Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.64436.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 7x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.60520\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60520 | 1.84215 | 0.921077 | − | 0.389381i | \(-0.127311\pi\) | ||||
0.921077 | + | 0.389381i | \(0.127311\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.78706 | 2.39353 | ||||||||
\(5\) | −3.78706 | −1.69362 | −0.846812 | − | 0.531892i | \(-0.821481\pi\) | ||||
−0.846812 | + | 0.531892i | \(0.821481\pi\) | |||||||
\(6\) | −2.60520 | −1.06357 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 7.26084 | 2.56709 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.86604 | −3.11992 | ||||||||
\(11\) | −2.55475 | −0.770287 | −0.385144 | − | 0.922857i | \(-0.625848\pi\) | ||||
−0.385144 | + | 0.922857i | \(0.625848\pi\) | |||||||
\(12\) | −4.78706 | −1.38190 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.60520 | 0.696269 | ||||||||
\(15\) | 3.78706 | 0.977814 | ||||||||
\(16\) | 9.34181 | 2.33545 | ||||||||
\(17\) | 3.21040 | 0.778636 | 0.389318 | − | 0.921103i | \(-0.372711\pi\) | ||||
0.389318 | + | 0.921103i | \(0.372711\pi\) | |||||||
\(18\) | 2.60520 | 0.614051 | ||||||||
\(19\) | −8.44270 | −1.93689 | −0.968444 | − | 0.249230i | \(-0.919822\pi\) | ||||
−0.968444 | + | 0.249230i | \(0.919822\pi\) | |||||||
\(20\) | −18.1289 | −4.05374 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −6.65564 | −1.41899 | ||||||||
\(23\) | −3.97809 | −0.829490 | −0.414745 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414745 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(24\) | −7.26084 | −1.48211 | ||||||||
\(25\) | 9.34181 | 1.86836 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.78706 | 0.904669 | ||||||||
\(29\) | −2.86858 | −0.532683 | −0.266341 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266341 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(30\) | 9.86604 | 1.80128 | ||||||||
\(31\) | 0.868584 | 0.156002 | 0.0780011 | − | 0.996953i | \(-0.475146\pi\) | ||||
0.0780011 | + | 0.996953i | \(0.475146\pi\) | |||||||
\(32\) | 9.81560 | 1.73517 | ||||||||
\(33\) | 2.55475 | 0.444726 | ||||||||
\(34\) | 8.36372 | 1.43437 | ||||||||
\(35\) | −3.78706 | −0.640130 | ||||||||
\(36\) | 4.78706 | 0.797843 | ||||||||
\(37\) | 5.10951 | 0.839998 | 0.419999 | − | 0.907525i | \(-0.362030\pi\) | ||||
0.419999 | + | 0.907525i | \(0.362030\pi\) | |||||||
\(38\) | −21.9949 | −3.56805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −27.4972 | −4.34769 | ||||||||
\(41\) | −3.34436 | −0.522301 | −0.261150 | − | 0.965298i | \(-0.584102\pi\) | ||||
−0.261150 | + | 0.965298i | \(0.584102\pi\) | |||||||
\(42\) | −2.60520 | −0.401991 | ||||||||
\(43\) | −4.86858 | −0.742452 | −0.371226 | − | 0.928543i | \(-0.621062\pi\) | ||||
−0.371226 | + | 0.928543i | \(0.621062\pi\) | |||||||
\(44\) | −12.2298 | −1.84371 | ||||||||
\(45\) | −3.78706 | −0.564541 | ||||||||
\(46\) | −10.3637 | −1.52805 | ||||||||
\(47\) | −11.0983 | −1.61886 | −0.809430 | − | 0.587217i | \(-0.800224\pi\) | ||||
−0.809430 | + | 0.587217i | \(0.800224\pi\) | |||||||
\(48\) | −9.34181 | −1.34837 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 24.3373 | 3.44181 | ||||||||
\(51\) | −3.21040 | −0.449545 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.33319 | 0.183128 | 0.0915640 | − | 0.995799i | \(-0.470813\pi\) | ||||
0.0915640 | + | 0.995799i | \(0.470813\pi\) | |||||||
\(54\) | −2.60520 | −0.354523 | ||||||||
\(55\) | 9.67501 | 1.30458 | ||||||||
\(56\) | 7.26084 | 0.970271 | ||||||||
\(57\) | 8.44270 | 1.11826 | ||||||||
\(58\) | −7.47323 | −0.981283 | ||||||||
\(59\) | −10.6556 | −1.38725 | −0.693623 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(60\) | 18.1289 | 2.34043 | ||||||||
\(61\) | −4.10089 | −0.525065 | −0.262532 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(62\) | 2.26283 | 0.287380 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 6.88795 | 0.860993 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.65564 | 0.819253 | ||||||||
\(67\) | −10.8467 | −1.32513 | −0.662566 | − | 0.749003i | \(-0.730533\pi\) | ||||
−0.662566 | + | 0.749003i | \(0.730533\pi\) | |||||||
\(68\) | 15.3684 | 1.86369 | ||||||||
\(69\) | 3.97809 | 0.478906 | ||||||||
\(70\) | −9.86604 | −1.17922 | ||||||||
\(71\) | −2.55475 | −0.303194 | −0.151597 | − | 0.988442i | \(-0.548442\pi\) | ||||
−0.151597 | + | 0.988442i | \(0.548442\pi\) | |||||||
\(72\) | 7.26084 | 0.855698 | ||||||||
\(73\) | 6.76770 | 0.792099 | 0.396049 | − | 0.918229i | \(-0.370381\pi\) | ||||
0.396049 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(74\) | 13.3113 | 1.54741 | ||||||||
\(75\) | −9.34181 | −1.07870 | ||||||||
\(76\) | −40.4157 | −4.63600 | ||||||||
\(77\) | −2.55475 | −0.291141 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.23230 | −0.138645 | −0.0693225 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693225 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(80\) | −35.3780 | −3.95538 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.71272 | −0.962158 | ||||||||
\(83\) | −11.0983 | −1.21820 | −0.609101 | − | 0.793093i | \(-0.708469\pi\) | ||||
−0.609101 | + | 0.793093i | \(0.708469\pi\) | |||||||
\(84\) | −4.78706 | −0.522311 | ||||||||
\(85\) | −12.1580 | −1.31872 | ||||||||
\(86\) | −12.6836 | −1.36771 | ||||||||
\(87\) | 2.86858 | 0.307544 | ||||||||
\(88\) | −18.5497 | −1.97740 | ||||||||
\(89\) | −5.52423 | −0.585567 | −0.292783 | − | 0.956179i | \(-0.594581\pi\) | ||||
−0.292783 | + | 0.956179i | \(0.594581\pi\) | |||||||
\(90\) | −9.86604 | −1.03997 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −19.0434 | −1.98541 | ||||||||
\(93\) | −0.868584 | −0.0900679 | ||||||||
\(94\) | −28.9134 | −2.98219 | ||||||||
\(95\) | 31.9730 | 3.28036 | ||||||||
\(96\) | −9.81560 | −1.00180 | ||||||||
\(97\) | 5.65819 | 0.574502 | 0.287251 | − | 0.957855i | \(-0.407259\pi\) | ||||
0.287251 | + | 0.957855i | \(0.407259\pi\) | |||||||
\(98\) | 2.60520 | 0.263165 | ||||||||
\(99\) | −2.55475 | −0.256762 | ||||||||
\(100\) | 44.7198 | 4.47198 | ||||||||
\(101\) | 8.94756 | 0.890316 | 0.445158 | − | 0.895452i | \(-0.353148\pi\) | ||||
0.445158 | + | 0.895452i | \(0.353148\pi\) | |||||||
\(102\) | −8.36372 | −0.828132 | ||||||||
\(103\) | 1.67501 | 0.165043 | 0.0825216 | − | 0.996589i | \(-0.473703\pi\) | ||||
0.0825216 | + | 0.996589i | \(0.473703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.78706 | 0.369579 | ||||||||
\(106\) | 3.47323 | 0.337350 | ||||||||
\(107\) | −0.846676 | −0.0818513 | −0.0409256 | − | 0.999162i | \(-0.513031\pi\) | ||||
−0.0409256 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(108\) | −4.78706 | −0.460635 | ||||||||
\(109\) | 17.9949 | 1.72360 | 0.861800 | − | 0.507248i | \(-0.169337\pi\) | ||||
0.861800 | + | 0.507248i | \(0.169337\pi\) | |||||||
\(110\) | 25.2053 | 2.40323 | ||||||||
\(111\) | −5.10951 | −0.484973 | ||||||||
\(112\) | 9.34181 | 0.882718 | ||||||||
\(113\) | 2.86858 | 0.269854 | 0.134927 | − | 0.990856i | \(-0.456920\pi\) | ||||
0.134927 | + | 0.990856i | \(0.456920\pi\) | |||||||
\(114\) | 21.9949 | 2.06001 | ||||||||
\(115\) | 15.0653 | 1.40484 | ||||||||
\(116\) | −13.7321 | −1.27499 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −27.7601 | −2.55552 | ||||||||
\(119\) | 3.21040 | 0.294297 | ||||||||
\(120\) | 27.4972 | 2.51014 | ||||||||
\(121\) | −4.47323 | −0.406657 | ||||||||
\(122\) | −10.6836 | −0.967250 | ||||||||
\(123\) | 3.34436 | 0.301551 | ||||||||
\(124\) | 4.15796 | 0.373396 | ||||||||
\(125\) | −16.4427 | −1.47068 | ||||||||
\(126\) | 2.60520 | 0.232090 | ||||||||
\(127\) | −17.2053 | −1.52672 | −0.763362 | − | 0.645971i | \(-0.776453\pi\) | ||||
−0.763362 | + | 0.645971i | \(0.776453\pi\) | |||||||
\(128\) | −1.68672 | −0.149087 | ||||||||
\(129\) | 4.86858 | 0.428655 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.6836 | 1.45766 | 0.728828 | − | 0.684697i | \(-0.240066\pi\) | ||||
0.728828 | + | 0.684697i | \(0.240066\pi\) | |||||||
\(132\) | 12.2298 | 1.06446 | ||||||||
\(133\) | −8.44270 | −0.732075 | ||||||||
\(134\) | −28.2577 | −2.44110 | ||||||||
\(135\) | 3.78706 | 0.325938 | ||||||||
\(136\) | 23.3102 | 1.99883 | ||||||||
\(137\) | 18.9134 | 1.61588 | 0.807940 | − | 0.589265i | \(-0.200583\pi\) | ||||
0.807940 | + | 0.589265i | \(0.200583\pi\) | |||||||
\(138\) | 10.3637 | 0.882218 | ||||||||
\(139\) | 5.67501 | 0.481348 | 0.240674 | − | 0.970606i | \(-0.422632\pi\) | ||||
0.240674 | + | 0.970606i | \(0.422632\pi\) | |||||||
\(140\) | −18.1289 | −1.53217 | ||||||||
\(141\) | 11.0983 | 0.934649 | ||||||||
\(142\) | −6.65564 | −0.558529 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.34181 | 0.778484 | ||||||||
\(145\) | 10.8635 | 0.902164 | ||||||||
\(146\) | 17.6312 | 1.45917 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 24.4595 | 2.01056 | ||||||||
\(149\) | 8.49259 | 0.695740 | 0.347870 | − | 0.937543i | \(-0.386905\pi\) | ||||
0.347870 | + | 0.937543i | \(0.386905\pi\) | |||||||
\(150\) | −24.3373 | −1.98713 | ||||||||
\(151\) | −14.2190 | −1.15713 | −0.578564 | − | 0.815637i | \(-0.696387\pi\) | ||||
−0.578564 | + | 0.815637i | \(0.696387\pi\) | |||||||
\(152\) | −61.3011 | −4.97218 | ||||||||
\(153\) | 3.21040 | 0.259545 | ||||||||
\(154\) | −6.65564 | −0.536327 | ||||||||
\(155\) | −3.28938 | −0.264209 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.42079 | 0.672052 | 0.336026 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(158\) | −3.21040 | −0.255405 | ||||||||
\(159\) | −1.33319 | −0.105729 | ||||||||
\(160\) | −37.1722 | −2.93872 | ||||||||
\(161\) | −3.97809 | −0.313518 | ||||||||
\(162\) | 2.60520 | 0.204684 | ||||||||
\(163\) | 3.77589 | 0.295751 | 0.147875 | − | 0.989006i | \(-0.452757\pi\) | ||||
0.147875 | + | 0.989006i | \(0.452757\pi\) | |||||||
\(164\) | −16.0096 | −1.25014 | ||||||||
\(165\) | −9.67501 | −0.753198 | ||||||||
\(166\) | −28.9134 | −2.24411 | ||||||||
\(167\) | −8.83551 | −0.683712 | −0.341856 | − | 0.939752i | \(-0.611056\pi\) | ||||
−0.341856 | + | 0.939752i | \(0.611056\pi\) | |||||||
\(168\) | −7.26084 | −0.560186 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −31.6739 | −2.42928 | ||||||||
\(171\) | −8.44270 | −0.645629 | ||||||||
\(172\) | −23.3062 | −1.77708 | ||||||||
\(173\) | −17.6750 | −1.34381 | −0.671903 | − | 0.740639i | \(-0.734523\pi\) | ||||
−0.671903 | + | 0.740639i | \(0.734523\pi\) | |||||||
\(174\) | 7.47323 | 0.566544 | ||||||||
\(175\) | 9.34181 | 0.706175 | ||||||||
\(176\) | −23.8660 | −1.79897 | ||||||||
\(177\) | 10.6556 | 0.800927 | ||||||||
\(178\) | −14.3917 | −1.07870 | ||||||||
\(179\) | −16.9073 | −1.26371 | −0.631856 | − | 0.775086i | \(-0.717707\pi\) | ||||
−0.631856 | + | 0.775086i | \(0.717707\pi\) | |||||||
\(180\) | −18.1289 | −1.35125 | ||||||||
\(181\) | −7.73717 | −0.575099 | −0.287550 | − | 0.957766i | \(-0.592841\pi\) | ||||
−0.287550 | + | 0.957766i | \(0.592841\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.10089 | 0.303146 | ||||||||
\(184\) | −28.8843 | −2.12938 | ||||||||
\(185\) | −19.3500 | −1.42264 | ||||||||
\(186\) | −2.26283 | −0.165919 | ||||||||
\(187\) | −8.20178 | −0.599773 | ||||||||
\(188\) | −53.1284 | −3.87479 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 83.2960 | 6.04293 | ||||||||
\(191\) | 5.57412 | 0.403329 | 0.201664 | − | 0.979455i | \(-0.435365\pi\) | ||||
0.201664 | + | 0.979455i | \(0.435365\pi\) | |||||||
\(192\) | −6.88795 | −0.497095 | ||||||||
\(193\) | 7.57412 | 0.545197 | 0.272598 | − | 0.962128i | \(-0.412117\pi\) | ||||
0.272598 | + | 0.962128i | \(0.412117\pi\) | |||||||
\(194\) | 14.7407 | 1.05832 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.78706 | 0.341933 | ||||||||
\(197\) | −13.3444 | −0.950746 | −0.475373 | − | 0.879784i | \(-0.657687\pi\) | ||||
−0.475373 | + | 0.879784i | \(0.657687\pi\) | |||||||
\(198\) | −6.65564 | −0.472996 | ||||||||
\(199\) | 16.8854 | 1.19697 | 0.598487 | − | 0.801132i | \(-0.295769\pi\) | ||||
0.598487 | + | 0.801132i | \(0.295769\pi\) | |||||||
\(200\) | 67.8294 | 4.79626 | ||||||||
\(201\) | 10.8467 | 0.765066 | ||||||||
\(202\) | 23.3102 | 1.64010 | ||||||||
\(203\) | −2.86858 | −0.201335 | ||||||||
\(204\) | −15.3684 | −1.07600 | ||||||||
\(205\) | 12.6653 | 0.884581 | ||||||||
\(206\) | 4.36372 | 0.304035 | ||||||||
\(207\) | −3.97809 | −0.276497 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.5690 | 1.49196 | ||||||||
\(210\) | 9.86604 | 0.680821 | ||||||||
\(211\) | 11.6969 | 0.805249 | 0.402624 | − | 0.915365i | \(-0.368098\pi\) | ||||
0.402624 | + | 0.915365i | \(0.368098\pi\) | |||||||
\(212\) | 6.38207 | 0.438322 | ||||||||
\(213\) | 2.55475 | 0.175049 | ||||||||
\(214\) | −2.20576 | −0.150783 | ||||||||
\(215\) | 18.4376 | 1.25743 | ||||||||
\(216\) | −7.26084 | −0.494038 | ||||||||
\(217\) | 0.868584 | 0.0589633 | ||||||||
\(218\) | 46.8803 | 3.17514 | ||||||||
\(219\) | −6.76770 | −0.457319 | ||||||||
\(220\) | 46.3148 | 3.12254 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.3113 | −0.893395 | ||||||||
\(223\) | 4.24093 | 0.283993 | 0.141997 | − | 0.989867i | \(-0.454648\pi\) | ||||
0.141997 | + | 0.989867i | \(0.454648\pi\) | |||||||
\(224\) | 9.81560 | 0.655832 | ||||||||
\(225\) | 9.34181 | 0.622788 | ||||||||
\(226\) | 7.47323 | 0.497112 | ||||||||
\(227\) | −1.72643 | −0.114587 | −0.0572934 | − | 0.998357i | \(-0.518247\pi\) | ||||
−0.0572934 | + | 0.998357i | \(0.518247\pi\) | |||||||
\(228\) | 40.4157 | 2.67660 | ||||||||
\(229\) | −6.82833 | −0.451229 | −0.225614 | − | 0.974217i | \(-0.572439\pi\) | ||||
−0.225614 | + | 0.974217i | \(0.572439\pi\) | |||||||
\(230\) | 39.2480 | 2.58794 | ||||||||
\(231\) | 2.55475 | 0.168091 | ||||||||
\(232\) | −20.8283 | −1.36745 | ||||||||
\(233\) | 1.33319 | 0.0873403 | 0.0436702 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436702 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 42.0301 | 2.74174 | ||||||||
\(236\) | −51.0092 | −3.32042 | ||||||||
\(237\) | 1.23230 | 0.0800468 | ||||||||
\(238\) | 8.36372 | 0.542139 | ||||||||
\(239\) | 3.90985 | 0.252907 | 0.126454 | − | 0.991973i | \(-0.459640\pi\) | ||||
0.126454 | + | 0.991973i | \(0.459640\pi\) | |||||||
\(240\) | 35.3780 | 2.28364 | ||||||||
\(241\) | 25.3903 | 1.63553 | 0.817765 | − | 0.575552i | \(-0.195213\pi\) | ||||
0.817765 | + | 0.575552i | \(0.195213\pi\) | |||||||
\(242\) | −11.6537 | −0.749125 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.6312 | −1.25676 | ||||||||
\(245\) | −3.78706 | −0.241946 | ||||||||
\(246\) | 8.71272 | 0.555502 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.30665 | 0.400473 | ||||||||
\(249\) | 11.0983 | 0.703329 | ||||||||
\(250\) | −42.8365 | −2.70922 | ||||||||
\(251\) | 25.7708 | 1.62664 | 0.813319 | − | 0.581818i | \(-0.197658\pi\) | ||||
0.813319 | + | 0.581818i | \(0.197658\pi\) | |||||||
\(252\) | 4.78706 | 0.301556 | ||||||||
\(253\) | 10.1631 | 0.638945 | ||||||||
\(254\) | −44.8232 | −2.81246 | ||||||||
\(255\) | 12.1580 | 0.761361 | ||||||||
\(256\) | −18.1701 | −1.13563 | ||||||||
\(257\) | −5.87678 | −0.366584 | −0.183292 | − | 0.983059i | \(-0.558675\pi\) | ||||
−0.183292 | + | 0.983059i | \(0.558675\pi\) | |||||||
\(258\) | 12.6836 | 0.789648 | ||||||||
\(259\) | 5.10951 | 0.317489 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.86858 | −0.177561 | ||||||||
\(262\) | 43.4642 | 2.68522 | ||||||||
\(263\) | −10.2409 | −0.631483 | −0.315741 | − | 0.948845i | \(-0.602253\pi\) | ||||
−0.315741 | + | 0.948845i | \(0.602253\pi\) | |||||||
\(264\) | 18.5497 | 1.14165 | ||||||||
\(265\) | −5.04888 | −0.310150 | ||||||||
\(266\) | −21.9949 | −1.34859 | ||||||||
\(267\) | 5.52423 | 0.338077 | ||||||||
\(268\) | −51.9237 | −3.17174 | ||||||||
\(269\) | −16.1396 | −0.984050 | −0.492025 | − | 0.870581i | \(-0.663743\pi\) | ||||
−0.492025 | + | 0.870581i | \(0.663743\pi\) | |||||||
\(270\) | 9.86604 | 0.600428 | ||||||||
\(271\) | 12.2577 | 0.744605 | 0.372302 | − | 0.928111i | \(-0.378568\pi\) | ||||
0.372302 | + | 0.928111i | \(0.378568\pi\) | |||||||
\(272\) | 29.9909 | 1.81847 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 49.2731 | 2.97670 | ||||||||
\(275\) | −23.8660 | −1.43918 | ||||||||
\(276\) | 19.0434 | 1.14628 | ||||||||
\(277\) | −9.81504 | −0.589729 | −0.294864 | − | 0.955539i | \(-0.595274\pi\) | ||||
−0.294864 | + | 0.955539i | \(0.595274\pi\) | |||||||
\(278\) | 14.7845 | 0.886716 | ||||||||
\(279\) | 0.868584 | 0.0520007 | ||||||||
\(280\) | −27.4972 | −1.64327 | ||||||||
\(281\) | −16.1910 | −0.965876 | −0.482938 | − | 0.875655i | \(-0.660430\pi\) | ||||
−0.482938 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(282\) | 28.9134 | 1.72177 | ||||||||
\(283\) | −19.1482 | −1.13824 | −0.569122 | − | 0.822253i | \(-0.692717\pi\) | ||||
−0.569122 | + | 0.822253i | \(0.692717\pi\) | |||||||
\(284\) | −12.2298 | −0.725703 | ||||||||
\(285\) | −31.9730 | −1.89392 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.34436 | −0.197411 | ||||||||
\(288\) | 9.81560 | 0.578389 | ||||||||
\(289\) | −6.69335 | −0.393727 | ||||||||
\(290\) | 28.3016 | 1.66192 | ||||||||
\(291\) | −5.65819 | −0.331689 | ||||||||
\(292\) | 32.3974 | 1.89591 | ||||||||
\(293\) | 24.6725 | 1.44138 | 0.720690 | − | 0.693257i | \(-0.243825\pi\) | ||||
0.720690 | + | 0.693257i | \(0.243825\pi\) | |||||||
\(294\) | −2.60520 | −0.151938 | ||||||||
\(295\) | 40.3535 | 2.34947 | ||||||||
\(296\) | 37.0993 | 2.15635 | ||||||||
\(297\) | 2.55475 | 0.148242 | ||||||||
\(298\) | 22.1249 | 1.28166 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −44.7198 | −2.58190 | ||||||||
\(301\) | −4.86858 | −0.280620 | ||||||||
\(302\) | −37.0434 | −2.13161 | ||||||||
\(303\) | −8.94756 | −0.514024 | ||||||||
\(304\) | −78.8701 | −4.52351 | ||||||||
\(305\) | 15.5303 | 0.889263 | ||||||||
\(306\) | 8.36372 | 0.478122 | ||||||||
\(307\) | 13.7540 | 0.784981 | 0.392491 | − | 0.919756i | \(-0.371614\pi\) | ||||
0.392491 | + | 0.919756i | \(0.371614\pi\) | |||||||
\(308\) | −12.2298 | −0.696855 | ||||||||
\(309\) | −1.67501 | −0.0952877 | ||||||||
\(310\) | −8.56948 | −0.486714 | ||||||||
\(311\) | −12.1580 | −0.689415 | −0.344707 | − | 0.938710i | \(-0.612022\pi\) | ||||
−0.344707 | + | 0.938710i | \(0.612022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6699 | 1.22486 | 0.612428 | − | 0.790526i | \(-0.290193\pi\) | ||||
0.612428 | + | 0.790526i | \(0.290193\pi\) | |||||||
\(314\) | 21.9378 | 1.23802 | ||||||||
\(315\) | −3.78706 | −0.213377 | ||||||||
\(316\) | −5.89911 | −0.331851 | ||||||||
\(317\) | −29.3780 | −1.65003 | −0.825016 | − | 0.565109i | \(-0.808834\pi\) | ||||
−0.825016 | + | 0.565109i | \(0.808834\pi\) | |||||||
\(318\) | −3.47323 | −0.194769 | ||||||||
\(319\) | 7.32853 | 0.410319 | ||||||||
\(320\) | −26.0851 | −1.45820 | ||||||||
\(321\) | 0.846676 | 0.0472569 | ||||||||
\(322\) | −10.3637 | −0.577548 | ||||||||
\(323\) | −27.1044 | −1.50813 | ||||||||
\(324\) | 4.78706 | 0.265948 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.83695 | 0.544818 | ||||||||
\(327\) | −17.9949 | −0.995121 | ||||||||
\(328\) | −24.2828 | −1.34080 | ||||||||
\(329\) | −11.0983 | −0.611871 | ||||||||
\(330\) | −25.2053 | −1.38751 | ||||||||
\(331\) | 23.9124 | 1.31434 | 0.657171 | − | 0.753741i | \(-0.271753\pi\) | ||||
0.657171 | + | 0.753741i | \(0.271753\pi\) | |||||||
\(332\) | −53.1284 | −2.91580 | ||||||||
\(333\) | 5.10951 | 0.279999 | ||||||||
\(334\) | −23.0183 | −1.25950 | ||||||||
\(335\) | 41.0770 | 2.24428 | ||||||||
\(336\) | −9.34181 | −0.509638 | ||||||||
\(337\) | 15.5706 | 0.848182 | 0.424091 | − | 0.905620i | \(-0.360594\pi\) | ||||
0.424091 | + | 0.905620i | \(0.360594\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.86858 | −0.155800 | ||||||||
\(340\) | −58.2009 | −3.15639 | ||||||||
\(341\) | −2.21902 | −0.120167 | ||||||||
\(342\) | −21.9949 | −1.18935 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −35.3500 | −1.90594 | ||||||||
\(345\) | −15.0653 | −0.811087 | ||||||||
\(346\) | −46.0469 | −2.47550 | ||||||||
\(347\) | 1.04845 | 0.0562838 | 0.0281419 | − | 0.999604i | \(-0.491041\pi\) | ||||
0.0281419 | + | 0.999604i | \(0.491041\pi\) | |||||||
\(348\) | 13.7321 | 0.736117 | ||||||||
\(349\) | −13.8721 | −0.742557 | −0.371279 | − | 0.928521i | \(-0.621081\pi\) | ||||
−0.371279 | + | 0.928521i | \(0.621081\pi\) | |||||||
\(350\) | 24.3373 | 1.30088 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.0764 | −1.33658 | ||||||||
\(353\) | −9.96693 | −0.530486 | −0.265243 | − | 0.964182i | \(-0.585452\pi\) | ||||
−0.265243 | + | 0.964182i | \(0.585452\pi\) | |||||||
\(354\) | 27.7601 | 1.47543 | ||||||||
\(355\) | 9.67501 | 0.513496 | ||||||||
\(356\) | −26.4448 | −1.40157 | ||||||||
\(357\) | −3.21040 | −0.169912 | ||||||||
\(358\) | −44.0469 | −2.32795 | ||||||||
\(359\) | 18.9705 | 1.00122 | 0.500611 | − | 0.865672i | \(-0.333109\pi\) | ||||
0.500611 | + | 0.865672i | \(0.333109\pi\) | |||||||
\(360\) | −27.4972 | −1.44923 | ||||||||
\(361\) | 52.2792 | 2.75154 | ||||||||
\(362\) | −20.1569 | −1.05942 | ||||||||
\(363\) | 4.47323 | 0.234784 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.6297 | −1.34152 | ||||||||
\(366\) | 10.6836 | 0.558442 | ||||||||
\(367\) | 22.3586 | 1.16711 | 0.583556 | − | 0.812073i | \(-0.301661\pi\) | ||||
0.583556 | + | 0.812073i | \(0.301661\pi\) | |||||||
\(368\) | −37.1626 | −1.93723 | ||||||||
\(369\) | −3.34436 | −0.174100 | ||||||||
\(370\) | −50.4106 | −2.62072 | ||||||||
\(371\) | 1.33319 | 0.0692159 | ||||||||
\(372\) | −4.15796 | −0.215580 | ||||||||
\(373\) | 26.0958 | 1.35119 | 0.675595 | − | 0.737273i | \(-0.263887\pi\) | ||||
0.675595 | + | 0.737273i | \(0.263887\pi\) | |||||||
\(374\) | −21.3673 | −1.10487 | ||||||||
\(375\) | 16.4427 | 0.849097 | ||||||||
\(376\) | −80.5833 | −4.15577 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.60520 | −0.133997 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 153.057 | 7.85164 | ||||||||
\(381\) | 17.2053 | 0.881455 | ||||||||
\(382\) | 14.5217 | 0.742994 | ||||||||
\(383\) | −4.96229 | −0.253561 | −0.126781 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126781 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(384\) | 1.68672 | 0.0860752 | ||||||||
\(385\) | 9.67501 | 0.493084 | ||||||||
\(386\) | 19.7321 | 1.00434 | ||||||||
\(387\) | −4.86858 | −0.247484 | ||||||||
\(388\) | 27.0861 | 1.37509 | ||||||||
\(389\) | −17.8757 | −0.906333 | −0.453166 | − | 0.891426i | \(-0.649706\pi\) | ||||
−0.453166 | + | 0.891426i | \(0.649706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7713 | −0.645870 | ||||||||
\(392\) | 7.26084 | 0.366728 | ||||||||
\(393\) | −16.6836 | −0.841578 | ||||||||
\(394\) | −34.7647 | −1.75142 | ||||||||
\(395\) | 4.66681 | 0.234813 | ||||||||
\(396\) | −12.2298 | −0.614569 | ||||||||
\(397\) | −7.06925 | −0.354796 | −0.177398 | − | 0.984139i | \(-0.556768\pi\) | ||||
−0.177398 | + | 0.984139i | \(0.556768\pi\) | |||||||
\(398\) | 43.9898 | 2.20501 | ||||||||
\(399\) | 8.44270 | 0.422664 | ||||||||
\(400\) | 87.2695 | 4.36347 | ||||||||
\(401\) | 9.12025 | 0.455444 | 0.227722 | − | 0.973726i | \(-0.426872\pi\) | ||||
0.227722 | + | 0.973726i | \(0.426872\pi\) | |||||||
\(402\) | 28.2577 | 1.40937 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 42.8325 | 2.13100 | ||||||||
\(405\) | −3.78706 | −0.188180 | ||||||||
\(406\) | −7.47323 | −0.370890 | ||||||||
\(407\) | −13.0535 | −0.647040 | ||||||||
\(408\) | −23.3102 | −1.15403 | ||||||||
\(409\) | −18.2542 | −0.902611 | −0.451306 | − | 0.892369i | \(-0.649042\pi\) | ||||
−0.451306 | + | 0.892369i | \(0.649042\pi\) | |||||||
\(410\) | 32.9956 | 1.62953 | ||||||||
\(411\) | −18.9134 | −0.932929 | ||||||||
\(412\) | 8.01835 | 0.395036 | ||||||||
\(413\) | −10.6556 | −0.524330 | ||||||||
\(414\) | −10.3637 | −0.509349 | ||||||||
\(415\) | 42.0301 | 2.06318 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.67501 | −0.277906 | ||||||||
\(418\) | 56.1916 | 2.74842 | ||||||||
\(419\) | 13.6934 | 0.668964 | 0.334482 | − | 0.942402i | \(-0.391439\pi\) | ||||
0.334482 | + | 0.942402i | \(0.391439\pi\) | |||||||
\(420\) | 18.1289 | 0.884598 | ||||||||
\(421\) | −33.8146 | −1.64802 | −0.824012 | − | 0.566573i | \(-0.808269\pi\) | ||||
−0.824012 | + | 0.566573i | \(0.808269\pi\) | |||||||
\(422\) | 30.4728 | 1.48339 | ||||||||
\(423\) | −11.0983 | −0.539620 | ||||||||
\(424\) | 9.68009 | 0.470107 | ||||||||
\(425\) | 29.9909 | 1.45477 | ||||||||
\(426\) | 6.65564 | 0.322467 | ||||||||
\(427\) | −4.10089 | −0.198456 | ||||||||
\(428\) | −4.05309 | −0.195913 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.0336 | 2.31639 | ||||||||
\(431\) | 20.3256 | 0.979048 | 0.489524 | − | 0.871990i | \(-0.337171\pi\) | ||||
0.489524 | + | 0.871990i | \(0.337171\pi\) | |||||||
\(432\) | −9.34181 | −0.449458 | ||||||||
\(433\) | 17.1106 | 0.822284 | 0.411142 | − | 0.911571i | \(-0.365130\pi\) | ||||
0.411142 | + | 0.911571i | \(0.365130\pi\) | |||||||
\(434\) | 2.26283 | 0.108619 | ||||||||
\(435\) | −10.8635 | −0.520865 | ||||||||
\(436\) | 86.1427 | 4.12549 | ||||||||
\(437\) | 33.5858 | 1.60663 | ||||||||
\(438\) | −17.6312 | −0.842451 | ||||||||
\(439\) | 1.67501 | 0.0799436 | 0.0399718 | − | 0.999201i | \(-0.487273\pi\) | ||||
0.0399718 | + | 0.999201i | \(0.487273\pi\) | |||||||
\(440\) | 70.2487 | 3.34897 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.9073 | −0.613245 | −0.306622 | − | 0.951831i | \(-0.599199\pi\) | ||||
−0.306622 | + | 0.951831i | \(0.599199\pi\) | |||||||
\(444\) | −24.4595 | −1.16080 | ||||||||
\(445\) | 20.9206 | 0.991730 | ||||||||
\(446\) | 11.0485 | 0.523159 | ||||||||
\(447\) | −8.49259 | −0.401686 | ||||||||
\(448\) | 6.88795 | 0.325425 | ||||||||
\(449\) | −21.1762 | −0.999368 | −0.499684 | − | 0.866208i | \(-0.666550\pi\) | ||||
−0.499684 | + | 0.866208i | \(0.666550\pi\) | |||||||
\(450\) | 24.3373 | 1.14727 | ||||||||
\(451\) | 8.54401 | 0.402322 | ||||||||
\(452\) | 13.7321 | 0.645903 | ||||||||
\(453\) | 14.2190 | 0.668068 | ||||||||
\(454\) | −4.49768 | −0.211087 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 61.3011 | 2.87069 | ||||||||
\(457\) | −8.41570 | −0.393670 | −0.196835 | − | 0.980437i | \(-0.563066\pi\) | ||||
−0.196835 | + | 0.980437i | \(0.563066\pi\) | |||||||
\(458\) | −17.7892 | −0.831232 | ||||||||
\(459\) | −3.21040 | −0.149848 | ||||||||
\(460\) | 72.1183 | 3.36253 | ||||||||
\(461\) | 1.76515 | 0.0822113 | 0.0411056 | − | 0.999155i | \(-0.486912\pi\) | ||||
0.0411056 | + | 0.999155i | \(0.486912\pi\) | |||||||
\(462\) | 6.65564 | 0.309649 | ||||||||
\(463\) | −38.9241 | −1.80896 | −0.904479 | − | 0.426519i | \(-0.859740\pi\) | ||||
−0.904479 | + | 0.426519i | \(0.859740\pi\) | |||||||
\(464\) | −26.7978 | −1.24406 | ||||||||
\(465\) | 3.28938 | 0.152541 | ||||||||
\(466\) | 3.47323 | 0.160894 | ||||||||
\(467\) | 30.4544 | 1.40926 | 0.704631 | − | 0.709573i | \(-0.251112\pi\) | ||||
0.704631 | + | 0.709573i | \(0.251112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8467 | −0.500853 | ||||||||
\(470\) | 109.497 | 5.05071 | ||||||||
\(471\) | −8.42079 | −0.388010 | ||||||||
\(472\) | −77.3689 | −3.56119 | ||||||||
\(473\) | 12.4380 | 0.571902 | ||||||||
\(474\) | 3.21040 | 0.147458 | ||||||||
\(475\) | −78.8701 | −3.61881 | ||||||||
\(476\) | 15.3684 | 0.704408 | ||||||||
\(477\) | 1.33319 | 0.0610427 | ||||||||
\(478\) | 10.1859 | 0.465894 | ||||||||
\(479\) | 3.54656 | 0.162046 | 0.0810232 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810232 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(480\) | 37.1722 | 1.69667 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 66.1467 | 3.01290 | ||||||||
\(483\) | 3.97809 | 0.181009 | ||||||||
\(484\) | −21.4136 | −0.973346 | ||||||||
\(485\) | −21.4279 | −0.972990 | ||||||||
\(486\) | −2.60520 | −0.118174 | ||||||||
\(487\) | 39.9898 | 1.81211 | 0.906056 | − | 0.423158i | \(-0.139078\pi\) | ||||
0.906056 | + | 0.423158i | \(0.139078\pi\) | |||||||
\(488\) | −29.7759 | −1.34789 | ||||||||
\(489\) | −3.77589 | −0.170752 | ||||||||
\(490\) | −9.86604 | −0.445702 | ||||||||
\(491\) | 9.69844 | 0.437685 | 0.218842 | − | 0.975760i | \(-0.429772\pi\) | ||||
0.218842 | + | 0.975760i | \(0.429772\pi\) | |||||||
\(492\) | 16.0096 | 0.721770 | ||||||||
\(493\) | −9.20929 | −0.414766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.67501 | 0.434859 | ||||||||
\(496\) | 8.11415 | 0.364336 | ||||||||
\(497\) | −2.55475 | −0.114596 | ||||||||
\(498\) | 28.9134 | 1.29564 | ||||||||
\(499\) | 24.0336 | 1.07589 | 0.537947 | − | 0.842979i | \(-0.319200\pi\) | ||||
0.537947 | + | 0.842979i | \(0.319200\pi\) | |||||||
\(500\) | −78.7122 | −3.52012 | ||||||||
\(501\) | 8.83551 | 0.394741 | ||||||||
\(502\) | 67.1381 | 2.99652 | ||||||||
\(503\) | 3.67390 | 0.163811 | 0.0819056 | − | 0.996640i | \(-0.473899\pi\) | ||||
0.0819056 | + | 0.996640i | \(0.473899\pi\) | |||||||
\(504\) | 7.26084 | 0.323424 | ||||||||
\(505\) | −33.8849 | −1.50786 | ||||||||
\(506\) | 26.4768 | 1.17704 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −82.3628 | −3.65426 | ||||||||
\(509\) | 19.3612 | 0.858169 | 0.429085 | − | 0.903264i | \(-0.358836\pi\) | ||||
0.429085 | + | 0.903264i | \(0.358836\pi\) | |||||||
\(510\) | 31.6739 | 1.40254 | ||||||||
\(511\) | 6.76770 | 0.299385 | ||||||||
\(512\) | −43.9634 | −1.94293 | ||||||||
\(513\) | 8.44270 | 0.372754 | ||||||||
\(514\) | −15.3102 | −0.675303 | ||||||||
\(515\) | −6.34334 | −0.279521 | ||||||||
\(516\) | 23.3062 | 1.02600 | ||||||||
\(517\) | 28.3535 | 1.24699 | ||||||||
\(518\) | 13.3113 | 0.584864 | ||||||||
\(519\) | 17.6750 | 0.775847 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.1130 | 1.49452 | 0.747260 | − | 0.664532i | \(-0.231369\pi\) | ||||
0.747260 | + | 0.664532i | \(0.231369\pi\) | |||||||
\(522\) | −7.47323 | −0.327094 | ||||||||
\(523\) | −33.0250 | −1.44408 | −0.722042 | − | 0.691850i | \(-0.756796\pi\) | ||||
−0.722042 | + | 0.691850i | \(0.756796\pi\) | |||||||
\(524\) | 79.8655 | 3.48894 | ||||||||
\(525\) | −9.34181 | −0.407710 | ||||||||
\(526\) | −26.6796 | −1.16329 | ||||||||
\(527\) | 2.78850 | 0.121469 | ||||||||
\(528\) | 23.8660 | 1.03864 | ||||||||
\(529\) | −7.17478 | −0.311947 | ||||||||
\(530\) | −13.1533 | −0.571344 | ||||||||
\(531\) | −10.6556 | −0.462415 | ||||||||
\(532\) | −40.4157 | −1.75224 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.3917 | 0.622790 | ||||||||
\(535\) | 3.20641 | 0.138625 | ||||||||
\(536\) | −78.7560 | −3.40174 | ||||||||
\(537\) | 16.9073 | 0.729604 | ||||||||
\(538\) | −42.0469 | −1.81277 | ||||||||
\(539\) | −2.55475 | −0.110041 | ||||||||
\(540\) | 18.1289 | 0.780142 | ||||||||
\(541\) | 24.8416 | 1.06802 | 0.534012 | − | 0.845477i | \(-0.320684\pi\) | ||||
0.534012 | + | 0.845477i | \(0.320684\pi\) | |||||||
\(542\) | 31.9339 | 1.37168 | ||||||||
\(543\) | 7.73717 | 0.332034 | ||||||||
\(544\) | 31.5120 | 1.35106 | ||||||||
\(545\) | −68.1478 | −2.91913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.14114 | 0.348090 | 0.174045 | − | 0.984738i | \(-0.444316\pi\) | ||||
0.174045 | + | 0.984738i | \(0.444316\pi\) | |||||||
\(548\) | 90.5395 | 3.86766 | ||||||||
\(549\) | −4.10089 | −0.175022 | ||||||||
\(550\) | −62.1758 | −2.65118 | ||||||||
\(551\) | 24.2186 | 1.03175 | ||||||||
\(552\) | 28.8843 | 1.22940 | ||||||||
\(553\) | −1.23230 | −0.0524029 | ||||||||
\(554\) | −25.5701 | −1.08637 | ||||||||
\(555\) | 19.3500 | 0.821362 | ||||||||
\(556\) | 27.1666 | 1.15212 | ||||||||
\(557\) | −8.11052 | −0.343654 | −0.171827 | − | 0.985127i | \(-0.554967\pi\) | ||||
−0.171827 | + | 0.985127i | \(0.554967\pi\) | |||||||
\(558\) | 2.26283 | 0.0957933 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −35.3780 | −1.49499 | ||||||||
\(561\) | 8.20178 | 0.346279 | ||||||||
\(562\) | −42.1809 | −1.77929 | ||||||||
\(563\) | −11.1044 | −0.467995 | −0.233998 | − | 0.972237i | \(-0.575181\pi\) | ||||
−0.233998 | + | 0.972237i | \(0.575181\pi\) | |||||||
\(564\) | 53.1284 | 2.23711 | ||||||||
\(565\) | −10.8635 | −0.457031 | ||||||||
\(566\) | −49.8849 | −2.09682 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −18.5497 | −0.778327 | ||||||||
\(569\) | −2.86858 | −0.120257 | −0.0601286 | − | 0.998191i | \(-0.519151\pi\) | ||||
−0.0601286 | + | 0.998191i | \(0.519151\pi\) | |||||||
\(570\) | −83.2960 | −3.48889 | ||||||||
\(571\) | −32.4947 | −1.35986 | −0.679930 | − | 0.733277i | \(-0.737990\pi\) | ||||
−0.679930 | + | 0.733277i | \(0.737990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.57412 | −0.232862 | ||||||||
\(574\) | −8.71272 | −0.363662 | ||||||||
\(575\) | −37.1626 | −1.54979 | ||||||||
\(576\) | 6.88795 | 0.286998 | ||||||||
\(577\) | −24.3759 | −1.01478 | −0.507390 | − | 0.861716i | \(-0.669390\pi\) | ||||
−0.507390 | + | 0.861716i | \(0.669390\pi\) | |||||||
\(578\) | −17.4375 | −0.725305 | ||||||||
\(579\) | −7.57412 | −0.314770 | ||||||||
\(580\) | 52.0042 | 2.15936 | ||||||||
\(581\) | −11.0983 | −0.460437 | ||||||||
\(582\) | −14.7407 | −0.611022 | ||||||||
\(583\) | −3.40598 | −0.141061 | ||||||||
\(584\) | 49.1392 | 2.03339 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 64.2767 | 2.65524 | ||||||||
\(587\) | −11.7483 | −0.484906 | −0.242453 | − | 0.970163i | \(-0.577952\pi\) | ||||
−0.242453 | + | 0.970163i | \(0.577952\pi\) | |||||||
\(588\) | −4.78706 | −0.197415 | ||||||||
\(589\) | −7.33319 | −0.302159 | ||||||||
\(590\) | 105.129 | 4.32809 | ||||||||
\(591\) | 13.3444 | 0.548914 | ||||||||
\(592\) | 47.7321 | 1.96178 | ||||||||
\(593\) | −46.6459 | −1.91552 | −0.957759 | − | 0.287574i | \(-0.907151\pi\) | ||||
−0.957759 | + | 0.287574i | \(0.907151\pi\) | |||||||
\(594\) | 6.65564 | 0.273084 | ||||||||
\(595\) | −12.1580 | −0.498428 | ||||||||
\(596\) | 40.6545 | 1.66527 | ||||||||
\(597\) | −16.8854 | −0.691073 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8197 | −0.850669 | −0.425335 | − | 0.905036i | \(-0.639844\pi\) | ||||
−0.425335 | + | 0.905036i | \(0.639844\pi\) | |||||||
\(600\) | −67.8294 | −2.76912 | ||||||||
\(601\) | 24.2588 | 0.989539 | 0.494770 | − | 0.869024i | \(-0.335252\pi\) | ||||
0.494770 | + | 0.869024i | \(0.335252\pi\) | |||||||
\(602\) | −12.6836 | −0.516946 | ||||||||
\(603\) | −10.8467 | −0.441711 | ||||||||
\(604\) | −68.0673 | −2.76962 | ||||||||
\(605\) | 16.9404 | 0.688724 | ||||||||
\(606\) | −23.3102 | −0.946911 | ||||||||
\(607\) | 6.20067 | 0.251677 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(608\) | −82.8701 | −3.36083 | ||||||||
\(609\) | 2.86858 | 0.116241 | ||||||||
\(610\) | 40.4595 | 1.63816 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.3684 | 0.621229 | ||||||||
\(613\) | −14.9026 | −0.601912 | −0.300956 | − | 0.953638i | \(-0.597306\pi\) | ||||
−0.300956 | + | 0.953638i | \(0.597306\pi\) | |||||||
\(614\) | 35.8319 | 1.44606 | ||||||||
\(615\) | −12.6653 | −0.510713 | ||||||||
\(616\) | −18.5497 | −0.747387 | ||||||||
\(617\) | −24.1472 | −0.972130 | −0.486065 | − | 0.873923i | \(-0.661568\pi\) | ||||
−0.486065 | + | 0.873923i | \(0.661568\pi\) | |||||||
\(618\) | −4.36372 | −0.175535 | ||||||||
\(619\) | −43.9339 | −1.76585 | −0.882925 | − | 0.469513i | \(-0.844429\pi\) | ||||
−0.882925 | + | 0.469513i | \(0.844429\pi\) | |||||||
\(620\) | −15.7464 | −0.632392 | ||||||||
\(621\) | 3.97809 | 0.159635 | ||||||||
\(622\) | −31.6739 | −1.27001 | ||||||||
\(623\) | −5.52423 | −0.221323 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5604 | 0.622416 | ||||||||
\(626\) | 56.4544 | 2.25637 | ||||||||
\(627\) | −21.5690 | −0.861384 | ||||||||
\(628\) | 40.3108 | 1.60858 | ||||||||
\(629\) | 16.4036 | 0.654052 | ||||||||
\(630\) | −9.86604 | −0.393072 | ||||||||
\(631\) | 25.9511 | 1.03310 | 0.516548 | − | 0.856258i | \(-0.327217\pi\) | ||||
0.516548 | + | 0.856258i | \(0.327217\pi\) | |||||||
\(632\) | −8.94756 | −0.355915 | ||||||||
\(633\) | −11.6969 | −0.464911 | ||||||||
\(634\) | −76.5355 | −3.03961 | ||||||||
\(635\) | 65.1575 | 2.58570 | ||||||||
\(636\) | −6.38207 | −0.253065 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 19.0923 | 0.755870 | ||||||||
\(639\) | −2.55475 | −0.101065 | ||||||||
\(640\) | 6.38772 | 0.252497 | ||||||||
\(641\) | 39.5858 | 1.56355 | 0.781773 | − | 0.623563i | \(-0.214315\pi\) | ||||
0.781773 | + | 0.623563i | \(0.214315\pi\) | |||||||
\(642\) | 2.20576 | 0.0870544 | ||||||||
\(643\) | −17.0434 | −0.672125 | −0.336062 | − | 0.941840i | \(-0.609095\pi\) | ||||
−0.336062 | + | 0.941840i | \(0.609095\pi\) | |||||||
\(644\) | −19.0434 | −0.750414 | ||||||||
\(645\) | −18.4376 | −0.725980 | ||||||||
\(646\) | −70.6124 | −2.77821 | ||||||||
\(647\) | 27.7544 | 1.09114 | 0.545569 | − | 0.838066i | \(-0.316313\pi\) | ||||
0.545569 | + | 0.838066i | \(0.316313\pi\) | |||||||
\(648\) | 7.26084 | 0.285233 | ||||||||
\(649\) | 27.2225 | 1.06858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.868584 | −0.0340425 | ||||||||
\(652\) | 18.0754 | 0.707888 | ||||||||
\(653\) | −7.77080 | −0.304095 | −0.152048 | − | 0.988373i | \(-0.548587\pi\) | ||||
−0.152048 | + | 0.988373i | \(0.548587\pi\) | |||||||
\(654\) | −46.8803 | −1.83317 | ||||||||
\(655\) | −63.1819 | −2.46872 | ||||||||
\(656\) | −31.2424 | −1.21981 | ||||||||
\(657\) | 6.76770 | 0.264033 | ||||||||
\(658\) | −28.9134 | −1.12716 | ||||||||
\(659\) | −4.74935 | −0.185008 | −0.0925042 | − | 0.995712i | \(-0.529487\pi\) | ||||
−0.0925042 | + | 0.995712i | \(0.529487\pi\) | |||||||
\(660\) | −46.3148 | −1.80280 | ||||||||
\(661\) | 38.0301 | 1.47920 | 0.739599 | − | 0.673047i | \(-0.235015\pi\) | ||||
0.739599 | + | 0.673047i | \(0.235015\pi\) | |||||||
\(662\) | 62.2965 | 2.42122 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −80.5833 | −3.12724 | ||||||||
\(665\) | 31.9730 | 1.23986 | ||||||||
\(666\) | 13.3113 | 0.515802 | ||||||||
\(667\) | 11.4115 | 0.441855 | ||||||||
\(668\) | −42.2961 | −1.63649 | ||||||||
\(669\) | −4.24093 | −0.163964 | ||||||||
\(670\) | 107.014 | 4.13430 | ||||||||
\(671\) | 10.4768 | 0.404451 | ||||||||
\(672\) | −9.81560 | −0.378645 | ||||||||
\(673\) | −23.0602 | −0.888905 | −0.444452 | − | 0.895803i | \(-0.646602\pi\) | ||||
−0.444452 | + | 0.895803i | \(0.646602\pi\) | |||||||
\(674\) | 40.5644 | 1.56248 | ||||||||
\(675\) | −9.34181 | −0.359567 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.3759 | −1.70550 | −0.852752 | − | 0.522317i | \(-0.825068\pi\) | ||||
−0.852752 | + | 0.522317i | \(0.825068\pi\) | |||||||
\(678\) | −7.47323 | −0.287008 | ||||||||
\(679\) | 5.65819 | 0.217141 | ||||||||
\(680\) | −88.2770 | −3.38527 | ||||||||
\(681\) | 1.72643 | 0.0661568 | ||||||||
\(682\) | −5.78098 | −0.221365 | ||||||||
\(683\) | −5.91494 | −0.226329 | −0.113165 | − | 0.993576i | \(-0.536099\pi\) | ||||
−0.113165 | + | 0.993576i | \(0.536099\pi\) | |||||||
\(684\) | −40.4157 | −1.54533 | ||||||||
\(685\) | −71.6261 | −2.73669 | ||||||||
\(686\) | 2.60520 | 0.0994669 | ||||||||
\(687\) | 6.82833 | 0.260517 | ||||||||
\(688\) | −45.4814 | −1.73396 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −39.2480 | −1.49415 | ||||||||
\(691\) | −12.6883 | −0.482685 | −0.241343 | − | 0.970440i | \(-0.577588\pi\) | ||||
−0.241343 | + | 0.970440i | \(0.577588\pi\) | |||||||
\(692\) | −84.6113 | −3.21644 | ||||||||
\(693\) | −2.55475 | −0.0970471 | ||||||||
\(694\) | 2.73143 | 0.103683 | ||||||||
\(695\) | −21.4916 | −0.815222 | ||||||||
\(696\) | 20.8283 | 0.789496 | ||||||||
\(697\) | −10.7367 | −0.406682 | ||||||||
\(698\) | −36.1396 | −1.36790 | ||||||||
\(699\) | −1.33319 | −0.0504260 | ||||||||
\(700\) | 44.7198 | 1.69025 | ||||||||
\(701\) | −25.8487 | −0.976291 | −0.488146 | − | 0.872762i | \(-0.662326\pi\) | ||||
−0.488146 | + | 0.872762i | \(0.662326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.1381 | −1.62698 | ||||||||
\(704\) | −17.5970 | −0.663212 | ||||||||
\(705\) | −42.0301 | −1.58294 | ||||||||
\(706\) | −25.9658 | −0.977237 | ||||||||
\(707\) | 8.94756 | 0.336508 | ||||||||
\(708\) | 51.0092 | 1.91704 | ||||||||
\(709\) | −18.8803 | −0.709065 | −0.354533 | − | 0.935044i | \(-0.615360\pi\) | ||||
−0.354533 | + | 0.935044i | \(0.615360\pi\) | |||||||
\(710\) | 25.2053 | 0.945938 | ||||||||
\(711\) | −1.23230 | −0.0462150 | ||||||||
\(712\) | −40.1105 | −1.50321 | ||||||||
\(713\) | −3.45531 | −0.129402 | ||||||||
\(714\) | −8.36372 | −0.313004 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −80.9363 | −3.02473 | ||||||||
\(717\) | −3.90985 | −0.146016 | ||||||||
\(718\) | 49.4218 | 1.84441 | ||||||||
\(719\) | 40.1580 | 1.49764 | 0.748820 | − | 0.662774i | \(-0.230621\pi\) | ||||
0.748820 | + | 0.662774i | \(0.230621\pi\) | |||||||
\(720\) | −35.3780 | −1.31846 | ||||||||
\(721\) | 1.67501 | 0.0623804 | ||||||||
\(722\) | 136.198 | 5.06875 | ||||||||
\(723\) | −25.3903 | −0.944274 | ||||||||
\(724\) | −37.0383 | −1.37652 | ||||||||
\(725\) | −26.7978 | −0.995244 | ||||||||
\(726\) | 11.6537 | 0.432508 | ||||||||
\(727\) | 32.0336 | 1.18806 | 0.594031 | − | 0.804442i | \(-0.297536\pi\) | ||||
0.594031 | + | 0.804442i | \(0.297536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −66.7704 | −2.47128 | ||||||||
\(731\) | −15.6301 | −0.578100 | ||||||||
\(732\) | 19.6312 | 0.725590 | ||||||||
\(733\) | 48.3265 | 1.78498 | 0.892491 | − | 0.451066i | \(-0.148956\pi\) | ||||
0.892491 | + | 0.451066i | \(0.148956\pi\) | |||||||
\(734\) | 58.2487 | 2.15000 | ||||||||
\(735\) | 3.78706 | 0.139688 | ||||||||
\(736\) | −39.0473 | −1.43930 | ||||||||
\(737\) | 27.7106 | 1.02073 | ||||||||
\(738\) | −8.71272 | −0.320719 | ||||||||
\(739\) | −35.7321 | −1.31443 | −0.657213 | − | 0.753705i | \(-0.728265\pi\) | ||||
−0.657213 | + | 0.753705i | \(0.728265\pi\) | |||||||
\(740\) | −92.6296 | −3.40513 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.47323 | 0.127506 | ||||||||
\(743\) | −45.0092 | −1.65123 | −0.825613 | − | 0.564236i | \(-0.809171\pi\) | ||||
−0.825613 | + | 0.564236i | \(0.809171\pi\) | |||||||
\(744\) | −6.30665 | −0.231213 | ||||||||
\(745\) | −32.1619 | −1.17832 | ||||||||
\(746\) | 67.9847 | 2.48910 | ||||||||
\(747\) | −11.0983 | −0.406067 | ||||||||
\(748\) | −39.2624 | −1.43557 | ||||||||
\(749\) | −0.846676 | −0.0309369 | ||||||||
\(750\) | 42.8365 | 1.56417 | ||||||||
\(751\) | −5.39425 | −0.196839 | −0.0984195 | − | 0.995145i | \(-0.531379\pi\) | ||||
−0.0984195 | + | 0.995145i | \(0.531379\pi\) | |||||||
\(752\) | −103.679 | −3.78077 | ||||||||
\(753\) | −25.7708 | −0.939140 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.8483 | 1.95974 | ||||||||
\(756\) | −4.78706 | −0.174104 | ||||||||
\(757\) | 13.7896 | 0.501191 | 0.250595 | − | 0.968092i | \(-0.419374\pi\) | ||||
0.250595 | + | 0.968092i | \(0.419374\pi\) | |||||||
\(758\) | −31.2624 | −1.13550 | ||||||||
\(759\) | −10.1631 | −0.368895 | ||||||||
\(760\) | 232.151 | 8.42100 | ||||||||
\(761\) | −30.6674 | −1.11169 | −0.555846 | − | 0.831286i | \(-0.687605\pi\) | ||||
−0.555846 | + | 0.831286i | \(0.687605\pi\) | |||||||
\(762\) | 44.8232 | 1.62377 | ||||||||
\(763\) | 17.9949 | 0.651460 | ||||||||
\(764\) | 26.6836 | 0.965380 | ||||||||
\(765\) | −12.1580 | −0.439572 | ||||||||
\(766\) | −12.9277 | −0.467099 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 18.1701 | 0.655659 | ||||||||
\(769\) | −48.6160 | −1.75314 | −0.876568 | − | 0.481278i | \(-0.840173\pi\) | ||||
−0.876568 | + | 0.481278i | \(0.840173\pi\) | |||||||
\(770\) | 25.2053 | 0.908336 | ||||||||
\(771\) | 5.87678 | 0.211647 | ||||||||
\(772\) | 36.2577 | 1.30494 | ||||||||
\(773\) | 18.6729 | 0.671617 | 0.335808 | − | 0.941930i | \(-0.390991\pi\) | ||||
0.335808 | + | 0.941930i | \(0.390991\pi\) | |||||||
\(774\) | −12.6836 | −0.455904 | ||||||||
\(775\) | 8.11415 | 0.291469 | ||||||||
\(776\) | 41.0832 | 1.47480 | ||||||||
\(777\) | −5.10951 | −0.183303 | ||||||||
\(778\) | −46.5697 | −1.66960 | ||||||||
\(779\) | 28.2354 | 1.01164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.52677 | 0.233546 | ||||||||
\(782\) | −33.2717 | −1.18979 | ||||||||
\(783\) | 2.86858 | 0.102515 | ||||||||
\(784\) | 9.34181 | 0.333636 | ||||||||
\(785\) | −31.8900 | −1.13820 | ||||||||
\(786\) | −43.4642 | −1.55032 | ||||||||
\(787\) | 9.61751 | 0.342827 | 0.171414 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171414 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(788\) | −63.8802 | −2.27564 | ||||||||
\(789\) | 10.2409 | 0.364587 | ||||||||
\(790\) | 12.1580 | 0.432561 | ||||||||
\(791\) | 2.86858 | 0.101995 | ||||||||
\(792\) | −18.5497 | −0.659134 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.4168 | −0.653588 | ||||||||
\(795\) | 5.04888 | 0.179065 | ||||||||
\(796\) | 80.8314 | 2.86499 | ||||||||
\(797\) | 3.73606 | 0.132338 | 0.0661691 | − | 0.997808i | \(-0.478922\pi\) | ||||
0.0661691 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(798\) | 21.9949 | 0.778611 | ||||||||
\(799\) | −35.6301 | −1.26050 | ||||||||
\(800\) | 91.6955 | 3.24192 | ||||||||
\(801\) | −5.52423 | −0.195189 | ||||||||
\(802\) | 23.7601 | 0.838997 | ||||||||
\(803\) | −17.2898 | −0.610144 | ||||||||
\(804\) | 51.9237 | 1.83121 | ||||||||
\(805\) | 15.0653 | 0.530981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1396 | 0.568141 | ||||||||
\(808\) | 64.9668 | 2.28553 | ||||||||
\(809\) | −10.1850 | −0.358084 | −0.179042 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179042 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(810\) | −9.86604 | −0.346657 | ||||||||
\(811\) | 6.21902 | 0.218379 | 0.109190 | − | 0.994021i | \(-0.465174\pi\) | ||||
0.109190 | + | 0.994021i | \(0.465174\pi\) | |||||||
\(812\) | −13.7321 | −0.481901 | ||||||||
\(813\) | −12.2577 | −0.429898 | ||||||||
\(814\) | −34.0071 | −1.19195 | ||||||||
\(815\) | −14.2995 | −0.500891 | ||||||||
\(816\) | −29.9909 | −1.04989 | ||||||||
\(817\) | 41.1040 | 1.43805 | ||||||||
\(818\) | −47.5558 | −1.66275 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.6294 | 2.11727 | ||||||||
\(821\) | −55.4534 | −1.93534 | −0.967669 | − | 0.252224i | \(-0.918838\pi\) | ||||
−0.967669 | + | 0.252224i | \(0.918838\pi\) | |||||||
\(822\) | −49.2731 | −1.71860 | ||||||||
\(823\) | 20.4380 | 0.712425 | 0.356213 | − | 0.934405i | \(-0.384068\pi\) | ||||
0.356213 | + | 0.934405i | \(0.384068\pi\) | |||||||
\(824\) | 12.1619 | 0.423681 | ||||||||
\(825\) | 23.8660 | 0.830909 | ||||||||
\(826\) | −27.7601 | −0.965896 | ||||||||
\(827\) | 14.1289 | 0.491309 | 0.245655 | − | 0.969357i | \(-0.420997\pi\) | ||||
0.245655 | + | 0.969357i | \(0.420997\pi\) | |||||||
\(828\) | −19.0434 | −0.661803 | ||||||||
\(829\) | −34.9159 | −1.21268 | −0.606340 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606340 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(830\) | 109.497 | 3.80069 | ||||||||
\(831\) | 9.81504 | 0.340480 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.21040 | 0.111234 | ||||||||
\(834\) | −14.7845 | −0.511946 | ||||||||
\(835\) | 33.4606 | 1.15795 | ||||||||
\(836\) | 103.252 | 3.57105 | ||||||||
\(837\) | −0.868584 | −0.0300226 | ||||||||
\(838\) | 35.6739 | 1.23233 | ||||||||
\(839\) | −46.4437 | −1.60341 | −0.801707 | − | 0.597717i | \(-0.796075\pi\) | ||||
−0.801707 | + | 0.597717i | \(0.796075\pi\) | |||||||
\(840\) | 27.4972 | 0.948745 | ||||||||
\(841\) | −20.7712 | −0.716249 | ||||||||
\(842\) | −88.0938 | −3.03591 | ||||||||
\(843\) | 16.1910 | 0.557649 | ||||||||
\(844\) | 55.9938 | 1.92739 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.9134 | −0.994063 | ||||||||
\(847\) | −4.47323 | −0.153702 | ||||||||
\(848\) | 12.4544 | 0.427687 | ||||||||
\(849\) | 19.1482 | 0.657166 | ||||||||
\(850\) | 78.1323 | 2.67992 | ||||||||
\(851\) | −20.3261 | −0.696770 | ||||||||
\(852\) | 12.2298 | 0.418985 | ||||||||
\(853\) | −41.4462 | −1.41909 | −0.709546 | − | 0.704659i | \(-0.751100\pi\) | ||||
−0.709546 | + | 0.704659i | \(0.751100\pi\) | |||||||
\(854\) | −10.6836 | −0.365586 | ||||||||
\(855\) | 31.9730 | 1.09345 | ||||||||
\(856\) | −6.14758 | −0.210120 | ||||||||
\(857\) | −33.8666 | −1.15686 | −0.578431 | − | 0.815732i | \(-0.696335\pi\) | ||||
−0.578431 | + | 0.815732i | \(0.696335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.2890 | −1.27228 | −0.636141 | − | 0.771573i | \(-0.719470\pi\) | ||||
−0.636141 | + | 0.771573i | \(0.719470\pi\) | |||||||
\(860\) | 88.2619 | 3.00971 | ||||||||
\(861\) | 3.34436 | 0.113975 | ||||||||
\(862\) | 52.9521 | 1.80356 | ||||||||
\(863\) | 38.7464 | 1.31894 | 0.659471 | − | 0.751730i | \(-0.270781\pi\) | ||||
0.659471 | + | 0.751730i | \(0.270781\pi\) | |||||||
\(864\) | −9.81560 | −0.333933 | ||||||||
\(865\) | 66.9363 | 2.27590 | ||||||||
\(866\) | 44.5765 | 1.51477 | ||||||||
\(867\) | 6.69335 | 0.227318 | ||||||||
\(868\) | 4.15796 | 0.141130 | ||||||||
\(869\) | 3.14823 | 0.106797 | ||||||||
\(870\) | −28.3016 | −0.959513 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 130.658 | 4.42464 | ||||||||
\(873\) | 5.65819 | 0.191501 | ||||||||
\(874\) | 87.4978 | 2.95966 | ||||||||
\(875\) | −16.4427 | −0.555865 | ||||||||
\(876\) | −32.3974 | −1.09461 | ||||||||
\(877\) | 51.8319 | 1.75024 | 0.875119 | − | 0.483908i | \(-0.160783\pi\) | ||||
0.875119 | + | 0.483908i | \(0.160783\pi\) | |||||||
\(878\) | 4.36372 | 0.147268 | ||||||||
\(879\) | −24.6725 | −0.832181 | ||||||||
\(880\) | 90.3821 | 3.04678 | ||||||||
\(881\) | −20.7896 | −0.700420 | −0.350210 | − | 0.936671i | \(-0.613890\pi\) | ||||
−0.350210 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(882\) | 2.60520 | 0.0877216 | ||||||||
\(883\) | −17.5292 | −0.589904 | −0.294952 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294952 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.3535 | −1.35647 | ||||||||
\(886\) | −33.6261 | −1.12969 | ||||||||
\(887\) | 9.53539 | 0.320167 | 0.160084 | − | 0.987103i | \(-0.448824\pi\) | ||||
0.160084 | + | 0.987103i | \(0.448824\pi\) | |||||||
\(888\) | −37.0993 | −1.24497 | ||||||||
\(889\) | −17.2053 | −0.577047 | ||||||||
\(890\) | 54.5022 | 1.82692 | ||||||||
\(891\) | −2.55475 | −0.0855875 | ||||||||
\(892\) | 20.3016 | 0.679746 | ||||||||
\(893\) | 93.7000 | 3.13555 | ||||||||
\(894\) | −22.1249 | −0.739967 | ||||||||
\(895\) | 64.0290 | 2.14025 | ||||||||
\(896\) | −1.68672 | −0.0563495 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.1683 | −1.84099 | ||||||||
\(899\) | −2.49160 | −0.0830997 | ||||||||
\(900\) | 44.7198 | 1.49066 | ||||||||
\(901\) | 4.28008 | 0.142590 | ||||||||
\(902\) | 22.2588 | 0.741139 | ||||||||
\(903\) | 4.86858 | 0.162016 | ||||||||
\(904\) | 20.8283 | 0.692740 | ||||||||
\(905\) | 29.3011 | 0.974002 | ||||||||
\(906\) | 37.0434 | 1.23068 | ||||||||
\(907\) | −27.3270 | −0.907378 | −0.453689 | − | 0.891160i | \(-0.649892\pi\) | ||||
−0.453689 | + | 0.891160i | \(0.649892\pi\) | |||||||
\(908\) | −8.26450 | −0.274267 | ||||||||
\(909\) | 8.94756 | 0.296772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.9582 | −1.29074 | −0.645371 | − | 0.763869i | \(-0.723297\pi\) | ||||
−0.645371 | + | 0.763869i | \(0.723297\pi\) | |||||||
\(912\) | 78.8701 | 2.61165 | ||||||||
\(913\) | 28.3535 | 0.938365 | ||||||||
\(914\) | −21.9246 | −0.725201 | ||||||||
\(915\) | −15.5303 | −0.513416 | ||||||||
\(916\) | −32.6876 | −1.08003 | ||||||||
\(917\) | 16.6836 | 0.550942 | ||||||||
\(918\) | −8.36372 | −0.276044 | ||||||||
\(919\) | 9.94293 | 0.327987 | 0.163993 | − | 0.986461i | \(-0.447562\pi\) | ||||
0.163993 | + | 0.986461i | \(0.447562\pi\) | |||||||
\(920\) | 109.387 | 3.60637 | ||||||||
\(921\) | −13.7540 | −0.453209 | ||||||||
\(922\) | 4.59857 | 0.151446 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.2298 | 0.402330 | ||||||||
\(925\) | 47.7321 | 1.56942 | ||||||||
\(926\) | −101.405 | −3.33238 | ||||||||
\(927\) | 1.67501 | 0.0550144 | ||||||||
\(928\) | −28.1569 | −0.924294 | ||||||||
\(929\) | −7.80854 | −0.256190 | −0.128095 | − | 0.991762i | \(-0.540886\pi\) | ||||
−0.128095 | + | 0.991762i | \(0.540886\pi\) | |||||||
\(930\) | 8.56948 | 0.281004 | ||||||||
\(931\) | −8.44270 | −0.276698 | ||||||||
\(932\) | 6.38207 | 0.209052 | ||||||||
\(933\) | 12.1580 | 0.398034 | ||||||||
\(934\) | 79.3398 | 2.59608 | ||||||||
\(935\) | 31.0606 | 1.01579 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.59246 | −0.313372 | −0.156686 | − | 0.987648i | \(-0.550081\pi\) | ||||
−0.156686 | + | 0.987648i | \(0.550081\pi\) | |||||||
\(938\) | −28.2577 | −0.922648 | ||||||||
\(939\) | −21.6699 | −0.707171 | ||||||||
\(940\) | 201.200 | 6.56243 | ||||||||
\(941\) | 28.5043 | 0.929214 | 0.464607 | − | 0.885517i | \(-0.346196\pi\) | ||||
0.464607 | + | 0.885517i | \(0.346196\pi\) | |||||||
\(942\) | −21.9378 | −0.714773 | ||||||||
\(943\) | 13.3042 | 0.433243 | ||||||||
\(944\) | −99.5430 | −3.23985 | ||||||||
\(945\) | 3.78706 | 0.123193 | ||||||||
\(946\) | 32.4036 | 1.05353 | ||||||||
\(947\) | −47.8997 | −1.55653 | −0.778265 | − | 0.627936i | \(-0.783900\pi\) | ||||
−0.778265 | + | 0.627936i | \(0.783900\pi\) | |||||||
\(948\) | 5.89911 | 0.191594 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −205.472 | −6.66640 | ||||||||
\(951\) | 29.3780 | 0.952647 | ||||||||
\(952\) | 23.3102 | 0.755487 | ||||||||
\(953\) | −32.5181 | −1.05337 | −0.526683 | − | 0.850062i | \(-0.676564\pi\) | ||||
−0.526683 | + | 0.850062i | \(0.676564\pi\) | |||||||
\(954\) | 3.47323 | 0.112450 | ||||||||
\(955\) | −21.1095 | −0.683088 | ||||||||
\(956\) | 18.7167 | 0.605341 | ||||||||
\(957\) | −7.32853 | −0.236898 | ||||||||
\(958\) | 9.23949 | 0.298514 | ||||||||
\(959\) | 18.9134 | 0.610745 | ||||||||
\(960\) | 26.0851 | 0.841892 | ||||||||
\(961\) | −30.2456 | −0.975663 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.846676 | −0.0272838 | ||||||||
\(964\) | 121.545 | 3.91469 | ||||||||
\(965\) | −28.6836 | −0.923359 | ||||||||
\(966\) | 10.3637 | 0.333447 | ||||||||
\(967\) | 18.0387 | 0.580086 | 0.290043 | − | 0.957014i | \(-0.406330\pi\) | ||||
0.290043 | + | 0.957014i | \(0.406330\pi\) | |||||||
\(968\) | −32.4794 | −1.04393 | ||||||||
\(969\) | 27.1044 | 0.870719 | ||||||||
\(970\) | −55.8239 | −1.79240 | ||||||||
\(971\) | 30.2190 | 0.969774 | 0.484887 | − | 0.874577i | \(-0.338861\pi\) | ||||
0.484887 | + | 0.874577i | \(0.338861\pi\) | |||||||
\(972\) | −4.78706 | −0.153545 | ||||||||
\(973\) | 5.67501 | 0.181932 | ||||||||
\(974\) | 104.181 | 3.33819 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.3097 | −1.22626 | ||||||||
\(977\) | −38.4652 | −1.23061 | −0.615305 | − | 0.788289i | \(-0.710967\pi\) | ||||
−0.615305 | + | 0.788289i | \(0.710967\pi\) | |||||||
\(978\) | −9.83695 | −0.314551 | ||||||||
\(979\) | 14.1130 | 0.451055 | ||||||||
\(980\) | −18.1289 | −0.579106 | ||||||||
\(981\) | 17.9949 | 0.574533 | ||||||||
\(982\) | 25.2664 | 0.806282 | ||||||||
\(983\) | −12.1742 | −0.388297 | −0.194149 | − | 0.980972i | \(-0.562194\pi\) | ||||
−0.194149 | + | 0.980972i | \(0.562194\pi\) | |||||||
\(984\) | 24.2828 | 0.774109 | ||||||||
\(985\) | 50.5359 | 1.61021 | ||||||||
\(986\) | −23.9920 | −0.764062 | ||||||||
\(987\) | 11.0983 | 0.353264 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.3677 | 0.615856 | ||||||||
\(990\) | 25.2053 | 0.801077 | ||||||||
\(991\) | 14.4982 | 0.460552 | 0.230276 | − | 0.973125i | \(-0.426037\pi\) | ||||
0.230276 | + | 0.973125i | \(0.426037\pi\) | |||||||
\(992\) | 8.52567 | 0.270690 | ||||||||
\(993\) | −23.9124 | −0.758836 | ||||||||
\(994\) | −6.65564 | −0.211104 | ||||||||
\(995\) | −63.9460 | −2.02722 | ||||||||
\(996\) | 53.1284 | 1.68344 | ||||||||
\(997\) | −9.35086 | −0.296145 | −0.148072 | − | 0.988977i | \(-0.547307\pi\) | ||||
−0.148072 | + | 0.988977i | \(0.547307\pi\) | |||||||
\(998\) | 62.6124 | 1.98196 | ||||||||
\(999\) | −5.10951 | −0.161658 |
(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 | 3549.2.a.v.1.4 | 4 | ||
13.5 | odd | 4 | 273.2.c.c.64.1 | ✓ | 8 | ||
13.8 | odd | 4 | 273.2.c.c.64.8 | yes | 8 | ||
13.12 | even | 2 | 3549.2.a.x.1.1 | 4 | |||
39.5 | even | 4 | 819.2.c.d.64.8 | 8 | |||
39.8 | even | 4 | 819.2.c.d.64.1 | 8 | |||
52.31 | even | 4 | 4368.2.h.q.337.8 | 8 | |||
52.47 | even | 4 | 4368.2.h.q.337.1 | 8 | |||
91.34 | even | 4 | 1911.2.c.l.883.8 | 8 | |||
91.83 | even | 4 | 1911.2.c.l.883.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.c.64.1 | ✓ | 8 | 13.5 | odd | 4 | ||
273.2.c.c.64.8 | yes | 8 | 13.8 | odd | 4 | ||
819.2.c.d.64.1 | 8 | 39.8 | even | 4 | |||
819.2.c.d.64.8 | 8 | 39.5 | even | 4 | |||
1911.2.c.l.883.1 | 8 | 91.83 | even | 4 | |||
1911.2.c.l.883.8 | 8 | 91.34 | even | 4 | |||
3549.2.a.v.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3549.2.a.x.1.1 | 4 | 13.12 | even | 2 | |||
4368.2.h.q.337.1 | 8 | 52.47 | even | 4 | |||
4368.2.h.q.337.8 | 8 | 52.31 | even | 4 |