Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22545.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.45106\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.894434 | −0.632460 | −0.316230 | − | 0.948683i | \(-0.602417\pi\) | ||||
−0.316230 | + | 0.948683i | \(0.602417\pi\) | |||||||
\(3\) | 2.74893 | 1.58710 | 0.793548 | − | 0.608508i | \(-0.208231\pi\) | ||||
0.793548 | + | 0.608508i | \(0.208231\pi\) | |||||||
\(4\) | −1.19999 | −0.599994 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.45874 | −1.00378 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.86218 | 1.01193 | ||||||||
\(9\) | 4.55662 | 1.51887 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.105566 | 0.0318294 | 0.0159147 | − | 0.999873i | \(-0.494934\pi\) | ||||
0.0159147 | + | 0.999873i | \(0.494934\pi\) | |||||||
\(12\) | −3.29869 | −0.952248 | ||||||||
\(13\) | 5.45106 | 1.51185 | 0.755926 | − | 0.654658i | \(-0.227187\pi\) | ||||
0.755926 | + | 0.654658i | \(0.227187\pi\) | |||||||
\(14\) | −0.894434 | −0.239047 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.160052 | −0.0400130 | ||||||||
\(17\) | 0.992320 | 0.240673 | 0.120336 | − | 0.992733i | \(-0.461603\pi\) | ||||
0.120336 | + | 0.992733i | \(0.461603\pi\) | |||||||
\(18\) | −4.07560 | −0.960628 | ||||||||
\(19\) | 3.34549 | 0.767508 | 0.383754 | − | 0.923435i | \(-0.374631\pi\) | ||||
0.383754 | + | 0.923435i | \(0.374631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.74893 | 0.599866 | ||||||||
\(22\) | −0.0944220 | −0.0201308 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 7.86793 | 1.60603 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.87561 | −0.956186 | ||||||||
\(27\) | 4.27905 | 0.823504 | ||||||||
\(28\) | −1.19999 | −0.226776 | ||||||||
\(29\) | 4.90211 | 0.910300 | 0.455150 | − | 0.890415i | \(-0.349586\pi\) | ||||
0.455150 | + | 0.890415i | \(0.349586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24760 | 0.762892 | 0.381446 | − | 0.924391i | \(-0.375426\pi\) | ||||
0.381446 | + | 0.924391i | \(0.375426\pi\) | |||||||
\(32\) | −5.58120 | −0.986626 | ||||||||
\(33\) | 0.290194 | 0.0505163 | ||||||||
\(34\) | −0.887564 | −0.152216 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.46789 | −0.911316 | ||||||||
\(37\) | −4.79655 | −0.788548 | −0.394274 | − | 0.918993i | \(-0.629004\pi\) | ||||
−0.394274 | + | 0.918993i | \(0.629004\pi\) | |||||||
\(38\) | −2.99232 | −0.485418 | ||||||||
\(39\) | 14.9846 | 2.39945 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.65873 | −0.727571 | −0.363785 | − | 0.931483i | \(-0.618516\pi\) | ||||
−0.363785 | + | 0.931483i | \(0.618516\pi\) | |||||||
\(42\) | −2.45874 | −0.379391 | ||||||||
\(43\) | 1.03994 | 0.158589 | 0.0792944 | − | 0.996851i | \(-0.474733\pi\) | ||||
0.0792944 | + | 0.996851i | \(0.474733\pi\) | |||||||
\(44\) | −0.126678 | −0.0190975 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.894434 | 0.131877 | ||||||||
\(47\) | 0.654509 | 0.0954700 | 0.0477350 | − | 0.998860i | \(-0.484800\pi\) | ||||
0.0477350 | + | 0.998860i | \(0.484800\pi\) | |||||||
\(48\) | −0.439972 | −0.0635044 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.72782 | 0.381971 | ||||||||
\(52\) | −6.54120 | −0.907102 | ||||||||
\(53\) | −6.49099 | −0.891606 | −0.445803 | − | 0.895131i | \(-0.647082\pi\) | ||||
−0.445803 | + | 0.895131i | \(0.647082\pi\) | |||||||
\(54\) | −3.82733 | −0.520833 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.86218 | 0.382475 | ||||||||
\(57\) | 9.19652 | 1.21811 | ||||||||
\(58\) | −4.38462 | −0.575728 | ||||||||
\(59\) | 4.54894 | 0.592222 | 0.296111 | − | 0.955154i | \(-0.404310\pi\) | ||||
0.296111 | + | 0.955154i | \(0.404310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.98886 | 0.254647 | 0.127323 | − | 0.991861i | \(-0.459361\pi\) | ||||
0.127323 | + | 0.991861i | \(0.459361\pi\) | |||||||
\(62\) | −3.79920 | −0.482499 | ||||||||
\(63\) | 4.55662 | 0.574081 | ||||||||
\(64\) | 5.31212 | 0.664015 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.259560 | −0.0319496 | ||||||||
\(67\) | −7.83567 | −0.957280 | −0.478640 | − | 0.878011i | \(-0.658870\pi\) | ||||
−0.478640 | + | 0.878011i | \(0.658870\pi\) | |||||||
\(68\) | −1.19077 | −0.144402 | ||||||||
\(69\) | −2.74893 | −0.330932 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.53433 | −0.894161 | −0.447081 | − | 0.894494i | \(-0.647536\pi\) | ||||
−0.447081 | + | 0.894494i | \(0.647536\pi\) | |||||||
\(72\) | 13.0419 | 1.53700 | ||||||||
\(73\) | 14.6798 | 1.71814 | 0.859072 | − | 0.511854i | \(-0.171041\pi\) | ||||
0.859072 | + | 0.511854i | \(0.171041\pi\) | |||||||
\(74\) | 4.29019 | 0.498725 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.01455 | −0.460500 | ||||||||
\(77\) | 0.105566 | 0.0120304 | ||||||||
\(78\) | −13.4027 | −1.51756 | ||||||||
\(79\) | 2.59656 | 0.292136 | 0.146068 | − | 0.989275i | \(-0.453338\pi\) | ||||
0.146068 | + | 0.989275i | \(0.453338\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.90705 | −0.211895 | ||||||||
\(82\) | 4.16692 | 0.460159 | ||||||||
\(83\) | −1.14469 | −0.125646 | −0.0628231 | − | 0.998025i | \(-0.520010\pi\) | ||||
−0.0628231 | + | 0.998025i | \(0.520010\pi\) | |||||||
\(84\) | −3.29869 | −0.359916 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.930154 | −0.100301 | ||||||||
\(87\) | 13.4756 | 1.44473 | ||||||||
\(88\) | 0.302149 | 0.0322092 | ||||||||
\(89\) | −14.3098 | −1.51683 | −0.758416 | − | 0.651770i | \(-0.774027\pi\) | ||||
−0.758416 | + | 0.651770i | \(0.774027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.45106 | 0.571426 | ||||||||
\(92\) | 1.19999 | 0.125107 | ||||||||
\(93\) | 11.6764 | 1.21078 | ||||||||
\(94\) | −0.585415 | −0.0603810 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.3423 | −1.56587 | ||||||||
\(97\) | 13.9455 | 1.41595 | 0.707973 | − | 0.706239i | \(-0.249610\pi\) | ||||
0.707973 | + | 0.706239i | \(0.249610\pi\) | |||||||
\(98\) | −0.894434 | −0.0903515 | ||||||||
\(99\) | 0.481025 | 0.0483449 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5677 | 1.44954 | 0.724771 | − | 0.688990i | \(-0.241946\pi\) | ||||
0.724771 | + | 0.688990i | \(0.241946\pi\) | |||||||
\(102\) | −2.43985 | −0.241582 | ||||||||
\(103\) | −10.7523 | −1.05946 | −0.529730 | − | 0.848167i | \(-0.677707\pi\) | ||||
−0.529730 | + | 0.848167i | \(0.677707\pi\) | |||||||
\(104\) | 15.6019 | 1.52989 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.80576 | 0.563906 | ||||||||
\(107\) | −2.16352 | −0.209155 | −0.104577 | − | 0.994517i | \(-0.533349\pi\) | ||||
−0.104577 | + | 0.994517i | \(0.533349\pi\) | |||||||
\(108\) | −5.13481 | −0.494097 | ||||||||
\(109\) | 9.77772 | 0.936536 | 0.468268 | − | 0.883586i | \(-0.344878\pi\) | ||||
0.468268 | + | 0.883586i | \(0.344878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.1854 | −1.25150 | ||||||||
\(112\) | −0.160052 | −0.0151235 | ||||||||
\(113\) | −9.08674 | −0.854809 | −0.427404 | − | 0.904061i | \(-0.640572\pi\) | ||||
−0.427404 | + | 0.904061i | \(0.640572\pi\) | |||||||
\(114\) | −8.22568 | −0.770406 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.88248 | −0.546174 | ||||||||
\(117\) | 24.8384 | 2.29631 | ||||||||
\(118\) | −4.06873 | −0.374557 | ||||||||
\(119\) | 0.992320 | 0.0909658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9889 | −0.998987 | ||||||||
\(122\) | −1.77890 | −0.161054 | ||||||||
\(123\) | −12.8065 | −1.15472 | ||||||||
\(124\) | −5.09708 | −0.457731 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.07560 | −0.363083 | ||||||||
\(127\) | −5.76083 | −0.511191 | −0.255595 | − | 0.966784i | \(-0.582271\pi\) | ||||
−0.255595 | + | 0.966784i | \(0.582271\pi\) | |||||||
\(128\) | 6.41106 | 0.566663 | ||||||||
\(129\) | 2.85871 | 0.251696 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3021 | 1.16221 | 0.581105 | − | 0.813829i | \(-0.302621\pi\) | ||||
0.581105 | + | 0.813829i | \(0.302621\pi\) | |||||||
\(132\) | −0.348230 | −0.0303095 | ||||||||
\(133\) | 3.34549 | 0.290091 | ||||||||
\(134\) | 7.00849 | 0.605441 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.84020 | 0.243545 | ||||||||
\(137\) | 8.06136 | 0.688728 | 0.344364 | − | 0.938836i | \(-0.388095\pi\) | ||||
0.344364 | + | 0.938836i | \(0.388095\pi\) | |||||||
\(138\) | 2.45874 | 0.209302 | ||||||||
\(139\) | 12.4910 | 1.05947 | 0.529736 | − | 0.848163i | \(-0.322291\pi\) | ||||
0.529736 | + | 0.848163i | \(0.322291\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.79920 | 0.151520 | ||||||||
\(142\) | 6.73896 | 0.565521 | ||||||||
\(143\) | 0.575447 | 0.0481213 | ||||||||
\(144\) | −0.729296 | −0.0607747 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.1301 | −1.08666 | ||||||||
\(147\) | 2.74893 | 0.226728 | ||||||||
\(148\) | 5.75580 | 0.473124 | ||||||||
\(149\) | 5.21188 | 0.426974 | 0.213487 | − | 0.976946i | \(-0.431518\pi\) | ||||
0.213487 | + | 0.976946i | \(0.431518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.5386 | −1.42727 | −0.713634 | − | 0.700519i | \(-0.752952\pi\) | ||||
−0.713634 | + | 0.700519i | \(0.752952\pi\) | |||||||
\(152\) | 9.57539 | 0.776667 | ||||||||
\(153\) | 4.52163 | 0.365552 | ||||||||
\(154\) | −0.0944220 | −0.00760874 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.9813 | −1.43966 | ||||||||
\(157\) | −9.19231 | −0.733626 | −0.366813 | − | 0.930295i | \(-0.619551\pi\) | ||||
−0.366813 | + | 0.930295i | \(0.619551\pi\) | |||||||
\(158\) | −2.32245 | −0.184764 | ||||||||
\(159\) | −17.8433 | −1.41507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 1.70573 | 0.134015 | ||||||||
\(163\) | −1.98464 | −0.155449 | −0.0777245 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777245 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(164\) | 5.59042 | 0.436538 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.02385 | 0.0794662 | ||||||||
\(167\) | −10.9121 | −0.844402 | −0.422201 | − | 0.906502i | \(-0.638742\pi\) | ||||
−0.422201 | + | 0.906502i | \(0.638742\pi\) | |||||||
\(168\) | 7.86793 | 0.607024 | ||||||||
\(169\) | 16.7140 | 1.28569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.2441 | 1.16575 | ||||||||
\(172\) | −1.24791 | −0.0951523 | ||||||||
\(173\) | 3.69866 | 0.281204 | 0.140602 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140602 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(174\) | −12.0530 | −0.913736 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.0168961 | −0.00127359 | ||||||||
\(177\) | 12.5047 | 0.939913 | ||||||||
\(178\) | 12.7991 | 0.959336 | ||||||||
\(179\) | 10.7812 | 0.805824 | 0.402912 | − | 0.915239i | \(-0.367998\pi\) | ||||
0.402912 | + | 0.915239i | \(0.367998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.2211 | −1.05705 | −0.528523 | − | 0.848919i | \(-0.677254\pi\) | ||||
−0.528523 | + | 0.848919i | \(0.677254\pi\) | |||||||
\(182\) | −4.87561 | −0.361404 | ||||||||
\(183\) | 5.46723 | 0.404149 | ||||||||
\(184\) | −2.86218 | −0.211003 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.4437 | −0.765772 | ||||||||
\(187\) | 0.104755 | 0.00766048 | ||||||||
\(188\) | −0.785403 | −0.0572814 | ||||||||
\(189\) | 4.27905 | 0.311255 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6536 | 1.56680 | 0.783401 | − | 0.621516i | \(-0.213483\pi\) | ||||
0.783401 | + | 0.621516i | \(0.213483\pi\) | |||||||
\(192\) | 14.6026 | 1.05386 | ||||||||
\(193\) | −0.548943 | −0.0395138 | −0.0197569 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197569 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(194\) | −12.4733 | −0.895530 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.19999 | −0.0857134 | ||||||||
\(197\) | 4.73438 | 0.337311 | 0.168655 | − | 0.985675i | \(-0.446058\pi\) | ||||
0.168655 | + | 0.985675i | \(0.446058\pi\) | |||||||
\(198\) | −0.430245 | −0.0305762 | ||||||||
\(199\) | 22.7300 | 1.61129 | 0.805645 | − | 0.592398i | \(-0.201819\pi\) | ||||
0.805645 | + | 0.592398i | \(0.201819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.5397 | −1.51930 | ||||||||
\(202\) | −13.0299 | −0.916777 | ||||||||
\(203\) | 4.90211 | 0.344061 | ||||||||
\(204\) | −3.27335 | −0.229180 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.61725 | 0.670066 | ||||||||
\(207\) | −4.55662 | −0.316707 | ||||||||
\(208\) | −0.872452 | −0.0604937 | ||||||||
\(209\) | 0.353171 | 0.0244293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9600 | 1.64947 | 0.824737 | − | 0.565516i | \(-0.191323\pi\) | ||||
0.824737 | + | 0.565516i | \(0.191323\pi\) | |||||||
\(212\) | 7.78912 | 0.534959 | ||||||||
\(213\) | −20.7114 | −1.41912 | ||||||||
\(214\) | 1.93512 | 0.132282 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.2474 | 0.833330 | ||||||||
\(217\) | 4.24760 | 0.288346 | ||||||||
\(218\) | −8.74553 | −0.592322 | ||||||||
\(219\) | 40.3539 | 2.72686 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.40919 | 0.363862 | ||||||||
\(222\) | 11.7934 | 0.791524 | ||||||||
\(223\) | 25.6917 | 1.72045 | 0.860223 | − | 0.509918i | \(-0.170324\pi\) | ||||
0.860223 | + | 0.509918i | \(0.170324\pi\) | |||||||
\(224\) | −5.58120 | −0.372910 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.12749 | 0.540633 | ||||||||
\(227\) | −15.5244 | −1.03039 | −0.515194 | − | 0.857073i | \(-0.672280\pi\) | ||||
−0.515194 | + | 0.857073i | \(0.672280\pi\) | |||||||
\(228\) | −11.0357 | −0.730858 | ||||||||
\(229\) | −5.21342 | −0.344512 | −0.172256 | − | 0.985052i | \(-0.555106\pi\) | ||||
−0.172256 | + | 0.985052i | \(0.555106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.290194 | 0.0190934 | ||||||||
\(232\) | 14.0307 | 0.921162 | ||||||||
\(233\) | −8.88594 | −0.582137 | −0.291069 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291069 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(234\) | −22.2163 | −1.45233 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.45868 | −0.355330 | ||||||||
\(237\) | 7.13776 | 0.463648 | ||||||||
\(238\) | −0.887564 | −0.0575323 | ||||||||
\(239\) | −4.87067 | −0.315057 | −0.157529 | − | 0.987514i | \(-0.550353\pi\) | ||||
−0.157529 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0065 | 1.22432 | 0.612158 | − | 0.790735i | \(-0.290302\pi\) | ||||
0.612158 | + | 0.790735i | \(0.290302\pi\) | |||||||
\(242\) | 9.82880 | 0.631819 | ||||||||
\(243\) | −18.0795 | −1.15980 | ||||||||
\(244\) | −2.38660 | −0.152787 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.4546 | 0.730317 | ||||||||
\(247\) | 18.2365 | 1.16036 | ||||||||
\(248\) | 12.1574 | 0.771996 | ||||||||
\(249\) | −3.14668 | −0.199413 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8902 | 1.06610 | 0.533049 | − | 0.846085i | \(-0.321046\pi\) | ||||
0.533049 | + | 0.846085i | \(0.321046\pi\) | |||||||
\(252\) | −5.46789 | −0.344445 | ||||||||
\(253\) | −0.105566 | −0.00663689 | ||||||||
\(254\) | 5.15268 | 0.323308 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.3585 | −1.02241 | ||||||||
\(257\) | −18.9751 | −1.18363 | −0.591816 | − | 0.806073i | \(-0.701589\pi\) | ||||
−0.591816 | + | 0.806073i | \(0.701589\pi\) | |||||||
\(258\) | −2.55693 | −0.159187 | ||||||||
\(259\) | −4.79655 | −0.298043 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.3371 | 1.38263 | ||||||||
\(262\) | −11.8978 | −0.735051 | ||||||||
\(263\) | −10.4978 | −0.647322 | −0.323661 | − | 0.946173i | \(-0.604914\pi\) | ||||
−0.323661 | + | 0.946173i | \(0.604914\pi\) | |||||||
\(264\) | 0.830588 | 0.0511191 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.99232 | −0.183471 | ||||||||
\(267\) | −39.3366 | −2.40736 | ||||||||
\(268\) | 9.40272 | 0.574362 | ||||||||
\(269\) | −24.2817 | −1.48048 | −0.740242 | − | 0.672341i | \(-0.765289\pi\) | ||||
−0.740242 | + | 0.672341i | \(0.765289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.6852 | 1.92474 | 0.962369 | − | 0.271748i | \(-0.0876016\pi\) | ||||
0.962369 | + | 0.271748i | \(0.0876016\pi\) | |||||||
\(272\) | −0.158823 | −0.00963004 | ||||||||
\(273\) | 14.9846 | 0.906908 | ||||||||
\(274\) | −7.21035 | −0.435593 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.29869 | 0.198558 | ||||||||
\(277\) | 3.74125 | 0.224790 | 0.112395 | − | 0.993664i | \(-0.464148\pi\) | ||||
0.112395 | + | 0.993664i | \(0.464148\pi\) | |||||||
\(278\) | −11.1724 | −0.670074 | ||||||||
\(279\) | 19.3547 | 1.15874 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2875 | 0.792668 | 0.396334 | − | 0.918106i | \(-0.370282\pi\) | ||||
0.396334 | + | 0.918106i | \(0.370282\pi\) | |||||||
\(282\) | −1.60927 | −0.0958304 | ||||||||
\(283\) | −1.11900 | −0.0665175 | −0.0332588 | − | 0.999447i | \(-0.510589\pi\) | ||||
−0.0332588 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(284\) | 9.04111 | 0.536491 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.514700 | −0.0304348 | ||||||||
\(287\) | −4.65873 | −0.274996 | ||||||||
\(288\) | −25.4314 | −1.49856 | ||||||||
\(289\) | −16.0153 | −0.942077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.3351 | 2.24724 | ||||||||
\(292\) | −17.6156 | −1.03088 | ||||||||
\(293\) | 32.0399 | 1.87179 | 0.935895 | − | 0.352280i | \(-0.114593\pi\) | ||||
0.935895 | + | 0.352280i | \(0.114593\pi\) | |||||||
\(294\) | −2.45874 | −0.143396 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.7286 | −0.797957 | ||||||||
\(297\) | 0.451723 | 0.0262116 | ||||||||
\(298\) | −4.66169 | −0.270044 | ||||||||
\(299\) | −5.45106 | −0.315243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.03994 | 0.0599409 | ||||||||
\(302\) | 15.6871 | 0.902690 | ||||||||
\(303\) | 40.0456 | 2.30056 | ||||||||
\(304\) | −0.535452 | −0.0307103 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.04430 | −0.231197 | ||||||||
\(307\) | 12.6484 | 0.721882 | 0.360941 | − | 0.932589i | \(-0.382456\pi\) | ||||
0.360941 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(308\) | −0.126678 | −0.00721816 | ||||||||
\(309\) | −29.5574 | −1.68146 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.72436 | −0.0977792 | −0.0488896 | − | 0.998804i | \(-0.515568\pi\) | ||||
−0.0488896 | + | 0.998804i | \(0.515568\pi\) | |||||||
\(312\) | 42.8885 | 2.42808 | ||||||||
\(313\) | −24.1880 | −1.36719 | −0.683594 | − | 0.729862i | \(-0.739584\pi\) | ||||
−0.683594 | + | 0.729862i | \(0.739584\pi\) | |||||||
\(314\) | 8.22191 | 0.463989 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.11584 | −0.175280 | ||||||||
\(317\) | −13.4599 | −0.755981 | −0.377990 | − | 0.925810i | \(-0.623385\pi\) | ||||
−0.377990 | + | 0.925810i | \(0.623385\pi\) | |||||||
\(318\) | 15.9596 | 0.894972 | ||||||||
\(319\) | 0.517498 | 0.0289743 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.94736 | −0.331949 | ||||||||
\(322\) | 0.894434 | 0.0498448 | ||||||||
\(323\) | 3.31980 | 0.184718 | ||||||||
\(324\) | 2.28844 | 0.127136 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.77513 | 0.0983153 | ||||||||
\(327\) | 26.8783 | 1.48637 | ||||||||
\(328\) | −13.3341 | −0.736252 | ||||||||
\(329\) | 0.654509 | 0.0360843 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5428 | −1.23907 | −0.619533 | − | 0.784971i | \(-0.712678\pi\) | ||||
−0.619533 | + | 0.784971i | \(0.712678\pi\) | |||||||
\(332\) | 1.37362 | 0.0753870 | ||||||||
\(333\) | −21.8561 | −1.19770 | ||||||||
\(334\) | 9.76013 | 0.534051 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.439972 | −0.0240024 | ||||||||
\(337\) | −30.6253 | −1.66827 | −0.834133 | − | 0.551563i | \(-0.814031\pi\) | ||||
−0.834133 | + | 0.551563i | \(0.814031\pi\) | |||||||
\(338\) | −14.9496 | −0.813150 | ||||||||
\(339\) | −24.9788 | −1.35666 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.448404 | 0.0242824 | ||||||||
\(342\) | −13.6349 | −0.737290 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.97648 | 0.160481 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.30821 | −0.177850 | ||||||||
\(347\) | 7.50208 | 0.402733 | 0.201366 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201366 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(348\) | −16.1705 | −0.866831 | ||||||||
\(349\) | −25.2041 | −1.34915 | −0.674573 | − | 0.738208i | \(-0.735672\pi\) | ||||
−0.674573 | + | 0.738208i | \(0.735672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.3253 | 1.24501 | ||||||||
\(352\) | −0.589186 | −0.0314037 | ||||||||
\(353\) | −16.9097 | −0.900014 | −0.450007 | − | 0.893025i | \(-0.648579\pi\) | ||||
−0.450007 | + | 0.893025i | \(0.648579\pi\) | |||||||
\(354\) | −11.1847 | −0.594458 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.1716 | 0.910091 | ||||||||
\(357\) | 2.72782 | 0.144372 | ||||||||
\(358\) | −9.64306 | −0.509651 | ||||||||
\(359\) | −7.06904 | −0.373089 | −0.186545 | − | 0.982446i | \(-0.559729\pi\) | ||||
−0.186545 | + | 0.982446i | \(0.559729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.80769 | −0.410931 | ||||||||
\(362\) | 12.7198 | 0.668540 | ||||||||
\(363\) | −30.2076 | −1.58549 | ||||||||
\(364\) | −6.54120 | −0.342852 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.89007 | −0.255608 | ||||||||
\(367\) | 14.8103 | 0.773091 | 0.386545 | − | 0.922270i | \(-0.373668\pi\) | ||||
0.386545 | + | 0.922270i | \(0.373668\pi\) | |||||||
\(368\) | 0.160052 | 0.00834328 | ||||||||
\(369\) | −21.2281 | −1.10509 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.49099 | −0.336996 | ||||||||
\(372\) | −14.0115 | −0.726463 | ||||||||
\(373\) | 11.6664 | 0.604064 | 0.302032 | − | 0.953298i | \(-0.402335\pi\) | ||||
0.302032 | + | 0.953298i | \(0.402335\pi\) | |||||||
\(374\) | −0.0936968 | −0.00484495 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.87332 | 0.0966092 | ||||||||
\(377\) | 26.7217 | 1.37624 | ||||||||
\(378\) | −3.82733 | −0.196856 | ||||||||
\(379\) | −24.4621 | −1.25654 | −0.628268 | − | 0.777997i | \(-0.716236\pi\) | ||||
−0.628268 | + | 0.777997i | \(0.716236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8361 | −0.811309 | ||||||||
\(382\) | −19.3677 | −0.990940 | ||||||||
\(383\) | −38.7880 | −1.98197 | −0.990987 | − | 0.133958i | \(-0.957231\pi\) | ||||
−0.990987 | + | 0.133958i | \(0.957231\pi\) | |||||||
\(384\) | 17.6236 | 0.899349 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.490993 | 0.0249909 | ||||||||
\(387\) | 4.73860 | 0.240876 | ||||||||
\(388\) | −16.7344 | −0.849560 | ||||||||
\(389\) | −6.28408 | −0.318615 | −0.159308 | − | 0.987229i | \(-0.550926\pi\) | ||||
−0.159308 | + | 0.987229i | \(0.550926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.992320 | −0.0501838 | ||||||||
\(392\) | 2.86218 | 0.144562 | ||||||||
\(393\) | 36.5665 | 1.84454 | ||||||||
\(394\) | −4.23459 | −0.213336 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.577225 | −0.0290066 | ||||||||
\(397\) | −13.9347 | −0.699361 | −0.349681 | − | 0.936869i | \(-0.613710\pi\) | ||||
−0.349681 | + | 0.936869i | \(0.613710\pi\) | |||||||
\(398\) | −20.3305 | −1.01908 | ||||||||
\(399\) | 9.19652 | 0.460402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8441 | 0.891092 | 0.445546 | − | 0.895259i | \(-0.353010\pi\) | ||||
0.445546 | + | 0.895259i | \(0.353010\pi\) | |||||||
\(402\) | 19.2659 | 0.960894 | ||||||||
\(403\) | 23.1539 | 1.15338 | ||||||||
\(404\) | −17.4811 | −0.869716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.38462 | −0.217605 | ||||||||
\(407\) | −0.506353 | −0.0250990 | ||||||||
\(408\) | 7.80750 | 0.386529 | ||||||||
\(409\) | 32.6510 | 1.61449 | 0.807244 | − | 0.590218i | \(-0.200958\pi\) | ||||
0.807244 | + | 0.590218i | \(0.200958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.1601 | 1.09308 | ||||||||
\(412\) | 12.9027 | 0.635669 | ||||||||
\(413\) | 4.54894 | 0.223839 | ||||||||
\(414\) | 4.07560 | 0.200305 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.4234 | −1.49163 | ||||||||
\(417\) | 34.3369 | 1.68148 | ||||||||
\(418\) | −0.315888 | −0.0154506 | ||||||||
\(419\) | 19.2687 | 0.941336 | 0.470668 | − | 0.882311i | \(-0.344013\pi\) | ||||
0.470668 | + | 0.882311i | \(0.344013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9182 | −1.45813 | −0.729063 | − | 0.684447i | \(-0.760044\pi\) | ||||
−0.729063 | + | 0.684447i | \(0.760044\pi\) | |||||||
\(422\) | −21.4306 | −1.04323 | ||||||||
\(423\) | 2.98235 | 0.145007 | ||||||||
\(424\) | −18.5784 | −0.902246 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.5249 | 0.897537 | ||||||||
\(427\) | 1.98886 | 0.0962475 | ||||||||
\(428\) | 2.59619 | 0.125492 | ||||||||
\(429\) | 1.58187 | 0.0763732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.9497 | −1.92431 | −0.962154 | − | 0.272506i | \(-0.912147\pi\) | ||||
−0.962154 | + | 0.272506i | \(0.912147\pi\) | |||||||
\(432\) | −0.684870 | −0.0329508 | ||||||||
\(433\) | 37.4107 | 1.79784 | 0.898922 | − | 0.438109i | \(-0.144352\pi\) | ||||
0.898922 | + | 0.438109i | \(0.144352\pi\) | |||||||
\(434\) | −3.79920 | −0.182367 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7332 | −0.561916 | ||||||||
\(437\) | −3.34549 | −0.160037 | ||||||||
\(438\) | −36.0939 | −1.72463 | ||||||||
\(439\) | −15.5531 | −0.742309 | −0.371154 | − | 0.928571i | \(-0.621038\pi\) | ||||
−0.371154 | + | 0.928571i | \(0.621038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.55662 | 0.216982 | ||||||||
\(442\) | −4.83816 | −0.230128 | ||||||||
\(443\) | −9.08836 | −0.431801 | −0.215901 | − | 0.976415i | \(-0.569269\pi\) | ||||
−0.215901 | + | 0.976415i | \(0.569269\pi\) | |||||||
\(444\) | 15.8223 | 0.750893 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22.9796 | −1.08811 | ||||||||
\(447\) | 14.3271 | 0.677649 | ||||||||
\(448\) | 5.31212 | 0.250974 | ||||||||
\(449\) | 26.2809 | 1.24027 | 0.620137 | − | 0.784494i | \(-0.287077\pi\) | ||||
0.620137 | + | 0.784494i | \(0.287077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.491804 | −0.0231581 | ||||||||
\(452\) | 10.9040 | 0.512880 | ||||||||
\(453\) | −48.2123 | −2.26521 | ||||||||
\(454\) | 13.8855 | 0.651680 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 26.3221 | 1.23264 | ||||||||
\(457\) | −41.4567 | −1.93926 | −0.969631 | − | 0.244572i | \(-0.921353\pi\) | ||||
−0.969631 | + | 0.244572i | \(0.921353\pi\) | |||||||
\(458\) | 4.66306 | 0.217890 | ||||||||
\(459\) | 4.24619 | 0.198195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.9094 | 1.90534 | 0.952670 | − | 0.304007i | \(-0.0983248\pi\) | ||||
0.952670 | + | 0.304007i | \(0.0983248\pi\) | |||||||
\(462\) | −0.259560 | −0.0120758 | ||||||||
\(463\) | 37.9028 | 1.76149 | 0.880746 | − | 0.473589i | \(-0.157042\pi\) | ||||
0.880746 | + | 0.473589i | \(0.157042\pi\) | |||||||
\(464\) | −0.784593 | −0.0364238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.94789 | 0.368179 | ||||||||
\(467\) | −27.2246 | −1.25980 | −0.629901 | − | 0.776675i | \(-0.716905\pi\) | ||||
−0.629901 | + | 0.776675i | \(0.716905\pi\) | |||||||
\(468\) | −29.8058 | −1.37777 | ||||||||
\(469\) | −7.83567 | −0.361818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2690 | −1.16434 | ||||||||
\(472\) | 13.0199 | 0.599289 | ||||||||
\(473\) | 0.109782 | 0.00504779 | ||||||||
\(474\) | −6.38426 | −0.293239 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.19077 | −0.0545790 | ||||||||
\(477\) | −29.5770 | −1.35424 | ||||||||
\(478\) | 4.35649 | 0.199261 | ||||||||
\(479\) | −21.1158 | −0.964807 | −0.482404 | − | 0.875949i | \(-0.660236\pi\) | ||||
−0.482404 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1463 | −1.19217 | ||||||||
\(482\) | −17.0001 | −0.774331 | ||||||||
\(483\) | −2.74893 | −0.125081 | ||||||||
\(484\) | 13.1865 | 0.599386 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.1709 | 0.733528 | ||||||||
\(487\) | −5.36085 | −0.242923 | −0.121462 | − | 0.992596i | \(-0.538758\pi\) | ||||
−0.121462 | + | 0.992596i | \(0.538758\pi\) | |||||||
\(488\) | 5.69246 | 0.257685 | ||||||||
\(489\) | −5.45564 | −0.246713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.8541 | 1.39243 | 0.696214 | − | 0.717835i | \(-0.254867\pi\) | ||||
0.696214 | + | 0.717835i | \(0.254867\pi\) | |||||||
\(492\) | 15.3677 | 0.692828 | ||||||||
\(493\) | 4.86447 | 0.219084 | ||||||||
\(494\) | −16.3113 | −0.733880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.679837 | −0.0305256 | ||||||||
\(497\) | −7.53433 | −0.337961 | ||||||||
\(498\) | 2.81450 | 0.126121 | ||||||||
\(499\) | −35.0798 | −1.57039 | −0.785194 | − | 0.619250i | \(-0.787437\pi\) | ||||
−0.785194 | + | 0.619250i | \(0.787437\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.9966 | −1.34015 | ||||||||
\(502\) | −15.1071 | −0.674264 | ||||||||
\(503\) | 10.1362 | 0.451951 | 0.225975 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225975 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(504\) | 13.0419 | 0.580931 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.0944220 | 0.00419757 | ||||||||
\(507\) | 45.9457 | 2.04052 | ||||||||
\(508\) | 6.91292 | 0.306711 | ||||||||
\(509\) | 42.1170 | 1.86680 | 0.933402 | − | 0.358831i | \(-0.116825\pi\) | ||||
0.933402 | + | 0.358831i | \(0.116825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6798 | 0.649398 | ||||||||
\(512\) | 1.80948 | 0.0799683 | ||||||||
\(513\) | 14.3155 | 0.632046 | ||||||||
\(514\) | 16.9719 | 0.748600 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.43042 | −0.151016 | ||||||||
\(517\) | 0.0690941 | 0.00303875 | ||||||||
\(518\) | 4.29019 | 0.188500 | ||||||||
\(519\) | 10.1674 | 0.446298 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.3370 | 1.15384 | 0.576922 | − | 0.816799i | \(-0.304253\pi\) | ||||
0.576922 | + | 0.816799i | \(0.304253\pi\) | |||||||
\(522\) | −19.9790 | −0.874459 | ||||||||
\(523\) | 34.1189 | 1.49192 | 0.745959 | − | 0.665992i | \(-0.231992\pi\) | ||||
0.745959 | + | 0.665992i | \(0.231992\pi\) | |||||||
\(524\) | −15.9624 | −0.697319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.38959 | 0.409406 | ||||||||
\(527\) | 4.21498 | 0.183608 | ||||||||
\(528\) | −0.0464461 | −0.00202131 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.7278 | 0.899511 | ||||||||
\(532\) | −4.01455 | −0.174053 | ||||||||
\(533\) | −25.3950 | −1.09998 | ||||||||
\(534\) | 35.1840 | 1.52256 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −22.4271 | −0.968703 | ||||||||
\(537\) | 29.6367 | 1.27892 | ||||||||
\(538\) | 21.7184 | 0.936347 | ||||||||
\(539\) | 0.105566 | 0.00454706 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.65414 | −0.372071 | −0.186035 | − | 0.982543i | \(-0.559564\pi\) | ||||
−0.186035 | + | 0.982543i | \(0.559564\pi\) | |||||||
\(542\) | −28.3403 | −1.21732 | ||||||||
\(543\) | −39.0928 | −1.67763 | ||||||||
\(544\) | −5.53834 | −0.237454 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.4027 | −0.573583 | ||||||||
\(547\) | −32.4714 | −1.38838 | −0.694188 | − | 0.719794i | \(-0.744236\pi\) | ||||
−0.694188 | + | 0.719794i | \(0.744236\pi\) | |||||||
\(548\) | −9.67353 | −0.413233 | ||||||||
\(549\) | 9.06247 | 0.386777 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4000 | 0.698662 | ||||||||
\(552\) | −7.86793 | −0.334881 | ||||||||
\(553\) | 2.59656 | 0.110417 | ||||||||
\(554\) | −3.34630 | −0.142171 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.9890 | −0.635677 | ||||||||
\(557\) | 27.3673 | 1.15959 | 0.579795 | − | 0.814763i | \(-0.303133\pi\) | ||||
0.579795 | + | 0.814763i | \(0.303133\pi\) | |||||||
\(558\) | −17.3115 | −0.732855 | ||||||||
\(559\) | 5.66875 | 0.239763 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.287966 | 0.0121579 | ||||||||
\(562\) | −11.8848 | −0.501331 | ||||||||
\(563\) | −15.5666 | −0.656054 | −0.328027 | − | 0.944668i | \(-0.606384\pi\) | ||||
−0.328027 | + | 0.944668i | \(0.606384\pi\) | |||||||
\(564\) | −2.15902 | −0.0909111 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.00087 | 0.0420697 | ||||||||
\(567\) | −1.90705 | −0.0800888 | ||||||||
\(568\) | −21.5646 | −0.904831 | ||||||||
\(569\) | −21.6863 | −0.909139 | −0.454569 | − | 0.890711i | \(-0.650207\pi\) | ||||
−0.454569 | + | 0.890711i | \(0.650207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0809 | −0.756663 | −0.378332 | − | 0.925670i | \(-0.623502\pi\) | ||||
−0.378332 | + | 0.925670i | \(0.623502\pi\) | |||||||
\(572\) | −0.690530 | −0.0288725 | ||||||||
\(573\) | 59.5244 | 2.48667 | ||||||||
\(574\) | 4.16692 | 0.173924 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.2053 | 1.00855 | ||||||||
\(577\) | −6.88594 | −0.286666 | −0.143333 | − | 0.989675i | \(-0.545782\pi\) | ||||
−0.143333 | + | 0.989675i | \(0.545782\pi\) | |||||||
\(578\) | 14.3246 | 0.595826 | ||||||||
\(579\) | −1.50901 | −0.0627122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.14469 | −0.0474898 | ||||||||
\(582\) | −34.2882 | −1.42129 | ||||||||
\(583\) | −0.685230 | −0.0283793 | ||||||||
\(584\) | 42.0163 | 1.73865 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.6575 | −1.18383 | ||||||||
\(587\) | −11.6871 | −0.482377 | −0.241189 | − | 0.970478i | \(-0.577537\pi\) | ||||
−0.241189 | + | 0.970478i | \(0.577537\pi\) | |||||||
\(588\) | −3.29869 | −0.136035 | ||||||||
\(589\) | 14.2103 | 0.585526 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0145 | 0.535345 | ||||||||
\(592\) | 0.767697 | 0.0315521 | ||||||||
\(593\) | −36.3009 | −1.49070 | −0.745349 | − | 0.666675i | \(-0.767717\pi\) | ||||
−0.745349 | + | 0.666675i | \(0.767717\pi\) | |||||||
\(594\) | −0.404036 | −0.0165778 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.25420 | −0.256182 | ||||||||
\(597\) | 62.4833 | 2.55727 | ||||||||
\(598\) | 4.87561 | 0.199378 | ||||||||
\(599\) | 5.81197 | 0.237471 | 0.118735 | − | 0.992926i | \(-0.462116\pi\) | ||||
0.118735 | + | 0.992926i | \(0.462116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7463 | 0.642304 | 0.321152 | − | 0.947028i | \(-0.395930\pi\) | ||||
0.321152 | + | 0.947028i | \(0.395930\pi\) | |||||||
\(602\) | −0.930154 | −0.0379103 | ||||||||
\(603\) | −35.7042 | −1.45399 | ||||||||
\(604\) | 21.0461 | 0.856352 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.8182 | −1.45501 | ||||||||
\(607\) | −0.243389 | −0.00987884 | −0.00493942 | − | 0.999988i | \(-0.501572\pi\) | ||||
−0.00493942 | + | 0.999988i | \(0.501572\pi\) | |||||||
\(608\) | −18.6719 | −0.757244 | ||||||||
\(609\) | 13.4756 | 0.546058 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.56777 | 0.144336 | ||||||||
\(612\) | −5.42590 | −0.219329 | ||||||||
\(613\) | 20.8065 | 0.840367 | 0.420184 | − | 0.907439i | \(-0.361966\pi\) | ||||
0.420184 | + | 0.907439i | \(0.361966\pi\) | |||||||
\(614\) | −11.3131 | −0.456562 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.302149 | 0.0121739 | ||||||||
\(617\) | −37.9224 | −1.52670 | −0.763348 | − | 0.645987i | \(-0.776446\pi\) | ||||
−0.763348 | + | 0.645987i | \(0.776446\pi\) | |||||||
\(618\) | 26.4372 | 1.06346 | ||||||||
\(619\) | 12.8967 | 0.518363 | 0.259182 | − | 0.965829i | \(-0.416547\pi\) | ||||
0.259182 | + | 0.965829i | \(0.416547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.27905 | −0.171712 | ||||||||
\(622\) | 1.54232 | 0.0618415 | ||||||||
\(623\) | −14.3098 | −0.573309 | ||||||||
\(624\) | −2.39831 | −0.0960093 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.6346 | 0.864692 | ||||||||
\(627\) | 0.970842 | 0.0387717 | ||||||||
\(628\) | 11.0307 | 0.440171 | ||||||||
\(629\) | −4.75971 | −0.189782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.1013 | −0.441935 | −0.220968 | − | 0.975281i | \(-0.570922\pi\) | ||||
−0.220968 | + | 0.975281i | \(0.570922\pi\) | |||||||
\(632\) | 7.43181 | 0.295622 | ||||||||
\(633\) | 65.8644 | 2.61788 | ||||||||
\(634\) | 12.0389 | 0.478128 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 21.4117 | 0.849031 | ||||||||
\(637\) | 5.45106 | 0.215979 | ||||||||
\(638\) | −0.462867 | −0.0183251 | ||||||||
\(639\) | −34.3311 | −1.35812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.8356 | −1.84990 | −0.924948 | − | 0.380094i | \(-0.875892\pi\) | ||||
−0.924948 | + | 0.380094i | \(0.875892\pi\) | |||||||
\(642\) | 5.31952 | 0.209945 | ||||||||
\(643\) | −8.58083 | −0.338395 | −0.169198 | − | 0.985582i | \(-0.554118\pi\) | ||||
−0.169198 | + | 0.985582i | \(0.554118\pi\) | |||||||
\(644\) | 1.19999 | 0.0472862 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.96934 | −0.116827 | ||||||||
\(647\) | 11.1584 | 0.438683 | 0.219342 | − | 0.975648i | \(-0.429609\pi\) | ||||
0.219342 | + | 0.975648i | \(0.429609\pi\) | |||||||
\(648\) | −5.45833 | −0.214423 | ||||||||
\(649\) | 0.480215 | 0.0188501 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.6764 | 0.457633 | ||||||||
\(652\) | 2.38154 | 0.0932685 | ||||||||
\(653\) | −44.5017 | −1.74148 | −0.870742 | − | 0.491740i | \(-0.836361\pi\) | ||||
−0.870742 | + | 0.491740i | \(0.836361\pi\) | |||||||
\(654\) | −24.0409 | −0.940072 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.745638 | 0.0291123 | ||||||||
\(657\) | 66.8905 | 2.60965 | ||||||||
\(658\) | −0.585415 | −0.0228219 | ||||||||
\(659\) | 1.71592 | 0.0668429 | 0.0334214 | − | 0.999441i | \(-0.489360\pi\) | ||||
0.0334214 | + | 0.999441i | \(0.489360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0568 | 0.857909 | 0.428955 | − | 0.903326i | \(-0.358882\pi\) | ||||
0.428955 | + | 0.903326i | \(0.358882\pi\) | |||||||
\(662\) | 20.1631 | 0.783660 | ||||||||
\(663\) | 14.8695 | 0.577483 | ||||||||
\(664\) | −3.27631 | −0.127146 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.5488 | 0.757501 | ||||||||
\(667\) | −4.90211 | −0.189811 | ||||||||
\(668\) | 13.0944 | 0.506636 | ||||||||
\(669\) | 70.6248 | 2.73051 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.209956 | 0.00810526 | ||||||||
\(672\) | −15.3423 | −0.591843 | ||||||||
\(673\) | 46.0825 | 1.77635 | 0.888174 | − | 0.459507i | \(-0.151974\pi\) | ||||
0.888174 | + | 0.459507i | \(0.151974\pi\) | |||||||
\(674\) | 27.3923 | 1.05511 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.0566 | −0.771409 | ||||||||
\(677\) | −4.82917 | −0.185600 | −0.0928000 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928000 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(678\) | 22.3419 | 0.858036 | ||||||||
\(679\) | 13.9455 | 0.535177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.6754 | −1.63533 | ||||||||
\(682\) | −0.401067 | −0.0153577 | ||||||||
\(683\) | −8.90248 | −0.340644 | −0.170322 | − | 0.985388i | \(-0.554481\pi\) | ||||
−0.170322 | + | 0.985388i | \(0.554481\pi\) | |||||||
\(684\) | −18.2928 | −0.699442 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.894434 | −0.0341496 | ||||||||
\(687\) | −14.3313 | −0.546774 | ||||||||
\(688\) | −0.166444 | −0.00634561 | ||||||||
\(689\) | −35.3828 | −1.34798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.3804 | 1.68831 | 0.844154 | − | 0.536100i | \(-0.180103\pi\) | ||||
0.844154 | + | 0.536100i | \(0.180103\pi\) | |||||||
\(692\) | −4.43835 | −0.168721 | ||||||||
\(693\) | 0.481025 | 0.0182726 | ||||||||
\(694\) | −6.71011 | −0.254712 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 38.5695 | 1.46197 | ||||||||
\(697\) | −4.62295 | −0.175107 | ||||||||
\(698\) | 22.5434 | 0.853282 | ||||||||
\(699\) | −24.4268 | −0.923908 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.2952 | −1.18200 | −0.591001 | − | 0.806671i | \(-0.701267\pi\) | ||||
−0.591001 | + | 0.806671i | \(0.701267\pi\) | |||||||
\(702\) | −20.8630 | −0.787422 | ||||||||
\(703\) | −16.0468 | −0.605217 | ||||||||
\(704\) | 0.560780 | 0.0211352 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1246 | 0.569223 | ||||||||
\(707\) | 14.5677 | 0.547875 | ||||||||
\(708\) | −15.0055 | −0.563942 | ||||||||
\(709\) | −7.13517 | −0.267967 | −0.133983 | − | 0.990984i | \(-0.542777\pi\) | ||||
−0.133983 | + | 0.990984i | \(0.542777\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.8315 | 0.443718 | ||||||||
\(712\) | −40.9571 | −1.53493 | ||||||||
\(713\) | −4.24760 | −0.159074 | ||||||||
\(714\) | −2.43985 | −0.0913092 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.9373 | −0.483490 | ||||||||
\(717\) | −13.3891 | −0.500026 | ||||||||
\(718\) | 6.32278 | 0.235964 | ||||||||
\(719\) | 10.5820 | 0.394642 | 0.197321 | − | 0.980339i | \(-0.436776\pi\) | ||||
0.197321 | + | 0.980339i | \(0.436776\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7523 | −0.400438 | ||||||||
\(722\) | 6.98346 | 0.259898 | ||||||||
\(723\) | 52.2476 | 1.94311 | ||||||||
\(724\) | 17.0652 | 0.634221 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 27.0187 | 1.00276 | ||||||||
\(727\) | 12.7386 | 0.472448 | 0.236224 | − | 0.971699i | \(-0.424090\pi\) | ||||
0.236224 | + | 0.971699i | \(0.424090\pi\) | |||||||
\(728\) | 15.6019 | 0.578245 | ||||||||
\(729\) | −43.9782 | −1.62882 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.03195 | 0.0381680 | ||||||||
\(732\) | −6.56061 | −0.242487 | ||||||||
\(733\) | 41.1734 | 1.52078 | 0.760388 | − | 0.649470i | \(-0.225009\pi\) | ||||
0.760388 | + | 0.649470i | \(0.225009\pi\) | |||||||
\(734\) | −13.2468 | −0.488949 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.58120 | 0.205726 | ||||||||
\(737\) | −0.827182 | −0.0304697 | ||||||||
\(738\) | 18.9871 | 0.698924 | ||||||||
\(739\) | −27.3862 | −1.00742 | −0.503708 | − | 0.863874i | \(-0.668031\pi\) | ||||
−0.503708 | + | 0.863874i | \(0.668031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.1308 | 1.84160 | ||||||||
\(742\) | 5.80576 | 0.213136 | ||||||||
\(743\) | 9.70101 | 0.355895 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(744\) | 33.4199 | 1.22523 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.4348 | −0.382046 | ||||||||
\(747\) | −5.21593 | −0.190841 | ||||||||
\(748\) | −0.125705 | −0.00459624 | ||||||||
\(749\) | −2.16352 | −0.0790532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.6502 | 0.972479 | 0.486239 | − | 0.873826i | \(-0.338368\pi\) | ||||
0.486239 | + | 0.873826i | \(0.338368\pi\) | |||||||
\(752\) | −0.104755 | −0.00382004 | ||||||||
\(753\) | 46.4299 | 1.69200 | ||||||||
\(754\) | −23.9008 | −0.870416 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.13481 | −0.186751 | ||||||||
\(757\) | −1.79649 | −0.0652945 | −0.0326472 | − | 0.999467i | \(-0.510394\pi\) | ||||
−0.0326472 | + | 0.999467i | \(0.510394\pi\) | |||||||
\(758\) | 21.8798 | 0.794709 | ||||||||
\(759\) | −0.290194 | −0.0105334 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9320 | −0.831285 | −0.415643 | − | 0.909528i | \(-0.636443\pi\) | ||||
−0.415643 | + | 0.909528i | \(0.636443\pi\) | |||||||
\(762\) | 14.1644 | 0.513121 | ||||||||
\(763\) | 9.77772 | 0.353977 | ||||||||
\(764\) | −25.9841 | −0.940072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.6933 | 1.25352 | ||||||||
\(767\) | 24.7965 | 0.895351 | ||||||||
\(768\) | −44.9684 | −1.62266 | ||||||||
\(769\) | −22.5274 | −0.812358 | −0.406179 | − | 0.913794i | \(-0.633139\pi\) | ||||
−0.406179 | + | 0.913794i | \(0.633139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.1611 | −1.87854 | ||||||||
\(772\) | 0.658725 | 0.0237080 | ||||||||
\(773\) | 19.8671 | 0.714571 | 0.357285 | − | 0.933995i | \(-0.383702\pi\) | ||||
0.357285 | + | 0.933995i | \(0.383702\pi\) | |||||||
\(774\) | −4.23836 | −0.152345 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 39.9144 | 1.43284 | ||||||||
\(777\) | −13.1854 | −0.473023 | ||||||||
\(778\) | 5.62069 | 0.201512 | ||||||||
\(779\) | −15.5857 | −0.558416 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.795371 | −0.0284606 | ||||||||
\(782\) | 0.887564 | 0.0317392 | ||||||||
\(783\) | 20.9764 | 0.749635 | ||||||||
\(784\) | −0.160052 | −0.00571614 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.7063 | −1.16660 | ||||||||
\(787\) | 41.8042 | 1.49016 | 0.745080 | − | 0.666975i | \(-0.232411\pi\) | ||||
0.745080 | + | 0.666975i | \(0.232411\pi\) | |||||||
\(788\) | −5.68120 | −0.202384 | ||||||||
\(789\) | −28.8577 | −1.02736 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.08674 | −0.323087 | ||||||||
\(792\) | 1.37678 | 0.0489218 | ||||||||
\(793\) | 10.8414 | 0.384988 | ||||||||
\(794\) | 12.4636 | 0.442318 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2758 | −0.966765 | ||||||||
\(797\) | −28.2806 | −1.00175 | −0.500874 | − | 0.865520i | \(-0.666988\pi\) | ||||
−0.500874 | + | 0.865520i | \(0.666988\pi\) | |||||||
\(798\) | −8.22568 | −0.291186 | ||||||||
\(799\) | 0.649483 | 0.0229770 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −65.2042 | −2.30388 | ||||||||
\(802\) | −15.9604 | −0.563580 | ||||||||
\(803\) | 1.54969 | 0.0546875 | ||||||||
\(804\) | 25.8474 | 0.911568 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.7097 | −0.729467 | ||||||||
\(807\) | −66.7488 | −2.34967 | ||||||||
\(808\) | 41.6954 | 1.46684 | ||||||||
\(809\) | 24.8076 | 0.872188 | 0.436094 | − | 0.899901i | \(-0.356362\pi\) | ||||
0.436094 | + | 0.899901i | \(0.356362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.1988 | −0.919965 | −0.459982 | − | 0.887928i | \(-0.652144\pi\) | ||||
−0.459982 | + | 0.887928i | \(0.652144\pi\) | |||||||
\(812\) | −5.88248 | −0.206435 | ||||||||
\(813\) | 87.1004 | 3.05474 | ||||||||
\(814\) | 0.452900 | 0.0158741 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.436593 | −0.0152838 | ||||||||
\(817\) | 3.47910 | 0.121718 | ||||||||
\(818\) | −29.2041 | −1.02110 | ||||||||
\(819\) | 24.8384 | 0.867924 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1447 | −0.423854 | −0.211927 | − | 0.977286i | \(-0.567974\pi\) | ||||
−0.211927 | + | 0.977286i | \(0.567974\pi\) | |||||||
\(822\) | −19.8208 | −0.691328 | ||||||||
\(823\) | 7.29212 | 0.254187 | 0.127094 | − | 0.991891i | \(-0.459435\pi\) | ||||
0.127094 | + | 0.991891i | \(0.459435\pi\) | |||||||
\(824\) | −30.7751 | −1.07210 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.06873 | −0.141569 | ||||||||
\(827\) | 24.8806 | 0.865182 | 0.432591 | − | 0.901590i | \(-0.357600\pi\) | ||||
0.432591 | + | 0.901590i | \(0.357600\pi\) | |||||||
\(828\) | 5.46789 | 0.190022 | ||||||||
\(829\) | 49.8882 | 1.73269 | 0.866344 | − | 0.499447i | \(-0.166463\pi\) | ||||
0.866344 | + | 0.499447i | \(0.166463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2844 | 0.356763 | ||||||||
\(832\) | 28.9567 | 1.00389 | ||||||||
\(833\) | 0.992320 | 0.0343818 | ||||||||
\(834\) | −30.7121 | −1.06347 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.423801 | −0.0146575 | ||||||||
\(837\) | 18.1757 | 0.628245 | ||||||||
\(838\) | −17.2345 | −0.595357 | ||||||||
\(839\) | −31.0352 | −1.07146 | −0.535728 | − | 0.844391i | \(-0.679963\pi\) | ||||
−0.535728 | + | 0.844391i | \(0.679963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.96928 | −0.171354 | ||||||||
\(842\) | 26.7599 | 0.922206 | ||||||||
\(843\) | 36.5265 | 1.25804 | ||||||||
\(844\) | −28.7517 | −0.989675 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.66752 | −0.0917111 | ||||||||
\(847\) | −10.9889 | −0.377582 | ||||||||
\(848\) | 1.03890 | 0.0356758 | ||||||||
\(849\) | −3.07605 | −0.105570 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.79655 | 0.164424 | ||||||||
\(852\) | 24.8534 | 0.851463 | ||||||||
\(853\) | 7.50702 | 0.257035 | 0.128518 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128518 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(854\) | −1.77890 | −0.0608727 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.19237 | −0.211651 | ||||||||
\(857\) | −40.9999 | −1.40053 | −0.700266 | − | 0.713882i | \(-0.746935\pi\) | ||||
−0.700266 | + | 0.713882i | \(0.746935\pi\) | |||||||
\(858\) | −1.41487 | −0.0483030 | ||||||||
\(859\) | −20.3735 | −0.695134 | −0.347567 | − | 0.937655i | \(-0.612992\pi\) | ||||
−0.347567 | + | 0.937655i | \(0.612992\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.8065 | −0.436445 | ||||||||
\(862\) | 35.7323 | 1.21705 | ||||||||
\(863\) | −17.5109 | −0.596077 | −0.298039 | − | 0.954554i | \(-0.596332\pi\) | ||||
−0.298039 | + | 0.954554i | \(0.596332\pi\) | |||||||
\(864\) | −23.8822 | −0.812490 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −33.4614 | −1.13706 | ||||||||
\(867\) | −44.0250 | −1.49517 | ||||||||
\(868\) | −5.09708 | −0.173006 | ||||||||
\(869\) | 0.274109 | 0.00929851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.7127 | −1.44726 | ||||||||
\(872\) | 27.9856 | 0.947711 | ||||||||
\(873\) | 63.5442 | 2.15064 | ||||||||
\(874\) | 2.99232 | 0.101217 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −48.4242 | −1.63610 | ||||||||
\(877\) | −12.2828 | −0.414761 | −0.207381 | − | 0.978260i | \(-0.566494\pi\) | ||||
−0.207381 | + | 0.978260i | \(0.566494\pi\) | |||||||
\(878\) | 13.9112 | 0.469481 | ||||||||
\(879\) | 88.0754 | 2.97071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.3811 | −1.69738 | −0.848691 | − | 0.528889i | \(-0.822609\pi\) | ||||
−0.848691 | + | 0.528889i | \(0.822609\pi\) | |||||||
\(882\) | −4.07560 | −0.137233 | ||||||||
\(883\) | −38.3258 | −1.28977 | −0.644883 | − | 0.764281i | \(-0.723094\pi\) | ||||
−0.644883 | + | 0.764281i | \(0.723094\pi\) | |||||||
\(884\) | −6.49097 | −0.218315 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.12894 | 0.273097 | ||||||||
\(887\) | −6.35245 | −0.213294 | −0.106647 | − | 0.994297i | \(-0.534012\pi\) | ||||
−0.106647 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(888\) | −37.7389 | −1.26643 | ||||||||
\(889\) | −5.76083 | −0.193212 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.201321 | −0.00674449 | ||||||||
\(892\) | −30.8298 | −1.03226 | ||||||||
\(893\) | 2.18965 | 0.0732740 | ||||||||
\(894\) | −12.8147 | −0.428586 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.41106 | 0.214179 | ||||||||
\(897\) | −14.9846 | −0.500321 | ||||||||
\(898\) | −23.5065 | −0.784423 | ||||||||
\(899\) | 20.8222 | 0.694461 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.44114 | −0.214586 | ||||||||
\(902\) | 0.439886 | 0.0146466 | ||||||||
\(903\) | 2.85871 | 0.0951320 | ||||||||
\(904\) | −26.0079 | −0.865009 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 43.1227 | 1.43266 | ||||||||
\(907\) | −46.6929 | −1.55041 | −0.775205 | − | 0.631709i | \(-0.782354\pi\) | ||||
−0.775205 | + | 0.631709i | \(0.782354\pi\) | |||||||
\(908\) | 18.6291 | 0.618227 | ||||||||
\(909\) | 66.3796 | 2.20167 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3014 | −0.506957 | −0.253478 | − | 0.967341i | \(-0.581575\pi\) | ||||
−0.253478 | + | 0.967341i | \(0.581575\pi\) | |||||||
\(912\) | −1.47192 | −0.0487402 | ||||||||
\(913\) | −0.120841 | −0.00399925 | ||||||||
\(914\) | 37.0803 | 1.22651 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.25604 | 0.206705 | ||||||||
\(917\) | 13.3021 | 0.439274 | ||||||||
\(918\) | −3.79793 | −0.125350 | ||||||||
\(919\) | −26.2441 | −0.865712 | −0.432856 | − | 0.901463i | \(-0.642494\pi\) | ||||
−0.432856 | + | 0.901463i | \(0.642494\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.7696 | 1.14570 | ||||||||
\(922\) | −36.5907 | −1.20505 | ||||||||
\(923\) | −41.0701 | −1.35184 | ||||||||
\(924\) | −0.348230 | −0.0114559 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.9015 | −1.11407 | ||||||||
\(927\) | −48.9943 | −1.60919 | ||||||||
\(928\) | −27.3597 | −0.898125 | ||||||||
\(929\) | −16.8945 | −0.554289 | −0.277145 | − | 0.960828i | \(-0.589388\pi\) | ||||
−0.277145 | + | 0.960828i | \(0.589388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.34549 | 0.109644 | ||||||||
\(932\) | 10.6630 | 0.349279 | ||||||||
\(933\) | −4.74013 | −0.155185 | ||||||||
\(934\) | 24.3506 | 0.796775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 71.0919 | 2.32371 | ||||||||
\(937\) | 14.2506 | 0.465548 | 0.232774 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232774 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(938\) | 7.00849 | 0.228835 | ||||||||
\(939\) | −66.4912 | −2.16986 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.36666 | −0.142349 | −0.0711746 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711746 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(942\) | 22.6015 | 0.736396 | ||||||||
\(943\) | 4.65873 | 0.151709 | ||||||||
\(944\) | −0.728067 | −0.0236966 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0981929 | −0.00319253 | ||||||||
\(947\) | −45.9017 | −1.49160 | −0.745802 | − | 0.666167i | \(-0.767934\pi\) | ||||
−0.745802 | + | 0.666167i | \(0.767934\pi\) | |||||||
\(948\) | −8.56523 | −0.278186 | ||||||||
\(949\) | 80.0206 | 2.59758 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.0002 | −1.19981 | ||||||||
\(952\) | 2.84020 | 0.0920513 | ||||||||
\(953\) | 32.4179 | 1.05012 | 0.525060 | − | 0.851065i | \(-0.324043\pi\) | ||||
0.525060 | + | 0.851065i | \(0.324043\pi\) | |||||||
\(954\) | 26.4547 | 0.856502 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.84474 | 0.189033 | ||||||||
\(957\) | 1.42257 | 0.0459850 | ||||||||
\(958\) | 18.8867 | 0.610202 | ||||||||
\(959\) | 8.06136 | 0.260315 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9579 | −0.417995 | ||||||||
\(962\) | 23.3861 | 0.753998 | ||||||||
\(963\) | −9.85833 | −0.317680 | ||||||||
\(964\) | −22.8076 | −0.734583 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.45874 | 0.0791086 | ||||||||
\(967\) | 44.8564 | 1.44248 | 0.721242 | − | 0.692683i | \(-0.243572\pi\) | ||||
0.721242 | + | 0.692683i | \(0.243572\pi\) | |||||||
\(968\) | −31.4521 | −1.01091 | ||||||||
\(969\) | 9.12589 | 0.293166 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.7244 | 0.344163 | 0.172081 | − | 0.985083i | \(-0.444951\pi\) | ||||
0.172081 | + | 0.985083i | \(0.444951\pi\) | |||||||
\(972\) | 21.6952 | 0.695874 | ||||||||
\(973\) | 12.4910 | 0.400443 | ||||||||
\(974\) | 4.79493 | 0.153639 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.318320 | −0.0101892 | ||||||||
\(977\) | −30.9305 | −0.989554 | −0.494777 | − | 0.869020i | \(-0.664750\pi\) | ||||
−0.494777 | + | 0.869020i | \(0.664750\pi\) | |||||||
\(978\) | 4.87971 | 0.156036 | ||||||||
\(979\) | −1.51063 | −0.0482799 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.5534 | 1.42248 | ||||||||
\(982\) | −27.5970 | −0.880655 | ||||||||
\(983\) | −24.0480 | −0.767012 | −0.383506 | − | 0.923538i | \(-0.625283\pi\) | ||||
−0.383506 | + | 0.923538i | \(0.625283\pi\) | |||||||
\(984\) | −36.6545 | −1.16850 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.35094 | −0.138562 | ||||||||
\(987\) | 1.79920 | 0.0572692 | ||||||||
\(988\) | −21.8835 | −0.696208 | ||||||||
\(989\) | −1.03994 | −0.0330681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.92365 | 0.251703 | 0.125852 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125852 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(992\) | −23.7067 | −0.752689 | ||||||||
\(993\) | −61.9687 | −1.96652 | ||||||||
\(994\) | 6.73896 | 0.213747 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.77598 | 0.119646 | ||||||||
\(997\) | −0.0645124 | −0.00204313 | −0.00102156 | − | 0.999999i | \(-0.500325\pi\) | ||||
−0.00102156 | + | 0.999999i | \(0.500325\pi\) | |||||||
\(998\) | 31.3766 | 0.993208 | ||||||||
\(999\) | −20.5247 | −0.649372 |
(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 | 4025.2.a.n.1.2 | 4 | ||
5.4 | even | 2 | 805.2.a.h.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 7245.2.a.be.1.2 | 4 | |||
35.34 | odd | 2 | 5635.2.a.t.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.h.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
4025.2.a.n.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5635.2.a.t.1.3 | 4 | 35.34 | odd | 2 | |||
7245.2.a.be.1.2 | 4 | 15.14 | odd | 2 |