Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(1,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, 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("575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.329727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.329727 | 0.233152 | 0.116576 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116576 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | −1.89128 | −0.945640 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.514886 | −0.210201 | ||||||||
\(7\) | −4.06562 | −1.53666 | −0.768330 | − | 0.640054i | \(-0.778912\pi\) | ||||
−0.768330 | + | 0.640054i | \(0.778912\pi\) | |||||||
\(8\) | −1.28306 | −0.453630 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.65945 | 0.801856 | 0.400928 | − | 0.916110i | \(-0.368688\pi\) | ||||
0.400928 | + | 0.916110i | \(0.368688\pi\) | |||||||
\(12\) | 2.95333 | 0.852554 | ||||||||
\(13\) | 5.91023 | 1.63920 | 0.819602 | − | 0.572933i | \(-0.194195\pi\) | ||||
0.819602 | + | 0.572933i | \(0.194195\pi\) | |||||||
\(14\) | −1.34055 | −0.358276 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.35950 | 0.839875 | ||||||||
\(17\) | 3.40617 | 0.826117 | 0.413058 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413058 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(18\) | −0.185159 | −0.0436424 | ||||||||
\(19\) | −2.65945 | −0.610121 | −0.305060 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305060 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.34868 | 1.38540 | ||||||||
\(22\) | 0.876894 | 0.186955 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.00357 | 0.408976 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.94876 | 0.382184 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 7.68923 | 1.45313 | ||||||||
\(29\) | 5.84461 | 1.08532 | 0.542659 | − | 0.839953i | \(-0.317418\pi\) | ||||
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.31640 | −1.67327 | −0.836637 | − | 0.547757i | \(-0.815482\pi\) | ||||
−0.836637 | + | 0.547757i | \(0.815482\pi\) | |||||||
\(32\) | 3.67384 | 0.649449 | ||||||||
\(33\) | −4.15288 | −0.722923 | ||||||||
\(34\) | 1.12311 | 0.192611 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.06205 | 0.177009 | ||||||||
\(37\) | 4.18059 | 0.687285 | 0.343642 | − | 0.939101i | \(-0.388339\pi\) | ||||
0.343642 | + | 0.939101i | \(0.388339\pi\) | |||||||
\(38\) | −0.876894 | −0.142251 | ||||||||
\(39\) | −9.22914 | −1.47785 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15539 | 0.336615 | 0.168307 | − | 0.985735i | \(-0.446170\pi\) | ||||
0.168307 | + | 0.985735i | \(0.446170\pi\) | |||||||
\(42\) | 2.09333 | 0.323008 | ||||||||
\(43\) | −2.34868 | −0.358171 | −0.179085 | − | 0.983834i | \(-0.557314\pi\) | ||||
−0.179085 | + | 0.983834i | \(0.557314\pi\) | |||||||
\(44\) | −5.02977 | −0.758267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.329727 | 0.0486156 | ||||||||
\(47\) | −0.242644 | −0.0353933 | −0.0176966 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176966 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(48\) | −5.24604 | −0.757200 | ||||||||
\(49\) | 9.52927 | 1.36132 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.31891 | −0.744796 | ||||||||
\(52\) | −11.1779 | −1.55010 | ||||||||
\(53\) | −9.03585 | −1.24117 | −0.620585 | − | 0.784140i | \(-0.713105\pi\) | ||||
−0.620585 | + | 0.784140i | \(0.713105\pi\) | |||||||
\(54\) | 1.83380 | 0.249548 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.21644 | 0.697076 | ||||||||
\(57\) | 4.15288 | 0.550062 | ||||||||
\(58\) | 1.92713 | 0.253044 | ||||||||
\(59\) | 14.4143 | 1.87658 | 0.938291 | − | 0.345846i | \(-0.112408\pi\) | ||||
0.938291 | + | 0.345846i | \(0.112408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46365 | 0.315438 | 0.157719 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157719 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(62\) | −3.07187 | −0.390128 | ||||||||
\(63\) | 2.28306 | 0.287639 | ||||||||
\(64\) | −5.50764 | −0.688454 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.36932 | −0.168551 | ||||||||
\(67\) | 7.75485 | 0.947405 | 0.473703 | − | 0.880685i | \(-0.342917\pi\) | ||||
0.473703 | + | 0.880685i | \(0.342917\pi\) | |||||||
\(68\) | −6.44201 | −0.781209 | ||||||||
\(69\) | −1.56155 | −0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4395 | 1.47630 | 0.738149 | − | 0.674638i | \(-0.235700\pi\) | ||||
0.738149 | + | 0.674638i | \(0.235700\pi\) | |||||||
\(72\) | 0.720506 | 0.0849125 | ||||||||
\(73\) | 2.08977 | 0.244589 | 0.122294 | − | 0.992494i | \(-0.460975\pi\) | ||||
0.122294 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(74\) | 1.37845 | 0.160242 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.02977 | 0.576955 | ||||||||
\(77\) | −10.8123 | −1.23218 | ||||||||
\(78\) | −3.04310 | −0.344563 | ||||||||
\(79\) | −4.15288 | −0.467235 | −0.233618 | − | 0.972329i | \(-0.575056\pi\) | ||||
−0.233618 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0.710689 | 0.0784825 | ||||||||
\(83\) | 12.5293 | 1.37527 | 0.687633 | − | 0.726058i | \(-0.258650\pi\) | ||||
0.687633 | + | 0.726058i | \(0.258650\pi\) | |||||||
\(84\) | −12.0071 | −1.31009 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.774424 | −0.0835083 | ||||||||
\(87\) | −9.12667 | −0.978482 | ||||||||
\(88\) | −3.41224 | −0.363746 | ||||||||
\(89\) | −9.35682 | −0.991821 | −0.495910 | − | 0.868374i | \(-0.665166\pi\) | ||||
−0.495910 | + | 0.868374i | \(0.665166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.0288 | −2.51890 | ||||||||
\(92\) | −1.89128 | −0.197180 | ||||||||
\(93\) | 14.5481 | 1.50856 | ||||||||
\(94\) | −0.0800064 | −0.00825203 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.73690 | −0.585519 | ||||||||
\(97\) | −3.47179 | −0.352507 | −0.176253 | − | 0.984345i | \(-0.556398\pi\) | ||||
−0.176253 | + | 0.984345i | \(0.556398\pi\) | |||||||
\(98\) | 3.14206 | 0.317396 | ||||||||
\(99\) | −1.49342 | −0.150095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.21036 | 0.916465 | 0.458233 | − | 0.888832i | \(-0.348483\pi\) | ||||
0.458233 | + | 0.888832i | \(0.348483\pi\) | |||||||
\(102\) | −1.75379 | −0.173651 | ||||||||
\(103\) | −4.69736 | −0.462845 | −0.231422 | − | 0.972853i | \(-0.574338\pi\) | ||||
−0.231422 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(104\) | −7.58319 | −0.743593 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.97936 | −0.289381 | ||||||||
\(107\) | 0.376394 | 0.0363873 | 0.0181937 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181937 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(108\) | −10.5185 | −1.01214 | ||||||||
\(109\) | 19.0369 | 1.82340 | 0.911702 | − | 0.410851i | \(-0.134768\pi\) | ||||
0.911702 | + | 0.410851i | \(0.134768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.52821 | −0.619631 | ||||||||
\(112\) | −13.6585 | −1.29060 | ||||||||
\(113\) | −2.94252 | −0.276809 | −0.138404 | − | 0.990376i | \(-0.544197\pi\) | ||||
−0.138404 | + | 0.990376i | \(0.544197\pi\) | |||||||
\(114\) | 1.36932 | 0.128248 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.0538 | −1.02632 | ||||||||
\(117\) | −3.31891 | −0.306833 | ||||||||
\(118\) | 4.75279 | 0.437530 | ||||||||
\(119\) | −13.8482 | −1.26946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.92730 | −0.357028 | ||||||||
\(122\) | 0.812333 | 0.0735452 | ||||||||
\(123\) | −3.36575 | −0.303479 | ||||||||
\(124\) | 17.6199 | 1.58232 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.752787 | 0.0670636 | ||||||||
\(127\) | −6.00357 | −0.532730 | −0.266365 | − | 0.963872i | \(-0.585823\pi\) | ||||
−0.266365 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(128\) | −9.16370 | −0.809964 | ||||||||
\(129\) | 3.66759 | 0.322913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.9606 | −1.74397 | −0.871985 | − | 0.489533i | \(-0.837167\pi\) | ||||
−0.871985 | + | 0.489533i | \(0.837167\pi\) | |||||||
\(132\) | 7.85426 | 0.683625 | ||||||||
\(133\) | 10.8123 | 0.937548 | ||||||||
\(134\) | 2.55698 | 0.220890 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.37032 | −0.374752 | ||||||||
\(137\) | 11.7609 | 1.00480 | 0.502402 | − | 0.864634i | \(-0.332450\pi\) | ||||
0.502402 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(138\) | −0.514886 | −0.0438300 | ||||||||
\(139\) | 12.3891 | 1.05083 | 0.525415 | − | 0.850846i | \(-0.323910\pi\) | ||||
0.525415 | + | 0.850846i | \(0.323910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.378902 | 0.0319093 | ||||||||
\(142\) | 4.10164 | 0.344202 | ||||||||
\(143\) | 15.7180 | 1.31441 | ||||||||
\(144\) | −1.88654 | −0.157211 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.689053 | 0.0570264 | ||||||||
\(147\) | −14.8805 | −1.22732 | ||||||||
\(148\) | −7.90667 | −0.649924 | ||||||||
\(149\) | −2.13124 | −0.174598 | −0.0872991 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0872991 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.787129 | −0.0640556 | −0.0320278 | − | 0.999487i | \(-0.510197\pi\) | ||||
−0.0320278 | + | 0.999487i | \(0.510197\pi\) | |||||||
\(152\) | 3.41224 | 0.276769 | ||||||||
\(153\) | −1.91274 | −0.154636 | ||||||||
\(154\) | −3.56512 | −0.287286 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 17.4549 | 1.39751 | ||||||||
\(157\) | 9.18873 | 0.733340 | 0.366670 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366670 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(158\) | −1.36932 | −0.108937 | ||||||||
\(159\) | 14.1100 | 1.11899 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.06562 | −0.320416 | ||||||||
\(162\) | −2.30809 | −0.181341 | ||||||||
\(163\) | 17.6928 | 1.38581 | 0.692903 | − | 0.721031i | \(-0.256331\pi\) | ||||
0.692903 | + | 0.721031i | \(0.256331\pi\) | |||||||
\(164\) | −4.07644 | −0.318316 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.13124 | 0.320647 | ||||||||
\(167\) | −14.2462 | −1.10240 | −0.551202 | − | 0.834372i | \(-0.685831\pi\) | ||||
−0.551202 | + | 0.834372i | \(0.685831\pi\) | |||||||
\(168\) | −8.14574 | −0.628458 | ||||||||
\(169\) | 21.9309 | 1.68699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.49342 | 0.114205 | ||||||||
\(172\) | 4.44201 | 0.338700 | ||||||||
\(173\) | 1.20394 | 0.0915338 | 0.0457669 | − | 0.998952i | \(-0.485427\pi\) | ||||
0.0457669 | + | 0.998952i | \(0.485427\pi\) | |||||||
\(174\) | −3.00931 | −0.228135 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.93444 | 0.673459 | ||||||||
\(177\) | −22.5087 | −1.69186 | ||||||||
\(178\) | −3.08520 | −0.231245 | ||||||||
\(179\) | 7.42495 | 0.554967 | 0.277483 | − | 0.960730i | \(-0.410500\pi\) | ||||
0.277483 | + | 0.960730i | \(0.410500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0450 | 1.78725 | 0.893627 | − | 0.448810i | \(-0.148152\pi\) | ||||
0.893627 | + | 0.448810i | \(0.148152\pi\) | |||||||
\(182\) | −7.92294 | −0.587287 | ||||||||
\(183\) | −3.84712 | −0.284387 | ||||||||
\(184\) | −1.28306 | −0.0945885 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.79689 | 0.351725 | ||||||||
\(187\) | 9.05854 | 0.662426 | ||||||||
\(188\) | 0.458908 | 0.0334693 | ||||||||
\(189\) | −22.6112 | −1.64472 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.87689 | −0.352880 | −0.176440 | − | 0.984311i | \(-0.556458\pi\) | ||||
−0.176440 | + | 0.984311i | \(0.556458\pi\) | |||||||
\(192\) | 8.60046 | 0.620685 | ||||||||
\(193\) | −10.2714 | −0.739353 | −0.369676 | − | 0.929161i | \(-0.620531\pi\) | ||||
−0.369676 | + | 0.929161i | \(0.620531\pi\) | |||||||
\(194\) | −1.14474 | −0.0821877 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.0225 | −1.28732 | ||||||||
\(197\) | −4.28557 | −0.305334 | −0.152667 | − | 0.988278i | \(-0.548786\pi\) | ||||
−0.152667 | + | 0.988278i | \(0.548786\pi\) | |||||||
\(198\) | −0.492423 | −0.0349949 | ||||||||
\(199\) | 4.02164 | 0.285086 | 0.142543 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142543 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.1096 | −0.854146 | ||||||||
\(202\) | 3.03691 | 0.213676 | ||||||||
\(203\) | −23.7620 | −1.66776 | ||||||||
\(204\) | 10.0595 | 0.704309 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.54885 | −0.107913 | ||||||||
\(207\) | −0.561553 | −0.0390306 | ||||||||
\(208\) | 19.8554 | 1.37673 | ||||||||
\(209\) | −7.07270 | −0.489229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3416 | 1.05616 | 0.528080 | − | 0.849195i | \(-0.322912\pi\) | ||||
0.528080 | + | 0.849195i | \(0.322912\pi\) | |||||||
\(212\) | 17.0893 | 1.17370 | ||||||||
\(213\) | −19.4249 | −1.33098 | ||||||||
\(214\) | 0.124107 | 0.00848379 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.13581 | −0.485530 | ||||||||
\(217\) | 37.8770 | 2.57126 | ||||||||
\(218\) | 6.27699 | 0.425131 | ||||||||
\(219\) | −3.26328 | −0.220512 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1312 | 1.35417 | ||||||||
\(222\) | −2.15253 | −0.144468 | ||||||||
\(223\) | 17.6801 | 1.18395 | 0.591973 | − | 0.805958i | \(-0.298349\pi\) | ||||
0.591973 | + | 0.805958i | \(0.298349\pi\) | |||||||
\(224\) | −14.9364 | −0.997983 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.970227 | −0.0645386 | ||||||||
\(227\) | −8.63817 | −0.573335 | −0.286668 | − | 0.958030i | \(-0.592548\pi\) | ||||
−0.286668 | + | 0.958030i | \(0.592548\pi\) | |||||||
\(228\) | −7.85426 | −0.520161 | ||||||||
\(229\) | −3.34055 | −0.220749 | −0.110375 | − | 0.993890i | \(-0.535205\pi\) | ||||
−0.110375 | + | 0.993890i | \(0.535205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.8840 | 1.11089 | ||||||||
\(232\) | −7.49899 | −0.492333 | ||||||||
\(233\) | −8.23728 | −0.539642 | −0.269821 | − | 0.962910i | \(-0.586965\pi\) | ||||
−0.269821 | + | 0.962910i | \(0.586965\pi\) | |||||||
\(234\) | −1.09433 | −0.0715389 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.2615 | −1.77457 | ||||||||
\(237\) | 6.48494 | 0.421242 | ||||||||
\(238\) | −4.56612 | −0.295978 | ||||||||
\(239\) | −2.86525 | −0.185338 | −0.0926688 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926688 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.68109 | 0.301536 | 0.150768 | − | 0.988569i | \(-0.451825\pi\) | ||||
0.150768 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(242\) | −1.29494 | −0.0832418 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | −4.65945 | −0.298291 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.10978 | −0.0707569 | ||||||||
\(247\) | −15.7180 | −1.00011 | ||||||||
\(248\) | 11.9535 | 0.759049 | ||||||||
\(249\) | −19.5651 | −1.23989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5824 | −1.17291 | −0.586455 | − | 0.809982i | \(-0.699477\pi\) | ||||
−0.586455 | + | 0.809982i | \(0.699477\pi\) | |||||||
\(252\) | −4.31791 | −0.272003 | ||||||||
\(253\) | 2.65945 | 0.167198 | ||||||||
\(254\) | −1.97954 | −0.124207 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.99375 | 0.499609 | ||||||||
\(257\) | 28.7226 | 1.79166 | 0.895832 | − | 0.444392i | \(-0.146580\pi\) | ||||
0.895832 | + | 0.444392i | \(0.146580\pi\) | |||||||
\(258\) | 1.20930 | 0.0752880 | ||||||||
\(259\) | −16.9967 | −1.05612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.28206 | −0.203154 | ||||||||
\(262\) | −6.58157 | −0.406611 | ||||||||
\(263\) | 9.20500 | 0.567604 | 0.283802 | − | 0.958883i | \(-0.408404\pi\) | ||||
0.283802 | + | 0.958883i | \(0.408404\pi\) | |||||||
\(264\) | 5.32840 | 0.327940 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.56512 | 0.218592 | ||||||||
\(267\) | 14.6112 | 0.894189 | ||||||||
\(268\) | −14.6666 | −0.895904 | ||||||||
\(269\) | 16.9194 | 1.03160 | 0.515798 | − | 0.856710i | \(-0.327496\pi\) | ||||
0.515798 | + | 0.856710i | \(0.327496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.15082 | 0.0699072 | 0.0349536 | − | 0.999389i | \(-0.488872\pi\) | ||||
0.0349536 | + | 0.999389i | \(0.488872\pi\) | |||||||
\(272\) | 11.4430 | 0.693835 | ||||||||
\(273\) | 37.5222 | 2.27095 | ||||||||
\(274\) | 3.87790 | 0.234272 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.95333 | 0.177770 | ||||||||
\(277\) | −2.57505 | −0.154720 | −0.0773600 | − | 0.997003i | \(-0.524649\pi\) | ||||
−0.0773600 | + | 0.997003i | \(0.524649\pi\) | |||||||
\(278\) | 4.08502 | 0.245003 | ||||||||
\(279\) | 5.23165 | 0.313211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.4718 | 1.63883 | 0.819415 | − | 0.573201i | \(-0.194299\pi\) | ||||
0.819415 | + | 0.573201i | \(0.194299\pi\) | |||||||
\(282\) | 0.124934 | 0.00743972 | ||||||||
\(283\) | 2.36389 | 0.140519 | 0.0702595 | − | 0.997529i | \(-0.477617\pi\) | ||||
0.0702595 | + | 0.997529i | \(0.477617\pi\) | |||||||
\(284\) | −23.5266 | −1.39605 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.18265 | 0.306457 | ||||||||
\(287\) | −8.76298 | −0.517263 | ||||||||
\(288\) | −2.06306 | −0.121567 | ||||||||
\(289\) | −5.39803 | −0.317531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.42138 | 0.317807 | ||||||||
\(292\) | −3.95233 | −0.231293 | ||||||||
\(293\) | −34.1198 | −1.99330 | −0.996650 | − | 0.0817846i | \(-0.973938\pi\) | ||||
−0.996650 | + | 0.0817846i | \(0.973938\pi\) | |||||||
\(294\) | −4.90649 | −0.286152 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.36395 | −0.311773 | ||||||||
\(297\) | 14.7907 | 0.858243 | ||||||||
\(298\) | −0.702728 | −0.0407080 | ||||||||
\(299\) | 5.91023 | 0.341798 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.54885 | 0.550386 | ||||||||
\(302\) | −0.259538 | −0.0149347 | ||||||||
\(303\) | −14.3825 | −0.826251 | ||||||||
\(304\) | −8.93444 | −0.512425 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.630683 | −0.0360538 | ||||||||
\(307\) | −1.49342 | −0.0852342 | −0.0426171 | − | 0.999091i | \(-0.513570\pi\) | ||||
−0.0426171 | + | 0.999091i | \(0.513570\pi\) | |||||||
\(308\) | 20.4491 | 1.16520 | ||||||||
\(309\) | 7.33518 | 0.417284 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1060 | −0.799880 | −0.399940 | − | 0.916541i | \(-0.630969\pi\) | ||||
−0.399940 | + | 0.916541i | \(0.630969\pi\) | |||||||
\(312\) | 11.8416 | 0.670396 | ||||||||
\(313\) | 32.8563 | 1.85715 | 0.928574 | − | 0.371146i | \(-0.121035\pi\) | ||||
0.928574 | + | 0.371146i | \(0.121035\pi\) | |||||||
\(314\) | 3.02977 | 0.170980 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.85426 | 0.441836 | ||||||||
\(317\) | −12.5824 | −0.706698 | −0.353349 | − | 0.935492i | \(-0.614957\pi\) | ||||
−0.353349 | + | 0.935492i | \(0.614957\pi\) | |||||||
\(318\) | 4.65244 | 0.260896 | ||||||||
\(319\) | 15.5435 | 0.870268 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.587758 | −0.0328055 | ||||||||
\(322\) | −1.34055 | −0.0747057 | ||||||||
\(323\) | −9.05854 | −0.504031 | ||||||||
\(324\) | 13.2390 | 0.735498 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.83380 | 0.323104 | ||||||||
\(327\) | −29.7271 | −1.64391 | ||||||||
\(328\) | −2.76549 | −0.152699 | ||||||||
\(329\) | 0.986499 | 0.0543874 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.57677 | 0.0866669 | 0.0433334 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433334 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(332\) | −23.6964 | −1.30051 | ||||||||
\(333\) | −2.34762 | −0.128649 | ||||||||
\(334\) | −4.69736 | −0.257028 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 21.3284 | 1.16356 | ||||||||
\(337\) | 15.4718 | 0.842802 | 0.421401 | − | 0.906874i | \(-0.361539\pi\) | ||||
0.421401 | + | 0.906874i | \(0.361539\pi\) | |||||||
\(338\) | 7.23120 | 0.393326 | ||||||||
\(339\) | 4.59489 | 0.249560 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.7765 | −1.34172 | ||||||||
\(342\) | 0.492423 | 0.0266272 | ||||||||
\(343\) | −10.2831 | −0.555233 | ||||||||
\(344\) | 3.01350 | 0.162477 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.396971 | 0.0213413 | ||||||||
\(347\) | 9.00312 | 0.483313 | 0.241656 | − | 0.970362i | \(-0.422309\pi\) | ||||
0.241656 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(348\) | 17.2611 | 0.925292 | ||||||||
\(349\) | 1.10398 | 0.0590945 | 0.0295473 | − | 0.999563i | \(-0.490593\pi\) | ||||
0.0295473 | + | 0.999563i | \(0.490593\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.8701 | 1.75448 | ||||||||
\(352\) | 9.77041 | 0.520765 | ||||||||
\(353\) | −1.96566 | −0.104621 | −0.0523107 | − | 0.998631i | \(-0.516659\pi\) | ||||
−0.0523107 | + | 0.998631i | \(0.516659\pi\) | |||||||
\(354\) | −7.42173 | −0.394460 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.6964 | 0.937905 | ||||||||
\(357\) | 21.6247 | 1.14450 | ||||||||
\(358\) | 2.44821 | 0.129392 | ||||||||
\(359\) | −2.60403 | −0.137435 | −0.0687177 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687177 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9273 | −0.627753 | ||||||||
\(362\) | 7.92830 | 0.416702 | ||||||||
\(363\) | 6.13269 | 0.321883 | ||||||||
\(364\) | 45.4451 | 2.38197 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.26850 | −0.0663056 | ||||||||
\(367\) | −6.98042 | −0.364375 | −0.182188 | − | 0.983264i | \(-0.558318\pi\) | ||||
−0.182188 | + | 0.983264i | \(0.558318\pi\) | |||||||
\(368\) | 3.35950 | 0.175126 | ||||||||
\(369\) | −1.21036 | −0.0630090 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 36.7363 | 1.90726 | ||||||||
\(372\) | −27.5144 | −1.42656 | ||||||||
\(373\) | −24.3220 | −1.25935 | −0.629673 | − | 0.776860i | \(-0.716811\pi\) | ||||
−0.629673 | + | 0.776860i | \(0.716811\pi\) | |||||||
\(374\) | 2.98685 | 0.154446 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.311327 | 0.0160555 | ||||||||
\(377\) | 34.5430 | 1.77906 | ||||||||
\(378\) | −7.45552 | −0.383470 | ||||||||
\(379\) | −24.6541 | −1.26640 | −0.633198 | − | 0.773990i | \(-0.718258\pi\) | ||||
−0.633198 | + | 0.773990i | \(0.718258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.37489 | 0.480290 | ||||||||
\(382\) | −1.60804 | −0.0822747 | ||||||||
\(383\) | 4.99292 | 0.255126 | 0.127563 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127563 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(384\) | 14.3096 | 0.730234 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.38676 | −0.172382 | ||||||||
\(387\) | 1.31891 | 0.0670439 | ||||||||
\(388\) | 6.56612 | 0.333344 | ||||||||
\(389\) | −32.0234 | −1.62365 | −0.811826 | − | 0.583900i | \(-0.801526\pi\) | ||||
−0.811826 | + | 0.583900i | \(0.801526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.40617 | 0.172257 | ||||||||
\(392\) | −12.2266 | −0.617538 | ||||||||
\(393\) | 31.1696 | 1.57230 | ||||||||
\(394\) | −1.41307 | −0.0711894 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.82448 | 0.141936 | ||||||||
\(397\) | 17.3441 | 0.870476 | 0.435238 | − | 0.900315i | \(-0.356664\pi\) | ||||
0.435238 | + | 0.900315i | \(0.356664\pi\) | |||||||
\(398\) | 1.32604 | 0.0664685 | ||||||||
\(399\) | −16.8840 | −0.845259 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.3352 | −1.06543 | −0.532714 | − | 0.846295i | \(-0.678828\pi\) | ||||
−0.532714 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(402\) | −3.99287 | −0.199146 | ||||||||
\(403\) | −55.0621 | −2.74284 | ||||||||
\(404\) | −17.4194 | −0.866646 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.83497 | −0.388843 | ||||||||
\(407\) | 11.1181 | 0.551103 | ||||||||
\(408\) | 6.82448 | 0.337862 | ||||||||
\(409\) | −12.5328 | −0.619709 | −0.309855 | − | 0.950784i | \(-0.600280\pi\) | ||||
−0.309855 | + | 0.950784i | \(0.600280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.3653 | −0.905894 | ||||||||
\(412\) | 8.88403 | 0.437685 | ||||||||
\(413\) | −58.6031 | −2.88367 | ||||||||
\(414\) | −0.185159 | −0.00910008 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.7133 | 1.06458 | ||||||||
\(417\) | −19.3462 | −0.947389 | ||||||||
\(418\) | −2.33206 | −0.114065 | ||||||||
\(419\) | 12.0288 | 0.587644 | 0.293822 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293822 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.3721 | −1.87014 | −0.935071 | − | 0.354462i | \(-0.884664\pi\) | ||||
−0.935071 | + | 0.354462i | \(0.884664\pi\) | |||||||
\(422\) | 5.05854 | 0.246246 | ||||||||
\(423\) | 0.136257 | 0.00662507 | ||||||||
\(424\) | 11.5935 | 0.563032 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.40493 | −0.310320 | ||||||||
\(427\) | −10.0163 | −0.484721 | ||||||||
\(428\) | −0.711866 | −0.0344093 | ||||||||
\(429\) | −24.5445 | −1.18502 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.4789 | −1.41995 | −0.709975 | − | 0.704227i | \(-0.751294\pi\) | ||||
−0.709975 | + | 0.704227i | \(0.751294\pi\) | |||||||
\(432\) | 18.6840 | 0.898936 | ||||||||
\(433\) | 12.0531 | 0.579236 | 0.289618 | − | 0.957142i | \(-0.406472\pi\) | ||||
0.289618 | + | 0.957142i | \(0.406472\pi\) | |||||||
\(434\) | 12.4891 | 0.599494 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.0041 | −1.72428 | ||||||||
\(437\) | −2.65945 | −0.127219 | ||||||||
\(438\) | −1.07599 | −0.0514129 | ||||||||
\(439\) | 16.1656 | 0.771541 | 0.385771 | − | 0.922595i | \(-0.373936\pi\) | ||||
0.385771 | + | 0.922595i | \(0.373936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.35119 | −0.254819 | ||||||||
\(442\) | 6.63782 | 0.315729 | ||||||||
\(443\) | −19.3729 | −0.920433 | −0.460217 | − | 0.887807i | \(-0.652228\pi\) | ||||
−0.460217 | + | 0.887807i | \(0.652228\pi\) | |||||||
\(444\) | 12.3467 | 0.585947 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.82961 | 0.276040 | ||||||||
\(447\) | 3.32805 | 0.157411 | ||||||||
\(448\) | 22.3920 | 1.05792 | ||||||||
\(449\) | 21.4728 | 1.01337 | 0.506683 | − | 0.862132i | \(-0.330871\pi\) | ||||
0.506683 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.73215 | 0.269916 | ||||||||
\(452\) | 5.56512 | 0.261761 | ||||||||
\(453\) | 1.22914 | 0.0577502 | ||||||||
\(454\) | −2.84824 | −0.133674 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.32840 | −0.249525 | ||||||||
\(457\) | 5.95602 | 0.278611 | 0.139305 | − | 0.990249i | \(-0.455513\pi\) | ||||
0.139305 | + | 0.990249i | \(0.455513\pi\) | |||||||
\(458\) | −1.10147 | −0.0514683 | ||||||||
\(459\) | 18.9436 | 0.884210 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.6918 | 1.61576 | 0.807879 | − | 0.589348i | \(-0.200615\pi\) | ||||
0.807879 | + | 0.589348i | \(0.200615\pi\) | |||||||
\(462\) | 5.56712 | 0.259006 | ||||||||
\(463\) | 30.6399 | 1.42396 | 0.711979 | − | 0.702200i | \(-0.247799\pi\) | ||||
0.711979 | + | 0.702200i | \(0.247799\pi\) | |||||||
\(464\) | 19.6350 | 0.911531 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.71605 | −0.125819 | ||||||||
\(467\) | 8.89547 | 0.411633 | 0.205817 | − | 0.978591i | \(-0.434015\pi\) | ||||
0.205817 | + | 0.978591i | \(0.434015\pi\) | |||||||
\(468\) | 6.27699 | 0.290154 | ||||||||
\(469\) | −31.5283 | −1.45584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.3487 | −0.661152 | ||||||||
\(472\) | −18.4944 | −0.851275 | ||||||||
\(473\) | −6.24621 | −0.287201 | ||||||||
\(474\) | 2.13826 | 0.0982136 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 26.1908 | 1.20045 | ||||||||
\(477\) | 5.07411 | 0.232327 | ||||||||
\(478\) | −0.944750 | −0.0432119 | ||||||||
\(479\) | −9.13224 | −0.417263 | −0.208631 | − | 0.977994i | \(-0.566901\pi\) | ||||
−0.208631 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.7083 | 1.12660 | ||||||||
\(482\) | 1.54348 | 0.0703037 | ||||||||
\(483\) | 6.34868 | 0.288875 | ||||||||
\(484\) | 7.42763 | 0.337619 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.89718 | −0.0860579 | ||||||||
\(487\) | −14.2085 | −0.643849 | −0.321924 | − | 0.946765i | \(-0.604330\pi\) | ||||
−0.321924 | + | 0.946765i | \(0.604330\pi\) | |||||||
\(488\) | −3.16101 | −0.143092 | ||||||||
\(489\) | −27.6282 | −1.24939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.1760 | −1.04592 | −0.522960 | − | 0.852357i | \(-0.675172\pi\) | ||||
−0.522960 | + | 0.852357i | \(0.675172\pi\) | |||||||
\(492\) | 6.36558 | 0.286982 | ||||||||
\(493\) | 19.9077 | 0.896599 | ||||||||
\(494\) | −5.18265 | −0.233179 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.2984 | −1.40534 | ||||||||
\(497\) | −50.5743 | −2.26857 | ||||||||
\(498\) | −6.45115 | −0.289083 | ||||||||
\(499\) | −2.19831 | −0.0984099 | −0.0492050 | − | 0.998789i | \(-0.515669\pi\) | ||||
−0.0492050 | + | 0.998789i | \(0.515669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.2462 | 0.993887 | ||||||||
\(502\) | −6.12712 | −0.273467 | ||||||||
\(503\) | 44.0461 | 1.96392 | 0.981959 | − | 0.189092i | \(-0.0605545\pi\) | ||||
0.981959 | + | 0.189092i | \(0.0605545\pi\) | |||||||
\(504\) | −2.92931 | −0.130482 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.876894 | 0.0389827 | ||||||||
\(507\) | −34.2462 | −1.52093 | ||||||||
\(508\) | 11.3544 | 0.503771 | ||||||||
\(509\) | −9.09254 | −0.403020 | −0.201510 | − | 0.979486i | \(-0.564585\pi\) | ||||
−0.201510 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.49619 | −0.375850 | ||||||||
\(512\) | 20.9632 | 0.926449 | ||||||||
\(513\) | −14.7907 | −0.653025 | ||||||||
\(514\) | 9.47061 | 0.417731 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.93644 | −0.305360 | ||||||||
\(517\) | −0.645301 | −0.0283803 | ||||||||
\(518\) | −5.60427 | −0.246238 | ||||||||
\(519\) | −1.88001 | −0.0825235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1231 | −0.750177 | −0.375088 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375088 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(522\) | −1.08218 | −0.0473659 | ||||||||
\(523\) | 26.6112 | 1.16362 | 0.581812 | − | 0.813323i | \(-0.302344\pi\) | ||||
0.581812 | + | 0.813323i | \(0.302344\pi\) | |||||||
\(524\) | 37.7512 | 1.64917 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.03514 | 0.132338 | ||||||||
\(527\) | −31.7332 | −1.38232 | ||||||||
\(528\) | −13.9516 | −0.607165 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.09439 | −0.351267 | ||||||||
\(532\) | −20.4491 | −0.886583 | ||||||||
\(533\) | 12.7388 | 0.551780 | ||||||||
\(534\) | 4.81770 | 0.208482 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.94994 | −0.429772 | ||||||||
\(537\) | −11.5944 | −0.500337 | ||||||||
\(538\) | 5.57880 | 0.240519 | ||||||||
\(539\) | 25.3427 | 1.09159 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.5941 | 1.35834 | 0.679168 | − | 0.733983i | \(-0.262341\pi\) | ||||
0.679168 | + | 0.733983i | \(0.262341\pi\) | |||||||
\(542\) | 0.379456 | 0.0162990 | ||||||||
\(543\) | −37.5476 | −1.61132 | ||||||||
\(544\) | 12.5137 | 0.536521 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.3721 | 0.529476 | ||||||||
\(547\) | −22.7009 | −0.970622 | −0.485311 | − | 0.874342i | \(-0.661294\pi\) | ||||
−0.485311 | + | 0.874342i | \(0.661294\pi\) | |||||||
\(548\) | −22.2432 | −0.950182 | ||||||||
\(549\) | −1.38347 | −0.0590451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5435 | −0.662175 | ||||||||
\(552\) | 2.00357 | 0.0852775 | ||||||||
\(553\) | 16.8840 | 0.717982 | ||||||||
\(554\) | −0.849065 | −0.0360733 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −23.4313 | −0.993706 | ||||||||
\(557\) | −35.1292 | −1.48847 | −0.744236 | − | 0.667917i | \(-0.767186\pi\) | ||||
−0.744236 | + | 0.667917i | \(0.767186\pi\) | |||||||
\(558\) | 1.72502 | 0.0730258 | ||||||||
\(559\) | −13.8813 | −0.587115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1454 | −0.597219 | ||||||||
\(562\) | 9.05819 | 0.382097 | ||||||||
\(563\) | −32.0511 | −1.35079 | −0.675397 | − | 0.737455i | \(-0.736028\pi\) | ||||
−0.675397 | + | 0.737455i | \(0.736028\pi\) | |||||||
\(564\) | −0.716609 | −0.0301747 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.779440 | 0.0327623 | ||||||||
\(567\) | 28.4593 | 1.19518 | ||||||||
\(568\) | −15.9606 | −0.669694 | ||||||||
\(569\) | −22.0575 | −0.924700 | −0.462350 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462350 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.49242 | 0.355397 | 0.177698 | − | 0.984085i | \(-0.443135\pi\) | ||||
0.177698 | + | 0.984085i | \(0.443135\pi\) | |||||||
\(572\) | −29.7271 | −1.24295 | ||||||||
\(573\) | 7.61553 | 0.318143 | ||||||||
\(574\) | −2.88939 | −0.120601 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.09283 | 0.128868 | ||||||||
\(577\) | −27.1554 | −1.13050 | −0.565248 | − | 0.824921i | \(-0.691220\pi\) | ||||
−0.565248 | + | 0.824921i | \(0.691220\pi\) | |||||||
\(578\) | −1.77988 | −0.0740331 | ||||||||
\(579\) | 16.0394 | 0.666573 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.9393 | −2.11332 | ||||||||
\(582\) | 1.78758 | 0.0740974 | ||||||||
\(583\) | −24.0304 | −0.995239 | ||||||||
\(584\) | −2.68130 | −0.110953 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.2502 | −0.464743 | ||||||||
\(587\) | 30.8322 | 1.27258 | 0.636290 | − | 0.771450i | \(-0.280468\pi\) | ||||
0.636290 | + | 0.771450i | \(0.280468\pi\) | |||||||
\(588\) | 28.1431 | 1.16060 | ||||||||
\(589\) | 24.7765 | 1.02090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.69214 | 0.275278 | ||||||||
\(592\) | 14.0447 | 0.577233 | ||||||||
\(593\) | 27.7559 | 1.13980 | 0.569899 | − | 0.821715i | \(-0.306982\pi\) | ||||
0.569899 | + | 0.821715i | \(0.306982\pi\) | |||||||
\(594\) | 4.87689 | 0.200101 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.03077 | 0.165107 | ||||||||
\(597\) | −6.28000 | −0.257023 | ||||||||
\(598\) | 1.94876 | 0.0796909 | ||||||||
\(599\) | −30.7712 | −1.25728 | −0.628638 | − | 0.777698i | \(-0.716387\pi\) | ||||
−0.628638 | + | 0.777698i | \(0.716387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9830 | −0.733541 | −0.366771 | − | 0.930311i | \(-0.619537\pi\) | ||||
−0.366771 | + | 0.930311i | \(0.619537\pi\) | |||||||
\(602\) | 3.14851 | 0.128324 | ||||||||
\(603\) | −4.35476 | −0.177339 | ||||||||
\(604\) | 1.48868 | 0.0605736 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.74229 | −0.192642 | ||||||||
\(607\) | 18.3220 | 0.743668 | 0.371834 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371834 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(608\) | −9.77041 | −0.396242 | ||||||||
\(609\) | 37.1056 | 1.50359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.43408 | −0.0580168 | ||||||||
\(612\) | 3.61753 | 0.146230 | ||||||||
\(613\) | −35.4451 | −1.43162 | −0.715808 | − | 0.698297i | \(-0.753941\pi\) | ||||
−0.715808 | + | 0.698297i | \(0.753941\pi\) | |||||||
\(614\) | −0.492423 | −0.0198726 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.8729 | 0.558954 | ||||||||
\(617\) | −43.1567 | −1.73742 | −0.868712 | − | 0.495318i | \(-0.835052\pi\) | ||||
−0.868712 | + | 0.495318i | \(0.835052\pi\) | |||||||
\(618\) | 2.41861 | 0.0972907 | ||||||||
\(619\) | 5.81133 | 0.233577 | 0.116789 | − | 0.993157i | \(-0.462740\pi\) | ||||
0.116789 | + | 0.993157i | \(0.462740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | −4.65114 | −0.186494 | ||||||||
\(623\) | 38.0413 | 1.52409 | ||||||||
\(624\) | −31.0053 | −1.24121 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.8336 | 0.432999 | ||||||||
\(627\) | 11.0444 | 0.441070 | ||||||||
\(628\) | −17.3785 | −0.693476 | ||||||||
\(629\) | 14.2398 | 0.567777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.4626 | −1.09327 | −0.546635 | − | 0.837371i | \(-0.684092\pi\) | ||||
−0.546635 | + | 0.837371i | \(0.684092\pi\) | |||||||
\(632\) | 5.32840 | 0.211952 | ||||||||
\(633\) | −23.9567 | −0.952194 | ||||||||
\(634\) | −4.14876 | −0.164768 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −26.6859 | −1.05816 | ||||||||
\(637\) | 56.3202 | 2.23149 | ||||||||
\(638\) | 5.12511 | 0.202905 | ||||||||
\(639\) | −6.98544 | −0.276340 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7938 | 1.49277 | 0.746383 | − | 0.665517i | \(-0.231789\pi\) | ||||
0.746383 | + | 0.665517i | \(0.231789\pi\) | |||||||
\(642\) | −0.193800 | −0.00764867 | ||||||||
\(643\) | −12.5343 | −0.494304 | −0.247152 | − | 0.968977i | \(-0.579495\pi\) | ||||
−0.247152 | + | 0.968977i | \(0.579495\pi\) | |||||||
\(644\) | 7.68923 | 0.302998 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.98685 | −0.117516 | ||||||||
\(647\) | 21.5133 | 0.845774 | 0.422887 | − | 0.906183i | \(-0.361017\pi\) | ||||
0.422887 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(648\) | 8.98143 | 0.352824 | ||||||||
\(649\) | 38.3342 | 1.50475 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −59.1469 | −2.31815 | ||||||||
\(652\) | −33.4620 | −1.31047 | ||||||||
\(653\) | −19.9011 | −0.778790 | −0.389395 | − | 0.921071i | \(-0.627316\pi\) | ||||
−0.389395 | + | 0.921071i | \(0.627316\pi\) | |||||||
\(654\) | −9.80184 | −0.383282 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.24102 | 0.282714 | ||||||||
\(657\) | −1.17351 | −0.0457831 | ||||||||
\(658\) | 0.325276 | 0.0126806 | ||||||||
\(659\) | −4.95773 | −0.193126 | −0.0965628 | − | 0.995327i | \(-0.530785\pi\) | ||||
−0.0965628 | + | 0.995327i | \(0.530785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0.519902 | 0.0202066 | ||||||||
\(663\) | −31.4360 | −1.22087 | ||||||||
\(664\) | −16.0758 | −0.623863 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.774075 | −0.0299948 | ||||||||
\(667\) | 5.84461 | 0.226304 | ||||||||
\(668\) | 26.9436 | 1.04248 | ||||||||
\(669\) | −27.6084 | −1.06740 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.55197 | 0.252936 | ||||||||
\(672\) | 23.3240 | 0.899744 | ||||||||
\(673\) | 28.5176 | 1.09927 | 0.549637 | − | 0.835404i | \(-0.314766\pi\) | ||||
0.549637 | + | 0.835404i | \(0.314766\pi\) | |||||||
\(674\) | 5.10147 | 0.196501 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −41.4774 | −1.59529 | ||||||||
\(677\) | −28.6214 | −1.10001 | −0.550004 | − | 0.835162i | \(-0.685374\pi\) | ||||
−0.550004 | + | 0.835162i | \(0.685374\pi\) | |||||||
\(678\) | 1.51506 | 0.0581856 | ||||||||
\(679\) | 14.1150 | 0.541683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4890 | 0.516898 | ||||||||
\(682\) | −8.16950 | −0.312826 | ||||||||
\(683\) | −11.3983 | −0.436144 | −0.218072 | − | 0.975933i | \(-0.569977\pi\) | ||||
−0.218072 | + | 0.975933i | \(0.569977\pi\) | |||||||
\(684\) | −2.82448 | −0.107997 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.39060 | −0.129454 | ||||||||
\(687\) | 5.21644 | 0.199020 | ||||||||
\(688\) | −7.89040 | −0.300819 | ||||||||
\(689\) | −53.4040 | −2.03453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.1898 | 1.71910 | 0.859550 | − | 0.511051i | \(-0.170744\pi\) | ||||
0.859550 | + | 0.511051i | \(0.170744\pi\) | |||||||
\(692\) | −2.27699 | −0.0865580 | ||||||||
\(693\) | 6.07170 | 0.230645 | ||||||||
\(694\) | 2.96857 | 0.112686 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.7101 | 0.443869 | ||||||||
\(697\) | 7.34160 | 0.278083 | ||||||||
\(698\) | 0.364011 | 0.0137780 | ||||||||
\(699\) | 12.8629 | 0.486521 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4871 | 1.52918 | 0.764588 | − | 0.644520i | \(-0.222943\pi\) | ||||
0.764588 | + | 0.644520i | \(0.222943\pi\) | |||||||
\(702\) | 10.8382 | 0.409060 | ||||||||
\(703\) | −11.1181 | −0.419327 | ||||||||
\(704\) | −14.6473 | −0.552041 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.648131 | −0.0243927 | ||||||||
\(707\) | −37.4458 | −1.40830 | ||||||||
\(708\) | 42.5702 | 1.59989 | ||||||||
\(709\) | −41.6443 | −1.56398 | −0.781992 | − | 0.623288i | \(-0.785796\pi\) | ||||
−0.781992 | + | 0.623288i | \(0.785796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.33206 | 0.0874591 | ||||||||
\(712\) | 12.0054 | 0.449920 | ||||||||
\(713\) | −9.31640 | −0.348902 | ||||||||
\(714\) | 7.13024 | 0.266843 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.0427 | −0.524799 | ||||||||
\(717\) | 4.47424 | 0.167093 | ||||||||
\(718\) | −0.858620 | −0.0320434 | ||||||||
\(719\) | 49.2288 | 1.83592 | 0.917961 | − | 0.396670i | \(-0.129834\pi\) | ||||
0.917961 | + | 0.396670i | \(0.129834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0977 | 0.711235 | ||||||||
\(722\) | −3.93276 | −0.146362 | ||||||||
\(723\) | −7.30977 | −0.271853 | ||||||||
\(724\) | −45.4759 | −1.69010 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.02211 | 0.0750477 | ||||||||
\(727\) | −27.9581 | −1.03691 | −0.518455 | − | 0.855105i | \(-0.673493\pi\) | ||||
−0.518455 | + | 0.855105i | \(0.673493\pi\) | |||||||
\(728\) | 30.8304 | 1.14265 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 7.27598 | 0.268928 | ||||||||
\(733\) | 18.6655 | 0.689427 | 0.344714 | − | 0.938708i | \(-0.387976\pi\) | ||||
0.344714 | + | 0.938708i | \(0.387976\pi\) | |||||||
\(734\) | −2.30164 | −0.0849549 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.67384 | 0.135420 | ||||||||
\(737\) | 20.6237 | 0.759682 | ||||||||
\(738\) | −0.399090 | −0.0146907 | ||||||||
\(739\) | 2.50407 | 0.0921136 | 0.0460568 | − | 0.998939i | \(-0.485334\pi\) | ||||
0.0460568 | + | 0.998939i | \(0.485334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.5445 | 0.901664 | ||||||||
\(742\) | 12.1130 | 0.444681 | ||||||||
\(743\) | −4.69736 | −0.172330 | −0.0861648 | − | 0.996281i | \(-0.527461\pi\) | ||||
−0.0861648 | + | 0.996281i | \(0.527461\pi\) | |||||||
\(744\) | −18.6660 | −0.684330 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.01963 | −0.293620 | ||||||||
\(747\) | −7.03585 | −0.257428 | ||||||||
\(748\) | −17.1322 | −0.626417 | ||||||||
\(749\) | −1.53027 | −0.0559150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0720 | −0.586477 | −0.293239 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293239 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(752\) | −0.815163 | −0.0297259 | ||||||||
\(753\) | 29.0174 | 1.05745 | ||||||||
\(754\) | 11.3898 | 0.414791 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 42.7640 | 1.55531 | ||||||||
\(757\) | 25.8357 | 0.939014 | 0.469507 | − | 0.882929i | \(-0.344432\pi\) | ||||
0.469507 | + | 0.882929i | \(0.344432\pi\) | |||||||
\(758\) | −8.12912 | −0.295263 | ||||||||
\(759\) | −4.15288 | −0.150740 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.6005 | 0.565518 | 0.282759 | − | 0.959191i | \(-0.408750\pi\) | ||||
0.282759 | + | 0.959191i | \(0.408750\pi\) | |||||||
\(762\) | 3.09116 | 0.111981 | ||||||||
\(763\) | −77.3968 | −2.80195 | ||||||||
\(764\) | 9.22357 | 0.333697 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.64630 | 0.0594833 | ||||||||
\(767\) | 85.1919 | 3.07610 | ||||||||
\(768\) | −12.4827 | −0.450429 | ||||||||
\(769\) | −37.7722 | −1.36210 | −0.681050 | − | 0.732237i | \(-0.738476\pi\) | ||||
−0.681050 | + | 0.732237i | \(0.738476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.8518 | −1.61530 | ||||||||
\(772\) | 19.4261 | 0.699161 | ||||||||
\(773\) | 42.9078 | 1.54329 | 0.771643 | − | 0.636056i | \(-0.219435\pi\) | ||||
0.771643 | + | 0.636056i | \(0.219435\pi\) | |||||||
\(774\) | 0.434880 | 0.0156314 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.45451 | 0.159908 | ||||||||
\(777\) | 26.5412 | 0.952162 | ||||||||
\(778\) | −10.5590 | −0.378558 | ||||||||
\(779\) | −5.73215 | −0.205376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.0823 | 1.18378 | ||||||||
\(782\) | 1.12311 | 0.0401622 | ||||||||
\(783\) | 32.5051 | 1.16164 | ||||||||
\(784\) | 32.0136 | 1.14334 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.2775 | 0.366585 | ||||||||
\(787\) | 33.5324 | 1.19530 | 0.597650 | − | 0.801757i | \(-0.296101\pi\) | ||||
0.597650 | + | 0.801757i | \(0.296101\pi\) | |||||||
\(788\) | 8.10521 | 0.288736 | ||||||||
\(789\) | −14.3741 | −0.511731 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9632 | 0.425361 | ||||||||
\(792\) | 1.91615 | 0.0680876 | ||||||||
\(793\) | 14.5608 | 0.517068 | ||||||||
\(794\) | 5.71883 | 0.202954 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.60604 | −0.269589 | ||||||||
\(797\) | −32.7488 | −1.16002 | −0.580012 | − | 0.814608i | \(-0.696952\pi\) | ||||
−0.580012 | + | 0.814608i | \(0.696952\pi\) | |||||||
\(798\) | −5.56712 | −0.197074 | ||||||||
\(799\) | −0.826486 | −0.0292390 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.25435 | 0.185653 | ||||||||
\(802\) | −7.03479 | −0.248407 | ||||||||
\(803\) | 5.55764 | 0.196125 | ||||||||
\(804\) | 22.9027 | 0.807714 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.1555 | −0.639499 | ||||||||
\(807\) | −26.4206 | −0.930049 | ||||||||
\(808\) | −11.8175 | −0.415737 | ||||||||
\(809\) | 28.8513 | 1.01436 | 0.507179 | − | 0.861841i | \(-0.330688\pi\) | ||||
0.507179 | + | 0.861841i | \(0.330688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.1791 | 1.27042 | 0.635211 | − | 0.772339i | \(-0.280913\pi\) | ||||
0.635211 | + | 0.772339i | \(0.280913\pi\) | |||||||
\(812\) | 44.9406 | 1.57710 | ||||||||
\(813\) | −1.79706 | −0.0630257 | ||||||||
\(814\) | 3.66594 | 0.128491 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17.8689 | −0.625536 | ||||||||
\(817\) | 6.24621 | 0.218527 | ||||||||
\(818\) | −4.13242 | −0.144487 | ||||||||
\(819\) | 13.4934 | 0.471498 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.73752 | 0.200241 | 0.100120 | − | 0.994975i | \(-0.468077\pi\) | ||||
0.100120 | + | 0.994975i | \(0.468077\pi\) | |||||||
\(822\) | −6.05554 | −0.211211 | ||||||||
\(823\) | 6.87333 | 0.239589 | 0.119795 | − | 0.992799i | \(-0.461776\pi\) | ||||
0.119795 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(824\) | 6.02700 | 0.209961 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.3230 | −0.672334 | ||||||||
\(827\) | 19.7332 | 0.686191 | 0.343095 | − | 0.939301i | \(-0.388525\pi\) | ||||
0.343095 | + | 0.939301i | \(0.388525\pi\) | |||||||
\(828\) | 1.06205 | 0.0369089 | ||||||||
\(829\) | −2.88833 | −0.100316 | −0.0501580 | − | 0.998741i | \(-0.515972\pi\) | ||||
−0.0501580 | + | 0.998741i | \(0.515972\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.02108 | 0.139490 | ||||||||
\(832\) | −32.5514 | −1.12852 | ||||||||
\(833\) | 32.4583 | 1.12461 | ||||||||
\(834\) | −6.37898 | −0.220886 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.3765 | 0.462634 | ||||||||
\(837\) | −51.8137 | −1.79094 | ||||||||
\(838\) | 3.96621 | 0.137011 | ||||||||
\(839\) | 24.1904 | 0.835147 | 0.417573 | − | 0.908643i | \(-0.362881\pi\) | ||||
0.417573 | + | 0.908643i | \(0.362881\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.15951 | 0.177914 | ||||||||
\(842\) | −12.6523 | −0.436028 | ||||||||
\(843\) | −42.8986 | −1.47751 | ||||||||
\(844\) | −29.0153 | −0.998747 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0449278 | 0.00154465 | ||||||||
\(847\) | 15.9669 | 0.548630 | ||||||||
\(848\) | −30.3559 | −1.04243 | ||||||||
\(849\) | −3.69135 | −0.126687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.18059 | 0.143309 | ||||||||
\(852\) | 36.7380 | 1.25862 | ||||||||
\(853\) | −27.5381 | −0.942887 | −0.471444 | − | 0.881896i | \(-0.656267\pi\) | ||||
−0.471444 | + | 0.881896i | \(0.656267\pi\) | |||||||
\(854\) | −3.30264 | −0.113014 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.482936 | −0.0165064 | ||||||||
\(857\) | 17.3995 | 0.594357 | 0.297178 | − | 0.954822i | \(-0.403954\pi\) | ||||
0.297178 | + | 0.954822i | \(0.403954\pi\) | |||||||
\(858\) | −8.09298 | −0.276290 | ||||||||
\(859\) | 1.24560 | 0.0424993 | 0.0212497 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212497 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6839 | 0.466345 | ||||||||
\(862\) | −9.72000 | −0.331065 | ||||||||
\(863\) | 4.60383 | 0.156716 | 0.0783580 | − | 0.996925i | \(-0.475032\pi\) | ||||
0.0783580 | + | 0.996925i | \(0.475032\pi\) | |||||||
\(864\) | 20.4323 | 0.695119 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.97424 | 0.135050 | ||||||||
\(867\) | 8.42931 | 0.286274 | ||||||||
\(868\) | −71.6359 | −2.43148 | ||||||||
\(869\) | −11.0444 | −0.374655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.8330 | 1.55299 | ||||||||
\(872\) | −24.4255 | −0.827152 | ||||||||
\(873\) | 1.94959 | 0.0659837 | ||||||||
\(874\) | −0.876894 | −0.0296614 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.17178 | 0.208525 | ||||||||
\(877\) | −33.8276 | −1.14228 | −0.571138 | − | 0.820854i | \(-0.693498\pi\) | ||||
−0.571138 | + | 0.820854i | \(0.693498\pi\) | |||||||
\(878\) | 5.33023 | 0.179887 | ||||||||
\(879\) | 53.2799 | 1.79709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.1134 | 0.879782 | 0.439891 | − | 0.898051i | \(-0.355017\pi\) | ||||
0.439891 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(882\) | −1.76443 | −0.0594115 | ||||||||
\(883\) | 54.5412 | 1.83546 | 0.917729 | − | 0.397206i | \(-0.130020\pi\) | ||||
0.917729 | + | 0.397206i | \(0.130020\pi\) | |||||||
\(884\) | −38.0738 | −1.28056 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.38777 | −0.214601 | ||||||||
\(887\) | −22.6201 | −0.759509 | −0.379754 | − | 0.925087i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925087i | \(0.623991\pi\) | |||||||
\(888\) | 8.37609 | 0.281083 | ||||||||
\(889\) | 24.4082 | 0.818626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.6162 | −0.623666 | ||||||||
\(892\) | −33.4380 | −1.11959 | ||||||||
\(893\) | 0.645301 | 0.0215942 | ||||||||
\(894\) | 1.09735 | 0.0367008 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.2561 | 1.24464 | ||||||||
\(897\) | −9.22914 | −0.308152 | ||||||||
\(898\) | 7.08018 | 0.236269 | ||||||||
\(899\) | −54.4508 | −1.81603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7776 | −1.02535 | ||||||||
\(902\) | 1.89005 | 0.0629317 | ||||||||
\(903\) | −14.9110 | −0.496208 | ||||||||
\(904\) | 3.77543 | 0.125569 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.405282 | 0.0134646 | ||||||||
\(907\) | 3.62149 | 0.120250 | 0.0601248 | − | 0.998191i | \(-0.480850\pi\) | ||||
0.0601248 | + | 0.998191i | \(0.480850\pi\) | |||||||
\(908\) | 16.3372 | 0.542169 | ||||||||
\(909\) | −5.17211 | −0.171548 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9241 | 0.892034 | 0.446017 | − | 0.895025i | \(-0.352842\pi\) | ||||
0.446017 | + | 0.895025i | \(0.352842\pi\) | |||||||
\(912\) | 13.9516 | 0.461983 | ||||||||
\(913\) | 33.3210 | 1.10277 | ||||||||
\(914\) | 1.96386 | 0.0649587 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.31791 | 0.208750 | ||||||||
\(917\) | 81.1524 | 2.67989 | ||||||||
\(918\) | 6.24621 | 0.206156 | ||||||||
\(919\) | −19.5059 | −0.643441 | −0.321721 | − | 0.946835i | \(-0.604261\pi\) | ||||
−0.321721 | + | 0.946835i | \(0.604261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.33206 | 0.0768440 | ||||||||
\(922\) | 11.4388 | 0.376718 | ||||||||
\(923\) | 73.5204 | 2.41995 | ||||||||
\(924\) | −31.9324 | −1.05050 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.1028 | 0.331999 | ||||||||
\(927\) | 2.63782 | 0.0866373 | ||||||||
\(928\) | 21.4722 | 0.704859 | ||||||||
\(929\) | 27.2139 | 0.892860 | 0.446430 | − | 0.894819i | \(-0.352695\pi\) | ||||
0.446430 | + | 0.894819i | \(0.352695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.3427 | −0.830572 | ||||||||
\(932\) | 15.5790 | 0.510307 | ||||||||
\(933\) | 22.0273 | 0.721142 | ||||||||
\(934\) | 2.93308 | 0.0959732 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.25836 | 0.139189 | ||||||||
\(937\) | −3.85626 | −0.125978 | −0.0629892 | − | 0.998014i | \(-0.520063\pi\) | ||||
−0.0629892 | + | 0.998014i | \(0.520063\pi\) | |||||||
\(938\) | −10.3957 | −0.339433 | ||||||||
\(939\) | −51.3069 | −1.67434 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.6471 | −1.97704 | −0.988519 | − | 0.151097i | \(-0.951720\pi\) | ||||
−0.988519 | + | 0.151097i | \(0.951720\pi\) | |||||||
\(942\) | −4.73115 | −0.154149 | ||||||||
\(943\) | 2.15539 | 0.0701890 | ||||||||
\(944\) | 48.4248 | 1.57609 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.05955 | −0.0669616 | ||||||||
\(947\) | 1.11954 | 0.0363801 | 0.0181901 | − | 0.999835i | \(-0.494210\pi\) | ||||
0.0181901 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(948\) | −12.2648 | −0.398343 | ||||||||
\(949\) | 12.3510 | 0.400931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.6481 | 0.637132 | ||||||||
\(952\) | 17.7681 | 0.575866 | ||||||||
\(953\) | −14.8590 | −0.481331 | −0.240666 | − | 0.970608i | \(-0.577366\pi\) | ||||
−0.240666 | + | 0.970608i | \(0.577366\pi\) | |||||||
\(954\) | 1.67307 | 0.0541677 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.41899 | 0.175263 | ||||||||
\(957\) | −24.2720 | −0.784601 | ||||||||
\(958\) | −3.01115 | −0.0972858 | ||||||||
\(959\) | −47.8155 | −1.54404 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.7953 | 1.79985 | ||||||||
\(962\) | 8.14699 | 0.262669 | ||||||||
\(963\) | −0.211365 | −0.00681114 | ||||||||
\(964\) | −8.85325 | −0.285144 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.09333 | 0.0673519 | ||||||||
\(967\) | −38.5718 | −1.24039 | −0.620193 | − | 0.784449i | \(-0.712946\pi\) | ||||
−0.620193 | + | 0.784449i | \(0.712946\pi\) | |||||||
\(968\) | 5.03897 | 0.161959 | ||||||||
\(969\) | 14.1454 | 0.454416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.4984 | −0.818284 | −0.409142 | − | 0.912471i | \(-0.634172\pi\) | ||||
−0.409142 | + | 0.912471i | \(0.634172\pi\) | |||||||
\(972\) | 10.8820 | 0.349041 | ||||||||
\(973\) | −50.3694 | −1.61477 | ||||||||
\(974\) | −4.68493 | −0.150115 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.27664 | 0.264929 | ||||||||
\(977\) | 15.8952 | 0.508533 | 0.254267 | − | 0.967134i | \(-0.418166\pi\) | ||||
0.254267 | + | 0.967134i | \(0.418166\pi\) | |||||||
\(978\) | −9.10978 | −0.291299 | ||||||||
\(979\) | −24.8840 | −0.795297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6902 | −0.341313 | ||||||||
\(982\) | −7.64176 | −0.243858 | ||||||||
\(983\) | 2.50587 | 0.0799247 | 0.0399624 | − | 0.999201i | \(-0.487276\pi\) | ||||
0.0399624 | + | 0.999201i | \(0.487276\pi\) | |||||||
\(984\) | 4.31846 | 0.137668 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.56412 | 0.209044 | ||||||||
\(987\) | −1.54047 | −0.0490337 | ||||||||
\(988\) | 29.7271 | 0.945746 | ||||||||
\(989\) | −2.34868 | −0.0746837 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5272 | 0.397938 | 0.198969 | − | 0.980006i | \(-0.436241\pi\) | ||||
0.198969 | + | 0.980006i | \(0.436241\pi\) | |||||||
\(992\) | −34.2270 | −1.08671 | ||||||||
\(993\) | −2.46220 | −0.0781356 | ||||||||
\(994\) | −16.6757 | −0.528922 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 37.0031 | 1.17249 | ||||||||
\(997\) | 9.34803 | 0.296055 | 0.148028 | − | 0.988983i | \(-0.452708\pi\) | ||||
0.148028 | + | 0.988983i | \(0.452708\pi\) | |||||||
\(998\) | −0.724843 | −0.0229445 | ||||||||
\(999\) | 23.2506 | 0.735616 |
(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 | 575.2.a.h.1.3 | 4 | ||
3.2 | odd | 2 | 5175.2.a.bx.1.2 | 4 | |||
4.3 | odd | 2 | 9200.2.a.cl.1.4 | 4 | |||
5.2 | odd | 4 | 575.2.b.e.24.5 | 8 | |||
5.3 | odd | 4 | 575.2.b.e.24.4 | 8 | |||
5.4 | even | 2 | 115.2.a.c.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 1035.2.a.o.1.3 | 4 | |||
20.19 | odd | 2 | 1840.2.a.u.1.1 | 4 | |||
35.34 | odd | 2 | 5635.2.a.v.1.2 | 4 | |||
40.19 | odd | 2 | 7360.2.a.cg.1.3 | 4 | |||
40.29 | even | 2 | 7360.2.a.cj.1.2 | 4 | |||
115.114 | odd | 2 | 2645.2.a.m.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.a.c.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
575.2.a.h.1.3 | 4 | 1.1 | even | 1 | trivial | ||
575.2.b.e.24.4 | 8 | 5.3 | odd | 4 | |||
575.2.b.e.24.5 | 8 | 5.2 | odd | 4 | |||
1035.2.a.o.1.3 | 4 | 15.14 | odd | 2 | |||
1840.2.a.u.1.1 | 4 | 20.19 | odd | 2 | |||
2645.2.a.m.1.2 | 4 | 115.114 | odd | 2 | |||
5175.2.a.bx.1.2 | 4 | 3.2 | odd | 2 | |||
5635.2.a.v.1.2 | 4 | 35.34 | odd | 2 | |||
7360.2.a.cg.1.3 | 4 | 40.19 | odd | 2 | |||
7360.2.a.cj.1.2 | 4 | 40.29 | even | 2 | |||
9200.2.a.cl.1.4 | 4 | 4.3 | odd | 2 |