Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.93688\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.93688 | 1.69561 | 0.847804 | − | 0.530310i | \(-0.177925\pi\) | ||||
0.847804 | + | 0.530310i | \(0.177925\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.167883 | −0.0750794 | −0.0375397 | − | 0.999295i | \(-0.511952\pi\) | ||||
−0.0375397 | + | 0.999295i | \(0.511952\pi\) | |||||||
\(6\) | 2.93688 | 1.19898 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.62525 | 1.87508 | ||||||||
\(10\) | −0.167883 | −0.0530892 | ||||||||
\(11\) | 5.85382 | 1.76499 | 0.882496 | − | 0.470320i | \(-0.155862\pi\) | ||||
0.882496 | + | 0.470320i | \(0.155862\pi\) | |||||||
\(12\) | 2.93688 | 0.847804 | ||||||||
\(13\) | 1.66176 | 0.460888 | 0.230444 | − | 0.973086i | \(-0.425982\pi\) | ||||
0.230444 | + | 0.973086i | \(0.425982\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.493051 | −0.127305 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.41436 | −0.343032 | −0.171516 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171516 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(18\) | 5.62525 | 1.32588 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.167883 | −0.0375397 | ||||||||
\(21\) | 2.93688 | 0.640879 | ||||||||
\(22\) | 5.85382 | 1.24804 | ||||||||
\(23\) | 8.26954 | 1.72432 | 0.862159 | − | 0.506637i | \(-0.169112\pi\) | ||||
0.862159 | + | 0.506637i | \(0.169112\pi\) | |||||||
\(24\) | 2.93688 | 0.599488 | ||||||||
\(25\) | −4.97182 | −0.994363 | ||||||||
\(26\) | 1.66176 | 0.325897 | ||||||||
\(27\) | 7.71005 | 1.48380 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.89591 | −1.28054 | −0.640269 | − | 0.768151i | \(-0.721177\pi\) | ||||
−0.640269 | + | 0.768151i | \(0.721177\pi\) | |||||||
\(30\) | −0.493051 | −0.0900184 | ||||||||
\(31\) | −8.06786 | −1.44903 | −0.724515 | − | 0.689259i | \(-0.757936\pi\) | ||||
−0.724515 | + | 0.689259i | \(0.757936\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 17.1919 | 2.99273 | ||||||||
\(34\) | −1.41436 | −0.242560 | ||||||||
\(35\) | −0.167883 | −0.0283774 | ||||||||
\(36\) | 5.62525 | 0.937542 | ||||||||
\(37\) | −6.18176 | −1.01628 | −0.508138 | − | 0.861276i | \(-0.669666\pi\) | ||||
−0.508138 | + | 0.861276i | \(0.669666\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.88037 | 0.781485 | ||||||||
\(40\) | −0.167883 | −0.0265446 | ||||||||
\(41\) | −4.84436 | −0.756561 | −0.378281 | − | 0.925691i | \(-0.623485\pi\) | ||||
−0.378281 | + | 0.925691i | \(0.623485\pi\) | |||||||
\(42\) | 2.93688 | 0.453170 | ||||||||
\(43\) | 1.16579 | 0.177782 | 0.0888908 | − | 0.996041i | \(-0.471668\pi\) | ||||
0.0888908 | + | 0.996041i | \(0.471668\pi\) | |||||||
\(44\) | 5.85382 | 0.882496 | ||||||||
\(45\) | −0.944382 | −0.140780 | ||||||||
\(46\) | 8.26954 | 1.21928 | ||||||||
\(47\) | 0.154029 | 0.0224675 | 0.0112337 | − | 0.999937i | \(-0.496424\pi\) | ||||
0.0112337 | + | 0.999937i | \(0.496424\pi\) | |||||||
\(48\) | 2.93688 | 0.423902 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.97182 | −0.703121 | ||||||||
\(51\) | −4.15379 | −0.581647 | ||||||||
\(52\) | 1.66176 | 0.230444 | ||||||||
\(53\) | −1.53808 | −0.211272 | −0.105636 | − | 0.994405i | \(-0.533688\pi\) | ||||
−0.105636 | + | 0.994405i | \(0.533688\pi\) | |||||||
\(54\) | 7.71005 | 1.04920 | ||||||||
\(55\) | −0.982754 | −0.132515 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.89591 | −0.905477 | ||||||||
\(59\) | −5.20856 | −0.678097 | −0.339049 | − | 0.940769i | \(-0.610105\pi\) | ||||
−0.339049 | + | 0.940769i | \(0.610105\pi\) | |||||||
\(60\) | −0.493051 | −0.0636526 | ||||||||
\(61\) | 12.3790 | 1.58497 | 0.792485 | − | 0.609891i | \(-0.208787\pi\) | ||||
0.792485 | + | 0.609891i | \(0.208787\pi\) | |||||||
\(62\) | −8.06786 | −1.02462 | ||||||||
\(63\) | 5.62525 | 0.708715 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.278980 | −0.0346032 | ||||||||
\(66\) | 17.1919 | 2.11618 | ||||||||
\(67\) | −2.21973 | −0.271184 | −0.135592 | − | 0.990765i | \(-0.543294\pi\) | ||||
−0.135592 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(68\) | −1.41436 | −0.171516 | ||||||||
\(69\) | 24.2866 | 2.92377 | ||||||||
\(70\) | −0.167883 | −0.0200658 | ||||||||
\(71\) | −8.24515 | −0.978519 | −0.489259 | − | 0.872138i | \(-0.662733\pi\) | ||||
−0.489259 | + | 0.872138i | \(0.662733\pi\) | |||||||
\(72\) | 5.62525 | 0.662942 | ||||||||
\(73\) | −10.6280 | −1.24391 | −0.621956 | − | 0.783052i | \(-0.713662\pi\) | ||||
−0.621956 | + | 0.783052i | \(0.713662\pi\) | |||||||
\(74\) | −6.18176 | −0.718615 | ||||||||
\(75\) | −14.6016 | −1.68605 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.85382 | 0.667104 | ||||||||
\(78\) | 4.88037 | 0.552594 | ||||||||
\(79\) | 5.69649 | 0.640905 | 0.320453 | − | 0.947265i | \(-0.396165\pi\) | ||||
0.320453 | + | 0.947265i | \(0.396165\pi\) | |||||||
\(80\) | −0.167883 | −0.0187699 | ||||||||
\(81\) | 5.76771 | 0.640856 | ||||||||
\(82\) | −4.84436 | −0.534970 | ||||||||
\(83\) | −9.93514 | −1.09052 | −0.545262 | − | 0.838266i | \(-0.683570\pi\) | ||||
−0.545262 | + | 0.838266i | \(0.683570\pi\) | |||||||
\(84\) | 2.93688 | 0.320440 | ||||||||
\(85\) | 0.237446 | 0.0257546 | ||||||||
\(86\) | 1.16579 | 0.125711 | ||||||||
\(87\) | −20.2524 | −2.17129 | ||||||||
\(88\) | 5.85382 | 0.624019 | ||||||||
\(89\) | 10.0204 | 1.06216 | 0.531081 | − | 0.847321i | \(-0.321786\pi\) | ||||
0.531081 | + | 0.847321i | \(0.321786\pi\) | |||||||
\(90\) | −0.944382 | −0.0995467 | ||||||||
\(91\) | 1.66176 | 0.174199 | ||||||||
\(92\) | 8.26954 | 0.862159 | ||||||||
\(93\) | −23.6943 | −2.45699 | ||||||||
\(94\) | 0.154029 | 0.0158869 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.93688 | 0.299744 | ||||||||
\(97\) | −12.2202 | −1.24077 | −0.620384 | − | 0.784298i | \(-0.713023\pi\) | ||||
−0.620384 | + | 0.784298i | \(0.713023\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 32.9292 | 3.30951 | ||||||||
\(100\) | −4.97182 | −0.497182 | ||||||||
\(101\) | 0.331346 | 0.0329701 | 0.0164851 | − | 0.999864i | \(-0.494752\pi\) | ||||
0.0164851 | + | 0.999864i | \(0.494752\pi\) | |||||||
\(102\) | −4.15379 | −0.411287 | ||||||||
\(103\) | 0.895065 | 0.0881934 | 0.0440967 | − | 0.999027i | \(-0.485959\pi\) | ||||
0.0440967 | + | 0.999027i | \(0.485959\pi\) | |||||||
\(104\) | 1.66176 | 0.162949 | ||||||||
\(105\) | −0.493051 | −0.0481168 | ||||||||
\(106\) | −1.53808 | −0.149392 | ||||||||
\(107\) | 10.1687 | 0.983045 | 0.491522 | − | 0.870865i | \(-0.336441\pi\) | ||||
0.491522 | + | 0.870865i | \(0.336441\pi\) | |||||||
\(108\) | 7.71005 | 0.741900 | ||||||||
\(109\) | 6.05462 | 0.579927 | 0.289964 | − | 0.957038i | \(-0.406357\pi\) | ||||
0.289964 | + | 0.957038i | \(0.406357\pi\) | |||||||
\(110\) | −0.982754 | −0.0937019 | ||||||||
\(111\) | −18.1551 | −1.72320 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 3.80616 | 0.358053 | 0.179027 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179027 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.38831 | −0.129461 | ||||||||
\(116\) | −6.89591 | −0.640269 | ||||||||
\(117\) | 9.34780 | 0.864204 | ||||||||
\(118\) | −5.20856 | −0.479487 | ||||||||
\(119\) | −1.41436 | −0.129654 | ||||||||
\(120\) | −0.493051 | −0.0450092 | ||||||||
\(121\) | 23.2672 | 2.11520 | ||||||||
\(122\) | 12.3790 | 1.12074 | ||||||||
\(123\) | −14.2273 | −1.28283 | ||||||||
\(124\) | −8.06786 | −0.724515 | ||||||||
\(125\) | 1.67410 | 0.149736 | ||||||||
\(126\) | 5.62525 | 0.501137 | ||||||||
\(127\) | 6.28735 | 0.557912 | 0.278956 | − | 0.960304i | \(-0.410012\pi\) | ||||
0.278956 | + | 0.960304i | \(0.410012\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.42379 | 0.301448 | ||||||||
\(130\) | −0.278980 | −0.0244682 | ||||||||
\(131\) | −18.9747 | −1.65782 | −0.828912 | − | 0.559380i | \(-0.811039\pi\) | ||||
−0.828912 | + | 0.559380i | \(0.811039\pi\) | |||||||
\(132\) | 17.1919 | 1.49637 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.21973 | −0.191756 | ||||||||
\(135\) | −1.29438 | −0.111403 | ||||||||
\(136\) | −1.41436 | −0.121280 | ||||||||
\(137\) | 10.2547 | 0.876119 | 0.438060 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438060 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(138\) | 24.2866 | 2.06742 | ||||||||
\(139\) | −17.3342 | −1.47027 | −0.735134 | − | 0.677921i | \(-0.762881\pi\) | ||||
−0.735134 | + | 0.677921i | \(0.762881\pi\) | |||||||
\(140\) | −0.167883 | −0.0141887 | ||||||||
\(141\) | 0.452366 | 0.0380961 | ||||||||
\(142\) | −8.24515 | −0.691917 | ||||||||
\(143\) | 9.72761 | 0.813464 | ||||||||
\(144\) | 5.62525 | 0.468771 | ||||||||
\(145\) | 1.15770 | 0.0961421 | ||||||||
\(146\) | −10.6280 | −0.879579 | ||||||||
\(147\) | 2.93688 | 0.242230 | ||||||||
\(148\) | −6.18176 | −0.508138 | ||||||||
\(149\) | 22.4619 | 1.84015 | 0.920074 | − | 0.391745i | \(-0.128129\pi\) | ||||
0.920074 | + | 0.391745i | \(0.128129\pi\) | |||||||
\(150\) | −14.6016 | −1.19222 | ||||||||
\(151\) | −11.9005 | −0.968452 | −0.484226 | − | 0.874943i | \(-0.660899\pi\) | ||||
−0.484226 | + | 0.874943i | \(0.660899\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.95611 | −0.643214 | ||||||||
\(154\) | 5.85382 | 0.471714 | ||||||||
\(155\) | 1.35445 | 0.108792 | ||||||||
\(156\) | 4.88037 | 0.390743 | ||||||||
\(157\) | −0.147652 | −0.0117839 | −0.00589195 | − | 0.999983i | \(-0.501875\pi\) | ||||
−0.00589195 | + | 0.999983i | \(0.501875\pi\) | |||||||
\(158\) | 5.69649 | 0.453189 | ||||||||
\(159\) | −4.51715 | −0.358234 | ||||||||
\(160\) | −0.167883 | −0.0132723 | ||||||||
\(161\) | 8.26954 | 0.651731 | ||||||||
\(162\) | 5.76771 | 0.453154 | ||||||||
\(163\) | −20.2248 | −1.58413 | −0.792063 | − | 0.610440i | \(-0.790993\pi\) | ||||
−0.792063 | + | 0.610440i | \(0.790993\pi\) | |||||||
\(164\) | −4.84436 | −0.378281 | ||||||||
\(165\) | −2.88623 | −0.224693 | ||||||||
\(166\) | −9.93514 | −0.771117 | ||||||||
\(167\) | 14.6174 | 1.13113 | 0.565565 | − | 0.824703i | \(-0.308658\pi\) | ||||
0.565565 | + | 0.824703i | \(0.308658\pi\) | |||||||
\(168\) | 2.93688 | 0.226585 | ||||||||
\(169\) | −10.2386 | −0.787582 | ||||||||
\(170\) | 0.237446 | 0.0182113 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.16579 | 0.0888908 | ||||||||
\(173\) | −16.5277 | −1.25658 | −0.628289 | − | 0.777980i | \(-0.716245\pi\) | ||||
−0.628289 | + | 0.777980i | \(0.716245\pi\) | |||||||
\(174\) | −20.2524 | −1.53533 | ||||||||
\(175\) | −4.97182 | −0.375834 | ||||||||
\(176\) | 5.85382 | 0.441248 | ||||||||
\(177\) | −15.2969 | −1.14979 | ||||||||
\(178\) | 10.0204 | 0.751062 | ||||||||
\(179\) | 11.8788 | 0.887861 | 0.443931 | − | 0.896061i | \(-0.353584\pi\) | ||||
0.443931 | + | 0.896061i | \(0.353584\pi\) | |||||||
\(180\) | −0.944382 | −0.0703901 | ||||||||
\(181\) | 14.3711 | 1.06820 | 0.534098 | − | 0.845423i | \(-0.320651\pi\) | ||||
0.534098 | + | 0.845423i | \(0.320651\pi\) | |||||||
\(182\) | 1.66176 | 0.123178 | ||||||||
\(183\) | 36.3557 | 2.68749 | ||||||||
\(184\) | 8.26954 | 0.609639 | ||||||||
\(185\) | 1.03781 | 0.0763013 | ||||||||
\(186\) | −23.6943 | −1.73735 | ||||||||
\(187\) | −8.27938 | −0.605448 | ||||||||
\(188\) | 0.154029 | 0.0112337 | ||||||||
\(189\) | 7.71005 | 0.560823 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.38259 | 0.678900 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(192\) | 2.93688 | 0.211951 | ||||||||
\(193\) | −25.0448 | −1.80276 | −0.901382 | − | 0.433025i | \(-0.857446\pi\) | ||||
−0.901382 | + | 0.433025i | \(0.857446\pi\) | |||||||
\(194\) | −12.2202 | −0.877356 | ||||||||
\(195\) | −0.819330 | −0.0586735 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.596816 | −0.0425214 | −0.0212607 | − | 0.999774i | \(-0.506768\pi\) | ||||
−0.0212607 | + | 0.999774i | \(0.506768\pi\) | |||||||
\(198\) | 32.9292 | 2.34018 | ||||||||
\(199\) | 23.0163 | 1.63158 | 0.815792 | − | 0.578345i | \(-0.196301\pi\) | ||||
0.815792 | + | 0.578345i | \(0.196301\pi\) | |||||||
\(200\) | −4.97182 | −0.351560 | ||||||||
\(201\) | −6.51908 | −0.459821 | ||||||||
\(202\) | 0.331346 | 0.0233134 | ||||||||
\(203\) | −6.89591 | −0.483998 | ||||||||
\(204\) | −4.15379 | −0.290824 | ||||||||
\(205\) | 0.813283 | 0.0568022 | ||||||||
\(206\) | 0.895065 | 0.0623621 | ||||||||
\(207\) | 46.5183 | 3.23324 | ||||||||
\(208\) | 1.66176 | 0.115222 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.493051 | −0.0340237 | ||||||||
\(211\) | 13.3969 | 0.922283 | 0.461142 | − | 0.887327i | \(-0.347440\pi\) | ||||
0.461142 | + | 0.887327i | \(0.347440\pi\) | |||||||
\(212\) | −1.53808 | −0.105636 | ||||||||
\(213\) | −24.2150 | −1.65918 | ||||||||
\(214\) | 10.1687 | 0.695117 | ||||||||
\(215\) | −0.195716 | −0.0133477 | ||||||||
\(216\) | 7.71005 | 0.524602 | ||||||||
\(217\) | −8.06786 | −0.547682 | ||||||||
\(218\) | 6.05462 | 0.410070 | ||||||||
\(219\) | −31.2131 | −2.10919 | ||||||||
\(220\) | −0.982754 | −0.0662573 | ||||||||
\(221\) | −2.35032 | −0.158099 | ||||||||
\(222\) | −18.1551 | −1.21849 | ||||||||
\(223\) | −7.31711 | −0.489990 | −0.244995 | − | 0.969524i | \(-0.578786\pi\) | ||||
−0.244995 | + | 0.969524i | \(0.578786\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −27.9677 | −1.86451 | ||||||||
\(226\) | 3.80616 | 0.253182 | ||||||||
\(227\) | 9.49511 | 0.630213 | 0.315106 | − | 0.949056i | \(-0.397960\pi\) | ||||
0.315106 | + | 0.949056i | \(0.397960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1411 | 0.802307 | 0.401153 | − | 0.916011i | \(-0.368609\pi\) | ||||
0.401153 | + | 0.916011i | \(0.368609\pi\) | |||||||
\(230\) | −1.38831 | −0.0915426 | ||||||||
\(231\) | 17.1919 | 1.13115 | ||||||||
\(232\) | −6.89591 | −0.452739 | ||||||||
\(233\) | −2.05744 | −0.134788 | −0.0673938 | − | 0.997726i | \(-0.521468\pi\) | ||||
−0.0673938 | + | 0.997726i | \(0.521468\pi\) | |||||||
\(234\) | 9.34780 | 0.611085 | ||||||||
\(235\) | −0.0258589 | −0.00168685 | ||||||||
\(236\) | −5.20856 | −0.339049 | ||||||||
\(237\) | 16.7299 | 1.08672 | ||||||||
\(238\) | −1.41436 | −0.0916791 | ||||||||
\(239\) | −6.66574 | −0.431171 | −0.215586 | − | 0.976485i | \(-0.569166\pi\) | ||||
−0.215586 | + | 0.976485i | \(0.569166\pi\) | |||||||
\(240\) | −0.493051 | −0.0318263 | ||||||||
\(241\) | −9.30578 | −0.599438 | −0.299719 | − | 0.954027i | \(-0.596893\pi\) | ||||
−0.299719 | + | 0.954027i | \(0.596893\pi\) | |||||||
\(242\) | 23.2672 | 1.49567 | ||||||||
\(243\) | −6.19108 | −0.397158 | ||||||||
\(244\) | 12.3790 | 0.792485 | ||||||||
\(245\) | −0.167883 | −0.0107256 | ||||||||
\(246\) | −14.2273 | −0.907098 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.06786 | −0.512310 | ||||||||
\(249\) | −29.1783 | −1.84910 | ||||||||
\(250\) | 1.67410 | 0.105879 | ||||||||
\(251\) | −10.4927 | −0.662296 | −0.331148 | − | 0.943579i | \(-0.607436\pi\) | ||||
−0.331148 | + | 0.943579i | \(0.607436\pi\) | |||||||
\(252\) | 5.62525 | 0.354358 | ||||||||
\(253\) | 48.4084 | 3.04341 | ||||||||
\(254\) | 6.28735 | 0.394503 | ||||||||
\(255\) | 0.697350 | 0.0436697 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.7324 | 1.48039 | 0.740194 | − | 0.672394i | \(-0.234734\pi\) | ||||
0.740194 | + | 0.672394i | \(0.234734\pi\) | |||||||
\(258\) | 3.42379 | 0.213156 | ||||||||
\(259\) | −6.18176 | −0.384116 | ||||||||
\(260\) | −0.278980 | −0.0173016 | ||||||||
\(261\) | −38.7912 | −2.40112 | ||||||||
\(262\) | −18.9747 | −1.17226 | ||||||||
\(263\) | 10.3381 | 0.637474 | 0.318737 | − | 0.947843i | \(-0.396741\pi\) | ||||
0.318737 | + | 0.947843i | \(0.396741\pi\) | |||||||
\(264\) | 17.1919 | 1.05809 | ||||||||
\(265\) | 0.258217 | 0.0158621 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.4288 | 1.80101 | ||||||||
\(268\) | −2.21973 | −0.135592 | ||||||||
\(269\) | 20.6722 | 1.26040 | 0.630202 | − | 0.776431i | \(-0.282972\pi\) | ||||
0.630202 | + | 0.776431i | \(0.282972\pi\) | |||||||
\(270\) | −1.29438 | −0.0787737 | ||||||||
\(271\) | 5.33469 | 0.324059 | 0.162030 | − | 0.986786i | \(-0.448196\pi\) | ||||
0.162030 | + | 0.986786i | \(0.448196\pi\) | |||||||
\(272\) | −1.41436 | −0.0857580 | ||||||||
\(273\) | 4.88037 | 0.295374 | ||||||||
\(274\) | 10.2547 | 0.619510 | ||||||||
\(275\) | −29.1041 | −1.75504 | ||||||||
\(276\) | 24.2866 | 1.46188 | ||||||||
\(277\) | 23.0145 | 1.38280 | 0.691402 | − | 0.722470i | \(-0.256993\pi\) | ||||
0.691402 | + | 0.722470i | \(0.256993\pi\) | |||||||
\(278\) | −17.3342 | −1.03964 | ||||||||
\(279\) | −45.3838 | −2.71705 | ||||||||
\(280\) | −0.167883 | −0.0100329 | ||||||||
\(281\) | 3.40916 | 0.203374 | 0.101687 | − | 0.994816i | \(-0.467576\pi\) | ||||
0.101687 | + | 0.994816i | \(0.467576\pi\) | |||||||
\(282\) | 0.452366 | 0.0269380 | ||||||||
\(283\) | 4.21235 | 0.250398 | 0.125199 | − | 0.992132i | \(-0.460043\pi\) | ||||
0.125199 | + | 0.992132i | \(0.460043\pi\) | |||||||
\(284\) | −8.24515 | −0.489259 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.72761 | 0.575206 | ||||||||
\(287\) | −4.84436 | −0.285953 | ||||||||
\(288\) | 5.62525 | 0.331471 | ||||||||
\(289\) | −14.9996 | −0.882329 | ||||||||
\(290\) | 1.15770 | 0.0679827 | ||||||||
\(291\) | −35.8891 | −2.10386 | ||||||||
\(292\) | −10.6280 | −0.621956 | ||||||||
\(293\) | −16.6053 | −0.970090 | −0.485045 | − | 0.874489i | \(-0.661197\pi\) | ||||
−0.485045 | + | 0.874489i | \(0.661197\pi\) | |||||||
\(294\) | 2.93688 | 0.171282 | ||||||||
\(295\) | 0.874428 | 0.0509112 | ||||||||
\(296\) | −6.18176 | −0.359307 | ||||||||
\(297\) | 45.1332 | 2.61889 | ||||||||
\(298\) | 22.4619 | 1.30118 | ||||||||
\(299\) | 13.7420 | 0.794718 | ||||||||
\(300\) | −14.6016 | −0.843025 | ||||||||
\(301\) | 1.16579 | 0.0671951 | ||||||||
\(302\) | −11.9005 | −0.684799 | ||||||||
\(303\) | 0.973122 | 0.0559044 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.07822 | −0.118999 | ||||||||
\(306\) | −7.95611 | −0.454821 | ||||||||
\(307\) | −13.7816 | −0.786560 | −0.393280 | − | 0.919419i | \(-0.628660\pi\) | ||||
−0.393280 | + | 0.919419i | \(0.628660\pi\) | |||||||
\(308\) | 5.85382 | 0.333552 | ||||||||
\(309\) | 2.62870 | 0.149541 | ||||||||
\(310\) | 1.35445 | 0.0769278 | ||||||||
\(311\) | −4.09294 | −0.232089 | −0.116045 | − | 0.993244i | \(-0.537022\pi\) | ||||
−0.116045 | + | 0.993244i | \(0.537022\pi\) | |||||||
\(312\) | 4.88037 | 0.276297 | ||||||||
\(313\) | 7.23396 | 0.408887 | 0.204444 | − | 0.978878i | \(-0.434461\pi\) | ||||
0.204444 | + | 0.978878i | \(0.434461\pi\) | |||||||
\(314\) | −0.147652 | −0.00833248 | ||||||||
\(315\) | −0.944382 | −0.0532099 | ||||||||
\(316\) | 5.69649 | 0.320453 | ||||||||
\(317\) | 31.7010 | 1.78050 | 0.890252 | − | 0.455468i | \(-0.150528\pi\) | ||||
0.890252 | + | 0.455468i | \(0.150528\pi\) | |||||||
\(318\) | −4.51715 | −0.253309 | ||||||||
\(319\) | −40.3674 | −2.26014 | ||||||||
\(320\) | −0.167883 | −0.00938493 | ||||||||
\(321\) | 29.8642 | 1.66686 | ||||||||
\(322\) | 8.26954 | 0.460843 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.76771 | 0.320428 | ||||||||
\(325\) | −8.26194 | −0.458290 | ||||||||
\(326\) | −20.2248 | −1.12015 | ||||||||
\(327\) | 17.7817 | 0.983329 | ||||||||
\(328\) | −4.84436 | −0.267485 | ||||||||
\(329\) | 0.154029 | 0.00849192 | ||||||||
\(330\) | −2.88623 | −0.158882 | ||||||||
\(331\) | 1.66753 | 0.0916557 | 0.0458278 | − | 0.998949i | \(-0.485407\pi\) | ||||
0.0458278 | + | 0.998949i | \(0.485407\pi\) | |||||||
\(332\) | −9.93514 | −0.545262 | ||||||||
\(333\) | −34.7740 | −1.90560 | ||||||||
\(334\) | 14.6174 | 0.799830 | ||||||||
\(335\) | 0.372655 | 0.0203603 | ||||||||
\(336\) | 2.93688 | 0.160220 | ||||||||
\(337\) | 23.1063 | 1.25868 | 0.629340 | − | 0.777130i | \(-0.283325\pi\) | ||||
0.629340 | + | 0.777130i | \(0.283325\pi\) | |||||||
\(338\) | −10.2386 | −0.556905 | ||||||||
\(339\) | 11.1782 | 0.607118 | ||||||||
\(340\) | 0.237446 | 0.0128773 | ||||||||
\(341\) | −47.2278 | −2.55753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.16579 | 0.0628553 | ||||||||
\(345\) | −4.07730 | −0.219515 | ||||||||
\(346\) | −16.5277 | −0.888535 | ||||||||
\(347\) | 35.3703 | 1.89878 | 0.949388 | − | 0.314106i | \(-0.101705\pi\) | ||||
0.949388 | + | 0.314106i | \(0.101705\pi\) | |||||||
\(348\) | −20.2524 | −1.08565 | ||||||||
\(349\) | 32.6789 | 1.74926 | 0.874632 | − | 0.484788i | \(-0.161103\pi\) | ||||
0.874632 | + | 0.484788i | \(0.161103\pi\) | |||||||
\(350\) | −4.97182 | −0.265755 | ||||||||
\(351\) | 12.8122 | 0.683865 | ||||||||
\(352\) | 5.85382 | 0.312009 | ||||||||
\(353\) | 16.5338 | 0.880006 | 0.440003 | − | 0.897996i | \(-0.354977\pi\) | ||||
0.440003 | + | 0.897996i | \(0.354977\pi\) | |||||||
\(354\) | −15.2969 | −0.813022 | ||||||||
\(355\) | 1.38422 | 0.0734666 | ||||||||
\(356\) | 10.0204 | 0.531081 | ||||||||
\(357\) | −4.15379 | −0.219842 | ||||||||
\(358\) | 11.8788 | 0.627813 | ||||||||
\(359\) | −6.82256 | −0.360081 | −0.180040 | − | 0.983659i | \(-0.557623\pi\) | ||||
−0.180040 | + | 0.983659i | \(0.557623\pi\) | |||||||
\(360\) | −0.944382 | −0.0497733 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 14.3711 | 0.755328 | ||||||||
\(363\) | 68.3328 | 3.58654 | ||||||||
\(364\) | 1.66176 | 0.0870997 | ||||||||
\(365\) | 1.78426 | 0.0933922 | ||||||||
\(366\) | 36.3557 | 1.90034 | ||||||||
\(367\) | 10.3686 | 0.541235 | 0.270617 | − | 0.962687i | \(-0.412772\pi\) | ||||
0.270617 | + | 0.962687i | \(0.412772\pi\) | |||||||
\(368\) | 8.26954 | 0.431080 | ||||||||
\(369\) | −27.2507 | −1.41862 | ||||||||
\(370\) | 1.03781 | 0.0539532 | ||||||||
\(371\) | −1.53808 | −0.0798531 | ||||||||
\(372\) | −23.6943 | −1.22849 | ||||||||
\(373\) | −9.75909 | −0.505306 | −0.252653 | − | 0.967557i | \(-0.581303\pi\) | ||||
−0.252653 | + | 0.967557i | \(0.581303\pi\) | |||||||
\(374\) | −8.27938 | −0.428117 | ||||||||
\(375\) | 4.91661 | 0.253893 | ||||||||
\(376\) | 0.154029 | 0.00794346 | ||||||||
\(377\) | −11.4593 | −0.590185 | ||||||||
\(378\) | 7.71005 | 0.396562 | ||||||||
\(379\) | 18.9676 | 0.974302 | 0.487151 | − | 0.873318i | \(-0.338036\pi\) | ||||
0.487151 | + | 0.873318i | \(0.338036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.4652 | 0.945999 | ||||||||
\(382\) | 9.38259 | 0.480055 | ||||||||
\(383\) | 7.57482 | 0.387055 | 0.193528 | − | 0.981095i | \(-0.438007\pi\) | ||||
0.193528 | + | 0.981095i | \(0.438007\pi\) | |||||||
\(384\) | 2.93688 | 0.149872 | ||||||||
\(385\) | −0.982754 | −0.0500858 | ||||||||
\(386\) | −25.0448 | −1.27475 | ||||||||
\(387\) | 6.55787 | 0.333355 | ||||||||
\(388\) | −12.2202 | −0.620384 | ||||||||
\(389\) | −19.4484 | −0.986073 | −0.493037 | − | 0.870009i | \(-0.664113\pi\) | ||||
−0.493037 | + | 0.870009i | \(0.664113\pi\) | |||||||
\(390\) | −0.819330 | −0.0414884 | ||||||||
\(391\) | −11.6961 | −0.591496 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −55.7262 | −2.81102 | ||||||||
\(394\) | −0.596816 | −0.0300672 | ||||||||
\(395\) | −0.956342 | −0.0481188 | ||||||||
\(396\) | 32.9292 | 1.65475 | ||||||||
\(397\) | −12.6930 | −0.637045 | −0.318523 | − | 0.947915i | \(-0.603187\pi\) | ||||
−0.318523 | + | 0.947915i | \(0.603187\pi\) | |||||||
\(398\) | 23.0163 | 1.15370 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.97182 | −0.248591 | ||||||||
\(401\) | −18.9738 | −0.947508 | −0.473754 | − | 0.880657i | \(-0.657101\pi\) | ||||
−0.473754 | + | 0.880657i | \(0.657101\pi\) | |||||||
\(402\) | −6.51908 | −0.325142 | ||||||||
\(403\) | −13.4068 | −0.667841 | ||||||||
\(404\) | 0.331346 | 0.0164851 | ||||||||
\(405\) | −0.968298 | −0.0481151 | ||||||||
\(406\) | −6.89591 | −0.342238 | ||||||||
\(407\) | −36.1869 | −1.79372 | ||||||||
\(408\) | −4.15379 | −0.205643 | ||||||||
\(409\) | −10.1298 | −0.500887 | −0.250443 | − | 0.968131i | \(-0.580576\pi\) | ||||
−0.250443 | + | 0.968131i | \(0.580576\pi\) | |||||||
\(410\) | 0.813283 | 0.0401652 | ||||||||
\(411\) | 30.1168 | 1.48555 | ||||||||
\(412\) | 0.895065 | 0.0440967 | ||||||||
\(413\) | −5.20856 | −0.256297 | ||||||||
\(414\) | 46.5183 | 2.28625 | ||||||||
\(415\) | 1.66794 | 0.0818759 | ||||||||
\(416\) | 1.66176 | 0.0814743 | ||||||||
\(417\) | −50.9085 | −2.49300 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.3112 | −1.28539 | −0.642694 | − | 0.766123i | \(-0.722183\pi\) | ||||
−0.642694 | + | 0.766123i | \(0.722183\pi\) | |||||||
\(420\) | −0.493051 | −0.0240584 | ||||||||
\(421\) | −26.5413 | −1.29354 | −0.646772 | − | 0.762683i | \(-0.723882\pi\) | ||||
−0.646772 | + | 0.762683i | \(0.723882\pi\) | |||||||
\(422\) | 13.3969 | 0.652153 | ||||||||
\(423\) | 0.866454 | 0.0421284 | ||||||||
\(424\) | −1.53808 | −0.0746958 | ||||||||
\(425\) | 7.03192 | 0.341098 | ||||||||
\(426\) | −24.2150 | −1.17322 | ||||||||
\(427\) | 12.3790 | 0.599063 | ||||||||
\(428\) | 10.1687 | 0.491522 | ||||||||
\(429\) | 28.5688 | 1.37932 | ||||||||
\(430\) | −0.195716 | −0.00943827 | ||||||||
\(431\) | −25.5907 | −1.23266 | −0.616331 | − | 0.787487i | \(-0.711382\pi\) | ||||
−0.616331 | + | 0.787487i | \(0.711382\pi\) | |||||||
\(432\) | 7.71005 | 0.370950 | ||||||||
\(433\) | 8.94247 | 0.429748 | 0.214874 | − | 0.976642i | \(-0.431066\pi\) | ||||
0.214874 | + | 0.976642i | \(0.431066\pi\) | |||||||
\(434\) | −8.06786 | −0.387270 | ||||||||
\(435\) | 3.40004 | 0.163019 | ||||||||
\(436\) | 6.05462 | 0.289964 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −31.2131 | −1.49142 | ||||||||
\(439\) | −12.4057 | −0.592090 | −0.296045 | − | 0.955174i | \(-0.595668\pi\) | ||||
−0.296045 | + | 0.955174i | \(0.595668\pi\) | |||||||
\(440\) | −0.982754 | −0.0468510 | ||||||||
\(441\) | 5.62525 | 0.267869 | ||||||||
\(442\) | −2.35032 | −0.111793 | ||||||||
\(443\) | −17.6686 | −0.839463 | −0.419731 | − | 0.907648i | \(-0.637876\pi\) | ||||
−0.419731 | + | 0.907648i | \(0.637876\pi\) | |||||||
\(444\) | −18.1551 | −0.861602 | ||||||||
\(445\) | −1.68225 | −0.0797465 | ||||||||
\(446\) | −7.31711 | −0.346475 | ||||||||
\(447\) | 65.9678 | 3.12017 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −14.1170 | −0.666220 | −0.333110 | − | 0.942888i | \(-0.608098\pi\) | ||||
−0.333110 | + | 0.942888i | \(0.608098\pi\) | |||||||
\(450\) | −27.9677 | −1.31841 | ||||||||
\(451\) | −28.3580 | −1.33532 | ||||||||
\(452\) | 3.80616 | 0.179027 | ||||||||
\(453\) | −34.9504 | −1.64211 | ||||||||
\(454\) | 9.49511 | 0.445628 | ||||||||
\(455\) | −0.278980 | −0.0130788 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.6332 | −1.05874 | −0.529369 | − | 0.848392i | \(-0.677571\pi\) | ||||
−0.529369 | + | 0.848392i | \(0.677571\pi\) | |||||||
\(458\) | 12.1411 | 0.567317 | ||||||||
\(459\) | −10.9048 | −0.508990 | ||||||||
\(460\) | −1.38831 | −0.0647304 | ||||||||
\(461\) | −28.3983 | −1.32264 | −0.661319 | − | 0.750104i | \(-0.730003\pi\) | ||||
−0.661319 | + | 0.750104i | \(0.730003\pi\) | |||||||
\(462\) | 17.1919 | 0.799842 | ||||||||
\(463\) | 2.08478 | 0.0968878 | 0.0484439 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484439 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(464\) | −6.89591 | −0.320135 | ||||||||
\(465\) | 3.97787 | 0.184469 | ||||||||
\(466\) | −2.05744 | −0.0953092 | ||||||||
\(467\) | −26.3159 | −1.21776 | −0.608878 | − | 0.793264i | \(-0.708380\pi\) | ||||
−0.608878 | + | 0.793264i | \(0.708380\pi\) | |||||||
\(468\) | 9.34780 | 0.432102 | ||||||||
\(469\) | −2.21973 | −0.102498 | ||||||||
\(470\) | −0.0258589 | −0.00119278 | ||||||||
\(471\) | −0.433636 | −0.0199809 | ||||||||
\(472\) | −5.20856 | −0.239744 | ||||||||
\(473\) | 6.82433 | 0.313783 | ||||||||
\(474\) | 16.7299 | 0.768430 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.41436 | −0.0648269 | ||||||||
\(477\) | −8.65209 | −0.396152 | ||||||||
\(478\) | −6.66574 | −0.304884 | ||||||||
\(479\) | −4.82538 | −0.220477 | −0.110239 | − | 0.993905i | \(-0.535161\pi\) | ||||
−0.110239 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(480\) | −0.493051 | −0.0225046 | ||||||||
\(481\) | −10.2726 | −0.468389 | ||||||||
\(482\) | −9.30578 | −0.423867 | ||||||||
\(483\) | 24.2866 | 1.10508 | ||||||||
\(484\) | 23.2672 | 1.05760 | ||||||||
\(485\) | 2.05155 | 0.0931562 | ||||||||
\(486\) | −6.19108 | −0.280833 | ||||||||
\(487\) | −24.0690 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683597\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683597\pi\) | |||||||
\(488\) | 12.3790 | 0.560372 | ||||||||
\(489\) | −59.3977 | −2.68605 | ||||||||
\(490\) | −0.167883 | −0.00758417 | ||||||||
\(491\) | 16.4774 | 0.743616 | 0.371808 | − | 0.928310i | \(-0.378738\pi\) | ||||
0.371808 | + | 0.928310i | \(0.378738\pi\) | |||||||
\(492\) | −14.2273 | −0.641415 | ||||||||
\(493\) | 9.75328 | 0.439265 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.52824 | −0.248476 | ||||||||
\(496\) | −8.06786 | −0.362258 | ||||||||
\(497\) | −8.24515 | −0.369845 | ||||||||
\(498\) | −29.1783 | −1.30751 | ||||||||
\(499\) | −33.9334 | −1.51907 | −0.759533 | − | 0.650469i | \(-0.774573\pi\) | ||||
−0.759533 | + | 0.650469i | \(0.774573\pi\) | |||||||
\(500\) | 1.67410 | 0.0748678 | ||||||||
\(501\) | 42.9296 | 1.91795 | ||||||||
\(502\) | −10.4927 | −0.468314 | ||||||||
\(503\) | −15.5750 | −0.694455 | −0.347227 | − | 0.937781i | \(-0.612877\pi\) | ||||
−0.347227 | + | 0.937781i | \(0.612877\pi\) | |||||||
\(504\) | 5.62525 | 0.250569 | ||||||||
\(505\) | −0.0556272 | −0.00247538 | ||||||||
\(506\) | 48.4084 | 2.15201 | ||||||||
\(507\) | −30.0694 | −1.33543 | ||||||||
\(508\) | 6.28735 | 0.278956 | ||||||||
\(509\) | −33.7611 | −1.49643 | −0.748217 | − | 0.663454i | \(-0.769090\pi\) | ||||
−0.748217 | + | 0.663454i | \(0.769090\pi\) | |||||||
\(510\) | 0.697350 | 0.0308792 | ||||||||
\(511\) | −10.6280 | −0.470154 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.7324 | 1.04679 | ||||||||
\(515\) | −0.150266 | −0.00662151 | ||||||||
\(516\) | 3.42379 | 0.150724 | ||||||||
\(517\) | 0.901660 | 0.0396549 | ||||||||
\(518\) | −6.18176 | −0.271611 | ||||||||
\(519\) | −48.5399 | −2.13066 | ||||||||
\(520\) | −0.278980 | −0.0122341 | ||||||||
\(521\) | −4.70124 | −0.205965 | −0.102982 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102982 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(522\) | −38.7912 | −1.69785 | ||||||||
\(523\) | −41.8308 | −1.82913 | −0.914566 | − | 0.404437i | \(-0.867468\pi\) | ||||
−0.914566 | + | 0.404437i | \(0.867468\pi\) | |||||||
\(524\) | −18.9747 | −0.828912 | ||||||||
\(525\) | −14.6016 | −0.637267 | ||||||||
\(526\) | 10.3381 | 0.450762 | ||||||||
\(527\) | 11.4108 | 0.497064 | ||||||||
\(528\) | 17.1919 | 0.748183 | ||||||||
\(529\) | 45.3853 | 1.97327 | ||||||||
\(530\) | 0.258217 | 0.0112162 | ||||||||
\(531\) | −29.2995 | −1.27149 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.05014 | −0.348690 | ||||||||
\(534\) | 29.4288 | 1.27351 | ||||||||
\(535\) | −1.70715 | −0.0738064 | ||||||||
\(536\) | −2.21973 | −0.0958779 | ||||||||
\(537\) | 34.8865 | 1.50546 | ||||||||
\(538\) | 20.6722 | 0.891240 | ||||||||
\(539\) | 5.85382 | 0.252142 | ||||||||
\(540\) | −1.29438 | −0.0557014 | ||||||||
\(541\) | −3.33966 | −0.143583 | −0.0717916 | − | 0.997420i | \(-0.522872\pi\) | ||||
−0.0717916 | + | 0.997420i | \(0.522872\pi\) | |||||||
\(542\) | 5.33469 | 0.229144 | ||||||||
\(543\) | 42.2062 | 1.81124 | ||||||||
\(544\) | −1.41436 | −0.0606400 | ||||||||
\(545\) | −1.01647 | −0.0435406 | ||||||||
\(546\) | 4.88037 | 0.208861 | ||||||||
\(547\) | 25.1993 | 1.07744 | 0.538722 | − | 0.842484i | \(-0.318907\pi\) | ||||
0.538722 | + | 0.842484i | \(0.318907\pi\) | |||||||
\(548\) | 10.2547 | 0.438060 | ||||||||
\(549\) | 69.6351 | 2.97195 | ||||||||
\(550\) | −29.1041 | −1.24100 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 24.2866 | 1.03371 | ||||||||
\(553\) | 5.69649 | 0.242239 | ||||||||
\(554\) | 23.0145 | 0.977791 | ||||||||
\(555\) | 3.04792 | 0.129377 | ||||||||
\(556\) | −17.3342 | −0.735134 | ||||||||
\(557\) | −20.4468 | −0.866359 | −0.433180 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433180 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(558\) | −45.3838 | −1.92125 | ||||||||
\(559\) | 1.93726 | 0.0819374 | ||||||||
\(560\) | −0.167883 | −0.00709434 | ||||||||
\(561\) | −24.3155 | −1.02660 | ||||||||
\(562\) | 3.40916 | 0.143807 | ||||||||
\(563\) | −6.79170 | −0.286236 | −0.143118 | − | 0.989706i | \(-0.545713\pi\) | ||||
−0.143118 | + | 0.989706i | \(0.545713\pi\) | |||||||
\(564\) | 0.452366 | 0.0190480 | ||||||||
\(565\) | −0.638988 | −0.0268824 | ||||||||
\(566\) | 4.21235 | 0.177058 | ||||||||
\(567\) | 5.76771 | 0.242221 | ||||||||
\(568\) | −8.24515 | −0.345959 | ||||||||
\(569\) | 23.1581 | 0.970836 | 0.485418 | − | 0.874282i | \(-0.338667\pi\) | ||||
0.485418 | + | 0.874282i | \(0.338667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.7662 | 1.20383 | 0.601914 | − | 0.798561i | \(-0.294405\pi\) | ||||
0.601914 | + | 0.798561i | \(0.294405\pi\) | |||||||
\(572\) | 9.72761 | 0.406732 | ||||||||
\(573\) | 27.5555 | 1.15115 | ||||||||
\(574\) | −4.84436 | −0.202199 | ||||||||
\(575\) | −41.1146 | −1.71460 | ||||||||
\(576\) | 5.62525 | 0.234386 | ||||||||
\(577\) | 18.3410 | 0.763547 | 0.381773 | − | 0.924256i | \(-0.375314\pi\) | ||||
0.381773 | + | 0.924256i | \(0.375314\pi\) | |||||||
\(578\) | −14.9996 | −0.623901 | ||||||||
\(579\) | −73.5535 | −3.05678 | ||||||||
\(580\) | 1.15770 | 0.0480710 | ||||||||
\(581\) | −9.93514 | −0.412179 | ||||||||
\(582\) | −35.8891 | −1.48765 | ||||||||
\(583\) | −9.00364 | −0.372893 | ||||||||
\(584\) | −10.6280 | −0.439789 | ||||||||
\(585\) | −1.56933 | −0.0648839 | ||||||||
\(586\) | −16.6053 | −0.685957 | ||||||||
\(587\) | −47.4916 | −1.96019 | −0.980095 | − | 0.198529i | \(-0.936384\pi\) | ||||
−0.980095 | + | 0.198529i | \(0.936384\pi\) | |||||||
\(588\) | 2.93688 | 0.121115 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.874428 | 0.0359996 | ||||||||
\(591\) | −1.75278 | −0.0720996 | ||||||||
\(592\) | −6.18176 | −0.254069 | ||||||||
\(593\) | 11.7283 | 0.481625 | 0.240812 | − | 0.970572i | \(-0.422586\pi\) | ||||
0.240812 | + | 0.970572i | \(0.422586\pi\) | |||||||
\(594\) | 45.1332 | 1.85184 | ||||||||
\(595\) | 0.237446 | 0.00973434 | ||||||||
\(596\) | 22.4619 | 0.920074 | ||||||||
\(597\) | 67.5961 | 2.76653 | ||||||||
\(598\) | 13.7420 | 0.561950 | ||||||||
\(599\) | −37.5795 | −1.53546 | −0.767728 | − | 0.640775i | \(-0.778613\pi\) | ||||
−0.767728 | + | 0.640775i | \(0.778613\pi\) | |||||||
\(600\) | −14.6016 | −0.596108 | ||||||||
\(601\) | −1.33987 | −0.0546545 | −0.0273273 | − | 0.999627i | \(-0.508700\pi\) | ||||
−0.0273273 | + | 0.999627i | \(0.508700\pi\) | |||||||
\(602\) | 1.16579 | 0.0475141 | ||||||||
\(603\) | −12.4866 | −0.508492 | ||||||||
\(604\) | −11.9005 | −0.484226 | ||||||||
\(605\) | −3.90615 | −0.158808 | ||||||||
\(606\) | 0.973122 | 0.0395304 | ||||||||
\(607\) | −5.32483 | −0.216128 | −0.108064 | − | 0.994144i | \(-0.534465\pi\) | ||||
−0.108064 | + | 0.994144i | \(0.534465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.2524 | −0.820671 | ||||||||
\(610\) | −2.07822 | −0.0841448 | ||||||||
\(611\) | 0.255959 | 0.0103550 | ||||||||
\(612\) | −7.95611 | −0.321607 | ||||||||
\(613\) | 15.3686 | 0.620733 | 0.310367 | − | 0.950617i | \(-0.399548\pi\) | ||||
0.310367 | + | 0.950617i | \(0.399548\pi\) | |||||||
\(614\) | −13.7816 | −0.556182 | ||||||||
\(615\) | 2.38851 | 0.0963142 | ||||||||
\(616\) | 5.85382 | 0.235857 | ||||||||
\(617\) | 27.8968 | 1.12308 | 0.561541 | − | 0.827449i | \(-0.310209\pi\) | ||||
0.561541 | + | 0.827449i | \(0.310209\pi\) | |||||||
\(618\) | 2.62870 | 0.105742 | ||||||||
\(619\) | 25.1582 | 1.01119 | 0.505597 | − | 0.862770i | \(-0.331272\pi\) | ||||
0.505597 | + | 0.862770i | \(0.331272\pi\) | |||||||
\(620\) | 1.35445 | 0.0543962 | ||||||||
\(621\) | 63.7585 | 2.55854 | ||||||||
\(622\) | −4.09294 | −0.164112 | ||||||||
\(623\) | 10.0204 | 0.401460 | ||||||||
\(624\) | 4.88037 | 0.195371 | ||||||||
\(625\) | 24.5780 | 0.983121 | ||||||||
\(626\) | 7.23396 | 0.289127 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.147652 | −0.00589195 | ||||||||
\(629\) | 8.74321 | 0.348615 | ||||||||
\(630\) | −0.944382 | −0.0376251 | ||||||||
\(631\) | 6.07571 | 0.241870 | 0.120935 | − | 0.992660i | \(-0.461411\pi\) | ||||
0.120935 | + | 0.992660i | \(0.461411\pi\) | |||||||
\(632\) | 5.69649 | 0.226594 | ||||||||
\(633\) | 39.3452 | 1.56383 | ||||||||
\(634\) | 31.7010 | 1.25901 | ||||||||
\(635\) | −1.05554 | −0.0418877 | ||||||||
\(636\) | −4.51715 | −0.179117 | ||||||||
\(637\) | 1.66176 | 0.0658412 | ||||||||
\(638\) | −40.3674 | −1.59816 | ||||||||
\(639\) | −46.3810 | −1.83481 | ||||||||
\(640\) | −0.167883 | −0.00663615 | ||||||||
\(641\) | −18.7683 | −0.741301 | −0.370651 | − | 0.928772i | \(-0.620865\pi\) | ||||
−0.370651 | + | 0.928772i | \(0.620865\pi\) | |||||||
\(642\) | 29.8642 | 1.17865 | ||||||||
\(643\) | 17.7478 | 0.699906 | 0.349953 | − | 0.936767i | \(-0.386198\pi\) | ||||
0.349953 | + | 0.936767i | \(0.386198\pi\) | |||||||
\(644\) | 8.26954 | 0.325866 | ||||||||
\(645\) | −0.574795 | −0.0226325 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.6137 | 1.91120 | 0.955601 | − | 0.294664i | \(-0.0952077\pi\) | ||||
0.955601 | + | 0.294664i | \(0.0952077\pi\) | |||||||
\(648\) | 5.76771 | 0.226577 | ||||||||
\(649\) | −30.4900 | −1.19684 | ||||||||
\(650\) | −8.26194 | −0.324060 | ||||||||
\(651\) | −23.6943 | −0.928654 | ||||||||
\(652\) | −20.2248 | −0.792063 | ||||||||
\(653\) | −35.4440 | −1.38703 | −0.693515 | − | 0.720442i | \(-0.743939\pi\) | ||||
−0.693515 | + | 0.720442i | \(0.743939\pi\) | |||||||
\(654\) | 17.7817 | 0.695318 | ||||||||
\(655\) | 3.18552 | 0.124468 | ||||||||
\(656\) | −4.84436 | −0.189140 | ||||||||
\(657\) | −59.7851 | −2.33244 | ||||||||
\(658\) | 0.154029 | 0.00600469 | ||||||||
\(659\) | 16.3470 | 0.636790 | 0.318395 | − | 0.947958i | \(-0.396856\pi\) | ||||
0.318395 | + | 0.947958i | \(0.396856\pi\) | |||||||
\(660\) | −2.88623 | −0.112346 | ||||||||
\(661\) | 23.7150 | 0.922405 | 0.461203 | − | 0.887295i | \(-0.347418\pi\) | ||||
0.461203 | + | 0.887295i | \(0.347418\pi\) | |||||||
\(662\) | 1.66753 | 0.0648104 | ||||||||
\(663\) | −6.90259 | −0.268074 | ||||||||
\(664\) | −9.93514 | −0.385558 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −34.7740 | −1.34746 | ||||||||
\(667\) | −57.0260 | −2.20806 | ||||||||
\(668\) | 14.6174 | 0.565565 | ||||||||
\(669\) | −21.4895 | −0.830831 | ||||||||
\(670\) | 0.372655 | 0.0143969 | ||||||||
\(671\) | 72.4645 | 2.79746 | ||||||||
\(672\) | 2.93688 | 0.113293 | ||||||||
\(673\) | 12.9809 | 0.500377 | 0.250188 | − | 0.968197i | \(-0.419507\pi\) | ||||
0.250188 | + | 0.968197i | \(0.419507\pi\) | |||||||
\(674\) | 23.1063 | 0.890022 | ||||||||
\(675\) | −38.3329 | −1.47544 | ||||||||
\(676\) | −10.2386 | −0.393791 | ||||||||
\(677\) | −17.3842 | −0.668129 | −0.334064 | − | 0.942550i | \(-0.608420\pi\) | ||||
−0.334064 | + | 0.942550i | \(0.608420\pi\) | |||||||
\(678\) | 11.1782 | 0.429297 | ||||||||
\(679\) | −12.2202 | −0.468966 | ||||||||
\(680\) | 0.237446 | 0.00910564 | ||||||||
\(681\) | 27.8860 | 1.06859 | ||||||||
\(682\) | −47.2278 | −1.80844 | ||||||||
\(683\) | 33.6737 | 1.28849 | 0.644243 | − | 0.764821i | \(-0.277172\pi\) | ||||
0.644243 | + | 0.764821i | \(0.277172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.72159 | −0.0657785 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 35.6570 | 1.36040 | ||||||||
\(688\) | 1.16579 | 0.0444454 | ||||||||
\(689\) | −2.55591 | −0.0973726 | ||||||||
\(690\) | −4.07730 | −0.155220 | ||||||||
\(691\) | 11.2788 | 0.429067 | 0.214533 | − | 0.976717i | \(-0.431177\pi\) | ||||
0.214533 | + | 0.976717i | \(0.431177\pi\) | |||||||
\(692\) | −16.5277 | −0.628289 | ||||||||
\(693\) | 32.9292 | 1.25088 | ||||||||
\(694\) | 35.3703 | 1.34264 | ||||||||
\(695\) | 2.91011 | 0.110387 | ||||||||
\(696\) | −20.2524 | −0.767667 | ||||||||
\(697\) | 6.85165 | 0.259525 | ||||||||
\(698\) | 32.6789 | 1.23692 | ||||||||
\(699\) | −6.04246 | −0.228547 | ||||||||
\(700\) | −4.97182 | −0.187917 | ||||||||
\(701\) | 15.0140 | 0.567071 | 0.283535 | − | 0.958962i | \(-0.408493\pi\) | ||||
0.283535 | + | 0.958962i | \(0.408493\pi\) | |||||||
\(702\) | 12.8122 | 0.483566 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.85382 | 0.220624 | ||||||||
\(705\) | −0.0759443 | −0.00286023 | ||||||||
\(706\) | 16.5338 | 0.622259 | ||||||||
\(707\) | 0.331346 | 0.0124615 | ||||||||
\(708\) | −15.2969 | −0.574893 | ||||||||
\(709\) | 43.3744 | 1.62896 | 0.814479 | − | 0.580192i | \(-0.197023\pi\) | ||||
0.814479 | + | 0.580192i | \(0.197023\pi\) | |||||||
\(710\) | 1.38422 | 0.0519488 | ||||||||
\(711\) | 32.0442 | 1.20175 | ||||||||
\(712\) | 10.0204 | 0.375531 | ||||||||
\(713\) | −66.7175 | −2.49859 | ||||||||
\(714\) | −4.15379 | −0.155452 | ||||||||
\(715\) | −1.63310 | −0.0610744 | ||||||||
\(716\) | 11.8788 | 0.443931 | ||||||||
\(717\) | −19.5765 | −0.731097 | ||||||||
\(718\) | −6.82256 | −0.254616 | ||||||||
\(719\) | 7.68558 | 0.286624 | 0.143312 | − | 0.989678i | \(-0.454225\pi\) | ||||
0.143312 | + | 0.989678i | \(0.454225\pi\) | |||||||
\(720\) | −0.944382 | −0.0351951 | ||||||||
\(721\) | 0.895065 | 0.0333340 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.3299 | −1.01641 | ||||||||
\(724\) | 14.3711 | 0.534098 | ||||||||
\(725\) | 34.2852 | 1.27332 | ||||||||
\(726\) | 68.3328 | 2.53607 | ||||||||
\(727\) | 12.4987 | 0.463551 | 0.231775 | − | 0.972769i | \(-0.425547\pi\) | ||||
0.231775 | + | 0.972769i | \(0.425547\pi\) | |||||||
\(728\) | 1.66176 | 0.0615888 | ||||||||
\(729\) | −35.4856 | −1.31428 | ||||||||
\(730\) | 1.78426 | 0.0660382 | ||||||||
\(731\) | −1.64884 | −0.0609847 | ||||||||
\(732\) | 36.3557 | 1.34374 | ||||||||
\(733\) | 28.5108 | 1.05307 | 0.526534 | − | 0.850154i | \(-0.323491\pi\) | ||||
0.526534 | + | 0.850154i | \(0.323491\pi\) | |||||||
\(734\) | 10.3686 | 0.382711 | ||||||||
\(735\) | −0.493051 | −0.0181865 | ||||||||
\(736\) | 8.26954 | 0.304819 | ||||||||
\(737\) | −12.9939 | −0.478637 | ||||||||
\(738\) | −27.2507 | −1.00311 | ||||||||
\(739\) | −50.0584 | −1.84143 | −0.920715 | − | 0.390237i | \(-0.872393\pi\) | ||||
−0.920715 | + | 0.390237i | \(0.872393\pi\) | |||||||
\(740\) | 1.03781 | 0.0381507 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.53808 | −0.0564647 | ||||||||
\(743\) | 6.73643 | 0.247136 | 0.123568 | − | 0.992336i | \(-0.460566\pi\) | ||||
0.123568 | + | 0.992336i | \(0.460566\pi\) | |||||||
\(744\) | −23.6943 | −0.868676 | ||||||||
\(745\) | −3.77096 | −0.138157 | ||||||||
\(746\) | −9.75909 | −0.357306 | ||||||||
\(747\) | −55.8877 | −2.04482 | ||||||||
\(748\) | −8.27938 | −0.302724 | ||||||||
\(749\) | 10.1687 | 0.371556 | ||||||||
\(750\) | 4.91661 | 0.179529 | ||||||||
\(751\) | −38.5477 | −1.40662 | −0.703312 | − | 0.710881i | \(-0.748296\pi\) | ||||
−0.703312 | + | 0.710881i | \(0.748296\pi\) | |||||||
\(752\) | 0.154029 | 0.00561687 | ||||||||
\(753\) | −30.8159 | −1.12299 | ||||||||
\(754\) | −11.4593 | −0.417324 | ||||||||
\(755\) | 1.99789 | 0.0727108 | ||||||||
\(756\) | 7.71005 | 0.280412 | ||||||||
\(757\) | −27.8178 | −1.01105 | −0.505527 | − | 0.862811i | \(-0.668702\pi\) | ||||
−0.505527 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(758\) | 18.9676 | 0.688936 | ||||||||
\(759\) | 142.169 | 5.16042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.533458 | −0.0193378 | −0.00966891 | − | 0.999953i | \(-0.503078\pi\) | ||||
−0.00966891 | + | 0.999953i | \(0.503078\pi\) | |||||||
\(762\) | 18.4652 | 0.668922 | ||||||||
\(763\) | 6.05462 | 0.219192 | ||||||||
\(764\) | 9.38259 | 0.339450 | ||||||||
\(765\) | 1.33569 | 0.0482921 | ||||||||
\(766\) | 7.57482 | 0.273689 | ||||||||
\(767\) | −8.65536 | −0.312527 | ||||||||
\(768\) | 2.93688 | 0.105975 | ||||||||
\(769\) | 43.0058 | 1.55083 | 0.775414 | − | 0.631453i | \(-0.217541\pi\) | ||||
0.775414 | + | 0.631453i | \(0.217541\pi\) | |||||||
\(770\) | −0.982754 | −0.0354160 | ||||||||
\(771\) | 69.6992 | 2.51016 | ||||||||
\(772\) | −25.0448 | −0.901382 | ||||||||
\(773\) | 19.1707 | 0.689523 | 0.344762 | − | 0.938690i | \(-0.387960\pi\) | ||||
0.344762 | + | 0.938690i | \(0.387960\pi\) | |||||||
\(774\) | 6.55787 | 0.235718 | ||||||||
\(775\) | 40.1119 | 1.44086 | ||||||||
\(776\) | −12.2202 | −0.438678 | ||||||||
\(777\) | −18.1551 | −0.651310 | ||||||||
\(778\) | −19.4484 | −0.697259 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.819330 | −0.0293367 | ||||||||
\(781\) | −48.2656 | −1.72708 | ||||||||
\(782\) | −11.6961 | −0.418251 | ||||||||
\(783\) | −53.1678 | −1.90006 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0.0247882 | 0.000884729 0 | ||||||||
\(786\) | −55.7262 | −1.98769 | ||||||||
\(787\) | −36.5017 | −1.30114 | −0.650572 | − | 0.759444i | \(-0.725471\pi\) | ||||
−0.650572 | + | 0.759444i | \(0.725471\pi\) | |||||||
\(788\) | −0.596816 | −0.0212607 | ||||||||
\(789\) | 30.3617 | 1.08091 | ||||||||
\(790\) | −0.956342 | −0.0340251 | ||||||||
\(791\) | 3.80616 | 0.135331 | ||||||||
\(792\) | 32.9292 | 1.17009 | ||||||||
\(793\) | 20.5709 | 0.730494 | ||||||||
\(794\) | −12.6930 | −0.450459 | ||||||||
\(795\) | 0.758352 | 0.0268960 | ||||||||
\(796\) | 23.0163 | 0.815792 | ||||||||
\(797\) | −24.7472 | −0.876590 | −0.438295 | − | 0.898831i | \(-0.644417\pi\) | ||||
−0.438295 | + | 0.898831i | \(0.644417\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.217852 | −0.00770707 | ||||||||
\(800\) | −4.97182 | −0.175780 | ||||||||
\(801\) | 56.3674 | 1.99164 | ||||||||
\(802\) | −18.9738 | −0.669989 | ||||||||
\(803\) | −62.2143 | −2.19549 | ||||||||
\(804\) | −6.51908 | −0.229910 | ||||||||
\(805\) | −1.38831 | −0.0489316 | ||||||||
\(806\) | −13.4068 | −0.472235 | ||||||||
\(807\) | 60.7116 | 2.13715 | ||||||||
\(808\) | 0.331346 | 0.0116567 | ||||||||
\(809\) | −1.07032 | −0.0376303 | −0.0188151 | − | 0.999823i | \(-0.505989\pi\) | ||||
−0.0188151 | + | 0.999823i | \(0.505989\pi\) | |||||||
\(810\) | −0.968298 | −0.0340225 | ||||||||
\(811\) | 19.1387 | 0.672049 | 0.336025 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336025 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(812\) | −6.89591 | −0.241999 | ||||||||
\(813\) | 15.6673 | 0.549477 | ||||||||
\(814\) | −36.1869 | −1.26835 | ||||||||
\(815\) | 3.39539 | 0.118935 | ||||||||
\(816\) | −4.15379 | −0.145412 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −10.1298 | −0.354180 | ||||||||
\(819\) | 9.34780 | 0.326638 | ||||||||
\(820\) | 0.813283 | 0.0284011 | ||||||||
\(821\) | 11.9598 | 0.417401 | 0.208701 | − | 0.977980i | \(-0.433077\pi\) | ||||
0.208701 | + | 0.977980i | \(0.433077\pi\) | |||||||
\(822\) | 30.1168 | 1.05045 | ||||||||
\(823\) | −1.13531 | −0.0395743 | −0.0197871 | − | 0.999804i | \(-0.506299\pi\) | ||||
−0.0197871 | + | 0.999804i | \(0.506299\pi\) | |||||||
\(824\) | 0.895065 | 0.0311811 | ||||||||
\(825\) | −85.4752 | −2.97586 | ||||||||
\(826\) | −5.20856 | −0.181229 | ||||||||
\(827\) | 40.9885 | 1.42531 | 0.712654 | − | 0.701515i | \(-0.247493\pi\) | ||||
0.712654 | + | 0.701515i | \(0.247493\pi\) | |||||||
\(828\) | 46.5183 | 1.61662 | ||||||||
\(829\) | 45.8211 | 1.59143 | 0.795716 | − | 0.605670i | \(-0.207095\pi\) | ||||
0.795716 | + | 0.605670i | \(0.207095\pi\) | |||||||
\(830\) | 1.66794 | 0.0578950 | ||||||||
\(831\) | 67.5907 | 2.34469 | ||||||||
\(832\) | 1.66176 | 0.0576110 | ||||||||
\(833\) | −1.41436 | −0.0490046 | ||||||||
\(834\) | −50.9085 | −1.76282 | ||||||||
\(835\) | −2.45401 | −0.0849246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.2036 | −2.15007 | ||||||||
\(838\) | −26.3112 | −0.908907 | ||||||||
\(839\) | 52.3712 | 1.80805 | 0.904027 | − | 0.427476i | \(-0.140597\pi\) | ||||
0.904027 | + | 0.427476i | \(0.140597\pi\) | |||||||
\(840\) | −0.493051 | −0.0170119 | ||||||||
\(841\) | 18.5536 | 0.639779 | ||||||||
\(842\) | −26.5413 | −0.914674 | ||||||||
\(843\) | 10.0123 | 0.344842 | ||||||||
\(844\) | 13.3969 | 0.461142 | ||||||||
\(845\) | 1.71888 | 0.0591312 | ||||||||
\(846\) | 0.866454 | 0.0297893 | ||||||||
\(847\) | 23.2672 | 0.799469 | ||||||||
\(848\) | −1.53808 | −0.0528179 | ||||||||
\(849\) | 12.3712 | 0.424577 | ||||||||
\(850\) | 7.03192 | 0.241193 | ||||||||
\(851\) | −51.1203 | −1.75238 | ||||||||
\(852\) | −24.2150 | −0.829592 | ||||||||
\(853\) | 0.305369 | 0.0104556 | 0.00522782 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522782 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(854\) | 12.3790 | 0.423601 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.1687 | 0.347559 | ||||||||
\(857\) | 12.5164 | 0.427550 | 0.213775 | − | 0.976883i | \(-0.431424\pi\) | ||||
0.213775 | + | 0.976883i | \(0.431424\pi\) | |||||||
\(858\) | 28.5688 | 0.975323 | ||||||||
\(859\) | −8.17940 | −0.279078 | −0.139539 | − | 0.990217i | \(-0.544562\pi\) | ||||
−0.139539 | + | 0.990217i | \(0.544562\pi\) | |||||||
\(860\) | −0.195716 | −0.00667387 | ||||||||
\(861\) | −14.2273 | −0.484864 | ||||||||
\(862\) | −25.5907 | −0.871624 | ||||||||
\(863\) | 12.3286 | 0.419669 | 0.209835 | − | 0.977737i | \(-0.432707\pi\) | ||||
0.209835 | + | 0.977737i | \(0.432707\pi\) | |||||||
\(864\) | 7.71005 | 0.262301 | ||||||||
\(865\) | 2.77472 | 0.0943432 | ||||||||
\(866\) | 8.94247 | 0.303878 | ||||||||
\(867\) | −44.0520 | −1.49608 | ||||||||
\(868\) | −8.06786 | −0.273841 | ||||||||
\(869\) | 33.3462 | 1.13119 | ||||||||
\(870\) | 3.40004 | 0.115272 | ||||||||
\(871\) | −3.68865 | −0.124985 | ||||||||
\(872\) | 6.05462 | 0.205035 | ||||||||
\(873\) | −68.7414 | −2.32655 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.67410 | 0.0565947 | ||||||||
\(876\) | −31.2131 | −1.05459 | ||||||||
\(877\) | 21.7354 | 0.733951 | 0.366976 | − | 0.930231i | \(-0.380393\pi\) | ||||
0.366976 | + | 0.930231i | \(0.380393\pi\) | |||||||
\(878\) | −12.4057 | −0.418671 | ||||||||
\(879\) | −48.7676 | −1.64489 | ||||||||
\(880\) | −0.982754 | −0.0331286 | ||||||||
\(881\) | 10.7650 | 0.362683 | 0.181341 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181341 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(882\) | 5.62525 | 0.189412 | ||||||||
\(883\) | −55.9766 | −1.88376 | −0.941881 | − | 0.335947i | \(-0.890944\pi\) | ||||
−0.941881 | + | 0.335947i | \(0.890944\pi\) | |||||||
\(884\) | −2.35032 | −0.0790497 | ||||||||
\(885\) | 2.56809 | 0.0863253 | ||||||||
\(886\) | −17.6686 | −0.593590 | ||||||||
\(887\) | −16.5852 | −0.556875 | −0.278437 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278437 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(888\) | −18.1551 | −0.609244 | ||||||||
\(889\) | 6.28735 | 0.210871 | ||||||||
\(890\) | −1.68225 | −0.0563893 | ||||||||
\(891\) | 33.7631 | 1.13111 | ||||||||
\(892\) | −7.31711 | −0.244995 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 65.9678 | 2.20629 | ||||||||
\(895\) | −1.99424 | −0.0666601 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 40.3585 | 1.34753 | ||||||||
\(898\) | −14.1170 | −0.471089 | ||||||||
\(899\) | 55.6353 | 1.85554 | ||||||||
\(900\) | −27.9677 | −0.932257 | ||||||||
\(901\) | 2.17539 | 0.0724729 | ||||||||
\(902\) | −28.3580 | −0.944217 | ||||||||
\(903\) | 3.42379 | 0.113936 | ||||||||
\(904\) | 3.80616 | 0.126591 | ||||||||
\(905\) | −2.41266 | −0.0801995 | ||||||||
\(906\) | −34.9504 | −1.16115 | ||||||||
\(907\) | −34.5946 | −1.14870 | −0.574348 | − | 0.818611i | \(-0.694744\pi\) | ||||
−0.574348 | + | 0.818611i | \(0.694744\pi\) | |||||||
\(908\) | 9.49511 | 0.315106 | ||||||||
\(909\) | 1.86390 | 0.0618218 | ||||||||
\(910\) | −0.278980 | −0.00924810 | ||||||||
\(911\) | 22.9274 | 0.759618 | 0.379809 | − | 0.925065i | \(-0.375990\pi\) | ||||
0.379809 | + | 0.925065i | \(0.375990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.1585 | −1.92477 | ||||||||
\(914\) | −22.6332 | −0.748641 | ||||||||
\(915\) | −6.10349 | −0.201775 | ||||||||
\(916\) | 12.1411 | 0.401153 | ||||||||
\(917\) | −18.9747 | −0.626598 | ||||||||
\(918\) | −10.9048 | −0.359911 | ||||||||
\(919\) | 4.19535 | 0.138392 | 0.0691958 | − | 0.997603i | \(-0.477957\pi\) | ||||
0.0691958 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(920\) | −1.38831 | −0.0457713 | ||||||||
\(921\) | −40.4750 | −1.33370 | ||||||||
\(922\) | −28.3983 | −0.935247 | ||||||||
\(923\) | −13.7014 | −0.450988 | ||||||||
\(924\) | 17.1919 | 0.565573 | ||||||||
\(925\) | 30.7346 | 1.01055 | ||||||||
\(926\) | 2.08478 | 0.0685100 | ||||||||
\(927\) | 5.03497 | 0.165370 | ||||||||
\(928\) | −6.89591 | −0.226369 | ||||||||
\(929\) | −18.6427 | −0.611647 | −0.305823 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305823 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(930\) | 3.97787 | 0.130439 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.05744 | −0.0673938 | ||||||||
\(933\) | −12.0205 | −0.393532 | ||||||||
\(934\) | −26.3159 | −0.861083 | ||||||||
\(935\) | 1.38996 | 0.0454567 | ||||||||
\(936\) | 9.34780 | 0.305542 | ||||||||
\(937\) | 34.7710 | 1.13592 | 0.567960 | − | 0.823056i | \(-0.307733\pi\) | ||||
0.567960 | + | 0.823056i | \(0.307733\pi\) | |||||||
\(938\) | −2.21973 | −0.0724768 | ||||||||
\(939\) | 21.2453 | 0.693313 | ||||||||
\(940\) | −0.0258589 | −0.000843423 0 | ||||||||
\(941\) | −20.8774 | −0.680583 | −0.340292 | − | 0.940320i | \(-0.610526\pi\) | ||||
−0.340292 | + | 0.940320i | \(0.610526\pi\) | |||||||
\(942\) | −0.433636 | −0.0141286 | ||||||||
\(943\) | −40.0606 | −1.30455 | ||||||||
\(944\) | −5.20856 | −0.169524 | ||||||||
\(945\) | −1.29438 | −0.0421063 | ||||||||
\(946\) | 6.82433 | 0.221878 | ||||||||
\(947\) | 15.9651 | 0.518797 | 0.259399 | − | 0.965770i | \(-0.416476\pi\) | ||||
0.259399 | + | 0.965770i | \(0.416476\pi\) | |||||||
\(948\) | 16.7299 | 0.543362 | ||||||||
\(949\) | −17.6611 | −0.573304 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 93.1019 | 3.01904 | ||||||||
\(952\) | −1.41436 | −0.0458396 | ||||||||
\(953\) | −33.4673 | −1.08411 | −0.542056 | − | 0.840343i | \(-0.682354\pi\) | ||||
−0.542056 | + | 0.840343i | \(0.682354\pi\) | |||||||
\(954\) | −8.65209 | −0.280122 | ||||||||
\(955\) | −1.57517 | −0.0509714 | ||||||||
\(956\) | −6.66574 | −0.215586 | ||||||||
\(957\) | −118.554 | −3.83231 | ||||||||
\(958\) | −4.82538 | −0.155901 | ||||||||
\(959\) | 10.2547 | 0.331142 | ||||||||
\(960\) | −0.493051 | −0.0159132 | ||||||||
\(961\) | 34.0904 | 1.09969 | ||||||||
\(962\) | −10.2726 | −0.331201 | ||||||||
\(963\) | 57.2015 | 1.84329 | ||||||||
\(964\) | −9.30578 | −0.299719 | ||||||||
\(965\) | 4.20459 | 0.135350 | ||||||||
\(966\) | 24.2866 | 0.781410 | ||||||||
\(967\) | −11.6426 | −0.374401 | −0.187201 | − | 0.982322i | \(-0.559941\pi\) | ||||
−0.187201 | + | 0.982322i | \(0.559941\pi\) | |||||||
\(968\) | 23.2672 | 0.747835 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.05155 | 0.0658714 | ||||||||
\(971\) | −48.8627 | −1.56808 | −0.784040 | − | 0.620711i | \(-0.786844\pi\) | ||||
−0.784040 | + | 0.620711i | \(0.786844\pi\) | |||||||
\(972\) | −6.19108 | −0.198579 | ||||||||
\(973\) | −17.3342 | −0.555709 | ||||||||
\(974\) | −24.0690 | −0.771220 | ||||||||
\(975\) | −24.2643 | −0.777080 | ||||||||
\(976\) | 12.3790 | 0.396243 | ||||||||
\(977\) | 13.7007 | 0.438325 | 0.219163 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219163 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(978\) | −59.3977 | −1.89933 | ||||||||
\(979\) | 58.6577 | 1.87471 | ||||||||
\(980\) | −0.167883 | −0.00536282 | ||||||||
\(981\) | 34.0588 | 1.08741 | ||||||||
\(982\) | 16.4774 | 0.525816 | ||||||||
\(983\) | 15.7814 | 0.503347 | 0.251674 | − | 0.967812i | \(-0.419019\pi\) | ||||
0.251674 | + | 0.967812i | \(0.419019\pi\) | |||||||
\(984\) | −14.2273 | −0.453549 | ||||||||
\(985\) | 0.100195 | 0.00319248 | ||||||||
\(986\) | 9.75328 | 0.310608 | ||||||||
\(987\) | 0.452366 | 0.0143990 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.64056 | 0.306552 | ||||||||
\(990\) | −5.52824 | −0.175699 | ||||||||
\(991\) | 2.61470 | 0.0830588 | 0.0415294 | − | 0.999137i | \(-0.486777\pi\) | ||||
0.0415294 | + | 0.999137i | \(0.486777\pi\) | |||||||
\(992\) | −8.06786 | −0.256155 | ||||||||
\(993\) | 4.89733 | 0.155412 | ||||||||
\(994\) | −8.24515 | −0.261520 | ||||||||
\(995\) | −3.86404 | −0.122498 | ||||||||
\(996\) | −29.1783 | −0.924550 | ||||||||
\(997\) | 20.7617 | 0.657529 | 0.328765 | − | 0.944412i | \(-0.393368\pi\) | ||||
0.328765 | + | 0.944412i | \(0.393368\pi\) | |||||||
\(998\) | −33.9334 | −1.07414 | ||||||||
\(999\) | −47.6617 | −1.50795 |
(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 | 5054.2.a.bm.1.10 | 12 | ||
19.3 | odd | 18 | 266.2.u.d.85.1 | ✓ | 24 | ||
19.13 | odd | 18 | 266.2.u.d.169.1 | yes | 24 | ||
19.18 | odd | 2 | 5054.2.a.bl.1.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.u.d.85.1 | ✓ | 24 | 19.3 | odd | 18 | ||
266.2.u.d.169.1 | yes | 24 | 19.13 | odd | 18 | ||
5054.2.a.bl.1.3 | 12 | 19.18 | odd | 2 | |||
5054.2.a.bm.1.10 | 12 | 1.1 | even | 1 | trivial |