Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67300 | 1.18299 | 0.591496 | − | 0.806308i | \(-0.298538\pi\) | ||||
0.591496 | + | 0.806308i | \(0.298538\pi\) | |||||||
\(3\) | −1.49184 | −0.861315 | −0.430657 | − | 0.902516i | \(-0.641718\pi\) | ||||
−0.430657 | + | 0.902516i | \(0.641718\pi\) | |||||||
\(4\) | 0.798939 | 0.399470 | ||||||||
\(5\) | −1.12664 | −0.503850 | −0.251925 | − | 0.967747i | \(-0.581064\pi\) | ||||
−0.251925 | + | 0.967747i | \(0.581064\pi\) | |||||||
\(6\) | −2.49585 | −1.01893 | ||||||||
\(7\) | −0.438386 | −0.165694 | −0.0828471 | − | 0.996562i | \(-0.526401\pi\) | ||||
−0.0828471 | + | 0.996562i | \(0.526401\pi\) | |||||||
\(8\) | −2.00938 | −0.710423 | ||||||||
\(9\) | −0.774411 | −0.258137 | ||||||||
\(10\) | −1.88488 | −0.596051 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.19189 | −0.344069 | ||||||||
\(13\) | 6.70892 | 1.86072 | 0.930359 | − | 0.366649i | \(-0.119495\pi\) | ||||
0.930359 | + | 0.366649i | \(0.119495\pi\) | |||||||
\(14\) | −0.733421 | −0.196015 | ||||||||
\(15\) | 1.68077 | 0.433973 | ||||||||
\(16\) | −4.95957 | −1.23989 | ||||||||
\(17\) | 0.414914 | 0.100631 | 0.0503157 | − | 0.998733i | \(-0.483977\pi\) | ||||
0.0503157 | + | 0.998733i | \(0.483977\pi\) | |||||||
\(18\) | −1.29559 | −0.305374 | ||||||||
\(19\) | 5.91492 | 1.35698 | 0.678488 | − | 0.734612i | \(-0.262636\pi\) | ||||
0.678488 | + | 0.734612i | \(0.262636\pi\) | |||||||
\(20\) | −0.900119 | −0.201273 | ||||||||
\(21\) | 0.654002 | 0.142715 | ||||||||
\(22\) | 1.67300 | 0.356685 | ||||||||
\(23\) | −8.48053 | −1.76831 | −0.884157 | − | 0.467191i | \(-0.845266\pi\) | ||||
−0.884157 | + | 0.467191i | \(0.845266\pi\) | |||||||
\(24\) | 2.99767 | 0.611897 | ||||||||
\(25\) | −3.73068 | −0.746135 | ||||||||
\(26\) | 11.2240 | 2.20122 | ||||||||
\(27\) | 5.63082 | 1.08365 | ||||||||
\(28\) | −0.350244 | −0.0661898 | ||||||||
\(29\) | 6.46992 | 1.20143 | 0.600717 | − | 0.799461i | \(-0.294882\pi\) | ||||
0.600717 | + | 0.799461i | \(0.294882\pi\) | |||||||
\(30\) | 2.81194 | 0.513387 | ||||||||
\(31\) | 8.15693 | 1.46503 | 0.732514 | − | 0.680752i | \(-0.238347\pi\) | ||||
0.732514 | + | 0.680752i | \(0.238347\pi\) | |||||||
\(32\) | −4.27863 | −0.756361 | ||||||||
\(33\) | −1.49184 | −0.259696 | ||||||||
\(34\) | 0.694152 | 0.119046 | ||||||||
\(35\) | 0.493904 | 0.0834851 | ||||||||
\(36\) | −0.618707 | −0.103118 | ||||||||
\(37\) | −0.0703706 | −0.0115689 | −0.00578443 | − | 0.999983i | \(-0.501841\pi\) | ||||
−0.00578443 | + | 0.999983i | \(0.501841\pi\) | |||||||
\(38\) | 9.89568 | 1.60529 | ||||||||
\(39\) | −10.0086 | −1.60266 | ||||||||
\(40\) | 2.26385 | 0.357947 | ||||||||
\(41\) | 10.4191 | 1.62719 | 0.813595 | − | 0.581432i | \(-0.197507\pi\) | ||||
0.813595 | + | 0.581432i | \(0.197507\pi\) | |||||||
\(42\) | 1.09415 | 0.168831 | ||||||||
\(43\) | 4.47503 | 0.682436 | 0.341218 | − | 0.939984i | \(-0.389161\pi\) | ||||
0.341218 | + | 0.939984i | \(0.389161\pi\) | |||||||
\(44\) | 0.798939 | 0.120445 | ||||||||
\(45\) | 0.872485 | 0.130062 | ||||||||
\(46\) | −14.1880 | −2.09190 | ||||||||
\(47\) | 4.80516 | 0.700904 | 0.350452 | − | 0.936581i | \(-0.386028\pi\) | ||||
0.350452 | + | 0.936581i | \(0.386028\pi\) | |||||||
\(48\) | 7.39890 | 1.06794 | ||||||||
\(49\) | −6.80782 | −0.972545 | ||||||||
\(50\) | −6.24143 | −0.882672 | ||||||||
\(51\) | −0.618985 | −0.0866753 | ||||||||
\(52\) | 5.36002 | 0.743300 | ||||||||
\(53\) | 14.4201 | 1.98075 | 0.990374 | − | 0.138418i | \(-0.0442016\pi\) | ||||
0.990374 | + | 0.138418i | \(0.0442016\pi\) | |||||||
\(54\) | 9.42038 | 1.28195 | ||||||||
\(55\) | −1.12664 | −0.151917 | ||||||||
\(56\) | 0.880883 | 0.117713 | ||||||||
\(57\) | −8.82412 | −1.16878 | ||||||||
\(58\) | 10.8242 | 1.42129 | ||||||||
\(59\) | 3.77174 | 0.491038 | 0.245519 | − | 0.969392i | \(-0.421042\pi\) | ||||
0.245519 | + | 0.969392i | \(0.421042\pi\) | |||||||
\(60\) | 1.34283 | 0.173359 | ||||||||
\(61\) | −11.5149 | −1.47433 | −0.737164 | − | 0.675714i | \(-0.763835\pi\) | ||||
−0.737164 | + | 0.675714i | \(0.763835\pi\) | |||||||
\(62\) | 13.6466 | 1.73312 | ||||||||
\(63\) | 0.339491 | 0.0427718 | ||||||||
\(64\) | 2.76100 | 0.345124 | ||||||||
\(65\) | −7.55856 | −0.937523 | ||||||||
\(66\) | −2.49585 | −0.307218 | ||||||||
\(67\) | 4.98056 | 0.608473 | 0.304236 | − | 0.952597i | \(-0.401599\pi\) | ||||
0.304236 | + | 0.952597i | \(0.401599\pi\) | |||||||
\(68\) | 0.331491 | 0.0401992 | ||||||||
\(69\) | 12.6516 | 1.52307 | ||||||||
\(70\) | 0.826304 | 0.0987622 | ||||||||
\(71\) | 12.8793 | 1.52850 | 0.764248 | − | 0.644923i | \(-0.223110\pi\) | ||||
0.764248 | + | 0.644923i | \(0.223110\pi\) | |||||||
\(72\) | 1.55609 | 0.183386 | ||||||||
\(73\) | −14.2632 | −1.66939 | −0.834693 | − | 0.550716i | \(-0.814355\pi\) | ||||
−0.834693 | + | 0.550716i | \(0.814355\pi\) | |||||||
\(74\) | −0.117730 | −0.0136859 | ||||||||
\(75\) | 5.56557 | 0.642657 | ||||||||
\(76\) | 4.72566 | 0.542070 | ||||||||
\(77\) | −0.438386 | −0.0499587 | ||||||||
\(78\) | −16.7445 | −1.89594 | ||||||||
\(79\) | −2.49267 | −0.280447 | −0.140224 | − | 0.990120i | \(-0.544782\pi\) | ||||
−0.140224 | + | 0.990120i | \(0.544782\pi\) | |||||||
\(80\) | 5.58767 | 0.624721 | ||||||||
\(81\) | −6.07705 | −0.675228 | ||||||||
\(82\) | 17.4312 | 1.92495 | ||||||||
\(83\) | 9.29253 | 1.01999 | 0.509994 | − | 0.860178i | \(-0.329648\pi\) | ||||
0.509994 | + | 0.860178i | \(0.329648\pi\) | |||||||
\(84\) | 0.522508 | 0.0570103 | ||||||||
\(85\) | −0.467460 | −0.0507031 | ||||||||
\(86\) | 7.48674 | 0.807316 | ||||||||
\(87\) | −9.65210 | −1.03481 | ||||||||
\(88\) | −2.00938 | −0.214200 | ||||||||
\(89\) | −0.995685 | −0.105542 | −0.0527712 | − | 0.998607i | \(-0.516805\pi\) | ||||
−0.0527712 | + | 0.998607i | \(0.516805\pi\) | |||||||
\(90\) | 1.45967 | 0.153863 | ||||||||
\(91\) | −2.94109 | −0.308310 | ||||||||
\(92\) | −6.77543 | −0.706387 | ||||||||
\(93\) | −12.1688 | −1.26185 | ||||||||
\(94\) | 8.03904 | 0.829164 | ||||||||
\(95\) | −6.66400 | −0.683712 | ||||||||
\(96\) | 6.38303 | 0.651465 | ||||||||
\(97\) | −0.687320 | −0.0697868 | −0.0348934 | − | 0.999391i | \(-0.511109\pi\) | ||||
−0.0348934 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(98\) | −11.3895 | −1.15051 | ||||||||
\(99\) | −0.774411 | −0.0778313 | ||||||||
\(100\) | −2.98058 | −0.298058 | ||||||||
\(101\) | −8.55380 | −0.851134 | −0.425567 | − | 0.904927i | \(-0.639925\pi\) | ||||
−0.425567 | + | 0.904927i | \(0.639925\pi\) | |||||||
\(102\) | −1.03556 | −0.102536 | ||||||||
\(103\) | −12.6617 | −1.24760 | −0.623800 | − | 0.781584i | \(-0.714412\pi\) | ||||
−0.623800 | + | 0.781584i | \(0.714412\pi\) | |||||||
\(104\) | −13.4808 | −1.32190 | ||||||||
\(105\) | −0.736827 | −0.0719069 | ||||||||
\(106\) | 24.1248 | 2.34321 | ||||||||
\(107\) | 5.66098 | 0.547268 | 0.273634 | − | 0.961834i | \(-0.411774\pi\) | ||||
0.273634 | + | 0.961834i | \(0.411774\pi\) | |||||||
\(108\) | 4.49868 | 0.432886 | ||||||||
\(109\) | −4.31049 | −0.412870 | −0.206435 | − | 0.978460i | \(-0.566186\pi\) | ||||
−0.206435 | + | 0.978460i | \(0.566186\pi\) | |||||||
\(110\) | −1.88488 | −0.179716 | ||||||||
\(111\) | 0.104982 | 0.00996443 | ||||||||
\(112\) | 2.17421 | 0.205443 | ||||||||
\(113\) | −10.2048 | −0.959988 | −0.479994 | − | 0.877272i | \(-0.659361\pi\) | ||||
−0.479994 | + | 0.877272i | \(0.659361\pi\) | |||||||
\(114\) | −14.7628 | −1.38266 | ||||||||
\(115\) | 9.55453 | 0.890965 | ||||||||
\(116\) | 5.16907 | 0.479937 | ||||||||
\(117\) | −5.19546 | −0.480321 | ||||||||
\(118\) | 6.31013 | 0.580894 | ||||||||
\(119\) | −0.181892 | −0.0166740 | ||||||||
\(120\) | −3.37731 | −0.308305 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −19.2644 | −1.74412 | ||||||||
\(123\) | −15.5436 | −1.40152 | ||||||||
\(124\) | 6.51689 | 0.585234 | ||||||||
\(125\) | 9.83635 | 0.879790 | ||||||||
\(126\) | 0.567969 | 0.0505987 | ||||||||
\(127\) | −17.4598 | −1.54931 | −0.774655 | − | 0.632385i | \(-0.782076\pi\) | ||||
−0.774655 | + | 0.632385i | \(0.782076\pi\) | |||||||
\(128\) | 13.1764 | 1.16464 | ||||||||
\(129\) | −6.67603 | −0.587792 | ||||||||
\(130\) | −12.6455 | −1.10908 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −1.19189 | −0.103741 | ||||||||
\(133\) | −2.59302 | −0.224843 | ||||||||
\(134\) | 8.33250 | 0.719818 | ||||||||
\(135\) | −6.34392 | −0.545998 | ||||||||
\(136\) | −0.833719 | −0.0714908 | ||||||||
\(137\) | 14.3718 | 1.22787 | 0.613935 | − | 0.789357i | \(-0.289586\pi\) | ||||
0.613935 | + | 0.789357i | \(0.289586\pi\) | |||||||
\(138\) | 21.1662 | 1.80178 | ||||||||
\(139\) | 8.98666 | 0.762239 | 0.381119 | − | 0.924526i | \(-0.375539\pi\) | ||||
0.381119 | + | 0.924526i | \(0.375539\pi\) | |||||||
\(140\) | 0.394599 | 0.0333497 | ||||||||
\(141\) | −7.16853 | −0.603699 | ||||||||
\(142\) | 21.5472 | 1.80820 | ||||||||
\(143\) | 6.70892 | 0.561028 | ||||||||
\(144\) | 3.84075 | 0.320063 | ||||||||
\(145\) | −7.28930 | −0.605343 | ||||||||
\(146\) | −23.8624 | −1.97487 | ||||||||
\(147\) | 10.1562 | 0.837668 | ||||||||
\(148\) | −0.0562218 | −0.00462141 | ||||||||
\(149\) | 10.6003 | 0.868409 | 0.434205 | − | 0.900814i | \(-0.357029\pi\) | ||||
0.434205 | + | 0.900814i | \(0.357029\pi\) | |||||||
\(150\) | 9.31122 | 0.760258 | ||||||||
\(151\) | −5.17506 | −0.421140 | −0.210570 | − | 0.977579i | \(-0.567532\pi\) | ||||
−0.210570 | + | 0.977579i | \(0.567532\pi\) | |||||||
\(152\) | −11.8853 | −0.964026 | ||||||||
\(153\) | −0.321314 | −0.0259767 | ||||||||
\(154\) | −0.733421 | −0.0591007 | ||||||||
\(155\) | −9.18994 | −0.738154 | ||||||||
\(156\) | −7.99629 | −0.640216 | ||||||||
\(157\) | 7.40190 | 0.590736 | 0.295368 | − | 0.955384i | \(-0.404558\pi\) | ||||
0.295368 | + | 0.955384i | \(0.404558\pi\) | |||||||
\(158\) | −4.17024 | −0.331767 | ||||||||
\(159\) | −21.5124 | −1.70605 | ||||||||
\(160\) | 4.82048 | 0.381093 | ||||||||
\(161\) | 3.71775 | 0.292999 | ||||||||
\(162\) | −10.1669 | −0.798789 | ||||||||
\(163\) | −22.5380 | −1.76531 | −0.882657 | − | 0.470018i | \(-0.844247\pi\) | ||||
−0.882657 | + | 0.470018i | \(0.844247\pi\) | |||||||
\(164\) | 8.32423 | 0.650013 | ||||||||
\(165\) | 1.68077 | 0.130848 | ||||||||
\(166\) | 15.5464 | 1.20664 | ||||||||
\(167\) | −6.28473 | −0.486327 | −0.243163 | − | 0.969985i | \(-0.578185\pi\) | ||||
−0.243163 | + | 0.969985i | \(0.578185\pi\) | |||||||
\(168\) | −1.31414 | −0.101388 | ||||||||
\(169\) | 32.0096 | 2.46228 | ||||||||
\(170\) | −0.782061 | −0.0599814 | ||||||||
\(171\) | −4.58058 | −0.350286 | ||||||||
\(172\) | 3.57528 | 0.272612 | ||||||||
\(173\) | 9.52170 | 0.723921 | 0.361961 | − | 0.932193i | \(-0.382107\pi\) | ||||
0.361961 | + | 0.932193i | \(0.382107\pi\) | |||||||
\(174\) | −16.1480 | −1.22418 | ||||||||
\(175\) | 1.63548 | 0.123630 | ||||||||
\(176\) | −4.95957 | −0.373842 | ||||||||
\(177\) | −5.62683 | −0.422939 | ||||||||
\(178\) | −1.66578 | −0.124856 | ||||||||
\(179\) | 11.7859 | 0.880917 | 0.440458 | − | 0.897773i | \(-0.354816\pi\) | ||||
0.440458 | + | 0.897773i | \(0.354816\pi\) | |||||||
\(180\) | 0.697062 | 0.0519560 | ||||||||
\(181\) | 18.2939 | 1.35978 | 0.679888 | − | 0.733316i | \(-0.262028\pi\) | ||||
0.679888 | + | 0.733316i | \(0.262028\pi\) | |||||||
\(182\) | −4.92046 | −0.364729 | ||||||||
\(183\) | 17.1783 | 1.26986 | ||||||||
\(184\) | 17.0406 | 1.25625 | ||||||||
\(185\) | 0.0792826 | 0.00582897 | ||||||||
\(186\) | −20.3585 | −1.49276 | ||||||||
\(187\) | 0.414914 | 0.0303415 | ||||||||
\(188\) | 3.83903 | 0.279990 | ||||||||
\(189\) | −2.46847 | −0.179555 | ||||||||
\(190\) | −11.1489 | −0.808826 | ||||||||
\(191\) | 3.21927 | 0.232938 | 0.116469 | − | 0.993194i | \(-0.462842\pi\) | ||||
0.116469 | + | 0.993194i | \(0.462842\pi\) | |||||||
\(192\) | −4.11897 | −0.297261 | ||||||||
\(193\) | −16.5162 | −1.18886 | −0.594430 | − | 0.804147i | \(-0.702622\pi\) | ||||
−0.594430 | + | 0.804147i | \(0.702622\pi\) | |||||||
\(194\) | −1.14989 | −0.0825572 | ||||||||
\(195\) | 11.2762 | 0.807503 | ||||||||
\(196\) | −5.43903 | −0.388502 | ||||||||
\(197\) | −19.8232 | −1.41235 | −0.706173 | − | 0.708039i | \(-0.749580\pi\) | ||||
−0.706173 | + | 0.708039i | \(0.749580\pi\) | |||||||
\(198\) | −1.29559 | −0.0920737 | ||||||||
\(199\) | 9.36808 | 0.664086 | 0.332043 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332043 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(200\) | 7.49634 | 0.530071 | ||||||||
\(201\) | −7.43021 | −0.524086 | ||||||||
\(202\) | −14.3105 | −1.00689 | ||||||||
\(203\) | −2.83632 | −0.199071 | ||||||||
\(204\) | −0.494531 | −0.0346241 | ||||||||
\(205\) | −11.7386 | −0.819860 | ||||||||
\(206\) | −21.1831 | −1.47590 | ||||||||
\(207\) | 6.56742 | 0.456467 | ||||||||
\(208\) | −33.2734 | −2.30709 | ||||||||
\(209\) | 5.91492 | 0.409144 | ||||||||
\(210\) | −1.23271 | −0.0850653 | ||||||||
\(211\) | 5.10895 | 0.351715 | 0.175857 | − | 0.984416i | \(-0.443730\pi\) | ||||
0.175857 | + | 0.984416i | \(0.443730\pi\) | |||||||
\(212\) | 11.5208 | 0.791248 | ||||||||
\(213\) | −19.2139 | −1.31652 | ||||||||
\(214\) | 9.47084 | 0.647413 | ||||||||
\(215\) | −5.04176 | −0.343845 | ||||||||
\(216\) | −11.3145 | −0.769851 | ||||||||
\(217\) | −3.57588 | −0.242747 | ||||||||
\(218\) | −7.21147 | −0.488422 | ||||||||
\(219\) | 21.2785 | 1.43787 | ||||||||
\(220\) | −0.900119 | −0.0606860 | ||||||||
\(221\) | 2.78362 | 0.187247 | ||||||||
\(222\) | 0.175635 | 0.0117878 | ||||||||
\(223\) | 4.23090 | 0.283322 | 0.141661 | − | 0.989915i | \(-0.454756\pi\) | ||||
0.141661 | + | 0.989915i | \(0.454756\pi\) | |||||||
\(224\) | 1.87569 | 0.125325 | ||||||||
\(225\) | 2.88908 | 0.192605 | ||||||||
\(226\) | −17.0727 | −1.13566 | ||||||||
\(227\) | 24.8258 | 1.64775 | 0.823873 | − | 0.566775i | \(-0.191809\pi\) | ||||
0.823873 | + | 0.566775i | \(0.191809\pi\) | |||||||
\(228\) | −7.04993 | −0.466893 | ||||||||
\(229\) | −23.3519 | −1.54314 | −0.771568 | − | 0.636147i | \(-0.780527\pi\) | ||||
−0.771568 | + | 0.636147i | \(0.780527\pi\) | |||||||
\(230\) | 15.9848 | 1.05400 | ||||||||
\(231\) | 0.654002 | 0.0430302 | ||||||||
\(232\) | −13.0005 | −0.853526 | ||||||||
\(233\) | 20.4182 | 1.33764 | 0.668820 | − | 0.743424i | \(-0.266800\pi\) | ||||
0.668820 | + | 0.743424i | \(0.266800\pi\) | |||||||
\(234\) | −8.69202 | −0.568215 | ||||||||
\(235\) | −5.41370 | −0.353151 | ||||||||
\(236\) | 3.01339 | 0.196155 | ||||||||
\(237\) | 3.71866 | 0.241553 | ||||||||
\(238\) | −0.304306 | −0.0197253 | ||||||||
\(239\) | 10.9109 | 0.705767 | 0.352883 | − | 0.935667i | \(-0.385201\pi\) | ||||
0.352883 | + | 0.935667i | \(0.385201\pi\) | |||||||
\(240\) | −8.33591 | −0.538081 | ||||||||
\(241\) | 2.19603 | 0.141459 | 0.0707293 | − | 0.997496i | \(-0.477467\pi\) | ||||
0.0707293 | + | 0.997496i | \(0.477467\pi\) | |||||||
\(242\) | 1.67300 | 0.107545 | ||||||||
\(243\) | −7.82647 | −0.502068 | ||||||||
\(244\) | −9.19968 | −0.588949 | ||||||||
\(245\) | 7.66998 | 0.490017 | ||||||||
\(246\) | −26.0046 | −1.65799 | ||||||||
\(247\) | 39.6827 | 2.52495 | ||||||||
\(248\) | −16.3904 | −1.04079 | ||||||||
\(249\) | −13.8630 | −0.878531 | ||||||||
\(250\) | 16.4563 | 1.04078 | ||||||||
\(251\) | 1.53382 | 0.0968140 | 0.0484070 | − | 0.998828i | \(-0.484586\pi\) | ||||
0.0484070 | + | 0.998828i | \(0.484586\pi\) | |||||||
\(252\) | 0.271233 | 0.0170860 | ||||||||
\(253\) | −8.48053 | −0.533166 | ||||||||
\(254\) | −29.2103 | −1.83282 | ||||||||
\(255\) | 0.697375 | 0.0436713 | ||||||||
\(256\) | 16.5222 | 1.03264 | ||||||||
\(257\) | 11.1972 | 0.698461 | 0.349230 | − | 0.937037i | \(-0.386443\pi\) | ||||
0.349230 | + | 0.937037i | \(0.386443\pi\) | |||||||
\(258\) | −11.1690 | −0.695353 | ||||||||
\(259\) | 0.0308495 | 0.00191689 | ||||||||
\(260\) | −6.03882 | −0.374512 | ||||||||
\(261\) | −5.01038 | −0.310135 | ||||||||
\(262\) | −1.67300 | −0.103358 | ||||||||
\(263\) | −8.27309 | −0.510140 | −0.255070 | − | 0.966923i | \(-0.582099\pi\) | ||||
−0.255070 | + | 0.966923i | \(0.582099\pi\) | |||||||
\(264\) | 2.99767 | 0.184494 | ||||||||
\(265\) | −16.2463 | −0.998000 | ||||||||
\(266\) | −4.33813 | −0.265988 | ||||||||
\(267\) | 1.48540 | 0.0909052 | ||||||||
\(268\) | 3.97917 | 0.243066 | ||||||||
\(269\) | −4.50079 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(270\) | −10.6134 | −0.645911 | ||||||||
\(271\) | 18.0644 | 1.09734 | 0.548668 | − | 0.836041i | \(-0.315135\pi\) | ||||
0.548668 | + | 0.836041i | \(0.315135\pi\) | |||||||
\(272\) | −2.05780 | −0.124772 | ||||||||
\(273\) | 4.38764 | 0.265552 | ||||||||
\(274\) | 24.0441 | 1.45256 | ||||||||
\(275\) | −3.73068 | −0.224968 | ||||||||
\(276\) | 10.1079 | 0.608422 | ||||||||
\(277\) | 19.2745 | 1.15809 | 0.579046 | − | 0.815295i | \(-0.303425\pi\) | ||||
0.579046 | + | 0.815295i | \(0.303425\pi\) | |||||||
\(278\) | 15.0347 | 0.901722 | ||||||||
\(279\) | −6.31681 | −0.378178 | ||||||||
\(280\) | −0.992441 | −0.0593097 | ||||||||
\(281\) | −25.8344 | −1.54115 | −0.770575 | − | 0.637350i | \(-0.780031\pi\) | ||||
−0.770575 | + | 0.637350i | \(0.780031\pi\) | |||||||
\(282\) | −11.9930 | −0.714171 | ||||||||
\(283\) | −2.86159 | −0.170104 | −0.0850519 | − | 0.996377i | \(-0.527106\pi\) | ||||
−0.0850519 | + | 0.996377i | \(0.527106\pi\) | |||||||
\(284\) | 10.2898 | 0.610587 | ||||||||
\(285\) | 9.94163 | 0.588891 | ||||||||
\(286\) | 11.2240 | 0.663691 | ||||||||
\(287\) | −4.56759 | −0.269616 | ||||||||
\(288\) | 3.31342 | 0.195245 | ||||||||
\(289\) | −16.8278 | −0.989873 | ||||||||
\(290\) | −12.1950 | −0.716116 | ||||||||
\(291\) | 1.02537 | 0.0601084 | ||||||||
\(292\) | −11.3955 | −0.666868 | ||||||||
\(293\) | 2.62110 | 0.153126 | 0.0765632 | − | 0.997065i | \(-0.475605\pi\) | ||||
0.0765632 | + | 0.997065i | \(0.475605\pi\) | |||||||
\(294\) | 16.9913 | 0.990954 | ||||||||
\(295\) | −4.24940 | −0.247410 | ||||||||
\(296\) | 0.141401 | 0.00821878 | ||||||||
\(297\) | 5.63082 | 0.326733 | ||||||||
\(298\) | 17.7343 | 1.02732 | ||||||||
\(299\) | −56.8952 | −3.29033 | ||||||||
\(300\) | 4.44655 | 0.256722 | ||||||||
\(301\) | −1.96179 | −0.113076 | ||||||||
\(302\) | −8.65789 | −0.498206 | ||||||||
\(303\) | 12.7609 | 0.733095 | ||||||||
\(304\) | −29.3355 | −1.68251 | ||||||||
\(305\) | 12.9731 | 0.742840 | ||||||||
\(306\) | −0.537559 | −0.0307302 | ||||||||
\(307\) | −4.23317 | −0.241600 | −0.120800 | − | 0.992677i | \(-0.538546\pi\) | ||||
−0.120800 | + | 0.992677i | \(0.538546\pi\) | |||||||
\(308\) | −0.350244 | −0.0199570 | ||||||||
\(309\) | 18.8893 | 1.07458 | ||||||||
\(310\) | −15.3748 | −0.873230 | ||||||||
\(311\) | −20.0593 | −1.13746 | −0.568728 | − | 0.822525i | \(-0.692564\pi\) | ||||
−0.568728 | + | 0.822525i | \(0.692564\pi\) | |||||||
\(312\) | 20.1111 | 1.13857 | ||||||||
\(313\) | −24.5329 | −1.38668 | −0.693340 | − | 0.720610i | \(-0.743862\pi\) | ||||
−0.693340 | + | 0.720610i | \(0.743862\pi\) | |||||||
\(314\) | 12.3834 | 0.698835 | ||||||||
\(315\) | −0.382485 | −0.0215506 | ||||||||
\(316\) | −1.99149 | −0.112030 | ||||||||
\(317\) | 14.9160 | 0.837768 | 0.418884 | − | 0.908040i | \(-0.362421\pi\) | ||||
0.418884 | + | 0.908040i | \(0.362421\pi\) | |||||||
\(318\) | −35.9904 | −2.01824 | ||||||||
\(319\) | 6.46992 | 0.362246 | ||||||||
\(320\) | −3.11066 | −0.173891 | ||||||||
\(321\) | −8.44528 | −0.471370 | ||||||||
\(322\) | 6.21980 | 0.346616 | ||||||||
\(323\) | 2.45418 | 0.136554 | ||||||||
\(324\) | −4.85520 | −0.269733 | ||||||||
\(325\) | −25.0288 | −1.38835 | ||||||||
\(326\) | −37.7062 | −2.08835 | ||||||||
\(327\) | 6.43057 | 0.355611 | ||||||||
\(328\) | −20.9359 | −1.15599 | ||||||||
\(329\) | −2.10651 | −0.116136 | ||||||||
\(330\) | 2.81194 | 0.154792 | ||||||||
\(331\) | 22.9280 | 1.26024 | 0.630118 | − | 0.776500i | \(-0.283007\pi\) | ||||
0.630118 | + | 0.776500i | \(0.283007\pi\) | |||||||
\(332\) | 7.42417 | 0.407454 | ||||||||
\(333\) | 0.0544958 | 0.00298635 | ||||||||
\(334\) | −10.5144 | −0.575321 | ||||||||
\(335\) | −5.61132 | −0.306579 | ||||||||
\(336\) | −3.24357 | −0.176951 | ||||||||
\(337\) | 6.15588 | 0.335332 | 0.167666 | − | 0.985844i | \(-0.446377\pi\) | ||||
0.167666 | + | 0.985844i | \(0.446377\pi\) | |||||||
\(338\) | 53.5521 | 2.91285 | ||||||||
\(339\) | 15.2240 | 0.826852 | ||||||||
\(340\) | −0.373472 | −0.0202544 | ||||||||
\(341\) | 8.15693 | 0.441722 | ||||||||
\(342\) | −7.66333 | −0.414385 | ||||||||
\(343\) | 6.05315 | 0.326839 | ||||||||
\(344\) | −8.99203 | −0.484818 | ||||||||
\(345\) | −14.2538 | −0.767401 | ||||||||
\(346\) | 15.9298 | 0.856393 | ||||||||
\(347\) | 9.08529 | 0.487724 | 0.243862 | − | 0.969810i | \(-0.421586\pi\) | ||||
0.243862 | + | 0.969810i | \(0.421586\pi\) | |||||||
\(348\) | −7.71144 | −0.413376 | ||||||||
\(349\) | −11.2493 | −0.602163 | −0.301082 | − | 0.953598i | \(-0.597348\pi\) | ||||
−0.301082 | + | 0.953598i | \(0.597348\pi\) | |||||||
\(350\) | 2.73616 | 0.146254 | ||||||||
\(351\) | 37.7767 | 2.01637 | ||||||||
\(352\) | −4.27863 | −0.228052 | ||||||||
\(353\) | −10.3092 | −0.548701 | −0.274351 | − | 0.961630i | \(-0.588463\pi\) | ||||
−0.274351 | + | 0.961630i | \(0.588463\pi\) | |||||||
\(354\) | −9.41371 | −0.500333 | ||||||||
\(355\) | −14.5104 | −0.770133 | ||||||||
\(356\) | −0.795492 | −0.0421610 | ||||||||
\(357\) | 0.271354 | 0.0143616 | ||||||||
\(358\) | 19.7178 | 1.04212 | ||||||||
\(359\) | −4.91736 | −0.259528 | −0.129764 | − | 0.991545i | \(-0.541422\pi\) | ||||
−0.129764 | + | 0.991545i | \(0.541422\pi\) | |||||||
\(360\) | −1.75315 | −0.0923993 | ||||||||
\(361\) | 15.9863 | 0.841383 | ||||||||
\(362\) | 30.6058 | 1.60860 | ||||||||
\(363\) | −1.49184 | −0.0783013 | ||||||||
\(364\) | −2.34976 | −0.123161 | ||||||||
\(365\) | 16.0696 | 0.841120 | ||||||||
\(366\) | 28.7394 | 1.50223 | ||||||||
\(367\) | 13.3846 | 0.698672 | 0.349336 | − | 0.936998i | \(-0.386407\pi\) | ||||
0.349336 | + | 0.936998i | \(0.386407\pi\) | |||||||
\(368\) | 42.0598 | 2.19252 | ||||||||
\(369\) | −8.06867 | −0.420038 | ||||||||
\(370\) | 0.132640 | 0.00689563 | ||||||||
\(371\) | −6.32155 | −0.328199 | ||||||||
\(372\) | −9.72216 | −0.504070 | ||||||||
\(373\) | −18.1922 | −0.941955 | −0.470977 | − | 0.882145i | \(-0.656099\pi\) | ||||
−0.470977 | + | 0.882145i | \(0.656099\pi\) | |||||||
\(374\) | 0.694152 | 0.0358937 | ||||||||
\(375\) | −14.6743 | −0.757776 | ||||||||
\(376\) | −9.65538 | −0.497938 | ||||||||
\(377\) | 43.4062 | 2.23553 | ||||||||
\(378\) | −4.12976 | −0.212412 | ||||||||
\(379\) | 11.4612 | 0.588724 | 0.294362 | − | 0.955694i | \(-0.404893\pi\) | ||||
0.294362 | + | 0.955694i | \(0.404893\pi\) | |||||||
\(380\) | −5.32413 | −0.273122 | ||||||||
\(381\) | 26.0473 | 1.33444 | ||||||||
\(382\) | 5.38584 | 0.275564 | ||||||||
\(383\) | 21.9494 | 1.12156 | 0.560782 | − | 0.827963i | \(-0.310500\pi\) | ||||
0.560782 | + | 0.827963i | \(0.310500\pi\) | |||||||
\(384\) | −19.6571 | −1.00312 | ||||||||
\(385\) | 0.493904 | 0.0251717 | ||||||||
\(386\) | −27.6316 | −1.40641 | ||||||||
\(387\) | −3.46551 | −0.176162 | ||||||||
\(388\) | −0.549127 | −0.0278777 | ||||||||
\(389\) | 22.4303 | 1.13726 | 0.568631 | − | 0.822592i | \(-0.307473\pi\) | ||||
0.568631 | + | 0.822592i | \(0.307473\pi\) | |||||||
\(390\) | 18.8651 | 0.955269 | ||||||||
\(391\) | −3.51869 | −0.177948 | ||||||||
\(392\) | 13.6795 | 0.690918 | ||||||||
\(393\) | 1.49184 | 0.0752534 | ||||||||
\(394\) | −33.1643 | −1.67079 | ||||||||
\(395\) | 2.80835 | 0.141303 | ||||||||
\(396\) | −0.618707 | −0.0310912 | ||||||||
\(397\) | −1.61878 | −0.0812443 | −0.0406221 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406221 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(398\) | 15.6728 | 0.785608 | ||||||||
\(399\) | 3.86837 | 0.193661 | ||||||||
\(400\) | 18.5026 | 0.925128 | ||||||||
\(401\) | −23.5568 | −1.17637 | −0.588185 | − | 0.808726i | \(-0.700157\pi\) | ||||
−0.588185 | + | 0.808726i | \(0.700157\pi\) | |||||||
\(402\) | −12.4308 | −0.619990 | ||||||||
\(403\) | 54.7241 | 2.72600 | ||||||||
\(404\) | −6.83396 | −0.340002 | ||||||||
\(405\) | 6.84667 | 0.340214 | ||||||||
\(406\) | −4.74518 | −0.235499 | ||||||||
\(407\) | −0.0703706 | −0.00348814 | ||||||||
\(408\) | 1.24378 | 0.0615761 | ||||||||
\(409\) | −15.0212 | −0.742749 | −0.371375 | − | 0.928483i | \(-0.621113\pi\) | ||||
−0.371375 | + | 0.928483i | \(0.621113\pi\) | |||||||
\(410\) | −19.6387 | −0.969888 | ||||||||
\(411\) | −21.4405 | −1.05758 | ||||||||
\(412\) | −10.1160 | −0.498378 | ||||||||
\(413\) | −1.65348 | −0.0813623 | ||||||||
\(414\) | 10.9873 | 0.539997 | ||||||||
\(415\) | −10.4694 | −0.513921 | ||||||||
\(416\) | −28.7049 | −1.40738 | ||||||||
\(417\) | −13.4067 | −0.656528 | ||||||||
\(418\) | 9.89568 | 0.484013 | ||||||||
\(419\) | −10.8982 | −0.532412 | −0.266206 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266206 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(420\) | −0.588680 | −0.0287246 | ||||||||
\(421\) | −23.0149 | −1.12168 | −0.560840 | − | 0.827924i | \(-0.689522\pi\) | ||||
−0.560840 | + | 0.827924i | \(0.689522\pi\) | |||||||
\(422\) | 8.54729 | 0.416075 | ||||||||
\(423\) | −3.72117 | −0.180929 | ||||||||
\(424\) | −28.9754 | −1.40717 | ||||||||
\(425\) | −1.54791 | −0.0750846 | ||||||||
\(426\) | −32.1449 | −1.55743 | ||||||||
\(427\) | 5.04795 | 0.244288 | ||||||||
\(428\) | 4.52278 | 0.218617 | ||||||||
\(429\) | −10.0086 | −0.483222 | ||||||||
\(430\) | −8.43488 | −0.406766 | ||||||||
\(431\) | 13.4907 | 0.649826 | 0.324913 | − | 0.945744i | \(-0.394665\pi\) | ||||
0.324913 | + | 0.945744i | \(0.394665\pi\) | |||||||
\(432\) | −27.9265 | −1.34361 | ||||||||
\(433\) | 13.7959 | 0.662986 | 0.331493 | − | 0.943458i | \(-0.392448\pi\) | ||||
0.331493 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(434\) | −5.98246 | −0.287167 | ||||||||
\(435\) | 10.8745 | 0.521391 | ||||||||
\(436\) | −3.44382 | −0.164929 | ||||||||
\(437\) | −50.1617 | −2.39956 | ||||||||
\(438\) | 35.5989 | 1.70098 | ||||||||
\(439\) | −0.877639 | −0.0418874 | −0.0209437 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209437 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(440\) | 2.26385 | 0.107925 | ||||||||
\(441\) | 5.27205 | 0.251050 | ||||||||
\(442\) | 4.65701 | 0.221511 | ||||||||
\(443\) | −8.61049 | −0.409097 | −0.204548 | − | 0.978856i | \(-0.565573\pi\) | ||||
−0.204548 | + | 0.978856i | \(0.565573\pi\) | |||||||
\(444\) | 0.0838740 | 0.00398049 | ||||||||
\(445\) | 1.12178 | 0.0531776 | ||||||||
\(446\) | 7.07830 | 0.335167 | ||||||||
\(447\) | −15.8139 | −0.747974 | ||||||||
\(448\) | −1.21038 | −0.0571851 | ||||||||
\(449\) | 9.07390 | 0.428224 | 0.214112 | − | 0.976809i | \(-0.431314\pi\) | ||||
0.214112 | + | 0.976809i | \(0.431314\pi\) | |||||||
\(450\) | 4.83343 | 0.227850 | ||||||||
\(451\) | 10.4191 | 0.490616 | ||||||||
\(452\) | −8.15302 | −0.383486 | ||||||||
\(453\) | 7.72036 | 0.362734 | ||||||||
\(454\) | 41.5336 | 1.94927 | ||||||||
\(455\) | 3.31356 | 0.155342 | ||||||||
\(456\) | 17.7310 | 0.830330 | ||||||||
\(457\) | −2.53270 | −0.118475 | −0.0592375 | − | 0.998244i | \(-0.518867\pi\) | ||||
−0.0592375 | + | 0.998244i | \(0.518867\pi\) | |||||||
\(458\) | −39.0678 | −1.82552 | ||||||||
\(459\) | 2.33630 | 0.109049 | ||||||||
\(460\) | 7.63349 | 0.355913 | ||||||||
\(461\) | −29.7019 | −1.38336 | −0.691678 | − | 0.722206i | \(-0.743128\pi\) | ||||
−0.691678 | + | 0.722206i | \(0.743128\pi\) | |||||||
\(462\) | 1.09415 | 0.0509043 | ||||||||
\(463\) | 3.11272 | 0.144660 | 0.0723301 | − | 0.997381i | \(-0.476956\pi\) | ||||
0.0723301 | + | 0.997381i | \(0.476956\pi\) | |||||||
\(464\) | −32.0881 | −1.48965 | ||||||||
\(465\) | 13.7099 | 0.635783 | ||||||||
\(466\) | 34.1597 | 1.58242 | ||||||||
\(467\) | 24.5855 | 1.13768 | 0.568840 | − | 0.822448i | \(-0.307392\pi\) | ||||
0.568840 | + | 0.822448i | \(0.307392\pi\) | |||||||
\(468\) | −4.15086 | −0.191873 | ||||||||
\(469\) | −2.18341 | −0.100820 | ||||||||
\(470\) | −9.05713 | −0.417774 | ||||||||
\(471\) | −11.0424 | −0.508809 | ||||||||
\(472\) | −7.57885 | −0.348845 | ||||||||
\(473\) | 4.47503 | 0.205762 | ||||||||
\(474\) | 6.22133 | 0.285755 | ||||||||
\(475\) | −22.0666 | −1.01249 | ||||||||
\(476\) | −0.145321 | −0.00666077 | ||||||||
\(477\) | −11.1671 | −0.511304 | ||||||||
\(478\) | 18.2540 | 0.834917 | ||||||||
\(479\) | 21.1814 | 0.967801 | 0.483900 | − | 0.875123i | \(-0.339220\pi\) | ||||
0.483900 | + | 0.875123i | \(0.339220\pi\) | |||||||
\(480\) | −7.19139 | −0.328241 | ||||||||
\(481\) | −0.472111 | −0.0215264 | ||||||||
\(482\) | 3.67396 | 0.167344 | ||||||||
\(483\) | −5.54628 | −0.252365 | ||||||||
\(484\) | 0.798939 | 0.0363154 | ||||||||
\(485\) | 0.774364 | 0.0351621 | ||||||||
\(486\) | −13.0937 | −0.593942 | ||||||||
\(487\) | 14.5726 | 0.660348 | 0.330174 | − | 0.943920i | \(-0.392893\pi\) | ||||
0.330174 | + | 0.943920i | \(0.392893\pi\) | |||||||
\(488\) | 23.1377 | 1.04740 | ||||||||
\(489\) | 33.6231 | 1.52049 | ||||||||
\(490\) | 12.8319 | 0.579686 | ||||||||
\(491\) | 26.7337 | 1.20648 | 0.603238 | − | 0.797562i | \(-0.293877\pi\) | ||||
0.603238 | + | 0.797562i | \(0.293877\pi\) | |||||||
\(492\) | −12.4184 | −0.559866 | ||||||||
\(493\) | 2.68446 | 0.120902 | ||||||||
\(494\) | 66.3893 | 2.98700 | ||||||||
\(495\) | 0.872485 | 0.0392153 | ||||||||
\(496\) | −40.4549 | −1.81648 | ||||||||
\(497\) | −5.64612 | −0.253263 | ||||||||
\(498\) | −23.1928 | −1.03929 | ||||||||
\(499\) | 9.76923 | 0.437331 | 0.218665 | − | 0.975800i | \(-0.429830\pi\) | ||||
0.218665 | + | 0.975800i | \(0.429830\pi\) | |||||||
\(500\) | 7.85865 | 0.351449 | ||||||||
\(501\) | 9.37581 | 0.418880 | ||||||||
\(502\) | 2.56609 | 0.114530 | ||||||||
\(503\) | −35.2664 | −1.57245 | −0.786225 | − | 0.617940i | \(-0.787967\pi\) | ||||
−0.786225 | + | 0.617940i | \(0.787967\pi\) | |||||||
\(504\) | −0.682166 | −0.0303861 | ||||||||
\(505\) | 9.63707 | 0.428844 | ||||||||
\(506\) | −14.1880 | −0.630732 | ||||||||
\(507\) | −47.7532 | −2.12079 | ||||||||
\(508\) | −13.9493 | −0.618902 | ||||||||
\(509\) | 37.0984 | 1.64436 | 0.822180 | − | 0.569228i | \(-0.192758\pi\) | ||||
0.822180 | + | 0.569228i | \(0.192758\pi\) | |||||||
\(510\) | 1.16671 | 0.0516628 | ||||||||
\(511\) | 6.25280 | 0.276608 | ||||||||
\(512\) | 1.28884 | 0.0569591 | ||||||||
\(513\) | 33.3059 | 1.47049 | ||||||||
\(514\) | 18.7329 | 0.826273 | ||||||||
\(515\) | 14.2653 | 0.628603 | ||||||||
\(516\) | −5.33374 | −0.234805 | ||||||||
\(517\) | 4.80516 | 0.211331 | ||||||||
\(518\) | 0.0516113 | 0.00226767 | ||||||||
\(519\) | −14.2049 | −0.623524 | ||||||||
\(520\) | 15.1880 | 0.666038 | ||||||||
\(521\) | −24.6016 | −1.07782 | −0.538908 | − | 0.842365i | \(-0.681163\pi\) | ||||
−0.538908 | + | 0.842365i | \(0.681163\pi\) | |||||||
\(522\) | −8.38238 | −0.366887 | ||||||||
\(523\) | −0.682719 | −0.0298532 | −0.0149266 | − | 0.999889i | \(-0.504751\pi\) | ||||
−0.0149266 | + | 0.999889i | \(0.504751\pi\) | |||||||
\(524\) | −0.798939 | −0.0349018 | ||||||||
\(525\) | −2.43987 | −0.106485 | ||||||||
\(526\) | −13.8409 | −0.603492 | ||||||||
\(527\) | 3.38442 | 0.147428 | ||||||||
\(528\) | 7.39890 | 0.321996 | ||||||||
\(529\) | 48.9194 | 2.12693 | ||||||||
\(530\) | −27.1800 | −1.18063 | ||||||||
\(531\) | −2.92088 | −0.126755 | ||||||||
\(532\) | −2.07166 | −0.0898180 | ||||||||
\(533\) | 69.9009 | 3.02774 | ||||||||
\(534\) | 2.48508 | 0.107540 | ||||||||
\(535\) | −6.37790 | −0.275741 | ||||||||
\(536\) | −10.0078 | −0.432273 | ||||||||
\(537\) | −17.5826 | −0.758747 | ||||||||
\(538\) | −7.52983 | −0.324634 | ||||||||
\(539\) | −6.80782 | −0.293233 | ||||||||
\(540\) | −5.06841 | −0.218110 | ||||||||
\(541\) | 32.5375 | 1.39889 | 0.699447 | − | 0.714684i | \(-0.253429\pi\) | ||||
0.699447 | + | 0.714684i | \(0.253429\pi\) | |||||||
\(542\) | 30.2218 | 1.29814 | ||||||||
\(543\) | −27.2916 | −1.17119 | ||||||||
\(544\) | −1.77526 | −0.0761137 | ||||||||
\(545\) | 4.85639 | 0.208025 | ||||||||
\(546\) | 7.34054 | 0.314146 | ||||||||
\(547\) | 42.0304 | 1.79709 | 0.898545 | − | 0.438881i | \(-0.144625\pi\) | ||||
0.898545 | + | 0.438881i | \(0.144625\pi\) | |||||||
\(548\) | 11.4822 | 0.490497 | ||||||||
\(549\) | 8.91724 | 0.380579 | ||||||||
\(550\) | −6.24143 | −0.266136 | ||||||||
\(551\) | 38.2691 | 1.63032 | ||||||||
\(552\) | −25.4219 | −1.08203 | ||||||||
\(553\) | 1.09275 | 0.0464685 | ||||||||
\(554\) | 32.2463 | 1.37001 | ||||||||
\(555\) | −0.118277 | −0.00502058 | ||||||||
\(556\) | 7.17980 | 0.304491 | ||||||||
\(557\) | −26.9423 | −1.14158 | −0.570790 | − | 0.821096i | \(-0.693363\pi\) | ||||
−0.570790 | + | 0.821096i | \(0.693363\pi\) | |||||||
\(558\) | −10.5681 | −0.447381 | ||||||||
\(559\) | 30.0226 | 1.26982 | ||||||||
\(560\) | −2.44956 | −0.103513 | ||||||||
\(561\) | −0.618985 | −0.0261336 | ||||||||
\(562\) | −43.2210 | −1.82317 | ||||||||
\(563\) | 0.439366 | 0.0185171 | 0.00925854 | − | 0.999957i | \(-0.497053\pi\) | ||||
0.00925854 | + | 0.999957i | \(0.497053\pi\) | |||||||
\(564\) | −5.72722 | −0.241159 | ||||||||
\(565\) | 11.4972 | 0.483690 | ||||||||
\(566\) | −4.78745 | −0.201231 | ||||||||
\(567\) | 2.66409 | 0.111881 | ||||||||
\(568\) | −25.8795 | −1.08588 | ||||||||
\(569\) | 17.7019 | 0.742101 | 0.371051 | − | 0.928613i | \(-0.378998\pi\) | ||||
0.371051 | + | 0.928613i | \(0.378998\pi\) | |||||||
\(570\) | 16.6324 | 0.696654 | ||||||||
\(571\) | −3.44776 | −0.144284 | −0.0721421 | − | 0.997394i | \(-0.522984\pi\) | ||||
−0.0721421 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(572\) | 5.36002 | 0.224114 | ||||||||
\(573\) | −4.80263 | −0.200633 | ||||||||
\(574\) | −7.64159 | −0.318954 | ||||||||
\(575\) | 31.6381 | 1.31940 | ||||||||
\(576\) | −2.13815 | −0.0890894 | ||||||||
\(577\) | 21.3780 | 0.889976 | 0.444988 | − | 0.895537i | \(-0.353208\pi\) | ||||
0.444988 | + | 0.895537i | \(0.353208\pi\) | |||||||
\(578\) | −28.1530 | −1.17101 | ||||||||
\(579\) | 24.6395 | 1.02398 | ||||||||
\(580\) | −5.82370 | −0.241816 | ||||||||
\(581\) | −4.07372 | −0.169006 | ||||||||
\(582\) | 1.71545 | 0.0711077 | ||||||||
\(583\) | 14.4201 | 0.597218 | ||||||||
\(584\) | 28.6602 | 1.18597 | ||||||||
\(585\) | 5.85343 | 0.242010 | ||||||||
\(586\) | 4.38511 | 0.181147 | ||||||||
\(587\) | −30.7139 | −1.26770 | −0.633848 | − | 0.773457i | \(-0.718526\pi\) | ||||
−0.633848 | + | 0.773457i | \(0.718526\pi\) | |||||||
\(588\) | 8.11417 | 0.334623 | ||||||||
\(589\) | 48.2476 | 1.98801 | ||||||||
\(590\) | −7.10926 | −0.292684 | ||||||||
\(591\) | 29.5731 | 1.21648 | ||||||||
\(592\) | 0.349008 | 0.0143442 | ||||||||
\(593\) | −4.55398 | −0.187009 | −0.0935047 | − | 0.995619i | \(-0.529807\pi\) | ||||
−0.0935047 | + | 0.995619i | \(0.529807\pi\) | |||||||
\(594\) | 9.42038 | 0.386523 | ||||||||
\(595\) | 0.204928 | 0.00840122 | ||||||||
\(596\) | 8.46898 | 0.346903 | ||||||||
\(597\) | −13.9757 | −0.571987 | ||||||||
\(598\) | −95.1858 | −3.89244 | ||||||||
\(599\) | 17.1227 | 0.699616 | 0.349808 | − | 0.936821i | \(-0.386247\pi\) | ||||
0.349808 | + | 0.936821i | \(0.386247\pi\) | |||||||
\(600\) | −11.1833 | −0.456558 | ||||||||
\(601\) | −2.42972 | −0.0991102 | −0.0495551 | − | 0.998771i | \(-0.515780\pi\) | ||||
−0.0495551 | + | 0.998771i | \(0.515780\pi\) | |||||||
\(602\) | −3.28208 | −0.133768 | ||||||||
\(603\) | −3.85700 | −0.157069 | ||||||||
\(604\) | −4.13456 | −0.168233 | ||||||||
\(605\) | −1.12664 | −0.0458046 | ||||||||
\(606\) | 21.3490 | 0.867245 | ||||||||
\(607\) | 0.497658 | 0.0201993 | 0.0100997 | − | 0.999949i | \(-0.496785\pi\) | ||||
0.0100997 | + | 0.999949i | \(0.496785\pi\) | |||||||
\(608\) | −25.3077 | −1.02636 | ||||||||
\(609\) | 4.23134 | 0.171463 | ||||||||
\(610\) | 21.7041 | 0.878774 | ||||||||
\(611\) | 32.2374 | 1.30419 | ||||||||
\(612\) | −0.256710 | −0.0103769 | ||||||||
\(613\) | 2.51525 | 0.101590 | 0.0507949 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507949 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(614\) | −7.08211 | −0.285811 | ||||||||
\(615\) | 17.5121 | 0.706157 | ||||||||
\(616\) | 0.880883 | 0.0354918 | ||||||||
\(617\) | −44.5175 | −1.79221 | −0.896103 | − | 0.443847i | \(-0.853613\pi\) | ||||
−0.896103 | + | 0.443847i | \(0.853613\pi\) | |||||||
\(618\) | 31.6019 | 1.27121 | ||||||||
\(619\) | −40.2898 | −1.61938 | −0.809692 | − | 0.586855i | \(-0.800366\pi\) | ||||
−0.809692 | + | 0.586855i | \(0.800366\pi\) | |||||||
\(620\) | −7.34220 | −0.294870 | ||||||||
\(621\) | −47.7524 | −1.91624 | ||||||||
\(622\) | −33.5592 | −1.34560 | ||||||||
\(623\) | 0.436494 | 0.0174878 | ||||||||
\(624\) | 49.6386 | 1.98713 | ||||||||
\(625\) | 7.57132 | 0.302853 | ||||||||
\(626\) | −41.0436 | −1.64043 | ||||||||
\(627\) | −8.82412 | −0.352401 | ||||||||
\(628\) | 5.91366 | 0.235981 | ||||||||
\(629\) | −0.0291977 | −0.00116419 | ||||||||
\(630\) | −0.639899 | −0.0254942 | ||||||||
\(631\) | −13.3359 | −0.530893 | −0.265447 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265447 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(632\) | 5.00871 | 0.199236 | ||||||||
\(633\) | −7.62174 | −0.302937 | ||||||||
\(634\) | 24.9546 | 0.991073 | ||||||||
\(635\) | 19.6710 | 0.780620 | ||||||||
\(636\) | −17.1871 | −0.681514 | ||||||||
\(637\) | −45.6731 | −1.80963 | ||||||||
\(638\) | 10.8242 | 0.428534 | ||||||||
\(639\) | −9.97390 | −0.394561 | ||||||||
\(640\) | −14.8451 | −0.586804 | ||||||||
\(641\) | −17.4992 | −0.691177 | −0.345588 | − | 0.938386i | \(-0.612321\pi\) | ||||
−0.345588 | + | 0.938386i | \(0.612321\pi\) | |||||||
\(642\) | −14.1290 | −0.557626 | ||||||||
\(643\) | 0.425674 | 0.0167869 | 0.00839347 | − | 0.999965i | \(-0.497328\pi\) | ||||
0.00839347 | + | 0.999965i | \(0.497328\pi\) | |||||||
\(644\) | 2.97025 | 0.117044 | ||||||||
\(645\) | 7.52150 | 0.296159 | ||||||||
\(646\) | 4.10585 | 0.161543 | ||||||||
\(647\) | 19.5613 | 0.769032 | 0.384516 | − | 0.923118i | \(-0.374368\pi\) | ||||
0.384516 | + | 0.923118i | \(0.374368\pi\) | |||||||
\(648\) | 12.2111 | 0.479697 | ||||||||
\(649\) | 3.77174 | 0.148054 | ||||||||
\(650\) | −41.8732 | −1.64240 | ||||||||
\(651\) | 5.33464 | 0.209081 | ||||||||
\(652\) | −18.0065 | −0.705189 | ||||||||
\(653\) | −35.4134 | −1.38583 | −0.692917 | − | 0.721018i | \(-0.743675\pi\) | ||||
−0.692917 | + | 0.721018i | \(0.743675\pi\) | |||||||
\(654\) | 10.7584 | 0.420685 | ||||||||
\(655\) | 1.12664 | 0.0440216 | ||||||||
\(656\) | −51.6743 | −2.01754 | ||||||||
\(657\) | 11.0456 | 0.430930 | ||||||||
\(658\) | −3.52420 | −0.137388 | ||||||||
\(659\) | 32.2081 | 1.25465 | 0.627325 | − | 0.778758i | \(-0.284150\pi\) | ||||
0.627325 | + | 0.778758i | \(0.284150\pi\) | |||||||
\(660\) | 1.34283 | 0.0522698 | ||||||||
\(661\) | 6.82312 | 0.265389 | 0.132694 | − | 0.991157i | \(-0.457637\pi\) | ||||
0.132694 | + | 0.991157i | \(0.457637\pi\) | |||||||
\(662\) | 38.3586 | 1.49085 | ||||||||
\(663\) | −4.15272 | −0.161278 | ||||||||
\(664\) | −18.6722 | −0.724623 | ||||||||
\(665\) | 2.92141 | 0.113287 | ||||||||
\(666\) | 0.0911717 | 0.00353283 | ||||||||
\(667\) | −54.8684 | −2.12451 | ||||||||
\(668\) | −5.02111 | −0.194273 | ||||||||
\(669\) | −6.31182 | −0.244029 | ||||||||
\(670\) | −9.38775 | −0.362680 | ||||||||
\(671\) | −11.5149 | −0.444526 | ||||||||
\(672\) | −2.79823 | −0.107944 | ||||||||
\(673\) | −50.9412 | −1.96364 | −0.981819 | − | 0.189818i | \(-0.939210\pi\) | ||||
−0.981819 | + | 0.189818i | \(0.939210\pi\) | |||||||
\(674\) | 10.2988 | 0.396695 | ||||||||
\(675\) | −21.0068 | −0.808551 | ||||||||
\(676\) | 25.5737 | 0.983604 | ||||||||
\(677\) | −27.1128 | −1.04203 | −0.521015 | − | 0.853548i | \(-0.674446\pi\) | ||||
−0.521015 | + | 0.853548i | \(0.674446\pi\) | |||||||
\(678\) | 25.4697 | 0.978159 | ||||||||
\(679\) | 0.301311 | 0.0115633 | ||||||||
\(680\) | 0.939303 | 0.0360206 | ||||||||
\(681\) | −37.0361 | −1.41923 | ||||||||
\(682\) | 13.6466 | 0.522554 | ||||||||
\(683\) | 19.8345 | 0.758947 | 0.379474 | − | 0.925203i | \(-0.376105\pi\) | ||||
0.379474 | + | 0.925203i | \(0.376105\pi\) | |||||||
\(684\) | −3.65960 | −0.139928 | ||||||||
\(685\) | −16.1919 | −0.618662 | ||||||||
\(686\) | 10.1269 | 0.386648 | ||||||||
\(687\) | 34.8373 | 1.32912 | ||||||||
\(688\) | −22.1942 | −0.846147 | ||||||||
\(689\) | 96.7430 | 3.68562 | ||||||||
\(690\) | −23.8467 | −0.907829 | ||||||||
\(691\) | −4.42320 | −0.168266 | −0.0841332 | − | 0.996455i | \(-0.526812\pi\) | ||||
−0.0841332 | + | 0.996455i | \(0.526812\pi\) | |||||||
\(692\) | 7.60726 | 0.289184 | ||||||||
\(693\) | 0.339491 | 0.0128962 | ||||||||
\(694\) | 15.1997 | 0.576974 | ||||||||
\(695\) | −10.1248 | −0.384054 | ||||||||
\(696\) | 19.3947 | 0.735155 | ||||||||
\(697\) | 4.32303 | 0.163746 | ||||||||
\(698\) | −18.8202 | −0.712354 | ||||||||
\(699\) | −30.4607 | −1.15213 | ||||||||
\(700\) | 1.30665 | 0.0493865 | ||||||||
\(701\) | −48.2511 | −1.82242 | −0.911210 | − | 0.411941i | \(-0.864851\pi\) | ||||
−0.911210 | + | 0.411941i | \(0.864851\pi\) | |||||||
\(702\) | 63.2005 | 2.38535 | ||||||||
\(703\) | −0.416237 | −0.0156987 | ||||||||
\(704\) | 2.76100 | 0.104059 | ||||||||
\(705\) | 8.07637 | 0.304174 | ||||||||
\(706\) | −17.2473 | −0.649109 | ||||||||
\(707\) | 3.74986 | 0.141028 | ||||||||
\(708\) | −4.49550 | −0.168951 | ||||||||
\(709\) | −39.4113 | −1.48012 | −0.740062 | − | 0.672539i | \(-0.765204\pi\) | ||||
−0.740062 | + | 0.672539i | \(0.765204\pi\) | |||||||
\(710\) | −24.2760 | −0.911060 | ||||||||
\(711\) | 1.93035 | 0.0723938 | ||||||||
\(712\) | 2.00071 | 0.0749797 | ||||||||
\(713\) | −69.1751 | −2.59063 | ||||||||
\(714\) | 0.453977 | 0.0169897 | ||||||||
\(715\) | −7.55856 | −0.282674 | ||||||||
\(716\) | 9.41619 | 0.351899 | ||||||||
\(717\) | −16.2773 | −0.607887 | ||||||||
\(718\) | −8.22676 | −0.307020 | ||||||||
\(719\) | −30.2623 | −1.12859 | −0.564296 | − | 0.825572i | \(-0.690852\pi\) | ||||
−0.564296 | + | 0.825572i | \(0.690852\pi\) | |||||||
\(720\) | −4.32715 | −0.161264 | ||||||||
\(721\) | 5.55073 | 0.206720 | ||||||||
\(722\) | 26.7451 | 0.995349 | ||||||||
\(723\) | −3.27612 | −0.121840 | ||||||||
\(724\) | 14.6157 | 0.543189 | ||||||||
\(725\) | −24.1372 | −0.896433 | ||||||||
\(726\) | −2.49585 | −0.0926298 | ||||||||
\(727\) | 24.6084 | 0.912675 | 0.456338 | − | 0.889807i | \(-0.349161\pi\) | ||||
0.456338 | + | 0.889807i | \(0.349161\pi\) | |||||||
\(728\) | 5.90977 | 0.219031 | ||||||||
\(729\) | 29.9070 | 1.10767 | ||||||||
\(730\) | 26.8844 | 0.995038 | ||||||||
\(731\) | 1.85675 | 0.0686744 | ||||||||
\(732\) | 13.7245 | 0.507270 | ||||||||
\(733\) | 36.7955 | 1.35907 | 0.679537 | − | 0.733641i | \(-0.262181\pi\) | ||||
0.679537 | + | 0.733641i | \(0.262181\pi\) | |||||||
\(734\) | 22.3925 | 0.826523 | ||||||||
\(735\) | −11.4424 | −0.422059 | ||||||||
\(736\) | 36.2850 | 1.33748 | ||||||||
\(737\) | 4.98056 | 0.183461 | ||||||||
\(738\) | −13.4989 | −0.496902 | ||||||||
\(739\) | 20.3502 | 0.748594 | 0.374297 | − | 0.927309i | \(-0.377884\pi\) | ||||
0.374297 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(740\) | 0.0633420 | 0.00232850 | ||||||||
\(741\) | −59.2003 | −2.17478 | ||||||||
\(742\) | −10.5760 | −0.388256 | ||||||||
\(743\) | −15.4255 | −0.565907 | −0.282954 | − | 0.959134i | \(-0.591314\pi\) | ||||
−0.282954 | + | 0.959134i | \(0.591314\pi\) | |||||||
\(744\) | 24.4518 | 0.896446 | ||||||||
\(745\) | −11.9427 | −0.437548 | ||||||||
\(746\) | −30.4356 | −1.11432 | ||||||||
\(747\) | −7.19624 | −0.263297 | ||||||||
\(748\) | 0.331491 | 0.0121205 | ||||||||
\(749\) | −2.48169 | −0.0906791 | ||||||||
\(750\) | −24.5501 | −0.896443 | ||||||||
\(751\) | −32.0431 | −1.16927 | −0.584635 | − | 0.811297i | \(-0.698762\pi\) | ||||
−0.584635 | + | 0.811297i | \(0.698762\pi\) | |||||||
\(752\) | −23.8315 | −0.869047 | ||||||||
\(753\) | −2.28822 | −0.0833873 | ||||||||
\(754\) | 72.6187 | 2.64462 | ||||||||
\(755\) | 5.83044 | 0.212192 | ||||||||
\(756\) | −1.97216 | −0.0717267 | ||||||||
\(757\) | −4.48845 | −0.163136 | −0.0815678 | − | 0.996668i | \(-0.525993\pi\) | ||||
−0.0815678 | + | 0.996668i | \(0.525993\pi\) | |||||||
\(758\) | 19.1747 | 0.696455 | ||||||||
\(759\) | 12.6516 | 0.459224 | ||||||||
\(760\) | 13.3905 | 0.485725 | ||||||||
\(761\) | −29.9584 | −1.08599 | −0.542996 | − | 0.839735i | \(-0.682710\pi\) | ||||
−0.542996 | + | 0.839735i | \(0.682710\pi\) | |||||||
\(762\) | 43.5772 | 1.57863 | ||||||||
\(763\) | 1.88966 | 0.0684103 | ||||||||
\(764\) | 2.57200 | 0.0930516 | ||||||||
\(765\) | 0.362006 | 0.0130884 | ||||||||
\(766\) | 36.7215 | 1.32680 | ||||||||
\(767\) | 25.3043 | 0.913685 | ||||||||
\(768\) | −24.6485 | −0.889424 | ||||||||
\(769\) | −12.9497 | −0.466979 | −0.233489 | − | 0.972359i | \(-0.575014\pi\) | ||||
−0.233489 | + | 0.972359i | \(0.575014\pi\) | |||||||
\(770\) | 0.826304 | 0.0297779 | ||||||||
\(771\) | −16.7044 | −0.601594 | ||||||||
\(772\) | −13.1954 | −0.474914 | ||||||||
\(773\) | −31.2913 | −1.12547 | −0.562734 | − | 0.826638i | \(-0.690251\pi\) | ||||
−0.562734 | + | 0.826638i | \(0.690251\pi\) | |||||||
\(774\) | −5.79781 | −0.208398 | ||||||||
\(775\) | −30.4308 | −1.09311 | ||||||||
\(776\) | 1.38109 | 0.0495781 | ||||||||
\(777\) | −0.0460225 | −0.00165105 | ||||||||
\(778\) | 37.5260 | 1.34537 | ||||||||
\(779\) | 61.6282 | 2.20806 | ||||||||
\(780\) | 9.00896 | 0.322573 | ||||||||
\(781\) | 12.8793 | 0.460859 | ||||||||
\(782\) | −5.88678 | −0.210511 | ||||||||
\(783\) | 36.4310 | 1.30194 | ||||||||
\(784\) | 33.7639 | 1.20585 | ||||||||
\(785\) | −8.33929 | −0.297642 | ||||||||
\(786\) | 2.49585 | 0.0890242 | ||||||||
\(787\) | 16.8323 | 0.600006 | 0.300003 | − | 0.953938i | \(-0.403012\pi\) | ||||
0.300003 | + | 0.953938i | \(0.403012\pi\) | |||||||
\(788\) | −15.8376 | −0.564190 | ||||||||
\(789\) | 12.3421 | 0.439391 | ||||||||
\(790\) | 4.69837 | 0.167161 | ||||||||
\(791\) | 4.47364 | 0.159064 | ||||||||
\(792\) | 1.55609 | 0.0552931 | ||||||||
\(793\) | −77.2523 | −2.74331 | ||||||||
\(794\) | −2.70822 | −0.0961113 | ||||||||
\(795\) | 24.2368 | 0.859592 | ||||||||
\(796\) | 7.48453 | 0.265282 | ||||||||
\(797\) | 14.3051 | 0.506712 | 0.253356 | − | 0.967373i | \(-0.418466\pi\) | ||||
0.253356 | + | 0.967373i | \(0.418466\pi\) | |||||||
\(798\) | 6.47179 | 0.229099 | ||||||||
\(799\) | 1.99373 | 0.0705329 | ||||||||
\(800\) | 15.9622 | 0.564348 | ||||||||
\(801\) | 0.771070 | 0.0272444 | ||||||||
\(802\) | −39.4106 | −1.39164 | ||||||||
\(803\) | −14.2632 | −0.503339 | ||||||||
\(804\) | −5.93628 | −0.209357 | ||||||||
\(805\) | −4.18857 | −0.147628 | ||||||||
\(806\) | 91.5537 | 3.22484 | ||||||||
\(807\) | 6.71446 | 0.236360 | ||||||||
\(808\) | 17.1878 | 0.604665 | ||||||||
\(809\) | 22.1051 | 0.777176 | 0.388588 | − | 0.921412i | \(-0.372963\pi\) | ||||
0.388588 | + | 0.921412i | \(0.372963\pi\) | |||||||
\(810\) | 11.4545 | 0.402470 | ||||||||
\(811\) | −27.9604 | −0.981823 | −0.490911 | − | 0.871210i | \(-0.663336\pi\) | ||||
−0.490911 | + | 0.871210i | \(0.663336\pi\) | |||||||
\(812\) | −2.26605 | −0.0795227 | ||||||||
\(813\) | −26.9492 | −0.945151 | ||||||||
\(814\) | −0.117730 | −0.00412644 | ||||||||
\(815\) | 25.3923 | 0.889453 | ||||||||
\(816\) | 3.06990 | 0.107468 | ||||||||
\(817\) | 26.4694 | 0.926048 | ||||||||
\(818\) | −25.1305 | −0.878666 | ||||||||
\(819\) | 2.27762 | 0.0795864 | ||||||||
\(820\) | −9.37843 | −0.327509 | ||||||||
\(821\) | −12.7474 | −0.444887 | −0.222443 | − | 0.974946i | \(-0.571403\pi\) | ||||
−0.222443 | + | 0.974946i | \(0.571403\pi\) | |||||||
\(822\) | −35.8700 | −1.25111 | ||||||||
\(823\) | 1.59217 | 0.0554994 | 0.0277497 | − | 0.999615i | \(-0.491166\pi\) | ||||
0.0277497 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(824\) | 25.4422 | 0.886323 | ||||||||
\(825\) | 5.56557 | 0.193768 | ||||||||
\(826\) | −2.76627 | −0.0962509 | ||||||||
\(827\) | −16.1370 | −0.561140 | −0.280570 | − | 0.959834i | \(-0.590524\pi\) | ||||
−0.280570 | + | 0.959834i | \(0.590524\pi\) | |||||||
\(828\) | 5.24697 | 0.182345 | ||||||||
\(829\) | −14.6192 | −0.507746 | −0.253873 | − | 0.967238i | \(-0.581705\pi\) | ||||
−0.253873 | + | 0.967238i | \(0.581705\pi\) | |||||||
\(830\) | −17.5153 | −0.607964 | ||||||||
\(831\) | −28.7545 | −0.997482 | ||||||||
\(832\) | 18.5233 | 0.642180 | ||||||||
\(833\) | −2.82466 | −0.0978686 | ||||||||
\(834\) | −22.4294 | −0.776667 | ||||||||
\(835\) | 7.08064 | 0.245036 | ||||||||
\(836\) | 4.72566 | 0.163440 | ||||||||
\(837\) | 45.9302 | 1.58758 | ||||||||
\(838\) | −18.2327 | −0.629839 | ||||||||
\(839\) | −47.0443 | −1.62415 | −0.812075 | − | 0.583554i | \(-0.801662\pi\) | ||||
−0.812075 | + | 0.583554i | \(0.801662\pi\) | |||||||
\(840\) | 1.48056 | 0.0510843 | ||||||||
\(841\) | 12.8599 | 0.443445 | ||||||||
\(842\) | −38.5041 | −1.32694 | ||||||||
\(843\) | 38.5408 | 1.32741 | ||||||||
\(844\) | 4.08174 | 0.140499 | ||||||||
\(845\) | −36.0634 | −1.24062 | ||||||||
\(846\) | −6.22552 | −0.214038 | ||||||||
\(847\) | −0.438386 | −0.0150631 | ||||||||
\(848\) | −71.5174 | −2.45592 | ||||||||
\(849\) | 4.26904 | 0.146513 | ||||||||
\(850\) | −2.58966 | −0.0888245 | ||||||||
\(851\) | 0.596780 | 0.0204574 | ||||||||
\(852\) | −15.3507 | −0.525908 | ||||||||
\(853\) | −40.2114 | −1.37681 | −0.688407 | − | 0.725325i | \(-0.741690\pi\) | ||||
−0.688407 | + | 0.725325i | \(0.741690\pi\) | |||||||
\(854\) | 8.44524 | 0.288990 | ||||||||
\(855\) | 5.16068 | 0.176492 | ||||||||
\(856\) | −11.3751 | −0.388791 | ||||||||
\(857\) | 15.4113 | 0.526439 | 0.263219 | − | 0.964736i | \(-0.415216\pi\) | ||||
0.263219 | + | 0.964736i | \(0.415216\pi\) | |||||||
\(858\) | −16.7445 | −0.571647 | ||||||||
\(859\) | 18.7549 | 0.639908 | 0.319954 | − | 0.947433i | \(-0.396333\pi\) | ||||
0.319954 | + | 0.947433i | \(0.396333\pi\) | |||||||
\(860\) | −4.02806 | −0.137356 | ||||||||
\(861\) | 6.81411 | 0.232224 | ||||||||
\(862\) | 22.5701 | 0.768739 | ||||||||
\(863\) | 14.2988 | 0.486738 | 0.243369 | − | 0.969934i | \(-0.421747\pi\) | ||||
0.243369 | + | 0.969934i | \(0.421747\pi\) | |||||||
\(864\) | −24.0922 | −0.819632 | ||||||||
\(865\) | −10.7276 | −0.364748 | ||||||||
\(866\) | 23.0805 | 0.784308 | ||||||||
\(867\) | 25.1045 | 0.852592 | ||||||||
\(868\) | −2.85691 | −0.0969699 | ||||||||
\(869\) | −2.49267 | −0.0845580 | ||||||||
\(870\) | 18.1930 | 0.616801 | ||||||||
\(871\) | 33.4142 | 1.13220 | ||||||||
\(872\) | 8.66141 | 0.293312 | ||||||||
\(873\) | 0.532268 | 0.0180146 | ||||||||
\(874\) | −83.9206 | −2.83866 | ||||||||
\(875\) | −4.31212 | −0.145776 | ||||||||
\(876\) | 17.0002 | 0.574384 | ||||||||
\(877\) | −20.5122 | −0.692646 | −0.346323 | − | 0.938115i | \(-0.612570\pi\) | ||||
−0.346323 | + | 0.938115i | \(0.612570\pi\) | |||||||
\(878\) | −1.46829 | −0.0495525 | ||||||||
\(879\) | −3.91027 | −0.131890 | ||||||||
\(880\) | 5.58767 | 0.188360 | ||||||||
\(881\) | 37.4254 | 1.26089 | 0.630446 | − | 0.776233i | \(-0.282872\pi\) | ||||
0.630446 | + | 0.776233i | \(0.282872\pi\) | |||||||
\(882\) | 8.82016 | 0.296990 | ||||||||
\(883\) | 5.24347 | 0.176457 | 0.0882284 | − | 0.996100i | \(-0.471879\pi\) | ||||
0.0882284 | + | 0.996100i | \(0.471879\pi\) | |||||||
\(884\) | 2.22394 | 0.0747993 | ||||||||
\(885\) | 6.33943 | 0.213098 | ||||||||
\(886\) | −14.4054 | −0.483958 | ||||||||
\(887\) | −28.8778 | −0.969623 | −0.484812 | − | 0.874619i | \(-0.661112\pi\) | ||||
−0.484812 | + | 0.874619i | \(0.661112\pi\) | |||||||
\(888\) | −0.210948 | −0.00707896 | ||||||||
\(889\) | 7.65414 | 0.256712 | ||||||||
\(890\) | 1.87674 | 0.0629086 | ||||||||
\(891\) | −6.07705 | −0.203589 | ||||||||
\(892\) | 3.38023 | 0.113178 | ||||||||
\(893\) | 28.4221 | 0.951110 | ||||||||
\(894\) | −26.4568 | −0.884847 | ||||||||
\(895\) | −13.2785 | −0.443850 | ||||||||
\(896\) | −5.77635 | −0.192974 | ||||||||
\(897\) | 84.8786 | 2.83401 | ||||||||
\(898\) | 15.1807 | 0.506585 | ||||||||
\(899\) | 52.7747 | 1.76013 | ||||||||
\(900\) | 2.30820 | 0.0769399 | ||||||||
\(901\) | 5.98308 | 0.199325 | ||||||||
\(902\) | 17.4312 | 0.580395 | ||||||||
\(903\) | 2.92668 | 0.0973937 | ||||||||
\(904\) | 20.5053 | 0.681997 | ||||||||
\(905\) | −20.6107 | −0.685123 | ||||||||
\(906\) | 12.9162 | 0.429112 | ||||||||
\(907\) | −40.2902 | −1.33781 | −0.668907 | − | 0.743346i | \(-0.733238\pi\) | ||||
−0.668907 | + | 0.743346i | \(0.733238\pi\) | |||||||
\(908\) | 19.8343 | 0.658224 | ||||||||
\(909\) | 6.62416 | 0.219709 | ||||||||
\(910\) | 5.54360 | 0.183769 | ||||||||
\(911\) | 34.6795 | 1.14898 | 0.574492 | − | 0.818510i | \(-0.305200\pi\) | ||||
0.574492 | + | 0.818510i | \(0.305200\pi\) | |||||||
\(912\) | 43.7639 | 1.44917 | ||||||||
\(913\) | 9.29253 | 0.307538 | ||||||||
\(914\) | −4.23722 | −0.140155 | ||||||||
\(915\) | −19.3539 | −0.639819 | ||||||||
\(916\) | −18.6567 | −0.616435 | ||||||||
\(917\) | 0.438386 | 0.0144768 | ||||||||
\(918\) | 3.90864 | 0.129005 | ||||||||
\(919\) | 34.1412 | 1.12621 | 0.563106 | − | 0.826384i | \(-0.309606\pi\) | ||||
0.563106 | + | 0.826384i | \(0.309606\pi\) | |||||||
\(920\) | −19.1987 | −0.632961 | ||||||||
\(921\) | 6.31522 | 0.208094 | ||||||||
\(922\) | −49.6914 | −1.63650 | ||||||||
\(923\) | 86.4064 | 2.84410 | ||||||||
\(924\) | 0.522508 | 0.0171892 | ||||||||
\(925\) | 0.262530 | 0.00863193 | ||||||||
\(926\) | 5.20759 | 0.171132 | ||||||||
\(927\) | 9.80540 | 0.322052 | ||||||||
\(928\) | −27.6824 | −0.908719 | ||||||||
\(929\) | 20.8883 | 0.685323 | 0.342662 | − | 0.939459i | \(-0.388672\pi\) | ||||
0.342662 | + | 0.939459i | \(0.388672\pi\) | |||||||
\(930\) | 22.9368 | 0.752126 | ||||||||
\(931\) | −40.2677 | −1.31972 | ||||||||
\(932\) | 16.3129 | 0.534347 | ||||||||
\(933\) | 29.9252 | 0.979708 | ||||||||
\(934\) | 41.1316 | 1.34587 | ||||||||
\(935\) | −0.467460 | −0.0152876 | ||||||||
\(936\) | 10.4396 | 0.341231 | ||||||||
\(937\) | 53.8849 | 1.76034 | 0.880171 | − | 0.474656i | \(-0.157427\pi\) | ||||
0.880171 | + | 0.474656i | \(0.157427\pi\) | |||||||
\(938\) | −3.65285 | −0.119270 | ||||||||
\(939\) | 36.5992 | 1.19437 | ||||||||
\(940\) | −4.32521 | −0.141073 | ||||||||
\(941\) | −23.1601 | −0.754998 | −0.377499 | − | 0.926010i | \(-0.623216\pi\) | ||||
−0.377499 | + | 0.926010i | \(0.623216\pi\) | |||||||
\(942\) | −18.4741 | −0.601917 | ||||||||
\(943\) | −88.3595 | −2.87738 | ||||||||
\(944\) | −18.7062 | −0.608836 | ||||||||
\(945\) | 2.78109 | 0.0904688 | ||||||||
\(946\) | 7.48674 | 0.243415 | ||||||||
\(947\) | −20.2719 | −0.658747 | −0.329374 | − | 0.944200i | \(-0.606838\pi\) | ||||
−0.329374 | + | 0.944200i | \(0.606838\pi\) | |||||||
\(948\) | 2.97099 | 0.0964931 | ||||||||
\(949\) | −95.6909 | −3.10626 | ||||||||
\(950\) | −36.9176 | −1.19776 | ||||||||
\(951\) | −22.2524 | −0.721582 | ||||||||
\(952\) | 0.365491 | 0.0118456 | ||||||||
\(953\) | −39.5410 | −1.28086 | −0.640430 | − | 0.768017i | \(-0.721244\pi\) | ||||
−0.640430 | + | 0.768017i | \(0.721244\pi\) | |||||||
\(954\) | −18.6825 | −0.604869 | ||||||||
\(955\) | −3.62697 | −0.117366 | ||||||||
\(956\) | 8.71714 | 0.281932 | ||||||||
\(957\) | −9.65210 | −0.312008 | ||||||||
\(958\) | 35.4365 | 1.14490 | ||||||||
\(959\) | −6.30042 | −0.203451 | ||||||||
\(960\) | 4.64060 | 0.149775 | ||||||||
\(961\) | 35.5354 | 1.14630 | ||||||||
\(962\) | −0.789843 | −0.0254656 | ||||||||
\(963\) | −4.38393 | −0.141270 | ||||||||
\(964\) | 1.75449 | 0.0565084 | ||||||||
\(965\) | 18.6078 | 0.599007 | ||||||||
\(966\) | −9.27895 | −0.298545 | ||||||||
\(967\) | −61.1084 | −1.96511 | −0.982557 | − | 0.185964i | \(-0.940459\pi\) | ||||
−0.982557 | + | 0.185964i | \(0.940459\pi\) | |||||||
\(968\) | −2.00938 | −0.0645839 | ||||||||
\(969\) | −3.66125 | −0.117616 | ||||||||
\(970\) | 1.29551 | 0.0415964 | ||||||||
\(971\) | −29.6739 | −0.952280 | −0.476140 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476140 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(972\) | −6.25287 | −0.200561 | ||||||||
\(973\) | −3.93963 | −0.126299 | ||||||||
\(974\) | 24.3800 | 0.781186 | ||||||||
\(975\) | 37.3390 | 1.19580 | ||||||||
\(976\) | 57.1088 | 1.82801 | ||||||||
\(977\) | −55.2813 | −1.76861 | −0.884303 | − | 0.466913i | \(-0.845366\pi\) | ||||
−0.884303 | + | 0.466913i | \(0.845366\pi\) | |||||||
\(978\) | 56.2516 | 1.79873 | ||||||||
\(979\) | −0.995685 | −0.0318222 | ||||||||
\(980\) | 6.12785 | 0.195747 | ||||||||
\(981\) | 3.33809 | 0.106577 | ||||||||
\(982\) | 44.7256 | 1.42725 | ||||||||
\(983\) | 55.5192 | 1.77079 | 0.885394 | − | 0.464842i | \(-0.153889\pi\) | ||||
0.885394 | + | 0.464842i | \(0.153889\pi\) | |||||||
\(984\) | 31.2331 | 0.995674 | ||||||||
\(985\) | 22.3337 | 0.711611 | ||||||||
\(986\) | 4.49111 | 0.143026 | ||||||||
\(987\) | 3.14258 | 0.100029 | ||||||||
\(988\) | 31.7041 | 1.00864 | ||||||||
\(989\) | −37.9506 | −1.20676 | ||||||||
\(990\) | 1.45967 | 0.0463914 | ||||||||
\(991\) | 38.2171 | 1.21401 | 0.607003 | − | 0.794700i | \(-0.292372\pi\) | ||||
0.607003 | + | 0.794700i | \(0.292372\pi\) | |||||||
\(992\) | −34.9004 | −1.10809 | ||||||||
\(993\) | −34.2049 | −1.08546 | ||||||||
\(994\) | −9.44597 | −0.299608 | ||||||||
\(995\) | −10.5545 | −0.334600 | ||||||||
\(996\) | −11.0757 | −0.350946 | ||||||||
\(997\) | 17.5447 | 0.555646 | 0.277823 | − | 0.960632i | \(-0.410387\pi\) | ||||
0.277823 | + | 0.960632i | \(0.410387\pi\) | |||||||
\(998\) | 16.3439 | 0.517359 | ||||||||
\(999\) | −0.396244 | −0.0125366 |
(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 | 1441.2.a.e.1.20 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.e.1.20 | ✓ | 28 | 1.1 | even | 1 | trivial |