Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97055 | −1.39339 | −0.696695 | − | 0.717367i | \(-0.745347\pi\) | ||||
−0.696695 | + | 0.717367i | \(0.745347\pi\) | |||||||
\(3\) | −1.02182 | −0.589948 | −0.294974 | − | 0.955505i | \(-0.595311\pi\) | ||||
−0.294974 | + | 0.955505i | \(0.595311\pi\) | |||||||
\(4\) | 1.88308 | 0.941538 | ||||||||
\(5\) | −1.99471 | −0.892061 | −0.446030 | − | 0.895018i | \(-0.647163\pi\) | ||||
−0.446030 | + | 0.895018i | \(0.647163\pi\) | |||||||
\(6\) | 2.01355 | 0.822029 | ||||||||
\(7\) | −4.59826 | −1.73798 | −0.868989 | − | 0.494832i | \(-0.835230\pi\) | ||||
−0.868989 | + | 0.494832i | \(0.835230\pi\) | |||||||
\(8\) | 0.230406 | 0.0814609 | ||||||||
\(9\) | −1.95588 | −0.651961 | ||||||||
\(10\) | 3.93068 | 1.24299 | ||||||||
\(11\) | 0.147869 | 0.0445843 | 0.0222922 | − | 0.999751i | \(-0.492904\pi\) | ||||
0.0222922 | + | 0.999751i | \(0.492904\pi\) | |||||||
\(12\) | −1.92416 | −0.555459 | ||||||||
\(13\) | −5.98055 | −1.65871 | −0.829353 | − | 0.558725i | \(-0.811291\pi\) | ||||
−0.829353 | + | 0.558725i | \(0.811291\pi\) | |||||||
\(14\) | 9.06110 | 2.42168 | ||||||||
\(15\) | 2.03823 | 0.526270 | ||||||||
\(16\) | −4.22018 | −1.05504 | ||||||||
\(17\) | 5.78675 | 1.40349 | 0.701746 | − | 0.712427i | \(-0.252404\pi\) | ||||
0.701746 | + | 0.712427i | \(0.252404\pi\) | |||||||
\(18\) | 3.85417 | 0.908436 | ||||||||
\(19\) | 4.95304 | 1.13631 | 0.568153 | − | 0.822923i | \(-0.307658\pi\) | ||||
0.568153 | + | 0.822923i | \(0.307658\pi\) | |||||||
\(20\) | −3.75619 | −0.839909 | ||||||||
\(21\) | 4.69859 | 1.02532 | ||||||||
\(22\) | −0.291384 | −0.0621234 | ||||||||
\(23\) | −4.12678 | −0.860493 | −0.430247 | − | 0.902711i | \(-0.641573\pi\) | ||||
−0.430247 | + | 0.902711i | \(0.641573\pi\) | |||||||
\(24\) | −0.235434 | −0.0480577 | ||||||||
\(25\) | −1.02114 | −0.204228 | ||||||||
\(26\) | 11.7850 | 2.31123 | ||||||||
\(27\) | 5.06402 | 0.974572 | ||||||||
\(28\) | −8.65886 | −1.63637 | ||||||||
\(29\) | −8.55493 | −1.58861 | −0.794306 | − | 0.607519i | \(-0.792165\pi\) | ||||
−0.794306 | + | 0.607519i | \(0.792165\pi\) | |||||||
\(30\) | −4.01645 | −0.733299 | ||||||||
\(31\) | −4.53282 | −0.814118 | −0.407059 | − | 0.913402i | \(-0.633446\pi\) | ||||
−0.407059 | + | 0.913402i | \(0.633446\pi\) | |||||||
\(32\) | 7.85527 | 1.38863 | ||||||||
\(33\) | −0.151096 | −0.0263024 | ||||||||
\(34\) | −11.4031 | −1.95561 | ||||||||
\(35\) | 9.17218 | 1.55038 | ||||||||
\(36\) | −3.68307 | −0.613846 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −9.76023 | −1.58332 | ||||||||
\(39\) | 6.11105 | 0.978551 | ||||||||
\(40\) | −0.459593 | −0.0726680 | ||||||||
\(41\) | 10.2013 | 1.59317 | 0.796587 | − | 0.604524i | \(-0.206637\pi\) | ||||
0.796587 | + | 0.604524i | \(0.206637\pi\) | |||||||
\(42\) | −9.25882 | −1.42867 | ||||||||
\(43\) | 7.52821 | 1.14804 | 0.574021 | − | 0.818841i | \(-0.305383\pi\) | ||||
0.574021 | + | 0.818841i | \(0.305383\pi\) | |||||||
\(44\) | 0.278449 | 0.0419778 | ||||||||
\(45\) | 3.90142 | 0.581589 | ||||||||
\(46\) | 8.13203 | 1.19900 | ||||||||
\(47\) | −3.29908 | −0.481221 | −0.240610 | − | 0.970622i | \(-0.577348\pi\) | ||||
−0.240610 | + | 0.970622i | \(0.577348\pi\) | |||||||
\(48\) | 4.31226 | 0.622422 | ||||||||
\(49\) | 14.1440 | 2.02057 | ||||||||
\(50\) | 2.01221 | 0.284569 | ||||||||
\(51\) | −5.91302 | −0.827988 | ||||||||
\(52\) | −11.2618 | −1.56173 | ||||||||
\(53\) | 8.58786 | 1.17963 | 0.589817 | − | 0.807537i | \(-0.299200\pi\) | ||||
0.589817 | + | 0.807537i | \(0.299200\pi\) | |||||||
\(54\) | −9.97892 | −1.35796 | ||||||||
\(55\) | −0.294956 | −0.0397719 | ||||||||
\(56\) | −1.05947 | −0.141577 | ||||||||
\(57\) | −5.06112 | −0.670362 | ||||||||
\(58\) | 16.8579 | 2.21356 | ||||||||
\(59\) | 2.91642 | 0.379686 | 0.189843 | − | 0.981814i | \(-0.439202\pi\) | ||||
0.189843 | + | 0.981814i | \(0.439202\pi\) | |||||||
\(60\) | 3.83815 | 0.495503 | ||||||||
\(61\) | 8.46825 | 1.08425 | 0.542124 | − | 0.840299i | \(-0.317620\pi\) | ||||
0.542124 | + | 0.840299i | \(0.317620\pi\) | |||||||
\(62\) | 8.93216 | 1.13438 | ||||||||
\(63\) | 8.99365 | 1.13309 | ||||||||
\(64\) | −7.03886 | −0.879857 | ||||||||
\(65\) | 11.9295 | 1.47967 | ||||||||
\(66\) | 0.297743 | 0.0366496 | ||||||||
\(67\) | −9.46516 | −1.15635 | −0.578177 | − | 0.815911i | \(-0.696236\pi\) | ||||
−0.578177 | + | 0.815911i | \(0.696236\pi\) | |||||||
\(68\) | 10.8969 | 1.32144 | ||||||||
\(69\) | 4.21683 | 0.507646 | ||||||||
\(70\) | −18.0743 | −2.16029 | ||||||||
\(71\) | 13.3751 | 1.58734 | 0.793668 | − | 0.608351i | \(-0.208169\pi\) | ||||
0.793668 | + | 0.608351i | \(0.208169\pi\) | |||||||
\(72\) | −0.450647 | −0.0531093 | ||||||||
\(73\) | −6.62409 | −0.775291 | −0.387646 | − | 0.921808i | \(-0.626712\pi\) | ||||
−0.387646 | + | 0.921808i | \(0.626712\pi\) | |||||||
\(74\) | 1.97055 | 0.229072 | ||||||||
\(75\) | 1.04342 | 0.120484 | ||||||||
\(76\) | 9.32695 | 1.06987 | ||||||||
\(77\) | −0.679942 | −0.0774866 | ||||||||
\(78\) | −12.0421 | −1.36350 | ||||||||
\(79\) | −9.72416 | −1.09405 | −0.547027 | − | 0.837115i | \(-0.684240\pi\) | ||||
−0.547027 | + | 0.837115i | \(0.684240\pi\) | |||||||
\(80\) | 8.41802 | 0.941164 | ||||||||
\(81\) | 0.693127 | 0.0770141 | ||||||||
\(82\) | −20.1022 | −2.21991 | ||||||||
\(83\) | −1.11380 | −0.122256 | −0.0611278 | − | 0.998130i | \(-0.519470\pi\) | ||||
−0.0611278 | + | 0.998130i | \(0.519470\pi\) | |||||||
\(84\) | 8.84780 | 0.965375 | ||||||||
\(85\) | −11.5429 | −1.25200 | ||||||||
\(86\) | −14.8347 | −1.59967 | ||||||||
\(87\) | 8.74160 | 0.937198 | ||||||||
\(88\) | 0.0340700 | 0.00363188 | ||||||||
\(89\) | 7.87689 | 0.834949 | 0.417474 | − | 0.908689i | \(-0.362915\pi\) | ||||
0.417474 | + | 0.908689i | \(0.362915\pi\) | |||||||
\(90\) | −7.68794 | −0.810380 | ||||||||
\(91\) | 27.5001 | 2.88279 | ||||||||
\(92\) | −7.77104 | −0.810187 | ||||||||
\(93\) | 4.63173 | 0.480288 | ||||||||
\(94\) | 6.50102 | 0.670529 | ||||||||
\(95\) | −9.87988 | −1.01365 | ||||||||
\(96\) | −8.02667 | −0.819219 | ||||||||
\(97\) | 17.5649 | 1.78345 | 0.891725 | − | 0.452577i | \(-0.149495\pi\) | ||||
0.891725 | + | 0.452577i | \(0.149495\pi\) | |||||||
\(98\) | −27.8714 | −2.81544 | ||||||||
\(99\) | −0.289215 | −0.0290672 | ||||||||
\(100\) | −1.92288 | −0.192288 | ||||||||
\(101\) | −12.7841 | −1.27207 | −0.636034 | − | 0.771661i | \(-0.719426\pi\) | ||||
−0.636034 | + | 0.771661i | \(0.719426\pi\) | |||||||
\(102\) | 11.6519 | 1.15371 | ||||||||
\(103\) | 1.20833 | 0.119060 | 0.0595302 | − | 0.998227i | \(-0.481040\pi\) | ||||
0.0595302 | + | 0.998227i | \(0.481040\pi\) | |||||||
\(104\) | −1.37796 | −0.135120 | ||||||||
\(105\) | −9.37232 | −0.914645 | ||||||||
\(106\) | −16.9228 | −1.64369 | ||||||||
\(107\) | −9.61471 | −0.929490 | −0.464745 | − | 0.885445i | \(-0.653854\pi\) | ||||
−0.464745 | + | 0.885445i | \(0.653854\pi\) | |||||||
\(108\) | 9.53594 | 0.917596 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 0.581227 | 0.0554178 | ||||||||
\(111\) | 1.02182 | 0.0969869 | ||||||||
\(112\) | 19.4055 | 1.83364 | ||||||||
\(113\) | −9.29285 | −0.874197 | −0.437099 | − | 0.899414i | \(-0.643994\pi\) | ||||
−0.437099 | + | 0.899414i | \(0.643994\pi\) | |||||||
\(114\) | 9.97320 | 0.934076 | ||||||||
\(115\) | 8.23172 | 0.767612 | ||||||||
\(116\) | −16.1096 | −1.49574 | ||||||||
\(117\) | 11.6973 | 1.08141 | ||||||||
\(118\) | −5.74697 | −0.529051 | ||||||||
\(119\) | −26.6090 | −2.43924 | ||||||||
\(120\) | 0.469622 | 0.0428704 | ||||||||
\(121\) | −10.9781 | −0.998012 | ||||||||
\(122\) | −16.6871 | −1.51078 | ||||||||
\(123\) | −10.4239 | −0.939890 | ||||||||
\(124\) | −8.53564 | −0.766523 | ||||||||
\(125\) | 12.0104 | 1.07424 | ||||||||
\(126\) | −17.7225 | −1.57884 | ||||||||
\(127\) | 18.8334 | 1.67119 | 0.835596 | − | 0.549345i | \(-0.185123\pi\) | ||||
0.835596 | + | 0.549345i | \(0.185123\pi\) | |||||||
\(128\) | −1.84010 | −0.162643 | ||||||||
\(129\) | −7.69248 | −0.677285 | ||||||||
\(130\) | −23.5076 | −2.06175 | ||||||||
\(131\) | 21.7971 | 1.90442 | 0.952210 | − | 0.305444i | \(-0.0988049\pi\) | ||||
0.952210 | + | 0.305444i | \(0.0988049\pi\) | |||||||
\(132\) | −0.284525 | −0.0247647 | ||||||||
\(133\) | −22.7754 | −1.97487 | ||||||||
\(134\) | 18.6516 | 1.61125 | ||||||||
\(135\) | −10.1012 | −0.869377 | ||||||||
\(136\) | 1.33330 | 0.114330 | ||||||||
\(137\) | −8.60123 | −0.734853 | −0.367426 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367426 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(138\) | −8.30948 | −0.707350 | ||||||||
\(139\) | 17.0727 | 1.44808 | 0.724042 | − | 0.689756i | \(-0.242282\pi\) | ||||
0.724042 | + | 0.689756i | \(0.242282\pi\) | |||||||
\(140\) | 17.2719 | 1.45974 | ||||||||
\(141\) | 3.37107 | 0.283896 | ||||||||
\(142\) | −26.3564 | −2.21178 | ||||||||
\(143\) | −0.884341 | −0.0739523 | ||||||||
\(144\) | 8.25417 | 0.687848 | ||||||||
\(145\) | 17.0646 | 1.41714 | ||||||||
\(146\) | 13.0531 | 1.08028 | ||||||||
\(147\) | −14.4526 | −1.19203 | ||||||||
\(148\) | −1.88308 | −0.154788 | ||||||||
\(149\) | 1.40424 | 0.115040 | 0.0575198 | − | 0.998344i | \(-0.481681\pi\) | ||||
0.0575198 | + | 0.998344i | \(0.481681\pi\) | |||||||
\(150\) | −2.05611 | −0.167881 | ||||||||
\(151\) | −6.12834 | −0.498717 | −0.249359 | − | 0.968411i | \(-0.580220\pi\) | ||||
−0.249359 | + | 0.968411i | \(0.580220\pi\) | |||||||
\(152\) | 1.14121 | 0.0925645 | ||||||||
\(153\) | −11.3182 | −0.915023 | ||||||||
\(154\) | 1.33986 | 0.107969 | ||||||||
\(155\) | 9.04165 | 0.726243 | ||||||||
\(156\) | 11.5076 | 0.921343 | ||||||||
\(157\) | −13.1395 | −1.04864 | −0.524322 | − | 0.851520i | \(-0.675681\pi\) | ||||
−0.524322 | + | 0.851520i | \(0.675681\pi\) | |||||||
\(158\) | 19.1620 | 1.52444 | ||||||||
\(159\) | −8.77526 | −0.695923 | ||||||||
\(160\) | −15.6690 | −1.23874 | ||||||||
\(161\) | 18.9760 | 1.49552 | ||||||||
\(162\) | −1.36584 | −0.107311 | ||||||||
\(163\) | −8.64246 | −0.676929 | −0.338465 | − | 0.940979i | \(-0.609908\pi\) | ||||
−0.338465 | + | 0.940979i | \(0.609908\pi\) | |||||||
\(164\) | 19.2098 | 1.50003 | ||||||||
\(165\) | 0.301393 | 0.0234634 | ||||||||
\(166\) | 2.19480 | 0.170350 | ||||||||
\(167\) | 6.36306 | 0.492388 | 0.246194 | − | 0.969221i | \(-0.420820\pi\) | ||||
0.246194 | + | 0.969221i | \(0.420820\pi\) | |||||||
\(168\) | 1.08258 | 0.0835232 | ||||||||
\(169\) | 22.7670 | 1.75131 | ||||||||
\(170\) | 22.7458 | 1.74453 | ||||||||
\(171\) | −9.68757 | −0.740827 | ||||||||
\(172\) | 14.1762 | 1.08092 | ||||||||
\(173\) | 16.9767 | 1.29071 | 0.645357 | − | 0.763881i | \(-0.276709\pi\) | ||||
0.645357 | + | 0.763881i | \(0.276709\pi\) | |||||||
\(174\) | −17.2258 | −1.30588 | ||||||||
\(175\) | 4.69545 | 0.354943 | ||||||||
\(176\) | −0.624035 | −0.0470384 | ||||||||
\(177\) | −2.98006 | −0.223995 | ||||||||
\(178\) | −15.5218 | −1.16341 | ||||||||
\(179\) | −1.68099 | −0.125643 | −0.0628216 | − | 0.998025i | \(-0.520010\pi\) | ||||
−0.0628216 | + | 0.998025i | \(0.520010\pi\) | |||||||
\(180\) | 7.34666 | 0.547588 | ||||||||
\(181\) | 17.1230 | 1.27274 | 0.636371 | − | 0.771383i | \(-0.280435\pi\) | ||||
0.636371 | + | 0.771383i | \(0.280435\pi\) | |||||||
\(182\) | −54.1904 | −4.01686 | ||||||||
\(183\) | −8.65303 | −0.639650 | ||||||||
\(184\) | −0.950835 | −0.0700965 | ||||||||
\(185\) | 1.99471 | 0.146654 | ||||||||
\(186\) | −9.12706 | −0.669228 | ||||||||
\(187\) | 0.855684 | 0.0625738 | ||||||||
\(188\) | −6.21243 | −0.453088 | ||||||||
\(189\) | −23.2857 | −1.69378 | ||||||||
\(190\) | 19.4688 | 1.41242 | ||||||||
\(191\) | −8.62110 | −0.623801 | −0.311901 | − | 0.950115i | \(-0.600966\pi\) | ||||
−0.311901 | + | 0.950115i | \(0.600966\pi\) | |||||||
\(192\) | 7.19245 | 0.519070 | ||||||||
\(193\) | −9.64784 | −0.694467 | −0.347233 | − | 0.937779i | \(-0.612879\pi\) | ||||
−0.347233 | + | 0.937779i | \(0.612879\pi\) | |||||||
\(194\) | −34.6126 | −2.48504 | ||||||||
\(195\) | −12.1898 | −0.872927 | ||||||||
\(196\) | 26.6342 | 1.90244 | ||||||||
\(197\) | −21.0894 | −1.50256 | −0.751280 | − | 0.659984i | \(-0.770563\pi\) | ||||
−0.751280 | + | 0.659984i | \(0.770563\pi\) | |||||||
\(198\) | 0.569914 | 0.0405020 | ||||||||
\(199\) | 14.6718 | 1.04006 | 0.520029 | − | 0.854148i | \(-0.325921\pi\) | ||||
0.520029 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(200\) | −0.235276 | −0.0166366 | ||||||||
\(201\) | 9.67170 | 0.682189 | ||||||||
\(202\) | 25.1918 | 1.77249 | ||||||||
\(203\) | 39.3378 | 2.76097 | ||||||||
\(204\) | −11.1347 | −0.779582 | ||||||||
\(205\) | −20.3486 | −1.42121 | ||||||||
\(206\) | −2.38108 | −0.165898 | ||||||||
\(207\) | 8.07150 | 0.561008 | ||||||||
\(208\) | 25.2390 | 1.75001 | ||||||||
\(209\) | 0.732404 | 0.0506614 | ||||||||
\(210\) | 18.4687 | 1.27446 | ||||||||
\(211\) | −12.2705 | −0.844736 | −0.422368 | − | 0.906425i | \(-0.638801\pi\) | ||||
−0.422368 | + | 0.906425i | \(0.638801\pi\) | |||||||
\(212\) | 16.1716 | 1.11067 | ||||||||
\(213\) | −13.6670 | −0.936447 | ||||||||
\(214\) | 18.9463 | 1.29514 | ||||||||
\(215\) | −15.0166 | −1.02412 | ||||||||
\(216\) | 1.16678 | 0.0793894 | ||||||||
\(217\) | 20.8431 | 1.41492 | ||||||||
\(218\) | 1.97055 | 0.133463 | ||||||||
\(219\) | 6.76863 | 0.457382 | ||||||||
\(220\) | −0.555425 | −0.0374468 | ||||||||
\(221\) | −34.6079 | −2.32798 | ||||||||
\(222\) | −2.01355 | −0.135141 | ||||||||
\(223\) | 8.42206 | 0.563983 | 0.281991 | − | 0.959417i | \(-0.409005\pi\) | ||||
0.281991 | + | 0.959417i | \(0.409005\pi\) | |||||||
\(224\) | −36.1205 | −2.41340 | ||||||||
\(225\) | 1.99723 | 0.133148 | ||||||||
\(226\) | 18.3120 | 1.21810 | ||||||||
\(227\) | −10.0213 | −0.665139 | −0.332570 | − | 0.943079i | \(-0.607916\pi\) | ||||
−0.332570 | + | 0.943079i | \(0.607916\pi\) | |||||||
\(228\) | −9.53047 | −0.631171 | ||||||||
\(229\) | 20.0915 | 1.32768 | 0.663841 | − | 0.747874i | \(-0.268925\pi\) | ||||
0.663841 | + | 0.747874i | \(0.268925\pi\) | |||||||
\(230\) | −16.2210 | −1.06958 | ||||||||
\(231\) | 0.694778 | 0.0457131 | ||||||||
\(232\) | −1.97111 | −0.129410 | ||||||||
\(233\) | −1.77267 | −0.116132 | −0.0580659 | − | 0.998313i | \(-0.518493\pi\) | ||||
−0.0580659 | + | 0.998313i | \(0.518493\pi\) | |||||||
\(234\) | −23.0501 | −1.50683 | ||||||||
\(235\) | 6.58071 | 0.429278 | ||||||||
\(236\) | 5.49185 | 0.357489 | ||||||||
\(237\) | 9.93635 | 0.645435 | ||||||||
\(238\) | 52.4343 | 3.39881 | ||||||||
\(239\) | 8.81715 | 0.570334 | 0.285167 | − | 0.958478i | \(-0.407951\pi\) | ||||
0.285167 | + | 0.958478i | \(0.407951\pi\) | |||||||
\(240\) | −8.60171 | −0.555238 | ||||||||
\(241\) | 6.64155 | 0.427820 | 0.213910 | − | 0.976853i | \(-0.431380\pi\) | ||||
0.213910 | + | 0.976853i | \(0.431380\pi\) | |||||||
\(242\) | 21.6330 | 1.39062 | ||||||||
\(243\) | −15.9003 | −1.02001 | ||||||||
\(244\) | 15.9463 | 1.02086 | ||||||||
\(245\) | −28.2131 | −1.80247 | ||||||||
\(246\) | 20.5408 | 1.30963 | ||||||||
\(247\) | −29.6219 | −1.88480 | ||||||||
\(248\) | −1.04439 | −0.0663188 | ||||||||
\(249\) | 1.13810 | 0.0721244 | ||||||||
\(250\) | −23.6671 | −1.49684 | ||||||||
\(251\) | 11.8620 | 0.748720 | 0.374360 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374360 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(252\) | 16.9357 | 1.06685 | ||||||||
\(253\) | −0.610225 | −0.0383645 | ||||||||
\(254\) | −37.1121 | −2.32862 | ||||||||
\(255\) | 11.7947 | 0.738616 | ||||||||
\(256\) | 17.7037 | 1.10648 | ||||||||
\(257\) | −18.7509 | −1.16965 | −0.584824 | − | 0.811160i | \(-0.698837\pi\) | ||||
−0.584824 | + | 0.811160i | \(0.698837\pi\) | |||||||
\(258\) | 15.1584 | 0.943723 | ||||||||
\(259\) | 4.59826 | 0.285722 | ||||||||
\(260\) | 22.4641 | 1.39316 | ||||||||
\(261\) | 16.7324 | 1.03571 | ||||||||
\(262\) | −42.9523 | −2.65360 | ||||||||
\(263\) | −12.7417 | −0.785685 | −0.392842 | − | 0.919606i | \(-0.628508\pi\) | ||||
−0.392842 | + | 0.919606i | \(0.628508\pi\) | |||||||
\(264\) | −0.0348134 | −0.00214262 | ||||||||
\(265\) | −17.1303 | −1.05231 | ||||||||
\(266\) | 44.8800 | 2.75177 | ||||||||
\(267\) | −8.04877 | −0.492577 | ||||||||
\(268\) | −17.8236 | −1.08875 | ||||||||
\(269\) | −20.3942 | −1.24345 | −0.621727 | − | 0.783234i | \(-0.713569\pi\) | ||||
−0.621727 | + | 0.783234i | \(0.713569\pi\) | |||||||
\(270\) | 19.9050 | 1.21138 | ||||||||
\(271\) | −15.1779 | −0.921992 | −0.460996 | − | 0.887402i | \(-0.652508\pi\) | ||||
−0.460996 | + | 0.887402i | \(0.652508\pi\) | |||||||
\(272\) | −24.4211 | −1.48075 | ||||||||
\(273\) | −28.1002 | −1.70070 | ||||||||
\(274\) | 16.9492 | 1.02394 | ||||||||
\(275\) | −0.150995 | −0.00910535 | ||||||||
\(276\) | 7.94061 | 0.477968 | ||||||||
\(277\) | 24.2305 | 1.45587 | 0.727935 | − | 0.685647i | \(-0.240480\pi\) | ||||
0.727935 | + | 0.685647i | \(0.240480\pi\) | |||||||
\(278\) | −33.6425 | −2.01775 | ||||||||
\(279\) | 8.86566 | 0.530773 | ||||||||
\(280\) | 2.11333 | 0.126295 | ||||||||
\(281\) | −2.17622 | −0.129822 | −0.0649111 | − | 0.997891i | \(-0.520676\pi\) | ||||
−0.0649111 | + | 0.997891i | \(0.520676\pi\) | |||||||
\(282\) | −6.64287 | −0.395577 | ||||||||
\(283\) | −7.25351 | −0.431177 | −0.215588 | − | 0.976484i | \(-0.569167\pi\) | ||||
−0.215588 | + | 0.976484i | \(0.569167\pi\) | |||||||
\(284\) | 25.1864 | 1.49454 | ||||||||
\(285\) | 10.0955 | 0.598003 | ||||||||
\(286\) | 1.74264 | 0.103044 | ||||||||
\(287\) | −46.9081 | −2.76890 | ||||||||
\(288\) | −15.3640 | −0.905331 | ||||||||
\(289\) | 16.4865 | 0.969792 | ||||||||
\(290\) | −33.6267 | −1.97463 | ||||||||
\(291\) | −17.9482 | −1.05214 | ||||||||
\(292\) | −12.4737 | −0.729966 | ||||||||
\(293\) | −15.6834 | −0.916234 | −0.458117 | − | 0.888892i | \(-0.651476\pi\) | ||||
−0.458117 | + | 0.888892i | \(0.651476\pi\) | |||||||
\(294\) | 28.4796 | 1.66096 | ||||||||
\(295\) | −5.81742 | −0.338703 | ||||||||
\(296\) | −0.230406 | −0.0133921 | ||||||||
\(297\) | 0.748814 | 0.0434506 | ||||||||
\(298\) | −2.76712 | −0.160295 | ||||||||
\(299\) | 24.6804 | 1.42731 | ||||||||
\(300\) | 1.96484 | 0.113440 | ||||||||
\(301\) | −34.6167 | −1.99527 | ||||||||
\(302\) | 12.0762 | 0.694908 | ||||||||
\(303\) | 13.0631 | 0.750455 | ||||||||
\(304\) | −20.9027 | −1.19885 | ||||||||
\(305\) | −16.8917 | −0.967215 | ||||||||
\(306\) | 22.3031 | 1.27498 | ||||||||
\(307\) | −5.37871 | −0.306979 | −0.153489 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153489 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(308\) | −1.28038 | −0.0729565 | ||||||||
\(309\) | −1.23470 | −0.0702394 | ||||||||
\(310\) | −17.8170 | −1.01194 | ||||||||
\(311\) | 6.01019 | 0.340807 | 0.170403 | − | 0.985374i | \(-0.445493\pi\) | ||||
0.170403 | + | 0.985374i | \(0.445493\pi\) | |||||||
\(312\) | 1.40802 | 0.0797136 | ||||||||
\(313\) | −0.833868 | −0.0471330 | −0.0235665 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235665 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(314\) | 25.8920 | 1.46117 | ||||||||
\(315\) | −17.9397 | −1.01079 | ||||||||
\(316\) | −18.3113 | −1.03009 | ||||||||
\(317\) | −2.80052 | −0.157293 | −0.0786465 | − | 0.996903i | \(-0.525060\pi\) | ||||
−0.0786465 | + | 0.996903i | \(0.525060\pi\) | |||||||
\(318\) | 17.2921 | 0.969693 | ||||||||
\(319\) | −1.26501 | −0.0708271 | ||||||||
\(320\) | 14.0405 | 0.784886 | ||||||||
\(321\) | 9.82451 | 0.548351 | ||||||||
\(322\) | −37.3932 | −2.08384 | ||||||||
\(323\) | 28.6620 | 1.59480 | ||||||||
\(324\) | 1.30521 | 0.0725117 | ||||||||
\(325\) | 6.10697 | 0.338754 | ||||||||
\(326\) | 17.0304 | 0.943227 | ||||||||
\(327\) | 1.02182 | 0.0565068 | ||||||||
\(328\) | 2.35044 | 0.129781 | ||||||||
\(329\) | 15.1700 | 0.836351 | ||||||||
\(330\) | −0.593910 | −0.0326937 | ||||||||
\(331\) | 13.2177 | 0.726513 | 0.363256 | − | 0.931689i | \(-0.381665\pi\) | ||||
0.363256 | + | 0.931689i | \(0.381665\pi\) | |||||||
\(332\) | −2.09737 | −0.115108 | ||||||||
\(333\) | 1.95588 | 0.107182 | ||||||||
\(334\) | −12.5387 | −0.686089 | ||||||||
\(335\) | 18.8802 | 1.03154 | ||||||||
\(336\) | −19.8289 | −1.08176 | ||||||||
\(337\) | −0.664361 | −0.0361900 | −0.0180950 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180950 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(338\) | −44.8635 | −2.44025 | ||||||||
\(339\) | 9.49562 | 0.515731 | ||||||||
\(340\) | −21.7361 | −1.17881 | ||||||||
\(341\) | −0.670266 | −0.0362969 | ||||||||
\(342\) | 19.0899 | 1.03226 | ||||||||
\(343\) | −32.8498 | −1.77372 | ||||||||
\(344\) | 1.73455 | 0.0935205 | ||||||||
\(345\) | −8.41134 | −0.452851 | ||||||||
\(346\) | −33.4535 | −1.79847 | ||||||||
\(347\) | −23.3057 | −1.25112 | −0.625558 | − | 0.780178i | \(-0.715129\pi\) | ||||
−0.625558 | + | 0.780178i | \(0.715129\pi\) | |||||||
\(348\) | 16.4611 | 0.882408 | ||||||||
\(349\) | −30.1020 | −1.61132 | −0.805662 | − | 0.592375i | \(-0.798190\pi\) | ||||
−0.805662 | + | 0.592375i | \(0.798190\pi\) | |||||||
\(350\) | −9.25264 | −0.494574 | ||||||||
\(351\) | −30.2856 | −1.61653 | ||||||||
\(352\) | 1.16155 | 0.0619111 | ||||||||
\(353\) | −30.6406 | −1.63083 | −0.815417 | − | 0.578874i | \(-0.803492\pi\) | ||||
−0.815417 | + | 0.578874i | \(0.803492\pi\) | |||||||
\(354\) | 5.87237 | 0.312113 | ||||||||
\(355\) | −26.6795 | −1.41600 | ||||||||
\(356\) | 14.8328 | 0.786136 | ||||||||
\(357\) | 27.1896 | 1.43903 | ||||||||
\(358\) | 3.31248 | 0.175070 | ||||||||
\(359\) | 22.9484 | 1.21117 | 0.605585 | − | 0.795781i | \(-0.292939\pi\) | ||||
0.605585 | + | 0.795781i | \(0.292939\pi\) | |||||||
\(360\) | 0.898910 | 0.0473767 | ||||||||
\(361\) | 5.53264 | 0.291191 | ||||||||
\(362\) | −33.7418 | −1.77343 | ||||||||
\(363\) | 11.2177 | 0.588776 | ||||||||
\(364\) | 51.7848 | 2.71426 | ||||||||
\(365\) | 13.2131 | 0.691607 | ||||||||
\(366\) | 17.0512 | 0.891283 | ||||||||
\(367\) | 30.3728 | 1.58545 | 0.792724 | − | 0.609580i | \(-0.208662\pi\) | ||||
0.792724 | + | 0.609580i | \(0.208662\pi\) | |||||||
\(368\) | 17.4157 | 0.907858 | ||||||||
\(369\) | −19.9525 | −1.03869 | ||||||||
\(370\) | −3.93068 | −0.204346 | ||||||||
\(371\) | −39.4892 | −2.05018 | ||||||||
\(372\) | 8.72189 | 0.452209 | ||||||||
\(373\) | 5.48861 | 0.284189 | 0.142095 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142095 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(374\) | −1.68617 | −0.0871897 | ||||||||
\(375\) | −12.2725 | −0.633749 | ||||||||
\(376\) | −0.760129 | −0.0392007 | ||||||||
\(377\) | 51.1632 | 2.63504 | ||||||||
\(378\) | 45.8856 | 2.36010 | ||||||||
\(379\) | 1.37247 | 0.0704992 | 0.0352496 | − | 0.999379i | \(-0.488777\pi\) | ||||
0.0352496 | + | 0.999379i | \(0.488777\pi\) | |||||||
\(380\) | −18.6046 | −0.954393 | ||||||||
\(381\) | −19.2443 | −0.985917 | ||||||||
\(382\) | 16.9883 | 0.869199 | ||||||||
\(383\) | 7.86117 | 0.401687 | 0.200844 | − | 0.979623i | \(-0.435632\pi\) | ||||
0.200844 | + | 0.979623i | \(0.435632\pi\) | |||||||
\(384\) | 1.88025 | 0.0959511 | ||||||||
\(385\) | 1.35629 | 0.0691227 | ||||||||
\(386\) | 19.0116 | 0.967664 | ||||||||
\(387\) | −14.7243 | −0.748479 | ||||||||
\(388\) | 33.0761 | 1.67919 | ||||||||
\(389\) | 24.1926 | 1.22661 | 0.613306 | − | 0.789846i | \(-0.289839\pi\) | ||||
0.613306 | + | 0.789846i | \(0.289839\pi\) | |||||||
\(390\) | 24.0206 | 1.21633 | ||||||||
\(391\) | −23.8806 | −1.20770 | ||||||||
\(392\) | 3.25886 | 0.164597 | ||||||||
\(393\) | −22.2727 | −1.12351 | ||||||||
\(394\) | 41.5578 | 2.09365 | ||||||||
\(395\) | 19.3969 | 0.975963 | ||||||||
\(396\) | −0.544614 | −0.0273679 | ||||||||
\(397\) | −24.4275 | −1.22598 | −0.612990 | − | 0.790091i | \(-0.710033\pi\) | ||||
−0.612990 | + | 0.790091i | \(0.710033\pi\) | |||||||
\(398\) | −28.9116 | −1.44921 | ||||||||
\(399\) | 23.2723 | 1.16507 | ||||||||
\(400\) | 4.30938 | 0.215469 | ||||||||
\(401\) | −30.6409 | −1.53013 | −0.765067 | − | 0.643950i | \(-0.777294\pi\) | ||||
−0.765067 | + | 0.643950i | \(0.777294\pi\) | |||||||
\(402\) | −19.0586 | −0.950556 | ||||||||
\(403\) | 27.1088 | 1.35038 | ||||||||
\(404\) | −24.0735 | −1.19770 | ||||||||
\(405\) | −1.38259 | −0.0687013 | ||||||||
\(406\) | −77.5171 | −3.84711 | ||||||||
\(407\) | −0.147869 | −0.00732962 | ||||||||
\(408\) | −1.36240 | −0.0674486 | ||||||||
\(409\) | −1.34065 | −0.0662908 | −0.0331454 | − | 0.999451i | \(-0.510552\pi\) | ||||
−0.0331454 | + | 0.999451i | \(0.510552\pi\) | |||||||
\(410\) | 40.0980 | 1.98030 | ||||||||
\(411\) | 8.78891 | 0.433525 | ||||||||
\(412\) | 2.27538 | 0.112100 | ||||||||
\(413\) | −13.4105 | −0.659886 | ||||||||
\(414\) | −15.9053 | −0.781703 | ||||||||
\(415\) | 2.22171 | 0.109059 | ||||||||
\(416\) | −46.9788 | −2.30333 | ||||||||
\(417\) | −17.4452 | −0.854294 | ||||||||
\(418\) | −1.44324 | −0.0705912 | ||||||||
\(419\) | 0.699066 | 0.0341516 | 0.0170758 | − | 0.999854i | \(-0.494564\pi\) | ||||
0.0170758 | + | 0.999854i | \(0.494564\pi\) | |||||||
\(420\) | −17.6488 | −0.861173 | ||||||||
\(421\) | 36.1837 | 1.76349 | 0.881744 | − | 0.471728i | \(-0.156370\pi\) | ||||
0.881744 | + | 0.471728i | \(0.156370\pi\) | |||||||
\(422\) | 24.1796 | 1.17705 | ||||||||
\(423\) | 6.45262 | 0.313737 | ||||||||
\(424\) | 1.97870 | 0.0960940 | ||||||||
\(425\) | −5.90907 | −0.286632 | ||||||||
\(426\) | 26.9315 | 1.30484 | ||||||||
\(427\) | −38.9392 | −1.88440 | ||||||||
\(428\) | −18.1052 | −0.875149 | ||||||||
\(429\) | 0.903637 | 0.0436280 | ||||||||
\(430\) | 29.5910 | 1.42700 | ||||||||
\(431\) | −19.3507 | −0.932088 | −0.466044 | − | 0.884761i | \(-0.654321\pi\) | ||||
−0.466044 | + | 0.884761i | \(0.654321\pi\) | |||||||
\(432\) | −21.3711 | −1.02822 | ||||||||
\(433\) | 37.5133 | 1.80277 | 0.901387 | − | 0.433014i | \(-0.142550\pi\) | ||||
0.901387 | + | 0.433014i | \(0.142550\pi\) | |||||||
\(434\) | −41.0723 | −1.97154 | ||||||||
\(435\) | −17.4370 | −0.836038 | ||||||||
\(436\) | −1.88308 | −0.0901830 | ||||||||
\(437\) | −20.4401 | −0.977783 | ||||||||
\(438\) | −13.3379 | −0.637312 | ||||||||
\(439\) | −20.9945 | −1.00201 | −0.501006 | − | 0.865444i | \(-0.667036\pi\) | ||||
−0.501006 | + | 0.865444i | \(0.667036\pi\) | |||||||
\(440\) | −0.0679598 | −0.00323985 | ||||||||
\(441\) | −27.6639 | −1.31733 | ||||||||
\(442\) | 68.1968 | 3.24379 | ||||||||
\(443\) | −15.6328 | −0.742737 | −0.371369 | − | 0.928485i | \(-0.621111\pi\) | ||||
−0.371369 | + | 0.928485i | \(0.621111\pi\) | |||||||
\(444\) | 1.92416 | 0.0913168 | ||||||||
\(445\) | −15.7121 | −0.744825 | ||||||||
\(446\) | −16.5961 | −0.785848 | ||||||||
\(447\) | −1.43488 | −0.0678674 | ||||||||
\(448\) | 32.3665 | 1.52917 | ||||||||
\(449\) | −19.5869 | −0.924364 | −0.462182 | − | 0.886785i | \(-0.652933\pi\) | ||||
−0.462182 | + | 0.886785i | \(0.652933\pi\) | |||||||
\(450\) | −3.93564 | −0.185528 | ||||||||
\(451\) | 1.50846 | 0.0710306 | ||||||||
\(452\) | −17.4991 | −0.823090 | ||||||||
\(453\) | 6.26207 | 0.294218 | ||||||||
\(454\) | 19.7476 | 0.926799 | ||||||||
\(455\) | −54.8547 | −2.57163 | ||||||||
\(456\) | −1.16611 | −0.0546082 | ||||||||
\(457\) | 28.8389 | 1.34903 | 0.674513 | − | 0.738263i | \(-0.264354\pi\) | ||||
0.674513 | + | 0.738263i | \(0.264354\pi\) | |||||||
\(458\) | −39.5913 | −1.84998 | ||||||||
\(459\) | 29.3042 | 1.36780 | ||||||||
\(460\) | 15.5010 | 0.722736 | ||||||||
\(461\) | −0.777552 | −0.0362142 | −0.0181071 | − | 0.999836i | \(-0.505764\pi\) | ||||
−0.0181071 | + | 0.999836i | \(0.505764\pi\) | |||||||
\(462\) | −1.36910 | −0.0636962 | ||||||||
\(463\) | −21.4915 | −0.998796 | −0.499398 | − | 0.866373i | \(-0.666445\pi\) | ||||
−0.499398 | + | 0.866373i | \(0.666445\pi\) | |||||||
\(464\) | 36.1033 | 1.67606 | ||||||||
\(465\) | −9.23895 | −0.428446 | ||||||||
\(466\) | 3.49315 | 0.161817 | ||||||||
\(467\) | −13.0787 | −0.605212 | −0.302606 | − | 0.953116i | \(-0.597857\pi\) | ||||
−0.302606 | + | 0.953116i | \(0.597857\pi\) | |||||||
\(468\) | 22.0268 | 1.01819 | ||||||||
\(469\) | 43.5233 | 2.00972 | ||||||||
\(470\) | −12.9676 | −0.598153 | ||||||||
\(471\) | 13.4262 | 0.618646 | ||||||||
\(472\) | 0.671962 | 0.0309296 | ||||||||
\(473\) | 1.11319 | 0.0511847 | ||||||||
\(474\) | −19.5801 | −0.899344 | ||||||||
\(475\) | −5.05774 | −0.232065 | ||||||||
\(476\) | −50.1067 | −2.29664 | ||||||||
\(477\) | −16.7969 | −0.769075 | ||||||||
\(478\) | −17.3746 | −0.794698 | ||||||||
\(479\) | −12.9537 | −0.591870 | −0.295935 | − | 0.955208i | \(-0.595631\pi\) | ||||
−0.295935 | + | 0.955208i | \(0.595631\pi\) | |||||||
\(480\) | 16.0109 | 0.730793 | ||||||||
\(481\) | 5.98055 | 0.272690 | ||||||||
\(482\) | −13.0875 | −0.596120 | ||||||||
\(483\) | −19.3901 | −0.882278 | ||||||||
\(484\) | −20.6727 | −0.939666 | ||||||||
\(485\) | −35.0370 | −1.59095 | ||||||||
\(486\) | 31.3324 | 1.42127 | ||||||||
\(487\) | 3.00195 | 0.136031 | 0.0680157 | − | 0.997684i | \(-0.478333\pi\) | ||||
0.0680157 | + | 0.997684i | \(0.478333\pi\) | |||||||
\(488\) | 1.95114 | 0.0883238 | ||||||||
\(489\) | 8.83104 | 0.399353 | ||||||||
\(490\) | 55.5954 | 2.51154 | ||||||||
\(491\) | 13.1521 | 0.593546 | 0.296773 | − | 0.954948i | \(-0.404089\pi\) | ||||
0.296773 | + | 0.954948i | \(0.404089\pi\) | |||||||
\(492\) | −19.6290 | −0.884942 | ||||||||
\(493\) | −49.5052 | −2.22960 | ||||||||
\(494\) | 58.3715 | 2.62626 | ||||||||
\(495\) | 0.576900 | 0.0259297 | ||||||||
\(496\) | 19.1293 | 0.858931 | ||||||||
\(497\) | −61.5023 | −2.75876 | ||||||||
\(498\) | −2.24269 | −0.100498 | ||||||||
\(499\) | 26.0363 | 1.16554 | 0.582772 | − | 0.812635i | \(-0.301968\pi\) | ||||
0.582772 | + | 0.812635i | \(0.301968\pi\) | |||||||
\(500\) | 22.6165 | 1.01144 | ||||||||
\(501\) | −6.50190 | −0.290484 | ||||||||
\(502\) | −23.3746 | −1.04326 | ||||||||
\(503\) | −40.9404 | −1.82544 | −0.912722 | − | 0.408582i | \(-0.866023\pi\) | ||||
−0.912722 | + | 0.408582i | \(0.866023\pi\) | |||||||
\(504\) | 2.07219 | 0.0923028 | ||||||||
\(505\) | 25.5006 | 1.13476 | ||||||||
\(506\) | 1.20248 | 0.0534567 | ||||||||
\(507\) | −23.2638 | −1.03318 | ||||||||
\(508\) | 35.4647 | 1.57349 | ||||||||
\(509\) | 5.31906 | 0.235763 | 0.117882 | − | 0.993028i | \(-0.462390\pi\) | ||||
0.117882 | + | 0.993028i | \(0.462390\pi\) | |||||||
\(510\) | −23.2422 | −1.02918 | ||||||||
\(511\) | 30.4593 | 1.34744 | ||||||||
\(512\) | −31.2059 | −1.37912 | ||||||||
\(513\) | 25.0823 | 1.10741 | ||||||||
\(514\) | 36.9496 | 1.62978 | ||||||||
\(515\) | −2.41027 | −0.106209 | ||||||||
\(516\) | −14.4855 | −0.637690 | ||||||||
\(517\) | −0.487834 | −0.0214549 | ||||||||
\(518\) | −9.06110 | −0.398122 | ||||||||
\(519\) | −17.3471 | −0.761455 | ||||||||
\(520\) | 2.74862 | 0.120535 | ||||||||
\(521\) | 11.9207 | 0.522254 | 0.261127 | − | 0.965304i | \(-0.415906\pi\) | ||||
0.261127 | + | 0.965304i | \(0.415906\pi\) | |||||||
\(522\) | −32.9722 | −1.44315 | ||||||||
\(523\) | −30.4181 | −1.33009 | −0.665045 | − | 0.746803i | \(-0.731588\pi\) | ||||
−0.665045 | + | 0.746803i | \(0.731588\pi\) | |||||||
\(524\) | 41.0456 | 1.79308 | ||||||||
\(525\) | −4.79791 | −0.209398 | ||||||||
\(526\) | 25.1081 | 1.09477 | ||||||||
\(527\) | −26.2303 | −1.14261 | ||||||||
\(528\) | 0.637652 | 0.0277502 | ||||||||
\(529\) | −5.96969 | −0.259552 | ||||||||
\(530\) | 33.7561 | 1.46627 | ||||||||
\(531\) | −5.70418 | −0.247541 | ||||||||
\(532\) | −42.8877 | −1.85942 | ||||||||
\(533\) | −61.0093 | −2.64261 | ||||||||
\(534\) | 15.8605 | 0.686352 | ||||||||
\(535\) | 19.1786 | 0.829161 | ||||||||
\(536\) | −2.18083 | −0.0941976 | ||||||||
\(537\) | 1.71767 | 0.0741230 | ||||||||
\(538\) | 40.1878 | 1.73262 | ||||||||
\(539\) | 2.09146 | 0.0900856 | ||||||||
\(540\) | −19.0214 | −0.818551 | ||||||||
\(541\) | 22.9775 | 0.987882 | 0.493941 | − | 0.869496i | \(-0.335556\pi\) | ||||
0.493941 | + | 0.869496i | \(0.335556\pi\) | |||||||
\(542\) | 29.9089 | 1.28470 | ||||||||
\(543\) | −17.4966 | −0.750852 | ||||||||
\(544\) | 45.4565 | 1.94893 | ||||||||
\(545\) | 1.99471 | 0.0854439 | ||||||||
\(546\) | 55.3728 | 2.36974 | ||||||||
\(547\) | −3.91647 | −0.167456 | −0.0837282 | − | 0.996489i | \(-0.526683\pi\) | ||||
−0.0837282 | + | 0.996489i | \(0.526683\pi\) | |||||||
\(548\) | −16.1968 | −0.691891 | ||||||||
\(549\) | −16.5629 | −0.706887 | ||||||||
\(550\) | 0.297544 | 0.0126873 | ||||||||
\(551\) | −42.3729 | −1.80515 | ||||||||
\(552\) | 0.971583 | 0.0413533 | ||||||||
\(553\) | 44.7142 | 1.90144 | ||||||||
\(554\) | −47.7474 | −2.02859 | ||||||||
\(555\) | −2.03823 | −0.0865182 | ||||||||
\(556\) | 32.1491 | 1.36342 | ||||||||
\(557\) | 31.8265 | 1.34853 | 0.674266 | − | 0.738488i | \(-0.264460\pi\) | ||||
0.674266 | + | 0.738488i | \(0.264460\pi\) | |||||||
\(558\) | −17.4703 | −0.739575 | ||||||||
\(559\) | −45.0229 | −1.90426 | ||||||||
\(560\) | −38.7082 | −1.63572 | ||||||||
\(561\) | −0.874355 | −0.0369153 | ||||||||
\(562\) | 4.28835 | 0.180893 | ||||||||
\(563\) | −45.5972 | −1.92169 | −0.960846 | − | 0.277082i | \(-0.910633\pi\) | ||||
−0.960846 | + | 0.277082i | \(0.910633\pi\) | |||||||
\(564\) | 6.34798 | 0.267298 | ||||||||
\(565\) | 18.5365 | 0.779837 | ||||||||
\(566\) | 14.2934 | 0.600797 | ||||||||
\(567\) | −3.18718 | −0.133849 | ||||||||
\(568\) | 3.08171 | 0.129306 | ||||||||
\(569\) | 36.6562 | 1.53671 | 0.768353 | − | 0.640026i | \(-0.221076\pi\) | ||||
0.768353 | + | 0.640026i | \(0.221076\pi\) | |||||||
\(570\) | −19.8936 | −0.833253 | ||||||||
\(571\) | −36.5350 | −1.52894 | −0.764471 | − | 0.644658i | \(-0.777000\pi\) | ||||
−0.764471 | + | 0.644658i | \(0.777000\pi\) | |||||||
\(572\) | −1.66528 | −0.0696289 | ||||||||
\(573\) | 8.80922 | 0.368010 | ||||||||
\(574\) | 92.4349 | 3.85816 | ||||||||
\(575\) | 4.21401 | 0.175736 | ||||||||
\(576\) | 13.7672 | 0.573633 | ||||||||
\(577\) | 44.5360 | 1.85406 | 0.927028 | − | 0.374992i | \(-0.122354\pi\) | ||||
0.927028 | + | 0.374992i | \(0.122354\pi\) | |||||||
\(578\) | −32.4874 | −1.35130 | ||||||||
\(579\) | 9.85836 | 0.409700 | ||||||||
\(580\) | 32.1339 | 1.33429 | ||||||||
\(581\) | 5.12154 | 0.212477 | ||||||||
\(582\) | 35.3679 | 1.46605 | ||||||||
\(583\) | 1.26988 | 0.0525932 | ||||||||
\(584\) | −1.52623 | −0.0631559 | ||||||||
\(585\) | −23.3326 | −0.964685 | ||||||||
\(586\) | 30.9049 | 1.27667 | ||||||||
\(587\) | 2.45740 | 0.101428 | 0.0507138 | − | 0.998713i | \(-0.483850\pi\) | ||||
0.0507138 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(588\) | −27.2153 | −1.12234 | ||||||||
\(589\) | −22.4512 | −0.925088 | ||||||||
\(590\) | 11.4635 | 0.471946 | ||||||||
\(591\) | 21.5496 | 0.886433 | ||||||||
\(592\) | 4.22018 | 0.173448 | ||||||||
\(593\) | −6.85210 | −0.281382 | −0.140691 | − | 0.990054i | \(-0.544932\pi\) | ||||
−0.140691 | + | 0.990054i | \(0.544932\pi\) | |||||||
\(594\) | −1.47558 | −0.0605437 | ||||||||
\(595\) | 53.0771 | 2.17595 | ||||||||
\(596\) | 2.64428 | 0.108314 | ||||||||
\(597\) | −14.9920 | −0.613581 | ||||||||
\(598\) | −48.6340 | −1.98879 | ||||||||
\(599\) | −9.11532 | −0.372442 | −0.186221 | − | 0.982508i | \(-0.559624\pi\) | ||||
−0.186221 | + | 0.982508i | \(0.559624\pi\) | |||||||
\(600\) | 0.240410 | 0.00981471 | ||||||||
\(601\) | 29.8340 | 1.21695 | 0.608477 | − | 0.793571i | \(-0.291781\pi\) | ||||
0.608477 | + | 0.793571i | \(0.291781\pi\) | |||||||
\(602\) | 68.2139 | 2.78019 | ||||||||
\(603\) | 18.5128 | 0.753898 | ||||||||
\(604\) | −11.5401 | −0.469561 | ||||||||
\(605\) | 21.8982 | 0.890288 | ||||||||
\(606\) | −25.7415 | −1.04568 | ||||||||
\(607\) | 14.1509 | 0.574368 | 0.287184 | − | 0.957875i | \(-0.407281\pi\) | ||||
0.287184 | + | 0.957875i | \(0.407281\pi\) | |||||||
\(608\) | 38.9075 | 1.57791 | ||||||||
\(609\) | −40.1961 | −1.62883 | ||||||||
\(610\) | 33.2859 | 1.34771 | ||||||||
\(611\) | 19.7303 | 0.798204 | ||||||||
\(612\) | −21.3130 | −0.861528 | ||||||||
\(613\) | −22.6702 | −0.915641 | −0.457820 | − | 0.889045i | \(-0.651370\pi\) | ||||
−0.457820 | + | 0.889045i | \(0.651370\pi\) | |||||||
\(614\) | 10.5990 | 0.427742 | ||||||||
\(615\) | 20.7926 | 0.838439 | ||||||||
\(616\) | −0.156663 | −0.00631212 | ||||||||
\(617\) | 36.9447 | 1.48734 | 0.743669 | − | 0.668548i | \(-0.233084\pi\) | ||||
0.743669 | + | 0.668548i | \(0.233084\pi\) | |||||||
\(618\) | 2.43303 | 0.0978710 | ||||||||
\(619\) | −42.5386 | −1.70977 | −0.854884 | − | 0.518818i | \(-0.826372\pi\) | ||||
−0.854884 | + | 0.518818i | \(0.826372\pi\) | |||||||
\(620\) | 17.0261 | 0.683785 | ||||||||
\(621\) | −20.8981 | −0.838612 | ||||||||
\(622\) | −11.8434 | −0.474877 | ||||||||
\(623\) | −36.2200 | −1.45112 | ||||||||
\(624\) | −25.7897 | −1.03241 | ||||||||
\(625\) | −18.8516 | −0.754064 | ||||||||
\(626\) | 1.64318 | 0.0656747 | ||||||||
\(627\) | −0.748385 | −0.0298876 | ||||||||
\(628\) | −24.7426 | −0.987338 | ||||||||
\(629\) | −5.78675 | −0.230733 | ||||||||
\(630\) | 35.3511 | 1.40842 | ||||||||
\(631\) | −38.7494 | −1.54259 | −0.771295 | − | 0.636478i | \(-0.780390\pi\) | ||||
−0.771295 | + | 0.636478i | \(0.780390\pi\) | |||||||
\(632\) | −2.24051 | −0.0891226 | ||||||||
\(633\) | 12.5382 | 0.498350 | ||||||||
\(634\) | 5.51858 | 0.219171 | ||||||||
\(635\) | −37.5671 | −1.49080 | ||||||||
\(636\) | −16.5245 | −0.655238 | ||||||||
\(637\) | −84.5887 | −3.35153 | ||||||||
\(638\) | 2.49277 | 0.0986899 | ||||||||
\(639\) | −26.1602 | −1.03488 | ||||||||
\(640\) | 3.67046 | 0.145088 | ||||||||
\(641\) | −25.7708 | −1.01789 | −0.508944 | − | 0.860800i | \(-0.669964\pi\) | ||||
−0.508944 | + | 0.860800i | \(0.669964\pi\) | |||||||
\(642\) | −19.3597 | −0.764067 | ||||||||
\(643\) | 12.1811 | 0.480374 | 0.240187 | − | 0.970727i | \(-0.422791\pi\) | ||||
0.240187 | + | 0.970727i | \(0.422791\pi\) | |||||||
\(644\) | 35.7332 | 1.40809 | ||||||||
\(645\) | 15.3443 | 0.604180 | ||||||||
\(646\) | −56.4800 | −2.22218 | ||||||||
\(647\) | −34.6555 | −1.36245 | −0.681224 | − | 0.732075i | \(-0.738552\pi\) | ||||
−0.681224 | + | 0.732075i | \(0.738552\pi\) | |||||||
\(648\) | 0.159701 | 0.00627363 | ||||||||
\(649\) | 0.431250 | 0.0169280 | ||||||||
\(650\) | −12.0341 | −0.472016 | ||||||||
\(651\) | −21.2979 | −0.834729 | ||||||||
\(652\) | −16.2744 | −0.637355 | ||||||||
\(653\) | 32.8451 | 1.28533 | 0.642665 | − | 0.766147i | \(-0.277829\pi\) | ||||
0.642665 | + | 0.766147i | \(0.277829\pi\) | |||||||
\(654\) | −2.01355 | −0.0787361 | ||||||||
\(655\) | −43.4788 | −1.69886 | ||||||||
\(656\) | −43.0513 | −1.68087 | ||||||||
\(657\) | 12.9560 | 0.505460 | ||||||||
\(658\) | −29.8934 | −1.16536 | ||||||||
\(659\) | 0.334015 | 0.0130114 | 0.00650569 | − | 0.999979i | \(-0.497929\pi\) | ||||
0.00650569 | + | 0.999979i | \(0.497929\pi\) | |||||||
\(660\) | 0.567545 | 0.0220917 | ||||||||
\(661\) | 35.1421 | 1.36687 | 0.683435 | − | 0.730011i | \(-0.260485\pi\) | ||||
0.683435 | + | 0.730011i | \(0.260485\pi\) | |||||||
\(662\) | −26.0462 | −1.01232 | ||||||||
\(663\) | 35.3631 | 1.37339 | ||||||||
\(664\) | −0.256627 | −0.00995904 | ||||||||
\(665\) | 45.4302 | 1.76171 | ||||||||
\(666\) | −3.85417 | −0.149346 | ||||||||
\(667\) | 35.3043 | 1.36699 | ||||||||
\(668\) | 11.9821 | 0.463602 | ||||||||
\(669\) | −8.60583 | −0.332721 | ||||||||
\(670\) | −37.2045 | −1.43734 | ||||||||
\(671\) | 1.25220 | 0.0483405 | ||||||||
\(672\) | 36.9087 | 1.42378 | ||||||||
\(673\) | −2.05265 | −0.0791240 | −0.0395620 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395620 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(674\) | 1.30916 | 0.0504269 | ||||||||
\(675\) | −5.17107 | −0.199034 | ||||||||
\(676\) | 42.8719 | 1.64892 | ||||||||
\(677\) | −37.4889 | −1.44081 | −0.720407 | − | 0.693552i | \(-0.756045\pi\) | ||||
−0.720407 | + | 0.693552i | \(0.756045\pi\) | |||||||
\(678\) | −18.7116 | −0.718615 | ||||||||
\(679\) | −80.7681 | −3.09960 | ||||||||
\(680\) | −2.65955 | −0.101989 | ||||||||
\(681\) | 10.2400 | 0.392398 | ||||||||
\(682\) | 1.32079 | 0.0505758 | ||||||||
\(683\) | −0.722222 | −0.0276351 | −0.0138175 | − | 0.999905i | \(-0.504398\pi\) | ||||
−0.0138175 | + | 0.999905i | \(0.504398\pi\) | |||||||
\(684\) | −18.2424 | −0.697517 | ||||||||
\(685\) | 17.1569 | 0.655533 | ||||||||
\(686\) | 64.7322 | 2.47149 | ||||||||
\(687\) | −20.5299 | −0.783263 | ||||||||
\(688\) | −31.7704 | −1.21124 | ||||||||
\(689\) | −51.3602 | −1.95667 | ||||||||
\(690\) | 16.5750 | 0.630999 | ||||||||
\(691\) | 35.6903 | 1.35772 | 0.678861 | − | 0.734266i | \(-0.262474\pi\) | ||||
0.678861 | + | 0.734266i | \(0.262474\pi\) | |||||||
\(692\) | 31.9684 | 1.21526 | ||||||||
\(693\) | 1.32989 | 0.0505182 | ||||||||
\(694\) | 45.9251 | 1.74329 | ||||||||
\(695\) | −34.0550 | −1.29178 | ||||||||
\(696\) | 2.01412 | 0.0763450 | ||||||||
\(697\) | 59.0323 | 2.23601 | ||||||||
\(698\) | 59.3176 | 2.24520 | ||||||||
\(699\) | 1.81135 | 0.0685117 | ||||||||
\(700\) | 8.84189 | 0.334192 | ||||||||
\(701\) | 21.8072 | 0.823648 | 0.411824 | − | 0.911263i | \(-0.364892\pi\) | ||||
0.411824 | + | 0.911263i | \(0.364892\pi\) | |||||||
\(702\) | 59.6794 | 2.25246 | ||||||||
\(703\) | −4.95304 | −0.186808 | ||||||||
\(704\) | −1.04083 | −0.0392278 | ||||||||
\(705\) | −6.72431 | −0.253252 | ||||||||
\(706\) | 60.3789 | 2.27239 | ||||||||
\(707\) | 58.7847 | 2.21083 | ||||||||
\(708\) | −5.61168 | −0.210900 | ||||||||
\(709\) | 6.15257 | 0.231065 | 0.115532 | − | 0.993304i | \(-0.463143\pi\) | ||||
0.115532 | + | 0.993304i | \(0.463143\pi\) | |||||||
\(710\) | 52.5733 | 1.97304 | ||||||||
\(711\) | 19.0193 | 0.713280 | ||||||||
\(712\) | 1.81488 | 0.0680156 | ||||||||
\(713\) | 18.7059 | 0.700543 | ||||||||
\(714\) | −53.5785 | −2.00512 | ||||||||
\(715\) | 1.76400 | 0.0659699 | ||||||||
\(716\) | −3.16544 | −0.118298 | ||||||||
\(717\) | −9.00954 | −0.336467 | ||||||||
\(718\) | −45.2210 | −1.68763 | ||||||||
\(719\) | 2.59823 | 0.0968977 | 0.0484489 | − | 0.998826i | \(-0.484572\pi\) | ||||
0.0484489 | + | 0.998826i | \(0.484572\pi\) | |||||||
\(720\) | −16.4647 | −0.613602 | ||||||||
\(721\) | −5.55621 | −0.206924 | ||||||||
\(722\) | −10.9023 | −0.405743 | ||||||||
\(723\) | −6.78647 | −0.252392 | ||||||||
\(724\) | 32.2439 | 1.19833 | ||||||||
\(725\) | 8.73577 | 0.324438 | ||||||||
\(726\) | −22.1050 | −0.820395 | ||||||||
\(727\) | −26.5290 | −0.983905 | −0.491953 | − | 0.870622i | \(-0.663717\pi\) | ||||
−0.491953 | + | 0.870622i | \(0.663717\pi\) | |||||||
\(728\) | 6.33619 | 0.234835 | ||||||||
\(729\) | 14.1679 | 0.524737 | ||||||||
\(730\) | −26.0372 | −0.963679 | ||||||||
\(731\) | 43.5639 | 1.61127 | ||||||||
\(732\) | −16.2943 | −0.602255 | ||||||||
\(733\) | −14.6904 | −0.542604 | −0.271302 | − | 0.962494i | \(-0.587454\pi\) | ||||
−0.271302 | + | 0.962494i | \(0.587454\pi\) | |||||||
\(734\) | −59.8512 | −2.20915 | ||||||||
\(735\) | 28.8287 | 1.06336 | ||||||||
\(736\) | −32.4170 | −1.19491 | ||||||||
\(737\) | −1.39961 | −0.0515552 | ||||||||
\(738\) | 39.3175 | 1.44730 | ||||||||
\(739\) | 5.78051 | 0.212639 | 0.106320 | − | 0.994332i | \(-0.466093\pi\) | ||||
0.106320 | + | 0.994332i | \(0.466093\pi\) | |||||||
\(740\) | 3.75619 | 0.138080 | ||||||||
\(741\) | 30.2683 | 1.11193 | ||||||||
\(742\) | 77.8155 | 2.85670 | ||||||||
\(743\) | −4.40453 | −0.161586 | −0.0807932 | − | 0.996731i | \(-0.525745\pi\) | ||||
−0.0807932 | + | 0.996731i | \(0.525745\pi\) | |||||||
\(744\) | 1.06718 | 0.0391246 | ||||||||
\(745\) | −2.80104 | −0.102622 | ||||||||
\(746\) | −10.8156 | −0.395987 | ||||||||
\(747\) | 2.17846 | 0.0797058 | ||||||||
\(748\) | 1.61132 | 0.0589156 | ||||||||
\(749\) | 44.2109 | 1.61543 | ||||||||
\(750\) | 24.1836 | 0.883059 | ||||||||
\(751\) | −17.5718 | −0.641202 | −0.320601 | − | 0.947214i | \(-0.603885\pi\) | ||||
−0.320601 | + | 0.947214i | \(0.603885\pi\) | |||||||
\(752\) | 13.9227 | 0.507710 | ||||||||
\(753\) | −12.1208 | −0.441706 | ||||||||
\(754\) | −100.820 | −3.67164 | ||||||||
\(755\) | 12.2243 | 0.444886 | ||||||||
\(756\) | −43.8487 | −1.59476 | ||||||||
\(757\) | 10.9831 | 0.399186 | 0.199593 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199593 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(758\) | −2.70453 | −0.0982329 | ||||||||
\(759\) | 0.623540 | 0.0226331 | ||||||||
\(760\) | −2.27638 | −0.0825731 | ||||||||
\(761\) | −4.03291 | −0.146193 | −0.0730964 | − | 0.997325i | \(-0.523288\pi\) | ||||
−0.0730964 | + | 0.997325i | \(0.523288\pi\) | |||||||
\(762\) | 37.9219 | 1.37377 | ||||||||
\(763\) | 4.59826 | 0.166468 | ||||||||
\(764\) | −16.2342 | −0.587332 | ||||||||
\(765\) | 22.5765 | 0.816256 | ||||||||
\(766\) | −15.4909 | −0.559707 | ||||||||
\(767\) | −17.4418 | −0.629788 | ||||||||
\(768\) | −18.0900 | −0.652768 | ||||||||
\(769\) | 28.2518 | 1.01879 | 0.509394 | − | 0.860533i | \(-0.329870\pi\) | ||||
0.509394 | + | 0.860533i | \(0.329870\pi\) | |||||||
\(770\) | −2.67263 | −0.0963150 | ||||||||
\(771\) | 19.1601 | 0.690032 | ||||||||
\(772\) | −18.1676 | −0.653867 | ||||||||
\(773\) | −35.9229 | −1.29206 | −0.646028 | − | 0.763314i | \(-0.723571\pi\) | ||||
−0.646028 | + | 0.763314i | \(0.723571\pi\) | |||||||
\(774\) | 29.0150 | 1.04292 | ||||||||
\(775\) | 4.62863 | 0.166265 | ||||||||
\(776\) | 4.04707 | 0.145281 | ||||||||
\(777\) | −4.69859 | −0.168561 | ||||||||
\(778\) | −47.6727 | −1.70915 | ||||||||
\(779\) | 50.5274 | 1.81033 | ||||||||
\(780\) | −22.9542 | −0.821894 | ||||||||
\(781\) | 1.97777 | 0.0707703 | ||||||||
\(782\) | 47.0580 | 1.68279 | ||||||||
\(783\) | −43.3224 | −1.54822 | ||||||||
\(784\) | −59.6900 | −2.13179 | ||||||||
\(785\) | 26.2094 | 0.935454 | ||||||||
\(786\) | 43.8895 | 1.56549 | ||||||||
\(787\) | 42.7074 | 1.52235 | 0.761177 | − | 0.648544i | \(-0.224622\pi\) | ||||
0.761177 | + | 0.648544i | \(0.224622\pi\) | |||||||
\(788\) | −39.7130 | −1.41472 | ||||||||
\(789\) | 13.0197 | 0.463513 | ||||||||
\(790\) | −38.2225 | −1.35990 | ||||||||
\(791\) | 42.7309 | 1.51934 | ||||||||
\(792\) | −0.0666370 | −0.00236784 | ||||||||
\(793\) | −50.6448 | −1.79845 | ||||||||
\(794\) | 48.1356 | 1.70827 | ||||||||
\(795\) | 17.5041 | 0.620806 | ||||||||
\(796\) | 27.6282 | 0.979254 | ||||||||
\(797\) | 39.0827 | 1.38438 | 0.692190 | − | 0.721716i | \(-0.256646\pi\) | ||||
0.692190 | + | 0.721716i | \(0.256646\pi\) | |||||||
\(798\) | −45.8593 | −1.62340 | ||||||||
\(799\) | −19.0910 | −0.675390 | ||||||||
\(800\) | −8.02131 | −0.283596 | ||||||||
\(801\) | −15.4063 | −0.544354 | ||||||||
\(802\) | 60.3795 | 2.13208 | ||||||||
\(803\) | −0.979501 | −0.0345658 | ||||||||
\(804\) | 18.2125 | 0.642307 | ||||||||
\(805\) | −37.8516 | −1.33409 | ||||||||
\(806\) | −53.4192 | −1.88161 | ||||||||
\(807\) | 20.8392 | 0.733574 | ||||||||
\(808\) | −2.94554 | −0.103624 | ||||||||
\(809\) | 4.36769 | 0.153560 | 0.0767800 | − | 0.997048i | \(-0.475536\pi\) | ||||
0.0767800 | + | 0.997048i | \(0.475536\pi\) | |||||||
\(810\) | 2.72446 | 0.0957277 | ||||||||
\(811\) | 18.2529 | 0.640945 | 0.320472 | − | 0.947258i | \(-0.396158\pi\) | ||||
0.320472 | + | 0.947258i | \(0.396158\pi\) | |||||||
\(812\) | 74.0760 | 2.59956 | ||||||||
\(813\) | 15.5091 | 0.543928 | ||||||||
\(814\) | 0.291384 | 0.0102130 | ||||||||
\(815\) | 17.2392 | 0.603862 | ||||||||
\(816\) | 24.9540 | 0.873564 | ||||||||
\(817\) | 37.2876 | 1.30453 | ||||||||
\(818\) | 2.64182 | 0.0923690 | ||||||||
\(819\) | −53.7870 | −1.87947 | ||||||||
\(820\) | −38.3179 | −1.33812 | ||||||||
\(821\) | 32.1393 | 1.12167 | 0.560835 | − | 0.827928i | \(-0.310480\pi\) | ||||
0.560835 | + | 0.827928i | \(0.310480\pi\) | |||||||
\(822\) | −17.3190 | −0.604070 | ||||||||
\(823\) | 40.7252 | 1.41959 | 0.709796 | − | 0.704407i | \(-0.248787\pi\) | ||||
0.709796 | + | 0.704407i | \(0.248787\pi\) | |||||||
\(824\) | 0.278407 | 0.00969875 | ||||||||
\(825\) | 0.154290 | 0.00537168 | ||||||||
\(826\) | 26.4260 | 0.919479 | ||||||||
\(827\) | −11.3478 | −0.394601 | −0.197300 | − | 0.980343i | \(-0.563217\pi\) | ||||
−0.197300 | + | 0.980343i | \(0.563217\pi\) | |||||||
\(828\) | 15.1992 | 0.528210 | ||||||||
\(829\) | −27.2925 | −0.947908 | −0.473954 | − | 0.880550i | \(-0.657174\pi\) | ||||
−0.473954 | + | 0.880550i | \(0.657174\pi\) | |||||||
\(830\) | −4.37799 | −0.151962 | ||||||||
\(831\) | −24.7592 | −0.858887 | ||||||||
\(832\) | 42.0962 | 1.45942 | ||||||||
\(833\) | 81.8476 | 2.83585 | ||||||||
\(834\) | 34.3766 | 1.19037 | ||||||||
\(835\) | −12.6924 | −0.439240 | ||||||||
\(836\) | 1.37917 | 0.0476996 | ||||||||
\(837\) | −22.9543 | −0.793417 | ||||||||
\(838\) | −1.37755 | −0.0475865 | ||||||||
\(839\) | 8.36928 | 0.288940 | 0.144470 | − | 0.989509i | \(-0.453852\pi\) | ||||
0.144470 | + | 0.989509i | \(0.453852\pi\) | |||||||
\(840\) | −2.15944 | −0.0745078 | ||||||||
\(841\) | 44.1869 | 1.52369 | ||||||||
\(842\) | −71.3020 | −2.45723 | ||||||||
\(843\) | 2.22370 | 0.0765884 | ||||||||
\(844\) | −23.1063 | −0.795350 | ||||||||
\(845\) | −45.4135 | −1.56227 | ||||||||
\(846\) | −12.7152 | −0.437159 | ||||||||
\(847\) | 50.4803 | 1.73452 | ||||||||
\(848\) | −36.2423 | −1.24457 | ||||||||
\(849\) | 7.41179 | 0.254372 | ||||||||
\(850\) | 11.6441 | 0.399390 | ||||||||
\(851\) | 4.12678 | 0.141464 | ||||||||
\(852\) | −25.7360 | −0.881700 | ||||||||
\(853\) | 31.4511 | 1.07686 | 0.538432 | − | 0.842669i | \(-0.319017\pi\) | ||||
0.538432 | + | 0.842669i | \(0.319017\pi\) | |||||||
\(854\) | 76.7317 | 2.62570 | ||||||||
\(855\) | 19.3239 | 0.660863 | ||||||||
\(856\) | −2.21529 | −0.0757170 | ||||||||
\(857\) | 53.5519 | 1.82930 | 0.914648 | − | 0.404251i | \(-0.132468\pi\) | ||||
0.914648 | + | 0.404251i | \(0.132468\pi\) | |||||||
\(858\) | −1.78066 | −0.0607909 | ||||||||
\(859\) | −17.6230 | −0.601290 | −0.300645 | − | 0.953736i | \(-0.597202\pi\) | ||||
−0.300645 | + | 0.953736i | \(0.597202\pi\) | |||||||
\(860\) | −28.2774 | −0.964251 | ||||||||
\(861\) | 47.9317 | 1.63351 | ||||||||
\(862\) | 38.1315 | 1.29876 | ||||||||
\(863\) | 30.2351 | 1.02921 | 0.514607 | − | 0.857426i | \(-0.327938\pi\) | ||||
0.514607 | + | 0.857426i | \(0.327938\pi\) | |||||||
\(864\) | 39.7793 | 1.35332 | ||||||||
\(865\) | −33.8636 | −1.15140 | ||||||||
\(866\) | −73.9219 | −2.51197 | ||||||||
\(867\) | −16.8462 | −0.572127 | ||||||||
\(868\) | 39.2491 | 1.33220 | ||||||||
\(869\) | −1.43791 | −0.0487777 | ||||||||
\(870\) | 34.3604 | 1.16493 | ||||||||
\(871\) | 56.6069 | 1.91805 | ||||||||
\(872\) | −0.230406 | −0.00780253 | ||||||||
\(873\) | −34.3550 | −1.16274 | ||||||||
\(874\) | 40.2783 | 1.36243 | ||||||||
\(875\) | −55.2270 | −1.86701 | ||||||||
\(876\) | 12.7458 | 0.430642 | ||||||||
\(877\) | 4.92419 | 0.166278 | 0.0831391 | − | 0.996538i | \(-0.473505\pi\) | ||||
0.0831391 | + | 0.996538i | \(0.473505\pi\) | |||||||
\(878\) | 41.3707 | 1.39619 | ||||||||
\(879\) | 16.0256 | 0.540531 | ||||||||
\(880\) | 1.24477 | 0.0419611 | ||||||||
\(881\) | 21.9024 | 0.737912 | 0.368956 | − | 0.929447i | \(-0.379715\pi\) | ||||
0.368956 | + | 0.929447i | \(0.379715\pi\) | |||||||
\(882\) | 54.5132 | 1.83556 | ||||||||
\(883\) | −34.0815 | −1.14693 | −0.573466 | − | 0.819229i | \(-0.694402\pi\) | ||||
−0.573466 | + | 0.819229i | \(0.694402\pi\) | |||||||
\(884\) | −65.1694 | −2.19188 | ||||||||
\(885\) | 5.94436 | 0.199817 | ||||||||
\(886\) | 30.8053 | 1.03492 | ||||||||
\(887\) | −14.6698 | −0.492565 | −0.246282 | − | 0.969198i | \(-0.579209\pi\) | ||||
−0.246282 | + | 0.969198i | \(0.579209\pi\) | |||||||
\(888\) | 0.235434 | 0.00790064 | ||||||||
\(889\) | −86.6007 | −2.90449 | ||||||||
\(890\) | 30.9615 | 1.03783 | ||||||||
\(891\) | 0.102492 | 0.00343362 | ||||||||
\(892\) | 15.8594 | 0.531011 | ||||||||
\(893\) | −16.3405 | −0.546814 | ||||||||
\(894\) | 2.82750 | 0.0945658 | ||||||||
\(895\) | 3.35309 | 0.112081 | ||||||||
\(896\) | 8.46125 | 0.282670 | ||||||||
\(897\) | −25.2190 | −0.842036 | ||||||||
\(898\) | 38.5971 | 1.28800 | ||||||||
\(899\) | 38.7780 | 1.29332 | ||||||||
\(900\) | 3.76093 | 0.125364 | ||||||||
\(901\) | 49.6958 | 1.65561 | ||||||||
\(902\) | −2.97250 | −0.0989733 | ||||||||
\(903\) | 35.3720 | 1.17711 | ||||||||
\(904\) | −2.14113 | −0.0712129 | ||||||||
\(905\) | −34.1554 | −1.13536 | ||||||||
\(906\) | −12.3397 | −0.409960 | ||||||||
\(907\) | 41.1637 | 1.36682 | 0.683409 | − | 0.730036i | \(-0.260497\pi\) | ||||
0.683409 | + | 0.730036i | \(0.260497\pi\) | |||||||
\(908\) | −18.8709 | −0.626254 | ||||||||
\(909\) | 25.0043 | 0.829339 | ||||||||
\(910\) | 108.094 | 3.58328 | ||||||||
\(911\) | −25.6140 | −0.848629 | −0.424315 | − | 0.905515i | \(-0.639485\pi\) | ||||
−0.424315 | + | 0.905515i | \(0.639485\pi\) | |||||||
\(912\) | 21.3588 | 0.707262 | ||||||||
\(913\) | −0.164697 | −0.00545068 | ||||||||
\(914\) | −56.8285 | −1.87972 | ||||||||
\(915\) | 17.2603 | 0.570607 | ||||||||
\(916\) | 37.8337 | 1.25006 | ||||||||
\(917\) | −100.229 | −3.30984 | ||||||||
\(918\) | −57.7455 | −1.90589 | ||||||||
\(919\) | 6.19134 | 0.204233 | 0.102117 | − | 0.994772i | \(-0.467438\pi\) | ||||
0.102117 | + | 0.994772i | \(0.467438\pi\) | |||||||
\(920\) | 1.89664 | 0.0625303 | ||||||||
\(921\) | 5.49607 | 0.181102 | ||||||||
\(922\) | 1.53221 | 0.0504606 | ||||||||
\(923\) | −79.9907 | −2.63293 | ||||||||
\(924\) | 1.30832 | 0.0430406 | ||||||||
\(925\) | 1.02114 | 0.0335748 | ||||||||
\(926\) | 42.3502 | 1.39171 | ||||||||
\(927\) | −2.36335 | −0.0776227 | ||||||||
\(928\) | −67.2013 | −2.20599 | ||||||||
\(929\) | −1.27625 | −0.0418723 | −0.0209361 | − | 0.999781i | \(-0.506665\pi\) | ||||
−0.0209361 | + | 0.999781i | \(0.506665\pi\) | |||||||
\(930\) | 18.2058 | 0.596992 | ||||||||
\(931\) | 70.0557 | 2.29598 | ||||||||
\(932\) | −3.33808 | −0.109342 | ||||||||
\(933\) | −6.14133 | −0.201058 | ||||||||
\(934\) | 25.7723 | 0.843297 | ||||||||
\(935\) | −1.70684 | −0.0558196 | ||||||||
\(936\) | 2.69512 | 0.0880927 | ||||||||
\(937\) | 19.3880 | 0.633378 | 0.316689 | − | 0.948529i | \(-0.397429\pi\) | ||||
0.316689 | + | 0.948529i | \(0.397429\pi\) | |||||||
\(938\) | −85.7648 | −2.80032 | ||||||||
\(939\) | 0.852064 | 0.0278061 | ||||||||
\(940\) | 12.3920 | 0.404182 | ||||||||
\(941\) | 44.8429 | 1.46184 | 0.730919 | − | 0.682464i | \(-0.239092\pi\) | ||||
0.730919 | + | 0.682464i | \(0.239092\pi\) | |||||||
\(942\) | −26.4570 | −0.862015 | ||||||||
\(943\) | −42.0985 | −1.37091 | ||||||||
\(944\) | −12.3078 | −0.400586 | ||||||||
\(945\) | 46.4481 | 1.51096 | ||||||||
\(946\) | −2.19360 | −0.0713202 | ||||||||
\(947\) | −44.8399 | −1.45710 | −0.728551 | − | 0.684992i | \(-0.759806\pi\) | ||||
−0.728551 | + | 0.684992i | \(0.759806\pi\) | |||||||
\(948\) | 18.7109 | 0.607702 | ||||||||
\(949\) | 39.6157 | 1.28598 | ||||||||
\(950\) | 9.96654 | 0.323357 | ||||||||
\(951\) | 2.86163 | 0.0927948 | ||||||||
\(952\) | −6.13087 | −0.198702 | ||||||||
\(953\) | 7.68868 | 0.249061 | 0.124530 | − | 0.992216i | \(-0.460258\pi\) | ||||
0.124530 | + | 0.992216i | \(0.460258\pi\) | |||||||
\(954\) | 33.0991 | 1.07162 | ||||||||
\(955\) | 17.1966 | 0.556469 | ||||||||
\(956\) | 16.6033 | 0.536991 | ||||||||
\(957\) | 1.29262 | 0.0417844 | ||||||||
\(958\) | 25.5259 | 0.824706 | ||||||||
\(959\) | 39.5507 | 1.27716 | ||||||||
\(960\) | −14.3468 | −0.463042 | ||||||||
\(961\) | −10.4536 | −0.337211 | ||||||||
\(962\) | −11.7850 | −0.379963 | ||||||||
\(963\) | 18.8053 | 0.605991 | ||||||||
\(964\) | 12.5065 | 0.402809 | ||||||||
\(965\) | 19.2446 | 0.619507 | ||||||||
\(966\) | 38.2091 | 1.22936 | ||||||||
\(967\) | 15.1427 | 0.486956 | 0.243478 | − | 0.969906i | \(-0.421712\pi\) | ||||
0.243478 | + | 0.969906i | \(0.421712\pi\) | |||||||
\(968\) | −2.52943 | −0.0812989 | ||||||||
\(969\) | −29.2874 | −0.940848 | ||||||||
\(970\) | 69.0421 | 2.21681 | ||||||||
\(971\) | 43.2548 | 1.38811 | 0.694056 | − | 0.719921i | \(-0.255822\pi\) | ||||
0.694056 | + | 0.719921i | \(0.255822\pi\) | |||||||
\(972\) | −29.9415 | −0.960374 | ||||||||
\(973\) | −78.5044 | −2.51674 | ||||||||
\(974\) | −5.91550 | −0.189545 | ||||||||
\(975\) | −6.24022 | −0.199847 | ||||||||
\(976\) | −35.7375 | −1.14393 | ||||||||
\(977\) | 51.2904 | 1.64093 | 0.820463 | − | 0.571700i | \(-0.193716\pi\) | ||||
0.820463 | + | 0.571700i | \(0.193716\pi\) | |||||||
\(978\) | −17.4020 | −0.556455 | ||||||||
\(979\) | 1.16475 | 0.0372256 | ||||||||
\(980\) | −53.1274 | −1.69709 | ||||||||
\(981\) | 1.95588 | 0.0624465 | ||||||||
\(982\) | −25.9169 | −0.827042 | ||||||||
\(983\) | 20.1997 | 0.644269 | 0.322134 | − | 0.946694i | \(-0.395600\pi\) | ||||
0.322134 | + | 0.946694i | \(0.395600\pi\) | |||||||
\(984\) | −2.40173 | −0.0765643 | ||||||||
\(985\) | 42.0673 | 1.34037 | ||||||||
\(986\) | 97.5527 | 3.10671 | ||||||||
\(987\) | −15.5011 | −0.493404 | ||||||||
\(988\) | −55.7803 | −1.77461 | ||||||||
\(989\) | −31.0673 | −0.987882 | ||||||||
\(990\) | −1.13681 | −0.0361303 | ||||||||
\(991\) | 35.6963 | 1.13393 | 0.566965 | − | 0.823742i | \(-0.308118\pi\) | ||||
0.566965 | + | 0.823742i | \(0.308118\pi\) | |||||||
\(992\) | −35.6065 | −1.13051 | ||||||||
\(993\) | −13.5062 | −0.428605 | ||||||||
\(994\) | 121.194 | 3.84402 | ||||||||
\(995\) | −29.2660 | −0.927795 | ||||||||
\(996\) | 2.14314 | 0.0679079 | ||||||||
\(997\) | 35.9659 | 1.13905 | 0.569526 | − | 0.821973i | \(-0.307127\pi\) | ||||
0.569526 | + | 0.821973i | \(0.307127\pi\) | |||||||
\(998\) | −51.3059 | −1.62406 | ||||||||
\(999\) | −5.06402 | −0.160219 |
(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 | 4033.2.a.d.1.17 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.17 | ✓ | 79 | 1.1 | even | 1 | trivial |