Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.244558277.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 29x^{2} + 5x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.847024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | 0 | ||||||||
\(3\) | 0.847024 | 0.489029 | 0.244515 | − | 0.969646i | \(-0.421371\pi\) | ||||
0.244515 | + | 0.969646i | \(0.421371\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.05840 | −0.920544 | −0.460272 | − | 0.887778i | \(-0.652248\pi\) | ||||
−0.460272 | + | 0.887778i | \(0.652248\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.28255 | −0.760850 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.74351 | −0.450173 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.00274 | 1.69841 | 0.849207 | − | 0.528060i | \(-0.177080\pi\) | ||||
0.849207 | + | 0.528060i | \(0.177080\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.01552 | −1.60947 | −0.804735 | − | 0.593634i | \(-0.797693\pi\) | ||||
−0.804735 | + | 0.593634i | \(0.797693\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.847024 | 0.184836 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.954888 | −0.199108 | −0.0995540 | − | 0.995032i | \(-0.531742\pi\) | ||||
−0.0995540 | + | 0.995032i | \(0.531742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.762993 | −0.152599 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.47445 | −0.861107 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.08403 | 0.201299 | 0.100650 | − | 0.994922i | \(-0.467908\pi\) | ||||
0.100650 | + | 0.994922i | \(0.467908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.96108 | 0.352221 | 0.176110 | − | 0.984370i | \(-0.443648\pi\) | ||||
0.176110 | + | 0.984370i | \(0.443648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.847024 | −0.147448 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.05840 | −0.347933 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.98989 | 1.64233 | 0.821164 | − | 0.570693i | \(-0.193325\pi\) | ||||
0.821164 | + | 0.570693i | \(0.193325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.847024 | −0.135632 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.778077 | 0.121515 | 0.0607576 | − | 0.998153i | \(-0.480648\pi\) | ||||
0.0607576 | + | 0.998153i | \(0.480648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.80191 | 0.884783 | 0.442392 | − | 0.896822i | \(-0.354130\pi\) | ||||
0.442392 | + | 0.896822i | \(0.354130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.69840 | 0.700396 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.446074 | −0.0650666 | −0.0325333 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325333 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.93149 | 0.830574 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.47486 | −1.30147 | −0.650736 | − | 0.759304i | \(-0.725540\pi\) | ||||
−0.650736 | + | 0.759304i | \(0.725540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.05840 | 0.277554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.94231 | −0.787078 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.7446 | −1.65921 | −0.829605 | − | 0.558350i | \(-0.811435\pi\) | ||||
−0.829605 | + | 0.558350i | \(0.811435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0588 | −1.80005 | −0.900024 | − | 0.435839i | \(-0.856452\pi\) | ||||
−0.900024 | + | 0.435839i | \(0.856452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.28255 | −0.287574 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.05840 | 0.255313 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.84479 | −0.347547 | −0.173773 | − | 0.984786i | \(-0.555596\pi\) | ||||
−0.173773 | + | 0.984786i | \(0.555596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.808813 | −0.0973696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.58850 | −0.425877 | −0.212939 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212939 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1969 | 1.42753 | 0.713767 | − | 0.700383i | \(-0.246987\pi\) | ||||
0.713767 | + | 0.700383i | \(0.246987\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.646273 | −0.0746252 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.36861 | 0.829034 | 0.414517 | − | 0.910042i | \(-0.363951\pi\) | ||||
0.414517 | + | 0.910042i | \(0.363951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.05769 | 0.339744 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7442 | 1.28910 | 0.644548 | − | 0.764564i | \(-0.277046\pi\) | ||||
0.644548 | + | 0.764564i | \(0.277046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4144 | −1.56346 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.918199 | 0.0984413 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1880 | 1.71592 | 0.857961 | − | 0.513715i | \(-0.171731\pi\) | ||||
0.857961 | + | 0.513715i | \(0.171731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.66108 | 0.172246 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.4407 | 1.48159 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.31966 | −0.235526 | −0.117763 | − | 0.993042i | \(-0.537572\pi\) | ||||
−0.117763 | + | 0.993042i | \(0.537572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.28255 | 0.229405 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5762 | 1.15187 | 0.575935 | − | 0.817495i | \(-0.304638\pi\) | ||||
0.575935 | + | 0.817495i | \(0.304638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.74351 | −0.170149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.72408 | 0.166673 | 0.0833363 | − | 0.996521i | \(-0.473442\pi\) | ||||
0.0833363 | + | 0.996521i | \(0.473442\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9315 | −1.14283 | −0.571415 | − | 0.820662i | \(-0.693605\pi\) | ||||
−0.571415 | + | 0.820662i | \(0.693605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.46167 | 0.803146 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.9821 | −1.59754 | −0.798770 | − | 0.601637i | \(-0.794515\pi\) | ||||
−0.798770 | + | 0.601637i | \(0.794515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.96554 | 0.183288 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.28255 | 0.211022 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.00274 | 0.641940 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.659050 | 0.0594245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8625 | 1.06102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.13628 | −0.367035 | −0.183518 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183518 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.91436 | 0.432685 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.36427 | 0.643420 | 0.321710 | − | 0.946838i | \(-0.395742\pi\) | ||||
0.321710 | + | 0.946838i | \(0.395742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.01552 | −0.608322 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.21019 | 0.792687 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.96108 | 0.680161 | 0.340081 | − | 0.940396i | \(-0.389546\pi\) | ||||
0.340081 | + | 0.940396i | \(0.389546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.81085 | 0.662507 | 0.331254 | − | 0.943542i | \(-0.392528\pi\) | ||||
0.331254 | + | 0.943542i | \(0.392528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.377836 | −0.0318195 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.23137 | −0.185305 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.847024 | 0.0698613 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.3196 | 1.58272 | 0.791361 | − | 0.611349i | \(-0.209373\pi\) | ||||
0.791361 | + | 0.611349i | \(0.209373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3075 | 1.40846 | 0.704231 | − | 0.709971i | \(-0.251292\pi\) | ||||
0.704231 | + | 0.709971i | \(0.251292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.9841 | −1.29224 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.03669 | −0.324235 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8929 | 1.18859 | 0.594293 | − | 0.804248i | \(-0.297432\pi\) | ||||
0.594293 | + | 0.804248i | \(0.297432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.02543 | −0.636458 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.954888 | −0.0752557 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.03934 | 0.708016 | 0.354008 | − | 0.935242i | \(-0.384819\pi\) | ||||
0.354008 | + | 0.935242i | \(0.384819\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.74351 | 0.135732 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.58894 | −0.122956 | −0.0614778 | − | 0.998108i | \(-0.519581\pi\) | ||||
−0.0614778 | + | 0.998108i | \(0.519581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.0133 | 1.22457 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4036 | −0.943029 | −0.471515 | − | 0.881858i | \(-0.656293\pi\) | ||||
−0.471515 | + | 0.881858i | \(0.656293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.762993 | −0.0576769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.7950 | −0.811403 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7913 | 0.806579 | 0.403289 | − | 0.915073i | \(-0.367867\pi\) | ||||
0.403289 | + | 0.915073i | \(0.367867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2294 | −1.35498 | −0.677492 | − | 0.735530i | \(-0.736933\pi\) | ||||
−0.677492 | + | 0.735530i | \(0.736933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9082 | −0.880277 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.5632 | −1.51183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.00274 | −0.512091 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.47445 | −0.325468 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7640 | −0.995928 | −0.497964 | − | 0.867198i | \(-0.665919\pi\) | ||||
−0.497964 | + | 0.867198i | \(0.665919\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7080 | 1.27465 | 0.637324 | − | 0.770596i | \(-0.280041\pi\) | ||||
0.637324 | + | 0.770596i | \(0.280041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.74351 | 0.124856 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.53507 | −0.608099 | −0.304049 | − | 0.952656i | \(-0.598339\pi\) | ||||
−0.304049 | + | 0.952656i | \(0.598339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4069 | 1.58838 | 0.794190 | − | 0.607669i | \(-0.207895\pi\) | ||||
0.794190 | + | 0.607669i | \(0.207895\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.40961 | −0.169961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.08403 | 0.0760840 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.60159 | −0.111860 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.17958 | 0.151491 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.01552 | 0.485273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7597 | −1.77337 | −0.886686 | − | 0.462372i | \(-0.846999\pi\) | ||||
−0.886686 | + | 0.462372i | \(0.846999\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.03955 | −0.208266 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9426 | −0.814482 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.96108 | 0.133127 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3310 | 0.698106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.00274 | −0.471055 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3058 | −1.49371 | −0.746853 | − | 0.664990i | \(-0.768436\pi\) | ||||
−0.746853 | + | 0.664990i | \(0.768436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.74157 | 0.116105 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.0432 | 1.46306 | 0.731530 | − | 0.681809i | \(-0.238807\pi\) | ||||
0.731530 | + | 0.681809i | \(0.238807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1420 | 1.26494 | 0.632468 | − | 0.774586i | \(-0.282042\pi\) | ||||
0.632468 | + | 0.774586i | \(0.282042\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.847024 | −0.0557301 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.614135 | 0.0402333 | 0.0201167 | − | 0.999798i | \(-0.493596\pi\) | ||||
0.0201167 | + | 0.999798i | \(0.493596\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.918199 | 0.0598967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.24139 | 0.405422 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.5486 | 1.71729 | 0.858643 | − | 0.512574i | \(-0.171308\pi\) | ||||
0.858643 | + | 0.512574i | \(0.171308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6212 | −0.877418 | −0.438709 | − | 0.898629i | \(-0.644564\pi\) | ||||
−0.438709 | + | 0.898629i | \(0.644564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0133 | 1.02725 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.05840 | −0.131506 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.01552 | 0.446387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.94763 | 0.630406 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.14862 | −0.135620 | −0.0678099 | − | 0.997698i | \(-0.521601\pi\) | ||||
−0.0678099 | + | 0.997698i | \(0.521601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.954888 | 0.0600333 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.2094 | −0.764580 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.58000 | 0.472828 | 0.236414 | − | 0.971652i | \(-0.424028\pi\) | ||||
0.236414 | + | 0.971652i | \(0.424028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.98989 | 0.620741 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.47435 | −0.153159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5846 | 0.652673 | 0.326337 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326337 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.5031 | 1.19806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.7116 | 0.839136 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.78702 | 0.108957 | 0.0544784 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544784 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4330 | 0.633761 | 0.316881 | − | 0.948465i | \(-0.397365\pi\) | ||||
0.316881 | + | 0.948465i | \(0.397365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.847024 | −0.0512642 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.762993 | 0.0460102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0759 | 0.725573 | 0.362787 | − | 0.931872i | \(-0.381825\pi\) | ||||
0.362787 | + | 0.931872i | \(0.381825\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.47627 | −0.267987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8892 | 1.48476 | 0.742382 | − | 0.669976i | \(-0.233696\pi\) | ||||
0.742382 | + | 0.669976i | \(0.233696\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.45416 | −0.205328 | −0.102664 | − | 0.994716i | \(-0.532737\pi\) | ||||
−0.102664 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.2316 | 0.724540 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.778077 | 0.0459285 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0384 | 1.88461 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.96481 | −0.115179 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.01926 | 0.351649 | 0.175824 | − | 0.984422i | \(-0.443741\pi\) | ||||
0.175824 | + | 0.984422i | \(0.443741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.2336 | 1.52738 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.47445 | 0.259634 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.954888 | 0.0552226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.80191 | 0.334417 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.80528 | 0.563299 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.9387 | 1.65702 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0598 | −1.65853 | −0.829266 | − | 0.558854i | \(-0.811241\pi\) | ||||
−0.829266 | + | 0.558854i | \(0.811241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.77619 | 0.385484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0052 | 1.13439 | 0.567196 | − | 0.823583i | \(-0.308028\pi\) | ||||
0.567196 | + | 0.823583i | \(0.308028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9725 | −0.902820 | −0.451410 | − | 0.892317i | \(-0.649079\pi\) | ||||
−0.451410 | + | 0.892317i | \(0.649079\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.69840 | 0.264725 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.67790 | 0.487399 | 0.243700 | − | 0.969851i | \(-0.421639\pi\) | ||||
0.243700 | + | 0.969851i | \(0.421639\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08403 | −0.0606940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.46033 | 0.0815078 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −49.1278 | −2.73355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.762993 | 0.0423233 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.1063 | −0.558877 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.446074 | −0.0245929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.49282 | 0.301913 | 0.150956 | − | 0.988540i | \(-0.451765\pi\) | ||||
0.150956 | + | 0.988540i | \(0.451765\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.8024 | −1.24957 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.85572 | 0.319932 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2610 | 0.776848 | 0.388424 | − | 0.921481i | \(-0.373020\pi\) | ||||
0.388424 | + | 0.921481i | \(0.373020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.3842 | −0.781244 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.96108 | −0.106199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.66486 | 0.0896330 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4487 | −0.829329 | −0.414664 | − | 0.909974i | \(-0.636101\pi\) | ||||
−0.414664 | + | 0.909974i | \(0.636101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8542 | 0.634540 | 0.317270 | − | 0.948335i | \(-0.397234\pi\) | ||||
0.317270 | + | 0.948335i | \(0.397234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47445 | 0.238828 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.2777 | −1.45185 | −0.725924 | − | 0.687775i | \(-0.758587\pi\) | ||||
−0.725924 | + | 0.687775i | \(0.758587\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.38657 | 0.392039 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.93149 | 0.313928 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5630 | −0.821382 | −0.410691 | − | 0.911775i | \(-0.634713\pi\) | ||||
−0.410691 | + | 0.911775i | \(0.634713\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.2175 | 1.59039 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.847024 | 0.0444572 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.1060 | −1.31411 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.566283 | 0.0295597 | 0.0147799 | − | 0.999891i | \(-0.495295\pi\) | ||||
0.0147799 | + | 0.999891i | \(0.495295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.77600 | −0.0924549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.47486 | −0.491910 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.8743 | 1.49505 | 0.747527 | − | 0.664231i | \(-0.231241\pi\) | ||||
0.747527 | + | 0.664231i | \(0.231241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0479 | 0.518869 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.08403 | −0.0558304 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1086 | −0.673341 | −0.336671 | − | 0.941622i | \(-0.609301\pi\) | ||||
−0.336671 | + | 0.941622i | \(0.609301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50353 | −0.179491 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8278 | 0.706566 | 0.353283 | − | 0.935516i | \(-0.385065\pi\) | ||||
0.353283 | + | 0.935516i | \(0.385065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.05840 | 0.104906 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2432 | −0.673188 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3584 | 0.728000 | 0.364000 | − | 0.931399i | \(-0.381411\pi\) | ||||
0.364000 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.68683 | −0.338168 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.23771 | 0.314651 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1675 | −0.763162 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0548 | 0.605011 | 0.302506 | − | 0.953148i | \(-0.402177\pi\) | ||||
0.302506 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.94231 | −0.297488 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.87701 | −0.243546 | −0.121773 | − | 0.992558i | \(-0.538858\pi\) | ||||
−0.121773 | + | 0.992558i | \(0.538858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.96108 | −0.0976884 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.29395 | −0.312749 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.98989 | −0.495180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.7296 | 1.12390 | 0.561952 | − | 0.827170i | \(-0.310050\pi\) | ||||
0.561952 | + | 0.827170i | \(0.310050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.74322 | 0.332619 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7446 | −0.627123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.1743 | −1.18667 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.61597 | 0.323985 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.3492 | −1.38495 | −0.692474 | − | 0.721443i | \(-0.743479\pi\) | ||||
−0.692474 | + | 0.721443i | \(0.743479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1169 | 0.931701 | 0.465850 | − | 0.884864i | \(-0.345749\pi\) | ||||
0.465850 | + | 0.884864i | \(0.345749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.01819 | 0.0495060 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.34304 | −0.259176 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.0588 | −0.680355 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.847024 | 0.0408947 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2876 | 0.880881 | 0.440440 | − | 0.897782i | \(-0.354822\pi\) | ||||
0.440440 | + | 0.897782i | \(0.354822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.8733 | −1.67590 | −0.837951 | − | 0.545745i | \(-0.816247\pi\) | ||||
−0.837951 | + | 0.545745i | \(0.816247\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.89002 | −0.0906195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.69903 | 0.320458 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.24713 | 0.154977 | 0.0774886 | − | 0.996993i | \(-0.475310\pi\) | ||||
0.0774886 | + | 0.996993i | \(0.475310\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.28255 | −0.108693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.51826 | −0.0721346 | −0.0360673 | − | 0.999349i | \(-0.511483\pi\) | ||||
−0.0360673 | + | 0.999349i | \(0.511483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.3213 | −1.57958 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3641 | 0.773997 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6637 | −1.39992 | −0.699958 | − | 0.714184i | \(-0.746798\pi\) | ||||
−0.699958 | + | 0.714184i | \(0.746798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.778077 | −0.0366382 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6598 | 0.688779 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.05840 | 0.0964992 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3474 | 0.484031 | 0.242015 | − | 0.970272i | \(-0.422192\pi\) | ||||
0.242015 | + | 0.970272i | \(0.422192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.3334 | −1.46252 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.8769 | 1.43808 | 0.719040 | − | 0.694969i | \(-0.244582\pi\) | ||||
0.719040 | + | 0.694969i | \(0.244582\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.1572 | 1.26210 | 0.631052 | − | 0.775741i | \(-0.282624\pi\) | ||||
0.631052 | + | 0.775741i | \(0.282624\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.41917 | −0.158560 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.54107 | 0.302685 | 0.151342 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151342 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.84479 | −0.131360 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6147 | 0.581254 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.80191 | −0.266772 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.35279 | 0.245603 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.6269 | 0.990226 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.9419 | 1.55085 | 0.775424 | − | 0.631441i | \(-0.217536\pi\) | ||||
0.775424 | + | 0.631441i | \(0.217536\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.98989 | −0.455500 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.808813 | −0.0368023 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.77478 | 0.216812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.51228 | 0.249785 | 0.124893 | − | 0.992170i | \(-0.460141\pi\) | ||||
0.124893 | + | 0.992170i | \(0.460141\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.65653 | 0.346240 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.04625 | −0.0923461 | −0.0461731 | − | 0.998933i | \(-0.514703\pi\) | ||||
−0.0461731 | + | 0.998933i | \(0.514703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.59118 | 0.341890 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.69840 | −0.211177 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.58850 | −0.160966 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7391 | −0.973177 | −0.486589 | − | 0.873631i | \(-0.661759\pi\) | ||||
−0.486589 | + | 0.873631i | \(0.661759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.34587 | −0.0601289 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.4668 | −1.58139 | −0.790693 | − | 0.612213i | \(-0.790280\pi\) | ||||
−0.790693 | + | 0.612213i | \(0.790280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.8284 | −1.06035 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.847024 | 0.0376176 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8093 | 0.656410 | 0.328205 | − | 0.944607i | \(-0.393556\pi\) | ||||
0.328205 | + | 0.944607i | \(0.393556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1969 | 0.539557 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.3905 | 1.38593 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.4672 | −0.725631 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.446074 | 0.0196183 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.5062 | −0.461169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.3786 | 1.33091 | 0.665456 | − | 0.746437i | \(-0.268237\pi\) | ||||
0.665456 | + | 0.746437i | \(0.268237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.28572 | −0.362309 | −0.181155 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181155 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.646273 | −0.0282057 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.7329 | 0.598217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0882 | −0.960356 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.0903 | 1.26241 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.778077 | −0.0337023 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.54883 | −0.153430 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.14047 | 0.394441 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.24152 | 0.182357 | 0.0911787 | − | 0.995835i | \(-0.470937\pi\) | ||||
0.0911787 | + | 0.995835i | \(0.470937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.4408 | −0.662627 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5598 | 1.05202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0700 | −1.28570 | −0.642850 | − | 0.765992i | \(-0.722248\pi\) | ||||
−0.642850 | + | 0.765992i | \(0.722248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.0900 | 1.36957 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.60503 | −0.323985 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.36861 | 0.313345 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.4175 | −0.739331 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9958 | 0.889619 | 0.444809 | − | 0.895625i | \(-0.353271\pi\) | ||||
0.444809 | + | 0.895625i | \(0.353271\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.80191 | −0.245395 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.93149 | −0.250428 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.07309 | −0.298095 | −0.149048 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149048 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.9559 | 1.47061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.05769 | 0.128411 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.2441 | 1.26790 | 0.633948 | − | 0.773375i | \(-0.281433\pi\) | ||||
0.633948 | + | 0.773375i | \(0.281433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.4850 | −1.86164 | −0.930820 | − | 0.365477i | \(-0.880906\pi\) | ||||
−0.930820 | + | 0.365477i | \(0.880906\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.6584 | −0.487038 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.728573 | 0.0303836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.1854 | −0.715436 | −0.357718 | − | 0.933830i | \(-0.616445\pi\) | ||||
−0.357718 | + | 0.933830i | \(0.616445\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9991 | 0.623340 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.7442 | 0.487232 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.47486 | 0.392409 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.69840 | −0.194255 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.7916 | 0.981986 | 0.490993 | − | 0.871164i | \(-0.336634\pi\) | ||||
0.490993 | + | 0.871164i | \(0.336634\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7580 | −0.566889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.22941 | −0.297378 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.5745 | 0.557440 | 0.278720 | − | 0.960372i | \(-0.410090\pi\) | ||||
0.278720 | + | 0.960372i | \(0.410090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4144 | −0.590934 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9791 | 0.776765 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.89645 | 0.240923 | 0.120461 | − | 0.992718i | \(-0.461563\pi\) | ||||
0.120461 | + | 0.992718i | \(0.461563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1942 | 1.35402 | 0.677009 | − | 0.735974i | \(-0.263276\pi\) | ||||
0.677009 | + | 0.735974i | \(0.263276\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.49339 | 0.264431 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.05840 | −0.0836858 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9580 | −0.850660 | −0.425330 | − | 0.905038i | \(-0.639842\pi\) | ||||
−0.425330 | + | 0.905038i | \(0.639842\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.918199 | 0.0372073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.446074 | 0.0180462 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.3458 | −0.498641 | −0.249321 | − | 0.968421i | \(-0.580207\pi\) | ||||
−0.249321 | + | 0.968421i | \(0.580207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.35659 | −0.0547029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32308 | −0.0532653 | −0.0266327 | − | 0.999645i | \(-0.508478\pi\) | ||||
−0.0266327 | + | 0.999645i | \(0.508478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3498 | −1.05909 | −0.529544 | − | 0.848282i | \(-0.677637\pi\) | ||||
−0.529544 | + | 0.848282i | \(0.677637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.27259 | 0.171453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.1880 | 0.648557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.6029 | −0.824115 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.94231 | 0.237313 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 69.9566 | 2.78935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4368 | −1.25148 | −0.625740 | − | 0.780032i | \(-0.715203\pi\) | ||||
−0.625740 | + | 0.780032i | \(0.715203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.8191 | −0.867231 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.51411 | 0.337872 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.19094 | 0.324029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2758 | −0.484865 | −0.242433 | − | 0.970168i | \(-0.577945\pi\) | ||||
−0.242433 | + | 0.970168i | \(0.577945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.29219 | 0.327012 | 0.163506 | − | 0.986542i | \(-0.447720\pi\) | ||||
0.163506 | + | 0.986542i | \(0.447720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.1157 | −0.398306 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.0570 | −0.788524 | −0.394262 | − | 0.918998i | \(-0.629000\pi\) | ||||
−0.394262 | + | 0.918998i | \(0.629000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.7446 | 0.500271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.66108 | 0.0651030 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.2082 | −0.595142 | −0.297571 | − | 0.954700i | \(-0.596176\pi\) | ||||
−0.297571 | + | 0.954700i | \(0.596176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.1586 | −0.592296 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.8400 | −1.08614 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.5095 | 1.03266 | 0.516332 | − | 0.856388i | \(-0.327297\pi\) | ||||
0.516332 | + | 0.856388i | \(0.327297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1291 | −1.79422 | −0.897108 | − | 0.441812i | \(-0.854336\pi\) | ||||
−0.897108 | + | 0.441812i | \(0.854336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.93149 | −0.230360 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4407 | 0.559988 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03513 | −0.0400803 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.8935 | −0.730466 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0588 | 0.542735 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.602701 | −0.0232324 | −0.0116162 | − | 0.999933i | \(-0.503698\pi\) | ||||
−0.0116162 | + | 0.999933i | \(0.503698\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.41397 | 0.131404 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.3981 | 1.70636 | 0.853178 | − | 0.521620i | \(-0.174672\pi\) | ||||
0.853178 | + | 0.521620i | \(0.174672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.31966 | −0.0890203 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.6711 | 0.715479 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.09430 | −0.194928 | −0.0974640 | − | 0.995239i | \(-0.531073\pi\) | ||||
−0.0974640 | + | 0.995239i | \(0.531073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.3871 | −0.626118 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.2137 | 0.618591 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.47486 | 0.360964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.70988 | −0.255256 | −0.127628 | − | 0.991822i | \(-0.540736\pi\) | ||||
−0.127628 | + | 0.991822i | \(0.540736\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.28255 | 0.0867069 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0778 | −0.609867 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.44867 | 0.206383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.520187 | 0.0196753 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.6510 | −0.440051 | −0.220025 | − | 0.975494i | \(-0.570614\pi\) | ||||
−0.220025 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −70.0842 | −2.64328 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.777736 | 0.0292912 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5762 | 0.435366 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.01867 | −0.0382569 | −0.0191284 | − | 0.999817i | \(-0.506089\pi\) | ||||
−0.0191284 | + | 0.999817i | \(0.506089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8192 | −0.630771 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.87261 | −0.0701299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.05840 | −0.0769798 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.4873 | 0.839803 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5816 | 0.879444 | 0.439722 | − | 0.898134i | \(-0.355077\pi\) | ||||
0.439722 | + | 0.898134i | \(0.355077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.5375 | −0.429083 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.827108 | −0.0307180 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.1740 | −0.414419 | −0.207210 | − | 0.978297i | \(-0.566438\pi\) | ||||
−0.207210 | + | 0.978297i | \(0.566438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.39055 | 0.162613 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.6293 | 1.50273 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.3061 | −0.897765 | −0.448883 | − | 0.893591i | \(-0.648178\pi\) | ||||
−0.448883 | + | 0.893591i | \(0.648178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.74351 | −0.0643104 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.84479 | 0.104789 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.5386 | 0.865882 | 0.432941 | − | 0.901422i | \(-0.357476\pi\) | ||||
0.432941 | + | 0.901422i | \(0.357476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.94231 | 0.218296 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0351 | 0.881763 | 0.440882 | − | 0.897565i | \(-0.354666\pi\) | ||||
0.440882 | + | 0.897565i | \(0.354666\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.7674 | −1.45697 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.8068 | −0.980809 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.72408 | 0.0629963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7741 | −0.466133 | −0.233066 | − | 0.972461i | \(-0.574876\pi\) | ||||
−0.233066 | + | 0.972461i | \(0.574876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.81993 | −0.0663221 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.6257 | −1.29655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.1026 | 1.74832 | 0.874159 | − | 0.485640i | \(-0.161413\pi\) | ||||
0.874159 | + | 0.485640i | \(0.161413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.808813 | 0.0293580 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.03639 | 0.255069 | 0.127534 | − | 0.991834i | \(-0.459294\pi\) | ||||
0.127534 | + | 0.991834i | \(0.459294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.9315 | −0.431949 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.9017 | 1.18956 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7446 | 0.460182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.1847 | −0.763939 | −0.381969 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381969 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.42044 | 0.231227 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.60216 | −0.165528 | −0.0827640 | − | 0.996569i | \(-0.526375\pi\) | ||||
−0.0827640 | + | 0.996569i | \(0.526375\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.49629 | −0.0537484 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.46167 | 0.303561 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.45862 | −0.195575 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.58850 | 0.128407 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.85043 | −0.173340 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.6556 | −1.09415 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.6855 | 1.62851 | 0.814255 | − | 0.580507i | \(-0.197146\pi\) | ||||
0.814255 | + | 0.580507i | \(0.197146\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.96539 | 0.319176 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.9821 | −0.603813 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0588 | 0.499244 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.5195 | 0.585888 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.4936 | 1.57604 | 0.788021 | − | 0.615648i | \(-0.211106\pi\) | ||||
0.788021 | + | 0.615648i | \(0.211106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.12374 | −0.110510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.9499 | −1.30556 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1969 | −0.430418 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.96554 | 0.0692762 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.51365 | 0.0532831 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.9932 | 0.808397 | 0.404199 | − | 0.914671i | \(-0.367550\pi\) | ||||
0.404199 | + | 0.914671i | \(0.367550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1126 | 0.952053 | 0.476027 | − | 0.879431i | \(-0.342077\pi\) | ||||
0.476027 | + | 0.879431i | \(0.342077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.83702 | 0.309928 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6066 | −0.651759 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.7034 | −1.42403 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.28255 | 0.0797588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.9418 | −1.21948 | −0.609739 | − | 0.792602i | \(-0.708726\pi\) | ||||
−0.609739 | + | 0.792602i | \(0.708726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.2465 | −0.775463 | −0.387731 | − | 0.921772i | \(-0.626741\pi\) | ||||
−0.387731 | + | 0.921772i | \(0.626741\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.646273 | 0.0225004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1421 | −0.909051 | −0.454525 | − | 0.890734i | \(-0.650191\pi\) | ||||
−0.454525 | + | 0.890734i | \(0.650191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4368 | −0.640336 | −0.320168 | − | 0.947361i | \(-0.603739\pi\) | ||||
−0.320168 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2286 | 0.354827 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.00274 | 0.242631 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.27066 | 0.113186 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.77475 | −0.303300 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7978 | 1.23588 | 0.617938 | − | 0.786227i | \(-0.287968\pi\) | ||||
0.617938 | + | 0.786227i | \(0.287968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8249 | −0.959479 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.0817 | 0.726093 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.05840 | −0.0708111 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.92575 | −0.100412 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.53922 | −0.327000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.48563 | 0.324782 | 0.162391 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162391 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.9617 | −1.12727 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.6406 | 1.42242 | 0.711208 | − | 0.702982i | \(-0.248148\pi\) | ||||
0.711208 | + | 0.702982i | \(0.248148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0745 | 0.548456 | 0.274228 | − | 0.961665i | \(-0.411578\pi\) | ||||
0.274228 | + | 0.961665i | \(0.411578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.659050 | 0.0224604 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1835 | 0.789175 | 0.394587 | − | 0.918858i | \(-0.370888\pi\) | ||||
0.394587 | + | 0.918858i | \(0.370888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.5316 | 0.868100 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.1373 | 0.921629 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.36861 | −0.249963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.84479 | 0.0963922 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.29474 | 0.179200 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.8625 | 0.401027 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1993 | 0.344407 | 0.172204 | − | 0.985061i | \(-0.444911\pi\) | ||||
0.172204 | + | 0.985061i | \(0.444911\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.09845 | 0.171967 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.98907 | −0.336540 | −0.168270 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168270 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5738 | 0.389489 | 0.194744 | − | 0.980854i | \(-0.437612\pi\) | ||||
0.194744 | + | 0.980854i | \(0.437612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.2204 | 0.746932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.8788 | 1.10396 | 0.551980 | − | 0.833857i | \(-0.313872\pi\) | ||||
0.551980 | + | 0.833857i | \(0.313872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.13628 | −0.138726 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.05769 | −0.102437 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.12944 | 0.104723 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.2128 | −0.742491 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.808813 | 0.0270055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.12587 | 0.0709018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −66.3500 | −2.21044 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.91436 | 0.163540 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.5235 | 1.24732 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.1471 | 0.768587 | 0.384294 | − | 0.923211i | \(-0.374445\pi\) | ||||
0.384294 | + | 0.923211i | \(0.374445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.4232 | −0.876401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.2258 | 0.703241 | 0.351621 | − | 0.936143i | \(-0.385631\pi\) | ||||
0.351621 | + | 0.936143i | \(0.385631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.7442 | −0.388677 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.5118 | 0.810333 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.36427 | 0.243190 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.3406 | −1.62760 | −0.813798 | − | 0.581147i | \(-0.802604\pi\) | ||||
−0.813798 | + | 0.581147i | \(0.802604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.6144 | −0.811071 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.58850 | 0.118117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.62222 | −0.250617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.2604 | −0.599750 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.4298 | 1.03118 | 0.515589 | − | 0.856836i | \(-0.327573\pi\) | ||||
0.515589 | + | 0.856836i | \(0.327573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.01552 | −0.229924 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.9449 | 0.554751 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.4144 | 0.471402 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6828 | −1.10037 | −0.550185 | − | 0.835043i | \(-0.685443\pi\) | ||||
−0.550185 | + | 0.835043i | \(0.685443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.5291 | −0.441505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.0345 | −1.07689 | −0.538447 | − | 0.842659i | \(-0.680989\pi\) | ||||
−0.538447 | + | 0.842659i | \(0.680989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.742977 | −0.0241947 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.21019 | 0.299608 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2385 | −0.885133 | −0.442567 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442567 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1969 | −0.395927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.35038 | 0.238352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.0094 | −1.42560 | −0.712802 | − | 0.701366i | \(-0.752574\pi\) | ||||
−0.712802 | + | 0.701366i | \(0.752574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.3318 | 0.916796 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.918199 | −0.0296812 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.96108 | 0.257077 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1542 | −0.875941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.93529 | −0.126813 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.4501 | −1.17337 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.8204 | −0.894644 | −0.447322 | − | 0.894373i | \(-0.647622\pi\) | ||||
−0.447322 | + | 0.894373i | \(0.647622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −41.6124 | −1.33678 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.1246 | −1.12720 | −0.563600 | − | 0.826048i | \(-0.690584\pi\) | ||||
−0.563600 | + | 0.826048i | \(0.690584\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.81085 | 0.250404 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.646273 | 0.0206973 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.8641 | −1.14739 | −0.573697 | − | 0.819067i | \(-0.694491\pi\) | ||||
−0.573697 | + | 0.819067i | \(0.694491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1880 | −0.517370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.2342 | 0.869522 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.0977 | 1.24702 | 0.623512 | − | 0.781814i | \(-0.285705\pi\) | ||||
0.623512 | + | 0.781814i | \(0.285705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5686 | 0.559782 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.377836 | −0.0120266 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.54018 | −0.176167 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.2785 | −0.453572 | −0.226786 | − | 0.973945i | \(-0.572822\pi\) | ||||
−0.226786 | + | 0.973945i | \(0.572822\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.65255 | 0.147644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46.1223 | −1.46217 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0422 | −0.603072 | −0.301536 | − | 0.953455i | \(-0.597499\pi\) | ||||
−0.301536 | + | 0.953455i | \(0.597499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.6992 | −1.41422 |
(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 | 8008.2.a.k.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.k.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial |