Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.54 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34450 | 1.65781 | 0.828904 | − | 0.559391i | \(-0.188965\pi\) | ||||
0.828904 | + | 0.559391i | \(0.188965\pi\) | |||||||
\(3\) | 3.18379 | 1.83816 | 0.919080 | − | 0.394072i | \(-0.128934\pi\) | ||||
0.919080 | + | 0.394072i | \(0.128934\pi\) | |||||||
\(4\) | 3.49666 | 1.74833 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 7.46437 | 3.04732 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.50891 | 1.24059 | ||||||||
\(9\) | 7.13649 | 2.37883 | ||||||||
\(10\) | −2.34450 | −0.741394 | ||||||||
\(11\) | 4.62370 | 1.39410 | 0.697049 | − | 0.717024i | \(-0.254496\pi\) | ||||
0.697049 | + | 0.717024i | \(0.254496\pi\) | |||||||
\(12\) | 11.1326 | 3.21371 | ||||||||
\(13\) | −6.35540 | −1.76267 | −0.881336 | − | 0.472490i | \(-0.843355\pi\) | ||||
−0.881336 | + | 0.472490i | \(0.843355\pi\) | |||||||
\(14\) | −2.34450 | −0.626593 | ||||||||
\(15\) | −3.18379 | −0.822050 | ||||||||
\(16\) | 1.23330 | 0.308324 | ||||||||
\(17\) | 7.67508 | 1.86148 | 0.930741 | − | 0.365680i | \(-0.119164\pi\) | ||||
0.930741 | + | 0.365680i | \(0.119164\pi\) | |||||||
\(18\) | 16.7315 | 3.94364 | ||||||||
\(19\) | 1.74190 | 0.399618 | 0.199809 | − | 0.979835i | \(-0.435968\pi\) | ||||
0.199809 | + | 0.979835i | \(0.435968\pi\) | |||||||
\(20\) | −3.49666 | −0.781876 | ||||||||
\(21\) | −3.18379 | −0.694759 | ||||||||
\(22\) | 10.8402 | 2.31115 | ||||||||
\(23\) | −2.85788 | −0.595909 | −0.297954 | − | 0.954580i | \(-0.596304\pi\) | ||||
−0.297954 | + | 0.954580i | \(0.596304\pi\) | |||||||
\(24\) | 11.1716 | 2.28039 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −14.9002 | −2.92217 | ||||||||
\(27\) | 13.1697 | 2.53451 | ||||||||
\(28\) | −3.49666 | −0.660806 | ||||||||
\(29\) | −0.436806 | −0.0811128 | −0.0405564 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405564 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(30\) | −7.46437 | −1.36280 | ||||||||
\(31\) | 6.66860 | 1.19772 | 0.598858 | − | 0.800855i | \(-0.295621\pi\) | ||||
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(32\) | −4.12635 | −0.729443 | ||||||||
\(33\) | 14.7209 | 2.56257 | ||||||||
\(34\) | 17.9942 | 3.08598 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 24.9539 | 4.15898 | ||||||||
\(37\) | 7.63350 | 1.25494 | 0.627470 | − | 0.778641i | \(-0.284091\pi\) | ||||
0.627470 | + | 0.778641i | \(0.284091\pi\) | |||||||
\(38\) | 4.08386 | 0.662490 | ||||||||
\(39\) | −20.2342 | −3.24007 | ||||||||
\(40\) | −3.50891 | −0.554807 | ||||||||
\(41\) | −6.26035 | −0.977702 | −0.488851 | − | 0.872367i | \(-0.662584\pi\) | ||||
−0.488851 | + | 0.872367i | \(0.662584\pi\) | |||||||
\(42\) | −7.46437 | −1.15178 | ||||||||
\(43\) | 3.17481 | 0.484154 | 0.242077 | − | 0.970257i | \(-0.422171\pi\) | ||||
0.242077 | + | 0.970257i | \(0.422171\pi\) | |||||||
\(44\) | 16.1675 | 2.43734 | ||||||||
\(45\) | −7.13649 | −1.06384 | ||||||||
\(46\) | −6.70028 | −0.987902 | ||||||||
\(47\) | 2.91581 | 0.425315 | 0.212658 | − | 0.977127i | \(-0.431788\pi\) | ||||
0.212658 | + | 0.977127i | \(0.431788\pi\) | |||||||
\(48\) | 3.92655 | 0.566749 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.34450 | 0.331562 | ||||||||
\(51\) | 24.4358 | 3.42170 | ||||||||
\(52\) | −22.2227 | −3.08173 | ||||||||
\(53\) | −5.81869 | −0.799259 | −0.399629 | − | 0.916677i | \(-0.630861\pi\) | ||||
−0.399629 | + | 0.916677i | \(0.630861\pi\) | |||||||
\(54\) | 30.8763 | 4.20173 | ||||||||
\(55\) | −4.62370 | −0.623460 | ||||||||
\(56\) | −3.50891 | −0.468897 | ||||||||
\(57\) | 5.54582 | 0.734562 | ||||||||
\(58\) | −1.02409 | −0.134469 | ||||||||
\(59\) | −12.2957 | −1.60077 | −0.800383 | − | 0.599489i | \(-0.795370\pi\) | ||||
−0.800383 | + | 0.599489i | \(0.795370\pi\) | |||||||
\(60\) | −11.1326 | −1.43721 | ||||||||
\(61\) | 6.19431 | 0.793100 | 0.396550 | − | 0.918013i | \(-0.370207\pi\) | ||||
0.396550 | + | 0.918013i | \(0.370207\pi\) | |||||||
\(62\) | 15.6345 | 1.98558 | ||||||||
\(63\) | −7.13649 | −0.899113 | ||||||||
\(64\) | −12.1408 | −1.51760 | ||||||||
\(65\) | 6.35540 | 0.788291 | ||||||||
\(66\) | 34.5130 | 4.24826 | ||||||||
\(67\) | 5.00419 | 0.611359 | 0.305680 | − | 0.952134i | \(-0.401116\pi\) | ||||
0.305680 | + | 0.952134i | \(0.401116\pi\) | |||||||
\(68\) | 26.8371 | 3.25448 | ||||||||
\(69\) | −9.09887 | −1.09538 | ||||||||
\(70\) | 2.34450 | 0.280221 | ||||||||
\(71\) | −9.58599 | −1.13765 | −0.568824 | − | 0.822459i | \(-0.692601\pi\) | ||||
−0.568824 | + | 0.822459i | \(0.692601\pi\) | |||||||
\(72\) | 25.0413 | 2.95114 | ||||||||
\(73\) | 11.9167 | 1.39474 | 0.697371 | − | 0.716711i | \(-0.254353\pi\) | ||||
0.697371 | + | 0.716711i | \(0.254353\pi\) | |||||||
\(74\) | 17.8967 | 2.08045 | ||||||||
\(75\) | 3.18379 | 0.367632 | ||||||||
\(76\) | 6.09081 | 0.698664 | ||||||||
\(77\) | −4.62370 | −0.526920 | ||||||||
\(78\) | −47.4391 | −5.37142 | ||||||||
\(79\) | −14.5034 | −1.63176 | −0.815878 | − | 0.578224i | \(-0.803746\pi\) | ||||
−0.815878 | + | 0.578224i | \(0.803746\pi\) | |||||||
\(80\) | −1.23330 | −0.137887 | ||||||||
\(81\) | 20.5200 | 2.28000 | ||||||||
\(82\) | −14.6774 | −1.62084 | ||||||||
\(83\) | −11.8857 | −1.30462 | −0.652311 | − | 0.757952i | \(-0.726200\pi\) | ||||
−0.652311 | + | 0.757952i | \(0.726200\pi\) | |||||||
\(84\) | −11.1326 | −1.21467 | ||||||||
\(85\) | −7.67508 | −0.832480 | ||||||||
\(86\) | 7.44332 | 0.802634 | ||||||||
\(87\) | −1.39070 | −0.149098 | ||||||||
\(88\) | 16.2241 | 1.72950 | ||||||||
\(89\) | −2.15278 | −0.228194 | −0.114097 | − | 0.993470i | \(-0.536398\pi\) | ||||
−0.114097 | + | 0.993470i | \(0.536398\pi\) | |||||||
\(90\) | −16.7315 | −1.76365 | ||||||||
\(91\) | 6.35540 | 0.666227 | ||||||||
\(92\) | −9.99302 | −1.04184 | ||||||||
\(93\) | 21.2314 | 2.20159 | ||||||||
\(94\) | 6.83611 | 0.705091 | ||||||||
\(95\) | −1.74190 | −0.178715 | ||||||||
\(96\) | −13.1374 | −1.34083 | ||||||||
\(97\) | −3.13335 | −0.318144 | −0.159072 | − | 0.987267i | \(-0.550850\pi\) | ||||
−0.159072 | + | 0.987267i | \(0.550850\pi\) | |||||||
\(98\) | 2.34450 | 0.236830 | ||||||||
\(99\) | 32.9970 | 3.31632 | ||||||||
\(100\) | 3.49666 | 0.349666 | ||||||||
\(101\) | 0.851516 | 0.0847290 | 0.0423645 | − | 0.999102i | \(-0.486511\pi\) | ||||
0.0423645 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(102\) | 57.2896 | 5.67252 | ||||||||
\(103\) | 13.5334 | 1.33349 | 0.666745 | − | 0.745286i | \(-0.267687\pi\) | ||||
0.666745 | + | 0.745286i | \(0.267687\pi\) | |||||||
\(104\) | −22.3005 | −2.18674 | ||||||||
\(105\) | 3.18379 | 0.310706 | ||||||||
\(106\) | −13.6419 | −1.32502 | ||||||||
\(107\) | −15.0392 | −1.45389 | −0.726947 | − | 0.686694i | \(-0.759061\pi\) | ||||
−0.726947 | + | 0.686694i | \(0.759061\pi\) | |||||||
\(108\) | 46.0499 | 4.43115 | ||||||||
\(109\) | −3.11964 | −0.298808 | −0.149404 | − | 0.988776i | \(-0.547735\pi\) | ||||
−0.149404 | + | 0.988776i | \(0.547735\pi\) | |||||||
\(110\) | −10.8402 | −1.03358 | ||||||||
\(111\) | 24.3034 | 2.30678 | ||||||||
\(112\) | −1.23330 | −0.116536 | ||||||||
\(113\) | 8.89667 | 0.836928 | 0.418464 | − | 0.908233i | \(-0.362569\pi\) | ||||
0.418464 | + | 0.908233i | \(0.362569\pi\) | |||||||
\(114\) | 13.0021 | 1.21776 | ||||||||
\(115\) | 2.85788 | 0.266498 | ||||||||
\(116\) | −1.52736 | −0.141812 | ||||||||
\(117\) | −45.3553 | −4.19310 | ||||||||
\(118\) | −28.8272 | −2.65376 | ||||||||
\(119\) | −7.67508 | −0.703574 | ||||||||
\(120\) | −11.1716 | −1.01982 | ||||||||
\(121\) | 10.3786 | 0.943509 | ||||||||
\(122\) | 14.5225 | 1.31481 | ||||||||
\(123\) | −19.9316 | −1.79717 | ||||||||
\(124\) | 23.3178 | 2.09400 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −16.7315 | −1.49056 | ||||||||
\(127\) | −9.71689 | −0.862234 | −0.431117 | − | 0.902296i | \(-0.641880\pi\) | ||||
−0.431117 | + | 0.902296i | \(0.641880\pi\) | |||||||
\(128\) | −20.2114 | −1.78645 | ||||||||
\(129\) | 10.1079 | 0.889952 | ||||||||
\(130\) | 14.9002 | 1.30684 | ||||||||
\(131\) | 21.9981 | 1.92199 | 0.960994 | − | 0.276571i | \(-0.0891981\pi\) | ||||
0.960994 | + | 0.276571i | \(0.0891981\pi\) | |||||||
\(132\) | 51.4738 | 4.48022 | ||||||||
\(133\) | −1.74190 | −0.151041 | ||||||||
\(134\) | 11.7323 | 1.01352 | ||||||||
\(135\) | −13.1697 | −1.13347 | ||||||||
\(136\) | 26.9311 | 2.30933 | ||||||||
\(137\) | 16.4551 | 1.40586 | 0.702929 | − | 0.711260i | \(-0.251875\pi\) | ||||
0.702929 | + | 0.711260i | \(0.251875\pi\) | |||||||
\(138\) | −21.3323 | −1.81592 | ||||||||
\(139\) | −8.30480 | −0.704404 | −0.352202 | − | 0.935924i | \(-0.614567\pi\) | ||||
−0.352202 | + | 0.935924i | \(0.614567\pi\) | |||||||
\(140\) | 3.49666 | 0.295521 | ||||||||
\(141\) | 9.28332 | 0.781797 | ||||||||
\(142\) | −22.4743 | −1.88600 | ||||||||
\(143\) | −29.3855 | −2.45734 | ||||||||
\(144\) | 8.80141 | 0.733450 | ||||||||
\(145\) | 0.436806 | 0.0362748 | ||||||||
\(146\) | 27.9386 | 2.31221 | ||||||||
\(147\) | 3.18379 | 0.262594 | ||||||||
\(148\) | 26.6917 | 2.19405 | ||||||||
\(149\) | 2.02340 | 0.165763 | 0.0828816 | − | 0.996559i | \(-0.473588\pi\) | ||||
0.0828816 | + | 0.996559i | \(0.473588\pi\) | |||||||
\(150\) | 7.46437 | 0.609463 | ||||||||
\(151\) | −1.07016 | −0.0870883 | −0.0435441 | − | 0.999052i | \(-0.513865\pi\) | ||||
−0.0435441 | + | 0.999052i | \(0.513865\pi\) | |||||||
\(152\) | 6.11214 | 0.495760 | ||||||||
\(153\) | 54.7731 | 4.42815 | ||||||||
\(154\) | −10.8402 | −0.873532 | ||||||||
\(155\) | −6.66860 | −0.535635 | ||||||||
\(156\) | −70.7522 | −5.66471 | ||||||||
\(157\) | −15.0419 | −1.20047 | −0.600237 | − | 0.799822i | \(-0.704927\pi\) | ||||
−0.600237 | + | 0.799822i | \(0.704927\pi\) | |||||||
\(158\) | −34.0031 | −2.70514 | ||||||||
\(159\) | −18.5255 | −1.46916 | ||||||||
\(160\) | 4.12635 | 0.326217 | ||||||||
\(161\) | 2.85788 | 0.225232 | ||||||||
\(162\) | 48.1090 | 3.77980 | ||||||||
\(163\) | −17.8488 | −1.39803 | −0.699014 | − | 0.715107i | \(-0.746378\pi\) | ||||
−0.699014 | + | 0.715107i | \(0.746378\pi\) | |||||||
\(164\) | −21.8903 | −1.70935 | ||||||||
\(165\) | −14.7209 | −1.14602 | ||||||||
\(166\) | −27.8659 | −2.16281 | ||||||||
\(167\) | 13.5074 | 1.04523 | 0.522616 | − | 0.852568i | \(-0.324956\pi\) | ||||
0.522616 | + | 0.852568i | \(0.324956\pi\) | |||||||
\(168\) | −11.1716 | −0.861908 | ||||||||
\(169\) | 27.3912 | 2.10701 | ||||||||
\(170\) | −17.9942 | −1.38009 | ||||||||
\(171\) | 12.4310 | 0.950623 | ||||||||
\(172\) | 11.1012 | 0.846460 | ||||||||
\(173\) | 4.93056 | 0.374864 | 0.187432 | − | 0.982278i | \(-0.439984\pi\) | ||||
0.187432 | + | 0.982278i | \(0.439984\pi\) | |||||||
\(174\) | −3.26048 | −0.247176 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 5.70239 | 0.429834 | ||||||||
\(177\) | −39.1469 | −2.94246 | ||||||||
\(178\) | −5.04719 | −0.378303 | ||||||||
\(179\) | −3.36333 | −0.251387 | −0.125694 | − | 0.992069i | \(-0.540116\pi\) | ||||
−0.125694 | + | 0.992069i | \(0.540116\pi\) | |||||||
\(180\) | −24.9539 | −1.85995 | ||||||||
\(181\) | 22.5617 | 1.67700 | 0.838500 | − | 0.544902i | \(-0.183433\pi\) | ||||
0.838500 | + | 0.544902i | \(0.183433\pi\) | |||||||
\(182\) | 14.9002 | 1.10448 | ||||||||
\(183\) | 19.7214 | 1.45784 | ||||||||
\(184\) | −10.0280 | −0.739276 | ||||||||
\(185\) | −7.63350 | −0.561226 | ||||||||
\(186\) | 49.7769 | 3.64982 | ||||||||
\(187\) | 35.4873 | 2.59509 | ||||||||
\(188\) | 10.1956 | 0.743591 | ||||||||
\(189\) | −13.1697 | −0.957954 | ||||||||
\(190\) | −4.08386 | −0.296275 | ||||||||
\(191\) | 4.12671 | 0.298598 | 0.149299 | − | 0.988792i | \(-0.452298\pi\) | ||||
0.149299 | + | 0.988792i | \(0.452298\pi\) | |||||||
\(192\) | −38.6537 | −2.78959 | ||||||||
\(193\) | −18.8951 | −1.36010 | −0.680050 | − | 0.733165i | \(-0.738042\pi\) | ||||
−0.680050 | + | 0.733165i | \(0.738042\pi\) | |||||||
\(194\) | −7.34613 | −0.527421 | ||||||||
\(195\) | 20.2342 | 1.44900 | ||||||||
\(196\) | 3.49666 | 0.249761 | ||||||||
\(197\) | −7.20048 | −0.513013 | −0.256506 | − | 0.966543i | \(-0.582571\pi\) | ||||
−0.256506 | + | 0.966543i | \(0.582571\pi\) | |||||||
\(198\) | 77.3613 | 5.49782 | ||||||||
\(199\) | 10.9880 | 0.778920 | 0.389460 | − | 0.921043i | \(-0.372662\pi\) | ||||
0.389460 | + | 0.921043i | \(0.372662\pi\) | |||||||
\(200\) | 3.50891 | 0.248117 | ||||||||
\(201\) | 15.9323 | 1.12378 | ||||||||
\(202\) | 1.99637 | 0.140464 | ||||||||
\(203\) | 0.436806 | 0.0306578 | ||||||||
\(204\) | 85.4437 | 5.98225 | ||||||||
\(205\) | 6.26035 | 0.437242 | ||||||||
\(206\) | 31.7291 | 2.21067 | ||||||||
\(207\) | −20.3952 | −1.41756 | ||||||||
\(208\) | −7.83810 | −0.543474 | ||||||||
\(209\) | 8.05400 | 0.557107 | ||||||||
\(210\) | 7.46437 | 0.515090 | ||||||||
\(211\) | −10.0405 | −0.691215 | −0.345607 | − | 0.938379i | \(-0.612327\pi\) | ||||
−0.345607 | + | 0.938379i | \(0.612327\pi\) | |||||||
\(212\) | −20.3460 | −1.39737 | ||||||||
\(213\) | −30.5197 | −2.09118 | ||||||||
\(214\) | −35.2593 | −2.41028 | ||||||||
\(215\) | −3.17481 | −0.216520 | ||||||||
\(216\) | 46.2112 | 3.14427 | ||||||||
\(217\) | −6.66860 | −0.452694 | ||||||||
\(218\) | −7.31399 | −0.495366 | ||||||||
\(219\) | 37.9401 | 2.56376 | ||||||||
\(220\) | −16.1675 | −1.09001 | ||||||||
\(221\) | −48.7782 | −3.28118 | ||||||||
\(222\) | 56.9793 | 3.82420 | ||||||||
\(223\) | −17.4845 | −1.17085 | −0.585425 | − | 0.810726i | \(-0.699073\pi\) | ||||
−0.585425 | + | 0.810726i | \(0.699073\pi\) | |||||||
\(224\) | 4.12635 | 0.275704 | ||||||||
\(225\) | 7.13649 | 0.475766 | ||||||||
\(226\) | 20.8582 | 1.38747 | ||||||||
\(227\) | 15.8550 | 1.05233 | 0.526166 | − | 0.850382i | \(-0.323629\pi\) | ||||
0.526166 | + | 0.850382i | \(0.323629\pi\) | |||||||
\(228\) | 19.3918 | 1.28426 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 6.70028 | 0.441803 | ||||||||
\(231\) | −14.7209 | −0.968562 | ||||||||
\(232\) | −1.53271 | −0.100627 | ||||||||
\(233\) | −26.8236 | −1.75727 | −0.878636 | − | 0.477491i | \(-0.841546\pi\) | ||||
−0.878636 | + | 0.477491i | \(0.841546\pi\) | |||||||
\(234\) | −106.335 | −6.95135 | ||||||||
\(235\) | −2.91581 | −0.190207 | ||||||||
\(236\) | −42.9939 | −2.79866 | ||||||||
\(237\) | −46.1756 | −2.99943 | ||||||||
\(238\) | −17.9942 | −1.16639 | ||||||||
\(239\) | −8.99690 | −0.581961 | −0.290980 | − | 0.956729i | \(-0.593981\pi\) | ||||
−0.290980 | + | 0.956729i | \(0.593981\pi\) | |||||||
\(240\) | −3.92655 | −0.253458 | ||||||||
\(241\) | 9.69859 | 0.624741 | 0.312370 | − | 0.949960i | \(-0.398877\pi\) | ||||
0.312370 | + | 0.949960i | \(0.398877\pi\) | |||||||
\(242\) | 24.3326 | 1.56416 | ||||||||
\(243\) | 25.8222 | 1.65649 | ||||||||
\(244\) | 21.6594 | 1.38660 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −46.7296 | −2.97937 | ||||||||
\(247\) | −11.0704 | −0.704396 | ||||||||
\(248\) | 23.3995 | 1.48587 | ||||||||
\(249\) | −37.8414 | −2.39810 | ||||||||
\(250\) | −2.34450 | −0.148279 | ||||||||
\(251\) | −19.8552 | −1.25325 | −0.626624 | − | 0.779322i | \(-0.715564\pi\) | ||||
−0.626624 | + | 0.779322i | \(0.715564\pi\) | |||||||
\(252\) | −24.9539 | −1.57194 | ||||||||
\(253\) | −13.2140 | −0.830755 | ||||||||
\(254\) | −22.7812 | −1.42942 | ||||||||
\(255\) | −24.4358 | −1.53023 | ||||||||
\(256\) | −23.1038 | −1.44399 | ||||||||
\(257\) | 2.34686 | 0.146393 | 0.0731965 | − | 0.997318i | \(-0.476680\pi\) | ||||
0.0731965 | + | 0.997318i | \(0.476680\pi\) | |||||||
\(258\) | 23.6979 | 1.47537 | ||||||||
\(259\) | −7.63350 | −0.474323 | ||||||||
\(260\) | 22.2227 | 1.37819 | ||||||||
\(261\) | −3.11726 | −0.192954 | ||||||||
\(262\) | 51.5745 | 3.18629 | ||||||||
\(263\) | 14.2690 | 0.879864 | 0.439932 | − | 0.898031i | \(-0.355003\pi\) | ||||
0.439932 | + | 0.898031i | \(0.355003\pi\) | |||||||
\(264\) | 51.6541 | 3.17909 | ||||||||
\(265\) | 5.81869 | 0.357439 | ||||||||
\(266\) | −4.08386 | −0.250398 | ||||||||
\(267\) | −6.85399 | −0.419458 | ||||||||
\(268\) | 17.4979 | 1.06886 | ||||||||
\(269\) | −3.29441 | −0.200864 | −0.100432 | − | 0.994944i | \(-0.532022\pi\) | ||||
−0.100432 | + | 0.994944i | \(0.532022\pi\) | |||||||
\(270\) | −30.8763 | −1.87907 | ||||||||
\(271\) | −19.1249 | −1.16175 | −0.580877 | − | 0.813991i | \(-0.697290\pi\) | ||||
−0.580877 | + | 0.813991i | \(0.697290\pi\) | |||||||
\(272\) | 9.46565 | 0.573939 | ||||||||
\(273\) | 20.2342 | 1.22463 | ||||||||
\(274\) | 38.5790 | 2.33064 | ||||||||
\(275\) | 4.62370 | 0.278820 | ||||||||
\(276\) | −31.8156 | −1.91508 | ||||||||
\(277\) | −31.8034 | −1.91088 | −0.955441 | − | 0.295181i | \(-0.904620\pi\) | ||||
−0.955441 | + | 0.295181i | \(0.904620\pi\) | |||||||
\(278\) | −19.4706 | −1.16777 | ||||||||
\(279\) | 47.5904 | 2.84916 | ||||||||
\(280\) | 3.50891 | 0.209697 | ||||||||
\(281\) | 11.2034 | 0.668341 | 0.334170 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334170 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(282\) | 21.7647 | 1.29607 | ||||||||
\(283\) | −19.2711 | −1.14555 | −0.572774 | − | 0.819713i | \(-0.694133\pi\) | ||||
−0.572774 | + | 0.819713i | \(0.694133\pi\) | |||||||
\(284\) | −33.5189 | −1.98898 | ||||||||
\(285\) | −5.54582 | −0.328506 | ||||||||
\(286\) | −68.8941 | −4.07379 | ||||||||
\(287\) | 6.26035 | 0.369537 | ||||||||
\(288\) | −29.4477 | −1.73522 | ||||||||
\(289\) | 41.9069 | 2.46511 | ||||||||
\(290\) | 1.02409 | 0.0601366 | ||||||||
\(291\) | −9.97592 | −0.584799 | ||||||||
\(292\) | 41.6685 | 2.43847 | ||||||||
\(293\) | −9.47060 | −0.553278 | −0.276639 | − | 0.960974i | \(-0.589221\pi\) | ||||
−0.276639 | + | 0.960974i | \(0.589221\pi\) | |||||||
\(294\) | 7.46437 | 0.435331 | ||||||||
\(295\) | 12.2957 | 0.715884 | ||||||||
\(296\) | 26.7852 | 1.55686 | ||||||||
\(297\) | 60.8927 | 3.53335 | ||||||||
\(298\) | 4.74385 | 0.274804 | ||||||||
\(299\) | 18.1630 | 1.05039 | ||||||||
\(300\) | 11.1326 | 0.642741 | ||||||||
\(301\) | −3.17481 | −0.182993 | ||||||||
\(302\) | −2.50898 | −0.144376 | ||||||||
\(303\) | 2.71104 | 0.155745 | ||||||||
\(304\) | 2.14827 | 0.123212 | ||||||||
\(305\) | −6.19431 | −0.354685 | ||||||||
\(306\) | 128.415 | 7.34102 | ||||||||
\(307\) | 1.81624 | 0.103658 | 0.0518292 | − | 0.998656i | \(-0.483495\pi\) | ||||
0.0518292 | + | 0.998656i | \(0.483495\pi\) | |||||||
\(308\) | −16.1675 | −0.921228 | ||||||||
\(309\) | 43.0876 | 2.45117 | ||||||||
\(310\) | −15.6345 | −0.887980 | ||||||||
\(311\) | −25.3930 | −1.43991 | −0.719953 | − | 0.694022i | \(-0.755837\pi\) | ||||
−0.719953 | + | 0.694022i | \(0.755837\pi\) | |||||||
\(312\) | −71.0000 | −4.01958 | ||||||||
\(313\) | −7.02854 | −0.397277 | −0.198638 | − | 0.980073i | \(-0.563652\pi\) | ||||
−0.198638 | + | 0.980073i | \(0.563652\pi\) | |||||||
\(314\) | −35.2657 | −1.99016 | ||||||||
\(315\) | 7.13649 | 0.402096 | ||||||||
\(316\) | −50.7133 | −2.85285 | ||||||||
\(317\) | −12.9572 | −0.727748 | −0.363874 | − | 0.931448i | \(-0.618546\pi\) | ||||
−0.363874 | + | 0.931448i | \(0.618546\pi\) | |||||||
\(318\) | −43.4329 | −2.43559 | ||||||||
\(319\) | −2.01966 | −0.113079 | ||||||||
\(320\) | 12.1408 | 0.678692 | ||||||||
\(321\) | −47.8816 | −2.67249 | ||||||||
\(322\) | 6.70028 | 0.373392 | ||||||||
\(323\) | 13.3692 | 0.743882 | ||||||||
\(324\) | 71.7514 | 3.98619 | ||||||||
\(325\) | −6.35540 | −0.352534 | ||||||||
\(326\) | −41.8465 | −2.31766 | ||||||||
\(327\) | −9.93228 | −0.549256 | ||||||||
\(328\) | −21.9670 | −1.21292 | ||||||||
\(329\) | −2.91581 | −0.160754 | ||||||||
\(330\) | −34.5130 | −1.89988 | ||||||||
\(331\) | −19.6652 | −1.08090 | −0.540450 | − | 0.841376i | \(-0.681746\pi\) | ||||
−0.540450 | + | 0.841376i | \(0.681746\pi\) | |||||||
\(332\) | −41.5601 | −2.28091 | ||||||||
\(333\) | 54.4764 | 2.98529 | ||||||||
\(334\) | 31.6679 | 1.73279 | ||||||||
\(335\) | −5.00419 | −0.273408 | ||||||||
\(336\) | −3.92655 | −0.214211 | ||||||||
\(337\) | 20.7344 | 1.12947 | 0.564737 | − | 0.825271i | \(-0.308978\pi\) | ||||
0.564737 | + | 0.825271i | \(0.308978\pi\) | |||||||
\(338\) | 64.2184 | 3.49302 | ||||||||
\(339\) | 28.3251 | 1.53841 | ||||||||
\(340\) | −26.8371 | −1.45545 | ||||||||
\(341\) | 30.8336 | 1.66973 | ||||||||
\(342\) | 29.1445 | 1.57595 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.1401 | 0.600634 | ||||||||
\(345\) | 9.09887 | 0.489867 | ||||||||
\(346\) | 11.5597 | 0.621452 | ||||||||
\(347\) | 4.30683 | 0.231203 | 0.115601 | − | 0.993296i | \(-0.463121\pi\) | ||||
0.115601 | + | 0.993296i | \(0.463121\pi\) | |||||||
\(348\) | −4.86279 | −0.260673 | ||||||||
\(349\) | −3.77394 | −0.202014 | −0.101007 | − | 0.994886i | \(-0.532207\pi\) | ||||
−0.101007 | + | 0.994886i | \(0.532207\pi\) | |||||||
\(350\) | −2.34450 | −0.125319 | ||||||||
\(351\) | −83.6987 | −4.46751 | ||||||||
\(352\) | −19.0790 | −1.01692 | ||||||||
\(353\) | 0.549800 | 0.0292629 | 0.0146315 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146315 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(354\) | −91.7798 | −4.87804 | ||||||||
\(355\) | 9.58599 | 0.508771 | ||||||||
\(356\) | −7.52754 | −0.398959 | ||||||||
\(357\) | −24.4358 | −1.29328 | ||||||||
\(358\) | −7.88532 | −0.416752 | ||||||||
\(359\) | −27.4370 | −1.44807 | −0.724033 | − | 0.689765i | \(-0.757714\pi\) | ||||
−0.724033 | + | 0.689765i | \(0.757714\pi\) | |||||||
\(360\) | −25.0413 | −1.31979 | ||||||||
\(361\) | −15.9658 | −0.840305 | ||||||||
\(362\) | 52.8959 | 2.78014 | ||||||||
\(363\) | 33.0432 | 1.73432 | ||||||||
\(364\) | 22.2227 | 1.16478 | ||||||||
\(365\) | −11.9167 | −0.623747 | ||||||||
\(366\) | 46.2366 | 2.41683 | ||||||||
\(367\) | 19.8255 | 1.03488 | 0.517442 | − | 0.855718i | \(-0.326884\pi\) | ||||
0.517442 | + | 0.855718i | \(0.326884\pi\) | |||||||
\(368\) | −3.52461 | −0.183733 | ||||||||
\(369\) | −44.6769 | −2.32579 | ||||||||
\(370\) | −17.8967 | −0.930405 | ||||||||
\(371\) | 5.81869 | 0.302091 | ||||||||
\(372\) | 74.2389 | 3.84911 | ||||||||
\(373\) | −5.02476 | −0.260172 | −0.130086 | − | 0.991503i | \(-0.541525\pi\) | ||||
−0.130086 | + | 0.991503i | \(0.541525\pi\) | |||||||
\(374\) | 83.1998 | 4.30216 | ||||||||
\(375\) | −3.18379 | −0.164410 | ||||||||
\(376\) | 10.2313 | 0.527640 | ||||||||
\(377\) | 2.77608 | 0.142975 | ||||||||
\(378\) | −30.8763 | −1.58810 | ||||||||
\(379\) | 10.1911 | 0.523484 | 0.261742 | − | 0.965138i | \(-0.415703\pi\) | ||||
0.261742 | + | 0.965138i | \(0.415703\pi\) | |||||||
\(380\) | −6.09081 | −0.312452 | ||||||||
\(381\) | −30.9365 | −1.58492 | ||||||||
\(382\) | 9.67504 | 0.495018 | ||||||||
\(383\) | 14.5669 | 0.744333 | 0.372167 | − | 0.928166i | \(-0.378615\pi\) | ||||
0.372167 | + | 0.928166i | \(0.378615\pi\) | |||||||
\(384\) | −64.3486 | −3.28378 | ||||||||
\(385\) | 4.62370 | 0.235646 | ||||||||
\(386\) | −44.2995 | −2.25479 | ||||||||
\(387\) | 22.6570 | 1.15172 | ||||||||
\(388\) | −10.9563 | −0.556220 | ||||||||
\(389\) | −22.9517 | −1.16370 | −0.581849 | − | 0.813297i | \(-0.697671\pi\) | ||||
−0.581849 | + | 0.813297i | \(0.697671\pi\) | |||||||
\(390\) | 47.4391 | 2.40217 | ||||||||
\(391\) | −21.9344 | −1.10927 | ||||||||
\(392\) | 3.50891 | 0.177226 | ||||||||
\(393\) | 70.0374 | 3.53292 | ||||||||
\(394\) | −16.8815 | −0.850477 | ||||||||
\(395\) | 14.5034 | 0.729743 | ||||||||
\(396\) | 115.379 | 5.79802 | ||||||||
\(397\) | 10.5328 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(398\) | 25.7614 | 1.29130 | ||||||||
\(399\) | −5.54582 | −0.277638 | ||||||||
\(400\) | 1.23330 | 0.0616648 | ||||||||
\(401\) | −18.8976 | −0.943699 | −0.471850 | − | 0.881679i | \(-0.656414\pi\) | ||||
−0.471850 | + | 0.881679i | \(0.656414\pi\) | |||||||
\(402\) | 37.3531 | 1.86300 | ||||||||
\(403\) | −42.3816 | −2.11118 | ||||||||
\(404\) | 2.97746 | 0.148134 | ||||||||
\(405\) | −20.5200 | −1.01965 | ||||||||
\(406\) | 1.02409 | 0.0508247 | ||||||||
\(407\) | 35.2950 | 1.74951 | ||||||||
\(408\) | 85.7430 | 4.24491 | ||||||||
\(409\) | −32.4892 | −1.60649 | −0.803243 | − | 0.595651i | \(-0.796894\pi\) | ||||
−0.803243 | + | 0.595651i | \(0.796894\pi\) | |||||||
\(410\) | 14.6774 | 0.724863 | ||||||||
\(411\) | 52.3896 | 2.58419 | ||||||||
\(412\) | 47.3218 | 2.33138 | ||||||||
\(413\) | 12.2957 | 0.605033 | ||||||||
\(414\) | −47.8165 | −2.35005 | ||||||||
\(415\) | 11.8857 | 0.583444 | ||||||||
\(416\) | 26.2246 | 1.28577 | ||||||||
\(417\) | −26.4407 | −1.29481 | ||||||||
\(418\) | 18.8826 | 0.923576 | ||||||||
\(419\) | −34.3633 | −1.67876 | −0.839378 | − | 0.543549i | \(-0.817080\pi\) | ||||
−0.839378 | + | 0.543549i | \(0.817080\pi\) | |||||||
\(420\) | 11.1326 | 0.543215 | ||||||||
\(421\) | 27.3474 | 1.33283 | 0.666416 | − | 0.745580i | \(-0.267828\pi\) | ||||
0.666416 | + | 0.745580i | \(0.267828\pi\) | |||||||
\(422\) | −23.5398 | −1.14590 | ||||||||
\(423\) | 20.8087 | 1.01175 | ||||||||
\(424\) | −20.4172 | −0.991549 | ||||||||
\(425\) | 7.67508 | 0.372296 | ||||||||
\(426\) | −71.5533 | −3.46677 | ||||||||
\(427\) | −6.19431 | −0.299764 | ||||||||
\(428\) | −52.5869 | −2.54188 | ||||||||
\(429\) | −93.5570 | −4.51698 | ||||||||
\(430\) | −7.44332 | −0.358949 | ||||||||
\(431\) | −30.5338 | −1.47076 | −0.735381 | − | 0.677653i | \(-0.762997\pi\) | ||||
−0.735381 | + | 0.677653i | \(0.762997\pi\) | |||||||
\(432\) | 16.2421 | 0.781450 | ||||||||
\(433\) | 24.8658 | 1.19497 | 0.597486 | − | 0.801879i | \(-0.296166\pi\) | ||||
0.597486 | + | 0.801879i | \(0.296166\pi\) | |||||||
\(434\) | −15.6345 | −0.750480 | ||||||||
\(435\) | 1.39070 | 0.0666788 | ||||||||
\(436\) | −10.9083 | −0.522414 | ||||||||
\(437\) | −4.97812 | −0.238136 | ||||||||
\(438\) | 88.9504 | 4.25022 | ||||||||
\(439\) | 3.57471 | 0.170612 | 0.0853059 | − | 0.996355i | \(-0.472813\pi\) | ||||
0.0853059 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(440\) | −16.2241 | −0.773455 | ||||||||
\(441\) | 7.13649 | 0.339833 | ||||||||
\(442\) | −114.360 | −5.43957 | ||||||||
\(443\) | −16.7373 | −0.795212 | −0.397606 | − | 0.917556i | \(-0.630159\pi\) | ||||
−0.397606 | + | 0.917556i | \(0.630159\pi\) | |||||||
\(444\) | 84.9808 | 4.03301 | ||||||||
\(445\) | 2.15278 | 0.102052 | ||||||||
\(446\) | −40.9924 | −1.94105 | ||||||||
\(447\) | 6.44207 | 0.304699 | ||||||||
\(448\) | 12.1408 | 0.573599 | ||||||||
\(449\) | 38.2407 | 1.80469 | 0.902345 | − | 0.431014i | \(-0.141844\pi\) | ||||
0.902345 | + | 0.431014i | \(0.141844\pi\) | |||||||
\(450\) | 16.7315 | 0.788729 | ||||||||
\(451\) | −28.9460 | −1.36301 | ||||||||
\(452\) | 31.1086 | 1.46323 | ||||||||
\(453\) | −3.40716 | −0.160082 | ||||||||
\(454\) | 37.1719 | 1.74456 | ||||||||
\(455\) | −6.35540 | −0.297946 | ||||||||
\(456\) | 19.4598 | 0.911287 | ||||||||
\(457\) | 4.23337 | 0.198029 | 0.0990144 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990144 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(458\) | 2.34450 | 0.109551 | ||||||||
\(459\) | 101.078 | 4.71794 | ||||||||
\(460\) | 9.99302 | 0.465927 | ||||||||
\(461\) | −3.07057 | −0.143011 | −0.0715054 | − | 0.997440i | \(-0.522780\pi\) | ||||
−0.0715054 | + | 0.997440i | \(0.522780\pi\) | |||||||
\(462\) | −34.5130 | −1.60569 | ||||||||
\(463\) | 4.29879 | 0.199781 | 0.0998907 | − | 0.994998i | \(-0.468151\pi\) | ||||
0.0998907 | + | 0.994998i | \(0.468151\pi\) | |||||||
\(464\) | −0.538711 | −0.0250090 | ||||||||
\(465\) | −21.2314 | −0.984582 | ||||||||
\(466\) | −62.8878 | −2.91322 | ||||||||
\(467\) | −25.9976 | −1.20302 | −0.601512 | − | 0.798863i | \(-0.705435\pi\) | ||||
−0.601512 | + | 0.798863i | \(0.705435\pi\) | |||||||
\(468\) | −158.592 | −7.33091 | ||||||||
\(469\) | −5.00419 | −0.231072 | ||||||||
\(470\) | −6.83611 | −0.315326 | ||||||||
\(471\) | −47.8902 | −2.20666 | ||||||||
\(472\) | −43.1445 | −1.98589 | ||||||||
\(473\) | 14.6794 | 0.674958 | ||||||||
\(474\) | −108.258 | −4.97247 | ||||||||
\(475\) | 1.74190 | 0.0799236 | ||||||||
\(476\) | −26.8371 | −1.23008 | ||||||||
\(477\) | −41.5250 | −1.90130 | ||||||||
\(478\) | −21.0932 | −0.964780 | ||||||||
\(479\) | 32.0979 | 1.46659 | 0.733296 | − | 0.679909i | \(-0.237981\pi\) | ||||
0.733296 | + | 0.679909i | \(0.237981\pi\) | |||||||
\(480\) | 13.1374 | 0.599638 | ||||||||
\(481\) | −48.5140 | −2.21205 | ||||||||
\(482\) | 22.7383 | 1.03570 | ||||||||
\(483\) | 9.09887 | 0.414013 | ||||||||
\(484\) | 36.2904 | 1.64956 | ||||||||
\(485\) | 3.13335 | 0.142278 | ||||||||
\(486\) | 60.5400 | 2.74615 | ||||||||
\(487\) | −16.7925 | −0.760939 | −0.380470 | − | 0.924793i | \(-0.624238\pi\) | ||||
−0.380470 | + | 0.924793i | \(0.624238\pi\) | |||||||
\(488\) | 21.7353 | 0.983909 | ||||||||
\(489\) | −56.8269 | −2.56980 | ||||||||
\(490\) | −2.34450 | −0.105913 | ||||||||
\(491\) | −2.17755 | −0.0982715 | −0.0491358 | − | 0.998792i | \(-0.515647\pi\) | ||||
−0.0491358 | + | 0.998792i | \(0.515647\pi\) | |||||||
\(492\) | −69.6940 | −3.14205 | ||||||||
\(493\) | −3.35252 | −0.150990 | ||||||||
\(494\) | −25.9546 | −1.16775 | ||||||||
\(495\) | −32.9970 | −1.48310 | ||||||||
\(496\) | 8.22436 | 0.369285 | ||||||||
\(497\) | 9.58599 | 0.429990 | ||||||||
\(498\) | −88.7190 | −3.97559 | ||||||||
\(499\) | 1.49228 | 0.0668038 | 0.0334019 | − | 0.999442i | \(-0.489366\pi\) | ||||
0.0334019 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(500\) | −3.49666 | −0.156375 | ||||||||
\(501\) | 43.0045 | 1.92130 | ||||||||
\(502\) | −46.5504 | −2.07765 | ||||||||
\(503\) | 7.02270 | 0.313127 | 0.156563 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156563 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(504\) | −25.0413 | −1.11543 | ||||||||
\(505\) | −0.851516 | −0.0378920 | ||||||||
\(506\) | −30.9801 | −1.37723 | ||||||||
\(507\) | 87.2075 | 3.87302 | ||||||||
\(508\) | −33.9766 | −1.50747 | ||||||||
\(509\) | 35.6581 | 1.58052 | 0.790260 | − | 0.612772i | \(-0.209946\pi\) | ||||
0.790260 | + | 0.612772i | \(0.209946\pi\) | |||||||
\(510\) | −57.2896 | −2.53683 | ||||||||
\(511\) | −11.9167 | −0.527163 | ||||||||
\(512\) | −13.7441 | −0.607407 | ||||||||
\(513\) | 22.9402 | 1.01284 | ||||||||
\(514\) | 5.50220 | 0.242692 | ||||||||
\(515\) | −13.5334 | −0.596355 | ||||||||
\(516\) | 35.3439 | 1.55593 | ||||||||
\(517\) | 13.4818 | 0.592931 | ||||||||
\(518\) | −17.8967 | −0.786336 | ||||||||
\(519\) | 15.6978 | 0.689059 | ||||||||
\(520\) | 22.3005 | 0.977942 | ||||||||
\(521\) | −13.5613 | −0.594131 | −0.297066 | − | 0.954857i | \(-0.596008\pi\) | ||||
−0.297066 | + | 0.954857i | \(0.596008\pi\) | |||||||
\(522\) | −7.30840 | −0.319880 | ||||||||
\(523\) | −16.1682 | −0.706988 | −0.353494 | − | 0.935437i | \(-0.615006\pi\) | ||||
−0.353494 | + | 0.935437i | \(0.615006\pi\) | |||||||
\(524\) | 76.9200 | 3.36026 | ||||||||
\(525\) | −3.18379 | −0.138952 | ||||||||
\(526\) | 33.4536 | 1.45865 | ||||||||
\(527\) | 51.1821 | 2.22953 | ||||||||
\(528\) | 18.1552 | 0.790103 | ||||||||
\(529\) | −14.8325 | −0.644893 | ||||||||
\(530\) | 13.6419 | 0.592566 | ||||||||
\(531\) | −87.7482 | −3.80795 | ||||||||
\(532\) | −6.09081 | −0.264070 | ||||||||
\(533\) | 39.7871 | 1.72337 | ||||||||
\(534\) | −16.0692 | −0.695380 | ||||||||
\(535\) | 15.0392 | 0.650201 | ||||||||
\(536\) | 17.5592 | 0.758443 | ||||||||
\(537\) | −10.7081 | −0.462090 | ||||||||
\(538\) | −7.72372 | −0.332993 | ||||||||
\(539\) | 4.62370 | 0.199157 | ||||||||
\(540\) | −46.0499 | −1.98167 | ||||||||
\(541\) | 10.6742 | 0.458921 | 0.229461 | − | 0.973318i | \(-0.426304\pi\) | ||||
0.229461 | + | 0.973318i | \(0.426304\pi\) | |||||||
\(542\) | −44.8382 | −1.92597 | ||||||||
\(543\) | 71.8317 | 3.08259 | ||||||||
\(544\) | −31.6701 | −1.35784 | ||||||||
\(545\) | 3.11964 | 0.133631 | ||||||||
\(546\) | 47.4391 | 2.03020 | ||||||||
\(547\) | −18.7787 | −0.802918 | −0.401459 | − | 0.915877i | \(-0.631497\pi\) | ||||
−0.401459 | + | 0.915877i | \(0.631497\pi\) | |||||||
\(548\) | 57.5380 | 2.45790 | ||||||||
\(549\) | 44.2056 | 1.88665 | ||||||||
\(550\) | 10.8402 | 0.462229 | ||||||||
\(551\) | −0.760870 | −0.0324142 | ||||||||
\(552\) | −31.9271 | −1.35891 | ||||||||
\(553\) | 14.5034 | 0.616746 | ||||||||
\(554\) | −74.5630 | −3.16788 | ||||||||
\(555\) | −24.3034 | −1.03162 | ||||||||
\(556\) | −29.0390 | −1.23153 | ||||||||
\(557\) | 35.3903 | 1.49954 | 0.749769 | − | 0.661700i | \(-0.230165\pi\) | ||||
0.749769 | + | 0.661700i | \(0.230165\pi\) | |||||||
\(558\) | 111.575 | 4.72336 | ||||||||
\(559\) | −20.1772 | −0.853404 | ||||||||
\(560\) | 1.23330 | 0.0521163 | ||||||||
\(561\) | 112.984 | 4.77018 | ||||||||
\(562\) | 26.2664 | 1.10798 | ||||||||
\(563\) | 15.4970 | 0.653119 | 0.326560 | − | 0.945177i | \(-0.394111\pi\) | ||||
0.326560 | + | 0.945177i | \(0.394111\pi\) | |||||||
\(564\) | 32.4606 | 1.36684 | ||||||||
\(565\) | −8.89667 | −0.374286 | ||||||||
\(566\) | −45.1810 | −1.89910 | ||||||||
\(567\) | −20.5200 | −0.861759 | ||||||||
\(568\) | −33.6363 | −1.41135 | ||||||||
\(569\) | −10.5479 | −0.442191 | −0.221095 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221095 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(570\) | −13.0021 | −0.544600 | ||||||||
\(571\) | 15.9870 | 0.669034 | 0.334517 | − | 0.942390i | \(-0.391427\pi\) | ||||
0.334517 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(572\) | −102.751 | −4.29623 | ||||||||
\(573\) | 13.1385 | 0.548871 | ||||||||
\(574\) | 14.6774 | 0.612621 | ||||||||
\(575\) | −2.85788 | −0.119182 | ||||||||
\(576\) | −86.6427 | −3.61011 | ||||||||
\(577\) | 8.13214 | 0.338546 | 0.169273 | − | 0.985569i | \(-0.445858\pi\) | ||||
0.169273 | + | 0.985569i | \(0.445858\pi\) | |||||||
\(578\) | 98.2505 | 4.08668 | ||||||||
\(579\) | −60.1580 | −2.50008 | ||||||||
\(580\) | 1.52736 | 0.0634202 | ||||||||
\(581\) | 11.8857 | 0.493101 | ||||||||
\(582\) | −23.3885 | −0.969484 | ||||||||
\(583\) | −26.9039 | −1.11424 | ||||||||
\(584\) | 41.8145 | 1.73030 | ||||||||
\(585\) | 45.3553 | 1.87521 | ||||||||
\(586\) | −22.2038 | −0.917229 | ||||||||
\(587\) | 44.4834 | 1.83603 | 0.918014 | − | 0.396548i | \(-0.129792\pi\) | ||||
0.918014 | + | 0.396548i | \(0.129792\pi\) | |||||||
\(588\) | 11.1326 | 0.459101 | ||||||||
\(589\) | 11.6160 | 0.478629 | ||||||||
\(590\) | 28.8272 | 1.18680 | ||||||||
\(591\) | −22.9248 | −0.942999 | ||||||||
\(592\) | 9.41437 | 0.386928 | ||||||||
\(593\) | 31.8482 | 1.30785 | 0.653925 | − | 0.756559i | \(-0.273121\pi\) | ||||
0.653925 | + | 0.756559i | \(0.273121\pi\) | |||||||
\(594\) | 142.763 | 5.85762 | ||||||||
\(595\) | 7.67508 | 0.314648 | ||||||||
\(596\) | 7.07513 | 0.289809 | ||||||||
\(597\) | 34.9835 | 1.43178 | ||||||||
\(598\) | 42.5830 | 1.74135 | ||||||||
\(599\) | 25.9005 | 1.05827 | 0.529133 | − | 0.848539i | \(-0.322517\pi\) | ||||
0.529133 | + | 0.848539i | \(0.322517\pi\) | |||||||
\(600\) | 11.1716 | 0.456079 | ||||||||
\(601\) | −1.11544 | −0.0454997 | −0.0227499 | − | 0.999741i | \(-0.507242\pi\) | ||||
−0.0227499 | + | 0.999741i | \(0.507242\pi\) | |||||||
\(602\) | −7.44332 | −0.303367 | ||||||||
\(603\) | 35.7123 | 1.45432 | ||||||||
\(604\) | −3.74198 | −0.152259 | ||||||||
\(605\) | −10.3786 | −0.421950 | ||||||||
\(606\) | 6.35603 | 0.258196 | ||||||||
\(607\) | 14.8404 | 0.602354 | 0.301177 | − | 0.953568i | \(-0.402621\pi\) | ||||
0.301177 | + | 0.953568i | \(0.402621\pi\) | |||||||
\(608\) | −7.18767 | −0.291499 | ||||||||
\(609\) | 1.39070 | 0.0563538 | ||||||||
\(610\) | −14.5225 | −0.588000 | ||||||||
\(611\) | −18.5312 | −0.749691 | ||||||||
\(612\) | 191.523 | 7.74185 | ||||||||
\(613\) | −29.1535 | −1.17750 | −0.588750 | − | 0.808315i | \(-0.700380\pi\) | ||||
−0.588750 | + | 0.808315i | \(0.700380\pi\) | |||||||
\(614\) | 4.25817 | 0.171846 | ||||||||
\(615\) | 19.9316 | 0.803720 | ||||||||
\(616\) | −16.2241 | −0.653689 | ||||||||
\(617\) | 7.88980 | 0.317631 | 0.158816 | − | 0.987308i | \(-0.449232\pi\) | ||||
0.158816 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(618\) | 101.019 | 4.06356 | ||||||||
\(619\) | −17.0250 | −0.684293 | −0.342146 | − | 0.939647i | \(-0.611154\pi\) | ||||
−0.342146 | + | 0.939647i | \(0.611154\pi\) | |||||||
\(620\) | −23.3178 | −0.936466 | ||||||||
\(621\) | −37.6374 | −1.51034 | ||||||||
\(622\) | −59.5338 | −2.38709 | ||||||||
\(623\) | 2.15278 | 0.0862494 | ||||||||
\(624\) | −24.9548 | −0.998992 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −16.4784 | −0.658609 | ||||||||
\(627\) | 25.6422 | 1.02405 | ||||||||
\(628\) | −52.5964 | −2.09882 | ||||||||
\(629\) | 58.5878 | 2.33605 | ||||||||
\(630\) | 16.7315 | 0.666597 | ||||||||
\(631\) | 48.1342 | 1.91619 | 0.958097 | − | 0.286444i | \(-0.0924733\pi\) | ||||
0.958097 | + | 0.286444i | \(0.0924733\pi\) | |||||||
\(632\) | −50.8909 | −2.02433 | ||||||||
\(633\) | −31.9667 | −1.27056 | ||||||||
\(634\) | −30.3781 | −1.20647 | ||||||||
\(635\) | 9.71689 | 0.385603 | ||||||||
\(636\) | −64.7772 | −2.56858 | ||||||||
\(637\) | −6.35540 | −0.251810 | ||||||||
\(638\) | −4.73508 | −0.187464 | ||||||||
\(639\) | −68.4103 | −2.70627 | ||||||||
\(640\) | 20.2114 | 0.798924 | ||||||||
\(641\) | 30.8315 | 1.21777 | 0.608885 | − | 0.793259i | \(-0.291617\pi\) | ||||
0.608885 | + | 0.793259i | \(0.291617\pi\) | |||||||
\(642\) | −112.258 | −4.43047 | ||||||||
\(643\) | −6.30659 | −0.248708 | −0.124354 | − | 0.992238i | \(-0.539686\pi\) | ||||
−0.124354 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(644\) | 9.99302 | 0.393780 | ||||||||
\(645\) | −10.1079 | −0.397998 | ||||||||
\(646\) | 31.3440 | 1.23321 | ||||||||
\(647\) | −12.0561 | −0.473974 | −0.236987 | − | 0.971513i | \(-0.576160\pi\) | ||||
−0.236987 | + | 0.971513i | \(0.576160\pi\) | |||||||
\(648\) | 72.0027 | 2.82853 | ||||||||
\(649\) | −56.8517 | −2.23162 | ||||||||
\(650\) | −14.9002 | −0.584434 | ||||||||
\(651\) | −21.2314 | −0.832124 | ||||||||
\(652\) | −62.4113 | −2.44421 | ||||||||
\(653\) | 14.3360 | 0.561012 | 0.280506 | − | 0.959852i | \(-0.409498\pi\) | ||||
0.280506 | + | 0.959852i | \(0.409498\pi\) | |||||||
\(654\) | −23.2862 | −0.910562 | ||||||||
\(655\) | −21.9981 | −0.859539 | ||||||||
\(656\) | −7.72087 | −0.301449 | ||||||||
\(657\) | 85.0432 | 3.31785 | ||||||||
\(658\) | −6.83611 | −0.266499 | ||||||||
\(659\) | 37.1853 | 1.44853 | 0.724267 | − | 0.689520i | \(-0.242178\pi\) | ||||
0.724267 | + | 0.689520i | \(0.242178\pi\) | |||||||
\(660\) | −51.4738 | −2.00362 | ||||||||
\(661\) | −46.3963 | −1.80461 | −0.902303 | − | 0.431102i | \(-0.858125\pi\) | ||||
−0.902303 | + | 0.431102i | \(0.858125\pi\) | |||||||
\(662\) | −46.1051 | −1.79192 | ||||||||
\(663\) | −155.299 | −6.03133 | ||||||||
\(664\) | −41.7057 | −1.61849 | ||||||||
\(665\) | 1.74190 | 0.0675478 | ||||||||
\(666\) | 127.720 | 4.94903 | ||||||||
\(667\) | 1.24834 | 0.0483358 | ||||||||
\(668\) | 47.2306 | 1.82741 | ||||||||
\(669\) | −55.6670 | −2.15221 | ||||||||
\(670\) | −11.7323 | −0.453258 | ||||||||
\(671\) | 28.6406 | 1.10566 | ||||||||
\(672\) | 13.1374 | 0.506787 | ||||||||
\(673\) | 17.1050 | 0.659349 | 0.329674 | − | 0.944095i | \(-0.393061\pi\) | ||||
0.329674 | + | 0.944095i | \(0.393061\pi\) | |||||||
\(674\) | 48.6116 | 1.87245 | ||||||||
\(675\) | 13.1697 | 0.506902 | ||||||||
\(676\) | 95.7775 | 3.68375 | ||||||||
\(677\) | 40.7373 | 1.56566 | 0.782832 | − | 0.622233i | \(-0.213775\pi\) | ||||
0.782832 | + | 0.622233i | \(0.213775\pi\) | |||||||
\(678\) | 66.4080 | 2.55038 | ||||||||
\(679\) | 3.13335 | 0.120247 | ||||||||
\(680\) | −26.9311 | −1.03276 | ||||||||
\(681\) | 50.4789 | 1.93435 | ||||||||
\(682\) | 72.2892 | 2.76810 | ||||||||
\(683\) | 17.6571 | 0.675631 | 0.337815 | − | 0.941212i | \(-0.390312\pi\) | ||||
0.337815 | + | 0.941212i | \(0.390312\pi\) | |||||||
\(684\) | 43.4670 | 1.66200 | ||||||||
\(685\) | −16.4551 | −0.628719 | ||||||||
\(686\) | −2.34450 | −0.0895132 | ||||||||
\(687\) | 3.18379 | 0.121469 | ||||||||
\(688\) | 3.91548 | 0.149276 | ||||||||
\(689\) | 36.9801 | 1.40883 | ||||||||
\(690\) | 21.3323 | 0.812105 | ||||||||
\(691\) | 46.4122 | 1.76560 | 0.882802 | − | 0.469746i | \(-0.155654\pi\) | ||||
0.882802 | + | 0.469746i | \(0.155654\pi\) | |||||||
\(692\) | 17.2405 | 0.655385 | ||||||||
\(693\) | −32.9970 | −1.25345 | ||||||||
\(694\) | 10.0973 | 0.383290 | ||||||||
\(695\) | 8.30480 | 0.315019 | ||||||||
\(696\) | −4.87982 | −0.184969 | ||||||||
\(697\) | −48.0487 | −1.81997 | ||||||||
\(698\) | −8.84799 | −0.334901 | ||||||||
\(699\) | −85.4006 | −3.23015 | ||||||||
\(700\) | −3.49666 | −0.132161 | ||||||||
\(701\) | −34.4033 | −1.29940 | −0.649698 | − | 0.760192i | \(-0.725105\pi\) | ||||
−0.649698 | + | 0.760192i | \(0.725105\pi\) | |||||||
\(702\) | −196.231 | −7.40627 | ||||||||
\(703\) | 13.2968 | 0.501497 | ||||||||
\(704\) | −56.1354 | −2.11568 | ||||||||
\(705\) | −9.28332 | −0.349630 | ||||||||
\(706\) | 1.28900 | 0.0485123 | ||||||||
\(707\) | −0.851516 | −0.0320245 | ||||||||
\(708\) | −136.883 | −5.14439 | ||||||||
\(709\) | 37.8527 | 1.42159 | 0.710794 | − | 0.703400i | \(-0.248336\pi\) | ||||
0.710794 | + | 0.703400i | \(0.248336\pi\) | |||||||
\(710\) | 22.4743 | 0.843445 | ||||||||
\(711\) | −103.503 | −3.88167 | ||||||||
\(712\) | −7.55391 | −0.283095 | ||||||||
\(713\) | −19.0580 | −0.713729 | ||||||||
\(714\) | −57.2896 | −2.14401 | ||||||||
\(715\) | 29.3855 | 1.09895 | ||||||||
\(716\) | −11.7604 | −0.439508 | ||||||||
\(717\) | −28.6442 | −1.06974 | ||||||||
\(718\) | −64.3258 | −2.40062 | ||||||||
\(719\) | 15.0869 | 0.562646 | 0.281323 | − | 0.959613i | \(-0.409227\pi\) | ||||
0.281323 | + | 0.959613i | \(0.409227\pi\) | |||||||
\(720\) | −8.80141 | −0.328009 | ||||||||
\(721\) | −13.5334 | −0.504012 | ||||||||
\(722\) | −37.4317 | −1.39307 | ||||||||
\(723\) | 30.8782 | 1.14837 | ||||||||
\(724\) | 78.8906 | 2.93195 | ||||||||
\(725\) | −0.436806 | −0.0162226 | ||||||||
\(726\) | 77.4697 | 2.87517 | ||||||||
\(727\) | −13.6374 | −0.505782 | −0.252891 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252891 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(728\) | 22.3005 | 0.826512 | ||||||||
\(729\) | 20.6523 | 0.764901 | ||||||||
\(730\) | −27.9386 | −1.03405 | ||||||||
\(731\) | 24.3669 | 0.901243 | ||||||||
\(732\) | 68.9588 | 2.54879 | ||||||||
\(733\) | −49.6747 | −1.83478 | −0.917388 | − | 0.397995i | \(-0.869706\pi\) | ||||
−0.917388 | + | 0.397995i | \(0.869706\pi\) | |||||||
\(734\) | 46.4808 | 1.71564 | ||||||||
\(735\) | −3.18379 | −0.117436 | ||||||||
\(736\) | 11.7926 | 0.434681 | ||||||||
\(737\) | 23.1379 | 0.852295 | ||||||||
\(738\) | −104.745 | −3.85571 | ||||||||
\(739\) | −0.419193 | −0.0154203 | −0.00771013 | − | 0.999970i | \(-0.502454\pi\) | ||||
−0.00771013 | + | 0.999970i | \(0.502454\pi\) | |||||||
\(740\) | −26.6917 | −0.981208 | ||||||||
\(741\) | −35.2459 | −1.29479 | ||||||||
\(742\) | 13.6419 | 0.500810 | ||||||||
\(743\) | −36.8714 | −1.35268 | −0.676341 | − | 0.736589i | \(-0.736435\pi\) | ||||
−0.676341 | + | 0.736589i | \(0.736435\pi\) | |||||||
\(744\) | 74.4989 | 2.73126 | ||||||||
\(745\) | −2.02340 | −0.0741316 | ||||||||
\(746\) | −11.7805 | −0.431316 | ||||||||
\(747\) | −84.8219 | −3.10347 | ||||||||
\(748\) | 124.087 | 4.53706 | ||||||||
\(749\) | 15.0392 | 0.549520 | ||||||||
\(750\) | −7.46437 | −0.272560 | ||||||||
\(751\) | 41.9205 | 1.52970 | 0.764850 | − | 0.644208i | \(-0.222813\pi\) | ||||
0.764850 | + | 0.644208i | \(0.222813\pi\) | |||||||
\(752\) | 3.59606 | 0.131135 | ||||||||
\(753\) | −63.2147 | −2.30367 | ||||||||
\(754\) | 6.50850 | 0.237026 | ||||||||
\(755\) | 1.07016 | 0.0389471 | ||||||||
\(756\) | −46.0499 | −1.67482 | ||||||||
\(757\) | −18.5801 | −0.675305 | −0.337652 | − | 0.941271i | \(-0.609633\pi\) | ||||
−0.337652 | + | 0.941271i | \(0.609633\pi\) | |||||||
\(758\) | 23.8931 | 0.867836 | ||||||||
\(759\) | −42.0704 | −1.52706 | ||||||||
\(760\) | −6.11214 | −0.221711 | ||||||||
\(761\) | 29.5000 | 1.06937 | 0.534687 | − | 0.845050i | \(-0.320429\pi\) | ||||
0.534687 | + | 0.845050i | \(0.320429\pi\) | |||||||
\(762\) | −72.5304 | −2.62750 | ||||||||
\(763\) | 3.11964 | 0.112939 | ||||||||
\(764\) | 14.4297 | 0.522047 | ||||||||
\(765\) | −54.7731 | −1.98033 | ||||||||
\(766\) | 34.1520 | 1.23396 | ||||||||
\(767\) | 78.1442 | 2.82162 | ||||||||
\(768\) | −73.5576 | −2.65428 | ||||||||
\(769\) | −41.4193 | −1.49362 | −0.746809 | − | 0.665039i | \(-0.768415\pi\) | ||||
−0.746809 | + | 0.665039i | \(0.768415\pi\) | |||||||
\(770\) | 10.8402 | 0.390655 | ||||||||
\(771\) | 7.47190 | 0.269094 | ||||||||
\(772\) | −66.0698 | −2.37790 | ||||||||
\(773\) | 11.3633 | 0.408710 | 0.204355 | − | 0.978897i | \(-0.434490\pi\) | ||||
0.204355 | + | 0.978897i | \(0.434490\pi\) | |||||||
\(774\) | 53.1192 | 1.90933 | ||||||||
\(775\) | 6.66860 | 0.239543 | ||||||||
\(776\) | −10.9946 | −0.394684 | ||||||||
\(777\) | −24.3034 | −0.871881 | ||||||||
\(778\) | −53.8102 | −1.92919 | ||||||||
\(779\) | −10.9049 | −0.390708 | ||||||||
\(780\) | 70.7522 | 2.53333 | ||||||||
\(781\) | −44.3227 | −1.58599 | ||||||||
\(782\) | −51.4252 | −1.83896 | ||||||||
\(783\) | −5.75260 | −0.205581 | ||||||||
\(784\) | 1.23330 | 0.0440463 | ||||||||
\(785\) | 15.0419 | 0.536869 | ||||||||
\(786\) | 164.202 | 5.85690 | ||||||||
\(787\) | 38.5960 | 1.37580 | 0.687900 | − | 0.725806i | \(-0.258533\pi\) | ||||
0.687900 | + | 0.725806i | \(0.258533\pi\) | |||||||
\(788\) | −25.1776 | −0.896915 | ||||||||
\(789\) | 45.4294 | 1.61733 | ||||||||
\(790\) | 34.0031 | 1.20977 | ||||||||
\(791\) | −8.89667 | −0.316329 | ||||||||
\(792\) | 115.783 | 4.11418 | ||||||||
\(793\) | −39.3674 | −1.39798 | ||||||||
\(794\) | 24.6941 | 0.876360 | ||||||||
\(795\) | 18.5255 | 0.657030 | ||||||||
\(796\) | 38.4213 | 1.36181 | ||||||||
\(797\) | −3.21061 | −0.113726 | −0.0568628 | − | 0.998382i | \(-0.518110\pi\) | ||||
−0.0568628 | + | 0.998382i | \(0.518110\pi\) | |||||||
\(798\) | −13.0021 | −0.460271 | ||||||||
\(799\) | 22.3791 | 0.791716 | ||||||||
\(800\) | −4.12635 | −0.145889 | ||||||||
\(801\) | −15.3633 | −0.542835 | ||||||||
\(802\) | −44.3053 | −1.56447 | ||||||||
\(803\) | 55.0991 | 1.94441 | ||||||||
\(804\) | 55.7097 | 1.96473 | ||||||||
\(805\) | −2.85788 | −0.100727 | ||||||||
\(806\) | −99.3636 | −3.49993 | ||||||||
\(807\) | −10.4887 | −0.369219 | ||||||||
\(808\) | 2.98789 | 0.105114 | ||||||||
\(809\) | −39.8833 | −1.40222 | −0.701111 | − | 0.713052i | \(-0.747312\pi\) | ||||
−0.701111 | + | 0.713052i | \(0.747312\pi\) | |||||||
\(810\) | −48.1090 | −1.69038 | ||||||||
\(811\) | 43.2414 | 1.51841 | 0.759206 | − | 0.650851i | \(-0.225588\pi\) | ||||
0.759206 | + | 0.650851i | \(0.225588\pi\) | |||||||
\(812\) | 1.52736 | 0.0535998 | ||||||||
\(813\) | −60.8895 | −2.13549 | ||||||||
\(814\) | 82.7490 | 2.90035 | ||||||||
\(815\) | 17.8488 | 0.625218 | ||||||||
\(816\) | 30.1366 | 1.05499 | ||||||||
\(817\) | 5.53018 | 0.193477 | ||||||||
\(818\) | −76.1707 | −2.66325 | ||||||||
\(819\) | 45.3553 | 1.58484 | ||||||||
\(820\) | 21.8903 | 0.764442 | ||||||||
\(821\) | 40.3195 | 1.40716 | 0.703579 | − | 0.710617i | \(-0.251584\pi\) | ||||
0.703579 | + | 0.710617i | \(0.251584\pi\) | |||||||
\(822\) | 122.827 | 4.28409 | ||||||||
\(823\) | 36.0043 | 1.25503 | 0.627516 | − | 0.778603i | \(-0.284072\pi\) | ||||
0.627516 | + | 0.778603i | \(0.284072\pi\) | |||||||
\(824\) | 47.4876 | 1.65431 | ||||||||
\(825\) | 14.7209 | 0.512515 | ||||||||
\(826\) | 28.8272 | 1.00303 | ||||||||
\(827\) | −11.2409 | −0.390886 | −0.195443 | − | 0.980715i | \(-0.562614\pi\) | ||||
−0.195443 | + | 0.980715i | \(0.562614\pi\) | |||||||
\(828\) | −71.3151 | −2.47837 | ||||||||
\(829\) | −5.03907 | −0.175014 | −0.0875070 | − | 0.996164i | \(-0.527890\pi\) | ||||
−0.0875070 | + | 0.996164i | \(0.527890\pi\) | |||||||
\(830\) | 27.8659 | 0.967239 | ||||||||
\(831\) | −101.255 | −3.51251 | ||||||||
\(832\) | 77.1597 | 2.67503 | ||||||||
\(833\) | 7.67508 | 0.265926 | ||||||||
\(834\) | −61.9901 | −2.14654 | ||||||||
\(835\) | −13.5074 | −0.467442 | ||||||||
\(836\) | 28.1621 | 0.974006 | ||||||||
\(837\) | 87.8234 | 3.03562 | ||||||||
\(838\) | −80.5645 | −2.78305 | ||||||||
\(839\) | −1.12900 | −0.0389774 | −0.0194887 | − | 0.999810i | \(-0.506204\pi\) | ||||
−0.0194887 | + | 0.999810i | \(0.506204\pi\) | |||||||
\(840\) | 11.1716 | 0.385457 | ||||||||
\(841\) | −28.8092 | −0.993421 | ||||||||
\(842\) | 64.1159 | 2.20958 | ||||||||
\(843\) | 35.6693 | 1.22852 | ||||||||
\(844\) | −35.1081 | −1.20847 | ||||||||
\(845\) | −27.3912 | −0.942284 | ||||||||
\(846\) | 48.7858 | 1.67729 | ||||||||
\(847\) | −10.3786 | −0.356613 | ||||||||
\(848\) | −7.17617 | −0.246431 | ||||||||
\(849\) | −61.3551 | −2.10570 | ||||||||
\(850\) | 17.9942 | 0.617196 | ||||||||
\(851\) | −21.8156 | −0.747830 | ||||||||
\(852\) | −106.717 | −3.65606 | ||||||||
\(853\) | 6.83009 | 0.233858 | 0.116929 | − | 0.993140i | \(-0.462695\pi\) | ||||
0.116929 | + | 0.993140i | \(0.462695\pi\) | |||||||
\(854\) | −14.5225 | −0.496951 | ||||||||
\(855\) | −12.4310 | −0.425132 | ||||||||
\(856\) | −52.7711 | −1.80368 | ||||||||
\(857\) | −22.3077 | −0.762016 | −0.381008 | − | 0.924572i | \(-0.624423\pi\) | ||||
−0.381008 | + | 0.924572i | \(0.624423\pi\) | |||||||
\(858\) | −219.344 | −7.48828 | ||||||||
\(859\) | 31.5613 | 1.07686 | 0.538429 | − | 0.842671i | \(-0.319018\pi\) | ||||
0.538429 | + | 0.842671i | \(0.319018\pi\) | |||||||
\(860\) | −11.1012 | −0.378548 | ||||||||
\(861\) | 19.9316 | 0.679267 | ||||||||
\(862\) | −71.5864 | −2.43824 | ||||||||
\(863\) | −23.5247 | −0.800791 | −0.400396 | − | 0.916342i | \(-0.631127\pi\) | ||||
−0.400396 | + | 0.916342i | \(0.631127\pi\) | |||||||
\(864\) | −54.3428 | −1.84878 | ||||||||
\(865\) | −4.93056 | −0.167644 | ||||||||
\(866\) | 58.2976 | 1.98103 | ||||||||
\(867\) | 133.423 | 4.53127 | ||||||||
\(868\) | −23.3178 | −0.791458 | ||||||||
\(869\) | −67.0592 | −2.27483 | ||||||||
\(870\) | 3.26048 | 0.110541 | ||||||||
\(871\) | −31.8037 | −1.07763 | ||||||||
\(872\) | −10.9465 | −0.370696 | ||||||||
\(873\) | −22.3611 | −0.756810 | ||||||||
\(874\) | −11.6712 | −0.394784 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 132.664 | 4.48229 | ||||||||
\(877\) | 25.5082 | 0.861352 | 0.430676 | − | 0.902507i | \(-0.358275\pi\) | ||||
0.430676 | + | 0.902507i | \(0.358275\pi\) | |||||||
\(878\) | 8.38090 | 0.282842 | ||||||||
\(879\) | −30.1524 | −1.01701 | ||||||||
\(880\) | −5.70239 | −0.192228 | ||||||||
\(881\) | −38.0860 | −1.28315 | −0.641575 | − | 0.767060i | \(-0.721719\pi\) | ||||
−0.641575 | + | 0.767060i | \(0.721719\pi\) | |||||||
\(882\) | 16.7315 | 0.563378 | ||||||||
\(883\) | −43.8969 | −1.47725 | −0.738624 | − | 0.674118i | \(-0.764524\pi\) | ||||
−0.738624 | + | 0.674118i | \(0.764524\pi\) | |||||||
\(884\) | −170.561 | −5.73658 | ||||||||
\(885\) | 39.1469 | 1.31591 | ||||||||
\(886\) | −39.2405 | −1.31831 | ||||||||
\(887\) | −45.5786 | −1.53038 | −0.765191 | − | 0.643804i | \(-0.777355\pi\) | ||||
−0.765191 | + | 0.643804i | \(0.777355\pi\) | |||||||
\(888\) | 85.2784 | 2.86176 | ||||||||
\(889\) | 9.71689 | 0.325894 | ||||||||
\(890\) | 5.04719 | 0.169182 | ||||||||
\(891\) | 94.8783 | 3.17854 | ||||||||
\(892\) | −61.1374 | −2.04703 | ||||||||
\(893\) | 5.07904 | 0.169964 | ||||||||
\(894\) | 15.1034 | 0.505133 | ||||||||
\(895\) | 3.36333 | 0.112424 | ||||||||
\(896\) | 20.2114 | 0.675214 | ||||||||
\(897\) | 57.8270 | 1.93079 | ||||||||
\(898\) | 89.6552 | 2.99183 | ||||||||
\(899\) | −2.91288 | −0.0971501 | ||||||||
\(900\) | 24.9539 | 0.831795 | ||||||||
\(901\) | −44.6589 | −1.48780 | ||||||||
\(902\) | −67.8637 | −2.25961 | ||||||||
\(903\) | −10.1079 | −0.336370 | ||||||||
\(904\) | 31.2176 | 1.03828 | ||||||||
\(905\) | −22.5617 | −0.749977 | ||||||||
\(906\) | −7.98806 | −0.265385 | ||||||||
\(907\) | 9.33152 | 0.309848 | 0.154924 | − | 0.987926i | \(-0.450487\pi\) | ||||
0.154924 | + | 0.987926i | \(0.450487\pi\) | |||||||
\(908\) | 55.4394 | 1.83982 | ||||||||
\(909\) | 6.07683 | 0.201556 | ||||||||
\(910\) | −14.9002 | −0.493937 | ||||||||
\(911\) | −10.3920 | −0.344303 | −0.172151 | − | 0.985071i | \(-0.555072\pi\) | ||||
−0.172151 | + | 0.985071i | \(0.555072\pi\) | |||||||
\(912\) | 6.83964 | 0.226483 | ||||||||
\(913\) | −54.9558 | −1.81877 | ||||||||
\(914\) | 9.92512 | 0.328294 | ||||||||
\(915\) | −19.7214 | −0.651968 | ||||||||
\(916\) | 3.49666 | 0.115533 | ||||||||
\(917\) | −21.9981 | −0.726443 | ||||||||
\(918\) | 236.978 | 7.82144 | ||||||||
\(919\) | −16.5206 | −0.544966 | −0.272483 | − | 0.962161i | \(-0.587845\pi\) | ||||
−0.272483 | + | 0.962161i | \(0.587845\pi\) | |||||||
\(920\) | 10.0280 | 0.330614 | ||||||||
\(921\) | 5.78253 | 0.190541 | ||||||||
\(922\) | −7.19894 | −0.237084 | ||||||||
\(923\) | 60.9228 | 2.00530 | ||||||||
\(924\) | −51.4738 | −1.69336 | ||||||||
\(925\) | 7.63350 | 0.250988 | ||||||||
\(926\) | 10.0785 | 0.331199 | ||||||||
\(927\) | 96.5813 | 3.17215 | ||||||||
\(928\) | 1.80242 | 0.0591672 | ||||||||
\(929\) | −21.9429 | −0.719923 | −0.359961 | − | 0.932967i | \(-0.617210\pi\) | ||||
−0.359961 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(930\) | −49.7769 | −1.63225 | ||||||||
\(931\) | 1.74190 | 0.0570883 | ||||||||
\(932\) | −93.7930 | −3.07229 | ||||||||
\(933\) | −80.8460 | −2.64678 | ||||||||
\(934\) | −60.9512 | −1.99438 | ||||||||
\(935\) | −35.4873 | −1.16056 | ||||||||
\(936\) | −159.147 | −5.20189 | ||||||||
\(937\) | −17.9933 | −0.587816 | −0.293908 | − | 0.955834i | \(-0.594956\pi\) | ||||
−0.293908 | + | 0.955834i | \(0.594956\pi\) | |||||||
\(938\) | −11.7323 | −0.383073 | ||||||||
\(939\) | −22.3774 | −0.730258 | ||||||||
\(940\) | −10.1956 | −0.332544 | ||||||||
\(941\) | 2.69099 | 0.0877237 | 0.0438618 | − | 0.999038i | \(-0.486034\pi\) | ||||
0.0438618 | + | 0.999038i | \(0.486034\pi\) | |||||||
\(942\) | −112.278 | −3.65823 | ||||||||
\(943\) | 17.8913 | 0.582621 | ||||||||
\(944\) | −15.1643 | −0.493555 | ||||||||
\(945\) | 13.1697 | 0.428410 | ||||||||
\(946\) | 34.4157 | 1.11895 | ||||||||
\(947\) | −26.6755 | −0.866839 | −0.433419 | − | 0.901192i | \(-0.642693\pi\) | ||||
−0.433419 | + | 0.901192i | \(0.642693\pi\) | |||||||
\(948\) | −161.460 | −5.24398 | ||||||||
\(949\) | −75.7353 | −2.45847 | ||||||||
\(950\) | 4.08386 | 0.132498 | ||||||||
\(951\) | −41.2529 | −1.33772 | ||||||||
\(952\) | −26.9311 | −0.872843 | ||||||||
\(953\) | 10.0982 | 0.327113 | 0.163557 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163557 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(954\) | −97.3552 | −3.15199 | ||||||||
\(955\) | −4.12671 | −0.133537 | ||||||||
\(956\) | −31.4591 | −1.01746 | ||||||||
\(957\) | −6.43016 | −0.207858 | ||||||||
\(958\) | 75.2535 | 2.43133 | ||||||||
\(959\) | −16.4551 | −0.531364 | ||||||||
\(960\) | 38.6537 | 1.24754 | ||||||||
\(961\) | 13.4702 | 0.434524 | ||||||||
\(962\) | −113.741 | −3.66715 | ||||||||
\(963\) | −107.327 | −3.45856 | ||||||||
\(964\) | 33.9126 | 1.09225 | ||||||||
\(965\) | 18.8951 | 0.608256 | ||||||||
\(966\) | 21.3323 | 0.686354 | ||||||||
\(967\) | 13.3090 | 0.427990 | 0.213995 | − | 0.976835i | \(-0.431352\pi\) | ||||
0.213995 | + | 0.976835i | \(0.431352\pi\) | |||||||
\(968\) | 36.4175 | 1.17050 | ||||||||
\(969\) | 42.5646 | 1.36737 | ||||||||
\(970\) | 7.34613 | 0.235870 | ||||||||
\(971\) | −26.7962 | −0.859931 | −0.429965 | − | 0.902845i | \(-0.641474\pi\) | ||||
−0.429965 | + | 0.902845i | \(0.641474\pi\) | |||||||
\(972\) | 90.2914 | 2.89610 | ||||||||
\(973\) | 8.30480 | 0.266240 | ||||||||
\(974\) | −39.3698 | −1.26149 | ||||||||
\(975\) | −20.2342 | −0.648014 | ||||||||
\(976\) | 7.63942 | 0.244532 | ||||||||
\(977\) | 15.2817 | 0.488904 | 0.244452 | − | 0.969661i | \(-0.421392\pi\) | ||||
0.244452 | + | 0.969661i | \(0.421392\pi\) | |||||||
\(978\) | −133.230 | −4.26024 | ||||||||
\(979\) | −9.95382 | −0.318125 | ||||||||
\(980\) | −3.49666 | −0.111697 | ||||||||
\(981\) | −22.2633 | −0.710813 | ||||||||
\(982\) | −5.10526 | −0.162915 | ||||||||
\(983\) | 2.31086 | 0.0737051 | 0.0368526 | − | 0.999321i | \(-0.488267\pi\) | ||||
0.0368526 | + | 0.999321i | \(0.488267\pi\) | |||||||
\(984\) | −69.9381 | −2.22955 | ||||||||
\(985\) | 7.20048 | 0.229426 | ||||||||
\(986\) | −7.85997 | −0.250312 | ||||||||
\(987\) | −9.28332 | −0.295491 | ||||||||
\(988\) | −38.7096 | −1.23151 | ||||||||
\(989\) | −9.07321 | −0.288511 | ||||||||
\(990\) | −77.3613 | −2.45870 | ||||||||
\(991\) | −27.1805 | −0.863418 | −0.431709 | − | 0.902013i | \(-0.642089\pi\) | ||||
−0.431709 | + | 0.902013i | \(0.642089\pi\) | |||||||
\(992\) | −27.5170 | −0.873666 | ||||||||
\(993\) | −62.6099 | −1.98687 | ||||||||
\(994\) | 22.4743 | 0.712842 | ||||||||
\(995\) | −10.9880 | −0.348344 | ||||||||
\(996\) | −132.318 | −4.19267 | ||||||||
\(997\) | 19.0305 | 0.602701 | 0.301351 | − | 0.953513i | \(-0.402563\pi\) | ||||
0.301351 | + | 0.953513i | \(0.402563\pi\) | |||||||
\(998\) | 3.49865 | 0.110748 | ||||||||
\(999\) | 100.531 | 3.18065 |
(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 | 8015.2.a.l.1.54 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.54 | ✓ | 62 | 1.1 | even | 1 | trivial |