Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38632 | −1.68738 | −0.843692 | − | 0.536827i | \(-0.819623\pi\) | ||||
−0.843692 | + | 0.536827i | \(0.819623\pi\) | |||||||
\(3\) | −0.731332 | −0.422235 | −0.211117 | − | 0.977461i | \(-0.567710\pi\) | ||||
−0.211117 | + | 0.977461i | \(0.567710\pi\) | |||||||
\(4\) | 3.69453 | 1.84727 | ||||||||
\(5\) | 1.80073 | 0.805313 | 0.402657 | − | 0.915351i | \(-0.368087\pi\) | ||||
0.402657 | + | 0.915351i | \(0.368087\pi\) | |||||||
\(6\) | 1.74519 | 0.712473 | ||||||||
\(7\) | −2.93364 | −1.10881 | −0.554406 | − | 0.832247i | \(-0.687054\pi\) | ||||
−0.554406 | + | 0.832247i | \(0.687054\pi\) | |||||||
\(8\) | −4.04370 | −1.42966 | ||||||||
\(9\) | −2.46515 | −0.821718 | ||||||||
\(10\) | −4.29713 | −1.35887 | ||||||||
\(11\) | 0.347932 | 0.104906 | 0.0524528 | − | 0.998623i | \(-0.483296\pi\) | ||||
0.0524528 | + | 0.998623i | \(0.483296\pi\) | |||||||
\(12\) | −2.70193 | −0.779980 | ||||||||
\(13\) | −1.80377 | −0.500277 | −0.250138 | − | 0.968210i | \(-0.580476\pi\) | ||||
−0.250138 | + | 0.968210i | \(0.580476\pi\) | |||||||
\(14\) | 7.00060 | 1.87099 | ||||||||
\(15\) | −1.31694 | −0.340031 | ||||||||
\(16\) | 2.26050 | 0.565124 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.88265 | 1.38655 | ||||||||
\(19\) | −1.44867 | −0.332348 | −0.166174 | − | 0.986096i | \(-0.553141\pi\) | ||||
−0.166174 | + | 0.986096i | \(0.553141\pi\) | |||||||
\(20\) | 6.65287 | 1.48763 | ||||||||
\(21\) | 2.14546 | 0.468179 | ||||||||
\(22\) | −0.830278 | −0.177016 | ||||||||
\(23\) | −1.89471 | −0.395073 | −0.197537 | − | 0.980295i | \(-0.563294\pi\) | ||||
−0.197537 | + | 0.980295i | \(0.563294\pi\) | |||||||
\(24\) | 2.95729 | 0.603653 | ||||||||
\(25\) | −1.75735 | −0.351471 | ||||||||
\(26\) | 4.30438 | 0.844159 | ||||||||
\(27\) | 3.99684 | 0.769193 | ||||||||
\(28\) | −10.8384 | −2.04827 | ||||||||
\(29\) | 1.23132 | 0.228651 | 0.114326 | − | 0.993443i | \(-0.463529\pi\) | ||||
0.114326 | + | 0.993443i | \(0.463529\pi\) | |||||||
\(30\) | 3.14263 | 0.573763 | ||||||||
\(31\) | −3.19162 | −0.573231 | −0.286616 | − | 0.958046i | \(-0.592530\pi\) | ||||
−0.286616 | + | 0.958046i | \(0.592530\pi\) | |||||||
\(32\) | 2.69312 | 0.476081 | ||||||||
\(33\) | −0.254454 | −0.0442948 | ||||||||
\(34\) | −2.38632 | −0.409251 | ||||||||
\(35\) | −5.28271 | −0.892940 | ||||||||
\(36\) | −9.10758 | −1.51793 | ||||||||
\(37\) | 7.85544 | 1.29143 | 0.645713 | − | 0.763580i | \(-0.276560\pi\) | ||||
0.645713 | + | 0.763580i | \(0.276560\pi\) | |||||||
\(38\) | 3.45699 | 0.560798 | ||||||||
\(39\) | 1.31916 | 0.211234 | ||||||||
\(40\) | −7.28162 | −1.15133 | ||||||||
\(41\) | 10.4853 | 1.63752 | 0.818761 | − | 0.574134i | \(-0.194661\pi\) | ||||
0.818761 | + | 0.574134i | \(0.194661\pi\) | |||||||
\(42\) | −5.11977 | −0.789997 | ||||||||
\(43\) | −5.61665 | −0.856531 | −0.428265 | − | 0.903653i | \(-0.640875\pi\) | ||||
−0.428265 | + | 0.903653i | \(0.640875\pi\) | |||||||
\(44\) | 1.28545 | 0.193788 | ||||||||
\(45\) | −4.43909 | −0.661740 | ||||||||
\(46\) | 4.52138 | 0.666641 | ||||||||
\(47\) | 6.76065 | 0.986143 | 0.493071 | − | 0.869989i | \(-0.335874\pi\) | ||||
0.493071 | + | 0.869989i | \(0.335874\pi\) | |||||||
\(48\) | −1.65317 | −0.238615 | ||||||||
\(49\) | 1.60623 | 0.229462 | ||||||||
\(50\) | 4.19361 | 0.593066 | ||||||||
\(51\) | −0.731332 | −0.102407 | ||||||||
\(52\) | −6.66410 | −0.924144 | ||||||||
\(53\) | 4.45378 | 0.611774 | 0.305887 | − | 0.952068i | \(-0.401047\pi\) | ||||
0.305887 | + | 0.952068i | \(0.401047\pi\) | |||||||
\(54\) | −9.53775 | −1.29792 | ||||||||
\(55\) | 0.626534 | 0.0844818 | ||||||||
\(56\) | 11.8627 | 1.58523 | ||||||||
\(57\) | 1.05946 | 0.140329 | ||||||||
\(58\) | −2.93834 | −0.385822 | ||||||||
\(59\) | 9.13356 | 1.18909 | 0.594544 | − | 0.804063i | \(-0.297333\pi\) | ||||
0.594544 | + | 0.804063i | \(0.297333\pi\) | |||||||
\(60\) | −4.86546 | −0.628128 | ||||||||
\(61\) | −4.99819 | −0.639953 | −0.319977 | − | 0.947425i | \(-0.603675\pi\) | ||||
−0.319977 | + | 0.947425i | \(0.603675\pi\) | |||||||
\(62\) | 7.61622 | 0.967261 | ||||||||
\(63\) | 7.23187 | 0.911130 | ||||||||
\(64\) | −10.9476 | −1.36846 | ||||||||
\(65\) | −3.24812 | −0.402879 | ||||||||
\(66\) | 0.607209 | 0.0747423 | ||||||||
\(67\) | 3.64704 | 0.445557 | 0.222779 | − | 0.974869i | \(-0.428487\pi\) | ||||
0.222779 | + | 0.974869i | \(0.428487\pi\) | |||||||
\(68\) | 3.69453 | 0.448028 | ||||||||
\(69\) | 1.38566 | 0.166814 | ||||||||
\(70\) | 12.6062 | 1.50673 | ||||||||
\(71\) | −1.83384 | −0.217637 | −0.108818 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108818 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(72\) | 9.96833 | 1.17478 | ||||||||
\(73\) | 11.1597 | 1.30615 | 0.653073 | − | 0.757295i | \(-0.273479\pi\) | ||||
0.653073 | + | 0.757295i | \(0.273479\pi\) | |||||||
\(74\) | −18.7456 | −2.17913 | ||||||||
\(75\) | 1.28521 | 0.148403 | ||||||||
\(76\) | −5.35216 | −0.613935 | ||||||||
\(77\) | −1.02071 | −0.116320 | ||||||||
\(78\) | −3.14794 | −0.356433 | ||||||||
\(79\) | 8.20187 | 0.922783 | 0.461391 | − | 0.887197i | \(-0.347350\pi\) | ||||
0.461391 | + | 0.887197i | \(0.347350\pi\) | |||||||
\(80\) | 4.07056 | 0.455102 | ||||||||
\(81\) | 4.47244 | 0.496938 | ||||||||
\(82\) | −25.0212 | −2.76313 | ||||||||
\(83\) | −1.21802 | −0.133695 | −0.0668475 | − | 0.997763i | \(-0.521294\pi\) | ||||
−0.0668475 | + | 0.997763i | \(0.521294\pi\) | |||||||
\(84\) | 7.92648 | 0.864850 | ||||||||
\(85\) | 1.80073 | 0.195317 | ||||||||
\(86\) | 13.4031 | 1.44530 | ||||||||
\(87\) | −0.900507 | −0.0965445 | ||||||||
\(88\) | −1.40693 | −0.149979 | ||||||||
\(89\) | −2.60146 | −0.275754 | −0.137877 | − | 0.990449i | \(-0.544028\pi\) | ||||
−0.137877 | + | 0.990449i | \(0.544028\pi\) | |||||||
\(90\) | 10.5931 | 1.11661 | ||||||||
\(91\) | 5.29162 | 0.554712 | ||||||||
\(92\) | −7.00005 | −0.729805 | ||||||||
\(93\) | 2.33413 | 0.242038 | ||||||||
\(94\) | −16.1331 | −1.66400 | ||||||||
\(95\) | −2.60867 | −0.267644 | ||||||||
\(96\) | −1.96957 | −0.201018 | ||||||||
\(97\) | 15.2585 | 1.54927 | 0.774635 | − | 0.632409i | \(-0.217934\pi\) | ||||
0.774635 | + | 0.632409i | \(0.217934\pi\) | |||||||
\(98\) | −3.83299 | −0.387191 | ||||||||
\(99\) | −0.857706 | −0.0862027 | ||||||||
\(100\) | −6.49260 | −0.649260 | ||||||||
\(101\) | −7.31205 | −0.727576 | −0.363788 | − | 0.931482i | \(-0.618517\pi\) | ||||
−0.363788 | + | 0.931482i | \(0.618517\pi\) | |||||||
\(102\) | 1.74519 | 0.172800 | ||||||||
\(103\) | 2.60750 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(104\) | 7.29391 | 0.715227 | ||||||||
\(105\) | 3.86341 | 0.377030 | ||||||||
\(106\) | −10.6282 | −1.03230 | ||||||||
\(107\) | 2.00243 | 0.193582 | 0.0967911 | − | 0.995305i | \(-0.469142\pi\) | ||||
0.0967911 | + | 0.995305i | \(0.469142\pi\) | |||||||
\(108\) | 14.7665 | 1.42090 | ||||||||
\(109\) | −1.94507 | −0.186304 | −0.0931518 | − | 0.995652i | \(-0.529694\pi\) | ||||
−0.0931518 | + | 0.995652i | \(0.529694\pi\) | |||||||
\(110\) | −1.49511 | −0.142553 | ||||||||
\(111\) | −5.74494 | −0.545285 | ||||||||
\(112\) | −6.63148 | −0.626616 | ||||||||
\(113\) | −14.2743 | −1.34281 | −0.671406 | − | 0.741090i | \(-0.734309\pi\) | ||||
−0.671406 | + | 0.741090i | \(0.734309\pi\) | |||||||
\(114\) | −2.52821 | −0.236789 | ||||||||
\(115\) | −3.41186 | −0.318158 | ||||||||
\(116\) | 4.54917 | 0.422379 | ||||||||
\(117\) | 4.44658 | 0.411086 | ||||||||
\(118\) | −21.7956 | −2.00645 | ||||||||
\(119\) | −2.93364 | −0.268926 | ||||||||
\(120\) | 5.32529 | 0.486130 | ||||||||
\(121\) | −10.8789 | −0.988995 | ||||||||
\(122\) | 11.9273 | 1.07985 | ||||||||
\(123\) | −7.66821 | −0.691419 | ||||||||
\(124\) | −11.7915 | −1.05891 | ||||||||
\(125\) | −12.1682 | −1.08836 | ||||||||
\(126\) | −17.2576 | −1.53743 | ||||||||
\(127\) | −2.58523 | −0.229402 | −0.114701 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114701 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(128\) | 20.7384 | 1.83303 | ||||||||
\(129\) | 4.10764 | 0.361657 | ||||||||
\(130\) | 7.75105 | 0.679812 | ||||||||
\(131\) | 7.25358 | 0.633748 | 0.316874 | − | 0.948468i | \(-0.397367\pi\) | ||||
0.316874 | + | 0.948468i | \(0.397367\pi\) | |||||||
\(132\) | −0.940088 | −0.0818242 | ||||||||
\(133\) | 4.24988 | 0.368511 | ||||||||
\(134\) | −8.70302 | −0.751826 | ||||||||
\(135\) | 7.19725 | 0.619441 | ||||||||
\(136\) | −4.04370 | −0.346744 | ||||||||
\(137\) | −16.2933 | −1.39203 | −0.696017 | − | 0.718025i | \(-0.745046\pi\) | ||||
−0.696017 | + | 0.718025i | \(0.745046\pi\) | |||||||
\(138\) | −3.30663 | −0.281479 | ||||||||
\(139\) | 0.813084 | 0.0689649 | 0.0344824 | − | 0.999405i | \(-0.489022\pi\) | ||||
0.0344824 | + | 0.999405i | \(0.489022\pi\) | |||||||
\(140\) | −19.5171 | −1.64950 | ||||||||
\(141\) | −4.94428 | −0.416384 | ||||||||
\(142\) | 4.37613 | 0.367237 | ||||||||
\(143\) | −0.627591 | −0.0524818 | ||||||||
\(144\) | −5.57247 | −0.464373 | ||||||||
\(145\) | 2.21729 | 0.184136 | ||||||||
\(146\) | −26.6307 | −2.20397 | ||||||||
\(147\) | −1.17469 | −0.0968869 | ||||||||
\(148\) | 29.0222 | 2.38561 | ||||||||
\(149\) | −5.41745 | −0.443815 | −0.221907 | − | 0.975068i | \(-0.571228\pi\) | ||||
−0.221907 | + | 0.975068i | \(0.571228\pi\) | |||||||
\(150\) | −3.06692 | −0.250413 | ||||||||
\(151\) | −15.9860 | −1.30093 | −0.650463 | − | 0.759538i | \(-0.725425\pi\) | ||||
−0.650463 | + | 0.759538i | \(0.725425\pi\) | |||||||
\(152\) | 5.85798 | 0.475145 | ||||||||
\(153\) | −2.46515 | −0.199296 | ||||||||
\(154\) | 2.43574 | 0.196277 | ||||||||
\(155\) | −5.74725 | −0.461630 | ||||||||
\(156\) | 4.87367 | 0.390206 | ||||||||
\(157\) | 15.9674 | 1.27434 | 0.637170 | − | 0.770723i | \(-0.280105\pi\) | ||||
0.637170 | + | 0.770723i | \(0.280105\pi\) | |||||||
\(158\) | −19.5723 | −1.55709 | ||||||||
\(159\) | −3.25720 | −0.258312 | ||||||||
\(160\) | 4.84959 | 0.383394 | ||||||||
\(161\) | 5.55838 | 0.438062 | ||||||||
\(162\) | −10.6727 | −0.838525 | ||||||||
\(163\) | −17.2121 | −1.34815 | −0.674077 | − | 0.738661i | \(-0.735458\pi\) | ||||
−0.674077 | + | 0.738661i | \(0.735458\pi\) | |||||||
\(164\) | 38.7381 | 3.02494 | ||||||||
\(165\) | −0.458204 | −0.0356712 | ||||||||
\(166\) | 2.90659 | 0.225595 | ||||||||
\(167\) | −6.95504 | −0.538197 | −0.269099 | − | 0.963113i | \(-0.586726\pi\) | ||||
−0.269099 | + | 0.963113i | \(0.586726\pi\) | |||||||
\(168\) | −8.67561 | −0.669338 | ||||||||
\(169\) | −9.74640 | −0.749723 | ||||||||
\(170\) | −4.29713 | −0.329575 | ||||||||
\(171\) | 3.57119 | 0.273096 | ||||||||
\(172\) | −20.7509 | −1.58224 | ||||||||
\(173\) | 15.5483 | 1.18212 | 0.591059 | − | 0.806629i | \(-0.298710\pi\) | ||||
0.591059 | + | 0.806629i | \(0.298710\pi\) | |||||||
\(174\) | 2.14890 | 0.162908 | ||||||||
\(175\) | 5.15544 | 0.389715 | ||||||||
\(176\) | 0.786500 | 0.0592846 | ||||||||
\(177\) | −6.67967 | −0.502075 | ||||||||
\(178\) | 6.20792 | 0.465303 | ||||||||
\(179\) | −16.8613 | −1.26028 | −0.630138 | − | 0.776483i | \(-0.717002\pi\) | ||||
−0.630138 | + | 0.776483i | \(0.717002\pi\) | |||||||
\(180\) | −16.4003 | −1.22241 | ||||||||
\(181\) | −8.87793 | −0.659892 | −0.329946 | − | 0.944000i | \(-0.607030\pi\) | ||||
−0.329946 | + | 0.944000i | \(0.607030\pi\) | |||||||
\(182\) | −12.6275 | −0.936013 | ||||||||
\(183\) | 3.65534 | 0.270211 | ||||||||
\(184\) | 7.66161 | 0.564822 | ||||||||
\(185\) | 14.1456 | 1.04000 | ||||||||
\(186\) | −5.56999 | −0.408411 | ||||||||
\(187\) | 0.347932 | 0.0254433 | ||||||||
\(188\) | 24.9774 | 1.82167 | ||||||||
\(189\) | −11.7253 | −0.852889 | ||||||||
\(190\) | 6.22513 | 0.451618 | ||||||||
\(191\) | −10.2305 | −0.740250 | −0.370125 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370125 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(192\) | 8.00636 | 0.577810 | ||||||||
\(193\) | −7.55672 | −0.543945 | −0.271972 | − | 0.962305i | \(-0.587676\pi\) | ||||
−0.271972 | + | 0.962305i | \(0.587676\pi\) | |||||||
\(194\) | −36.4118 | −2.61421 | ||||||||
\(195\) | 2.37545 | 0.170110 | ||||||||
\(196\) | 5.93428 | 0.423877 | ||||||||
\(197\) | 8.75809 | 0.623988 | 0.311994 | − | 0.950084i | \(-0.399003\pi\) | ||||
0.311994 | + | 0.950084i | \(0.399003\pi\) | |||||||
\(198\) | 2.04676 | 0.145457 | ||||||||
\(199\) | −27.7511 | −1.96722 | −0.983611 | − | 0.180303i | \(-0.942292\pi\) | ||||
−0.983611 | + | 0.180303i | \(0.942292\pi\) | |||||||
\(200\) | 7.10620 | 0.502484 | ||||||||
\(201\) | −2.66720 | −0.188130 | ||||||||
\(202\) | 17.4489 | 1.22770 | ||||||||
\(203\) | −3.61226 | −0.253531 | ||||||||
\(204\) | −2.70193 | −0.189173 | ||||||||
\(205\) | 18.8812 | 1.31872 | ||||||||
\(206\) | −6.22233 | −0.433530 | ||||||||
\(207\) | 4.67074 | 0.324639 | ||||||||
\(208\) | −4.07742 | −0.282718 | ||||||||
\(209\) | −0.504039 | −0.0348651 | ||||||||
\(210\) | −9.21935 | −0.636195 | ||||||||
\(211\) | −21.8646 | −1.50522 | −0.752610 | − | 0.658467i | \(-0.771205\pi\) | ||||
−0.752610 | + | 0.658467i | \(0.771205\pi\) | |||||||
\(212\) | 16.4546 | 1.13011 | ||||||||
\(213\) | 1.34115 | 0.0918938 | ||||||||
\(214\) | −4.77844 | −0.326647 | ||||||||
\(215\) | −10.1141 | −0.689775 | ||||||||
\(216\) | −16.1620 | −1.09969 | ||||||||
\(217\) | 9.36305 | 0.635605 | ||||||||
\(218\) | 4.64155 | 0.314366 | ||||||||
\(219\) | −8.16146 | −0.551500 | ||||||||
\(220\) | 2.31475 | 0.156060 | ||||||||
\(221\) | −1.80377 | −0.121335 | ||||||||
\(222\) | 13.7093 | 0.920106 | ||||||||
\(223\) | 14.0179 | 0.938709 | 0.469354 | − | 0.883010i | \(-0.344487\pi\) | ||||
0.469354 | + | 0.883010i | \(0.344487\pi\) | |||||||
\(224\) | −7.90064 | −0.527884 | ||||||||
\(225\) | 4.33215 | 0.288810 | ||||||||
\(226\) | 34.0630 | 2.26584 | ||||||||
\(227\) | 2.91981 | 0.193795 | 0.0968973 | − | 0.995294i | \(-0.469108\pi\) | ||||
0.0968973 | + | 0.995294i | \(0.469108\pi\) | |||||||
\(228\) | 3.91421 | 0.259225 | ||||||||
\(229\) | 14.8579 | 0.981835 | 0.490917 | − | 0.871206i | \(-0.336662\pi\) | ||||
0.490917 | + | 0.871206i | \(0.336662\pi\) | |||||||
\(230\) | 8.14180 | 0.536854 | ||||||||
\(231\) | 0.746476 | 0.0491145 | ||||||||
\(232\) | −4.97910 | −0.326894 | ||||||||
\(233\) | 9.89756 | 0.648411 | 0.324205 | − | 0.945987i | \(-0.394903\pi\) | ||||
0.324205 | + | 0.945987i | \(0.394903\pi\) | |||||||
\(234\) | −10.6110 | −0.693661 | ||||||||
\(235\) | 12.1741 | 0.794154 | ||||||||
\(236\) | 33.7442 | 2.19656 | ||||||||
\(237\) | −5.99829 | −0.389631 | ||||||||
\(238\) | 7.00060 | 0.453782 | ||||||||
\(239\) | −9.07454 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(240\) | −2.97693 | −0.192160 | ||||||||
\(241\) | 22.4628 | 1.44695 | 0.723477 | − | 0.690348i | \(-0.242543\pi\) | ||||
0.723477 | + | 0.690348i | \(0.242543\pi\) | |||||||
\(242\) | 25.9607 | 1.66881 | ||||||||
\(243\) | −15.2614 | −0.979017 | ||||||||
\(244\) | −18.4660 | −1.18216 | ||||||||
\(245\) | 2.89240 | 0.184789 | ||||||||
\(246\) | 18.2988 | 1.16669 | ||||||||
\(247\) | 2.61307 | 0.166266 | ||||||||
\(248\) | 12.9059 | 0.819527 | ||||||||
\(249\) | 0.890777 | 0.0564507 | ||||||||
\(250\) | 29.0372 | 1.83648 | ||||||||
\(251\) | 2.12835 | 0.134340 | 0.0671702 | − | 0.997742i | \(-0.478603\pi\) | ||||
0.0671702 | + | 0.997742i | \(0.478603\pi\) | |||||||
\(252\) | 26.7184 | 1.68310 | ||||||||
\(253\) | −0.659229 | −0.0414454 | ||||||||
\(254\) | 6.16919 | 0.387090 | ||||||||
\(255\) | −1.31694 | −0.0824697 | ||||||||
\(256\) | −27.5931 | −1.72457 | ||||||||
\(257\) | −28.0764 | −1.75136 | −0.875679 | − | 0.482894i | \(-0.839586\pi\) | ||||
−0.875679 | + | 0.482894i | \(0.839586\pi\) | |||||||
\(258\) | −9.80214 | −0.610255 | ||||||||
\(259\) | −23.0450 | −1.43195 | ||||||||
\(260\) | −12.0003 | −0.744225 | ||||||||
\(261\) | −3.03540 | −0.187887 | ||||||||
\(262\) | −17.3094 | −1.06938 | ||||||||
\(263\) | −16.3530 | −1.00837 | −0.504185 | − | 0.863596i | \(-0.668207\pi\) | ||||
−0.504185 | + | 0.863596i | \(0.668207\pi\) | |||||||
\(264\) | 1.02893 | 0.0633266 | ||||||||
\(265\) | 8.02008 | 0.492670 | ||||||||
\(266\) | −10.1416 | −0.621820 | ||||||||
\(267\) | 1.90253 | 0.116433 | ||||||||
\(268\) | 13.4741 | 0.823063 | ||||||||
\(269\) | 24.8267 | 1.51371 | 0.756855 | − | 0.653583i | \(-0.226735\pi\) | ||||
0.756855 | + | 0.653583i | \(0.226735\pi\) | |||||||
\(270\) | −17.1750 | −1.04524 | ||||||||
\(271\) | 21.5124 | 1.30678 | 0.653392 | − | 0.757020i | \(-0.273345\pi\) | ||||
0.653392 | + | 0.757020i | \(0.273345\pi\) | |||||||
\(272\) | 2.26050 | 0.137063 | ||||||||
\(273\) | −3.86993 | −0.234219 | ||||||||
\(274\) | 38.8812 | 2.34890 | ||||||||
\(275\) | −0.611440 | −0.0368712 | ||||||||
\(276\) | 5.11936 | 0.308149 | ||||||||
\(277\) | −18.1491 | −1.09048 | −0.545238 | − | 0.838281i | \(-0.683561\pi\) | ||||
−0.545238 | + | 0.838281i | \(0.683561\pi\) | |||||||
\(278\) | −1.94028 | −0.116370 | ||||||||
\(279\) | 7.86782 | 0.471034 | ||||||||
\(280\) | 21.3617 | 1.27660 | ||||||||
\(281\) | 9.52494 | 0.568210 | 0.284105 | − | 0.958793i | \(-0.408304\pi\) | ||||
0.284105 | + | 0.958793i | \(0.408304\pi\) | |||||||
\(282\) | 11.7987 | 0.702600 | ||||||||
\(283\) | 28.4718 | 1.69247 | 0.846237 | − | 0.532806i | \(-0.178863\pi\) | ||||
0.846237 | + | 0.532806i | \(0.178863\pi\) | |||||||
\(284\) | −6.77517 | −0.402033 | ||||||||
\(285\) | 1.90781 | 0.113009 | ||||||||
\(286\) | 1.49763 | 0.0885570 | ||||||||
\(287\) | −30.7600 | −1.81570 | ||||||||
\(288\) | −6.63895 | −0.391204 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.29116 | −0.310708 | ||||||||
\(291\) | −11.1591 | −0.654155 | ||||||||
\(292\) | 41.2299 | 2.41280 | ||||||||
\(293\) | 6.76742 | 0.395357 | 0.197678 | − | 0.980267i | \(-0.436660\pi\) | ||||
0.197678 | + | 0.980267i | \(0.436660\pi\) | |||||||
\(294\) | 2.80319 | 0.163485 | ||||||||
\(295\) | 16.4471 | 0.957588 | ||||||||
\(296\) | −31.7650 | −1.84630 | ||||||||
\(297\) | 1.39063 | 0.0806926 | ||||||||
\(298\) | 12.9278 | 0.748886 | ||||||||
\(299\) | 3.41762 | 0.197646 | ||||||||
\(300\) | 4.74825 | 0.274140 | ||||||||
\(301\) | 16.4772 | 0.949731 | ||||||||
\(302\) | 38.1478 | 2.19516 | ||||||||
\(303\) | 5.34754 | 0.307208 | ||||||||
\(304\) | −3.27471 | −0.187818 | ||||||||
\(305\) | −9.00042 | −0.515363 | ||||||||
\(306\) | 5.88265 | 0.336289 | ||||||||
\(307\) | 13.3185 | 0.760130 | 0.380065 | − | 0.924960i | \(-0.375902\pi\) | ||||
0.380065 | + | 0.924960i | \(0.375902\pi\) | |||||||
\(308\) | −3.77103 | −0.214875 | ||||||||
\(309\) | −1.90695 | −0.108482 | ||||||||
\(310\) | 13.7148 | 0.778948 | ||||||||
\(311\) | −14.9468 | −0.847553 | −0.423777 | − | 0.905767i | \(-0.639296\pi\) | ||||
−0.423777 | + | 0.905767i | \(0.639296\pi\) | |||||||
\(312\) | −5.33427 | −0.301994 | ||||||||
\(313\) | 10.8435 | 0.612911 | 0.306455 | − | 0.951885i | \(-0.400857\pi\) | ||||
0.306455 | + | 0.951885i | \(0.400857\pi\) | |||||||
\(314\) | −38.1034 | −2.15030 | ||||||||
\(315\) | 13.0227 | 0.733745 | ||||||||
\(316\) | 30.3021 | 1.70462 | ||||||||
\(317\) | 28.0955 | 1.57800 | 0.789001 | − | 0.614392i | \(-0.210599\pi\) | ||||
0.789001 | + | 0.614392i | \(0.210599\pi\) | |||||||
\(318\) | 7.77272 | 0.435872 | ||||||||
\(319\) | 0.428417 | 0.0239868 | ||||||||
\(320\) | −19.7138 | −1.10204 | ||||||||
\(321\) | −1.46444 | −0.0817371 | ||||||||
\(322\) | −13.2641 | −0.739179 | ||||||||
\(323\) | −1.44867 | −0.0806062 | ||||||||
\(324\) | 16.5236 | 0.917976 | ||||||||
\(325\) | 3.16987 | 0.175833 | ||||||||
\(326\) | 41.0735 | 2.27485 | ||||||||
\(327\) | 1.42249 | 0.0786638 | ||||||||
\(328\) | −42.3992 | −2.34110 | ||||||||
\(329\) | −19.8333 | −1.09345 | ||||||||
\(330\) | 1.09342 | 0.0601910 | ||||||||
\(331\) | 6.19250 | 0.340371 | 0.170185 | − | 0.985412i | \(-0.445563\pi\) | ||||
0.170185 | + | 0.985412i | \(0.445563\pi\) | |||||||
\(332\) | −4.50001 | −0.246970 | ||||||||
\(333\) | −19.3649 | −1.06119 | ||||||||
\(334\) | 16.5970 | 0.908145 | ||||||||
\(335\) | 6.56736 | 0.358813 | ||||||||
\(336\) | 4.84982 | 0.264579 | ||||||||
\(337\) | 27.5485 | 1.50066 | 0.750332 | − | 0.661061i | \(-0.229894\pi\) | ||||
0.750332 | + | 0.661061i | \(0.229894\pi\) | |||||||
\(338\) | 23.2580 | 1.26507 | ||||||||
\(339\) | 10.4392 | 0.566982 | ||||||||
\(340\) | 6.65287 | 0.360803 | ||||||||
\(341\) | −1.11047 | −0.0601351 | ||||||||
\(342\) | −8.52202 | −0.460818 | ||||||||
\(343\) | 15.8234 | 0.854381 | ||||||||
\(344\) | 22.7120 | 1.22455 | ||||||||
\(345\) | 2.49521 | 0.134337 | ||||||||
\(346\) | −37.1033 | −1.99469 | ||||||||
\(347\) | −3.93699 | −0.211349 | −0.105674 | − | 0.994401i | \(-0.533700\pi\) | ||||
−0.105674 | + | 0.994401i | \(0.533700\pi\) | |||||||
\(348\) | −3.32695 | −0.178343 | ||||||||
\(349\) | 3.06845 | 0.164251 | 0.0821253 | − | 0.996622i | \(-0.473829\pi\) | ||||
0.0821253 | + | 0.996622i | \(0.473829\pi\) | |||||||
\(350\) | −12.3025 | −0.657598 | ||||||||
\(351\) | −7.20940 | −0.384809 | ||||||||
\(352\) | 0.937023 | 0.0499435 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 15.9398 | 0.847193 | ||||||||
\(355\) | −3.30226 | −0.175266 | ||||||||
\(356\) | −9.61117 | −0.509391 | ||||||||
\(357\) | 2.14546 | 0.113550 | ||||||||
\(358\) | 40.2366 | 2.12657 | ||||||||
\(359\) | −12.8218 | −0.676707 | −0.338354 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338354 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(360\) | 17.9503 | 0.946065 | ||||||||
\(361\) | −16.9014 | −0.889545 | ||||||||
\(362\) | 21.1856 | 1.11349 | ||||||||
\(363\) | 7.95612 | 0.417588 | ||||||||
\(364\) | 19.5501 | 1.02470 | ||||||||
\(365\) | 20.0957 | 1.05186 | ||||||||
\(366\) | −8.72282 | −0.455949 | ||||||||
\(367\) | −23.3278 | −1.21770 | −0.608849 | − | 0.793286i | \(-0.708369\pi\) | ||||
−0.608849 | + | 0.793286i | \(0.708369\pi\) | |||||||
\(368\) | −4.28298 | −0.223266 | ||||||||
\(369\) | −25.8478 | −1.34558 | ||||||||
\(370\) | −33.7559 | −1.75488 | ||||||||
\(371\) | −13.0658 | −0.678342 | ||||||||
\(372\) | 8.62352 | 0.447109 | ||||||||
\(373\) | −28.1304 | −1.45654 | −0.728268 | − | 0.685293i | \(-0.759674\pi\) | ||||
−0.728268 | + | 0.685293i | \(0.759674\pi\) | |||||||
\(374\) | −0.830278 | −0.0429327 | ||||||||
\(375\) | 8.89900 | 0.459542 | ||||||||
\(376\) | −27.3380 | −1.40985 | ||||||||
\(377\) | −2.22103 | −0.114389 | ||||||||
\(378\) | 27.9803 | 1.43915 | ||||||||
\(379\) | −12.4012 | −0.637004 | −0.318502 | − | 0.947922i | \(-0.603180\pi\) | ||||
−0.318502 | + | 0.947922i | \(0.603180\pi\) | |||||||
\(380\) | −9.63782 | −0.494410 | ||||||||
\(381\) | 1.89066 | 0.0968616 | ||||||||
\(382\) | 24.4132 | 1.24909 | ||||||||
\(383\) | −19.9183 | −1.01778 | −0.508888 | − | 0.860833i | \(-0.669943\pi\) | ||||
−0.508888 | + | 0.860833i | \(0.669943\pi\) | |||||||
\(384\) | −15.1666 | −0.773969 | ||||||||
\(385\) | −1.83802 | −0.0936743 | ||||||||
\(386\) | 18.0328 | 0.917844 | ||||||||
\(387\) | 13.8459 | 0.703826 | ||||||||
\(388\) | 56.3731 | 2.86191 | ||||||||
\(389\) | 1.68839 | 0.0856048 | 0.0428024 | − | 0.999084i | \(-0.486371\pi\) | ||||
0.0428024 | + | 0.999084i | \(0.486371\pi\) | |||||||
\(390\) | −5.66860 | −0.287041 | ||||||||
\(391\) | −1.89471 | −0.0958194 | ||||||||
\(392\) | −6.49512 | −0.328053 | ||||||||
\(393\) | −5.30478 | −0.267591 | ||||||||
\(394\) | −20.8996 | −1.05291 | ||||||||
\(395\) | 14.7694 | 0.743129 | ||||||||
\(396\) | −3.16882 | −0.159239 | ||||||||
\(397\) | −36.3951 | −1.82662 | −0.913308 | − | 0.407269i | \(-0.866481\pi\) | ||||
−0.913308 | + | 0.407269i | \(0.866481\pi\) | |||||||
\(398\) | 66.2230 | 3.31946 | ||||||||
\(399\) | −3.10807 | −0.155598 | ||||||||
\(400\) | −3.97249 | −0.198625 | ||||||||
\(401\) | 21.1548 | 1.05642 | 0.528210 | − | 0.849114i | \(-0.322863\pi\) | ||||
0.528210 | + | 0.849114i | \(0.322863\pi\) | |||||||
\(402\) | 6.36480 | 0.317447 | ||||||||
\(403\) | 5.75695 | 0.286774 | ||||||||
\(404\) | −27.0146 | −1.34403 | ||||||||
\(405\) | 8.05368 | 0.400190 | ||||||||
\(406\) | 8.62001 | 0.427804 | ||||||||
\(407\) | 2.73316 | 0.135478 | ||||||||
\(408\) | 2.95729 | 0.146407 | ||||||||
\(409\) | 6.03160 | 0.298243 | 0.149122 | − | 0.988819i | \(-0.452355\pi\) | ||||
0.149122 | + | 0.988819i | \(0.452355\pi\) | |||||||
\(410\) | −45.0565 | −2.22518 | ||||||||
\(411\) | 11.9158 | 0.587765 | ||||||||
\(412\) | 9.63348 | 0.474607 | ||||||||
\(413\) | −26.7946 | −1.31847 | ||||||||
\(414\) | −11.1459 | −0.547790 | ||||||||
\(415\) | −2.19333 | −0.107666 | ||||||||
\(416\) | −4.85778 | −0.238172 | ||||||||
\(417\) | −0.594635 | −0.0291194 | ||||||||
\(418\) | 1.20280 | 0.0588308 | ||||||||
\(419\) | −28.7800 | −1.40599 | −0.702996 | − | 0.711193i | \(-0.748155\pi\) | ||||
−0.702996 | + | 0.711193i | \(0.748155\pi\) | |||||||
\(420\) | 14.2735 | 0.696475 | ||||||||
\(421\) | −26.4896 | −1.29102 | −0.645512 | − | 0.763750i | \(-0.723356\pi\) | ||||
−0.645512 | + | 0.763750i | \(0.723356\pi\) | |||||||
\(422\) | 52.1759 | 2.53988 | ||||||||
\(423\) | −16.6660 | −0.810331 | ||||||||
\(424\) | −18.0097 | −0.874630 | ||||||||
\(425\) | −1.75735 | −0.0852442 | ||||||||
\(426\) | −3.20040 | −0.155060 | ||||||||
\(427\) | 14.6629 | 0.709587 | ||||||||
\(428\) | 7.39804 | 0.357598 | ||||||||
\(429\) | 0.458978 | 0.0221596 | ||||||||
\(430\) | 24.1355 | 1.16392 | ||||||||
\(431\) | −19.0198 | −0.916154 | −0.458077 | − | 0.888913i | \(-0.651462\pi\) | ||||
−0.458077 | + | 0.888913i | \(0.651462\pi\) | |||||||
\(432\) | 9.03485 | 0.434689 | ||||||||
\(433\) | 27.3321 | 1.31350 | 0.656748 | − | 0.754110i | \(-0.271931\pi\) | ||||
0.656748 | + | 0.754110i | \(0.271931\pi\) | |||||||
\(434\) | −22.3432 | −1.07251 | ||||||||
\(435\) | −1.62157 | −0.0777486 | ||||||||
\(436\) | −7.18611 | −0.344152 | ||||||||
\(437\) | 2.74480 | 0.131302 | ||||||||
\(438\) | 19.4759 | 0.930593 | ||||||||
\(439\) | 8.16086 | 0.389497 | 0.194748 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194748 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(440\) | −2.53351 | −0.120780 | ||||||||
\(441\) | −3.95961 | −0.188553 | ||||||||
\(442\) | 4.30438 | 0.204739 | ||||||||
\(443\) | −29.3754 | −1.39567 | −0.697835 | − | 0.716259i | \(-0.745853\pi\) | ||||
−0.697835 | + | 0.716259i | \(0.745853\pi\) | |||||||
\(444\) | −21.2248 | −1.00729 | ||||||||
\(445\) | −4.68454 | −0.222068 | ||||||||
\(446\) | −33.4512 | −1.58396 | ||||||||
\(447\) | 3.96196 | 0.187394 | ||||||||
\(448\) | 32.1164 | 1.51736 | ||||||||
\(449\) | 14.1923 | 0.669775 | 0.334888 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334888 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(450\) | −10.3379 | −0.487333 | ||||||||
\(451\) | 3.64816 | 0.171785 | ||||||||
\(452\) | −52.7368 | −2.48053 | ||||||||
\(453\) | 11.6911 | 0.549296 | ||||||||
\(454\) | −6.96760 | −0.327006 | ||||||||
\(455\) | 9.52880 | 0.446717 | ||||||||
\(456\) | −4.28413 | −0.200623 | ||||||||
\(457\) | −13.6666 | −0.639296 | −0.319648 | − | 0.947536i | \(-0.603565\pi\) | ||||
−0.319648 | + | 0.947536i | \(0.603565\pi\) | |||||||
\(458\) | −35.4556 | −1.65673 | ||||||||
\(459\) | 3.99684 | 0.186557 | ||||||||
\(460\) | −12.6052 | −0.587722 | ||||||||
\(461\) | −22.9365 | −1.06826 | −0.534129 | − | 0.845403i | \(-0.679360\pi\) | ||||
−0.534129 | + | 0.845403i | \(0.679360\pi\) | |||||||
\(462\) | −1.78133 | −0.0828751 | ||||||||
\(463\) | −10.9090 | −0.506985 | −0.253492 | − | 0.967337i | \(-0.581579\pi\) | ||||
−0.253492 | + | 0.967337i | \(0.581579\pi\) | |||||||
\(464\) | 2.78340 | 0.129216 | ||||||||
\(465\) | 4.20315 | 0.194916 | ||||||||
\(466\) | −23.6188 | −1.09412 | ||||||||
\(467\) | −15.6351 | −0.723507 | −0.361753 | − | 0.932274i | \(-0.617822\pi\) | ||||
−0.361753 | + | 0.932274i | \(0.617822\pi\) | |||||||
\(468\) | 16.4280 | 0.759385 | ||||||||
\(469\) | −10.6991 | −0.494039 | ||||||||
\(470\) | −29.0514 | −1.34004 | ||||||||
\(471\) | −11.6775 | −0.538071 | ||||||||
\(472\) | −36.9333 | −1.69999 | ||||||||
\(473\) | −1.95421 | −0.0898548 | ||||||||
\(474\) | 14.3139 | 0.657457 | ||||||||
\(475\) | 2.54583 | 0.116811 | ||||||||
\(476\) | −10.8384 | −0.496778 | ||||||||
\(477\) | −10.9793 | −0.502706 | ||||||||
\(478\) | 21.6548 | 0.990466 | ||||||||
\(479\) | 26.1414 | 1.19443 | 0.597216 | − | 0.802080i | \(-0.296273\pi\) | ||||
0.597216 | + | 0.802080i | \(0.296273\pi\) | |||||||
\(480\) | −3.54666 | −0.161882 | ||||||||
\(481\) | −14.1694 | −0.646071 | ||||||||
\(482\) | −53.6034 | −2.44157 | ||||||||
\(483\) | −4.06502 | −0.184965 | ||||||||
\(484\) | −40.1926 | −1.82694 | ||||||||
\(485\) | 27.4766 | 1.24765 | ||||||||
\(486\) | 36.4185 | 1.65198 | ||||||||
\(487\) | 28.9095 | 1.31002 | 0.655008 | − | 0.755622i | \(-0.272665\pi\) | ||||
0.655008 | + | 0.755622i | \(0.272665\pi\) | |||||||
\(488\) | 20.2112 | 0.914917 | ||||||||
\(489\) | 12.5877 | 0.569237 | ||||||||
\(490\) | −6.90220 | −0.311810 | ||||||||
\(491\) | 6.07604 | 0.274208 | 0.137104 | − | 0.990557i | \(-0.456221\pi\) | ||||
0.137104 | + | 0.990557i | \(0.456221\pi\) | |||||||
\(492\) | −28.3304 | −1.27723 | ||||||||
\(493\) | 1.23132 | 0.0554561 | ||||||||
\(494\) | −6.23563 | −0.280554 | ||||||||
\(495\) | −1.54450 | −0.0694202 | ||||||||
\(496\) | −7.21464 | −0.323947 | ||||||||
\(497\) | 5.37982 | 0.241318 | ||||||||
\(498\) | −2.12568 | −0.0952541 | ||||||||
\(499\) | 38.8961 | 1.74123 | 0.870614 | − | 0.491966i | \(-0.163722\pi\) | ||||
0.870614 | + | 0.491966i | \(0.163722\pi\) | |||||||
\(500\) | −44.9558 | −2.01048 | ||||||||
\(501\) | 5.08645 | 0.227246 | ||||||||
\(502\) | −5.07893 | −0.226684 | ||||||||
\(503\) | −32.4758 | −1.44802 | −0.724012 | − | 0.689787i | \(-0.757704\pi\) | ||||
−0.724012 | + | 0.689787i | \(0.757704\pi\) | |||||||
\(504\) | −29.2435 | −1.30261 | ||||||||
\(505\) | −13.1671 | −0.585926 | ||||||||
\(506\) | 1.57313 | 0.0699343 | ||||||||
\(507\) | 7.12786 | 0.316559 | ||||||||
\(508\) | −9.55122 | −0.423767 | ||||||||
\(509\) | −24.7597 | −1.09746 | −0.548728 | − | 0.836001i | \(-0.684888\pi\) | ||||
−0.548728 | + | 0.836001i | \(0.684888\pi\) | |||||||
\(510\) | 3.14263 | 0.139158 | ||||||||
\(511\) | −32.7386 | −1.44827 | ||||||||
\(512\) | 24.3693 | 1.07698 | ||||||||
\(513\) | −5.79011 | −0.255640 | ||||||||
\(514\) | 66.9993 | 2.95521 | ||||||||
\(515\) | 4.69541 | 0.206905 | ||||||||
\(516\) | 15.1758 | 0.668077 | ||||||||
\(517\) | 2.35225 | 0.103452 | ||||||||
\(518\) | 54.9928 | 2.41625 | ||||||||
\(519\) | −11.3710 | −0.499131 | ||||||||
\(520\) | 13.1344 | 0.575982 | ||||||||
\(521\) | −41.3687 | −1.81240 | −0.906198 | − | 0.422853i | \(-0.861029\pi\) | ||||
−0.906198 | + | 0.422853i | \(0.861029\pi\) | |||||||
\(522\) | 7.24345 | 0.317037 | ||||||||
\(523\) | 9.02974 | 0.394843 | 0.197422 | − | 0.980319i | \(-0.436743\pi\) | ||||
0.197422 | + | 0.980319i | \(0.436743\pi\) | |||||||
\(524\) | 26.7986 | 1.17070 | ||||||||
\(525\) | −3.77034 | −0.164551 | ||||||||
\(526\) | 39.0236 | 1.70151 | ||||||||
\(527\) | −3.19162 | −0.139029 | ||||||||
\(528\) | −0.575193 | −0.0250320 | ||||||||
\(529\) | −19.4101 | −0.843917 | ||||||||
\(530\) | −19.1385 | −0.831323 | ||||||||
\(531\) | −22.5156 | −0.977095 | ||||||||
\(532\) | 15.7013 | 0.680738 | ||||||||
\(533\) | −18.9130 | −0.819214 | ||||||||
\(534\) | −4.54005 | −0.196467 | ||||||||
\(535\) | 3.60584 | 0.155894 | ||||||||
\(536\) | −14.7475 | −0.636996 | ||||||||
\(537\) | 12.3312 | 0.532132 | ||||||||
\(538\) | −59.2445 | −2.55421 | ||||||||
\(539\) | 0.558861 | 0.0240718 | ||||||||
\(540\) | 26.5905 | 1.14427 | ||||||||
\(541\) | −39.1174 | −1.68179 | −0.840895 | − | 0.541198i | \(-0.817971\pi\) | ||||
−0.840895 | + | 0.541198i | \(0.817971\pi\) | |||||||
\(542\) | −51.3354 | −2.20505 | ||||||||
\(543\) | 6.49272 | 0.278629 | ||||||||
\(544\) | 2.69312 | 0.115467 | ||||||||
\(545\) | −3.50255 | −0.150033 | ||||||||
\(546\) | 9.23490 | 0.395217 | ||||||||
\(547\) | −33.1264 | −1.41638 | −0.708192 | − | 0.706020i | \(-0.750489\pi\) | ||||
−0.708192 | + | 0.706020i | \(0.750489\pi\) | |||||||
\(548\) | −60.1963 | −2.57146 | ||||||||
\(549\) | 12.3213 | 0.525861 | ||||||||
\(550\) | 1.45909 | 0.0622159 | ||||||||
\(551\) | −1.78378 | −0.0759917 | ||||||||
\(552\) | −5.60318 | −0.238487 | ||||||||
\(553\) | −24.0613 | −1.02319 | ||||||||
\(554\) | 43.3097 | 1.84005 | ||||||||
\(555\) | −10.3451 | −0.439125 | ||||||||
\(556\) | 3.00396 | 0.127396 | ||||||||
\(557\) | 11.8344 | 0.501439 | 0.250719 | − | 0.968060i | \(-0.419333\pi\) | ||||
0.250719 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(558\) | −18.7751 | −0.794815 | ||||||||
\(559\) | 10.1312 | 0.428502 | ||||||||
\(560\) | −11.9415 | −0.504622 | ||||||||
\(561\) | −0.254454 | −0.0107431 | ||||||||
\(562\) | −22.7296 | −0.958789 | ||||||||
\(563\) | 1.38282 | 0.0582788 | 0.0291394 | − | 0.999575i | \(-0.490723\pi\) | ||||
0.0291394 | + | 0.999575i | \(0.490723\pi\) | |||||||
\(564\) | −18.2668 | −0.769172 | ||||||||
\(565\) | −25.7042 | −1.08138 | ||||||||
\(566\) | −67.9429 | −2.85585 | ||||||||
\(567\) | −13.1205 | −0.551010 | ||||||||
\(568\) | 7.41548 | 0.311147 | ||||||||
\(569\) | 14.2588 | 0.597760 | 0.298880 | − | 0.954291i | \(-0.403387\pi\) | ||||
0.298880 | + | 0.954291i | \(0.403387\pi\) | |||||||
\(570\) | −4.55264 | −0.190689 | ||||||||
\(571\) | −12.7902 | −0.535254 | −0.267627 | − | 0.963523i | \(-0.586239\pi\) | ||||
−0.267627 | + | 0.963523i | \(0.586239\pi\) | |||||||
\(572\) | −2.31865 | −0.0969478 | ||||||||
\(573\) | 7.48187 | 0.312560 | ||||||||
\(574\) | 73.4032 | 3.06379 | ||||||||
\(575\) | 3.32967 | 0.138857 | ||||||||
\(576\) | 26.9876 | 1.12448 | ||||||||
\(577\) | −15.9144 | −0.662525 | −0.331262 | − | 0.943539i | \(-0.607475\pi\) | ||||
−0.331262 | + | 0.943539i | \(0.607475\pi\) | |||||||
\(578\) | −2.38632 | −0.0992579 | ||||||||
\(579\) | 5.52648 | 0.229673 | ||||||||
\(580\) | 8.19184 | 0.340148 | ||||||||
\(581\) | 3.57323 | 0.148243 | ||||||||
\(582\) | 26.6291 | 1.10381 | ||||||||
\(583\) | 1.54961 | 0.0641785 | ||||||||
\(584\) | −45.1265 | −1.86735 | ||||||||
\(585\) | 8.00711 | 0.331053 | ||||||||
\(586\) | −16.1492 | −0.667119 | ||||||||
\(587\) | −23.6222 | −0.974992 | −0.487496 | − | 0.873125i | \(-0.662090\pi\) | ||||
−0.487496 | + | 0.873125i | \(0.662090\pi\) | |||||||
\(588\) | −4.33993 | −0.178976 | ||||||||
\(589\) | 4.62360 | 0.190512 | ||||||||
\(590\) | −39.2481 | −1.61582 | ||||||||
\(591\) | −6.40507 | −0.263469 | ||||||||
\(592\) | 17.7572 | 0.729816 | ||||||||
\(593\) | 25.4016 | 1.04312 | 0.521560 | − | 0.853215i | \(-0.325350\pi\) | ||||
0.521560 | + | 0.853215i | \(0.325350\pi\) | |||||||
\(594\) | −3.31849 | −0.136159 | ||||||||
\(595\) | −5.28271 | −0.216570 | ||||||||
\(596\) | −20.0149 | −0.819844 | ||||||||
\(597\) | 20.2953 | 0.830630 | ||||||||
\(598\) | −8.15554 | −0.333505 | ||||||||
\(599\) | −19.8692 | −0.811833 | −0.405916 | − | 0.913910i | \(-0.633048\pi\) | ||||
−0.405916 | + | 0.913910i | \(0.633048\pi\) | |||||||
\(600\) | −5.19700 | −0.212166 | ||||||||
\(601\) | −2.68442 | −0.109500 | −0.0547500 | − | 0.998500i | \(-0.517436\pi\) | ||||
−0.0547500 | + | 0.998500i | \(0.517436\pi\) | |||||||
\(602\) | −39.3199 | −1.60256 | ||||||||
\(603\) | −8.99052 | −0.366122 | ||||||||
\(604\) | −59.0609 | −2.40315 | ||||||||
\(605\) | −19.5901 | −0.796451 | ||||||||
\(606\) | −12.7609 | −0.518378 | ||||||||
\(607\) | 48.1090 | 1.95268 | 0.976342 | − | 0.216233i | \(-0.0693770\pi\) | ||||
0.976342 | + | 0.216233i | \(0.0693770\pi\) | |||||||
\(608\) | −3.90144 | −0.158224 | ||||||||
\(609\) | 2.64176 | 0.107050 | ||||||||
\(610\) | 21.4779 | 0.869615 | ||||||||
\(611\) | −12.1947 | −0.493344 | ||||||||
\(612\) | −9.10758 | −0.368152 | ||||||||
\(613\) | −8.90899 | −0.359831 | −0.179915 | − | 0.983682i | \(-0.557582\pi\) | ||||
−0.179915 | + | 0.983682i | \(0.557582\pi\) | |||||||
\(614\) | −31.7823 | −1.28263 | ||||||||
\(615\) | −13.8084 | −0.556809 | ||||||||
\(616\) | 4.12743 | 0.166299 | ||||||||
\(617\) | 16.7211 | 0.673165 | 0.336582 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336582 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(618\) | 4.55059 | 0.183052 | ||||||||
\(619\) | −1.04364 | −0.0419474 | −0.0209737 | − | 0.999780i | \(-0.506677\pi\) | ||||
−0.0209737 | + | 0.999780i | \(0.506677\pi\) | |||||||
\(620\) | −21.2334 | −0.852754 | ||||||||
\(621\) | −7.57284 | −0.303888 | ||||||||
\(622\) | 35.6678 | 1.43015 | ||||||||
\(623\) | 7.63174 | 0.305759 | ||||||||
\(624\) | 2.98195 | 0.119374 | ||||||||
\(625\) | −13.1249 | −0.524998 | ||||||||
\(626\) | −25.8761 | −1.03422 | ||||||||
\(627\) | 0.368620 | 0.0147213 | ||||||||
\(628\) | 58.9922 | 2.35404 | ||||||||
\(629\) | 7.85544 | 0.313217 | ||||||||
\(630\) | −31.0763 | −1.23811 | ||||||||
\(631\) | −23.6152 | −0.940108 | −0.470054 | − | 0.882638i | \(-0.655766\pi\) | ||||
−0.470054 | + | 0.882638i | \(0.655766\pi\) | |||||||
\(632\) | −33.1659 | −1.31927 | ||||||||
\(633\) | 15.9903 | 0.635556 | ||||||||
\(634\) | −67.0450 | −2.66270 | ||||||||
\(635\) | −4.65532 | −0.184741 | ||||||||
\(636\) | −12.0338 | −0.477172 | ||||||||
\(637\) | −2.89728 | −0.114795 | ||||||||
\(638\) | −1.02234 | −0.0404749 | ||||||||
\(639\) | 4.52069 | 0.178836 | ||||||||
\(640\) | 37.3443 | 1.47616 | ||||||||
\(641\) | 22.5720 | 0.891541 | 0.445770 | − | 0.895147i | \(-0.352930\pi\) | ||||
0.445770 | + | 0.895147i | \(0.352930\pi\) | |||||||
\(642\) | 3.49463 | 0.137922 | ||||||||
\(643\) | −37.5789 | −1.48197 | −0.740984 | − | 0.671522i | \(-0.765641\pi\) | ||||
−0.740984 | + | 0.671522i | \(0.765641\pi\) | |||||||
\(644\) | 20.5356 | 0.809216 | ||||||||
\(645\) | 7.39676 | 0.291247 | ||||||||
\(646\) | 3.45699 | 0.136014 | ||||||||
\(647\) | −7.42682 | −0.291978 | −0.145989 | − | 0.989286i | \(-0.546636\pi\) | ||||
−0.145989 | + | 0.989286i | \(0.546636\pi\) | |||||||
\(648\) | −18.0852 | −0.710453 | ||||||||
\(649\) | 3.17786 | 0.124742 | ||||||||
\(650\) | −7.56433 | −0.296697 | ||||||||
\(651\) | −6.84750 | −0.268375 | ||||||||
\(652\) | −63.5905 | −2.49040 | ||||||||
\(653\) | 32.5806 | 1.27498 | 0.637488 | − | 0.770460i | \(-0.279973\pi\) | ||||
0.637488 | + | 0.770460i | \(0.279973\pi\) | |||||||
\(654\) | −3.39452 | −0.132736 | ||||||||
\(655\) | 13.0618 | 0.510366 | ||||||||
\(656\) | 23.7019 | 0.925403 | ||||||||
\(657\) | −27.5104 | −1.07328 | ||||||||
\(658\) | 47.3287 | 1.84506 | ||||||||
\(659\) | 33.3575 | 1.29942 | 0.649712 | − | 0.760181i | \(-0.274890\pi\) | ||||
0.649712 | + | 0.760181i | \(0.274890\pi\) | |||||||
\(660\) | −1.69285 | −0.0658941 | ||||||||
\(661\) | 13.0929 | 0.509256 | 0.254628 | − | 0.967039i | \(-0.418047\pi\) | ||||
0.254628 | + | 0.967039i | \(0.418047\pi\) | |||||||
\(662\) | −14.7773 | −0.574336 | ||||||||
\(663\) | 1.31916 | 0.0512318 | ||||||||
\(664\) | 4.92530 | 0.191139 | ||||||||
\(665\) | 7.65290 | 0.296767 | ||||||||
\(666\) | 46.2108 | 1.79063 | ||||||||
\(667\) | −2.33300 | −0.0903340 | ||||||||
\(668\) | −25.6956 | −0.994193 | ||||||||
\(669\) | −10.2517 | −0.396356 | ||||||||
\(670\) | −15.6718 | −0.605456 | ||||||||
\(671\) | −1.73903 | −0.0671346 | ||||||||
\(672\) | 5.77799 | 0.222891 | ||||||||
\(673\) | −13.4103 | −0.516931 | −0.258465 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258465 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(674\) | −65.7397 | −2.53220 | ||||||||
\(675\) | −7.02387 | −0.270349 | ||||||||
\(676\) | −36.0084 | −1.38494 | ||||||||
\(677\) | −27.3196 | −1.04998 | −0.524989 | − | 0.851109i | \(-0.675931\pi\) | ||||
−0.524989 | + | 0.851109i | \(0.675931\pi\) | |||||||
\(678\) | −24.9114 | −0.956717 | ||||||||
\(679\) | −44.7630 | −1.71785 | ||||||||
\(680\) | −7.28162 | −0.279238 | ||||||||
\(681\) | −2.13535 | −0.0818268 | ||||||||
\(682\) | 2.64993 | 0.101471 | ||||||||
\(683\) | −3.80562 | −0.145618 | −0.0728089 | − | 0.997346i | \(-0.523196\pi\) | ||||
−0.0728089 | + | 0.997346i | \(0.523196\pi\) | |||||||
\(684\) | 13.1939 | 0.504481 | ||||||||
\(685\) | −29.3400 | −1.12102 | ||||||||
\(686\) | −37.7596 | −1.44167 | ||||||||
\(687\) | −10.8660 | −0.414565 | ||||||||
\(688\) | −12.6964 | −0.484046 | ||||||||
\(689\) | −8.03362 | −0.306056 | ||||||||
\(690\) | −5.95436 | −0.226679 | ||||||||
\(691\) | −19.2715 | −0.733123 | −0.366562 | − | 0.930394i | \(-0.619465\pi\) | ||||
−0.366562 | + | 0.930394i | \(0.619465\pi\) | |||||||
\(692\) | 57.4438 | 2.18368 | ||||||||
\(693\) | 2.51620 | 0.0955825 | ||||||||
\(694\) | 9.39493 | 0.356627 | ||||||||
\(695\) | 1.46415 | 0.0555383 | ||||||||
\(696\) | 3.64138 | 0.138026 | ||||||||
\(697\) | 10.4853 | 0.397158 | ||||||||
\(698\) | −7.32232 | −0.277154 | ||||||||
\(699\) | −7.23841 | −0.273782 | ||||||||
\(700\) | 19.0469 | 0.719906 | ||||||||
\(701\) | −45.4262 | −1.71572 | −0.857862 | − | 0.513880i | \(-0.828208\pi\) | ||||
−0.857862 | + | 0.513880i | \(0.828208\pi\) | |||||||
\(702\) | 17.2039 | 0.649321 | ||||||||
\(703\) | −11.3799 | −0.429203 | ||||||||
\(704\) | −3.80904 | −0.143559 | ||||||||
\(705\) | −8.90335 | −0.335319 | ||||||||
\(706\) | −2.38632 | −0.0898104 | ||||||||
\(707\) | 21.4509 | 0.806744 | ||||||||
\(708\) | −24.6782 | −0.927465 | ||||||||
\(709\) | −5.02016 | −0.188536 | −0.0942680 | − | 0.995547i | \(-0.530051\pi\) | ||||
−0.0942680 | + | 0.995547i | \(0.530051\pi\) | |||||||
\(710\) | 7.88025 | 0.295740 | ||||||||
\(711\) | −20.2189 | −0.758267 | ||||||||
\(712\) | 10.5195 | 0.394235 | ||||||||
\(713\) | 6.04717 | 0.226468 | ||||||||
\(714\) | −5.11977 | −0.191603 | ||||||||
\(715\) | −1.13013 | −0.0422643 | ||||||||
\(716\) | −62.2947 | −2.32806 | ||||||||
\(717\) | 6.63651 | 0.247845 | ||||||||
\(718\) | 30.5969 | 1.14186 | ||||||||
\(719\) | 0.626950 | 0.0233813 | 0.0116907 | − | 0.999932i | \(-0.496279\pi\) | ||||
0.0116907 | + | 0.999932i | \(0.496279\pi\) | |||||||
\(720\) | −10.0345 | −0.373965 | ||||||||
\(721\) | −7.64945 | −0.284881 | ||||||||
\(722\) | 40.3321 | 1.50100 | ||||||||
\(723\) | −16.4277 | −0.610955 | ||||||||
\(724\) | −32.7998 | −1.21899 | ||||||||
\(725\) | −2.16387 | −0.0803642 | ||||||||
\(726\) | −18.9859 | −0.704632 | ||||||||
\(727\) | 8.82628 | 0.327349 | 0.163674 | − | 0.986514i | \(-0.447665\pi\) | ||||
0.163674 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(728\) | −21.3977 | −0.793051 | ||||||||
\(729\) | −2.25619 | −0.0835624 | ||||||||
\(730\) | −47.9548 | −1.77489 | ||||||||
\(731\) | −5.61665 | −0.207739 | ||||||||
\(732\) | 13.5048 | 0.499151 | ||||||||
\(733\) | 41.5035 | 1.53297 | 0.766484 | − | 0.642263i | \(-0.222004\pi\) | ||||
0.766484 | + | 0.642263i | \(0.222004\pi\) | |||||||
\(734\) | 55.6675 | 2.05473 | ||||||||
\(735\) | −2.11531 | −0.0780243 | ||||||||
\(736\) | −5.10267 | −0.188087 | ||||||||
\(737\) | 1.26892 | 0.0467414 | ||||||||
\(738\) | 61.6811 | 2.27051 | ||||||||
\(739\) | −20.0707 | −0.738312 | −0.369156 | − | 0.929367i | \(-0.620353\pi\) | ||||
−0.369156 | + | 0.929367i | \(0.620353\pi\) | |||||||
\(740\) | 52.2612 | 1.92116 | ||||||||
\(741\) | −1.91103 | −0.0702033 | ||||||||
\(742\) | 31.1792 | 1.14462 | ||||||||
\(743\) | 24.6198 | 0.903211 | 0.451606 | − | 0.892218i | \(-0.350851\pi\) | ||||
0.451606 | + | 0.892218i | \(0.350851\pi\) | |||||||
\(744\) | −9.43852 | −0.346033 | ||||||||
\(745\) | −9.75539 | −0.357410 | ||||||||
\(746\) | 67.1281 | 2.45774 | ||||||||
\(747\) | 3.00261 | 0.109860 | ||||||||
\(748\) | 1.28545 | 0.0470006 | ||||||||
\(749\) | −5.87440 | −0.214646 | ||||||||
\(750\) | −21.2359 | −0.775425 | ||||||||
\(751\) | 20.2311 | 0.738242 | 0.369121 | − | 0.929381i | \(-0.379659\pi\) | ||||
0.369121 | + | 0.929381i | \(0.379659\pi\) | |||||||
\(752\) | 15.2824 | 0.557293 | ||||||||
\(753\) | −1.55653 | −0.0567232 | ||||||||
\(754\) | 5.30009 | 0.193018 | ||||||||
\(755\) | −28.7866 | −1.04765 | ||||||||
\(756\) | −43.3195 | −1.57551 | ||||||||
\(757\) | 1.00053 | 0.0363648 | 0.0181824 | − | 0.999835i | \(-0.494212\pi\) | ||||
0.0181824 | + | 0.999835i | \(0.494212\pi\) | |||||||
\(758\) | 29.5931 | 1.07487 | ||||||||
\(759\) | 0.482116 | 0.0174997 | ||||||||
\(760\) | 10.5487 | 0.382641 | ||||||||
\(761\) | −10.7841 | −0.390925 | −0.195462 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195462 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(762\) | −4.51173 | −0.163443 | ||||||||
\(763\) | 5.70612 | 0.206575 | ||||||||
\(764\) | −37.7968 | −1.36744 | ||||||||
\(765\) | −4.43909 | −0.160496 | ||||||||
\(766\) | 47.5314 | 1.71738 | ||||||||
\(767\) | −16.4749 | −0.594873 | ||||||||
\(768\) | 20.1797 | 0.728173 | ||||||||
\(769\) | 9.46018 | 0.341143 | 0.170571 | − | 0.985345i | \(-0.445439\pi\) | ||||
0.170571 | + | 0.985345i | \(0.445439\pi\) | |||||||
\(770\) | 4.38611 | 0.158065 | ||||||||
\(771\) | 20.5332 | 0.739484 | ||||||||
\(772\) | −27.9185 | −1.00481 | ||||||||
\(773\) | −26.8074 | −0.964196 | −0.482098 | − | 0.876117i | \(-0.660125\pi\) | ||||
−0.482098 | + | 0.876117i | \(0.660125\pi\) | |||||||
\(774\) | −33.0408 | −1.18763 | ||||||||
\(775\) | 5.60880 | 0.201474 | ||||||||
\(776\) | −61.7009 | −2.21493 | ||||||||
\(777\) | 16.8536 | 0.604618 | ||||||||
\(778\) | −4.02904 | −0.144448 | ||||||||
\(779\) | −15.1897 | −0.544227 | ||||||||
\(780\) | 8.77619 | 0.314238 | ||||||||
\(781\) | −0.638051 | −0.0228313 | ||||||||
\(782\) | 4.52138 | 0.161684 | ||||||||
\(783\) | 4.92141 | 0.175877 | ||||||||
\(784\) | 3.63089 | 0.129675 | ||||||||
\(785\) | 28.7531 | 1.02624 | ||||||||
\(786\) | 12.6589 | 0.451528 | ||||||||
\(787\) | −32.6755 | −1.16476 | −0.582378 | − | 0.812918i | \(-0.697878\pi\) | ||||
−0.582378 | + | 0.812918i | \(0.697878\pi\) | |||||||
\(788\) | 32.3570 | 1.15267 | ||||||||
\(789\) | 11.9595 | 0.425769 | ||||||||
\(790\) | −35.2445 | −1.25394 | ||||||||
\(791\) | 41.8756 | 1.48892 | ||||||||
\(792\) | 3.46830 | 0.123241 | ||||||||
\(793\) | 9.01561 | 0.320154 | ||||||||
\(794\) | 86.8504 | 3.08220 | ||||||||
\(795\) | −5.86535 | −0.208022 | ||||||||
\(796\) | −102.527 | −3.63398 | ||||||||
\(797\) | 25.4005 | 0.899730 | 0.449865 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449865 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(798\) | 7.41686 | 0.262554 | ||||||||
\(799\) | 6.76065 | 0.239175 | ||||||||
\(800\) | −4.73276 | −0.167328 | ||||||||
\(801\) | 6.41300 | 0.226592 | ||||||||
\(802\) | −50.4821 | −1.78259 | ||||||||
\(803\) | 3.88283 | 0.137022 | ||||||||
\(804\) | −9.85406 | −0.347526 | ||||||||
\(805\) | 10.0092 | 0.352777 | ||||||||
\(806\) | −13.7379 | −0.483898 | ||||||||
\(807\) | −18.1566 | −0.639141 | ||||||||
\(808\) | 29.5677 | 1.04019 | ||||||||
\(809\) | −50.4976 | −1.77540 | −0.887701 | − | 0.460420i | \(-0.847699\pi\) | ||||
−0.887701 | + | 0.460420i | \(0.847699\pi\) | |||||||
\(810\) | −19.2187 | −0.675275 | ||||||||
\(811\) | −40.3610 | −1.41727 | −0.708633 | − | 0.705577i | \(-0.750688\pi\) | ||||
−0.708633 | + | 0.705577i | \(0.750688\pi\) | |||||||
\(812\) | −13.3456 | −0.468339 | ||||||||
\(813\) | −15.7327 | −0.551770 | ||||||||
\(814\) | −6.52220 | −0.228603 | ||||||||
\(815\) | −30.9944 | −1.08569 | ||||||||
\(816\) | −1.65317 | −0.0578727 | ||||||||
\(817\) | 8.13667 | 0.284666 | ||||||||
\(818\) | −14.3933 | −0.503251 | ||||||||
\(819\) | −13.0447 | −0.455817 | ||||||||
\(820\) | 69.7571 | 2.43602 | ||||||||
\(821\) | −11.2198 | −0.391575 | −0.195788 | − | 0.980646i | \(-0.562726\pi\) | ||||
−0.195788 | + | 0.980646i | \(0.562726\pi\) | |||||||
\(822\) | −28.4350 | −0.991786 | ||||||||
\(823\) | 15.4730 | 0.539356 | 0.269678 | − | 0.962951i | \(-0.413083\pi\) | ||||
0.269678 | + | 0.962951i | \(0.413083\pi\) | |||||||
\(824\) | −10.5439 | −0.367315 | ||||||||
\(825\) | 0.447166 | 0.0155683 | ||||||||
\(826\) | 63.9404 | 2.22477 | ||||||||
\(827\) | −54.6475 | −1.90028 | −0.950139 | − | 0.311826i | \(-0.899059\pi\) | ||||
−0.950139 | + | 0.311826i | \(0.899059\pi\) | |||||||
\(828\) | 17.2562 | 0.599694 | ||||||||
\(829\) | 26.8692 | 0.933206 | 0.466603 | − | 0.884467i | \(-0.345478\pi\) | ||||
0.466603 | + | 0.884467i | \(0.345478\pi\) | |||||||
\(830\) | 5.23399 | 0.181675 | ||||||||
\(831\) | 13.2730 | 0.460437 | ||||||||
\(832\) | 19.7471 | 0.684606 | ||||||||
\(833\) | 1.60623 | 0.0556527 | ||||||||
\(834\) | 1.41899 | 0.0491356 | ||||||||
\(835\) | −12.5242 | −0.433417 | ||||||||
\(836\) | −1.86219 | −0.0644051 | ||||||||
\(837\) | −12.7564 | −0.440925 | ||||||||
\(838\) | 68.6782 | 2.37245 | ||||||||
\(839\) | −36.2163 | −1.25033 | −0.625163 | − | 0.780494i | \(-0.714968\pi\) | ||||
−0.625163 | + | 0.780494i | \(0.714968\pi\) | |||||||
\(840\) | −15.6225 | −0.539026 | ||||||||
\(841\) | −27.4838 | −0.947719 | ||||||||
\(842\) | 63.2127 | 2.17845 | ||||||||
\(843\) | −6.96589 | −0.239918 | ||||||||
\(844\) | −80.7794 | −2.78054 | ||||||||
\(845\) | −17.5507 | −0.603762 | ||||||||
\(846\) | 39.7705 | 1.36734 | ||||||||
\(847\) | 31.9149 | 1.09661 | ||||||||
\(848\) | 10.0678 | 0.345728 | ||||||||
\(849\) | −20.8224 | −0.714622 | ||||||||
\(850\) | 4.19361 | 0.143840 | ||||||||
\(851\) | −14.8837 | −0.510208 | ||||||||
\(852\) | 4.95490 | 0.169752 | ||||||||
\(853\) | 36.0100 | 1.23296 | 0.616480 | − | 0.787371i | \(-0.288558\pi\) | ||||
0.616480 | + | 0.787371i | \(0.288558\pi\) | |||||||
\(854\) | −34.9904 | −1.19735 | ||||||||
\(855\) | 6.43077 | 0.219928 | ||||||||
\(856\) | −8.09721 | −0.276757 | ||||||||
\(857\) | −22.7172 | −0.776005 | −0.388002 | − | 0.921658i | \(-0.626835\pi\) | ||||
−0.388002 | + | 0.921658i | \(0.626835\pi\) | |||||||
\(858\) | −1.09527 | −0.0373918 | ||||||||
\(859\) | 37.6812 | 1.28567 | 0.642833 | − | 0.766006i | \(-0.277759\pi\) | ||||
0.642833 | + | 0.766006i | \(0.277759\pi\) | |||||||
\(860\) | −37.3668 | −1.27420 | ||||||||
\(861\) | 22.4958 | 0.766653 | ||||||||
\(862\) | 45.3875 | 1.54590 | ||||||||
\(863\) | −0.110067 | −0.00374674 | −0.00187337 | − | 0.999998i | \(-0.500596\pi\) | ||||
−0.00187337 | + | 0.999998i | \(0.500596\pi\) | |||||||
\(864\) | 10.7640 | 0.366198 | ||||||||
\(865\) | 27.9984 | 0.951975 | ||||||||
\(866\) | −65.2232 | −2.21637 | ||||||||
\(867\) | −0.731332 | −0.0248373 | ||||||||
\(868\) | 34.5921 | 1.17413 | ||||||||
\(869\) | 2.85370 | 0.0968050 | ||||||||
\(870\) | 3.86960 | 0.131192 | ||||||||
\(871\) | −6.57844 | −0.222902 | ||||||||
\(872\) | 7.86525 | 0.266351 | ||||||||
\(873\) | −37.6146 | −1.27306 | ||||||||
\(874\) | −6.54999 | −0.221557 | ||||||||
\(875\) | 35.6971 | 1.20678 | ||||||||
\(876\) | −30.1528 | −1.01877 | ||||||||
\(877\) | 20.4861 | 0.691766 | 0.345883 | − | 0.938278i | \(-0.387579\pi\) | ||||
0.345883 | + | 0.938278i | \(0.387579\pi\) | |||||||
\(878\) | −19.4744 | −0.657230 | ||||||||
\(879\) | −4.94923 | −0.166934 | ||||||||
\(880\) | 1.41628 | 0.0477427 | ||||||||
\(881\) | 14.5965 | 0.491768 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(882\) | 9.44891 | 0.318161 | ||||||||
\(883\) | −13.8615 | −0.466478 | −0.233239 | − | 0.972419i | \(-0.574932\pi\) | ||||
−0.233239 | + | 0.972419i | \(0.574932\pi\) | |||||||
\(884\) | −6.66410 | −0.224138 | ||||||||
\(885\) | −12.0283 | −0.404327 | ||||||||
\(886\) | 70.0992 | 2.35503 | ||||||||
\(887\) | 25.1704 | 0.845138 | 0.422569 | − | 0.906331i | \(-0.361128\pi\) | ||||
0.422569 | + | 0.906331i | \(0.361128\pi\) | |||||||
\(888\) | 23.2308 | 0.779574 | ||||||||
\(889\) | 7.58413 | 0.254364 | ||||||||
\(890\) | 11.1788 | 0.374715 | ||||||||
\(891\) | 1.55611 | 0.0521315 | ||||||||
\(892\) | 51.7896 | 1.73404 | ||||||||
\(893\) | −9.79396 | −0.327742 | ||||||||
\(894\) | −9.45450 | −0.316206 | ||||||||
\(895\) | −30.3628 | −1.01492 | ||||||||
\(896\) | −60.8388 | −2.03248 | ||||||||
\(897\) | −2.49942 | −0.0834531 | ||||||||
\(898\) | −33.8674 | −1.13017 | ||||||||
\(899\) | −3.92991 | −0.131070 | ||||||||
\(900\) | 16.0052 | 0.533508 | ||||||||
\(901\) | 4.45378 | 0.148377 | ||||||||
\(902\) | −8.70568 | −0.289868 | ||||||||
\(903\) | −12.0503 | −0.401009 | ||||||||
\(904\) | 57.7209 | 1.91977 | ||||||||
\(905\) | −15.9868 | −0.531419 | ||||||||
\(906\) | −27.8987 | −0.926874 | ||||||||
\(907\) | 34.5184 | 1.14616 | 0.573082 | − | 0.819498i | \(-0.305748\pi\) | ||||
0.573082 | + | 0.819498i | \(0.305748\pi\) | |||||||
\(908\) | 10.7873 | 0.357990 | ||||||||
\(909\) | 18.0253 | 0.597862 | ||||||||
\(910\) | −22.7388 | −0.753784 | ||||||||
\(911\) | −37.5898 | −1.24541 | −0.622704 | − | 0.782458i | \(-0.713966\pi\) | ||||
−0.622704 | + | 0.782458i | \(0.713966\pi\) | |||||||
\(912\) | 2.39490 | 0.0793032 | ||||||||
\(913\) | −0.423788 | −0.0140254 | ||||||||
\(914\) | 32.6129 | 1.07874 | ||||||||
\(915\) | 6.58230 | 0.217604 | ||||||||
\(916\) | 54.8928 | 1.81371 | ||||||||
\(917\) | −21.2794 | −0.702707 | ||||||||
\(918\) | −9.53775 | −0.314793 | ||||||||
\(919\) | 7.78236 | 0.256717 | 0.128358 | − | 0.991728i | \(-0.459029\pi\) | ||||
0.128358 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(920\) | 13.7965 | 0.454858 | ||||||||
\(921\) | −9.74029 | −0.320953 | ||||||||
\(922\) | 54.7338 | 1.80256 | ||||||||
\(923\) | 3.30783 | 0.108879 | ||||||||
\(924\) | 2.75788 | 0.0907276 | ||||||||
\(925\) | −13.8048 | −0.453899 | ||||||||
\(926\) | 26.0324 | 0.855478 | ||||||||
\(927\) | −6.42788 | −0.211119 | ||||||||
\(928\) | 3.31610 | 0.108856 | ||||||||
\(929\) | 20.6721 | 0.678231 | 0.339115 | − | 0.940745i | \(-0.389872\pi\) | ||||
0.339115 | + | 0.940745i | \(0.389872\pi\) | |||||||
\(930\) | −10.0301 | −0.328899 | ||||||||
\(931\) | −2.32690 | −0.0762612 | ||||||||
\(932\) | 36.5668 | 1.19779 | ||||||||
\(933\) | 10.9311 | 0.357867 | ||||||||
\(934\) | 37.3104 | 1.22083 | ||||||||
\(935\) | 0.626534 | 0.0204898 | ||||||||
\(936\) | −17.9806 | −0.587715 | ||||||||
\(937\) | 49.1773 | 1.60655 | 0.803277 | − | 0.595606i | \(-0.203088\pi\) | ||||
0.803277 | + | 0.595606i | \(0.203088\pi\) | |||||||
\(938\) | 25.5315 | 0.833633 | ||||||||
\(939\) | −7.93020 | −0.258792 | ||||||||
\(940\) | 44.9778 | 1.46701 | ||||||||
\(941\) | −32.3644 | −1.05505 | −0.527524 | − | 0.849540i | \(-0.676880\pi\) | ||||
−0.527524 | + | 0.849540i | \(0.676880\pi\) | |||||||
\(942\) | 27.8663 | 0.907932 | ||||||||
\(943\) | −19.8665 | −0.646942 | ||||||||
\(944\) | 20.6464 | 0.671983 | ||||||||
\(945\) | −21.1141 | −0.686843 | ||||||||
\(946\) | 4.66338 | 0.151620 | ||||||||
\(947\) | 36.6625 | 1.19137 | 0.595685 | − | 0.803218i | \(-0.296881\pi\) | ||||
0.595685 | + | 0.803218i | \(0.296881\pi\) | |||||||
\(948\) | −22.1609 | −0.719752 | ||||||||
\(949\) | −20.1296 | −0.653435 | ||||||||
\(950\) | −6.07516 | −0.197104 | ||||||||
\(951\) | −20.5472 | −0.666288 | ||||||||
\(952\) | 11.8627 | 0.384474 | ||||||||
\(953\) | −37.0481 | −1.20011 | −0.600053 | − | 0.799960i | \(-0.704854\pi\) | ||||
−0.600053 | + | 0.799960i | \(0.704854\pi\) | |||||||
\(954\) | 26.2000 | 0.848258 | ||||||||
\(955\) | −18.4224 | −0.596133 | ||||||||
\(956\) | −33.5262 | −1.08431 | ||||||||
\(957\) | −0.313315 | −0.0101281 | ||||||||
\(958\) | −62.3818 | −2.01547 | ||||||||
\(959\) | 47.7988 | 1.54350 | ||||||||
\(960\) | 14.4173 | 0.465318 | ||||||||
\(961\) | −20.8136 | −0.671406 | ||||||||
\(962\) | 33.8128 | 1.09017 | ||||||||
\(963\) | −4.93629 | −0.159070 | ||||||||
\(964\) | 82.9894 | 2.67291 | ||||||||
\(965\) | −13.6077 | −0.438046 | ||||||||
\(966\) | 9.70045 | 0.312107 | ||||||||
\(967\) | 48.9858 | 1.57528 | 0.787639 | − | 0.616138i | \(-0.211303\pi\) | ||||
0.787639 | + | 0.616138i | \(0.211303\pi\) | |||||||
\(968\) | 43.9911 | 1.41393 | ||||||||
\(969\) | 1.05946 | 0.0340347 | ||||||||
\(970\) | −65.5679 | −2.10526 | ||||||||
\(971\) | −28.5391 | −0.915865 | −0.457932 | − | 0.888987i | \(-0.651410\pi\) | ||||
−0.457932 | + | 0.888987i | \(0.651410\pi\) | |||||||
\(972\) | −56.3836 | −1.80850 | ||||||||
\(973\) | −2.38529 | −0.0764690 | ||||||||
\(974\) | −68.9875 | −2.21050 | ||||||||
\(975\) | −2.31823 | −0.0742427 | ||||||||
\(976\) | −11.2984 | −0.361653 | ||||||||
\(977\) | −13.5098 | −0.432216 | −0.216108 | − | 0.976369i | \(-0.569336\pi\) | ||||
−0.216108 | + | 0.976369i | \(0.569336\pi\) | |||||||
\(978\) | −30.0384 | −0.960522 | ||||||||
\(979\) | −0.905132 | −0.0289281 | ||||||||
\(980\) | 10.6861 | 0.341354 | ||||||||
\(981\) | 4.79489 | 0.153089 | ||||||||
\(982\) | −14.4994 | −0.462694 | ||||||||
\(983\) | 39.6418 | 1.26438 | 0.632188 | − | 0.774815i | \(-0.282157\pi\) | ||||
0.632188 | + | 0.774815i | \(0.282157\pi\) | |||||||
\(984\) | 31.0079 | 0.988496 | ||||||||
\(985\) | 15.7710 | 0.502506 | ||||||||
\(986\) | −2.93834 | −0.0935757 | ||||||||
\(987\) | 14.5047 | 0.461691 | ||||||||
\(988\) | 9.65408 | 0.307137 | ||||||||
\(989\) | 10.6419 | 0.338393 | ||||||||
\(990\) | 3.68568 | 0.117139 | ||||||||
\(991\) | 1.60031 | 0.0508355 | 0.0254178 | − | 0.999677i | \(-0.491908\pi\) | ||||
0.0254178 | + | 0.999677i | \(0.491908\pi\) | |||||||
\(992\) | −8.59540 | −0.272904 | ||||||||
\(993\) | −4.52878 | −0.143716 | ||||||||
\(994\) | −12.8380 | −0.407196 | ||||||||
\(995\) | −49.9723 | −1.58423 | ||||||||
\(996\) | 3.29100 | 0.104279 | ||||||||
\(997\) | 30.0064 | 0.950313 | 0.475157 | − | 0.879901i | \(-0.342391\pi\) | ||||
0.475157 | + | 0.879901i | \(0.342391\pi\) | |||||||
\(998\) | −92.8186 | −2.93812 | ||||||||
\(999\) | 31.3970 | 0.993356 |
(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 | 6001.2.a.b.1.11 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.11 | ✓ | 114 | 1.1 | even | 1 | trivial |