Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(172\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58576 | −1.82841 | −0.914203 | − | 0.405257i | \(-0.867182\pi\) | ||||
−0.914203 | + | 0.405257i | \(0.867182\pi\) | |||||||
\(3\) | 1.51660 | 0.875612 | 0.437806 | − | 0.899069i | \(-0.355756\pi\) | ||||
0.437806 | + | 0.899069i | \(0.355756\pi\) | |||||||
\(4\) | 4.68613 | 2.34307 | ||||||||
\(5\) | −3.91728 | −1.75186 | −0.875930 | − | 0.482438i | \(-0.839751\pi\) | ||||
−0.875930 | + | 0.482438i | \(0.839751\pi\) | |||||||
\(6\) | −3.92157 | −1.60097 | ||||||||
\(7\) | −1.90750 | −0.720966 | −0.360483 | − | 0.932766i | \(-0.617388\pi\) | ||||
−0.360483 | + | 0.932766i | \(0.617388\pi\) | |||||||
\(8\) | −6.94569 | −2.45567 | ||||||||
\(9\) | −0.699911 | −0.233304 | ||||||||
\(10\) | 10.1291 | 3.20311 | ||||||||
\(11\) | 3.75612 | 1.13251 | 0.566256 | − | 0.824229i | \(-0.308391\pi\) | ||||
0.566256 | + | 0.824229i | \(0.308391\pi\) | |||||||
\(12\) | 7.10701 | 2.05162 | ||||||||
\(13\) | 0.142589 | 0.0395470 | 0.0197735 | − | 0.999804i | \(-0.493705\pi\) | ||||
0.0197735 | + | 0.999804i | \(0.493705\pi\) | |||||||
\(14\) | 4.93232 | 1.31822 | ||||||||
\(15\) | −5.94096 | −1.53395 | ||||||||
\(16\) | 8.58758 | 2.14690 | ||||||||
\(17\) | 0.966060 | 0.234304 | 0.117152 | − | 0.993114i | \(-0.462624\pi\) | ||||
0.117152 | + | 0.993114i | \(0.462624\pi\) | |||||||
\(18\) | 1.80980 | 0.426574 | ||||||||
\(19\) | 3.91278 | 0.897653 | 0.448826 | − | 0.893619i | \(-0.351842\pi\) | ||||
0.448826 | + | 0.893619i | \(0.351842\pi\) | |||||||
\(20\) | −18.3569 | −4.10473 | ||||||||
\(21\) | −2.89292 | −0.631287 | ||||||||
\(22\) | −9.71241 | −2.07069 | ||||||||
\(23\) | 8.94661 | 1.86550 | 0.932749 | − | 0.360527i | \(-0.117403\pi\) | ||||
0.932749 | + | 0.360527i | \(0.117403\pi\) | |||||||
\(24\) | −10.5339 | −2.15021 | ||||||||
\(25\) | 10.3451 | 2.06901 | ||||||||
\(26\) | −0.368700 | −0.0723080 | ||||||||
\(27\) | −5.61130 | −1.07990 | ||||||||
\(28\) | −8.93879 | −1.68927 | ||||||||
\(29\) | −1.33204 | −0.247353 | −0.123677 | − | 0.992323i | \(-0.539469\pi\) | ||||
−0.123677 | + | 0.992323i | \(0.539469\pi\) | |||||||
\(30\) | 15.3619 | 2.80468 | ||||||||
\(31\) | 5.78221 | 1.03851 | 0.519257 | − | 0.854618i | \(-0.326209\pi\) | ||||
0.519257 | + | 0.854618i | \(0.326209\pi\) | |||||||
\(32\) | −8.31402 | −1.46972 | ||||||||
\(33\) | 5.69655 | 0.991641 | ||||||||
\(34\) | −2.49799 | −0.428403 | ||||||||
\(35\) | 7.47220 | 1.26303 | ||||||||
\(36\) | −3.27988 | −0.546646 | ||||||||
\(37\) | 8.39609 | 1.38031 | 0.690155 | − | 0.723662i | \(-0.257543\pi\) | ||||
0.690155 | + | 0.723662i | \(0.257543\pi\) | |||||||
\(38\) | −10.1175 | −1.64127 | ||||||||
\(39\) | 0.216251 | 0.0346278 | ||||||||
\(40\) | 27.2082 | 4.30199 | ||||||||
\(41\) | −7.06425 | −1.10325 | −0.551626 | − | 0.834092i | \(-0.685992\pi\) | ||||
−0.551626 | + | 0.834092i | \(0.685992\pi\) | |||||||
\(42\) | 7.48038 | 1.15425 | ||||||||
\(43\) | −10.2633 | −1.56514 | −0.782568 | − | 0.622565i | \(-0.786091\pi\) | ||||
−0.782568 | + | 0.622565i | \(0.786091\pi\) | |||||||
\(44\) | 17.6017 | 2.65355 | ||||||||
\(45\) | 2.74175 | 0.408716 | ||||||||
\(46\) | −23.1338 | −3.41089 | ||||||||
\(47\) | −5.88279 | −0.858092 | −0.429046 | − | 0.903283i | \(-0.641150\pi\) | ||||
−0.429046 | + | 0.903283i | \(0.641150\pi\) | |||||||
\(48\) | 13.0240 | 1.87985 | ||||||||
\(49\) | −3.36145 | −0.480207 | ||||||||
\(50\) | −26.7498 | −3.78300 | ||||||||
\(51\) | 1.46513 | 0.205159 | ||||||||
\(52\) | 0.668190 | 0.0926613 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 14.5095 | 1.97449 | ||||||||
\(55\) | −14.7138 | −1.98400 | ||||||||
\(56\) | 13.2489 | 1.77046 | ||||||||
\(57\) | 5.93414 | 0.785995 | ||||||||
\(58\) | 3.44432 | 0.452262 | ||||||||
\(59\) | 10.5720 | 1.37636 | 0.688179 | − | 0.725541i | \(-0.258411\pi\) | ||||
0.688179 | + | 0.725541i | \(0.258411\pi\) | |||||||
\(60\) | −27.8401 | −3.59415 | ||||||||
\(61\) | 10.9931 | 1.40752 | 0.703761 | − | 0.710437i | \(-0.251503\pi\) | ||||
0.703761 | + | 0.710437i | \(0.251503\pi\) | |||||||
\(62\) | −14.9514 | −1.89883 | ||||||||
\(63\) | 1.33508 | 0.168204 | ||||||||
\(64\) | 4.32286 | 0.540357 | ||||||||
\(65\) | −0.558560 | −0.0692808 | ||||||||
\(66\) | −14.7299 | −1.81312 | ||||||||
\(67\) | 4.88864 | 0.597243 | 0.298621 | − | 0.954372i | \(-0.403473\pi\) | ||||
0.298621 | + | 0.954372i | \(0.403473\pi\) | |||||||
\(68\) | 4.52709 | 0.548990 | ||||||||
\(69\) | 13.5685 | 1.63345 | ||||||||
\(70\) | −19.3213 | −2.30934 | ||||||||
\(71\) | −5.62361 | −0.667400 | −0.333700 | − | 0.942679i | \(-0.608297\pi\) | ||||
−0.333700 | + | 0.942679i | \(0.608297\pi\) | |||||||
\(72\) | 4.86136 | 0.572917 | ||||||||
\(73\) | 2.67486 | 0.313068 | 0.156534 | − | 0.987673i | \(-0.449968\pi\) | ||||
0.156534 | + | 0.987673i | \(0.449968\pi\) | |||||||
\(74\) | −21.7102 | −2.52377 | ||||||||
\(75\) | 15.6894 | 1.81165 | ||||||||
\(76\) | 18.3358 | 2.10326 | ||||||||
\(77\) | −7.16479 | −0.816503 | ||||||||
\(78\) | −0.559172 | −0.0633137 | ||||||||
\(79\) | −12.4486 | −1.40058 | −0.700288 | − | 0.713860i | \(-0.746945\pi\) | ||||
−0.700288 | + | 0.713860i | \(0.746945\pi\) | |||||||
\(80\) | −33.6400 | −3.76106 | ||||||||
\(81\) | −6.41039 | −0.712266 | ||||||||
\(82\) | 18.2664 | 2.01719 | ||||||||
\(83\) | −4.48555 | −0.492353 | −0.246177 | − | 0.969225i | \(-0.579174\pi\) | ||||
−0.246177 | + | 0.969225i | \(0.579174\pi\) | |||||||
\(84\) | −13.5566 | −1.47915 | ||||||||
\(85\) | −3.78433 | −0.410468 | ||||||||
\(86\) | 26.5383 | 2.86170 | ||||||||
\(87\) | −2.02017 | −0.216585 | ||||||||
\(88\) | −26.0888 | −2.78108 | ||||||||
\(89\) | −4.37845 | −0.464115 | −0.232057 | − | 0.972702i | \(-0.574546\pi\) | ||||
−0.232057 | + | 0.972702i | \(0.574546\pi\) | |||||||
\(90\) | −7.08949 | −0.747298 | ||||||||
\(91\) | −0.271988 | −0.0285121 | ||||||||
\(92\) | 41.9250 | 4.37099 | ||||||||
\(93\) | 8.76932 | 0.909336 | ||||||||
\(94\) | 15.2114 | 1.56894 | ||||||||
\(95\) | −15.3274 | −1.57256 | ||||||||
\(96\) | −12.6091 | −1.28691 | ||||||||
\(97\) | 7.22950 | 0.734045 | 0.367022 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367022 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(98\) | 8.69190 | 0.878014 | ||||||||
\(99\) | −2.62895 | −0.264219 | ||||||||
\(100\) | 48.4784 | 4.84784 | ||||||||
\(101\) | −12.0889 | −1.20289 | −0.601446 | − | 0.798913i | \(-0.705409\pi\) | ||||
−0.601446 | + | 0.798913i | \(0.705409\pi\) | |||||||
\(102\) | −3.78847 | −0.375114 | ||||||||
\(103\) | 2.36405 | 0.232937 | 0.116468 | − | 0.993194i | \(-0.462843\pi\) | ||||
0.116468 | + | 0.993194i | \(0.462843\pi\) | |||||||
\(104\) | −0.990377 | −0.0971144 | ||||||||
\(105\) | 11.3324 | 1.10593 | ||||||||
\(106\) | 2.58576 | 0.251151 | ||||||||
\(107\) | 9.13710 | 0.883317 | 0.441658 | − | 0.897183i | \(-0.354390\pi\) | ||||
0.441658 | + | 0.897183i | \(0.354390\pi\) | |||||||
\(108\) | −26.2953 | −2.53027 | ||||||||
\(109\) | 9.16055 | 0.877422 | 0.438711 | − | 0.898628i | \(-0.355435\pi\) | ||||
0.438711 | + | 0.898628i | \(0.355435\pi\) | |||||||
\(110\) | 38.0462 | 3.62756 | ||||||||
\(111\) | 12.7336 | 1.20862 | ||||||||
\(112\) | −16.3808 | −1.54784 | ||||||||
\(113\) | 5.92505 | 0.557382 | 0.278691 | − | 0.960381i | \(-0.410100\pi\) | ||||
0.278691 | + | 0.960381i | \(0.410100\pi\) | |||||||
\(114\) | −15.3442 | −1.43712 | ||||||||
\(115\) | −35.0464 | −3.26809 | ||||||||
\(116\) | −6.24211 | −0.579565 | ||||||||
\(117\) | −0.0997995 | −0.00922647 | ||||||||
\(118\) | −27.3366 | −2.51654 | ||||||||
\(119\) | −1.84276 | −0.168925 | ||||||||
\(120\) | 41.2641 | 3.76688 | ||||||||
\(121\) | 3.10843 | 0.282584 | ||||||||
\(122\) | −28.4255 | −2.57352 | ||||||||
\(123\) | −10.7137 | −0.966020 | ||||||||
\(124\) | 27.0962 | 2.43331 | ||||||||
\(125\) | −20.9381 | −1.87276 | ||||||||
\(126\) | −3.45219 | −0.307545 | ||||||||
\(127\) | 17.4134 | 1.54519 | 0.772595 | − | 0.634899i | \(-0.218958\pi\) | ||||
0.772595 | + | 0.634899i | \(0.218958\pi\) | |||||||
\(128\) | 5.45018 | 0.481732 | ||||||||
\(129\) | −15.5653 | −1.37045 | ||||||||
\(130\) | 1.44430 | 0.126673 | ||||||||
\(131\) | −12.0533 | −1.05310 | −0.526550 | − | 0.850144i | \(-0.676515\pi\) | ||||
−0.526550 | + | 0.850144i | \(0.676515\pi\) | |||||||
\(132\) | 26.6948 | 2.32348 | ||||||||
\(133\) | −7.46361 | −0.647177 | ||||||||
\(134\) | −12.6408 | −1.09200 | ||||||||
\(135\) | 21.9810 | 1.89183 | ||||||||
\(136\) | −6.70995 | −0.575373 | ||||||||
\(137\) | −5.13529 | −0.438737 | −0.219369 | − | 0.975642i | \(-0.570400\pi\) | ||||
−0.219369 | + | 0.975642i | \(0.570400\pi\) | |||||||
\(138\) | −35.0848 | −2.98661 | ||||||||
\(139\) | −15.2916 | −1.29702 | −0.648509 | − | 0.761207i | \(-0.724607\pi\) | ||||
−0.648509 | + | 0.761207i | \(0.724607\pi\) | |||||||
\(140\) | 35.0157 | 2.95937 | ||||||||
\(141\) | −8.92186 | −0.751356 | ||||||||
\(142\) | 14.5413 | 1.22028 | ||||||||
\(143\) | 0.535580 | 0.0447875 | ||||||||
\(144\) | −6.01055 | −0.500879 | ||||||||
\(145\) | 5.21796 | 0.433328 | ||||||||
\(146\) | −6.91653 | −0.572416 | ||||||||
\(147\) | −5.09799 | −0.420475 | ||||||||
\(148\) | 39.3452 | 3.23416 | ||||||||
\(149\) | −22.5918 | −1.85079 | −0.925395 | − | 0.379005i | \(-0.876266\pi\) | ||||
−0.925395 | + | 0.379005i | \(0.876266\pi\) | |||||||
\(150\) | −40.5689 | −3.31244 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | −27.1769 | −2.20434 | ||||||||
\(153\) | −0.676156 | −0.0546640 | ||||||||
\(154\) | 18.5264 | 1.49290 | ||||||||
\(155\) | −22.6505 | −1.81933 | ||||||||
\(156\) | 1.01338 | 0.0811353 | ||||||||
\(157\) | 7.94569 | 0.634135 | 0.317067 | − | 0.948403i | \(-0.397302\pi\) | ||||
0.317067 | + | 0.948403i | \(0.397302\pi\) | |||||||
\(158\) | 32.1890 | 2.56082 | ||||||||
\(159\) | −1.51660 | −0.120275 | ||||||||
\(160\) | 32.5683 | 2.57475 | ||||||||
\(161\) | −17.0656 | −1.34496 | ||||||||
\(162\) | 16.5757 | 1.30231 | ||||||||
\(163\) | 16.5204 | 1.29398 | 0.646989 | − | 0.762499i | \(-0.276028\pi\) | ||||
0.646989 | + | 0.762499i | \(0.276028\pi\) | |||||||
\(164\) | −33.1040 | −2.58499 | ||||||||
\(165\) | −22.3150 | −1.73722 | ||||||||
\(166\) | 11.5985 | 0.900221 | ||||||||
\(167\) | −25.1452 | −1.94579 | −0.972897 | − | 0.231240i | \(-0.925722\pi\) | ||||
−0.972897 | + | 0.231240i | \(0.925722\pi\) | |||||||
\(168\) | 20.0933 | 1.55023 | ||||||||
\(169\) | −12.9797 | −0.998436 | ||||||||
\(170\) | 9.78534 | 0.750501 | ||||||||
\(171\) | −2.73860 | −0.209426 | ||||||||
\(172\) | −48.0951 | −3.66722 | ||||||||
\(173\) | −10.5848 | −0.804745 | −0.402372 | − | 0.915476i | \(-0.631814\pi\) | ||||
−0.402372 | + | 0.915476i | \(0.631814\pi\) | |||||||
\(174\) | 5.22368 | 0.396006 | ||||||||
\(175\) | −19.7332 | −1.49169 | ||||||||
\(176\) | 32.2560 | 2.43139 | ||||||||
\(177\) | 16.0335 | 1.20515 | ||||||||
\(178\) | 11.3216 | 0.848590 | ||||||||
\(179\) | −24.0504 | −1.79761 | −0.898807 | − | 0.438344i | \(-0.855565\pi\) | ||||
−0.898807 | + | 0.438344i | \(0.855565\pi\) | |||||||
\(180\) | 12.8482 | 0.957648 | ||||||||
\(181\) | 6.86739 | 0.510449 | 0.255225 | − | 0.966882i | \(-0.417851\pi\) | ||||
0.255225 | + | 0.966882i | \(0.417851\pi\) | |||||||
\(182\) | 0.703294 | 0.0521316 | ||||||||
\(183\) | 16.6722 | 1.23244 | ||||||||
\(184\) | −62.1404 | −4.58105 | ||||||||
\(185\) | −32.8898 | −2.41811 | ||||||||
\(186\) | −22.6753 | −1.66264 | ||||||||
\(187\) | 3.62863 | 0.265352 | ||||||||
\(188\) | −27.5675 | −2.01057 | ||||||||
\(189\) | 10.7035 | 0.778568 | ||||||||
\(190\) | 39.6330 | 2.87528 | ||||||||
\(191\) | 15.7699 | 1.14107 | 0.570533 | − | 0.821275i | \(-0.306737\pi\) | ||||
0.570533 | + | 0.821275i | \(0.306737\pi\) | |||||||
\(192\) | 6.55607 | 0.473143 | ||||||||
\(193\) | 18.8268 | 1.35519 | 0.677593 | − | 0.735437i | \(-0.263023\pi\) | ||||
0.677593 | + | 0.735437i | \(0.263023\pi\) | |||||||
\(194\) | −18.6937 | −1.34213 | ||||||||
\(195\) | −0.847114 | −0.0606631 | ||||||||
\(196\) | −15.7522 | −1.12516 | ||||||||
\(197\) | −6.29805 | −0.448718 | −0.224359 | − | 0.974507i | \(-0.572029\pi\) | ||||
−0.224359 | + | 0.974507i | \(0.572029\pi\) | |||||||
\(198\) | 6.79782 | 0.483100 | ||||||||
\(199\) | 17.5297 | 1.24265 | 0.621325 | − | 0.783553i | \(-0.286595\pi\) | ||||
0.621325 | + | 0.783553i | \(0.286595\pi\) | |||||||
\(200\) | −71.8536 | −5.08082 | ||||||||
\(201\) | 7.41414 | 0.522953 | ||||||||
\(202\) | 31.2590 | 2.19937 | ||||||||
\(203\) | 2.54086 | 0.178333 | ||||||||
\(204\) | 6.86580 | 0.480702 | ||||||||
\(205\) | 27.6727 | 1.93274 | ||||||||
\(206\) | −6.11285 | −0.425902 | ||||||||
\(207\) | −6.26184 | −0.435228 | ||||||||
\(208\) | 1.22449 | 0.0849033 | ||||||||
\(209\) | 14.6969 | 1.01660 | ||||||||
\(210\) | −29.3027 | −2.02208 | ||||||||
\(211\) | −16.3640 | −1.12654 | −0.563271 | − | 0.826273i | \(-0.690457\pi\) | ||||
−0.563271 | + | 0.826273i | \(0.690457\pi\) | |||||||
\(212\) | −4.68613 | −0.321845 | ||||||||
\(213\) | −8.52879 | −0.584383 | ||||||||
\(214\) | −23.6263 | −1.61506 | ||||||||
\(215\) | 40.2041 | 2.74190 | ||||||||
\(216\) | 38.9743 | 2.65187 | ||||||||
\(217\) | −11.0295 | −0.748734 | ||||||||
\(218\) | −23.6870 | −1.60428 | ||||||||
\(219\) | 4.05670 | 0.274126 | ||||||||
\(220\) | −68.9507 | −4.64865 | ||||||||
\(221\) | 0.137749 | 0.00926602 | ||||||||
\(222\) | −32.9259 | −2.20984 | ||||||||
\(223\) | −14.1502 | −0.947565 | −0.473782 | − | 0.880642i | \(-0.657112\pi\) | ||||
−0.473782 | + | 0.880642i | \(0.657112\pi\) | |||||||
\(224\) | 15.8590 | 1.05962 | ||||||||
\(225\) | −7.24063 | −0.482709 | ||||||||
\(226\) | −15.3207 | −1.01912 | ||||||||
\(227\) | 25.6179 | 1.70032 | 0.850160 | − | 0.526525i | \(-0.176505\pi\) | ||||
0.850160 | + | 0.526525i | \(0.176505\pi\) | |||||||
\(228\) | 27.8082 | 1.84164 | ||||||||
\(229\) | 21.4403 | 1.41681 | 0.708407 | − | 0.705804i | \(-0.249414\pi\) | ||||
0.708407 | + | 0.705804i | \(0.249414\pi\) | |||||||
\(230\) | 90.6214 | 5.97540 | ||||||||
\(231\) | −10.8661 | −0.714940 | ||||||||
\(232\) | 9.25192 | 0.607418 | ||||||||
\(233\) | 5.55659 | 0.364025 | 0.182012 | − | 0.983296i | \(-0.441739\pi\) | ||||
0.182012 | + | 0.983296i | \(0.441739\pi\) | |||||||
\(234\) | 0.258057 | 0.0168697 | ||||||||
\(235\) | 23.0445 | 1.50326 | ||||||||
\(236\) | 49.5418 | 3.22490 | ||||||||
\(237\) | −18.8796 | −1.22636 | ||||||||
\(238\) | 4.76492 | 0.308864 | ||||||||
\(239\) | 3.49503 | 0.226075 | 0.113037 | − | 0.993591i | \(-0.463942\pi\) | ||||
0.113037 | + | 0.993591i | \(0.463942\pi\) | |||||||
\(240\) | −51.0185 | −3.29323 | ||||||||
\(241\) | 27.1249 | 1.74727 | 0.873633 | − | 0.486585i | \(-0.161758\pi\) | ||||
0.873633 | + | 0.486585i | \(0.161758\pi\) | |||||||
\(242\) | −8.03763 | −0.516679 | ||||||||
\(243\) | 7.11188 | 0.456227 | ||||||||
\(244\) | 51.5151 | 3.29792 | ||||||||
\(245\) | 13.1677 | 0.841256 | ||||||||
\(246\) | 27.7030 | 1.76628 | ||||||||
\(247\) | 0.557918 | 0.0354995 | ||||||||
\(248\) | −40.1614 | −2.55025 | ||||||||
\(249\) | −6.80280 | −0.431110 | ||||||||
\(250\) | 54.1409 | 3.42417 | ||||||||
\(251\) | −2.17259 | −0.137132 | −0.0685662 | − | 0.997647i | \(-0.521842\pi\) | ||||
−0.0685662 | + | 0.997647i | \(0.521842\pi\) | |||||||
\(252\) | 6.25636 | 0.394114 | ||||||||
\(253\) | 33.6045 | 2.11270 | ||||||||
\(254\) | −45.0268 | −2.82524 | ||||||||
\(255\) | −5.73932 | −0.359410 | ||||||||
\(256\) | −22.7386 | −1.42116 | ||||||||
\(257\) | −5.50631 | −0.343474 | −0.171737 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171737 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(258\) | 40.2482 | 2.50574 | ||||||||
\(259\) | −16.0155 | −0.995157 | ||||||||
\(260\) | −2.61749 | −0.162330 | ||||||||
\(261\) | 0.932308 | 0.0577084 | ||||||||
\(262\) | 31.1668 | 1.92549 | ||||||||
\(263\) | −4.71111 | −0.290499 | −0.145250 | − | 0.989395i | \(-0.546399\pi\) | ||||
−0.145250 | + | 0.989395i | \(0.546399\pi\) | |||||||
\(264\) | −39.5664 | −2.43514 | ||||||||
\(265\) | 3.91728 | 0.240637 | ||||||||
\(266\) | 19.2991 | 1.18330 | ||||||||
\(267\) | −6.64037 | −0.406384 | ||||||||
\(268\) | 22.9088 | 1.39938 | ||||||||
\(269\) | −4.71700 | −0.287601 | −0.143800 | − | 0.989607i | \(-0.545932\pi\) | ||||
−0.143800 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(270\) | −56.8376 | −3.45903 | ||||||||
\(271\) | 18.7886 | 1.14132 | 0.570662 | − | 0.821185i | \(-0.306687\pi\) | ||||
0.570662 | + | 0.821185i | \(0.306687\pi\) | |||||||
\(272\) | 8.29612 | 0.503026 | ||||||||
\(273\) | −0.412498 | −0.0249655 | ||||||||
\(274\) | 13.2786 | 0.802190 | ||||||||
\(275\) | 38.8573 | 2.34318 | ||||||||
\(276\) | 63.5837 | 3.82729 | ||||||||
\(277\) | 26.3472 | 1.58305 | 0.791526 | − | 0.611136i | \(-0.209287\pi\) | ||||
0.791526 | + | 0.611136i | \(0.209287\pi\) | |||||||
\(278\) | 39.5404 | 2.37147 | ||||||||
\(279\) | −4.04703 | −0.242289 | ||||||||
\(280\) | −51.8996 | −3.10159 | ||||||||
\(281\) | −4.57799 | −0.273100 | −0.136550 | − | 0.990633i | \(-0.543601\pi\) | ||||
−0.136550 | + | 0.990633i | \(0.543601\pi\) | |||||||
\(282\) | 23.0697 | 1.37378 | ||||||||
\(283\) | −19.9392 | −1.18526 | −0.592631 | − | 0.805474i | \(-0.701911\pi\) | ||||
−0.592631 | + | 0.805474i | \(0.701911\pi\) | |||||||
\(284\) | −26.3530 | −1.56376 | ||||||||
\(285\) | −23.2457 | −1.37695 | ||||||||
\(286\) | −1.38488 | −0.0818897 | ||||||||
\(287\) | 13.4751 | 0.795407 | ||||||||
\(288\) | 5.81908 | 0.342892 | ||||||||
\(289\) | −16.0667 | −0.945102 | ||||||||
\(290\) | −13.4924 | −0.792300 | ||||||||
\(291\) | 10.9643 | 0.642738 | ||||||||
\(292\) | 12.5347 | 0.733540 | ||||||||
\(293\) | 17.2198 | 1.00599 | 0.502996 | − | 0.864289i | \(-0.332231\pi\) | ||||
0.502996 | + | 0.864289i | \(0.332231\pi\) | |||||||
\(294\) | 13.1822 | 0.768800 | ||||||||
\(295\) | −41.4135 | −2.41119 | ||||||||
\(296\) | −58.3166 | −3.38959 | ||||||||
\(297\) | −21.0767 | −1.22299 | ||||||||
\(298\) | 58.4168 | 3.38399 | ||||||||
\(299\) | 1.27569 | 0.0737749 | ||||||||
\(300\) | 73.5225 | 4.24483 | ||||||||
\(301\) | 19.5772 | 1.12841 | ||||||||
\(302\) | −2.58576 | −0.148794 | ||||||||
\(303\) | −18.3341 | −1.05327 | ||||||||
\(304\) | 33.6013 | 1.92717 | ||||||||
\(305\) | −43.0630 | −2.46578 | ||||||||
\(306\) | 1.74837 | 0.0999479 | ||||||||
\(307\) | 24.9304 | 1.42286 | 0.711428 | − | 0.702759i | \(-0.248049\pi\) | ||||
0.711428 | + | 0.702759i | \(0.248049\pi\) | |||||||
\(308\) | −33.5752 | −1.91312 | ||||||||
\(309\) | 3.58532 | 0.203962 | ||||||||
\(310\) | 58.5687 | 3.32648 | ||||||||
\(311\) | 23.5635 | 1.33616 | 0.668081 | − | 0.744088i | \(-0.267116\pi\) | ||||
0.668081 | + | 0.744088i | \(0.267116\pi\) | |||||||
\(312\) | −1.50201 | −0.0850346 | ||||||||
\(313\) | 0.606690 | 0.0342922 | 0.0171461 | − | 0.999853i | \(-0.494542\pi\) | ||||
0.0171461 | + | 0.999853i | \(0.494542\pi\) | |||||||
\(314\) | −20.5456 | −1.15946 | ||||||||
\(315\) | −5.22988 | −0.294670 | ||||||||
\(316\) | −58.3358 | −3.28164 | ||||||||
\(317\) | −3.08402 | −0.173216 | −0.0866080 | − | 0.996242i | \(-0.527603\pi\) | ||||
−0.0866080 | + | 0.996242i | \(0.527603\pi\) | |||||||
\(318\) | 3.92157 | 0.219911 | ||||||||
\(319\) | −5.00329 | −0.280131 | ||||||||
\(320\) | −16.9338 | −0.946631 | ||||||||
\(321\) | 13.8574 | 0.773443 | ||||||||
\(322\) | 44.1276 | 2.45913 | ||||||||
\(323\) | 3.77998 | 0.210324 | ||||||||
\(324\) | −30.0399 | −1.66889 | ||||||||
\(325\) | 1.47509 | 0.0818233 | ||||||||
\(326\) | −42.7177 | −2.36592 | ||||||||
\(327\) | 13.8929 | 0.768281 | ||||||||
\(328\) | 49.0661 | 2.70922 | ||||||||
\(329\) | 11.2214 | 0.618656 | ||||||||
\(330\) | 57.7010 | 3.17634 | ||||||||
\(331\) | −3.76482 | −0.206933 | −0.103467 | − | 0.994633i | \(-0.532993\pi\) | ||||
−0.103467 | + | 0.994633i | \(0.532993\pi\) | |||||||
\(332\) | −21.0199 | −1.15362 | ||||||||
\(333\) | −5.87652 | −0.322031 | ||||||||
\(334\) | 65.0193 | 3.55770 | ||||||||
\(335\) | −19.1502 | −1.04629 | ||||||||
\(336\) | −24.8432 | −1.35531 | ||||||||
\(337\) | 30.3197 | 1.65162 | 0.825810 | − | 0.563948i | \(-0.190718\pi\) | ||||
0.825810 | + | 0.563948i | \(0.190718\pi\) | |||||||
\(338\) | 33.5623 | 1.82555 | ||||||||
\(339\) | 8.98595 | 0.488050 | ||||||||
\(340\) | −17.7339 | −0.961753 | ||||||||
\(341\) | 21.7187 | 1.17613 | ||||||||
\(342\) | 7.08135 | 0.382915 | ||||||||
\(343\) | 19.7644 | 1.06718 | ||||||||
\(344\) | 71.2855 | 3.84346 | ||||||||
\(345\) | −53.1515 | −2.86158 | ||||||||
\(346\) | 27.3696 | 1.47140 | ||||||||
\(347\) | −7.44001 | −0.399401 | −0.199700 | − | 0.979857i | \(-0.563997\pi\) | ||||
−0.199700 | + | 0.979857i | \(0.563997\pi\) | |||||||
\(348\) | −9.46681 | −0.507474 | ||||||||
\(349\) | −8.69386 | −0.465372 | −0.232686 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232686 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(350\) | 51.0252 | 2.72741 | ||||||||
\(351\) | −0.800109 | −0.0427066 | ||||||||
\(352\) | −31.2284 | −1.66448 | ||||||||
\(353\) | 18.5627 | 0.987991 | 0.493995 | − | 0.869464i | \(-0.335536\pi\) | ||||
0.493995 | + | 0.869464i | \(0.335536\pi\) | |||||||
\(354\) | −41.4588 | −2.20351 | ||||||||
\(355\) | 22.0292 | 1.16919 | ||||||||
\(356\) | −20.5180 | −1.08745 | ||||||||
\(357\) | −2.79473 | −0.147913 | ||||||||
\(358\) | 62.1886 | 3.28677 | ||||||||
\(359\) | 28.2132 | 1.48904 | 0.744519 | − | 0.667602i | \(-0.232679\pi\) | ||||
0.744519 | + | 0.667602i | \(0.232679\pi\) | |||||||
\(360\) | −19.0433 | −1.00367 | ||||||||
\(361\) | −3.69017 | −0.194219 | ||||||||
\(362\) | −17.7574 | −0.933308 | ||||||||
\(363\) | 4.71425 | 0.247434 | ||||||||
\(364\) | −1.27457 | −0.0668057 | ||||||||
\(365\) | −10.4782 | −0.548452 | ||||||||
\(366\) | −43.1102 | −2.25340 | ||||||||
\(367\) | 3.67470 | 0.191818 | 0.0959089 | − | 0.995390i | \(-0.469424\pi\) | ||||
0.0959089 | + | 0.995390i | \(0.469424\pi\) | |||||||
\(368\) | 76.8298 | 4.00503 | ||||||||
\(369\) | 4.94435 | 0.257393 | ||||||||
\(370\) | 85.0451 | 4.42128 | ||||||||
\(371\) | 1.90750 | 0.0990323 | ||||||||
\(372\) | 41.0942 | 2.13064 | ||||||||
\(373\) | −31.7582 | −1.64438 | −0.822189 | − | 0.569215i | \(-0.807247\pi\) | ||||
−0.822189 | + | 0.569215i | \(0.807247\pi\) | |||||||
\(374\) | −9.38276 | −0.485171 | ||||||||
\(375\) | −31.7549 | −1.63981 | ||||||||
\(376\) | 40.8600 | 2.10719 | ||||||||
\(377\) | −0.189934 | −0.00978208 | ||||||||
\(378\) | −27.6768 | −1.42354 | ||||||||
\(379\) | 6.69828 | 0.344068 | 0.172034 | − | 0.985091i | \(-0.444966\pi\) | ||||
0.172034 | + | 0.985091i | \(0.444966\pi\) | |||||||
\(380\) | −71.8264 | −3.68462 | ||||||||
\(381\) | 26.4093 | 1.35299 | ||||||||
\(382\) | −40.7770 | −2.08633 | ||||||||
\(383\) | 18.4508 | 0.942793 | 0.471396 | − | 0.881921i | \(-0.343750\pi\) | ||||
0.471396 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(384\) | 8.26577 | 0.421811 | ||||||||
\(385\) | 28.0665 | 1.43040 | ||||||||
\(386\) | −48.6816 | −2.47783 | ||||||||
\(387\) | 7.18339 | 0.365152 | ||||||||
\(388\) | 33.8784 | 1.71992 | ||||||||
\(389\) | 31.1220 | 1.57795 | 0.788974 | − | 0.614427i | \(-0.210613\pi\) | ||||
0.788974 | + | 0.614427i | \(0.210613\pi\) | |||||||
\(390\) | 2.19043 | 0.110917 | ||||||||
\(391\) | 8.64296 | 0.437093 | ||||||||
\(392\) | 23.3476 | 1.17923 | ||||||||
\(393\) | −18.2801 | −0.922107 | ||||||||
\(394\) | 16.2852 | 0.820438 | ||||||||
\(395\) | 48.7646 | 2.45361 | ||||||||
\(396\) | −12.3196 | −0.619084 | ||||||||
\(397\) | 5.73702 | 0.287933 | 0.143966 | − | 0.989583i | \(-0.454014\pi\) | ||||
0.143966 | + | 0.989583i | \(0.454014\pi\) | |||||||
\(398\) | −45.3276 | −2.27207 | ||||||||
\(399\) | −11.3194 | −0.566676 | ||||||||
\(400\) | 88.8392 | 4.44196 | ||||||||
\(401\) | −0.256250 | −0.0127965 | −0.00639826 | − | 0.999980i | \(-0.502037\pi\) | ||||
−0.00639826 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(402\) | −19.1712 | −0.956170 | ||||||||
\(403\) | 0.824478 | 0.0410702 | ||||||||
\(404\) | −56.6503 | −2.81846 | ||||||||
\(405\) | 25.1113 | 1.24779 | ||||||||
\(406\) | −6.57004 | −0.326066 | ||||||||
\(407\) | 31.5367 | 1.56322 | ||||||||
\(408\) | −10.1763 | −0.503804 | ||||||||
\(409\) | −38.3070 | −1.89416 | −0.947079 | − | 0.321002i | \(-0.895980\pi\) | ||||
−0.947079 | + | 0.321002i | \(0.895980\pi\) | |||||||
\(410\) | −71.5547 | −3.53384 | ||||||||
\(411\) | −7.78820 | −0.384164 | ||||||||
\(412\) | 11.0782 | 0.545786 | ||||||||
\(413\) | −20.1661 | −0.992307 | ||||||||
\(414\) | 16.1916 | 0.795773 | ||||||||
\(415\) | 17.5711 | 0.862534 | ||||||||
\(416\) | −1.18549 | −0.0581232 | ||||||||
\(417\) | −23.1913 | −1.13568 | ||||||||
\(418\) | −38.0025 | −1.85876 | ||||||||
\(419\) | 34.8432 | 1.70220 | 0.851101 | − | 0.525002i | \(-0.175936\pi\) | ||||
0.851101 | + | 0.525002i | \(0.175936\pi\) | |||||||
\(420\) | 53.1050 | 2.59126 | ||||||||
\(421\) | 2.30563 | 0.112370 | 0.0561848 | − | 0.998420i | \(-0.482106\pi\) | ||||
0.0561848 | + | 0.998420i | \(0.482106\pi\) | |||||||
\(422\) | 42.3132 | 2.05977 | ||||||||
\(423\) | 4.11743 | 0.200196 | ||||||||
\(424\) | 6.94569 | 0.337312 | ||||||||
\(425\) | 9.99396 | 0.484778 | ||||||||
\(426\) | 22.0534 | 1.06849 | ||||||||
\(427\) | −20.9693 | −1.01478 | ||||||||
\(428\) | 42.8177 | 2.06967 | ||||||||
\(429\) | 0.812263 | 0.0392164 | ||||||||
\(430\) | −103.958 | −5.01330 | ||||||||
\(431\) | −3.04894 | −0.146862 | −0.0734312 | − | 0.997300i | \(-0.523395\pi\) | ||||
−0.0734312 | + | 0.997300i | \(0.523395\pi\) | |||||||
\(432\) | −48.1875 | −2.31842 | ||||||||
\(433\) | −16.6336 | −0.799358 | −0.399679 | − | 0.916655i | \(-0.630878\pi\) | ||||
−0.399679 | + | 0.916655i | \(0.630878\pi\) | |||||||
\(434\) | 28.5197 | 1.36899 | ||||||||
\(435\) | 7.91358 | 0.379427 | ||||||||
\(436\) | 42.9276 | 2.05586 | ||||||||
\(437\) | 35.0061 | 1.67457 | ||||||||
\(438\) | −10.4896 | −0.501214 | ||||||||
\(439\) | −15.1998 | −0.725447 | −0.362724 | − | 0.931897i | \(-0.618153\pi\) | ||||
−0.362724 | + | 0.931897i | \(0.618153\pi\) | |||||||
\(440\) | 102.197 | 4.87206 | ||||||||
\(441\) | 2.35272 | 0.112034 | ||||||||
\(442\) | −0.356186 | −0.0169420 | ||||||||
\(443\) | −5.99981 | −0.285060 | −0.142530 | − | 0.989791i | \(-0.545524\pi\) | ||||
−0.142530 | + | 0.989791i | \(0.545524\pi\) | |||||||
\(444\) | 59.6711 | 2.83187 | ||||||||
\(445\) | 17.1516 | 0.813064 | ||||||||
\(446\) | 36.5889 | 1.73253 | ||||||||
\(447\) | −34.2628 | −1.62057 | ||||||||
\(448\) | −8.24584 | −0.389579 | ||||||||
\(449\) | −28.4475 | −1.34252 | −0.671260 | − | 0.741222i | \(-0.734247\pi\) | ||||
−0.671260 | + | 0.741222i | \(0.734247\pi\) | |||||||
\(450\) | 18.7225 | 0.882588 | ||||||||
\(451\) | −26.5342 | −1.24945 | ||||||||
\(452\) | 27.7656 | 1.30598 | ||||||||
\(453\) | 1.51660 | 0.0712563 | ||||||||
\(454\) | −66.2416 | −3.10887 | ||||||||
\(455\) | 1.06545 | 0.0499491 | ||||||||
\(456\) | −41.2166 | −1.93015 | ||||||||
\(457\) | −17.1863 | −0.803942 | −0.401971 | − | 0.915653i | \(-0.631675\pi\) | ||||
−0.401971 | + | 0.915653i | \(0.631675\pi\) | |||||||
\(458\) | −55.4393 | −2.59051 | ||||||||
\(459\) | −5.42085 | −0.253024 | ||||||||
\(460\) | −164.232 | −7.65736 | ||||||||
\(461\) | 0.275645 | 0.0128381 | 0.00641904 | − | 0.999979i | \(-0.497957\pi\) | ||||
0.00641904 | + | 0.999979i | \(0.497957\pi\) | |||||||
\(462\) | 28.0972 | 1.30720 | ||||||||
\(463\) | 0.821586 | 0.0381823 | 0.0190912 | − | 0.999818i | \(-0.493923\pi\) | ||||
0.0190912 | + | 0.999818i | \(0.493923\pi\) | |||||||
\(464\) | −11.4390 | −0.531041 | ||||||||
\(465\) | −34.3519 | −1.59303 | ||||||||
\(466\) | −14.3680 | −0.665585 | ||||||||
\(467\) | 18.6468 | 0.862872 | 0.431436 | − | 0.902144i | \(-0.358007\pi\) | ||||
0.431436 | + | 0.902144i | \(0.358007\pi\) | |||||||
\(468\) | −0.467674 | −0.0216182 | ||||||||
\(469\) | −9.32508 | −0.430592 | ||||||||
\(470\) | −59.5875 | −2.74857 | ||||||||
\(471\) | 12.0505 | 0.555256 | ||||||||
\(472\) | −73.4298 | −3.37988 | ||||||||
\(473\) | −38.5501 | −1.77254 | ||||||||
\(474\) | 48.8180 | 2.24229 | ||||||||
\(475\) | 40.4780 | 1.85726 | ||||||||
\(476\) | −8.63540 | −0.395803 | ||||||||
\(477\) | 0.699911 | 0.0320467 | ||||||||
\(478\) | −9.03730 | −0.413356 | ||||||||
\(479\) | 18.2930 | 0.835828 | 0.417914 | − | 0.908487i | \(-0.362761\pi\) | ||||
0.417914 | + | 0.908487i | \(0.362761\pi\) | |||||||
\(480\) | 49.3933 | 2.25448 | ||||||||
\(481\) | 1.19719 | 0.0545871 | ||||||||
\(482\) | −70.1383 | −3.19471 | ||||||||
\(483\) | −25.8818 | −1.17766 | ||||||||
\(484\) | 14.5665 | 0.662114 | ||||||||
\(485\) | −28.3200 | −1.28594 | ||||||||
\(486\) | −18.3896 | −0.834169 | ||||||||
\(487\) | 26.4988 | 1.20077 | 0.600387 | − | 0.799709i | \(-0.295013\pi\) | ||||
0.600387 | + | 0.799709i | \(0.295013\pi\) | |||||||
\(488\) | −76.3546 | −3.45641 | ||||||||
\(489\) | 25.0549 | 1.13302 | ||||||||
\(490\) | −34.0486 | −1.53816 | ||||||||
\(491\) | 27.5508 | 1.24335 | 0.621675 | − | 0.783276i | \(-0.286453\pi\) | ||||
0.621675 | + | 0.783276i | \(0.286453\pi\) | |||||||
\(492\) | −50.2057 | −2.26345 | ||||||||
\(493\) | −1.28683 | −0.0579558 | ||||||||
\(494\) | −1.44264 | −0.0649074 | ||||||||
\(495\) | 10.2983 | 0.462876 | ||||||||
\(496\) | 49.6552 | 2.22958 | ||||||||
\(497\) | 10.7270 | 0.481173 | ||||||||
\(498\) | 17.5904 | 0.788244 | ||||||||
\(499\) | 7.01388 | 0.313984 | 0.156992 | − | 0.987600i | \(-0.449820\pi\) | ||||
0.156992 | + | 0.987600i | \(0.449820\pi\) | |||||||
\(500\) | −98.1189 | −4.38801 | ||||||||
\(501\) | −38.1353 | −1.70376 | ||||||||
\(502\) | 5.61778 | 0.250734 | ||||||||
\(503\) | 16.2687 | 0.725385 | 0.362693 | − | 0.931909i | \(-0.381857\pi\) | ||||
0.362693 | + | 0.931909i | \(0.381857\pi\) | |||||||
\(504\) | −9.27304 | −0.413054 | ||||||||
\(505\) | 47.3557 | 2.10730 | ||||||||
\(506\) | −86.8931 | −3.86287 | ||||||||
\(507\) | −19.6850 | −0.874242 | ||||||||
\(508\) | 81.6016 | 3.62049 | ||||||||
\(509\) | −7.12948 | −0.316009 | −0.158004 | − | 0.987438i | \(-0.550506\pi\) | ||||
−0.158004 | + | 0.987438i | \(0.550506\pi\) | |||||||
\(510\) | 14.8405 | 0.657148 | ||||||||
\(511\) | −5.10229 | −0.225712 | ||||||||
\(512\) | 47.8960 | 2.11672 | ||||||||
\(513\) | −21.9558 | −0.969371 | ||||||||
\(514\) | 14.2380 | 0.628011 | ||||||||
\(515\) | −9.26063 | −0.408072 | ||||||||
\(516\) | −72.9413 | −3.21106 | ||||||||
\(517\) | −22.0964 | −0.971800 | ||||||||
\(518\) | 41.4122 | 1.81955 | ||||||||
\(519\) | −16.0529 | −0.704644 | ||||||||
\(520\) | 3.87958 | 0.170131 | ||||||||
\(521\) | 29.9032 | 1.31008 | 0.655041 | − | 0.755593i | \(-0.272651\pi\) | ||||
0.655041 | + | 0.755593i | \(0.272651\pi\) | |||||||
\(522\) | −2.41072 | −0.105514 | ||||||||
\(523\) | −15.4246 | −0.674471 | −0.337235 | − | 0.941420i | \(-0.609492\pi\) | ||||
−0.337235 | + | 0.941420i | \(0.609492\pi\) | |||||||
\(524\) | −56.4833 | −2.46748 | ||||||||
\(525\) | −29.9275 | −1.30614 | ||||||||
\(526\) | 12.1818 | 0.531151 | ||||||||
\(527\) | 5.58596 | 0.243328 | ||||||||
\(528\) | 48.9196 | 2.12895 | ||||||||
\(529\) | 57.0419 | 2.48008 | ||||||||
\(530\) | −10.1291 | −0.439981 | ||||||||
\(531\) | −7.39946 | −0.321109 | ||||||||
\(532\) | −34.9755 | −1.51638 | ||||||||
\(533\) | −1.00728 | −0.0436303 | ||||||||
\(534\) | 17.1704 | 0.743035 | ||||||||
\(535\) | −35.7926 | −1.54745 | ||||||||
\(536\) | −33.9550 | −1.46663 | ||||||||
\(537\) | −36.4750 | −1.57401 | ||||||||
\(538\) | 12.1970 | 0.525851 | ||||||||
\(539\) | −12.6260 | −0.543841 | ||||||||
\(540\) | 103.006 | 4.43267 | ||||||||
\(541\) | −22.2568 | −0.956894 | −0.478447 | − | 0.878116i | \(-0.658800\pi\) | ||||
−0.478447 | + | 0.878116i | \(0.658800\pi\) | |||||||
\(542\) | −48.5826 | −2.08680 | ||||||||
\(543\) | 10.4151 | 0.446956 | ||||||||
\(544\) | −8.03184 | −0.344362 | ||||||||
\(545\) | −35.8844 | −1.53712 | ||||||||
\(546\) | 1.06662 | 0.0456471 | ||||||||
\(547\) | −35.8183 | −1.53148 | −0.765740 | − | 0.643150i | \(-0.777627\pi\) | ||||
−0.765740 | + | 0.643150i | \(0.777627\pi\) | |||||||
\(548\) | −24.0646 | −1.02799 | ||||||||
\(549\) | −7.69419 | −0.328380 | ||||||||
\(550\) | −100.476 | −4.28429 | ||||||||
\(551\) | −5.21197 | −0.222037 | ||||||||
\(552\) | −94.2424 | −4.01122 | ||||||||
\(553\) | 23.7457 | 1.00977 | ||||||||
\(554\) | −68.1275 | −2.89446 | ||||||||
\(555\) | −49.8809 | −2.11732 | ||||||||
\(556\) | −71.6585 | −3.03900 | ||||||||
\(557\) | −9.46947 | −0.401234 | −0.200617 | − | 0.979670i | \(-0.564295\pi\) | ||||
−0.200617 | + | 0.979670i | \(0.564295\pi\) | |||||||
\(558\) | 10.4646 | 0.443003 | ||||||||
\(559\) | −1.46343 | −0.0618964 | ||||||||
\(560\) | 64.1681 | 2.71160 | ||||||||
\(561\) | 5.50320 | 0.232345 | ||||||||
\(562\) | 11.8376 | 0.499337 | ||||||||
\(563\) | 16.6832 | 0.703115 | 0.351558 | − | 0.936166i | \(-0.385652\pi\) | ||||
0.351558 | + | 0.936166i | \(0.385652\pi\) | |||||||
\(564\) | −41.8090 | −1.76048 | ||||||||
\(565\) | −23.2101 | −0.976455 | ||||||||
\(566\) | 51.5579 | 2.16714 | ||||||||
\(567\) | 12.2278 | 0.513520 | ||||||||
\(568\) | 39.0598 | 1.63891 | ||||||||
\(569\) | −46.6921 | −1.95743 | −0.978717 | − | 0.205216i | \(-0.934210\pi\) | ||||
−0.978717 | + | 0.205216i | \(0.934210\pi\) | |||||||
\(570\) | 60.1076 | 2.51763 | ||||||||
\(571\) | 17.6507 | 0.738658 | 0.369329 | − | 0.929299i | \(-0.379587\pi\) | ||||
0.369329 | + | 0.929299i | \(0.379587\pi\) | |||||||
\(572\) | 2.50980 | 0.104940 | ||||||||
\(573\) | 23.9166 | 0.999131 | ||||||||
\(574\) | −34.8432 | −1.45433 | ||||||||
\(575\) | 92.5534 | 3.85974 | ||||||||
\(576\) | −3.02562 | −0.126067 | ||||||||
\(577\) | −7.85004 | −0.326802 | −0.163401 | − | 0.986560i | \(-0.552246\pi\) | ||||
−0.163401 | + | 0.986560i | \(0.552246\pi\) | |||||||
\(578\) | 41.5446 | 1.72803 | ||||||||
\(579\) | 28.5529 | 1.18662 | ||||||||
\(580\) | 24.4521 | 1.01532 | ||||||||
\(581\) | 8.55618 | 0.354970 | ||||||||
\(582\) | −28.3510 | −1.17519 | ||||||||
\(583\) | −3.75612 | −0.155563 | ||||||||
\(584\) | −18.5787 | −0.768793 | ||||||||
\(585\) | 0.390942 | 0.0161635 | ||||||||
\(586\) | −44.5262 | −1.83936 | ||||||||
\(587\) | −34.9831 | −1.44391 | −0.721954 | − | 0.691941i | \(-0.756756\pi\) | ||||
−0.721954 | + | 0.691941i | \(0.756756\pi\) | |||||||
\(588\) | −23.8899 | −0.985202 | ||||||||
\(589\) | 22.6245 | 0.932226 | ||||||||
\(590\) | 107.085 | 4.40863 | ||||||||
\(591\) | −9.55165 | −0.392902 | ||||||||
\(592\) | 72.1021 | 2.96338 | ||||||||
\(593\) | −8.61073 | −0.353600 | −0.176800 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176800 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(594\) | 54.4992 | 2.23613 | ||||||||
\(595\) | 7.21859 | 0.295933 | ||||||||
\(596\) | −105.868 | −4.33652 | ||||||||
\(597\) | 26.5857 | 1.08808 | ||||||||
\(598\) | −3.29861 | −0.134890 | ||||||||
\(599\) | −19.6518 | −0.802950 | −0.401475 | − | 0.915870i | \(-0.631502\pi\) | ||||
−0.401475 | + | 0.915870i | \(0.631502\pi\) | |||||||
\(600\) | −108.974 | −4.44883 | ||||||||
\(601\) | −27.8365 | −1.13547 | −0.567737 | − | 0.823210i | \(-0.692181\pi\) | ||||
−0.567737 | + | 0.823210i | \(0.692181\pi\) | |||||||
\(602\) | −50.6218 | −2.06319 | ||||||||
\(603\) | −3.42162 | −0.139339 | ||||||||
\(604\) | 4.68613 | 0.190676 | ||||||||
\(605\) | −12.1766 | −0.495048 | ||||||||
\(606\) | 47.4075 | 1.92580 | ||||||||
\(607\) | 28.8503 | 1.17100 | 0.585499 | − | 0.810673i | \(-0.300898\pi\) | ||||
0.585499 | + | 0.810673i | \(0.300898\pi\) | |||||||
\(608\) | −32.5309 | −1.31930 | ||||||||
\(609\) | 3.85348 | 0.156151 | ||||||||
\(610\) | 111.350 | 4.50845 | ||||||||
\(611\) | −0.838819 | −0.0339350 | ||||||||
\(612\) | −3.16856 | −0.128081 | ||||||||
\(613\) | 45.9035 | 1.85402 | 0.927012 | − | 0.375033i | \(-0.122369\pi\) | ||||
0.927012 | + | 0.375033i | \(0.122369\pi\) | |||||||
\(614\) | −64.4640 | −2.60156 | ||||||||
\(615\) | 41.9685 | 1.69233 | ||||||||
\(616\) | 49.7644 | 2.00506 | ||||||||
\(617\) | 30.4913 | 1.22753 | 0.613766 | − | 0.789488i | \(-0.289654\pi\) | ||||
0.613766 | + | 0.789488i | \(0.289654\pi\) | |||||||
\(618\) | −9.27077 | −0.372925 | ||||||||
\(619\) | 31.7620 | 1.27662 | 0.638311 | − | 0.769779i | \(-0.279634\pi\) | ||||
0.638311 | + | 0.769779i | \(0.279634\pi\) | |||||||
\(620\) | −106.143 | −4.26282 | ||||||||
\(621\) | −50.2021 | −2.01454 | ||||||||
\(622\) | −60.9294 | −2.44305 | ||||||||
\(623\) | 8.35188 | 0.334611 | ||||||||
\(624\) | 1.85707 | 0.0743423 | ||||||||
\(625\) | 30.2952 | 1.21181 | ||||||||
\(626\) | −1.56875 | −0.0627000 | ||||||||
\(627\) | 22.2893 | 0.890150 | ||||||||
\(628\) | 37.2345 | 1.48582 | ||||||||
\(629\) | 8.11113 | 0.323412 | ||||||||
\(630\) | 13.5232 | 0.538777 | ||||||||
\(631\) | −10.4816 | −0.417265 | −0.208632 | − | 0.977994i | \(-0.566901\pi\) | ||||
−0.208632 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(632\) | 86.4641 | 3.43936 | ||||||||
\(633\) | −24.8176 | −0.986413 | ||||||||
\(634\) | 7.97453 | 0.316709 | ||||||||
\(635\) | −68.2132 | −2.70696 | ||||||||
\(636\) | −7.10701 | −0.281811 | ||||||||
\(637\) | −0.479305 | −0.0189908 | ||||||||
\(638\) | 12.9373 | 0.512192 | ||||||||
\(639\) | 3.93603 | 0.155707 | ||||||||
\(640\) | −21.3499 | −0.843928 | ||||||||
\(641\) | 6.16145 | 0.243363 | 0.121681 | − | 0.992569i | \(-0.461171\pi\) | ||||
0.121681 | + | 0.992569i | \(0.461171\pi\) | |||||||
\(642\) | −35.8318 | −1.41417 | ||||||||
\(643\) | −11.0271 | −0.434866 | −0.217433 | − | 0.976075i | \(-0.569768\pi\) | ||||
−0.217433 | + | 0.976075i | \(0.569768\pi\) | |||||||
\(644\) | −79.9719 | −3.15133 | ||||||||
\(645\) | 60.9738 | 2.40084 | ||||||||
\(646\) | −9.77410 | −0.384557 | ||||||||
\(647\) | 20.1232 | 0.791125 | 0.395562 | − | 0.918439i | \(-0.370550\pi\) | ||||
0.395562 | + | 0.918439i | \(0.370550\pi\) | |||||||
\(648\) | 44.5246 | 1.74909 | ||||||||
\(649\) | 39.7097 | 1.55874 | ||||||||
\(650\) | −3.81423 | −0.149606 | ||||||||
\(651\) | −16.7275 | −0.655601 | ||||||||
\(652\) | 77.4169 | 3.03188 | ||||||||
\(653\) | −17.9445 | −0.702224 | −0.351112 | − | 0.936333i | \(-0.614196\pi\) | ||||
−0.351112 | + | 0.936333i | \(0.614196\pi\) | |||||||
\(654\) | −35.9237 | −1.40473 | ||||||||
\(655\) | 47.2161 | 1.84488 | ||||||||
\(656\) | −60.6649 | −2.36857 | ||||||||
\(657\) | −1.87216 | −0.0730401 | ||||||||
\(658\) | −29.0158 | −1.13115 | ||||||||
\(659\) | −8.14962 | −0.317464 | −0.158732 | − | 0.987322i | \(-0.550741\pi\) | ||||
−0.158732 | + | 0.987322i | \(0.550741\pi\) | |||||||
\(660\) | −104.571 | −4.07042 | ||||||||
\(661\) | 4.92480 | 0.191553 | 0.0957763 | − | 0.995403i | \(-0.469467\pi\) | ||||
0.0957763 | + | 0.995403i | \(0.469467\pi\) | |||||||
\(662\) | 9.73490 | 0.378358 | ||||||||
\(663\) | 0.208911 | 0.00811344 | ||||||||
\(664\) | 31.1552 | 1.20906 | ||||||||
\(665\) | 29.2371 | 1.13376 | ||||||||
\(666\) | 15.1952 | 0.588804 | ||||||||
\(667\) | −11.9172 | −0.461437 | ||||||||
\(668\) | −117.834 | −4.55912 | ||||||||
\(669\) | −21.4602 | −0.829699 | ||||||||
\(670\) | 49.5177 | 1.91304 | ||||||||
\(671\) | 41.2914 | 1.59404 | ||||||||
\(672\) | 24.0518 | 0.927818 | ||||||||
\(673\) | −10.5249 | −0.405704 | −0.202852 | − | 0.979209i | \(-0.565021\pi\) | ||||
−0.202852 | + | 0.979209i | \(0.565021\pi\) | |||||||
\(674\) | −78.3994 | −3.01983 | ||||||||
\(675\) | −58.0493 | −2.23432 | ||||||||
\(676\) | −60.8245 | −2.33940 | ||||||||
\(677\) | 18.6657 | 0.717381 | 0.358691 | − | 0.933457i | \(-0.383223\pi\) | ||||
0.358691 | + | 0.933457i | \(0.383223\pi\) | |||||||
\(678\) | −23.2355 | −0.892353 | ||||||||
\(679\) | −13.7903 | −0.529222 | ||||||||
\(680\) | 26.2847 | 1.00797 | ||||||||
\(681\) | 38.8522 | 1.48882 | ||||||||
\(682\) | −56.1591 | −2.15044 | ||||||||
\(683\) | −37.7647 | −1.44503 | −0.722513 | − | 0.691357i | \(-0.757013\pi\) | ||||
−0.722513 | + | 0.691357i | \(0.757013\pi\) | |||||||
\(684\) | −12.8334 | −0.490699 | ||||||||
\(685\) | 20.1164 | 0.768606 | ||||||||
\(686\) | −51.1060 | −1.95124 | ||||||||
\(687\) | 32.5164 | 1.24058 | ||||||||
\(688\) | −88.1368 | −3.36018 | ||||||||
\(689\) | −0.142589 | −0.00543220 | ||||||||
\(690\) | 137.437 | 5.23213 | ||||||||
\(691\) | −9.96020 | −0.378904 | −0.189452 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189452 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(692\) | −49.6016 | −1.88557 | ||||||||
\(693\) | 5.01472 | 0.190493 | ||||||||
\(694\) | 19.2380 | 0.730266 | ||||||||
\(695\) | 59.9015 | 2.27219 | ||||||||
\(696\) | 14.0315 | 0.531862 | ||||||||
\(697\) | −6.82449 | −0.258496 | ||||||||
\(698\) | 22.4802 | 0.850888 | ||||||||
\(699\) | 8.42715 | 0.318744 | ||||||||
\(700\) | −92.4724 | −3.49513 | ||||||||
\(701\) | −8.51557 | −0.321629 | −0.160814 | − | 0.986985i | \(-0.551412\pi\) | ||||
−0.160814 | + | 0.986985i | \(0.551412\pi\) | |||||||
\(702\) | 2.06889 | 0.0780850 | ||||||||
\(703\) | 32.8520 | 1.23904 | ||||||||
\(704\) | 16.2372 | 0.611961 | ||||||||
\(705\) | 34.9494 | 1.31627 | ||||||||
\(706\) | −47.9985 | −1.80645 | ||||||||
\(707\) | 23.0596 | 0.867245 | ||||||||
\(708\) | 75.1353 | 2.82376 | ||||||||
\(709\) | 14.2980 | 0.536973 | 0.268487 | − | 0.963283i | \(-0.413476\pi\) | ||||
0.268487 | + | 0.963283i | \(0.413476\pi\) | |||||||
\(710\) | −56.9623 | −2.13776 | ||||||||
\(711\) | 8.71291 | 0.326760 | ||||||||
\(712\) | 30.4113 | 1.13971 | ||||||||
\(713\) | 51.7312 | 1.93735 | ||||||||
\(714\) | 7.22650 | 0.270445 | ||||||||
\(715\) | −2.09802 | −0.0784614 | ||||||||
\(716\) | −112.704 | −4.21193 | ||||||||
\(717\) | 5.30058 | 0.197954 | ||||||||
\(718\) | −72.9525 | −2.72256 | ||||||||
\(719\) | −8.40001 | −0.313268 | −0.156634 | − | 0.987657i | \(-0.550064\pi\) | ||||
−0.156634 | + | 0.987657i | \(0.550064\pi\) | |||||||
\(720\) | 23.5450 | 0.877470 | ||||||||
\(721\) | −4.50942 | −0.167939 | ||||||||
\(722\) | 9.54188 | 0.355112 | ||||||||
\(723\) | 41.1377 | 1.52993 | ||||||||
\(724\) | 32.1815 | 1.19602 | ||||||||
\(725\) | −13.7800 | −0.511777 | ||||||||
\(726\) | −12.1899 | −0.452410 | ||||||||
\(727\) | 27.9374 | 1.03614 | 0.518069 | − | 0.855339i | \(-0.326651\pi\) | ||||
0.518069 | + | 0.855339i | \(0.326651\pi\) | |||||||
\(728\) | 1.88914 | 0.0700162 | ||||||||
\(729\) | 30.0171 | 1.11174 | ||||||||
\(730\) | 27.0940 | 1.00279 | ||||||||
\(731\) | −9.91495 | −0.366718 | ||||||||
\(732\) | 78.1280 | 2.88770 | ||||||||
\(733\) | −43.6711 | −1.61303 | −0.806514 | − | 0.591215i | \(-0.798648\pi\) | ||||
−0.806514 | + | 0.591215i | \(0.798648\pi\) | |||||||
\(734\) | −9.50188 | −0.350721 | ||||||||
\(735\) | 19.9703 | 0.736614 | ||||||||
\(736\) | −74.3823 | −2.74177 | ||||||||
\(737\) | 18.3623 | 0.676385 | ||||||||
\(738\) | −12.7849 | −0.470618 | ||||||||
\(739\) | 2.08967 | 0.0768698 | 0.0384349 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384349 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(740\) | −154.126 | −5.66579 | ||||||||
\(741\) | 0.846141 | 0.0310838 | ||||||||
\(742\) | −4.93232 | −0.181071 | ||||||||
\(743\) | 18.9152 | 0.693931 | 0.346965 | − | 0.937878i | \(-0.387212\pi\) | ||||
0.346965 | + | 0.937878i | \(0.387212\pi\) | |||||||
\(744\) | −60.9089 | −2.23303 | ||||||||
\(745\) | 88.4982 | 3.24232 | ||||||||
\(746\) | 82.1190 | 3.00659 | ||||||||
\(747\) | 3.13949 | 0.114868 | ||||||||
\(748\) | 17.0043 | 0.621738 | ||||||||
\(749\) | −17.4290 | −0.636842 | ||||||||
\(750\) | 82.1103 | 2.99825 | ||||||||
\(751\) | 0.164356 | 0.00599743 | 0.00299871 | − | 0.999996i | \(-0.499045\pi\) | ||||
0.00299871 | + | 0.999996i | \(0.499045\pi\) | |||||||
\(752\) | −50.5189 | −1.84223 | ||||||||
\(753\) | −3.29495 | −0.120075 | ||||||||
\(754\) | 0.491122 | 0.0178856 | ||||||||
\(755\) | −3.91728 | −0.142564 | ||||||||
\(756\) | 50.1582 | 1.82424 | ||||||||
\(757\) | −41.5741 | −1.51104 | −0.755518 | − | 0.655128i | \(-0.772615\pi\) | ||||
−0.755518 | + | 0.655128i | \(0.772615\pi\) | |||||||
\(758\) | −17.3201 | −0.629095 | ||||||||
\(759\) | 50.9648 | 1.84990 | ||||||||
\(760\) | 106.460 | 3.86170 | ||||||||
\(761\) | −6.44288 | −0.233554 | −0.116777 | − | 0.993158i | \(-0.537256\pi\) | ||||
−0.116777 | + | 0.993158i | \(0.537256\pi\) | |||||||
\(762\) | −68.2879 | −2.47381 | ||||||||
\(763\) | −17.4737 | −0.632592 | ||||||||
\(764\) | 73.8996 | 2.67359 | ||||||||
\(765\) | 2.64869 | 0.0957637 | ||||||||
\(766\) | −47.7093 | −1.72381 | ||||||||
\(767\) | 1.50745 | 0.0544308 | ||||||||
\(768\) | −34.4854 | −1.24438 | ||||||||
\(769\) | 38.0509 | 1.37215 | 0.686075 | − | 0.727531i | \(-0.259332\pi\) | ||||
0.686075 | + | 0.727531i | \(0.259332\pi\) | |||||||
\(770\) | −72.5730 | −2.61535 | ||||||||
\(771\) | −8.35090 | −0.300750 | ||||||||
\(772\) | 88.2251 | 3.17529 | ||||||||
\(773\) | 26.9944 | 0.970921 | 0.485460 | − | 0.874259i | \(-0.338652\pi\) | ||||
0.485460 | + | 0.874259i | \(0.338652\pi\) | |||||||
\(774\) | −18.5745 | −0.667646 | ||||||||
\(775\) | 59.8173 | 2.14870 | ||||||||
\(776\) | −50.2139 | −1.80257 | ||||||||
\(777\) | −24.2892 | −0.871371 | ||||||||
\(778\) | −80.4739 | −2.88513 | ||||||||
\(779\) | −27.6409 | −0.990337 | ||||||||
\(780\) | −3.96969 | −0.142138 | ||||||||
\(781\) | −21.1229 | −0.755838 | ||||||||
\(782\) | −22.3486 | −0.799184 | ||||||||
\(783\) | 7.47446 | 0.267116 | ||||||||
\(784\) | −28.8667 | −1.03096 | ||||||||
\(785\) | −31.1255 | −1.11092 | ||||||||
\(786\) | 47.2678 | 1.68599 | ||||||||
\(787\) | 5.34202 | 0.190423 | 0.0952113 | − | 0.995457i | \(-0.469647\pi\) | ||||
0.0952113 | + | 0.995457i | \(0.469647\pi\) | |||||||
\(788\) | −29.5135 | −1.05138 | ||||||||
\(789\) | −7.14489 | −0.254365 | ||||||||
\(790\) | −126.093 | −4.48620 | ||||||||
\(791\) | −11.3020 | −0.401853 | ||||||||
\(792\) | 18.2599 | 0.648836 | ||||||||
\(793\) | 1.56749 | 0.0556633 | ||||||||
\(794\) | −14.8345 | −0.526458 | ||||||||
\(795\) | 5.94096 | 0.210704 | ||||||||
\(796\) | 82.1467 | 2.91161 | ||||||||
\(797\) | 23.2653 | 0.824101 | 0.412050 | − | 0.911161i | \(-0.364813\pi\) | ||||
0.412050 | + | 0.911161i | \(0.364813\pi\) | |||||||
\(798\) | 29.2691 | 1.03611 | ||||||||
\(799\) | −5.68312 | −0.201054 | ||||||||
\(800\) | −86.0091 | −3.04088 | ||||||||
\(801\) | 3.06453 | 0.108280 | ||||||||
\(802\) | 0.662600 | 0.0233972 | ||||||||
\(803\) | 10.0471 | 0.354554 | ||||||||
\(804\) | 34.7436 | 1.22531 | ||||||||
\(805\) | 66.8509 | 2.35618 | ||||||||
\(806\) | −2.13190 | −0.0750929 | ||||||||
\(807\) | −7.15382 | −0.251827 | ||||||||
\(808\) | 83.9658 | 2.95391 | ||||||||
\(809\) | 14.1968 | 0.499134 | 0.249567 | − | 0.968358i | \(-0.419712\pi\) | ||||
0.249567 | + | 0.968358i | \(0.419712\pi\) | |||||||
\(810\) | −64.9317 | −2.28147 | ||||||||
\(811\) | 37.6255 | 1.32121 | 0.660604 | − | 0.750734i | \(-0.270300\pi\) | ||||
0.660604 | + | 0.750734i | \(0.270300\pi\) | |||||||
\(812\) | 11.9068 | 0.417847 | ||||||||
\(813\) | 28.4948 | 0.999357 | ||||||||
\(814\) | −81.5463 | −2.85820 | ||||||||
\(815\) | −64.7151 | −2.26687 | ||||||||
\(816\) | 12.5819 | 0.440456 | ||||||||
\(817\) | −40.1579 | −1.40495 | ||||||||
\(818\) | 99.0524 | 3.46329 | ||||||||
\(819\) | 0.190367 | 0.00665197 | ||||||||
\(820\) | 129.678 | 4.52854 | ||||||||
\(821\) | 49.9913 | 1.74471 | 0.872354 | − | 0.488875i | \(-0.162593\pi\) | ||||
0.872354 | + | 0.488875i | \(0.162593\pi\) | |||||||
\(822\) | 20.1384 | 0.702407 | ||||||||
\(823\) | 40.3708 | 1.40724 | 0.703619 | − | 0.710578i | \(-0.251566\pi\) | ||||
0.703619 | + | 0.710578i | \(0.251566\pi\) | |||||||
\(824\) | −16.4199 | −0.572015 | ||||||||
\(825\) | 58.9312 | 2.05172 | ||||||||
\(826\) | 52.1445 | 1.81434 | ||||||||
\(827\) | 18.0366 | 0.627195 | 0.313598 | − | 0.949556i | \(-0.398466\pi\) | ||||
0.313598 | + | 0.949556i | \(0.398466\pi\) | |||||||
\(828\) | −29.3438 | −1.01977 | ||||||||
\(829\) | −23.6846 | −0.822601 | −0.411300 | − | 0.911500i | \(-0.634925\pi\) | ||||
−0.411300 | + | 0.911500i | \(0.634925\pi\) | |||||||
\(830\) | −45.4347 | −1.57706 | ||||||||
\(831\) | 39.9583 | 1.38614 | ||||||||
\(832\) | 0.616391 | 0.0213695 | ||||||||
\(833\) | −3.24736 | −0.112514 | ||||||||
\(834\) | 59.9671 | 2.07649 | ||||||||
\(835\) | 98.5007 | 3.40876 | ||||||||
\(836\) | 68.8714 | 2.38197 | ||||||||
\(837\) | −32.4457 | −1.12149 | ||||||||
\(838\) | −90.0960 | −3.11232 | ||||||||
\(839\) | 21.8035 | 0.752739 | 0.376370 | − | 0.926470i | \(-0.377172\pi\) | ||||
0.376370 | + | 0.926470i | \(0.377172\pi\) | |||||||
\(840\) | −78.7111 | −2.71579 | ||||||||
\(841\) | −27.2257 | −0.938816 | ||||||||
\(842\) | −5.96180 | −0.205457 | ||||||||
\(843\) | −6.94300 | −0.239130 | ||||||||
\(844\) | −76.6837 | −2.63956 | ||||||||
\(845\) | 50.8450 | 1.74912 | ||||||||
\(846\) | −10.6467 | −0.366040 | ||||||||
\(847\) | −5.92932 | −0.203734 | ||||||||
\(848\) | −8.58758 | −0.294899 | ||||||||
\(849\) | −30.2399 | −1.03783 | ||||||||
\(850\) | −25.8419 | −0.886371 | ||||||||
\(851\) | 75.1166 | 2.57496 | ||||||||
\(852\) | −39.9671 | −1.36925 | ||||||||
\(853\) | 32.2129 | 1.10295 | 0.551474 | − | 0.834192i | \(-0.314065\pi\) | ||||
0.551474 | + | 0.834192i | \(0.314065\pi\) | |||||||
\(854\) | 54.2215 | 1.85542 | ||||||||
\(855\) | 10.7279 | 0.366885 | ||||||||
\(856\) | −63.4634 | −2.16914 | ||||||||
\(857\) | 41.0072 | 1.40078 | 0.700390 | − | 0.713760i | \(-0.253009\pi\) | ||||
0.700390 | + | 0.713760i | \(0.253009\pi\) | |||||||
\(858\) | −2.10031 | −0.0717036 | ||||||||
\(859\) | −24.6072 | −0.839588 | −0.419794 | − | 0.907619i | \(-0.637898\pi\) | ||||
−0.419794 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(860\) | 188.402 | 6.42445 | ||||||||
\(861\) | 20.4363 | 0.696468 | ||||||||
\(862\) | 7.88382 | 0.268524 | ||||||||
\(863\) | −20.0106 | −0.681170 | −0.340585 | − | 0.940214i | \(-0.610625\pi\) | ||||
−0.340585 | + | 0.940214i | \(0.610625\pi\) | |||||||
\(864\) | 46.6525 | 1.58715 | ||||||||
\(865\) | 41.4635 | 1.40980 | ||||||||
\(866\) | 43.0103 | 1.46155 | ||||||||
\(867\) | −24.3669 | −0.827542 | ||||||||
\(868\) | −51.6859 | −1.75433 | ||||||||
\(869\) | −46.7584 | −1.58617 | ||||||||
\(870\) | −20.4626 | −0.693747 | ||||||||
\(871\) | 0.697066 | 0.0236192 | ||||||||
\(872\) | −63.6263 | −2.15466 | ||||||||
\(873\) | −5.06001 | −0.171255 | ||||||||
\(874\) | −90.5173 | −3.06179 | ||||||||
\(875\) | 39.9395 | 1.35020 | ||||||||
\(876\) | 19.0102 | 0.642297 | ||||||||
\(877\) | 48.7666 | 1.64673 | 0.823366 | − | 0.567511i | \(-0.192094\pi\) | ||||
0.823366 | + | 0.567511i | \(0.192094\pi\) | |||||||
\(878\) | 39.3030 | 1.32641 | ||||||||
\(879\) | 26.1156 | 0.880858 | ||||||||
\(880\) | −126.356 | −4.25945 | ||||||||
\(881\) | 40.1845 | 1.35385 | 0.676925 | − | 0.736052i | \(-0.263312\pi\) | ||||
0.676925 | + | 0.736052i | \(0.263312\pi\) | |||||||
\(882\) | −6.08356 | −0.204844 | ||||||||
\(883\) | −15.2135 | −0.511977 | −0.255988 | − | 0.966680i | \(-0.582401\pi\) | ||||
−0.255988 | + | 0.966680i | \(0.582401\pi\) | |||||||
\(884\) | 0.645511 | 0.0217109 | ||||||||
\(885\) | −62.8079 | −2.11126 | ||||||||
\(886\) | 15.5140 | 0.521204 | ||||||||
\(887\) | 41.2413 | 1.38475 | 0.692374 | − | 0.721539i | \(-0.256565\pi\) | ||||
0.692374 | + | 0.721539i | \(0.256565\pi\) | |||||||
\(888\) | −88.4433 | −2.96796 | ||||||||
\(889\) | −33.2161 | −1.11403 | ||||||||
\(890\) | −44.3499 | −1.48661 | ||||||||
\(891\) | −24.0782 | −0.806650 | ||||||||
\(892\) | −66.3095 | −2.22021 | ||||||||
\(893\) | −23.0180 | −0.770269 | ||||||||
\(894\) | 88.5951 | 2.96306 | ||||||||
\(895\) | 94.2123 | 3.14917 | ||||||||
\(896\) | −10.3962 | −0.347313 | ||||||||
\(897\) | 1.93471 | 0.0645981 | ||||||||
\(898\) | 73.5583 | 2.45467 | ||||||||
\(899\) | −7.70212 | −0.256880 | ||||||||
\(900\) | −33.9306 | −1.13102 | ||||||||
\(901\) | −0.966060 | −0.0321841 | ||||||||
\(902\) | 68.6109 | 2.28449 | ||||||||
\(903\) | 29.6909 | 0.988050 | ||||||||
\(904\) | −41.1535 | −1.36875 | ||||||||
\(905\) | −26.9015 | −0.894236 | ||||||||
\(906\) | −3.92157 | −0.130285 | ||||||||
\(907\) | −11.4689 | −0.380819 | −0.190409 | − | 0.981705i | \(-0.560982\pi\) | ||||
−0.190409 | + | 0.981705i | \(0.560982\pi\) | |||||||
\(908\) | 120.049 | 3.98396 | ||||||||
\(909\) | 8.46117 | 0.280639 | ||||||||
\(910\) | −2.75500 | −0.0913273 | ||||||||
\(911\) | −12.6546 | −0.419265 | −0.209632 | − | 0.977780i | \(-0.567227\pi\) | ||||
−0.209632 | + | 0.977780i | \(0.567227\pi\) | |||||||
\(912\) | 50.9599 | 1.68745 | ||||||||
\(913\) | −16.8483 | −0.557596 | ||||||||
\(914\) | 44.4396 | 1.46993 | ||||||||
\(915\) | −65.3095 | −2.15907 | ||||||||
\(916\) | 100.472 | 3.31969 | ||||||||
\(917\) | 22.9916 | 0.759250 | ||||||||
\(918\) | 14.0170 | 0.462630 | ||||||||
\(919\) | −5.85207 | −0.193042 | −0.0965209 | − | 0.995331i | \(-0.530771\pi\) | ||||
−0.0965209 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(920\) | 243.421 | 8.02536 | ||||||||
\(921\) | 37.8096 | 1.24587 | ||||||||
\(922\) | −0.712751 | −0.0234732 | ||||||||
\(923\) | −0.801863 | −0.0263937 | ||||||||
\(924\) | −50.9202 | −1.67515 | ||||||||
\(925\) | 86.8582 | 2.85588 | ||||||||
\(926\) | −2.12442 | −0.0698128 | ||||||||
\(927\) | −1.65462 | −0.0543450 | ||||||||
\(928\) | 11.0746 | 0.363541 | ||||||||
\(929\) | −12.8196 | −0.420596 | −0.210298 | − | 0.977637i | \(-0.567443\pi\) | ||||
−0.210298 | + | 0.977637i | \(0.567443\pi\) | |||||||
\(930\) | 88.8255 | 2.91270 | ||||||||
\(931\) | −13.1526 | −0.431060 | ||||||||
\(932\) | 26.0389 | 0.852934 | ||||||||
\(933\) | 35.7365 | 1.16996 | ||||||||
\(934\) | −48.2161 | −1.57768 | ||||||||
\(935\) | −14.2144 | −0.464860 | ||||||||
\(936\) | 0.693176 | 0.0226572 | ||||||||
\(937\) | −35.8178 | −1.17012 | −0.585058 | − | 0.810992i | \(-0.698928\pi\) | ||||
−0.585058 | + | 0.810992i | \(0.698928\pi\) | |||||||
\(938\) | 24.1124 | 0.787297 | ||||||||
\(939\) | 0.920109 | 0.0300266 | ||||||||
\(940\) | 107.990 | 3.52223 | ||||||||
\(941\) | 52.9402 | 1.72580 | 0.862900 | − | 0.505375i | \(-0.168646\pi\) | ||||
0.862900 | + | 0.505375i | \(0.168646\pi\) | |||||||
\(942\) | −31.1596 | −1.01523 | ||||||||
\(943\) | −63.2012 | −2.05811 | ||||||||
\(944\) | 90.7879 | 2.95490 | ||||||||
\(945\) | −41.9288 | −1.36394 | ||||||||
\(946\) | 99.6812 | 3.24091 | ||||||||
\(947\) | −26.0614 | −0.846883 | −0.423441 | − | 0.905924i | \(-0.639178\pi\) | ||||
−0.423441 | + | 0.905924i | \(0.639178\pi\) | |||||||
\(948\) | −88.4723 | −2.87345 | ||||||||
\(949\) | 0.381405 | 0.0123809 | ||||||||
\(950\) | −104.666 | −3.39582 | ||||||||
\(951\) | −4.67724 | −0.151670 | ||||||||
\(952\) | 12.7992 | 0.414825 | ||||||||
\(953\) | −30.6756 | −0.993679 | −0.496839 | − | 0.867843i | \(-0.665506\pi\) | ||||
−0.496839 | + | 0.867843i | \(0.665506\pi\) | |||||||
\(954\) | −1.80980 | −0.0585944 | ||||||||
\(955\) | −61.7749 | −1.99899 | ||||||||
\(956\) | 16.3782 | 0.529708 | ||||||||
\(957\) | −7.58801 | −0.245286 | ||||||||
\(958\) | −47.3012 | −1.52823 | ||||||||
\(959\) | 9.79555 | 0.316315 | ||||||||
\(960\) | −25.6819 | −0.828881 | ||||||||
\(961\) | 2.43391 | 0.0785132 | ||||||||
\(962\) | −3.09564 | −0.0998073 | ||||||||
\(963\) | −6.39516 | −0.206081 | ||||||||
\(964\) | 127.111 | 4.09396 | ||||||||
\(965\) | −73.7500 | −2.37410 | ||||||||
\(966\) | 66.9241 | 2.15325 | ||||||||
\(967\) | −17.3466 | −0.557830 | −0.278915 | − | 0.960316i | \(-0.589975\pi\) | ||||
−0.278915 | + | 0.960316i | \(0.589975\pi\) | |||||||
\(968\) | −21.5902 | −0.693934 | ||||||||
\(969\) | 5.73273 | 0.184162 | ||||||||
\(970\) | 73.2286 | 2.35123 | ||||||||
\(971\) | 14.9833 | 0.480838 | 0.240419 | − | 0.970669i | \(-0.422715\pi\) | ||||
0.240419 | + | 0.970669i | \(0.422715\pi\) | |||||||
\(972\) | 33.3272 | 1.06897 | ||||||||
\(973\) | 29.1687 | 0.935106 | ||||||||
\(974\) | −68.5194 | −2.19550 | ||||||||
\(975\) | 2.23713 | 0.0716455 | ||||||||
\(976\) | 94.4041 | 3.02180 | ||||||||
\(977\) | 41.3195 | 1.32193 | 0.660964 | − | 0.750417i | \(-0.270148\pi\) | ||||
0.660964 | + | 0.750417i | \(0.270148\pi\) | |||||||
\(978\) | −64.7859 | −2.07163 | ||||||||
\(979\) | −16.4460 | −0.525615 | ||||||||
\(980\) | 61.7058 | 1.97112 | ||||||||
\(981\) | −6.41158 | −0.204706 | ||||||||
\(982\) | −71.2396 | −2.27335 | ||||||||
\(983\) | −49.6718 | −1.58429 | −0.792143 | − | 0.610336i | \(-0.791034\pi\) | ||||
−0.792143 | + | 0.610336i | \(0.791034\pi\) | |||||||
\(984\) | 74.4139 | 2.37223 | ||||||||
\(985\) | 24.6712 | 0.786091 | ||||||||
\(986\) | 3.32742 | 0.105967 | ||||||||
\(987\) | 17.0184 | 0.541702 | ||||||||
\(988\) | 2.61448 | 0.0831777 | ||||||||
\(989\) | −91.8216 | −2.91976 | ||||||||
\(990\) | −26.6290 | −0.846324 | ||||||||
\(991\) | −4.59118 | −0.145844 | −0.0729219 | − | 0.997338i | \(-0.523232\pi\) | ||||
−0.0729219 | + | 0.997338i | \(0.523232\pi\) | |||||||
\(992\) | −48.0734 | −1.52633 | ||||||||
\(993\) | −5.70974 | −0.181193 | ||||||||
\(994\) | −27.7375 | −0.879779 | ||||||||
\(995\) | −68.6688 | −2.17695 | ||||||||
\(996\) | −31.8789 | −1.01012 | ||||||||
\(997\) | −7.02084 | −0.222352 | −0.111176 | − | 0.993801i | \(-0.535462\pi\) | ||||
−0.111176 | + | 0.993801i | \(0.535462\pi\) | |||||||
\(998\) | −18.1362 | −0.574091 | ||||||||
\(999\) | −47.1130 | −1.49059 |
(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 | 8003.2.a.c.1.9 | ✓ | 172 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.c.1.9 | ✓ | 172 | 1.1 | even | 1 | trivial |