Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.23488 | −1.29031 | −0.645154 | − | 0.764053i | \(-0.723207\pi\) | ||||
−0.645154 | + | 0.764053i | \(0.723207\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.812592 | 0.363402 | 0.181701 | − | 0.983354i | \(-0.441840\pi\) | ||||
0.181701 | + | 0.983354i | \(0.441840\pi\) | |||||||
\(6\) | −2.23488 | −0.912385 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.99468 | 0.664893 | ||||||||
\(10\) | 0.812592 | 0.256964 | ||||||||
\(11\) | 3.26531 | 0.984529 | 0.492265 | − | 0.870446i | \(-0.336169\pi\) | ||||
0.492265 | + | 0.870446i | \(0.336169\pi\) | |||||||
\(12\) | −2.23488 | −0.645154 | ||||||||
\(13\) | 2.96305 | 0.821801 | 0.410900 | − | 0.911680i | \(-0.365214\pi\) | ||||
0.410900 | + | 0.911680i | \(0.365214\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.81604 | −0.468900 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.78329 | −0.675047 | −0.337523 | − | 0.941317i | \(-0.609589\pi\) | ||||
−0.337523 | + | 0.941317i | \(0.609589\pi\) | |||||||
\(18\) | 1.99468 | 0.470150 | ||||||||
\(19\) | −4.32376 | −0.991938 | −0.495969 | − | 0.868340i | \(-0.665187\pi\) | ||||
−0.495969 | + | 0.868340i | \(0.665187\pi\) | |||||||
\(20\) | 0.812592 | 0.181701 | ||||||||
\(21\) | −2.23488 | −0.487690 | ||||||||
\(22\) | 3.26531 | 0.696167 | ||||||||
\(23\) | −8.63879 | −1.80131 | −0.900656 | − | 0.434533i | \(-0.856913\pi\) | ||||
−0.900656 | + | 0.434533i | \(0.856913\pi\) | |||||||
\(24\) | −2.23488 | −0.456193 | ||||||||
\(25\) | −4.33969 | −0.867939 | ||||||||
\(26\) | 2.96305 | 0.581101 | ||||||||
\(27\) | 2.24677 | 0.432391 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −9.37575 | −1.74103 | −0.870517 | − | 0.492139i | \(-0.836215\pi\) | ||||
−0.870517 | + | 0.492139i | \(0.836215\pi\) | |||||||
\(30\) | −1.81604 | −0.331563 | ||||||||
\(31\) | 5.70390 | 1.02445 | 0.512226 | − | 0.858851i | \(-0.328821\pi\) | ||||
0.512226 | + | 0.858851i | \(0.328821\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.29758 | −1.27035 | ||||||||
\(34\) | −2.78329 | −0.477330 | ||||||||
\(35\) | 0.812592 | 0.137353 | ||||||||
\(36\) | 1.99468 | 0.332446 | ||||||||
\(37\) | 7.34378 | 1.20731 | 0.603655 | − | 0.797246i | \(-0.293710\pi\) | ||||
0.603655 | + | 0.797246i | \(0.293710\pi\) | |||||||
\(38\) | −4.32376 | −0.701406 | ||||||||
\(39\) | −6.62204 | −1.06038 | ||||||||
\(40\) | 0.812592 | 0.128482 | ||||||||
\(41\) | 1.76139 | 0.275083 | 0.137541 | − | 0.990496i | \(-0.456080\pi\) | ||||
0.137541 | + | 0.990496i | \(0.456080\pi\) | |||||||
\(42\) | −2.23488 | −0.344849 | ||||||||
\(43\) | −1.70416 | −0.259882 | −0.129941 | − | 0.991522i | \(-0.541479\pi\) | ||||
−0.129941 | + | 0.991522i | \(0.541479\pi\) | |||||||
\(44\) | 3.26531 | 0.492265 | ||||||||
\(45\) | 1.62086 | 0.241624 | ||||||||
\(46\) | −8.63879 | −1.27372 | ||||||||
\(47\) | −9.53234 | −1.39043 | −0.695217 | − | 0.718800i | \(-0.744692\pi\) | ||||
−0.695217 | + | 0.718800i | \(0.744692\pi\) | |||||||
\(48\) | −2.23488 | −0.322577 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.33969 | −0.613725 | ||||||||
\(51\) | 6.22031 | 0.871018 | ||||||||
\(52\) | 2.96305 | 0.410900 | ||||||||
\(53\) | −11.7502 | −1.61401 | −0.807007 | − | 0.590541i | \(-0.798914\pi\) | ||||
−0.807007 | + | 0.590541i | \(0.798914\pi\) | |||||||
\(54\) | 2.24677 | 0.305747 | ||||||||
\(55\) | 2.65337 | 0.357780 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 9.66307 | 1.27990 | ||||||||
\(58\) | −9.37575 | −1.23110 | ||||||||
\(59\) | −8.71482 | −1.13457 | −0.567287 | − | 0.823520i | \(-0.692007\pi\) | ||||
−0.567287 | + | 0.823520i | \(0.692007\pi\) | |||||||
\(60\) | −1.81604 | −0.234450 | ||||||||
\(61\) | −4.63923 | −0.593992 | −0.296996 | − | 0.954879i | \(-0.595985\pi\) | ||||
−0.296996 | + | 0.954879i | \(0.595985\pi\) | |||||||
\(62\) | 5.70390 | 0.724396 | ||||||||
\(63\) | 1.99468 | 0.251306 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.40775 | 0.298644 | ||||||||
\(66\) | −7.29758 | −0.898270 | ||||||||
\(67\) | 9.29319 | 1.13534 | 0.567672 | − | 0.823255i | \(-0.307844\pi\) | ||||
0.567672 | + | 0.823255i | \(0.307844\pi\) | |||||||
\(68\) | −2.78329 | −0.337523 | ||||||||
\(69\) | 19.3066 | 2.32425 | ||||||||
\(70\) | 0.812592 | 0.0971233 | ||||||||
\(71\) | −16.1273 | −1.91396 | −0.956979 | − | 0.290156i | \(-0.906293\pi\) | ||||
−0.956979 | + | 0.290156i | \(0.906293\pi\) | |||||||
\(72\) | 1.99468 | 0.235075 | ||||||||
\(73\) | −11.0969 | −1.29879 | −0.649397 | − | 0.760450i | \(-0.724979\pi\) | ||||
−0.649397 | + | 0.760450i | \(0.724979\pi\) | |||||||
\(74\) | 7.34378 | 0.853697 | ||||||||
\(75\) | 9.69869 | 1.11991 | ||||||||
\(76\) | −4.32376 | −0.495969 | ||||||||
\(77\) | 3.26531 | 0.372117 | ||||||||
\(78\) | −6.62204 | −0.749799 | ||||||||
\(79\) | 9.75479 | 1.09750 | 0.548750 | − | 0.835987i | \(-0.315104\pi\) | ||||
0.548750 | + | 0.835987i | \(0.315104\pi\) | |||||||
\(80\) | 0.812592 | 0.0908505 | ||||||||
\(81\) | −11.0053 | −1.22281 | ||||||||
\(82\) | 1.76139 | 0.194513 | ||||||||
\(83\) | 10.2662 | 1.12686 | 0.563432 | − | 0.826163i | \(-0.309481\pi\) | ||||
0.563432 | + | 0.826163i | \(0.309481\pi\) | |||||||
\(84\) | −2.23488 | −0.243845 | ||||||||
\(85\) | −2.26168 | −0.245313 | ||||||||
\(86\) | −1.70416 | −0.183764 | ||||||||
\(87\) | 20.9537 | 2.24647 | ||||||||
\(88\) | 3.26531 | 0.348084 | ||||||||
\(89\) | 6.52666 | 0.691825 | 0.345912 | − | 0.938267i | \(-0.387569\pi\) | ||||
0.345912 | + | 0.938267i | \(0.387569\pi\) | |||||||
\(90\) | 1.62086 | 0.170854 | ||||||||
\(91\) | 2.96305 | 0.310612 | ||||||||
\(92\) | −8.63879 | −0.900656 | ||||||||
\(93\) | −12.7475 | −1.32186 | ||||||||
\(94\) | −9.53234 | −0.983186 | ||||||||
\(95\) | −3.51345 | −0.360472 | ||||||||
\(96\) | −2.23488 | −0.228096 | ||||||||
\(97\) | −1.25240 | −0.127162 | −0.0635812 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635812 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 6.51325 | 0.654607 | ||||||||
\(100\) | −4.33969 | −0.433969 | ||||||||
\(101\) | 13.8258 | 1.37572 | 0.687859 | − | 0.725845i | \(-0.258551\pi\) | ||||
0.687859 | + | 0.725845i | \(0.258551\pi\) | |||||||
\(102\) | 6.22031 | 0.615903 | ||||||||
\(103\) | 3.59568 | 0.354293 | 0.177147 | − | 0.984184i | \(-0.443313\pi\) | ||||
0.177147 | + | 0.984184i | \(0.443313\pi\) | |||||||
\(104\) | 2.96305 | 0.290551 | ||||||||
\(105\) | −1.81604 | −0.177228 | ||||||||
\(106\) | −11.7502 | −1.14128 | ||||||||
\(107\) | −0.761019 | −0.0735705 | −0.0367852 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367852 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(108\) | 2.24677 | 0.216196 | ||||||||
\(109\) | 8.13333 | 0.779031 | 0.389516 | − | 0.921020i | \(-0.372642\pi\) | ||||
0.389516 | + | 0.921020i | \(0.372642\pi\) | |||||||
\(110\) | 2.65337 | 0.252989 | ||||||||
\(111\) | −16.4125 | −1.55780 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −5.97693 | −0.562262 | −0.281131 | − | 0.959669i | \(-0.590710\pi\) | ||||
−0.281131 | + | 0.959669i | \(0.590710\pi\) | |||||||
\(114\) | 9.66307 | 0.905029 | ||||||||
\(115\) | −7.01981 | −0.654601 | ||||||||
\(116\) | −9.37575 | −0.870517 | ||||||||
\(117\) | 5.91032 | 0.546410 | ||||||||
\(118\) | −8.71482 | −0.802265 | ||||||||
\(119\) | −2.78329 | −0.255144 | ||||||||
\(120\) | −1.81604 | −0.165781 | ||||||||
\(121\) | −0.337724 | −0.0307022 | ||||||||
\(122\) | −4.63923 | −0.420016 | ||||||||
\(123\) | −3.93649 | −0.354942 | ||||||||
\(124\) | 5.70390 | 0.512226 | ||||||||
\(125\) | −7.58936 | −0.678813 | ||||||||
\(126\) | 1.99468 | 0.177700 | ||||||||
\(127\) | 6.98647 | 0.619949 | 0.309974 | − | 0.950745i | \(-0.399680\pi\) | ||||
0.309974 | + | 0.950745i | \(0.399680\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.80859 | 0.335327 | ||||||||
\(130\) | 2.40775 | 0.211173 | ||||||||
\(131\) | −0.0906462 | −0.00791980 | −0.00395990 | − | 0.999992i | \(-0.501260\pi\) | ||||
−0.00395990 | + | 0.999992i | \(0.501260\pi\) | |||||||
\(132\) | −7.29758 | −0.635173 | ||||||||
\(133\) | −4.32376 | −0.374917 | ||||||||
\(134\) | 9.29319 | 0.802809 | ||||||||
\(135\) | 1.82571 | 0.157132 | ||||||||
\(136\) | −2.78329 | −0.238665 | ||||||||
\(137\) | −12.7735 | −1.09131 | −0.545655 | − | 0.838010i | \(-0.683719\pi\) | ||||
−0.545655 | + | 0.838010i | \(0.683719\pi\) | |||||||
\(138\) | 19.3066 | 1.64349 | ||||||||
\(139\) | 14.4342 | 1.22429 | 0.612146 | − | 0.790745i | \(-0.290307\pi\) | ||||
0.612146 | + | 0.790745i | \(0.290307\pi\) | |||||||
\(140\) | 0.812592 | 0.0686766 | ||||||||
\(141\) | 21.3036 | 1.79409 | ||||||||
\(142\) | −16.1273 | −1.35337 | ||||||||
\(143\) | 9.67527 | 0.809087 | ||||||||
\(144\) | 1.99468 | 0.166223 | ||||||||
\(145\) | −7.61866 | −0.632695 | ||||||||
\(146\) | −11.0969 | −0.918386 | ||||||||
\(147\) | −2.23488 | −0.184330 | ||||||||
\(148\) | 7.34378 | 0.603655 | ||||||||
\(149\) | −16.3307 | −1.33786 | −0.668931 | − | 0.743324i | \(-0.733248\pi\) | ||||
−0.668931 | + | 0.743324i | \(0.733248\pi\) | |||||||
\(150\) | 9.69869 | 0.791894 | ||||||||
\(151\) | −4.18363 | −0.340459 | −0.170230 | − | 0.985404i | \(-0.554451\pi\) | ||||
−0.170230 | + | 0.985404i | \(0.554451\pi\) | |||||||
\(152\) | −4.32376 | −0.350703 | ||||||||
\(153\) | −5.55177 | −0.448834 | ||||||||
\(154\) | 3.26531 | 0.263127 | ||||||||
\(155\) | 4.63495 | 0.372288 | ||||||||
\(156\) | −6.62204 | −0.530188 | ||||||||
\(157\) | 22.1358 | 1.76663 | 0.883314 | − | 0.468782i | \(-0.155307\pi\) | ||||
0.883314 | + | 0.468782i | \(0.155307\pi\) | |||||||
\(158\) | 9.75479 | 0.776050 | ||||||||
\(159\) | 26.2603 | 2.08257 | ||||||||
\(160\) | 0.812592 | 0.0642410 | ||||||||
\(161\) | −8.63879 | −0.680832 | ||||||||
\(162\) | −11.0053 | −0.864657 | ||||||||
\(163\) | 0.335627 | 0.0262884 | 0.0131442 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131442 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(164\) | 1.76139 | 0.137541 | ||||||||
\(165\) | −5.92995 | −0.461646 | ||||||||
\(166\) | 10.2662 | 0.796813 | ||||||||
\(167\) | 11.5237 | 0.891727 | 0.445864 | − | 0.895101i | \(-0.352897\pi\) | ||||
0.445864 | + | 0.895101i | \(0.352897\pi\) | |||||||
\(168\) | −2.23488 | −0.172425 | ||||||||
\(169\) | −4.22036 | −0.324643 | ||||||||
\(170\) | −2.26168 | −0.173463 | ||||||||
\(171\) | −8.62451 | −0.659532 | ||||||||
\(172\) | −1.70416 | −0.129941 | ||||||||
\(173\) | −9.73755 | −0.740332 | −0.370166 | − | 0.928966i | \(-0.620699\pi\) | ||||
−0.370166 | + | 0.928966i | \(0.620699\pi\) | |||||||
\(174\) | 20.9537 | 1.58849 | ||||||||
\(175\) | −4.33969 | −0.328050 | ||||||||
\(176\) | 3.26531 | 0.246132 | ||||||||
\(177\) | 19.4766 | 1.46395 | ||||||||
\(178\) | 6.52666 | 0.489194 | ||||||||
\(179\) | −23.6562 | −1.76815 | −0.884075 | − | 0.467346i | \(-0.845210\pi\) | ||||
−0.884075 | + | 0.467346i | \(0.845210\pi\) | |||||||
\(180\) | 1.62086 | 0.120812 | ||||||||
\(181\) | −14.9888 | −1.11411 | −0.557053 | − | 0.830477i | \(-0.688068\pi\) | ||||
−0.557053 | + | 0.830477i | \(0.688068\pi\) | |||||||
\(182\) | 2.96305 | 0.219636 | ||||||||
\(183\) | 10.3681 | 0.766433 | ||||||||
\(184\) | −8.63879 | −0.636860 | ||||||||
\(185\) | 5.96750 | 0.438739 | ||||||||
\(186\) | −12.7475 | −0.934694 | ||||||||
\(187\) | −9.08831 | −0.664603 | ||||||||
\(188\) | −9.53234 | −0.695217 | ||||||||
\(189\) | 2.24677 | 0.163428 | ||||||||
\(190\) | −3.51345 | −0.254892 | ||||||||
\(191\) | −9.26422 | −0.670335 | −0.335168 | − | 0.942158i | \(-0.608793\pi\) | ||||
−0.335168 | + | 0.942158i | \(0.608793\pi\) | |||||||
\(192\) | −2.23488 | −0.161288 | ||||||||
\(193\) | 23.5608 | 1.69594 | 0.847971 | − | 0.530043i | \(-0.177824\pi\) | ||||
0.847971 | + | 0.530043i | \(0.177824\pi\) | |||||||
\(194\) | −1.25240 | −0.0899174 | ||||||||
\(195\) | −5.38102 | −0.385343 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.7432 | −1.76288 | −0.881438 | − | 0.472299i | \(-0.843424\pi\) | ||||
−0.881438 | + | 0.472299i | \(0.843424\pi\) | |||||||
\(198\) | 6.51325 | 0.462877 | ||||||||
\(199\) | −9.00585 | −0.638408 | −0.319204 | − | 0.947686i | \(-0.603415\pi\) | ||||
−0.319204 | + | 0.947686i | \(0.603415\pi\) | |||||||
\(200\) | −4.33969 | −0.306863 | ||||||||
\(201\) | −20.7691 | −1.46494 | ||||||||
\(202\) | 13.8258 | 0.972779 | ||||||||
\(203\) | −9.37575 | −0.658049 | ||||||||
\(204\) | 6.22031 | 0.435509 | ||||||||
\(205\) | 1.43129 | 0.0999657 | ||||||||
\(206\) | 3.59568 | 0.250523 | ||||||||
\(207\) | −17.2316 | −1.19768 | ||||||||
\(208\) | 2.96305 | 0.205450 | ||||||||
\(209\) | −14.1184 | −0.976592 | ||||||||
\(210\) | −1.81604 | −0.125319 | ||||||||
\(211\) | −9.99153 | −0.687845 | −0.343923 | − | 0.938998i | \(-0.611756\pi\) | ||||
−0.343923 | + | 0.938998i | \(0.611756\pi\) | |||||||
\(212\) | −11.7502 | −0.807007 | ||||||||
\(213\) | 36.0426 | 2.46960 | ||||||||
\(214\) | −0.761019 | −0.0520222 | ||||||||
\(215\) | −1.38479 | −0.0944416 | ||||||||
\(216\) | 2.24677 | 0.152873 | ||||||||
\(217\) | 5.70390 | 0.387206 | ||||||||
\(218\) | 8.13333 | 0.550858 | ||||||||
\(219\) | 24.8002 | 1.67584 | ||||||||
\(220\) | 2.65337 | 0.178890 | ||||||||
\(221\) | −8.24701 | −0.554754 | ||||||||
\(222\) | −16.4125 | −1.10153 | ||||||||
\(223\) | −18.8022 | −1.25909 | −0.629546 | − | 0.776964i | \(-0.716759\pi\) | ||||
−0.629546 | + | 0.776964i | \(0.716759\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −8.65630 | −0.577086 | ||||||||
\(226\) | −5.97693 | −0.397579 | ||||||||
\(227\) | 4.48248 | 0.297513 | 0.148756 | − | 0.988874i | \(-0.452473\pi\) | ||||
0.148756 | + | 0.988874i | \(0.452473\pi\) | |||||||
\(228\) | 9.66307 | 0.639952 | ||||||||
\(229\) | 12.8191 | 0.847110 | 0.423555 | − | 0.905870i | \(-0.360782\pi\) | ||||
0.423555 | + | 0.905870i | \(0.360782\pi\) | |||||||
\(230\) | −7.01981 | −0.462872 | ||||||||
\(231\) | −7.29758 | −0.480145 | ||||||||
\(232\) | −9.37575 | −0.615548 | ||||||||
\(233\) | −5.91773 | −0.387683 | −0.193842 | − | 0.981033i | \(-0.562095\pi\) | ||||
−0.193842 | + | 0.981033i | \(0.562095\pi\) | |||||||
\(234\) | 5.91032 | 0.386370 | ||||||||
\(235\) | −7.74590 | −0.505287 | ||||||||
\(236\) | −8.71482 | −0.567287 | ||||||||
\(237\) | −21.8008 | −1.41611 | ||||||||
\(238\) | −2.78329 | −0.180414 | ||||||||
\(239\) | 18.0461 | 1.16731 | 0.583654 | − | 0.812003i | \(-0.301623\pi\) | ||||
0.583654 | + | 0.812003i | \(0.301623\pi\) | |||||||
\(240\) | −1.81604 | −0.117225 | ||||||||
\(241\) | −29.1393 | −1.87703 | −0.938513 | − | 0.345243i | \(-0.887796\pi\) | ||||
−0.938513 | + | 0.345243i | \(0.887796\pi\) | |||||||
\(242\) | −0.337724 | −0.0217097 | ||||||||
\(243\) | 17.8552 | 1.14541 | ||||||||
\(244\) | −4.63923 | −0.296996 | ||||||||
\(245\) | 0.812592 | 0.0519146 | ||||||||
\(246\) | −3.93649 | −0.250982 | ||||||||
\(247\) | −12.8115 | −0.815175 | ||||||||
\(248\) | 5.70390 | 0.362198 | ||||||||
\(249\) | −22.9437 | −1.45400 | ||||||||
\(250\) | −7.58936 | −0.479993 | ||||||||
\(251\) | 20.6603 | 1.30407 | 0.652034 | − | 0.758190i | \(-0.273916\pi\) | ||||
0.652034 | + | 0.758190i | \(0.273916\pi\) | |||||||
\(252\) | 1.99468 | 0.125653 | ||||||||
\(253\) | −28.2084 | −1.77344 | ||||||||
\(254\) | 6.98647 | 0.438370 | ||||||||
\(255\) | 5.05457 | 0.316530 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.83777 | −0.177015 | −0.0885075 | − | 0.996076i | \(-0.528210\pi\) | ||||
−0.0885075 | + | 0.996076i | \(0.528210\pi\) | |||||||
\(258\) | 3.80859 | 0.237112 | ||||||||
\(259\) | 7.34378 | 0.456320 | ||||||||
\(260\) | 2.40775 | 0.149322 | ||||||||
\(261\) | −18.7016 | −1.15760 | ||||||||
\(262\) | −0.0906462 | −0.00560014 | ||||||||
\(263\) | 18.9655 | 1.16947 | 0.584733 | − | 0.811226i | \(-0.301199\pi\) | ||||
0.584733 | + | 0.811226i | \(0.301199\pi\) | |||||||
\(264\) | −7.29758 | −0.449135 | ||||||||
\(265\) | −9.54812 | −0.586536 | ||||||||
\(266\) | −4.32376 | −0.265107 | ||||||||
\(267\) | −14.5863 | −0.892666 | ||||||||
\(268\) | 9.29319 | 0.567672 | ||||||||
\(269\) | 21.4827 | 1.30982 | 0.654912 | − | 0.755705i | \(-0.272706\pi\) | ||||
0.654912 | + | 0.755705i | \(0.272706\pi\) | |||||||
\(270\) | 1.82571 | 0.111109 | ||||||||
\(271\) | −31.6824 | −1.92457 | −0.962284 | − | 0.272047i | \(-0.912299\pi\) | ||||
−0.962284 | + | 0.272047i | \(0.912299\pi\) | |||||||
\(272\) | −2.78329 | −0.168762 | ||||||||
\(273\) | −6.62204 | −0.400784 | ||||||||
\(274\) | −12.7735 | −0.771673 | ||||||||
\(275\) | −14.1705 | −0.854511 | ||||||||
\(276\) | 19.3066 | 1.16212 | ||||||||
\(277\) | −13.8100 | −0.829763 | −0.414882 | − | 0.909875i | \(-0.636177\pi\) | ||||
−0.414882 | + | 0.909875i | \(0.636177\pi\) | |||||||
\(278\) | 14.4342 | 0.865705 | ||||||||
\(279\) | 11.3775 | 0.681150 | ||||||||
\(280\) | 0.812592 | 0.0485617 | ||||||||
\(281\) | −4.97958 | −0.297057 | −0.148528 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148528 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(282\) | 21.3036 | 1.26861 | ||||||||
\(283\) | −20.3586 | −1.21019 | −0.605096 | − | 0.796153i | \(-0.706865\pi\) | ||||
−0.605096 | + | 0.796153i | \(0.706865\pi\) | |||||||
\(284\) | −16.1273 | −0.956979 | ||||||||
\(285\) | 7.85213 | 0.465120 | ||||||||
\(286\) | 9.67527 | 0.572111 | ||||||||
\(287\) | 1.76139 | 0.103972 | ||||||||
\(288\) | 1.99468 | 0.117538 | ||||||||
\(289\) | −9.25330 | −0.544312 | ||||||||
\(290\) | −7.61866 | −0.447383 | ||||||||
\(291\) | 2.79897 | 0.164079 | ||||||||
\(292\) | −11.0969 | −0.649397 | ||||||||
\(293\) | −6.82559 | −0.398755 | −0.199377 | − | 0.979923i | \(-0.563892\pi\) | ||||
−0.199377 | + | 0.979923i | \(0.563892\pi\) | |||||||
\(294\) | −2.23488 | −0.130341 | ||||||||
\(295\) | −7.08160 | −0.412306 | ||||||||
\(296\) | 7.34378 | 0.426849 | ||||||||
\(297\) | 7.33641 | 0.425702 | ||||||||
\(298\) | −16.3307 | −0.946012 | ||||||||
\(299\) | −25.5971 | −1.48032 | ||||||||
\(300\) | 9.69869 | 0.559954 | ||||||||
\(301\) | −1.70416 | −0.0982261 | ||||||||
\(302\) | −4.18363 | −0.240741 | ||||||||
\(303\) | −30.8989 | −1.77510 | ||||||||
\(304\) | −4.32376 | −0.247984 | ||||||||
\(305\) | −3.76980 | −0.215858 | ||||||||
\(306\) | −5.55177 | −0.317373 | ||||||||
\(307\) | 20.6120 | 1.17639 | 0.588194 | − | 0.808720i | \(-0.299839\pi\) | ||||
0.588194 | + | 0.808720i | \(0.299839\pi\) | |||||||
\(308\) | 3.26531 | 0.186059 | ||||||||
\(309\) | −8.03591 | −0.457147 | ||||||||
\(310\) | 4.63495 | 0.263247 | ||||||||
\(311\) | 1.90679 | 0.108124 | 0.0540620 | − | 0.998538i | \(-0.482783\pi\) | ||||
0.0540620 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(312\) | −6.62204 | −0.374899 | ||||||||
\(313\) | −23.7618 | −1.34309 | −0.671547 | − | 0.740962i | \(-0.734370\pi\) | ||||
−0.671547 | + | 0.740962i | \(0.734370\pi\) | |||||||
\(314\) | 22.1358 | 1.24919 | ||||||||
\(315\) | 1.62086 | 0.0913251 | ||||||||
\(316\) | 9.75479 | 0.548750 | ||||||||
\(317\) | −7.97081 | −0.447685 | −0.223843 | − | 0.974625i | \(-0.571860\pi\) | ||||
−0.223843 | + | 0.974625i | \(0.571860\pi\) | |||||||
\(318\) | 26.2603 | 1.47260 | ||||||||
\(319\) | −30.6148 | −1.71410 | ||||||||
\(320\) | 0.812592 | 0.0454253 | ||||||||
\(321\) | 1.70078 | 0.0949285 | ||||||||
\(322\) | −8.63879 | −0.481421 | ||||||||
\(323\) | 12.0343 | 0.669604 | ||||||||
\(324\) | −11.0053 | −0.611405 | ||||||||
\(325\) | −12.8587 | −0.713273 | ||||||||
\(326\) | 0.335627 | 0.0185887 | ||||||||
\(327\) | −18.1770 | −1.00519 | ||||||||
\(328\) | 1.76139 | 0.0972565 | ||||||||
\(329\) | −9.53234 | −0.525535 | ||||||||
\(330\) | −5.92995 | −0.326433 | ||||||||
\(331\) | −20.3369 | −1.11782 | −0.558908 | − | 0.829230i | \(-0.688779\pi\) | ||||
−0.558908 | + | 0.829230i | \(0.688779\pi\) | |||||||
\(332\) | 10.2662 | 0.563432 | ||||||||
\(333\) | 14.6485 | 0.802732 | ||||||||
\(334\) | 11.5237 | 0.630546 | ||||||||
\(335\) | 7.55157 | 0.412586 | ||||||||
\(336\) | −2.23488 | −0.121923 | ||||||||
\(337\) | 25.4833 | 1.38817 | 0.694083 | − | 0.719895i | \(-0.255810\pi\) | ||||
0.694083 | + | 0.719895i | \(0.255810\pi\) | |||||||
\(338\) | −4.22036 | −0.229557 | ||||||||
\(339\) | 13.3577 | 0.725491 | ||||||||
\(340\) | −2.26168 | −0.122657 | ||||||||
\(341\) | 18.6250 | 1.00860 | ||||||||
\(342\) | −8.62451 | −0.466360 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −1.70416 | −0.0918821 | ||||||||
\(345\) | 15.6884 | 0.844636 | ||||||||
\(346\) | −9.73755 | −0.523494 | ||||||||
\(347\) | −25.6592 | −1.37746 | −0.688728 | − | 0.725020i | \(-0.741831\pi\) | ||||
−0.688728 | + | 0.725020i | \(0.741831\pi\) | |||||||
\(348\) | 20.9537 | 1.12323 | ||||||||
\(349\) | 20.7876 | 1.11274 | 0.556368 | − | 0.830936i | \(-0.312194\pi\) | ||||
0.556368 | + | 0.830936i | \(0.312194\pi\) | |||||||
\(350\) | −4.33969 | −0.231966 | ||||||||
\(351\) | 6.65728 | 0.355339 | ||||||||
\(352\) | 3.26531 | 0.174042 | ||||||||
\(353\) | −6.60536 | −0.351568 | −0.175784 | − | 0.984429i | \(-0.556246\pi\) | ||||
−0.175784 | + | 0.984429i | \(0.556246\pi\) | |||||||
\(354\) | 19.4766 | 1.03517 | ||||||||
\(355\) | −13.1049 | −0.695537 | ||||||||
\(356\) | 6.52666 | 0.345912 | ||||||||
\(357\) | 6.22031 | 0.329214 | ||||||||
\(358\) | −23.6562 | −1.25027 | ||||||||
\(359\) | −5.63025 | −0.297153 | −0.148577 | − | 0.988901i | \(-0.547469\pi\) | ||||
−0.148577 | + | 0.988901i | \(0.547469\pi\) | |||||||
\(360\) | 1.62086 | 0.0854268 | ||||||||
\(361\) | −0.305127 | −0.0160593 | ||||||||
\(362\) | −14.9888 | −0.787792 | ||||||||
\(363\) | 0.754771 | 0.0396152 | ||||||||
\(364\) | 2.96305 | 0.155306 | ||||||||
\(365\) | −9.01725 | −0.471985 | ||||||||
\(366\) | 10.3681 | 0.541950 | ||||||||
\(367\) | 6.20611 | 0.323956 | 0.161978 | − | 0.986794i | \(-0.448213\pi\) | ||||
0.161978 | + | 0.986794i | \(0.448213\pi\) | |||||||
\(368\) | −8.63879 | −0.450328 | ||||||||
\(369\) | 3.51341 | 0.182901 | ||||||||
\(370\) | 5.96750 | 0.310235 | ||||||||
\(371\) | −11.7502 | −0.610040 | ||||||||
\(372\) | −12.7475 | −0.660928 | ||||||||
\(373\) | −11.4320 | −0.591927 | −0.295964 | − | 0.955199i | \(-0.595641\pi\) | ||||
−0.295964 | + | 0.955199i | \(0.595641\pi\) | |||||||
\(374\) | −9.08831 | −0.469945 | ||||||||
\(375\) | 16.9613 | 0.875877 | ||||||||
\(376\) | −9.53234 | −0.491593 | ||||||||
\(377\) | −27.7808 | −1.43078 | ||||||||
\(378\) | 2.24677 | 0.115561 | ||||||||
\(379\) | 25.5794 | 1.31393 | 0.656963 | − | 0.753923i | \(-0.271841\pi\) | ||||
0.656963 | + | 0.753923i | \(0.271841\pi\) | |||||||
\(380\) | −3.51345 | −0.180236 | ||||||||
\(381\) | −15.6139 | −0.799924 | ||||||||
\(382\) | −9.26422 | −0.473999 | ||||||||
\(383\) | 22.9519 | 1.17279 | 0.586394 | − | 0.810026i | \(-0.300547\pi\) | ||||
0.586394 | + | 0.810026i | \(0.300547\pi\) | |||||||
\(384\) | −2.23488 | −0.114048 | ||||||||
\(385\) | 2.65337 | 0.135228 | ||||||||
\(386\) | 23.5608 | 1.19921 | ||||||||
\(387\) | −3.39925 | −0.172794 | ||||||||
\(388\) | −1.25240 | −0.0635812 | ||||||||
\(389\) | −20.9052 | −1.05994 | −0.529969 | − | 0.848017i | \(-0.677796\pi\) | ||||
−0.529969 | + | 0.848017i | \(0.677796\pi\) | |||||||
\(390\) | −5.38102 | −0.272479 | ||||||||
\(391\) | 24.0442 | 1.21597 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0.202583 | 0.0102190 | ||||||||
\(394\) | −24.7432 | −1.24654 | ||||||||
\(395\) | 7.92667 | 0.398834 | ||||||||
\(396\) | 6.51325 | 0.327303 | ||||||||
\(397\) | 14.8338 | 0.744489 | 0.372244 | − | 0.928135i | \(-0.378588\pi\) | ||||
0.372244 | + | 0.928135i | \(0.378588\pi\) | |||||||
\(398\) | −9.00585 | −0.451422 | ||||||||
\(399\) | 9.66307 | 0.483758 | ||||||||
\(400\) | −4.33969 | −0.216985 | ||||||||
\(401\) | −1.99975 | −0.0998630 | −0.0499315 | − | 0.998753i | \(-0.515900\pi\) | ||||
−0.0499315 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(402\) | −20.7691 | −1.03587 | ||||||||
\(403\) | 16.9009 | 0.841895 | ||||||||
\(404\) | 13.8258 | 0.687859 | ||||||||
\(405\) | −8.94281 | −0.444372 | ||||||||
\(406\) | −9.37575 | −0.465311 | ||||||||
\(407\) | 23.9798 | 1.18863 | ||||||||
\(408\) | 6.22031 | 0.307951 | ||||||||
\(409\) | −38.6230 | −1.90978 | −0.954892 | − | 0.296953i | \(-0.904029\pi\) | ||||
−0.954892 | + | 0.296953i | \(0.904029\pi\) | |||||||
\(410\) | 1.43129 | 0.0706865 | ||||||||
\(411\) | 28.5471 | 1.40812 | ||||||||
\(412\) | 3.59568 | 0.177147 | ||||||||
\(413\) | −8.71482 | −0.428828 | ||||||||
\(414\) | −17.2316 | −0.846887 | ||||||||
\(415\) | 8.34224 | 0.409505 | ||||||||
\(416\) | 2.96305 | 0.145275 | ||||||||
\(417\) | −32.2586 | −1.57971 | ||||||||
\(418\) | −14.1184 | −0.690555 | ||||||||
\(419\) | 2.18635 | 0.106810 | 0.0534051 | − | 0.998573i | \(-0.482993\pi\) | ||||
0.0534051 | + | 0.998573i | \(0.482993\pi\) | |||||||
\(420\) | −1.81604 | −0.0886139 | ||||||||
\(421\) | 10.6823 | 0.520624 | 0.260312 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260312 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(422\) | −9.99153 | −0.486380 | ||||||||
\(423\) | −19.0140 | −0.924490 | ||||||||
\(424\) | −11.7502 | −0.570640 | ||||||||
\(425\) | 12.0786 | 0.585899 | ||||||||
\(426\) | 36.0426 | 1.74627 | ||||||||
\(427\) | −4.63923 | −0.224508 | ||||||||
\(428\) | −0.761019 | −0.0367852 | ||||||||
\(429\) | −21.6231 | −1.04397 | ||||||||
\(430\) | −1.38479 | −0.0667803 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 2.24677 | 0.108098 | ||||||||
\(433\) | 8.63850 | 0.415140 | 0.207570 | − | 0.978220i | \(-0.433445\pi\) | ||||
0.207570 | + | 0.978220i | \(0.433445\pi\) | |||||||
\(434\) | 5.70390 | 0.273796 | ||||||||
\(435\) | 17.0268 | 0.816371 | ||||||||
\(436\) | 8.13333 | 0.389516 | ||||||||
\(437\) | 37.3520 | 1.78679 | ||||||||
\(438\) | 24.8002 | 1.18500 | ||||||||
\(439\) | 12.0109 | 0.573248 | 0.286624 | − | 0.958043i | \(-0.407467\pi\) | ||||
0.286624 | + | 0.958043i | \(0.407467\pi\) | |||||||
\(440\) | 2.65337 | 0.126494 | ||||||||
\(441\) | 1.99468 | 0.0949847 | ||||||||
\(442\) | −8.24701 | −0.392270 | ||||||||
\(443\) | 17.0802 | 0.811505 | 0.405752 | − | 0.913983i | \(-0.367010\pi\) | ||||
0.405752 | + | 0.913983i | \(0.367010\pi\) | |||||||
\(444\) | −16.4125 | −0.778901 | ||||||||
\(445\) | 5.30351 | 0.251411 | ||||||||
\(446\) | −18.8022 | −0.890312 | ||||||||
\(447\) | 36.4971 | 1.72625 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −22.2276 | −1.04899 | −0.524493 | − | 0.851415i | \(-0.675745\pi\) | ||||
−0.524493 | + | 0.851415i | \(0.675745\pi\) | |||||||
\(450\) | −8.65630 | −0.408062 | ||||||||
\(451\) | 5.75149 | 0.270827 | ||||||||
\(452\) | −5.97693 | −0.281131 | ||||||||
\(453\) | 9.34991 | 0.439297 | ||||||||
\(454\) | 4.48248 | 0.210373 | ||||||||
\(455\) | 2.40775 | 0.112877 | ||||||||
\(456\) | 9.66307 | 0.452515 | ||||||||
\(457\) | −37.6890 | −1.76302 | −0.881508 | − | 0.472169i | \(-0.843471\pi\) | ||||
−0.881508 | + | 0.472169i | \(0.843471\pi\) | |||||||
\(458\) | 12.8191 | 0.598997 | ||||||||
\(459\) | −6.25341 | −0.291884 | ||||||||
\(460\) | −7.01981 | −0.327300 | ||||||||
\(461\) | −4.33600 | −0.201948 | −0.100974 | − | 0.994889i | \(-0.532196\pi\) | ||||
−0.100974 | + | 0.994889i | \(0.532196\pi\) | |||||||
\(462\) | −7.29758 | −0.339514 | ||||||||
\(463\) | 29.7916 | 1.38453 | 0.692265 | − | 0.721643i | \(-0.256613\pi\) | ||||
0.692265 | + | 0.721643i | \(0.256613\pi\) | |||||||
\(464\) | −9.37575 | −0.435258 | ||||||||
\(465\) | −10.3585 | −0.480366 | ||||||||
\(466\) | −5.91773 | −0.274134 | ||||||||
\(467\) | −27.6527 | −1.27962 | −0.639808 | − | 0.768535i | \(-0.720986\pi\) | ||||
−0.639808 | + | 0.768535i | \(0.720986\pi\) | |||||||
\(468\) | 5.91032 | 0.273205 | ||||||||
\(469\) | 9.29319 | 0.429119 | ||||||||
\(470\) | −7.74590 | −0.357292 | ||||||||
\(471\) | −49.4708 | −2.27949 | ||||||||
\(472\) | −8.71482 | −0.401132 | ||||||||
\(473\) | −5.56461 | −0.255861 | ||||||||
\(474\) | −21.8008 | −1.00134 | ||||||||
\(475\) | 18.7638 | 0.860941 | ||||||||
\(476\) | −2.78329 | −0.127572 | ||||||||
\(477\) | −23.4379 | −1.07315 | ||||||||
\(478\) | 18.0461 | 0.825411 | ||||||||
\(479\) | 4.07882 | 0.186366 | 0.0931830 | − | 0.995649i | \(-0.470296\pi\) | ||||
0.0931830 | + | 0.995649i | \(0.470296\pi\) | |||||||
\(480\) | −1.81604 | −0.0828907 | ||||||||
\(481\) | 21.7600 | 0.992169 | ||||||||
\(482\) | −29.1393 | −1.32726 | ||||||||
\(483\) | 19.3066 | 0.878482 | ||||||||
\(484\) | −0.337724 | −0.0153511 | ||||||||
\(485\) | −1.01769 | −0.0462111 | ||||||||
\(486\) | 17.8552 | 0.809927 | ||||||||
\(487\) | 27.6331 | 1.25217 | 0.626087 | − | 0.779753i | \(-0.284655\pi\) | ||||
0.626087 | + | 0.779753i | \(0.284655\pi\) | |||||||
\(488\) | −4.63923 | −0.210008 | ||||||||
\(489\) | −0.750086 | −0.0339201 | ||||||||
\(490\) | 0.812592 | 0.0367092 | ||||||||
\(491\) | 20.9329 | 0.944691 | 0.472345 | − | 0.881414i | \(-0.343408\pi\) | ||||
0.472345 | + | 0.881414i | \(0.343408\pi\) | |||||||
\(492\) | −3.93649 | −0.177471 | ||||||||
\(493\) | 26.0954 | 1.17528 | ||||||||
\(494\) | −12.8115 | −0.576416 | ||||||||
\(495\) | 5.29262 | 0.237885 | ||||||||
\(496\) | 5.70390 | 0.256113 | ||||||||
\(497\) | −16.1273 | −0.723408 | ||||||||
\(498\) | −22.9437 | −1.02813 | ||||||||
\(499\) | −28.6722 | −1.28354 | −0.641771 | − | 0.766896i | \(-0.721800\pi\) | ||||
−0.641771 | + | 0.766896i | \(0.721800\pi\) | |||||||
\(500\) | −7.58936 | −0.339407 | ||||||||
\(501\) | −25.7540 | −1.15060 | ||||||||
\(502\) | 20.6603 | 0.922116 | ||||||||
\(503\) | −5.59086 | −0.249284 | −0.124642 | − | 0.992202i | \(-0.539778\pi\) | ||||
−0.124642 | + | 0.992202i | \(0.539778\pi\) | |||||||
\(504\) | 1.99468 | 0.0888501 | ||||||||
\(505\) | 11.2347 | 0.499939 | ||||||||
\(506\) | −28.2084 | −1.25401 | ||||||||
\(507\) | 9.43199 | 0.418890 | ||||||||
\(508\) | 6.98647 | 0.309974 | ||||||||
\(509\) | 4.78285 | 0.211996 | 0.105998 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.105998 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(510\) | 5.05457 | 0.223820 | ||||||||
\(511\) | −11.0969 | −0.490898 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.71449 | −0.428905 | ||||||||
\(514\) | −2.83777 | −0.125169 | ||||||||
\(515\) | 2.92182 | 0.128751 | ||||||||
\(516\) | 3.80859 | 0.167664 | ||||||||
\(517\) | −31.1261 | −1.36892 | ||||||||
\(518\) | 7.34378 | 0.322667 | ||||||||
\(519\) | 21.7622 | 0.955256 | ||||||||
\(520\) | 2.40775 | 0.105587 | ||||||||
\(521\) | 30.0690 | 1.31734 | 0.658672 | − | 0.752430i | \(-0.271118\pi\) | ||||
0.658672 | + | 0.752430i | \(0.271118\pi\) | |||||||
\(522\) | −18.7016 | −0.818547 | ||||||||
\(523\) | −3.59089 | −0.157018 | −0.0785092 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785092 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(524\) | −0.0906462 | −0.00395990 | ||||||||
\(525\) | 9.69869 | 0.423285 | ||||||||
\(526\) | 18.9655 | 0.826937 | ||||||||
\(527\) | −15.8756 | −0.691552 | ||||||||
\(528\) | −7.29758 | −0.317586 | ||||||||
\(529\) | 51.6286 | 2.24472 | ||||||||
\(530\) | −9.54812 | −0.414744 | ||||||||
\(531\) | −17.3833 | −0.754370 | ||||||||
\(532\) | −4.32376 | −0.187459 | ||||||||
\(533\) | 5.21908 | 0.226063 | ||||||||
\(534\) | −14.5863 | −0.631210 | ||||||||
\(535\) | −0.618398 | −0.0267357 | ||||||||
\(536\) | 9.29319 | 0.401404 | ||||||||
\(537\) | 52.8688 | 2.28146 | ||||||||
\(538\) | 21.4827 | 0.926185 | ||||||||
\(539\) | 3.26531 | 0.140647 | ||||||||
\(540\) | 1.82571 | 0.0785659 | ||||||||
\(541\) | −28.5645 | −1.22808 | −0.614041 | − | 0.789274i | \(-0.710457\pi\) | ||||
−0.614041 | + | 0.789274i | \(0.710457\pi\) | |||||||
\(542\) | −31.6824 | −1.36087 | ||||||||
\(543\) | 33.4981 | 1.43754 | ||||||||
\(544\) | −2.78329 | −0.119333 | ||||||||
\(545\) | 6.60907 | 0.283102 | ||||||||
\(546\) | −6.62204 | −0.283397 | ||||||||
\(547\) | −41.4043 | −1.77032 | −0.885160 | − | 0.465287i | \(-0.845951\pi\) | ||||
−0.885160 | + | 0.465287i | \(0.845951\pi\) | |||||||
\(548\) | −12.7735 | −0.545655 | ||||||||
\(549\) | −9.25377 | −0.394941 | ||||||||
\(550\) | −14.1705 | −0.604231 | ||||||||
\(551\) | 40.5385 | 1.72700 | ||||||||
\(552\) | 19.3066 | 0.821745 | ||||||||
\(553\) | 9.75479 | 0.414816 | ||||||||
\(554\) | −13.8100 | −0.586731 | ||||||||
\(555\) | −13.3366 | −0.566108 | ||||||||
\(556\) | 14.4342 | 0.612146 | ||||||||
\(557\) | −10.5996 | −0.449119 | −0.224559 | − | 0.974460i | \(-0.572094\pi\) | ||||
−0.224559 | + | 0.974460i | \(0.572094\pi\) | |||||||
\(558\) | 11.3775 | 0.481646 | ||||||||
\(559\) | −5.04950 | −0.213571 | ||||||||
\(560\) | 0.812592 | 0.0343383 | ||||||||
\(561\) | 20.3113 | 0.857542 | ||||||||
\(562\) | −4.97958 | −0.210051 | ||||||||
\(563\) | 15.3788 | 0.648138 | 0.324069 | − | 0.946034i | \(-0.394949\pi\) | ||||
0.324069 | + | 0.946034i | \(0.394949\pi\) | |||||||
\(564\) | 21.3036 | 0.897044 | ||||||||
\(565\) | −4.85680 | −0.204327 | ||||||||
\(566\) | −20.3586 | −0.855735 | ||||||||
\(567\) | −11.0053 | −0.462179 | ||||||||
\(568\) | −16.1273 | −0.676687 | ||||||||
\(569\) | 19.3679 | 0.811943 | 0.405972 | − | 0.913886i | \(-0.366933\pi\) | ||||
0.405972 | + | 0.913886i | \(0.366933\pi\) | |||||||
\(570\) | 7.85213 | 0.328890 | ||||||||
\(571\) | 20.1297 | 0.842400 | 0.421200 | − | 0.906968i | \(-0.361609\pi\) | ||||
0.421200 | + | 0.906968i | \(0.361609\pi\) | |||||||
\(572\) | 9.67527 | 0.404544 | ||||||||
\(573\) | 20.7044 | 0.864939 | ||||||||
\(574\) | 1.76139 | 0.0735190 | ||||||||
\(575\) | 37.4897 | 1.56343 | ||||||||
\(576\) | 1.99468 | 0.0831116 | ||||||||
\(577\) | 24.7523 | 1.03045 | 0.515226 | − | 0.857054i | \(-0.327708\pi\) | ||||
0.515226 | + | 0.857054i | \(0.327708\pi\) | |||||||
\(578\) | −9.25330 | −0.384887 | ||||||||
\(579\) | −52.6555 | −2.18829 | ||||||||
\(580\) | −7.61866 | −0.316348 | ||||||||
\(581\) | 10.2662 | 0.425914 | ||||||||
\(582\) | 2.79897 | 0.116021 | ||||||||
\(583\) | −38.3681 | −1.58904 | ||||||||
\(584\) | −11.0969 | −0.459193 | ||||||||
\(585\) | 4.80268 | 0.198566 | ||||||||
\(586\) | −6.82559 | −0.281962 | ||||||||
\(587\) | 24.9304 | 1.02899 | 0.514493 | − | 0.857495i | \(-0.327980\pi\) | ||||
0.514493 | + | 0.857495i | \(0.327980\pi\) | |||||||
\(588\) | −2.23488 | −0.0921648 | ||||||||
\(589\) | −24.6623 | −1.01619 | ||||||||
\(590\) | −7.08160 | −0.291545 | ||||||||
\(591\) | 55.2979 | 2.27465 | ||||||||
\(592\) | 7.34378 | 0.301828 | ||||||||
\(593\) | −19.1377 | −0.785893 | −0.392947 | − | 0.919561i | \(-0.628544\pi\) | ||||
−0.392947 | + | 0.919561i | \(0.628544\pi\) | |||||||
\(594\) | 7.33641 | 0.301017 | ||||||||
\(595\) | −2.26168 | −0.0927198 | ||||||||
\(596\) | −16.3307 | −0.668931 | ||||||||
\(597\) | 20.1270 | 0.823742 | ||||||||
\(598\) | −25.5971 | −1.04674 | ||||||||
\(599\) | 24.8622 | 1.01584 | 0.507922 | − | 0.861403i | \(-0.330414\pi\) | ||||
0.507922 | + | 0.861403i | \(0.330414\pi\) | |||||||
\(600\) | 9.69869 | 0.395947 | ||||||||
\(601\) | −20.4523 | −0.834266 | −0.417133 | − | 0.908846i | \(-0.636965\pi\) | ||||
−0.417133 | + | 0.908846i | \(0.636965\pi\) | |||||||
\(602\) | −1.70416 | −0.0694563 | ||||||||
\(603\) | 18.5369 | 0.754882 | ||||||||
\(604\) | −4.18363 | −0.170230 | ||||||||
\(605\) | −0.274432 | −0.0111572 | ||||||||
\(606\) | −30.8989 | −1.25518 | ||||||||
\(607\) | −3.54318 | −0.143813 | −0.0719066 | − | 0.997411i | \(-0.522908\pi\) | ||||
−0.0719066 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(608\) | −4.32376 | −0.175351 | ||||||||
\(609\) | 20.9537 | 0.849085 | ||||||||
\(610\) | −3.76980 | −0.152635 | ||||||||
\(611\) | −28.2448 | −1.14266 | ||||||||
\(612\) | −5.55177 | −0.224417 | ||||||||
\(613\) | −32.3409 | −1.30624 | −0.653118 | − | 0.757256i | \(-0.726540\pi\) | ||||
−0.653118 | + | 0.757256i | \(0.726540\pi\) | |||||||
\(614\) | 20.6120 | 0.831832 | ||||||||
\(615\) | −3.19876 | −0.128987 | ||||||||
\(616\) | 3.26531 | 0.131563 | ||||||||
\(617\) | 5.03574 | 0.202731 | 0.101366 | − | 0.994849i | \(-0.467679\pi\) | ||||
0.101366 | + | 0.994849i | \(0.467679\pi\) | |||||||
\(618\) | −8.03591 | −0.323252 | ||||||||
\(619\) | −1.01794 | −0.0409144 | −0.0204572 | − | 0.999791i | \(-0.506512\pi\) | ||||
−0.0204572 | + | 0.999791i | \(0.506512\pi\) | |||||||
\(620\) | 4.63495 | 0.186144 | ||||||||
\(621\) | −19.4094 | −0.778871 | ||||||||
\(622\) | 1.90679 | 0.0764553 | ||||||||
\(623\) | 6.52666 | 0.261485 | ||||||||
\(624\) | −6.62204 | −0.265094 | ||||||||
\(625\) | 15.5314 | 0.621257 | ||||||||
\(626\) | −23.7618 | −0.949711 | ||||||||
\(627\) | 31.5530 | 1.26010 | ||||||||
\(628\) | 22.1358 | 0.883314 | ||||||||
\(629\) | −20.4399 | −0.814991 | ||||||||
\(630\) | 1.62086 | 0.0645766 | ||||||||
\(631\) | −40.2620 | −1.60280 | −0.801402 | − | 0.598126i | \(-0.795912\pi\) | ||||
−0.801402 | + | 0.598126i | \(0.795912\pi\) | |||||||
\(632\) | 9.75479 | 0.388025 | ||||||||
\(633\) | 22.3299 | 0.887532 | ||||||||
\(634\) | −7.97081 | −0.316561 | ||||||||
\(635\) | 5.67715 | 0.225291 | ||||||||
\(636\) | 26.2603 | 1.04129 | ||||||||
\(637\) | 2.96305 | 0.117400 | ||||||||
\(638\) | −30.6148 | −1.21205 | ||||||||
\(639\) | −32.1688 | −1.27258 | ||||||||
\(640\) | 0.812592 | 0.0321205 | ||||||||
\(641\) | 40.7674 | 1.61022 | 0.805108 | − | 0.593128i | \(-0.202107\pi\) | ||||
0.805108 | + | 0.593128i | \(0.202107\pi\) | |||||||
\(642\) | 1.70078 | 0.0671246 | ||||||||
\(643\) | 44.3194 | 1.74779 | 0.873893 | − | 0.486119i | \(-0.161588\pi\) | ||||
0.873893 | + | 0.486119i | \(0.161588\pi\) | |||||||
\(644\) | −8.63879 | −0.340416 | ||||||||
\(645\) | 3.09483 | 0.121859 | ||||||||
\(646\) | 12.0343 | 0.473482 | ||||||||
\(647\) | 36.3016 | 1.42716 | 0.713581 | − | 0.700573i | \(-0.247072\pi\) | ||||
0.713581 | + | 0.700573i | \(0.247072\pi\) | |||||||
\(648\) | −11.0053 | −0.432329 | ||||||||
\(649\) | −28.4566 | −1.11702 | ||||||||
\(650\) | −12.8587 | −0.504360 | ||||||||
\(651\) | −12.7475 | −0.499615 | ||||||||
\(652\) | 0.335627 | 0.0131442 | ||||||||
\(653\) | −42.3260 | −1.65634 | −0.828172 | − | 0.560474i | \(-0.810619\pi\) | ||||
−0.828172 | + | 0.560474i | \(0.810619\pi\) | |||||||
\(654\) | −18.1770 | −0.710776 | ||||||||
\(655\) | −0.0736584 | −0.00287807 | ||||||||
\(656\) | 1.76139 | 0.0687707 | ||||||||
\(657\) | −22.1348 | −0.863559 | ||||||||
\(658\) | −9.53234 | −0.371609 | ||||||||
\(659\) | 47.6809 | 1.85738 | 0.928692 | − | 0.370851i | \(-0.120934\pi\) | ||||
0.928692 | + | 0.370851i | \(0.120934\pi\) | |||||||
\(660\) | −5.92995 | −0.230823 | ||||||||
\(661\) | −16.5427 | −0.643435 | −0.321718 | − | 0.946836i | \(-0.604260\pi\) | ||||
−0.321718 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(662\) | −20.3369 | −0.790415 | ||||||||
\(663\) | 18.4311 | 0.715803 | ||||||||
\(664\) | 10.2662 | 0.398406 | ||||||||
\(665\) | −3.51345 | −0.136246 | ||||||||
\(666\) | 14.6485 | 0.567617 | ||||||||
\(667\) | 80.9951 | 3.13614 | ||||||||
\(668\) | 11.5237 | 0.445864 | ||||||||
\(669\) | 42.0207 | 1.62461 | ||||||||
\(670\) | 7.55157 | 0.291743 | ||||||||
\(671\) | −15.1485 | −0.584803 | ||||||||
\(672\) | −2.23488 | −0.0862123 | ||||||||
\(673\) | 42.0819 | 1.62214 | 0.811069 | − | 0.584950i | \(-0.198886\pi\) | ||||
0.811069 | + | 0.584950i | \(0.198886\pi\) | |||||||
\(674\) | 25.4833 | 0.981581 | ||||||||
\(675\) | −9.75029 | −0.375289 | ||||||||
\(676\) | −4.22036 | −0.162322 | ||||||||
\(677\) | 7.22910 | 0.277837 | 0.138918 | − | 0.990304i | \(-0.455637\pi\) | ||||
0.138918 | + | 0.990304i | \(0.455637\pi\) | |||||||
\(678\) | 13.3577 | 0.512999 | ||||||||
\(679\) | −1.25240 | −0.0480629 | ||||||||
\(680\) | −2.26168 | −0.0867314 | ||||||||
\(681\) | −10.0178 | −0.383883 | ||||||||
\(682\) | 18.6250 | 0.713189 | ||||||||
\(683\) | −11.6165 | −0.444493 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(684\) | −8.62451 | −0.329766 | ||||||||
\(685\) | −10.3796 | −0.396584 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −28.6491 | −1.09303 | ||||||||
\(688\) | −1.70416 | −0.0649704 | ||||||||
\(689\) | −34.8164 | −1.32640 | ||||||||
\(690\) | 15.6884 | 0.597248 | ||||||||
\(691\) | −17.0283 | −0.647787 | −0.323894 | − | 0.946093i | \(-0.604992\pi\) | ||||
−0.323894 | + | 0.946093i | \(0.604992\pi\) | |||||||
\(692\) | −9.73755 | −0.370166 | ||||||||
\(693\) | 6.51325 | 0.247418 | ||||||||
\(694\) | −25.6592 | −0.974008 | ||||||||
\(695\) | 11.7291 | 0.444910 | ||||||||
\(696\) | 20.9537 | 0.794246 | ||||||||
\(697\) | −4.90246 | −0.185694 | ||||||||
\(698\) | 20.7876 | 0.786824 | ||||||||
\(699\) | 13.2254 | 0.500231 | ||||||||
\(700\) | −4.33969 | −0.164025 | ||||||||
\(701\) | −3.01004 | −0.113688 | −0.0568439 | − | 0.998383i | \(-0.518104\pi\) | ||||
−0.0568439 | + | 0.998383i | \(0.518104\pi\) | |||||||
\(702\) | 6.65728 | 0.251263 | ||||||||
\(703\) | −31.7527 | −1.19758 | ||||||||
\(704\) | 3.26531 | 0.123066 | ||||||||
\(705\) | 17.3111 | 0.651975 | ||||||||
\(706\) | −6.60536 | −0.248596 | ||||||||
\(707\) | 13.8258 | 0.519972 | ||||||||
\(708\) | 19.4766 | 0.731974 | ||||||||
\(709\) | 27.5541 | 1.03482 | 0.517408 | − | 0.855739i | \(-0.326897\pi\) | ||||
0.517408 | + | 0.855739i | \(0.326897\pi\) | |||||||
\(710\) | −13.1049 | −0.491819 | ||||||||
\(711\) | 19.4577 | 0.729720 | ||||||||
\(712\) | 6.52666 | 0.244597 | ||||||||
\(713\) | −49.2748 | −1.84536 | ||||||||
\(714\) | 6.22031 | 0.232789 | ||||||||
\(715\) | 7.86205 | 0.294024 | ||||||||
\(716\) | −23.6562 | −0.884075 | ||||||||
\(717\) | −40.3309 | −1.50619 | ||||||||
\(718\) | −5.63025 | −0.210119 | ||||||||
\(719\) | −27.5142 | −1.02611 | −0.513053 | − | 0.858357i | \(-0.671486\pi\) | ||||
−0.513053 | + | 0.858357i | \(0.671486\pi\) | |||||||
\(720\) | 1.62086 | 0.0604059 | ||||||||
\(721\) | 3.59568 | 0.133910 | ||||||||
\(722\) | −0.305127 | −0.0113557 | ||||||||
\(723\) | 65.1227 | 2.42194 | ||||||||
\(724\) | −14.9888 | −0.557053 | ||||||||
\(725\) | 40.6879 | 1.51111 | ||||||||
\(726\) | 0.754771 | 0.0280122 | ||||||||
\(727\) | 39.0112 | 1.44685 | 0.723423 | − | 0.690406i | \(-0.242568\pi\) | ||||
0.723423 | + | 0.690406i | \(0.242568\pi\) | |||||||
\(728\) | 2.96305 | 0.109818 | ||||||||
\(729\) | −6.88826 | −0.255121 | ||||||||
\(730\) | −9.01725 | −0.333743 | ||||||||
\(731\) | 4.74317 | 0.175432 | ||||||||
\(732\) | 10.3681 | 0.383216 | ||||||||
\(733\) | −49.3662 | −1.82338 | −0.911690 | − | 0.410878i | \(-0.865222\pi\) | ||||
−0.911690 | + | 0.410878i | \(0.865222\pi\) | |||||||
\(734\) | 6.20611 | 0.229072 | ||||||||
\(735\) | −1.81604 | −0.0669858 | ||||||||
\(736\) | −8.63879 | −0.318430 | ||||||||
\(737\) | 30.3452 | 1.11778 | ||||||||
\(738\) | 3.51341 | 0.129330 | ||||||||
\(739\) | 3.28671 | 0.120903 | 0.0604517 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604517 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(740\) | 5.96750 | 0.219370 | ||||||||
\(741\) | 28.6321 | 1.05183 | ||||||||
\(742\) | −11.7502 | −0.431364 | ||||||||
\(743\) | 11.6914 | 0.428915 | 0.214458 | − | 0.976733i | \(-0.431202\pi\) | ||||
0.214458 | + | 0.976733i | \(0.431202\pi\) | |||||||
\(744\) | −12.7475 | −0.467347 | ||||||||
\(745\) | −13.2702 | −0.486182 | ||||||||
\(746\) | −11.4320 | −0.418556 | ||||||||
\(747\) | 20.4778 | 0.749243 | ||||||||
\(748\) | −9.08831 | −0.332302 | ||||||||
\(749\) | −0.761019 | −0.0278070 | ||||||||
\(750\) | 16.9613 | 0.619339 | ||||||||
\(751\) | −6.49083 | −0.236854 | −0.118427 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118427 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(752\) | −9.53234 | −0.347609 | ||||||||
\(753\) | −46.1733 | −1.68265 | ||||||||
\(754\) | −27.7808 | −1.01172 | ||||||||
\(755\) | −3.39959 | −0.123724 | ||||||||
\(756\) | 2.24677 | 0.0817142 | ||||||||
\(757\) | 11.4748 | 0.417059 | 0.208530 | − | 0.978016i | \(-0.433132\pi\) | ||||
0.208530 | + | 0.978016i | \(0.433132\pi\) | |||||||
\(758\) | 25.5794 | 0.929086 | ||||||||
\(759\) | 63.0422 | 2.28829 | ||||||||
\(760\) | −3.51345 | −0.127446 | ||||||||
\(761\) | 6.25685 | 0.226811 | 0.113405 | − | 0.993549i | \(-0.463824\pi\) | ||||
0.113405 | + | 0.993549i | \(0.463824\pi\) | |||||||
\(762\) | −15.6139 | −0.565632 | ||||||||
\(763\) | 8.13333 | 0.294446 | ||||||||
\(764\) | −9.26422 | −0.335168 | ||||||||
\(765\) | −4.51132 | −0.163107 | ||||||||
\(766\) | 22.9519 | 0.829286 | ||||||||
\(767\) | −25.8224 | −0.932394 | ||||||||
\(768\) | −2.23488 | −0.0806442 | ||||||||
\(769\) | 38.5889 | 1.39155 | 0.695775 | − | 0.718259i | \(-0.255061\pi\) | ||||
0.695775 | + | 0.718259i | \(0.255061\pi\) | |||||||
\(770\) | 2.65337 | 0.0956207 | ||||||||
\(771\) | 6.34206 | 0.228404 | ||||||||
\(772\) | 23.5608 | 0.847971 | ||||||||
\(773\) | −7.19501 | −0.258787 | −0.129393 | − | 0.991593i | \(-0.541303\pi\) | ||||
−0.129393 | + | 0.991593i | \(0.541303\pi\) | |||||||
\(774\) | −3.39925 | −0.122183 | ||||||||
\(775\) | −24.7532 | −0.889161 | ||||||||
\(776\) | −1.25240 | −0.0449587 | ||||||||
\(777\) | −16.4125 | −0.588794 | ||||||||
\(778\) | −20.9052 | −0.749489 | ||||||||
\(779\) | −7.61582 | −0.272865 | ||||||||
\(780\) | −5.38102 | −0.192671 | ||||||||
\(781\) | −52.6607 | −1.88435 | ||||||||
\(782\) | 24.0442 | 0.859820 | ||||||||
\(783\) | −21.0652 | −0.752807 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.9874 | 0.641996 | ||||||||
\(786\) | 0.202583 | 0.00722590 | ||||||||
\(787\) | −8.86735 | −0.316087 | −0.158043 | − | 0.987432i | \(-0.550519\pi\) | ||||
−0.158043 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(788\) | −24.7432 | −0.881438 | ||||||||
\(789\) | −42.3857 | −1.50897 | ||||||||
\(790\) | 7.92667 | 0.282018 | ||||||||
\(791\) | −5.97693 | −0.212515 | ||||||||
\(792\) | 6.51325 | 0.231438 | ||||||||
\(793\) | −13.7462 | −0.488143 | ||||||||
\(794\) | 14.8338 | 0.526433 | ||||||||
\(795\) | 21.3389 | 0.756812 | ||||||||
\(796\) | −9.00585 | −0.319204 | ||||||||
\(797\) | 1.87871 | 0.0665474 | 0.0332737 | − | 0.999446i | \(-0.489407\pi\) | ||||
0.0332737 | + | 0.999446i | \(0.489407\pi\) | |||||||
\(798\) | 9.66307 | 0.342069 | ||||||||
\(799\) | 26.5313 | 0.938608 | ||||||||
\(800\) | −4.33969 | −0.153431 | ||||||||
\(801\) | 13.0186 | 0.459989 | ||||||||
\(802\) | −1.99975 | −0.0706138 | ||||||||
\(803\) | −36.2349 | −1.27870 | ||||||||
\(804\) | −20.7691 | −0.732471 | ||||||||
\(805\) | −7.01981 | −0.247416 | ||||||||
\(806\) | 16.9009 | 0.595310 | ||||||||
\(807\) | −48.0112 | −1.69008 | ||||||||
\(808\) | 13.8258 | 0.486389 | ||||||||
\(809\) | −46.3154 | −1.62836 | −0.814182 | − | 0.580610i | \(-0.802814\pi\) | ||||
−0.814182 | + | 0.580610i | \(0.802814\pi\) | |||||||
\(810\) | −8.94281 | −0.314218 | ||||||||
\(811\) | 15.1610 | 0.532374 | 0.266187 | − | 0.963921i | \(-0.414236\pi\) | ||||
0.266187 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(812\) | −9.37575 | −0.329024 | ||||||||
\(813\) | 70.8063 | 2.48328 | ||||||||
\(814\) | 23.9798 | 0.840490 | ||||||||
\(815\) | 0.272728 | 0.00955325 | ||||||||
\(816\) | 6.22031 | 0.217754 | ||||||||
\(817\) | 7.36837 | 0.257787 | ||||||||
\(818\) | −38.6230 | −1.35042 | ||||||||
\(819\) | 5.91032 | 0.206523 | ||||||||
\(820\) | 1.43129 | 0.0499829 | ||||||||
\(821\) | −17.2740 | −0.602868 | −0.301434 | − | 0.953487i | \(-0.597465\pi\) | ||||
−0.301434 | + | 0.953487i | \(0.597465\pi\) | |||||||
\(822\) | 28.5471 | 0.995695 | ||||||||
\(823\) | 36.5942 | 1.27559 | 0.637796 | − | 0.770205i | \(-0.279846\pi\) | ||||
0.637796 | + | 0.770205i | \(0.279846\pi\) | |||||||
\(824\) | 3.59568 | 0.125262 | ||||||||
\(825\) | 31.6693 | 1.10258 | ||||||||
\(826\) | −8.71482 | −0.303228 | ||||||||
\(827\) | −6.57553 | −0.228654 | −0.114327 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114327 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(828\) | −17.2316 | −0.598840 | ||||||||
\(829\) | 16.3087 | 0.566424 | 0.283212 | − | 0.959057i | \(-0.408600\pi\) | ||||
0.283212 | + | 0.959057i | \(0.408600\pi\) | |||||||
\(830\) | 8.34224 | 0.289563 | ||||||||
\(831\) | 30.8637 | 1.07065 | ||||||||
\(832\) | 2.96305 | 0.102725 | ||||||||
\(833\) | −2.78329 | −0.0964353 | ||||||||
\(834\) | −32.2586 | −1.11703 | ||||||||
\(835\) | 9.36403 | 0.324056 | ||||||||
\(836\) | −14.1184 | −0.488296 | ||||||||
\(837\) | 12.8154 | 0.442964 | ||||||||
\(838\) | 2.18635 | 0.0755263 | ||||||||
\(839\) | −49.1941 | −1.69837 | −0.849184 | − | 0.528097i | \(-0.822906\pi\) | ||||
−0.849184 | + | 0.528097i | \(0.822906\pi\) | |||||||
\(840\) | −1.81604 | −0.0626595 | ||||||||
\(841\) | 58.9047 | 2.03120 | ||||||||
\(842\) | 10.6823 | 0.368137 | ||||||||
\(843\) | 11.1288 | 0.383295 | ||||||||
\(844\) | −9.99153 | −0.343923 | ||||||||
\(845\) | −3.42943 | −0.117976 | ||||||||
\(846\) | −19.0140 | −0.653713 | ||||||||
\(847\) | −0.337724 | −0.0116043 | ||||||||
\(848\) | −11.7502 | −0.403504 | ||||||||
\(849\) | 45.4989 | 1.56152 | ||||||||
\(850\) | 12.0786 | 0.414293 | ||||||||
\(851\) | −63.4414 | −2.17474 | ||||||||
\(852\) | 36.0426 | 1.23480 | ||||||||
\(853\) | −52.0438 | −1.78195 | −0.890973 | − | 0.454056i | \(-0.849977\pi\) | ||||
−0.890973 | + | 0.454056i | \(0.849977\pi\) | |||||||
\(854\) | −4.63923 | −0.158751 | ||||||||
\(855\) | −7.00820 | −0.239676 | ||||||||
\(856\) | −0.761019 | −0.0260111 | ||||||||
\(857\) | 7.18768 | 0.245527 | 0.122763 | − | 0.992436i | \(-0.460824\pi\) | ||||
0.122763 | + | 0.992436i | \(0.460824\pi\) | |||||||
\(858\) | −21.6231 | −0.738199 | ||||||||
\(859\) | −8.75697 | −0.298784 | −0.149392 | − | 0.988778i | \(-0.547732\pi\) | ||||
−0.149392 | + | 0.988778i | \(0.547732\pi\) | |||||||
\(860\) | −1.38479 | −0.0472208 | ||||||||
\(861\) | −3.93649 | −0.134155 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −25.7682 | −0.877159 | −0.438579 | − | 0.898693i | \(-0.644518\pi\) | ||||
−0.438579 | + | 0.898693i | \(0.644518\pi\) | |||||||
\(864\) | 2.24677 | 0.0764367 | ||||||||
\(865\) | −7.91266 | −0.269038 | ||||||||
\(866\) | 8.63850 | 0.293548 | ||||||||
\(867\) | 20.6800 | 0.702330 | ||||||||
\(868\) | 5.70390 | 0.193603 | ||||||||
\(869\) | 31.8525 | 1.08052 | ||||||||
\(870\) | 17.0268 | 0.577262 | ||||||||
\(871\) | 27.5361 | 0.933026 | ||||||||
\(872\) | 8.13333 | 0.275429 | ||||||||
\(873\) | −2.49815 | −0.0845494 | ||||||||
\(874\) | 37.3520 | 1.26345 | ||||||||
\(875\) | −7.58936 | −0.256567 | ||||||||
\(876\) | 24.8002 | 0.837922 | ||||||||
\(877\) | 46.4632 | 1.56895 | 0.784476 | − | 0.620159i | \(-0.212932\pi\) | ||||
0.784476 | + | 0.620159i | \(0.212932\pi\) | |||||||
\(878\) | 12.0109 | 0.405347 | ||||||||
\(879\) | 15.2543 | 0.514516 | ||||||||
\(880\) | 2.65337 | 0.0894450 | ||||||||
\(881\) | 23.4137 | 0.788827 | 0.394414 | − | 0.918933i | \(-0.370948\pi\) | ||||
0.394414 | + | 0.918933i | \(0.370948\pi\) | |||||||
\(882\) | 1.99468 | 0.0671643 | ||||||||
\(883\) | −32.3704 | −1.08935 | −0.544675 | − | 0.838647i | \(-0.683347\pi\) | ||||
−0.544675 | + | 0.838647i | \(0.683347\pi\) | |||||||
\(884\) | −8.24701 | −0.277377 | ||||||||
\(885\) | 15.8265 | 0.532002 | ||||||||
\(886\) | 17.0802 | 0.573821 | ||||||||
\(887\) | −0.832155 | −0.0279410 | −0.0139705 | − | 0.999902i | \(-0.504447\pi\) | ||||
−0.0139705 | + | 0.999902i | \(0.504447\pi\) | |||||||
\(888\) | −16.4125 | −0.550766 | ||||||||
\(889\) | 6.98647 | 0.234319 | ||||||||
\(890\) | 5.30351 | 0.177774 | ||||||||
\(891\) | −35.9357 | −1.20389 | ||||||||
\(892\) | −18.8022 | −0.629546 | ||||||||
\(893\) | 41.2155 | 1.37922 | ||||||||
\(894\) | 36.4971 | 1.22065 | ||||||||
\(895\) | −19.2229 | −0.642549 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 57.2064 | 1.91007 | ||||||||
\(898\) | −22.2276 | −0.741746 | ||||||||
\(899\) | −53.4784 | −1.78360 | ||||||||
\(900\) | −8.65630 | −0.288543 | ||||||||
\(901\) | 32.7042 | 1.08954 | ||||||||
\(902\) | 5.75149 | 0.191504 | ||||||||
\(903\) | 3.80859 | 0.126742 | ||||||||
\(904\) | −5.97693 | −0.198790 | ||||||||
\(905\) | −12.1798 | −0.404869 | ||||||||
\(906\) | 9.34991 | 0.310630 | ||||||||
\(907\) | 14.3369 | 0.476049 | 0.238024 | − | 0.971259i | \(-0.423500\pi\) | ||||
0.238024 | + | 0.971259i | \(0.423500\pi\) | |||||||
\(908\) | 4.48248 | 0.148756 | ||||||||
\(909\) | 27.5780 | 0.914705 | ||||||||
\(910\) | 2.40775 | 0.0798160 | ||||||||
\(911\) | 12.1591 | 0.402850 | 0.201425 | − | 0.979504i | \(-0.435443\pi\) | ||||
0.201425 | + | 0.979504i | \(0.435443\pi\) | |||||||
\(912\) | 9.66307 | 0.319976 | ||||||||
\(913\) | 33.5224 | 1.10943 | ||||||||
\(914\) | −37.6890 | −1.24664 | ||||||||
\(915\) | 8.42504 | 0.278523 | ||||||||
\(916\) | 12.8191 | 0.423555 | ||||||||
\(917\) | −0.0906462 | −0.00299340 | ||||||||
\(918\) | −6.25341 | −0.206393 | ||||||||
\(919\) | −45.3983 | −1.49755 | −0.748775 | − | 0.662824i | \(-0.769358\pi\) | ||||
−0.748775 | + | 0.662824i | \(0.769358\pi\) | |||||||
\(920\) | −7.01981 | −0.231436 | ||||||||
\(921\) | −46.0652 | −1.51790 | ||||||||
\(922\) | −4.33600 | −0.142799 | ||||||||
\(923\) | −47.7859 | −1.57289 | ||||||||
\(924\) | −7.29758 | −0.240073 | ||||||||
\(925\) | −31.8698 | −1.04787 | ||||||||
\(926\) | 29.7916 | 0.979011 | ||||||||
\(927\) | 7.17223 | 0.235567 | ||||||||
\(928\) | −9.37575 | −0.307774 | ||||||||
\(929\) | 0.869939 | 0.0285418 | 0.0142709 | − | 0.999898i | \(-0.495457\pi\) | ||||
0.0142709 | + | 0.999898i | \(0.495457\pi\) | |||||||
\(930\) | −10.3585 | −0.339670 | ||||||||
\(931\) | −4.32376 | −0.141705 | ||||||||
\(932\) | −5.91773 | −0.193842 | ||||||||
\(933\) | −4.26144 | −0.139513 | ||||||||
\(934\) | −27.6527 | −0.904826 | ||||||||
\(935\) | −7.38509 | −0.241518 | ||||||||
\(936\) | 5.91032 | 0.193185 | ||||||||
\(937\) | −1.89466 | −0.0618958 | −0.0309479 | − | 0.999521i | \(-0.509853\pi\) | ||||
−0.0309479 | + | 0.999521i | \(0.509853\pi\) | |||||||
\(938\) | 9.29319 | 0.303433 | ||||||||
\(939\) | 53.1046 | 1.73300 | ||||||||
\(940\) | −7.74590 | −0.252643 | ||||||||
\(941\) | 34.2486 | 1.11647 | 0.558236 | − | 0.829682i | \(-0.311478\pi\) | ||||
0.558236 | + | 0.829682i | \(0.311478\pi\) | |||||||
\(942\) | −49.4708 | −1.61184 | ||||||||
\(943\) | −15.2163 | −0.495510 | ||||||||
\(944\) | −8.71482 | −0.283643 | ||||||||
\(945\) | 1.82571 | 0.0593903 | ||||||||
\(946\) | −5.56461 | −0.180921 | ||||||||
\(947\) | 58.6802 | 1.90685 | 0.953425 | − | 0.301631i | \(-0.0975312\pi\) | ||||
0.953425 | + | 0.301631i | \(0.0975312\pi\) | |||||||
\(948\) | −21.8008 | −0.708056 | ||||||||
\(949\) | −32.8806 | −1.06735 | ||||||||
\(950\) | 18.7638 | 0.608777 | ||||||||
\(951\) | 17.8138 | 0.577652 | ||||||||
\(952\) | −2.78329 | −0.0902069 | ||||||||
\(953\) | 37.1216 | 1.20249 | 0.601244 | − | 0.799066i | \(-0.294672\pi\) | ||||
0.601244 | + | 0.799066i | \(0.294672\pi\) | |||||||
\(954\) | −23.4379 | −0.758830 | ||||||||
\(955\) | −7.52803 | −0.243601 | ||||||||
\(956\) | 18.0461 | 0.583654 | ||||||||
\(957\) | 68.4203 | 2.21171 | ||||||||
\(958\) | 4.07882 | 0.131781 | ||||||||
\(959\) | −12.7735 | −0.412476 | ||||||||
\(960\) | −1.81604 | −0.0586126 | ||||||||
\(961\) | 1.53450 | 0.0495001 | ||||||||
\(962\) | 21.7600 | 0.701569 | ||||||||
\(963\) | −1.51799 | −0.0489165 | ||||||||
\(964\) | −29.1393 | −0.938513 | ||||||||
\(965\) | 19.1453 | 0.616309 | ||||||||
\(966\) | 19.3066 | 0.621181 | ||||||||
\(967\) | −4.43537 | −0.142632 | −0.0713159 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713159 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(968\) | −0.337724 | −0.0108549 | ||||||||
\(969\) | −26.8951 | −0.863995 | ||||||||
\(970\) | −1.01769 | −0.0326762 | ||||||||
\(971\) | −44.7507 | −1.43612 | −0.718059 | − | 0.695982i | \(-0.754969\pi\) | ||||
−0.718059 | + | 0.695982i | \(0.754969\pi\) | |||||||
\(972\) | 17.8552 | 0.572705 | ||||||||
\(973\) | 14.4342 | 0.462739 | ||||||||
\(974\) | 27.6331 | 0.885421 | ||||||||
\(975\) | 28.7376 | 0.920341 | ||||||||
\(976\) | −4.63923 | −0.148498 | ||||||||
\(977\) | −12.5393 | −0.401168 | −0.200584 | − | 0.979677i | \(-0.564284\pi\) | ||||
−0.200584 | + | 0.979677i | \(0.564284\pi\) | |||||||
\(978\) | −0.750086 | −0.0239851 | ||||||||
\(979\) | 21.3116 | 0.681122 | ||||||||
\(980\) | 0.812592 | 0.0259573 | ||||||||
\(981\) | 16.2234 | 0.517972 | ||||||||
\(982\) | 20.9329 | 0.667997 | ||||||||
\(983\) | −4.61837 | −0.147303 | −0.0736516 | − | 0.997284i | \(-0.523465\pi\) | ||||
−0.0736516 | + | 0.997284i | \(0.523465\pi\) | |||||||
\(984\) | −3.93649 | −0.125491 | ||||||||
\(985\) | −20.1061 | −0.640633 | ||||||||
\(986\) | 26.0954 | 0.831048 | ||||||||
\(987\) | 21.3036 | 0.678102 | ||||||||
\(988\) | −12.8115 | −0.407588 | ||||||||
\(989\) | 14.7219 | 0.468128 | ||||||||
\(990\) | 5.29262 | 0.168210 | ||||||||
\(991\) | 37.7918 | 1.20050 | 0.600248 | − | 0.799814i | \(-0.295068\pi\) | ||||
0.600248 | + | 0.799814i | \(0.295068\pi\) | |||||||
\(992\) | 5.70390 | 0.181099 | ||||||||
\(993\) | 45.4504 | 1.44233 | ||||||||
\(994\) | −16.1273 | −0.511527 | ||||||||
\(995\) | −7.31808 | −0.231999 | ||||||||
\(996\) | −22.9437 | −0.727000 | ||||||||
\(997\) | −52.4042 | −1.65966 | −0.829828 | − | 0.558019i | \(-0.811562\pi\) | ||||
−0.829828 | + | 0.558019i | \(0.811562\pi\) | |||||||
\(998\) | −28.6722 | −0.907602 | ||||||||
\(999\) | 16.4998 | 0.522030 |
(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 | 6034.2.a.m.1.5 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.m.1.5 | ✓ | 21 | 1.1 | even | 1 | trivial |