Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71030 | −1.91647 | −0.958235 | − | 0.285983i | \(-0.907680\pi\) | ||||
−0.958235 | + | 0.285983i | \(0.907680\pi\) | |||||||
\(3\) | −2.41604 | −1.39490 | −0.697451 | − | 0.716633i | \(-0.745682\pi\) | ||||
−0.697451 | + | 0.716633i | \(0.745682\pi\) | |||||||
\(4\) | 5.34571 | 2.67285 | ||||||||
\(5\) | 3.72865 | 1.66750 | 0.833751 | − | 0.552140i | \(-0.186189\pi\) | ||||
0.833751 | + | 0.552140i | \(0.186189\pi\) | |||||||
\(6\) | 6.54819 | 2.67329 | ||||||||
\(7\) | −2.88700 | −1.09118 | −0.545591 | − | 0.838052i | \(-0.683695\pi\) | ||||
−0.545591 | + | 0.838052i | \(0.683695\pi\) | |||||||
\(8\) | −9.06786 | −3.20597 | ||||||||
\(9\) | 2.83725 | 0.945751 | ||||||||
\(10\) | −10.1057 | −3.19572 | ||||||||
\(11\) | −4.46651 | −1.34670 | −0.673352 | − | 0.739322i | \(-0.735146\pi\) | ||||
−0.673352 | + | 0.739322i | \(0.735146\pi\) | |||||||
\(12\) | −12.9155 | −3.72837 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 7.82461 | 2.09122 | ||||||||
\(15\) | −9.00857 | −2.32600 | ||||||||
\(16\) | 13.8852 | 3.47130 | ||||||||
\(17\) | −1.88158 | −0.456351 | −0.228175 | − | 0.973620i | \(-0.573276\pi\) | ||||
−0.228175 | + | 0.973620i | \(0.573276\pi\) | |||||||
\(18\) | −7.68980 | −1.81250 | ||||||||
\(19\) | −8.12116 | −1.86312 | −0.931561 | − | 0.363584i | \(-0.881553\pi\) | ||||
−0.931561 | + | 0.363584i | \(0.881553\pi\) | |||||||
\(20\) | 19.9323 | 4.45699 | ||||||||
\(21\) | 6.97510 | 1.52209 | ||||||||
\(22\) | 12.1056 | 2.58092 | ||||||||
\(23\) | −2.19223 | −0.457112 | −0.228556 | − | 0.973531i | \(-0.573400\pi\) | ||||
−0.228556 | + | 0.973531i | \(0.573400\pi\) | |||||||
\(24\) | 21.9083 | 4.47202 | ||||||||
\(25\) | 8.90282 | 1.78056 | ||||||||
\(26\) | 2.71030 | 0.531533 | ||||||||
\(27\) | 0.393202 | 0.0756717 | ||||||||
\(28\) | −15.4330 | −2.91657 | ||||||||
\(29\) | 8.82158 | 1.63813 | 0.819063 | − | 0.573703i | \(-0.194494\pi\) | ||||
0.819063 | + | 0.573703i | \(0.194494\pi\) | |||||||
\(30\) | 24.4159 | 4.45771 | ||||||||
\(31\) | 5.98295 | 1.07457 | 0.537285 | − | 0.843401i | \(-0.319450\pi\) | ||||
0.537285 | + | 0.843401i | \(0.319450\pi\) | |||||||
\(32\) | −19.4972 | −3.44666 | ||||||||
\(33\) | 10.7913 | 1.87852 | ||||||||
\(34\) | 5.09965 | 0.874583 | ||||||||
\(35\) | −10.7646 | −1.81955 | ||||||||
\(36\) | 15.1671 | 2.52786 | ||||||||
\(37\) | −9.44386 | −1.55256 | −0.776281 | − | 0.630387i | \(-0.782896\pi\) | ||||
−0.776281 | + | 0.630387i | \(0.782896\pi\) | |||||||
\(38\) | 22.0108 | 3.57062 | ||||||||
\(39\) | 2.41604 | 0.386876 | ||||||||
\(40\) | −33.8109 | −5.34597 | ||||||||
\(41\) | −6.21801 | −0.971089 | −0.485545 | − | 0.874212i | \(-0.661379\pi\) | ||||
−0.485545 | + | 0.874212i | \(0.661379\pi\) | |||||||
\(42\) | −18.9046 | −2.91704 | ||||||||
\(43\) | −0.0964750 | −0.0147123 | −0.00735615 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735615 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(44\) | −23.8767 | −3.59954 | ||||||||
\(45\) | 10.5791 | 1.57704 | ||||||||
\(46\) | 5.94159 | 0.876040 | ||||||||
\(47\) | 4.49548 | 0.655733 | 0.327866 | − | 0.944724i | \(-0.393670\pi\) | ||||
0.327866 | + | 0.944724i | \(0.393670\pi\) | |||||||
\(48\) | −33.5472 | −4.84212 | ||||||||
\(49\) | 1.33474 | 0.190678 | ||||||||
\(50\) | −24.1293 | −3.41240 | ||||||||
\(51\) | 4.54598 | 0.636565 | ||||||||
\(52\) | −5.34571 | −0.741316 | ||||||||
\(53\) | 1.45631 | 0.200040 | 0.100020 | − | 0.994985i | \(-0.468109\pi\) | ||||
0.100020 | + | 0.994985i | \(0.468109\pi\) | |||||||
\(54\) | −1.06569 | −0.145023 | ||||||||
\(55\) | −16.6540 | −2.24563 | ||||||||
\(56\) | 26.1789 | 3.49830 | ||||||||
\(57\) | 19.6211 | 2.59887 | ||||||||
\(58\) | −23.9091 | −3.13942 | ||||||||
\(59\) | 8.09604 | 1.05402 | 0.527008 | − | 0.849861i | \(-0.323314\pi\) | ||||
0.527008 | + | 0.849861i | \(0.323314\pi\) | |||||||
\(60\) | −48.1572 | −6.21707 | ||||||||
\(61\) | 1.81432 | 0.232299 | 0.116150 | − | 0.993232i | \(-0.462945\pi\) | ||||
0.116150 | + | 0.993232i | \(0.462945\pi\) | |||||||
\(62\) | −16.2156 | −2.05938 | ||||||||
\(63\) | −8.19114 | −1.03199 | ||||||||
\(64\) | 25.0729 | 3.13412 | ||||||||
\(65\) | −3.72865 | −0.462482 | ||||||||
\(66\) | −29.2475 | −3.60012 | ||||||||
\(67\) | 7.20656 | 0.880422 | 0.440211 | − | 0.897894i | \(-0.354904\pi\) | ||||
0.440211 | + | 0.897894i | \(0.354904\pi\) | |||||||
\(68\) | −10.0584 | −1.21976 | ||||||||
\(69\) | 5.29652 | 0.637626 | ||||||||
\(70\) | 29.1752 | 3.48711 | ||||||||
\(71\) | 10.0084 | 1.18778 | 0.593889 | − | 0.804547i | \(-0.297592\pi\) | ||||
0.593889 | + | 0.804547i | \(0.297592\pi\) | |||||||
\(72\) | −25.7278 | −3.03205 | ||||||||
\(73\) | −3.27988 | −0.383881 | −0.191940 | − | 0.981407i | \(-0.561478\pi\) | ||||
−0.191940 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(74\) | 25.5957 | 2.97544 | ||||||||
\(75\) | −21.5096 | −2.48371 | ||||||||
\(76\) | −43.4134 | −4.97986 | ||||||||
\(77\) | 12.8948 | 1.46950 | ||||||||
\(78\) | −6.54819 | −0.741436 | ||||||||
\(79\) | −2.69531 | −0.303246 | −0.151623 | − | 0.988438i | \(-0.548450\pi\) | ||||
−0.151623 | + | 0.988438i | \(0.548450\pi\) | |||||||
\(80\) | 51.7730 | 5.78839 | ||||||||
\(81\) | −9.46175 | −1.05131 | ||||||||
\(82\) | 16.8526 | 1.86106 | ||||||||
\(83\) | −8.82524 | −0.968696 | −0.484348 | − | 0.874875i | \(-0.660943\pi\) | ||||
−0.484348 | + | 0.874875i | \(0.660943\pi\) | |||||||
\(84\) | 37.2868 | 4.06833 | ||||||||
\(85\) | −7.01576 | −0.760966 | ||||||||
\(86\) | 0.261476 | 0.0281957 | ||||||||
\(87\) | −21.3133 | −2.28503 | ||||||||
\(88\) | 40.5017 | 4.31750 | ||||||||
\(89\) | 11.4254 | 1.21109 | 0.605545 | − | 0.795811i | \(-0.292955\pi\) | ||||
0.605545 | + | 0.795811i | \(0.292955\pi\) | |||||||
\(90\) | −28.6726 | −3.02235 | ||||||||
\(91\) | 2.88700 | 0.302639 | ||||||||
\(92\) | −11.7190 | −1.22179 | ||||||||
\(93\) | −14.4550 | −1.49892 | ||||||||
\(94\) | −12.1841 | −1.25669 | ||||||||
\(95\) | −30.2810 | −3.10676 | ||||||||
\(96\) | 47.1061 | 4.80775 | ||||||||
\(97\) | −3.79001 | −0.384817 | −0.192409 | − | 0.981315i | \(-0.561630\pi\) | ||||
−0.192409 | + | 0.981315i | \(0.561630\pi\) | |||||||
\(98\) | −3.61755 | −0.365428 | ||||||||
\(99\) | −12.6726 | −1.27365 | ||||||||
\(100\) | 47.5919 | 4.75919 | ||||||||
\(101\) | 17.7796 | 1.76914 | 0.884570 | − | 0.466407i | \(-0.154452\pi\) | ||||
0.884570 | + | 0.466407i | \(0.154452\pi\) | |||||||
\(102\) | −12.3210 | −1.21996 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 9.06786 | 0.889177 | ||||||||
\(105\) | 26.0077 | 2.53809 | ||||||||
\(106\) | −3.94704 | −0.383370 | ||||||||
\(107\) | 5.63431 | 0.544690 | 0.272345 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272345 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(108\) | 2.10194 | 0.202259 | ||||||||
\(109\) | 8.39968 | 0.804543 | 0.402272 | − | 0.915520i | \(-0.368221\pi\) | ||||
0.402272 | + | 0.915520i | \(0.368221\pi\) | |||||||
\(110\) | 45.1374 | 4.30368 | ||||||||
\(111\) | 22.8168 | 2.16567 | ||||||||
\(112\) | −40.0865 | −3.78781 | ||||||||
\(113\) | 1.62078 | 0.152470 | 0.0762352 | − | 0.997090i | \(-0.475710\pi\) | ||||
0.0762352 | + | 0.997090i | \(0.475710\pi\) | |||||||
\(114\) | −53.1789 | −4.98066 | ||||||||
\(115\) | −8.17406 | −0.762235 | ||||||||
\(116\) | 47.1576 | 4.37847 | ||||||||
\(117\) | −2.83725 | −0.262304 | ||||||||
\(118\) | −21.9427 | −2.01999 | ||||||||
\(119\) | 5.43212 | 0.497962 | ||||||||
\(120\) | 81.6885 | 7.45710 | ||||||||
\(121\) | 8.94971 | 0.813610 | ||||||||
\(122\) | −4.91733 | −0.445195 | ||||||||
\(123\) | 15.0230 | 1.35457 | ||||||||
\(124\) | 31.9831 | 2.87217 | ||||||||
\(125\) | 14.5522 | 1.30159 | ||||||||
\(126\) | 22.2004 | 1.97777 | ||||||||
\(127\) | −8.95322 | −0.794470 | −0.397235 | − | 0.917717i | \(-0.630030\pi\) | ||||
−0.397235 | + | 0.917717i | \(0.630030\pi\) | |||||||
\(128\) | −28.9606 | −2.55978 | ||||||||
\(129\) | 0.233088 | 0.0205222 | ||||||||
\(130\) | 10.1057 | 0.886332 | ||||||||
\(131\) | 4.50594 | 0.393686 | 0.196843 | − | 0.980435i | \(-0.436931\pi\) | ||||
0.196843 | + | 0.980435i | \(0.436931\pi\) | |||||||
\(132\) | 57.6870 | 5.02101 | ||||||||
\(133\) | 23.4458 | 2.03301 | ||||||||
\(134\) | −19.5319 | −1.68730 | ||||||||
\(135\) | 1.46611 | 0.126183 | ||||||||
\(136\) | 17.0619 | 1.46305 | ||||||||
\(137\) | −11.9373 | −1.01987 | −0.509935 | − | 0.860213i | \(-0.670331\pi\) | ||||
−0.509935 | + | 0.860213i | \(0.670331\pi\) | |||||||
\(138\) | −14.3551 | −1.22199 | ||||||||
\(139\) | −12.6510 | −1.07304 | −0.536520 | − | 0.843888i | \(-0.680261\pi\) | ||||
−0.536520 | + | 0.843888i | \(0.680261\pi\) | |||||||
\(140\) | −57.5444 | −4.86339 | ||||||||
\(141\) | −10.8613 | −0.914683 | ||||||||
\(142\) | −27.1257 | −2.27634 | ||||||||
\(143\) | 4.46651 | 0.373508 | ||||||||
\(144\) | 39.3958 | 3.28298 | ||||||||
\(145\) | 32.8926 | 2.73158 | ||||||||
\(146\) | 8.88945 | 0.735696 | ||||||||
\(147\) | −3.22479 | −0.265977 | ||||||||
\(148\) | −50.4842 | −4.14977 | ||||||||
\(149\) | −3.00561 | −0.246229 | −0.123115 | − | 0.992392i | \(-0.539288\pi\) | ||||
−0.123115 | + | 0.992392i | \(0.539288\pi\) | |||||||
\(150\) | 58.2973 | 4.75996 | ||||||||
\(151\) | −12.6213 | −1.02711 | −0.513554 | − | 0.858057i | \(-0.671671\pi\) | ||||
−0.513554 | + | 0.858057i | \(0.671671\pi\) | |||||||
\(152\) | 73.6416 | 5.97312 | ||||||||
\(153\) | −5.33853 | −0.431594 | ||||||||
\(154\) | −34.9487 | −2.81625 | ||||||||
\(155\) | 22.3083 | 1.79185 | ||||||||
\(156\) | 12.9155 | 1.03406 | ||||||||
\(157\) | −1.39969 | −0.111707 | −0.0558536 | − | 0.998439i | \(-0.517788\pi\) | ||||
−0.0558536 | + | 0.998439i | \(0.517788\pi\) | |||||||
\(158\) | 7.30509 | 0.581161 | ||||||||
\(159\) | −3.51851 | −0.279036 | ||||||||
\(160\) | −72.6984 | −5.74731 | ||||||||
\(161\) | 6.32896 | 0.498792 | ||||||||
\(162\) | 25.6442 | 2.01480 | ||||||||
\(163\) | 22.1668 | 1.73624 | 0.868118 | − | 0.496358i | \(-0.165330\pi\) | ||||
0.868118 | + | 0.496358i | \(0.165330\pi\) | |||||||
\(164\) | −33.2397 | −2.59558 | ||||||||
\(165\) | 40.2369 | 3.13244 | ||||||||
\(166\) | 23.9190 | 1.85648 | ||||||||
\(167\) | 23.6661 | 1.83134 | 0.915668 | − | 0.401934i | \(-0.131662\pi\) | ||||
0.915668 | + | 0.401934i | \(0.131662\pi\) | |||||||
\(168\) | −63.2492 | −4.87979 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 19.0148 | 1.45837 | ||||||||
\(171\) | −23.0418 | −1.76205 | ||||||||
\(172\) | −0.515727 | −0.0393238 | ||||||||
\(173\) | 22.0669 | 1.67771 | 0.838857 | − | 0.544351i | \(-0.183224\pi\) | ||||
0.838857 | + | 0.544351i | \(0.183224\pi\) | |||||||
\(174\) | 57.7654 | 4.37918 | ||||||||
\(175\) | −25.7024 | −1.94292 | ||||||||
\(176\) | −62.0183 | −4.67481 | ||||||||
\(177\) | −19.5604 | −1.47025 | ||||||||
\(178\) | −30.9662 | −2.32102 | ||||||||
\(179\) | 16.2811 | 1.21691 | 0.608453 | − | 0.793590i | \(-0.291790\pi\) | ||||
0.608453 | + | 0.793590i | \(0.291790\pi\) | |||||||
\(180\) | 56.5529 | 4.21520 | ||||||||
\(181\) | −14.4397 | −1.07329 | −0.536646 | − | 0.843808i | \(-0.680309\pi\) | ||||
−0.536646 | + | 0.843808i | \(0.680309\pi\) | |||||||
\(182\) | −7.82461 | −0.579999 | ||||||||
\(183\) | −4.38346 | −0.324035 | ||||||||
\(184\) | 19.8788 | 1.46549 | ||||||||
\(185\) | −35.2129 | −2.58890 | ||||||||
\(186\) | 39.1775 | 2.87263 | ||||||||
\(187\) | 8.40411 | 0.614569 | ||||||||
\(188\) | 24.0315 | 1.75268 | ||||||||
\(189\) | −1.13517 | −0.0825716 | ||||||||
\(190\) | 82.0704 | 5.95401 | ||||||||
\(191\) | 8.61603 | 0.623434 | 0.311717 | − | 0.950175i | \(-0.399096\pi\) | ||||
0.311717 | + | 0.950175i | \(0.399096\pi\) | |||||||
\(192\) | −60.5773 | −4.37179 | ||||||||
\(193\) | 13.6430 | 0.982045 | 0.491022 | − | 0.871147i | \(-0.336623\pi\) | ||||
0.491022 | + | 0.871147i | \(0.336623\pi\) | |||||||
\(194\) | 10.2721 | 0.737490 | ||||||||
\(195\) | 9.00857 | 0.645117 | ||||||||
\(196\) | 7.13515 | 0.509653 | ||||||||
\(197\) | −16.9346 | −1.20654 | −0.603269 | − | 0.797538i | \(-0.706135\pi\) | ||||
−0.603269 | + | 0.797538i | \(0.706135\pi\) | |||||||
\(198\) | 34.3466 | 2.44090 | ||||||||
\(199\) | 6.04968 | 0.428850 | 0.214425 | − | 0.976740i | \(-0.431212\pi\) | ||||
0.214425 | + | 0.976740i | \(0.431212\pi\) | |||||||
\(200\) | −80.7296 | −5.70844 | ||||||||
\(201\) | −17.4114 | −1.22810 | ||||||||
\(202\) | −48.1881 | −3.39050 | ||||||||
\(203\) | −25.4679 | −1.78749 | ||||||||
\(204\) | 24.3015 | 1.70144 | ||||||||
\(205\) | −23.1848 | −1.61929 | ||||||||
\(206\) | −2.71030 | −0.188835 | ||||||||
\(207\) | −6.21991 | −0.432314 | ||||||||
\(208\) | −13.8852 | −0.962764 | ||||||||
\(209\) | 36.2733 | 2.50907 | ||||||||
\(210\) | −70.4886 | −4.86417 | ||||||||
\(211\) | −1.32862 | −0.0914657 | −0.0457328 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457328 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(212\) | 7.78502 | 0.534677 | ||||||||
\(213\) | −24.1807 | −1.65683 | ||||||||
\(214\) | −15.2707 | −1.04388 | ||||||||
\(215\) | −0.359721 | −0.0245328 | ||||||||
\(216\) | −3.56550 | −0.242602 | ||||||||
\(217\) | −17.2727 | −1.17255 | ||||||||
\(218\) | −22.7656 | −1.54188 | ||||||||
\(219\) | 7.92433 | 0.535476 | ||||||||
\(220\) | −89.0277 | −6.00224 | ||||||||
\(221\) | 1.88158 | 0.126569 | ||||||||
\(222\) | −61.8402 | −4.15044 | ||||||||
\(223\) | −21.5713 | −1.44452 | −0.722261 | − | 0.691620i | \(-0.756897\pi\) | ||||
−0.722261 | + | 0.691620i | \(0.756897\pi\) | |||||||
\(224\) | 56.2885 | 3.76093 | ||||||||
\(225\) | 25.2596 | 1.68397 | ||||||||
\(226\) | −4.39280 | −0.292205 | ||||||||
\(227\) | 10.9540 | 0.727041 | 0.363521 | − | 0.931586i | \(-0.381575\pi\) | ||||
0.363521 | + | 0.931586i | \(0.381575\pi\) | |||||||
\(228\) | 104.888 | 6.94641 | ||||||||
\(229\) | −12.8148 | −0.846825 | −0.423412 | − | 0.905937i | \(-0.639168\pi\) | ||||
−0.423412 | + | 0.905937i | \(0.639168\pi\) | |||||||
\(230\) | 22.1541 | 1.46080 | ||||||||
\(231\) | −31.1544 | −2.04981 | ||||||||
\(232\) | −79.9929 | −5.25179 | ||||||||
\(233\) | 7.56663 | 0.495706 | 0.247853 | − | 0.968798i | \(-0.420275\pi\) | ||||
0.247853 | + | 0.968798i | \(0.420275\pi\) | |||||||
\(234\) | 7.68980 | 0.502698 | ||||||||
\(235\) | 16.7621 | 1.09344 | ||||||||
\(236\) | 43.2791 | 2.81723 | ||||||||
\(237\) | 6.51198 | 0.422998 | ||||||||
\(238\) | −14.7227 | −0.954328 | ||||||||
\(239\) | 5.69918 | 0.368649 | 0.184325 | − | 0.982865i | \(-0.440990\pi\) | ||||
0.184325 | + | 0.982865i | \(0.440990\pi\) | |||||||
\(240\) | −125.086 | −8.07424 | ||||||||
\(241\) | 15.1300 | 0.974612 | 0.487306 | − | 0.873231i | \(-0.337980\pi\) | ||||
0.487306 | + | 0.873231i | \(0.337980\pi\) | |||||||
\(242\) | −24.2564 | −1.55926 | ||||||||
\(243\) | 21.6804 | 1.39080 | ||||||||
\(244\) | 9.69880 | 0.620902 | ||||||||
\(245\) | 4.97679 | 0.317955 | ||||||||
\(246\) | −40.7167 | −2.59600 | ||||||||
\(247\) | 8.12116 | 0.516737 | ||||||||
\(248\) | −54.2526 | −3.44504 | ||||||||
\(249\) | 21.3222 | 1.35124 | ||||||||
\(250\) | −39.4409 | −2.49446 | ||||||||
\(251\) | −24.2446 | −1.53031 | −0.765153 | − | 0.643849i | \(-0.777336\pi\) | ||||
−0.765153 | + | 0.643849i | \(0.777336\pi\) | |||||||
\(252\) | −43.7874 | −2.75835 | ||||||||
\(253\) | 9.79162 | 0.615594 | ||||||||
\(254\) | 24.2659 | 1.52258 | ||||||||
\(255\) | 16.9504 | 1.06147 | ||||||||
\(256\) | 28.3460 | 1.77163 | ||||||||
\(257\) | 18.4097 | 1.14837 | 0.574184 | − | 0.818726i | \(-0.305319\pi\) | ||||
0.574184 | + | 0.818726i | \(0.305319\pi\) | |||||||
\(258\) | −0.631736 | −0.0393302 | ||||||||
\(259\) | 27.2644 | 1.69413 | ||||||||
\(260\) | −19.9323 | −1.23615 | ||||||||
\(261\) | 25.0291 | 1.54926 | ||||||||
\(262\) | −12.2124 | −0.754487 | ||||||||
\(263\) | 21.0436 | 1.29760 | 0.648802 | − | 0.760957i | \(-0.275270\pi\) | ||||
0.648802 | + | 0.760957i | \(0.275270\pi\) | |||||||
\(264\) | −97.8538 | −6.02248 | ||||||||
\(265\) | 5.43007 | 0.333567 | ||||||||
\(266\) | −63.5450 | −3.89619 | ||||||||
\(267\) | −27.6042 | −1.68935 | ||||||||
\(268\) | 38.5242 | 2.35324 | ||||||||
\(269\) | −29.0529 | −1.77139 | −0.885694 | − | 0.464269i | \(-0.846317\pi\) | ||||
−0.885694 | + | 0.464269i | \(0.846317\pi\) | |||||||
\(270\) | −3.97360 | −0.241825 | ||||||||
\(271\) | 21.6941 | 1.31782 | 0.658912 | − | 0.752220i | \(-0.271017\pi\) | ||||
0.658912 | + | 0.752220i | \(0.271017\pi\) | |||||||
\(272\) | −26.1261 | −1.58413 | ||||||||
\(273\) | −6.97510 | −0.422152 | ||||||||
\(274\) | 32.3536 | 1.95455 | ||||||||
\(275\) | −39.7645 | −2.39789 | ||||||||
\(276\) | 28.3136 | 1.70428 | ||||||||
\(277\) | 3.12197 | 0.187581 | 0.0937904 | − | 0.995592i | \(-0.470102\pi\) | ||||
0.0937904 | + | 0.995592i | \(0.470102\pi\) | |||||||
\(278\) | 34.2879 | 2.05645 | ||||||||
\(279\) | 16.9751 | 1.01628 | ||||||||
\(280\) | 97.6119 | 5.83342 | ||||||||
\(281\) | −23.0923 | −1.37757 | −0.688785 | − | 0.724965i | \(-0.741856\pi\) | ||||
−0.688785 | + | 0.724965i | \(0.741856\pi\) | |||||||
\(282\) | 29.4372 | 1.75296 | ||||||||
\(283\) | 19.4513 | 1.15626 | 0.578131 | − | 0.815944i | \(-0.303782\pi\) | ||||
0.578131 | + | 0.815944i | \(0.303782\pi\) | |||||||
\(284\) | 53.5019 | 3.17476 | ||||||||
\(285\) | 73.1600 | 4.33363 | ||||||||
\(286\) | −12.1056 | −0.715817 | ||||||||
\(287\) | 17.9514 | 1.05964 | ||||||||
\(288\) | −55.3186 | −3.25968 | ||||||||
\(289\) | −13.4596 | −0.791744 | ||||||||
\(290\) | −89.1487 | −5.23499 | ||||||||
\(291\) | 9.15682 | 0.536782 | ||||||||
\(292\) | −17.5333 | −1.02606 | ||||||||
\(293\) | 10.1827 | 0.594882 | 0.297441 | − | 0.954740i | \(-0.403867\pi\) | ||||
0.297441 | + | 0.954740i | \(0.403867\pi\) | |||||||
\(294\) | 8.74015 | 0.509736 | ||||||||
\(295\) | 30.1873 | 1.75757 | ||||||||
\(296\) | 85.6357 | 4.97747 | ||||||||
\(297\) | −1.75624 | −0.101907 | ||||||||
\(298\) | 8.14609 | 0.471890 | ||||||||
\(299\) | 2.19223 | 0.126780 | ||||||||
\(300\) | −114.984 | −6.63860 | ||||||||
\(301\) | 0.278523 | 0.0160538 | ||||||||
\(302\) | 34.2075 | 1.96842 | ||||||||
\(303\) | −42.9563 | −2.46778 | ||||||||
\(304\) | −112.764 | −6.46745 | ||||||||
\(305\) | 6.76495 | 0.387360 | ||||||||
\(306\) | 14.4690 | 0.827138 | ||||||||
\(307\) | 0.443021 | 0.0252845 | 0.0126423 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126423 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(308\) | 68.9318 | 3.92775 | ||||||||
\(309\) | −2.41604 | −0.137444 | ||||||||
\(310\) | −60.4621 | −3.43402 | ||||||||
\(311\) | 24.7475 | 1.40330 | 0.701650 | − | 0.712522i | \(-0.252447\pi\) | ||||
0.701650 | + | 0.712522i | \(0.252447\pi\) | |||||||
\(312\) | −21.9083 | −1.24031 | ||||||||
\(313\) | −10.8305 | −0.612173 | −0.306087 | − | 0.952004i | \(-0.599020\pi\) | ||||
−0.306087 | + | 0.952004i | \(0.599020\pi\) | |||||||
\(314\) | 3.79357 | 0.214084 | ||||||||
\(315\) | −30.5419 | −1.72084 | ||||||||
\(316\) | −14.4083 | −0.810532 | ||||||||
\(317\) | 27.3315 | 1.53509 | 0.767544 | − | 0.640997i | \(-0.221479\pi\) | ||||
0.767544 | + | 0.640997i | \(0.221479\pi\) | |||||||
\(318\) | 9.53620 | 0.534764 | ||||||||
\(319\) | −39.4017 | −2.20607 | ||||||||
\(320\) | 93.4882 | 5.22615 | ||||||||
\(321\) | −13.6127 | −0.759789 | ||||||||
\(322\) | −17.1534 | −0.955919 | ||||||||
\(323\) | 15.2806 | 0.850238 | ||||||||
\(324\) | −50.5798 | −2.80999 | ||||||||
\(325\) | −8.90282 | −0.493840 | ||||||||
\(326\) | −60.0785 | −3.32744 | ||||||||
\(327\) | −20.2940 | −1.12226 | ||||||||
\(328\) | 56.3840 | 3.11329 | ||||||||
\(329\) | −12.9784 | −0.715524 | ||||||||
\(330\) | −109.054 | −6.00322 | ||||||||
\(331\) | 14.4478 | 0.794123 | 0.397061 | − | 0.917792i | \(-0.370030\pi\) | ||||
0.397061 | + | 0.917792i | \(0.370030\pi\) | |||||||
\(332\) | −47.1772 | −2.58918 | ||||||||
\(333\) | −26.7946 | −1.46834 | ||||||||
\(334\) | −64.1421 | −3.50970 | ||||||||
\(335\) | 26.8707 | 1.46811 | ||||||||
\(336\) | 96.8505 | 5.28363 | ||||||||
\(337\) | 14.3299 | 0.780599 | 0.390300 | − | 0.920688i | \(-0.372371\pi\) | ||||
0.390300 | + | 0.920688i | \(0.372371\pi\) | |||||||
\(338\) | −2.71030 | −0.147421 | ||||||||
\(339\) | −3.91588 | −0.212681 | ||||||||
\(340\) | −37.5042 | −2.03395 | ||||||||
\(341\) | −26.7229 | −1.44713 | ||||||||
\(342\) | 62.4501 | 3.37692 | ||||||||
\(343\) | 16.3556 | 0.883118 | ||||||||
\(344\) | 0.874822 | 0.0471672 | ||||||||
\(345\) | 19.7489 | 1.06324 | ||||||||
\(346\) | −59.8078 | −3.21529 | ||||||||
\(347\) | 31.1467 | 1.67204 | 0.836020 | − | 0.548699i | \(-0.184877\pi\) | ||||
0.836020 | + | 0.548699i | \(0.184877\pi\) | |||||||
\(348\) | −113.935 | −6.10754 | ||||||||
\(349\) | 2.40158 | 0.128554 | 0.0642769 | − | 0.997932i | \(-0.479526\pi\) | ||||
0.0642769 | + | 0.997932i | \(0.479526\pi\) | |||||||
\(350\) | 69.6611 | 3.72354 | ||||||||
\(351\) | −0.393202 | −0.0209876 | ||||||||
\(352\) | 87.0846 | 4.64163 | ||||||||
\(353\) | 20.4095 | 1.08629 | 0.543144 | − | 0.839640i | \(-0.317234\pi\) | ||||
0.543144 | + | 0.839640i | \(0.317234\pi\) | |||||||
\(354\) | 53.0144 | 2.81768 | ||||||||
\(355\) | 37.3178 | 1.98062 | ||||||||
\(356\) | 61.0768 | 3.23707 | ||||||||
\(357\) | −13.1242 | −0.694608 | ||||||||
\(358\) | −44.1266 | −2.33216 | ||||||||
\(359\) | −30.6694 | −1.61867 | −0.809334 | − | 0.587349i | \(-0.800172\pi\) | ||||
−0.809334 | + | 0.587349i | \(0.800172\pi\) | |||||||
\(360\) | −95.9300 | −5.05596 | ||||||||
\(361\) | 46.9533 | 2.47123 | ||||||||
\(362\) | 39.1357 | 2.05693 | ||||||||
\(363\) | −21.6229 | −1.13491 | ||||||||
\(364\) | 15.4330 | 0.808911 | ||||||||
\(365\) | −12.2295 | −0.640122 | ||||||||
\(366\) | 11.8805 | 0.621003 | ||||||||
\(367\) | −0.968271 | −0.0505433 | −0.0252717 | − | 0.999681i | \(-0.508045\pi\) | ||||
−0.0252717 | + | 0.999681i | \(0.508045\pi\) | |||||||
\(368\) | −30.4395 | −1.58677 | ||||||||
\(369\) | −17.6421 | −0.918409 | ||||||||
\(370\) | 95.4373 | 4.96155 | ||||||||
\(371\) | −4.20436 | −0.218280 | ||||||||
\(372\) | −77.2725 | −4.00639 | ||||||||
\(373\) | 20.0505 | 1.03817 | 0.519087 | − | 0.854721i | \(-0.326272\pi\) | ||||
0.519087 | + | 0.854721i | \(0.326272\pi\) | |||||||
\(374\) | −22.7776 | −1.17780 | ||||||||
\(375\) | −35.1588 | −1.81559 | ||||||||
\(376\) | −40.7644 | −2.10226 | ||||||||
\(377\) | −8.82158 | −0.454335 | ||||||||
\(378\) | 3.07665 | 0.158246 | ||||||||
\(379\) | −4.26123 | −0.218884 | −0.109442 | − | 0.993993i | \(-0.534906\pi\) | ||||
−0.109442 | + | 0.993993i | \(0.534906\pi\) | |||||||
\(380\) | −161.873 | −8.30392 | ||||||||
\(381\) | 21.6313 | 1.10821 | ||||||||
\(382\) | −23.3520 | −1.19479 | ||||||||
\(383\) | −6.57977 | −0.336210 | −0.168105 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168105 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(384\) | 69.9701 | 3.57065 | ||||||||
\(385\) | 48.0802 | 2.45039 | ||||||||
\(386\) | −36.9766 | −1.88206 | ||||||||
\(387\) | −0.273724 | −0.0139142 | ||||||||
\(388\) | −20.2603 | −1.02856 | ||||||||
\(389\) | 14.0220 | 0.710941 | 0.355471 | − | 0.934687i | \(-0.384321\pi\) | ||||
0.355471 | + | 0.934687i | \(0.384321\pi\) | |||||||
\(390\) | −24.4159 | −1.23635 | ||||||||
\(391\) | 4.12486 | 0.208603 | ||||||||
\(392\) | −12.1033 | −0.611307 | ||||||||
\(393\) | −10.8865 | −0.549153 | ||||||||
\(394\) | 45.8977 | 2.31229 | ||||||||
\(395\) | −10.0499 | −0.505663 | ||||||||
\(396\) | −67.7441 | −3.40427 | ||||||||
\(397\) | −18.0146 | −0.904125 | −0.452063 | − | 0.891986i | \(-0.649312\pi\) | ||||
−0.452063 | + | 0.891986i | \(0.649312\pi\) | |||||||
\(398\) | −16.3964 | −0.821878 | ||||||||
\(399\) | −56.6459 | −2.83584 | ||||||||
\(400\) | 123.617 | 6.18087 | ||||||||
\(401\) | −35.9551 | −1.79551 | −0.897755 | − | 0.440495i | \(-0.854803\pi\) | ||||
−0.897755 | + | 0.440495i | \(0.854803\pi\) | |||||||
\(402\) | 47.1899 | 2.35362 | ||||||||
\(403\) | −5.98295 | −0.298032 | ||||||||
\(404\) | 95.0448 | 4.72866 | ||||||||
\(405\) | −35.2796 | −1.75305 | ||||||||
\(406\) | 69.0255 | 3.42568 | ||||||||
\(407\) | 42.1811 | 2.09084 | ||||||||
\(408\) | −41.2223 | −2.04081 | ||||||||
\(409\) | 13.3433 | 0.659786 | 0.329893 | − | 0.944018i | \(-0.392987\pi\) | ||||
0.329893 | + | 0.944018i | \(0.392987\pi\) | |||||||
\(410\) | 62.8376 | 3.10333 | ||||||||
\(411\) | 28.8410 | 1.42262 | ||||||||
\(412\) | 5.34571 | 0.263364 | ||||||||
\(413\) | −23.3732 | −1.15012 | ||||||||
\(414\) | 16.8578 | 0.828516 | ||||||||
\(415\) | −32.9062 | −1.61530 | ||||||||
\(416\) | 19.4972 | 0.955931 | ||||||||
\(417\) | 30.5652 | 1.49679 | ||||||||
\(418\) | −98.3113 | −4.80856 | ||||||||
\(419\) | −15.5375 | −0.759058 | −0.379529 | − | 0.925180i | \(-0.623914\pi\) | ||||
−0.379529 | + | 0.925180i | \(0.623914\pi\) | |||||||
\(420\) | 139.030 | 6.78395 | ||||||||
\(421\) | 4.30962 | 0.210038 | 0.105019 | − | 0.994470i | \(-0.466510\pi\) | ||||
0.105019 | + | 0.994470i | \(0.466510\pi\) | |||||||
\(422\) | 3.60094 | 0.175291 | ||||||||
\(423\) | 12.7548 | 0.620160 | ||||||||
\(424\) | −13.2056 | −0.641322 | ||||||||
\(425\) | −16.7514 | −0.812562 | ||||||||
\(426\) | 65.5368 | 3.17527 | ||||||||
\(427\) | −5.23792 | −0.253481 | ||||||||
\(428\) | 30.1194 | 1.45588 | ||||||||
\(429\) | −10.7913 | −0.521007 | ||||||||
\(430\) | 0.974952 | 0.0470163 | ||||||||
\(431\) | −20.3114 | −0.978366 | −0.489183 | − | 0.872181i | \(-0.662705\pi\) | ||||
−0.489183 | + | 0.872181i | \(0.662705\pi\) | |||||||
\(432\) | 5.45968 | 0.262679 | ||||||||
\(433\) | 18.7669 | 0.901878 | 0.450939 | − | 0.892555i | \(-0.351089\pi\) | ||||
0.450939 | + | 0.892555i | \(0.351089\pi\) | |||||||
\(434\) | 46.8143 | 2.24716 | ||||||||
\(435\) | −79.4698 | −3.81029 | ||||||||
\(436\) | 44.9022 | 2.15043 | ||||||||
\(437\) | 17.8035 | 0.851655 | ||||||||
\(438\) | −21.4773 | −1.02622 | ||||||||
\(439\) | 23.3941 | 1.11654 | 0.558269 | − | 0.829660i | \(-0.311466\pi\) | ||||
0.558269 | + | 0.829660i | \(0.311466\pi\) | |||||||
\(440\) | 151.017 | 7.19943 | ||||||||
\(441\) | 3.78701 | 0.180334 | ||||||||
\(442\) | −5.09965 | −0.242566 | ||||||||
\(443\) | −25.8019 | −1.22588 | −0.612942 | − | 0.790128i | \(-0.710014\pi\) | ||||
−0.612942 | + | 0.790128i | \(0.710014\pi\) | |||||||
\(444\) | 121.972 | 5.78852 | ||||||||
\(445\) | 42.6013 | 2.01949 | ||||||||
\(446\) | 58.4647 | 2.76838 | ||||||||
\(447\) | 7.26167 | 0.343465 | ||||||||
\(448\) | −72.3855 | −3.41989 | ||||||||
\(449\) | 8.48971 | 0.400654 | 0.200327 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200327 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(450\) | −68.4609 | −3.22728 | ||||||||
\(451\) | 27.7728 | 1.30777 | ||||||||
\(452\) | 8.66423 | 0.407531 | ||||||||
\(453\) | 30.4936 | 1.43271 | ||||||||
\(454\) | −29.6885 | −1.39335 | ||||||||
\(455\) | 10.7646 | 0.504652 | ||||||||
\(456\) | −177.921 | −8.33192 | ||||||||
\(457\) | 13.6623 | 0.639096 | 0.319548 | − | 0.947570i | \(-0.396469\pi\) | ||||
0.319548 | + | 0.947570i | \(0.396469\pi\) | |||||||
\(458\) | 34.7319 | 1.62291 | ||||||||
\(459\) | −0.739842 | −0.0345329 | ||||||||
\(460\) | −43.6961 | −2.03734 | ||||||||
\(461\) | −22.8686 | −1.06510 | −0.532549 | − | 0.846399i | \(-0.678766\pi\) | ||||
−0.532549 | + | 0.846399i | \(0.678766\pi\) | |||||||
\(462\) | 84.4375 | 3.92839 | ||||||||
\(463\) | 3.21950 | 0.149623 | 0.0748115 | − | 0.997198i | \(-0.476164\pi\) | ||||
0.0748115 | + | 0.997198i | \(0.476164\pi\) | |||||||
\(464\) | 122.489 | 5.68642 | ||||||||
\(465\) | −53.8978 | −2.49945 | ||||||||
\(466\) | −20.5078 | −0.950006 | ||||||||
\(467\) | 26.8827 | 1.24398 | 0.621991 | − | 0.783025i | \(-0.286324\pi\) | ||||
0.621991 | + | 0.783025i | \(0.286324\pi\) | |||||||
\(468\) | −15.1671 | −0.701101 | ||||||||
\(469\) | −20.8053 | −0.960700 | ||||||||
\(470\) | −45.4302 | −2.09554 | ||||||||
\(471\) | 3.38170 | 0.155821 | ||||||||
\(472\) | −73.4138 | −3.37915 | ||||||||
\(473\) | 0.430906 | 0.0198131 | ||||||||
\(474\) | −17.6494 | −0.810663 | ||||||||
\(475\) | −72.3013 | −3.31741 | ||||||||
\(476\) | 29.0385 | 1.33098 | ||||||||
\(477\) | 4.13192 | 0.189188 | ||||||||
\(478\) | −15.4465 | −0.706505 | ||||||||
\(479\) | −18.2753 | −0.835021 | −0.417511 | − | 0.908672i | \(-0.637097\pi\) | ||||
−0.417511 | + | 0.908672i | \(0.637097\pi\) | |||||||
\(480\) | 175.642 | 8.01693 | ||||||||
\(481\) | 9.44386 | 0.430603 | ||||||||
\(482\) | −41.0069 | −1.86781 | ||||||||
\(483\) | −15.2910 | −0.695766 | ||||||||
\(484\) | 47.8425 | 2.17466 | ||||||||
\(485\) | −14.1316 | −0.641684 | ||||||||
\(486\) | −58.7603 | −2.66542 | ||||||||
\(487\) | 26.4880 | 1.20028 | 0.600142 | − | 0.799894i | \(-0.295111\pi\) | ||||
0.600142 | + | 0.799894i | \(0.295111\pi\) | |||||||
\(488\) | −16.4520 | −0.744746 | ||||||||
\(489\) | −53.5558 | −2.42188 | ||||||||
\(490\) | −13.4886 | −0.609352 | ||||||||
\(491\) | 21.4783 | 0.969301 | 0.484650 | − | 0.874708i | \(-0.338947\pi\) | ||||
0.484650 | + | 0.874708i | \(0.338947\pi\) | |||||||
\(492\) | 80.3084 | 3.62058 | ||||||||
\(493\) | −16.5985 | −0.747561 | ||||||||
\(494\) | −22.0108 | −0.990311 | ||||||||
\(495\) | −47.2518 | −2.12381 | ||||||||
\(496\) | 83.0743 | 3.73015 | ||||||||
\(497\) | −28.8942 | −1.29608 | ||||||||
\(498\) | −57.7894 | −2.58960 | ||||||||
\(499\) | 10.4746 | 0.468908 | 0.234454 | − | 0.972127i | \(-0.424670\pi\) | ||||
0.234454 | + | 0.972127i | \(0.424670\pi\) | |||||||
\(500\) | 77.7921 | 3.47897 | ||||||||
\(501\) | −57.1782 | −2.55454 | ||||||||
\(502\) | 65.7100 | 2.93278 | ||||||||
\(503\) | −15.8868 | −0.708358 | −0.354179 | − | 0.935178i | \(-0.615240\pi\) | ||||
−0.354179 | + | 0.935178i | \(0.615240\pi\) | |||||||
\(504\) | 74.2761 | 3.30852 | ||||||||
\(505\) | 66.2940 | 2.95005 | ||||||||
\(506\) | −26.5382 | −1.17977 | ||||||||
\(507\) | −2.41604 | −0.107300 | ||||||||
\(508\) | −47.8613 | −2.12350 | ||||||||
\(509\) | 18.2970 | 0.811002 | 0.405501 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405501 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(510\) | −45.9405 | −2.03428 | ||||||||
\(511\) | 9.46900 | 0.418884 | ||||||||
\(512\) | −18.9049 | −0.835487 | ||||||||
\(513\) | −3.19326 | −0.140986 | ||||||||
\(514\) | −49.8958 | −2.20081 | ||||||||
\(515\) | 3.72865 | 0.164304 | ||||||||
\(516\) | 1.24602 | 0.0548529 | ||||||||
\(517\) | −20.0791 | −0.883078 | ||||||||
\(518\) | −73.8946 | −3.24674 | ||||||||
\(519\) | −53.3145 | −2.34025 | ||||||||
\(520\) | 33.8109 | 1.48271 | ||||||||
\(521\) | −13.4600 | −0.589695 | −0.294847 | − | 0.955544i | \(-0.595269\pi\) | ||||
−0.294847 | + | 0.955544i | \(0.595269\pi\) | |||||||
\(522\) | −67.8362 | −2.96911 | ||||||||
\(523\) | −36.0870 | −1.57798 | −0.788988 | − | 0.614409i | \(-0.789395\pi\) | ||||
−0.788988 | + | 0.614409i | \(0.789395\pi\) | |||||||
\(524\) | 24.0874 | 1.05226 | ||||||||
\(525\) | 62.0981 | 2.71018 | ||||||||
\(526\) | −57.0344 | −2.48682 | ||||||||
\(527\) | −11.2574 | −0.490381 | ||||||||
\(528\) | 149.839 | 6.52090 | ||||||||
\(529\) | −18.1941 | −0.791049 | ||||||||
\(530\) | −14.7171 | −0.639270 | ||||||||
\(531\) | 22.9705 | 0.996836 | ||||||||
\(532\) | 125.334 | 5.43393 | ||||||||
\(533\) | 6.21801 | 0.269332 | ||||||||
\(534\) | 74.8156 | 3.23759 | ||||||||
\(535\) | 21.0084 | 0.908271 | ||||||||
\(536\) | −65.3481 | −2.82261 | ||||||||
\(537\) | −39.3358 | −1.69746 | ||||||||
\(538\) | 78.7421 | 3.39481 | ||||||||
\(539\) | −5.96164 | −0.256786 | ||||||||
\(540\) | 7.83740 | 0.337268 | ||||||||
\(541\) | −11.2553 | −0.483901 | −0.241951 | − | 0.970289i | \(-0.577787\pi\) | ||||
−0.241951 | + | 0.970289i | \(0.577787\pi\) | |||||||
\(542\) | −58.7975 | −2.52557 | ||||||||
\(543\) | 34.8868 | 1.49714 | ||||||||
\(544\) | 36.6857 | 1.57289 | ||||||||
\(545\) | 31.3194 | 1.34158 | ||||||||
\(546\) | 18.9046 | 0.809042 | ||||||||
\(547\) | −22.0034 | −0.940798 | −0.470399 | − | 0.882454i | \(-0.655890\pi\) | ||||
−0.470399 | + | 0.882454i | \(0.655890\pi\) | |||||||
\(548\) | −63.8132 | −2.72597 | ||||||||
\(549\) | 5.14767 | 0.219697 | ||||||||
\(550\) | 107.774 | 4.59549 | ||||||||
\(551\) | −71.6415 | −3.05203 | ||||||||
\(552\) | −48.0281 | −2.04421 | ||||||||
\(553\) | 7.78134 | 0.330896 | ||||||||
\(554\) | −8.46145 | −0.359493 | ||||||||
\(555\) | 85.0757 | 3.61126 | ||||||||
\(556\) | −67.6283 | −2.86808 | ||||||||
\(557\) | 20.2468 | 0.857886 | 0.428943 | − | 0.903331i | \(-0.358886\pi\) | ||||
0.428943 | + | 0.903331i | \(0.358886\pi\) | |||||||
\(558\) | −46.0077 | −1.94766 | ||||||||
\(559\) | 0.0964750 | 0.00408046 | ||||||||
\(560\) | −149.468 | −6.31619 | ||||||||
\(561\) | −20.3047 | −0.857264 | ||||||||
\(562\) | 62.5870 | 2.64007 | ||||||||
\(563\) | 24.4794 | 1.03169 | 0.515843 | − | 0.856683i | \(-0.327479\pi\) | ||||
0.515843 | + | 0.856683i | \(0.327479\pi\) | |||||||
\(564\) | −58.0611 | −2.44481 | ||||||||
\(565\) | 6.04333 | 0.254245 | ||||||||
\(566\) | −52.7189 | −2.21594 | ||||||||
\(567\) | 27.3160 | 1.14717 | ||||||||
\(568\) | −90.7547 | −3.80798 | ||||||||
\(569\) | 13.1464 | 0.551125 | 0.275563 | − | 0.961283i | \(-0.411136\pi\) | ||||
0.275563 | + | 0.961283i | \(0.411136\pi\) | |||||||
\(570\) | −198.285 | −8.30526 | ||||||||
\(571\) | −32.5556 | −1.36241 | −0.681205 | − | 0.732092i | \(-0.738544\pi\) | ||||
−0.681205 | + | 0.732092i | \(0.738544\pi\) | |||||||
\(572\) | 23.8767 | 0.998333 | ||||||||
\(573\) | −20.8167 | −0.869629 | ||||||||
\(574\) | −48.6535 | −2.03076 | ||||||||
\(575\) | −19.5170 | −0.813917 | ||||||||
\(576\) | 71.1383 | 2.96410 | ||||||||
\(577\) | −36.0583 | −1.50113 | −0.750564 | − | 0.660798i | \(-0.770218\pi\) | ||||
−0.750564 | + | 0.660798i | \(0.770218\pi\) | |||||||
\(578\) | 36.4796 | 1.51735 | ||||||||
\(579\) | −32.9621 | −1.36986 | ||||||||
\(580\) | 175.834 | 7.30112 | ||||||||
\(581\) | 25.4784 | 1.05702 | ||||||||
\(582\) | −24.8177 | −1.02873 | ||||||||
\(583\) | −6.50463 | −0.269394 | ||||||||
\(584\) | 29.7415 | 1.23071 | ||||||||
\(585\) | −10.5791 | −0.437393 | ||||||||
\(586\) | −27.5983 | −1.14007 | ||||||||
\(587\) | −29.2925 | −1.20903 | −0.604516 | − | 0.796593i | \(-0.706633\pi\) | ||||
−0.604516 | + | 0.796593i | \(0.706633\pi\) | |||||||
\(588\) | −17.2388 | −0.710917 | ||||||||
\(589\) | −48.5885 | −2.00205 | ||||||||
\(590\) | −81.8166 | −3.36833 | ||||||||
\(591\) | 40.9146 | 1.68300 | ||||||||
\(592\) | −131.130 | −5.38940 | ||||||||
\(593\) | 14.8347 | 0.609190 | 0.304595 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304595 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(594\) | 4.75993 | 0.195302 | ||||||||
\(595\) | 20.2545 | 0.830352 | ||||||||
\(596\) | −16.0671 | −0.658134 | ||||||||
\(597\) | −14.6163 | −0.598204 | ||||||||
\(598\) | −5.94159 | −0.242970 | ||||||||
\(599\) | −23.5377 | −0.961724 | −0.480862 | − | 0.876796i | \(-0.659676\pi\) | ||||
−0.480862 | + | 0.876796i | \(0.659676\pi\) | |||||||
\(600\) | 195.046 | 7.96272 | ||||||||
\(601\) | 15.2715 | 0.622936 | 0.311468 | − | 0.950257i | \(-0.399179\pi\) | ||||
0.311468 | + | 0.950257i | \(0.399179\pi\) | |||||||
\(602\) | −0.754880 | −0.0307666 | ||||||||
\(603\) | 20.4469 | 0.832660 | ||||||||
\(604\) | −67.4698 | −2.74531 | ||||||||
\(605\) | 33.3703 | 1.35670 | ||||||||
\(606\) | 116.424 | 4.72942 | ||||||||
\(607\) | 14.1425 | 0.574026 | 0.287013 | − | 0.957927i | \(-0.407338\pi\) | ||||
0.287013 | + | 0.957927i | \(0.407338\pi\) | |||||||
\(608\) | 158.340 | 6.42155 | ||||||||
\(609\) | 61.5314 | 2.49338 | ||||||||
\(610\) | −18.3350 | −0.742363 | ||||||||
\(611\) | −4.49548 | −0.181868 | ||||||||
\(612\) | −28.5382 | −1.15359 | ||||||||
\(613\) | 13.6543 | 0.551493 | 0.275747 | − | 0.961230i | \(-0.411075\pi\) | ||||
0.275747 | + | 0.961230i | \(0.411075\pi\) | |||||||
\(614\) | −1.20072 | −0.0484570 | ||||||||
\(615\) | 56.0153 | 2.25876 | ||||||||
\(616\) | −116.928 | −4.71117 | ||||||||
\(617\) | −20.9206 | −0.842231 | −0.421116 | − | 0.907007i | \(-0.638361\pi\) | ||||
−0.421116 | + | 0.907007i | \(0.638361\pi\) | |||||||
\(618\) | 6.54819 | 0.263407 | ||||||||
\(619\) | 45.8833 | 1.84421 | 0.922104 | − | 0.386943i | \(-0.126469\pi\) | ||||
0.922104 | + | 0.386943i | \(0.126469\pi\) | |||||||
\(620\) | 119.254 | 4.78935 | ||||||||
\(621\) | −0.861989 | −0.0345904 | ||||||||
\(622\) | −67.0730 | −2.68938 | ||||||||
\(623\) | −32.9851 | −1.32152 | ||||||||
\(624\) | 33.5472 | 1.34296 | ||||||||
\(625\) | 9.74611 | 0.389844 | ||||||||
\(626\) | 29.3537 | 1.17321 | ||||||||
\(627\) | −87.6377 | −3.49991 | ||||||||
\(628\) | −7.48233 | −0.298577 | ||||||||
\(629\) | 17.7694 | 0.708513 | ||||||||
\(630\) | 82.7776 | 3.29794 | ||||||||
\(631\) | −10.8853 | −0.433336 | −0.216668 | − | 0.976245i | \(-0.569519\pi\) | ||||
−0.216668 | + | 0.976245i | \(0.569519\pi\) | |||||||
\(632\) | 24.4407 | 0.972198 | ||||||||
\(633\) | 3.20999 | 0.127586 | ||||||||
\(634\) | −74.0763 | −2.94195 | ||||||||
\(635\) | −33.3834 | −1.32478 | ||||||||
\(636\) | −18.8089 | −0.745822 | ||||||||
\(637\) | −1.33474 | −0.0528845 | ||||||||
\(638\) | 106.790 | 4.22787 | ||||||||
\(639\) | 28.3963 | 1.12334 | ||||||||
\(640\) | −107.984 | −4.26844 | ||||||||
\(641\) | −2.82436 | −0.111555 | −0.0557777 | − | 0.998443i | \(-0.517764\pi\) | ||||
−0.0557777 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(642\) | 36.8945 | 1.45611 | ||||||||
\(643\) | −37.6914 | −1.48640 | −0.743202 | − | 0.669067i | \(-0.766694\pi\) | ||||
−0.743202 | + | 0.669067i | \(0.766694\pi\) | |||||||
\(644\) | 33.8328 | 1.33320 | ||||||||
\(645\) | 0.869101 | 0.0342208 | ||||||||
\(646\) | −41.4151 | −1.62945 | ||||||||
\(647\) | 3.17982 | 0.125012 | 0.0625059 | − | 0.998045i | \(-0.480091\pi\) | ||||
0.0625059 | + | 0.998045i | \(0.480091\pi\) | |||||||
\(648\) | 85.7979 | 3.37046 | ||||||||
\(649\) | −36.1611 | −1.41945 | ||||||||
\(650\) | 24.1293 | 0.946428 | ||||||||
\(651\) | 41.7317 | 1.63559 | ||||||||
\(652\) | 118.497 | 4.64071 | ||||||||
\(653\) | −7.12183 | −0.278699 | −0.139349 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139349 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(654\) | 55.0027 | 2.15077 | ||||||||
\(655\) | 16.8011 | 0.656472 | ||||||||
\(656\) | −86.3382 | −3.37094 | ||||||||
\(657\) | −9.30585 | −0.363056 | ||||||||
\(658\) | 35.1754 | 1.37128 | ||||||||
\(659\) | 17.8612 | 0.695775 | 0.347887 | − | 0.937536i | \(-0.386899\pi\) | ||||
0.347887 | + | 0.937536i | \(0.386899\pi\) | |||||||
\(660\) | 215.095 | 8.37254 | ||||||||
\(661\) | 6.58887 | 0.256277 | 0.128139 | − | 0.991756i | \(-0.459100\pi\) | ||||
0.128139 | + | 0.991756i | \(0.459100\pi\) | |||||||
\(662\) | −39.1578 | −1.52191 | ||||||||
\(663\) | −4.54598 | −0.176551 | ||||||||
\(664\) | 80.0261 | 3.10562 | ||||||||
\(665\) | 87.4210 | 3.39004 | ||||||||
\(666\) | 72.6214 | 2.81402 | ||||||||
\(667\) | −19.3389 | −0.748807 | ||||||||
\(668\) | 126.512 | 4.89490 | ||||||||
\(669\) | 52.1172 | 2.01497 | ||||||||
\(670\) | −72.8277 | −2.81358 | ||||||||
\(671\) | −8.10366 | −0.312838 | ||||||||
\(672\) | −135.995 | −5.24613 | ||||||||
\(673\) | 11.4750 | 0.442328 | 0.221164 | − | 0.975237i | \(-0.429014\pi\) | ||||
0.221164 | + | 0.975237i | \(0.429014\pi\) | |||||||
\(674\) | −38.8383 | −1.49599 | ||||||||
\(675\) | 3.50060 | 0.134738 | ||||||||
\(676\) | 5.34571 | 0.205604 | ||||||||
\(677\) | −35.1193 | −1.34974 | −0.674872 | − | 0.737934i | \(-0.735801\pi\) | ||||
−0.674872 | + | 0.737934i | \(0.735801\pi\) | |||||||
\(678\) | 10.6132 | 0.407597 | ||||||||
\(679\) | 10.9417 | 0.419906 | ||||||||
\(680\) | 63.6180 | 2.43964 | ||||||||
\(681\) | −26.4653 | −1.01415 | ||||||||
\(682\) | 72.4270 | 2.77337 | ||||||||
\(683\) | −5.01898 | −0.192046 | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) | ||||
−0.0960230 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(684\) | −123.175 | −4.70970 | ||||||||
\(685\) | −44.5099 | −1.70064 | ||||||||
\(686\) | −44.3285 | −1.69247 | ||||||||
\(687\) | 30.9610 | 1.18124 | ||||||||
\(688\) | −1.33957 | −0.0510707 | ||||||||
\(689\) | −1.45631 | −0.0554810 | ||||||||
\(690\) | −53.5253 | −2.03767 | ||||||||
\(691\) | 12.4329 | 0.472968 | 0.236484 | − | 0.971635i | \(-0.424005\pi\) | ||||
0.236484 | + | 0.971635i | \(0.424005\pi\) | |||||||
\(692\) | 117.963 | 4.48429 | ||||||||
\(693\) | 36.5858 | 1.38978 | ||||||||
\(694\) | −84.4167 | −3.20441 | ||||||||
\(695\) | −47.1710 | −1.78930 | ||||||||
\(696\) | 193.266 | 7.32573 | ||||||||
\(697\) | 11.6997 | 0.443158 | ||||||||
\(698\) | −6.50900 | −0.246369 | ||||||||
\(699\) | −18.2813 | −0.691462 | ||||||||
\(700\) | −137.398 | −5.19314 | ||||||||
\(701\) | 3.05709 | 0.115465 | 0.0577323 | − | 0.998332i | \(-0.481613\pi\) | ||||
0.0577323 | + | 0.998332i | \(0.481613\pi\) | |||||||
\(702\) | 1.06569 | 0.0402220 | ||||||||
\(703\) | 76.6952 | 2.89261 | ||||||||
\(704\) | −111.989 | −4.22073 | ||||||||
\(705\) | −40.4978 | −1.52524 | ||||||||
\(706\) | −55.3158 | −2.08184 | ||||||||
\(707\) | −51.3298 | −1.93045 | ||||||||
\(708\) | −104.564 | −3.92976 | ||||||||
\(709\) | 15.7066 | 0.589874 | 0.294937 | − | 0.955517i | \(-0.404701\pi\) | ||||
0.294937 | + | 0.955517i | \(0.404701\pi\) | |||||||
\(710\) | −101.142 | −3.79580 | ||||||||
\(711\) | −7.64727 | −0.286795 | ||||||||
\(712\) | −103.604 | −3.88272 | ||||||||
\(713\) | −13.1160 | −0.491198 | ||||||||
\(714\) | 35.5706 | 1.33119 | ||||||||
\(715\) | 16.6540 | 0.622826 | ||||||||
\(716\) | 87.0340 | 3.25261 | ||||||||
\(717\) | −13.7695 | −0.514230 | ||||||||
\(718\) | 83.1231 | 3.10213 | ||||||||
\(719\) | 20.0098 | 0.746238 | 0.373119 | − | 0.927784i | \(-0.378288\pi\) | ||||
0.373119 | + | 0.927784i | \(0.378288\pi\) | |||||||
\(720\) | 146.893 | 5.47438 | ||||||||
\(721\) | −2.88700 | −0.107517 | ||||||||
\(722\) | −127.257 | −4.73603 | ||||||||
\(723\) | −36.5548 | −1.35949 | ||||||||
\(724\) | −77.1902 | −2.86875 | ||||||||
\(725\) | 78.5370 | 2.91679 | ||||||||
\(726\) | 58.6044 | 2.17501 | ||||||||
\(727\) | 8.61430 | 0.319487 | 0.159743 | − | 0.987159i | \(-0.448933\pi\) | ||||
0.159743 | + | 0.987159i | \(0.448933\pi\) | |||||||
\(728\) | −26.1789 | −0.970254 | ||||||||
\(729\) | −23.9954 | −0.888719 | ||||||||
\(730\) | 33.1456 | 1.22678 | ||||||||
\(731\) | 0.181526 | 0.00671397 | ||||||||
\(732\) | −23.4327 | −0.866098 | ||||||||
\(733\) | −8.17582 | −0.301981 | −0.150990 | − | 0.988535i | \(-0.548246\pi\) | ||||
−0.150990 | + | 0.988535i | \(0.548246\pi\) | |||||||
\(734\) | 2.62430 | 0.0968648 | ||||||||
\(735\) | −12.0241 | −0.443517 | ||||||||
\(736\) | 42.7424 | 1.57551 | ||||||||
\(737\) | −32.1882 | −1.18567 | ||||||||
\(738\) | 47.8152 | 1.76010 | ||||||||
\(739\) | 15.1353 | 0.556759 | 0.278380 | − | 0.960471i | \(-0.410203\pi\) | ||||
0.278380 | + | 0.960471i | \(0.410203\pi\) | |||||||
\(740\) | −188.238 | −6.91975 | ||||||||
\(741\) | −19.6211 | −0.720798 | ||||||||
\(742\) | 11.3951 | 0.418326 | ||||||||
\(743\) | −40.8558 | −1.49885 | −0.749426 | − | 0.662088i | \(-0.769671\pi\) | ||||
−0.749426 | + | 0.662088i | \(0.769671\pi\) | |||||||
\(744\) | 131.076 | 4.80549 | ||||||||
\(745\) | −11.2069 | −0.410587 | ||||||||
\(746\) | −54.3427 | −1.98963 | ||||||||
\(747\) | −25.0395 | −0.916146 | ||||||||
\(748\) | 44.9259 | 1.64265 | ||||||||
\(749\) | −16.2662 | −0.594355 | ||||||||
\(750\) | 95.2908 | 3.47953 | ||||||||
\(751\) | −8.91979 | −0.325488 | −0.162744 | − | 0.986668i | \(-0.552034\pi\) | ||||
−0.162744 | + | 0.986668i | \(0.552034\pi\) | |||||||
\(752\) | 62.4205 | 2.27624 | ||||||||
\(753\) | 58.5759 | 2.13463 | ||||||||
\(754\) | 23.9091 | 0.870718 | ||||||||
\(755\) | −47.0604 | −1.71270 | ||||||||
\(756\) | −6.06830 | −0.220702 | ||||||||
\(757\) | −6.76209 | −0.245772 | −0.122886 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122886 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(758\) | 11.5492 | 0.419485 | ||||||||
\(759\) | −23.6570 | −0.858693 | ||||||||
\(760\) | 274.584 | 9.96020 | ||||||||
\(761\) | −42.8735 | −1.55416 | −0.777081 | − | 0.629401i | \(-0.783300\pi\) | ||||
−0.777081 | + | 0.629401i | \(0.783300\pi\) | |||||||
\(762\) | −58.6274 | −2.12385 | ||||||||
\(763\) | −24.2498 | −0.877903 | ||||||||
\(764\) | 46.0588 | 1.66635 | ||||||||
\(765\) | −19.9055 | −0.719685 | ||||||||
\(766\) | 17.8331 | 0.644337 | ||||||||
\(767\) | −8.09604 | −0.292331 | ||||||||
\(768\) | −68.4852 | −2.47125 | ||||||||
\(769\) | 3.60879 | 0.130136 | 0.0650681 | − | 0.997881i | \(-0.479274\pi\) | ||||
0.0650681 | + | 0.997881i | \(0.479274\pi\) | |||||||
\(770\) | −130.311 | −4.69610 | ||||||||
\(771\) | −44.4787 | −1.60186 | ||||||||
\(772\) | 72.9315 | 2.62486 | ||||||||
\(773\) | −23.6267 | −0.849794 | −0.424897 | − | 0.905242i | \(-0.639690\pi\) | ||||
−0.424897 | + | 0.905242i | \(0.639690\pi\) | |||||||
\(774\) | 0.741873 | 0.0266661 | ||||||||
\(775\) | 53.2651 | 1.91334 | ||||||||
\(776\) | 34.3673 | 1.23371 | ||||||||
\(777\) | −65.8719 | −2.36314 | ||||||||
\(778\) | −38.0036 | −1.36250 | ||||||||
\(779\) | 50.4974 | 1.80926 | ||||||||
\(780\) | 48.1572 | 1.72430 | ||||||||
\(781\) | −44.7026 | −1.59958 | ||||||||
\(782\) | −11.1796 | −0.399782 | ||||||||
\(783\) | 3.46866 | 0.123960 | ||||||||
\(784\) | 18.5332 | 0.661898 | ||||||||
\(785\) | −5.21895 | −0.186272 | ||||||||
\(786\) | 29.5057 | 1.05243 | ||||||||
\(787\) | 13.7575 | 0.490401 | 0.245201 | − | 0.969472i | \(-0.421146\pi\) | ||||
0.245201 | + | 0.969472i | \(0.421146\pi\) | |||||||
\(788\) | −90.5272 | −3.22490 | ||||||||
\(789\) | −50.8422 | −1.81003 | ||||||||
\(790\) | 27.2381 | 0.969088 | ||||||||
\(791\) | −4.67919 | −0.166373 | ||||||||
\(792\) | 114.914 | 4.08328 | ||||||||
\(793\) | −1.81432 | −0.0644282 | ||||||||
\(794\) | 48.8248 | 1.73273 | ||||||||
\(795\) | −13.1193 | −0.465293 | ||||||||
\(796\) | 32.3398 | 1.14625 | ||||||||
\(797\) | 20.2972 | 0.718965 | 0.359483 | − | 0.933152i | \(-0.382953\pi\) | ||||
0.359483 | + | 0.933152i | \(0.382953\pi\) | |||||||
\(798\) | 153.527 | 5.43481 | ||||||||
\(799\) | −8.45862 | −0.299244 | ||||||||
\(800\) | −173.580 | −6.13700 | ||||||||
\(801\) | 32.4168 | 1.14539 | ||||||||
\(802\) | 97.4489 | 3.44104 | ||||||||
\(803\) | 14.6496 | 0.516974 | ||||||||
\(804\) | −93.0760 | −3.28254 | ||||||||
\(805\) | 23.5985 | 0.831737 | ||||||||
\(806\) | 16.2156 | 0.571169 | ||||||||
\(807\) | 70.1931 | 2.47091 | ||||||||
\(808\) | −161.223 | −5.67182 | ||||||||
\(809\) | 22.4195 | 0.788229 | 0.394114 | − | 0.919061i | \(-0.371051\pi\) | ||||
0.394114 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(810\) | 95.6181 | 3.35968 | ||||||||
\(811\) | −30.0963 | −1.05682 | −0.528412 | − | 0.848988i | \(-0.677213\pi\) | ||||
−0.528412 | + | 0.848988i | \(0.677213\pi\) | |||||||
\(812\) | −136.144 | −4.77771 | ||||||||
\(813\) | −52.4139 | −1.83824 | ||||||||
\(814\) | −114.323 | −4.00703 | ||||||||
\(815\) | 82.6521 | 2.89518 | ||||||||
\(816\) | 63.1218 | 2.20970 | ||||||||
\(817\) | 0.783489 | 0.0274108 | ||||||||
\(818\) | −36.1644 | −1.26446 | ||||||||
\(819\) | 8.19114 | 0.286222 | ||||||||
\(820\) | −123.939 | −4.32814 | ||||||||
\(821\) | −46.3978 | −1.61929 | −0.809647 | − | 0.586917i | \(-0.800342\pi\) | ||||
−0.809647 | + | 0.586917i | \(0.800342\pi\) | |||||||
\(822\) | −78.1676 | −2.72641 | ||||||||
\(823\) | 4.02324 | 0.140241 | 0.0701206 | − | 0.997539i | \(-0.477662\pi\) | ||||
0.0701206 | + | 0.997539i | \(0.477662\pi\) | |||||||
\(824\) | −9.06786 | −0.315894 | ||||||||
\(825\) | 96.0727 | 3.34482 | ||||||||
\(826\) | 63.3484 | 2.20417 | ||||||||
\(827\) | 50.0728 | 1.74120 | 0.870600 | − | 0.491991i | \(-0.163731\pi\) | ||||
0.870600 | + | 0.491991i | \(0.163731\pi\) | |||||||
\(828\) | −33.2498 | −1.15551 | ||||||||
\(829\) | 32.1441 | 1.11641 | 0.558206 | − | 0.829703i | \(-0.311490\pi\) | ||||
0.558206 | + | 0.829703i | \(0.311490\pi\) | |||||||
\(830\) | 89.1857 | 3.09568 | ||||||||
\(831\) | −7.54280 | −0.261657 | ||||||||
\(832\) | −25.0729 | −0.869248 | ||||||||
\(833\) | −2.51143 | −0.0870159 | ||||||||
\(834\) | −82.8409 | −2.86854 | ||||||||
\(835\) | 88.2425 | 3.05376 | ||||||||
\(836\) | 193.906 | 6.70639 | ||||||||
\(837\) | 2.35251 | 0.0813145 | ||||||||
\(838\) | 42.1113 | 1.45471 | ||||||||
\(839\) | 34.0270 | 1.17474 | 0.587371 | − | 0.809318i | \(-0.300163\pi\) | ||||
0.587371 | + | 0.809318i | \(0.300163\pi\) | |||||||
\(840\) | −235.834 | −8.13705 | ||||||||
\(841\) | 48.8203 | 1.68346 | ||||||||
\(842\) | −11.6803 | −0.402531 | ||||||||
\(843\) | 55.7919 | 1.92158 | ||||||||
\(844\) | −7.10239 | −0.244474 | ||||||||
\(845\) | 3.72865 | 0.128269 | ||||||||
\(846\) | −34.5693 | −1.18852 | ||||||||
\(847\) | −25.8378 | −0.887796 | ||||||||
\(848\) | 20.2212 | 0.694397 | ||||||||
\(849\) | −46.9952 | −1.61287 | ||||||||
\(850\) | 45.4013 | 1.55725 | ||||||||
\(851\) | 20.7031 | 0.709694 | ||||||||
\(852\) | −129.263 | −4.42847 | ||||||||
\(853\) | −25.1406 | −0.860796 | −0.430398 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430398 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(854\) | 14.1963 | 0.485788 | ||||||||
\(855\) | −85.9148 | −2.93822 | ||||||||
\(856\) | −51.0912 | −1.74626 | ||||||||
\(857\) | −4.22334 | −0.144266 | −0.0721332 | − | 0.997395i | \(-0.522981\pi\) | ||||
−0.0721332 | + | 0.997395i | \(0.522981\pi\) | |||||||
\(858\) | 29.2475 | 0.998495 | ||||||||
\(859\) | −2.87834 | −0.0982077 | −0.0491038 | − | 0.998794i | \(-0.515637\pi\) | ||||
−0.0491038 | + | 0.998794i | \(0.515637\pi\) | |||||||
\(860\) | −1.92297 | −0.0655726 | ||||||||
\(861\) | −43.3712 | −1.47809 | ||||||||
\(862\) | 55.0500 | 1.87501 | ||||||||
\(863\) | −6.79893 | −0.231438 | −0.115719 | − | 0.993282i | \(-0.536917\pi\) | ||||
−0.115719 | + | 0.993282i | \(0.536917\pi\) | |||||||
\(864\) | −7.66635 | −0.260815 | ||||||||
\(865\) | 82.2797 | 2.79759 | ||||||||
\(866\) | −50.8638 | −1.72842 | ||||||||
\(867\) | 32.5191 | 1.10440 | ||||||||
\(868\) | −92.3351 | −3.13406 | ||||||||
\(869\) | 12.0386 | 0.408382 | ||||||||
\(870\) | 215.387 | 7.30230 | ||||||||
\(871\) | −7.20656 | −0.244185 | ||||||||
\(872\) | −76.1671 | −2.57934 | ||||||||
\(873\) | −10.7532 | −0.363941 | ||||||||
\(874\) | −48.2527 | −1.63217 | ||||||||
\(875\) | −42.0123 | −1.42027 | ||||||||
\(876\) | 42.3611 | 1.43125 | ||||||||
\(877\) | 7.24349 | 0.244595 | 0.122298 | − | 0.992493i | \(-0.460974\pi\) | ||||
0.122298 | + | 0.992493i | \(0.460974\pi\) | |||||||
\(878\) | −63.4049 | −2.13981 | ||||||||
\(879\) | −24.6019 | −0.829802 | ||||||||
\(880\) | −231.244 | −7.79525 | ||||||||
\(881\) | −40.3317 | −1.35881 | −0.679406 | − | 0.733763i | \(-0.737762\pi\) | ||||
−0.679406 | + | 0.733763i | \(0.737762\pi\) | |||||||
\(882\) | −10.2639 | −0.345604 | ||||||||
\(883\) | 10.4924 | 0.353097 | 0.176548 | − | 0.984292i | \(-0.443507\pi\) | ||||
0.176548 | + | 0.984292i | \(0.443507\pi\) | |||||||
\(884\) | 10.0584 | 0.338300 | ||||||||
\(885\) | −72.9338 | −2.45164 | ||||||||
\(886\) | 69.9308 | 2.34937 | ||||||||
\(887\) | −20.6936 | −0.694823 | −0.347411 | − | 0.937713i | \(-0.612939\pi\) | ||||
−0.347411 | + | 0.937713i | \(0.612939\pi\) | |||||||
\(888\) | −206.899 | −6.94309 | ||||||||
\(889\) | 25.8479 | 0.866911 | ||||||||
\(890\) | −115.462 | −3.87030 | ||||||||
\(891\) | 42.2610 | 1.41580 | ||||||||
\(892\) | −115.314 | −3.86100 | ||||||||
\(893\) | −36.5085 | −1.22171 | ||||||||
\(894\) | −19.6813 | −0.658241 | ||||||||
\(895\) | 60.7065 | 2.02919 | ||||||||
\(896\) | 83.6092 | 2.79319 | ||||||||
\(897\) | −5.29652 | −0.176846 | ||||||||
\(898\) | −23.0096 | −0.767841 | ||||||||
\(899\) | 52.7791 | 1.76028 | ||||||||
\(900\) | 135.030 | 4.50101 | ||||||||
\(901\) | −2.74017 | −0.0912883 | ||||||||
\(902\) | −75.2725 | −2.50630 | ||||||||
\(903\) | −0.672923 | −0.0223935 | ||||||||
\(904\) | −14.6970 | −0.488816 | ||||||||
\(905\) | −53.8404 | −1.78972 | ||||||||
\(906\) | −82.6467 | −2.74575 | ||||||||
\(907\) | 8.46304 | 0.281011 | 0.140505 | − | 0.990080i | \(-0.455127\pi\) | ||||
0.140505 | + | 0.990080i | \(0.455127\pi\) | |||||||
\(908\) | 58.5568 | 1.94328 | ||||||||
\(909\) | 50.4454 | 1.67317 | ||||||||
\(910\) | −29.1752 | −0.967150 | ||||||||
\(911\) | −31.2749 | −1.03618 | −0.518091 | − | 0.855325i | \(-0.673357\pi\) | ||||
−0.518091 | + | 0.855325i | \(0.673357\pi\) | |||||||
\(912\) | 272.442 | 9.02146 | ||||||||
\(913\) | 39.4180 | 1.30455 | ||||||||
\(914\) | −37.0289 | −1.22481 | ||||||||
\(915\) | −16.3444 | −0.540329 | ||||||||
\(916\) | −68.5041 | −2.26344 | ||||||||
\(917\) | −13.0086 | −0.429583 | ||||||||
\(918\) | 2.00519 | 0.0661812 | ||||||||
\(919\) | −17.9054 | −0.590645 | −0.295323 | − | 0.955398i | \(-0.595427\pi\) | ||||
−0.295323 | + | 0.955398i | \(0.595427\pi\) | |||||||
\(920\) | 74.1212 | 2.44370 | ||||||||
\(921\) | −1.07036 | −0.0352694 | ||||||||
\(922\) | 61.9808 | 2.04123 | ||||||||
\(923\) | −10.0084 | −0.329430 | ||||||||
\(924\) | −166.542 | −5.47883 | ||||||||
\(925\) | −84.0770 | −2.76444 | ||||||||
\(926\) | −8.72581 | −0.286748 | ||||||||
\(927\) | 2.83725 | 0.0931876 | ||||||||
\(928\) | −171.997 | −5.64606 | ||||||||
\(929\) | 35.9314 | 1.17887 | 0.589436 | − | 0.807815i | \(-0.299350\pi\) | ||||
0.589436 | + | 0.807815i | \(0.299350\pi\) | |||||||
\(930\) | 146.079 | 4.79012 | ||||||||
\(931\) | −10.8397 | −0.355256 | ||||||||
\(932\) | 40.4490 | 1.32495 | ||||||||
\(933\) | −59.7909 | −1.95747 | ||||||||
\(934\) | −72.8600 | −2.38405 | ||||||||
\(935\) | 31.3360 | 1.02480 | ||||||||
\(936\) | 25.7278 | 0.840940 | ||||||||
\(937\) | 35.2537 | 1.15169 | 0.575845 | − | 0.817559i | \(-0.304673\pi\) | ||||
0.575845 | + | 0.817559i | \(0.304673\pi\) | |||||||
\(938\) | 56.3886 | 1.84115 | ||||||||
\(939\) | 26.1668 | 0.853922 | ||||||||
\(940\) | 89.6051 | 2.92260 | ||||||||
\(941\) | 43.7224 | 1.42531 | 0.712654 | − | 0.701515i | \(-0.247493\pi\) | ||||
0.712654 | + | 0.701515i | \(0.247493\pi\) | |||||||
\(942\) | −9.16542 | −0.298626 | ||||||||
\(943\) | 13.6313 | 0.443896 | ||||||||
\(944\) | 112.415 | 3.65880 | ||||||||
\(945\) | −4.23266 | −0.137688 | ||||||||
\(946\) | −1.16788 | −0.0379712 | ||||||||
\(947\) | −3.03635 | −0.0986680 | −0.0493340 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493340 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(948\) | 34.8111 | 1.13061 | ||||||||
\(949\) | 3.27988 | 0.106469 | ||||||||
\(950\) | 195.958 | 6.35771 | ||||||||
\(951\) | −66.0339 | −2.14130 | ||||||||
\(952\) | −49.2577 | −1.59645 | ||||||||
\(953\) | 44.3886 | 1.43789 | 0.718944 | − | 0.695068i | \(-0.244626\pi\) | ||||
0.718944 | + | 0.695068i | \(0.244626\pi\) | |||||||
\(954\) | −11.1987 | −0.362573 | ||||||||
\(955\) | 32.1261 | 1.03958 | ||||||||
\(956\) | 30.4662 | 0.985346 | ||||||||
\(957\) | 95.1961 | 3.07725 | ||||||||
\(958\) | 49.5316 | 1.60029 | ||||||||
\(959\) | 34.4629 | 1.11286 | ||||||||
\(960\) | −225.871 | −7.28997 | ||||||||
\(961\) | 4.79567 | 0.154699 | ||||||||
\(962\) | −25.5957 | −0.825238 | ||||||||
\(963\) | 15.9860 | 0.515141 | ||||||||
\(964\) | 80.8808 | 2.60500 | ||||||||
\(965\) | 50.8700 | 1.63756 | ||||||||
\(966\) | 41.4432 | 1.33341 | ||||||||
\(967\) | −6.85729 | −0.220516 | −0.110258 | − | 0.993903i | \(-0.535168\pi\) | ||||
−0.110258 | + | 0.993903i | \(0.535168\pi\) | |||||||
\(968\) | −81.1548 | −2.60841 | ||||||||
\(969\) | −36.9187 | −1.18600 | ||||||||
\(970\) | 38.3009 | 1.22977 | ||||||||
\(971\) | 34.8877 | 1.11960 | 0.559799 | − | 0.828628i | \(-0.310878\pi\) | ||||
0.559799 | + | 0.828628i | \(0.310878\pi\) | |||||||
\(972\) | 115.897 | 3.71740 | ||||||||
\(973\) | 36.5233 | 1.17088 | ||||||||
\(974\) | −71.7902 | −2.30031 | ||||||||
\(975\) | 21.5096 | 0.688858 | ||||||||
\(976\) | 25.1921 | 0.806380 | ||||||||
\(977\) | 12.7827 | 0.408954 | 0.204477 | − | 0.978871i | \(-0.434451\pi\) | ||||
0.204477 | + | 0.978871i | \(0.434451\pi\) | |||||||
\(978\) | 145.152 | 4.64146 | ||||||||
\(979\) | −51.0316 | −1.63098 | ||||||||
\(980\) | 26.6045 | 0.849848 | ||||||||
\(981\) | 23.8320 | 0.760898 | ||||||||
\(982\) | −58.2125 | −1.85764 | ||||||||
\(983\) | −26.7457 | −0.853054 | −0.426527 | − | 0.904475i | \(-0.640263\pi\) | ||||
−0.426527 | + | 0.904475i | \(0.640263\pi\) | |||||||
\(984\) | −136.226 | −4.34273 | ||||||||
\(985\) | −63.1430 | −2.01190 | ||||||||
\(986\) | 44.9870 | 1.43268 | ||||||||
\(987\) | 31.3564 | 0.998085 | ||||||||
\(988\) | 43.4134 | 1.38116 | ||||||||
\(989\) | 0.211495 | 0.00672516 | ||||||||
\(990\) | 128.066 | 4.07021 | ||||||||
\(991\) | −58.9088 | −1.87130 | −0.935649 | − | 0.352931i | \(-0.885185\pi\) | ||||
−0.935649 | + | 0.352931i | \(0.885185\pi\) | |||||||
\(992\) | −116.651 | −3.70367 | ||||||||
\(993\) | −34.9065 | −1.10772 | ||||||||
\(994\) | 78.3118 | 2.48390 | ||||||||
\(995\) | 22.5571 | 0.715109 | ||||||||
\(996\) | 113.982 | 3.61166 | ||||||||
\(997\) | 22.9734 | 0.727574 | 0.363787 | − | 0.931482i | \(-0.381484\pi\) | ||||
0.363787 | + | 0.931482i | \(0.381484\pi\) | |||||||
\(998\) | −28.3893 | −0.898648 | ||||||||
\(999\) | −3.71334 | −0.117485 |
(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 | 1339.2.a.g.1.1 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.g.1.1 | ✓ | 30 | 1.1 | even | 1 | trivial |