Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, 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("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.974241.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} - 2x^{2} + 11x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.47364\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-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 | ||||||||
\(3\) | 3.09718 | 1.78816 | 0.894080 | − | 0.447907i | \(-0.147830\pi\) | ||||
0.894080 | + | 0.447907i | \(0.147830\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.78950 | −1.24750 | −0.623752 | − | 0.781623i | \(-0.714392\pi\) | ||||
−0.623752 | + | 0.781623i | \(0.714392\pi\) | |||||||
\(6\) | −3.09718 | −1.26442 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.59255 | 2.19752 | ||||||||
\(10\) | 2.78950 | 0.882118 | ||||||||
\(11\) | 2.80305 | 0.845151 | 0.422575 | − | 0.906328i | \(-0.361126\pi\) | ||||
0.422575 | + | 0.906328i | \(0.361126\pi\) | |||||||
\(12\) | 3.09718 | 0.894080 | ||||||||
\(13\) | −3.76778 | −1.04499 | −0.522497 | − | 0.852641i | \(-0.674999\pi\) | ||||
−0.522497 | + | 0.852641i | \(0.674999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.63960 | −2.23074 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.21609 | 1.50762 | 0.753812 | − | 0.657090i | \(-0.228213\pi\) | ||||
0.753812 | + | 0.657090i | \(0.228213\pi\) | |||||||
\(18\) | −6.59255 | −1.55388 | ||||||||
\(19\) | −1.46546 | −0.336201 | −0.168100 | − | 0.985770i | \(-0.553763\pi\) | ||||
−0.168100 | + | 0.985770i | \(0.553763\pi\) | |||||||
\(20\) | −2.78950 | −0.623752 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.80305 | −0.597612 | ||||||||
\(23\) | −6.75033 | −1.40754 | −0.703771 | − | 0.710427i | \(-0.748502\pi\) | ||||
−0.703771 | + | 0.710427i | \(0.748502\pi\) | |||||||
\(24\) | −3.09718 | −0.632210 | ||||||||
\(25\) | 2.78132 | 0.556265 | ||||||||
\(26\) | 3.76778 | 0.738922 | ||||||||
\(27\) | 11.1268 | 2.14135 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 8.63960 | 1.57737 | ||||||||
\(31\) | 8.37388 | 1.50399 | 0.751996 | − | 0.659167i | \(-0.229091\pi\) | ||||
0.751996 | + | 0.659167i | \(0.229091\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.68156 | 1.51127 | ||||||||
\(34\) | −6.21609 | −1.06605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.59255 | 1.09876 | ||||||||
\(37\) | 2.28596 | 0.375809 | 0.187905 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187905 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(38\) | 1.46546 | 0.237730 | ||||||||
\(39\) | −11.6695 | −1.86862 | ||||||||
\(40\) | 2.78950 | 0.441059 | ||||||||
\(41\) | 8.55060 | 1.33538 | 0.667689 | − | 0.744440i | \(-0.267283\pi\) | ||||
0.667689 | + | 0.744440i | \(0.267283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.71375 | 1.17634 | 0.588168 | − | 0.808739i | \(-0.299849\pi\) | ||||
0.588168 | + | 0.808739i | \(0.299849\pi\) | |||||||
\(44\) | 2.80305 | 0.422575 | ||||||||
\(45\) | −18.3899 | −2.74141 | ||||||||
\(46\) | 6.75033 | 0.995282 | ||||||||
\(47\) | 12.2347 | 1.78462 | 0.892310 | − | 0.451423i | \(-0.149084\pi\) | ||||
0.892310 | + | 0.451423i | \(0.149084\pi\) | |||||||
\(48\) | 3.09718 | 0.447040 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.78132 | −0.393339 | ||||||||
\(51\) | 19.2524 | 2.69587 | ||||||||
\(52\) | −3.76778 | −0.522497 | ||||||||
\(53\) | −1.12428 | −0.154431 | −0.0772156 | − | 0.997014i | \(-0.524603\pi\) | ||||
−0.0772156 | + | 0.997014i | \(0.524603\pi\) | |||||||
\(54\) | −11.1268 | −1.51416 | ||||||||
\(55\) | −7.81911 | −1.05433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.53881 | −0.601181 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 3.38006 | 0.440047 | 0.220023 | − | 0.975495i | \(-0.429387\pi\) | ||||
0.220023 | + | 0.975495i | \(0.429387\pi\) | |||||||
\(60\) | −8.63960 | −1.11537 | ||||||||
\(61\) | 3.70947 | 0.474949 | 0.237474 | − | 0.971394i | \(-0.423680\pi\) | ||||
0.237474 | + | 0.971394i | \(0.423680\pi\) | |||||||
\(62\) | −8.37388 | −1.06348 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5102 | 1.30363 | ||||||||
\(66\) | −8.68156 | −1.06863 | ||||||||
\(67\) | −6.57312 | −0.803034 | −0.401517 | − | 0.915852i | \(-0.631517\pi\) | ||||
−0.401517 | + | 0.915852i | \(0.631517\pi\) | |||||||
\(68\) | 6.21609 | 0.753812 | ||||||||
\(69\) | −20.9070 | −2.51691 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.45620 | 1.00357 | 0.501783 | − | 0.864994i | \(-0.332678\pi\) | ||||
0.501783 | + | 0.864994i | \(0.332678\pi\) | |||||||
\(72\) | −6.59255 | −0.776940 | ||||||||
\(73\) | −1.41841 | −0.166013 | −0.0830063 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830063 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(74\) | −2.28596 | −0.265737 | ||||||||
\(75\) | 8.61427 | 0.994691 | ||||||||
\(76\) | −1.46546 | −0.168100 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.6695 | 1.32131 | ||||||||
\(79\) | −12.8464 | −1.44534 | −0.722668 | − | 0.691195i | \(-0.757084\pi\) | ||||
−0.722668 | + | 0.691195i | \(0.757084\pi\) | |||||||
\(80\) | −2.78950 | −0.311876 | ||||||||
\(81\) | 14.6841 | 1.63156 | ||||||||
\(82\) | −8.55060 | −0.944256 | ||||||||
\(83\) | 7.72073 | 0.847460 | 0.423730 | − | 0.905789i | \(-0.360721\pi\) | ||||
0.423730 | + | 0.905789i | \(0.360721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3398 | −1.88077 | ||||||||
\(86\) | −7.71375 | −0.831795 | ||||||||
\(87\) | −3.09718 | −0.332053 | ||||||||
\(88\) | −2.80305 | −0.298806 | ||||||||
\(89\) | −9.99993 | −1.05999 | −0.529995 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529995 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(90\) | 18.3899 | 1.93847 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.75033 | −0.703771 | ||||||||
\(93\) | 25.9354 | 2.68938 | ||||||||
\(94\) | −12.2347 | −1.26192 | ||||||||
\(95\) | 4.08792 | 0.419411 | ||||||||
\(96\) | −3.09718 | −0.316105 | ||||||||
\(97\) | 1.13474 | 0.115216 | 0.0576078 | − | 0.998339i | \(-0.481653\pi\) | ||||
0.0576078 | + | 0.998339i | \(0.481653\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.4792 | 1.85723 | ||||||||
\(100\) | 2.78132 | 0.278132 | ||||||||
\(101\) | −13.7492 | −1.36810 | −0.684050 | − | 0.729435i | \(-0.739783\pi\) | ||||
−0.684050 | + | 0.729435i | \(0.739783\pi\) | |||||||
\(102\) | −19.2524 | −1.90627 | ||||||||
\(103\) | 3.31557 | 0.326692 | 0.163346 | − | 0.986569i | \(-0.447771\pi\) | ||||
0.163346 | + | 0.986569i | \(0.447771\pi\) | |||||||
\(104\) | 3.76778 | 0.369461 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.12428 | 0.109199 | ||||||||
\(107\) | 6.61427 | 0.639426 | 0.319713 | − | 0.947514i | \(-0.396413\pi\) | ||||
0.319713 | + | 0.947514i | \(0.396413\pi\) | |||||||
\(108\) | 11.1268 | 1.07068 | ||||||||
\(109\) | 14.7237 | 1.41028 | 0.705139 | − | 0.709069i | \(-0.250885\pi\) | ||||
0.705139 | + | 0.709069i | \(0.250885\pi\) | |||||||
\(110\) | 7.81911 | 0.745523 | ||||||||
\(111\) | 7.08003 | 0.672007 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.56133 | −0.335022 | −0.167511 | − | 0.985870i | \(-0.553573\pi\) | ||||
−0.167511 | + | 0.985870i | \(0.553573\pi\) | |||||||
\(114\) | 4.53881 | 0.425099 | ||||||||
\(115\) | 18.8301 | 1.75591 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −24.8393 | −2.29639 | ||||||||
\(118\) | −3.38006 | −0.311160 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.63960 | 0.788684 | ||||||||
\(121\) | −3.14292 | −0.285720 | ||||||||
\(122\) | −3.70947 | −0.335840 | ||||||||
\(123\) | 26.4828 | 2.38787 | ||||||||
\(124\) | 8.37388 | 0.751996 | ||||||||
\(125\) | 6.18900 | 0.553561 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.10668 | −0.808087 | −0.404044 | − | 0.914740i | \(-0.632396\pi\) | ||||
−0.404044 | + | 0.914740i | \(0.632396\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 23.8909 | 2.10348 | ||||||||
\(130\) | −10.5102 | −0.921808 | ||||||||
\(131\) | 1.86931 | 0.163322 | 0.0816611 | − | 0.996660i | \(-0.473977\pi\) | ||||
0.0816611 | + | 0.996660i | \(0.473977\pi\) | |||||||
\(132\) | 8.68156 | 0.755633 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.57312 | 0.567831 | ||||||||
\(135\) | −31.0382 | −2.67134 | ||||||||
\(136\) | −6.21609 | −0.533026 | ||||||||
\(137\) | 13.5477 | 1.15746 | 0.578730 | − | 0.815519i | \(-0.303549\pi\) | ||||
0.578730 | + | 0.815519i | \(0.303549\pi\) | |||||||
\(138\) | 20.9070 | 1.77972 | ||||||||
\(139\) | 4.55837 | 0.386636 | 0.193318 | − | 0.981136i | \(-0.438075\pi\) | ||||
0.193318 | + | 0.981136i | \(0.438075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.8932 | 3.19119 | ||||||||
\(142\) | −8.45620 | −0.709628 | ||||||||
\(143\) | −10.5613 | −0.883177 | ||||||||
\(144\) | 6.59255 | 0.549379 | ||||||||
\(145\) | 2.78950 | 0.231656 | ||||||||
\(146\) | 1.41841 | 0.117389 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.28596 | 0.187905 | ||||||||
\(149\) | 15.6004 | 1.27804 | 0.639019 | − | 0.769191i | \(-0.279341\pi\) | ||||
0.639019 | + | 0.769191i | \(0.279341\pi\) | |||||||
\(150\) | −8.61427 | −0.703353 | ||||||||
\(151\) | −7.61559 | −0.619748 | −0.309874 | − | 0.950778i | \(-0.600287\pi\) | ||||
−0.309874 | + | 0.950778i | \(0.600287\pi\) | |||||||
\(152\) | 1.46546 | 0.118865 | ||||||||
\(153\) | 40.9799 | 3.31303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.3589 | −1.87624 | ||||||||
\(156\) | −11.6695 | −0.934308 | ||||||||
\(157\) | 18.7723 | 1.49819 | 0.749096 | − | 0.662462i | \(-0.230488\pi\) | ||||
0.749096 | + | 0.662462i | \(0.230488\pi\) | |||||||
\(158\) | 12.8464 | 1.02201 | ||||||||
\(159\) | −3.48209 | −0.276148 | ||||||||
\(160\) | 2.78950 | 0.220530 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −14.6841 | −1.15369 | ||||||||
\(163\) | −8.47804 | −0.664051 | −0.332026 | − | 0.943270i | \(-0.607732\pi\) | ||||
−0.332026 | + | 0.943270i | \(0.607732\pi\) | |||||||
\(164\) | 8.55060 | 0.667689 | ||||||||
\(165\) | −24.2172 | −1.88531 | ||||||||
\(166\) | −7.72073 | −0.599245 | ||||||||
\(167\) | 17.6261 | 1.36395 | 0.681973 | − | 0.731378i | \(-0.261122\pi\) | ||||
0.681973 | + | 0.731378i | \(0.261122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.19616 | 0.0920121 | ||||||||
\(170\) | 17.3398 | 1.32990 | ||||||||
\(171\) | −9.66115 | −0.738807 | ||||||||
\(172\) | 7.71375 | 0.588168 | ||||||||
\(173\) | 18.4928 | 1.40598 | 0.702990 | − | 0.711200i | \(-0.251848\pi\) | ||||
0.702990 | + | 0.711200i | \(0.251848\pi\) | |||||||
\(174\) | 3.09718 | 0.234797 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.80305 | 0.211288 | ||||||||
\(177\) | 10.4687 | 0.786874 | ||||||||
\(178\) | 9.99993 | 0.749527 | ||||||||
\(179\) | −13.8700 | −1.03670 | −0.518348 | − | 0.855170i | \(-0.673453\pi\) | ||||
−0.518348 | + | 0.855170i | \(0.673453\pi\) | |||||||
\(180\) | −18.3899 | −1.37070 | ||||||||
\(181\) | −22.3876 | −1.66406 | −0.832030 | − | 0.554730i | \(-0.812822\pi\) | ||||
−0.832030 | + | 0.554730i | \(0.812822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4889 | 0.849285 | ||||||||
\(184\) | 6.75033 | 0.497641 | ||||||||
\(185\) | −6.37669 | −0.468823 | ||||||||
\(186\) | −25.9354 | −1.90168 | ||||||||
\(187\) | 17.4240 | 1.27417 | ||||||||
\(188\) | 12.2347 | 0.892310 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.08792 | −0.296569 | ||||||||
\(191\) | −7.97033 | −0.576713 | −0.288356 | − | 0.957523i | \(-0.593109\pi\) | ||||
−0.288356 | + | 0.957523i | \(0.593109\pi\) | |||||||
\(192\) | 3.09718 | 0.223520 | ||||||||
\(193\) | −11.4871 | −0.826861 | −0.413431 | − | 0.910536i | \(-0.635670\pi\) | ||||
−0.413431 | + | 0.910536i | \(0.635670\pi\) | |||||||
\(194\) | −1.13474 | −0.0814698 | ||||||||
\(195\) | 32.5521 | 2.33111 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.59563 | −0.469919 | −0.234960 | − | 0.972005i | \(-0.575496\pi\) | ||||
−0.234960 | + | 0.972005i | \(0.575496\pi\) | |||||||
\(198\) | −18.4792 | −1.31326 | ||||||||
\(199\) | −12.3980 | −0.878871 | −0.439436 | − | 0.898274i | \(-0.644822\pi\) | ||||
−0.439436 | + | 0.898274i | \(0.644822\pi\) | |||||||
\(200\) | −2.78132 | −0.196669 | ||||||||
\(201\) | −20.3582 | −1.43595 | ||||||||
\(202\) | 13.7492 | 0.967393 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 19.2524 | 1.34794 | ||||||||
\(205\) | −23.8519 | −1.66589 | ||||||||
\(206\) | −3.31557 | −0.231006 | ||||||||
\(207\) | −44.5019 | −3.09310 | ||||||||
\(208\) | −3.76778 | −0.261248 | ||||||||
\(209\) | −4.10777 | −0.284140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3981 | 1.67964 | 0.839818 | − | 0.542868i | \(-0.182662\pi\) | ||||
0.839818 | + | 0.542868i | \(0.182662\pi\) | |||||||
\(212\) | −1.12428 | −0.0772156 | ||||||||
\(213\) | 26.1904 | 1.79454 | ||||||||
\(214\) | −6.61427 | −0.452142 | ||||||||
\(215\) | −21.5175 | −1.46748 | ||||||||
\(216\) | −11.1268 | −0.757082 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.7237 | −0.997217 | ||||||||
\(219\) | −4.39308 | −0.296857 | ||||||||
\(220\) | −7.81911 | −0.527164 | ||||||||
\(221\) | −23.4209 | −1.57546 | ||||||||
\(222\) | −7.08003 | −0.475181 | ||||||||
\(223\) | −12.1316 | −0.812391 | −0.406196 | − | 0.913786i | \(-0.633145\pi\) | ||||
−0.406196 | + | 0.913786i | \(0.633145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.3360 | 1.22240 | ||||||||
\(226\) | 3.56133 | 0.236896 | ||||||||
\(227\) | 11.8788 | 0.788424 | 0.394212 | − | 0.919020i | \(-0.371018\pi\) | ||||
0.394212 | + | 0.919020i | \(0.371018\pi\) | |||||||
\(228\) | −4.53881 | −0.300590 | ||||||||
\(229\) | −11.5572 | −0.763719 | −0.381859 | − | 0.924220i | \(-0.624716\pi\) | ||||
−0.381859 | + | 0.924220i | \(0.624716\pi\) | |||||||
\(230\) | −18.8301 | −1.24162 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −16.8242 | −1.10219 | −0.551095 | − | 0.834442i | \(-0.685790\pi\) | ||||
−0.551095 | + | 0.834442i | \(0.685790\pi\) | |||||||
\(234\) | 24.8393 | 1.62379 | ||||||||
\(235\) | −34.1288 | −2.22632 | ||||||||
\(236\) | 3.38006 | 0.220023 | ||||||||
\(237\) | −39.7878 | −2.58449 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.97828 | −0.516072 | −0.258036 | − | 0.966135i | \(-0.583075\pi\) | ||||
−0.258036 | + | 0.966135i | \(0.583075\pi\) | |||||||
\(240\) | −8.63960 | −0.557684 | ||||||||
\(241\) | 12.9498 | 0.834170 | 0.417085 | − | 0.908867i | \(-0.363052\pi\) | ||||
0.417085 | + | 0.908867i | \(0.363052\pi\) | |||||||
\(242\) | 3.14292 | 0.202035 | ||||||||
\(243\) | 12.0989 | 0.776145 | ||||||||
\(244\) | 3.70947 | 0.237474 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.4828 | −1.68848 | ||||||||
\(247\) | 5.52155 | 0.351328 | ||||||||
\(248\) | −8.37388 | −0.531742 | ||||||||
\(249\) | 23.9125 | 1.51539 | ||||||||
\(250\) | −6.18900 | −0.391427 | ||||||||
\(251\) | −0.655438 | −0.0413709 | −0.0206854 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206854 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.9215 | −1.18959 | ||||||||
\(254\) | 9.10668 | 0.571404 | ||||||||
\(255\) | −53.7046 | −3.36311 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.1143 | 1.06756 | 0.533781 | − | 0.845622i | \(-0.320770\pi\) | ||||
0.533781 | + | 0.845622i | \(0.320770\pi\) | |||||||
\(258\) | −23.8909 | −1.48738 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.5102 | 0.651817 | ||||||||
\(261\) | −6.59255 | −0.408069 | ||||||||
\(262\) | −1.86931 | −0.115486 | ||||||||
\(263\) | 11.8065 | 0.728022 | 0.364011 | − | 0.931395i | \(-0.381407\pi\) | ||||
0.364011 | + | 0.931395i | \(0.381407\pi\) | |||||||
\(264\) | −8.68156 | −0.534313 | ||||||||
\(265\) | 3.13617 | 0.192653 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.9716 | −1.89543 | ||||||||
\(268\) | −6.57312 | −0.401517 | ||||||||
\(269\) | 31.9259 | 1.94656 | 0.973279 | − | 0.229624i | \(-0.0737496\pi\) | ||||
0.973279 | + | 0.229624i | \(0.0737496\pi\) | |||||||
\(270\) | 31.0382 | 1.88893 | ||||||||
\(271\) | 5.43740 | 0.330299 | 0.165149 | − | 0.986269i | \(-0.447189\pi\) | ||||
0.165149 | + | 0.986269i | \(0.447189\pi\) | |||||||
\(272\) | 6.21609 | 0.376906 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.5477 | −0.818448 | ||||||||
\(275\) | 7.79619 | 0.470128 | ||||||||
\(276\) | −20.9070 | −1.25846 | ||||||||
\(277\) | 14.2018 | 0.853301 | 0.426650 | − | 0.904417i | \(-0.359693\pi\) | ||||
0.426650 | + | 0.904417i | \(0.359693\pi\) | |||||||
\(278\) | −4.55837 | −0.273393 | ||||||||
\(279\) | 55.2052 | 3.30505 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.11893 | −0.186060 | −0.0930300 | − | 0.995663i | \(-0.529655\pi\) | ||||
−0.0930300 | + | 0.995663i | \(0.529655\pi\) | |||||||
\(282\) | −37.8932 | −2.25651 | ||||||||
\(283\) | −9.65027 | −0.573649 | −0.286825 | − | 0.957983i | \(-0.592600\pi\) | ||||
−0.286825 | + | 0.957983i | \(0.592600\pi\) | |||||||
\(284\) | 8.45620 | 0.501783 | ||||||||
\(285\) | 12.6610 | 0.749975 | ||||||||
\(286\) | 10.5613 | 0.624501 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.59255 | −0.388470 | ||||||||
\(289\) | 21.6398 | 1.27293 | ||||||||
\(290\) | −2.78950 | −0.163805 | ||||||||
\(291\) | 3.51451 | 0.206024 | ||||||||
\(292\) | −1.41841 | −0.0830063 | ||||||||
\(293\) | 19.6730 | 1.14931 | 0.574654 | − | 0.818396i | \(-0.305137\pi\) | ||||
0.574654 | + | 0.818396i | \(0.305137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.42870 | −0.548960 | ||||||||
\(296\) | −2.28596 | −0.132869 | ||||||||
\(297\) | 31.1889 | 1.80977 | ||||||||
\(298\) | −15.6004 | −0.903709 | ||||||||
\(299\) | 25.4338 | 1.47087 | ||||||||
\(300\) | 8.61427 | 0.497345 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.61559 | 0.438228 | ||||||||
\(303\) | −42.5839 | −2.44638 | ||||||||
\(304\) | −1.46546 | −0.0840502 | ||||||||
\(305\) | −10.3476 | −0.592500 | ||||||||
\(306\) | −40.9799 | −2.34267 | ||||||||
\(307\) | −18.2644 | −1.04240 | −0.521202 | − | 0.853433i | \(-0.674516\pi\) | ||||
−0.521202 | + | 0.853433i | \(0.674516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2689 | 0.584178 | ||||||||
\(310\) | 23.3589 | 1.32670 | ||||||||
\(311\) | −30.3270 | −1.71969 | −0.859843 | − | 0.510559i | \(-0.829438\pi\) | ||||
−0.859843 | + | 0.510559i | \(0.829438\pi\) | |||||||
\(312\) | 11.6695 | 0.660656 | ||||||||
\(313\) | −18.6417 | −1.05369 | −0.526846 | − | 0.849961i | \(-0.676626\pi\) | ||||
−0.526846 | + | 0.849961i | \(0.676626\pi\) | |||||||
\(314\) | −18.7723 | −1.05938 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.8464 | −0.722668 | ||||||||
\(317\) | 14.9125 | 0.837570 | 0.418785 | − | 0.908085i | \(-0.362456\pi\) | ||||
0.418785 | + | 0.908085i | \(0.362456\pi\) | |||||||
\(318\) | 3.48209 | 0.195266 | ||||||||
\(319\) | −2.80305 | −0.156941 | ||||||||
\(320\) | −2.78950 | −0.155938 | ||||||||
\(321\) | 20.4856 | 1.14340 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.10946 | −0.506864 | ||||||||
\(324\) | 14.6841 | 0.815782 | ||||||||
\(325\) | −10.4794 | −0.581293 | ||||||||
\(326\) | 8.47804 | 0.469555 | ||||||||
\(327\) | 45.6021 | 2.52180 | ||||||||
\(328\) | −8.55060 | −0.472128 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 24.2172 | 1.33311 | ||||||||
\(331\) | −19.0518 | −1.04718 | −0.523592 | − | 0.851969i | \(-0.675408\pi\) | ||||
−0.523592 | + | 0.851969i | \(0.675408\pi\) | |||||||
\(332\) | 7.72073 | 0.423730 | ||||||||
\(333\) | 15.0703 | 0.825847 | ||||||||
\(334\) | −17.6261 | −0.964455 | ||||||||
\(335\) | 18.3357 | 1.00179 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7396 | −0.802916 | −0.401458 | − | 0.915878i | \(-0.631496\pi\) | ||||
−0.401458 | + | 0.915878i | \(0.631496\pi\) | |||||||
\(338\) | −1.19616 | −0.0650624 | ||||||||
\(339\) | −11.0301 | −0.599073 | ||||||||
\(340\) | −17.3398 | −0.940383 | ||||||||
\(341\) | 23.4724 | 1.27110 | ||||||||
\(342\) | 9.66115 | 0.522415 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.71375 | −0.415897 | ||||||||
\(345\) | 58.3202 | 3.13985 | ||||||||
\(346\) | −18.4928 | −0.994178 | ||||||||
\(347\) | 11.1550 | 0.598830 | 0.299415 | − | 0.954123i | \(-0.403208\pi\) | ||||
0.299415 | + | 0.954123i | \(0.403208\pi\) | |||||||
\(348\) | −3.09718 | −0.166027 | ||||||||
\(349\) | −31.8123 | −1.70288 | −0.851438 | − | 0.524456i | \(-0.824269\pi\) | ||||
−0.851438 | + | 0.524456i | \(0.824269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −41.9233 | −2.23770 | ||||||||
\(352\) | −2.80305 | −0.149403 | ||||||||
\(353\) | 1.86046 | 0.0990221 | 0.0495111 | − | 0.998774i | \(-0.484234\pi\) | ||||
0.0495111 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(354\) | −10.4687 | −0.556404 | ||||||||
\(355\) | −23.5886 | −1.25195 | ||||||||
\(356\) | −9.99993 | −0.529995 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.8700 | 0.733054 | ||||||||
\(359\) | −31.2924 | −1.65155 | −0.825775 | − | 0.564000i | \(-0.809262\pi\) | ||||
−0.825775 | + | 0.564000i | \(0.809262\pi\) | |||||||
\(360\) | 18.3899 | 0.969235 | ||||||||
\(361\) | −16.8524 | −0.886969 | ||||||||
\(362\) | 22.3876 | 1.17667 | ||||||||
\(363\) | −9.73420 | −0.510913 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.95666 | 0.207101 | ||||||||
\(366\) | −11.4889 | −0.600535 | ||||||||
\(367\) | −0.872346 | −0.0455361 | −0.0227681 | − | 0.999741i | \(-0.507248\pi\) | ||||
−0.0227681 | + | 0.999741i | \(0.507248\pi\) | |||||||
\(368\) | −6.75033 | −0.351885 | ||||||||
\(369\) | 56.3702 | 2.93452 | ||||||||
\(370\) | 6.37669 | 0.331508 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 25.9354 | 1.34469 | ||||||||
\(373\) | 11.3493 | 0.587644 | 0.293822 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293822 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(374\) | −17.4240 | −0.900974 | ||||||||
\(375\) | 19.1685 | 0.989856 | ||||||||
\(376\) | −12.2347 | −0.630958 | ||||||||
\(377\) | 3.76778 | 0.194050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.3212 | −1.09519 | −0.547597 | − | 0.836742i | \(-0.684457\pi\) | ||||
−0.547597 | + | 0.836742i | \(0.684457\pi\) | |||||||
\(380\) | 4.08792 | 0.209706 | ||||||||
\(381\) | −28.2051 | −1.44499 | ||||||||
\(382\) | 7.97033 | 0.407797 | ||||||||
\(383\) | 11.6863 | 0.597140 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(384\) | −3.09718 | −0.158053 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4871 | 0.584679 | ||||||||
\(387\) | 50.8533 | 2.58502 | ||||||||
\(388\) | 1.13474 | 0.0576078 | ||||||||
\(389\) | 8.79559 | 0.445954 | 0.222977 | − | 0.974824i | \(-0.428422\pi\) | ||||
0.222977 | + | 0.974824i | \(0.428422\pi\) | |||||||
\(390\) | −32.5521 | −1.64834 | ||||||||
\(391\) | −41.9607 | −2.12204 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.78959 | 0.292046 | ||||||||
\(394\) | 6.59563 | 0.332283 | ||||||||
\(395\) | 35.8351 | 1.80306 | ||||||||
\(396\) | 18.4792 | 0.928617 | ||||||||
\(397\) | 24.4533 | 1.22728 | 0.613639 | − | 0.789587i | \(-0.289705\pi\) | ||||
0.613639 | + | 0.789587i | \(0.289705\pi\) | |||||||
\(398\) | 12.3980 | 0.621456 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.78132 | 0.139066 | ||||||||
\(401\) | −22.6628 | −1.13173 | −0.565863 | − | 0.824499i | \(-0.691457\pi\) | ||||
−0.565863 | + | 0.824499i | \(0.691457\pi\) | |||||||
\(402\) | 20.3582 | 1.01537 | ||||||||
\(403\) | −31.5509 | −1.57166 | ||||||||
\(404\) | −13.7492 | −0.684050 | ||||||||
\(405\) | −40.9613 | −2.03538 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.40765 | 0.317615 | ||||||||
\(408\) | −19.2524 | −0.953135 | ||||||||
\(409\) | 1.81284 | 0.0896390 | 0.0448195 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448195 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(410\) | 23.8519 | 1.17796 | ||||||||
\(411\) | 41.9598 | 2.06972 | ||||||||
\(412\) | 3.31557 | 0.163346 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 44.5019 | 2.18715 | ||||||||
\(415\) | −21.5370 | −1.05721 | ||||||||
\(416\) | 3.76778 | 0.184731 | ||||||||
\(417\) | 14.1181 | 0.691367 | ||||||||
\(418\) | 4.10777 | 0.200917 | ||||||||
\(419\) | 14.4468 | 0.705773 | 0.352887 | − | 0.935666i | \(-0.385200\pi\) | ||||
0.352887 | + | 0.935666i | \(0.385200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8483 | −0.674925 | −0.337463 | − | 0.941339i | \(-0.609569\pi\) | ||||
−0.337463 | + | 0.941339i | \(0.609569\pi\) | |||||||
\(422\) | −24.3981 | −1.18768 | ||||||||
\(423\) | 80.6581 | 3.92173 | ||||||||
\(424\) | 1.12428 | 0.0545997 | ||||||||
\(425\) | 17.2890 | 0.838638 | ||||||||
\(426\) | −26.1904 | −1.26893 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.61427 | 0.319713 | ||||||||
\(429\) | −32.7102 | −1.57926 | ||||||||
\(430\) | 21.5175 | 1.03767 | ||||||||
\(431\) | −12.5908 | −0.606476 | −0.303238 | − | 0.952915i | \(-0.598068\pi\) | ||||
−0.303238 | + | 0.952915i | \(0.598068\pi\) | |||||||
\(432\) | 11.1268 | 0.535338 | ||||||||
\(433\) | −9.09118 | −0.436894 | −0.218447 | − | 0.975849i | \(-0.570099\pi\) | ||||
−0.218447 | + | 0.975849i | \(0.570099\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.63960 | 0.414237 | ||||||||
\(436\) | 14.7237 | 0.705139 | ||||||||
\(437\) | 9.89237 | 0.473216 | ||||||||
\(438\) | 4.39308 | 0.209910 | ||||||||
\(439\) | −23.9511 | −1.14312 | −0.571561 | − | 0.820560i | \(-0.693662\pi\) | ||||
−0.571561 | + | 0.820560i | \(0.693662\pi\) | |||||||
\(440\) | 7.81911 | 0.372761 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.4209 | 1.11402 | ||||||||
\(443\) | 26.2769 | 1.24845 | 0.624225 | − | 0.781244i | \(-0.285415\pi\) | ||||
0.624225 | + | 0.781244i | \(0.285415\pi\) | |||||||
\(444\) | 7.08003 | 0.336004 | ||||||||
\(445\) | 27.8948 | 1.32234 | ||||||||
\(446\) | 12.1316 | 0.574448 | ||||||||
\(447\) | 48.3174 | 2.28534 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.06619 | 0.144703 | 0.0723513 | − | 0.997379i | \(-0.476950\pi\) | ||||
0.0723513 | + | 0.997379i | \(0.476950\pi\) | |||||||
\(450\) | −18.3360 | −0.864368 | ||||||||
\(451\) | 23.9677 | 1.12860 | ||||||||
\(452\) | −3.56133 | −0.167511 | ||||||||
\(453\) | −23.5869 | −1.10821 | ||||||||
\(454\) | −11.8788 | −0.557500 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.53881 | 0.212549 | ||||||||
\(457\) | 15.6802 | 0.733488 | 0.366744 | − | 0.930322i | \(-0.380473\pi\) | ||||
0.366744 | + | 0.930322i | \(0.380473\pi\) | |||||||
\(458\) | 11.5572 | 0.540031 | ||||||||
\(459\) | 69.1652 | 3.22835 | ||||||||
\(460\) | 18.8301 | 0.877957 | ||||||||
\(461\) | −1.66602 | −0.0775941 | −0.0387971 | − | 0.999247i | \(-0.512353\pi\) | ||||
−0.0387971 | + | 0.999247i | \(0.512353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2509 | 0.801718 | 0.400859 | − | 0.916140i | \(-0.368712\pi\) | ||||
0.400859 | + | 0.916140i | \(0.368712\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −72.3470 | −3.35501 | ||||||||
\(466\) | 16.8242 | 0.779366 | ||||||||
\(467\) | −11.1793 | −0.517317 | −0.258659 | − | 0.965969i | \(-0.583280\pi\) | ||||
−0.258659 | + | 0.965969i | \(0.583280\pi\) | |||||||
\(468\) | −24.8393 | −1.14820 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 34.1288 | 1.57425 | ||||||||
\(471\) | 58.1412 | 2.67901 | ||||||||
\(472\) | −3.38006 | −0.155580 | ||||||||
\(473\) | 21.6220 | 0.994181 | ||||||||
\(474\) | 39.7878 | 1.82751 | ||||||||
\(475\) | −4.07593 | −0.187017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.41184 | −0.339365 | ||||||||
\(478\) | 7.97828 | 0.364918 | ||||||||
\(479\) | −13.0826 | −0.597760 | −0.298880 | − | 0.954291i | \(-0.596613\pi\) | ||||
−0.298880 | + | 0.954291i | \(0.596613\pi\) | |||||||
\(480\) | 8.63960 | 0.394342 | ||||||||
\(481\) | −8.61298 | −0.392718 | ||||||||
\(482\) | −12.9498 | −0.589847 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.14292 | −0.142860 | ||||||||
\(485\) | −3.16537 | −0.143732 | ||||||||
\(486\) | −12.0989 | −0.548818 | ||||||||
\(487\) | 6.75769 | 0.306220 | 0.153110 | − | 0.988209i | \(-0.451071\pi\) | ||||
0.153110 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(488\) | −3.70947 | −0.167920 | ||||||||
\(489\) | −26.2580 | −1.18743 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.53271 | 0.430205 | 0.215103 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215103 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(492\) | 26.4828 | 1.19394 | ||||||||
\(493\) | −6.21609 | −0.279959 | ||||||||
\(494\) | −5.52155 | −0.248426 | ||||||||
\(495\) | −51.5479 | −2.31690 | ||||||||
\(496\) | 8.37388 | 0.375998 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −23.9125 | −1.07155 | ||||||||
\(499\) | −21.0060 | −0.940358 | −0.470179 | − | 0.882571i | \(-0.655811\pi\) | ||||
−0.470179 | + | 0.882571i | \(0.655811\pi\) | |||||||
\(500\) | 6.18900 | 0.276781 | ||||||||
\(501\) | 54.5912 | 2.43895 | ||||||||
\(502\) | 0.655438 | 0.0292536 | ||||||||
\(503\) | −43.2476 | −1.92831 | −0.964157 | − | 0.265333i | \(-0.914518\pi\) | ||||
−0.964157 | + | 0.265333i | \(0.914518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.3536 | 1.70671 | ||||||||
\(506\) | 18.9215 | 0.841164 | ||||||||
\(507\) | 3.70472 | 0.164532 | ||||||||
\(508\) | −9.10668 | −0.404044 | ||||||||
\(509\) | −8.51537 | −0.377437 | −0.188719 | − | 0.982031i | \(-0.560433\pi\) | ||||
−0.188719 | + | 0.982031i | \(0.560433\pi\) | |||||||
\(510\) | 53.7046 | 2.37808 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.3059 | −0.719924 | ||||||||
\(514\) | −17.1143 | −0.754881 | ||||||||
\(515\) | −9.24878 | −0.407550 | ||||||||
\(516\) | 23.8909 | 1.05174 | ||||||||
\(517\) | 34.2946 | 1.50827 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.2756 | 2.51412 | ||||||||
\(520\) | −10.5102 | −0.460904 | ||||||||
\(521\) | −16.6592 | −0.729855 | −0.364927 | − | 0.931036i | \(-0.618906\pi\) | ||||
−0.364927 | + | 0.931036i | \(0.618906\pi\) | |||||||
\(522\) | 6.59255 | 0.288548 | ||||||||
\(523\) | 5.33917 | 0.233466 | 0.116733 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116733 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(524\) | 1.86931 | 0.0816611 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.8065 | −0.514789 | ||||||||
\(527\) | 52.0528 | 2.26745 | ||||||||
\(528\) | 8.68156 | 0.377816 | ||||||||
\(529\) | 22.5670 | 0.981174 | ||||||||
\(530\) | −3.13617 | −0.136227 | ||||||||
\(531\) | 22.2832 | 0.967010 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.2168 | −1.39546 | ||||||||
\(534\) | 30.9716 | 1.34027 | ||||||||
\(535\) | −18.4505 | −0.797686 | ||||||||
\(536\) | 6.57312 | 0.283915 | ||||||||
\(537\) | −42.9581 | −1.85378 | ||||||||
\(538\) | −31.9259 | −1.37643 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −31.0382 | −1.33567 | ||||||||
\(541\) | −15.5363 | −0.667956 | −0.333978 | − | 0.942581i | \(-0.608391\pi\) | ||||
−0.333978 | + | 0.942581i | \(0.608391\pi\) | |||||||
\(542\) | −5.43740 | −0.233556 | ||||||||
\(543\) | −69.3387 | −2.97561 | ||||||||
\(544\) | −6.21609 | −0.266513 | ||||||||
\(545\) | −41.0719 | −1.75933 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2836 | −1.59413 | −0.797067 | − | 0.603891i | \(-0.793616\pi\) | ||||
−0.797067 | + | 0.603891i | \(0.793616\pi\) | |||||||
\(548\) | 13.5477 | 0.578730 | ||||||||
\(549\) | 24.4549 | 1.04371 | ||||||||
\(550\) | −7.79619 | −0.332431 | ||||||||
\(551\) | 1.46546 | 0.0624309 | ||||||||
\(552\) | 20.9070 | 0.889862 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2018 | −0.603375 | ||||||||
\(555\) | −19.7498 | −0.838331 | ||||||||
\(556\) | 4.55837 | 0.193318 | ||||||||
\(557\) | 5.64481 | 0.239178 | 0.119589 | − | 0.992823i | \(-0.461842\pi\) | ||||
0.119589 | + | 0.992823i | \(0.461842\pi\) | |||||||
\(558\) | −55.2052 | −2.33702 | ||||||||
\(559\) | −29.0637 | −1.22926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 53.9654 | 2.27842 | ||||||||
\(562\) | 3.11893 | 0.131564 | ||||||||
\(563\) | 17.3517 | 0.731286 | 0.365643 | − | 0.930755i | \(-0.380849\pi\) | ||||
0.365643 | + | 0.930755i | \(0.380849\pi\) | |||||||
\(564\) | 37.8932 | 1.59559 | ||||||||
\(565\) | 9.93435 | 0.417941 | ||||||||
\(566\) | 9.65027 | 0.405631 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.45620 | −0.354814 | ||||||||
\(569\) | 7.88927 | 0.330735 | 0.165368 | − | 0.986232i | \(-0.447119\pi\) | ||||
0.165368 | + | 0.986232i | \(0.447119\pi\) | |||||||
\(570\) | −12.6610 | −0.530312 | ||||||||
\(571\) | 15.5879 | 0.652332 | 0.326166 | − | 0.945313i | \(-0.394243\pi\) | ||||
0.326166 | + | 0.945313i | \(0.394243\pi\) | |||||||
\(572\) | −10.5613 | −0.441589 | ||||||||
\(573\) | −24.6856 | −1.03125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.7749 | −0.782966 | ||||||||
\(576\) | 6.59255 | 0.274690 | ||||||||
\(577\) | −28.9405 | −1.20481 | −0.602405 | − | 0.798191i | \(-0.705791\pi\) | ||||
−0.602405 | + | 0.798191i | \(0.705791\pi\) | |||||||
\(578\) | −21.6398 | −0.900097 | ||||||||
\(579\) | −35.5777 | −1.47856 | ||||||||
\(580\) | 2.78950 | 0.115828 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.51451 | −0.145681 | ||||||||
\(583\) | −3.15140 | −0.130518 | ||||||||
\(584\) | 1.41841 | 0.0586943 | ||||||||
\(585\) | 69.2892 | 2.86476 | ||||||||
\(586\) | −19.6730 | −0.812684 | ||||||||
\(587\) | −39.0368 | −1.61122 | −0.805611 | − | 0.592444i | \(-0.798163\pi\) | ||||
−0.805611 | + | 0.592444i | \(0.798163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.2716 | −0.505643 | ||||||||
\(590\) | 9.42870 | 0.388173 | ||||||||
\(591\) | −20.4279 | −0.840291 | ||||||||
\(592\) | 2.28596 | 0.0939523 | ||||||||
\(593\) | 29.2986 | 1.20315 | 0.601576 | − | 0.798816i | \(-0.294540\pi\) | ||||
0.601576 | + | 0.798816i | \(0.294540\pi\) | |||||||
\(594\) | −31.1889 | −1.27970 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.6004 | 0.639019 | ||||||||
\(597\) | −38.3989 | −1.57156 | ||||||||
\(598\) | −25.4338 | −1.04006 | ||||||||
\(599\) | −4.87633 | −0.199241 | −0.0996207 | − | 0.995025i | \(-0.531763\pi\) | ||||
−0.0996207 | + | 0.995025i | \(0.531763\pi\) | |||||||
\(600\) | −8.61427 | −0.351676 | ||||||||
\(601\) | −13.4240 | −0.547578 | −0.273789 | − | 0.961790i | \(-0.588277\pi\) | ||||
−0.273789 | + | 0.961790i | \(0.588277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −43.3336 | −1.76468 | ||||||||
\(604\) | −7.61559 | −0.309874 | ||||||||
\(605\) | 8.76719 | 0.356437 | ||||||||
\(606\) | 42.5839 | 1.72985 | ||||||||
\(607\) | −27.3793 | −1.11129 | −0.555645 | − | 0.831420i | \(-0.687529\pi\) | ||||
−0.555645 | + | 0.831420i | \(0.687529\pi\) | |||||||
\(608\) | 1.46546 | 0.0594324 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.3476 | 0.418961 | ||||||||
\(611\) | −46.0978 | −1.86492 | ||||||||
\(612\) | 40.9799 | 1.65651 | ||||||||
\(613\) | −10.0025 | −0.403998 | −0.201999 | − | 0.979386i | \(-0.564744\pi\) | ||||
−0.201999 | + | 0.979386i | \(0.564744\pi\) | |||||||
\(614\) | 18.2644 | 0.737091 | ||||||||
\(615\) | −73.8738 | −2.97888 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0833 | −1.09033 | −0.545167 | − | 0.838327i | \(-0.683534\pi\) | ||||
−0.545167 | + | 0.838327i | \(0.683534\pi\) | |||||||
\(618\) | −10.2689 | −0.413076 | ||||||||
\(619\) | −30.5470 | −1.22779 | −0.613894 | − | 0.789388i | \(-0.710398\pi\) | ||||
−0.613894 | + | 0.789388i | \(0.710398\pi\) | |||||||
\(620\) | −23.3589 | −0.938118 | ||||||||
\(621\) | −75.1096 | −3.01404 | ||||||||
\(622\) | 30.3270 | 1.21600 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.6695 | −0.467154 | ||||||||
\(625\) | −31.1709 | −1.24683 | ||||||||
\(626\) | 18.6417 | 0.745073 | ||||||||
\(627\) | −12.7225 | −0.508088 | ||||||||
\(628\) | 18.7723 | 0.749096 | ||||||||
\(629\) | 14.2097 | 0.566579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0961 | 0.600965 | 0.300483 | − | 0.953787i | \(-0.402852\pi\) | ||||
0.300483 | + | 0.953787i | \(0.402852\pi\) | |||||||
\(632\) | 12.8464 | 0.511004 | ||||||||
\(633\) | 75.5655 | 3.00346 | ||||||||
\(634\) | −14.9125 | −0.592251 | ||||||||
\(635\) | 25.4031 | 1.00809 | ||||||||
\(636\) | −3.48209 | −0.138074 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.80305 | 0.110974 | ||||||||
\(639\) | 55.7479 | 2.20535 | ||||||||
\(640\) | 2.78950 | 0.110265 | ||||||||
\(641\) | −47.6686 | −1.88280 | −0.941398 | − | 0.337297i | \(-0.890487\pi\) | ||||
−0.941398 | + | 0.337297i | \(0.890487\pi\) | |||||||
\(642\) | −20.4856 | −0.808503 | ||||||||
\(643\) | 22.5917 | 0.890929 | 0.445465 | − | 0.895299i | \(-0.353038\pi\) | ||||
0.445465 | + | 0.895299i | \(0.353038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −66.6437 | −2.62409 | ||||||||
\(646\) | 9.10946 | 0.358407 | ||||||||
\(647\) | −40.6976 | −1.59999 | −0.799994 | − | 0.600008i | \(-0.795164\pi\) | ||||
−0.799994 | + | 0.600008i | \(0.795164\pi\) | |||||||
\(648\) | −14.6841 | −0.576845 | ||||||||
\(649\) | 9.47448 | 0.371906 | ||||||||
\(650\) | 10.4794 | 0.411036 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.47804 | −0.332026 | ||||||||
\(653\) | −11.8914 | −0.465346 | −0.232673 | − | 0.972555i | \(-0.574747\pi\) | ||||
−0.232673 | + | 0.972555i | \(0.574747\pi\) | |||||||
\(654\) | −45.6021 | −1.78318 | ||||||||
\(655\) | −5.21444 | −0.203745 | ||||||||
\(656\) | 8.55060 | 0.333845 | ||||||||
\(657\) | −9.35095 | −0.364815 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.2919 | 1.41373 | 0.706866 | − | 0.707348i | \(-0.250108\pi\) | ||||
0.706866 | + | 0.707348i | \(0.250108\pi\) | |||||||
\(660\) | −24.2172 | −0.942654 | ||||||||
\(661\) | 23.6776 | 0.920952 | 0.460476 | − | 0.887672i | \(-0.347679\pi\) | ||||
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(662\) | 19.0518 | 0.740470 | ||||||||
\(663\) | −72.5387 | −2.81717 | ||||||||
\(664\) | −7.72073 | −0.299622 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.0703 | −0.583962 | ||||||||
\(667\) | 6.75033 | 0.261374 | ||||||||
\(668\) | 17.6261 | 0.681973 | ||||||||
\(669\) | −37.5738 | −1.45269 | ||||||||
\(670\) | −18.3357 | −0.708371 | ||||||||
\(671\) | 10.3978 | 0.401403 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.1605 | −1.23970 | −0.619848 | − | 0.784722i | \(-0.712806\pi\) | ||||
−0.619848 | + | 0.784722i | \(0.712806\pi\) | |||||||
\(674\) | 14.7396 | 0.567747 | ||||||||
\(675\) | 30.9472 | 1.19116 | ||||||||
\(676\) | 1.19616 | 0.0460060 | ||||||||
\(677\) | 6.02635 | 0.231611 | 0.115806 | − | 0.993272i | \(-0.463055\pi\) | ||||
0.115806 | + | 0.993272i | \(0.463055\pi\) | |||||||
\(678\) | 11.0301 | 0.423609 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.3398 | 0.664951 | ||||||||
\(681\) | 36.7908 | 1.40983 | ||||||||
\(682\) | −23.4724 | −0.898804 | ||||||||
\(683\) | −16.1649 | −0.618534 | −0.309267 | − | 0.950975i | \(-0.600084\pi\) | ||||
−0.309267 | + | 0.950975i | \(0.600084\pi\) | |||||||
\(684\) | −9.66115 | −0.369403 | ||||||||
\(685\) | −37.7914 | −1.44394 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −35.7947 | −1.36565 | ||||||||
\(688\) | 7.71375 | 0.294084 | ||||||||
\(689\) | 4.23602 | 0.161380 | ||||||||
\(690\) | −58.3202 | −2.22021 | ||||||||
\(691\) | 6.25698 | 0.238027 | 0.119013 | − | 0.992893i | \(-0.462027\pi\) | ||||
0.119013 | + | 0.992893i | \(0.462027\pi\) | |||||||
\(692\) | 18.4928 | 0.702990 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.1550 | −0.423437 | ||||||||
\(695\) | −12.7156 | −0.482330 | ||||||||
\(696\) | 3.09718 | 0.117398 | ||||||||
\(697\) | 53.1513 | 2.01325 | ||||||||
\(698\) | 31.8123 | 1.20411 | ||||||||
\(699\) | −52.1077 | −1.97089 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7051 | −1.23525 | −0.617627 | − | 0.786471i | \(-0.711906\pi\) | ||||
−0.617627 | + | 0.786471i | \(0.711906\pi\) | |||||||
\(702\) | 41.9233 | 1.58229 | ||||||||
\(703\) | −3.34999 | −0.126347 | ||||||||
\(704\) | 2.80305 | 0.105644 | ||||||||
\(705\) | −105.703 | −3.98102 | ||||||||
\(706\) | −1.86046 | −0.0700192 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.4687 | 0.393437 | ||||||||
\(709\) | 7.02322 | 0.263763 | 0.131881 | − | 0.991266i | \(-0.457898\pi\) | ||||
0.131881 | + | 0.991266i | \(0.457898\pi\) | |||||||
\(710\) | 23.5886 | 0.885264 | ||||||||
\(711\) | −84.6907 | −3.17615 | ||||||||
\(712\) | 9.99993 | 0.374763 | ||||||||
\(713\) | −56.5265 | −2.11693 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.4607 | 1.10177 | ||||||||
\(716\) | −13.8700 | −0.518348 | ||||||||
\(717\) | −24.7102 | −0.922819 | ||||||||
\(718\) | 31.2924 | 1.16782 | ||||||||
\(719\) | 2.25327 | 0.0840326 | 0.0420163 | − | 0.999117i | \(-0.486622\pi\) | ||||
0.0420163 | + | 0.999117i | \(0.486622\pi\) | |||||||
\(720\) | −18.3899 | −0.685352 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.8524 | 0.627182 | ||||||||
\(723\) | 40.1079 | 1.49163 | ||||||||
\(724\) | −22.3876 | −0.832030 | ||||||||
\(725\) | −2.78132 | −0.103296 | ||||||||
\(726\) | 9.73420 | 0.361270 | ||||||||
\(727\) | 34.0513 | 1.26289 | 0.631447 | − | 0.775419i | \(-0.282461\pi\) | ||||
0.631447 | + | 0.775419i | \(0.282461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.57968 | −0.243692 | ||||||||
\(730\) | −3.95666 | −0.146443 | ||||||||
\(731\) | 47.9494 | 1.77347 | ||||||||
\(732\) | 11.4889 | 0.424642 | ||||||||
\(733\) | −11.3601 | −0.419595 | −0.209797 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209797 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(734\) | 0.872346 | 0.0321989 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.75033 | 0.248821 | ||||||||
\(737\) | −18.4248 | −0.678685 | ||||||||
\(738\) | −56.3702 | −2.07502 | ||||||||
\(739\) | 11.8858 | 0.437227 | 0.218614 | − | 0.975811i | \(-0.429847\pi\) | ||||
0.218614 | + | 0.975811i | \(0.429847\pi\) | |||||||
\(740\) | −6.37669 | −0.234412 | ||||||||
\(741\) | 17.1012 | 0.628230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.1441 | −0.959133 | −0.479566 | − | 0.877506i | \(-0.659206\pi\) | ||||
−0.479566 | + | 0.877506i | \(0.659206\pi\) | |||||||
\(744\) | −25.9354 | −0.950839 | ||||||||
\(745\) | −43.5175 | −1.59436 | ||||||||
\(746\) | −11.3493 | −0.415527 | ||||||||
\(747\) | 50.8993 | 1.86231 | ||||||||
\(748\) | 17.4240 | 0.637085 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.1685 | −0.699934 | ||||||||
\(751\) | −0.657023 | −0.0239751 | −0.0119875 | − | 0.999928i | \(-0.503816\pi\) | ||||
−0.0119875 | + | 0.999928i | \(0.503816\pi\) | |||||||
\(752\) | 12.2347 | 0.446155 | ||||||||
\(753\) | −2.03001 | −0.0739778 | ||||||||
\(754\) | −3.76778 | −0.137214 | ||||||||
\(755\) | 21.2437 | 0.773138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.6633 | 1.11448 | 0.557239 | − | 0.830352i | \(-0.311861\pi\) | ||||
0.557239 | + | 0.830352i | \(0.311861\pi\) | |||||||
\(758\) | 21.3212 | 0.774419 | ||||||||
\(759\) | −58.6034 | −2.12717 | ||||||||
\(760\) | −4.08792 | −0.148284 | ||||||||
\(761\) | 11.4045 | 0.413411 | 0.206706 | − | 0.978403i | \(-0.433726\pi\) | ||||
0.206706 | + | 0.978403i | \(0.433726\pi\) | |||||||
\(762\) | 28.2051 | 1.02176 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.97033 | −0.288356 | ||||||||
\(765\) | −114.314 | −4.13302 | ||||||||
\(766\) | −11.6863 | −0.422241 | ||||||||
\(767\) | −12.7353 | −0.459846 | ||||||||
\(768\) | 3.09718 | 0.111760 | ||||||||
\(769\) | 26.3916 | 0.951704 | 0.475852 | − | 0.879525i | \(-0.342140\pi\) | ||||
0.475852 | + | 0.879525i | \(0.342140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.0063 | 1.90897 | ||||||||
\(772\) | −11.4871 | −0.413431 | ||||||||
\(773\) | 36.2068 | 1.30227 | 0.651134 | − | 0.758962i | \(-0.274293\pi\) | ||||
0.651134 | + | 0.758962i | \(0.274293\pi\) | |||||||
\(774\) | −50.8533 | −1.82788 | ||||||||
\(775\) | 23.2905 | 0.836618 | ||||||||
\(776\) | −1.13474 | −0.0407349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.79559 | −0.315337 | ||||||||
\(779\) | −12.5306 | −0.448955 | ||||||||
\(780\) | 32.5521 | 1.16555 | ||||||||
\(781\) | 23.7031 | 0.848165 | ||||||||
\(782\) | 41.9607 | 1.50051 | ||||||||
\(783\) | −11.1268 | −0.397639 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52.3653 | −1.86900 | ||||||||
\(786\) | −5.78959 | −0.206508 | ||||||||
\(787\) | −18.9730 | −0.676314 | −0.338157 | − | 0.941090i | \(-0.609804\pi\) | ||||
−0.338157 | + | 0.941090i | \(0.609804\pi\) | |||||||
\(788\) | −6.59563 | −0.234960 | ||||||||
\(789\) | 36.5670 | 1.30182 | ||||||||
\(790\) | −35.8351 | −1.27496 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −18.4792 | −0.656631 | ||||||||
\(793\) | −13.9765 | −0.496319 | ||||||||
\(794\) | −24.4533 | −0.867817 | ||||||||
\(795\) | 9.71330 | 0.344495 | ||||||||
\(796\) | −12.3980 | −0.439436 | ||||||||
\(797\) | 2.45142 | 0.0868339 | 0.0434169 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434169 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.0523 | 2.69054 | ||||||||
\(800\) | −2.78132 | −0.0983347 | ||||||||
\(801\) | −65.9251 | −2.32935 | ||||||||
\(802\) | 22.6628 | 0.800251 | ||||||||
\(803\) | −3.97588 | −0.140306 | ||||||||
\(804\) | −20.3582 | −0.717977 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.5509 | 1.11133 | ||||||||
\(807\) | 98.8805 | 3.48076 | ||||||||
\(808\) | 13.7492 | 0.483697 | ||||||||
\(809\) | −42.7136 | −1.50173 | −0.750866 | − | 0.660455i | \(-0.770363\pi\) | ||||
−0.750866 | + | 0.660455i | \(0.770363\pi\) | |||||||
\(810\) | 40.9613 | 1.43923 | ||||||||
\(811\) | 13.4951 | 0.473878 | 0.236939 | − | 0.971524i | \(-0.423856\pi\) | ||||
0.236939 | + | 0.971524i | \(0.423856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.8406 | 0.590627 | ||||||||
\(814\) | −6.40765 | −0.224588 | ||||||||
\(815\) | 23.6495 | 0.828406 | ||||||||
\(816\) | 19.2524 | 0.673968 | ||||||||
\(817\) | −11.3042 | −0.395485 | ||||||||
\(818\) | −1.81284 | −0.0633844 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.8519 | −0.832945 | ||||||||
\(821\) | 5.48451 | 0.191411 | 0.0957054 | − | 0.995410i | \(-0.469489\pi\) | ||||
0.0957054 | + | 0.995410i | \(0.469489\pi\) | |||||||
\(822\) | −41.9598 | −1.46352 | ||||||||
\(823\) | 2.39007 | 0.0833124 | 0.0416562 | − | 0.999132i | \(-0.486737\pi\) | ||||
0.0416562 | + | 0.999132i | \(0.486737\pi\) | |||||||
\(824\) | −3.31557 | −0.115503 | ||||||||
\(825\) | 24.1462 | 0.840664 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.6211 | −0.612745 | −0.306372 | − | 0.951912i | \(-0.599115\pi\) | ||||
−0.306372 | + | 0.951912i | \(0.599115\pi\) | |||||||
\(828\) | −44.5019 | −1.54655 | ||||||||
\(829\) | 3.99053 | 0.138597 | 0.0692984 | − | 0.997596i | \(-0.477924\pi\) | ||||
0.0692984 | + | 0.997596i | \(0.477924\pi\) | |||||||
\(830\) | 21.5370 | 0.747560 | ||||||||
\(831\) | 43.9855 | 1.52584 | ||||||||
\(832\) | −3.76778 | −0.130624 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.1181 | −0.488870 | ||||||||
\(835\) | −49.1679 | −1.70153 | ||||||||
\(836\) | −4.10777 | −0.142070 | ||||||||
\(837\) | 93.1744 | 3.22058 | ||||||||
\(838\) | −14.4468 | −0.499057 | ||||||||
\(839\) | 52.4049 | 1.80922 | 0.904610 | − | 0.426241i | \(-0.140162\pi\) | ||||
0.904610 | + | 0.426241i | \(0.140162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 13.8483 | 0.477244 | ||||||||
\(843\) | −9.65991 | −0.332705 | ||||||||
\(844\) | 24.3981 | 0.839818 | ||||||||
\(845\) | −3.33668 | −0.114785 | ||||||||
\(846\) | −80.6581 | −2.77308 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.12428 | −0.0386078 | ||||||||
\(849\) | −29.8887 | −1.02578 | ||||||||
\(850\) | −17.2890 | −0.593007 | ||||||||
\(851\) | −15.4310 | −0.528967 | ||||||||
\(852\) | 26.1904 | 0.897268 | ||||||||
\(853\) | 23.3084 | 0.798064 | 0.399032 | − | 0.916937i | \(-0.369346\pi\) | ||||
0.399032 | + | 0.916937i | \(0.369346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.9498 | 0.921664 | ||||||||
\(856\) | −6.61427 | −0.226071 | ||||||||
\(857\) | −42.7990 | −1.46199 | −0.730993 | − | 0.682385i | \(-0.760943\pi\) | ||||
−0.730993 | + | 0.682385i | \(0.760943\pi\) | |||||||
\(858\) | 32.7102 | 1.11671 | ||||||||
\(859\) | 28.9445 | 0.987575 | 0.493788 | − | 0.869583i | \(-0.335612\pi\) | ||||
0.493788 | + | 0.869583i | \(0.335612\pi\) | |||||||
\(860\) | −21.5175 | −0.733741 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.5908 | 0.428843 | ||||||||
\(863\) | −53.6213 | −1.82529 | −0.912644 | − | 0.408755i | \(-0.865963\pi\) | ||||
−0.912644 | + | 0.408755i | \(0.865963\pi\) | |||||||
\(864\) | −11.1268 | −0.378541 | ||||||||
\(865\) | −51.5857 | −1.75397 | ||||||||
\(866\) | 9.09118 | 0.308931 | ||||||||
\(867\) | 67.0225 | 2.27620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.0092 | −1.22153 | ||||||||
\(870\) | −8.63960 | −0.292910 | ||||||||
\(871\) | 24.7660 | 0.839165 | ||||||||
\(872\) | −14.7237 | −0.498609 | ||||||||
\(873\) | 7.48085 | 0.253188 | ||||||||
\(874\) | −9.89237 | −0.334615 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.39308 | −0.148429 | ||||||||
\(877\) | 28.6402 | 0.967110 | 0.483555 | − | 0.875314i | \(-0.339345\pi\) | ||||
0.483555 | + | 0.875314i | \(0.339345\pi\) | |||||||
\(878\) | 23.9511 | 0.808309 | ||||||||
\(879\) | 60.9309 | 2.05515 | ||||||||
\(880\) | −7.81911 | −0.263582 | ||||||||
\(881\) | 13.6171 | 0.458773 | 0.229386 | − | 0.973335i | \(-0.426328\pi\) | ||||
0.229386 | + | 0.973335i | \(0.426328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.8344 | −1.30688 | −0.653441 | − | 0.756978i | \(-0.726675\pi\) | ||||
−0.653441 | + | 0.756978i | \(0.726675\pi\) | |||||||
\(884\) | −23.4209 | −0.787729 | ||||||||
\(885\) | −29.2024 | −0.981628 | ||||||||
\(886\) | −26.2769 | −0.882788 | ||||||||
\(887\) | −33.4467 | −1.12303 | −0.561515 | − | 0.827467i | \(-0.689781\pi\) | ||||
−0.561515 | + | 0.827467i | \(0.689781\pi\) | |||||||
\(888\) | −7.08003 | −0.237590 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.8948 | −0.935037 | ||||||||
\(891\) | 41.1602 | 1.37892 | ||||||||
\(892\) | −12.1316 | −0.406196 | ||||||||
\(893\) | −17.9296 | −0.599990 | ||||||||
\(894\) | −48.3174 | −1.61598 | ||||||||
\(895\) | 38.6905 | 1.29328 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 78.7731 | 2.63016 | ||||||||
\(898\) | −3.06619 | −0.102320 | ||||||||
\(899\) | −8.37388 | −0.279284 | ||||||||
\(900\) | 18.3360 | 0.611201 | ||||||||
\(901\) | −6.98860 | −0.232824 | ||||||||
\(902\) | −23.9677 | −0.798038 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.56133 | 0.118448 | ||||||||
\(905\) | 62.4504 | 2.07592 | ||||||||
\(906\) | 23.5869 | 0.783622 | ||||||||
\(907\) | −6.20968 | −0.206189 | −0.103095 | − | 0.994672i | \(-0.532874\pi\) | ||||
−0.103095 | + | 0.994672i | \(0.532874\pi\) | |||||||
\(908\) | 11.8788 | 0.394212 | ||||||||
\(909\) | −90.6426 | −3.00643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.9816 | −1.85475 | −0.927377 | − | 0.374127i | \(-0.877942\pi\) | ||||
−0.927377 | + | 0.374127i | \(0.877942\pi\) | |||||||
\(912\) | −4.53881 | −0.150295 | ||||||||
\(913\) | 21.6416 | 0.716231 | ||||||||
\(914\) | −15.6802 | −0.518654 | ||||||||
\(915\) | −32.0483 | −1.05949 | ||||||||
\(916\) | −11.5572 | −0.381859 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −69.1652 | −2.28279 | ||||||||
\(919\) | −33.8594 | −1.11692 | −0.558460 | − | 0.829532i | \(-0.688607\pi\) | ||||
−0.558460 | + | 0.829532i | \(0.688607\pi\) | |||||||
\(920\) | −18.8301 | −0.620809 | ||||||||
\(921\) | −56.5682 | −1.86399 | ||||||||
\(922\) | 1.66602 | 0.0548673 | ||||||||
\(923\) | −31.8611 | −1.04872 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.35799 | 0.209049 | ||||||||
\(926\) | −17.2509 | −0.566900 | ||||||||
\(927\) | 21.8580 | 0.717912 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 59.7885 | 1.96160 | 0.980798 | − | 0.195025i | \(-0.0624789\pi\) | ||||
0.980798 | + | 0.195025i | \(0.0624789\pi\) | |||||||
\(930\) | 72.3470 | 2.37235 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.8242 | −0.551095 | ||||||||
\(933\) | −93.9283 | −3.07507 | ||||||||
\(934\) | 11.1793 | 0.365799 | ||||||||
\(935\) | −48.6043 | −1.58953 | ||||||||
\(936\) | 24.8393 | 0.811897 | ||||||||
\(937\) | −27.6720 | −0.904004 | −0.452002 | − | 0.892017i | \(-0.649290\pi\) | ||||
−0.452002 | + | 0.892017i | \(0.649290\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.7368 | −1.88417 | ||||||||
\(940\) | −34.1288 | −1.11316 | ||||||||
\(941\) | 20.2724 | 0.660862 | 0.330431 | − | 0.943830i | \(-0.392806\pi\) | ||||
0.330431 | + | 0.943830i | \(0.392806\pi\) | |||||||
\(942\) | −58.1412 | −1.89434 | ||||||||
\(943\) | −57.7194 | −1.87960 | ||||||||
\(944\) | 3.38006 | 0.110012 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.6220 | −0.702992 | ||||||||
\(947\) | 40.4969 | 1.31597 | 0.657986 | − | 0.753030i | \(-0.271409\pi\) | ||||
0.657986 | + | 0.753030i | \(0.271409\pi\) | |||||||
\(948\) | −39.7878 | −1.29225 | ||||||||
\(949\) | 5.34426 | 0.173482 | ||||||||
\(950\) | 4.07593 | 0.132241 | ||||||||
\(951\) | 46.1868 | 1.49771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.5977 | 0.991156 | 0.495578 | − | 0.868564i | \(-0.334956\pi\) | ||||
0.495578 | + | 0.868564i | \(0.334956\pi\) | |||||||
\(954\) | 7.41184 | 0.239967 | ||||||||
\(955\) | 22.2332 | 0.719451 | ||||||||
\(956\) | −7.97828 | −0.258036 | ||||||||
\(957\) | −8.68156 | −0.280635 | ||||||||
\(958\) | 13.0826 | 0.422680 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.63960 | −0.278842 | ||||||||
\(961\) | 39.1218 | 1.26199 | ||||||||
\(962\) | 8.61298 | 0.277694 | ||||||||
\(963\) | 43.6049 | 1.40515 | ||||||||
\(964\) | 12.9498 | 0.417085 | ||||||||
\(965\) | 32.0434 | 1.03151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5129 | 0.627491 | 0.313746 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313746 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(968\) | 3.14292 | 0.101017 | ||||||||
\(969\) | −28.2137 | −0.906354 | ||||||||
\(970\) | 3.16537 | 0.101634 | ||||||||
\(971\) | −27.5801 | −0.885087 | −0.442543 | − | 0.896747i | \(-0.645924\pi\) | ||||
−0.442543 | + | 0.896747i | \(0.645924\pi\) | |||||||
\(972\) | 12.0989 | 0.388073 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.75769 | −0.216530 | ||||||||
\(975\) | −32.4567 | −1.03945 | ||||||||
\(976\) | 3.70947 | 0.118737 | ||||||||
\(977\) | −19.7213 | −0.630940 | −0.315470 | − | 0.948936i | \(-0.602162\pi\) | ||||
−0.315470 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(978\) | 26.2580 | 0.839640 | ||||||||
\(979\) | −28.0303 | −0.895852 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 97.0670 | 3.09911 | ||||||||
\(982\) | −9.53271 | −0.304201 | ||||||||
\(983\) | 8.91791 | 0.284437 | 0.142219 | − | 0.989835i | \(-0.454576\pi\) | ||||
0.142219 | + | 0.989835i | \(0.454576\pi\) | |||||||
\(984\) | −26.4828 | −0.844240 | ||||||||
\(985\) | 18.3985 | 0.586226 | ||||||||
\(986\) | 6.21609 | 0.197961 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.52155 | 0.175664 | ||||||||
\(989\) | −52.0704 | −1.65574 | ||||||||
\(990\) | 51.5479 | 1.63830 | ||||||||
\(991\) | 55.1794 | 1.75283 | 0.876416 | − | 0.481555i | \(-0.159928\pi\) | ||||
0.876416 | + | 0.481555i | \(0.159928\pi\) | |||||||
\(992\) | −8.37388 | −0.265871 | ||||||||
\(993\) | −59.0070 | −1.87253 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.5843 | 1.09639 | ||||||||
\(996\) | 23.9125 | 0.757697 | ||||||||
\(997\) | 45.0444 | 1.42657 | 0.713285 | − | 0.700874i | \(-0.247207\pi\) | ||||
0.713285 | + | 0.700874i | \(0.247207\pi\) | |||||||
\(998\) | 21.0060 | 0.664933 | ||||||||
\(999\) | 25.4354 | 0.804740 |
(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 | 2842.2.a.u.1.5 | 5 | ||
7.3 | odd | 6 | 406.2.e.d.233.5 | ✓ | 10 | ||
7.5 | odd | 6 | 406.2.e.d.291.5 | yes | 10 | ||
7.6 | odd | 2 | 2842.2.a.t.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.d.233.5 | ✓ | 10 | 7.3 | odd | 6 | ||
406.2.e.d.291.5 | yes | 10 | 7.5 | odd | 6 | ||
2842.2.a.t.1.1 | 5 | 7.6 | odd | 2 | |||
2842.2.a.u.1.5 | 5 | 1.1 | even | 1 | trivial |