Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32771 | −1.64594 | −0.822970 | − | 0.568085i | \(-0.807685\pi\) | ||||
−0.822970 | + | 0.568085i | \(0.807685\pi\) | |||||||
\(3\) | −1.02581 | −0.592251 | −0.296125 | − | 0.955149i | \(-0.595695\pi\) | ||||
−0.296125 | + | 0.955149i | \(0.595695\pi\) | |||||||
\(4\) | 3.41824 | 1.70912 | ||||||||
\(5\) | 4.27433 | 1.91154 | 0.955768 | − | 0.294121i | \(-0.0950269\pi\) | ||||
0.955768 | + | 0.294121i | \(0.0950269\pi\) | |||||||
\(6\) | 2.38779 | 0.974809 | ||||||||
\(7\) | 1.70170 | 0.643182 | 0.321591 | − | 0.946879i | \(-0.395782\pi\) | ||||
0.321591 | + | 0.946879i | \(0.395782\pi\) | |||||||
\(8\) | −3.30124 | −1.16717 | ||||||||
\(9\) | −1.94772 | −0.649239 | ||||||||
\(10\) | −9.94939 | −3.14627 | ||||||||
\(11\) | 2.00974 | 0.605959 | 0.302980 | − | 0.952997i | \(-0.402019\pi\) | ||||
0.302980 | + | 0.952997i | \(0.402019\pi\) | |||||||
\(12\) | −3.50646 | −1.01223 | ||||||||
\(13\) | 1.61811 | 0.448782 | 0.224391 | − | 0.974499i | \(-0.427961\pi\) | ||||
0.224391 | + | 0.974499i | \(0.427961\pi\) | |||||||
\(14\) | −3.96106 | −1.05864 | ||||||||
\(15\) | −4.38464 | −1.13211 | ||||||||
\(16\) | 0.847868 | 0.211967 | ||||||||
\(17\) | −6.17530 | −1.49773 | −0.748865 | − | 0.662723i | \(-0.769401\pi\) | ||||
−0.748865 | + | 0.662723i | \(0.769401\pi\) | |||||||
\(18\) | 4.53372 | 1.06861 | ||||||||
\(19\) | 4.28930 | 0.984032 | 0.492016 | − | 0.870586i | \(-0.336260\pi\) | ||||
0.492016 | + | 0.870586i | \(0.336260\pi\) | |||||||
\(20\) | 14.6107 | 3.26704 | ||||||||
\(21\) | −1.74562 | −0.380925 | ||||||||
\(22\) | −4.67809 | −0.997372 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.38644 | 0.691255 | ||||||||
\(25\) | 13.2699 | 2.65397 | ||||||||
\(26\) | −3.76649 | −0.738669 | ||||||||
\(27\) | 5.07541 | 0.976763 | ||||||||
\(28\) | 5.81681 | 1.09927 | ||||||||
\(29\) | 0.608216 | 0.112943 | 0.0564714 | − | 0.998404i | \(-0.482015\pi\) | ||||
0.0564714 | + | 0.998404i | \(0.482015\pi\) | |||||||
\(30\) | 10.2062 | 1.86338 | ||||||||
\(31\) | 5.38009 | 0.966292 | 0.483146 | − | 0.875540i | \(-0.339494\pi\) | ||||
0.483146 | + | 0.875540i | \(0.339494\pi\) | |||||||
\(32\) | 4.62890 | 0.818281 | ||||||||
\(33\) | −2.06161 | −0.358880 | ||||||||
\(34\) | 14.3743 | 2.46517 | ||||||||
\(35\) | 7.27362 | 1.22947 | ||||||||
\(36\) | −6.65776 | −1.10963 | ||||||||
\(37\) | 1.89650 | 0.311783 | 0.155892 | − | 0.987774i | \(-0.450175\pi\) | ||||
0.155892 | + | 0.987774i | \(0.450175\pi\) | |||||||
\(38\) | −9.98424 | −1.61966 | ||||||||
\(39\) | −1.65987 | −0.265792 | ||||||||
\(40\) | −14.1106 | −2.23108 | ||||||||
\(41\) | −5.00330 | −0.781384 | −0.390692 | − | 0.920521i | \(-0.627764\pi\) | ||||
−0.390692 | + | 0.920521i | \(0.627764\pi\) | |||||||
\(42\) | 4.06329 | 0.626980 | ||||||||
\(43\) | 9.86830 | 1.50490 | 0.752451 | − | 0.658648i | \(-0.228872\pi\) | ||||
0.752451 | + | 0.658648i | \(0.228872\pi\) | |||||||
\(44\) | 6.86976 | 1.03566 | ||||||||
\(45\) | −8.32518 | −1.24104 | ||||||||
\(46\) | −2.32771 | −0.343202 | ||||||||
\(47\) | −8.33383 | −1.21561 | −0.607807 | − | 0.794085i | \(-0.707951\pi\) | ||||
−0.607807 | + | 0.794085i | \(0.707951\pi\) | |||||||
\(48\) | −0.869750 | −0.125538 | ||||||||
\(49\) | −4.10422 | −0.586317 | ||||||||
\(50\) | −30.8884 | −4.36828 | ||||||||
\(51\) | 6.33467 | 0.887031 | ||||||||
\(52\) | 5.53107 | 0.767022 | ||||||||
\(53\) | −12.1363 | −1.66705 | −0.833526 | − | 0.552480i | \(-0.813681\pi\) | ||||
−0.833526 | + | 0.552480i | \(0.813681\pi\) | |||||||
\(54\) | −11.8141 | −1.60769 | ||||||||
\(55\) | 8.59028 | 1.15831 | ||||||||
\(56\) | −5.61772 | −0.750700 | ||||||||
\(57\) | −4.40000 | −0.582794 | ||||||||
\(58\) | −1.41575 | −0.185897 | ||||||||
\(59\) | 13.2643 | 1.72687 | 0.863435 | − | 0.504460i | \(-0.168308\pi\) | ||||
0.863435 | + | 0.504460i | \(0.168308\pi\) | |||||||
\(60\) | −14.9877 | −1.93491 | ||||||||
\(61\) | −1.11954 | −0.143342 | −0.0716712 | − | 0.997428i | \(-0.522833\pi\) | ||||
−0.0716712 | + | 0.997428i | \(0.522833\pi\) | |||||||
\(62\) | −12.5233 | −1.59046 | ||||||||
\(63\) | −3.31443 | −0.417579 | ||||||||
\(64\) | −12.4705 | −1.55881 | ||||||||
\(65\) | 6.91632 | 0.857863 | ||||||||
\(66\) | 4.79882 | 0.590694 | ||||||||
\(67\) | 5.17780 | 0.632569 | 0.316285 | − | 0.948664i | \(-0.397565\pi\) | ||||
0.316285 | + | 0.948664i | \(0.397565\pi\) | |||||||
\(68\) | −21.1086 | −2.55980 | ||||||||
\(69\) | −1.02581 | −0.123493 | ||||||||
\(70\) | −16.9309 | −2.02363 | ||||||||
\(71\) | −9.04501 | −1.07345 | −0.536723 | − | 0.843759i | \(-0.680338\pi\) | ||||
−0.536723 | + | 0.843759i | \(0.680338\pi\) | |||||||
\(72\) | 6.42989 | 0.757770 | ||||||||
\(73\) | 11.1757 | 1.30802 | 0.654008 | − | 0.756488i | \(-0.273086\pi\) | ||||
0.654008 | + | 0.756488i | \(0.273086\pi\) | |||||||
\(74\) | −4.41451 | −0.513176 | ||||||||
\(75\) | −13.6123 | −1.57182 | ||||||||
\(76\) | 14.6618 | 1.68183 | ||||||||
\(77\) | 3.41997 | 0.389742 | ||||||||
\(78\) | 3.86369 | 0.437477 | ||||||||
\(79\) | −7.67606 | −0.863624 | −0.431812 | − | 0.901964i | \(-0.642126\pi\) | ||||
−0.431812 | + | 0.901964i | \(0.642126\pi\) | |||||||
\(80\) | 3.62406 | 0.405183 | ||||||||
\(81\) | 0.636753 | 0.0707504 | ||||||||
\(82\) | 11.6462 | 1.28611 | ||||||||
\(83\) | 0.460957 | 0.0505966 | 0.0252983 | − | 0.999680i | \(-0.491946\pi\) | ||||
0.0252983 | + | 0.999680i | \(0.491946\pi\) | |||||||
\(84\) | −5.96693 | −0.651046 | ||||||||
\(85\) | −26.3952 | −2.86296 | ||||||||
\(86\) | −22.9705 | −2.47698 | ||||||||
\(87\) | −0.623913 | −0.0668905 | ||||||||
\(88\) | −6.63464 | −0.707255 | ||||||||
\(89\) | 8.95569 | 0.949301 | 0.474651 | − | 0.880174i | \(-0.342574\pi\) | ||||
0.474651 | + | 0.880174i | \(0.342574\pi\) | |||||||
\(90\) | 19.3786 | 2.04268 | ||||||||
\(91\) | 2.75353 | 0.288649 | ||||||||
\(92\) | 3.41824 | 0.356376 | ||||||||
\(93\) | −5.51894 | −0.572287 | ||||||||
\(94\) | 19.3987 | 2.00083 | ||||||||
\(95\) | 18.3339 | 1.88101 | ||||||||
\(96\) | −4.74836 | −0.484628 | ||||||||
\(97\) | 12.0748 | 1.22601 | 0.613007 | − | 0.790078i | \(-0.289960\pi\) | ||||
0.613007 | + | 0.790078i | \(0.289960\pi\) | |||||||
\(98\) | 9.55344 | 0.965043 | ||||||||
\(99\) | −3.91440 | −0.393412 | ||||||||
\(100\) | 45.3595 | 4.53595 | ||||||||
\(101\) | 1.50920 | 0.150171 | 0.0750853 | − | 0.997177i | \(-0.476077\pi\) | ||||
0.0750853 | + | 0.997177i | \(0.476077\pi\) | |||||||
\(102\) | −14.7453 | −1.46000 | ||||||||
\(103\) | −10.6660 | −1.05095 | −0.525474 | − | 0.850810i | \(-0.676112\pi\) | ||||
−0.525474 | + | 0.850810i | \(0.676112\pi\) | |||||||
\(104\) | −5.34177 | −0.523803 | ||||||||
\(105\) | −7.46134 | −0.728152 | ||||||||
\(106\) | 28.2498 | 2.74387 | ||||||||
\(107\) | 5.01926 | 0.485230 | 0.242615 | − | 0.970123i | \(-0.421995\pi\) | ||||
0.242615 | + | 0.970123i | \(0.421995\pi\) | |||||||
\(108\) | 17.3490 | 1.66940 | ||||||||
\(109\) | −9.42712 | −0.902954 | −0.451477 | − | 0.892283i | \(-0.649103\pi\) | ||||
−0.451477 | + | 0.892283i | \(0.649103\pi\) | |||||||
\(110\) | −19.9957 | −1.90651 | ||||||||
\(111\) | −1.94545 | −0.184654 | ||||||||
\(112\) | 1.44282 | 0.136333 | ||||||||
\(113\) | 16.2427 | 1.52798 | 0.763990 | − | 0.645228i | \(-0.223238\pi\) | ||||
0.763990 | + | 0.645228i | \(0.223238\pi\) | |||||||
\(114\) | 10.2419 | 0.959244 | ||||||||
\(115\) | 4.27433 | 0.398583 | ||||||||
\(116\) | 2.07903 | 0.193033 | ||||||||
\(117\) | −3.15162 | −0.291367 | ||||||||
\(118\) | −30.8756 | −2.84232 | ||||||||
\(119\) | −10.5085 | −0.963312 | ||||||||
\(120\) | 14.4748 | 1.32136 | ||||||||
\(121\) | −6.96095 | −0.632814 | ||||||||
\(122\) | 2.60596 | 0.235933 | ||||||||
\(123\) | 5.13243 | 0.462775 | ||||||||
\(124\) | 18.3904 | 1.65151 | ||||||||
\(125\) | 35.3481 | 3.16163 | ||||||||
\(126\) | 7.71503 | 0.687310 | ||||||||
\(127\) | −14.1448 | −1.25515 | −0.627575 | − | 0.778556i | \(-0.715952\pi\) | ||||
−0.627575 | + | 0.778556i | \(0.715952\pi\) | |||||||
\(128\) | 19.7698 | 1.74742 | ||||||||
\(129\) | −10.1230 | −0.891279 | ||||||||
\(130\) | −16.0992 | −1.41199 | ||||||||
\(131\) | −6.85130 | −0.598601 | −0.299300 | − | 0.954159i | \(-0.596753\pi\) | ||||
−0.299300 | + | 0.954159i | \(0.596753\pi\) | |||||||
\(132\) | −7.04706 | −0.613368 | ||||||||
\(133\) | 7.29909 | 0.632912 | ||||||||
\(134\) | −12.0524 | −1.04117 | ||||||||
\(135\) | 21.6940 | 1.86712 | ||||||||
\(136\) | 20.3862 | 1.74810 | ||||||||
\(137\) | 11.5482 | 0.986633 | 0.493317 | − | 0.869850i | \(-0.335784\pi\) | ||||
0.493317 | + | 0.869850i | \(0.335784\pi\) | |||||||
\(138\) | 2.38779 | 0.203262 | ||||||||
\(139\) | 11.0022 | 0.933197 | 0.466598 | − | 0.884469i | \(-0.345479\pi\) | ||||
0.466598 | + | 0.884469i | \(0.345479\pi\) | |||||||
\(140\) | 24.8629 | 2.10130 | ||||||||
\(141\) | 8.54891 | 0.719948 | ||||||||
\(142\) | 21.0542 | 1.76683 | ||||||||
\(143\) | 3.25197 | 0.271944 | ||||||||
\(144\) | −1.65141 | −0.137617 | ||||||||
\(145\) | 2.59971 | 0.215894 | ||||||||
\(146\) | −26.0138 | −2.15292 | ||||||||
\(147\) | 4.21014 | 0.347247 | ||||||||
\(148\) | 6.48270 | 0.532874 | ||||||||
\(149\) | 11.2261 | 0.919682 | 0.459841 | − | 0.888001i | \(-0.347906\pi\) | ||||
0.459841 | + | 0.888001i | \(0.347906\pi\) | |||||||
\(150\) | 31.6856 | 2.58712 | ||||||||
\(151\) | 7.28367 | 0.592737 | 0.296368 | − | 0.955074i | \(-0.404224\pi\) | ||||
0.296368 | + | 0.955074i | \(0.404224\pi\) | |||||||
\(152\) | −14.1600 | −1.14853 | ||||||||
\(153\) | 12.0277 | 0.972385 | ||||||||
\(154\) | −7.96070 | −0.641492 | ||||||||
\(155\) | 22.9962 | 1.84710 | ||||||||
\(156\) | −5.67382 | −0.454269 | ||||||||
\(157\) | 11.7311 | 0.936246 | 0.468123 | − | 0.883663i | \(-0.344930\pi\) | ||||
0.468123 | + | 0.883663i | \(0.344930\pi\) | |||||||
\(158\) | 17.8676 | 1.42147 | ||||||||
\(159\) | 12.4495 | 0.987313 | ||||||||
\(160\) | 19.7854 | 1.56417 | ||||||||
\(161\) | 1.70170 | 0.134113 | ||||||||
\(162\) | −1.48218 | −0.116451 | ||||||||
\(163\) | 7.53172 | 0.589930 | 0.294965 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294965 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(164\) | −17.1025 | −1.33548 | ||||||||
\(165\) | −8.81198 | −0.686012 | ||||||||
\(166\) | −1.07297 | −0.0832789 | ||||||||
\(167\) | 16.9939 | 1.31503 | 0.657515 | − | 0.753441i | \(-0.271607\pi\) | ||||
0.657515 | + | 0.753441i | \(0.271607\pi\) | |||||||
\(168\) | 5.76271 | 0.444603 | ||||||||
\(169\) | −10.3817 | −0.798595 | ||||||||
\(170\) | 61.4405 | 4.71227 | ||||||||
\(171\) | −8.35434 | −0.638872 | ||||||||
\(172\) | 33.7322 | 2.57205 | ||||||||
\(173\) | 6.48923 | 0.493367 | 0.246683 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246683 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(174\) | 1.45229 | 0.110098 | ||||||||
\(175\) | 22.5813 | 1.70699 | ||||||||
\(176\) | 1.70399 | 0.128443 | ||||||||
\(177\) | −13.6067 | −1.02274 | ||||||||
\(178\) | −20.8463 | −1.56249 | ||||||||
\(179\) | −14.4878 | −1.08287 | −0.541435 | − | 0.840743i | \(-0.682119\pi\) | ||||
−0.541435 | + | 0.840743i | \(0.682119\pi\) | |||||||
\(180\) | −28.4574 | −2.12109 | ||||||||
\(181\) | 12.0057 | 0.892379 | 0.446190 | − | 0.894938i | \(-0.352781\pi\) | ||||
0.446190 | + | 0.894938i | \(0.352781\pi\) | |||||||
\(182\) | −6.40942 | −0.475098 | ||||||||
\(183\) | 1.14843 | 0.0848946 | ||||||||
\(184\) | −3.30124 | −0.243371 | ||||||||
\(185\) | 8.10627 | 0.595985 | ||||||||
\(186\) | 12.8465 | 0.941950 | ||||||||
\(187\) | −12.4107 | −0.907563 | ||||||||
\(188\) | −28.4870 | −2.07763 | ||||||||
\(189\) | 8.63682 | 0.628236 | ||||||||
\(190\) | −42.6759 | −3.09604 | ||||||||
\(191\) | −22.3997 | −1.62079 | −0.810393 | − | 0.585887i | \(-0.800746\pi\) | ||||
−0.810393 | + | 0.585887i | \(0.800746\pi\) | |||||||
\(192\) | 12.7923 | 0.923206 | ||||||||
\(193\) | −13.6594 | −0.983222 | −0.491611 | − | 0.870815i | \(-0.663592\pi\) | ||||
−0.491611 | + | 0.870815i | \(0.663592\pi\) | |||||||
\(194\) | −28.1067 | −2.01794 | ||||||||
\(195\) | −7.09482 | −0.508070 | ||||||||
\(196\) | −14.0292 | −1.00209 | ||||||||
\(197\) | −9.60206 | −0.684118 | −0.342059 | − | 0.939678i | \(-0.611124\pi\) | ||||
−0.342059 | + | 0.939678i | \(0.611124\pi\) | |||||||
\(198\) | 9.11160 | 0.647533 | ||||||||
\(199\) | 13.0056 | 0.921945 | 0.460972 | − | 0.887414i | \(-0.347501\pi\) | ||||
0.460972 | + | 0.887414i | \(0.347501\pi\) | |||||||
\(200\) | −43.8070 | −3.09763 | ||||||||
\(201\) | −5.31143 | −0.374640 | ||||||||
\(202\) | −3.51297 | −0.247172 | ||||||||
\(203\) | 1.03500 | 0.0726428 | ||||||||
\(204\) | 21.6534 | 1.51604 | ||||||||
\(205\) | −21.3857 | −1.49364 | ||||||||
\(206\) | 24.8273 | 1.72980 | ||||||||
\(207\) | −1.94772 | −0.135376 | ||||||||
\(208\) | 1.37194 | 0.0951270 | ||||||||
\(209\) | 8.62037 | 0.596283 | ||||||||
\(210\) | 17.3678 | 1.19849 | ||||||||
\(211\) | −14.3769 | −0.989748 | −0.494874 | − | 0.868965i | \(-0.664786\pi\) | ||||
−0.494874 | + | 0.868965i | \(0.664786\pi\) | |||||||
\(212\) | −41.4848 | −2.84919 | ||||||||
\(213\) | 9.27845 | 0.635749 | ||||||||
\(214\) | −11.6834 | −0.798660 | ||||||||
\(215\) | 42.1803 | 2.87667 | ||||||||
\(216\) | −16.7552 | −1.14004 | ||||||||
\(217\) | 9.15529 | 0.621501 | ||||||||
\(218\) | 21.9436 | 1.48621 | ||||||||
\(219\) | −11.4641 | −0.774673 | ||||||||
\(220\) | 29.3636 | 1.97969 | ||||||||
\(221\) | −9.99229 | −0.672154 | ||||||||
\(222\) | 4.52844 | 0.303929 | ||||||||
\(223\) | 24.7345 | 1.65635 | 0.828174 | − | 0.560471i | \(-0.189380\pi\) | ||||
0.828174 | + | 0.560471i | \(0.189380\pi\) | |||||||
\(224\) | 7.87699 | 0.526304 | ||||||||
\(225\) | −25.8459 | −1.72306 | ||||||||
\(226\) | −37.8082 | −2.51496 | ||||||||
\(227\) | −14.2027 | −0.942667 | −0.471333 | − | 0.881955i | \(-0.656227\pi\) | ||||
−0.471333 | + | 0.881955i | \(0.656227\pi\) | |||||||
\(228\) | −15.0402 | −0.996064 | ||||||||
\(229\) | −5.01020 | −0.331083 | −0.165542 | − | 0.986203i | \(-0.552937\pi\) | ||||
−0.165542 | + | 0.986203i | \(0.552937\pi\) | |||||||
\(230\) | −9.94939 | −0.656043 | ||||||||
\(231\) | −3.50823 | −0.230825 | ||||||||
\(232\) | −2.00787 | −0.131823 | ||||||||
\(233\) | −17.8985 | −1.17257 | −0.586285 | − | 0.810105i | \(-0.699410\pi\) | ||||
−0.586285 | + | 0.810105i | \(0.699410\pi\) | |||||||
\(234\) | 7.33605 | 0.479572 | ||||||||
\(235\) | −35.6215 | −2.32369 | ||||||||
\(236\) | 45.3407 | 2.95143 | ||||||||
\(237\) | 7.87416 | 0.511482 | ||||||||
\(238\) | 24.4607 | 1.58555 | ||||||||
\(239\) | 17.4463 | 1.12851 | 0.564255 | − | 0.825600i | \(-0.309163\pi\) | ||||
0.564255 | + | 0.825600i | \(0.309163\pi\) | |||||||
\(240\) | −3.71759 | −0.239970 | ||||||||
\(241\) | 6.26578 | 0.403614 | 0.201807 | − | 0.979425i | \(-0.435319\pi\) | ||||
0.201807 | + | 0.979425i | \(0.435319\pi\) | |||||||
\(242\) | 16.2031 | 1.04157 | ||||||||
\(243\) | −15.8794 | −1.01867 | ||||||||
\(244\) | −3.82685 | −0.244989 | ||||||||
\(245\) | −17.5428 | −1.12077 | ||||||||
\(246\) | −11.9468 | −0.761700 | ||||||||
\(247\) | 6.94054 | 0.441616 | ||||||||
\(248\) | −17.7610 | −1.12782 | ||||||||
\(249\) | −0.472853 | −0.0299659 | ||||||||
\(250\) | −82.2800 | −5.20385 | ||||||||
\(251\) | 24.6239 | 1.55425 | 0.777123 | − | 0.629349i | \(-0.216678\pi\) | ||||
0.777123 | + | 0.629349i | \(0.216678\pi\) | |||||||
\(252\) | −11.3295 | −0.713691 | ||||||||
\(253\) | 2.00974 | 0.126351 | ||||||||
\(254\) | 32.9251 | 2.06590 | ||||||||
\(255\) | 27.0764 | 1.69559 | ||||||||
\(256\) | −21.0775 | −1.31735 | ||||||||
\(257\) | 6.79868 | 0.424090 | 0.212045 | − | 0.977260i | \(-0.431988\pi\) | ||||
0.212045 | + | 0.977260i | \(0.431988\pi\) | |||||||
\(258\) | 23.5634 | 1.46699 | ||||||||
\(259\) | 3.22728 | 0.200533 | ||||||||
\(260\) | 23.6416 | 1.46619 | ||||||||
\(261\) | −1.18463 | −0.0733269 | ||||||||
\(262\) | 15.9478 | 0.985261 | ||||||||
\(263\) | −4.80455 | −0.296261 | −0.148131 | − | 0.988968i | \(-0.547326\pi\) | ||||
−0.148131 | + | 0.988968i | \(0.547326\pi\) | |||||||
\(264\) | 6.80587 | 0.418872 | ||||||||
\(265\) | −51.8746 | −3.18663 | ||||||||
\(266\) | −16.9902 | −1.04173 | ||||||||
\(267\) | −9.18682 | −0.562224 | ||||||||
\(268\) | 17.6990 | 1.08114 | ||||||||
\(269\) | 16.2703 | 0.992018 | 0.496009 | − | 0.868317i | \(-0.334798\pi\) | ||||
0.496009 | + | 0.868317i | \(0.334798\pi\) | |||||||
\(270\) | −50.4972 | −3.07316 | ||||||||
\(271\) | 14.1453 | 0.859264 | 0.429632 | − | 0.903004i | \(-0.358643\pi\) | ||||
0.429632 | + | 0.903004i | \(0.358643\pi\) | |||||||
\(272\) | −5.23584 | −0.317469 | ||||||||
\(273\) | −2.82460 | −0.170952 | ||||||||
\(274\) | −26.8810 | −1.62394 | ||||||||
\(275\) | 26.6689 | 1.60820 | ||||||||
\(276\) | −3.50646 | −0.211064 | ||||||||
\(277\) | −3.49890 | −0.210228 | −0.105114 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105114 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(278\) | −25.6100 | −1.53599 | ||||||||
\(279\) | −10.4789 | −0.627354 | ||||||||
\(280\) | −24.0120 | −1.43499 | ||||||||
\(281\) | −27.0853 | −1.61577 | −0.807887 | − | 0.589338i | \(-0.799389\pi\) | ||||
−0.807887 | + | 0.589338i | \(0.799389\pi\) | |||||||
\(282\) | −19.8994 | −1.18499 | ||||||||
\(283\) | 32.2220 | 1.91540 | 0.957699 | − | 0.287772i | \(-0.0929147\pi\) | ||||
0.957699 | + | 0.287772i | \(0.0929147\pi\) | |||||||
\(284\) | −30.9180 | −1.83464 | ||||||||
\(285\) | −18.8070 | −1.11403 | ||||||||
\(286\) | −7.56965 | −0.447603 | ||||||||
\(287\) | −8.51411 | −0.502572 | ||||||||
\(288\) | −9.01578 | −0.531260 | ||||||||
\(289\) | 21.1343 | 1.24319 | ||||||||
\(290\) | −6.05138 | −0.355349 | ||||||||
\(291\) | −12.3865 | −0.726108 | ||||||||
\(292\) | 38.2012 | 2.23555 | ||||||||
\(293\) | 12.3090 | 0.719099 | 0.359549 | − | 0.933126i | \(-0.382930\pi\) | ||||
0.359549 | + | 0.933126i | \(0.382930\pi\) | |||||||
\(294\) | −9.80000 | −0.571547 | ||||||||
\(295\) | 56.6961 | 3.30098 | ||||||||
\(296\) | −6.26082 | −0.363903 | ||||||||
\(297\) | 10.2002 | 0.591878 | ||||||||
\(298\) | −26.1312 | −1.51374 | ||||||||
\(299\) | 1.61811 | 0.0935776 | ||||||||
\(300\) | −46.5302 | −2.68642 | ||||||||
\(301\) | 16.7929 | 0.967925 | ||||||||
\(302\) | −16.9543 | −0.975609 | ||||||||
\(303\) | −1.54815 | −0.0889386 | ||||||||
\(304\) | 3.63676 | 0.208582 | ||||||||
\(305\) | −4.78528 | −0.274004 | ||||||||
\(306\) | −27.9971 | −1.60049 | ||||||||
\(307\) | 19.4108 | 1.10783 | 0.553916 | − | 0.832572i | \(-0.313133\pi\) | ||||
0.553916 | + | 0.832572i | \(0.313133\pi\) | |||||||
\(308\) | 11.6903 | 0.666115 | ||||||||
\(309\) | 10.9412 | 0.622425 | ||||||||
\(310\) | −53.5286 | −3.04022 | ||||||||
\(311\) | −11.1369 | −0.631514 | −0.315757 | − | 0.948840i | \(-0.602258\pi\) | ||||
−0.315757 | + | 0.948840i | \(0.602258\pi\) | |||||||
\(312\) | 5.47963 | 0.310223 | ||||||||
\(313\) | −1.19380 | −0.0674775 | −0.0337387 | − | 0.999431i | \(-0.510741\pi\) | ||||
−0.0337387 | + | 0.999431i | \(0.510741\pi\) | |||||||
\(314\) | −27.3067 | −1.54100 | ||||||||
\(315\) | −14.1669 | −0.798217 | ||||||||
\(316\) | −26.2386 | −1.47604 | ||||||||
\(317\) | 10.3650 | 0.582155 | 0.291077 | − | 0.956700i | \(-0.405986\pi\) | ||||
0.291077 | + | 0.956700i | \(0.405986\pi\) | |||||||
\(318\) | −28.9789 | −1.62506 | ||||||||
\(319\) | 1.22236 | 0.0684388 | ||||||||
\(320\) | −53.3028 | −2.97972 | ||||||||
\(321\) | −5.14880 | −0.287378 | ||||||||
\(322\) | −3.96106 | −0.220741 | ||||||||
\(323\) | −26.4877 | −1.47381 | ||||||||
\(324\) | 2.17657 | 0.120921 | ||||||||
\(325\) | 21.4720 | 1.19105 | ||||||||
\(326\) | −17.5317 | −0.970989 | ||||||||
\(327\) | 9.67042 | 0.534775 | ||||||||
\(328\) | 16.5171 | 0.912005 | ||||||||
\(329\) | −14.1817 | −0.781861 | ||||||||
\(330\) | 20.5117 | 1.12913 | ||||||||
\(331\) | 5.14683 | 0.282895 | 0.141448 | − | 0.989946i | \(-0.454824\pi\) | ||||
0.141448 | + | 0.989946i | \(0.454824\pi\) | |||||||
\(332\) | 1.57566 | 0.0864756 | ||||||||
\(333\) | −3.69385 | −0.202422 | ||||||||
\(334\) | −39.5570 | −2.16446 | ||||||||
\(335\) | 22.1316 | 1.20918 | ||||||||
\(336\) | −1.48005 | −0.0807435 | ||||||||
\(337\) | −14.3182 | −0.779964 | −0.389982 | − | 0.920823i | \(-0.627519\pi\) | ||||
−0.389982 | + | 0.920823i | \(0.627519\pi\) | |||||||
\(338\) | 24.1657 | 1.31444 | ||||||||
\(339\) | −16.6618 | −0.904947 | ||||||||
\(340\) | −90.2251 | −4.89314 | ||||||||
\(341\) | 10.8126 | 0.585533 | ||||||||
\(342\) | 19.4465 | 1.05155 | ||||||||
\(343\) | −18.8960 | −1.02029 | ||||||||
\(344\) | −32.5777 | −1.75647 | ||||||||
\(345\) | −4.38464 | −0.236061 | ||||||||
\(346\) | −15.1050 | −0.812052 | ||||||||
\(347\) | 7.02408 | 0.377072 | 0.188536 | − | 0.982066i | \(-0.439626\pi\) | ||||
0.188536 | + | 0.982066i | \(0.439626\pi\) | |||||||
\(348\) | −2.13268 | −0.114324 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −52.5627 | −2.80960 | ||||||||
\(351\) | 8.21256 | 0.438354 | ||||||||
\(352\) | 9.30287 | 0.495845 | ||||||||
\(353\) | −1.94258 | −0.103393 | −0.0516965 | − | 0.998663i | \(-0.516463\pi\) | ||||
−0.0516965 | + | 0.998663i | \(0.516463\pi\) | |||||||
\(354\) | 31.6724 | 1.68337 | ||||||||
\(355\) | −38.6613 | −2.05193 | ||||||||
\(356\) | 30.6127 | 1.62247 | ||||||||
\(357\) | 10.7797 | 0.570522 | ||||||||
\(358\) | 33.7234 | 1.78234 | ||||||||
\(359\) | 21.8606 | 1.15376 | 0.576879 | − | 0.816830i | \(-0.304271\pi\) | ||||
0.576879 | + | 0.816830i | \(0.304271\pi\) | |||||||
\(360\) | 27.4834 | 1.44850 | ||||||||
\(361\) | −0.601929 | −0.0316805 | ||||||||
\(362\) | −27.9459 | −1.46880 | ||||||||
\(363\) | 7.14060 | 0.374784 | ||||||||
\(364\) | 9.41222 | 0.493334 | ||||||||
\(365\) | 47.7685 | 2.50032 | ||||||||
\(366\) | −2.67322 | −0.139731 | ||||||||
\(367\) | −17.8826 | −0.933462 | −0.466731 | − | 0.884399i | \(-0.654568\pi\) | ||||
−0.466731 | + | 0.884399i | \(0.654568\pi\) | |||||||
\(368\) | 0.847868 | 0.0441982 | ||||||||
\(369\) | 9.74501 | 0.507305 | ||||||||
\(370\) | −18.8691 | −0.980955 | ||||||||
\(371\) | −20.6524 | −1.07222 | ||||||||
\(372\) | −18.8650 | −0.978106 | ||||||||
\(373\) | −4.41097 | −0.228391 | −0.114196 | − | 0.993458i | \(-0.536429\pi\) | ||||
−0.114196 | + | 0.993458i | \(0.536429\pi\) | |||||||
\(374\) | 28.8886 | 1.49379 | ||||||||
\(375\) | −36.2603 | −1.87248 | ||||||||
\(376\) | 27.5120 | 1.41882 | ||||||||
\(377\) | 0.984159 | 0.0506868 | ||||||||
\(378\) | −20.1040 | −1.03404 | ||||||||
\(379\) | 27.0213 | 1.38799 | 0.693995 | − | 0.719980i | \(-0.255849\pi\) | ||||
0.693995 | + | 0.719980i | \(0.255849\pi\) | |||||||
\(380\) | 62.6694 | 3.21487 | ||||||||
\(381\) | 14.5099 | 0.743364 | ||||||||
\(382\) | 52.1400 | 2.66772 | ||||||||
\(383\) | −34.4391 | −1.75976 | −0.879879 | − | 0.475197i | \(-0.842377\pi\) | ||||
−0.879879 | + | 0.475197i | \(0.842377\pi\) | |||||||
\(384\) | −20.2801 | −1.03491 | ||||||||
\(385\) | 14.6181 | 0.745006 | ||||||||
\(386\) | 31.7950 | 1.61832 | ||||||||
\(387\) | −19.2207 | −0.977041 | ||||||||
\(388\) | 41.2746 | 2.09540 | ||||||||
\(389\) | −17.6612 | −0.895458 | −0.447729 | − | 0.894169i | \(-0.647767\pi\) | ||||
−0.447729 | + | 0.894169i | \(0.647767\pi\) | |||||||
\(390\) | 16.5147 | 0.836253 | ||||||||
\(391\) | −6.17530 | −0.312298 | ||||||||
\(392\) | 13.5490 | 0.684330 | ||||||||
\(393\) | 7.02812 | 0.354522 | ||||||||
\(394\) | 22.3508 | 1.12602 | ||||||||
\(395\) | −32.8100 | −1.65085 | ||||||||
\(396\) | −13.3804 | −0.672388 | ||||||||
\(397\) | 15.5929 | 0.782585 | 0.391292 | − | 0.920266i | \(-0.372028\pi\) | ||||
0.391292 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(398\) | −30.2733 | −1.51747 | ||||||||
\(399\) | −7.48747 | −0.374842 | ||||||||
\(400\) | 11.2511 | 0.562554 | ||||||||
\(401\) | 23.8802 | 1.19252 | 0.596259 | − | 0.802792i | \(-0.296653\pi\) | ||||
0.596259 | + | 0.802792i | \(0.296653\pi\) | |||||||
\(402\) | 12.3635 | 0.616634 | ||||||||
\(403\) | 8.70556 | 0.433655 | ||||||||
\(404\) | 5.15879 | 0.256659 | ||||||||
\(405\) | 2.72169 | 0.135242 | ||||||||
\(406\) | −2.40918 | −0.119566 | ||||||||
\(407\) | 3.81148 | 0.188928 | ||||||||
\(408\) | −20.9123 | −1.03531 | ||||||||
\(409\) | −13.8778 | −0.686212 | −0.343106 | − | 0.939297i | \(-0.611479\pi\) | ||||
−0.343106 | + | 0.939297i | \(0.611479\pi\) | |||||||
\(410\) | 49.7798 | 2.45845 | ||||||||
\(411\) | −11.8463 | −0.584334 | ||||||||
\(412\) | −36.4588 | −1.79619 | ||||||||
\(413\) | 22.5719 | 1.11069 | ||||||||
\(414\) | 4.53372 | 0.222820 | ||||||||
\(415\) | 1.97028 | 0.0967172 | ||||||||
\(416\) | 7.49005 | 0.367230 | ||||||||
\(417\) | −11.2862 | −0.552686 | ||||||||
\(418\) | −20.0657 | −0.981446 | ||||||||
\(419\) | −27.1245 | −1.32512 | −0.662559 | − | 0.749010i | \(-0.730530\pi\) | ||||
−0.662559 | + | 0.749010i | \(0.730530\pi\) | |||||||
\(420\) | −25.5046 | −1.24450 | ||||||||
\(421\) | −26.7887 | −1.30560 | −0.652800 | − | 0.757531i | \(-0.726406\pi\) | ||||
−0.652800 | + | 0.757531i | \(0.726406\pi\) | |||||||
\(422\) | 33.4653 | 1.62907 | ||||||||
\(423\) | 16.2319 | 0.789224 | ||||||||
\(424\) | 40.0650 | 1.94573 | ||||||||
\(425\) | −81.9453 | −3.97493 | ||||||||
\(426\) | −21.5975 | −1.04640 | ||||||||
\(427\) | −1.90512 | −0.0921952 | ||||||||
\(428\) | 17.1570 | 0.829316 | ||||||||
\(429\) | −3.33590 | −0.161059 | ||||||||
\(430\) | −98.1836 | −4.73483 | ||||||||
\(431\) | 29.2686 | 1.40982 | 0.704909 | − | 0.709297i | \(-0.250988\pi\) | ||||
0.704909 | + | 0.709297i | \(0.250988\pi\) | |||||||
\(432\) | 4.30328 | 0.207042 | ||||||||
\(433\) | −26.6150 | −1.27903 | −0.639517 | − | 0.768777i | \(-0.720866\pi\) | ||||
−0.639517 | + | 0.768777i | \(0.720866\pi\) | |||||||
\(434\) | −21.3109 | −1.02295 | ||||||||
\(435\) | −2.66681 | −0.127864 | ||||||||
\(436\) | −32.2241 | −1.54326 | ||||||||
\(437\) | 4.28930 | 0.205185 | ||||||||
\(438\) | 26.6851 | 1.27507 | ||||||||
\(439\) | 4.97431 | 0.237411 | 0.118705 | − | 0.992930i | \(-0.462126\pi\) | ||||
0.118705 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(440\) | −28.3586 | −1.35194 | ||||||||
\(441\) | 7.99386 | 0.380660 | ||||||||
\(442\) | 23.2592 | 1.10633 | ||||||||
\(443\) | −40.2880 | −1.91414 | −0.957071 | − | 0.289853i | \(-0.906394\pi\) | ||||
−0.957071 | + | 0.289853i | \(0.906394\pi\) | |||||||
\(444\) | −6.65000 | −0.315595 | ||||||||
\(445\) | 38.2795 | 1.81462 | ||||||||
\(446\) | −57.5749 | −2.72625 | ||||||||
\(447\) | −11.5159 | −0.544682 | ||||||||
\(448\) | −21.2210 | −1.00260 | ||||||||
\(449\) | −29.6619 | −1.39983 | −0.699915 | − | 0.714226i | \(-0.746779\pi\) | ||||
−0.699915 | + | 0.714226i | \(0.746779\pi\) | |||||||
\(450\) | 60.1618 | 2.83606 | ||||||||
\(451\) | −10.0553 | −0.473487 | ||||||||
\(452\) | 55.5212 | 2.61150 | ||||||||
\(453\) | −7.47165 | −0.351049 | ||||||||
\(454\) | 33.0598 | 1.55157 | ||||||||
\(455\) | 11.7695 | 0.551762 | ||||||||
\(456\) | 14.5255 | 0.680217 | ||||||||
\(457\) | 20.0955 | 0.940028 | 0.470014 | − | 0.882659i | \(-0.344249\pi\) | ||||
0.470014 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(458\) | 11.6623 | 0.544943 | ||||||||
\(459\) | −31.3422 | −1.46293 | ||||||||
\(460\) | 14.6107 | 0.681225 | ||||||||
\(461\) | −15.2847 | −0.711880 | −0.355940 | − | 0.934509i | \(-0.615839\pi\) | ||||
−0.355940 | + | 0.934509i | \(0.615839\pi\) | |||||||
\(462\) | 8.16616 | 0.379924 | ||||||||
\(463\) | −18.5771 | −0.863351 | −0.431676 | − | 0.902029i | \(-0.642078\pi\) | ||||
−0.431676 | + | 0.902029i | \(0.642078\pi\) | |||||||
\(464\) | 0.515687 | 0.0239402 | ||||||||
\(465\) | −23.5897 | −1.09395 | ||||||||
\(466\) | 41.6626 | 1.92998 | ||||||||
\(467\) | 36.3534 | 1.68224 | 0.841118 | − | 0.540852i | \(-0.181898\pi\) | ||||
0.841118 | + | 0.540852i | \(0.181898\pi\) | |||||||
\(468\) | −10.7730 | −0.497981 | ||||||||
\(469\) | 8.81106 | 0.406857 | ||||||||
\(470\) | 82.9165 | 3.82465 | ||||||||
\(471\) | −12.0339 | −0.554492 | ||||||||
\(472\) | −43.7888 | −2.01554 | ||||||||
\(473\) | 19.8327 | 0.911909 | ||||||||
\(474\) | −18.3288 | −0.841869 | ||||||||
\(475\) | 56.9184 | 2.61159 | ||||||||
\(476\) | −35.9205 | −1.64641 | ||||||||
\(477\) | 23.6381 | 1.08232 | ||||||||
\(478\) | −40.6100 | −1.85746 | ||||||||
\(479\) | −16.6557 | −0.761018 | −0.380509 | − | 0.924777i | \(-0.624251\pi\) | ||||
−0.380509 | + | 0.924777i | \(0.624251\pi\) | |||||||
\(480\) | −20.2960 | −0.926383 | ||||||||
\(481\) | 3.06875 | 0.139923 | ||||||||
\(482\) | −14.5849 | −0.664325 | ||||||||
\(483\) | −1.74562 | −0.0794283 | ||||||||
\(484\) | −23.7942 | −1.08155 | ||||||||
\(485\) | 51.6118 | 2.34357 | ||||||||
\(486\) | 36.9627 | 1.67666 | ||||||||
\(487\) | 21.6123 | 0.979345 | 0.489672 | − | 0.871907i | \(-0.337116\pi\) | ||||
0.489672 | + | 0.871907i | \(0.337116\pi\) | |||||||
\(488\) | 3.69587 | 0.167304 | ||||||||
\(489\) | −7.72610 | −0.349386 | ||||||||
\(490\) | 40.8345 | 1.84471 | ||||||||
\(491\) | −26.6400 | −1.20225 | −0.601123 | − | 0.799156i | \(-0.705280\pi\) | ||||
−0.601123 | + | 0.799156i | \(0.705280\pi\) | |||||||
\(492\) | 17.5438 | 0.790938 | ||||||||
\(493\) | −3.75591 | −0.169158 | ||||||||
\(494\) | −16.1556 | −0.726874 | ||||||||
\(495\) | −16.7314 | −0.752022 | ||||||||
\(496\) | 4.56160 | 0.204822 | ||||||||
\(497\) | −15.3919 | −0.690420 | ||||||||
\(498\) | 1.10067 | 0.0493220 | ||||||||
\(499\) | −22.1313 | −0.990732 | −0.495366 | − | 0.868684i | \(-0.664966\pi\) | ||||
−0.495366 | + | 0.868684i | \(0.664966\pi\) | |||||||
\(500\) | 120.828 | 5.40359 | ||||||||
\(501\) | −17.4325 | −0.778828 | ||||||||
\(502\) | −57.3173 | −2.55819 | ||||||||
\(503\) | −24.3122 | −1.08403 | −0.542013 | − | 0.840370i | \(-0.682338\pi\) | ||||
−0.542013 | + | 0.840370i | \(0.682338\pi\) | |||||||
\(504\) | 10.9417 | 0.487384 | ||||||||
\(505\) | 6.45079 | 0.287057 | ||||||||
\(506\) | −4.67809 | −0.207966 | ||||||||
\(507\) | 10.6497 | 0.472968 | ||||||||
\(508\) | −48.3503 | −2.14520 | ||||||||
\(509\) | 16.9018 | 0.749158 | 0.374579 | − | 0.927195i | \(-0.377787\pi\) | ||||
0.374579 | + | 0.927195i | \(0.377787\pi\) | |||||||
\(510\) | −63.0261 | −2.79084 | ||||||||
\(511\) | 19.0177 | 0.841292 | ||||||||
\(512\) | 9.52273 | 0.420849 | ||||||||
\(513\) | 21.7699 | 0.961166 | ||||||||
\(514\) | −15.8254 | −0.698026 | ||||||||
\(515\) | −45.5898 | −2.00893 | ||||||||
\(516\) | −34.6028 | −1.52330 | ||||||||
\(517\) | −16.7488 | −0.736612 | ||||||||
\(518\) | −7.51217 | −0.330066 | ||||||||
\(519\) | −6.65670 | −0.292197 | ||||||||
\(520\) | −22.8324 | −1.00127 | ||||||||
\(521\) | 27.6484 | 1.21130 | 0.605650 | − | 0.795731i | \(-0.292913\pi\) | ||||
0.605650 | + | 0.795731i | \(0.292913\pi\) | |||||||
\(522\) | 2.75748 | 0.120692 | ||||||||
\(523\) | 25.4626 | 1.11340 | 0.556701 | − | 0.830713i | \(-0.312067\pi\) | ||||
0.556701 | + | 0.830713i | \(0.312067\pi\) | |||||||
\(524\) | −23.4194 | −1.02308 | ||||||||
\(525\) | −23.1641 | −1.01096 | ||||||||
\(526\) | 11.1836 | 0.487628 | ||||||||
\(527\) | −33.2236 | −1.44724 | ||||||||
\(528\) | −1.74797 | −0.0760707 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 120.749 | 5.24500 | ||||||||
\(531\) | −25.8352 | −1.12115 | ||||||||
\(532\) | 24.9500 | 1.08172 | ||||||||
\(533\) | −8.09587 | −0.350671 | ||||||||
\(534\) | 21.3843 | 0.925388 | ||||||||
\(535\) | 21.4539 | 0.927535 | ||||||||
\(536\) | −17.0932 | −0.738313 | ||||||||
\(537\) | 14.8617 | 0.641330 | ||||||||
\(538\) | −37.8725 | −1.63280 | ||||||||
\(539\) | −8.24841 | −0.355284 | ||||||||
\(540\) | 74.1551 | 3.19113 | ||||||||
\(541\) | 17.6280 | 0.757887 | 0.378943 | − | 0.925420i | \(-0.376288\pi\) | ||||
0.378943 | + | 0.925420i | \(0.376288\pi\) | |||||||
\(542\) | −32.9261 | −1.41430 | ||||||||
\(543\) | −12.3156 | −0.528512 | ||||||||
\(544\) | −28.5848 | −1.22556 | ||||||||
\(545\) | −40.2946 | −1.72603 | ||||||||
\(546\) | 6.57484 | 0.281377 | ||||||||
\(547\) | 0.0364265 | 0.00155749 | 0.000778743 | − | 1.00000i | \(-0.499752\pi\) | ||||
0.000778743 | 1.00000i | \(0.499752\pi\) | ||||||||
\(548\) | 39.4746 | 1.68627 | ||||||||
\(549\) | 2.18055 | 0.0930635 | ||||||||
\(550\) | −62.0776 | −2.64700 | ||||||||
\(551\) | 2.60882 | 0.111139 | ||||||||
\(552\) | 3.38644 | 0.144137 | ||||||||
\(553\) | −13.0623 | −0.555467 | ||||||||
\(554\) | 8.14442 | 0.346023 | ||||||||
\(555\) | −8.31548 | −0.352972 | ||||||||
\(556\) | 37.6082 | 1.59494 | ||||||||
\(557\) | −9.67931 | −0.410126 | −0.205063 | − | 0.978749i | \(-0.565740\pi\) | ||||
−0.205063 | + | 0.978749i | \(0.565740\pi\) | |||||||
\(558\) | 24.3918 | 1.03259 | ||||||||
\(559\) | 15.9680 | 0.675373 | ||||||||
\(560\) | 6.16707 | 0.260606 | ||||||||
\(561\) | 12.7310 | 0.537505 | ||||||||
\(562\) | 63.0467 | 2.65947 | ||||||||
\(563\) | −6.93225 | −0.292160 | −0.146080 | − | 0.989273i | \(-0.546666\pi\) | ||||
−0.146080 | + | 0.989273i | \(0.546666\pi\) | |||||||
\(564\) | 29.2222 | 1.23048 | ||||||||
\(565\) | 69.4264 | 2.92079 | ||||||||
\(566\) | −75.0034 | −3.15263 | ||||||||
\(567\) | 1.08356 | 0.0455054 | ||||||||
\(568\) | 29.8598 | 1.25289 | ||||||||
\(569\) | 45.7594 | 1.91833 | 0.959167 | − | 0.282840i | \(-0.0912766\pi\) | ||||
0.959167 | + | 0.282840i | \(0.0912766\pi\) | |||||||
\(570\) | 43.7773 | 1.83363 | ||||||||
\(571\) | −23.5660 | −0.986208 | −0.493104 | − | 0.869970i | \(-0.664138\pi\) | ||||
−0.493104 | + | 0.869970i | \(0.664138\pi\) | |||||||
\(572\) | 11.1160 | 0.464784 | ||||||||
\(573\) | 22.9778 | 0.959912 | ||||||||
\(574\) | 19.8184 | 0.827203 | ||||||||
\(575\) | 13.2699 | 0.553391 | ||||||||
\(576\) | 24.2889 | 1.01204 | ||||||||
\(577\) | 44.5555 | 1.85487 | 0.927435 | − | 0.373984i | \(-0.122009\pi\) | ||||
0.927435 | + | 0.373984i | \(0.122009\pi\) | |||||||
\(578\) | −49.1945 | −2.04622 | ||||||||
\(579\) | 14.0119 | 0.582314 | ||||||||
\(580\) | 8.88643 | 0.368989 | ||||||||
\(581\) | 0.784410 | 0.0325428 | ||||||||
\(582\) | 28.8321 | 1.19513 | ||||||||
\(583\) | −24.3908 | −1.01017 | ||||||||
\(584\) | −36.8937 | −1.52667 | ||||||||
\(585\) | −13.4710 | −0.556958 | ||||||||
\(586\) | −28.6518 | −1.18359 | ||||||||
\(587\) | −0.704570 | −0.0290807 | −0.0145404 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145404 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(588\) | 14.3913 | 0.593486 | ||||||||
\(589\) | 23.0768 | 0.950862 | ||||||||
\(590\) | −131.972 | −5.43321 | ||||||||
\(591\) | 9.84987 | 0.405170 | ||||||||
\(592\) | 1.60798 | 0.0660877 | ||||||||
\(593\) | 39.4417 | 1.61968 | 0.809839 | − | 0.586653i | \(-0.199555\pi\) | ||||
0.809839 | + | 0.586653i | \(0.199555\pi\) | |||||||
\(594\) | −23.7432 | −0.974196 | ||||||||
\(595\) | −44.9167 | −1.84141 | ||||||||
\(596\) | 38.3736 | 1.57184 | ||||||||
\(597\) | −13.3413 | −0.546022 | ||||||||
\(598\) | −3.76649 | −0.154023 | ||||||||
\(599\) | −22.5458 | −0.921196 | −0.460598 | − | 0.887609i | \(-0.652365\pi\) | ||||
−0.460598 | + | 0.887609i | \(0.652365\pi\) | |||||||
\(600\) | 44.9376 | 1.83457 | ||||||||
\(601\) | 18.0719 | 0.737166 | 0.368583 | − | 0.929595i | \(-0.379843\pi\) | ||||
0.368583 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(602\) | −39.0890 | −1.59315 | ||||||||
\(603\) | −10.0849 | −0.410689 | ||||||||
\(604\) | 24.8973 | 1.01306 | ||||||||
\(605\) | −29.7534 | −1.20965 | ||||||||
\(606\) | 3.60364 | 0.146388 | ||||||||
\(607\) | −4.73812 | −0.192315 | −0.0961573 | − | 0.995366i | \(-0.530655\pi\) | ||||
−0.0961573 | + | 0.995366i | \(0.530655\pi\) | |||||||
\(608\) | 19.8547 | 0.805215 | ||||||||
\(609\) | −1.06171 | −0.0430228 | ||||||||
\(610\) | 11.1387 | 0.450994 | ||||||||
\(611\) | −13.4850 | −0.545546 | ||||||||
\(612\) | 41.1136 | 1.66192 | ||||||||
\(613\) | −11.0776 | −0.447420 | −0.223710 | − | 0.974656i | \(-0.571817\pi\) | ||||
−0.223710 | + | 0.974656i | \(0.571817\pi\) | |||||||
\(614\) | −45.1827 | −1.82343 | ||||||||
\(615\) | 21.9377 | 0.884612 | ||||||||
\(616\) | −11.2902 | −0.454893 | ||||||||
\(617\) | −46.8859 | −1.88756 | −0.943778 | − | 0.330579i | \(-0.892756\pi\) | ||||
−0.943778 | + | 0.330579i | \(0.892756\pi\) | |||||||
\(618\) | −25.4680 | −1.02447 | ||||||||
\(619\) | −22.0795 | −0.887451 | −0.443725 | − | 0.896163i | \(-0.646343\pi\) | ||||
−0.443725 | + | 0.896163i | \(0.646343\pi\) | |||||||
\(620\) | 78.6066 | 3.15692 | ||||||||
\(621\) | 5.07541 | 0.203669 | ||||||||
\(622\) | 25.9234 | 1.03943 | ||||||||
\(623\) | 15.2399 | 0.610573 | ||||||||
\(624\) | −1.40735 | −0.0563390 | ||||||||
\(625\) | 84.7398 | 3.38959 | ||||||||
\(626\) | 2.77882 | 0.111064 | ||||||||
\(627\) | −8.84285 | −0.353149 | ||||||||
\(628\) | 40.0998 | 1.60015 | ||||||||
\(629\) | −11.7115 | −0.466967 | ||||||||
\(630\) | 32.9765 | 1.31382 | ||||||||
\(631\) | 42.2089 | 1.68031 | 0.840154 | − | 0.542348i | \(-0.182464\pi\) | ||||
0.840154 | + | 0.542348i | \(0.182464\pi\) | |||||||
\(632\) | 25.3405 | 1.00799 | ||||||||
\(633\) | 14.7480 | 0.586179 | ||||||||
\(634\) | −24.1266 | −0.958192 | ||||||||
\(635\) | −60.4596 | −2.39926 | ||||||||
\(636\) | 42.5555 | 1.68743 | ||||||||
\(637\) | −6.64107 | −0.263129 | ||||||||
\(638\) | −2.84529 | −0.112646 | ||||||||
\(639\) | 17.6171 | 0.696922 | ||||||||
\(640\) | 84.5028 | 3.34026 | ||||||||
\(641\) | 28.4238 | 1.12267 | 0.561337 | − | 0.827587i | \(-0.310287\pi\) | ||||
0.561337 | + | 0.827587i | \(0.310287\pi\) | |||||||
\(642\) | 11.9849 | 0.473007 | ||||||||
\(643\) | −2.51831 | −0.0993126 | −0.0496563 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496563 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(644\) | 5.81681 | 0.229214 | ||||||||
\(645\) | −43.2689 | −1.70371 | ||||||||
\(646\) | 61.6557 | 2.42581 | ||||||||
\(647\) | 42.1876 | 1.65857 | 0.829283 | − | 0.558829i | \(-0.188749\pi\) | ||||
0.829283 | + | 0.558829i | \(0.188749\pi\) | |||||||
\(648\) | −2.10208 | −0.0825774 | ||||||||
\(649\) | 26.6579 | 1.04641 | ||||||||
\(650\) | −49.9807 | −1.96040 | ||||||||
\(651\) | −9.39157 | −0.368085 | ||||||||
\(652\) | 25.7452 | 1.00826 | ||||||||
\(653\) | 11.2829 | 0.441534 | 0.220767 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220767 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(654\) | −22.5099 | −0.880208 | ||||||||
\(655\) | −29.2847 | −1.14425 | ||||||||
\(656\) | −4.24214 | −0.165628 | ||||||||
\(657\) | −21.7671 | −0.849215 | ||||||||
\(658\) | 33.0108 | 1.28690 | ||||||||
\(659\) | −41.5918 | −1.62018 | −0.810092 | − | 0.586302i | \(-0.800583\pi\) | ||||
−0.810092 | + | 0.586302i | \(0.800583\pi\) | |||||||
\(660\) | −30.1214 | −1.17247 | ||||||||
\(661\) | 20.7577 | 0.807380 | 0.403690 | − | 0.914896i | \(-0.367727\pi\) | ||||
0.403690 | + | 0.914896i | \(0.367727\pi\) | |||||||
\(662\) | −11.9803 | −0.465629 | ||||||||
\(663\) | 10.2502 | 0.398084 | ||||||||
\(664\) | −1.52173 | −0.0590546 | ||||||||
\(665\) | 31.1987 | 1.20983 | ||||||||
\(666\) | 8.59822 | 0.333174 | ||||||||
\(667\) | 0.608216 | 0.0235502 | ||||||||
\(668\) | 58.0893 | 2.24754 | ||||||||
\(669\) | −25.3729 | −0.980973 | ||||||||
\(670\) | −51.5160 | −1.99024 | ||||||||
\(671\) | −2.24998 | −0.0868596 | ||||||||
\(672\) | −8.08028 | −0.311704 | ||||||||
\(673\) | −4.93686 | −0.190302 | −0.0951509 | − | 0.995463i | \(-0.530333\pi\) | ||||
−0.0951509 | + | 0.995463i | \(0.530333\pi\) | |||||||
\(674\) | 33.3287 | 1.28377 | ||||||||
\(675\) | 67.3500 | 2.59230 | ||||||||
\(676\) | −35.4872 | −1.36489 | ||||||||
\(677\) | −9.42202 | −0.362118 | −0.181059 | − | 0.983472i | \(-0.557952\pi\) | ||||
−0.181059 | + | 0.983472i | \(0.557952\pi\) | |||||||
\(678\) | 38.7840 | 1.48949 | ||||||||
\(679\) | 20.5477 | 0.788550 | ||||||||
\(680\) | 87.1371 | 3.34156 | ||||||||
\(681\) | 14.5693 | 0.558295 | ||||||||
\(682\) | −25.1685 | −0.963753 | ||||||||
\(683\) | 9.24765 | 0.353852 | 0.176926 | − | 0.984224i | \(-0.443385\pi\) | ||||
0.176926 | + | 0.984224i | \(0.443385\pi\) | |||||||
\(684\) | −28.5571 | −1.09191 | ||||||||
\(685\) | 49.3610 | 1.88598 | ||||||||
\(686\) | 43.9845 | 1.67934 | ||||||||
\(687\) | 5.13950 | 0.196084 | ||||||||
\(688\) | 8.36702 | 0.318989 | ||||||||
\(689\) | −19.6379 | −0.748143 | ||||||||
\(690\) | 10.2062 | 0.388542 | ||||||||
\(691\) | −49.8540 | −1.89654 | −0.948268 | − | 0.317470i | \(-0.897167\pi\) | ||||
−0.948268 | + | 0.317470i | \(0.897167\pi\) | |||||||
\(692\) | 22.1817 | 0.843222 | ||||||||
\(693\) | −6.66114 | −0.253036 | ||||||||
\(694\) | −16.3500 | −0.620638 | ||||||||
\(695\) | 47.0271 | 1.78384 | ||||||||
\(696\) | 2.05969 | 0.0780723 | ||||||||
\(697\) | 30.8969 | 1.17030 | ||||||||
\(698\) | 2.32771 | 0.0881051 | ||||||||
\(699\) | 18.3604 | 0.694456 | ||||||||
\(700\) | 77.1882 | 2.91744 | ||||||||
\(701\) | −32.1548 | −1.21447 | −0.607235 | − | 0.794522i | \(-0.707722\pi\) | ||||
−0.607235 | + | 0.794522i | \(0.707722\pi\) | |||||||
\(702\) | −19.1165 | −0.721504 | ||||||||
\(703\) | 8.13467 | 0.306805 | ||||||||
\(704\) | −25.0624 | −0.944574 | ||||||||
\(705\) | 36.5408 | 1.37621 | ||||||||
\(706\) | 4.52176 | 0.170179 | ||||||||
\(707\) | 2.56820 | 0.0965870 | ||||||||
\(708\) | −46.5108 | −1.74798 | ||||||||
\(709\) | 7.32416 | 0.275065 | 0.137532 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137532 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(710\) | 89.9923 | 3.37735 | ||||||||
\(711\) | 14.9508 | 0.560698 | ||||||||
\(712\) | −29.5649 | −1.10799 | ||||||||
\(713\) | 5.38009 | 0.201486 | ||||||||
\(714\) | −25.0920 | −0.939046 | ||||||||
\(715\) | 13.9000 | 0.519830 | ||||||||
\(716\) | −49.5227 | −1.85075 | ||||||||
\(717\) | −17.8966 | −0.668361 | ||||||||
\(718\) | −50.8851 | −1.89902 | ||||||||
\(719\) | −28.8645 | −1.07646 | −0.538232 | − | 0.842797i | \(-0.680908\pi\) | ||||
−0.538232 | + | 0.842797i | \(0.680908\pi\) | |||||||
\(720\) | −7.05865 | −0.263060 | ||||||||
\(721\) | −18.1503 | −0.675951 | ||||||||
\(722\) | 1.40112 | 0.0521442 | ||||||||
\(723\) | −6.42749 | −0.239041 | ||||||||
\(724\) | 41.0384 | 1.52518 | ||||||||
\(725\) | 8.07094 | 0.299747 | ||||||||
\(726\) | −16.6213 | −0.616873 | ||||||||
\(727\) | 4.45516 | 0.165233 | 0.0826164 | − | 0.996581i | \(-0.473672\pi\) | ||||
0.0826164 | + | 0.996581i | \(0.473672\pi\) | |||||||
\(728\) | −9.09008 | −0.336901 | ||||||||
\(729\) | 14.3790 | 0.532555 | ||||||||
\(730\) | −111.191 | −4.11538 | ||||||||
\(731\) | −60.9397 | −2.25394 | ||||||||
\(732\) | 3.92562 | 0.145095 | ||||||||
\(733\) | 11.8779 | 0.438721 | 0.219360 | − | 0.975644i | \(-0.429603\pi\) | ||||
0.219360 | + | 0.975644i | \(0.429603\pi\) | |||||||
\(734\) | 41.6254 | 1.53642 | ||||||||
\(735\) | 17.9955 | 0.663775 | ||||||||
\(736\) | 4.62890 | 0.170623 | ||||||||
\(737\) | 10.4060 | 0.383311 | ||||||||
\(738\) | −22.6836 | −0.834994 | ||||||||
\(739\) | −6.82724 | −0.251144 | −0.125572 | − | 0.992085i | \(-0.540077\pi\) | ||||
−0.125572 | + | 0.992085i | \(0.540077\pi\) | |||||||
\(740\) | 27.7092 | 1.01861 | ||||||||
\(741\) | −7.11967 | −0.261547 | ||||||||
\(742\) | 48.0727 | 1.76481 | ||||||||
\(743\) | −0.685788 | −0.0251591 | −0.0125796 | − | 0.999921i | \(-0.504004\pi\) | ||||
−0.0125796 | + | 0.999921i | \(0.504004\pi\) | |||||||
\(744\) | 18.2194 | 0.667954 | ||||||||
\(745\) | 47.9842 | 1.75800 | ||||||||
\(746\) | 10.2675 | 0.375918 | ||||||||
\(747\) | −0.897814 | −0.0328493 | ||||||||
\(748\) | −42.4228 | −1.55113 | ||||||||
\(749\) | 8.54127 | 0.312091 | ||||||||
\(750\) | 84.4035 | 3.08198 | ||||||||
\(751\) | 42.7148 | 1.55869 | 0.779343 | − | 0.626598i | \(-0.215553\pi\) | ||||
0.779343 | + | 0.626598i | \(0.215553\pi\) | |||||||
\(752\) | −7.06599 | −0.257670 | ||||||||
\(753\) | −25.2594 | −0.920503 | ||||||||
\(754\) | −2.29084 | −0.0834274 | ||||||||
\(755\) | 31.1328 | 1.13304 | ||||||||
\(756\) | 29.5227 | 1.07373 | ||||||||
\(757\) | 31.7729 | 1.15481 | 0.577404 | − | 0.816459i | \(-0.304066\pi\) | ||||
0.577404 | + | 0.816459i | \(0.304066\pi\) | |||||||
\(758\) | −62.8977 | −2.28455 | ||||||||
\(759\) | −2.06161 | −0.0748316 | ||||||||
\(760\) | −60.5245 | −2.19546 | ||||||||
\(761\) | 39.1843 | 1.42043 | 0.710215 | − | 0.703985i | \(-0.248598\pi\) | ||||
0.710215 | + | 0.703985i | \(0.248598\pi\) | |||||||
\(762\) | −33.7748 | −1.22353 | ||||||||
\(763\) | −16.0421 | −0.580764 | ||||||||
\(764\) | −76.5675 | −2.77011 | ||||||||
\(765\) | 51.4104 | 1.85875 | ||||||||
\(766\) | 80.1644 | 2.89646 | ||||||||
\(767\) | 21.4631 | 0.774989 | ||||||||
\(768\) | 21.6215 | 0.780200 | ||||||||
\(769\) | 24.4316 | 0.881027 | 0.440514 | − | 0.897746i | \(-0.354796\pi\) | ||||
0.440514 | + | 0.897746i | \(0.354796\pi\) | |||||||
\(770\) | −34.0266 | −1.22623 | ||||||||
\(771\) | −6.97414 | −0.251168 | ||||||||
\(772\) | −46.6909 | −1.68044 | ||||||||
\(773\) | −10.8754 | −0.391160 | −0.195580 | − | 0.980688i | \(-0.562659\pi\) | ||||
−0.195580 | + | 0.980688i | \(0.562659\pi\) | |||||||
\(774\) | 44.7401 | 1.60815 | ||||||||
\(775\) | 71.3930 | 2.56451 | ||||||||
\(776\) | −39.8620 | −1.43096 | ||||||||
\(777\) | −3.31057 | −0.118766 | ||||||||
\(778\) | 41.1101 | 1.47387 | ||||||||
\(779\) | −21.4606 | −0.768907 | ||||||||
\(780\) | −24.2518 | −0.868352 | ||||||||
\(781\) | −18.1781 | −0.650464 | ||||||||
\(782\) | 14.3743 | 0.514024 | ||||||||
\(783\) | 3.08695 | 0.110318 | ||||||||
\(784\) | −3.47984 | −0.124280 | ||||||||
\(785\) | 50.1426 | 1.78967 | ||||||||
\(786\) | −16.3594 | −0.583521 | ||||||||
\(787\) | 13.2611 | 0.472706 | 0.236353 | − | 0.971667i | \(-0.424048\pi\) | ||||
0.236353 | + | 0.971667i | \(0.424048\pi\) | |||||||
\(788\) | −32.8221 | −1.16924 | ||||||||
\(789\) | 4.92855 | 0.175461 | ||||||||
\(790\) | 76.3721 | 2.71720 | ||||||||
\(791\) | 27.6401 | 0.982769 | ||||||||
\(792\) | 12.9224 | 0.459177 | ||||||||
\(793\) | −1.81154 | −0.0643295 | ||||||||
\(794\) | −36.2957 | −1.28809 | ||||||||
\(795\) | 53.2134 | 1.88728 | ||||||||
\(796\) | 44.4563 | 1.57571 | ||||||||
\(797\) | −47.0003 | −1.66483 | −0.832417 | − | 0.554149i | \(-0.813044\pi\) | ||||
−0.832417 | + | 0.554149i | \(0.813044\pi\) | |||||||
\(798\) | 17.4287 | 0.616968 | ||||||||
\(799\) | 51.4639 | 1.82066 | ||||||||
\(800\) | 61.4248 | 2.17169 | ||||||||
\(801\) | −17.4432 | −0.616324 | ||||||||
\(802\) | −55.5861 | −1.96281 | ||||||||
\(803\) | 22.4602 | 0.792604 | ||||||||
\(804\) | −18.1557 | −0.640303 | ||||||||
\(805\) | 7.27362 | 0.256361 | ||||||||
\(806\) | −20.2640 | −0.713769 | ||||||||
\(807\) | −16.6902 | −0.587523 | ||||||||
\(808\) | −4.98222 | −0.175274 | ||||||||
\(809\) | −13.7566 | −0.483658 | −0.241829 | − | 0.970319i | \(-0.577747\pi\) | ||||
−0.241829 | + | 0.970319i | \(0.577747\pi\) | |||||||
\(810\) | −6.33531 | −0.222600 | ||||||||
\(811\) | −3.44967 | −0.121134 | −0.0605672 | − | 0.998164i | \(-0.519291\pi\) | ||||
−0.0605672 | + | 0.998164i | \(0.519291\pi\) | |||||||
\(812\) | 3.53788 | 0.124155 | ||||||||
\(813\) | −14.5103 | −0.508900 | ||||||||
\(814\) | −8.87201 | −0.310964 | ||||||||
\(815\) | 32.1930 | 1.12767 | ||||||||
\(816\) | 5.37097 | 0.188021 | ||||||||
\(817\) | 42.3281 | 1.48087 | ||||||||
\(818\) | 32.3034 | 1.12946 | ||||||||
\(819\) | −5.36310 | −0.187402 | ||||||||
\(820\) | −73.1015 | −2.55281 | ||||||||
\(821\) | 6.01932 | 0.210076 | 0.105038 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105038 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(822\) | 27.5747 | 0.961779 | ||||||||
\(823\) | −10.2270 | −0.356490 | −0.178245 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178245 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(824\) | 35.2109 | 1.22663 | ||||||||
\(825\) | −27.3572 | −0.952456 | ||||||||
\(826\) | −52.5409 | −1.82813 | ||||||||
\(827\) | −11.2946 | −0.392751 | −0.196376 | − | 0.980529i | \(-0.562917\pi\) | ||||
−0.196376 | + | 0.980529i | \(0.562917\pi\) | |||||||
\(828\) | −6.65776 | −0.231373 | ||||||||
\(829\) | 45.1632 | 1.56858 | 0.784291 | − | 0.620394i | \(-0.213027\pi\) | ||||
0.784291 | + | 0.620394i | \(0.213027\pi\) | |||||||
\(830\) | −4.58624 | −0.159191 | ||||||||
\(831\) | 3.58920 | 0.124508 | ||||||||
\(832\) | −20.1786 | −0.699566 | ||||||||
\(833\) | 25.3448 | 0.878145 | ||||||||
\(834\) | 26.2710 | 0.909689 | ||||||||
\(835\) | 72.6376 | 2.51373 | ||||||||
\(836\) | 29.4665 | 1.01912 | ||||||||
\(837\) | 27.3061 | 0.943838 | ||||||||
\(838\) | 63.1379 | 2.18106 | ||||||||
\(839\) | 25.8740 | 0.893270 | 0.446635 | − | 0.894716i | \(-0.352622\pi\) | ||||
0.446635 | + | 0.894716i | \(0.352622\pi\) | |||||||
\(840\) | 24.6317 | 0.849874 | ||||||||
\(841\) | −28.6301 | −0.987244 | ||||||||
\(842\) | 62.3562 | 2.14894 | ||||||||
\(843\) | 27.7843 | 0.956943 | ||||||||
\(844\) | −49.1437 | −1.69160 | ||||||||
\(845\) | −44.3749 | −1.52654 | ||||||||
\(846\) | −37.7833 | −1.29902 | ||||||||
\(847\) | −11.8454 | −0.407014 | ||||||||
\(848\) | −10.2900 | −0.353360 | ||||||||
\(849\) | −33.0536 | −1.13440 | ||||||||
\(850\) | 190.745 | 6.54250 | ||||||||
\(851\) | 1.89650 | 0.0650113 | ||||||||
\(852\) | 31.7159 | 1.08657 | ||||||||
\(853\) | −11.6416 | −0.398599 | −0.199300 | − | 0.979939i | \(-0.563867\pi\) | ||||
−0.199300 | + | 0.979939i | \(0.563867\pi\) | |||||||
\(854\) | 4.43457 | 0.151748 | ||||||||
\(855\) | −35.7092 | −1.22123 | ||||||||
\(856\) | −16.5698 | −0.566344 | ||||||||
\(857\) | 51.6165 | 1.76319 | 0.881593 | − | 0.472010i | \(-0.156471\pi\) | ||||
0.881593 | + | 0.472010i | \(0.156471\pi\) | |||||||
\(858\) | 7.76501 | 0.265093 | ||||||||
\(859\) | −38.2249 | −1.30422 | −0.652109 | − | 0.758125i | \(-0.726116\pi\) | ||||
−0.652109 | + | 0.758125i | \(0.726116\pi\) | |||||||
\(860\) | 144.182 | 4.91658 | ||||||||
\(861\) | 8.73384 | 0.297649 | ||||||||
\(862\) | −68.1288 | −2.32048 | ||||||||
\(863\) | 7.79497 | 0.265344 | 0.132672 | − | 0.991160i | \(-0.457644\pi\) | ||||
0.132672 | + | 0.991160i | \(0.457644\pi\) | |||||||
\(864\) | 23.4935 | 0.799267 | ||||||||
\(865\) | 27.7371 | 0.943089 | ||||||||
\(866\) | 61.9520 | 2.10521 | ||||||||
\(867\) | −21.6797 | −0.736282 | ||||||||
\(868\) | 31.2949 | 1.06222 | ||||||||
\(869\) | −15.4269 | −0.523321 | ||||||||
\(870\) | 6.20756 | 0.210456 | ||||||||
\(871\) | 8.37824 | 0.283886 | ||||||||
\(872\) | 31.1212 | 1.05390 | ||||||||
\(873\) | −23.5184 | −0.795976 | ||||||||
\(874\) | −9.98424 | −0.337722 | ||||||||
\(875\) | 60.1517 | 2.03350 | ||||||||
\(876\) | −39.1871 | −1.32401 | ||||||||
\(877\) | 21.4478 | 0.724242 | 0.362121 | − | 0.932131i | \(-0.382053\pi\) | ||||
0.362121 | + | 0.932131i | \(0.382053\pi\) | |||||||
\(878\) | −11.5788 | −0.390764 | ||||||||
\(879\) | −12.6267 | −0.425887 | ||||||||
\(880\) | 7.28342 | 0.245524 | ||||||||
\(881\) | −8.51828 | −0.286988 | −0.143494 | − | 0.989651i | \(-0.545834\pi\) | ||||
−0.143494 | + | 0.989651i | \(0.545834\pi\) | |||||||
\(882\) | −18.6074 | −0.626544 | ||||||||
\(883\) | 34.6783 | 1.16702 | 0.583509 | − | 0.812106i | \(-0.301679\pi\) | ||||
0.583509 | + | 0.812106i | \(0.301679\pi\) | |||||||
\(884\) | −34.1560 | −1.14879 | ||||||||
\(885\) | −58.1594 | −1.95501 | ||||||||
\(886\) | 93.7789 | 3.15056 | ||||||||
\(887\) | −33.8190 | −1.13553 | −0.567766 | − | 0.823190i | \(-0.692192\pi\) | ||||
−0.567766 | + | 0.823190i | \(0.692192\pi\) | |||||||
\(888\) | 6.42240 | 0.215522 | ||||||||
\(889\) | −24.0702 | −0.807290 | ||||||||
\(890\) | −89.1037 | −2.98676 | ||||||||
\(891\) | 1.27971 | 0.0428718 | ||||||||
\(892\) | 84.5485 | 2.83089 | ||||||||
\(893\) | −35.7463 | −1.19620 | ||||||||
\(894\) | 26.8056 | 0.896514 | ||||||||
\(895\) | −61.9256 | −2.06994 | ||||||||
\(896\) | 33.6423 | 1.12391 | ||||||||
\(897\) | −1.65987 | −0.0554214 | ||||||||
\(898\) | 69.0442 | 2.30404 | ||||||||
\(899\) | 3.27225 | 0.109136 | ||||||||
\(900\) | −88.3475 | −2.94492 | ||||||||
\(901\) | 74.9454 | 2.49679 | ||||||||
\(902\) | 23.4059 | 0.779331 | ||||||||
\(903\) | −17.2263 | −0.573254 | ||||||||
\(904\) | −53.6210 | −1.78341 | ||||||||
\(905\) | 51.3164 | 1.70582 | ||||||||
\(906\) | 17.3918 | 0.577805 | ||||||||
\(907\) | 50.3773 | 1.67275 | 0.836376 | − | 0.548156i | \(-0.184670\pi\) | ||||
0.836376 | + | 0.548156i | \(0.184670\pi\) | |||||||
\(908\) | −48.5482 | −1.61113 | ||||||||
\(909\) | −2.93949 | −0.0974966 | ||||||||
\(910\) | −27.3960 | −0.908167 | ||||||||
\(911\) | −9.70175 | −0.321433 | −0.160717 | − | 0.987001i | \(-0.551381\pi\) | ||||
−0.160717 | + | 0.987001i | \(0.551381\pi\) | |||||||
\(912\) | −3.73062 | −0.123533 | ||||||||
\(913\) | 0.926403 | 0.0306595 | ||||||||
\(914\) | −46.7765 | −1.54723 | ||||||||
\(915\) | 4.90878 | 0.162279 | ||||||||
\(916\) | −17.1260 | −0.565860 | ||||||||
\(917\) | −11.6588 | −0.385009 | ||||||||
\(918\) | 72.9555 | 2.40789 | ||||||||
\(919\) | −55.0373 | −1.81551 | −0.907756 | − | 0.419498i | \(-0.862206\pi\) | ||||
−0.907756 | + | 0.419498i | \(0.862206\pi\) | |||||||
\(920\) | −14.1106 | −0.465212 | ||||||||
\(921\) | −19.9118 | −0.656115 | ||||||||
\(922\) | 35.5784 | 1.17171 | ||||||||
\(923\) | −14.6358 | −0.481743 | ||||||||
\(924\) | −11.9920 | −0.394507 | ||||||||
\(925\) | 25.1663 | 0.827464 | ||||||||
\(926\) | 43.2421 | 1.42102 | ||||||||
\(927\) | 20.7743 | 0.682317 | ||||||||
\(928\) | 2.81537 | 0.0924190 | ||||||||
\(929\) | 14.9212 | 0.489548 | 0.244774 | − | 0.969580i | \(-0.421286\pi\) | ||||
0.244774 | + | 0.969580i | \(0.421286\pi\) | |||||||
\(930\) | 54.9101 | 1.80057 | ||||||||
\(931\) | −17.6042 | −0.576955 | ||||||||
\(932\) | −61.1813 | −2.00406 | ||||||||
\(933\) | 11.4243 | 0.374014 | ||||||||
\(934\) | −84.6203 | −2.76886 | ||||||||
\(935\) | −53.0475 | −1.73484 | ||||||||
\(936\) | 10.4043 | 0.340074 | ||||||||
\(937\) | 20.7962 | 0.679382 | 0.339691 | − | 0.940537i | \(-0.389677\pi\) | ||||
0.339691 | + | 0.940537i | \(0.389677\pi\) | |||||||
\(938\) | −20.5096 | −0.669662 | ||||||||
\(939\) | 1.22461 | 0.0399636 | ||||||||
\(940\) | −121.763 | −3.97146 | ||||||||
\(941\) | −25.7833 | −0.840510 | −0.420255 | − | 0.907406i | \(-0.638059\pi\) | ||||
−0.420255 | + | 0.907406i | \(0.638059\pi\) | |||||||
\(942\) | 28.0114 | 0.912661 | ||||||||
\(943\) | −5.00330 | −0.162930 | ||||||||
\(944\) | 11.2464 | 0.366040 | ||||||||
\(945\) | 36.9166 | 1.20090 | ||||||||
\(946\) | −46.1648 | −1.50095 | ||||||||
\(947\) | −37.5575 | −1.22046 | −0.610228 | − | 0.792226i | \(-0.708922\pi\) | ||||
−0.610228 | + | 0.792226i | \(0.708922\pi\) | |||||||
\(948\) | 26.9158 | 0.874183 | ||||||||
\(949\) | 18.0835 | 0.587014 | ||||||||
\(950\) | −132.489 | −4.29853 | ||||||||
\(951\) | −10.6325 | −0.344782 | ||||||||
\(952\) | 34.6911 | 1.12435 | ||||||||
\(953\) | 6.96993 | 0.225778 | 0.112889 | − | 0.993608i | \(-0.463990\pi\) | ||||
0.112889 | + | 0.993608i | \(0.463990\pi\) | |||||||
\(954\) | −55.0227 | −1.78143 | ||||||||
\(955\) | −95.7436 | −3.09819 | ||||||||
\(956\) | 59.6357 | 1.92876 | ||||||||
\(957\) | −1.25390 | −0.0405329 | ||||||||
\(958\) | 38.7696 | 1.25259 | ||||||||
\(959\) | 19.6516 | 0.634584 | ||||||||
\(960\) | 54.6785 | 1.76474 | ||||||||
\(961\) | −2.05468 | −0.0662799 | ||||||||
\(962\) | −7.14315 | −0.230304 | ||||||||
\(963\) | −9.77610 | −0.315030 | ||||||||
\(964\) | 21.4179 | 0.689825 | ||||||||
\(965\) | −58.3845 | −1.87947 | ||||||||
\(966\) | 4.06329 | 0.130734 | ||||||||
\(967\) | 24.8235 | 0.798271 | 0.399135 | − | 0.916892i | \(-0.369310\pi\) | ||||
0.399135 | + | 0.916892i | \(0.369310\pi\) | |||||||
\(968\) | 22.9798 | 0.738599 | ||||||||
\(969\) | 27.1713 | 0.872868 | ||||||||
\(970\) | −120.137 | −3.85737 | ||||||||
\(971\) | −25.9555 | −0.832952 | −0.416476 | − | 0.909147i | \(-0.636735\pi\) | ||||
−0.416476 | + | 0.909147i | \(0.636735\pi\) | |||||||
\(972\) | −54.2796 | −1.74102 | ||||||||
\(973\) | 18.7225 | 0.600215 | ||||||||
\(974\) | −50.3071 | −1.61194 | ||||||||
\(975\) | −22.0262 | −0.705403 | ||||||||
\(976\) | −0.949222 | −0.0303839 | ||||||||
\(977\) | 9.32928 | 0.298470 | 0.149235 | − | 0.988802i | \(-0.452319\pi\) | ||||
0.149235 | + | 0.988802i | \(0.452319\pi\) | |||||||
\(978\) | 17.9841 | 0.575069 | ||||||||
\(979\) | 17.9986 | 0.575238 | ||||||||
\(980\) | −59.9653 | −1.91552 | ||||||||
\(981\) | 18.3614 | 0.586233 | ||||||||
\(982\) | 62.0102 | 1.97883 | ||||||||
\(983\) | 15.4183 | 0.491766 | 0.245883 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245883 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(984\) | −16.9434 | −0.540136 | ||||||||
\(985\) | −41.0423 | −1.30772 | ||||||||
\(986\) | 8.74268 | 0.278424 | ||||||||
\(987\) | 14.5477 | 0.463058 | ||||||||
\(988\) | 23.7244 | 0.754774 | ||||||||
\(989\) | 9.86830 | 0.313794 | ||||||||
\(990\) | 38.9459 | 1.23778 | ||||||||
\(991\) | 11.2765 | 0.358211 | 0.179105 | − | 0.983830i | \(-0.442680\pi\) | ||||
0.179105 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(992\) | 24.9039 | 0.790698 | ||||||||
\(993\) | −5.27966 | −0.167545 | ||||||||
\(994\) | 35.8278 | 1.13639 | ||||||||
\(995\) | 55.5903 | 1.76233 | ||||||||
\(996\) | −1.61632 | −0.0512152 | ||||||||
\(997\) | 12.1855 | 0.385919 | 0.192959 | − | 0.981207i | \(-0.438191\pi\) | ||||
0.192959 | + | 0.981207i | \(0.438191\pi\) | |||||||
\(998\) | 51.5152 | 1.63068 | ||||||||
\(999\) | 9.62553 | 0.304538 |
(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 | 8027.2.a.f.1.18 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.f.1.18 | ✓ | 176 | 1.1 | even | 1 | trivial |