Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.414764096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 20x^{3} + 29x^{2} - 42x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.52844\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52844 | −1.08077 | −0.540386 | − | 0.841417i | \(-0.681722\pi\) | ||||
−0.540386 | + | 0.841417i | \(0.681722\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.336137 | 0.168068 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.52844 | 0.623984 | ||||||||
\(7\) | −3.11578 | −1.17765 | −0.588827 | − | 0.808259i | \(-0.700410\pi\) | ||||
−0.588827 | + | 0.808259i | \(0.700410\pi\) | |||||||
\(8\) | 2.54312 | 0.899129 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.66386 | 0.803185 | 0.401593 | − | 0.915818i | \(-0.368457\pi\) | ||||
0.401593 | + | 0.915818i | \(0.368457\pi\) | |||||||
\(12\) | −0.336137 | −0.0970343 | ||||||||
\(13\) | −5.03002 | −1.39508 | −0.697538 | − | 0.716547i | \(-0.745721\pi\) | ||||
−0.697538 | + | 0.716547i | \(0.745721\pi\) | |||||||
\(14\) | 4.76229 | 1.27278 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.55929 | −1.13982 | ||||||||
\(17\) | 5.03002 | 1.21996 | 0.609980 | − | 0.792417i | \(-0.291178\pi\) | ||||
0.609980 | + | 0.792417i | \(0.291178\pi\) | |||||||
\(18\) | −1.52844 | −0.360257 | ||||||||
\(19\) | 8.43772 | 1.93575 | 0.967873 | − | 0.251440i | \(-0.0809042\pi\) | ||||
0.967873 | + | 0.251440i | \(0.0809042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.11578 | 0.679919 | ||||||||
\(22\) | −4.07156 | −0.868060 | ||||||||
\(23\) | 3.11578 | 0.649685 | 0.324842 | − | 0.945768i | \(-0.394689\pi\) | ||||
0.324842 | + | 0.945768i | \(0.394689\pi\) | |||||||
\(24\) | −2.54312 | −0.519112 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.68810 | 1.50776 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.04733 | −0.197926 | ||||||||
\(29\) | 5.61965 | 1.04354 | 0.521771 | − | 0.853086i | \(-0.325272\pi\) | ||||
0.521771 | + | 0.853086i | \(0.325272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.86076 | −1.77105 | −0.885523 | − | 0.464596i | \(-0.846199\pi\) | ||||
−0.885523 | + | 0.464596i | \(0.846199\pi\) | |||||||
\(32\) | 1.88237 | 0.332759 | ||||||||
\(33\) | −2.66386 | −0.463719 | ||||||||
\(34\) | −7.68810 | −1.31850 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.336137 | 0.0560228 | ||||||||
\(37\) | −4.66386 | −0.766734 | −0.383367 | − | 0.923596i | \(-0.625236\pi\) | ||||
−0.383367 | + | 0.923596i | \(0.625236\pi\) | |||||||
\(38\) | −12.8966 | −2.09210 | ||||||||
\(39\) | 5.03002 | 0.805448 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.06955 | −1.41643 | −0.708213 | − | 0.705999i | \(-0.750498\pi\) | ||||
−0.708213 | + | 0.705999i | \(0.750498\pi\) | |||||||
\(42\) | −4.76229 | −0.734837 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0.895422 | 0.134990 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.76229 | −0.702161 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 4.55929 | 0.658076 | ||||||||
\(49\) | 2.70808 | 0.386869 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.03002 | −0.704344 | ||||||||
\(52\) | −1.69077 | −0.234468 | ||||||||
\(53\) | 0.958459 | 0.131654 | 0.0658272 | − | 0.997831i | \(-0.479031\pi\) | ||||
0.0658272 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(54\) | 1.52844 | 0.207995 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.92380 | −1.05886 | ||||||||
\(57\) | −8.43772 | −1.11760 | ||||||||
\(58\) | −8.58931 | −1.12783 | ||||||||
\(59\) | −3.70540 | −0.482403 | −0.241201 | − | 0.970475i | \(-0.577541\pi\) | ||||
−0.241201 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29192 | 0.549524 | 0.274762 | − | 0.961512i | \(-0.411401\pi\) | ||||
0.274762 | + | 0.961512i | \(0.411401\pi\) | |||||||
\(62\) | 15.0716 | 1.91410 | ||||||||
\(63\) | −3.11578 | −0.392551 | ||||||||
\(64\) | 6.24148 | 0.780185 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.07156 | 0.501175 | ||||||||
\(67\) | 15.0354 | 1.83687 | 0.918435 | − | 0.395571i | \(-0.129453\pi\) | ||||
0.918435 | + | 0.395571i | \(0.129453\pi\) | |||||||
\(68\) | 1.69077 | 0.205036 | ||||||||
\(69\) | −3.11578 | −0.375096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.14690 | −0.848181 | −0.424091 | − | 0.905620i | \(-0.639406\pi\) | ||||
−0.424091 | + | 0.905620i | \(0.639406\pi\) | |||||||
\(72\) | 2.54312 | 0.299710 | ||||||||
\(73\) | 11.8608 | 1.38820 | 0.694099 | − | 0.719880i | \(-0.255803\pi\) | ||||
0.694099 | + | 0.719880i | \(0.255803\pi\) | |||||||
\(74\) | 7.12845 | 0.828665 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.83623 | 0.325337 | ||||||||
\(77\) | −8.30001 | −0.945874 | ||||||||
\(78\) | −7.68810 | −0.870506 | ||||||||
\(79\) | −10.9555 | −1.23259 | −0.616293 | − | 0.787517i | \(-0.711366\pi\) | ||||
−0.616293 | + | 0.787517i | \(0.711366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.8623 | 1.53083 | ||||||||
\(83\) | −12.8754 | −1.41326 | −0.706632 | − | 0.707582i | \(-0.749786\pi\) | ||||
−0.706632 | + | 0.707582i | \(0.749786\pi\) | |||||||
\(84\) | 1.04733 | 0.114273 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.61965 | −0.602489 | ||||||||
\(88\) | 6.77452 | 0.722167 | ||||||||
\(89\) | 14.3632 | 1.52249 | 0.761246 | − | 0.648463i | \(-0.224588\pi\) | ||||
0.761246 | + | 0.648463i | \(0.224588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.6724 | 1.64292 | ||||||||
\(92\) | 1.04733 | 0.109191 | ||||||||
\(93\) | 9.86076 | 1.02251 | ||||||||
\(94\) | −1.52844 | −0.157647 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.88237 | −0.192118 | ||||||||
\(97\) | −8.96387 | −0.910143 | −0.455072 | − | 0.890455i | \(-0.650386\pi\) | ||||
−0.455072 | + | 0.890455i | \(0.650386\pi\) | |||||||
\(98\) | −4.13915 | −0.418117 | ||||||||
\(99\) | 2.66386 | 0.267728 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.51306 | −0.946585 | −0.473292 | − | 0.880905i | \(-0.656935\pi\) | ||||
−0.473292 | + | 0.880905i | \(0.656935\pi\) | |||||||
\(102\) | 7.68810 | 0.761235 | ||||||||
\(103\) | 7.74494 | 0.763131 | 0.381566 | − | 0.924342i | \(-0.375385\pi\) | ||||
0.381566 | + | 0.924342i | \(0.375385\pi\) | |||||||
\(104\) | −12.7919 | −1.25435 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.46495 | −0.142288 | ||||||||
\(107\) | 0.319993 | 0.0309349 | 0.0154674 | − | 0.999880i | \(-0.495076\pi\) | ||||
0.0154674 | + | 0.999880i | \(0.495076\pi\) | |||||||
\(108\) | −0.336137 | −0.0323448 | ||||||||
\(109\) | −10.9470 | −1.04853 | −0.524266 | − | 0.851554i | \(-0.675660\pi\) | ||||
−0.524266 | + | 0.851554i | \(0.675660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.66386 | 0.442674 | ||||||||
\(112\) | 14.2057 | 1.34232 | ||||||||
\(113\) | 14.8670 | 1.39857 | 0.699286 | − | 0.714842i | \(-0.253501\pi\) | ||||
0.699286 | + | 0.714842i | \(0.253501\pi\) | |||||||
\(114\) | 12.8966 | 1.20787 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.88897 | 0.175386 | ||||||||
\(117\) | −5.03002 | −0.465026 | ||||||||
\(118\) | 5.66350 | 0.521367 | ||||||||
\(119\) | −15.6724 | −1.43669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.90383 | −0.354894 | ||||||||
\(122\) | −6.55995 | −0.593910 | ||||||||
\(123\) | 9.06955 | 0.817774 | ||||||||
\(124\) | −3.31456 | −0.297657 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.76229 | 0.424258 | ||||||||
\(127\) | −5.36988 | −0.476500 | −0.238250 | − | 0.971204i | \(-0.576574\pi\) | ||||
−0.238250 | + | 0.971204i | \(0.576574\pi\) | |||||||
\(128\) | −13.3045 | −1.17596 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.06841 | −0.268088 | −0.134044 | − | 0.990975i | \(-0.542796\pi\) | ||||
−0.134044 | + | 0.990975i | \(0.542796\pi\) | |||||||
\(132\) | −0.895422 | −0.0779365 | ||||||||
\(133\) | −26.2901 | −2.27964 | ||||||||
\(134\) | −22.9808 | −1.98524 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.7919 | 1.09690 | ||||||||
\(137\) | −8.42841 | −0.720088 | −0.360044 | − | 0.932935i | \(-0.617238\pi\) | ||||
−0.360044 | + | 0.932935i | \(0.617238\pi\) | |||||||
\(138\) | 4.76229 | 0.405393 | ||||||||
\(139\) | 3.51605 | 0.298228 | 0.149114 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149114 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 10.9236 | 0.916691 | ||||||||
\(143\) | −13.3993 | −1.12050 | ||||||||
\(144\) | −4.55929 | −0.379940 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.1285 | −1.50032 | ||||||||
\(147\) | −2.70808 | −0.223359 | ||||||||
\(148\) | −1.56770 | −0.128864 | ||||||||
\(149\) | 7.20994 | 0.590661 | 0.295331 | − | 0.955395i | \(-0.404570\pi\) | ||||
0.295331 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8792 | 1.61775 | 0.808874 | − | 0.587982i | \(-0.200078\pi\) | ||||
0.808874 | + | 0.587982i | \(0.200078\pi\) | |||||||
\(152\) | 21.4581 | 1.74048 | ||||||||
\(153\) | 5.03002 | 0.406653 | ||||||||
\(154\) | 12.6861 | 1.02227 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.69077 | 0.135370 | ||||||||
\(157\) | −10.9292 | −0.872243 | −0.436121 | − | 0.899888i | \(-0.643648\pi\) | ||||
−0.436121 | + | 0.899888i | \(0.643648\pi\) | |||||||
\(158\) | 16.7448 | 1.33214 | ||||||||
\(159\) | −0.958459 | −0.0760107 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.70808 | −0.765104 | ||||||||
\(162\) | −1.52844 | −0.120086 | ||||||||
\(163\) | −19.9046 | −1.55905 | −0.779525 | − | 0.626371i | \(-0.784539\pi\) | ||||
−0.779525 | + | 0.626371i | \(0.784539\pi\) | |||||||
\(164\) | −3.04861 | −0.238056 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.6794 | 1.52742 | ||||||||
\(167\) | 22.5373 | 1.74399 | 0.871994 | − | 0.489516i | \(-0.162827\pi\) | ||||
0.871994 | + | 0.489516i | \(0.162827\pi\) | |||||||
\(168\) | 7.92380 | 0.611334 | ||||||||
\(169\) | 12.3011 | 0.946239 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.43772 | 0.645249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.54687 | −0.421720 | −0.210860 | − | 0.977516i | \(-0.567626\pi\) | ||||
−0.210860 | + | 0.977516i | \(0.567626\pi\) | |||||||
\(174\) | 8.58931 | 0.651154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1453 | −0.915487 | ||||||||
\(177\) | 3.70540 | 0.278515 | ||||||||
\(178\) | −21.9533 | −1.64547 | ||||||||
\(179\) | 4.74389 | 0.354575 | 0.177287 | − | 0.984159i | \(-0.443268\pi\) | ||||
0.177287 | + | 0.984159i | \(0.443268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.43542 | 0.329682 | 0.164841 | − | 0.986320i | \(-0.447289\pi\) | ||||
0.164841 | + | 0.986320i | \(0.447289\pi\) | |||||||
\(182\) | −23.9544 | −1.77562 | ||||||||
\(183\) | −4.29192 | −0.317268 | ||||||||
\(184\) | 7.92380 | 0.584150 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.0716 | −1.10510 | ||||||||
\(187\) | 13.3993 | 0.979853 | ||||||||
\(188\) | 0.336137 | 0.0245153 | ||||||||
\(189\) | 3.11578 | 0.226640 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.931595 | −0.0674078 | −0.0337039 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337039 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(192\) | −6.24148 | −0.450440 | ||||||||
\(193\) | 8.18076 | 0.588864 | 0.294432 | − | 0.955672i | \(-0.404870\pi\) | ||||
0.294432 | + | 0.955672i | \(0.404870\pi\) | |||||||
\(194\) | 13.7008 | 0.983658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.910285 | 0.0650204 | ||||||||
\(197\) | 3.79293 | 0.270235 | 0.135118 | − | 0.990830i | \(-0.456859\pi\) | ||||
0.135118 | + | 0.990830i | \(0.456859\pi\) | |||||||
\(198\) | −4.07156 | −0.289353 | ||||||||
\(199\) | 17.3669 | 1.23111 | 0.615553 | − | 0.788095i | \(-0.288933\pi\) | ||||
0.615553 | + | 0.788095i | \(0.288933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0354 | −1.06052 | ||||||||
\(202\) | 14.5402 | 1.02304 | ||||||||
\(203\) | −17.5096 | −1.22893 | ||||||||
\(204\) | −1.69077 | −0.118378 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.8377 | −0.824771 | ||||||||
\(207\) | 3.11578 | 0.216562 | ||||||||
\(208\) | 22.9333 | 1.59014 | ||||||||
\(209\) | 22.4769 | 1.55476 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.6762 | −1.14803 | −0.574017 | − | 0.818843i | \(-0.694616\pi\) | ||||
−0.574017 | + | 0.818843i | \(0.694616\pi\) | |||||||
\(212\) | 0.322173 | 0.0221269 | ||||||||
\(213\) | 7.14690 | 0.489698 | ||||||||
\(214\) | −0.489091 | −0.0334335 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.54312 | −0.173037 | ||||||||
\(217\) | 30.7240 | 2.08568 | ||||||||
\(218\) | 16.7319 | 1.13322 | ||||||||
\(219\) | −11.8608 | −0.801476 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.3011 | −1.70194 | ||||||||
\(222\) | −7.12845 | −0.478430 | ||||||||
\(223\) | 15.4877 | 1.03713 | 0.518567 | − | 0.855037i | \(-0.326466\pi\) | ||||
0.518567 | + | 0.855037i | \(0.326466\pi\) | |||||||
\(224\) | −5.86504 | −0.391874 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −22.7234 | −1.51154 | ||||||||
\(227\) | 22.8120 | 1.51408 | 0.757042 | − | 0.653366i | \(-0.226644\pi\) | ||||
0.757042 | + | 0.653366i | \(0.226644\pi\) | |||||||
\(228\) | −2.83623 | −0.187834 | ||||||||
\(229\) | 22.7755 | 1.50505 | 0.752523 | − | 0.658566i | \(-0.228837\pi\) | ||||
0.752523 | + | 0.658566i | \(0.228837\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.30001 | 0.546101 | ||||||||
\(232\) | 14.2914 | 0.938279 | ||||||||
\(233\) | 17.2393 | 1.12938 | 0.564692 | − | 0.825302i | \(-0.308995\pi\) | ||||
0.564692 | + | 0.825302i | \(0.308995\pi\) | |||||||
\(234\) | 7.68810 | 0.502587 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.24552 | −0.0810766 | ||||||||
\(237\) | 10.9555 | 0.711634 | ||||||||
\(238\) | 23.9544 | 1.55273 | ||||||||
\(239\) | 15.2115 | 0.983952 | 0.491976 | − | 0.870609i | \(-0.336275\pi\) | ||||
0.491976 | + | 0.870609i | \(0.336275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7510 | 1.20786 | 0.603930 | − | 0.797038i | \(-0.293601\pi\) | ||||
0.603930 | + | 0.797038i | \(0.293601\pi\) | |||||||
\(242\) | 5.96678 | 0.383559 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.44267 | 0.0923576 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.8623 | −0.883827 | ||||||||
\(247\) | −42.4419 | −2.70051 | ||||||||
\(248\) | −25.0771 | −1.59240 | ||||||||
\(249\) | 12.8754 | 0.815948 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.77476 | 0.112022 | 0.0560111 | − | 0.998430i | \(-0.482162\pi\) | ||||
0.0560111 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(252\) | −1.04733 | −0.0659754 | ||||||||
\(253\) | 8.30001 | 0.521817 | ||||||||
\(254\) | 8.20756 | 0.514988 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.85217 | 0.490761 | ||||||||
\(257\) | 15.9731 | 0.996372 | 0.498186 | − | 0.867070i | \(-0.334000\pi\) | ||||
0.498186 | + | 0.867070i | \(0.334000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.5316 | 0.902948 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.61965 | 0.347847 | ||||||||
\(262\) | 4.68988 | 0.289742 | ||||||||
\(263\) | −26.3400 | −1.62420 | −0.812098 | − | 0.583521i | \(-0.801675\pi\) | ||||
−0.812098 | + | 0.583521i | \(0.801675\pi\) | |||||||
\(264\) | −6.77452 | −0.416943 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 40.1829 | 2.46377 | ||||||||
\(267\) | −14.3632 | −0.879011 | ||||||||
\(268\) | 5.05396 | 0.308720 | ||||||||
\(269\) | −13.5477 | −0.826019 | −0.413009 | − | 0.910727i | \(-0.635522\pi\) | ||||
−0.413009 | + | 0.910727i | \(0.635522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.05373 | 0.246246 | 0.123123 | − | 0.992391i | \(-0.460709\pi\) | ||||
0.123123 | + | 0.992391i | \(0.460709\pi\) | |||||||
\(272\) | −22.9333 | −1.39054 | ||||||||
\(273\) | −15.6724 | −0.948539 | ||||||||
\(274\) | 12.8823 | 0.778251 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.04733 | −0.0630417 | ||||||||
\(277\) | 2.57543 | 0.154743 | 0.0773713 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773713 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(278\) | −5.37409 | −0.322316 | ||||||||
\(279\) | −9.86076 | −0.590348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.8589 | −1.24434 | −0.622170 | − | 0.782882i | \(-0.713749\pi\) | ||||
−0.622170 | + | 0.782882i | \(0.713749\pi\) | |||||||
\(282\) | 1.52844 | 0.0910174 | ||||||||
\(283\) | 14.9101 | 0.886316 | 0.443158 | − | 0.896443i | \(-0.353858\pi\) | ||||
0.443158 | + | 0.896443i | \(0.353858\pi\) | |||||||
\(284\) | −2.40234 | −0.142552 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.4800 | 1.21101 | ||||||||
\(287\) | 28.2587 | 1.66806 | ||||||||
\(288\) | 1.88237 | 0.110920 | ||||||||
\(289\) | 8.30111 | 0.488301 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.96387 | 0.525472 | ||||||||
\(292\) | 3.98684 | 0.233312 | ||||||||
\(293\) | −9.41310 | −0.549919 | −0.274960 | − | 0.961456i | \(-0.588665\pi\) | ||||
−0.274960 | + | 0.961456i | \(0.588665\pi\) | |||||||
\(294\) | 4.13915 | 0.241400 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.8608 | −0.689393 | ||||||||
\(297\) | −2.66386 | −0.154573 | ||||||||
\(298\) | −11.0200 | −0.638370 | ||||||||
\(299\) | −15.6724 | −0.906360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −30.3842 | −1.74842 | ||||||||
\(303\) | 9.51306 | 0.546511 | ||||||||
\(304\) | −38.4700 | −2.20640 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.68810 | −0.439499 | ||||||||
\(307\) | 13.5134 | 0.771249 | 0.385625 | − | 0.922656i | \(-0.373986\pi\) | ||||
0.385625 | + | 0.922656i | \(0.373986\pi\) | |||||||
\(308\) | −2.78994 | −0.158971 | ||||||||
\(309\) | −7.74494 | −0.440594 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9323 | 1.41378 | 0.706891 | − | 0.707322i | \(-0.250097\pi\) | ||||
0.706891 | + | 0.707322i | \(0.250097\pi\) | |||||||
\(312\) | 12.7919 | 0.724201 | ||||||||
\(313\) | 21.1922 | 1.19786 | 0.598928 | − | 0.800803i | \(-0.295594\pi\) | ||||
0.598928 | + | 0.800803i | \(0.295594\pi\) | |||||||
\(314\) | 16.7046 | 0.942695 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.68253 | −0.207159 | ||||||||
\(317\) | −11.6193 | −0.652606 | −0.326303 | − | 0.945265i | \(-0.605803\pi\) | ||||
−0.326303 | + | 0.945265i | \(0.605803\pi\) | |||||||
\(318\) | 1.46495 | 0.0821503 | ||||||||
\(319\) | 14.9700 | 0.838157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.319993 | −0.0178603 | ||||||||
\(322\) | 14.8382 | 0.826903 | ||||||||
\(323\) | 42.4419 | 2.36153 | ||||||||
\(324\) | 0.336137 | 0.0186743 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.4231 | 1.68498 | ||||||||
\(327\) | 10.9470 | 0.605371 | ||||||||
\(328\) | −23.0650 | −1.27355 | ||||||||
\(329\) | −3.11578 | −0.171778 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0022 | 0.769631 | 0.384815 | − | 0.922994i | \(-0.374265\pi\) | ||||
0.384815 | + | 0.922994i | \(0.374265\pi\) | |||||||
\(332\) | −4.32791 | −0.237525 | ||||||||
\(333\) | −4.66386 | −0.255578 | ||||||||
\(334\) | −34.4470 | −1.88485 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.2057 | −0.774986 | ||||||||
\(337\) | −30.1370 | −1.64167 | −0.820834 | − | 0.571167i | \(-0.806491\pi\) | ||||
−0.820834 | + | 0.571167i | \(0.806491\pi\) | |||||||
\(338\) | −18.8015 | −1.02267 | ||||||||
\(339\) | −14.8670 | −0.807466 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.2677 | −1.42248 | ||||||||
\(342\) | −12.8966 | −0.697367 | ||||||||
\(343\) | 13.3727 | 0.722057 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.47807 | 0.455784 | ||||||||
\(347\) | −16.2010 | −0.869713 | −0.434857 | − | 0.900500i | \(-0.643201\pi\) | ||||
−0.434857 | + | 0.900500i | \(0.643201\pi\) | |||||||
\(348\) | −1.88897 | −0.101259 | ||||||||
\(349\) | −4.26621 | −0.228365 | −0.114183 | − | 0.993460i | \(-0.536425\pi\) | ||||
−0.114183 | + | 0.993460i | \(0.536425\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.03002 | 0.268483 | ||||||||
\(352\) | 5.01437 | 0.267267 | ||||||||
\(353\) | −11.2178 | −0.597066 | −0.298533 | − | 0.954399i | \(-0.596497\pi\) | ||||
−0.298533 | + | 0.954399i | \(0.596497\pi\) | |||||||
\(354\) | −5.66350 | −0.301012 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.82798 | 0.255883 | ||||||||
\(357\) | 15.6724 | 0.829473 | ||||||||
\(358\) | −7.25076 | −0.383215 | ||||||||
\(359\) | 23.3092 | 1.23021 | 0.615106 | − | 0.788444i | \(-0.289113\pi\) | ||||
0.615106 | + | 0.788444i | \(0.289113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.1951 | 2.74711 | ||||||||
\(362\) | −6.77928 | −0.356311 | ||||||||
\(363\) | 3.90383 | 0.204898 | ||||||||
\(364\) | 5.26808 | 0.276122 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.55995 | 0.342894 | ||||||||
\(367\) | 24.2748 | 1.26713 | 0.633567 | − | 0.773688i | \(-0.281590\pi\) | ||||
0.633567 | + | 0.773688i | \(0.281590\pi\) | |||||||
\(368\) | −14.2057 | −0.740525 | ||||||||
\(369\) | −9.06955 | −0.472142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.98635 | −0.155043 | ||||||||
\(372\) | 3.31456 | 0.171852 | ||||||||
\(373\) | 6.09003 | 0.315330 | 0.157665 | − | 0.987493i | \(-0.449603\pi\) | ||||
0.157665 | + | 0.987493i | \(0.449603\pi\) | |||||||
\(374\) | −20.4800 | −1.05900 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.54312 | 0.131151 | ||||||||
\(377\) | −28.2669 | −1.45582 | ||||||||
\(378\) | −4.76229 | −0.244946 | ||||||||
\(379\) | 17.3523 | 0.891329 | 0.445664 | − | 0.895200i | \(-0.352967\pi\) | ||||
0.445664 | + | 0.895200i | \(0.352967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.36988 | 0.275107 | ||||||||
\(382\) | 1.42389 | 0.0728525 | ||||||||
\(383\) | 16.4053 | 0.838273 | 0.419136 | − | 0.907923i | \(-0.362333\pi\) | ||||
0.419136 | + | 0.907923i | \(0.362333\pi\) | |||||||
\(384\) | 13.3045 | 0.678941 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.5038 | −0.636427 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.01309 | −0.152966 | ||||||||
\(389\) | 0.943355 | 0.0478300 | 0.0239150 | − | 0.999714i | \(-0.492387\pi\) | ||||
0.0239150 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.6724 | 0.792589 | ||||||||
\(392\) | 6.88697 | 0.347845 | ||||||||
\(393\) | 3.06841 | 0.154781 | ||||||||
\(394\) | −5.79728 | −0.292063 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.895422 | 0.0449966 | ||||||||
\(397\) | 20.0762 | 1.00760 | 0.503798 | − | 0.863821i | \(-0.331935\pi\) | ||||
0.503798 | + | 0.863821i | \(0.331935\pi\) | |||||||
\(398\) | −26.5443 | −1.33055 | ||||||||
\(399\) | 26.2901 | 1.31615 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42992 | 0.0714070 | 0.0357035 | − | 0.999362i | \(-0.488633\pi\) | ||||
0.0357035 | + | 0.999362i | \(0.488633\pi\) | |||||||
\(402\) | 22.9808 | 1.14618 | ||||||||
\(403\) | 49.5998 | 2.47074 | ||||||||
\(404\) | −3.19769 | −0.159091 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.7624 | 1.32819 | ||||||||
\(407\) | −12.4239 | −0.615830 | ||||||||
\(408\) | −12.7919 | −0.633296 | ||||||||
\(409\) | −34.8124 | −1.72136 | −0.860681 | − | 0.509145i | \(-0.829962\pi\) | ||||
−0.860681 | + | 0.509145i | \(0.829962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.42841 | 0.415743 | ||||||||
\(412\) | 2.60336 | 0.128258 | ||||||||
\(413\) | 11.5452 | 0.568103 | ||||||||
\(414\) | −4.76229 | −0.234054 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.46834 | −0.464224 | ||||||||
\(417\) | −3.51605 | −0.172182 | ||||||||
\(418\) | −34.3547 | −1.68034 | ||||||||
\(419\) | 31.0798 | 1.51835 | 0.759175 | − | 0.650887i | \(-0.225603\pi\) | ||||
0.759175 | + | 0.650887i | \(0.225603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.93452 | 0.337968 | 0.168984 | − | 0.985619i | \(-0.445951\pi\) | ||||
0.168984 | + | 0.985619i | \(0.445951\pi\) | |||||||
\(422\) | 25.4886 | 1.24076 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 2.43748 | 0.118374 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.9236 | −0.529252 | ||||||||
\(427\) | −13.3727 | −0.647149 | ||||||||
\(428\) | 0.107561 | 0.00519917 | ||||||||
\(429\) | 13.3993 | 0.646924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.1517 | 1.74137 | 0.870683 | − | 0.491844i | \(-0.163677\pi\) | ||||
0.870683 | + | 0.491844i | \(0.163677\pi\) | |||||||
\(432\) | 4.55929 | 0.219359 | ||||||||
\(433\) | 8.83317 | 0.424495 | 0.212247 | − | 0.977216i | \(-0.431922\pi\) | ||||
0.212247 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(434\) | −46.9598 | −2.25414 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.67969 | −0.176225 | ||||||||
\(437\) | 26.2901 | 1.25762 | ||||||||
\(438\) | 18.1285 | 0.866213 | ||||||||
\(439\) | −14.1162 | −0.673729 | −0.336865 | − | 0.941553i | \(-0.609366\pi\) | ||||
−0.336865 | + | 0.941553i | \(0.609366\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.70808 | 0.128956 | ||||||||
\(442\) | 38.6713 | 1.83941 | ||||||||
\(443\) | −21.3002 | −1.01200 | −0.506002 | − | 0.862533i | \(-0.668877\pi\) | ||||
−0.506002 | + | 0.862533i | \(0.668877\pi\) | |||||||
\(444\) | 1.56770 | 0.0743995 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.6721 | −1.12091 | ||||||||
\(447\) | −7.20994 | −0.341018 | ||||||||
\(448\) | −19.4471 | −0.918788 | ||||||||
\(449\) | 14.0828 | 0.664607 | 0.332303 | − | 0.943173i | \(-0.392174\pi\) | ||||
0.332303 | + | 0.943173i | \(0.392174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.1601 | −1.13765 | ||||||||
\(452\) | 4.99735 | 0.235056 | ||||||||
\(453\) | −19.8792 | −0.934007 | ||||||||
\(454\) | −34.8668 | −1.63638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.4581 | −1.00487 | ||||||||
\(457\) | −8.39150 | −0.392538 | −0.196269 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196269 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(458\) | −34.8110 | −1.62661 | ||||||||
\(459\) | −5.03002 | −0.234781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2745 | 0.711404 | 0.355702 | − | 0.934599i | \(-0.384242\pi\) | ||||
0.355702 | + | 0.934599i | \(0.384242\pi\) | |||||||
\(462\) | −12.6861 | −0.590210 | ||||||||
\(463\) | −29.7434 | −1.38229 | −0.691146 | − | 0.722715i | \(-0.742894\pi\) | ||||
−0.691146 | + | 0.722715i | \(0.742894\pi\) | |||||||
\(464\) | −25.6216 | −1.18945 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.3493 | −1.22061 | ||||||||
\(467\) | 3.29265 | 0.152366 | 0.0761828 | − | 0.997094i | \(-0.475727\pi\) | ||||
0.0761828 | + | 0.997094i | \(0.475727\pi\) | |||||||
\(468\) | −1.69077 | −0.0781561 | ||||||||
\(469\) | −46.8471 | −2.16320 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.9292 | 0.503589 | ||||||||
\(472\) | −9.42329 | −0.433742 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −16.7448 | −0.769114 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.26808 | −0.241462 | ||||||||
\(477\) | 0.958459 | 0.0438848 | ||||||||
\(478\) | −23.2499 | −1.06343 | ||||||||
\(479\) | 24.6208 | 1.12496 | 0.562478 | − | 0.826812i | \(-0.309848\pi\) | ||||
0.562478 | + | 0.826812i | \(0.309848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4593 | 1.06965 | ||||||||
\(482\) | −28.6599 | −1.30542 | ||||||||
\(483\) | 9.70808 | 0.441733 | ||||||||
\(484\) | −1.31222 | −0.0596464 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.52844 | 0.0693316 | ||||||||
\(487\) | −29.4221 | −1.33324 | −0.666621 | − | 0.745396i | \(-0.732260\pi\) | ||||
−0.666621 | + | 0.745396i | \(0.732260\pi\) | |||||||
\(488\) | 10.9149 | 0.494093 | ||||||||
\(489\) | 19.9046 | 0.900118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.22405 | −0.371146 | −0.185573 | − | 0.982630i | \(-0.559414\pi\) | ||||
−0.185573 | + | 0.982630i | \(0.559414\pi\) | |||||||
\(492\) | 3.04861 | 0.137442 | ||||||||
\(493\) | 28.2669 | 1.27308 | ||||||||
\(494\) | 64.8700 | 2.91864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 44.9580 | 2.01868 | ||||||||
\(497\) | 22.2682 | 0.998864 | ||||||||
\(498\) | −19.6794 | −0.881854 | ||||||||
\(499\) | 39.1301 | 1.75170 | 0.875852 | − | 0.482579i | \(-0.160300\pi\) | ||||
0.875852 | + | 0.482579i | \(0.160300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.5373 | −1.00689 | ||||||||
\(502\) | −2.71263 | −0.121070 | ||||||||
\(503\) | 18.2344 | 0.813029 | 0.406515 | − | 0.913644i | \(-0.366744\pi\) | ||||
0.406515 | + | 0.913644i | \(0.366744\pi\) | |||||||
\(504\) | −7.92380 | −0.352954 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.6861 | −0.563965 | ||||||||
\(507\) | −12.3011 | −0.546312 | ||||||||
\(508\) | −1.80501 | −0.0800845 | ||||||||
\(509\) | −18.0666 | −0.800787 | −0.400394 | − | 0.916343i | \(-0.631127\pi\) | ||||
−0.400394 | + | 0.916343i | \(0.631127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.9555 | −1.63482 | ||||||||
\(512\) | 14.6074 | 0.645561 | ||||||||
\(513\) | −8.43772 | −0.372534 | ||||||||
\(514\) | −24.4139 | −1.07685 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.66386 | 0.117157 | ||||||||
\(518\) | −22.2107 | −0.975881 | ||||||||
\(519\) | 5.54687 | 0.243480 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.38242 | 0.411051 | 0.205526 | − | 0.978652i | \(-0.434110\pi\) | ||||
0.205526 | + | 0.978652i | \(0.434110\pi\) | |||||||
\(522\) | −8.58931 | −0.375944 | ||||||||
\(523\) | 6.06882 | 0.265371 | 0.132686 | − | 0.991158i | \(-0.457640\pi\) | ||||
0.132686 | + | 0.991158i | \(0.457640\pi\) | |||||||
\(524\) | −1.03140 | −0.0450571 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.2592 | 1.75539 | ||||||||
\(527\) | −49.5998 | −2.16060 | ||||||||
\(528\) | 12.1453 | 0.528557 | ||||||||
\(529\) | −13.2919 | −0.577910 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.70540 | −0.160801 | ||||||||
\(532\) | −8.83706 | −0.383135 | ||||||||
\(533\) | 45.6200 | 1.97602 | ||||||||
\(534\) | 21.9533 | 0.950011 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 38.2369 | 1.65158 | ||||||||
\(537\) | −4.74389 | −0.204714 | ||||||||
\(538\) | 20.7069 | 0.892738 | ||||||||
\(539\) | 7.21396 | 0.310727 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5419 | −0.840173 | −0.420086 | − | 0.907484i | \(-0.638000\pi\) | ||||
−0.420086 | + | 0.907484i | \(0.638000\pi\) | |||||||
\(542\) | −6.19589 | −0.266136 | ||||||||
\(543\) | −4.43542 | −0.190342 | ||||||||
\(544\) | 9.46834 | 0.405952 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 23.9544 | 1.02515 | ||||||||
\(547\) | 2.32009 | 0.0991997 | 0.0495999 | − | 0.998769i | \(-0.484205\pi\) | ||||
0.0495999 | + | 0.998769i | \(0.484205\pi\) | |||||||
\(548\) | −2.83310 | −0.121024 | ||||||||
\(549\) | 4.29192 | 0.183175 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.4170 | 2.02003 | ||||||||
\(552\) | −7.92380 | −0.337259 | ||||||||
\(553\) | 34.1348 | 1.45156 | ||||||||
\(554\) | −3.93640 | −0.167241 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.18187 | 0.0501226 | ||||||||
\(557\) | 20.5653 | 0.871380 | 0.435690 | − | 0.900097i | \(-0.356504\pi\) | ||||
0.435690 | + | 0.900097i | \(0.356504\pi\) | |||||||
\(558\) | 15.0716 | 0.638032 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.3993 | −0.565718 | ||||||||
\(562\) | 31.8817 | 1.34485 | ||||||||
\(563\) | 22.8577 | 0.963335 | 0.481668 | − | 0.876354i | \(-0.340031\pi\) | ||||
0.481668 | + | 0.876354i | \(0.340031\pi\) | |||||||
\(564\) | −0.336137 | −0.0141539 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.7893 | −0.957906 | ||||||||
\(567\) | −3.11578 | −0.130850 | ||||||||
\(568\) | −18.1754 | −0.762624 | ||||||||
\(569\) | −8.53537 | −0.357821 | −0.178911 | − | 0.983865i | \(-0.557257\pi\) | ||||
−0.178911 | + | 0.983865i | \(0.557257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.1926 | 1.17982 | 0.589911 | − | 0.807468i | \(-0.299163\pi\) | ||||
0.589911 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(572\) | −4.50399 | −0.188321 | ||||||||
\(573\) | 0.931595 | 0.0389179 | ||||||||
\(574\) | −43.1918 | −1.80279 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.24148 | 0.260062 | ||||||||
\(577\) | 8.26475 | 0.344066 | 0.172033 | − | 0.985091i | \(-0.444966\pi\) | ||||
0.172033 | + | 0.985091i | \(0.444966\pi\) | |||||||
\(578\) | −12.6878 | −0.527742 | ||||||||
\(579\) | −8.18076 | −0.339981 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.1170 | 1.66433 | ||||||||
\(582\) | −13.7008 | −0.567915 | ||||||||
\(583\) | 2.55320 | 0.105743 | ||||||||
\(584\) | 30.1633 | 1.24817 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.3874 | 0.594338 | ||||||||
\(587\) | 25.3501 | 1.04631 | 0.523156 | − | 0.852237i | \(-0.324755\pi\) | ||||
0.523156 | + | 0.852237i | \(0.324755\pi\) | |||||||
\(588\) | −0.910285 | −0.0375395 | ||||||||
\(589\) | −83.2024 | −3.42829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.79293 | −0.156020 | ||||||||
\(592\) | 21.2639 | 0.873940 | ||||||||
\(593\) | −4.29599 | −0.176415 | −0.0882076 | − | 0.996102i | \(-0.528114\pi\) | ||||
−0.0882076 | + | 0.996102i | \(0.528114\pi\) | |||||||
\(594\) | 4.07156 | 0.167058 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.42352 | 0.0992714 | ||||||||
\(597\) | −17.3669 | −0.710779 | ||||||||
\(598\) | 23.9544 | 0.979569 | ||||||||
\(599\) | −24.7662 | −1.01192 | −0.505959 | − | 0.862557i | \(-0.668861\pi\) | ||||
−0.505959 | + | 0.862557i | \(0.668861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.1635 | −0.944857 | −0.472429 | − | 0.881369i | \(-0.656623\pi\) | ||||
−0.472429 | + | 0.881369i | \(0.656623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.0354 | 0.612290 | ||||||||
\(604\) | 6.68213 | 0.271892 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.5402 | −0.590654 | ||||||||
\(607\) | −26.7755 | −1.08679 | −0.543393 | − | 0.839479i | \(-0.682861\pi\) | ||||
−0.543393 | + | 0.839479i | \(0.682861\pi\) | |||||||
\(608\) | 15.8829 | 0.644136 | ||||||||
\(609\) | 17.5096 | 0.709524 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.03002 | −0.203493 | ||||||||
\(612\) | 1.69077 | 0.0683455 | ||||||||
\(613\) | −5.66244 | −0.228704 | −0.114352 | − | 0.993440i | \(-0.536479\pi\) | ||||
−0.114352 | + | 0.993440i | \(0.536479\pi\) | |||||||
\(614\) | −20.6544 | −0.833545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.1079 | −0.850462 | ||||||||
\(617\) | −4.44702 | −0.179030 | −0.0895151 | − | 0.995985i | \(-0.528532\pi\) | ||||
−0.0895151 | + | 0.995985i | \(0.528532\pi\) | |||||||
\(618\) | 11.8377 | 0.476182 | ||||||||
\(619\) | −17.7123 | −0.711917 | −0.355958 | − | 0.934502i | \(-0.615845\pi\) | ||||
−0.355958 | + | 0.934502i | \(0.615845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.11578 | −0.125032 | ||||||||
\(622\) | −38.1076 | −1.52798 | ||||||||
\(623\) | −44.7524 | −1.79297 | ||||||||
\(624\) | −22.9333 | −0.918067 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.3911 | −1.29461 | ||||||||
\(627\) | −22.4769 | −0.897642 | ||||||||
\(628\) | −3.67369 | −0.146596 | ||||||||
\(629\) | −23.4593 | −0.935385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.3177 | 1.08750 | 0.543751 | − | 0.839247i | \(-0.317004\pi\) | ||||
0.543751 | + | 0.839247i | \(0.317004\pi\) | |||||||
\(632\) | −27.8611 | −1.10825 | ||||||||
\(633\) | 16.6762 | 0.662818 | ||||||||
\(634\) | 17.7595 | 0.705319 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.322173 | −0.0127750 | ||||||||
\(637\) | −13.6217 | −0.539711 | ||||||||
\(638\) | −22.8807 | −0.905857 | ||||||||
\(639\) | −7.14690 | −0.282727 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.3024 | −1.19687 | −0.598437 | − | 0.801170i | \(-0.704211\pi\) | ||||
−0.598437 | + | 0.801170i | \(0.704211\pi\) | |||||||
\(642\) | 0.489091 | 0.0193029 | ||||||||
\(643\) | 44.2436 | 1.74480 | 0.872399 | − | 0.488795i | \(-0.162563\pi\) | ||||
0.872399 | + | 0.488795i | \(0.162563\pi\) | |||||||
\(644\) | −3.26324 | −0.128590 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −64.8700 | −2.55228 | ||||||||
\(647\) | −14.2147 | −0.558839 | −0.279420 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279420 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(648\) | 2.54312 | 0.0999032 | ||||||||
\(649\) | −9.87069 | −0.387459 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.7240 | −1.20417 | ||||||||
\(652\) | −6.69067 | −0.262027 | ||||||||
\(653\) | 30.6915 | 1.20105 | 0.600526 | − | 0.799605i | \(-0.294958\pi\) | ||||
0.600526 | + | 0.799605i | \(0.294958\pi\) | |||||||
\(654\) | −16.7319 | −0.654268 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.3507 | 1.61447 | ||||||||
\(657\) | 11.8608 | 0.462732 | ||||||||
\(658\) | 4.76229 | 0.185653 | ||||||||
\(659\) | 8.18820 | 0.318967 | 0.159484 | − | 0.987201i | \(-0.449017\pi\) | ||||
0.159484 | + | 0.987201i | \(0.449017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9503 | −0.542606 | −0.271303 | − | 0.962494i | \(-0.587454\pi\) | ||||
−0.271303 | + | 0.962494i | \(0.587454\pi\) | |||||||
\(662\) | −21.4016 | −0.831795 | ||||||||
\(663\) | 25.3011 | 0.982614 | ||||||||
\(664\) | −32.7438 | −1.27071 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.12845 | 0.276222 | ||||||||
\(667\) | 17.5096 | 0.677974 | ||||||||
\(668\) | 7.57561 | 0.293109 | ||||||||
\(669\) | −15.4877 | −0.598790 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4331 | 0.441369 | ||||||||
\(672\) | 5.86504 | 0.226249 | ||||||||
\(673\) | 39.4082 | 1.51908 | 0.759538 | − | 0.650463i | \(-0.225425\pi\) | ||||
0.759538 | + | 0.650463i | \(0.225425\pi\) | |||||||
\(674\) | 46.0627 | 1.77427 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.13485 | 0.159033 | ||||||||
\(677\) | −19.9254 | −0.765797 | −0.382898 | − | 0.923790i | \(-0.625074\pi\) | ||||
−0.382898 | + | 0.923790i | \(0.625074\pi\) | |||||||
\(678\) | 22.7234 | 0.872687 | ||||||||
\(679\) | 27.9295 | 1.07183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.8120 | −0.874157 | ||||||||
\(682\) | 40.1487 | 1.53737 | ||||||||
\(683\) | −18.4694 | −0.706713 | −0.353357 | − | 0.935489i | \(-0.614960\pi\) | ||||
−0.353357 | + | 0.935489i | \(0.614960\pi\) | |||||||
\(684\) | 2.83623 | 0.108446 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.4394 | −0.780379 | ||||||||
\(687\) | −22.7755 | −0.868939 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.82107 | −0.183668 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.10226 | −0.0799737 | −0.0399869 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399869 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(692\) | −1.86450 | −0.0708778 | ||||||||
\(693\) | −8.30001 | −0.315291 | ||||||||
\(694\) | 24.7622 | 0.939962 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.2914 | −0.541715 | ||||||||
\(697\) | −45.6200 | −1.72798 | ||||||||
\(698\) | 6.52066 | 0.246811 | ||||||||
\(699\) | −17.2393 | −0.652050 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.5251 | −1.49284 | −0.746421 | − | 0.665474i | \(-0.768230\pi\) | ||||
−0.746421 | + | 0.665474i | \(0.768230\pi\) | |||||||
\(702\) | −7.68810 | −0.290169 | ||||||||
\(703\) | −39.3524 | −1.48420 | ||||||||
\(704\) | 16.6265 | 0.626633 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1458 | 0.645292 | ||||||||
\(707\) | 29.6406 | 1.11475 | ||||||||
\(708\) | 1.24552 | 0.0468096 | ||||||||
\(709\) | 18.6737 | 0.701307 | 0.350653 | − | 0.936505i | \(-0.385960\pi\) | ||||
0.350653 | + | 0.936505i | \(0.385960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.9555 | −0.410862 | ||||||||
\(712\) | 36.5272 | 1.36892 | ||||||||
\(713\) | −30.7240 | −1.15062 | ||||||||
\(714\) | −23.9544 | −0.896472 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.59459 | 0.0595928 | ||||||||
\(717\) | −15.2115 | −0.568085 | ||||||||
\(718\) | −35.6268 | −1.32958 | ||||||||
\(719\) | −20.1777 | −0.752500 | −0.376250 | − | 0.926518i | \(-0.622787\pi\) | ||||
−0.376250 | + | 0.926518i | \(0.622787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.1315 | −0.898704 | ||||||||
\(722\) | −79.7772 | −2.96900 | ||||||||
\(723\) | −18.7510 | −0.697358 | ||||||||
\(724\) | 1.49091 | 0.0554091 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.96678 | −0.221448 | ||||||||
\(727\) | 36.0615 | 1.33745 | 0.668724 | − | 0.743511i | \(-0.266841\pi\) | ||||
0.668724 | + | 0.743511i | \(0.266841\pi\) | |||||||
\(728\) | 39.8569 | 1.47719 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.44267 | −0.0533227 | ||||||||
\(733\) | −27.2648 | −1.00705 | −0.503525 | − | 0.863981i | \(-0.667964\pi\) | ||||
−0.503525 | + | 0.863981i | \(0.667964\pi\) | |||||||
\(734\) | −37.1026 | −1.36948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.86504 | 0.216188 | ||||||||
\(737\) | 40.0523 | 1.47535 | ||||||||
\(738\) | 13.8623 | 0.510278 | ||||||||
\(739\) | −1.62581 | −0.0598066 | −0.0299033 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299033 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.4419 | 1.55914 | ||||||||
\(742\) | 4.56446 | 0.167567 | ||||||||
\(743\) | 20.8088 | 0.763401 | 0.381701 | − | 0.924286i | \(-0.375339\pi\) | ||||
0.381701 | + | 0.924286i | \(0.375339\pi\) | |||||||
\(744\) | 25.0771 | 0.919371 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.30825 | −0.340799 | ||||||||
\(747\) | −12.8754 | −0.471088 | ||||||||
\(748\) | 4.50399 | 0.164682 | ||||||||
\(749\) | −0.997027 | −0.0364306 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9762 | −1.09385 | −0.546923 | − | 0.837183i | \(-0.684201\pi\) | ||||
−0.546923 | + | 0.837183i | \(0.684201\pi\) | |||||||
\(752\) | −4.55929 | −0.166260 | ||||||||
\(753\) | −1.77476 | −0.0646760 | ||||||||
\(754\) | 43.2044 | 1.57341 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.04733 | 0.0380909 | ||||||||
\(757\) | −4.79797 | −0.174385 | −0.0871925 | − | 0.996191i | \(-0.527790\pi\) | ||||
−0.0871925 | + | 0.996191i | \(0.527790\pi\) | |||||||
\(758\) | −26.5220 | −0.963323 | ||||||||
\(759\) | −8.30001 | −0.301271 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5039 | −0.852014 | −0.426007 | − | 0.904720i | \(-0.640080\pi\) | ||||
−0.426007 | + | 0.904720i | \(0.640080\pi\) | |||||||
\(762\) | −8.20756 | −0.297328 | ||||||||
\(763\) | 34.1084 | 1.23481 | ||||||||
\(764\) | −0.313143 | −0.0113291 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.0746 | −0.905982 | ||||||||
\(767\) | 18.6383 | 0.672989 | ||||||||
\(768\) | −7.85217 | −0.283341 | ||||||||
\(769\) | −34.7708 | −1.25387 | −0.626933 | − | 0.779073i | \(-0.715690\pi\) | ||||
−0.626933 | + | 0.779073i | \(0.715690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.9731 | −0.575256 | ||||||||
\(772\) | 2.74985 | 0.0989693 | ||||||||
\(773\) | −18.9562 | −0.681807 | −0.340903 | − | 0.940098i | \(-0.610733\pi\) | ||||
−0.340903 | + | 0.940098i | \(0.610733\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −22.7962 | −0.818336 | ||||||||
\(777\) | −14.5316 | −0.521317 | ||||||||
\(778\) | −1.44186 | −0.0516933 | ||||||||
\(779\) | −76.5263 | −2.74184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.0384 | −0.681246 | ||||||||
\(782\) | −23.9544 | −0.856608 | ||||||||
\(783\) | −5.61965 | −0.200830 | ||||||||
\(784\) | −12.3469 | −0.440961 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.68988 | −0.167283 | ||||||||
\(787\) | 42.9210 | 1.52997 | 0.764984 | − | 0.644050i | \(-0.222747\pi\) | ||||
0.764984 | + | 0.644050i | \(0.222747\pi\) | |||||||
\(788\) | 1.27494 | 0.0454180 | ||||||||
\(789\) | 26.3400 | 0.937730 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.3224 | −1.64703 | ||||||||
\(792\) | 6.77452 | 0.240722 | ||||||||
\(793\) | −21.5884 | −0.766628 | ||||||||
\(794\) | −30.6854 | −1.08898 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.83765 | 0.206910 | ||||||||
\(797\) | −49.6483 | −1.75863 | −0.879317 | − | 0.476237i | \(-0.842000\pi\) | ||||
−0.879317 | + | 0.476237i | \(0.842000\pi\) | |||||||
\(798\) | −40.1829 | −1.42246 | ||||||||
\(799\) | 5.03002 | 0.177949 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3632 | 0.507497 | ||||||||
\(802\) | −2.18556 | −0.0771747 | ||||||||
\(803\) | 31.5955 | 1.11498 | ||||||||
\(804\) | −5.05396 | −0.178239 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −75.8105 | −2.67031 | ||||||||
\(807\) | 13.5477 | 0.476902 | ||||||||
\(808\) | −24.1928 | −0.851101 | ||||||||
\(809\) | −34.5440 | −1.21450 | −0.607251 | − | 0.794510i | \(-0.707728\pi\) | ||||
−0.607251 | + | 0.794510i | \(0.707728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3409 | 1.06541 | 0.532707 | − | 0.846300i | \(-0.321175\pi\) | ||||
0.532707 | + | 0.846300i | \(0.321175\pi\) | |||||||
\(812\) | −5.88561 | −0.206544 | ||||||||
\(813\) | −4.05373 | −0.142170 | ||||||||
\(814\) | 18.9892 | 0.665571 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.9333 | 0.802826 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 53.2087 | 1.86040 | ||||||||
\(819\) | 15.6724 | 0.547639 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.7336 | 1.59611 | 0.798057 | − | 0.602582i | \(-0.205861\pi\) | ||||
0.798057 | + | 0.602582i | \(0.205861\pi\) | |||||||
\(822\) | −12.8823 | −0.449323 | ||||||||
\(823\) | −5.32543 | −0.185633 | −0.0928164 | − | 0.995683i | \(-0.529587\pi\) | ||||
−0.0928164 | + | 0.995683i | \(0.529587\pi\) | |||||||
\(824\) | 19.6963 | 0.686153 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.6462 | −0.613990 | ||||||||
\(827\) | −50.7215 | −1.76376 | −0.881880 | − | 0.471474i | \(-0.843722\pi\) | ||||
−0.881880 | + | 0.471474i | \(0.843722\pi\) | |||||||
\(828\) | 1.04733 | 0.0363971 | ||||||||
\(829\) | 40.3932 | 1.40291 | 0.701456 | − | 0.712713i | \(-0.252534\pi\) | ||||
0.701456 | + | 0.712713i | \(0.252534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.57543 | −0.0893406 | ||||||||
\(832\) | −31.3948 | −1.08842 | ||||||||
\(833\) | 13.6217 | 0.471964 | ||||||||
\(834\) | 5.37409 | 0.186089 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.55532 | 0.261306 | ||||||||
\(837\) | 9.86076 | 0.340838 | ||||||||
\(838\) | −47.5038 | −1.64099 | ||||||||
\(839\) | 52.2100 | 1.80249 | 0.901244 | − | 0.433311i | \(-0.142655\pi\) | ||||
0.901244 | + | 0.433311i | \(0.142655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.58042 | 0.0889801 | ||||||||
\(842\) | −10.5990 | −0.365266 | ||||||||
\(843\) | 20.8589 | 0.718420 | ||||||||
\(844\) | −5.60547 | −0.192948 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.52844 | −0.0525489 | ||||||||
\(847\) | 12.1635 | 0.417942 | ||||||||
\(848\) | −4.36989 | −0.150063 | ||||||||
\(849\) | −14.9101 | −0.511715 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.5316 | −0.498136 | ||||||||
\(852\) | 2.40234 | 0.0823026 | ||||||||
\(853\) | 17.3940 | 0.595559 | 0.297779 | − | 0.954635i | \(-0.403754\pi\) | ||||
0.297779 | + | 0.954635i | \(0.403754\pi\) | |||||||
\(854\) | 20.4394 | 0.699421 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.813780 | 0.0278144 | ||||||||
\(857\) | 3.12067 | 0.106600 | 0.0533000 | − | 0.998579i | \(-0.483026\pi\) | ||||
0.0533000 | + | 0.998579i | \(0.483026\pi\) | |||||||
\(858\) | −20.4800 | −0.699177 | ||||||||
\(859\) | 34.9054 | 1.19096 | 0.595478 | − | 0.803372i | \(-0.296963\pi\) | ||||
0.595478 | + | 0.803372i | \(0.296963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.2587 | −0.963055 | ||||||||
\(862\) | −55.2558 | −1.88202 | ||||||||
\(863\) | 15.0786 | 0.513282 | 0.256641 | − | 0.966507i | \(-0.417384\pi\) | ||||
0.256641 | + | 0.966507i | \(0.417384\pi\) | |||||||
\(864\) | −1.88237 | −0.0640394 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.5010 | −0.458782 | ||||||||
\(867\) | −8.30111 | −0.281921 | ||||||||
\(868\) | 10.3274 | 0.350536 | ||||||||
\(869\) | −29.1839 | −0.989995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −75.6286 | −2.56258 | ||||||||
\(872\) | −27.8395 | −0.942766 | ||||||||
\(873\) | −8.96387 | −0.303381 | ||||||||
\(874\) | −40.1829 | −1.35921 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.98684 | −0.134703 | ||||||||
\(877\) | −47.0622 | −1.58918 | −0.794588 | − | 0.607149i | \(-0.792313\pi\) | ||||
−0.794588 | + | 0.607149i | \(0.792313\pi\) | |||||||
\(878\) | 21.5758 | 0.728147 | ||||||||
\(879\) | 9.41310 | 0.317496 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.5544 | −0.524040 | −0.262020 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262020 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(882\) | −4.13915 | −0.139372 | ||||||||
\(883\) | 0.575056 | 0.0193522 | 0.00967609 | − | 0.999953i | \(-0.496920\pi\) | ||||
0.00967609 | + | 0.999953i | \(0.496920\pi\) | |||||||
\(884\) | −8.50463 | −0.286042 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.5561 | 1.09374 | ||||||||
\(887\) | −58.0626 | −1.94955 | −0.974775 | − | 0.223189i | \(-0.928353\pi\) | ||||
−0.974775 | + | 0.223189i | \(0.928353\pi\) | |||||||
\(888\) | 11.8608 | 0.398021 | ||||||||
\(889\) | 16.7314 | 0.561152 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.66386 | 0.0892428 | ||||||||
\(892\) | 5.20599 | 0.174309 | ||||||||
\(893\) | 8.43772 | 0.282358 | ||||||||
\(894\) | 11.0200 | 0.368563 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 41.4538 | 1.38487 | ||||||||
\(897\) | 15.6724 | 0.523287 | ||||||||
\(898\) | −21.5247 | −0.718288 | ||||||||
\(899\) | −55.4140 | −1.84816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.82107 | 0.160613 | ||||||||
\(902\) | 36.9272 | 1.22954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.8086 | 1.25750 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.3842 | 1.00945 | ||||||||
\(907\) | 3.58681 | 0.119098 | 0.0595490 | − | 0.998225i | \(-0.481034\pi\) | ||||
0.0595490 | + | 0.998225i | \(0.481034\pi\) | |||||||
\(908\) | 7.66794 | 0.254469 | ||||||||
\(909\) | −9.51306 | −0.315528 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5531 | 0.813482 | 0.406741 | − | 0.913544i | \(-0.366665\pi\) | ||||
0.406741 | + | 0.913544i | \(0.366665\pi\) | |||||||
\(912\) | 38.4700 | 1.27387 | ||||||||
\(913\) | −34.2984 | −1.13511 | ||||||||
\(914\) | 12.8259 | 0.424244 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.65567 | 0.252951 | ||||||||
\(917\) | 9.56047 | 0.315715 | ||||||||
\(918\) | 7.68810 | 0.253745 | ||||||||
\(919\) | 0.157692 | 0.00520177 | 0.00260089 | − | 0.999997i | \(-0.499172\pi\) | ||||
0.00260089 | + | 0.999997i | \(0.499172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5134 | −0.445281 | ||||||||
\(922\) | −23.3462 | −0.768866 | ||||||||
\(923\) | 35.9491 | 1.18328 | ||||||||
\(924\) | 2.78994 | 0.0917822 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 45.4610 | 1.49394 | ||||||||
\(927\) | 7.74494 | 0.254377 | ||||||||
\(928\) | 10.5782 | 0.347248 | ||||||||
\(929\) | −30.8470 | −1.01206 | −0.506029 | − | 0.862516i | \(-0.668887\pi\) | ||||
−0.506029 | + | 0.862516i | \(0.668887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.8500 | 0.748879 | ||||||||
\(932\) | 5.79476 | 0.189814 | ||||||||
\(933\) | −24.9323 | −0.816248 | ||||||||
\(934\) | −5.03262 | −0.164672 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.7919 | −0.418118 | ||||||||
\(937\) | 40.0853 | 1.30953 | 0.654764 | − | 0.755833i | \(-0.272768\pi\) | ||||
0.654764 | + | 0.755833i | \(0.272768\pi\) | |||||||
\(938\) | 71.6031 | 2.33792 | ||||||||
\(939\) | −21.1922 | −0.691582 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.88673 | 0.257100 | 0.128550 | − | 0.991703i | \(-0.458968\pi\) | ||||
0.128550 | + | 0.991703i | \(0.458968\pi\) | |||||||
\(942\) | −16.7046 | −0.544265 | ||||||||
\(943\) | −28.2587 | −0.920231 | ||||||||
\(944\) | 16.8940 | 0.549853 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1577 | 1.33745 | 0.668723 | − | 0.743512i | \(-0.266841\pi\) | ||||
0.668723 | + | 0.743512i | \(0.266841\pi\) | |||||||
\(948\) | 3.68253 | 0.119603 | ||||||||
\(949\) | −59.6599 | −1.93664 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6193 | 0.376783 | ||||||||
\(952\) | −39.8569 | −1.29177 | ||||||||
\(953\) | 10.5683 | 0.342340 | 0.171170 | − | 0.985242i | \(-0.445245\pi\) | ||||
0.171170 | + | 0.985242i | \(0.445245\pi\) | |||||||
\(954\) | −1.46495 | −0.0474295 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.11315 | 0.165371 | ||||||||
\(957\) | −14.9700 | −0.483910 | ||||||||
\(958\) | −37.6316 | −1.21582 | ||||||||
\(959\) | 26.2611 | 0.848014 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.2346 | 2.13660 | ||||||||
\(962\) | −35.8562 | −1.15605 | ||||||||
\(963\) | 0.319993 | 0.0103116 | ||||||||
\(964\) | 6.30290 | 0.203003 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.8382 | −0.477413 | ||||||||
\(967\) | 10.1161 | 0.325311 | 0.162655 | − | 0.986683i | \(-0.447994\pi\) | ||||
0.162655 | + | 0.986683i | \(0.447994\pi\) | |||||||
\(968\) | −9.92791 | −0.319095 | ||||||||
\(969\) | −42.4419 | −1.36343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.70212 | −0.279264 | −0.139632 | − | 0.990203i | \(-0.544592\pi\) | ||||
−0.139632 | + | 0.990203i | \(0.544592\pi\) | |||||||
\(972\) | −0.336137 | −0.0107816 | ||||||||
\(973\) | −10.9552 | −0.351209 | ||||||||
\(974\) | 44.9700 | 1.44093 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.5681 | −0.626359 | ||||||||
\(977\) | 0.883840 | 0.0282766 | 0.0141383 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141383 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(978\) | −30.4231 | −0.972822 | ||||||||
\(979\) | 38.2615 | 1.22284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.9470 | −0.349511 | ||||||||
\(982\) | 12.5700 | 0.401124 | ||||||||
\(983\) | 4.23814 | 0.135176 | 0.0675878 | − | 0.997713i | \(-0.478470\pi\) | ||||
0.0675878 | + | 0.997713i | \(0.478470\pi\) | |||||||
\(984\) | 23.0650 | 0.735284 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.2044 | −1.37591 | ||||||||
\(987\) | 3.11578 | 0.0991763 | ||||||||
\(988\) | −14.2663 | −0.453871 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.3971 | −1.21972 | −0.609862 | − | 0.792508i | \(-0.708775\pi\) | ||||
−0.609862 | + | 0.792508i | \(0.708775\pi\) | |||||||
\(992\) | −18.5616 | −0.589330 | ||||||||
\(993\) | −14.0022 | −0.444346 | ||||||||
\(994\) | −34.0356 | −1.07954 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.32791 | 0.137135 | ||||||||
\(997\) | 19.8902 | 0.629930 | 0.314965 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314965 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(998\) | −59.8081 | −1.89319 | ||||||||
\(999\) | 4.66386 | 0.147558 |
(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 | 3525.2.a.w.1.3 | 6 | ||
5.4 | even | 2 | 705.2.a.m.1.4 | ✓ | 6 | ||
15.14 | odd | 2 | 2115.2.a.s.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.a.m.1.4 | ✓ | 6 | 5.4 | even | 2 | ||
2115.2.a.s.1.3 | 6 | 15.14 | odd | 2 | |||
3525.2.a.w.1.3 | 6 | 1.1 | even | 1 | trivial |