Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 6x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.86205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48008 | 1.75368 | 0.876842 | − | 0.480779i | \(-0.159646\pi\) | ||||
0.876842 | + | 0.480779i | \(0.159646\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.15081 | 2.07540 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.48008 | −1.01249 | ||||||||
\(7\) | 4.39482 | 1.66109 | 0.830544 | − | 0.556954i | \(-0.188030\pi\) | ||||
0.830544 | + | 0.556954i | \(0.188030\pi\) | |||||||
\(8\) | 5.33418 | 1.88592 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.48008 | −0.784271 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −4.15081 | −1.19824 | ||||||||
\(13\) | 2.13795 | 0.592961 | 0.296481 | − | 0.955039i | \(-0.404187\pi\) | ||||
0.296481 | + | 0.955039i | \(0.404187\pi\) | |||||||
\(14\) | 10.8995 | 2.91302 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 4.92760 | 1.23190 | ||||||||
\(17\) | −3.96017 | −0.960481 | −0.480241 | − | 0.877137i | \(-0.659451\pi\) | ||||
−0.480241 | + | 0.877137i | \(0.659451\pi\) | |||||||
\(18\) | 2.48008 | 0.584561 | ||||||||
\(19\) | 2.15081 | 0.493429 | 0.246715 | − | 0.969088i | \(-0.420649\pi\) | ||||
0.246715 | + | 0.969088i | \(0.420649\pi\) | |||||||
\(20\) | −4.15081 | −0.928149 | ||||||||
\(21\) | −4.39482 | −0.959029 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.16367 | 1.07670 | 0.538350 | − | 0.842722i | \(-0.319048\pi\) | ||||
0.538350 | + | 0.842722i | \(0.319048\pi\) | |||||||
\(24\) | −5.33418 | −1.08884 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.30230 | 1.03987 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 18.2421 | 3.44743 | ||||||||
\(29\) | −7.93936 | −1.47430 | −0.737151 | − | 0.675728i | \(-0.763829\pi\) | ||||
−0.737151 | + | 0.675728i | \(0.763829\pi\) | |||||||
\(30\) | 2.48008 | 0.452799 | ||||||||
\(31\) | 6.19132 | 1.11199 | 0.555997 | − | 0.831184i | \(-0.312337\pi\) | ||||
0.555997 | + | 0.831184i | \(0.312337\pi\) | |||||||
\(32\) | 1.55248 | 0.274443 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.82154 | −1.68438 | ||||||||
\(35\) | −4.39482 | −0.742861 | ||||||||
\(36\) | 4.15081 | 0.691802 | ||||||||
\(37\) | −8.57025 | −1.40894 | −0.704470 | − | 0.709733i | \(-0.748815\pi\) | ||||
−0.704470 | + | 0.709733i | \(0.748815\pi\) | |||||||
\(38\) | 5.33418 | 0.865319 | ||||||||
\(39\) | −2.13795 | −0.342346 | ||||||||
\(40\) | −5.33418 | −0.843409 | ||||||||
\(41\) | 7.63089 | 1.19175 | 0.595873 | − | 0.803079i | \(-0.296806\pi\) | ||||
0.595873 | + | 0.803079i | \(0.296806\pi\) | |||||||
\(42\) | −10.8995 | −1.68183 | ||||||||
\(43\) | 2.22321 | 0.339036 | 0.169518 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169518 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 12.8063 | 1.88819 | ||||||||
\(47\) | 6.88285 | 1.00397 | 0.501984 | − | 0.864877i | \(-0.332604\pi\) | ||||
0.501984 | + | 0.864877i | \(0.332604\pi\) | |||||||
\(48\) | −4.92760 | −0.711238 | ||||||||
\(49\) | 12.3145 | 1.75921 | ||||||||
\(50\) | 2.48008 | 0.350737 | ||||||||
\(51\) | 3.96017 | 0.554534 | ||||||||
\(52\) | 8.87423 | 1.23063 | ||||||||
\(53\) | −5.69644 | −0.782467 | −0.391233 | − | 0.920292i | \(-0.627951\pi\) | ||||
−0.391233 | + | 0.920292i | \(0.627951\pi\) | |||||||
\(54\) | −2.48008 | −0.337496 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.4428 | 3.13268 | ||||||||
\(57\) | −2.15081 | −0.284882 | ||||||||
\(58\) | −19.6903 | −2.58546 | ||||||||
\(59\) | 3.78170 | 0.492336 | 0.246168 | − | 0.969227i | \(-0.420829\pi\) | ||||
0.246168 | + | 0.969227i | \(0.420829\pi\) | |||||||
\(60\) | 4.15081 | 0.535867 | ||||||||
\(61\) | −4.83439 | −0.618981 | −0.309490 | − | 0.950903i | \(-0.600158\pi\) | ||||
−0.309490 | + | 0.950903i | \(0.600158\pi\) | |||||||
\(62\) | 15.3550 | 1.95009 | ||||||||
\(63\) | 4.39482 | 0.553696 | ||||||||
\(64\) | −6.00491 | −0.750614 | ||||||||
\(65\) | −2.13795 | −0.265180 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.57025 | 1.16919 | 0.584596 | − | 0.811324i | \(-0.301253\pi\) | ||||
0.584596 | + | 0.811324i | \(0.301253\pi\) | |||||||
\(68\) | −16.4379 | −1.99339 | ||||||||
\(69\) | −5.16367 | −0.621632 | ||||||||
\(70\) | −10.8995 | −1.30274 | ||||||||
\(71\) | −2.11030 | −0.250446 | −0.125223 | − | 0.992129i | \(-0.539965\pi\) | ||||
−0.125223 | + | 0.992129i | \(0.539965\pi\) | |||||||
\(72\) | 5.33418 | 0.628640 | ||||||||
\(73\) | 14.6506 | 1.71472 | 0.857362 | − | 0.514715i | \(-0.172102\pi\) | ||||
0.857362 | + | 0.514715i | \(0.172102\pi\) | |||||||
\(74\) | −21.2549 | −2.47084 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 8.92760 | 1.02407 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.30230 | −0.600367 | ||||||||
\(79\) | −3.26111 | −0.366903 | −0.183452 | − | 0.983029i | \(-0.558727\pi\) | ||||
−0.183452 | + | 0.983029i | \(0.558727\pi\) | |||||||
\(80\) | −4.92760 | −0.550922 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 18.9252 | 2.08994 | ||||||||
\(83\) | −10.6635 | −1.17047 | −0.585233 | − | 0.810865i | \(-0.698997\pi\) | ||||
−0.585233 | + | 0.810865i | \(0.698997\pi\) | |||||||
\(84\) | −18.2421 | −1.99037 | ||||||||
\(85\) | 3.96017 | 0.429540 | ||||||||
\(86\) | 5.51374 | 0.594562 | ||||||||
\(87\) | 7.93936 | 0.851189 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.64375 | −0.810236 | −0.405118 | − | 0.914264i | \(-0.632770\pi\) | ||||
−0.405118 | + | 0.914264i | \(0.632770\pi\) | |||||||
\(90\) | −2.48008 | −0.261424 | ||||||||
\(91\) | 9.39592 | 0.984960 | ||||||||
\(92\) | 21.4334 | 2.23459 | ||||||||
\(93\) | −6.19132 | −0.642010 | ||||||||
\(94\) | 17.0700 | 1.76064 | ||||||||
\(95\) | −2.15081 | −0.220668 | ||||||||
\(96\) | −1.55248 | −0.158450 | ||||||||
\(97\) | −5.67073 | −0.575775 | −0.287888 | − | 0.957664i | \(-0.592953\pi\) | ||||
−0.287888 | + | 0.957664i | \(0.592953\pi\) | |||||||
\(98\) | 30.5409 | 3.08510 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.15081 | 0.415081 | ||||||||
\(101\) | 7.03366 | 0.699876 | 0.349938 | − | 0.936773i | \(-0.386203\pi\) | ||||
0.349938 | + | 0.936773i | \(0.386203\pi\) | |||||||
\(102\) | 9.82154 | 0.972477 | ||||||||
\(103\) | 0.622945 | 0.0613806 | 0.0306903 | − | 0.999529i | \(-0.490229\pi\) | ||||
0.0306903 | + | 0.999529i | \(0.490229\pi\) | |||||||
\(104\) | 11.4042 | 1.11828 | ||||||||
\(105\) | 4.39482 | 0.428891 | ||||||||
\(106\) | −14.1276 | −1.37220 | ||||||||
\(107\) | −17.8847 | −1.72898 | −0.864491 | − | 0.502648i | \(-0.832359\pi\) | ||||
−0.864491 | + | 0.502648i | \(0.832359\pi\) | |||||||
\(108\) | −4.15081 | −0.399412 | ||||||||
\(109\) | −13.1041 | −1.25515 | −0.627574 | − | 0.778557i | \(-0.715952\pi\) | ||||
−0.627574 | + | 0.778557i | \(0.715952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.57025 | 0.813452 | ||||||||
\(112\) | 21.6559 | 2.04629 | ||||||||
\(113\) | −8.38755 | −0.789035 | −0.394517 | − | 0.918888i | \(-0.629088\pi\) | ||||
−0.394517 | + | 0.918888i | \(0.629088\pi\) | |||||||
\(114\) | −5.33418 | −0.499592 | ||||||||
\(115\) | −5.16367 | −0.481514 | ||||||||
\(116\) | −32.9548 | −3.05977 | ||||||||
\(117\) | 2.13795 | 0.197654 | ||||||||
\(118\) | 9.37893 | 0.863401 | ||||||||
\(119\) | −17.4042 | −1.59544 | ||||||||
\(120\) | 5.33418 | 0.486942 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.9897 | −1.08550 | ||||||||
\(123\) | −7.63089 | −0.688054 | ||||||||
\(124\) | 25.6990 | 2.30784 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 10.8995 | 0.971007 | ||||||||
\(127\) | −10.9828 | −0.974570 | −0.487285 | − | 0.873243i | \(-0.662013\pi\) | ||||
−0.487285 | + | 0.873243i | \(0.662013\pi\) | |||||||
\(128\) | −17.9976 | −1.59078 | ||||||||
\(129\) | −2.22321 | −0.195743 | ||||||||
\(130\) | −5.30230 | −0.465042 | ||||||||
\(131\) | 7.33115 | 0.640525 | 0.320263 | − | 0.947329i | \(-0.396229\pi\) | ||||
0.320263 | + | 0.947329i | \(0.396229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.45243 | 0.819629 | ||||||||
\(134\) | 23.7350 | 2.05039 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −21.1243 | −1.81139 | ||||||||
\(137\) | −16.6774 | −1.42485 | −0.712424 | − | 0.701750i | \(-0.752403\pi\) | ||||
−0.712424 | + | 0.701750i | \(0.752403\pi\) | |||||||
\(138\) | −12.8063 | −1.09015 | ||||||||
\(139\) | 11.0386 | 0.936280 | 0.468140 | − | 0.883654i | \(-0.344924\pi\) | ||||
0.468140 | + | 0.883654i | \(0.344924\pi\) | |||||||
\(140\) | −18.2421 | −1.54174 | ||||||||
\(141\) | −6.88285 | −0.579641 | ||||||||
\(142\) | −5.23371 | −0.439203 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.92760 | 0.410633 | ||||||||
\(145\) | 7.93936 | 0.659328 | ||||||||
\(146\) | 36.3347 | 3.00708 | ||||||||
\(147\) | −12.3145 | −1.01568 | ||||||||
\(148\) | −35.5735 | −2.92412 | ||||||||
\(149\) | −4.61118 | −0.377763 | −0.188881 | − | 0.982000i | \(-0.560486\pi\) | ||||
−0.188881 | + | 0.982000i | \(0.560486\pi\) | |||||||
\(150\) | −2.48008 | −0.202498 | ||||||||
\(151\) | 9.00914 | 0.733154 | 0.366577 | − | 0.930388i | \(-0.380530\pi\) | ||||
0.366577 | + | 0.930388i | \(0.380530\pi\) | |||||||
\(152\) | 11.4728 | 0.930568 | ||||||||
\(153\) | −3.96017 | −0.320160 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.19132 | −0.497299 | ||||||||
\(156\) | −8.87423 | −0.710507 | ||||||||
\(157\) | 2.98902 | 0.238550 | 0.119275 | − | 0.992861i | \(-0.461943\pi\) | ||||
0.119275 | + | 0.992861i | \(0.461943\pi\) | |||||||
\(158\) | −8.08781 | −0.643432 | ||||||||
\(159\) | 5.69644 | 0.451757 | ||||||||
\(160\) | −1.55248 | −0.122735 | ||||||||
\(161\) | 22.6934 | 1.78849 | ||||||||
\(162\) | 2.48008 | 0.194854 | ||||||||
\(163\) | −2.89571 | −0.226810 | −0.113405 | − | 0.993549i | \(-0.536176\pi\) | ||||
−0.113405 | + | 0.993549i | \(0.536176\pi\) | |||||||
\(164\) | 31.6744 | 2.47335 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.4463 | −2.05263 | ||||||||
\(167\) | 3.80512 | 0.294449 | 0.147225 | − | 0.989103i | \(-0.452966\pi\) | ||||
0.147225 | + | 0.989103i | \(0.452966\pi\) | |||||||
\(168\) | −23.4428 | −1.80865 | ||||||||
\(169\) | −8.42916 | −0.648397 | ||||||||
\(170\) | 9.82154 | 0.753277 | ||||||||
\(171\) | 2.15081 | 0.164476 | ||||||||
\(172\) | 9.22812 | 0.703638 | ||||||||
\(173\) | 1.11291 | 0.0846132 | 0.0423066 | − | 0.999105i | \(-0.486529\pi\) | ||||
0.0423066 | + | 0.999105i | \(0.486529\pi\) | |||||||
\(174\) | 19.6903 | 1.49272 | ||||||||
\(175\) | 4.39482 | 0.332217 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.78170 | −0.284250 | ||||||||
\(178\) | −18.9571 | −1.42090 | ||||||||
\(179\) | −4.81918 | −0.360202 | −0.180101 | − | 0.983648i | \(-0.557643\pi\) | ||||
−0.180101 | + | 0.983648i | \(0.557643\pi\) | |||||||
\(180\) | −4.15081 | −0.309383 | ||||||||
\(181\) | −21.4623 | −1.59528 | −0.797638 | − | 0.603136i | \(-0.793918\pi\) | ||||
−0.797638 | + | 0.603136i | \(0.793918\pi\) | |||||||
\(182\) | 23.3027 | 1.72731 | ||||||||
\(183\) | 4.83439 | 0.357369 | ||||||||
\(184\) | 27.5440 | 2.03057 | ||||||||
\(185\) | 8.57025 | 0.630097 | ||||||||
\(186\) | −15.3550 | −1.12588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 28.5694 | 2.08364 | ||||||||
\(189\) | −4.39482 | −0.319676 | ||||||||
\(190\) | −5.33418 | −0.386982 | ||||||||
\(191\) | −9.36184 | −0.677399 | −0.338699 | − | 0.940895i | \(-0.609987\pi\) | ||||
−0.338699 | + | 0.940895i | \(0.609987\pi\) | |||||||
\(192\) | 6.00491 | 0.433367 | ||||||||
\(193\) | 18.4088 | 1.32509 | 0.662546 | − | 0.749021i | \(-0.269476\pi\) | ||||
0.662546 | + | 0.749021i | \(0.269476\pi\) | |||||||
\(194\) | −14.0639 | −1.00973 | ||||||||
\(195\) | 2.13795 | 0.153102 | ||||||||
\(196\) | 51.1150 | 3.65107 | ||||||||
\(197\) | 4.67182 | 0.332854 | 0.166427 | − | 0.986054i | \(-0.446777\pi\) | ||||
0.166427 | + | 0.986054i | \(0.446777\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2018 | −1.14852 | −0.574258 | − | 0.818674i | \(-0.694710\pi\) | ||||
−0.574258 | + | 0.818674i | \(0.694710\pi\) | |||||||
\(200\) | 5.33418 | 0.377184 | ||||||||
\(201\) | −9.57025 | −0.675034 | ||||||||
\(202\) | 17.4441 | 1.22736 | ||||||||
\(203\) | −34.8921 | −2.44894 | ||||||||
\(204\) | 16.4379 | 1.15088 | ||||||||
\(205\) | −7.63089 | −0.532965 | ||||||||
\(206\) | 1.54496 | 0.107642 | ||||||||
\(207\) | 5.16367 | 0.358900 | ||||||||
\(208\) | 10.5350 | 0.730469 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 10.8995 | 0.752139 | ||||||||
\(211\) | 6.40465 | 0.440914 | 0.220457 | − | 0.975397i | \(-0.429245\pi\) | ||||
0.220457 | + | 0.975397i | \(0.429245\pi\) | |||||||
\(212\) | −23.6448 | −1.62393 | ||||||||
\(213\) | 2.11030 | 0.144595 | ||||||||
\(214\) | −44.3556 | −3.03209 | ||||||||
\(215\) | −2.22321 | −0.151622 | ||||||||
\(216\) | −5.33418 | −0.362945 | ||||||||
\(217\) | 27.2098 | 1.84712 | ||||||||
\(218\) | −32.4993 | −2.20113 | ||||||||
\(219\) | −14.6506 | −0.989996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.46664 | −0.569528 | ||||||||
\(222\) | 21.2549 | 1.42654 | ||||||||
\(223\) | −14.3520 | −0.961078 | −0.480539 | − | 0.876973i | \(-0.659559\pi\) | ||||
−0.480539 | + | 0.876973i | \(0.659559\pi\) | |||||||
\(224\) | 6.82289 | 0.455874 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −20.8018 | −1.38372 | ||||||||
\(227\) | −18.3113 | −1.21537 | −0.607683 | − | 0.794180i | \(-0.707901\pi\) | ||||
−0.607683 | + | 0.794180i | \(0.707901\pi\) | |||||||
\(228\) | −8.92760 | −0.591245 | ||||||||
\(229\) | −18.9191 | −1.25021 | −0.625104 | − | 0.780542i | \(-0.714943\pi\) | ||||
−0.625104 | + | 0.780542i | \(0.714943\pi\) | |||||||
\(230\) | −12.8063 | −0.844424 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −42.3500 | −2.78041 | ||||||||
\(233\) | 6.35813 | 0.416535 | 0.208267 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208267 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(234\) | 5.30230 | 0.346622 | ||||||||
\(235\) | −6.88285 | −0.448988 | ||||||||
\(236\) | 15.6971 | 1.02180 | ||||||||
\(237\) | 3.26111 | 0.211832 | ||||||||
\(238\) | −43.1639 | −2.79790 | ||||||||
\(239\) | 13.6150 | 0.880681 | 0.440341 | − | 0.897831i | \(-0.354858\pi\) | ||||
0.440341 | + | 0.897831i | \(0.354858\pi\) | |||||||
\(240\) | 4.92760 | 0.318075 | ||||||||
\(241\) | −10.1564 | −0.654231 | −0.327116 | − | 0.944984i | \(-0.606077\pi\) | ||||
−0.327116 | + | 0.944984i | \(0.606077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −20.0666 | −1.28464 | ||||||||
\(245\) | −12.3145 | −0.786743 | ||||||||
\(246\) | −18.9252 | −1.20663 | ||||||||
\(247\) | 4.59833 | 0.292584 | ||||||||
\(248\) | 33.0257 | 2.09713 | ||||||||
\(249\) | 10.6635 | 0.675769 | ||||||||
\(250\) | −2.48008 | −0.156854 | ||||||||
\(251\) | 15.7579 | 0.994627 | 0.497314 | − | 0.867571i | \(-0.334320\pi\) | ||||
0.497314 | + | 0.867571i | \(0.334320\pi\) | |||||||
\(252\) | 18.2421 | 1.14914 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −27.2384 | −1.70909 | ||||||||
\(255\) | −3.96017 | −0.247995 | ||||||||
\(256\) | −32.6258 | −2.03911 | ||||||||
\(257\) | −1.36335 | −0.0850437 | −0.0425218 | − | 0.999096i | \(-0.513539\pi\) | ||||
−0.0425218 | + | 0.999096i | \(0.513539\pi\) | |||||||
\(258\) | −5.51374 | −0.343271 | ||||||||
\(259\) | −37.6647 | −2.34037 | ||||||||
\(260\) | −8.87423 | −0.550356 | ||||||||
\(261\) | −7.93936 | −0.491434 | ||||||||
\(262\) | 18.1819 | 1.12328 | ||||||||
\(263\) | 8.12002 | 0.500702 | 0.250351 | − | 0.968155i | \(-0.419454\pi\) | ||||
0.250351 | + | 0.968155i | \(0.419454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.69644 | 0.349930 | ||||||||
\(266\) | 23.4428 | 1.43737 | ||||||||
\(267\) | 7.64375 | 0.467790 | ||||||||
\(268\) | 39.7243 | 2.42655 | ||||||||
\(269\) | −11.7112 | −0.714047 | −0.357023 | − | 0.934095i | \(-0.616208\pi\) | ||||
−0.357023 | + | 0.934095i | \(0.616208\pi\) | |||||||
\(270\) | 2.48008 | 0.150933 | ||||||||
\(271\) | −2.18651 | −0.132821 | −0.0664106 | − | 0.997792i | \(-0.521155\pi\) | ||||
−0.0664106 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(272\) | −19.5141 | −1.18322 | ||||||||
\(273\) | −9.39592 | −0.568667 | ||||||||
\(274\) | −41.3614 | −2.49873 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −21.4334 | −1.29014 | ||||||||
\(277\) | −10.6733 | −0.641295 | −0.320648 | − | 0.947199i | \(-0.603901\pi\) | ||||
−0.320648 | + | 0.947199i | \(0.603901\pi\) | |||||||
\(278\) | 27.3766 | 1.64194 | ||||||||
\(279\) | 6.19132 | 0.370665 | ||||||||
\(280\) | −23.4428 | −1.40098 | ||||||||
\(281\) | −5.43272 | −0.324089 | −0.162044 | − | 0.986783i | \(-0.551809\pi\) | ||||
−0.162044 | + | 0.986783i | \(0.551809\pi\) | |||||||
\(282\) | −17.0700 | −1.01651 | ||||||||
\(283\) | −18.2401 | −1.08426 | −0.542132 | − | 0.840293i | \(-0.682383\pi\) | ||||
−0.542132 | + | 0.840293i | \(0.682383\pi\) | |||||||
\(284\) | −8.75944 | −0.519777 | ||||||||
\(285\) | 2.15081 | 0.127403 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33.5364 | 1.97959 | ||||||||
\(288\) | 1.55248 | 0.0914810 | ||||||||
\(289\) | −1.31709 | −0.0774761 | ||||||||
\(290\) | 19.6903 | 1.15625 | ||||||||
\(291\) | 5.67073 | 0.332424 | ||||||||
\(292\) | 60.8118 | 3.55874 | ||||||||
\(293\) | 15.8594 | 0.926518 | 0.463259 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463259 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(294\) | −30.5409 | −1.78118 | ||||||||
\(295\) | −3.78170 | −0.220179 | ||||||||
\(296\) | −45.7153 | −2.65715 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.4361 | −0.662476 | ||||||||
\(299\) | 11.0397 | 0.638441 | ||||||||
\(300\) | −4.15081 | −0.239647 | ||||||||
\(301\) | 9.77062 | 0.563169 | ||||||||
\(302\) | 22.3434 | 1.28572 | ||||||||
\(303\) | −7.03366 | −0.404073 | ||||||||
\(304\) | 10.5983 | 0.607856 | ||||||||
\(305\) | 4.83439 | 0.276817 | ||||||||
\(306\) | −9.82154 | −0.561460 | ||||||||
\(307\) | 18.1026 | 1.03317 | 0.516585 | − | 0.856236i | \(-0.327203\pi\) | ||||
0.516585 | + | 0.856236i | \(0.327203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.622945 | −0.0354381 | ||||||||
\(310\) | −15.3550 | −0.872105 | ||||||||
\(311\) | −18.3391 | −1.03991 | −0.519957 | − | 0.854192i | \(-0.674052\pi\) | ||||
−0.519957 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(312\) | −11.4042 | −0.645637 | ||||||||
\(313\) | 30.2483 | 1.70974 | 0.854869 | − | 0.518844i | \(-0.173638\pi\) | ||||
0.854869 | + | 0.518844i | \(0.173638\pi\) | |||||||
\(314\) | 7.41301 | 0.418340 | ||||||||
\(315\) | −4.39482 | −0.247620 | ||||||||
\(316\) | −13.5362 | −0.761472 | ||||||||
\(317\) | 30.5985 | 1.71858 | 0.859292 | − | 0.511485i | \(-0.170904\pi\) | ||||
0.859292 | + | 0.511485i | \(0.170904\pi\) | |||||||
\(318\) | 14.1276 | 0.792239 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 6.00491 | 0.335685 | ||||||||
\(321\) | 17.8847 | 0.998228 | ||||||||
\(322\) | 56.2815 | 3.13645 | ||||||||
\(323\) | −8.51756 | −0.473930 | ||||||||
\(324\) | 4.15081 | 0.230601 | ||||||||
\(325\) | 2.13795 | 0.118592 | ||||||||
\(326\) | −7.18160 | −0.397752 | ||||||||
\(327\) | 13.1041 | 0.724660 | ||||||||
\(328\) | 40.7046 | 2.24753 | ||||||||
\(329\) | 30.2489 | 1.66768 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.09362 | −0.0601110 | −0.0300555 | − | 0.999548i | \(-0.509568\pi\) | ||||
−0.0300555 | + | 0.999548i | \(0.509568\pi\) | |||||||
\(332\) | −44.2620 | −2.42919 | ||||||||
\(333\) | −8.57025 | −0.469647 | ||||||||
\(334\) | 9.43702 | 0.516371 | ||||||||
\(335\) | −9.57025 | −0.522879 | ||||||||
\(336\) | −21.6559 | −1.18143 | ||||||||
\(337\) | −16.2674 | −0.886140 | −0.443070 | − | 0.896487i | \(-0.646111\pi\) | ||||
−0.443070 | + | 0.896487i | \(0.646111\pi\) | |||||||
\(338\) | −20.9050 | −1.13708 | ||||||||
\(339\) | 8.38755 | 0.455549 | ||||||||
\(340\) | 16.4379 | 0.891470 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.33418 | 0.288440 | ||||||||
\(343\) | 23.3562 | 1.26112 | ||||||||
\(344\) | 11.8590 | 0.639395 | ||||||||
\(345\) | 5.16367 | 0.278002 | ||||||||
\(346\) | 2.76012 | 0.148385 | ||||||||
\(347\) | −7.88599 | −0.423342 | −0.211671 | − | 0.977341i | \(-0.567891\pi\) | ||||
−0.211671 | + | 0.977341i | \(0.567891\pi\) | |||||||
\(348\) | 32.9548 | 1.76656 | ||||||||
\(349\) | 12.4119 | 0.664395 | 0.332197 | − | 0.943210i | \(-0.392210\pi\) | ||||
0.332197 | + | 0.943210i | \(0.392210\pi\) | |||||||
\(350\) | 10.8995 | 0.582604 | ||||||||
\(351\) | −2.13795 | −0.114115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7984 | −0.734413 | −0.367207 | − | 0.930139i | \(-0.619686\pi\) | ||||
−0.367207 | + | 0.930139i | \(0.619686\pi\) | |||||||
\(354\) | −9.37893 | −0.498485 | ||||||||
\(355\) | 2.11030 | 0.112003 | ||||||||
\(356\) | −31.7277 | −1.68157 | ||||||||
\(357\) | 17.4042 | 0.921129 | ||||||||
\(358\) | −11.9520 | −0.631681 | ||||||||
\(359\) | 21.6248 | 1.14131 | 0.570657 | − | 0.821188i | \(-0.306689\pi\) | ||||
0.570657 | + | 0.821188i | \(0.306689\pi\) | |||||||
\(360\) | −5.33418 | −0.281136 | ||||||||
\(361\) | −14.3740 | −0.756527 | ||||||||
\(362\) | −53.2282 | −2.79761 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 39.0007 | 2.04419 | ||||||||
\(365\) | −14.6506 | −0.766847 | ||||||||
\(366\) | 11.9897 | 0.626711 | ||||||||
\(367\) | 23.1283 | 1.20729 | 0.603644 | − | 0.797254i | \(-0.293715\pi\) | ||||
0.603644 | + | 0.797254i | \(0.293715\pi\) | |||||||
\(368\) | 25.4445 | 1.32639 | ||||||||
\(369\) | 7.63089 | 0.397248 | ||||||||
\(370\) | 21.2549 | 1.10499 | ||||||||
\(371\) | −25.0349 | −1.29975 | ||||||||
\(372\) | −25.6990 | −1.33243 | ||||||||
\(373\) | 23.7304 | 1.22871 | 0.614356 | − | 0.789029i | \(-0.289416\pi\) | ||||
0.614356 | + | 0.789029i | \(0.289416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 36.7144 | 1.89340 | ||||||||
\(377\) | −16.9740 | −0.874204 | ||||||||
\(378\) | −10.8995 | −0.560611 | ||||||||
\(379\) | −33.0484 | −1.69758 | −0.848791 | − | 0.528728i | \(-0.822669\pi\) | ||||
−0.848791 | + | 0.528728i | \(0.822669\pi\) | |||||||
\(380\) | −8.92760 | −0.457976 | ||||||||
\(381\) | 10.9828 | 0.562668 | ||||||||
\(382\) | −23.2181 | −1.18794 | ||||||||
\(383\) | −7.97370 | −0.407437 | −0.203719 | − | 0.979029i | \(-0.565303\pi\) | ||||
−0.203719 | + | 0.979029i | \(0.565303\pi\) | |||||||
\(384\) | 17.9976 | 0.918438 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.6553 | 2.32379 | ||||||||
\(387\) | 2.22321 | 0.113012 | ||||||||
\(388\) | −23.5381 | −1.19497 | ||||||||
\(389\) | 4.28766 | 0.217393 | 0.108697 | − | 0.994075i | \(-0.465332\pi\) | ||||
0.108697 | + | 0.994075i | \(0.465332\pi\) | |||||||
\(390\) | 5.30230 | 0.268492 | ||||||||
\(391\) | −20.4490 | −1.03415 | ||||||||
\(392\) | 65.6877 | 3.31773 | ||||||||
\(393\) | −7.33115 | −0.369808 | ||||||||
\(394\) | 11.5865 | 0.583720 | ||||||||
\(395\) | 3.26111 | 0.164084 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.21087 | −0.110961 | −0.0554803 | − | 0.998460i | \(-0.517669\pi\) | ||||
−0.0554803 | + | 0.998460i | \(0.517669\pi\) | |||||||
\(398\) | −40.1819 | −2.01413 | ||||||||
\(399\) | −9.45243 | −0.473213 | ||||||||
\(400\) | 4.92760 | 0.246380 | ||||||||
\(401\) | 12.1478 | 0.606631 | 0.303315 | − | 0.952890i | \(-0.401906\pi\) | ||||
0.303315 | + | 0.952890i | \(0.401906\pi\) | |||||||
\(402\) | −23.7350 | −1.18379 | ||||||||
\(403\) | 13.2367 | 0.659369 | ||||||||
\(404\) | 29.1954 | 1.45252 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −86.5353 | −4.29467 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 21.1243 | 1.04581 | ||||||||
\(409\) | −33.8603 | −1.67428 | −0.837142 | − | 0.546985i | \(-0.815775\pi\) | ||||
−0.837142 | + | 0.546985i | \(0.815775\pi\) | |||||||
\(410\) | −18.9252 | −0.934651 | ||||||||
\(411\) | 16.6774 | 0.822636 | ||||||||
\(412\) | 2.58573 | 0.127390 | ||||||||
\(413\) | 16.6199 | 0.817812 | ||||||||
\(414\) | 12.8063 | 0.629396 | ||||||||
\(415\) | 10.6635 | 0.523449 | ||||||||
\(416\) | 3.31913 | 0.162734 | ||||||||
\(417\) | −11.0386 | −0.540561 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.1583 | 0.887093 | 0.443546 | − | 0.896251i | \(-0.353720\pi\) | ||||
0.443546 | + | 0.896251i | \(0.353720\pi\) | |||||||
\(420\) | 18.2421 | 0.890122 | ||||||||
\(421\) | 39.1558 | 1.90834 | 0.954169 | − | 0.299269i | \(-0.0967428\pi\) | ||||
0.954169 | + | 0.299269i | \(0.0967428\pi\) | |||||||
\(422\) | 15.8841 | 0.773224 | ||||||||
\(423\) | 6.88285 | 0.334656 | ||||||||
\(424\) | −30.3859 | −1.47567 | ||||||||
\(425\) | −3.96017 | −0.192096 | ||||||||
\(426\) | 5.23371 | 0.253574 | ||||||||
\(427\) | −21.2463 | −1.02818 | ||||||||
\(428\) | −74.2361 | −3.58834 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.51374 | −0.265896 | ||||||||
\(431\) | −22.8319 | −1.09978 | −0.549888 | − | 0.835239i | \(-0.685330\pi\) | ||||
−0.549888 | + | 0.835239i | \(0.685330\pi\) | |||||||
\(432\) | −4.92760 | −0.237079 | ||||||||
\(433\) | 5.89190 | 0.283146 | 0.141573 | − | 0.989928i | \(-0.454784\pi\) | ||||
0.141573 | + | 0.989928i | \(0.454784\pi\) | |||||||
\(434\) | 67.4825 | 3.23926 | ||||||||
\(435\) | −7.93936 | −0.380663 | ||||||||
\(436\) | −54.3927 | −2.60494 | ||||||||
\(437\) | 11.1061 | 0.531275 | ||||||||
\(438\) | −36.3347 | −1.73614 | ||||||||
\(439\) | −5.46570 | −0.260864 | −0.130432 | − | 0.991457i | \(-0.541636\pi\) | ||||
−0.130432 | + | 0.991457i | \(0.541636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.3145 | 0.586404 | ||||||||
\(442\) | −20.9980 | −0.998771 | ||||||||
\(443\) | 25.2148 | 1.19799 | 0.598995 | − | 0.800753i | \(-0.295567\pi\) | ||||
0.598995 | + | 0.800753i | \(0.295567\pi\) | |||||||
\(444\) | 35.5735 | 1.68824 | ||||||||
\(445\) | 7.64375 | 0.362348 | ||||||||
\(446\) | −35.5940 | −1.68543 | ||||||||
\(447\) | 4.61118 | 0.218102 | ||||||||
\(448\) | −26.3905 | −1.24684 | ||||||||
\(449\) | 14.8612 | 0.701344 | 0.350672 | − | 0.936498i | \(-0.385953\pi\) | ||||
0.350672 | + | 0.936498i | \(0.385953\pi\) | |||||||
\(450\) | 2.48008 | 0.116912 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −34.8151 | −1.63757 | ||||||||
\(453\) | −9.00914 | −0.423287 | ||||||||
\(454\) | −45.4136 | −2.13137 | ||||||||
\(455\) | −9.39592 | −0.440488 | ||||||||
\(456\) | −11.4728 | −0.537264 | ||||||||
\(457\) | 38.6831 | 1.80952 | 0.904760 | − | 0.425923i | \(-0.140050\pi\) | ||||
0.904760 | + | 0.425923i | \(0.140050\pi\) | |||||||
\(458\) | −46.9209 | −2.19247 | ||||||||
\(459\) | 3.96017 | 0.184845 | ||||||||
\(460\) | −21.4334 | −0.999337 | ||||||||
\(461\) | 4.32624 | 0.201493 | 0.100746 | − | 0.994912i | \(-0.467877\pi\) | ||||
0.100746 | + | 0.994912i | \(0.467877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.723001 | 0.0336007 | 0.0168003 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0168003 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(464\) | −39.1220 | −1.81619 | ||||||||
\(465\) | 6.19132 | 0.287116 | ||||||||
\(466\) | 15.7687 | 0.730470 | ||||||||
\(467\) | −19.8965 | −0.920700 | −0.460350 | − | 0.887738i | \(-0.652276\pi\) | ||||
−0.460350 | + | 0.887738i | \(0.652276\pi\) | |||||||
\(468\) | 8.87423 | 0.410211 | ||||||||
\(469\) | 42.0596 | 1.94213 | ||||||||
\(470\) | −17.0700 | −0.787382 | ||||||||
\(471\) | −2.98902 | −0.137727 | ||||||||
\(472\) | 20.1723 | 0.928505 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.08781 | 0.371486 | ||||||||
\(475\) | 2.15081 | 0.0986859 | ||||||||
\(476\) | −72.2416 | −3.31119 | ||||||||
\(477\) | −5.69644 | −0.260822 | ||||||||
\(478\) | 33.7663 | 1.54444 | ||||||||
\(479\) | 18.7395 | 0.856230 | 0.428115 | − | 0.903724i | \(-0.359178\pi\) | ||||
0.428115 | + | 0.903724i | \(0.359178\pi\) | |||||||
\(480\) | 1.55248 | 0.0708608 | ||||||||
\(481\) | −18.3228 | −0.835447 | ||||||||
\(482\) | −25.1887 | −1.14731 | ||||||||
\(483\) | −22.6934 | −1.03259 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.67073 | 0.257494 | ||||||||
\(486\) | −2.48008 | −0.112499 | ||||||||
\(487\) | −0.524245 | −0.0237558 | −0.0118779 | − | 0.999929i | \(-0.503781\pi\) | ||||
−0.0118779 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(488\) | −25.7875 | −1.16735 | ||||||||
\(489\) | 2.89571 | 0.130949 | ||||||||
\(490\) | −30.5409 | −1.37970 | ||||||||
\(491\) | −20.4709 | −0.923838 | −0.461919 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461919 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(492\) | −31.6744 | −1.42799 | ||||||||
\(493\) | 31.4412 | 1.41604 | ||||||||
\(494\) | 11.4042 | 0.513100 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.5084 | 1.36987 | ||||||||
\(497\) | −9.27438 | −0.416013 | ||||||||
\(498\) | 26.4463 | 1.18509 | ||||||||
\(499\) | −4.56237 | −0.204240 | −0.102120 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102120 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(500\) | −4.15081 | −0.185630 | ||||||||
\(501\) | −3.80512 | −0.170000 | ||||||||
\(502\) | 39.0808 | 1.74426 | ||||||||
\(503\) | 23.4683 | 1.04640 | 0.523199 | − | 0.852211i | \(-0.324738\pi\) | ||||
0.523199 | + | 0.852211i | \(0.324738\pi\) | |||||||
\(504\) | 23.4428 | 1.04423 | ||||||||
\(505\) | −7.03366 | −0.312994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.42916 | 0.374352 | ||||||||
\(508\) | −45.5877 | −2.02263 | ||||||||
\(509\) | 4.74119 | 0.210149 | 0.105075 | − | 0.994464i | \(-0.466492\pi\) | ||||
0.105075 | + | 0.994464i | \(0.466492\pi\) | |||||||
\(510\) | −9.82154 | −0.434905 | ||||||||
\(511\) | 64.3868 | 2.84830 | ||||||||
\(512\) | −44.9194 | −1.98518 | ||||||||
\(513\) | −2.15081 | −0.0949605 | ||||||||
\(514\) | −3.38123 | −0.149140 | ||||||||
\(515\) | −0.622945 | −0.0274502 | ||||||||
\(516\) | −9.22812 | −0.406245 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −93.4117 | −4.10427 | ||||||||
\(519\) | −1.11291 | −0.0488515 | ||||||||
\(520\) | −11.4042 | −0.500108 | ||||||||
\(521\) | −33.8092 | −1.48121 | −0.740604 | − | 0.671942i | \(-0.765460\pi\) | ||||
−0.740604 | + | 0.671942i | \(0.765460\pi\) | |||||||
\(522\) | −19.6903 | −0.861820 | ||||||||
\(523\) | 28.1112 | 1.22922 | 0.614609 | − | 0.788832i | \(-0.289314\pi\) | ||||
0.614609 | + | 0.788832i | \(0.289314\pi\) | |||||||
\(524\) | 30.4302 | 1.32935 | ||||||||
\(525\) | −4.39482 | −0.191806 | ||||||||
\(526\) | 20.1383 | 0.878072 | ||||||||
\(527\) | −24.5187 | −1.06805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.66346 | 0.159281 | ||||||||
\(530\) | 14.1276 | 0.613666 | ||||||||
\(531\) | 3.78170 | 0.164112 | ||||||||
\(532\) | 39.2352 | 1.70106 | ||||||||
\(533\) | 16.3145 | 0.706658 | ||||||||
\(534\) | 18.9571 | 0.820355 | ||||||||
\(535\) | 17.8847 | 0.773224 | ||||||||
\(536\) | 51.0495 | 2.20500 | ||||||||
\(537\) | 4.81918 | 0.207963 | ||||||||
\(538\) | −29.0448 | −1.25221 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.15081 | 0.178622 | ||||||||
\(541\) | −14.1474 | −0.608242 | −0.304121 | − | 0.952633i | \(-0.598363\pi\) | ||||
−0.304121 | + | 0.952633i | \(0.598363\pi\) | |||||||
\(542\) | −5.42273 | −0.232926 | ||||||||
\(543\) | 21.4623 | 0.921033 | ||||||||
\(544\) | −6.14809 | −0.263597 | ||||||||
\(545\) | 13.1041 | 0.561319 | ||||||||
\(546\) | −23.3027 | −0.997262 | ||||||||
\(547\) | 31.6553 | 1.35348 | 0.676742 | − | 0.736220i | \(-0.263391\pi\) | ||||
0.676742 | + | 0.736220i | \(0.263391\pi\) | |||||||
\(548\) | −69.2248 | −2.95713 | ||||||||
\(549\) | −4.83439 | −0.206327 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.0761 | −0.727464 | ||||||||
\(552\) | −27.5440 | −1.17235 | ||||||||
\(553\) | −14.3320 | −0.609458 | ||||||||
\(554\) | −26.4706 | −1.12463 | ||||||||
\(555\) | −8.57025 | −0.363787 | ||||||||
\(556\) | 45.8190 | 1.94316 | ||||||||
\(557\) | 27.1124 | 1.14879 | 0.574395 | − | 0.818578i | \(-0.305237\pi\) | ||||
0.574395 | + | 0.818578i | \(0.305237\pi\) | |||||||
\(558\) | 15.3550 | 0.650029 | ||||||||
\(559\) | 4.75312 | 0.201035 | ||||||||
\(560\) | −21.6559 | −0.915130 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.4736 | −0.568349 | ||||||||
\(563\) | 24.0556 | 1.01382 | 0.506911 | − | 0.861999i | \(-0.330787\pi\) | ||||
0.506911 | + | 0.861999i | \(0.330787\pi\) | |||||||
\(564\) | −28.5694 | −1.20299 | ||||||||
\(565\) | 8.38755 | 0.352867 | ||||||||
\(566\) | −45.2370 | −1.90145 | ||||||||
\(567\) | 4.39482 | 0.184565 | ||||||||
\(568\) | −11.2567 | −0.472321 | ||||||||
\(569\) | −27.8406 | −1.16714 | −0.583569 | − | 0.812063i | \(-0.698344\pi\) | ||||
−0.583569 | + | 0.812063i | \(0.698344\pi\) | |||||||
\(570\) | 5.33418 | 0.223424 | ||||||||
\(571\) | 33.5792 | 1.40525 | 0.702624 | − | 0.711562i | \(-0.252012\pi\) | ||||
0.702624 | + | 0.711562i | \(0.252012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.36184 | 0.391096 | ||||||||
\(574\) | 83.1731 | 3.47158 | ||||||||
\(575\) | 5.16367 | 0.215340 | ||||||||
\(576\) | −6.00491 | −0.250205 | ||||||||
\(577\) | −19.1012 | −0.795191 | −0.397596 | − | 0.917561i | \(-0.630155\pi\) | ||||
−0.397596 | + | 0.917561i | \(0.630155\pi\) | |||||||
\(578\) | −3.26650 | −0.135868 | ||||||||
\(579\) | −18.4088 | −0.765043 | ||||||||
\(580\) | 32.9548 | 1.36837 | ||||||||
\(581\) | −46.8640 | −1.94425 | ||||||||
\(582\) | 14.0639 | 0.582966 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 78.1490 | 3.23383 | ||||||||
\(585\) | −2.13795 | −0.0883934 | ||||||||
\(586\) | 39.3327 | 1.62482 | ||||||||
\(587\) | −21.3648 | −0.881820 | −0.440910 | − | 0.897551i | \(-0.645344\pi\) | ||||
−0.440910 | + | 0.897551i | \(0.645344\pi\) | |||||||
\(588\) | −51.1150 | −2.10795 | ||||||||
\(589\) | 13.3164 | 0.548691 | ||||||||
\(590\) | −9.37893 | −0.386124 | ||||||||
\(591\) | −4.67182 | −0.192173 | ||||||||
\(592\) | −42.2308 | −1.73567 | ||||||||
\(593\) | 9.16002 | 0.376157 | 0.188078 | − | 0.982154i | \(-0.439774\pi\) | ||||
0.188078 | + | 0.982154i | \(0.439774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.4042 | 0.713504 | ||||||||
\(596\) | −19.1401 | −0.784011 | ||||||||
\(597\) | 16.2018 | 0.663096 | ||||||||
\(598\) | 27.3793 | 1.11962 | ||||||||
\(599\) | −3.39567 | −0.138743 | −0.0693716 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693716 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(600\) | −5.33418 | −0.217767 | ||||||||
\(601\) | 14.4385 | 0.588958 | 0.294479 | − | 0.955658i | \(-0.404854\pi\) | ||||
0.294479 | + | 0.955658i | \(0.404854\pi\) | |||||||
\(602\) | 24.2319 | 0.987620 | ||||||||
\(603\) | 9.57025 | 0.389731 | ||||||||
\(604\) | 37.3952 | 1.52159 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.4441 | −0.708617 | ||||||||
\(607\) | −1.37689 | −0.0558862 | −0.0279431 | − | 0.999610i | \(-0.508896\pi\) | ||||
−0.0279431 | + | 0.999610i | \(0.508896\pi\) | |||||||
\(608\) | 3.33910 | 0.135418 | ||||||||
\(609\) | 34.8921 | 1.41390 | ||||||||
\(610\) | 11.9897 | 0.485449 | ||||||||
\(611\) | 14.7152 | 0.595313 | ||||||||
\(612\) | −16.4379 | −0.664462 | ||||||||
\(613\) | −1.19074 | −0.0480934 | −0.0240467 | − | 0.999711i | \(-0.507655\pi\) | ||||
−0.0240467 | + | 0.999711i | \(0.507655\pi\) | |||||||
\(614\) | 44.8960 | 1.81185 | ||||||||
\(615\) | 7.63089 | 0.307707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.9076 | −0.439122 | −0.219561 | − | 0.975599i | \(-0.570463\pi\) | ||||
−0.219561 | + | 0.975599i | \(0.570463\pi\) | |||||||
\(618\) | −1.54496 | −0.0621472 | ||||||||
\(619\) | −28.7339 | −1.15491 | −0.577457 | − | 0.816421i | \(-0.695955\pi\) | ||||
−0.577457 | + | 0.816421i | \(0.695955\pi\) | |||||||
\(620\) | −25.6990 | −1.03210 | ||||||||
\(621\) | −5.16367 | −0.207211 | ||||||||
\(622\) | −45.4825 | −1.82368 | ||||||||
\(623\) | −33.5929 | −1.34587 | ||||||||
\(624\) | −10.5350 | −0.421736 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 75.0184 | 2.99834 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.4068 | 0.495087 | ||||||||
\(629\) | 33.9396 | 1.35326 | ||||||||
\(630\) | −10.8995 | −0.434247 | ||||||||
\(631\) | 33.7376 | 1.34307 | 0.671536 | − | 0.740972i | \(-0.265635\pi\) | ||||
0.671536 | + | 0.740972i | \(0.265635\pi\) | |||||||
\(632\) | −17.3953 | −0.691950 | ||||||||
\(633\) | −6.40465 | −0.254562 | ||||||||
\(634\) | 75.8869 | 3.01385 | ||||||||
\(635\) | 10.9828 | 0.435841 | ||||||||
\(636\) | 23.6448 | 0.937579 | ||||||||
\(637\) | 26.3278 | 1.04314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.11030 | −0.0834821 | ||||||||
\(640\) | 17.9976 | 0.711419 | ||||||||
\(641\) | −17.5210 | −0.692036 | −0.346018 | − | 0.938228i | \(-0.612466\pi\) | ||||
−0.346018 | + | 0.938228i | \(0.612466\pi\) | |||||||
\(642\) | 44.3556 | 1.75058 | ||||||||
\(643\) | −0.699059 | −0.0275682 | −0.0137841 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137841 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(644\) | 94.1960 | 3.71184 | ||||||||
\(645\) | 2.22321 | 0.0875388 | ||||||||
\(646\) | −21.1243 | −0.831123 | ||||||||
\(647\) | 45.4242 | 1.78581 | 0.892905 | − | 0.450246i | \(-0.148664\pi\) | ||||
0.892905 | + | 0.450246i | \(0.148664\pi\) | |||||||
\(648\) | 5.33418 | 0.209547 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.30230 | 0.207973 | ||||||||
\(651\) | −27.2098 | −1.06643 | ||||||||
\(652\) | −12.0195 | −0.470722 | ||||||||
\(653\) | 37.1061 | 1.45207 | 0.726036 | − | 0.687656i | \(-0.241360\pi\) | ||||
0.726036 | + | 0.687656i | \(0.241360\pi\) | |||||||
\(654\) | 32.4993 | 1.27082 | ||||||||
\(655\) | −7.33115 | −0.286452 | ||||||||
\(656\) | 37.6020 | 1.46811 | ||||||||
\(657\) | 14.6506 | 0.571574 | ||||||||
\(658\) | 75.0198 | 2.92458 | ||||||||
\(659\) | −16.0716 | −0.626061 | −0.313031 | − | 0.949743i | \(-0.601344\pi\) | ||||
−0.313031 | + | 0.949743i | \(0.601344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.1478 | 1.63936 | 0.819680 | − | 0.572822i | \(-0.194151\pi\) | ||||
0.819680 | + | 0.572822i | \(0.194151\pi\) | |||||||
\(662\) | −2.71228 | −0.105416 | ||||||||
\(663\) | 8.46664 | 0.328817 | ||||||||
\(664\) | −56.8809 | −2.20741 | ||||||||
\(665\) | −9.45243 | −0.366549 | ||||||||
\(666\) | −21.2549 | −0.823612 | ||||||||
\(667\) | −40.9962 | −1.58738 | ||||||||
\(668\) | 15.7943 | 0.611101 | ||||||||
\(669\) | 14.3520 | 0.554879 | ||||||||
\(670\) | −23.7350 | −0.916964 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −6.82289 | −0.263199 | ||||||||
\(673\) | 38.9658 | 1.50202 | 0.751010 | − | 0.660291i | \(-0.229567\pi\) | ||||
0.751010 | + | 0.660291i | \(0.229567\pi\) | |||||||
\(674\) | −40.3444 | −1.55401 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −34.9879 | −1.34569 | ||||||||
\(677\) | 1.42510 | 0.0547709 | 0.0273854 | − | 0.999625i | \(-0.491282\pi\) | ||||
0.0273854 | + | 0.999625i | \(0.491282\pi\) | |||||||
\(678\) | 20.8018 | 0.798889 | ||||||||
\(679\) | −24.9218 | −0.956413 | ||||||||
\(680\) | 21.1243 | 0.810078 | ||||||||
\(681\) | 18.3113 | 0.701692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.1490 | −0.809245 | −0.404623 | − | 0.914484i | \(-0.632597\pi\) | ||||
−0.404623 | + | 0.914484i | \(0.632597\pi\) | |||||||
\(684\) | 8.92760 | 0.341355 | ||||||||
\(685\) | 16.6774 | 0.637211 | ||||||||
\(686\) | 57.9253 | 2.21160 | ||||||||
\(687\) | 18.9191 | 0.721807 | ||||||||
\(688\) | 10.9551 | 0.417659 | ||||||||
\(689\) | −12.1787 | −0.463972 | ||||||||
\(690\) | 12.8063 | 0.487528 | ||||||||
\(691\) | 27.8197 | 1.05831 | 0.529155 | − | 0.848525i | \(-0.322509\pi\) | ||||
0.529155 | + | 0.848525i | \(0.322509\pi\) | |||||||
\(692\) | 4.61949 | 0.175607 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.5579 | −0.742408 | ||||||||
\(695\) | −11.0386 | −0.418717 | ||||||||
\(696\) | 42.3500 | 1.60527 | ||||||||
\(697\) | −30.2196 | −1.14465 | ||||||||
\(698\) | 30.7826 | 1.16514 | ||||||||
\(699\) | −6.35813 | −0.240486 | ||||||||
\(700\) | 18.2421 | 0.689486 | ||||||||
\(701\) | −1.45437 | −0.0549307 | −0.0274653 | − | 0.999623i | \(-0.508744\pi\) | ||||
−0.0274653 | + | 0.999623i | \(0.508744\pi\) | |||||||
\(702\) | −5.30230 | −0.200122 | ||||||||
\(703\) | −18.4330 | −0.695213 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.88285 | 0.259223 | ||||||||
\(706\) | −34.2211 | −1.28793 | ||||||||
\(707\) | 30.9117 | 1.16255 | ||||||||
\(708\) | −15.6971 | −0.589934 | ||||||||
\(709\) | −12.3696 | −0.464551 | −0.232275 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232275 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(710\) | 5.23371 | 0.196418 | ||||||||
\(711\) | −3.26111 | −0.122301 | ||||||||
\(712\) | −40.7732 | −1.52804 | ||||||||
\(713\) | 31.9699 | 1.19728 | ||||||||
\(714\) | 43.1639 | 1.61537 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.0035 | −0.747566 | ||||||||
\(717\) | −13.6150 | −0.508461 | ||||||||
\(718\) | 53.6313 | 2.00150 | ||||||||
\(719\) | 30.4067 | 1.13398 | 0.566989 | − | 0.823725i | \(-0.308108\pi\) | ||||
0.566989 | + | 0.823725i | \(0.308108\pi\) | |||||||
\(720\) | −4.92760 | −0.183641 | ||||||||
\(721\) | 2.73773 | 0.101959 | ||||||||
\(722\) | −35.6488 | −1.32671 | ||||||||
\(723\) | 10.1564 | 0.377721 | ||||||||
\(724\) | −89.0857 | −3.31084 | ||||||||
\(725\) | −7.93936 | −0.294860 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.7184 | 1.36181 | 0.680906 | − | 0.732371i | \(-0.261586\pi\) | ||||
0.680906 | + | 0.732371i | \(0.261586\pi\) | |||||||
\(728\) | 50.1196 | 1.85755 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −36.3347 | −1.34481 | ||||||||
\(731\) | −8.80428 | −0.325638 | ||||||||
\(732\) | 20.0666 | 0.741685 | ||||||||
\(733\) | −42.8001 | −1.58086 | −0.790429 | − | 0.612554i | \(-0.790142\pi\) | ||||
−0.790429 | + | 0.612554i | \(0.790142\pi\) | |||||||
\(734\) | 57.3602 | 2.11720 | ||||||||
\(735\) | 12.3145 | 0.454226 | ||||||||
\(736\) | 8.01651 | 0.295492 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.9252 | 0.696648 | ||||||||
\(739\) | 32.2616 | 1.18676 | 0.593381 | − | 0.804921i | \(-0.297793\pi\) | ||||
0.593381 | + | 0.804921i | \(0.297793\pi\) | |||||||
\(740\) | 35.5735 | 1.30771 | ||||||||
\(741\) | −4.59833 | −0.168924 | ||||||||
\(742\) | −62.0885 | −2.27934 | ||||||||
\(743\) | −40.5472 | −1.48753 | −0.743767 | − | 0.668439i | \(-0.766963\pi\) | ||||
−0.743767 | + | 0.668439i | \(0.766963\pi\) | |||||||
\(744\) | −33.0257 | −1.21078 | ||||||||
\(745\) | 4.61118 | 0.168941 | ||||||||
\(746\) | 58.8533 | 2.15477 | ||||||||
\(747\) | −10.6635 | −0.390156 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −78.6002 | −2.87199 | ||||||||
\(750\) | 2.48008 | 0.0905598 | ||||||||
\(751\) | −33.5276 | −1.22344 | −0.611720 | − | 0.791074i | \(-0.709522\pi\) | ||||
−0.611720 | + | 0.791074i | \(0.709522\pi\) | |||||||
\(752\) | 33.9159 | 1.23679 | ||||||||
\(753\) | −15.7579 | −0.574248 | ||||||||
\(754\) | −42.0968 | −1.53308 | ||||||||
\(755\) | −9.00914 | −0.327876 | ||||||||
\(756\) | −18.2421 | −0.663458 | ||||||||
\(757\) | 10.8866 | 0.395679 | 0.197839 | − | 0.980234i | \(-0.436608\pi\) | ||||
0.197839 | + | 0.980234i | \(0.436608\pi\) | |||||||
\(758\) | −81.9627 | −2.97702 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.4728 | −0.416163 | ||||||||
\(761\) | 21.7351 | 0.787896 | 0.393948 | − | 0.919133i | \(-0.371109\pi\) | ||||
0.393948 | + | 0.919133i | \(0.371109\pi\) | |||||||
\(762\) | 27.2384 | 0.986742 | ||||||||
\(763\) | −57.5903 | −2.08491 | ||||||||
\(764\) | −38.8592 | −1.40588 | ||||||||
\(765\) | 3.96017 | 0.143180 | ||||||||
\(766\) | −19.7754 | −0.714516 | ||||||||
\(767\) | 8.08509 | 0.291936 | ||||||||
\(768\) | 32.6258 | 1.17728 | ||||||||
\(769\) | 38.6384 | 1.39333 | 0.696667 | − | 0.717394i | \(-0.254665\pi\) | ||||
0.696667 | + | 0.717394i | \(0.254665\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.36335 | 0.0491000 | ||||||||
\(772\) | 76.4113 | 2.75010 | ||||||||
\(773\) | −7.50909 | −0.270083 | −0.135042 | − | 0.990840i | \(-0.543117\pi\) | ||||
−0.135042 | + | 0.990840i | \(0.543117\pi\) | |||||||
\(774\) | 5.51374 | 0.198187 | ||||||||
\(775\) | 6.19132 | 0.222399 | ||||||||
\(776\) | −30.2487 | −1.08587 | ||||||||
\(777\) | 37.6647 | 1.35122 | ||||||||
\(778\) | 10.6338 | 0.381239 | ||||||||
\(779\) | 16.4126 | 0.588042 | ||||||||
\(780\) | 8.87423 | 0.317748 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −50.7151 | −1.81357 | ||||||||
\(783\) | 7.93936 | 0.283730 | ||||||||
\(784\) | 60.6808 | 2.16717 | ||||||||
\(785\) | −2.98902 | −0.106683 | ||||||||
\(786\) | −18.1819 | −0.648525 | ||||||||
\(787\) | 37.4105 | 1.33354 | 0.666770 | − | 0.745264i | \(-0.267676\pi\) | ||||
0.666770 | + | 0.745264i | \(0.267676\pi\) | |||||||
\(788\) | 19.3918 | 0.690806 | ||||||||
\(789\) | −8.12002 | −0.289080 | ||||||||
\(790\) | 8.08781 | 0.287751 | ||||||||
\(791\) | −36.8618 | −1.31066 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3357 | −0.367031 | ||||||||
\(794\) | −5.48315 | −0.194590 | ||||||||
\(795\) | −5.69644 | −0.202032 | ||||||||
\(796\) | −67.2507 | −2.38364 | ||||||||
\(797\) | 10.7695 | 0.381476 | 0.190738 | − | 0.981641i | \(-0.438912\pi\) | ||||
0.190738 | + | 0.981641i | \(0.438912\pi\) | |||||||
\(798\) | −23.4428 | −0.829866 | ||||||||
\(799\) | −27.2572 | −0.964292 | ||||||||
\(800\) | 1.55248 | 0.0548886 | ||||||||
\(801\) | −7.64375 | −0.270079 | ||||||||
\(802\) | 30.1275 | 1.06384 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −39.7243 | −1.40097 | ||||||||
\(805\) | −22.6934 | −0.799838 | ||||||||
\(806\) | 32.8282 | 1.15632 | ||||||||
\(807\) | 11.7112 | 0.412255 | ||||||||
\(808\) | 37.5189 | 1.31991 | ||||||||
\(809\) | −20.1705 | −0.709155 | −0.354578 | − | 0.935027i | \(-0.615375\pi\) | ||||
−0.354578 | + | 0.935027i | \(0.615375\pi\) | |||||||
\(810\) | −2.48008 | −0.0871412 | ||||||||
\(811\) | −4.33664 | −0.152280 | −0.0761399 | − | 0.997097i | \(-0.524260\pi\) | ||||
−0.0761399 | + | 0.997097i | \(0.524260\pi\) | |||||||
\(812\) | −144.830 | −5.08255 | ||||||||
\(813\) | 2.18651 | 0.0766843 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.89571 | 0.101432 | ||||||||
\(816\) | 19.5141 | 0.683130 | ||||||||
\(817\) | 4.78170 | 0.167291 | ||||||||
\(818\) | −83.9764 | −2.93616 | ||||||||
\(819\) | 9.39592 | 0.328320 | ||||||||
\(820\) | −31.6744 | −1.10612 | ||||||||
\(821\) | −44.7129 | −1.56049 | −0.780246 | − | 0.625472i | \(-0.784906\pi\) | ||||
−0.780246 | + | 0.625472i | \(0.784906\pi\) | |||||||
\(822\) | 41.3614 | 1.44264 | ||||||||
\(823\) | −23.8721 | −0.832130 | −0.416065 | − | 0.909335i | \(-0.636591\pi\) | ||||
−0.416065 | + | 0.909335i | \(0.636591\pi\) | |||||||
\(824\) | 3.32290 | 0.115759 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41.2187 | 1.43418 | ||||||||
\(827\) | −3.43278 | −0.119370 | −0.0596848 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596848 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(828\) | 21.4334 | 0.744862 | ||||||||
\(829\) | 23.8429 | 0.828097 | 0.414048 | − | 0.910255i | \(-0.364114\pi\) | ||||
0.414048 | + | 0.910255i | \(0.364114\pi\) | |||||||
\(830\) | 26.4463 | 0.917963 | ||||||||
\(831\) | 10.6733 | 0.370252 | ||||||||
\(832\) | −12.8382 | −0.445085 | ||||||||
\(833\) | −48.7674 | −1.68969 | ||||||||
\(834\) | −27.3766 | −0.947973 | ||||||||
\(835\) | −3.80512 | −0.131682 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.19132 | −0.214003 | ||||||||
\(838\) | 45.0342 | 1.55568 | ||||||||
\(839\) | −16.6444 | −0.574629 | −0.287315 | − | 0.957836i | \(-0.592763\pi\) | ||||
−0.287315 | + | 0.957836i | \(0.592763\pi\) | |||||||
\(840\) | 23.4428 | 0.808853 | ||||||||
\(841\) | 34.0334 | 1.17357 | ||||||||
\(842\) | 97.1096 | 3.34662 | ||||||||
\(843\) | 5.43272 | 0.187113 | ||||||||
\(844\) | 26.5845 | 0.915075 | ||||||||
\(845\) | 8.42916 | 0.289972 | ||||||||
\(846\) | 17.0700 | 0.586880 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28.0698 | −0.963920 | ||||||||
\(849\) | 18.2401 | 0.626000 | ||||||||
\(850\) | −9.82154 | −0.336876 | ||||||||
\(851\) | −44.2539 | −1.51701 | ||||||||
\(852\) | 8.75944 | 0.300093 | ||||||||
\(853\) | −4.76800 | −0.163253 | −0.0816266 | − | 0.996663i | \(-0.526011\pi\) | ||||
−0.0816266 | + | 0.996663i | \(0.526011\pi\) | |||||||
\(854\) | −52.6926 | −1.80310 | ||||||||
\(855\) | −2.15081 | −0.0735561 | ||||||||
\(856\) | −95.4004 | −3.26072 | ||||||||
\(857\) | 27.8195 | 0.950296 | 0.475148 | − | 0.879906i | \(-0.342395\pi\) | ||||
0.475148 | + | 0.879906i | \(0.342395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1802 | −0.859139 | −0.429569 | − | 0.903034i | \(-0.641335\pi\) | ||||
−0.429569 | + | 0.903034i | \(0.641335\pi\) | |||||||
\(860\) | −9.22812 | −0.314676 | ||||||||
\(861\) | −33.5364 | −1.14292 | ||||||||
\(862\) | −56.6251 | −1.92866 | ||||||||
\(863\) | 21.9684 | 0.747812 | 0.373906 | − | 0.927467i | \(-0.378018\pi\) | ||||
0.373906 | + | 0.927467i | \(0.378018\pi\) | |||||||
\(864\) | −1.55248 | −0.0528166 | ||||||||
\(865\) | −1.11291 | −0.0378402 | ||||||||
\(866\) | 14.6124 | 0.496549 | ||||||||
\(867\) | 1.31709 | 0.0447308 | ||||||||
\(868\) | 112.943 | 3.83352 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −19.6903 | −0.667563 | ||||||||
\(871\) | 20.4607 | 0.693286 | ||||||||
\(872\) | −69.8998 | −2.36711 | ||||||||
\(873\) | −5.67073 | −0.191925 | ||||||||
\(874\) | 27.5440 | 0.931688 | ||||||||
\(875\) | −4.39482 | −0.148572 | ||||||||
\(876\) | −60.8118 | −2.05464 | ||||||||
\(877\) | −33.0169 | −1.11490 | −0.557451 | − | 0.830210i | \(-0.688221\pi\) | ||||
−0.557451 | + | 0.830210i | \(0.688221\pi\) | |||||||
\(878\) | −13.5554 | −0.457473 | ||||||||
\(879\) | −15.8594 | −0.534925 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26357 | 0.0762615 | 0.0381307 | − | 0.999273i | \(-0.487860\pi\) | ||||
0.0381307 | + | 0.999273i | \(0.487860\pi\) | |||||||
\(882\) | 30.5409 | 1.02837 | ||||||||
\(883\) | −28.9534 | −0.974360 | −0.487180 | − | 0.873302i | \(-0.661974\pi\) | ||||
−0.487180 | + | 0.873302i | \(0.661974\pi\) | |||||||
\(884\) | −35.1434 | −1.18200 | ||||||||
\(885\) | 3.78170 | 0.127120 | ||||||||
\(886\) | 62.5347 | 2.10090 | ||||||||
\(887\) | −36.6047 | −1.22907 | −0.614533 | − | 0.788891i | \(-0.710655\pi\) | ||||
−0.614533 | + | 0.788891i | \(0.710655\pi\) | |||||||
\(888\) | 45.7153 | 1.53411 | ||||||||
\(889\) | −48.2677 | −1.61885 | ||||||||
\(890\) | 18.9571 | 0.635444 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −59.5722 | −1.99463 | ||||||||
\(893\) | 14.8037 | 0.495387 | ||||||||
\(894\) | 11.4361 | 0.382481 | ||||||||
\(895\) | 4.81918 | 0.161087 | ||||||||
\(896\) | −79.0965 | −2.64243 | ||||||||
\(897\) | −11.0397 | −0.368604 | ||||||||
\(898\) | 36.8570 | 1.22993 | ||||||||
\(899\) | −49.1551 | −1.63942 | ||||||||
\(900\) | 4.15081 | 0.138360 | ||||||||
\(901\) | 22.5589 | 0.751544 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.77062 | −0.325146 | ||||||||
\(904\) | −44.7408 | −1.48806 | ||||||||
\(905\) | 21.4623 | 0.713429 | ||||||||
\(906\) | −22.3434 | −0.742311 | ||||||||
\(907\) | 23.2651 | 0.772506 | 0.386253 | − | 0.922393i | \(-0.373769\pi\) | ||||
0.386253 | + | 0.922393i | \(0.373769\pi\) | |||||||
\(908\) | −76.0069 | −2.52238 | ||||||||
\(909\) | 7.03366 | 0.233292 | ||||||||
\(910\) | −23.3027 | −0.772476 | ||||||||
\(911\) | 32.5851 | 1.07959 | 0.539796 | − | 0.841796i | \(-0.318501\pi\) | ||||
0.539796 | + | 0.841796i | \(0.318501\pi\) | |||||||
\(912\) | −10.5983 | −0.350946 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 95.9373 | 3.17332 | ||||||||
\(915\) | −4.83439 | −0.159820 | ||||||||
\(916\) | −78.5294 | −2.59469 | ||||||||
\(917\) | 32.2191 | 1.06397 | ||||||||
\(918\) | 9.82154 | 0.324159 | ||||||||
\(919\) | −4.19869 | −0.138502 | −0.0692511 | − | 0.997599i | \(-0.522061\pi\) | ||||
−0.0692511 | + | 0.997599i | \(0.522061\pi\) | |||||||
\(920\) | −27.5440 | −0.908097 | ||||||||
\(921\) | −18.1026 | −0.596501 | ||||||||
\(922\) | 10.7294 | 0.353355 | ||||||||
\(923\) | −4.51171 | −0.148505 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.57025 | −0.281788 | ||||||||
\(926\) | 1.79310 | 0.0589250 | ||||||||
\(927\) | 0.622945 | 0.0204602 | ||||||||
\(928\) | −12.3257 | −0.404612 | ||||||||
\(929\) | −35.9774 | −1.18038 | −0.590189 | − | 0.807265i | \(-0.700947\pi\) | ||||
−0.590189 | + | 0.807265i | \(0.700947\pi\) | |||||||
\(930\) | 15.3550 | 0.503510 | ||||||||
\(931\) | 26.4861 | 0.868047 | ||||||||
\(932\) | 26.3914 | 0.864478 | ||||||||
\(933\) | 18.3391 | 0.600395 | ||||||||
\(934\) | −49.3449 | −1.61462 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.4042 | 0.372759 | ||||||||
\(937\) | −20.6219 | −0.673689 | −0.336845 | − | 0.941560i | \(-0.609360\pi\) | ||||
−0.336845 | + | 0.941560i | \(0.609360\pi\) | |||||||
\(938\) | 104.311 | 3.40588 | ||||||||
\(939\) | −30.2483 | −0.987117 | ||||||||
\(940\) | −28.5694 | −0.931831 | ||||||||
\(941\) | 37.4439 | 1.22064 | 0.610318 | − | 0.792156i | \(-0.291042\pi\) | ||||
0.610318 | + | 0.792156i | \(0.291042\pi\) | |||||||
\(942\) | −7.41301 | −0.241529 | ||||||||
\(943\) | 39.4034 | 1.28315 | ||||||||
\(944\) | 18.6347 | 0.606508 | ||||||||
\(945\) | 4.39482 | 0.142964 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.3928 | 1.50756 | 0.753781 | − | 0.657126i | \(-0.228228\pi\) | ||||
0.753781 | + | 0.657126i | \(0.228228\pi\) | |||||||
\(948\) | 13.5362 | 0.439636 | ||||||||
\(949\) | 31.3223 | 1.01676 | ||||||||
\(950\) | 5.33418 | 0.173064 | ||||||||
\(951\) | −30.5985 | −0.992225 | ||||||||
\(952\) | −92.8374 | −3.00888 | ||||||||
\(953\) | 44.0854 | 1.42806 | 0.714032 | − | 0.700113i | \(-0.246867\pi\) | ||||
0.714032 | + | 0.700113i | \(0.246867\pi\) | |||||||
\(954\) | −14.1276 | −0.457399 | ||||||||
\(955\) | 9.36184 | 0.302942 | ||||||||
\(956\) | 56.5133 | 1.82777 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 46.4755 | 1.50156 | ||||||||
\(959\) | −73.2943 | −2.36680 | ||||||||
\(960\) | −6.00491 | −0.193808 | ||||||||
\(961\) | 7.33247 | 0.236531 | ||||||||
\(962\) | −45.4420 | −1.46511 | ||||||||
\(963\) | −17.8847 | −0.576327 | ||||||||
\(964\) | −42.1573 | −1.35779 | ||||||||
\(965\) | −18.4088 | −0.592600 | ||||||||
\(966\) | −56.2815 | −1.81083 | ||||||||
\(967\) | −18.7661 | −0.603476 | −0.301738 | − | 0.953391i | \(-0.597567\pi\) | ||||
−0.301738 | + | 0.953391i | \(0.597567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.51756 | 0.273623 | ||||||||
\(970\) | 14.0639 | 0.451564 | ||||||||
\(971\) | −48.7690 | −1.56507 | −0.782536 | − | 0.622605i | \(-0.786074\pi\) | ||||
−0.782536 | + | 0.622605i | \(0.786074\pi\) | |||||||
\(972\) | −4.15081 | −0.133137 | ||||||||
\(973\) | 48.5126 | 1.55524 | ||||||||
\(974\) | −1.30017 | −0.0416601 | ||||||||
\(975\) | −2.13795 | −0.0684692 | ||||||||
\(976\) | −23.8220 | −0.762522 | ||||||||
\(977\) | 18.6971 | 0.598174 | 0.299087 | − | 0.954226i | \(-0.403318\pi\) | ||||
0.299087 | + | 0.954226i | \(0.403318\pi\) | |||||||
\(978\) | 7.18160 | 0.229642 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −51.1150 | −1.63281 | ||||||||
\(981\) | −13.1041 | −0.418382 | ||||||||
\(982\) | −50.7695 | −1.62012 | ||||||||
\(983\) | −39.6527 | −1.26473 | −0.632363 | − | 0.774672i | \(-0.717915\pi\) | ||||
−0.632363 | + | 0.774672i | \(0.717915\pi\) | |||||||
\(984\) | −40.7046 | −1.29761 | ||||||||
\(985\) | −4.67182 | −0.148857 | ||||||||
\(986\) | 77.9767 | 2.48328 | ||||||||
\(987\) | −30.2489 | −0.962834 | ||||||||
\(988\) | 19.0868 | 0.607231 | ||||||||
\(989\) | 11.4799 | 0.365040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4204 | −0.489846 | −0.244923 | − | 0.969542i | \(-0.578763\pi\) | ||||
−0.244923 | + | 0.969542i | \(0.578763\pi\) | |||||||
\(992\) | 9.61192 | 0.305179 | ||||||||
\(993\) | 1.09362 | 0.0347051 | ||||||||
\(994\) | −23.0012 | −0.729555 | ||||||||
\(995\) | 16.2018 | 0.513632 | ||||||||
\(996\) | 44.2620 | 1.40249 | ||||||||
\(997\) | −15.3415 | −0.485869 | −0.242934 | − | 0.970043i | \(-0.578110\pi\) | ||||
−0.242934 | + | 0.970043i | \(0.578110\pi\) | |||||||
\(998\) | −11.3151 | −0.358172 | ||||||||
\(999\) | 8.57025 | 0.271151 |
(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 | 1815.2.a.r.1.4 | 4 | ||
3.2 | odd | 2 | 5445.2.a.br.1.1 | 4 | |||
5.4 | even | 2 | 9075.2.a.dg.1.1 | 4 | |||
11.2 | odd | 10 | 165.2.m.b.136.2 | yes | 8 | ||
11.6 | odd | 10 | 165.2.m.b.91.2 | ✓ | 8 | ||
11.10 | odd | 2 | 1815.2.a.v.1.1 | 4 | |||
33.2 | even | 10 | 495.2.n.b.136.1 | 8 | |||
33.17 | even | 10 | 495.2.n.b.91.1 | 8 | |||
33.32 | even | 2 | 5445.2.a.bk.1.4 | 4 | |||
55.2 | even | 20 | 825.2.bx.g.499.1 | 16 | |||
55.13 | even | 20 | 825.2.bx.g.499.4 | 16 | |||
55.17 | even | 20 | 825.2.bx.g.124.4 | 16 | |||
55.24 | odd | 10 | 825.2.n.i.301.1 | 8 | |||
55.28 | even | 20 | 825.2.bx.g.124.1 | 16 | |||
55.39 | odd | 10 | 825.2.n.i.751.1 | 8 | |||
55.54 | odd | 2 | 9075.2.a.cq.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.b.91.2 | ✓ | 8 | 11.6 | odd | 10 | ||
165.2.m.b.136.2 | yes | 8 | 11.2 | odd | 10 | ||
495.2.n.b.91.1 | 8 | 33.17 | even | 10 | |||
495.2.n.b.136.1 | 8 | 33.2 | even | 10 | |||
825.2.n.i.301.1 | 8 | 55.24 | odd | 10 | |||
825.2.n.i.751.1 | 8 | 55.39 | odd | 10 | |||
825.2.bx.g.124.1 | 16 | 55.28 | even | 20 | |||
825.2.bx.g.124.4 | 16 | 55.17 | even | 20 | |||
825.2.bx.g.499.1 | 16 | 55.2 | even | 20 | |||
825.2.bx.g.499.4 | 16 | 55.13 | even | 20 | |||
1815.2.a.r.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.v.1.1 | 4 | 11.10 | odd | 2 | |||
5445.2.a.bk.1.4 | 4 | 33.32 | even | 2 | |||
5445.2.a.br.1.1 | 4 | 3.2 | odd | 2 | |||
9075.2.a.cq.1.4 | 4 | 55.54 | odd | 2 | |||
9075.2.a.dg.1.1 | 4 | 5.4 | even | 2 |