Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −0.354737 | −0.204807 | −0.102404 | − | 0.994743i | \(-0.532653\pi\) | ||||
−0.102404 | + | 0.994743i | \(0.532653\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.50160 | 1.11875 | 0.559375 | − | 0.828915i | \(-0.311041\pi\) | ||||
0.559375 | + | 0.828915i | \(0.311041\pi\) | |||||||
\(6\) | −0.354737 | −0.144821 | ||||||||
\(7\) | 4.23908 | 1.60222 | 0.801110 | − | 0.598517i | \(-0.204243\pi\) | ||||
0.801110 | + | 0.598517i | \(0.204243\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.87416 | −0.958054 | ||||||||
\(10\) | 2.50160 | 0.791076 | ||||||||
\(11\) | 5.05191 | 1.52321 | 0.761605 | − | 0.648042i | \(-0.224412\pi\) | ||||
0.761605 | + | 0.648042i | \(0.224412\pi\) | |||||||
\(12\) | −0.354737 | −0.102404 | ||||||||
\(13\) | 1.44576 | 0.400981 | 0.200490 | − | 0.979696i | \(-0.435746\pi\) | ||||
0.200490 | + | 0.979696i | \(0.435746\pi\) | |||||||
\(14\) | 4.23908 | 1.13294 | ||||||||
\(15\) | −0.887411 | −0.229128 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.70292 | 0.655554 | 0.327777 | − | 0.944755i | \(-0.393700\pi\) | ||||
0.327777 | + | 0.944755i | \(0.393700\pi\) | |||||||
\(18\) | −2.87416 | −0.677446 | ||||||||
\(19\) | 0.309796 | 0.0710722 | 0.0355361 | − | 0.999368i | \(-0.488686\pi\) | ||||
0.0355361 | + | 0.999368i | \(0.488686\pi\) | |||||||
\(20\) | 2.50160 | 0.559375 | ||||||||
\(21\) | −1.50376 | −0.328147 | ||||||||
\(22\) | 5.05191 | 1.07707 | ||||||||
\(23\) | −6.04785 | −1.26106 | −0.630532 | − | 0.776163i | \(-0.717163\pi\) | ||||
−0.630532 | + | 0.776163i | \(0.717163\pi\) | |||||||
\(24\) | −0.354737 | −0.0724104 | ||||||||
\(25\) | 1.25801 | 0.251603 | ||||||||
\(26\) | 1.44576 | 0.283536 | ||||||||
\(27\) | 2.08378 | 0.401024 | ||||||||
\(28\) | 4.23908 | 0.801110 | ||||||||
\(29\) | 7.09884 | 1.31822 | 0.659110 | − | 0.752046i | \(-0.270933\pi\) | ||||
0.659110 | + | 0.752046i | \(0.270933\pi\) | |||||||
\(30\) | −0.887411 | −0.162018 | ||||||||
\(31\) | 7.08818 | 1.27307 | 0.636537 | − | 0.771246i | \(-0.280366\pi\) | ||||
0.636537 | + | 0.771246i | \(0.280366\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.79210 | −0.311965 | ||||||||
\(34\) | 2.70292 | 0.463547 | ||||||||
\(35\) | 10.6045 | 1.79249 | ||||||||
\(36\) | −2.87416 | −0.479027 | ||||||||
\(37\) | −10.0196 | −1.64721 | −0.823605 | − | 0.567163i | \(-0.808041\pi\) | ||||
−0.823605 | + | 0.567163i | \(0.808041\pi\) | |||||||
\(38\) | 0.309796 | 0.0502556 | ||||||||
\(39\) | −0.512863 | −0.0821239 | ||||||||
\(40\) | 2.50160 | 0.395538 | ||||||||
\(41\) | −3.19650 | −0.499209 | −0.249605 | − | 0.968348i | \(-0.580301\pi\) | ||||
−0.249605 | + | 0.968348i | \(0.580301\pi\) | |||||||
\(42\) | −1.50376 | −0.232035 | ||||||||
\(43\) | −6.59282 | −1.00540 | −0.502698 | − | 0.864462i | \(-0.667659\pi\) | ||||
−0.502698 | + | 0.864462i | \(0.667659\pi\) | |||||||
\(44\) | 5.05191 | 0.761605 | ||||||||
\(45\) | −7.19001 | −1.07182 | ||||||||
\(46\) | −6.04785 | −0.891707 | ||||||||
\(47\) | −6.47974 | −0.945167 | −0.472583 | − | 0.881286i | \(-0.656678\pi\) | ||||
−0.472583 | + | 0.881286i | \(0.656678\pi\) | |||||||
\(48\) | −0.354737 | −0.0512019 | ||||||||
\(49\) | 10.9698 | 1.56711 | ||||||||
\(50\) | 1.25801 | 0.177910 | ||||||||
\(51\) | −0.958825 | −0.134262 | ||||||||
\(52\) | 1.44576 | 0.200490 | ||||||||
\(53\) | 7.51170 | 1.03181 | 0.515906 | − | 0.856645i | \(-0.327455\pi\) | ||||
0.515906 | + | 0.856645i | \(0.327455\pi\) | |||||||
\(54\) | 2.08378 | 0.283567 | ||||||||
\(55\) | 12.6379 | 1.70409 | ||||||||
\(56\) | 4.23908 | 0.566471 | ||||||||
\(57\) | −0.109896 | −0.0145561 | ||||||||
\(58\) | 7.09884 | 0.932123 | ||||||||
\(59\) | −9.36687 | −1.21946 | −0.609731 | − | 0.792608i | \(-0.708723\pi\) | ||||
−0.609731 | + | 0.792608i | \(0.708723\pi\) | |||||||
\(60\) | −0.887411 | −0.114564 | ||||||||
\(61\) | −6.79492 | −0.870001 | −0.435000 | − | 0.900430i | \(-0.643252\pi\) | ||||
−0.435000 | + | 0.900430i | \(0.643252\pi\) | |||||||
\(62\) | 7.08818 | 0.900200 | ||||||||
\(63\) | −12.1838 | −1.53501 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.61671 | 0.448598 | ||||||||
\(66\) | −1.79210 | −0.220592 | ||||||||
\(67\) | 3.57920 | 0.437268 | 0.218634 | − | 0.975807i | \(-0.429840\pi\) | ||||
0.218634 | + | 0.975807i | \(0.429840\pi\) | |||||||
\(68\) | 2.70292 | 0.327777 | ||||||||
\(69\) | 2.14539 | 0.258275 | ||||||||
\(70\) | 10.6045 | 1.26748 | ||||||||
\(71\) | −10.2708 | −1.21891 | −0.609457 | − | 0.792819i | \(-0.708613\pi\) | ||||
−0.609457 | + | 0.792819i | \(0.708613\pi\) | |||||||
\(72\) | −2.87416 | −0.338723 | ||||||||
\(73\) | −11.4207 | −1.33670 | −0.668349 | − | 0.743848i | \(-0.732999\pi\) | ||||
−0.668349 | + | 0.743848i | \(0.732999\pi\) | |||||||
\(74\) | −10.0196 | −1.16475 | ||||||||
\(75\) | −0.446264 | −0.0515302 | ||||||||
\(76\) | 0.309796 | 0.0355361 | ||||||||
\(77\) | 21.4155 | 2.44052 | ||||||||
\(78\) | −0.512863 | −0.0580704 | ||||||||
\(79\) | 15.8549 | 1.78382 | 0.891909 | − | 0.452215i | \(-0.149366\pi\) | ||||
0.891909 | + | 0.452215i | \(0.149366\pi\) | |||||||
\(80\) | 2.50160 | 0.279688 | ||||||||
\(81\) | 7.88329 | 0.875921 | ||||||||
\(82\) | −3.19650 | −0.352994 | ||||||||
\(83\) | −11.9598 | −1.31276 | −0.656379 | − | 0.754431i | \(-0.727913\pi\) | ||||
−0.656379 | + | 0.754431i | \(0.727913\pi\) | |||||||
\(84\) | −1.50376 | −0.164073 | ||||||||
\(85\) | 6.76163 | 0.733402 | ||||||||
\(86\) | −6.59282 | −0.710922 | ||||||||
\(87\) | −2.51822 | −0.269981 | ||||||||
\(88\) | 5.05191 | 0.538536 | ||||||||
\(89\) | 8.41688 | 0.892187 | 0.446094 | − | 0.894986i | \(-0.352815\pi\) | ||||
0.446094 | + | 0.894986i | \(0.352815\pi\) | |||||||
\(90\) | −7.19001 | −0.757894 | ||||||||
\(91\) | 6.12868 | 0.642460 | ||||||||
\(92\) | −6.04785 | −0.630532 | ||||||||
\(93\) | −2.51444 | −0.260735 | ||||||||
\(94\) | −6.47974 | −0.668334 | ||||||||
\(95\) | 0.774988 | 0.0795120 | ||||||||
\(96\) | −0.354737 | −0.0362052 | ||||||||
\(97\) | 13.0362 | 1.32363 | 0.661814 | − | 0.749668i | \(-0.269787\pi\) | ||||
0.661814 | + | 0.749668i | \(0.269787\pi\) | |||||||
\(98\) | 10.9698 | 1.10812 | ||||||||
\(99\) | −14.5200 | −1.45932 | ||||||||
\(100\) | 1.25801 | 0.125801 | ||||||||
\(101\) | 13.4570 | 1.33902 | 0.669509 | − | 0.742804i | \(-0.266505\pi\) | ||||
0.669509 | + | 0.742804i | \(0.266505\pi\) | |||||||
\(102\) | −0.958825 | −0.0949379 | ||||||||
\(103\) | −19.4082 | −1.91235 | −0.956175 | − | 0.292795i | \(-0.905415\pi\) | ||||
−0.956175 | + | 0.292795i | \(0.905415\pi\) | |||||||
\(104\) | 1.44576 | 0.141768 | ||||||||
\(105\) | −3.76180 | −0.367114 | ||||||||
\(106\) | 7.51170 | 0.729601 | ||||||||
\(107\) | −6.49107 | −0.627516 | −0.313758 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313758 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(108\) | 2.08378 | 0.200512 | ||||||||
\(109\) | 1.54816 | 0.148287 | 0.0741433 | − | 0.997248i | \(-0.476378\pi\) | ||||
0.0741433 | + | 0.997248i | \(0.476378\pi\) | |||||||
\(110\) | 12.6379 | 1.20497 | ||||||||
\(111\) | 3.55432 | 0.337361 | ||||||||
\(112\) | 4.23908 | 0.400555 | ||||||||
\(113\) | −16.0403 | −1.50894 | −0.754472 | − | 0.656332i | \(-0.772107\pi\) | ||||
−0.754472 | + | 0.656332i | \(0.772107\pi\) | |||||||
\(114\) | −0.109896 | −0.0102927 | ||||||||
\(115\) | −15.1293 | −1.41082 | ||||||||
\(116\) | 7.09884 | 0.659110 | ||||||||
\(117\) | −4.15534 | −0.384161 | ||||||||
\(118\) | −9.36687 | −0.862290 | ||||||||
\(119\) | 11.4579 | 1.05034 | ||||||||
\(120\) | −0.887411 | −0.0810091 | ||||||||
\(121\) | 14.5218 | 1.32017 | ||||||||
\(122\) | −6.79492 | −0.615184 | ||||||||
\(123\) | 1.13392 | 0.102242 | ||||||||
\(124\) | 7.08818 | 0.636537 | ||||||||
\(125\) | −9.36096 | −0.837270 | ||||||||
\(126\) | −12.1838 | −1.08542 | ||||||||
\(127\) | −15.5297 | −1.37804 | −0.689021 | − | 0.724741i | \(-0.741959\pi\) | ||||
−0.689021 | + | 0.724741i | \(0.741959\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.33872 | 0.205913 | ||||||||
\(130\) | 3.61671 | 0.317206 | ||||||||
\(131\) | 5.60410 | 0.489632 | 0.244816 | − | 0.969570i | \(-0.421272\pi\) | ||||
0.244816 | + | 0.969570i | \(0.421272\pi\) | |||||||
\(132\) | −1.79210 | −0.155982 | ||||||||
\(133\) | 1.31325 | 0.113873 | ||||||||
\(134\) | 3.57920 | 0.309196 | ||||||||
\(135\) | 5.21279 | 0.448646 | ||||||||
\(136\) | 2.70292 | 0.231773 | ||||||||
\(137\) | −16.7378 | −1.43000 | −0.715001 | − | 0.699123i | \(-0.753574\pi\) | ||||
−0.715001 | + | 0.699123i | \(0.753574\pi\) | |||||||
\(138\) | 2.14539 | 0.182628 | ||||||||
\(139\) | 5.63400 | 0.477870 | 0.238935 | − | 0.971036i | \(-0.423202\pi\) | ||||
0.238935 | + | 0.971036i | \(0.423202\pi\) | |||||||
\(140\) | 10.6045 | 0.896243 | ||||||||
\(141\) | 2.29860 | 0.193577 | ||||||||
\(142\) | −10.2708 | −0.861903 | ||||||||
\(143\) | 7.30384 | 0.610778 | ||||||||
\(144\) | −2.87416 | −0.239513 | ||||||||
\(145\) | 17.7585 | 1.47476 | ||||||||
\(146\) | −11.4207 | −0.945188 | ||||||||
\(147\) | −3.89139 | −0.320956 | ||||||||
\(148\) | −10.0196 | −0.823605 | ||||||||
\(149\) | −11.6511 | −0.954494 | −0.477247 | − | 0.878769i | \(-0.658365\pi\) | ||||
−0.477247 | + | 0.878769i | \(0.658365\pi\) | |||||||
\(150\) | −0.446264 | −0.0364373 | ||||||||
\(151\) | −18.8620 | −1.53497 | −0.767485 | − | 0.641066i | \(-0.778492\pi\) | ||||
−0.767485 | + | 0.641066i | \(0.778492\pi\) | |||||||
\(152\) | 0.309796 | 0.0251278 | ||||||||
\(153\) | −7.76863 | −0.628056 | ||||||||
\(154\) | 21.4155 | 1.72571 | ||||||||
\(155\) | 17.7318 | 1.42425 | ||||||||
\(156\) | −0.512863 | −0.0410619 | ||||||||
\(157\) | 6.74126 | 0.538011 | 0.269006 | − | 0.963139i | \(-0.413305\pi\) | ||||
0.269006 | + | 0.963139i | \(0.413305\pi\) | |||||||
\(158\) | 15.8549 | 1.26135 | ||||||||
\(159\) | −2.66468 | −0.211323 | ||||||||
\(160\) | 2.50160 | 0.197769 | ||||||||
\(161\) | −25.6373 | −2.02050 | ||||||||
\(162\) | 7.88329 | 0.619370 | ||||||||
\(163\) | 16.2878 | 1.27576 | 0.637878 | − | 0.770137i | \(-0.279812\pi\) | ||||
0.637878 | + | 0.770137i | \(0.279812\pi\) | |||||||
\(164\) | −3.19650 | −0.249605 | ||||||||
\(165\) | −4.48312 | −0.349011 | ||||||||
\(166\) | −11.9598 | −0.928260 | ||||||||
\(167\) | 12.3546 | 0.956025 | 0.478013 | − | 0.878353i | \(-0.341357\pi\) | ||||
0.478013 | + | 0.878353i | \(0.341357\pi\) | |||||||
\(168\) | −1.50376 | −0.116017 | ||||||||
\(169\) | −10.9098 | −0.839214 | ||||||||
\(170\) | 6.76163 | 0.518593 | ||||||||
\(171\) | −0.890405 | −0.0680910 | ||||||||
\(172\) | −6.59282 | −0.502698 | ||||||||
\(173\) | −5.34997 | −0.406751 | −0.203376 | − | 0.979101i | \(-0.565191\pi\) | ||||
−0.203376 | + | 0.979101i | \(0.565191\pi\) | |||||||
\(174\) | −2.51822 | −0.190906 | ||||||||
\(175\) | 5.33282 | 0.403123 | ||||||||
\(176\) | 5.05191 | 0.380802 | ||||||||
\(177\) | 3.32277 | 0.249755 | ||||||||
\(178\) | 8.41688 | 0.630872 | ||||||||
\(179\) | 16.1423 | 1.20653 | 0.603265 | − | 0.797541i | \(-0.293866\pi\) | ||||
0.603265 | + | 0.797541i | \(0.293866\pi\) | |||||||
\(180\) | −7.19001 | −0.535912 | ||||||||
\(181\) | −16.4804 | −1.22498 | −0.612490 | − | 0.790478i | \(-0.709832\pi\) | ||||
−0.612490 | + | 0.790478i | \(0.709832\pi\) | |||||||
\(182\) | 6.12868 | 0.454288 | ||||||||
\(183\) | 2.41041 | 0.178183 | ||||||||
\(184\) | −6.04785 | −0.445853 | ||||||||
\(185\) | −25.0650 | −1.84282 | ||||||||
\(186\) | −2.51444 | −0.184368 | ||||||||
\(187\) | 13.6549 | 0.998546 | ||||||||
\(188\) | −6.47974 | −0.472583 | ||||||||
\(189\) | 8.83331 | 0.642529 | ||||||||
\(190\) | 0.774988 | 0.0562235 | ||||||||
\(191\) | 25.8262 | 1.86872 | 0.934358 | − | 0.356337i | \(-0.115974\pi\) | ||||
0.934358 | + | 0.356337i | \(0.115974\pi\) | |||||||
\(192\) | −0.354737 | −0.0256009 | ||||||||
\(193\) | 24.2074 | 1.74249 | 0.871245 | − | 0.490849i | \(-0.163313\pi\) | ||||
0.871245 | + | 0.490849i | \(0.163313\pi\) | |||||||
\(194\) | 13.0362 | 0.935947 | ||||||||
\(195\) | −1.28298 | −0.0918761 | ||||||||
\(196\) | 10.9698 | 0.783556 | ||||||||
\(197\) | −7.28644 | −0.519137 | −0.259569 | − | 0.965725i | \(-0.583580\pi\) | ||||
−0.259569 | + | 0.965725i | \(0.583580\pi\) | |||||||
\(198\) | −14.5200 | −1.03189 | ||||||||
\(199\) | 7.55110 | 0.535283 | 0.267642 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267642 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(200\) | 1.25801 | 0.0889551 | ||||||||
\(201\) | −1.26967 | −0.0895558 | ||||||||
\(202\) | 13.4570 | 0.946829 | ||||||||
\(203\) | 30.0925 | 2.11208 | ||||||||
\(204\) | −0.958825 | −0.0671312 | ||||||||
\(205\) | −7.99637 | −0.558491 | ||||||||
\(206\) | −19.4082 | −1.35224 | ||||||||
\(207\) | 17.3825 | 1.20817 | ||||||||
\(208\) | 1.44576 | 0.100245 | ||||||||
\(209\) | 1.56506 | 0.108258 | ||||||||
\(210\) | −3.76180 | −0.259589 | ||||||||
\(211\) | 16.1594 | 1.11246 | 0.556230 | − | 0.831029i | \(-0.312248\pi\) | ||||
0.556230 | + | 0.831029i | \(0.312248\pi\) | |||||||
\(212\) | 7.51170 | 0.515906 | ||||||||
\(213\) | 3.64342 | 0.249643 | ||||||||
\(214\) | −6.49107 | −0.443721 | ||||||||
\(215\) | −16.4926 | −1.12479 | ||||||||
\(216\) | 2.08378 | 0.141783 | ||||||||
\(217\) | 30.0473 | 2.03975 | ||||||||
\(218\) | 1.54816 | 0.104854 | ||||||||
\(219\) | 4.05136 | 0.273766 | ||||||||
\(220\) | 12.6379 | 0.852046 | ||||||||
\(221\) | 3.90777 | 0.262865 | ||||||||
\(222\) | 3.55432 | 0.238550 | ||||||||
\(223\) | −17.6469 | −1.18172 | −0.590861 | − | 0.806774i | \(-0.701212\pi\) | ||||
−0.590861 | + | 0.806774i | \(0.701212\pi\) | |||||||
\(224\) | 4.23908 | 0.283235 | ||||||||
\(225\) | −3.61574 | −0.241049 | ||||||||
\(226\) | −16.0403 | −1.06698 | ||||||||
\(227\) | −1.29779 | −0.0861371 | −0.0430686 | − | 0.999072i | \(-0.513713\pi\) | ||||
−0.0430686 | + | 0.999072i | \(0.513713\pi\) | |||||||
\(228\) | −0.109896 | −0.00727806 | ||||||||
\(229\) | 23.9469 | 1.58245 | 0.791227 | − | 0.611523i | \(-0.209443\pi\) | ||||
0.791227 | + | 0.611523i | \(0.209443\pi\) | |||||||
\(230\) | −15.1293 | −0.997597 | ||||||||
\(231\) | −7.59685 | −0.499836 | ||||||||
\(232\) | 7.09884 | 0.466061 | ||||||||
\(233\) | 7.87004 | 0.515584 | 0.257792 | − | 0.966200i | \(-0.417005\pi\) | ||||
0.257792 | + | 0.966200i | \(0.417005\pi\) | |||||||
\(234\) | −4.15534 | −0.271643 | ||||||||
\(235\) | −16.2097 | −1.05741 | ||||||||
\(236\) | −9.36687 | −0.609731 | ||||||||
\(237\) | −5.62432 | −0.365339 | ||||||||
\(238\) | 11.4579 | 0.742705 | ||||||||
\(239\) | 19.2985 | 1.24831 | 0.624157 | − | 0.781299i | \(-0.285443\pi\) | ||||
0.624157 | + | 0.781299i | \(0.285443\pi\) | |||||||
\(240\) | −0.887411 | −0.0572821 | ||||||||
\(241\) | 6.99523 | 0.450602 | 0.225301 | − | 0.974289i | \(-0.427663\pi\) | ||||
0.225301 | + | 0.974289i | \(0.427663\pi\) | |||||||
\(242\) | 14.5218 | 0.933498 | ||||||||
\(243\) | −9.04784 | −0.580419 | ||||||||
\(244\) | −6.79492 | −0.435000 | ||||||||
\(245\) | 27.4420 | 1.75321 | ||||||||
\(246\) | 1.13392 | 0.0722958 | ||||||||
\(247\) | 0.447890 | 0.0284986 | ||||||||
\(248\) | 7.08818 | 0.450100 | ||||||||
\(249\) | 4.24258 | 0.268863 | ||||||||
\(250\) | −9.36096 | −0.592039 | ||||||||
\(251\) | 15.3312 | 0.967696 | 0.483848 | − | 0.875152i | \(-0.339239\pi\) | ||||
0.483848 | + | 0.875152i | \(0.339239\pi\) | |||||||
\(252\) | −12.1838 | −0.767507 | ||||||||
\(253\) | −30.5532 | −1.92086 | ||||||||
\(254\) | −15.5297 | −0.974423 | ||||||||
\(255\) | −2.39860 | −0.150206 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.6485 | −1.53753 | −0.768766 | − | 0.639530i | \(-0.779129\pi\) | ||||
−0.768766 | + | 0.639530i | \(0.779129\pi\) | |||||||
\(258\) | 2.33872 | 0.145602 | ||||||||
\(259\) | −42.4738 | −2.63919 | ||||||||
\(260\) | 3.61671 | 0.224299 | ||||||||
\(261\) | −20.4032 | −1.26293 | ||||||||
\(262\) | 5.60410 | 0.346222 | ||||||||
\(263\) | 10.2955 | 0.634848 | 0.317424 | − | 0.948284i | \(-0.397182\pi\) | ||||
0.317424 | + | 0.948284i | \(0.397182\pi\) | |||||||
\(264\) | −1.79210 | −0.110296 | ||||||||
\(265\) | 18.7913 | 1.15434 | ||||||||
\(266\) | 1.31325 | 0.0805206 | ||||||||
\(267\) | −2.98578 | −0.182727 | ||||||||
\(268\) | 3.57920 | 0.218634 | ||||||||
\(269\) | 14.6922 | 0.895801 | 0.447901 | − | 0.894083i | \(-0.352172\pi\) | ||||
0.447901 | + | 0.894083i | \(0.352172\pi\) | |||||||
\(270\) | 5.21279 | 0.317241 | ||||||||
\(271\) | −6.98204 | −0.424129 | −0.212064 | − | 0.977256i | \(-0.568019\pi\) | ||||
−0.212064 | + | 0.977256i | \(0.568019\pi\) | |||||||
\(272\) | 2.70292 | 0.163889 | ||||||||
\(273\) | −2.17407 | −0.131581 | ||||||||
\(274\) | −16.7378 | −1.01116 | ||||||||
\(275\) | 6.35538 | 0.383244 | ||||||||
\(276\) | 2.14539 | 0.129138 | ||||||||
\(277\) | 16.0138 | 0.962177 | 0.481089 | − | 0.876672i | \(-0.340242\pi\) | ||||
0.481089 | + | 0.876672i | \(0.340242\pi\) | |||||||
\(278\) | 5.63400 | 0.337905 | ||||||||
\(279\) | −20.3726 | −1.21967 | ||||||||
\(280\) | 10.6045 | 0.633739 | ||||||||
\(281\) | 17.5241 | 1.04540 | 0.522700 | − | 0.852517i | \(-0.324925\pi\) | ||||
0.522700 | + | 0.852517i | \(0.324925\pi\) | |||||||
\(282\) | 2.29860 | 0.136880 | ||||||||
\(283\) | −6.47177 | −0.384707 | −0.192353 | − | 0.981326i | \(-0.561612\pi\) | ||||
−0.192353 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(284\) | −10.2708 | −0.609457 | ||||||||
\(285\) | −0.274917 | −0.0162847 | ||||||||
\(286\) | 7.30384 | 0.431885 | ||||||||
\(287\) | −13.5502 | −0.799843 | ||||||||
\(288\) | −2.87416 | −0.169362 | ||||||||
\(289\) | −9.69422 | −0.570248 | ||||||||
\(290\) | 17.7585 | 1.04281 | ||||||||
\(291\) | −4.62443 | −0.271089 | ||||||||
\(292\) | −11.4207 | −0.668349 | ||||||||
\(293\) | −15.8101 | −0.923636 | −0.461818 | − | 0.886975i | \(-0.652803\pi\) | ||||
−0.461818 | + | 0.886975i | \(0.652803\pi\) | |||||||
\(294\) | −3.89139 | −0.226950 | ||||||||
\(295\) | −23.4322 | −1.36427 | ||||||||
\(296\) | −10.0196 | −0.582377 | ||||||||
\(297\) | 10.5271 | 0.610843 | ||||||||
\(298\) | −11.6511 | −0.674929 | ||||||||
\(299\) | −8.74372 | −0.505662 | ||||||||
\(300\) | −0.446264 | −0.0257651 | ||||||||
\(301\) | −27.9475 | −1.61087 | ||||||||
\(302\) | −18.8620 | −1.08539 | ||||||||
\(303\) | −4.77368 | −0.274241 | ||||||||
\(304\) | 0.309796 | 0.0177680 | ||||||||
\(305\) | −16.9982 | −0.973314 | ||||||||
\(306\) | −7.76863 | −0.444103 | ||||||||
\(307\) | −11.6136 | −0.662825 | −0.331412 | − | 0.943486i | \(-0.607525\pi\) | ||||
−0.331412 | + | 0.943486i | \(0.607525\pi\) | |||||||
\(308\) | 21.4155 | 1.22026 | ||||||||
\(309\) | 6.88482 | 0.391664 | ||||||||
\(310\) | 17.7318 | 1.00710 | ||||||||
\(311\) | −18.7925 | −1.06562 | −0.532812 | − | 0.846234i | \(-0.678865\pi\) | ||||
−0.532812 | + | 0.846234i | \(0.678865\pi\) | |||||||
\(312\) | −0.512863 | −0.0290352 | ||||||||
\(313\) | −3.58821 | −0.202818 | −0.101409 | − | 0.994845i | \(-0.532335\pi\) | ||||
−0.101409 | + | 0.994845i | \(0.532335\pi\) | |||||||
\(314\) | 6.74126 | 0.380431 | ||||||||
\(315\) | −30.4790 | −1.71730 | ||||||||
\(316\) | 15.8549 | 0.891909 | ||||||||
\(317\) | 19.8340 | 1.11399 | 0.556993 | − | 0.830517i | \(-0.311955\pi\) | ||||
0.556993 | + | 0.830517i | \(0.311955\pi\) | |||||||
\(318\) | −2.66468 | −0.149428 | ||||||||
\(319\) | 35.8627 | 2.00793 | ||||||||
\(320\) | 2.50160 | 0.139844 | ||||||||
\(321\) | 2.30262 | 0.128520 | ||||||||
\(322\) | −25.6373 | −1.42871 | ||||||||
\(323\) | 0.837355 | 0.0465917 | ||||||||
\(324\) | 7.88329 | 0.437961 | ||||||||
\(325\) | 1.81878 | 0.100888 | ||||||||
\(326\) | 16.2878 | 0.902096 | ||||||||
\(327\) | −0.549189 | −0.0303702 | ||||||||
\(328\) | −3.19650 | −0.176497 | ||||||||
\(329\) | −27.4681 | −1.51437 | ||||||||
\(330\) | −4.48312 | −0.246788 | ||||||||
\(331\) | 14.8735 | 0.817519 | 0.408760 | − | 0.912642i | \(-0.365961\pi\) | ||||
0.408760 | + | 0.912642i | \(0.365961\pi\) | |||||||
\(332\) | −11.9598 | −0.656379 | ||||||||
\(333\) | 28.7979 | 1.57812 | ||||||||
\(334\) | 12.3546 | 0.676012 | ||||||||
\(335\) | 8.95373 | 0.489194 | ||||||||
\(336\) | −1.50376 | −0.0820367 | ||||||||
\(337\) | −12.2061 | −0.664908 | −0.332454 | − | 0.943120i | \(-0.607877\pi\) | ||||
−0.332454 | + | 0.943120i | \(0.607877\pi\) | |||||||
\(338\) | −10.9098 | −0.593414 | ||||||||
\(339\) | 5.69008 | 0.309043 | ||||||||
\(340\) | 6.76163 | 0.366701 | ||||||||
\(341\) | 35.8089 | 1.93916 | ||||||||
\(342\) | −0.890405 | −0.0481476 | ||||||||
\(343\) | 16.8282 | 0.908637 | ||||||||
\(344\) | −6.59282 | −0.355461 | ||||||||
\(345\) | 5.36692 | 0.288946 | ||||||||
\(346\) | −5.34997 | −0.287616 | ||||||||
\(347\) | 25.9128 | 1.39107 | 0.695535 | − | 0.718492i | \(-0.255167\pi\) | ||||
0.695535 | + | 0.718492i | \(0.255167\pi\) | |||||||
\(348\) | −2.51822 | −0.134991 | ||||||||
\(349\) | −1.96325 | −0.105090 | −0.0525452 | − | 0.998619i | \(-0.516733\pi\) | ||||
−0.0525452 | + | 0.998619i | \(0.516733\pi\) | |||||||
\(350\) | 5.33282 | 0.285051 | ||||||||
\(351\) | 3.01264 | 0.160803 | ||||||||
\(352\) | 5.05191 | 0.269268 | ||||||||
\(353\) | 7.06061 | 0.375798 | 0.187899 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187899 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(354\) | 3.32277 | 0.176603 | ||||||||
\(355\) | −25.6934 | −1.36366 | ||||||||
\(356\) | 8.41688 | 0.446094 | ||||||||
\(357\) | −4.06454 | −0.215118 | ||||||||
\(358\) | 16.1423 | 0.853146 | ||||||||
\(359\) | 8.10653 | 0.427847 | 0.213923 | − | 0.976850i | \(-0.431376\pi\) | ||||
0.213923 | + | 0.976850i | \(0.431376\pi\) | |||||||
\(360\) | −7.19001 | −0.378947 | ||||||||
\(361\) | −18.9040 | −0.994949 | ||||||||
\(362\) | −16.4804 | −0.866192 | ||||||||
\(363\) | −5.15143 | −0.270380 | ||||||||
\(364\) | 6.12868 | 0.321230 | ||||||||
\(365\) | −28.5702 | −1.49543 | ||||||||
\(366\) | 2.41041 | 0.125994 | ||||||||
\(367\) | 30.2287 | 1.57792 | 0.788962 | − | 0.614441i | \(-0.210619\pi\) | ||||
0.788962 | + | 0.614441i | \(0.210619\pi\) | |||||||
\(368\) | −6.04785 | −0.315266 | ||||||||
\(369\) | 9.18725 | 0.478269 | ||||||||
\(370\) | −25.0650 | −1.30307 | ||||||||
\(371\) | 31.8427 | 1.65319 | ||||||||
\(372\) | −2.51444 | −0.130368 | ||||||||
\(373\) | −3.53242 | −0.182902 | −0.0914508 | − | 0.995810i | \(-0.529150\pi\) | ||||
−0.0914508 | + | 0.995810i | \(0.529150\pi\) | |||||||
\(374\) | 13.6549 | 0.706079 | ||||||||
\(375\) | 3.32068 | 0.171479 | ||||||||
\(376\) | −6.47974 | −0.334167 | ||||||||
\(377\) | 10.2632 | 0.528581 | ||||||||
\(378\) | 8.83331 | 0.454337 | ||||||||
\(379\) | 37.2454 | 1.91317 | 0.956584 | − | 0.291456i | \(-0.0941398\pi\) | ||||
0.956584 | + | 0.291456i | \(0.0941398\pi\) | |||||||
\(380\) | 0.774988 | 0.0397560 | ||||||||
\(381\) | 5.50898 | 0.282233 | ||||||||
\(382\) | 25.8262 | 1.32138 | ||||||||
\(383\) | −36.2812 | −1.85388 | −0.926940 | − | 0.375209i | \(-0.877571\pi\) | ||||
−0.926940 | + | 0.375209i | \(0.877571\pi\) | |||||||
\(384\) | −0.354737 | −0.0181026 | ||||||||
\(385\) | 53.5729 | 2.73033 | ||||||||
\(386\) | 24.2074 | 1.23213 | ||||||||
\(387\) | 18.9488 | 0.963224 | ||||||||
\(388\) | 13.0362 | 0.661814 | ||||||||
\(389\) | −25.5490 | −1.29539 | −0.647693 | − | 0.761901i | \(-0.724266\pi\) | ||||
−0.647693 | + | 0.761901i | \(0.724266\pi\) | |||||||
\(390\) | −1.28298 | −0.0649662 | ||||||||
\(391\) | −16.3468 | −0.826696 | ||||||||
\(392\) | 10.9698 | 0.554058 | ||||||||
\(393\) | −1.98798 | −0.100280 | ||||||||
\(394\) | −7.28644 | −0.367086 | ||||||||
\(395\) | 39.6627 | 1.99565 | ||||||||
\(396\) | −14.5200 | −0.729658 | ||||||||
\(397\) | 17.4966 | 0.878127 | 0.439064 | − | 0.898456i | \(-0.355310\pi\) | ||||
0.439064 | + | 0.898456i | \(0.355310\pi\) | |||||||
\(398\) | 7.55110 | 0.378502 | ||||||||
\(399\) | −0.465859 | −0.0233221 | ||||||||
\(400\) | 1.25801 | 0.0629007 | ||||||||
\(401\) | −30.2755 | −1.51189 | −0.755943 | − | 0.654638i | \(-0.772821\pi\) | ||||
−0.755943 | + | 0.654638i | \(0.772821\pi\) | |||||||
\(402\) | −1.26967 | −0.0633255 | ||||||||
\(403\) | 10.2478 | 0.510479 | ||||||||
\(404\) | 13.4570 | 0.669509 | ||||||||
\(405\) | 19.7209 | 0.979937 | ||||||||
\(406\) | 30.0925 | 1.49347 | ||||||||
\(407\) | −50.6181 | −2.50905 | ||||||||
\(408\) | −0.958825 | −0.0474689 | ||||||||
\(409\) | 29.7996 | 1.47350 | 0.736749 | − | 0.676167i | \(-0.236360\pi\) | ||||
0.736749 | + | 0.676167i | \(0.236360\pi\) | |||||||
\(410\) | −7.99637 | −0.394912 | ||||||||
\(411\) | 5.93750 | 0.292875 | ||||||||
\(412\) | −19.4082 | −0.956175 | ||||||||
\(413\) | −39.7069 | −1.95385 | ||||||||
\(414\) | 17.3825 | 0.854303 | ||||||||
\(415\) | −29.9187 | −1.46865 | ||||||||
\(416\) | 1.44576 | 0.0708841 | ||||||||
\(417\) | −1.99859 | −0.0978713 | ||||||||
\(418\) | 1.56506 | 0.0765498 | ||||||||
\(419\) | −8.07295 | −0.394389 | −0.197195 | − | 0.980364i | \(-0.563183\pi\) | ||||
−0.197195 | + | 0.980364i | \(0.563183\pi\) | |||||||
\(420\) | −3.76180 | −0.183557 | ||||||||
\(421\) | −23.5149 | −1.14605 | −0.573023 | − | 0.819539i | \(-0.694230\pi\) | ||||
−0.573023 | + | 0.819539i | \(0.694230\pi\) | |||||||
\(422\) | 16.1594 | 0.786627 | ||||||||
\(423\) | 18.6238 | 0.905521 | ||||||||
\(424\) | 7.51170 | 0.364800 | ||||||||
\(425\) | 3.40031 | 0.164939 | ||||||||
\(426\) | 3.64342 | 0.176524 | ||||||||
\(427\) | −28.8042 | −1.39393 | ||||||||
\(428\) | −6.49107 | −0.313758 | ||||||||
\(429\) | −2.59094 | −0.125092 | ||||||||
\(430\) | −16.4926 | −0.795345 | ||||||||
\(431\) | −12.5117 | −0.602667 | −0.301334 | − | 0.953519i | \(-0.597432\pi\) | ||||
−0.301334 | + | 0.953519i | \(0.597432\pi\) | |||||||
\(432\) | 2.08378 | 0.100256 | ||||||||
\(433\) | −12.9160 | −0.620705 | −0.310353 | − | 0.950621i | \(-0.600447\pi\) | ||||
−0.310353 | + | 0.950621i | \(0.600447\pi\) | |||||||
\(434\) | 30.0473 | 1.44232 | ||||||||
\(435\) | −6.29958 | −0.302042 | ||||||||
\(436\) | 1.54816 | 0.0741433 | ||||||||
\(437\) | −1.87360 | −0.0896265 | ||||||||
\(438\) | 4.05136 | 0.193581 | ||||||||
\(439\) | −7.03100 | −0.335571 | −0.167786 | − | 0.985824i | \(-0.553662\pi\) | ||||
−0.167786 | + | 0.985824i | \(0.553662\pi\) | |||||||
\(440\) | 12.6379 | 0.602487 | ||||||||
\(441\) | −31.5289 | −1.50138 | ||||||||
\(442\) | 3.90777 | 0.185873 | ||||||||
\(443\) | 33.5400 | 1.59353 | 0.796767 | − | 0.604287i | \(-0.206542\pi\) | ||||
0.796767 | + | 0.604287i | \(0.206542\pi\) | |||||||
\(444\) | 3.55432 | 0.168680 | ||||||||
\(445\) | 21.0557 | 0.998135 | ||||||||
\(446\) | −17.6469 | −0.835603 | ||||||||
\(447\) | 4.13307 | 0.195488 | ||||||||
\(448\) | 4.23908 | 0.200278 | ||||||||
\(449\) | −22.6121 | −1.06713 | −0.533566 | − | 0.845759i | \(-0.679148\pi\) | ||||
−0.533566 | + | 0.845759i | \(0.679148\pi\) | |||||||
\(450\) | −3.61574 | −0.170448 | ||||||||
\(451\) | −16.1484 | −0.760400 | ||||||||
\(452\) | −16.0403 | −0.754472 | ||||||||
\(453\) | 6.69106 | 0.314373 | ||||||||
\(454\) | −1.29779 | −0.0609081 | ||||||||
\(455\) | 15.3315 | 0.718752 | ||||||||
\(456\) | −0.109896 | −0.00514636 | ||||||||
\(457\) | −13.0858 | −0.612126 | −0.306063 | − | 0.952011i | \(-0.599012\pi\) | ||||
−0.306063 | + | 0.952011i | \(0.599012\pi\) | |||||||
\(458\) | 23.9469 | 1.11896 | ||||||||
\(459\) | 5.63230 | 0.262893 | ||||||||
\(460\) | −15.1293 | −0.705408 | ||||||||
\(461\) | −17.0440 | −0.793817 | −0.396909 | − | 0.917858i | \(-0.629917\pi\) | ||||
−0.396909 | + | 0.917858i | \(0.629917\pi\) | |||||||
\(462\) | −7.59685 | −0.353437 | ||||||||
\(463\) | −16.6959 | −0.775925 | −0.387962 | − | 0.921675i | \(-0.626821\pi\) | ||||
−0.387962 | + | 0.921675i | \(0.626821\pi\) | |||||||
\(464\) | 7.09884 | 0.329555 | ||||||||
\(465\) | −6.29013 | −0.291698 | ||||||||
\(466\) | 7.87004 | 0.364573 | ||||||||
\(467\) | −32.5843 | −1.50782 | −0.753912 | − | 0.656976i | \(-0.771835\pi\) | ||||
−0.753912 | + | 0.656976i | \(0.771835\pi\) | |||||||
\(468\) | −4.15534 | −0.192081 | ||||||||
\(469\) | 15.1725 | 0.700601 | ||||||||
\(470\) | −16.2097 | −0.747699 | ||||||||
\(471\) | −2.39137 | −0.110189 | ||||||||
\(472\) | −9.36687 | −0.431145 | ||||||||
\(473\) | −33.3064 | −1.53143 | ||||||||
\(474\) | −5.62432 | −0.258334 | ||||||||
\(475\) | 0.389729 | 0.0178820 | ||||||||
\(476\) | 11.4579 | 0.525171 | ||||||||
\(477\) | −21.5898 | −0.988531 | ||||||||
\(478\) | 19.2985 | 0.882691 | ||||||||
\(479\) | 38.3198 | 1.75088 | 0.875439 | − | 0.483329i | \(-0.160572\pi\) | ||||
0.875439 | + | 0.483329i | \(0.160572\pi\) | |||||||
\(480\) | −0.887411 | −0.0405046 | ||||||||
\(481\) | −14.4859 | −0.660500 | ||||||||
\(482\) | 6.99523 | 0.318624 | ||||||||
\(483\) | 9.09450 | 0.413814 | ||||||||
\(484\) | 14.5218 | 0.660083 | ||||||||
\(485\) | 32.6115 | 1.48081 | ||||||||
\(486\) | −9.04784 | −0.410418 | ||||||||
\(487\) | −14.7907 | −0.670233 | −0.335116 | − | 0.942177i | \(-0.608776\pi\) | ||||
−0.335116 | + | 0.942177i | \(0.608776\pi\) | |||||||
\(488\) | −6.79492 | −0.307592 | ||||||||
\(489\) | −5.77787 | −0.261284 | ||||||||
\(490\) | 27.4420 | 1.23970 | ||||||||
\(491\) | 16.2154 | 0.731793 | 0.365896 | − | 0.930656i | \(-0.380762\pi\) | ||||
0.365896 | + | 0.930656i | \(0.380762\pi\) | |||||||
\(492\) | 1.13392 | 0.0511209 | ||||||||
\(493\) | 19.1876 | 0.864165 | ||||||||
\(494\) | 0.447890 | 0.0201515 | ||||||||
\(495\) | −36.3233 | −1.63261 | ||||||||
\(496\) | 7.08818 | 0.318269 | ||||||||
\(497\) | −43.5385 | −1.95297 | ||||||||
\(498\) | 4.24258 | 0.190115 | ||||||||
\(499\) | −20.0826 | −0.899022 | −0.449511 | − | 0.893275i | \(-0.648402\pi\) | ||||
−0.449511 | + | 0.893275i | \(0.648402\pi\) | |||||||
\(500\) | −9.36096 | −0.418635 | ||||||||
\(501\) | −4.38262 | −0.195801 | ||||||||
\(502\) | 15.3312 | 0.684264 | ||||||||
\(503\) | 27.8342 | 1.24107 | 0.620533 | − | 0.784180i | \(-0.286916\pi\) | ||||
0.620533 | + | 0.784180i | \(0.286916\pi\) | |||||||
\(504\) | −12.1838 | −0.542709 | ||||||||
\(505\) | 33.6640 | 1.49803 | ||||||||
\(506\) | −30.5532 | −1.35826 | ||||||||
\(507\) | 3.87010 | 0.171877 | ||||||||
\(508\) | −15.5297 | −0.689021 | ||||||||
\(509\) | 13.3063 | 0.589793 | 0.294897 | − | 0.955529i | \(-0.404715\pi\) | ||||
0.294897 | + | 0.955529i | \(0.404715\pi\) | |||||||
\(510\) | −2.39860 | −0.106212 | ||||||||
\(511\) | −48.4134 | −2.14168 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.645548 | 0.0285017 | ||||||||
\(514\) | −24.6485 | −1.08720 | ||||||||
\(515\) | −48.5517 | −2.13944 | ||||||||
\(516\) | 2.33872 | 0.102956 | ||||||||
\(517\) | −32.7351 | −1.43969 | ||||||||
\(518\) | −42.4738 | −1.86619 | ||||||||
\(519\) | 1.89783 | 0.0833056 | ||||||||
\(520\) | 3.61671 | 0.158603 | ||||||||
\(521\) | −4.20936 | −0.184416 | −0.0922078 | − | 0.995740i | \(-0.529392\pi\) | ||||
−0.0922078 | + | 0.995740i | \(0.529392\pi\) | |||||||
\(522\) | −20.4032 | −0.893024 | ||||||||
\(523\) | 19.9416 | 0.871987 | 0.435993 | − | 0.899950i | \(-0.356397\pi\) | ||||
0.435993 | + | 0.899950i | \(0.356397\pi\) | |||||||
\(524\) | 5.60410 | 0.244816 | ||||||||
\(525\) | −1.89175 | −0.0825627 | ||||||||
\(526\) | 10.2955 | 0.448906 | ||||||||
\(527\) | 19.1588 | 0.834570 | ||||||||
\(528\) | −1.79210 | −0.0779911 | ||||||||
\(529\) | 13.5765 | 0.590281 | ||||||||
\(530\) | 18.7913 | 0.816241 | ||||||||
\(531\) | 26.9219 | 1.16831 | ||||||||
\(532\) | 1.31325 | 0.0569367 | ||||||||
\(533\) | −4.62136 | −0.200173 | ||||||||
\(534\) | −2.98578 | −0.129207 | ||||||||
\(535\) | −16.2381 | −0.702034 | ||||||||
\(536\) | 3.57920 | 0.154598 | ||||||||
\(537\) | −5.72626 | −0.247106 | ||||||||
\(538\) | 14.6922 | 0.633427 | ||||||||
\(539\) | 55.4184 | 2.38704 | ||||||||
\(540\) | 5.21279 | 0.224323 | ||||||||
\(541\) | 16.8684 | 0.725228 | 0.362614 | − | 0.931939i | \(-0.381884\pi\) | ||||
0.362614 | + | 0.931939i | \(0.381884\pi\) | |||||||
\(542\) | −6.98204 | −0.299904 | ||||||||
\(543\) | 5.84621 | 0.250885 | ||||||||
\(544\) | 2.70292 | 0.115887 | ||||||||
\(545\) | 3.87288 | 0.165896 | ||||||||
\(546\) | −2.17407 | −0.0930415 | ||||||||
\(547\) | −31.6926 | −1.35508 | −0.677538 | − | 0.735488i | \(-0.736953\pi\) | ||||
−0.677538 | + | 0.735488i | \(0.736953\pi\) | |||||||
\(548\) | −16.7378 | −0.715001 | ||||||||
\(549\) | 19.5297 | 0.833508 | ||||||||
\(550\) | 6.35538 | 0.270994 | ||||||||
\(551\) | 2.19919 | 0.0936888 | ||||||||
\(552\) | 2.14539 | 0.0913141 | ||||||||
\(553\) | 67.2102 | 2.85807 | ||||||||
\(554\) | 16.0138 | 0.680362 | ||||||||
\(555\) | 8.89149 | 0.377423 | ||||||||
\(556\) | 5.63400 | 0.238935 | ||||||||
\(557\) | 47.1291 | 1.99693 | 0.998463 | − | 0.0554225i | \(-0.0176506\pi\) | ||||
0.998463 | + | 0.0554225i | \(0.0176506\pi\) | |||||||
\(558\) | −20.3726 | −0.862440 | ||||||||
\(559\) | −9.53162 | −0.403145 | ||||||||
\(560\) | 10.6045 | 0.448121 | ||||||||
\(561\) | −4.84390 | −0.204510 | ||||||||
\(562\) | 17.5241 | 0.739209 | ||||||||
\(563\) | 35.3170 | 1.48843 | 0.744216 | − | 0.667939i | \(-0.232823\pi\) | ||||
0.744216 | + | 0.667939i | \(0.232823\pi\) | |||||||
\(564\) | 2.29860 | 0.0967886 | ||||||||
\(565\) | −40.1264 | −1.68813 | ||||||||
\(566\) | −6.47177 | −0.272029 | ||||||||
\(567\) | 33.4179 | 1.40342 | ||||||||
\(568\) | −10.2708 | −0.430952 | ||||||||
\(569\) | 3.88606 | 0.162912 | 0.0814560 | − | 0.996677i | \(-0.474043\pi\) | ||||
0.0814560 | + | 0.996677i | \(0.474043\pi\) | |||||||
\(570\) | −0.274917 | −0.0115150 | ||||||||
\(571\) | −38.2602 | −1.60114 | −0.800569 | − | 0.599241i | \(-0.795469\pi\) | ||||
−0.800569 | + | 0.599241i | \(0.795469\pi\) | |||||||
\(572\) | 7.30384 | 0.305389 | ||||||||
\(573\) | −9.16149 | −0.382727 | ||||||||
\(574\) | −13.5502 | −0.565575 | ||||||||
\(575\) | −7.60828 | −0.317287 | ||||||||
\(576\) | −2.87416 | −0.119757 | ||||||||
\(577\) | −40.4946 | −1.68581 | −0.842907 | − | 0.538060i | \(-0.819157\pi\) | ||||
−0.842907 | + | 0.538060i | \(0.819157\pi\) | |||||||
\(578\) | −9.69422 | −0.403227 | ||||||||
\(579\) | −8.58727 | −0.356875 | ||||||||
\(580\) | 17.7585 | 0.737380 | ||||||||
\(581\) | −50.6985 | −2.10333 | ||||||||
\(582\) | −4.62443 | −0.191689 | ||||||||
\(583\) | 37.9485 | 1.57166 | ||||||||
\(584\) | −11.4207 | −0.472594 | ||||||||
\(585\) | −10.3950 | −0.429781 | ||||||||
\(586\) | −15.8101 | −0.653109 | ||||||||
\(587\) | −30.8235 | −1.27222 | −0.636110 | − | 0.771598i | \(-0.719458\pi\) | ||||
−0.636110 | + | 0.771598i | \(0.719458\pi\) | |||||||
\(588\) | −3.89139 | −0.160478 | ||||||||
\(589\) | 2.19589 | 0.0904802 | ||||||||
\(590\) | −23.4322 | −0.964688 | ||||||||
\(591\) | 2.58477 | 0.106323 | ||||||||
\(592\) | −10.0196 | −0.411803 | ||||||||
\(593\) | −31.2460 | −1.28312 | −0.641560 | − | 0.767073i | \(-0.721713\pi\) | ||||
−0.641560 | + | 0.767073i | \(0.721713\pi\) | |||||||
\(594\) | 10.5271 | 0.431932 | ||||||||
\(595\) | 28.6631 | 1.17507 | ||||||||
\(596\) | −11.6511 | −0.477247 | ||||||||
\(597\) | −2.67865 | −0.109630 | ||||||||
\(598\) | −8.74372 | −0.357557 | ||||||||
\(599\) | 18.7749 | 0.767122 | 0.383561 | − | 0.923516i | \(-0.374698\pi\) | ||||
0.383561 | + | 0.923516i | \(0.374698\pi\) | |||||||
\(600\) | −0.446264 | −0.0182187 | ||||||||
\(601\) | −19.8542 | −0.809871 | −0.404935 | − | 0.914345i | \(-0.632706\pi\) | ||||
−0.404935 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(602\) | −27.9475 | −1.13905 | ||||||||
\(603\) | −10.2872 | −0.418927 | ||||||||
\(604\) | −18.8620 | −0.767485 | ||||||||
\(605\) | 36.3278 | 1.47694 | ||||||||
\(606\) | −4.77368 | −0.193918 | ||||||||
\(607\) | 28.0675 | 1.13923 | 0.569613 | − | 0.821913i | \(-0.307093\pi\) | ||||
0.569613 | + | 0.821913i | \(0.307093\pi\) | |||||||
\(608\) | 0.309796 | 0.0125639 | ||||||||
\(609\) | −10.6749 | −0.432570 | ||||||||
\(610\) | −16.9982 | −0.688237 | ||||||||
\(611\) | −9.36813 | −0.378994 | ||||||||
\(612\) | −7.76863 | −0.314028 | ||||||||
\(613\) | 8.57039 | 0.346155 | 0.173077 | − | 0.984908i | \(-0.444629\pi\) | ||||
0.173077 | + | 0.984908i | \(0.444629\pi\) | |||||||
\(614\) | −11.6136 | −0.468688 | ||||||||
\(615\) | 2.83661 | 0.114383 | ||||||||
\(616\) | 21.4155 | 0.862853 | ||||||||
\(617\) | 11.8838 | 0.478423 | 0.239211 | − | 0.970968i | \(-0.423111\pi\) | ||||
0.239211 | + | 0.970968i | \(0.423111\pi\) | |||||||
\(618\) | 6.88482 | 0.276948 | ||||||||
\(619\) | −2.01662 | −0.0810547 | −0.0405274 | − | 0.999178i | \(-0.512904\pi\) | ||||
−0.0405274 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(620\) | 17.7318 | 0.712127 | ||||||||
\(621\) | −12.6024 | −0.505717 | ||||||||
\(622\) | −18.7925 | −0.753509 | ||||||||
\(623\) | 35.6798 | 1.42948 | ||||||||
\(624\) | −0.512863 | −0.0205310 | ||||||||
\(625\) | −29.7075 | −1.18830 | ||||||||
\(626\) | −3.58821 | −0.143414 | ||||||||
\(627\) | −0.555186 | −0.0221720 | ||||||||
\(628\) | 6.74126 | 0.269006 | ||||||||
\(629\) | −27.0822 | −1.07984 | ||||||||
\(630\) | −30.4790 | −1.21431 | ||||||||
\(631\) | −6.64381 | −0.264486 | −0.132243 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132243 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(632\) | 15.8549 | 0.630675 | ||||||||
\(633\) | −5.73234 | −0.227840 | ||||||||
\(634\) | 19.8340 | 0.787707 | ||||||||
\(635\) | −38.8493 | −1.54169 | ||||||||
\(636\) | −2.66468 | −0.105661 | ||||||||
\(637\) | 15.8596 | 0.628382 | ||||||||
\(638\) | 35.8627 | 1.41982 | ||||||||
\(639\) | 29.5198 | 1.16779 | ||||||||
\(640\) | 2.50160 | 0.0988845 | ||||||||
\(641\) | −24.0254 | −0.948946 | −0.474473 | − | 0.880270i | \(-0.657361\pi\) | ||||
−0.474473 | + | 0.880270i | \(0.657361\pi\) | |||||||
\(642\) | 2.30262 | 0.0908773 | ||||||||
\(643\) | −13.2150 | −0.521148 | −0.260574 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260574 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(644\) | −25.6373 | −1.01025 | ||||||||
\(645\) | 5.85054 | 0.230365 | ||||||||
\(646\) | 0.837355 | 0.0329453 | ||||||||
\(647\) | 1.28356 | 0.0504619 | 0.0252309 | − | 0.999682i | \(-0.491968\pi\) | ||||
0.0252309 | + | 0.999682i | \(0.491968\pi\) | |||||||
\(648\) | 7.88329 | 0.309685 | ||||||||
\(649\) | −47.3206 | −1.85750 | ||||||||
\(650\) | 1.81878 | 0.0713386 | ||||||||
\(651\) | −10.6589 | −0.417755 | ||||||||
\(652\) | 16.2878 | 0.637878 | ||||||||
\(653\) | 14.8806 | 0.582324 | 0.291162 | − | 0.956674i | \(-0.405958\pi\) | ||||
0.291162 | + | 0.956674i | \(0.405958\pi\) | |||||||
\(654\) | −0.549189 | −0.0214750 | ||||||||
\(655\) | 14.0192 | 0.547776 | ||||||||
\(656\) | −3.19650 | −0.124802 | ||||||||
\(657\) | 32.8251 | 1.28063 | ||||||||
\(658\) | −27.4681 | −1.07082 | ||||||||
\(659\) | −25.0699 | −0.976583 | −0.488291 | − | 0.872681i | \(-0.662380\pi\) | ||||
−0.488291 | + | 0.872681i | \(0.662380\pi\) | |||||||
\(660\) | −4.48312 | −0.174505 | ||||||||
\(661\) | −9.12341 | −0.354859 | −0.177430 | − | 0.984133i | \(-0.556778\pi\) | ||||
−0.177430 | + | 0.984133i | \(0.556778\pi\) | |||||||
\(662\) | 14.8735 | 0.578073 | ||||||||
\(663\) | −1.38623 | −0.0538367 | ||||||||
\(664\) | −11.9598 | −0.464130 | ||||||||
\(665\) | 3.28523 | 0.127396 | ||||||||
\(666\) | 28.7979 | 1.11590 | ||||||||
\(667\) | −42.9327 | −1.66236 | ||||||||
\(668\) | 12.3546 | 0.478013 | ||||||||
\(669\) | 6.25999 | 0.242025 | ||||||||
\(670\) | 8.95373 | 0.345913 | ||||||||
\(671\) | −34.3274 | −1.32519 | ||||||||
\(672\) | −1.50376 | −0.0580087 | ||||||||
\(673\) | −42.0482 | −1.62084 | −0.810419 | − | 0.585850i | \(-0.800761\pi\) | ||||
−0.810419 | + | 0.585850i | \(0.800761\pi\) | |||||||
\(674\) | −12.2061 | −0.470161 | ||||||||
\(675\) | 2.62143 | 0.100899 | ||||||||
\(676\) | −10.9098 | −0.419607 | ||||||||
\(677\) | −6.22762 | −0.239347 | −0.119673 | − | 0.992813i | \(-0.538185\pi\) | ||||
−0.119673 | + | 0.992813i | \(0.538185\pi\) | |||||||
\(678\) | 5.69008 | 0.218526 | ||||||||
\(679\) | 55.2616 | 2.12075 | ||||||||
\(680\) | 6.76163 | 0.259297 | ||||||||
\(681\) | 0.460373 | 0.0176415 | ||||||||
\(682\) | 35.8089 | 1.37119 | ||||||||
\(683\) | −28.8127 | −1.10249 | −0.551244 | − | 0.834344i | \(-0.685847\pi\) | ||||
−0.551244 | + | 0.834344i | \(0.685847\pi\) | |||||||
\(684\) | −0.890405 | −0.0340455 | ||||||||
\(685\) | −41.8712 | −1.59982 | ||||||||
\(686\) | 16.8282 | 0.642504 | ||||||||
\(687\) | −8.49483 | −0.324098 | ||||||||
\(688\) | −6.59282 | −0.251349 | ||||||||
\(689\) | 10.8601 | 0.413737 | ||||||||
\(690\) | 5.36692 | 0.204315 | ||||||||
\(691\) | 8.66669 | 0.329697 | 0.164848 | − | 0.986319i | \(-0.447287\pi\) | ||||
0.164848 | + | 0.986319i | \(0.447287\pi\) | |||||||
\(692\) | −5.34997 | −0.203376 | ||||||||
\(693\) | −61.5515 | −2.33815 | ||||||||
\(694\) | 25.9128 | 0.983636 | ||||||||
\(695\) | 14.0940 | 0.534617 | ||||||||
\(696\) | −2.51822 | −0.0954529 | ||||||||
\(697\) | −8.63988 | −0.327259 | ||||||||
\(698\) | −1.96325 | −0.0743101 | ||||||||
\(699\) | −2.79180 | −0.105595 | ||||||||
\(700\) | 5.33282 | 0.201562 | ||||||||
\(701\) | 9.38131 | 0.354327 | 0.177164 | − | 0.984181i | \(-0.443308\pi\) | ||||
0.177164 | + | 0.984181i | \(0.443308\pi\) | |||||||
\(702\) | 3.01264 | 0.113705 | ||||||||
\(703\) | −3.10403 | −0.117071 | ||||||||
\(704\) | 5.05191 | 0.190401 | ||||||||
\(705\) | 5.75019 | 0.216565 | ||||||||
\(706\) | 7.06061 | 0.265730 | ||||||||
\(707\) | 57.0451 | 2.14540 | ||||||||
\(708\) | 3.32277 | 0.124877 | ||||||||
\(709\) | 17.7703 | 0.667379 | 0.333690 | − | 0.942683i | \(-0.391706\pi\) | ||||
0.333690 | + | 0.942683i | \(0.391706\pi\) | |||||||
\(710\) | −25.6934 | −0.964255 | ||||||||
\(711\) | −45.5696 | −1.70899 | ||||||||
\(712\) | 8.41688 | 0.315436 | ||||||||
\(713\) | −42.8682 | −1.60543 | ||||||||
\(714\) | −4.06454 | −0.152111 | ||||||||
\(715\) | 18.2713 | 0.683308 | ||||||||
\(716\) | 16.1423 | 0.603265 | ||||||||
\(717\) | −6.84588 | −0.255664 | ||||||||
\(718\) | 8.10653 | 0.302533 | ||||||||
\(719\) | 28.9435 | 1.07941 | 0.539704 | − | 0.841855i | \(-0.318536\pi\) | ||||
0.539704 | + | 0.841855i | \(0.318536\pi\) | |||||||
\(720\) | −7.19001 | −0.267956 | ||||||||
\(721\) | −82.2730 | −3.06401 | ||||||||
\(722\) | −18.9040 | −0.703535 | ||||||||
\(723\) | −2.48146 | −0.0922867 | ||||||||
\(724\) | −16.4804 | −0.612490 | ||||||||
\(725\) | 8.93044 | 0.331668 | ||||||||
\(726\) | −5.15143 | −0.191187 | ||||||||
\(727\) | −8.66942 | −0.321531 | −0.160766 | − | 0.986993i | \(-0.551396\pi\) | ||||
−0.160766 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(728\) | 6.12868 | 0.227144 | ||||||||
\(729\) | −20.4403 | −0.757047 | ||||||||
\(730\) | −28.5702 | −1.05743 | ||||||||
\(731\) | −17.8199 | −0.659092 | ||||||||
\(732\) | 2.41041 | 0.0890913 | ||||||||
\(733\) | −12.5526 | −0.463641 | −0.231820 | − | 0.972759i | \(-0.574468\pi\) | ||||
−0.231820 | + | 0.972759i | \(0.574468\pi\) | |||||||
\(734\) | 30.2287 | 1.11576 | ||||||||
\(735\) | −9.73470 | −0.359070 | ||||||||
\(736\) | −6.04785 | −0.222927 | ||||||||
\(737\) | 18.0818 | 0.666051 | ||||||||
\(738\) | 9.18725 | 0.338187 | ||||||||
\(739\) | −25.8355 | −0.950373 | −0.475186 | − | 0.879885i | \(-0.657619\pi\) | ||||
−0.475186 | + | 0.879885i | \(0.657619\pi\) | |||||||
\(740\) | −25.0650 | −0.921409 | ||||||||
\(741\) | −0.158883 | −0.00583672 | ||||||||
\(742\) | 31.8427 | 1.16898 | ||||||||
\(743\) | 20.2761 | 0.743857 | 0.371928 | − | 0.928261i | \(-0.378697\pi\) | ||||
0.371928 | + | 0.928261i | \(0.378697\pi\) | |||||||
\(744\) | −2.51444 | −0.0921838 | ||||||||
\(745\) | −29.1464 | −1.06784 | ||||||||
\(746\) | −3.53242 | −0.129331 | ||||||||
\(747\) | 34.3744 | 1.25769 | ||||||||
\(748\) | 13.6549 | 0.499273 | ||||||||
\(749\) | −27.5162 | −1.00542 | ||||||||
\(750\) | 3.32068 | 0.121254 | ||||||||
\(751\) | 21.7713 | 0.794446 | 0.397223 | − | 0.917722i | \(-0.369974\pi\) | ||||
0.397223 | + | 0.917722i | \(0.369974\pi\) | |||||||
\(752\) | −6.47974 | −0.236292 | ||||||||
\(753\) | −5.43854 | −0.198191 | ||||||||
\(754\) | 10.2632 | 0.373764 | ||||||||
\(755\) | −47.1853 | −1.71725 | ||||||||
\(756\) | 8.83331 | 0.321264 | ||||||||
\(757\) | −12.1926 | −0.443147 | −0.221574 | − | 0.975144i | \(-0.571119\pi\) | ||||
−0.221574 | + | 0.975144i | \(0.571119\pi\) | |||||||
\(758\) | 37.2454 | 1.35281 | ||||||||
\(759\) | 10.8383 | 0.393407 | ||||||||
\(760\) | 0.774988 | 0.0281118 | ||||||||
\(761\) | −29.6438 | −1.07459 | −0.537294 | − | 0.843395i | \(-0.680553\pi\) | ||||
−0.537294 | + | 0.843395i | \(0.680553\pi\) | |||||||
\(762\) | 5.50898 | 0.199569 | ||||||||
\(763\) | 6.56276 | 0.237588 | ||||||||
\(764\) | 25.8262 | 0.934358 | ||||||||
\(765\) | −19.4340 | −0.702639 | ||||||||
\(766\) | −36.2812 | −1.31089 | ||||||||
\(767\) | −13.5422 | −0.488981 | ||||||||
\(768\) | −0.354737 | −0.0128005 | ||||||||
\(769\) | 10.7597 | 0.388005 | 0.194002 | − | 0.981001i | \(-0.437853\pi\) | ||||
0.194002 | + | 0.981001i | \(0.437853\pi\) | |||||||
\(770\) | 53.5729 | 1.93063 | ||||||||
\(771\) | 8.74374 | 0.314898 | ||||||||
\(772\) | 24.2074 | 0.871245 | ||||||||
\(773\) | 43.5593 | 1.56672 | 0.783360 | − | 0.621569i | \(-0.213504\pi\) | ||||
0.783360 | + | 0.621569i | \(0.213504\pi\) | |||||||
\(774\) | 18.9488 | 0.681102 | ||||||||
\(775\) | 8.91704 | 0.320309 | ||||||||
\(776\) | 13.0362 | 0.467973 | ||||||||
\(777\) | 15.0670 | 0.540527 | ||||||||
\(778\) | −25.5490 | −0.915976 | ||||||||
\(779\) | −0.990264 | −0.0354799 | ||||||||
\(780\) | −1.28298 | −0.0459381 | ||||||||
\(781\) | −51.8870 | −1.85666 | ||||||||
\(782\) | −16.3468 | −0.584562 | ||||||||
\(783\) | 14.7924 | 0.528638 | ||||||||
\(784\) | 10.9698 | 0.391778 | ||||||||
\(785\) | 16.8640 | 0.601900 | ||||||||
\(786\) | −1.98798 | −0.0709089 | ||||||||
\(787\) | 29.0027 | 1.03384 | 0.516918 | − | 0.856035i | \(-0.327079\pi\) | ||||
0.516918 | + | 0.856035i | \(0.327079\pi\) | |||||||
\(788\) | −7.28644 | −0.259569 | ||||||||
\(789\) | −3.65220 | −0.130022 | ||||||||
\(790\) | 39.6627 | 1.41114 | ||||||||
\(791\) | −67.9960 | −2.41766 | ||||||||
\(792\) | −14.5200 | −0.515946 | ||||||||
\(793\) | −9.82381 | −0.348854 | ||||||||
\(794\) | 17.4966 | 0.620930 | ||||||||
\(795\) | −6.66596 | −0.236417 | ||||||||
\(796\) | 7.55110 | 0.267642 | ||||||||
\(797\) | 43.8518 | 1.55331 | 0.776655 | − | 0.629926i | \(-0.216915\pi\) | ||||
0.776655 | + | 0.629926i | \(0.216915\pi\) | |||||||
\(798\) | −0.465859 | −0.0164912 | ||||||||
\(799\) | −17.5142 | −0.619608 | ||||||||
\(800\) | 1.25801 | 0.0444775 | ||||||||
\(801\) | −24.1915 | −0.854763 | ||||||||
\(802\) | −30.2755 | −1.06906 | ||||||||
\(803\) | −57.6966 | −2.03607 | ||||||||
\(804\) | −1.26967 | −0.0447779 | ||||||||
\(805\) | −64.1343 | −2.26044 | ||||||||
\(806\) | 10.2478 | 0.360963 | ||||||||
\(807\) | −5.21188 | −0.183467 | ||||||||
\(808\) | 13.4570 | 0.473414 | ||||||||
\(809\) | −47.9146 | −1.68459 | −0.842294 | − | 0.539018i | \(-0.818795\pi\) | ||||
−0.842294 | + | 0.539018i | \(0.818795\pi\) | |||||||
\(810\) | 19.7209 | 0.692920 | ||||||||
\(811\) | 22.3056 | 0.783255 | 0.391628 | − | 0.920124i | \(-0.371912\pi\) | ||||
0.391628 | + | 0.920124i | \(0.371912\pi\) | |||||||
\(812\) | 30.0925 | 1.05604 | ||||||||
\(813\) | 2.47679 | 0.0868648 | ||||||||
\(814\) | −50.6181 | −1.77416 | ||||||||
\(815\) | 40.7455 | 1.42725 | ||||||||
\(816\) | −0.958825 | −0.0335656 | ||||||||
\(817\) | −2.04243 | −0.0714557 | ||||||||
\(818\) | 29.7996 | 1.04192 | ||||||||
\(819\) | −17.6148 | −0.615511 | ||||||||
\(820\) | −7.99637 | −0.279245 | ||||||||
\(821\) | −19.2376 | −0.671397 | −0.335699 | − | 0.941969i | \(-0.608972\pi\) | ||||
−0.335699 | + | 0.941969i | \(0.608972\pi\) | |||||||
\(822\) | 5.93750 | 0.207094 | ||||||||
\(823\) | 0.114474 | 0.00399032 | 0.00199516 | − | 0.999998i | \(-0.499365\pi\) | ||||
0.00199516 | + | 0.999998i | \(0.499365\pi\) | |||||||
\(824\) | −19.4082 | −0.676118 | ||||||||
\(825\) | −2.25449 | −0.0784912 | ||||||||
\(826\) | −39.7069 | −1.38158 | ||||||||
\(827\) | 27.2801 | 0.948622 | 0.474311 | − | 0.880357i | \(-0.342697\pi\) | ||||
0.474311 | + | 0.880357i | \(0.342697\pi\) | |||||||
\(828\) | 17.3825 | 0.604083 | ||||||||
\(829\) | −52.3424 | −1.81793 | −0.908964 | − | 0.416876i | \(-0.863125\pi\) | ||||
−0.908964 | + | 0.416876i | \(0.863125\pi\) | |||||||
\(830\) | −29.9187 | −1.03849 | ||||||||
\(831\) | −5.68069 | −0.197061 | ||||||||
\(832\) | 1.44576 | 0.0501226 | ||||||||
\(833\) | 29.6504 | 1.02733 | ||||||||
\(834\) | −1.99859 | −0.0692054 | ||||||||
\(835\) | 30.9062 | 1.06955 | ||||||||
\(836\) | 1.56506 | 0.0541289 | ||||||||
\(837\) | 14.7702 | 0.510534 | ||||||||
\(838\) | −8.07295 | −0.278875 | ||||||||
\(839\) | −18.9473 | −0.654132 | −0.327066 | − | 0.945001i | \(-0.606060\pi\) | ||||
−0.327066 | + | 0.945001i | \(0.606060\pi\) | |||||||
\(840\) | −3.76180 | −0.129795 | ||||||||
\(841\) | 21.3935 | 0.737706 | ||||||||
\(842\) | −23.5149 | −0.810377 | ||||||||
\(843\) | −6.21644 | −0.214106 | ||||||||
\(844\) | 16.1594 | 0.556230 | ||||||||
\(845\) | −27.2919 | −0.938872 | ||||||||
\(846\) | 18.6238 | 0.640300 | ||||||||
\(847\) | 61.5591 | 2.11520 | ||||||||
\(848\) | 7.51170 | 0.257953 | ||||||||
\(849\) | 2.29578 | 0.0787908 | ||||||||
\(850\) | 3.40031 | 0.116630 | ||||||||
\(851\) | 60.5970 | 2.07724 | ||||||||
\(852\) | 3.64342 | 0.124821 | ||||||||
\(853\) | 10.8118 | 0.370190 | 0.185095 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185095 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(854\) | −28.8042 | −0.985660 | ||||||||
\(855\) | −2.22744 | −0.0761768 | ||||||||
\(856\) | −6.49107 | −0.221860 | ||||||||
\(857\) | 3.33892 | 0.114055 | 0.0570277 | − | 0.998373i | \(-0.481838\pi\) | ||||
0.0570277 | + | 0.998373i | \(0.481838\pi\) | |||||||
\(858\) | −2.59094 | −0.0884533 | ||||||||
\(859\) | −27.3932 | −0.934643 | −0.467321 | − | 0.884087i | \(-0.654781\pi\) | ||||
−0.467321 | + | 0.884087i | \(0.654781\pi\) | |||||||
\(860\) | −16.4926 | −0.562394 | ||||||||
\(861\) | 4.80676 | 0.163814 | ||||||||
\(862\) | −12.5117 | −0.426150 | ||||||||
\(863\) | 41.7515 | 1.42124 | 0.710619 | − | 0.703577i | \(-0.248415\pi\) | ||||
0.710619 | + | 0.703577i | \(0.248415\pi\) | |||||||
\(864\) | 2.08378 | 0.0708917 | ||||||||
\(865\) | −13.3835 | −0.455053 | ||||||||
\(866\) | −12.9160 | −0.438905 | ||||||||
\(867\) | 3.43890 | 0.116791 | ||||||||
\(868\) | 30.0473 | 1.01987 | ||||||||
\(869\) | 80.0977 | 2.71713 | ||||||||
\(870\) | −6.29958 | −0.213576 | ||||||||
\(871\) | 5.17465 | 0.175336 | ||||||||
\(872\) | 1.54816 | 0.0524272 | ||||||||
\(873\) | −37.4682 | −1.26811 | ||||||||
\(874\) | −1.87360 | −0.0633755 | ||||||||
\(875\) | −39.6818 | −1.34149 | ||||||||
\(876\) | 4.05136 | 0.136883 | ||||||||
\(877\) | −33.2160 | −1.12162 | −0.560812 | − | 0.827943i | \(-0.689511\pi\) | ||||
−0.560812 | + | 0.827943i | \(0.689511\pi\) | |||||||
\(878\) | −7.03100 | −0.237285 | ||||||||
\(879\) | 5.60843 | 0.189168 | ||||||||
\(880\) | 12.6379 | 0.426023 | ||||||||
\(881\) | −6.70460 | −0.225884 | −0.112942 | − | 0.993602i | \(-0.536027\pi\) | ||||
−0.112942 | + | 0.993602i | \(0.536027\pi\) | |||||||
\(882\) | −31.5289 | −1.06163 | ||||||||
\(883\) | −25.6609 | −0.863559 | −0.431780 | − | 0.901979i | \(-0.642114\pi\) | ||||
−0.431780 | + | 0.901979i | \(0.642114\pi\) | |||||||
\(884\) | 3.90777 | 0.131432 | ||||||||
\(885\) | 8.31226 | 0.279414 | ||||||||
\(886\) | 33.5400 | 1.12680 | ||||||||
\(887\) | −33.6357 | −1.12938 | −0.564689 | − | 0.825304i | \(-0.691004\pi\) | ||||
−0.564689 | + | 0.825304i | \(0.691004\pi\) | |||||||
\(888\) | 3.55432 | 0.119275 | ||||||||
\(889\) | −65.8318 | −2.20793 | ||||||||
\(890\) | 21.0557 | 0.705788 | ||||||||
\(891\) | 39.8257 | 1.33421 | ||||||||
\(892\) | −17.6469 | −0.590861 | ||||||||
\(893\) | −2.00740 | −0.0671751 | ||||||||
\(894\) | 4.13307 | 0.138231 | ||||||||
\(895\) | 40.3816 | 1.34981 | ||||||||
\(896\) | 4.23908 | 0.141618 | ||||||||
\(897\) | 3.10172 | 0.103563 | ||||||||
\(898\) | −22.6121 | −0.754576 | ||||||||
\(899\) | 50.3178 | 1.67819 | ||||||||
\(900\) | −3.61574 | −0.120525 | ||||||||
\(901\) | 20.3035 | 0.676409 | ||||||||
\(902\) | −16.1484 | −0.537684 | ||||||||
\(903\) | 9.91400 | 0.329917 | ||||||||
\(904\) | −16.0403 | −0.533492 | ||||||||
\(905\) | −41.2275 | −1.37045 | ||||||||
\(906\) | 6.69106 | 0.222296 | ||||||||
\(907\) | −36.4738 | −1.21109 | −0.605546 | − | 0.795810i | \(-0.707045\pi\) | ||||
−0.605546 | + | 0.795810i | \(0.707045\pi\) | |||||||
\(908\) | −1.29779 | −0.0430686 | ||||||||
\(909\) | −38.6775 | −1.28285 | ||||||||
\(910\) | 15.3315 | 0.508235 | ||||||||
\(911\) | −1.97399 | −0.0654013 | −0.0327006 | − | 0.999465i | \(-0.510411\pi\) | ||||
−0.0327006 | + | 0.999465i | \(0.510411\pi\) | |||||||
\(912\) | −0.109896 | −0.00363903 | ||||||||
\(913\) | −60.4199 | −1.99961 | ||||||||
\(914\) | −13.0858 | −0.432838 | ||||||||
\(915\) | 6.02989 | 0.199342 | ||||||||
\(916\) | 23.9469 | 0.791227 | ||||||||
\(917\) | 23.7562 | 0.784499 | ||||||||
\(918\) | 5.63230 | 0.185893 | ||||||||
\(919\) | −28.9746 | −0.955783 | −0.477891 | − | 0.878419i | \(-0.658599\pi\) | ||||
−0.477891 | + | 0.878419i | \(0.658599\pi\) | |||||||
\(920\) | −15.1293 | −0.498799 | ||||||||
\(921\) | 4.11978 | 0.135751 | ||||||||
\(922\) | −17.0440 | −0.561314 | ||||||||
\(923\) | −14.8490 | −0.488762 | ||||||||
\(924\) | −7.59685 | −0.249918 | ||||||||
\(925\) | −12.6048 | −0.414443 | ||||||||
\(926\) | −16.6959 | −0.548662 | ||||||||
\(927\) | 55.7824 | 1.83214 | ||||||||
\(928\) | 7.09884 | 0.233031 | ||||||||
\(929\) | 45.3451 | 1.48772 | 0.743862 | − | 0.668334i | \(-0.232992\pi\) | ||||
0.743862 | + | 0.668334i | \(0.232992\pi\) | |||||||
\(930\) | −6.29013 | −0.206261 | ||||||||
\(931\) | 3.39840 | 0.111378 | ||||||||
\(932\) | 7.87004 | 0.257792 | ||||||||
\(933\) | 6.66638 | 0.218248 | ||||||||
\(934\) | −32.5843 | −1.06619 | ||||||||
\(935\) | 34.1592 | 1.11712 | ||||||||
\(936\) | −4.15534 | −0.135822 | ||||||||
\(937\) | 36.7042 | 1.19907 | 0.599537 | − | 0.800347i | \(-0.295352\pi\) | ||||
0.599537 | + | 0.800347i | \(0.295352\pi\) | |||||||
\(938\) | 15.1725 | 0.495399 | ||||||||
\(939\) | 1.27287 | 0.0415386 | ||||||||
\(940\) | −16.2097 | −0.528703 | ||||||||
\(941\) | −50.6447 | −1.65097 | −0.825484 | − | 0.564425i | \(-0.809098\pi\) | ||||
−0.825484 | + | 0.564425i | \(0.809098\pi\) | |||||||
\(942\) | −2.39137 | −0.0779152 | ||||||||
\(943\) | 19.3319 | 0.629535 | ||||||||
\(944\) | −9.36687 | −0.304866 | ||||||||
\(945\) | 22.0974 | 0.718830 | ||||||||
\(946\) | −33.3064 | −1.08288 | ||||||||
\(947\) | −47.2660 | −1.53594 | −0.767969 | − | 0.640487i | \(-0.778732\pi\) | ||||
−0.767969 | + | 0.640487i | \(0.778732\pi\) | |||||||
\(948\) | −5.62432 | −0.182670 | ||||||||
\(949\) | −16.5116 | −0.535990 | ||||||||
\(950\) | 0.389729 | 0.0126445 | ||||||||
\(951\) | −7.03584 | −0.228153 | ||||||||
\(952\) | 11.4579 | 0.371352 | ||||||||
\(953\) | 32.6629 | 1.05806 | 0.529028 | − | 0.848604i | \(-0.322557\pi\) | ||||
0.529028 | + | 0.848604i | \(0.322557\pi\) | |||||||
\(954\) | −21.5898 | −0.698997 | ||||||||
\(955\) | 64.6068 | 2.09063 | ||||||||
\(956\) | 19.2985 | 0.624157 | ||||||||
\(957\) | −12.7218 | −0.411238 | ||||||||
\(958\) | 38.3198 | 1.23806 | ||||||||
\(959\) | −70.9526 | −2.29118 | ||||||||
\(960\) | −0.887411 | −0.0286411 | ||||||||
\(961\) | 19.2423 | 0.620719 | ||||||||
\(962\) | −14.4859 | −0.467044 | ||||||||
\(963\) | 18.6564 | 0.601194 | ||||||||
\(964\) | 6.99523 | 0.225301 | ||||||||
\(965\) | 60.5574 | 1.94941 | ||||||||
\(966\) | 9.09450 | 0.292611 | ||||||||
\(967\) | 31.4235 | 1.01051 | 0.505256 | − | 0.862969i | \(-0.331398\pi\) | ||||
0.505256 | + | 0.862969i | \(0.331398\pi\) | |||||||
\(968\) | 14.5218 | 0.466749 | ||||||||
\(969\) | −0.297041 | −0.00954232 | ||||||||
\(970\) | 32.6115 | 1.04709 | ||||||||
\(971\) | −13.6162 | −0.436966 | −0.218483 | − | 0.975841i | \(-0.570111\pi\) | ||||
−0.218483 | + | 0.975841i | \(0.570111\pi\) | |||||||
\(972\) | −9.04784 | −0.290210 | ||||||||
\(973\) | 23.8830 | 0.765653 | ||||||||
\(974\) | −14.7907 | −0.473926 | ||||||||
\(975\) | −0.645190 | −0.0206626 | ||||||||
\(976\) | −6.79492 | −0.217500 | ||||||||
\(977\) | 23.1193 | 0.739651 | 0.369825 | − | 0.929101i | \(-0.379417\pi\) | ||||
0.369825 | + | 0.929101i | \(0.379417\pi\) | |||||||
\(978\) | −5.77787 | −0.184756 | ||||||||
\(979\) | 42.5213 | 1.35899 | ||||||||
\(980\) | 27.4420 | 0.876603 | ||||||||
\(981\) | −4.44966 | −0.142067 | ||||||||
\(982\) | 16.2154 | 0.517456 | ||||||||
\(983\) | −39.2107 | −1.25063 | −0.625314 | − | 0.780373i | \(-0.715029\pi\) | ||||
−0.625314 | + | 0.780373i | \(0.715029\pi\) | |||||||
\(984\) | 1.13392 | 0.0361479 | ||||||||
\(985\) | −18.2278 | −0.580785 | ||||||||
\(986\) | 19.1876 | 0.611057 | ||||||||
\(987\) | 9.74395 | 0.310153 | ||||||||
\(988\) | 0.447890 | 0.0142493 | ||||||||
\(989\) | 39.8724 | 1.26787 | ||||||||
\(990\) | −36.3233 | −1.15443 | ||||||||
\(991\) | 26.0106 | 0.826253 | 0.413127 | − | 0.910674i | \(-0.364437\pi\) | ||||
0.413127 | + | 0.910674i | \(0.364437\pi\) | |||||||
\(992\) | 7.08818 | 0.225050 | ||||||||
\(993\) | −5.27616 | −0.167434 | ||||||||
\(994\) | −43.5385 | −1.38096 | ||||||||
\(995\) | 18.8898 | 0.598848 | ||||||||
\(996\) | 4.24258 | 0.134431 | ||||||||
\(997\) | −10.5925 | −0.335467 | −0.167733 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167733 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(998\) | −20.0826 | −0.635705 | ||||||||
\(999\) | −20.8786 | −0.660571 |
(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 | 4006.2.a.i.1.17 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.i.1.17 | ✓ | 46 | 1.1 | even | 1 | trivial |