Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56568 | −1.81421 | −0.907106 | − | 0.420903i | \(-0.861713\pi\) | ||||
−0.907106 | + | 0.420903i | \(0.861713\pi\) | |||||||
\(3\) | −3.40788 | −1.96754 | −0.983769 | − | 0.179438i | \(-0.942572\pi\) | ||||
−0.983769 | + | 0.179438i | \(0.942572\pi\) | |||||||
\(4\) | 4.58273 | 2.29136 | ||||||||
\(5\) | 3.86072 | 1.72656 | 0.863282 | − | 0.504721i | \(-0.168405\pi\) | ||||
0.863282 | + | 0.504721i | \(0.168405\pi\) | |||||||
\(6\) | 8.74353 | 3.56953 | ||||||||
\(7\) | 2.70727 | 1.02325 | 0.511625 | − | 0.859209i | \(-0.329044\pi\) | ||||
0.511625 | + | 0.859209i | \(0.329044\pi\) | |||||||
\(8\) | −6.62646 | −2.34281 | ||||||||
\(9\) | 8.61362 | 2.87121 | ||||||||
\(10\) | −9.90537 | −3.13235 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −15.6174 | −4.50835 | ||||||||
\(13\) | 2.11448 | 0.586450 | 0.293225 | − | 0.956043i | \(-0.405271\pi\) | ||||
0.293225 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(14\) | −6.94599 | −1.85639 | ||||||||
\(15\) | −13.1568 | −3.39708 | ||||||||
\(16\) | 7.83593 | 1.95898 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −22.0998 | −5.20898 | ||||||||
\(19\) | −1.30765 | −0.299995 | −0.149997 | − | 0.988686i | \(-0.547926\pi\) | ||||
−0.149997 | + | 0.988686i | \(0.547926\pi\) | |||||||
\(20\) | 17.6926 | 3.95619 | ||||||||
\(21\) | −9.22603 | −2.01329 | ||||||||
\(22\) | 2.56568 | 0.547005 | ||||||||
\(23\) | −2.98860 | −0.623165 | −0.311583 | − | 0.950219i | \(-0.600859\pi\) | ||||
−0.311583 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(24\) | 22.5821 | 4.60956 | ||||||||
\(25\) | 9.90513 | 1.98103 | ||||||||
\(26\) | −5.42507 | −1.06394 | ||||||||
\(27\) | −19.1305 | −3.68167 | ||||||||
\(28\) | 12.4067 | 2.34464 | ||||||||
\(29\) | −10.3624 | −1.92424 | −0.962121 | − | 0.272622i | \(-0.912109\pi\) | ||||
−0.962121 | + | 0.272622i | \(0.912109\pi\) | |||||||
\(30\) | 33.7563 | 6.16303 | ||||||||
\(31\) | −6.85908 | −1.23193 | −0.615963 | − | 0.787775i | \(-0.711233\pi\) | ||||
−0.615963 | + | 0.787775i | \(0.711233\pi\) | |||||||
\(32\) | −6.85160 | −1.21120 | ||||||||
\(33\) | 3.40788 | 0.593235 | ||||||||
\(34\) | −2.56568 | −0.440011 | ||||||||
\(35\) | 10.4520 | 1.76671 | ||||||||
\(36\) | 39.4739 | 6.57898 | ||||||||
\(37\) | 10.9443 | 1.79922 | 0.899612 | − | 0.436690i | \(-0.143849\pi\) | ||||
0.899612 | + | 0.436690i | \(0.143849\pi\) | |||||||
\(38\) | 3.35500 | 0.544254 | ||||||||
\(39\) | −7.20587 | −1.15386 | ||||||||
\(40\) | −25.5829 | −4.04501 | ||||||||
\(41\) | 2.34438 | 0.366131 | 0.183065 | − | 0.983101i | \(-0.441398\pi\) | ||||
0.183065 | + | 0.983101i | \(0.441398\pi\) | |||||||
\(42\) | 23.6711 | 3.65252 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −4.58273 | −0.690872 | ||||||||
\(45\) | 33.2548 | 4.95733 | ||||||||
\(46\) | 7.66779 | 1.13055 | ||||||||
\(47\) | −3.62217 | −0.528348 | −0.264174 | − | 0.964475i | \(-0.585099\pi\) | ||||
−0.264174 | + | 0.964475i | \(0.585099\pi\) | |||||||
\(48\) | −26.7039 | −3.85437 | ||||||||
\(49\) | 0.329292 | 0.0470417 | ||||||||
\(50\) | −25.4134 | −3.59400 | ||||||||
\(51\) | −3.40788 | −0.477198 | ||||||||
\(52\) | 9.69007 | 1.34377 | ||||||||
\(53\) | −5.18840 | −0.712681 | −0.356341 | − | 0.934356i | \(-0.615976\pi\) | ||||
−0.356341 | + | 0.934356i | \(0.615976\pi\) | |||||||
\(54\) | 49.0829 | 6.67934 | ||||||||
\(55\) | −3.86072 | −0.520579 | ||||||||
\(56\) | −17.9396 | −2.39728 | ||||||||
\(57\) | 4.45630 | 0.590251 | ||||||||
\(58\) | 26.5865 | 3.49098 | ||||||||
\(59\) | −3.01490 | −0.392506 | −0.196253 | − | 0.980553i | \(-0.562877\pi\) | ||||
−0.196253 | + | 0.980553i | \(0.562877\pi\) | |||||||
\(60\) | −60.2942 | −7.78395 | ||||||||
\(61\) | −0.942345 | −0.120655 | −0.0603275 | − | 0.998179i | \(-0.519214\pi\) | ||||
−0.0603275 | + | 0.998179i | \(0.519214\pi\) | |||||||
\(62\) | 17.5982 | 2.23498 | ||||||||
\(63\) | 23.3194 | 2.93797 | ||||||||
\(64\) | 1.90716 | 0.238395 | ||||||||
\(65\) | 8.16339 | 1.01254 | ||||||||
\(66\) | −8.74353 | −1.07625 | ||||||||
\(67\) | 8.07080 | 0.986005 | 0.493003 | − | 0.870028i | \(-0.335899\pi\) | ||||
0.493003 | + | 0.870028i | \(0.335899\pi\) | |||||||
\(68\) | 4.58273 | 0.555737 | ||||||||
\(69\) | 10.1848 | 1.22610 | ||||||||
\(70\) | −26.8165 | −3.20518 | ||||||||
\(71\) | 1.22037 | 0.144832 | 0.0724158 | − | 0.997375i | \(-0.476929\pi\) | ||||
0.0724158 | + | 0.997375i | \(0.476929\pi\) | |||||||
\(72\) | −57.0778 | −6.72668 | ||||||||
\(73\) | 0.756085 | 0.0884931 | 0.0442465 | − | 0.999021i | \(-0.485911\pi\) | ||||
0.0442465 | + | 0.999021i | \(0.485911\pi\) | |||||||
\(74\) | −28.0795 | −3.26417 | ||||||||
\(75\) | −33.7555 | −3.89775 | ||||||||
\(76\) | −5.99258 | −0.687397 | ||||||||
\(77\) | −2.70727 | −0.308522 | ||||||||
\(78\) | 18.4880 | 2.09335 | ||||||||
\(79\) | 7.66163 | 0.862001 | 0.431000 | − | 0.902352i | \(-0.358161\pi\) | ||||
0.431000 | + | 0.902352i | \(0.358161\pi\) | |||||||
\(80\) | 30.2523 | 3.38231 | ||||||||
\(81\) | 39.3537 | 4.37263 | ||||||||
\(82\) | −6.01494 | −0.664239 | ||||||||
\(83\) | −0.00863659 | −0.000947989 0 | −0.000473995 | − | 1.00000i | \(-0.500151\pi\) | ||||
−0.000473995 | 1.00000i | \(0.500151\pi\) | ||||||||
\(84\) | −42.2804 | −4.61317 | ||||||||
\(85\) | 3.86072 | 0.418753 | ||||||||
\(86\) | −2.56568 | −0.276665 | ||||||||
\(87\) | 35.3137 | 3.78602 | ||||||||
\(88\) | 6.62646 | 0.706383 | ||||||||
\(89\) | −0.141453 | −0.0149940 | −0.00749698 | − | 0.999972i | \(-0.502386\pi\) | ||||
−0.00749698 | + | 0.999972i | \(0.502386\pi\) | |||||||
\(90\) | −85.3212 | −8.99364 | ||||||||
\(91\) | 5.72445 | 0.600086 | ||||||||
\(92\) | −13.6959 | −1.42790 | ||||||||
\(93\) | 23.3749 | 2.42386 | ||||||||
\(94\) | 9.29334 | 0.958535 | ||||||||
\(95\) | −5.04845 | −0.517960 | ||||||||
\(96\) | 23.3494 | 2.38309 | ||||||||
\(97\) | −12.3113 | −1.25002 | −0.625011 | − | 0.780616i | \(-0.714905\pi\) | ||||
−0.625011 | + | 0.780616i | \(0.714905\pi\) | |||||||
\(98\) | −0.844859 | −0.0853436 | ||||||||
\(99\) | −8.61362 | −0.865702 | ||||||||
\(100\) | 45.3925 | 4.53925 | ||||||||
\(101\) | −9.54345 | −0.949609 | −0.474804 | − | 0.880091i | \(-0.657481\pi\) | ||||
−0.474804 | + | 0.880091i | \(0.657481\pi\) | |||||||
\(102\) | 8.74353 | 0.865738 | ||||||||
\(103\) | −17.1049 | −1.68539 | −0.842696 | − | 0.538390i | \(-0.819033\pi\) | ||||
−0.842696 | + | 0.538390i | \(0.819033\pi\) | |||||||
\(104\) | −14.0115 | −1.37394 | ||||||||
\(105\) | −35.6191 | −3.47607 | ||||||||
\(106\) | 13.3118 | 1.29295 | ||||||||
\(107\) | −8.20583 | −0.793287 | −0.396644 | − | 0.917973i | \(-0.629825\pi\) | ||||
−0.396644 | + | 0.917973i | \(0.629825\pi\) | |||||||
\(108\) | −87.6700 | −8.43605 | ||||||||
\(109\) | −13.7576 | −1.31774 | −0.658872 | − | 0.752255i | \(-0.728966\pi\) | ||||
−0.658872 | + | 0.752255i | \(0.728966\pi\) | |||||||
\(110\) | 9.90537 | 0.944440 | ||||||||
\(111\) | −37.2967 | −3.54004 | ||||||||
\(112\) | 21.2140 | 2.00453 | ||||||||
\(113\) | −1.41681 | −0.133282 | −0.0666411 | − | 0.997777i | \(-0.521228\pi\) | ||||
−0.0666411 | + | 0.997777i | \(0.521228\pi\) | |||||||
\(114\) | −11.4334 | −1.07084 | ||||||||
\(115\) | −11.5381 | −1.07594 | ||||||||
\(116\) | −47.4879 | −4.40914 | ||||||||
\(117\) | 18.2133 | 1.68382 | ||||||||
\(118\) | 7.73527 | 0.712089 | ||||||||
\(119\) | 2.70727 | 0.248175 | ||||||||
\(120\) | 87.1833 | 7.95871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.41776 | 0.218894 | ||||||||
\(123\) | −7.98936 | −0.720376 | ||||||||
\(124\) | −31.4333 | −2.82279 | ||||||||
\(125\) | 18.9373 | 1.69381 | ||||||||
\(126\) | −59.8301 | −5.33009 | ||||||||
\(127\) | −18.2538 | −1.61976 | −0.809881 | − | 0.586594i | \(-0.800469\pi\) | ||||
−0.809881 | + | 0.586594i | \(0.800469\pi\) | |||||||
\(128\) | 8.81002 | 0.778703 | ||||||||
\(129\) | −3.40788 | −0.300047 | ||||||||
\(130\) | −20.9447 | −1.83697 | ||||||||
\(131\) | −16.5568 | −1.44657 | −0.723285 | − | 0.690549i | \(-0.757369\pi\) | ||||
−0.723285 | + | 0.690549i | \(0.757369\pi\) | |||||||
\(132\) | 15.6174 | 1.35932 | ||||||||
\(133\) | −3.54015 | −0.306970 | ||||||||
\(134\) | −20.7071 | −1.78882 | ||||||||
\(135\) | −73.8576 | −6.35665 | ||||||||
\(136\) | −6.62646 | −0.568214 | ||||||||
\(137\) | −2.11635 | −0.180812 | −0.0904058 | − | 0.995905i | \(-0.528816\pi\) | ||||
−0.0904058 | + | 0.995905i | \(0.528816\pi\) | |||||||
\(138\) | −26.1309 | −2.22441 | ||||||||
\(139\) | 0.360905 | 0.0306115 | 0.0153058 | − | 0.999883i | \(-0.495128\pi\) | ||||
0.0153058 | + | 0.999883i | \(0.495128\pi\) | |||||||
\(140\) | 47.8986 | 4.04817 | ||||||||
\(141\) | 12.3439 | 1.03955 | ||||||||
\(142\) | −3.13109 | −0.262755 | ||||||||
\(143\) | −2.11448 | −0.176821 | ||||||||
\(144\) | 67.4958 | 5.62465 | ||||||||
\(145\) | −40.0061 | −3.32233 | ||||||||
\(146\) | −1.93987 | −0.160545 | ||||||||
\(147\) | −1.12219 | −0.0925564 | ||||||||
\(148\) | 50.1545 | 4.12268 | ||||||||
\(149\) | −21.5462 | −1.76514 | −0.882568 | − | 0.470184i | \(-0.844188\pi\) | ||||
−0.882568 | + | 0.470184i | \(0.844188\pi\) | |||||||
\(150\) | 86.6058 | 7.07133 | ||||||||
\(151\) | −16.0295 | −1.30446 | −0.652231 | − | 0.758021i | \(-0.726167\pi\) | ||||
−0.652231 | + | 0.758021i | \(0.726167\pi\) | |||||||
\(152\) | 8.66506 | 0.702829 | ||||||||
\(153\) | 8.61362 | 0.696370 | ||||||||
\(154\) | 6.94599 | 0.559724 | ||||||||
\(155\) | −26.4810 | −2.12700 | ||||||||
\(156\) | −33.0226 | −2.64392 | ||||||||
\(157\) | 21.0322 | 1.67855 | 0.839275 | − | 0.543707i | \(-0.182980\pi\) | ||||
0.839275 | + | 0.543707i | \(0.182980\pi\) | |||||||
\(158\) | −19.6573 | −1.56385 | ||||||||
\(159\) | 17.6814 | 1.40223 | ||||||||
\(160\) | −26.4521 | −2.09122 | ||||||||
\(161\) | −8.09093 | −0.637654 | ||||||||
\(162\) | −100.969 | −7.93287 | ||||||||
\(163\) | −14.9750 | −1.17293 | −0.586464 | − | 0.809975i | \(-0.699481\pi\) | ||||
−0.586464 | + | 0.809975i | \(0.699481\pi\) | |||||||
\(164\) | 10.7437 | 0.838939 | ||||||||
\(165\) | 13.1568 | 1.02426 | ||||||||
\(166\) | 0.0221588 | 0.00171985 | ||||||||
\(167\) | 0.440321 | 0.0340731 | 0.0170365 | − | 0.999855i | \(-0.494577\pi\) | ||||
0.0170365 | + | 0.999855i | \(0.494577\pi\) | |||||||
\(168\) | 61.1359 | 4.71674 | ||||||||
\(169\) | −8.52899 | −0.656076 | ||||||||
\(170\) | −9.90537 | −0.759707 | ||||||||
\(171\) | −11.2636 | −0.861347 | ||||||||
\(172\) | 4.58273 | 0.349430 | ||||||||
\(173\) | 10.8300 | 0.823386 | 0.411693 | − | 0.911322i | \(-0.364938\pi\) | ||||
0.411693 | + | 0.911322i | \(0.364938\pi\) | |||||||
\(174\) | −90.6036 | −6.86864 | ||||||||
\(175\) | 26.8158 | 2.02709 | ||||||||
\(176\) | −7.83593 | −0.590656 | ||||||||
\(177\) | 10.2744 | 0.772271 | ||||||||
\(178\) | 0.362923 | 0.0272022 | ||||||||
\(179\) | 16.0754 | 1.20153 | 0.600765 | − | 0.799426i | \(-0.294863\pi\) | ||||
0.600765 | + | 0.799426i | \(0.294863\pi\) | |||||||
\(180\) | 152.397 | 11.3590 | ||||||||
\(181\) | 18.6761 | 1.38818 | 0.694091 | − | 0.719887i | \(-0.255807\pi\) | ||||
0.694091 | + | 0.719887i | \(0.255807\pi\) | |||||||
\(182\) | −14.6871 | −1.08868 | ||||||||
\(183\) | 3.21140 | 0.237393 | ||||||||
\(184\) | 19.8038 | 1.45996 | ||||||||
\(185\) | 42.2526 | 3.10648 | ||||||||
\(186\) | −59.9726 | −4.39740 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −16.5994 | −1.21064 | ||||||||
\(189\) | −51.7915 | −3.76728 | ||||||||
\(190\) | 12.9527 | 0.939689 | ||||||||
\(191\) | 1.25058 | 0.0904885 | 0.0452443 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452443 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(192\) | −6.49937 | −0.469052 | ||||||||
\(193\) | −6.39972 | −0.460662 | −0.230331 | − | 0.973112i | \(-0.573981\pi\) | ||||
−0.230331 | + | 0.973112i | \(0.573981\pi\) | |||||||
\(194\) | 31.5868 | 2.26780 | ||||||||
\(195\) | −27.8198 | −1.99222 | ||||||||
\(196\) | 1.50906 | 0.107790 | ||||||||
\(197\) | 17.0074 | 1.21173 | 0.605863 | − | 0.795569i | \(-0.292828\pi\) | ||||
0.605863 | + | 0.795569i | \(0.292828\pi\) | |||||||
\(198\) | 22.0998 | 1.57057 | ||||||||
\(199\) | −6.05693 | −0.429364 | −0.214682 | − | 0.976684i | \(-0.568872\pi\) | ||||
−0.214682 | + | 0.976684i | \(0.568872\pi\) | |||||||
\(200\) | −65.6359 | −4.64116 | ||||||||
\(201\) | −27.5043 | −1.94000 | ||||||||
\(202\) | 24.4855 | 1.72279 | ||||||||
\(203\) | −28.0537 | −1.96898 | ||||||||
\(204\) | −15.6174 | −1.09343 | ||||||||
\(205\) | 9.05099 | 0.632148 | ||||||||
\(206\) | 43.8856 | 3.05766 | ||||||||
\(207\) | −25.7427 | −1.78924 | ||||||||
\(208\) | 16.5689 | 1.14885 | ||||||||
\(209\) | 1.30765 | 0.0904518 | ||||||||
\(210\) | 91.3873 | 6.30632 | ||||||||
\(211\) | −1.15209 | −0.0793133 | −0.0396566 | − | 0.999213i | \(-0.512626\pi\) | ||||
−0.0396566 | + | 0.999213i | \(0.512626\pi\) | |||||||
\(212\) | −23.7770 | −1.63301 | ||||||||
\(213\) | −4.15888 | −0.284962 | ||||||||
\(214\) | 21.0535 | 1.43919 | ||||||||
\(215\) | 3.86072 | 0.263299 | ||||||||
\(216\) | 126.768 | 8.62545 | ||||||||
\(217\) | −18.5694 | −1.26057 | ||||||||
\(218\) | 35.2977 | 2.39066 | ||||||||
\(219\) | −2.57664 | −0.174113 | ||||||||
\(220\) | −17.6926 | −1.19284 | ||||||||
\(221\) | 2.11448 | 0.142235 | ||||||||
\(222\) | 95.6914 | 6.42239 | ||||||||
\(223\) | 25.4941 | 1.70721 | 0.853606 | − | 0.520919i | \(-0.174411\pi\) | ||||
0.853606 | + | 0.520919i | \(0.174411\pi\) | |||||||
\(224\) | −18.5491 | −1.23936 | ||||||||
\(225\) | 85.3191 | 5.68794 | ||||||||
\(226\) | 3.63508 | 0.241802 | ||||||||
\(227\) | 19.0502 | 1.26441 | 0.632203 | − | 0.774803i | \(-0.282151\pi\) | ||||
0.632203 | + | 0.774803i | \(0.282151\pi\) | |||||||
\(228\) | 20.4220 | 1.35248 | ||||||||
\(229\) | −10.5112 | −0.694598 | −0.347299 | − | 0.937754i | \(-0.612901\pi\) | ||||
−0.347299 | + | 0.937754i | \(0.612901\pi\) | |||||||
\(230\) | 29.6032 | 1.95197 | ||||||||
\(231\) | 9.22603 | 0.607028 | ||||||||
\(232\) | 68.6658 | 4.50813 | ||||||||
\(233\) | −17.6216 | −1.15443 | −0.577215 | − | 0.816592i | \(-0.695860\pi\) | ||||
−0.577215 | + | 0.816592i | \(0.695860\pi\) | |||||||
\(234\) | −46.7296 | −3.05481 | ||||||||
\(235\) | −13.9842 | −0.912227 | ||||||||
\(236\) | −13.8164 | −0.899374 | ||||||||
\(237\) | −26.1099 | −1.69602 | ||||||||
\(238\) | −6.94599 | −0.450241 | ||||||||
\(239\) | −6.19205 | −0.400530 | −0.200265 | − | 0.979742i | \(-0.564180\pi\) | ||||
−0.200265 | + | 0.979742i | \(0.564180\pi\) | |||||||
\(240\) | −103.096 | −6.65483 | ||||||||
\(241\) | 9.01722 | 0.580850 | 0.290425 | − | 0.956898i | \(-0.406203\pi\) | ||||
0.290425 | + | 0.956898i | \(0.406203\pi\) | |||||||
\(242\) | −2.56568 | −0.164928 | ||||||||
\(243\) | −76.7208 | −4.92164 | ||||||||
\(244\) | −4.31851 | −0.276464 | ||||||||
\(245\) | 1.27130 | 0.0812206 | ||||||||
\(246\) | 20.4982 | 1.30692 | ||||||||
\(247\) | −2.76499 | −0.175932 | ||||||||
\(248\) | 45.4514 | 2.88617 | ||||||||
\(249\) | 0.0294325 | 0.00186521 | ||||||||
\(250\) | −48.5871 | −3.07292 | ||||||||
\(251\) | 5.54169 | 0.349789 | 0.174894 | − | 0.984587i | \(-0.444042\pi\) | ||||
0.174894 | + | 0.984587i | \(0.444042\pi\) | |||||||
\(252\) | 106.866 | 6.73195 | ||||||||
\(253\) | 2.98860 | 0.187891 | ||||||||
\(254\) | 46.8335 | 2.93859 | ||||||||
\(255\) | −13.1568 | −0.823914 | ||||||||
\(256\) | −26.4180 | −1.65113 | ||||||||
\(257\) | −28.4209 | −1.77285 | −0.886424 | − | 0.462874i | \(-0.846818\pi\) | ||||
−0.886424 | + | 0.462874i | \(0.846818\pi\) | |||||||
\(258\) | 8.74353 | 0.544348 | ||||||||
\(259\) | 29.6290 | 1.84106 | ||||||||
\(260\) | 37.4106 | 2.32011 | ||||||||
\(261\) | −89.2575 | −5.52490 | ||||||||
\(262\) | 42.4794 | 2.62438 | ||||||||
\(263\) | 9.97055 | 0.614811 | 0.307405 | − | 0.951579i | \(-0.400539\pi\) | ||||
0.307405 | + | 0.951579i | \(0.400539\pi\) | |||||||
\(264\) | −22.5821 | −1.38984 | ||||||||
\(265\) | −20.0309 | −1.23049 | ||||||||
\(266\) | 9.08289 | 0.556908 | ||||||||
\(267\) | 0.482053 | 0.0295012 | ||||||||
\(268\) | 36.9863 | 2.25930 | ||||||||
\(269\) | −32.1793 | −1.96201 | −0.981004 | − | 0.193989i | \(-0.937857\pi\) | ||||
−0.981004 | + | 0.193989i | \(0.937857\pi\) | |||||||
\(270\) | 189.495 | 11.5323 | ||||||||
\(271\) | −10.8929 | −0.661697 | −0.330849 | − | 0.943684i | \(-0.607335\pi\) | ||||
−0.330849 | + | 0.943684i | \(0.607335\pi\) | |||||||
\(272\) | 7.83593 | 0.475123 | ||||||||
\(273\) | −19.5082 | −1.18069 | ||||||||
\(274\) | 5.42987 | 0.328030 | ||||||||
\(275\) | −9.90513 | −0.597302 | ||||||||
\(276\) | 46.6740 | 2.80945 | ||||||||
\(277\) | 3.98110 | 0.239201 | 0.119600 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119600 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(278\) | −0.925967 | −0.0555358 | ||||||||
\(279\) | −59.0815 | −3.53712 | ||||||||
\(280\) | −69.2596 | −4.13906 | ||||||||
\(281\) | −19.8292 | −1.18291 | −0.591456 | − | 0.806337i | \(-0.701447\pi\) | ||||
−0.591456 | + | 0.806337i | \(0.701447\pi\) | |||||||
\(282\) | −31.6706 | −1.88596 | ||||||||
\(283\) | 17.4932 | 1.03986 | 0.519931 | − | 0.854208i | \(-0.325958\pi\) | ||||
0.519931 | + | 0.854208i | \(0.325958\pi\) | |||||||
\(284\) | 5.59264 | 0.331862 | ||||||||
\(285\) | 17.2045 | 1.01911 | ||||||||
\(286\) | 5.42507 | 0.320791 | ||||||||
\(287\) | 6.34686 | 0.374643 | ||||||||
\(288\) | −59.0171 | −3.47762 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 102.643 | 6.02741 | ||||||||
\(291\) | 41.9553 | 2.45947 | ||||||||
\(292\) | 3.46493 | 0.202770 | ||||||||
\(293\) | −16.1550 | −0.943783 | −0.471891 | − | 0.881657i | \(-0.656429\pi\) | ||||
−0.471891 | + | 0.881657i | \(0.656429\pi\) | |||||||
\(294\) | 2.87918 | 0.167917 | ||||||||
\(295\) | −11.6397 | −0.677687 | ||||||||
\(296\) | −72.5216 | −4.21523 | ||||||||
\(297\) | 19.1305 | 1.11007 | ||||||||
\(298\) | 55.2808 | 3.20233 | ||||||||
\(299\) | −6.31932 | −0.365456 | ||||||||
\(300\) | −154.692 | −8.93115 | ||||||||
\(301\) | 2.70727 | 0.156044 | ||||||||
\(302\) | 41.1266 | 2.36657 | ||||||||
\(303\) | 32.5229 | 1.86839 | ||||||||
\(304\) | −10.2466 | −0.587684 | ||||||||
\(305\) | −3.63813 | −0.208319 | ||||||||
\(306\) | −22.0998 | −1.26336 | ||||||||
\(307\) | −27.0549 | −1.54411 | −0.772053 | − | 0.635558i | \(-0.780770\pi\) | ||||
−0.772053 | + | 0.635558i | \(0.780770\pi\) | |||||||
\(308\) | −12.4067 | −0.706935 | ||||||||
\(309\) | 58.2913 | 3.31607 | ||||||||
\(310\) | 67.9417 | 3.85883 | ||||||||
\(311\) | 1.31805 | 0.0747399 | 0.0373700 | − | 0.999301i | \(-0.488102\pi\) | ||||
0.0373700 | + | 0.999301i | \(0.488102\pi\) | |||||||
\(312\) | 47.7494 | 2.70328 | ||||||||
\(313\) | 24.6020 | 1.39059 | 0.695293 | − | 0.718727i | \(-0.255275\pi\) | ||||
0.695293 | + | 0.718727i | \(0.255275\pi\) | |||||||
\(314\) | −53.9619 | −3.04525 | ||||||||
\(315\) | 90.0295 | 5.07259 | ||||||||
\(316\) | 35.1112 | 1.97516 | ||||||||
\(317\) | 18.4036 | 1.03365 | 0.516824 | − | 0.856092i | \(-0.327114\pi\) | ||||
0.516824 | + | 0.856092i | \(0.327114\pi\) | |||||||
\(318\) | −45.3649 | −2.54394 | ||||||||
\(319\) | 10.3624 | 0.580181 | ||||||||
\(320\) | 7.36301 | 0.411605 | ||||||||
\(321\) | 27.9644 | 1.56082 | ||||||||
\(322\) | 20.7588 | 1.15684 | ||||||||
\(323\) | −1.30765 | −0.0727594 | ||||||||
\(324\) | 180.347 | 10.0193 | ||||||||
\(325\) | 20.9442 | 1.16177 | ||||||||
\(326\) | 38.4210 | 2.12794 | ||||||||
\(327\) | 46.8844 | 2.59271 | ||||||||
\(328\) | −15.5349 | −0.857773 | ||||||||
\(329\) | −9.80619 | −0.540632 | ||||||||
\(330\) | −33.7563 | −1.85822 | ||||||||
\(331\) | −0.955814 | −0.0525363 | −0.0262681 | − | 0.999655i | \(-0.508362\pi\) | ||||
−0.0262681 | + | 0.999655i | \(0.508362\pi\) | |||||||
\(332\) | −0.0395792 | −0.00217219 | ||||||||
\(333\) | 94.2697 | 5.16595 | ||||||||
\(334\) | −1.12972 | −0.0618158 | ||||||||
\(335\) | 31.1591 | 1.70240 | ||||||||
\(336\) | −72.2945 | −3.94399 | ||||||||
\(337\) | −9.94283 | −0.541621 | −0.270810 | − | 0.962633i | \(-0.587292\pi\) | ||||
−0.270810 | + | 0.962633i | \(0.587292\pi\) | |||||||
\(338\) | 21.8827 | 1.19026 | ||||||||
\(339\) | 4.82831 | 0.262238 | ||||||||
\(340\) | 17.6926 | 0.959516 | ||||||||
\(341\) | 6.85908 | 0.371440 | ||||||||
\(342\) | 28.8987 | 1.56267 | ||||||||
\(343\) | −18.0594 | −0.975115 | ||||||||
\(344\) | −6.62646 | −0.357275 | ||||||||
\(345\) | 39.3205 | 2.11694 | ||||||||
\(346\) | −27.7862 | −1.49380 | ||||||||
\(347\) | −2.24529 | −0.120534 | −0.0602668 | − | 0.998182i | \(-0.519195\pi\) | ||||
−0.0602668 | + | 0.998182i | \(0.519195\pi\) | |||||||
\(348\) | 161.833 | 8.67515 | ||||||||
\(349\) | −2.51558 | −0.134656 | −0.0673279 | − | 0.997731i | \(-0.521447\pi\) | ||||
−0.0673279 | + | 0.997731i | \(0.521447\pi\) | |||||||
\(350\) | −68.8009 | −3.67756 | ||||||||
\(351\) | −40.4511 | −2.15912 | ||||||||
\(352\) | 6.85160 | 0.365191 | ||||||||
\(353\) | 19.7090 | 1.04900 | 0.524501 | − | 0.851410i | \(-0.324252\pi\) | ||||
0.524501 | + | 0.851410i | \(0.324252\pi\) | |||||||
\(354\) | −26.3608 | −1.40106 | ||||||||
\(355\) | 4.71151 | 0.250061 | ||||||||
\(356\) | −0.648239 | −0.0343566 | ||||||||
\(357\) | −9.22603 | −0.488293 | ||||||||
\(358\) | −41.2443 | −2.17983 | ||||||||
\(359\) | −35.9132 | −1.89543 | −0.947714 | − | 0.319120i | \(-0.896613\pi\) | ||||
−0.947714 | + | 0.319120i | \(0.896613\pi\) | |||||||
\(360\) | −220.361 | −11.6141 | ||||||||
\(361\) | −17.2901 | −0.910003 | ||||||||
\(362\) | −47.9169 | −2.51846 | ||||||||
\(363\) | −3.40788 | −0.178867 | ||||||||
\(364\) | 26.2336 | 1.37501 | ||||||||
\(365\) | 2.91903 | 0.152789 | ||||||||
\(366\) | −8.23942 | −0.430682 | ||||||||
\(367\) | 6.06250 | 0.316460 | 0.158230 | − | 0.987402i | \(-0.449421\pi\) | ||||
0.158230 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(368\) | −23.4184 | −1.22077 | ||||||||
\(369\) | 20.1936 | 1.05124 | ||||||||
\(370\) | −108.407 | −5.63581 | ||||||||
\(371\) | −14.0464 | −0.729252 | ||||||||
\(372\) | 107.121 | 5.55395 | ||||||||
\(373\) | 13.4398 | 0.695889 | 0.347944 | − | 0.937515i | \(-0.386880\pi\) | ||||
0.347944 | + | 0.937515i | \(0.386880\pi\) | |||||||
\(374\) | 2.56568 | 0.132668 | ||||||||
\(375\) | −64.5360 | −3.33263 | ||||||||
\(376\) | 24.0022 | 1.23782 | ||||||||
\(377\) | −21.9110 | −1.12847 | ||||||||
\(378\) | 132.880 | 6.83463 | ||||||||
\(379\) | 10.1209 | 0.519875 | 0.259937 | − | 0.965626i | \(-0.416298\pi\) | ||||
0.259937 | + | 0.965626i | \(0.416298\pi\) | |||||||
\(380\) | −23.1357 | −1.18683 | ||||||||
\(381\) | 62.2067 | 3.18695 | ||||||||
\(382\) | −3.20858 | −0.164165 | ||||||||
\(383\) | −4.32059 | −0.220772 | −0.110386 | − | 0.993889i | \(-0.535209\pi\) | ||||
−0.110386 | + | 0.993889i | \(0.535209\pi\) | |||||||
\(384\) | −30.0235 | −1.53213 | ||||||||
\(385\) | −10.4520 | −0.532683 | ||||||||
\(386\) | 16.4197 | 0.835739 | ||||||||
\(387\) | 8.61362 | 0.437855 | ||||||||
\(388\) | −56.4192 | −2.86425 | ||||||||
\(389\) | −7.04567 | −0.357229 | −0.178615 | − | 0.983919i | \(-0.557162\pi\) | ||||
−0.178615 | + | 0.983919i | \(0.557162\pi\) | |||||||
\(390\) | 71.3769 | 3.61431 | ||||||||
\(391\) | −2.98860 | −0.151140 | ||||||||
\(392\) | −2.18204 | −0.110210 | ||||||||
\(393\) | 56.4234 | 2.84618 | ||||||||
\(394\) | −43.6355 | −2.19833 | ||||||||
\(395\) | 29.5794 | 1.48830 | ||||||||
\(396\) | −39.4739 | −1.98364 | ||||||||
\(397\) | 14.7016 | 0.737850 | 0.368925 | − | 0.929459i | \(-0.379726\pi\) | ||||
0.368925 | + | 0.929459i | \(0.379726\pi\) | |||||||
\(398\) | 15.5402 | 0.778958 | ||||||||
\(399\) | 12.0644 | 0.603975 | ||||||||
\(400\) | 77.6159 | 3.88080 | ||||||||
\(401\) | 0.564011 | 0.0281653 | 0.0140827 | − | 0.999901i | \(-0.495517\pi\) | ||||
0.0140827 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(402\) | 70.5673 | 3.51958 | ||||||||
\(403\) | −14.5034 | −0.722464 | ||||||||
\(404\) | −43.7350 | −2.17590 | ||||||||
\(405\) | 151.933 | 7.54963 | ||||||||
\(406\) | 71.9768 | 3.57215 | ||||||||
\(407\) | −10.9443 | −0.542486 | ||||||||
\(408\) | 22.5821 | 1.11798 | ||||||||
\(409\) | −24.8056 | −1.22656 | −0.613279 | − | 0.789866i | \(-0.710150\pi\) | ||||
−0.613279 | + | 0.789866i | \(0.710150\pi\) | |||||||
\(410\) | −23.2220 | −1.14685 | ||||||||
\(411\) | 7.21224 | 0.355754 | ||||||||
\(412\) | −78.3869 | −3.86185 | ||||||||
\(413\) | −8.16213 | −0.401632 | ||||||||
\(414\) | 66.0475 | 3.24606 | ||||||||
\(415\) | −0.0333434 | −0.00163677 | ||||||||
\(416\) | −14.4875 | −0.710310 | ||||||||
\(417\) | −1.22992 | −0.0602294 | ||||||||
\(418\) | −3.35500 | −0.164099 | ||||||||
\(419\) | −29.2810 | −1.43047 | −0.715234 | − | 0.698885i | \(-0.753680\pi\) | ||||
−0.715234 | + | 0.698885i | \(0.753680\pi\) | |||||||
\(420\) | −163.233 | −7.96493 | ||||||||
\(421\) | 16.2275 | 0.790882 | 0.395441 | − | 0.918491i | \(-0.370592\pi\) | ||||
0.395441 | + | 0.918491i | \(0.370592\pi\) | |||||||
\(422\) | 2.95590 | 0.143891 | ||||||||
\(423\) | −31.2000 | −1.51700 | ||||||||
\(424\) | 34.3807 | 1.66967 | ||||||||
\(425\) | 9.90513 | 0.480469 | ||||||||
\(426\) | 10.6704 | 0.516981 | ||||||||
\(427\) | −2.55118 | −0.123460 | ||||||||
\(428\) | −37.6051 | −1.81771 | ||||||||
\(429\) | 7.20587 | 0.347903 | ||||||||
\(430\) | −9.90537 | −0.477679 | ||||||||
\(431\) | 7.83107 | 0.377209 | 0.188605 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188605 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(432\) | −149.906 | −7.21234 | ||||||||
\(433\) | −28.5758 | −1.37327 | −0.686633 | − | 0.727004i | \(-0.740912\pi\) | ||||
−0.686633 | + | 0.727004i | \(0.740912\pi\) | |||||||
\(434\) | 47.6431 | 2.28694 | ||||||||
\(435\) | 136.336 | 6.53681 | ||||||||
\(436\) | −63.0475 | −3.01943 | ||||||||
\(437\) | 3.90803 | 0.186946 | ||||||||
\(438\) | 6.61085 | 0.315879 | ||||||||
\(439\) | −20.2106 | −0.964599 | −0.482300 | − | 0.876006i | \(-0.660198\pi\) | ||||
−0.482300 | + | 0.876006i | \(0.660198\pi\) | |||||||
\(440\) | 25.5829 | 1.21962 | ||||||||
\(441\) | 2.83640 | 0.135067 | ||||||||
\(442\) | −5.42507 | −0.258044 | ||||||||
\(443\) | −34.1256 | −1.62136 | −0.810678 | − | 0.585492i | \(-0.800901\pi\) | ||||
−0.810678 | + | 0.585492i | \(0.800901\pi\) | |||||||
\(444\) | −170.920 | −8.11152 | ||||||||
\(445\) | −0.546109 | −0.0258880 | ||||||||
\(446\) | −65.4098 | −3.09724 | ||||||||
\(447\) | 73.4269 | 3.47298 | ||||||||
\(448\) | 5.16319 | 0.243938 | ||||||||
\(449\) | −35.3516 | −1.66834 | −0.834172 | − | 0.551505i | \(-0.814054\pi\) | ||||
−0.834172 | + | 0.551505i | \(0.814054\pi\) | |||||||
\(450\) | −218.902 | −10.3191 | ||||||||
\(451\) | −2.34438 | −0.110393 | ||||||||
\(452\) | −6.49285 | −0.305398 | ||||||||
\(453\) | 54.6265 | 2.56658 | ||||||||
\(454\) | −48.8767 | −2.29390 | ||||||||
\(455\) | 22.1005 | 1.03609 | ||||||||
\(456\) | −29.5295 | −1.38284 | ||||||||
\(457\) | 27.6520 | 1.29350 | 0.646752 | − | 0.762700i | \(-0.276127\pi\) | ||||
0.646752 | + | 0.762700i | \(0.276127\pi\) | |||||||
\(458\) | 26.9683 | 1.26015 | ||||||||
\(459\) | −19.1305 | −0.892937 | ||||||||
\(460\) | −52.8761 | −2.46536 | ||||||||
\(461\) | 21.7082 | 1.01105 | 0.505527 | − | 0.862811i | \(-0.331298\pi\) | ||||
0.505527 | + | 0.862811i | \(0.331298\pi\) | |||||||
\(462\) | −23.6711 | −1.10128 | ||||||||
\(463\) | 16.8349 | 0.782383 | 0.391192 | − | 0.920309i | \(-0.372063\pi\) | ||||
0.391192 | + | 0.920309i | \(0.372063\pi\) | |||||||
\(464\) | −81.1988 | −3.76956 | ||||||||
\(465\) | 90.2438 | 4.18496 | ||||||||
\(466\) | 45.2114 | 2.09438 | ||||||||
\(467\) | −19.3987 | −0.897666 | −0.448833 | − | 0.893616i | \(-0.648160\pi\) | ||||
−0.448833 | + | 0.893616i | \(0.648160\pi\) | |||||||
\(468\) | 83.4666 | 3.85825 | ||||||||
\(469\) | 21.8498 | 1.00893 | ||||||||
\(470\) | 35.8790 | 1.65497 | ||||||||
\(471\) | −71.6751 | −3.30261 | ||||||||
\(472\) | 19.9781 | 0.919566 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 66.9897 | 3.07694 | ||||||||
\(475\) | −12.9524 | −0.594297 | ||||||||
\(476\) | 12.4067 | 0.568658 | ||||||||
\(477\) | −44.6909 | −2.04626 | ||||||||
\(478\) | 15.8868 | 0.726646 | ||||||||
\(479\) | −31.8295 | −1.45433 | −0.727163 | − | 0.686465i | \(-0.759161\pi\) | ||||
−0.727163 | + | 0.686465i | \(0.759161\pi\) | |||||||
\(480\) | 90.1454 | 4.11456 | ||||||||
\(481\) | 23.1414 | 1.05516 | ||||||||
\(482\) | −23.1353 | −1.05378 | ||||||||
\(483\) | 27.5729 | 1.25461 | ||||||||
\(484\) | 4.58273 | 0.208306 | ||||||||
\(485\) | −47.5304 | −2.15824 | ||||||||
\(486\) | 196.841 | 8.92890 | ||||||||
\(487\) | 12.8515 | 0.582355 | 0.291177 | − | 0.956669i | \(-0.405953\pi\) | ||||
0.291177 | + | 0.956669i | \(0.405953\pi\) | |||||||
\(488\) | 6.24441 | 0.282671 | ||||||||
\(489\) | 51.0328 | 2.30778 | ||||||||
\(490\) | −3.26176 | −0.147351 | ||||||||
\(491\) | −22.7255 | −1.02559 | −0.512794 | − | 0.858512i | \(-0.671390\pi\) | ||||
−0.512794 | + | 0.858512i | \(0.671390\pi\) | |||||||
\(492\) | −36.6131 | −1.65064 | ||||||||
\(493\) | −10.3624 | −0.466697 | ||||||||
\(494\) | 7.09408 | 0.319178 | ||||||||
\(495\) | −33.2548 | −1.49469 | ||||||||
\(496\) | −53.7473 | −2.41332 | ||||||||
\(497\) | 3.30388 | 0.148199 | ||||||||
\(498\) | −0.0755143 | −0.00338388 | ||||||||
\(499\) | 39.9822 | 1.78985 | 0.894924 | − | 0.446219i | \(-0.147230\pi\) | ||||
0.894924 | + | 0.446219i | \(0.147230\pi\) | |||||||
\(500\) | 86.7846 | 3.88112 | ||||||||
\(501\) | −1.50056 | −0.0670401 | ||||||||
\(502\) | −14.2182 | −0.634590 | ||||||||
\(503\) | 37.8385 | 1.68713 | 0.843567 | − | 0.537024i | \(-0.180452\pi\) | ||||
0.843567 | + | 0.537024i | \(0.180452\pi\) | |||||||
\(504\) | −154.525 | −6.88308 | ||||||||
\(505\) | −36.8446 | −1.63956 | ||||||||
\(506\) | −7.66779 | −0.340875 | ||||||||
\(507\) | 29.0657 | 1.29086 | ||||||||
\(508\) | −83.6522 | −3.71147 | ||||||||
\(509\) | 36.9633 | 1.63837 | 0.819185 | − | 0.573529i | \(-0.194426\pi\) | ||||
0.819185 | + | 0.573529i | \(0.194426\pi\) | |||||||
\(510\) | 33.7563 | 1.49475 | ||||||||
\(511\) | 2.04692 | 0.0905506 | ||||||||
\(512\) | 50.1603 | 2.21679 | ||||||||
\(513\) | 25.0160 | 1.10448 | ||||||||
\(514\) | 72.9190 | 3.21632 | ||||||||
\(515\) | −66.0370 | −2.90994 | ||||||||
\(516\) | −15.6174 | −0.687516 | ||||||||
\(517\) | 3.62217 | 0.159303 | ||||||||
\(518\) | −76.0186 | −3.34007 | ||||||||
\(519\) | −36.9072 | −1.62004 | ||||||||
\(520\) | −54.0944 | −2.37220 | ||||||||
\(521\) | −0.366090 | −0.0160387 | −0.00801935 | − | 0.999968i | \(-0.502553\pi\) | ||||
−0.00801935 | + | 0.999968i | \(0.502553\pi\) | |||||||
\(522\) | 229.006 | 10.0233 | ||||||||
\(523\) | −28.1275 | −1.22993 | −0.614965 | − | 0.788554i | \(-0.710830\pi\) | ||||
−0.614965 | + | 0.788554i | \(0.710830\pi\) | |||||||
\(524\) | −75.8751 | −3.31462 | ||||||||
\(525\) | −91.3850 | −3.98837 | ||||||||
\(526\) | −25.5813 | −1.11540 | ||||||||
\(527\) | −6.85908 | −0.298786 | ||||||||
\(528\) | 26.7039 | 1.16214 | ||||||||
\(529\) | −14.0683 | −0.611665 | ||||||||
\(530\) | 51.3930 | 2.23237 | ||||||||
\(531\) | −25.9692 | −1.12697 | ||||||||
\(532\) | −16.2235 | −0.703379 | ||||||||
\(533\) | 4.95714 | 0.214717 | ||||||||
\(534\) | −1.23680 | −0.0535214 | ||||||||
\(535\) | −31.6804 | −1.36966 | ||||||||
\(536\) | −53.4808 | −2.31002 | ||||||||
\(537\) | −54.7829 | −2.36406 | ||||||||
\(538\) | 82.5619 | 3.55950 | ||||||||
\(539\) | −0.329292 | −0.0141836 | ||||||||
\(540\) | −338.469 | −14.5654 | ||||||||
\(541\) | 34.4124 | 1.47951 | 0.739753 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739753 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(542\) | 27.9477 | 1.20046 | ||||||||
\(543\) | −63.6458 | −2.73130 | ||||||||
\(544\) | −6.85160 | −0.293760 | ||||||||
\(545\) | −53.1144 | −2.27517 | ||||||||
\(546\) | 50.0519 | 2.14202 | ||||||||
\(547\) | −1.29007 | −0.0551594 | −0.0275797 | − | 0.999620i | \(-0.508780\pi\) | ||||
−0.0275797 | + | 0.999620i | \(0.508780\pi\) | |||||||
\(548\) | −9.69863 | −0.414305 | ||||||||
\(549\) | −8.11701 | −0.346425 | ||||||||
\(550\) | 25.4134 | 1.08363 | ||||||||
\(551\) | 13.5503 | 0.577262 | ||||||||
\(552\) | −67.4889 | −2.87252 | ||||||||
\(553\) | 20.7421 | 0.882043 | ||||||||
\(554\) | −10.2142 | −0.433961 | ||||||||
\(555\) | −143.992 | −6.11211 | ||||||||
\(556\) | 1.65393 | 0.0701422 | ||||||||
\(557\) | −45.4436 | −1.92551 | −0.962754 | − | 0.270378i | \(-0.912851\pi\) | ||||
−0.962754 | + | 0.270378i | \(0.912851\pi\) | |||||||
\(558\) | 151.584 | 6.41708 | ||||||||
\(559\) | 2.11448 | 0.0894328 | ||||||||
\(560\) | 81.9011 | 3.46095 | ||||||||
\(561\) | 3.40788 | 0.143881 | ||||||||
\(562\) | 50.8755 | 2.14605 | ||||||||
\(563\) | 8.41519 | 0.354658 | 0.177329 | − | 0.984152i | \(-0.443254\pi\) | ||||
0.177329 | + | 0.984152i | \(0.443254\pi\) | |||||||
\(564\) | 56.5688 | 2.38198 | ||||||||
\(565\) | −5.46990 | −0.230120 | ||||||||
\(566\) | −44.8820 | −1.88653 | ||||||||
\(567\) | 106.541 | 4.47429 | ||||||||
\(568\) | −8.08675 | −0.339313 | ||||||||
\(569\) | −46.3552 | −1.94331 | −0.971656 | − | 0.236399i | \(-0.924033\pi\) | ||||
−0.971656 | + | 0.236399i | \(0.924033\pi\) | |||||||
\(570\) | −44.1413 | −1.84887 | ||||||||
\(571\) | 7.28218 | 0.304750 | 0.152375 | − | 0.988323i | \(-0.451308\pi\) | ||||
0.152375 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(572\) | −9.69007 | −0.405162 | ||||||||
\(573\) | −4.26181 | −0.178040 | ||||||||
\(574\) | −16.2840 | −0.679683 | ||||||||
\(575\) | −29.6024 | −1.23451 | ||||||||
\(576\) | 16.4276 | 0.684482 | ||||||||
\(577\) | 11.9159 | 0.496064 | 0.248032 | − | 0.968752i | \(-0.420216\pi\) | ||||
0.248032 | + | 0.968752i | \(0.420216\pi\) | |||||||
\(578\) | −2.56568 | −0.106718 | ||||||||
\(579\) | 21.8095 | 0.906371 | ||||||||
\(580\) | −183.337 | −7.61266 | ||||||||
\(581\) | −0.0233816 | −0.000970031 0 | ||||||||
\(582\) | −107.644 | −4.46199 | ||||||||
\(583\) | 5.18840 | 0.214882 | ||||||||
\(584\) | −5.01016 | −0.207322 | ||||||||
\(585\) | 70.3164 | 2.90723 | ||||||||
\(586\) | 41.4485 | 1.71222 | ||||||||
\(587\) | 10.1705 | 0.419781 | 0.209890 | − | 0.977725i | \(-0.432689\pi\) | ||||
0.209890 | + | 0.977725i | \(0.432689\pi\) | |||||||
\(588\) | −5.14268 | −0.212080 | ||||||||
\(589\) | 8.96925 | 0.369571 | ||||||||
\(590\) | 29.8637 | 1.22947 | ||||||||
\(591\) | −57.9591 | −2.38412 | ||||||||
\(592\) | 85.7584 | 3.52465 | ||||||||
\(593\) | 30.9156 | 1.26955 | 0.634775 | − | 0.772697i | \(-0.281093\pi\) | ||||
0.634775 | + | 0.772697i | \(0.281093\pi\) | |||||||
\(594\) | −49.0829 | −2.01390 | ||||||||
\(595\) | 10.4520 | 0.428490 | ||||||||
\(596\) | −98.7405 | −4.04457 | ||||||||
\(597\) | 20.6413 | 0.844791 | ||||||||
\(598\) | 16.2134 | 0.663014 | ||||||||
\(599\) | −0.676568 | −0.0276438 | −0.0138219 | − | 0.999904i | \(-0.504400\pi\) | ||||
−0.0138219 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(600\) | 223.679 | 9.13166 | ||||||||
\(601\) | −29.3939 | −1.19900 | −0.599502 | − | 0.800374i | \(-0.704634\pi\) | ||||
−0.599502 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(602\) | −6.94599 | −0.283097 | ||||||||
\(603\) | 69.5188 | 2.83103 | ||||||||
\(604\) | −73.4588 | −2.98900 | ||||||||
\(605\) | 3.86072 | 0.156960 | ||||||||
\(606\) | −83.4434 | −3.38966 | ||||||||
\(607\) | 29.0313 | 1.17834 | 0.589172 | − | 0.808008i | \(-0.299454\pi\) | ||||
0.589172 | + | 0.808008i | \(0.299454\pi\) | |||||||
\(608\) | 8.95946 | 0.363354 | ||||||||
\(609\) | 95.6035 | 3.87405 | ||||||||
\(610\) | 9.33428 | 0.377934 | ||||||||
\(611\) | −7.65900 | −0.309850 | ||||||||
\(612\) | 39.4739 | 1.59564 | ||||||||
\(613\) | −3.04225 | −0.122875 | −0.0614376 | − | 0.998111i | \(-0.519569\pi\) | ||||
−0.0614376 | + | 0.998111i | \(0.519569\pi\) | |||||||
\(614\) | 69.4143 | 2.80134 | ||||||||
\(615\) | −30.8447 | −1.24378 | ||||||||
\(616\) | 17.9396 | 0.722806 | ||||||||
\(617\) | 40.9708 | 1.64942 | 0.824712 | − | 0.565553i | \(-0.191337\pi\) | ||||
0.824712 | + | 0.565553i | \(0.191337\pi\) | |||||||
\(618\) | −149.557 | −6.01606 | ||||||||
\(619\) | 40.1960 | 1.61561 | 0.807807 | − | 0.589447i | \(-0.200654\pi\) | ||||
0.807807 | + | 0.589447i | \(0.200654\pi\) | |||||||
\(620\) | −121.355 | −4.87373 | ||||||||
\(621\) | 57.1735 | 2.29429 | ||||||||
\(622\) | −3.38170 | −0.135594 | ||||||||
\(623\) | −0.382950 | −0.0153426 | ||||||||
\(624\) | −56.4647 | −2.26040 | ||||||||
\(625\) | 23.5860 | 0.943438 | ||||||||
\(626\) | −63.1208 | −2.52282 | ||||||||
\(627\) | −4.45630 | −0.177967 | ||||||||
\(628\) | 96.3847 | 3.84617 | ||||||||
\(629\) | 10.9443 | 0.436376 | ||||||||
\(630\) | −230.987 | −9.20275 | ||||||||
\(631\) | 41.3771 | 1.64720 | 0.823598 | − | 0.567173i | \(-0.191963\pi\) | ||||
0.823598 | + | 0.567173i | \(0.191963\pi\) | |||||||
\(632\) | −50.7695 | −2.01950 | ||||||||
\(633\) | 3.92619 | 0.156052 | ||||||||
\(634\) | −47.2177 | −1.87526 | ||||||||
\(635\) | −70.4727 | −2.79663 | ||||||||
\(636\) | 81.0291 | 3.21301 | ||||||||
\(637\) | 0.696280 | 0.0275876 | ||||||||
\(638\) | −26.5865 | −1.05257 | ||||||||
\(639\) | 10.5118 | 0.415842 | ||||||||
\(640\) | 34.0130 | 1.34448 | ||||||||
\(641\) | 21.9811 | 0.868203 | 0.434101 | − | 0.900864i | \(-0.357066\pi\) | ||||
0.434101 | + | 0.900864i | \(0.357066\pi\) | |||||||
\(642\) | −71.7479 | −2.83166 | ||||||||
\(643\) | −1.54304 | −0.0608517 | −0.0304258 | − | 0.999537i | \(-0.509686\pi\) | ||||
−0.0304258 | + | 0.999537i | \(0.509686\pi\) | |||||||
\(644\) | −37.0785 | −1.46110 | ||||||||
\(645\) | −13.1568 | −0.518050 | ||||||||
\(646\) | 3.35500 | 0.132001 | ||||||||
\(647\) | 26.3907 | 1.03753 | 0.518763 | − | 0.854918i | \(-0.326393\pi\) | ||||
0.518763 | + | 0.854918i | \(0.326393\pi\) | |||||||
\(648\) | −260.775 | −10.2442 | ||||||||
\(649\) | 3.01490 | 0.118345 | ||||||||
\(650\) | −53.7361 | −2.10770 | ||||||||
\(651\) | 63.2821 | 2.48022 | ||||||||
\(652\) | −68.6261 | −2.68761 | ||||||||
\(653\) | 2.11721 | 0.0828529 | 0.0414265 | − | 0.999142i | \(-0.486810\pi\) | ||||
0.0414265 | + | 0.999142i | \(0.486810\pi\) | |||||||
\(654\) | −120.290 | −4.70373 | ||||||||
\(655\) | −63.9209 | −2.49760 | ||||||||
\(656\) | 18.3704 | 0.717244 | ||||||||
\(657\) | 6.51263 | 0.254082 | ||||||||
\(658\) | 25.1596 | 0.980822 | ||||||||
\(659\) | 37.8061 | 1.47272 | 0.736359 | − | 0.676591i | \(-0.236544\pi\) | ||||
0.736359 | + | 0.676591i | \(0.236544\pi\) | |||||||
\(660\) | 60.2942 | 2.34695 | ||||||||
\(661\) | −35.6988 | −1.38852 | −0.694261 | − | 0.719723i | \(-0.744269\pi\) | ||||
−0.694261 | + | 0.719723i | \(0.744269\pi\) | |||||||
\(662\) | 2.45231 | 0.0953119 | ||||||||
\(663\) | −7.20587 | −0.279853 | ||||||||
\(664\) | 0.0572300 | 0.00222096 | ||||||||
\(665\) | −13.6675 | −0.530003 | ||||||||
\(666\) | −241.866 | −9.37212 | ||||||||
\(667\) | 30.9689 | 1.19912 | ||||||||
\(668\) | 2.01787 | 0.0780738 | ||||||||
\(669\) | −86.8808 | −3.35901 | ||||||||
\(670\) | −79.9443 | −3.08852 | ||||||||
\(671\) | 0.942345 | 0.0363788 | ||||||||
\(672\) | 63.2130 | 2.43850 | ||||||||
\(673\) | 4.92558 | 0.189867 | 0.0949336 | − | 0.995484i | \(-0.469736\pi\) | ||||
0.0949336 | + | 0.995484i | \(0.469736\pi\) | |||||||
\(674\) | 25.5101 | 0.982614 | ||||||||
\(675\) | −189.491 | −7.29349 | ||||||||
\(676\) | −39.0860 | −1.50331 | ||||||||
\(677\) | −5.70818 | −0.219383 | −0.109692 | − | 0.993966i | \(-0.534986\pi\) | ||||
−0.109692 | + | 0.993966i | \(0.534986\pi\) | |||||||
\(678\) | −12.3879 | −0.475755 | ||||||||
\(679\) | −33.3299 | −1.27909 | ||||||||
\(680\) | −25.5829 | −0.981058 | ||||||||
\(681\) | −64.9207 | −2.48777 | ||||||||
\(682\) | −17.5982 | −0.673871 | ||||||||
\(683\) | −0.00484862 | −0.000185527 0 | −9.27636e−5 | − | 1.00000i | \(-0.500030\pi\) | ||||
−9.27636e−5 | 1.00000i | \(0.500030\pi\) | ||||||||
\(684\) | −51.6179 | −1.97366 | ||||||||
\(685\) | −8.17061 | −0.312183 | ||||||||
\(686\) | 46.3346 | 1.76907 | ||||||||
\(687\) | 35.8208 | 1.36665 | ||||||||
\(688\) | 7.83593 | 0.298742 | ||||||||
\(689\) | −10.9707 | −0.417952 | ||||||||
\(690\) | −100.884 | −3.84059 | ||||||||
\(691\) | 27.5741 | 1.04897 | 0.524485 | − | 0.851420i | \(-0.324258\pi\) | ||||
0.524485 | + | 0.851420i | \(0.324258\pi\) | |||||||
\(692\) | 49.6307 | 1.88668 | ||||||||
\(693\) | −23.3194 | −0.885830 | ||||||||
\(694\) | 5.76071 | 0.218674 | ||||||||
\(695\) | 1.39335 | 0.0528528 | ||||||||
\(696\) | −234.004 | −8.86991 | ||||||||
\(697\) | 2.34438 | 0.0887997 | ||||||||
\(698\) | 6.45418 | 0.244294 | ||||||||
\(699\) | 60.0522 | 2.27138 | ||||||||
\(700\) | 122.890 | 4.64479 | ||||||||
\(701\) | −17.1734 | −0.648630 | −0.324315 | − | 0.945949i | \(-0.605134\pi\) | ||||
−0.324315 | + | 0.945949i | \(0.605134\pi\) | |||||||
\(702\) | 103.785 | 3.91710 | ||||||||
\(703\) | −14.3112 | −0.539757 | ||||||||
\(704\) | −1.90716 | −0.0718789 | ||||||||
\(705\) | 47.6564 | 1.79484 | ||||||||
\(706\) | −50.5670 | −1.90311 | ||||||||
\(707\) | −25.8367 | −0.971688 | ||||||||
\(708\) | 47.0847 | 1.76955 | ||||||||
\(709\) | −44.5725 | −1.67396 | −0.836978 | − | 0.547237i | \(-0.815680\pi\) | ||||
−0.836978 | + | 0.547237i | \(0.815680\pi\) | |||||||
\(710\) | −12.0883 | −0.453664 | ||||||||
\(711\) | 65.9944 | 2.47498 | ||||||||
\(712\) | 0.937330 | 0.0351279 | ||||||||
\(713\) | 20.4990 | 0.767694 | ||||||||
\(714\) | 23.6711 | 0.885867 | ||||||||
\(715\) | −8.16339 | −0.305294 | ||||||||
\(716\) | 73.6691 | 2.75314 | ||||||||
\(717\) | 21.1017 | 0.788059 | ||||||||
\(718\) | 92.1420 | 3.43871 | ||||||||
\(719\) | 16.7672 | 0.625310 | 0.312655 | − | 0.949867i | \(-0.398782\pi\) | ||||
0.312655 | + | 0.949867i | \(0.398782\pi\) | |||||||
\(720\) | 260.582 | 9.71132 | ||||||||
\(721\) | −46.3074 | −1.72458 | ||||||||
\(722\) | 44.3608 | 1.65094 | ||||||||
\(723\) | −30.7296 | −1.14284 | ||||||||
\(724\) | 85.5874 | 3.18083 | ||||||||
\(725\) | −102.641 | −3.81197 | ||||||||
\(726\) | 8.74353 | 0.324503 | ||||||||
\(727\) | −22.9888 | −0.852609 | −0.426304 | − | 0.904580i | \(-0.640185\pi\) | ||||
−0.426304 | + | 0.904580i | \(0.640185\pi\) | |||||||
\(728\) | −37.9328 | −1.40588 | ||||||||
\(729\) | 143.394 | 5.31089 | ||||||||
\(730\) | −7.48930 | −0.277192 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 14.7170 | 0.543954 | ||||||||
\(733\) | −5.52678 | −0.204136 | −0.102068 | − | 0.994777i | \(-0.532546\pi\) | ||||
−0.102068 | + | 0.994777i | \(0.532546\pi\) | |||||||
\(734\) | −15.5545 | −0.574126 | ||||||||
\(735\) | −4.33245 | −0.159805 | ||||||||
\(736\) | 20.4767 | 0.754780 | ||||||||
\(737\) | −8.07080 | −0.297292 | ||||||||
\(738\) | −51.8104 | −1.90717 | ||||||||
\(739\) | 8.55475 | 0.314692 | 0.157346 | − | 0.987544i | \(-0.449706\pi\) | ||||
0.157346 | + | 0.987544i | \(0.449706\pi\) | |||||||
\(740\) | 193.632 | 7.11807 | ||||||||
\(741\) | 9.42273 | 0.346153 | ||||||||
\(742\) | 36.0385 | 1.32302 | ||||||||
\(743\) | −14.7440 | −0.540904 | −0.270452 | − | 0.962734i | \(-0.587173\pi\) | ||||
−0.270452 | + | 0.962734i | \(0.587173\pi\) | |||||||
\(744\) | −154.893 | −5.67864 | ||||||||
\(745\) | −83.1839 | −3.04762 | ||||||||
\(746\) | −34.4824 | −1.26249 | ||||||||
\(747\) | −0.0743924 | −0.00272187 | ||||||||
\(748\) | −4.58273 | −0.167561 | ||||||||
\(749\) | −22.2154 | −0.811732 | ||||||||
\(750\) | 165.579 | 6.04609 | ||||||||
\(751\) | −10.7666 | −0.392879 | −0.196440 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196440 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(752\) | −28.3831 | −1.03502 | ||||||||
\(753\) | −18.8854 | −0.688222 | ||||||||
\(754\) | 56.2166 | 2.04729 | ||||||||
\(755\) | −61.8853 | −2.25224 | ||||||||
\(756\) | −237.346 | −8.63220 | ||||||||
\(757\) | −19.4914 | −0.708426 | −0.354213 | − | 0.935165i | \(-0.615251\pi\) | ||||
−0.354213 | + | 0.935165i | \(0.615251\pi\) | |||||||
\(758\) | −25.9670 | −0.943162 | ||||||||
\(759\) | −10.1848 | −0.369684 | ||||||||
\(760\) | 33.4533 | 1.21348 | ||||||||
\(761\) | −31.5916 | −1.14519 | −0.572597 | − | 0.819837i | \(-0.694064\pi\) | ||||
−0.572597 | + | 0.819837i | \(0.694064\pi\) | |||||||
\(762\) | −159.603 | −5.78179 | ||||||||
\(763\) | −37.2456 | −1.34838 | ||||||||
\(764\) | 5.73105 | 0.207342 | ||||||||
\(765\) | 33.2548 | 1.20233 | ||||||||
\(766\) | 11.0853 | 0.400527 | ||||||||
\(767\) | −6.37493 | −0.230185 | ||||||||
\(768\) | 90.0295 | 3.24866 | ||||||||
\(769\) | 31.8259 | 1.14767 | 0.573835 | − | 0.818971i | \(-0.305455\pi\) | ||||
0.573835 | + | 0.818971i | \(0.305455\pi\) | |||||||
\(770\) | 26.8165 | 0.966399 | ||||||||
\(771\) | 96.8550 | 3.48815 | ||||||||
\(772\) | −29.3282 | −1.05554 | ||||||||
\(773\) | 53.1704 | 1.91241 | 0.956203 | − | 0.292705i | \(-0.0945554\pi\) | ||||
0.956203 | + | 0.292705i | \(0.0945554\pi\) | |||||||
\(774\) | −22.0998 | −0.794362 | ||||||||
\(775\) | −67.9401 | −2.44048 | ||||||||
\(776\) | 81.5802 | 2.92856 | ||||||||
\(777\) | −100.972 | −3.62235 | ||||||||
\(778\) | 18.0769 | 0.648090 | ||||||||
\(779\) | −3.06562 | −0.109837 | ||||||||
\(780\) | −127.491 | −4.56490 | ||||||||
\(781\) | −1.22037 | −0.0436684 | ||||||||
\(782\) | 7.66779 | 0.274200 | ||||||||
\(783\) | 198.238 | 7.08443 | ||||||||
\(784\) | 2.58031 | 0.0921539 | ||||||||
\(785\) | 81.1993 | 2.89813 | ||||||||
\(786\) | −144.764 | −5.16358 | ||||||||
\(787\) | −3.52470 | −0.125642 | −0.0628210 | − | 0.998025i | \(-0.520010\pi\) | ||||
−0.0628210 | + | 0.998025i | \(0.520010\pi\) | |||||||
\(788\) | 77.9402 | 2.77650 | ||||||||
\(789\) | −33.9784 | −1.20966 | ||||||||
\(790\) | −75.8913 | −2.70009 | ||||||||
\(791\) | −3.83568 | −0.136381 | ||||||||
\(792\) | 57.0778 | 2.02817 | ||||||||
\(793\) | −1.99257 | −0.0707581 | ||||||||
\(794\) | −37.7195 | −1.33862 | ||||||||
\(795\) | 68.2630 | 2.42104 | ||||||||
\(796\) | −27.7573 | −0.983830 | ||||||||
\(797\) | −0.945700 | −0.0334984 | −0.0167492 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167492 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(798\) | −30.9534 | −1.09574 | ||||||||
\(799\) | −3.62217 | −0.128143 | ||||||||
\(800\) | −67.8660 | −2.39942 | ||||||||
\(801\) | −1.21842 | −0.0430508 | ||||||||
\(802\) | −1.44707 | −0.0510979 | ||||||||
\(803\) | −0.756085 | −0.0266817 | ||||||||
\(804\) | −126.045 | −4.44525 | ||||||||
\(805\) | −31.2368 | −1.10095 | ||||||||
\(806\) | 37.2110 | 1.31070 | ||||||||
\(807\) | 109.663 | 3.86033 | ||||||||
\(808\) | 63.2393 | 2.22475 | ||||||||
\(809\) | 12.0201 | 0.422605 | 0.211303 | − | 0.977421i | \(-0.432229\pi\) | ||||
0.211303 | + | 0.977421i | \(0.432229\pi\) | |||||||
\(810\) | −389.813 | −13.6966 | ||||||||
\(811\) | 21.9589 | 0.771082 | 0.385541 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385541 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(812\) | −128.562 | −4.51165 | ||||||||
\(813\) | 37.1217 | 1.30191 | ||||||||
\(814\) | 28.0795 | 0.984185 | ||||||||
\(815\) | −57.8140 | −2.02514 | ||||||||
\(816\) | −26.7039 | −0.934823 | ||||||||
\(817\) | −1.30765 | −0.0457487 | ||||||||
\(818\) | 63.6433 | 2.22524 | ||||||||
\(819\) | 49.3083 | 1.72297 | ||||||||
\(820\) | 41.4782 | 1.44848 | ||||||||
\(821\) | −11.8731 | −0.414376 | −0.207188 | − | 0.978301i | \(-0.566431\pi\) | ||||
−0.207188 | + | 0.978301i | \(0.566431\pi\) | |||||||
\(822\) | −18.5043 | −0.645413 | ||||||||
\(823\) | −6.29351 | −0.219378 | −0.109689 | − | 0.993966i | \(-0.534986\pi\) | ||||
−0.109689 | + | 0.993966i | \(0.534986\pi\) | |||||||
\(824\) | 113.345 | 3.94855 | ||||||||
\(825\) | 33.7555 | 1.17521 | ||||||||
\(826\) | 20.9414 | 0.728646 | ||||||||
\(827\) | −29.2252 | −1.01626 | −0.508131 | − | 0.861280i | \(-0.669663\pi\) | ||||
−0.508131 | + | 0.861280i | \(0.669663\pi\) | |||||||
\(828\) | −117.972 | −4.09979 | ||||||||
\(829\) | −1.43924 | −0.0499869 | −0.0249935 | − | 0.999688i | \(-0.507956\pi\) | ||||
−0.0249935 | + | 0.999688i | \(0.507956\pi\) | |||||||
\(830\) | 0.0855487 | 0.00296944 | ||||||||
\(831\) | −13.5671 | −0.470637 | ||||||||
\(832\) | 4.03265 | 0.139807 | ||||||||
\(833\) | 0.329292 | 0.0114093 | ||||||||
\(834\) | 3.15558 | 0.109269 | ||||||||
\(835\) | 1.69996 | 0.0588294 | ||||||||
\(836\) | 5.99258 | 0.207258 | ||||||||
\(837\) | 131.218 | 4.53555 | ||||||||
\(838\) | 75.1256 | 2.59517 | ||||||||
\(839\) | 10.1147 | 0.349199 | 0.174600 | − | 0.984639i | \(-0.444137\pi\) | ||||
0.174600 | + | 0.984639i | \(0.444137\pi\) | |||||||
\(840\) | 236.028 | 8.14375 | ||||||||
\(841\) | 78.3786 | 2.70271 | ||||||||
\(842\) | −41.6347 | −1.43483 | ||||||||
\(843\) | 67.5756 | 2.32743 | ||||||||
\(844\) | −5.27972 | −0.181736 | ||||||||
\(845\) | −32.9280 | −1.13276 | ||||||||
\(846\) | 80.0494 | 2.75215 | ||||||||
\(847\) | 2.70727 | 0.0930228 | ||||||||
\(848\) | −40.6559 | −1.39613 | ||||||||
\(849\) | −59.6146 | −2.04597 | ||||||||
\(850\) | −25.4134 | −0.871673 | ||||||||
\(851\) | −32.7080 | −1.12121 | ||||||||
\(852\) | −19.0590 | −0.652951 | ||||||||
\(853\) | 20.9007 | 0.715625 | 0.357812 | − | 0.933793i | \(-0.383523\pi\) | ||||
0.357812 | + | 0.933793i | \(0.383523\pi\) | |||||||
\(854\) | 6.54552 | 0.223983 | ||||||||
\(855\) | −43.4855 | −1.48717 | ||||||||
\(856\) | 54.3756 | 1.85852 | ||||||||
\(857\) | −52.1008 | −1.77973 | −0.889864 | − | 0.456225i | \(-0.849201\pi\) | ||||
−0.889864 | + | 0.456225i | \(0.849201\pi\) | |||||||
\(858\) | −18.4880 | −0.631169 | ||||||||
\(859\) | −1.88418 | −0.0642873 | −0.0321436 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321436 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(860\) | 17.6926 | 0.603313 | ||||||||
\(861\) | −21.6293 | −0.737126 | ||||||||
\(862\) | −20.0920 | −0.684338 | ||||||||
\(863\) | −22.6315 | −0.770385 | −0.385193 | − | 0.922836i | \(-0.625865\pi\) | ||||
−0.385193 | + | 0.922836i | \(0.625865\pi\) | |||||||
\(864\) | 131.075 | 4.45925 | ||||||||
\(865\) | 41.8114 | 1.42163 | ||||||||
\(866\) | 73.3164 | 2.49139 | ||||||||
\(867\) | −3.40788 | −0.115738 | ||||||||
\(868\) | −85.0983 | −2.88842 | ||||||||
\(869\) | −7.66163 | −0.259903 | ||||||||
\(870\) | −349.795 | −11.8592 | ||||||||
\(871\) | 17.0655 | 0.578243 | ||||||||
\(872\) | 91.1644 | 3.08722 | ||||||||
\(873\) | −106.045 | −3.58907 | ||||||||
\(874\) | −10.0268 | −0.339160 | ||||||||
\(875\) | 51.2684 | 1.73319 | ||||||||
\(876\) | −11.8081 | −0.398957 | ||||||||
\(877\) | 11.3175 | 0.382165 | 0.191083 | − | 0.981574i | \(-0.438800\pi\) | ||||
0.191083 | + | 0.981574i | \(0.438800\pi\) | |||||||
\(878\) | 51.8540 | 1.74999 | ||||||||
\(879\) | 55.0541 | 1.85693 | ||||||||
\(880\) | −30.2523 | −1.01981 | ||||||||
\(881\) | 50.7352 | 1.70931 | 0.854656 | − | 0.519194i | \(-0.173768\pi\) | ||||
0.854656 | + | 0.519194i | \(0.173768\pi\) | |||||||
\(882\) | −7.27730 | −0.245039 | ||||||||
\(883\) | 4.87912 | 0.164195 | 0.0820977 | − | 0.996624i | \(-0.473838\pi\) | ||||
0.0820977 | + | 0.996624i | \(0.473838\pi\) | |||||||
\(884\) | 9.69007 | 0.325912 | ||||||||
\(885\) | 39.6665 | 1.33338 | ||||||||
\(886\) | 87.5555 | 2.94148 | ||||||||
\(887\) | −35.6547 | −1.19717 | −0.598584 | − | 0.801060i | \(-0.704270\pi\) | ||||
−0.598584 | + | 0.801060i | \(0.704270\pi\) | |||||||
\(888\) | 247.145 | 8.29363 | ||||||||
\(889\) | −49.4179 | −1.65742 | ||||||||
\(890\) | 1.40114 | 0.0469664 | ||||||||
\(891\) | −39.3537 | −1.31840 | ||||||||
\(892\) | 116.833 | 3.91184 | ||||||||
\(893\) | 4.73652 | 0.158502 | ||||||||
\(894\) | −188.390 | −6.30071 | ||||||||
\(895\) | 62.0625 | 2.07452 | ||||||||
\(896\) | 23.8511 | 0.796809 | ||||||||
\(897\) | 21.5355 | 0.719048 | ||||||||
\(898\) | 90.7009 | 3.02673 | ||||||||
\(899\) | 71.0763 | 2.37053 | ||||||||
\(900\) | 390.994 | 13.0331 | ||||||||
\(901\) | −5.18840 | −0.172851 | ||||||||
\(902\) | 6.01494 | 0.200275 | ||||||||
\(903\) | −9.22603 | −0.307023 | ||||||||
\(904\) | 9.38842 | 0.312254 | ||||||||
\(905\) | 72.1030 | 2.39679 | ||||||||
\(906\) | −140.154 | −4.65632 | ||||||||
\(907\) | 36.0153 | 1.19587 | 0.597934 | − | 0.801546i | \(-0.295989\pi\) | ||||
0.597934 | + | 0.801546i | \(0.295989\pi\) | |||||||
\(908\) | 87.3018 | 2.89721 | ||||||||
\(909\) | −82.2037 | −2.72652 | ||||||||
\(910\) | −56.7028 | −1.87968 | ||||||||
\(911\) | 13.9844 | 0.463322 | 0.231661 | − | 0.972797i | \(-0.425584\pi\) | ||||
0.231661 | + | 0.972797i | \(0.425584\pi\) | |||||||
\(912\) | 34.9192 | 1.15629 | ||||||||
\(913\) | 0.00863659 | 0.000285830 0 | ||||||||
\(914\) | −70.9462 | −2.34669 | ||||||||
\(915\) | 12.3983 | 0.409875 | ||||||||
\(916\) | −48.1698 | −1.59158 | ||||||||
\(917\) | −44.8235 | −1.48020 | ||||||||
\(918\) | 49.0829 | 1.61998 | ||||||||
\(919\) | −32.3409 | −1.06683 | −0.533413 | − | 0.845855i | \(-0.679091\pi\) | ||||
−0.533413 | + | 0.845855i | \(0.679091\pi\) | |||||||
\(920\) | 76.4569 | 2.52071 | ||||||||
\(921\) | 92.1999 | 3.03809 | ||||||||
\(922\) | −55.6965 | −1.83426 | ||||||||
\(923\) | 2.58045 | 0.0849366 | ||||||||
\(924\) | 42.2804 | 1.39092 | ||||||||
\(925\) | 108.404 | 3.56431 | ||||||||
\(926\) | −43.1930 | −1.41941 | ||||||||
\(927\) | −147.335 | −4.83911 | ||||||||
\(928\) | 70.9987 | 2.33065 | ||||||||
\(929\) | −21.1655 | −0.694416 | −0.347208 | − | 0.937788i | \(-0.612870\pi\) | ||||
−0.347208 | + | 0.937788i | \(0.612870\pi\) | |||||||
\(930\) | −231.537 | −7.59240 | ||||||||
\(931\) | −0.430597 | −0.0141123 | ||||||||
\(932\) | −80.7550 | −2.64522 | ||||||||
\(933\) | −4.49176 | −0.147054 | ||||||||
\(934\) | 49.7710 | 1.62856 | ||||||||
\(935\) | −3.86072 | −0.126259 | ||||||||
\(936\) | −120.690 | −3.94487 | ||||||||
\(937\) | −7.21528 | −0.235713 | −0.117856 | − | 0.993031i | \(-0.537602\pi\) | ||||
−0.117856 | + | 0.993031i | \(0.537602\pi\) | |||||||
\(938\) | −56.0597 | −1.83041 | ||||||||
\(939\) | −83.8405 | −2.73603 | ||||||||
\(940\) | −64.0857 | −2.09024 | ||||||||
\(941\) | 20.6129 | 0.671962 | 0.335981 | − | 0.941869i | \(-0.390932\pi\) | ||||
0.335981 | + | 0.941869i | \(0.390932\pi\) | |||||||
\(942\) | 183.895 | 5.99164 | ||||||||
\(943\) | −7.00641 | −0.228160 | ||||||||
\(944\) | −23.6245 | −0.768913 | ||||||||
\(945\) | −199.952 | −6.50445 | ||||||||
\(946\) | 2.56568 | 0.0834175 | ||||||||
\(947\) | −58.1824 | −1.89067 | −0.945337 | − | 0.326095i | \(-0.894267\pi\) | ||||
−0.945337 | + | 0.326095i | \(0.894267\pi\) | |||||||
\(948\) | −119.655 | −3.88620 | ||||||||
\(949\) | 1.59872 | 0.0518968 | ||||||||
\(950\) | 33.2318 | 1.07818 | ||||||||
\(951\) | −62.7171 | −2.03374 | ||||||||
\(952\) | −17.9396 | −0.581425 | ||||||||
\(953\) | 43.2160 | 1.39990 | 0.699952 | − | 0.714190i | \(-0.253205\pi\) | ||||
0.699952 | + | 0.714190i | \(0.253205\pi\) | |||||||
\(954\) | 114.663 | 3.71234 | ||||||||
\(955\) | 4.82812 | 0.156234 | ||||||||
\(956\) | −28.3765 | −0.917760 | ||||||||
\(957\) | −35.3137 | −1.14153 | ||||||||
\(958\) | 81.6643 | 2.63845 | ||||||||
\(959\) | −5.72951 | −0.185016 | ||||||||
\(960\) | −25.0922 | −0.809848 | ||||||||
\(961\) | 16.0470 | 0.517644 | ||||||||
\(962\) | −59.3734 | −1.91427 | ||||||||
\(963\) | −70.6819 | −2.27769 | ||||||||
\(964\) | 41.3234 | 1.33094 | ||||||||
\(965\) | −24.7075 | −0.795363 | ||||||||
\(966\) | −70.7433 | −2.27613 | ||||||||
\(967\) | −49.2721 | −1.58448 | −0.792242 | − | 0.610208i | \(-0.791086\pi\) | ||||
−0.792242 | + | 0.610208i | \(0.791086\pi\) | |||||||
\(968\) | −6.62646 | −0.212982 | ||||||||
\(969\) | 4.45630 | 0.143157 | ||||||||
\(970\) | 121.948 | 3.91551 | ||||||||
\(971\) | 59.4975 | 1.90937 | 0.954683 | − | 0.297624i | \(-0.0961943\pi\) | ||||
0.954683 | + | 0.297624i | \(0.0961943\pi\) | |||||||
\(972\) | −351.590 | −11.2773 | ||||||||
\(973\) | 0.977065 | 0.0313233 | ||||||||
\(974\) | −32.9727 | −1.05651 | ||||||||
\(975\) | −71.3751 | −2.28583 | ||||||||
\(976\) | −7.38415 | −0.236361 | ||||||||
\(977\) | 34.9544 | 1.11829 | 0.559145 | − | 0.829070i | \(-0.311129\pi\) | ||||
0.559145 | + | 0.829070i | \(0.311129\pi\) | |||||||
\(978\) | −130.934 | −4.18681 | ||||||||
\(979\) | 0.141453 | 0.00452085 | ||||||||
\(980\) | 5.82604 | 0.186106 | ||||||||
\(981\) | −118.503 | −3.78352 | ||||||||
\(982\) | 58.3065 | 1.86063 | ||||||||
\(983\) | −19.3716 | −0.617859 | −0.308929 | − | 0.951085i | \(-0.599971\pi\) | ||||
−0.308929 | + | 0.951085i | \(0.599971\pi\) | |||||||
\(984\) | 52.9412 | 1.68770 | ||||||||
\(985\) | 65.6607 | 2.09212 | ||||||||
\(986\) | 26.5865 | 0.846688 | ||||||||
\(987\) | 33.4183 | 1.06372 | ||||||||
\(988\) | −12.6712 | −0.403124 | ||||||||
\(989\) | −2.98860 | −0.0950318 | ||||||||
\(990\) | 85.3212 | 2.71168 | ||||||||
\(991\) | 9.99236 | 0.317418 | 0.158709 | − | 0.987325i | \(-0.449267\pi\) | ||||
0.158709 | + | 0.987325i | \(0.449267\pi\) | |||||||
\(992\) | 46.9956 | 1.49211 | ||||||||
\(993\) | 3.25729 | 0.103367 | ||||||||
\(994\) | −8.47670 | −0.268864 | ||||||||
\(995\) | −23.3841 | −0.741325 | ||||||||
\(996\) | 0.134881 | 0.00427386 | ||||||||
\(997\) | 20.6367 | 0.653571 | 0.326786 | − | 0.945098i | \(-0.394034\pi\) | ||||
0.326786 | + | 0.945098i | \(0.394034\pi\) | |||||||
\(998\) | −102.582 | −3.24716 | ||||||||
\(999\) | −209.369 | −6.62416 |
(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 | 8041.2.a.g.1.5 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.5 | ✓ | 69 | 1.1 | even | 1 | trivial |