Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.561553 | −0.155747 | −0.0778734 | − | 0.996963i | \(-0.524813\pi\) | ||||
−0.0778734 | + | 0.996963i | \(0.524813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.56155 | −0.378732 | −0.189366 | − | 0.981907i | \(-0.560643\pi\) | ||||
−0.189366 | + | 0.981907i | \(0.560643\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.12311 | 0.394251 | 0.197125 | − | 0.980378i | \(-0.436839\pi\) | ||||
0.197125 | + | 0.980378i | \(0.436839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.24621 | −1.66067 | −0.830334 | − | 0.557266i | \(-0.811851\pi\) | ||||
−0.830334 | + | 0.557266i | \(0.811851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.12311 | 0.891818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.56155 | 0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.438447 | 0.0720803 | 0.0360401 | − | 0.999350i | \(-0.488526\pi\) | ||||
0.0360401 | + | 0.999350i | \(0.488526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.43845 | 0.230336 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.12311 | −0.643921 | −0.321960 | − | 0.946753i | \(-0.604342\pi\) | ||||
−0.321960 | + | 0.946753i | \(0.604342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.56155 | −0.530925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.68466 | −1.12092 | −0.560461 | − | 0.828181i | \(-0.689376\pi\) | ||||
−0.560461 | + | 0.828181i | \(0.689376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.438447 | 0.0602254 | 0.0301127 | − | 0.999547i | \(-0.490413\pi\) | ||||
0.0301127 | + | 0.999547i | \(0.490413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.3693 | 2.03572 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.68466 | −1.13065 | −0.565323 | − | 0.824870i | \(-0.691249\pi\) | ||||
−0.565323 | + | 0.824870i | \(0.691249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12311 | −0.143799 | −0.0718995 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0718995 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.56155 | −0.700690 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.561553 | 0.0696521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.43845 | 0.542243 | 0.271121 | − | 0.962545i | \(-0.412606\pi\) | ||||
0.271121 | + | 0.962545i | \(0.412606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.56155 | −0.308375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.87689 | 0.222746 | 0.111373 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111373 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.56155 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.12311 | 0.355911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.1231 | 1.47646 | 0.738232 | − | 0.674546i | \(-0.235661\pi\) | ||||
0.738232 | + | 0.674546i | \(0.235661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.9309 | −1.63888 | −0.819438 | − | 0.573168i | \(-0.805714\pi\) | ||||
−0.819438 | + | 0.573168i | \(0.805714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56155 | 0.169374 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.43845 | −0.583063 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.24621 | −0.238098 | −0.119049 | − | 0.992888i | \(-0.537985\pi\) | ||||
−0.119049 | + | 0.992888i | \(0.537985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.876894 | 0.0919235 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.6847 | 2.45598 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.87689 | −0.495174 | −0.247587 | − | 0.968866i | \(-0.579638\pi\) | ||||
−0.247587 | + | 0.968866i | \(0.579638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.12311 | −0.715899 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.31534 | 0.528896 | 0.264448 | − | 0.964400i | \(-0.414810\pi\) | ||||
0.264448 | + | 0.964400i | \(0.414810\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.56155 | −0.731003 | −0.365501 | − | 0.930811i | \(-0.619102\pi\) | ||||
−0.365501 | + | 0.930811i | \(0.619102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.36932 | 0.897418 | 0.448709 | − | 0.893678i | \(-0.351884\pi\) | ||||
0.448709 | + | 0.893678i | \(0.351884\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.12311 | −0.106600 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.80776 | −0.734493 | −0.367246 | − | 0.930124i | \(-0.619699\pi\) | ||||
−0.367246 | + | 0.930124i | \(0.619699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.43845 | 0.223532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5616 | 0.952303 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8078 | −1.13651 | −0.568253 | − | 0.822854i | \(-0.692380\pi\) | ||||
−0.568253 | + | 0.822854i | \(0.692380\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.8078 | −1.81798 | −0.908991 | − | 0.416815i | \(-0.863146\pi\) | ||||
−0.908991 | + | 0.416815i | \(0.863146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.36932 | 0.812423 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.43845 | 0.123802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1231 | 1.29205 | 0.646027 | − | 0.763315i | \(-0.276429\pi\) | ||||
0.646027 | + | 0.763315i | \(0.276429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.24621 | −0.444978 | −0.222489 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222489 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.6847 | 1.65775 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.12311 | 0.0939188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.12311 | −0.176314 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.6847 | 0.963734 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3693 | −1.25910 | −0.629552 | − | 0.776959i | \(-0.716761\pi\) | ||||
−0.629552 | + | 0.776959i | \(0.716761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.0540 | 1.87611 | 0.938053 | − | 0.346492i | \(-0.112627\pi\) | ||||
0.938053 | + | 0.346492i | \(0.112627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.56155 | −0.449625 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.24621 | 0.742674 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6847 | 1.33158 | 0.665790 | − | 0.746139i | \(-0.268095\pi\) | ||||
0.665790 | + | 0.746139i | \(0.268095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.12311 | −0.0890681 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.56155 | −0.123068 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.9309 | 0.934498 | 0.467249 | − | 0.884126i | \(-0.345245\pi\) | ||||
0.467249 | + | 0.884126i | \(0.345245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.12311 | −0.398833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.3693 | −1.63415 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3693 | 1.47262 | 0.736311 | − | 0.676643i | \(-0.236566\pi\) | ||||
0.736311 | + | 0.676643i | \(0.236566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56155 | −0.118042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.2462 | 1.67213 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9309 | −1.63919 | −0.819595 | − | 0.572943i | \(-0.805802\pi\) | ||||
−0.819595 | + | 0.572943i | \(0.805802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.3693 | −1.43971 | −0.719855 | − | 0.694124i | \(-0.755792\pi\) | ||||
−0.719855 | + | 0.694124i | \(0.755792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.87689 | 0.212666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.438447 | −0.0322353 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.12311 | 0.228384 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.24621 | 0.163388 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.36932 | −0.533225 | −0.266613 | − | 0.963804i | \(-0.585904\pi\) | ||||
−0.266613 | + | 0.963804i | \(0.585904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.56155 | 0.472311 | 0.236155 | − | 0.971715i | \(-0.424113\pi\) | ||||
0.236155 | + | 0.971715i | \(0.424113\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.43845 | −0.103009 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.31534 | 0.449949 | 0.224975 | − | 0.974365i | \(-0.427770\pi\) | ||||
0.224975 | + | 0.974365i | \(0.427770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3693 | −0.801930 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.31534 | −0.232691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.12311 | 0.287970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.56155 | 0.247545 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6847 | −0.873248 | −0.436624 | − | 0.899644i | \(-0.643826\pi\) | ||||
−0.436624 | + | 0.899644i | \(0.643826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.80776 | −0.329423 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4384 | 0.980146 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.9309 | 1.48195 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.876894 | 0.0589863 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6155 | 1.58141 | 0.790706 | − | 0.612196i | \(-0.209713\pi\) | ||||
0.790706 | + | 0.612196i | \(0.209713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.75379 | −0.647382 | −0.323691 | − | 0.946163i | \(-0.604924\pi\) | ||||
−0.323691 | + | 0.946163i | \(0.604924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.7386 | −1.50261 | −0.751306 | − | 0.659954i | \(-0.770576\pi\) | ||||
−0.751306 | + | 0.659954i | \(0.770576\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6847 | 0.765487 | 0.382744 | − | 0.923855i | \(-0.374979\pi\) | ||||
0.382744 | + | 0.923855i | \(0.374979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.68466 | 0.501292 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.6155 | −2.18356 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2462 | 1.24493 | 0.622467 | − | 0.782646i | \(-0.286131\pi\) | ||||
0.622467 | + | 0.782646i | \(0.286131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.56155 | 0.291427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.36932 | 0.214384 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.2462 | 2.42376 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3693 | −1.09634 | −0.548171 | − | 0.836366i | \(-0.684676\pi\) | ||||
−0.548171 | + | 0.836366i | \(0.684676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.1922 | 0.698152 | 0.349076 | − | 0.937094i | \(-0.386495\pi\) | ||||
0.349076 | + | 0.937094i | \(0.386495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.684658 | −0.0425426 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.56155 | 0.468048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.9309 | 1.78395 | 0.891977 | − | 0.452081i | \(-0.149318\pi\) | ||||
0.891977 | + | 0.452081i | \(0.149318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.438447 | −0.0269336 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.75379 | 0.352126 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.75379 | −0.411786 | −0.205893 | − | 0.978575i | \(-0.566010\pi\) | ||||
−0.205893 | + | 0.978575i | \(0.566010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.93087 | −0.421020 | −0.210510 | − | 0.977592i | \(-0.567513\pi\) | ||||
−0.210510 | + | 0.977592i | \(0.567513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.24621 | −0.135947 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.68466 | −0.341558 | −0.170779 | − | 0.985309i | \(-0.554628\pi\) | ||||
−0.170779 | + | 0.985309i | \(0.554628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −32.9309 | −1.97152 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1231 | −0.902169 | −0.451084 | − | 0.892481i | \(-0.648963\pi\) | ||||
−0.451084 | + | 0.892481i | \(0.648963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.80776 | 0.345236 | 0.172618 | − | 0.984989i | \(-0.444777\pi\) | ||||
0.172618 | + | 0.984989i | \(0.444777\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.3693 | −0.910400 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.43845 | 0.380050 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5616 | −0.856562 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.4924 | 0.732319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.80776 | −0.222452 | −0.111226 | − | 0.993795i | \(-0.535478\pi\) | ||||
−0.111226 | + | 0.993795i | \(0.535478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.68466 | 0.505640 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.87689 | 0.166934 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.561553 | −0.0324754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.6155 | −0.782192 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.12311 | 0.0643088 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8769 | 0.734923 | 0.367462 | − | 0.930039i | \(-0.380227\pi\) | ||||
0.367462 | + | 0.930039i | \(0.380227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.9848 | 2.33155 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.68466 | −0.208938 | −0.104469 | − | 0.994528i | \(-0.533314\pi\) | ||||
−0.104469 | + | 0.994528i | \(0.533314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8078 | 1.11960 | 0.559801 | − | 0.828627i | \(-0.310878\pi\) | ||||
0.559801 | + | 0.828627i | \(0.310878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.56155 | 0.313358 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.87689 | −0.386245 | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193122 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.24621 | −0.237742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.3693 | 1.08109 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.36932 | 0.521323 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.561553 | −0.0311493 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0000 | −1.32720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6155 | 0.693412 | 0.346706 | − | 0.937974i | \(-0.387300\pi\) | ||||
0.346706 | + | 0.937974i | \(0.387300\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.56155 | 0.0855726 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.43845 | −0.242498 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.6155 | −1.50431 | −0.752157 | − | 0.658984i | \(-0.770986\pi\) | ||||
−0.752157 | + | 0.658984i | \(0.770986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0000 | 1.08625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.4924 | 1.00142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.56155 | 0.137909 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4924 | 0.885360 | 0.442680 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442680 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.63068 | 0.0872885 | 0.0436442 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436442 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.807764 | 0.0431153 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.0540 | 1.86573 | 0.932867 | − | 0.360220i | \(-0.117298\pi\) | ||||
0.932867 | + | 0.360220i | \(0.117298\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.87689 | −0.0996152 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.24621 | −0.330585 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.6155 | −1.35194 | −0.675968 | − | 0.736931i | \(-0.736274\pi\) | ||||
−0.675968 | + | 0.736931i | \(0.736274\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.9309 | 0.941127 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.56155 | 0.448132 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.4384 | −0.962479 | −0.481240 | − | 0.876589i | \(-0.659813\pi\) | ||||
−0.481240 | + | 0.876589i | \(0.659813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.6847 | −0.764453 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.684658 | −0.0355457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.75379 | 0.194364 | 0.0971819 | − | 0.995267i | \(-0.469017\pi\) | ||||
0.0971819 | + | 0.995267i | \(0.469017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.56155 | 0.132278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.19224 | −0.0614033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.50758 | 0.180172 | 0.0900861 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900861 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.8078 | 1.68079 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8078 | 1.21652 | 0.608260 | − | 0.793738i | \(-0.291868\pi\) | ||||
0.608260 | + | 0.793738i | \(0.291868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.12311 | −0.159168 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.1231 | 0.969580 | 0.484790 | − | 0.874631i | \(-0.338896\pi\) | ||||
0.484790 | + | 0.874631i | \(0.338896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.56155 | −0.0789711 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 53.3002 | 2.68864 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1231 | −0.660295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.5464 | 1.78402 | 0.892011 | − | 0.452013i | \(-0.149294\pi\) | ||||
0.892011 | + | 0.452013i | \(0.149294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.0000 | −1.20150 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.19224 | 0.258644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.876894 | −0.0434660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9848 | 1.48266 | 0.741328 | − | 0.671143i | \(-0.234197\pi\) | ||||
0.741328 | + | 0.671143i | \(0.234197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.7386 | −1.91084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.5616 | 0.667320 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.9309 | 0.732928 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4384 | 0.658084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.1231 | 1.32505 | 0.662525 | − | 0.749040i | \(-0.269485\pi\) | ||||
0.662525 | + | 0.749040i | \(0.269485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8769 | −0.822530 | −0.411265 | − | 0.911516i | \(-0.634913\pi\) | ||||
−0.411265 | + | 0.911516i | \(0.634913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.3693 | −1.33074 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.56155 | −0.0757464 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.75379 | 0.0848718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.87689 | −0.138898 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.24621 | 0.300869 | 0.150435 | − | 0.988620i | \(-0.451933\pi\) | ||||
0.150435 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0691 | 0.531948 | 0.265974 | − | 0.963980i | \(-0.414306\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.43845 | 0.260754 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.807764 | −0.0385525 | −0.0192762 | − | 0.999814i | \(-0.506136\pi\) | ||||
−0.0192762 | + | 0.999814i | \(0.506136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.2462 | −0.773629 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.80776 | −0.418469 | −0.209235 | − | 0.977865i | \(-0.567097\pi\) | ||||
−0.209235 | + | 0.977865i | \(0.567097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.24621 | 0.106481 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.3693 | 1.86210 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.31534 | −0.439618 | −0.219809 | − | 0.975543i | \(-0.570543\pi\) | ||||
−0.219809 | + | 0.975543i | \(0.570543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.24621 | 0.388299 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −59.0540 | −2.77460 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.876894 | −0.0411094 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.5616 | 0.634383 | 0.317191 | − | 0.948362i | \(-0.397260\pi\) | ||||
0.317191 | + | 0.948362i | \(0.397260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.24621 | 0.104844 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0691 | 0.562115 | 0.281058 | − | 0.959691i | \(-0.409315\pi\) | ||||
0.281058 | + | 0.959691i | \(0.409315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.63068 | −0.308154 | −0.154077 | − | 0.988059i | \(-0.549240\pi\) | ||||
−0.154077 | + | 0.988059i | \(0.549240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.6847 | −1.09835 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.6847 | 1.60501 | 0.802507 | − | 0.596642i | \(-0.203499\pi\) | ||||
0.802507 | + | 0.596642i | \(0.203499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.93087 | −0.320038 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.7386 | −1.96929 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.56155 | 0.0714986 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.2311 | 1.79251 | 0.896256 | − | 0.443536i | \(-0.146276\pi\) | ||||
0.896256 | + | 0.443536i | \(0.146276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.246211 | −0.0112263 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.87689 | 0.221448 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8078 | −0.580375 | −0.290188 | − | 0.956970i | \(-0.593718\pi\) | ||||
−0.290188 | + | 0.956970i | \(0.593718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.5616 | −1.38204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.4924 | 0.969939 | 0.484970 | − | 0.874531i | \(-0.338831\pi\) | ||||
0.484970 | + | 0.874531i | \(0.338831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.31534 | −0.149315 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.12311 | 0.320160 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.93087 | −0.131467 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6155 | 0.833345 | 0.416673 | − | 0.909057i | \(-0.363196\pi\) | ||||
0.416673 | + | 0.909057i | \(0.363196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.4924 | 0.915534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.9309 | 1.11161 | 0.555806 | − | 0.831312i | \(-0.312410\pi\) | ||||
0.555806 | + | 0.831312i | \(0.312410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.31534 | −0.236530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.4924 | 1.44304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.1771 | −0.805685 | −0.402842 | − | 0.915269i | \(-0.631978\pi\) | ||||
−0.402842 | + | 0.915269i | \(0.631978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3693 | 0.591424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.63068 | 0.381054 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3693 | 0.675942 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.6155 | −2.17788 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.6155 | 1.20986 | 0.604929 | − | 0.796279i | \(-0.293201\pi\) | ||||
0.604929 | + | 0.796279i | \(0.293201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7386 | −1.51901 | −0.759507 | − | 0.650499i | \(-0.774560\pi\) | ||||
−0.759507 | + | 0.650499i | \(0.774560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4384 | 0.628949 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.9309 | −1.34229 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.31534 | 0.100289 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.56155 | 0.326914 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 56.1771 | 2.42422 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.12311 | 0.392960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.68466 | −0.416376 | −0.208188 | − | 0.978089i | \(-0.566757\pi\) | ||||
−0.208188 | + | 0.978089i | \(0.566757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.6155 | 2.12921 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.36932 | −0.401337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1771 | −1.03374 | −0.516869 | − | 0.856065i | \(-0.672902\pi\) | ||||
−0.516869 | + | 0.856065i | \(0.672902\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | −0.170716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7386 | −0.542684 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4924 | −0.871426 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.12311 | 0.0476732 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.31534 | 0.140476 | 0.0702378 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702378 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.6695 | 1.92474 | 0.962370 | − | 0.271742i | \(-0.0875998\pi\) | ||||
0.962370 | + | 0.271742i | \(0.0875998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.80776 | 0.328475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.9309 | 0.459053 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.7386 | −1.37247 | −0.686237 | − | 0.727378i | \(-0.740739\pi\) | ||||
−0.686237 | + | 0.727378i | \(0.740739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0000 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.8769 | 0.788594 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.4384 | −1.05902 | −0.529508 | − | 0.848305i | \(-0.677624\pi\) | ||||
−0.529508 | + | 0.848305i | \(0.677624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.8078 | −0.698507 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.3153 | 0.967283 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.876894 | −0.0363173 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.9309 | −1.48303 | −0.741513 | − | 0.670939i | \(-0.765891\pi\) | ||||
−0.741513 | + | 0.670939i | \(0.765891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.4773 | 2.28590 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.1771 | −0.665436 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.6155 | −1.05190 | −0.525952 | − | 0.850514i | \(-0.676291\pi\) | ||||
−0.525952 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.43845 | −0.0999666 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.6155 | 1.04837 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9848 | 1.34772 | 0.673862 | − | 0.738857i | \(-0.264634\pi\) | ||||
0.673862 | + | 0.738857i | \(0.264634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6307 | 0.474425 | 0.237213 | − | 0.971458i | \(-0.423766\pi\) | ||||
0.237213 | + | 0.971458i | \(0.423766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.8078 | 0.643742 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.4924 | −0.994117 | −0.497058 | − | 0.867717i | \(-0.665587\pi\) | ||||
−0.497058 | + | 0.867717i | \(0.665587\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.49242 | 0.344130 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.31534 | 0.174580 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.6155 | −1.43850 | −0.719249 | − | 0.694753i | \(-0.755514\pi\) | ||||
−0.719249 | + | 0.694753i | \(0.755514\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.5616 | −0.425883 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.56155 | −0.143383 | −0.0716914 | − | 0.997427i | \(-0.522840\pi\) | ||||
−0.0716914 | + | 0.997427i | \(0.522840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4924 | 0.823660 | 0.411830 | − | 0.911261i | \(-0.364890\pi\) | ||||
0.411830 | + | 0.911261i | \(0.364890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.43845 | −0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.50758 | 0.140528 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.7386 | −1.22758 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.684658 | −0.0272991 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.7538 | 0.547530 | 0.273765 | − | 0.961797i | \(-0.411731\pi\) | ||||
0.273765 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.4924 | 1.29146 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.8078 | 0.508261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.56155 | 0.101492 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.68466 | 0.264441 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1231 | 0.597327 | 0.298663 | − | 0.954359i | \(-0.403459\pi\) | ||||
0.298663 | + | 0.954359i | \(0.403459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.4233 | 1.63358 | 0.816788 | − | 0.576939i | \(-0.195753\pi\) | ||||
0.816788 | + | 0.576939i | \(0.195753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6847 | 0.695256 | 0.347628 | − | 0.937633i | \(-0.386987\pi\) | ||||
0.347628 | + | 0.937633i | \(0.386987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3693 | 0.681805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.9848 | −1.44955 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.6695 | 1.51325 | 0.756627 | − | 0.653846i | \(-0.226846\pi\) | ||||
0.756627 | + | 0.653846i | \(0.226846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8078 | 0.813027 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.4924 | −1.18962 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.36932 | 0.364977 | 0.182488 | − | 0.983208i | \(-0.441585\pi\) | ||||
0.182488 | + | 0.983208i | \(0.441585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4924 | −1.03044 | −0.515218 | − | 0.857059i | \(-0.672289\pi\) | ||||
−0.515218 | + | 0.857059i | \(0.672289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.24621 | −0.0872356 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.36932 | −0.363327 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.12311 | 0.0822070 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −60.4924 | −2.33877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.24621 | 0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.5464 | −1.37021 | −0.685106 | − | 0.728443i | \(-0.740244\pi\) | ||||
−0.685106 | + | 0.728443i | \(0.740244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.43845 | −0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.19224 | −0.237987 | −0.118993 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118993 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.61553 | 0.292257 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.9848 | 0.957421 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.94602 | −0.189254 | −0.0946272 | − | 0.995513i | \(-0.530166\pi\) | ||||
−0.0946272 | + | 0.995513i | \(0.530166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.1231 | −0.577824 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 58.2462 | 2.22223 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.246211 | −0.00937990 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4924 | 0.627401 | 0.313701 | − | 0.949522i | \(-0.398431\pi\) | ||||
0.313701 | + | 0.949522i | \(0.398431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.1231 | 0.422532 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.24621 | 0.199000 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.43845 | 0.243874 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.9309 | −1.13209 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.2462 | 0.689150 | 0.344575 | − | 0.938759i | \(-0.388023\pi\) | ||||
0.344575 | + | 0.938759i | \(0.388023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.63068 | −0.0992181 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.6847 | −0.741367 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.30019 | −0.312161 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.2462 | −1.73681 | −0.868406 | − | 0.495853i | \(-0.834855\pi\) | ||||
−0.868406 | + | 0.495853i | \(0.834855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.7386 | 1.75284 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.24621 | −0.346273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.12311 | −0.0420018 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.3002 | −1.84115 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0540 | −0.673300 | −0.336650 | − | 0.941630i | \(-0.609294\pi\) | ||||
−0.336650 | + | 0.941630i | \(0.609294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.9848 | 0.930484 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.3693 | −0.571591 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.12311 | 0.0788502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.8078 | −1.55056 | −0.775282 | − | 0.631615i | \(-0.782392\pi\) | ||||
−0.775282 | + | 0.631615i | \(0.782392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6847 | −0.468519 | −0.234259 | − | 0.972174i | \(-0.575266\pi\) | ||||
−0.234259 | + | 0.972174i | \(0.575266\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.6847 | −0.430995 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.87689 | −0.326985 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.6155 | 1.49407 | 0.747033 | − | 0.664787i | \(-0.231478\pi\) | ||||
0.747033 | + | 0.664787i | \(0.231478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.63068 | −0.317056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.4924 | 1.33878 | 0.669389 | − | 0.742912i | \(-0.266556\pi\) | ||||
0.669389 | + | 0.742912i | \(0.266556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.3693 | 0.563088 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −53.1771 | −1.94565 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.8078 | 0.431446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.87689 | −0.177960 | −0.0889802 | − | 0.996033i | \(-0.528361\pi\) | ||||
−0.0889802 | + | 0.996033i | \(0.528361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.4924 | 1.62139 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.0540 | −0.839020 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.43845 | −0.306701 | −0.153350 | − | 0.988172i | \(-0.549006\pi\) | ||||
−0.153350 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.12311 | 0.185957 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9848 | 0.796950 | 0.398475 | − | 0.917179i | \(-0.369540\pi\) | ||||
0.398475 | + | 0.917179i | \(0.369540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6307 | −0.529666 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.56155 | 0.201078 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.87689 | 0.176094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.3693 | −1.27545 | −0.637725 | − | 0.770264i | \(-0.720124\pi\) | ||||
−0.637725 | + | 0.770264i | \(0.720124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.6695 | −1.03251 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.8769 | 1.18250 | 0.591250 | − | 0.806488i | \(-0.298635\pi\) | ||||
0.591250 | + | 0.806488i | \(0.298635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.24621 | −0.332134 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.75379 | 0.0629168 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.7386 | 0.886354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.75379 | −0.134321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.05398 | −0.109140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.6847 | −0.595501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3153 | 0.973687 | 0.486843 | − | 0.873489i | \(-0.338148\pi\) | ||||
0.486843 | + | 0.873489i | \(0.338148\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −74.1080 | −2.63831 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.1922 | 0.433506 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.630683 | 0.0223962 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.12311 | 0.0398325 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.42329 | −0.333790 | −0.166895 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166895 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00000 | −0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.1231 | 0.604261 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.56155 | 0.0550375 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3002 | 0.608995 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.82292 | −0.310197 | −0.155099 | − | 0.987899i | \(-0.549570\pi\) | ||||
−0.155099 | + | 0.987899i | \(0.549570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.7538 | −1.07991 | −0.539956 | − | 0.841693i | \(-0.681559\pi\) | ||||
−0.539956 | + | 0.841693i | \(0.681559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7538 | 0.622653 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.9309 | −0.417920 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.12311 | 0.109130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50758 | 0.0526148 | 0.0263074 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263074 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.946025 | −0.0329763 | −0.0164882 | − | 0.999864i | \(-0.505249\pi\) | ||||
−0.0164882 | + | 0.999864i | \(0.505249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.12311 | 0.178364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.31534 | −0.254379 | −0.127190 | − | 0.991878i | \(-0.540596\pi\) | ||||
−0.127190 | + | 0.991878i | \(0.540596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.5464 | −1.40823 | −0.704117 | − | 0.710084i | \(-0.748657\pi\) | ||||
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5616 | 0.505135 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.12311 | 0.246801 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.3002 | 0.459722 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.1231 | −1.76497 | −0.882483 | − | 0.470345i | \(-0.844130\pi\) | ||||
−0.882483 | + | 0.470345i | \(0.844130\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4924 | −0.844566 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.7386 | 1.33423 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6847 | 0.436366 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9309 | 0.375589 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.8769 | −0.510574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.438447 | 0.0150298 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.75379 | 0.128527 | 0.0642636 | − | 0.997933i | \(-0.479530\pi\) | ||||
0.0642636 | + | 0.997933i | \(0.479530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.3693 | 0.730815 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.6847 | −1.56056 | −0.780279 | − | 0.625431i | \(-0.784923\pi\) | ||||
−0.780279 | + | 0.625431i | \(0.784923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.4924 | 1.62042 | 0.810210 | − | 0.586139i | \(-0.199353\pi\) | ||||
0.810210 | + | 0.586139i | \(0.199353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.4924 | −0.562060 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.43845 | −0.117046 | −0.0585231 | − | 0.998286i | \(-0.518639\pi\) | ||||
−0.0585231 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.3693 | −0.658577 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.3002 | 1.26678 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.2462 | −0.890342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.49242 | −0.0844525 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.3693 | −0.587862 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.56155 | 0.0527901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.9848 | −1.58657 | −0.793283 | − | 0.608853i | \(-0.791630\pi\) | ||||
−0.793283 | + | 0.608853i | \(0.791630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.75379 | 0.328987 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.4773 | −1.93646 | −0.968229 | − | 0.250065i | \(-0.919548\pi\) | ||||
−0.968229 | + | 0.250065i | \(0.919548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.7386 | 1.30366 | 0.651829 | − | 0.758366i | \(-0.274002\pi\) | ||||
0.651829 | + | 0.758366i | \(0.274002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.2462 | −0.747798 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.7926 | −1.47041 | −0.735206 | − | 0.677844i | \(-0.762915\pi\) | ||||
−0.735206 | + | 0.677844i | \(0.762915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | 0.670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0000 | 0.469018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.1080 | 1.54294 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.9309 | 0.733068 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.43845 | 0.0480284 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.6307 | −0.654720 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.684658 | −0.0228093 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.3693 | 0.643858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.31534 | −0.309311 | −0.154655 | − | 0.987968i | \(-0.549427\pi\) | ||||
−0.154655 | + | 0.987968i | \(0.549427\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.9309 | 0.627897 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.12311 | 0.169736 | 0.0848680 | − | 0.996392i | \(-0.472953\pi\) | ||||
0.0848680 | + | 0.996392i | \(0.472953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.8617 | 0.988279 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.87689 | −0.0951072 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.4924 | 1.07299 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.73863 | −0.0903392 | −0.0451696 | − | 0.998979i | \(-0.514383\pi\) | ||||
−0.0451696 | + | 0.998979i | \(0.514383\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.9848 | −1.08689 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.05398 | −0.0346920 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.438447 | 0.0144161 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −56.9848 | −1.87163 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.7235 | 1.92665 | 0.963327 | − | 0.268329i | \(-0.0864713\pi\) | ||||
0.963327 | + | 0.268329i | \(0.0864713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.3693 | 0.896993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.43845 | 0.309001 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.12311 | −0.102136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.246211 | 0.00804337 | 0.00402169 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402169 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.7386 | −1.65579 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.2462 | 1.76838 | 0.884188 | − | 0.467131i | \(-0.154712\pi\) | ||||
0.884188 | + | 0.467131i | \(0.154712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.12311 | −0.134267 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.24621 | −0.0730693 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.3153 | −1.44006 | −0.720028 | − | 0.693945i | \(-0.755871\pi\) | ||||
−0.720028 | + | 0.693945i | \(0.755871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.80776 | 0.156067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.6155 | 0.571223 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.50758 | −0.178408 | −0.0892040 | − | 0.996013i | \(-0.528432\pi\) | ||||
−0.0892040 | + | 0.996013i | \(0.528432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.36932 | 0.238465 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.8769 | 0.351600 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.6155 | −0.762585 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.4924 | 1.75782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.9309 | −0.867835 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.56155 | −0.211224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.3153 | −1.42509 | −0.712543 | − | 0.701629i | \(-0.752457\pi\) | ||||
−0.712543 | + | 0.701629i | \(0.752457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3693 | 1.52015 | 0.760077 | − | 0.649833i | \(-0.225161\pi\) | ||||
0.760077 | + | 0.649833i | \(0.225161\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.19224 | 0.262631 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.43845 | 0.0460672 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.7926 | −0.857172 | −0.428586 | − | 0.903501i | \(-0.640988\pi\) | ||||
−0.428586 | + | 0.903501i | \(0.640988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.49242 | 0.143578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.3693 | 1.06540 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.0539753 | 0.00172155 | 0.000860773 | − | 1.00000i | \(-0.499726\pi\) | ||||
0.000860773 | 1.00000i | \(0.499726\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.31534 | −0.201224 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.7386 | −0.978421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.300187 | −0.00953574 | −0.00476787 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476787 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.3153 | −1.02550 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.3845 | −0.455561 | −0.227780 | − | 0.973713i | \(-0.573147\pi\) | ||||
−0.227780 | + | 0.973713i | \(0.573147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.630683 | −0.0199539 |
(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 | 7360.2.a.bi.1.1 | 2 | ||
4.3 | odd | 2 | 7360.2.a.bo.1.2 | 2 | |||
8.3 | odd | 2 | 1840.2.a.m.1.1 | 2 | |||
8.5 | even | 2 | 460.2.a.e.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 4140.2.a.m.1.1 | 2 | |||
40.13 | odd | 4 | 2300.2.c.h.1749.4 | 4 | |||
40.19 | odd | 2 | 9200.2.a.bv.1.2 | 2 | |||
40.29 | even | 2 | 2300.2.a.i.1.1 | 2 | |||
40.37 | odd | 4 | 2300.2.c.h.1749.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.a.e.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
1840.2.a.m.1.1 | 2 | 8.3 | odd | 2 | |||
2300.2.a.i.1.1 | 2 | 40.29 | even | 2 | |||
2300.2.c.h.1749.1 | 4 | 40.37 | odd | 4 | |||
2300.2.c.h.1749.4 | 4 | 40.13 | odd | 4 | |||
4140.2.a.m.1.1 | 2 | 24.5 | odd | 2 | |||
7360.2.a.bi.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7360.2.a.bo.1.2 | 2 | 4.3 | odd | 2 | |||
9200.2.a.bv.1.2 | 2 | 40.19 | odd | 2 |