Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65345 | −1.87627 | −0.938135 | − | 0.346270i | \(-0.887448\pi\) | ||||
−0.938135 | + | 0.346270i | \(0.887448\pi\) | |||||||
\(3\) | 0.515937 | 0.297876 | 0.148938 | − | 0.988847i | \(-0.452414\pi\) | ||||
0.148938 | + | 0.988847i | \(0.452414\pi\) | |||||||
\(4\) | 5.04077 | 2.52039 | ||||||||
\(5\) | −0.00500829 | −0.00223978 | −0.00111989 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111989 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(6\) | −1.36901 | −0.558896 | ||||||||
\(7\) | 0.475978 | 0.179903 | 0.0899514 | − | 0.995946i | \(-0.471329\pi\) | ||||
0.0899514 | + | 0.995946i | \(0.471329\pi\) | |||||||
\(8\) | −8.06853 | −2.85266 | ||||||||
\(9\) | −2.73381 | −0.911270 | ||||||||
\(10\) | 0.0132892 | 0.00420242 | ||||||||
\(11\) | 1.65099 | 0.497793 | 0.248896 | − | 0.968530i | \(-0.419932\pi\) | ||||
0.248896 | + | 0.968530i | \(0.419932\pi\) | |||||||
\(12\) | 2.60072 | 0.750764 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.26298 | −0.337546 | ||||||||
\(15\) | −0.00258396 | −0.000667176 0 | ||||||||
\(16\) | 11.3279 | 2.83197 | ||||||||
\(17\) | 3.63802 | 0.882350 | 0.441175 | − | 0.897421i | \(-0.354562\pi\) | ||||
0.441175 | + | 0.897421i | \(0.354562\pi\) | |||||||
\(18\) | 7.25401 | 1.70979 | ||||||||
\(19\) | −5.84505 | −1.34095 | −0.670473 | − | 0.741934i | \(-0.733909\pi\) | ||||
−0.670473 | + | 0.741934i | \(0.733909\pi\) | |||||||
\(20\) | −0.0252457 | −0.00564510 | ||||||||
\(21\) | 0.245575 | 0.0535888 | ||||||||
\(22\) | −4.38082 | −0.933993 | ||||||||
\(23\) | −7.42216 | −1.54763 | −0.773814 | − | 0.633413i | \(-0.781653\pi\) | ||||
−0.773814 | + | 0.633413i | \(0.781653\pi\) | |||||||
\(24\) | −4.16285 | −0.849739 | ||||||||
\(25\) | −4.99997 | −0.999995 | ||||||||
\(26\) | 2.65345 | 0.520384 | ||||||||
\(27\) | −2.95828 | −0.569322 | ||||||||
\(28\) | 2.39930 | 0.453425 | ||||||||
\(29\) | −0.0556594 | −0.0103357 | −0.00516784 | − | 0.999987i | \(-0.501645\pi\) | ||||
−0.00516784 | + | 0.999987i | \(0.501645\pi\) | |||||||
\(30\) | 0.00685641 | 0.00125180 | ||||||||
\(31\) | 2.36468 | 0.424710 | 0.212355 | − | 0.977193i | \(-0.431887\pi\) | ||||
0.212355 | + | 0.977193i | \(0.431887\pi\) | |||||||
\(32\) | −13.9208 | −2.46087 | ||||||||
\(33\) | 0.851808 | 0.148281 | ||||||||
\(34\) | −9.65330 | −1.65553 | ||||||||
\(35\) | −0.00238384 | −0.000402942 0 | ||||||||
\(36\) | −13.7805 | −2.29675 | ||||||||
\(37\) | −6.53383 | −1.07416 | −0.537078 | − | 0.843533i | \(-0.680472\pi\) | ||||
−0.537078 | + | 0.843533i | \(0.680472\pi\) | |||||||
\(38\) | 15.5095 | 2.51598 | ||||||||
\(39\) | −0.515937 | −0.0826161 | ||||||||
\(40\) | 0.0404096 | 0.00638931 | ||||||||
\(41\) | −8.86805 | −1.38496 | −0.692478 | − | 0.721439i | \(-0.743481\pi\) | ||||
−0.692478 | + | 0.721439i | \(0.743481\pi\) | |||||||
\(42\) | −0.651619 | −0.100547 | ||||||||
\(43\) | 5.29287 | 0.807156 | 0.403578 | − | 0.914945i | \(-0.367766\pi\) | ||||
0.403578 | + | 0.914945i | \(0.367766\pi\) | |||||||
\(44\) | 8.32228 | 1.25463 | ||||||||
\(45\) | 0.0136917 | 0.00204104 | ||||||||
\(46\) | 19.6943 | 2.90377 | ||||||||
\(47\) | 7.95646 | 1.16057 | 0.580284 | − | 0.814414i | \(-0.302941\pi\) | ||||
0.580284 | + | 0.814414i | \(0.302941\pi\) | |||||||
\(48\) | 5.84446 | 0.843576 | ||||||||
\(49\) | −6.77344 | −0.967635 | ||||||||
\(50\) | 13.2672 | 1.87626 | ||||||||
\(51\) | 1.87699 | 0.262831 | ||||||||
\(52\) | −5.04077 | −0.699030 | ||||||||
\(53\) | −8.94334 | −1.22846 | −0.614231 | − | 0.789126i | \(-0.710534\pi\) | ||||
−0.614231 | + | 0.789126i | \(0.710534\pi\) | |||||||
\(54\) | 7.84965 | 1.06820 | ||||||||
\(55\) | −0.00826865 | −0.00111494 | ||||||||
\(56\) | −3.84044 | −0.513201 | ||||||||
\(57\) | −3.01568 | −0.399436 | ||||||||
\(58\) | 0.147689 | 0.0193925 | ||||||||
\(59\) | 2.92756 | 0.381136 | 0.190568 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190568 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(60\) | −0.0130252 | −0.00168154 | ||||||||
\(61\) | 2.66939 | 0.341780 | 0.170890 | − | 0.985290i | \(-0.445336\pi\) | ||||
0.170890 | + | 0.985290i | \(0.445336\pi\) | |||||||
\(62\) | −6.27456 | −0.796870 | ||||||||
\(63\) | −1.30123 | −0.163940 | ||||||||
\(64\) | 14.2824 | 1.78530 | ||||||||
\(65\) | 0.00500829 | 0.000621202 0 | ||||||||
\(66\) | −2.26023 | −0.278215 | ||||||||
\(67\) | 3.28724 | 0.401601 | 0.200800 | − | 0.979632i | \(-0.435646\pi\) | ||||
0.200800 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(68\) | 18.3385 | 2.22386 | ||||||||
\(69\) | −3.82937 | −0.461002 | ||||||||
\(70\) | 0.00632538 | 0.000756028 0 | ||||||||
\(71\) | 2.08943 | 0.247969 | 0.123985 | − | 0.992284i | \(-0.460433\pi\) | ||||
0.123985 | + | 0.992284i | \(0.460433\pi\) | |||||||
\(72\) | 22.0578 | 2.59954 | ||||||||
\(73\) | −2.96308 | −0.346802 | −0.173401 | − | 0.984851i | \(-0.555476\pi\) | ||||
−0.173401 | + | 0.984851i | \(0.555476\pi\) | |||||||
\(74\) | 17.3372 | 2.01541 | ||||||||
\(75\) | −2.57967 | −0.297875 | ||||||||
\(76\) | −29.4636 | −3.37970 | ||||||||
\(77\) | 0.785836 | 0.0895543 | ||||||||
\(78\) | 1.36901 | 0.155010 | ||||||||
\(79\) | 10.7511 | 1.20959 | 0.604797 | − | 0.796379i | \(-0.293254\pi\) | ||||
0.604797 | + | 0.796379i | \(0.293254\pi\) | |||||||
\(80\) | −0.0567332 | −0.00634297 | ||||||||
\(81\) | 6.67514 | 0.741682 | ||||||||
\(82\) | 23.5309 | 2.59855 | ||||||||
\(83\) | 15.5905 | 1.71128 | 0.855639 | − | 0.517574i | \(-0.173165\pi\) | ||||
0.855639 | + | 0.517574i | \(0.173165\pi\) | |||||||
\(84\) | 1.23789 | 0.135065 | ||||||||
\(85\) | −0.0182203 | −0.00197627 | ||||||||
\(86\) | −14.0444 | −1.51444 | ||||||||
\(87\) | −0.0287167 | −0.00307876 | ||||||||
\(88\) | −13.3211 | −1.42003 | ||||||||
\(89\) | 0.666900 | 0.0706913 | 0.0353457 | − | 0.999375i | \(-0.488747\pi\) | ||||
0.0353457 | + | 0.999375i | \(0.488747\pi\) | |||||||
\(90\) | −0.0363302 | −0.00382954 | ||||||||
\(91\) | −0.475978 | −0.0498961 | ||||||||
\(92\) | −37.4134 | −3.90062 | ||||||||
\(93\) | 1.22003 | 0.126511 | ||||||||
\(94\) | −21.1120 | −2.17754 | ||||||||
\(95\) | 0.0292737 | 0.00300342 | ||||||||
\(96\) | −7.18226 | −0.733036 | ||||||||
\(97\) | −8.96468 | −0.910225 | −0.455113 | − | 0.890434i | \(-0.650401\pi\) | ||||
−0.455113 | + | 0.890434i | \(0.650401\pi\) | |||||||
\(98\) | 17.9730 | 1.81554 | ||||||||
\(99\) | −4.51350 | −0.453623 | ||||||||
\(100\) | −25.2037 | −2.52037 | ||||||||
\(101\) | 3.30741 | 0.329100 | 0.164550 | − | 0.986369i | \(-0.447383\pi\) | ||||
0.164550 | + | 0.986369i | \(0.447383\pi\) | |||||||
\(102\) | −4.98050 | −0.493143 | ||||||||
\(103\) | −12.8857 | −1.26967 | −0.634833 | − | 0.772650i | \(-0.718931\pi\) | ||||
−0.634833 | + | 0.772650i | \(0.718931\pi\) | |||||||
\(104\) | 8.06853 | 0.791185 | ||||||||
\(105\) | −0.00122991 | −0.000120027 0 | ||||||||
\(106\) | 23.7307 | 2.30493 | ||||||||
\(107\) | 10.4861 | 1.01373 | 0.506866 | − | 0.862025i | \(-0.330804\pi\) | ||||
0.506866 | + | 0.862025i | \(0.330804\pi\) | |||||||
\(108\) | −14.9120 | −1.43491 | ||||||||
\(109\) | 7.93761 | 0.760285 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(110\) | 0.0219404 | 0.00209194 | ||||||||
\(111\) | −3.37105 | −0.319966 | ||||||||
\(112\) | 5.39181 | 0.509479 | ||||||||
\(113\) | −8.11503 | −0.763398 | −0.381699 | − | 0.924287i | \(-0.624661\pi\) | ||||
−0.381699 | + | 0.924287i | \(0.624661\pi\) | |||||||
\(114\) | 8.00194 | 0.749450 | ||||||||
\(115\) | 0.0371723 | 0.00346634 | ||||||||
\(116\) | −0.280566 | −0.0260499 | ||||||||
\(117\) | 2.73381 | 0.252741 | ||||||||
\(118\) | −7.76813 | −0.715114 | ||||||||
\(119\) | 1.73162 | 0.158737 | ||||||||
\(120\) | 0.0208488 | 0.00190323 | ||||||||
\(121\) | −8.27423 | −0.752202 | ||||||||
\(122\) | −7.08308 | −0.641271 | ||||||||
\(123\) | −4.57536 | −0.412546 | ||||||||
\(124\) | 11.9198 | 1.07043 | ||||||||
\(125\) | 0.0500828 | 0.00447954 | ||||||||
\(126\) | 3.45275 | 0.307596 | ||||||||
\(127\) | 7.74521 | 0.687276 | 0.343638 | − | 0.939102i | \(-0.388341\pi\) | ||||
0.343638 | + | 0.939102i | \(0.388341\pi\) | |||||||
\(128\) | −10.0559 | −0.888825 | ||||||||
\(129\) | 2.73079 | 0.240433 | ||||||||
\(130\) | −0.0132892 | −0.00116554 | ||||||||
\(131\) | −5.88653 | −0.514308 | −0.257154 | − | 0.966370i | \(-0.582785\pi\) | ||||
−0.257154 | + | 0.966370i | \(0.582785\pi\) | |||||||
\(132\) | 4.29377 | 0.373725 | ||||||||
\(133\) | −2.78211 | −0.241240 | ||||||||
\(134\) | −8.72253 | −0.753511 | ||||||||
\(135\) | 0.0148160 | 0.00127515 | ||||||||
\(136\) | −29.3535 | −2.51704 | ||||||||
\(137\) | 13.4566 | 1.14968 | 0.574839 | − | 0.818267i | \(-0.305065\pi\) | ||||
0.574839 | + | 0.818267i | \(0.305065\pi\) | |||||||
\(138\) | 10.1610 | 0.864963 | ||||||||
\(139\) | −17.2788 | −1.46557 | −0.732786 | − | 0.680459i | \(-0.761780\pi\) | ||||
−0.732786 | + | 0.680459i | \(0.761780\pi\) | |||||||
\(140\) | −0.0120164 | −0.00101557 | ||||||||
\(141\) | 4.10503 | 0.345706 | ||||||||
\(142\) | −5.54418 | −0.465258 | ||||||||
\(143\) | −1.65099 | −0.138063 | ||||||||
\(144\) | −30.9682 | −2.58068 | ||||||||
\(145\) | 0.000278758 0 | 2.31496e−5 0 | ||||||||
\(146\) | 7.86237 | 0.650695 | ||||||||
\(147\) | −3.49467 | −0.288236 | ||||||||
\(148\) | −32.9356 | −2.70729 | ||||||||
\(149\) | 12.5580 | 1.02879 | 0.514395 | − | 0.857554i | \(-0.328017\pi\) | ||||
0.514395 | + | 0.857554i | \(0.328017\pi\) | |||||||
\(150\) | 6.84502 | 0.558894 | ||||||||
\(151\) | 15.7683 | 1.28320 | 0.641601 | − | 0.767038i | \(-0.278270\pi\) | ||||
0.641601 | + | 0.767038i | \(0.278270\pi\) | |||||||
\(152\) | 47.1609 | 3.82526 | ||||||||
\(153\) | −9.94566 | −0.804059 | ||||||||
\(154\) | −2.08517 | −0.168028 | ||||||||
\(155\) | −0.0118430 | −0.000951254 0 | ||||||||
\(156\) | −2.60072 | −0.208224 | ||||||||
\(157\) | 23.4257 | 1.86957 | 0.934786 | − | 0.355212i | \(-0.115591\pi\) | ||||
0.934786 | + | 0.355212i | \(0.115591\pi\) | |||||||
\(158\) | −28.5275 | −2.26953 | ||||||||
\(159\) | −4.61420 | −0.365930 | ||||||||
\(160\) | 0.0697194 | 0.00551181 | ||||||||
\(161\) | −3.53279 | −0.278423 | ||||||||
\(162\) | −17.7121 | −1.39160 | ||||||||
\(163\) | −4.10226 | −0.321314 | −0.160657 | − | 0.987010i | \(-0.551361\pi\) | ||||
−0.160657 | + | 0.987010i | \(0.551361\pi\) | |||||||
\(164\) | −44.7018 | −3.49063 | ||||||||
\(165\) | −0.00426610 | −0.000332116 0 | ||||||||
\(166\) | −41.3685 | −3.21082 | ||||||||
\(167\) | −3.44344 | −0.266462 | −0.133231 | − | 0.991085i | \(-0.542535\pi\) | ||||
−0.133231 | + | 0.991085i | \(0.542535\pi\) | |||||||
\(168\) | −1.98143 | −0.152870 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.0483465 | 0.00370801 | ||||||||
\(171\) | 15.9792 | 1.22196 | ||||||||
\(172\) | 26.6802 | 2.03435 | ||||||||
\(173\) | 11.5721 | 0.879811 | 0.439906 | − | 0.898044i | \(-0.355012\pi\) | ||||
0.439906 | + | 0.898044i | \(0.355012\pi\) | |||||||
\(174\) | 0.0761983 | 0.00577658 | ||||||||
\(175\) | −2.37988 | −0.179902 | ||||||||
\(176\) | 18.7022 | 1.40973 | ||||||||
\(177\) | 1.51044 | 0.113532 | ||||||||
\(178\) | −1.76958 | −0.132636 | ||||||||
\(179\) | 8.58201 | 0.641449 | 0.320725 | − | 0.947172i | \(-0.396074\pi\) | ||||
0.320725 | + | 0.947172i | \(0.396074\pi\) | |||||||
\(180\) | 0.0690168 | 0.00514421 | ||||||||
\(181\) | −8.74813 | −0.650243 | −0.325122 | − | 0.945672i | \(-0.605405\pi\) | ||||
−0.325122 | + | 0.945672i | \(0.605405\pi\) | |||||||
\(182\) | 1.26298 | 0.0936185 | ||||||||
\(183\) | 1.37724 | 0.101808 | ||||||||
\(184\) | 59.8859 | 4.41485 | ||||||||
\(185\) | 0.0327233 | 0.00240587 | ||||||||
\(186\) | −3.23728 | −0.237369 | ||||||||
\(187\) | 6.00635 | 0.439228 | ||||||||
\(188\) | 40.1067 | 2.92508 | ||||||||
\(189\) | −1.40808 | −0.102423 | ||||||||
\(190\) | −0.0776762 | −0.00563522 | ||||||||
\(191\) | 17.5140 | 1.26727 | 0.633634 | − | 0.773633i | \(-0.281562\pi\) | ||||
0.633634 | + | 0.773633i | \(0.281562\pi\) | |||||||
\(192\) | 7.36881 | 0.531798 | ||||||||
\(193\) | 3.43729 | 0.247421 | 0.123711 | − | 0.992318i | \(-0.460521\pi\) | ||||
0.123711 | + | 0.992318i | \(0.460521\pi\) | |||||||
\(194\) | 23.7873 | 1.70783 | ||||||||
\(195\) | 0.00258396 | 0.000185041 0 | ||||||||
\(196\) | −34.1434 | −2.43882 | ||||||||
\(197\) | −2.59164 | −0.184647 | −0.0923234 | − | 0.995729i | \(-0.529429\pi\) | ||||
−0.0923234 | + | 0.995729i | \(0.529429\pi\) | |||||||
\(198\) | 11.9763 | 0.851120 | ||||||||
\(199\) | −7.46291 | −0.529032 | −0.264516 | − | 0.964381i | \(-0.585212\pi\) | ||||
−0.264516 | + | 0.964381i | \(0.585212\pi\) | |||||||
\(200\) | 40.3425 | 2.85264 | ||||||||
\(201\) | 1.69601 | 0.119627 | ||||||||
\(202\) | −8.77604 | −0.617480 | ||||||||
\(203\) | −0.0264927 | −0.00185942 | ||||||||
\(204\) | 9.46149 | 0.662437 | ||||||||
\(205\) | 0.0444138 | 0.00310199 | ||||||||
\(206\) | 34.1915 | 2.38223 | ||||||||
\(207\) | 20.2908 | 1.41031 | ||||||||
\(208\) | −11.3279 | −0.785446 | ||||||||
\(209\) | −9.65012 | −0.667513 | ||||||||
\(210\) | 0.00326350 | 0.000225203 0 | ||||||||
\(211\) | −4.59355 | −0.316233 | −0.158117 | − | 0.987420i | \(-0.550542\pi\) | ||||
−0.158117 | + | 0.987420i | \(0.550542\pi\) | |||||||
\(212\) | −45.0814 | −3.09620 | ||||||||
\(213\) | 1.07801 | 0.0738643 | ||||||||
\(214\) | −27.8243 | −1.90203 | ||||||||
\(215\) | −0.0265083 | −0.00180785 | ||||||||
\(216\) | 23.8690 | 1.62408 | ||||||||
\(217\) | 1.12554 | 0.0764064 | ||||||||
\(218\) | −21.0620 | −1.42650 | ||||||||
\(219\) | −1.52876 | −0.103304 | ||||||||
\(220\) | −0.0416804 | −0.00281009 | ||||||||
\(221\) | −3.63802 | −0.244720 | ||||||||
\(222\) | 8.94489 | 0.600342 | ||||||||
\(223\) | 22.7650 | 1.52446 | 0.762228 | − | 0.647308i | \(-0.224105\pi\) | ||||
0.762228 | + | 0.647308i | \(0.224105\pi\) | |||||||
\(224\) | −6.62600 | −0.442718 | ||||||||
\(225\) | 13.6690 | 0.911265 | ||||||||
\(226\) | 21.5328 | 1.43234 | ||||||||
\(227\) | 14.7090 | 0.976267 | 0.488134 | − | 0.872769i | \(-0.337678\pi\) | ||||
0.488134 | + | 0.872769i | \(0.337678\pi\) | |||||||
\(228\) | −15.2013 | −1.00673 | ||||||||
\(229\) | 10.5556 | 0.697531 | 0.348766 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348766 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(230\) | −0.0986348 | −0.00650379 | ||||||||
\(231\) | 0.405442 | 0.0266761 | ||||||||
\(232\) | 0.449090 | 0.0294842 | ||||||||
\(233\) | −3.19984 | −0.209629 | −0.104814 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104814 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(234\) | −7.25401 | −0.474210 | ||||||||
\(235\) | −0.0398483 | −0.00259941 | ||||||||
\(236\) | 14.7572 | 0.960611 | ||||||||
\(237\) | 5.54690 | 0.360310 | ||||||||
\(238\) | −4.59476 | −0.297834 | ||||||||
\(239\) | 23.3898 | 1.51296 | 0.756482 | − | 0.654015i | \(-0.226917\pi\) | ||||
0.756482 | + | 0.654015i | \(0.226917\pi\) | |||||||
\(240\) | −0.0292708 | −0.00188942 | ||||||||
\(241\) | −17.0415 | −1.09774 | −0.548871 | − | 0.835907i | \(-0.684942\pi\) | ||||
−0.548871 | + | 0.835907i | \(0.684942\pi\) | |||||||
\(242\) | 21.9552 | 1.41133 | ||||||||
\(243\) | 12.3188 | 0.790252 | ||||||||
\(244\) | 13.4558 | 0.861418 | ||||||||
\(245\) | 0.0339234 | 0.00216729 | ||||||||
\(246\) | 12.1405 | 0.774048 | ||||||||
\(247\) | 5.84505 | 0.371911 | ||||||||
\(248\) | −19.0795 | −1.21155 | ||||||||
\(249\) | 8.04371 | 0.509749 | ||||||||
\(250\) | −0.132892 | −0.00840483 | ||||||||
\(251\) | 12.3446 | 0.779185 | 0.389592 | − | 0.920987i | \(-0.372616\pi\) | ||||
0.389592 | + | 0.920987i | \(0.372616\pi\) | |||||||
\(252\) | −6.55922 | −0.413192 | ||||||||
\(253\) | −12.2539 | −0.770398 | ||||||||
\(254\) | −20.5515 | −1.28951 | ||||||||
\(255\) | −0.00940052 | −0.000588683 0 | ||||||||
\(256\) | −1.88195 | −0.117622 | ||||||||
\(257\) | 2.39685 | 0.149511 | 0.0747556 | − | 0.997202i | \(-0.476182\pi\) | ||||
0.0747556 | + | 0.997202i | \(0.476182\pi\) | |||||||
\(258\) | −7.24600 | −0.451117 | ||||||||
\(259\) | −3.10996 | −0.193244 | ||||||||
\(260\) | 0.0252457 | 0.00156567 | ||||||||
\(261\) | 0.152162 | 0.00941860 | ||||||||
\(262\) | 15.6196 | 0.964981 | ||||||||
\(263\) | −12.6291 | −0.778745 | −0.389372 | − | 0.921080i | \(-0.627308\pi\) | ||||
−0.389372 | + | 0.921080i | \(0.627308\pi\) | |||||||
\(264\) | −6.87284 | −0.422994 | ||||||||
\(265\) | 0.0447909 | 0.00275148 | ||||||||
\(266\) | 7.38219 | 0.452631 | ||||||||
\(267\) | 0.344079 | 0.0210573 | ||||||||
\(268\) | 16.5703 | 1.01219 | ||||||||
\(269\) | 6.53901 | 0.398690 | 0.199345 | − | 0.979929i | \(-0.436119\pi\) | ||||
0.199345 | + | 0.979929i | \(0.436119\pi\) | |||||||
\(270\) | −0.0393133 | −0.00239253 | ||||||||
\(271\) | 3.69104 | 0.224215 | 0.112107 | − | 0.993696i | \(-0.464240\pi\) | ||||
0.112107 | + | 0.993696i | \(0.464240\pi\) | |||||||
\(272\) | 41.2110 | 2.49879 | ||||||||
\(273\) | −0.245575 | −0.0148629 | ||||||||
\(274\) | −35.7064 | −2.15710 | ||||||||
\(275\) | −8.25492 | −0.497790 | ||||||||
\(276\) | −19.3030 | −1.16190 | ||||||||
\(277\) | −10.5010 | −0.630947 | −0.315473 | − | 0.948934i | \(-0.602163\pi\) | ||||
−0.315473 | + | 0.948934i | \(0.602163\pi\) | |||||||
\(278\) | 45.8485 | 2.74981 | ||||||||
\(279\) | −6.46459 | −0.387025 | ||||||||
\(280\) | 0.0192341 | 0.00114946 | ||||||||
\(281\) | 12.3150 | 0.734654 | 0.367327 | − | 0.930092i | \(-0.380273\pi\) | ||||
0.367327 | + | 0.930092i | \(0.380273\pi\) | |||||||
\(282\) | −10.8925 | −0.648638 | ||||||||
\(283\) | 6.98483 | 0.415205 | 0.207603 | − | 0.978213i | \(-0.433434\pi\) | ||||
0.207603 | + | 0.978213i | \(0.433434\pi\) | |||||||
\(284\) | 10.5323 | 0.624979 | ||||||||
\(285\) | 0.0151034 | 0.000894647 0 | ||||||||
\(286\) | 4.38082 | 0.259043 | ||||||||
\(287\) | −4.22100 | −0.249158 | ||||||||
\(288\) | 38.0568 | 2.24252 | ||||||||
\(289\) | −3.76478 | −0.221458 | ||||||||
\(290\) | −0.000739670 0 | −4.34349e−5 0 | ||||||||
\(291\) | −4.62521 | −0.271135 | ||||||||
\(292\) | −14.9362 | −0.874076 | ||||||||
\(293\) | 0.0137949 | 0.000805909 0 | 0.000402954 | − | 1.00000i | \(-0.499872\pi\) | ||||
0.000402954 | 1.00000i | \(0.499872\pi\) | ||||||||
\(294\) | 9.27292 | 0.540808 | ||||||||
\(295\) | −0.0146621 | −0.000853660 0 | ||||||||
\(296\) | 52.7184 | 3.06420 | ||||||||
\(297\) | −4.88410 | −0.283404 | ||||||||
\(298\) | −33.3219 | −1.93029 | ||||||||
\(299\) | 7.42216 | 0.429235 | ||||||||
\(300\) | −13.0035 | −0.750760 | ||||||||
\(301\) | 2.51929 | 0.145210 | ||||||||
\(302\) | −41.8402 | −2.40763 | ||||||||
\(303\) | 1.70642 | 0.0980311 | ||||||||
\(304\) | −66.2119 | −3.79751 | ||||||||
\(305\) | −0.0133691 | −0.000765511 0 | ||||||||
\(306\) | 26.3903 | 1.50863 | ||||||||
\(307\) | 12.7245 | 0.726225 | 0.363113 | − | 0.931745i | \(-0.381714\pi\) | ||||
0.363113 | + | 0.931745i | \(0.381714\pi\) | |||||||
\(308\) | 3.96122 | 0.225712 | ||||||||
\(309\) | −6.64821 | −0.378203 | ||||||||
\(310\) | 0.0314248 | 0.00178481 | ||||||||
\(311\) | 22.8436 | 1.29534 | 0.647670 | − | 0.761921i | \(-0.275743\pi\) | ||||
0.647670 | + | 0.761921i | \(0.275743\pi\) | |||||||
\(312\) | 4.16285 | 0.235675 | ||||||||
\(313\) | 6.11890 | 0.345860 | 0.172930 | − | 0.984934i | \(-0.444676\pi\) | ||||
0.172930 | + | 0.984934i | \(0.444676\pi\) | |||||||
\(314\) | −62.1587 | −3.50782 | ||||||||
\(315\) | 0.00651695 | 0.000367189 0 | ||||||||
\(316\) | 54.1939 | 3.04865 | ||||||||
\(317\) | 10.8002 | 0.606601 | 0.303300 | − | 0.952895i | \(-0.401911\pi\) | ||||
0.303300 | + | 0.952895i | \(0.401911\pi\) | |||||||
\(318\) | 12.2435 | 0.686584 | ||||||||
\(319\) | −0.0918932 | −0.00514503 | ||||||||
\(320\) | −0.0715303 | −0.00399867 | ||||||||
\(321\) | 5.41018 | 0.301967 | ||||||||
\(322\) | 9.37406 | 0.522396 | ||||||||
\(323\) | −21.2644 | −1.18318 | ||||||||
\(324\) | 33.6479 | 1.86933 | ||||||||
\(325\) | 4.99997 | 0.277349 | ||||||||
\(326\) | 10.8851 | 0.602871 | ||||||||
\(327\) | 4.09531 | 0.226471 | ||||||||
\(328\) | 71.5522 | 3.95081 | ||||||||
\(329\) | 3.78710 | 0.208790 | ||||||||
\(330\) | 0.0113199 | 0.000623138 0 | ||||||||
\(331\) | 9.59881 | 0.527599 | 0.263799 | − | 0.964578i | \(-0.415024\pi\) | ||||
0.263799 | + | 0.964578i | \(0.415024\pi\) | |||||||
\(332\) | 78.5881 | 4.31308 | ||||||||
\(333\) | 17.8623 | 0.978845 | ||||||||
\(334\) | 9.13699 | 0.499954 | ||||||||
\(335\) | −0.0164635 | −0.000899496 0 | ||||||||
\(336\) | 2.78184 | 0.151762 | ||||||||
\(337\) | 2.52387 | 0.137484 | 0.0687420 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687420 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(338\) | −2.65345 | −0.144328 | ||||||||
\(339\) | −4.18684 | −0.227398 | ||||||||
\(340\) | −0.0918443 | −0.00498096 | ||||||||
\(341\) | 3.90407 | 0.211417 | ||||||||
\(342\) | −42.4001 | −2.29273 | ||||||||
\(343\) | −6.55586 | −0.353983 | ||||||||
\(344\) | −42.7057 | −2.30254 | ||||||||
\(345\) | 0.0191786 | 0.00103254 | ||||||||
\(346\) | −30.7060 | −1.65076 | ||||||||
\(347\) | 12.6819 | 0.680801 | 0.340401 | − | 0.940280i | \(-0.389437\pi\) | ||||
0.340401 | + | 0.940280i | \(0.389437\pi\) | |||||||
\(348\) | −0.144755 | −0.00775966 | ||||||||
\(349\) | 0.762243 | 0.0408020 | 0.0204010 | − | 0.999792i | \(-0.493506\pi\) | ||||
0.0204010 | + | 0.999792i | \(0.493506\pi\) | |||||||
\(350\) | 6.31488 | 0.337544 | ||||||||
\(351\) | 2.95828 | 0.157902 | ||||||||
\(352\) | −22.9831 | −1.22501 | ||||||||
\(353\) | 35.0468 | 1.86535 | 0.932675 | − | 0.360717i | \(-0.117468\pi\) | ||||
0.932675 | + | 0.360717i | \(0.117468\pi\) | |||||||
\(354\) | −4.00787 | −0.213016 | ||||||||
\(355\) | −0.0104645 | −0.000555396 0 | ||||||||
\(356\) | 3.36170 | 0.178169 | ||||||||
\(357\) | 0.893407 | 0.0472841 | ||||||||
\(358\) | −22.7719 | −1.20353 | ||||||||
\(359\) | −28.3780 | −1.49774 | −0.748868 | − | 0.662720i | \(-0.769402\pi\) | ||||
−0.748868 | + | 0.662720i | \(0.769402\pi\) | |||||||
\(360\) | −0.110472 | −0.00582239 | ||||||||
\(361\) | 15.1646 | 0.798136 | ||||||||
\(362\) | 23.2127 | 1.22003 | ||||||||
\(363\) | −4.26898 | −0.224063 | ||||||||
\(364\) | −2.39930 | −0.125757 | ||||||||
\(365\) | 0.0148400 | 0.000776759 0 | ||||||||
\(366\) | −3.65442 | −0.191020 | ||||||||
\(367\) | −22.7527 | −1.18768 | −0.593840 | − | 0.804583i | \(-0.702389\pi\) | ||||
−0.593840 | + | 0.804583i | \(0.702389\pi\) | |||||||
\(368\) | −84.0772 | −4.38283 | ||||||||
\(369\) | 24.2436 | 1.26207 | ||||||||
\(370\) | −0.0868296 | −0.00451406 | ||||||||
\(371\) | −4.25684 | −0.221004 | ||||||||
\(372\) | 6.14988 | 0.318857 | ||||||||
\(373\) | −31.8029 | −1.64669 | −0.823346 | − | 0.567540i | \(-0.807895\pi\) | ||||
−0.823346 | + | 0.567540i | \(0.807895\pi\) | |||||||
\(374\) | −15.9375 | −0.824109 | ||||||||
\(375\) | 0.0258396 | 0.00133435 | ||||||||
\(376\) | −64.1969 | −3.31070 | ||||||||
\(377\) | 0.0556594 | 0.00286660 | ||||||||
\(378\) | 3.73626 | 0.192173 | ||||||||
\(379\) | −27.8757 | −1.43188 | −0.715940 | − | 0.698162i | \(-0.754001\pi\) | ||||
−0.715940 | + | 0.698162i | \(0.754001\pi\) | |||||||
\(380\) | 0.147562 | 0.00756978 | ||||||||
\(381\) | 3.99604 | 0.204723 | ||||||||
\(382\) | −46.4725 | −2.37774 | ||||||||
\(383\) | 3.33238 | 0.170277 | 0.0851384 | − | 0.996369i | \(-0.472867\pi\) | ||||
0.0851384 | + | 0.996369i | \(0.472867\pi\) | |||||||
\(384\) | −5.18822 | −0.264760 | ||||||||
\(385\) | −0.00393569 | −0.000200582 0 | ||||||||
\(386\) | −9.12065 | −0.464229 | ||||||||
\(387\) | −14.4697 | −0.735537 | ||||||||
\(388\) | −45.1889 | −2.29412 | ||||||||
\(389\) | −21.2115 | −1.07547 | −0.537734 | − | 0.843115i | \(-0.680719\pi\) | ||||
−0.537734 | + | 0.843115i | \(0.680719\pi\) | |||||||
\(390\) | −0.00685641 | −0.000347188 0 | ||||||||
\(391\) | −27.0020 | −1.36555 | ||||||||
\(392\) | 54.6518 | 2.76033 | ||||||||
\(393\) | −3.03708 | −0.153200 | ||||||||
\(394\) | 6.87678 | 0.346447 | ||||||||
\(395\) | −0.0538447 | −0.00270922 | ||||||||
\(396\) | −22.7515 | −1.14331 | ||||||||
\(397\) | 4.20883 | 0.211235 | 0.105618 | − | 0.994407i | \(-0.466318\pi\) | ||||
0.105618 | + | 0.994407i | \(0.466318\pi\) | |||||||
\(398\) | 19.8024 | 0.992607 | ||||||||
\(399\) | −1.43540 | −0.0718597 | ||||||||
\(400\) | −56.6390 | −2.83195 | ||||||||
\(401\) | −33.8744 | −1.69161 | −0.845803 | − | 0.533496i | \(-0.820878\pi\) | ||||
−0.845803 | + | 0.533496i | \(0.820878\pi\) | |||||||
\(402\) | −4.50027 | −0.224453 | ||||||||
\(403\) | −2.36468 | −0.117793 | ||||||||
\(404\) | 16.6719 | 0.829460 | ||||||||
\(405\) | −0.0334310 | −0.00166120 | ||||||||
\(406\) | 0.0702968 | 0.00348877 | ||||||||
\(407\) | −10.7873 | −0.534707 | ||||||||
\(408\) | −15.1446 | −0.749768 | ||||||||
\(409\) | −34.8372 | −1.72259 | −0.861293 | − | 0.508108i | \(-0.830345\pi\) | ||||
−0.861293 | + | 0.508108i | \(0.830345\pi\) | |||||||
\(410\) | −0.117850 | −0.00582017 | ||||||||
\(411\) | 6.94277 | 0.342462 | ||||||||
\(412\) | −64.9539 | −3.20005 | ||||||||
\(413\) | 1.39346 | 0.0685675 | ||||||||
\(414\) | −53.8405 | −2.64611 | ||||||||
\(415\) | −0.0780816 | −0.00383288 | ||||||||
\(416\) | 13.9208 | 0.682524 | ||||||||
\(417\) | −8.91479 | −0.436559 | ||||||||
\(418\) | 25.6061 | 1.25243 | ||||||||
\(419\) | −30.4052 | −1.48539 | −0.742697 | − | 0.669628i | \(-0.766454\pi\) | ||||
−0.742697 | + | 0.669628i | \(0.766454\pi\) | |||||||
\(420\) | −0.00619970 | −0.000302514 0 | ||||||||
\(421\) | 9.98329 | 0.486556 | 0.243278 | − | 0.969957i | \(-0.421777\pi\) | ||||
0.243278 | + | 0.969957i | \(0.421777\pi\) | |||||||
\(422\) | 12.1887 | 0.593338 | ||||||||
\(423\) | −21.7514 | −1.05759 | ||||||||
\(424\) | 72.1597 | 3.50438 | ||||||||
\(425\) | −18.1900 | −0.882346 | ||||||||
\(426\) | −2.86045 | −0.138589 | ||||||||
\(427\) | 1.27057 | 0.0614872 | ||||||||
\(428\) | 52.8581 | 2.55499 | ||||||||
\(429\) | −0.851808 | −0.0411257 | ||||||||
\(430\) | 0.0703382 | 0.00339201 | ||||||||
\(431\) | −4.65355 | −0.224153 | −0.112077 | − | 0.993700i | \(-0.535750\pi\) | ||||
−0.112077 | + | 0.993700i | \(0.535750\pi\) | |||||||
\(432\) | −33.5110 | −1.61230 | ||||||||
\(433\) | −12.7533 | −0.612884 | −0.306442 | − | 0.951889i | \(-0.599139\pi\) | ||||
−0.306442 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(434\) | −2.98655 | −0.143359 | ||||||||
\(435\) | 0.000143822 0 | 6.89573e−6 0 | ||||||||
\(436\) | 40.0117 | 1.91621 | ||||||||
\(437\) | 43.3829 | 2.07528 | ||||||||
\(438\) | 4.05649 | 0.193827 | ||||||||
\(439\) | 9.54567 | 0.455590 | 0.227795 | − | 0.973709i | \(-0.426848\pi\) | ||||
0.227795 | + | 0.973709i | \(0.426848\pi\) | |||||||
\(440\) | 0.0667158 | 0.00318055 | ||||||||
\(441\) | 18.5173 | 0.881776 | ||||||||
\(442\) | 9.65330 | 0.459161 | ||||||||
\(443\) | 38.2436 | 1.81701 | 0.908504 | − | 0.417877i | \(-0.137226\pi\) | ||||
0.908504 | + | 0.417877i | \(0.137226\pi\) | |||||||
\(444\) | −16.9927 | −0.806437 | ||||||||
\(445\) | −0.00334003 | −0.000158333 0 | ||||||||
\(446\) | −60.4057 | −2.86029 | ||||||||
\(447\) | 6.47913 | 0.306452 | ||||||||
\(448\) | 6.79810 | 0.321180 | ||||||||
\(449\) | −9.31882 | −0.439783 | −0.219891 | − | 0.975524i | \(-0.570570\pi\) | ||||
−0.219891 | + | 0.975524i | \(0.570570\pi\) | |||||||
\(450\) | −36.2699 | −1.70978 | ||||||||
\(451\) | −14.6411 | −0.689421 | ||||||||
\(452\) | −40.9060 | −1.92406 | ||||||||
\(453\) | 8.13543 | 0.382236 | ||||||||
\(454\) | −39.0294 | −1.83174 | ||||||||
\(455\) | 0.00238384 | 0.000111756 0 | ||||||||
\(456\) | 24.3321 | 1.13945 | ||||||||
\(457\) | −2.09500 | −0.0980000 | −0.0490000 | − | 0.998799i | \(-0.515603\pi\) | ||||
−0.0490000 | + | 0.998799i | \(0.515603\pi\) | |||||||
\(458\) | −28.0086 | −1.30876 | ||||||||
\(459\) | −10.7623 | −0.502342 | ||||||||
\(460\) | 0.187377 | 0.00873652 | ||||||||
\(461\) | 7.03041 | 0.327439 | 0.163719 | − | 0.986507i | \(-0.447651\pi\) | ||||
0.163719 | + | 0.986507i | \(0.447651\pi\) | |||||||
\(462\) | −1.07582 | −0.0500516 | ||||||||
\(463\) | −41.7166 | −1.93873 | −0.969367 | − | 0.245618i | \(-0.921009\pi\) | ||||
−0.969367 | + | 0.245618i | \(0.921009\pi\) | |||||||
\(464\) | −0.630502 | −0.0292703 | ||||||||
\(465\) | −0.00611025 | −0.000283356 0 | ||||||||
\(466\) | 8.49060 | 0.393320 | ||||||||
\(467\) | −10.0452 | −0.464836 | −0.232418 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232418 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(468\) | 13.7805 | 0.637005 | ||||||||
\(469\) | 1.56466 | 0.0722491 | ||||||||
\(470\) | 0.105735 | 0.00487720 | ||||||||
\(471\) | 12.0862 | 0.556901 | ||||||||
\(472\) | −23.6211 | −1.08725 | ||||||||
\(473\) | 8.73849 | 0.401796 | ||||||||
\(474\) | −14.7184 | −0.676038 | ||||||||
\(475\) | 29.2251 | 1.34094 | ||||||||
\(476\) | 8.72871 | 0.400080 | ||||||||
\(477\) | 24.4494 | 1.11946 | ||||||||
\(478\) | −62.0637 | −2.83873 | ||||||||
\(479\) | −39.0021 | −1.78205 | −0.891026 | − | 0.453952i | \(-0.850014\pi\) | ||||
−0.891026 | + | 0.453952i | \(0.850014\pi\) | |||||||
\(480\) | 0.0359708 | 0.00164184 | ||||||||
\(481\) | 6.53383 | 0.297917 | ||||||||
\(482\) | 45.2188 | 2.05966 | ||||||||
\(483\) | −1.82270 | −0.0829355 | ||||||||
\(484\) | −41.7085 | −1.89584 | ||||||||
\(485\) | 0.0448977 | 0.00203870 | ||||||||
\(486\) | −32.6873 | −1.48273 | ||||||||
\(487\) | 6.16441 | 0.279336 | 0.139668 | − | 0.990198i | \(-0.455396\pi\) | ||||
0.139668 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(488\) | −21.5380 | −0.974981 | ||||||||
\(489\) | −2.11651 | −0.0957117 | ||||||||
\(490\) | −0.0900139 | −0.00406641 | ||||||||
\(491\) | −17.4046 | −0.785458 | −0.392729 | − | 0.919654i | \(-0.628469\pi\) | ||||
−0.392729 | + | 0.919654i | \(0.628469\pi\) | |||||||
\(492\) | −23.0633 | −1.03978 | ||||||||
\(493\) | −0.202490 | −0.00911970 | ||||||||
\(494\) | −15.5095 | −0.697806 | ||||||||
\(495\) | 0.0226049 | 0.00101601 | ||||||||
\(496\) | 26.7868 | 1.20276 | ||||||||
\(497\) | 0.994522 | 0.0446104 | ||||||||
\(498\) | −21.3435 | −0.956427 | ||||||||
\(499\) | 33.9519 | 1.51990 | 0.759948 | − | 0.649983i | \(-0.225224\pi\) | ||||
0.759948 | + | 0.649983i | \(0.225224\pi\) | |||||||
\(500\) | 0.252456 | 0.0112902 | ||||||||
\(501\) | −1.77660 | −0.0793726 | ||||||||
\(502\) | −32.7557 | −1.46196 | ||||||||
\(503\) | 12.1637 | 0.542351 | 0.271176 | − | 0.962530i | \(-0.412588\pi\) | ||||
0.271176 | + | 0.962530i | \(0.412588\pi\) | |||||||
\(504\) | 10.4990 | 0.467664 | ||||||||
\(505\) | −0.0165645 | −0.000737110 0 | ||||||||
\(506\) | 32.5151 | 1.44547 | ||||||||
\(507\) | 0.515937 | 0.0229136 | ||||||||
\(508\) | 39.0418 | 1.73220 | ||||||||
\(509\) | 33.1871 | 1.47099 | 0.735496 | − | 0.677529i | \(-0.236949\pi\) | ||||
0.735496 | + | 0.677529i | \(0.236949\pi\) | |||||||
\(510\) | 0.0249438 | 0.00110453 | ||||||||
\(511\) | −1.41036 | −0.0623907 | ||||||||
\(512\) | 25.1055 | 1.10952 | ||||||||
\(513\) | 17.2913 | 0.763430 | ||||||||
\(514\) | −6.35990 | −0.280523 | ||||||||
\(515\) | 0.0645353 | 0.00284377 | ||||||||
\(516\) | 13.7653 | 0.605983 | ||||||||
\(517\) | 13.1360 | 0.577723 | ||||||||
\(518\) | 8.25211 | 0.362577 | ||||||||
\(519\) | 5.97048 | 0.262075 | ||||||||
\(520\) | −0.0404096 | −0.00177208 | ||||||||
\(521\) | 12.2627 | 0.537238 | 0.268619 | − | 0.963246i | \(-0.413433\pi\) | ||||
0.268619 | + | 0.963246i | \(0.413433\pi\) | |||||||
\(522\) | −0.403754 | −0.0176718 | ||||||||
\(523\) | 10.6567 | 0.465986 | 0.232993 | − | 0.972478i | \(-0.425148\pi\) | ||||
0.232993 | + | 0.972478i | \(0.425148\pi\) | |||||||
\(524\) | −29.6727 | −1.29626 | ||||||||
\(525\) | −1.22787 | −0.0535885 | ||||||||
\(526\) | 33.5107 | 1.46114 | ||||||||
\(527\) | 8.60277 | 0.374743 | ||||||||
\(528\) | 9.64916 | 0.419926 | ||||||||
\(529\) | 32.0885 | 1.39515 | ||||||||
\(530\) | −0.118850 | −0.00516252 | ||||||||
\(531\) | −8.00340 | −0.347318 | ||||||||
\(532\) | −14.0240 | −0.608018 | ||||||||
\(533\) | 8.86805 | 0.384118 | ||||||||
\(534\) | −0.912994 | −0.0395091 | ||||||||
\(535\) | −0.0525175 | −0.00227053 | ||||||||
\(536\) | −26.5232 | −1.14563 | ||||||||
\(537\) | 4.42778 | 0.191073 | ||||||||
\(538\) | −17.3509 | −0.748050 | ||||||||
\(539\) | −11.1829 | −0.481682 | ||||||||
\(540\) | 0.0746839 | 0.00321388 | ||||||||
\(541\) | 12.0032 | 0.516058 | 0.258029 | − | 0.966137i | \(-0.416927\pi\) | ||||
0.258029 | + | 0.966137i | \(0.416927\pi\) | |||||||
\(542\) | −9.79398 | −0.420687 | ||||||||
\(543\) | −4.51348 | −0.193692 | ||||||||
\(544\) | −50.6442 | −2.17135 | ||||||||
\(545\) | −0.0397539 | −0.00170287 | ||||||||
\(546\) | 0.651619 | 0.0278867 | ||||||||
\(547\) | −27.8620 | −1.19129 | −0.595647 | − | 0.803246i | \(-0.703104\pi\) | ||||
−0.595647 | + | 0.803246i | \(0.703104\pi\) | |||||||
\(548\) | 67.8318 | 2.89763 | ||||||||
\(549\) | −7.29760 | −0.311454 | ||||||||
\(550\) | 21.9040 | 0.933989 | ||||||||
\(551\) | 0.325332 | 0.0138596 | ||||||||
\(552\) | 30.8974 | 1.31508 | ||||||||
\(553\) | 5.11729 | 0.217609 | ||||||||
\(554\) | 27.8640 | 1.18383 | ||||||||
\(555\) | 0.0168832 | 0.000716651 0 | ||||||||
\(556\) | −87.0987 | −3.69381 | ||||||||
\(557\) | 14.7421 | 0.624644 | 0.312322 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312322 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(558\) | 17.1534 | 0.726163 | ||||||||
\(559\) | −5.29287 | −0.223865 | ||||||||
\(560\) | −0.0270038 | −0.00114112 | ||||||||
\(561\) | 3.09890 | 0.130836 | ||||||||
\(562\) | −32.6773 | −1.37841 | ||||||||
\(563\) | −3.37440 | −0.142214 | −0.0711069 | − | 0.997469i | \(-0.522653\pi\) | ||||
−0.0711069 | + | 0.997469i | \(0.522653\pi\) | |||||||
\(564\) | 20.6925 | 0.871313 | ||||||||
\(565\) | 0.0406424 | 0.00170984 | ||||||||
\(566\) | −18.5339 | −0.779037 | ||||||||
\(567\) | 3.17722 | 0.133431 | ||||||||
\(568\) | −16.8586 | −0.707372 | ||||||||
\(569\) | −8.57801 | −0.359609 | −0.179804 | − | 0.983702i | \(-0.557546\pi\) | ||||
−0.179804 | + | 0.983702i | \(0.557546\pi\) | |||||||
\(570\) | −0.0400760 | −0.00167860 | ||||||||
\(571\) | −34.5580 | −1.44621 | −0.723104 | − | 0.690739i | \(-0.757285\pi\) | ||||
−0.723104 | + | 0.690739i | \(0.757285\pi\) | |||||||
\(572\) | −8.32228 | −0.347972 | ||||||||
\(573\) | 9.03612 | 0.377489 | ||||||||
\(574\) | 11.2002 | 0.467487 | ||||||||
\(575\) | 37.1106 | 1.54762 | ||||||||
\(576\) | −39.0453 | −1.62689 | ||||||||
\(577\) | 41.5208 | 1.72853 | 0.864267 | − | 0.503033i | \(-0.167783\pi\) | ||||
0.864267 | + | 0.503033i | \(0.167783\pi\) | |||||||
\(578\) | 9.98964 | 0.415514 | ||||||||
\(579\) | 1.77342 | 0.0737010 | ||||||||
\(580\) | 0.00140516 | 5.83460e−5 0 | ||||||||
\(581\) | 7.42073 | 0.307864 | ||||||||
\(582\) | 12.2727 | 0.508722 | ||||||||
\(583\) | −14.7654 | −0.611520 | ||||||||
\(584\) | 23.9077 | 0.989308 | ||||||||
\(585\) | −0.0136917 | −0.000566083 0 | ||||||||
\(586\) | −0.0366041 | −0.00151210 | ||||||||
\(587\) | 41.0504 | 1.69433 | 0.847166 | − | 0.531328i | \(-0.178307\pi\) | ||||
0.847166 | + | 0.531328i | \(0.178307\pi\) | |||||||
\(588\) | −17.6159 | −0.726466 | ||||||||
\(589\) | −13.8217 | −0.569512 | ||||||||
\(590\) | 0.0389051 | 0.00160170 | ||||||||
\(591\) | −1.33712 | −0.0550019 | ||||||||
\(592\) | −74.0144 | −3.04197 | ||||||||
\(593\) | 6.70002 | 0.275137 | 0.137568 | − | 0.990492i | \(-0.456071\pi\) | ||||
0.137568 | + | 0.990492i | \(0.456071\pi\) | |||||||
\(594\) | 12.9597 | 0.531743 | ||||||||
\(595\) | −0.00867246 | −0.000355536 0 | ||||||||
\(596\) | 63.3019 | 2.59295 | ||||||||
\(597\) | −3.85039 | −0.157586 | ||||||||
\(598\) | −19.6943 | −0.805360 | ||||||||
\(599\) | −31.5675 | −1.28981 | −0.644906 | − | 0.764262i | \(-0.723103\pi\) | ||||
−0.644906 | + | 0.764262i | \(0.723103\pi\) | |||||||
\(600\) | 20.8142 | 0.849735 | ||||||||
\(601\) | 8.44281 | 0.344389 | 0.172195 | − | 0.985063i | \(-0.444914\pi\) | ||||
0.172195 | + | 0.985063i | \(0.444914\pi\) | |||||||
\(602\) | −6.68481 | −0.272452 | ||||||||
\(603\) | −8.98670 | −0.365967 | ||||||||
\(604\) | 79.4842 | 3.23417 | ||||||||
\(605\) | 0.0414397 | 0.00168476 | ||||||||
\(606\) | −4.52789 | −0.183933 | ||||||||
\(607\) | −27.4718 | −1.11505 | −0.557524 | − | 0.830161i | \(-0.688249\pi\) | ||||
−0.557524 | + | 0.830161i | \(0.688249\pi\) | |||||||
\(608\) | 81.3678 | 3.29990 | ||||||||
\(609\) | −0.0136685 | −0.000553877 0 | ||||||||
\(610\) | 0.0354741 | 0.00143630 | ||||||||
\(611\) | −7.95646 | −0.321884 | ||||||||
\(612\) | −50.1338 | −2.02654 | ||||||||
\(613\) | −34.8804 | −1.40881 | −0.704403 | − | 0.709800i | \(-0.748785\pi\) | ||||
−0.704403 | + | 0.709800i | \(0.748785\pi\) | |||||||
\(614\) | −33.7638 | −1.36259 | ||||||||
\(615\) | 0.0229147 | 0.000924011 0 | ||||||||
\(616\) | −6.34054 | −0.255468 | ||||||||
\(617\) | 32.4039 | 1.30453 | 0.652266 | − | 0.757990i | \(-0.273818\pi\) | ||||
0.652266 | + | 0.757990i | \(0.273818\pi\) | |||||||
\(618\) | 17.6407 | 0.709611 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −0.0596980 | −0.00239753 | ||||||||
\(621\) | 21.9569 | 0.881099 | ||||||||
\(622\) | −60.6142 | −2.43041 | ||||||||
\(623\) | 0.317430 | 0.0127176 | ||||||||
\(624\) | −5.84446 | −0.233966 | ||||||||
\(625\) | 24.9996 | 0.999985 | ||||||||
\(626\) | −16.2362 | −0.648927 | ||||||||
\(627\) | −4.97886 | −0.198836 | ||||||||
\(628\) | 118.084 | 4.71204 | ||||||||
\(629\) | −23.7702 | −0.947782 | ||||||||
\(630\) | −0.0172924 | −0.000688945 0 | ||||||||
\(631\) | 1.94293 | 0.0773467 | 0.0386734 | − | 0.999252i | \(-0.487687\pi\) | ||||
0.0386734 | + | 0.999252i | \(0.487687\pi\) | |||||||
\(632\) | −86.7457 | −3.45056 | ||||||||
\(633\) | −2.36998 | −0.0941984 | ||||||||
\(634\) | −28.6578 | −1.13815 | ||||||||
\(635\) | −0.0387902 | −0.00153934 | ||||||||
\(636\) | −23.2592 | −0.922286 | ||||||||
\(637\) | 6.77344 | 0.268374 | ||||||||
\(638\) | 0.243834 | 0.00965347 | ||||||||
\(639\) | −5.71210 | −0.225967 | ||||||||
\(640\) | 0.0503629 | 0.00199077 | ||||||||
\(641\) | 6.59171 | 0.260357 | 0.130178 | − | 0.991491i | \(-0.458445\pi\) | ||||
0.130178 | + | 0.991491i | \(0.458445\pi\) | |||||||
\(642\) | −14.3556 | −0.566571 | ||||||||
\(643\) | 31.1716 | 1.22929 | 0.614643 | − | 0.788805i | \(-0.289300\pi\) | ||||
0.614643 | + | 0.788805i | \(0.289300\pi\) | |||||||
\(644\) | −17.8080 | −0.701733 | ||||||||
\(645\) | −0.0136766 | −0.000538515 0 | ||||||||
\(646\) | 56.4240 | 2.21997 | ||||||||
\(647\) | 42.8632 | 1.68513 | 0.842563 | − | 0.538597i | \(-0.181045\pi\) | ||||
0.842563 | + | 0.538597i | \(0.181045\pi\) | |||||||
\(648\) | −53.8586 | −2.11576 | ||||||||
\(649\) | 4.83338 | 0.189727 | ||||||||
\(650\) | −13.2672 | −0.520381 | ||||||||
\(651\) | 0.580706 | 0.0227597 | ||||||||
\(652\) | −20.6786 | −0.809835 | ||||||||
\(653\) | −4.52802 | −0.177195 | −0.0885975 | − | 0.996068i | \(-0.528238\pi\) | ||||
−0.0885975 | + | 0.996068i | \(0.528238\pi\) | |||||||
\(654\) | −10.8667 | −0.424921 | ||||||||
\(655\) | 0.0294814 | 0.00115194 | ||||||||
\(656\) | −100.456 | −3.92215 | ||||||||
\(657\) | 8.10050 | 0.316030 | ||||||||
\(658\) | −10.0489 | −0.391746 | ||||||||
\(659\) | 6.97938 | 0.271878 | 0.135939 | − | 0.990717i | \(-0.456595\pi\) | ||||
0.135939 | + | 0.990717i | \(0.456595\pi\) | |||||||
\(660\) | −0.0215045 | −0.000837060 0 | ||||||||
\(661\) | −16.7494 | −0.651475 | −0.325737 | − | 0.945460i | \(-0.605612\pi\) | ||||
−0.325737 | + | 0.945460i | \(0.605612\pi\) | |||||||
\(662\) | −25.4699 | −0.989917 | ||||||||
\(663\) | −1.87699 | −0.0728963 | ||||||||
\(664\) | −125.792 | −4.88169 | ||||||||
\(665\) | 0.0139336 | 0.000540323 0 | ||||||||
\(666\) | −47.3965 | −1.83658 | ||||||||
\(667\) | 0.413113 | 0.0159958 | ||||||||
\(668\) | −17.3576 | −0.671587 | ||||||||
\(669\) | 11.7453 | 0.454100 | ||||||||
\(670\) | 0.0436849 | 0.00168770 | ||||||||
\(671\) | 4.40714 | 0.170136 | ||||||||
\(672\) | −3.41860 | −0.131875 | ||||||||
\(673\) | 38.4954 | 1.48389 | 0.741944 | − | 0.670462i | \(-0.233904\pi\) | ||||
0.741944 | + | 0.670462i | \(0.233904\pi\) | |||||||
\(674\) | −6.69696 | −0.257957 | ||||||||
\(675\) | 14.7913 | 0.569319 | ||||||||
\(676\) | 5.04077 | 0.193876 | ||||||||
\(677\) | −18.4536 | −0.709229 | −0.354615 | − | 0.935013i | \(-0.615388\pi\) | ||||
−0.354615 | + | 0.935013i | \(0.615388\pi\) | |||||||
\(678\) | 11.1096 | 0.426660 | ||||||||
\(679\) | −4.26699 | −0.163752 | ||||||||
\(680\) | 0.147011 | 0.00563761 | ||||||||
\(681\) | 7.58889 | 0.290807 | ||||||||
\(682\) | −10.3592 | −0.396676 | ||||||||
\(683\) | −7.28490 | −0.278749 | −0.139375 | − | 0.990240i | \(-0.544509\pi\) | ||||
−0.139375 | + | 0.990240i | \(0.544509\pi\) | |||||||
\(684\) | 80.5478 | 3.07982 | ||||||||
\(685\) | −0.0673947 | −0.00257502 | ||||||||
\(686\) | 17.3956 | 0.664168 | ||||||||
\(687\) | 5.44600 | 0.207778 | ||||||||
\(688\) | 59.9570 | 2.28584 | ||||||||
\(689\) | 8.94334 | 0.340714 | ||||||||
\(690\) | −0.0508893 | −0.00193732 | ||||||||
\(691\) | 21.5639 | 0.820330 | 0.410165 | − | 0.912011i | \(-0.365471\pi\) | ||||
0.410165 | + | 0.912011i | \(0.365471\pi\) | |||||||
\(692\) | 58.3324 | 2.21747 | ||||||||
\(693\) | −2.14833 | −0.0816081 | ||||||||
\(694\) | −33.6508 | −1.27737 | ||||||||
\(695\) | 0.0865374 | 0.00328255 | ||||||||
\(696\) | 0.231702 | 0.00878264 | ||||||||
\(697\) | −32.2622 | −1.22202 | ||||||||
\(698\) | −2.02257 | −0.0765555 | ||||||||
\(699\) | −1.65092 | −0.0624434 | ||||||||
\(700\) | −11.9964 | −0.453423 | ||||||||
\(701\) | −26.4193 | −0.997842 | −0.498921 | − | 0.866648i | \(-0.666270\pi\) | ||||
−0.498921 | + | 0.866648i | \(0.666270\pi\) | |||||||
\(702\) | −7.84965 | −0.296266 | ||||||||
\(703\) | 38.1906 | 1.44038 | ||||||||
\(704\) | 23.5801 | 0.888708 | ||||||||
\(705\) | −0.0205592 | −0.000774304 0 | ||||||||
\(706\) | −92.9947 | −3.49990 | ||||||||
\(707\) | 1.57426 | 0.0592060 | ||||||||
\(708\) | 7.61378 | 0.286143 | ||||||||
\(709\) | 41.6078 | 1.56261 | 0.781306 | − | 0.624148i | \(-0.214554\pi\) | ||||
0.781306 | + | 0.624148i | \(0.214554\pi\) | |||||||
\(710\) | 0.0277669 | 0.00104207 | ||||||||
\(711\) | −29.3915 | −1.10227 | ||||||||
\(712\) | −5.38091 | −0.201658 | ||||||||
\(713\) | −17.5511 | −0.657292 | ||||||||
\(714\) | −2.37061 | −0.0887177 | ||||||||
\(715\) | 0.00826865 | 0.000309230 0 | ||||||||
\(716\) | 43.2600 | 1.61670 | ||||||||
\(717\) | 12.0677 | 0.450676 | ||||||||
\(718\) | 75.2996 | 2.81016 | ||||||||
\(719\) | 30.9501 | 1.15424 | 0.577122 | − | 0.816658i | \(-0.304176\pi\) | ||||
0.577122 | + | 0.816658i | \(0.304176\pi\) | |||||||
\(720\) | 0.155098 | 0.00578015 | ||||||||
\(721\) | −6.13331 | −0.228416 | ||||||||
\(722\) | −40.2384 | −1.49752 | ||||||||
\(723\) | −8.79236 | −0.326992 | ||||||||
\(724\) | −44.0974 | −1.63887 | ||||||||
\(725\) | 0.278296 | 0.0103356 | ||||||||
\(726\) | 11.3275 | 0.420403 | ||||||||
\(727\) | −12.1071 | −0.449028 | −0.224514 | − | 0.974471i | \(-0.572079\pi\) | ||||
−0.224514 | + | 0.974471i | \(0.572079\pi\) | |||||||
\(728\) | 3.84044 | 0.142336 | ||||||||
\(729\) | −13.6697 | −0.506285 | ||||||||
\(730\) | −0.0393771 | −0.00145741 | ||||||||
\(731\) | 19.2556 | 0.712194 | ||||||||
\(732\) | 6.94234 | 0.256596 | ||||||||
\(733\) | −1.86559 | −0.0689070 | −0.0344535 | − | 0.999406i | \(-0.510969\pi\) | ||||
−0.0344535 | + | 0.999406i | \(0.510969\pi\) | |||||||
\(734\) | 60.3730 | 2.22841 | ||||||||
\(735\) | 0.0175023 | 0.000645583 0 | ||||||||
\(736\) | 103.322 | 3.80852 | ||||||||
\(737\) | 5.42721 | 0.199914 | ||||||||
\(738\) | −64.3290 | −2.36798 | ||||||||
\(739\) | 7.80076 | 0.286956 | 0.143478 | − | 0.989654i | \(-0.454171\pi\) | ||||
0.143478 | + | 0.989654i | \(0.454171\pi\) | |||||||
\(740\) | 0.164951 | 0.00606372 | ||||||||
\(741\) | 3.01568 | 0.110784 | ||||||||
\(742\) | 11.2953 | 0.414663 | ||||||||
\(743\) | 12.6571 | 0.464343 | 0.232172 | − | 0.972675i | \(-0.425417\pi\) | ||||
0.232172 | + | 0.972675i | \(0.425417\pi\) | |||||||
\(744\) | −9.84383 | −0.360892 | ||||||||
\(745\) | −0.0628940 | −0.00230426 | ||||||||
\(746\) | 84.3872 | 3.08964 | ||||||||
\(747\) | −42.6214 | −1.55944 | ||||||||
\(748\) | 30.2766 | 1.10702 | ||||||||
\(749\) | 4.99116 | 0.182373 | ||||||||
\(750\) | −0.0685639 | −0.00250360 | ||||||||
\(751\) | −17.7165 | −0.646486 | −0.323243 | − | 0.946316i | \(-0.604773\pi\) | ||||
−0.323243 | + | 0.946316i | \(0.604773\pi\) | |||||||
\(752\) | 90.1297 | 3.28669 | ||||||||
\(753\) | 6.36904 | 0.232101 | ||||||||
\(754\) | −0.147689 | −0.00537852 | ||||||||
\(755\) | −0.0789720 | −0.00287409 | ||||||||
\(756\) | −7.09781 | −0.258145 | ||||||||
\(757\) | 2.58644 | 0.0940059 | 0.0470029 | − | 0.998895i | \(-0.485033\pi\) | ||||
0.0470029 | + | 0.998895i | \(0.485033\pi\) | |||||||
\(758\) | 73.9667 | 2.68659 | ||||||||
\(759\) | −6.32225 | −0.229483 | ||||||||
\(760\) | −0.236196 | −0.00856772 | ||||||||
\(761\) | 17.0680 | 0.618713 | 0.309357 | − | 0.950946i | \(-0.399886\pi\) | ||||
0.309357 | + | 0.950946i | \(0.399886\pi\) | |||||||
\(762\) | −10.6033 | −0.384116 | ||||||||
\(763\) | 3.77813 | 0.136777 | ||||||||
\(764\) | 88.2841 | 3.19401 | ||||||||
\(765\) | 0.0498108 | 0.00180091 | ||||||||
\(766\) | −8.84230 | −0.319485 | ||||||||
\(767\) | −2.92756 | −0.105708 | ||||||||
\(768\) | −0.970967 | −0.0350368 | ||||||||
\(769\) | −7.51879 | −0.271134 | −0.135567 | − | 0.990768i | \(-0.543286\pi\) | ||||
−0.135567 | + | 0.990768i | \(0.543286\pi\) | |||||||
\(770\) | 0.0104432 | 0.000376345 0 | ||||||||
\(771\) | 1.23662 | 0.0445358 | ||||||||
\(772\) | 17.3266 | 0.623598 | ||||||||
\(773\) | 7.85500 | 0.282525 | 0.141262 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141262 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(774\) | 38.3946 | 1.38006 | ||||||||
\(775\) | −11.8234 | −0.424707 | ||||||||
\(776\) | 72.3318 | 2.59656 | ||||||||
\(777\) | −1.60454 | −0.0575627 | ||||||||
\(778\) | 56.2836 | 2.01787 | ||||||||
\(779\) | 51.8342 | 1.85715 | ||||||||
\(780\) | 0.0130252 | 0.000466376 0 | ||||||||
\(781\) | 3.44963 | 0.123437 | ||||||||
\(782\) | 71.6483 | 2.56214 | ||||||||
\(783\) | 0.164656 | 0.00588434 | ||||||||
\(784\) | −76.7286 | −2.74031 | ||||||||
\(785\) | −0.117323 | −0.00418742 | ||||||||
\(786\) | 8.05872 | 0.287445 | ||||||||
\(787\) | 39.3063 | 1.40112 | 0.700560 | − | 0.713594i | \(-0.252934\pi\) | ||||
0.700560 | + | 0.713594i | \(0.252934\pi\) | |||||||
\(788\) | −13.0639 | −0.465381 | ||||||||
\(789\) | −6.51583 | −0.231970 | ||||||||
\(790\) | 0.142874 | 0.00508323 | ||||||||
\(791\) | −3.86258 | −0.137337 | ||||||||
\(792\) | 36.4173 | 1.29403 | ||||||||
\(793\) | −2.66939 | −0.0947927 | ||||||||
\(794\) | −11.1679 | −0.396334 | ||||||||
\(795\) | 0.0231093 | 0.000819601 0 | ||||||||
\(796\) | −37.6189 | −1.33337 | ||||||||
\(797\) | 13.3509 | 0.472913 | 0.236457 | − | 0.971642i | \(-0.424014\pi\) | ||||
0.236457 | + | 0.971642i | \(0.424014\pi\) | |||||||
\(798\) | 3.80875 | 0.134828 | ||||||||
\(799\) | 28.9458 | 1.02403 | ||||||||
\(800\) | 69.6037 | 2.46086 | ||||||||
\(801\) | −1.82318 | −0.0644188 | ||||||||
\(802\) | 89.8838 | 3.17391 | ||||||||
\(803\) | −4.89202 | −0.172636 | ||||||||
\(804\) | 8.54921 | 0.301507 | ||||||||
\(805\) | 0.0176932 | 0.000623604 0 | ||||||||
\(806\) | 6.27456 | 0.221012 | ||||||||
\(807\) | 3.37372 | 0.118760 | ||||||||
\(808\) | −26.6860 | −0.938809 | ||||||||
\(809\) | −1.11585 | −0.0392311 | −0.0196156 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196156 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(810\) | 0.0887074 | 0.00311686 | ||||||||
\(811\) | −18.3014 | −0.642648 | −0.321324 | − | 0.946969i | \(-0.604128\pi\) | ||||
−0.321324 | + | 0.946969i | \(0.604128\pi\) | |||||||
\(812\) | −0.133543 | −0.00468646 | ||||||||
\(813\) | 1.90434 | 0.0667883 | ||||||||
\(814\) | 28.6235 | 1.00325 | ||||||||
\(815\) | 0.0205453 | 0.000719670 0 | ||||||||
\(816\) | 21.2623 | 0.744329 | ||||||||
\(817\) | −30.9371 | −1.08235 | ||||||||
\(818\) | 92.4385 | 3.23204 | ||||||||
\(819\) | 1.30123 | 0.0454688 | ||||||||
\(820\) | 0.223880 | 0.00781822 | ||||||||
\(821\) | −9.42950 | −0.329092 | −0.164546 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164546 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(822\) | −18.4223 | −0.642551 | ||||||||
\(823\) | 19.3028 | 0.672854 | 0.336427 | − | 0.941710i | \(-0.390781\pi\) | ||||
0.336427 | + | 0.941710i | \(0.390781\pi\) | |||||||
\(824\) | 103.969 | 3.62192 | ||||||||
\(825\) | −4.25902 | −0.148280 | ||||||||
\(826\) | −3.69746 | −0.128651 | ||||||||
\(827\) | −12.1323 | −0.421881 | −0.210941 | − | 0.977499i | \(-0.567653\pi\) | ||||
−0.210941 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(828\) | 102.281 | 3.55452 | ||||||||
\(829\) | −23.7879 | −0.826188 | −0.413094 | − | 0.910688i | \(-0.635552\pi\) | ||||
−0.413094 | + | 0.910688i | \(0.635552\pi\) | |||||||
\(830\) | 0.207185 | 0.00719151 | ||||||||
\(831\) | −5.41788 | −0.187944 | ||||||||
\(832\) | −14.2824 | −0.495152 | ||||||||
\(833\) | −24.6420 | −0.853793 | ||||||||
\(834\) | 23.6549 | 0.819103 | ||||||||
\(835\) | 0.0172458 | 0.000596814 0 | ||||||||
\(836\) | −48.6441 | −1.68239 | ||||||||
\(837\) | −6.99540 | −0.241797 | ||||||||
\(838\) | 80.6787 | 2.78700 | ||||||||
\(839\) | 24.3103 | 0.839285 | 0.419643 | − | 0.907689i | \(-0.362155\pi\) | ||||
0.419643 | + | 0.907689i | \(0.362155\pi\) | |||||||
\(840\) | 0.00992357 | 0.000342396 0 | ||||||||
\(841\) | −28.9969 | −0.999893 | ||||||||
\(842\) | −26.4901 | −0.912910 | ||||||||
\(843\) | 6.35379 | 0.218836 | ||||||||
\(844\) | −23.1551 | −0.797030 | ||||||||
\(845\) | −0.00500829 | −0.000172290 0 | ||||||||
\(846\) | 57.7163 | 1.98433 | ||||||||
\(847\) | −3.93835 | −0.135323 | ||||||||
\(848\) | −101.309 | −3.47896 | ||||||||
\(849\) | 3.60373 | 0.123680 | ||||||||
\(850\) | 48.2663 | 1.65552 | ||||||||
\(851\) | 48.4952 | 1.66239 | ||||||||
\(852\) | 5.43402 | 0.186167 | ||||||||
\(853\) | −20.3283 | −0.696028 | −0.348014 | − | 0.937489i | \(-0.613144\pi\) | ||||
−0.348014 | + | 0.937489i | \(0.613144\pi\) | |||||||
\(854\) | −3.37139 | −0.115367 | ||||||||
\(855\) | −0.0800287 | −0.00273692 | ||||||||
\(856\) | −84.6076 | −2.89183 | ||||||||
\(857\) | −5.81877 | −0.198766 | −0.0993828 | − | 0.995049i | \(-0.531687\pi\) | ||||
−0.0993828 | + | 0.995049i | \(0.531687\pi\) | |||||||
\(858\) | 2.26023 | 0.0771628 | ||||||||
\(859\) | 17.2590 | 0.588871 | 0.294435 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294435 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(860\) | −0.133622 | −0.00455648 | ||||||||
\(861\) | −2.17777 | −0.0742182 | ||||||||
\(862\) | 12.3479 | 0.420572 | ||||||||
\(863\) | −39.7257 | −1.35228 | −0.676139 | − | 0.736774i | \(-0.736348\pi\) | ||||
−0.676139 | + | 0.736774i | \(0.736348\pi\) | |||||||
\(864\) | 41.1817 | 1.40103 | ||||||||
\(865\) | −0.0579565 | −0.00197058 | ||||||||
\(866\) | 33.8402 | 1.14994 | ||||||||
\(867\) | −1.94239 | −0.0659670 | ||||||||
\(868\) | 5.67358 | 0.192574 | ||||||||
\(869\) | 17.7500 | 0.602127 | ||||||||
\(870\) | −0.000381623 0 | −1.29382e−5 0 | ||||||||
\(871\) | −3.28724 | −0.111384 | ||||||||
\(872\) | −64.0449 | −2.16883 | ||||||||
\(873\) | 24.5077 | 0.829461 | ||||||||
\(874\) | −115.114 | −3.89379 | ||||||||
\(875\) | 0.0238383 | 0.000805882 0 | ||||||||
\(876\) | −7.70615 | −0.260367 | ||||||||
\(877\) | 13.6176 | 0.459835 | 0.229917 | − | 0.973210i | \(-0.426154\pi\) | ||||
0.229917 | + | 0.973210i | \(0.426154\pi\) | |||||||
\(878\) | −25.3289 | −0.854810 | ||||||||
\(879\) | 0.00711732 | 0.000240061 0 | ||||||||
\(880\) | −0.0936661 | −0.00315748 | ||||||||
\(881\) | −30.9788 | −1.04370 | −0.521851 | − | 0.853036i | \(-0.674758\pi\) | ||||
−0.521851 | + | 0.853036i | \(0.674758\pi\) | |||||||
\(882\) | −49.1347 | −1.65445 | ||||||||
\(883\) | 46.0102 | 1.54837 | 0.774184 | − | 0.632960i | \(-0.218160\pi\) | ||||
0.774184 | + | 0.632960i | \(0.218160\pi\) | |||||||
\(884\) | −18.3385 | −0.616789 | ||||||||
\(885\) | −0.00756472 | −0.000254285 0 | ||||||||
\(886\) | −101.477 | −3.40920 | ||||||||
\(887\) | −11.4962 | −0.386005 | −0.193002 | − | 0.981198i | \(-0.561823\pi\) | ||||
−0.193002 | + | 0.981198i | \(0.561823\pi\) | |||||||
\(888\) | 27.1994 | 0.912752 | ||||||||
\(889\) | 3.68655 | 0.123643 | ||||||||
\(890\) | 0.00886259 | 0.000297075 0 | ||||||||
\(891\) | 11.0206 | 0.369204 | ||||||||
\(892\) | 114.753 | 3.84222 | ||||||||
\(893\) | −46.5059 | −1.55626 | ||||||||
\(894\) | −17.1920 | −0.574987 | ||||||||
\(895\) | −0.0429812 | −0.00143670 | ||||||||
\(896\) | −4.78639 | −0.159902 | ||||||||
\(897\) | 3.82937 | 0.127859 | ||||||||
\(898\) | 24.7270 | 0.825151 | ||||||||
\(899\) | −0.131617 | −0.00438967 | ||||||||
\(900\) | 68.9022 | 2.29674 | ||||||||
\(901\) | −32.5361 | −1.08393 | ||||||||
\(902\) | 38.8493 | 1.29354 | ||||||||
\(903\) | 1.29980 | 0.0432545 | ||||||||
\(904\) | 65.4764 | 2.17771 | ||||||||
\(905\) | 0.0438132 | 0.00145640 | ||||||||
\(906\) | −21.5869 | −0.717177 | ||||||||
\(907\) | 2.07117 | 0.0687722 | 0.0343861 | − | 0.999409i | \(-0.489052\pi\) | ||||
0.0343861 | + | 0.999409i | \(0.489052\pi\) | |||||||
\(908\) | 74.1445 | 2.46057 | ||||||||
\(909\) | −9.04184 | −0.299899 | ||||||||
\(910\) | −0.00632538 | −0.000209684 0 | ||||||||
\(911\) | 26.3507 | 0.873038 | 0.436519 | − | 0.899695i | \(-0.356211\pi\) | ||||
0.436519 | + | 0.899695i | \(0.356211\pi\) | |||||||
\(912\) | −34.1612 | −1.13119 | ||||||||
\(913\) | 25.7398 | 0.851861 | ||||||||
\(914\) | 5.55897 | 0.183874 | ||||||||
\(915\) | −0.00689760 | −0.000228028 0 | ||||||||
\(916\) | 53.2082 | 1.75805 | ||||||||
\(917\) | −2.80186 | −0.0925255 | ||||||||
\(918\) | 28.5572 | 0.942528 | ||||||||
\(919\) | 7.01806 | 0.231504 | 0.115752 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115752 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(920\) | −0.299926 | −0.00988827 | ||||||||
\(921\) | 6.56504 | 0.216325 | ||||||||
\(922\) | −18.6548 | −0.614364 | ||||||||
\(923\) | −2.08943 | −0.0687744 | ||||||||
\(924\) | 2.04374 | 0.0672342 | ||||||||
\(925\) | 32.6690 | 1.07415 | ||||||||
\(926\) | 110.693 | 3.63759 | ||||||||
\(927\) | 35.2270 | 1.15701 | ||||||||
\(928\) | 0.774824 | 0.0254348 | ||||||||
\(929\) | 33.7765 | 1.10817 | 0.554086 | − | 0.832459i | \(-0.313068\pi\) | ||||
0.554086 | + | 0.832459i | \(0.313068\pi\) | |||||||
\(930\) | 0.0162132 | 0.000531653 0 | ||||||||
\(931\) | 39.5911 | 1.29755 | ||||||||
\(932\) | −16.1297 | −0.528345 | ||||||||
\(933\) | 11.7858 | 0.385851 | ||||||||
\(934\) | 26.6544 | 0.872158 | ||||||||
\(935\) | −0.0300815 | −0.000983771 0 | ||||||||
\(936\) | −22.0578 | −0.720983 | ||||||||
\(937\) | −41.2222 | −1.34667 | −0.673335 | − | 0.739338i | \(-0.735139\pi\) | ||||
−0.673335 | + | 0.739338i | \(0.735139\pi\) | |||||||
\(938\) | −4.15173 | −0.135559 | ||||||||
\(939\) | 3.15697 | 0.103024 | ||||||||
\(940\) | −0.200866 | −0.00655153 | ||||||||
\(941\) | 46.8750 | 1.52808 | 0.764040 | − | 0.645169i | \(-0.223213\pi\) | ||||
0.764040 | + | 0.645169i | \(0.223213\pi\) | |||||||
\(942\) | −32.0700 | −1.04490 | ||||||||
\(943\) | 65.8201 | 2.14340 | ||||||||
\(944\) | 33.1630 | 1.07936 | ||||||||
\(945\) | 0.00705207 | 0.000229404 0 | ||||||||
\(946\) | −23.1871 | −0.753878 | ||||||||
\(947\) | −55.3568 | −1.79885 | −0.899426 | − | 0.437072i | \(-0.856015\pi\) | ||||
−0.899426 | + | 0.437072i | \(0.856015\pi\) | |||||||
\(948\) | 27.9607 | 0.908120 | ||||||||
\(949\) | 2.96308 | 0.0961857 | ||||||||
\(950\) | −77.5472 | −2.51596 | ||||||||
\(951\) | 5.57223 | 0.180692 | ||||||||
\(952\) | −13.9716 | −0.452823 | ||||||||
\(953\) | 35.7661 | 1.15858 | 0.579289 | − | 0.815122i | \(-0.303330\pi\) | ||||
0.579289 | + | 0.815122i | \(0.303330\pi\) | |||||||
\(954\) | −64.8751 | −2.10041 | ||||||||
\(955\) | −0.0877152 | −0.00283840 | ||||||||
\(956\) | 117.903 | 3.81325 | ||||||||
\(957\) | −0.0474111 | −0.00153258 | ||||||||
\(958\) | 103.490 | 3.34361 | ||||||||
\(959\) | 6.40506 | 0.206830 | ||||||||
\(960\) | −0.0369051 | −0.00119111 | ||||||||
\(961\) | −25.4083 | −0.819622 | ||||||||
\(962\) | −17.3372 | −0.558973 | ||||||||
\(963\) | −28.6670 | −0.923782 | ||||||||
\(964\) | −85.9026 | −2.76674 | ||||||||
\(965\) | −0.0172149 | −0.000554168 0 | ||||||||
\(966\) | 4.83642 | 0.155609 | ||||||||
\(967\) | 6.61843 | 0.212835 | 0.106417 | − | 0.994322i | \(-0.466062\pi\) | ||||
0.106417 | + | 0.994322i | \(0.466062\pi\) | |||||||
\(968\) | 66.7609 | 2.14578 | ||||||||
\(969\) | −10.9711 | −0.352443 | ||||||||
\(970\) | −0.119134 | −0.00382515 | ||||||||
\(971\) | 26.7164 | 0.857371 | 0.428686 | − | 0.903454i | \(-0.358977\pi\) | ||||
0.428686 | + | 0.903454i | \(0.358977\pi\) | |||||||
\(972\) | 62.0963 | 1.99174 | ||||||||
\(973\) | −8.22435 | −0.263660 | ||||||||
\(974\) | −16.3569 | −0.524110 | ||||||||
\(975\) | 2.57967 | 0.0826156 | ||||||||
\(976\) | 30.2385 | 0.967909 | ||||||||
\(977\) | 30.1264 | 0.963828 | 0.481914 | − | 0.876219i | \(-0.339942\pi\) | ||||
0.481914 | + | 0.876219i | \(0.339942\pi\) | |||||||
\(978\) | 5.61604 | 0.179581 | ||||||||
\(979\) | 1.10105 | 0.0351896 | ||||||||
\(980\) | 0.171000 | 0.00546240 | ||||||||
\(981\) | −21.6999 | −0.692825 | ||||||||
\(982\) | 46.1821 | 1.47373 | ||||||||
\(983\) | −6.58163 | −0.209921 | −0.104961 | − | 0.994476i | \(-0.533472\pi\) | ||||
−0.104961 | + | 0.994476i | \(0.533472\pi\) | |||||||
\(984\) | 36.9164 | 1.17685 | ||||||||
\(985\) | 0.0129797 | 0.000413567 0 | ||||||||
\(986\) | 0.537297 | 0.0171110 | ||||||||
\(987\) | 1.95391 | 0.0621935 | ||||||||
\(988\) | 29.4636 | 0.937361 | ||||||||
\(989\) | −39.2846 | −1.24918 | ||||||||
\(990\) | −0.0599809 | −0.00190632 | ||||||||
\(991\) | 59.2791 | 1.88306 | 0.941531 | − | 0.336928i | \(-0.109388\pi\) | ||||
0.941531 | + | 0.336928i | \(0.109388\pi\) | |||||||
\(992\) | −32.9183 | −1.04516 | ||||||||
\(993\) | 4.95238 | 0.157159 | ||||||||
\(994\) | −2.63891 | −0.0837011 | ||||||||
\(995\) | 0.0373764 | 0.00118491 | ||||||||
\(996\) | 40.5465 | 1.28477 | ||||||||
\(997\) | 36.8420 | 1.16680 | 0.583399 | − | 0.812186i | \(-0.301723\pi\) | ||||
0.583399 | + | 0.812186i | \(0.301723\pi\) | |||||||
\(998\) | −90.0896 | −2.85174 | ||||||||
\(999\) | 19.3289 | 0.611541 |
(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 | 8047.2.a.d.1.5 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.5 | ✓ | 156 | 1.1 | even | 1 | trivial |