Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(113\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14256 | −1.51502 | −0.757508 | − | 0.652826i | \(-0.773583\pi\) | ||||
−0.757508 | + | 0.652826i | \(0.773583\pi\) | |||||||
\(3\) | −2.11238 | −1.21958 | −0.609792 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609792 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(4\) | 2.59055 | 1.29527 | ||||||||
\(5\) | 1.25903 | 0.563054 | 0.281527 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281527 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(6\) | 4.52589 | 1.84769 | ||||||||
\(7\) | 1.44603 | 0.546548 | 0.273274 | − | 0.961936i | \(-0.411893\pi\) | ||||
0.273274 | + | 0.961936i | \(0.411893\pi\) | |||||||
\(8\) | −1.26528 | −0.447345 | ||||||||
\(9\) | 1.46215 | 0.487383 | ||||||||
\(10\) | −2.69753 | −0.853035 | ||||||||
\(11\) | 4.85189 | 1.46290 | 0.731450 | − | 0.681895i | \(-0.238844\pi\) | ||||
0.731450 | + | 0.681895i | \(0.238844\pi\) | |||||||
\(12\) | −5.47222 | −1.57969 | ||||||||
\(13\) | −5.39622 | −1.49664 | −0.748320 | − | 0.663337i | \(-0.769139\pi\) | ||||
−0.748320 | + | 0.663337i | \(0.769139\pi\) | |||||||
\(14\) | −3.09820 | −0.828029 | ||||||||
\(15\) | −2.65954 | −0.686691 | ||||||||
\(16\) | −2.47016 | −0.617540 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −3.13274 | −0.738393 | ||||||||
\(19\) | −0.860517 | −0.197416 | −0.0987081 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987081 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(20\) | 3.26157 | 0.729309 | ||||||||
\(21\) | −3.05457 | −0.666561 | ||||||||
\(22\) | −10.3955 | −2.21632 | ||||||||
\(23\) | 2.81301 | 0.586552 | 0.293276 | − | 0.956028i | \(-0.405254\pi\) | ||||
0.293276 | + | 0.956028i | \(0.405254\pi\) | |||||||
\(24\) | 2.67275 | 0.545574 | ||||||||
\(25\) | −3.41485 | −0.682971 | ||||||||
\(26\) | 11.5617 | 2.26744 | ||||||||
\(27\) | 3.24853 | 0.625179 | ||||||||
\(28\) | 3.74601 | 0.707929 | ||||||||
\(29\) | 4.40407 | 0.817815 | 0.408907 | − | 0.912576i | \(-0.365910\pi\) | ||||
0.408907 | + | 0.912576i | \(0.365910\pi\) | |||||||
\(30\) | 5.69822 | 1.04035 | ||||||||
\(31\) | 4.93268 | 0.885935 | 0.442968 | − | 0.896538i | \(-0.353926\pi\) | ||||
0.442968 | + | 0.896538i | \(0.353926\pi\) | |||||||
\(32\) | 7.82302 | 1.38293 | ||||||||
\(33\) | −10.2490 | −1.78413 | ||||||||
\(34\) | 2.14256 | 0.367445 | ||||||||
\(35\) | 1.82059 | 0.307736 | ||||||||
\(36\) | 3.78777 | 0.631294 | ||||||||
\(37\) | 4.46799 | 0.734533 | 0.367266 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367266 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(38\) | 1.84371 | 0.299089 | ||||||||
\(39\) | 11.3989 | 1.82528 | ||||||||
\(40\) | −1.59302 | −0.251879 | ||||||||
\(41\) | −1.43011 | −0.223346 | −0.111673 | − | 0.993745i | \(-0.535621\pi\) | ||||
−0.111673 | + | 0.993745i | \(0.535621\pi\) | |||||||
\(42\) | 6.54458 | 1.00985 | ||||||||
\(43\) | −12.0014 | −1.83020 | −0.915098 | − | 0.403231i | \(-0.867887\pi\) | ||||
−0.915098 | + | 0.403231i | \(0.867887\pi\) | |||||||
\(44\) | 12.5691 | 1.89486 | ||||||||
\(45\) | 1.84088 | 0.274423 | ||||||||
\(46\) | −6.02702 | −0.888636 | ||||||||
\(47\) | 9.34116 | 1.36255 | 0.681274 | − | 0.732029i | \(-0.261426\pi\) | ||||
0.681274 | + | 0.732029i | \(0.261426\pi\) | |||||||
\(48\) | 5.21791 | 0.753141 | ||||||||
\(49\) | −4.90900 | −0.701285 | ||||||||
\(50\) | 7.31651 | 1.03471 | ||||||||
\(51\) | 2.11238 | 0.295792 | ||||||||
\(52\) | −13.9792 | −1.93856 | ||||||||
\(53\) | 4.19720 | 0.576530 | 0.288265 | − | 0.957551i | \(-0.406922\pi\) | ||||
0.288265 | + | 0.957551i | \(0.406922\pi\) | |||||||
\(54\) | −6.96015 | −0.947156 | ||||||||
\(55\) | 6.10866 | 0.823691 | ||||||||
\(56\) | −1.82964 | −0.244495 | ||||||||
\(57\) | 1.81774 | 0.240765 | ||||||||
\(58\) | −9.43596 | −1.23900 | ||||||||
\(59\) | −11.5846 | −1.50819 | −0.754094 | − | 0.656766i | \(-0.771924\pi\) | ||||
−0.754094 | + | 0.656766i | \(0.771924\pi\) | |||||||
\(60\) | −6.88967 | −0.889452 | ||||||||
\(61\) | −11.6645 | −1.49349 | −0.746746 | − | 0.665110i | \(-0.768385\pi\) | ||||
−0.746746 | + | 0.665110i | \(0.768385\pi\) | |||||||
\(62\) | −10.5685 | −1.34221 | ||||||||
\(63\) | 2.11431 | 0.266378 | ||||||||
\(64\) | −11.8209 | −1.47762 | ||||||||
\(65\) | −6.79398 | −0.842689 | ||||||||
\(66\) | 21.9591 | 2.70298 | ||||||||
\(67\) | 10.9973 | 1.34353 | 0.671767 | − | 0.740763i | \(-0.265536\pi\) | ||||
0.671767 | + | 0.740763i | \(0.265536\pi\) | |||||||
\(68\) | −2.59055 | −0.314150 | ||||||||
\(69\) | −5.94214 | −0.715349 | ||||||||
\(70\) | −3.90072 | −0.466225 | ||||||||
\(71\) | −10.7868 | −1.28016 | −0.640081 | − | 0.768307i | \(-0.721099\pi\) | ||||
−0.640081 | + | 0.768307i | \(0.721099\pi\) | |||||||
\(72\) | −1.85003 | −0.218028 | ||||||||
\(73\) | −5.27905 | −0.617866 | −0.308933 | − | 0.951084i | \(-0.599972\pi\) | ||||
−0.308933 | + | 0.951084i | \(0.599972\pi\) | |||||||
\(74\) | −9.57291 | −1.11283 | ||||||||
\(75\) | 7.21347 | 0.832939 | ||||||||
\(76\) | −2.22921 | −0.255708 | ||||||||
\(77\) | 7.01598 | 0.799546 | ||||||||
\(78\) | −24.4227 | −2.76533 | ||||||||
\(79\) | −11.9667 | −1.34636 | −0.673181 | − | 0.739478i | \(-0.735073\pi\) | ||||
−0.673181 | + | 0.739478i | \(0.735073\pi\) | |||||||
\(80\) | −3.10999 | −0.347708 | ||||||||
\(81\) | −11.2486 | −1.24984 | ||||||||
\(82\) | 3.06409 | 0.338372 | ||||||||
\(83\) | −0.0276943 | −0.00303985 | −0.00151992 | − | 0.999999i | \(-0.500484\pi\) | ||||
−0.00151992 | + | 0.999999i | \(0.500484\pi\) | |||||||
\(84\) | −7.91300 | −0.863379 | ||||||||
\(85\) | −1.25903 | −0.136561 | ||||||||
\(86\) | 25.7137 | 2.77278 | ||||||||
\(87\) | −9.30306 | −0.997393 | ||||||||
\(88\) | −6.13901 | −0.654421 | ||||||||
\(89\) | −15.4679 | −1.63959 | −0.819796 | − | 0.572656i | \(-0.805913\pi\) | ||||
−0.819796 | + | 0.572656i | \(0.805913\pi\) | |||||||
\(90\) | −3.94420 | −0.415755 | ||||||||
\(91\) | −7.80309 | −0.817986 | ||||||||
\(92\) | 7.28722 | 0.759746 | ||||||||
\(93\) | −10.4197 | −1.08047 | ||||||||
\(94\) | −20.0140 | −2.06428 | ||||||||
\(95\) | −1.08341 | −0.111156 | ||||||||
\(96\) | −16.5252 | −1.68659 | ||||||||
\(97\) | 1.90368 | 0.193289 | 0.0966447 | − | 0.995319i | \(-0.469189\pi\) | ||||
0.0966447 | + | 0.995319i | \(0.469189\pi\) | |||||||
\(98\) | 10.5178 | 1.06246 | ||||||||
\(99\) | 7.09419 | 0.712993 | ||||||||
\(100\) | −8.84634 | −0.884634 | ||||||||
\(101\) | 14.8528 | 1.47791 | 0.738957 | − | 0.673753i | \(-0.235319\pi\) | ||||
0.738957 | + | 0.673753i | \(0.235319\pi\) | |||||||
\(102\) | −4.52589 | −0.448130 | ||||||||
\(103\) | 8.13194 | 0.801264 | 0.400632 | − | 0.916239i | \(-0.368791\pi\) | ||||
0.400632 | + | 0.916239i | \(0.368791\pi\) | |||||||
\(104\) | 6.82773 | 0.669514 | ||||||||
\(105\) | −3.84578 | −0.375310 | ||||||||
\(106\) | −8.99274 | −0.873452 | ||||||||
\(107\) | 11.7474 | 1.13566 | 0.567831 | − | 0.823145i | \(-0.307783\pi\) | ||||
0.567831 | + | 0.823145i | \(0.307783\pi\) | |||||||
\(108\) | 8.41546 | 0.809778 | ||||||||
\(109\) | −7.55948 | −0.724067 | −0.362033 | − | 0.932165i | \(-0.617917\pi\) | ||||
−0.362033 | + | 0.932165i | \(0.617917\pi\) | |||||||
\(110\) | −13.0881 | −1.24791 | ||||||||
\(111\) | −9.43809 | −0.895823 | ||||||||
\(112\) | −3.57192 | −0.337515 | ||||||||
\(113\) | −8.61277 | −0.810221 | −0.405110 | − | 0.914268i | \(-0.632767\pi\) | ||||
−0.405110 | + | 0.914268i | \(0.632767\pi\) | |||||||
\(114\) | −3.89461 | −0.364763 | ||||||||
\(115\) | 3.54165 | 0.330260 | ||||||||
\(116\) | 11.4089 | 1.05929 | ||||||||
\(117\) | −7.89007 | −0.729437 | ||||||||
\(118\) | 24.8207 | 2.28493 | ||||||||
\(119\) | −1.44603 | −0.132557 | ||||||||
\(120\) | 3.36507 | 0.307187 | ||||||||
\(121\) | 12.5409 | 1.14008 | ||||||||
\(122\) | 24.9919 | 2.26266 | ||||||||
\(123\) | 3.02094 | 0.272389 | ||||||||
\(124\) | 12.7783 | 1.14753 | ||||||||
\(125\) | −10.5945 | −0.947603 | ||||||||
\(126\) | −4.53003 | −0.403567 | ||||||||
\(127\) | 20.3232 | 1.80339 | 0.901697 | − | 0.432369i | \(-0.142322\pi\) | ||||
0.901697 | + | 0.432369i | \(0.142322\pi\) | |||||||
\(128\) | 9.68099 | 0.855687 | ||||||||
\(129\) | 25.3515 | 2.23208 | ||||||||
\(130\) | 14.5565 | 1.27669 | ||||||||
\(131\) | 6.50414 | 0.568269 | 0.284135 | − | 0.958784i | \(-0.408294\pi\) | ||||
0.284135 | + | 0.958784i | \(0.408294\pi\) | |||||||
\(132\) | −26.5506 | −2.31094 | ||||||||
\(133\) | −1.24433 | −0.107897 | ||||||||
\(134\) | −23.5623 | −2.03547 | ||||||||
\(135\) | 4.08998 | 0.352009 | ||||||||
\(136\) | 1.26528 | 0.108497 | ||||||||
\(137\) | −2.78341 | −0.237803 | −0.118902 | − | 0.992906i | \(-0.537937\pi\) | ||||
−0.118902 | + | 0.992906i | \(0.537937\pi\) | |||||||
\(138\) | 12.7314 | 1.08377 | ||||||||
\(139\) | −11.4915 | −0.974697 | −0.487349 | − | 0.873208i | \(-0.662036\pi\) | ||||
−0.487349 | + | 0.873208i | \(0.662036\pi\) | |||||||
\(140\) | 4.71633 | 0.398602 | ||||||||
\(141\) | −19.7321 | −1.66174 | ||||||||
\(142\) | 23.1114 | 1.93947 | ||||||||
\(143\) | −26.1819 | −2.18944 | ||||||||
\(144\) | −3.61174 | −0.300978 | ||||||||
\(145\) | 5.54484 | 0.460474 | ||||||||
\(146\) | 11.3107 | 0.936076 | ||||||||
\(147\) | 10.3697 | 0.855275 | ||||||||
\(148\) | 11.5745 | 0.951421 | ||||||||
\(149\) | −18.3441 | −1.50281 | −0.751405 | − | 0.659841i | \(-0.770624\pi\) | ||||
−0.751405 | + | 0.659841i | \(0.770624\pi\) | |||||||
\(150\) | −15.4553 | −1.26192 | ||||||||
\(151\) | 2.12540 | 0.172963 | 0.0864814 | − | 0.996253i | \(-0.472438\pi\) | ||||
0.0864814 | + | 0.996253i | \(0.472438\pi\) | |||||||
\(152\) | 1.08880 | 0.0883130 | ||||||||
\(153\) | −1.46215 | −0.118208 | ||||||||
\(154\) | −15.0321 | −1.21132 | ||||||||
\(155\) | 6.21037 | 0.498829 | ||||||||
\(156\) | 29.5293 | 2.36423 | ||||||||
\(157\) | 4.01364 | 0.320323 | 0.160162 | − | 0.987091i | \(-0.448798\pi\) | ||||
0.160162 | + | 0.987091i | \(0.448798\pi\) | |||||||
\(158\) | 25.6394 | 2.03976 | ||||||||
\(159\) | −8.86608 | −0.703126 | ||||||||
\(160\) | 9.84938 | 0.778662 | ||||||||
\(161\) | 4.06769 | 0.320579 | ||||||||
\(162\) | 24.1007 | 1.89353 | ||||||||
\(163\) | 12.1998 | 0.955561 | 0.477781 | − | 0.878479i | \(-0.341441\pi\) | ||||
0.477781 | + | 0.878479i | \(0.341441\pi\) | |||||||
\(164\) | −3.70477 | −0.289294 | ||||||||
\(165\) | −12.9038 | −1.00456 | ||||||||
\(166\) | 0.0593367 | 0.00460542 | ||||||||
\(167\) | −15.5593 | −1.20401 | −0.602006 | − | 0.798492i | \(-0.705632\pi\) | ||||
−0.602006 | + | 0.798492i | \(0.705632\pi\) | |||||||
\(168\) | 3.86489 | 0.298182 | ||||||||
\(169\) | 16.1191 | 1.23993 | ||||||||
\(170\) | 2.69753 | 0.206891 | ||||||||
\(171\) | −1.25820 | −0.0962173 | ||||||||
\(172\) | −31.0902 | −2.37060 | ||||||||
\(173\) | 4.00343 | 0.304375 | 0.152187 | − | 0.988352i | \(-0.451368\pi\) | ||||
0.152187 | + | 0.988352i | \(0.451368\pi\) | |||||||
\(174\) | 19.9323 | 1.51107 | ||||||||
\(175\) | −4.93798 | −0.373276 | ||||||||
\(176\) | −11.9849 | −0.903399 | ||||||||
\(177\) | 24.4711 | 1.83936 | ||||||||
\(178\) | 33.1408 | 2.48401 | ||||||||
\(179\) | −20.7365 | −1.54992 | −0.774960 | − | 0.632010i | \(-0.782230\pi\) | ||||
−0.774960 | + | 0.632010i | \(0.782230\pi\) | |||||||
\(180\) | 4.76890 | 0.355453 | ||||||||
\(181\) | −12.6564 | −0.940739 | −0.470370 | − | 0.882469i | \(-0.655879\pi\) | ||||
−0.470370 | + | 0.882469i | \(0.655879\pi\) | |||||||
\(182\) | 16.7186 | 1.23926 | ||||||||
\(183\) | 24.6399 | 1.82144 | ||||||||
\(184\) | −3.55924 | −0.262391 | ||||||||
\(185\) | 5.62531 | 0.413581 | ||||||||
\(186\) | 22.3248 | 1.63693 | ||||||||
\(187\) | −4.85189 | −0.354805 | ||||||||
\(188\) | 24.1987 | 1.76487 | ||||||||
\(189\) | 4.69747 | 0.341690 | ||||||||
\(190\) | 2.32127 | 0.168403 | ||||||||
\(191\) | 22.8301 | 1.65193 | 0.825963 | − | 0.563725i | \(-0.190632\pi\) | ||||
0.825963 | + | 0.563725i | \(0.190632\pi\) | |||||||
\(192\) | 24.9703 | 1.80208 | ||||||||
\(193\) | 17.6885 | 1.27324 | 0.636622 | − | 0.771176i | \(-0.280331\pi\) | ||||
0.636622 | + | 0.771176i | \(0.280331\pi\) | |||||||
\(194\) | −4.07874 | −0.292837 | ||||||||
\(195\) | 14.3515 | 1.02773 | ||||||||
\(196\) | −12.7170 | −0.908356 | ||||||||
\(197\) | 8.87651 | 0.632425 | 0.316213 | − | 0.948688i | \(-0.397589\pi\) | ||||
0.316213 | + | 0.948688i | \(0.397589\pi\) | |||||||
\(198\) | −15.1997 | −1.08020 | ||||||||
\(199\) | 21.3147 | 1.51096 | 0.755478 | − | 0.655174i | \(-0.227405\pi\) | ||||
0.755478 | + | 0.655174i | \(0.227405\pi\) | |||||||
\(200\) | 4.32075 | 0.305523 | ||||||||
\(201\) | −23.2305 | −1.63855 | ||||||||
\(202\) | −31.8231 | −2.23906 | ||||||||
\(203\) | 6.36842 | 0.446975 | ||||||||
\(204\) | 5.47222 | 0.383132 | ||||||||
\(205\) | −1.80055 | −0.125756 | ||||||||
\(206\) | −17.4231 | −1.21393 | ||||||||
\(207\) | 4.11303 | 0.285876 | ||||||||
\(208\) | 13.3295 | 0.924235 | ||||||||
\(209\) | −4.17514 | −0.288800 | ||||||||
\(210\) | 8.23980 | 0.568600 | ||||||||
\(211\) | −10.0900 | −0.694623 | −0.347312 | − | 0.937750i | \(-0.612905\pi\) | ||||
−0.347312 | + | 0.937750i | \(0.612905\pi\) | |||||||
\(212\) | 10.8730 | 0.746764 | ||||||||
\(213\) | 22.7859 | 1.56126 | ||||||||
\(214\) | −25.1694 | −1.72055 | ||||||||
\(215\) | −15.1101 | −1.03050 | ||||||||
\(216\) | −4.11030 | −0.279670 | ||||||||
\(217\) | 7.13280 | 0.484206 | ||||||||
\(218\) | 16.1966 | 1.09697 | ||||||||
\(219\) | 11.1514 | 0.753538 | ||||||||
\(220\) | 15.8248 | 1.06691 | ||||||||
\(221\) | 5.39622 | 0.362989 | ||||||||
\(222\) | 20.2216 | 1.35719 | ||||||||
\(223\) | −10.7813 | −0.721968 | −0.360984 | − | 0.932572i | \(-0.617559\pi\) | ||||
−0.360984 | + | 0.932572i | \(0.617559\pi\) | |||||||
\(224\) | 11.3123 | 0.755836 | ||||||||
\(225\) | −4.99302 | −0.332868 | ||||||||
\(226\) | 18.4533 | 1.22750 | ||||||||
\(227\) | 5.18809 | 0.344346 | 0.172173 | − | 0.985067i | \(-0.444921\pi\) | ||||
0.172173 | + | 0.985067i | \(0.444921\pi\) | |||||||
\(228\) | 4.70894 | 0.311857 | ||||||||
\(229\) | −19.6840 | −1.30076 | −0.650378 | − | 0.759611i | \(-0.725389\pi\) | ||||
−0.650378 | + | 0.759611i | \(0.725389\pi\) | |||||||
\(230\) | −7.58818 | −0.500350 | ||||||||
\(231\) | −14.8204 | −0.975112 | ||||||||
\(232\) | −5.57239 | −0.365845 | ||||||||
\(233\) | 2.73430 | 0.179130 | 0.0895650 | − | 0.995981i | \(-0.471452\pi\) | ||||
0.0895650 | + | 0.995981i | \(0.471452\pi\) | |||||||
\(234\) | 16.9049 | 1.10511 | ||||||||
\(235\) | 11.7608 | 0.767187 | ||||||||
\(236\) | −30.0105 | −1.95352 | ||||||||
\(237\) | 25.2783 | 1.64200 | ||||||||
\(238\) | 3.09820 | 0.200827 | ||||||||
\(239\) | 6.00842 | 0.388653 | 0.194326 | − | 0.980937i | \(-0.437748\pi\) | ||||
0.194326 | + | 0.980937i | \(0.437748\pi\) | |||||||
\(240\) | 6.56949 | 0.424059 | ||||||||
\(241\) | −4.29472 | −0.276647 | −0.138324 | − | 0.990387i | \(-0.544171\pi\) | ||||
−0.138324 | + | 0.990387i | \(0.544171\pi\) | |||||||
\(242\) | −26.8695 | −1.72724 | ||||||||
\(243\) | 14.0157 | 0.899106 | ||||||||
\(244\) | −30.2175 | −1.93448 | ||||||||
\(245\) | −6.18055 | −0.394861 | ||||||||
\(246\) | −6.47253 | −0.412673 | ||||||||
\(247\) | 4.64353 | 0.295461 | ||||||||
\(248\) | −6.24122 | −0.396318 | ||||||||
\(249\) | 0.0585010 | 0.00370735 | ||||||||
\(250\) | 22.6994 | 1.43563 | ||||||||
\(251\) | −1.17799 | −0.0743539 | −0.0371770 | − | 0.999309i | \(-0.511837\pi\) | ||||
−0.0371770 | + | 0.999309i | \(0.511837\pi\) | |||||||
\(252\) | 5.47722 | 0.345033 | ||||||||
\(253\) | 13.6484 | 0.858067 | ||||||||
\(254\) | −43.5436 | −2.73217 | ||||||||
\(255\) | 2.65954 | 0.166547 | ||||||||
\(256\) | 2.89981 | 0.181238 | ||||||||
\(257\) | −20.6085 | −1.28553 | −0.642763 | − | 0.766065i | \(-0.722212\pi\) | ||||
−0.642763 | + | 0.766065i | \(0.722212\pi\) | |||||||
\(258\) | −54.3170 | −3.38163 | ||||||||
\(259\) | 6.46084 | 0.401457 | ||||||||
\(260\) | −17.6001 | −1.09151 | ||||||||
\(261\) | 6.43940 | 0.398589 | ||||||||
\(262\) | −13.9355 | −0.860937 | ||||||||
\(263\) | −21.3263 | −1.31504 | −0.657518 | − | 0.753439i | \(-0.728394\pi\) | ||||
−0.657518 | + | 0.753439i | \(0.728394\pi\) | |||||||
\(264\) | 12.9679 | 0.798120 | ||||||||
\(265\) | 5.28438 | 0.324617 | ||||||||
\(266\) | 2.66606 | 0.163466 | ||||||||
\(267\) | 32.6740 | 1.99962 | ||||||||
\(268\) | 28.4890 | 1.74024 | ||||||||
\(269\) | −22.5415 | −1.37438 | −0.687189 | − | 0.726478i | \(-0.741156\pi\) | ||||
−0.687189 | + | 0.726478i | \(0.741156\pi\) | |||||||
\(270\) | −8.76301 | −0.533300 | ||||||||
\(271\) | 13.2512 | 0.804953 | 0.402477 | − | 0.915430i | \(-0.368149\pi\) | ||||
0.402477 | + | 0.915430i | \(0.368149\pi\) | |||||||
\(272\) | 2.47016 | 0.149775 | ||||||||
\(273\) | 16.4831 | 0.997602 | ||||||||
\(274\) | 5.96362 | 0.360276 | ||||||||
\(275\) | −16.5685 | −0.999118 | ||||||||
\(276\) | −15.3934 | −0.926573 | ||||||||
\(277\) | 6.16242 | 0.370264 | 0.185132 | − | 0.982714i | \(-0.440729\pi\) | ||||
0.185132 | + | 0.982714i | \(0.440729\pi\) | |||||||
\(278\) | 24.6212 | 1.47668 | ||||||||
\(279\) | 7.21231 | 0.431790 | ||||||||
\(280\) | −2.30356 | −0.137664 | ||||||||
\(281\) | 10.1465 | 0.605288 | 0.302644 | − | 0.953104i | \(-0.402131\pi\) | ||||
0.302644 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(282\) | 42.2771 | 2.51756 | ||||||||
\(283\) | −16.1457 | −0.959762 | −0.479881 | − | 0.877333i | \(-0.659320\pi\) | ||||
−0.479881 | + | 0.877333i | \(0.659320\pi\) | |||||||
\(284\) | −27.9438 | −1.65816 | ||||||||
\(285\) | 2.28858 | 0.135564 | ||||||||
\(286\) | 56.0961 | 3.31703 | ||||||||
\(287\) | −2.06798 | −0.122069 | ||||||||
\(288\) | 11.4384 | 0.674015 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −11.8801 | −0.697625 | ||||||||
\(291\) | −4.02130 | −0.235733 | ||||||||
\(292\) | −13.6756 | −0.800305 | ||||||||
\(293\) | 29.1061 | 1.70040 | 0.850198 | − | 0.526462i | \(-0.176482\pi\) | ||||
0.850198 | + | 0.526462i | \(0.176482\pi\) | |||||||
\(294\) | −22.2176 | −1.29576 | ||||||||
\(295\) | −14.5853 | −0.849191 | ||||||||
\(296\) | −5.65326 | −0.328589 | ||||||||
\(297\) | 15.7615 | 0.914575 | ||||||||
\(298\) | 39.3034 | 2.27678 | ||||||||
\(299\) | −15.1796 | −0.877858 | ||||||||
\(300\) | 18.6868 | 1.07888 | ||||||||
\(301\) | −17.3544 | −1.00029 | ||||||||
\(302\) | −4.55379 | −0.262041 | ||||||||
\(303\) | −31.3749 | −1.80244 | ||||||||
\(304\) | 2.12561 | 0.121912 | ||||||||
\(305\) | −14.6860 | −0.840916 | ||||||||
\(306\) | 3.13274 | 0.179087 | ||||||||
\(307\) | −16.4458 | −0.938609 | −0.469304 | − | 0.883036i | \(-0.655495\pi\) | ||||
−0.469304 | + | 0.883036i | \(0.655495\pi\) | |||||||
\(308\) | 18.1752 | 1.03563 | ||||||||
\(309\) | −17.1777 | −0.977207 | ||||||||
\(310\) | −13.3061 | −0.755734 | ||||||||
\(311\) | 24.9437 | 1.41443 | 0.707213 | − | 0.707000i | \(-0.249952\pi\) | ||||
0.707213 | + | 0.707000i | \(0.249952\pi\) | |||||||
\(312\) | −14.4228 | −0.816528 | ||||||||
\(313\) | −28.2448 | −1.59649 | −0.798246 | − | 0.602331i | \(-0.794239\pi\) | ||||
−0.798246 | + | 0.602331i | \(0.794239\pi\) | |||||||
\(314\) | −8.59945 | −0.485295 | ||||||||
\(315\) | 2.66197 | 0.149985 | ||||||||
\(316\) | −31.0004 | −1.74391 | ||||||||
\(317\) | −27.4623 | −1.54244 | −0.771219 | − | 0.636570i | \(-0.780352\pi\) | ||||
−0.771219 | + | 0.636570i | \(0.780352\pi\) | |||||||
\(318\) | 18.9961 | 1.06525 | ||||||||
\(319\) | 21.3681 | 1.19638 | ||||||||
\(320\) | −14.8829 | −0.831978 | ||||||||
\(321\) | −24.8149 | −1.38503 | ||||||||
\(322\) | −8.71526 | −0.485682 | ||||||||
\(323\) | 0.860517 | 0.0478804 | ||||||||
\(324\) | −29.1399 | −1.61889 | ||||||||
\(325\) | 18.4273 | 1.02216 | ||||||||
\(326\) | −26.1387 | −1.44769 | ||||||||
\(327\) | 15.9685 | 0.883060 | ||||||||
\(328\) | 1.80949 | 0.0999125 | ||||||||
\(329\) | 13.5076 | 0.744698 | ||||||||
\(330\) | 27.6471 | 1.52192 | ||||||||
\(331\) | −4.50743 | −0.247751 | −0.123875 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123875 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(332\) | −0.0717435 | −0.00393744 | ||||||||
\(333\) | 6.53286 | 0.357999 | ||||||||
\(334\) | 33.3366 | 1.82410 | ||||||||
\(335\) | 13.8459 | 0.756481 | ||||||||
\(336\) | 7.54526 | 0.411628 | ||||||||
\(337\) | 2.12518 | 0.115766 | 0.0578831 | − | 0.998323i | \(-0.481565\pi\) | ||||
0.0578831 | + | 0.998323i | \(0.481565\pi\) | |||||||
\(338\) | −34.5362 | −1.87852 | ||||||||
\(339\) | 18.1934 | 0.988132 | ||||||||
\(340\) | −3.26157 | −0.176883 | ||||||||
\(341\) | 23.9328 | 1.29603 | ||||||||
\(342\) | 2.69577 | 0.145771 | ||||||||
\(343\) | −17.2208 | −0.929834 | ||||||||
\(344\) | 15.1851 | 0.818728 | ||||||||
\(345\) | −7.48131 | −0.402780 | ||||||||
\(346\) | −8.57757 | −0.461133 | ||||||||
\(347\) | −11.2330 | −0.603018 | −0.301509 | − | 0.953463i | \(-0.597490\pi\) | ||||
−0.301509 | + | 0.953463i | \(0.597490\pi\) | |||||||
\(348\) | −24.1000 | −1.29190 | ||||||||
\(349\) | 26.0958 | 1.39688 | 0.698439 | − | 0.715670i | \(-0.253878\pi\) | ||||
0.698439 | + | 0.715670i | \(0.253878\pi\) | |||||||
\(350\) | 10.5799 | 0.565520 | ||||||||
\(351\) | −17.5297 | −0.935669 | ||||||||
\(352\) | 37.9564 | 2.02308 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −52.4307 | −2.78666 | ||||||||
\(355\) | −13.5809 | −0.720800 | ||||||||
\(356\) | −40.0703 | −2.12372 | ||||||||
\(357\) | 3.05457 | 0.161665 | ||||||||
\(358\) | 44.4292 | 2.34815 | ||||||||
\(359\) | 32.2363 | 1.70137 | 0.850684 | − | 0.525677i | \(-0.176188\pi\) | ||||
0.850684 | + | 0.525677i | \(0.176188\pi\) | |||||||
\(360\) | −2.32924 | −0.122762 | ||||||||
\(361\) | −18.2595 | −0.961027 | ||||||||
\(362\) | 27.1170 | 1.42524 | ||||||||
\(363\) | −26.4911 | −1.39042 | ||||||||
\(364\) | −20.2143 | −1.05952 | ||||||||
\(365\) | −6.64646 | −0.347891 | ||||||||
\(366\) | −52.7924 | −2.75951 | ||||||||
\(367\) | −6.89914 | −0.360132 | −0.180066 | − | 0.983654i | \(-0.557631\pi\) | ||||
−0.180066 | + | 0.983654i | \(0.557631\pi\) | |||||||
\(368\) | −6.94857 | −0.362219 | ||||||||
\(369\) | −2.09103 | −0.108855 | ||||||||
\(370\) | −12.0525 | −0.626582 | ||||||||
\(371\) | 6.06928 | 0.315101 | ||||||||
\(372\) | −26.9927 | −1.39951 | ||||||||
\(373\) | 19.6813 | 1.01906 | 0.509529 | − | 0.860454i | \(-0.329820\pi\) | ||||
0.509529 | + | 0.860454i | \(0.329820\pi\) | |||||||
\(374\) | 10.3955 | 0.537536 | ||||||||
\(375\) | 22.3797 | 1.15568 | ||||||||
\(376\) | −11.8192 | −0.609528 | ||||||||
\(377\) | −23.7653 | −1.22398 | ||||||||
\(378\) | −10.0646 | −0.517667 | ||||||||
\(379\) | −28.6601 | −1.47217 | −0.736085 | − | 0.676889i | \(-0.763328\pi\) | ||||
−0.736085 | + | 0.676889i | \(0.763328\pi\) | |||||||
\(380\) | −2.80663 | −0.143977 | ||||||||
\(381\) | −42.9304 | −2.19939 | ||||||||
\(382\) | −48.9147 | −2.50269 | ||||||||
\(383\) | −19.9905 | −1.02147 | −0.510734 | − | 0.859739i | \(-0.670626\pi\) | ||||
−0.510734 | + | 0.859739i | \(0.670626\pi\) | |||||||
\(384\) | −20.4499 | −1.04358 | ||||||||
\(385\) | 8.83331 | 0.450187 | ||||||||
\(386\) | −37.8985 | −1.92898 | ||||||||
\(387\) | −17.5478 | −0.892006 | ||||||||
\(388\) | 4.93157 | 0.250363 | ||||||||
\(389\) | 25.8923 | 1.31279 | 0.656396 | − | 0.754417i | \(-0.272080\pi\) | ||||
0.656396 | + | 0.754417i | \(0.272080\pi\) | |||||||
\(390\) | −30.7488 | −1.55703 | ||||||||
\(391\) | −2.81301 | −0.142260 | ||||||||
\(392\) | 6.21126 | 0.313716 | ||||||||
\(393\) | −13.7392 | −0.693051 | ||||||||
\(394\) | −19.0184 | −0.958135 | ||||||||
\(395\) | −15.0664 | −0.758074 | ||||||||
\(396\) | 18.3778 | 0.923521 | ||||||||
\(397\) | 32.8009 | 1.64623 | 0.823115 | − | 0.567874i | \(-0.192234\pi\) | ||||
0.823115 | + | 0.567874i | \(0.192234\pi\) | |||||||
\(398\) | −45.6679 | −2.28912 | ||||||||
\(399\) | 2.62851 | 0.131590 | ||||||||
\(400\) | 8.43523 | 0.421761 | ||||||||
\(401\) | 21.5362 | 1.07546 | 0.537732 | − | 0.843116i | \(-0.319281\pi\) | ||||
0.537732 | + | 0.843116i | \(0.319281\pi\) | |||||||
\(402\) | 49.7726 | 2.48243 | ||||||||
\(403\) | −26.6178 | −1.32593 | ||||||||
\(404\) | 38.4770 | 1.91430 | ||||||||
\(405\) | −14.1622 | −0.703727 | ||||||||
\(406\) | −13.6447 | −0.677175 | ||||||||
\(407\) | 21.6782 | 1.07455 | ||||||||
\(408\) | −2.67275 | −0.132321 | ||||||||
\(409\) | 6.95199 | 0.343754 | 0.171877 | − | 0.985118i | \(-0.445017\pi\) | ||||
0.171877 | + | 0.985118i | \(0.445017\pi\) | |||||||
\(410\) | 3.85777 | 0.190522 | ||||||||
\(411\) | 5.87963 | 0.290021 | ||||||||
\(412\) | 21.0662 | 1.03786 | ||||||||
\(413\) | −16.7517 | −0.824297 | ||||||||
\(414\) | −8.81240 | −0.433106 | ||||||||
\(415\) | −0.0348679 | −0.00171160 | ||||||||
\(416\) | −42.2147 | −2.06975 | ||||||||
\(417\) | 24.2744 | 1.18872 | ||||||||
\(418\) | 8.94546 | 0.437537 | ||||||||
\(419\) | 6.48010 | 0.316574 | 0.158287 | − | 0.987393i | \(-0.449403\pi\) | ||||
0.158287 | + | 0.987393i | \(0.449403\pi\) | |||||||
\(420\) | −9.96267 | −0.486129 | ||||||||
\(421\) | 14.8094 | 0.721768 | 0.360884 | − | 0.932611i | \(-0.382475\pi\) | ||||
0.360884 | + | 0.932611i | \(0.382475\pi\) | |||||||
\(422\) | 21.6184 | 1.05237 | ||||||||
\(423\) | 13.6582 | 0.664082 | ||||||||
\(424\) | −5.31064 | −0.257907 | ||||||||
\(425\) | 3.41485 | 0.165645 | ||||||||
\(426\) | −48.8201 | −2.36534 | ||||||||
\(427\) | −16.8673 | −0.816265 | ||||||||
\(428\) | 30.4321 | 1.47099 | ||||||||
\(429\) | 55.3060 | 2.67020 | ||||||||
\(430\) | 32.3742 | 1.56122 | ||||||||
\(431\) | 13.2015 | 0.635895 | 0.317948 | − | 0.948108i | \(-0.397006\pi\) | ||||
0.317948 | + | 0.948108i | \(0.397006\pi\) | |||||||
\(432\) | −8.02437 | −0.386073 | ||||||||
\(433\) | −3.37603 | −0.162241 | −0.0811207 | − | 0.996704i | \(-0.525850\pi\) | ||||
−0.0811207 | + | 0.996704i | \(0.525850\pi\) | |||||||
\(434\) | −15.2824 | −0.733580 | ||||||||
\(435\) | −11.7128 | −0.561586 | ||||||||
\(436\) | −19.5832 | −0.937865 | ||||||||
\(437\) | −2.42064 | −0.115795 | ||||||||
\(438\) | −23.8924 | −1.14162 | ||||||||
\(439\) | −1.52581 | −0.0728227 | −0.0364114 | − | 0.999337i | \(-0.511593\pi\) | ||||
−0.0364114 | + | 0.999337i | \(0.511593\pi\) | |||||||
\(440\) | −7.72917 | −0.368474 | ||||||||
\(441\) | −7.17768 | −0.341794 | ||||||||
\(442\) | −11.5617 | −0.549934 | ||||||||
\(443\) | 10.0461 | 0.477306 | 0.238653 | − | 0.971105i | \(-0.423294\pi\) | ||||
0.238653 | + | 0.971105i | \(0.423294\pi\) | |||||||
\(444\) | −24.4498 | −1.16034 | ||||||||
\(445\) | −19.4745 | −0.923178 | ||||||||
\(446\) | 23.0995 | 1.09379 | ||||||||
\(447\) | 38.7498 | 1.83280 | ||||||||
\(448\) | −17.0934 | −0.807589 | ||||||||
\(449\) | −26.6886 | −1.25951 | −0.629756 | − | 0.776793i | \(-0.716845\pi\) | ||||
−0.629756 | + | 0.776793i | \(0.716845\pi\) | |||||||
\(450\) | 10.6978 | 0.504301 | ||||||||
\(451\) | −6.93874 | −0.326733 | ||||||||
\(452\) | −22.3118 | −1.04946 | ||||||||
\(453\) | −4.48966 | −0.210943 | ||||||||
\(454\) | −11.1158 | −0.521689 | ||||||||
\(455\) | −9.82430 | −0.460570 | ||||||||
\(456\) | −2.29995 | −0.107705 | ||||||||
\(457\) | −6.03441 | −0.282278 | −0.141139 | − | 0.989990i | \(-0.545076\pi\) | ||||
−0.141139 | + | 0.989990i | \(0.545076\pi\) | |||||||
\(458\) | 42.1741 | 1.97067 | ||||||||
\(459\) | −3.24853 | −0.151628 | ||||||||
\(460\) | 9.17481 | 0.427778 | ||||||||
\(461\) | 15.0232 | 0.699699 | 0.349849 | − | 0.936806i | \(-0.386233\pi\) | ||||
0.349849 | + | 0.936806i | \(0.386233\pi\) | |||||||
\(462\) | 31.7536 | 1.47731 | ||||||||
\(463\) | 4.78332 | 0.222300 | 0.111150 | − | 0.993804i | \(-0.464547\pi\) | ||||
0.111150 | + | 0.993804i | \(0.464547\pi\) | |||||||
\(464\) | −10.8787 | −0.505033 | ||||||||
\(465\) | −13.1187 | −0.608363 | ||||||||
\(466\) | −5.85840 | −0.271385 | ||||||||
\(467\) | −17.1328 | −0.792810 | −0.396405 | − | 0.918076i | \(-0.629742\pi\) | ||||
−0.396405 | + | 0.918076i | \(0.629742\pi\) | |||||||
\(468\) | −20.4396 | −0.944821 | ||||||||
\(469\) | 15.9024 | 0.734306 | ||||||||
\(470\) | −25.1981 | −1.16230 | ||||||||
\(471\) | −8.47834 | −0.390661 | ||||||||
\(472\) | 14.6578 | 0.674680 | ||||||||
\(473\) | −58.2295 | −2.67739 | ||||||||
\(474\) | −54.1601 | −2.48766 | ||||||||
\(475\) | 2.93854 | 0.134829 | ||||||||
\(476\) | −3.74601 | −0.171698 | ||||||||
\(477\) | 6.13693 | 0.280991 | ||||||||
\(478\) | −12.8734 | −0.588815 | ||||||||
\(479\) | 22.9247 | 1.04746 | 0.523729 | − | 0.851885i | \(-0.324541\pi\) | ||||
0.523729 | + | 0.851885i | \(0.324541\pi\) | |||||||
\(480\) | −20.8056 | −0.949643 | ||||||||
\(481\) | −24.1102 | −1.09933 | ||||||||
\(482\) | 9.20167 | 0.419125 | ||||||||
\(483\) | −8.59251 | −0.390973 | ||||||||
\(484\) | 32.4877 | 1.47671 | ||||||||
\(485\) | 2.39678 | 0.108832 | ||||||||
\(486\) | −30.0294 | −1.36216 | ||||||||
\(487\) | −9.04444 | −0.409843 | −0.204921 | − | 0.978778i | \(-0.565694\pi\) | ||||
−0.204921 | + | 0.978778i | \(0.565694\pi\) | |||||||
\(488\) | 14.7589 | 0.668105 | ||||||||
\(489\) | −25.7706 | −1.16539 | ||||||||
\(490\) | 13.2422 | 0.598221 | ||||||||
\(491\) | −8.42855 | −0.380375 | −0.190188 | − | 0.981748i | \(-0.560910\pi\) | ||||
−0.190188 | + | 0.981748i | \(0.560910\pi\) | |||||||
\(492\) | 7.82588 | 0.352818 | ||||||||
\(493\) | −4.40407 | −0.198349 | ||||||||
\(494\) | −9.94904 | −0.447628 | ||||||||
\(495\) | 8.93177 | 0.401453 | ||||||||
\(496\) | −12.1845 | −0.547100 | ||||||||
\(497\) | −15.5981 | −0.699671 | ||||||||
\(498\) | −0.125342 | −0.00561669 | ||||||||
\(499\) | 7.46498 | 0.334178 | 0.167089 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167089 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(500\) | −27.4456 | −1.22740 | ||||||||
\(501\) | 32.8671 | 1.46839 | ||||||||
\(502\) | 2.52391 | 0.112647 | ||||||||
\(503\) | −9.87757 | −0.440419 | −0.220210 | − | 0.975453i | \(-0.570674\pi\) | ||||
−0.220210 | + | 0.975453i | \(0.570674\pi\) | |||||||
\(504\) | −2.67520 | −0.119163 | ||||||||
\(505\) | 18.7001 | 0.832145 | ||||||||
\(506\) | −29.2425 | −1.29999 | ||||||||
\(507\) | −34.0497 | −1.51220 | ||||||||
\(508\) | 52.6483 | 2.33589 | ||||||||
\(509\) | −25.0389 | −1.10983 | −0.554914 | − | 0.831908i | \(-0.687249\pi\) | ||||
−0.554914 | + | 0.831908i | \(0.687249\pi\) | |||||||
\(510\) | −5.69822 | −0.252321 | ||||||||
\(511\) | −7.63366 | −0.337693 | ||||||||
\(512\) | −25.5750 | −1.13027 | ||||||||
\(513\) | −2.79541 | −0.123420 | ||||||||
\(514\) | 44.1550 | 1.94759 | ||||||||
\(515\) | 10.2383 | 0.451154 | ||||||||
\(516\) | 65.6743 | 2.89115 | ||||||||
\(517\) | 45.3223 | 1.99327 | ||||||||
\(518\) | −13.8427 | −0.608214 | ||||||||
\(519\) | −8.45676 | −0.371210 | ||||||||
\(520\) | 8.59629 | 0.376972 | ||||||||
\(521\) | −16.4977 | −0.722777 | −0.361389 | − | 0.932415i | \(-0.617697\pi\) | ||||
−0.361389 | + | 0.932415i | \(0.617697\pi\) | |||||||
\(522\) | −13.7968 | −0.603869 | ||||||||
\(523\) | −9.83004 | −0.429837 | −0.214919 | − | 0.976632i | \(-0.568949\pi\) | ||||
−0.214919 | + | 0.976632i | \(0.568949\pi\) | |||||||
\(524\) | 16.8493 | 0.736064 | ||||||||
\(525\) | 10.4309 | 0.455241 | ||||||||
\(526\) | 45.6928 | 1.99230 | ||||||||
\(527\) | −4.93268 | −0.214871 | ||||||||
\(528\) | 25.3168 | 1.10177 | ||||||||
\(529\) | −15.0870 | −0.655957 | ||||||||
\(530\) | −11.3221 | −0.491800 | ||||||||
\(531\) | −16.9384 | −0.735065 | ||||||||
\(532\) | −3.22351 | −0.139757 | ||||||||
\(533\) | 7.71718 | 0.334268 | ||||||||
\(534\) | −70.0059 | −3.02945 | ||||||||
\(535\) | 14.7903 | 0.639438 | ||||||||
\(536\) | −13.9147 | −0.601022 | ||||||||
\(537\) | 43.8034 | 1.89026 | ||||||||
\(538\) | 48.2964 | 2.08221 | ||||||||
\(539\) | −23.8179 | −1.02591 | ||||||||
\(540\) | 10.5953 | 0.455949 | ||||||||
\(541\) | 31.7712 | 1.36595 | 0.682976 | − | 0.730441i | \(-0.260685\pi\) | ||||
0.682976 | + | 0.730441i | \(0.260685\pi\) | |||||||
\(542\) | −28.3914 | −1.21952 | ||||||||
\(543\) | 26.7350 | 1.14731 | ||||||||
\(544\) | −7.82302 | −0.335409 | ||||||||
\(545\) | −9.51759 | −0.407689 | ||||||||
\(546\) | −35.3160 | −1.51138 | ||||||||
\(547\) | 6.28505 | 0.268729 | 0.134365 | − | 0.990932i | \(-0.457101\pi\) | ||||
0.134365 | + | 0.990932i | \(0.457101\pi\) | |||||||
\(548\) | −7.21057 | −0.308020 | ||||||||
\(549\) | −17.0553 | −0.727902 | ||||||||
\(550\) | 35.4989 | 1.51368 | ||||||||
\(551\) | −3.78978 | −0.161450 | ||||||||
\(552\) | 7.51847 | 0.320008 | ||||||||
\(553\) | −17.3043 | −0.735852 | ||||||||
\(554\) | −13.2033 | −0.560956 | ||||||||
\(555\) | −11.8828 | −0.504397 | ||||||||
\(556\) | −29.7693 | −1.26250 | ||||||||
\(557\) | −1.62184 | −0.0687196 | −0.0343598 | − | 0.999410i | \(-0.510939\pi\) | ||||
−0.0343598 | + | 0.999410i | \(0.510939\pi\) | |||||||
\(558\) | −15.4528 | −0.654168 | ||||||||
\(559\) | 64.7621 | 2.73915 | ||||||||
\(560\) | −4.49715 | −0.190039 | ||||||||
\(561\) | 10.2490 | 0.432715 | ||||||||
\(562\) | −21.7394 | −0.917021 | ||||||||
\(563\) | 24.9610 | 1.05198 | 0.525991 | − | 0.850490i | \(-0.323694\pi\) | ||||
0.525991 | + | 0.850490i | \(0.323694\pi\) | |||||||
\(564\) | −51.1169 | −2.15241 | ||||||||
\(565\) | −10.8437 | −0.456198 | ||||||||
\(566\) | 34.5931 | 1.45406 | ||||||||
\(567\) | −16.2658 | −0.683098 | ||||||||
\(568\) | 13.6484 | 0.572674 | ||||||||
\(569\) | −32.9797 | −1.38258 | −0.691291 | − | 0.722576i | \(-0.742958\pi\) | ||||
−0.691291 | + | 0.722576i | \(0.742958\pi\) | |||||||
\(570\) | −4.90341 | −0.205381 | ||||||||
\(571\) | −43.3587 | −1.81451 | −0.907253 | − | 0.420585i | \(-0.861825\pi\) | ||||
−0.907253 | + | 0.420585i | \(0.861825\pi\) | |||||||
\(572\) | −67.8253 | −2.83592 | ||||||||
\(573\) | −48.2258 | −2.01466 | ||||||||
\(574\) | 4.43077 | 0.184937 | ||||||||
\(575\) | −9.60600 | −0.400598 | ||||||||
\(576\) | −17.2840 | −0.720165 | ||||||||
\(577\) | 34.0482 | 1.41745 | 0.708723 | − | 0.705487i | \(-0.249272\pi\) | ||||
0.708723 | + | 0.705487i | \(0.249272\pi\) | |||||||
\(578\) | −2.14256 | −0.0891186 | ||||||||
\(579\) | −37.3648 | −1.55283 | ||||||||
\(580\) | 14.3642 | 0.596439 | ||||||||
\(581\) | −0.0400469 | −0.00166142 | ||||||||
\(582\) | 8.61585 | 0.357139 | ||||||||
\(583\) | 20.3644 | 0.843406 | ||||||||
\(584\) | 6.67948 | 0.276399 | ||||||||
\(585\) | −9.93380 | −0.410712 | ||||||||
\(586\) | −62.3615 | −2.57613 | ||||||||
\(587\) | −37.5840 | −1.55126 | −0.775628 | − | 0.631190i | \(-0.782567\pi\) | ||||
−0.775628 | + | 0.631190i | \(0.782567\pi\) | |||||||
\(588\) | 26.8631 | 1.10782 | ||||||||
\(589\) | −4.24465 | −0.174898 | ||||||||
\(590\) | 31.2499 | 1.28654 | ||||||||
\(591\) | −18.7506 | −0.771295 | ||||||||
\(592\) | −11.0366 | −0.453603 | ||||||||
\(593\) | 6.91019 | 0.283768 | 0.141884 | − | 0.989883i | \(-0.454684\pi\) | ||||
0.141884 | + | 0.989883i | \(0.454684\pi\) | |||||||
\(594\) | −33.7699 | −1.38560 | ||||||||
\(595\) | −1.82059 | −0.0746369 | ||||||||
\(596\) | −47.5214 | −1.94655 | ||||||||
\(597\) | −45.0247 | −1.84274 | ||||||||
\(598\) | 32.5231 | 1.32997 | ||||||||
\(599\) | −28.2377 | −1.15376 | −0.576880 | − | 0.816829i | \(-0.695730\pi\) | ||||
−0.576880 | + | 0.816829i | \(0.695730\pi\) | |||||||
\(600\) | −9.12707 | −0.372611 | ||||||||
\(601\) | 34.3753 | 1.40220 | 0.701100 | − | 0.713063i | \(-0.252693\pi\) | ||||
0.701100 | + | 0.713063i | \(0.252693\pi\) | |||||||
\(602\) | 37.1828 | 1.51546 | ||||||||
\(603\) | 16.0797 | 0.654815 | ||||||||
\(604\) | 5.50596 | 0.224034 | ||||||||
\(605\) | 15.7893 | 0.641925 | ||||||||
\(606\) | 67.2224 | 2.73072 | ||||||||
\(607\) | −28.4971 | −1.15666 | −0.578332 | − | 0.815802i | \(-0.696296\pi\) | ||||
−0.578332 | + | 0.815802i | \(0.696296\pi\) | |||||||
\(608\) | −6.73184 | −0.273012 | ||||||||
\(609\) | −13.4525 | −0.545123 | ||||||||
\(610\) | 31.4655 | 1.27400 | ||||||||
\(611\) | −50.4069 | −2.03924 | ||||||||
\(612\) | −3.78777 | −0.153111 | ||||||||
\(613\) | −40.8237 | −1.64885 | −0.824426 | − | 0.565969i | \(-0.808502\pi\) | ||||
−0.824426 | + | 0.565969i | \(0.808502\pi\) | |||||||
\(614\) | 35.2359 | 1.42201 | ||||||||
\(615\) | 3.80344 | 0.153369 | ||||||||
\(616\) | −8.87719 | −0.357672 | ||||||||
\(617\) | −4.03369 | −0.162390 | −0.0811951 | − | 0.996698i | \(-0.525874\pi\) | ||||
−0.0811951 | + | 0.996698i | \(0.525874\pi\) | |||||||
\(618\) | 36.8043 | 1.48049 | ||||||||
\(619\) | 4.27327 | 0.171757 | 0.0858786 | − | 0.996306i | \(-0.472630\pi\) | ||||
0.0858786 | + | 0.996306i | \(0.472630\pi\) | |||||||
\(620\) | 16.0883 | 0.646120 | ||||||||
\(621\) | 9.13812 | 0.366700 | ||||||||
\(622\) | −53.4432 | −2.14288 | ||||||||
\(623\) | −22.3670 | −0.896116 | ||||||||
\(624\) | −28.1570 | −1.12718 | ||||||||
\(625\) | 3.73549 | 0.149419 | ||||||||
\(626\) | 60.5161 | 2.41871 | ||||||||
\(627\) | 8.81947 | 0.352216 | ||||||||
\(628\) | 10.3975 | 0.414907 | ||||||||
\(629\) | −4.46799 | −0.178150 | ||||||||
\(630\) | −5.70343 | −0.227230 | ||||||||
\(631\) | −11.1461 | −0.443719 | −0.221860 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221860 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(632\) | 15.1413 | 0.602288 | ||||||||
\(633\) | 21.3139 | 0.847151 | ||||||||
\(634\) | 58.8396 | 2.33682 | ||||||||
\(635\) | 25.5875 | 1.01541 | ||||||||
\(636\) | −22.9680 | −0.910741 | ||||||||
\(637\) | 26.4900 | 1.04957 | ||||||||
\(638\) | −45.7823 | −1.81254 | ||||||||
\(639\) | −15.7720 | −0.623930 | ||||||||
\(640\) | 12.1886 | 0.481797 | ||||||||
\(641\) | −40.5431 | −1.60135 | −0.800677 | − | 0.599096i | \(-0.795527\pi\) | ||||
−0.800677 | + | 0.599096i | \(0.795527\pi\) | |||||||
\(642\) | 53.1674 | 2.09835 | ||||||||
\(643\) | −9.29223 | −0.366450 | −0.183225 | − | 0.983071i | \(-0.558654\pi\) | ||||
−0.183225 | + | 0.983071i | \(0.558654\pi\) | |||||||
\(644\) | 10.5375 | 0.415238 | ||||||||
\(645\) | 31.9182 | 1.25678 | ||||||||
\(646\) | −1.84371 | −0.0725396 | ||||||||
\(647\) | −29.6720 | −1.16653 | −0.583263 | − | 0.812283i | \(-0.698224\pi\) | ||||
−0.583263 | + | 0.812283i | \(0.698224\pi\) | |||||||
\(648\) | 14.2326 | 0.559109 | ||||||||
\(649\) | −56.2073 | −2.20633 | ||||||||
\(650\) | −39.4815 | −1.54859 | ||||||||
\(651\) | −15.0672 | −0.590530 | ||||||||
\(652\) | 31.6041 | 1.23771 | ||||||||
\(653\) | 27.3242 | 1.06928 | 0.534638 | − | 0.845081i | \(-0.320448\pi\) | ||||
0.534638 | + | 0.845081i | \(0.320448\pi\) | |||||||
\(654\) | −34.2134 | −1.33785 | ||||||||
\(655\) | 8.18888 | 0.319966 | ||||||||
\(656\) | 3.53260 | 0.137925 | ||||||||
\(657\) | −7.71875 | −0.301137 | ||||||||
\(658\) | −28.9408 | −1.12823 | ||||||||
\(659\) | −0.301844 | −0.0117582 | −0.00587909 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587909 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(660\) | −33.4279 | −1.30118 | ||||||||
\(661\) | −42.6379 | −1.65842 | −0.829210 | − | 0.558937i | \(-0.811209\pi\) | ||||
−0.829210 | + | 0.558937i | \(0.811209\pi\) | |||||||
\(662\) | 9.65743 | 0.375347 | ||||||||
\(663\) | −11.3989 | −0.442695 | ||||||||
\(664\) | 0.0350411 | 0.00135986 | ||||||||
\(665\) | −1.56665 | −0.0607520 | ||||||||
\(666\) | −13.9970 | −0.542374 | ||||||||
\(667\) | 12.3887 | 0.479691 | ||||||||
\(668\) | −40.3070 | −1.55952 | ||||||||
\(669\) | 22.7742 | 0.880500 | ||||||||
\(670\) | −29.6656 | −1.14608 | ||||||||
\(671\) | −56.5951 | −2.18483 | ||||||||
\(672\) | −23.8959 | −0.921805 | ||||||||
\(673\) | 3.89457 | 0.150125 | 0.0750623 | − | 0.997179i | \(-0.476084\pi\) | ||||
0.0750623 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(674\) | −4.55333 | −0.175388 | ||||||||
\(675\) | −11.0932 | −0.426979 | ||||||||
\(676\) | 41.7574 | 1.60605 | ||||||||
\(677\) | −23.3401 | −0.897034 | −0.448517 | − | 0.893774i | \(-0.648048\pi\) | ||||
−0.448517 | + | 0.893774i | \(0.648048\pi\) | |||||||
\(678\) | −38.9805 | −1.49704 | ||||||||
\(679\) | 2.75278 | 0.105642 | ||||||||
\(680\) | 1.59302 | 0.0610896 | ||||||||
\(681\) | −10.9592 | −0.419958 | ||||||||
\(682\) | −51.2774 | −1.96351 | ||||||||
\(683\) | −38.7929 | −1.48437 | −0.742185 | − | 0.670195i | \(-0.766211\pi\) | ||||
−0.742185 | + | 0.670195i | \(0.766211\pi\) | |||||||
\(684\) | −3.25944 | −0.124628 | ||||||||
\(685\) | −3.50439 | −0.133896 | ||||||||
\(686\) | 36.8965 | 1.40871 | ||||||||
\(687\) | 41.5801 | 1.58638 | ||||||||
\(688\) | 29.6454 | 1.13022 | ||||||||
\(689\) | −22.6490 | −0.862858 | ||||||||
\(690\) | 16.0291 | 0.610218 | ||||||||
\(691\) | 3.05375 | 0.116170 | 0.0580850 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580850 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(692\) | 10.3711 | 0.394249 | ||||||||
\(693\) | 10.2584 | 0.389685 | ||||||||
\(694\) | 24.0673 | 0.913583 | ||||||||
\(695\) | −14.4681 | −0.548807 | ||||||||
\(696\) | 11.7710 | 0.446178 | ||||||||
\(697\) | 1.43011 | 0.0541693 | ||||||||
\(698\) | −55.9118 | −2.11629 | ||||||||
\(699\) | −5.77588 | −0.218464 | ||||||||
\(700\) | −12.7921 | −0.483495 | ||||||||
\(701\) | 4.41130 | 0.166612 | 0.0833062 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833062 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(702\) | 37.5585 | 1.41755 | ||||||||
\(703\) | −3.84478 | −0.145009 | ||||||||
\(704\) | −57.3539 | −2.16161 | ||||||||
\(705\) | −24.8432 | −0.935649 | ||||||||
\(706\) | 2.14256 | 0.0806362 | ||||||||
\(707\) | 21.4777 | 0.807751 | ||||||||
\(708\) | 63.3936 | 2.38248 | ||||||||
\(709\) | −12.7835 | −0.480096 | −0.240048 | − | 0.970761i | \(-0.577163\pi\) | ||||
−0.240048 | + | 0.970761i | \(0.577163\pi\) | |||||||
\(710\) | 29.0979 | 1.09202 | ||||||||
\(711\) | −17.4971 | −0.656194 | ||||||||
\(712\) | 19.5712 | 0.733462 | ||||||||
\(713\) | 13.8756 | 0.519647 | ||||||||
\(714\) | −6.54458 | −0.244925 | ||||||||
\(715\) | −32.9636 | −1.23277 | ||||||||
\(716\) | −53.7190 | −2.00757 | ||||||||
\(717\) | −12.6921 | −0.473994 | ||||||||
\(718\) | −69.0681 | −2.57760 | ||||||||
\(719\) | −4.46156 | −0.166388 | −0.0831940 | − | 0.996533i | \(-0.526512\pi\) | ||||
−0.0831940 | + | 0.996533i | \(0.526512\pi\) | |||||||
\(720\) | −4.54727 | −0.169467 | ||||||||
\(721\) | 11.7590 | 0.437929 | ||||||||
\(722\) | 39.1220 | 1.45597 | ||||||||
\(723\) | 9.07207 | 0.337394 | ||||||||
\(724\) | −32.7869 | −1.21852 | ||||||||
\(725\) | −15.0392 | −0.558544 | ||||||||
\(726\) | 56.7586 | 2.10651 | ||||||||
\(727\) | −8.58580 | −0.318430 | −0.159215 | − | 0.987244i | \(-0.550896\pi\) | ||||
−0.159215 | + | 0.987244i | \(0.550896\pi\) | |||||||
\(728\) | 9.87311 | 0.365922 | ||||||||
\(729\) | 4.13928 | 0.153307 | ||||||||
\(730\) | 14.2404 | 0.527061 | ||||||||
\(731\) | 12.0014 | 0.443888 | ||||||||
\(732\) | 63.8309 | 2.35926 | ||||||||
\(733\) | 13.2110 | 0.487958 | 0.243979 | − | 0.969780i | \(-0.421547\pi\) | ||||
0.243979 | + | 0.969780i | \(0.421547\pi\) | |||||||
\(734\) | 14.7818 | 0.545606 | ||||||||
\(735\) | 13.0557 | 0.481566 | ||||||||
\(736\) | 22.0062 | 0.811159 | ||||||||
\(737\) | 53.3577 | 1.96546 | ||||||||
\(738\) | 4.48016 | 0.164917 | ||||||||
\(739\) | 45.7908 | 1.68444 | 0.842220 | − | 0.539133i | \(-0.181248\pi\) | ||||
0.842220 | + | 0.539133i | \(0.181248\pi\) | |||||||
\(740\) | 14.5726 | 0.535701 | ||||||||
\(741\) | −9.80891 | −0.360339 | ||||||||
\(742\) | −13.0038 | −0.477383 | ||||||||
\(743\) | −43.5356 | −1.59717 | −0.798583 | − | 0.601884i | \(-0.794417\pi\) | ||||
−0.798583 | + | 0.601884i | \(0.794417\pi\) | |||||||
\(744\) | 13.1838 | 0.483343 | ||||||||
\(745\) | −23.0958 | −0.846163 | ||||||||
\(746\) | −42.1682 | −1.54389 | ||||||||
\(747\) | −0.0404932 | −0.00148157 | ||||||||
\(748\) | −12.5691 | −0.459570 | ||||||||
\(749\) | 16.9871 | 0.620694 | ||||||||
\(750\) | −47.9497 | −1.75087 | ||||||||
\(751\) | −45.7345 | −1.66888 | −0.834438 | − | 0.551102i | \(-0.814208\pi\) | ||||
−0.834438 | + | 0.551102i | \(0.814208\pi\) | |||||||
\(752\) | −23.0741 | −0.841427 | ||||||||
\(753\) | 2.48836 | 0.0906808 | ||||||||
\(754\) | 50.9185 | 1.85434 | ||||||||
\(755\) | 2.67594 | 0.0973873 | ||||||||
\(756\) | 12.1690 | 0.442583 | ||||||||
\(757\) | 35.1277 | 1.27674 | 0.638368 | − | 0.769731i | \(-0.279610\pi\) | ||||
0.638368 | + | 0.769731i | \(0.279610\pi\) | |||||||
\(758\) | 61.4059 | 2.23036 | ||||||||
\(759\) | −28.8306 | −1.04648 | ||||||||
\(760\) | 1.37082 | 0.0497250 | ||||||||
\(761\) | −22.1947 | −0.804559 | −0.402279 | − | 0.915517i | \(-0.631782\pi\) | ||||
−0.402279 | + | 0.915517i | \(0.631782\pi\) | |||||||
\(762\) | 91.9807 | 3.33211 | ||||||||
\(763\) | −10.9312 | −0.395737 | ||||||||
\(764\) | 59.1424 | 2.13970 | ||||||||
\(765\) | −1.84088 | −0.0665573 | ||||||||
\(766\) | 42.8308 | 1.54754 | ||||||||
\(767\) | 62.5131 | 2.25722 | ||||||||
\(768\) | −6.12550 | −0.221035 | ||||||||
\(769\) | −19.4933 | −0.702948 | −0.351474 | − | 0.936198i | \(-0.614319\pi\) | ||||
−0.351474 | + | 0.936198i | \(0.614319\pi\) | |||||||
\(770\) | −18.9259 | −0.682041 | ||||||||
\(771\) | 43.5331 | 1.56781 | ||||||||
\(772\) | 45.8228 | 1.64920 | ||||||||
\(773\) | 30.2999 | 1.08981 | 0.544905 | − | 0.838498i | \(-0.316566\pi\) | ||||
0.544905 | + | 0.838498i | \(0.316566\pi\) | |||||||
\(774\) | 37.5972 | 1.35140 | ||||||||
\(775\) | −16.8444 | −0.605068 | ||||||||
\(776\) | −2.40869 | −0.0864670 | ||||||||
\(777\) | −13.6478 | −0.489611 | ||||||||
\(778\) | −55.4757 | −1.98890 | ||||||||
\(779\) | 1.23063 | 0.0440920 | ||||||||
\(780\) | 37.1781 | 1.33119 | ||||||||
\(781\) | −52.3366 | −1.87275 | ||||||||
\(782\) | 6.02702 | 0.215526 | ||||||||
\(783\) | 14.3067 | 0.511281 | ||||||||
\(784\) | 12.1260 | 0.433071 | ||||||||
\(785\) | 5.05328 | 0.180359 | ||||||||
\(786\) | 29.4370 | 1.04998 | ||||||||
\(787\) | −10.7649 | −0.383727 | −0.191864 | − | 0.981422i | \(-0.561453\pi\) | ||||
−0.191864 | + | 0.981422i | \(0.561453\pi\) | |||||||
\(788\) | 22.9950 | 0.819164 | ||||||||
\(789\) | 45.0493 | 1.60380 | ||||||||
\(790\) | 32.2807 | 1.14849 | ||||||||
\(791\) | −12.4543 | −0.442825 | ||||||||
\(792\) | −8.97614 | −0.318953 | ||||||||
\(793\) | 62.9444 | 2.23522 | ||||||||
\(794\) | −70.2778 | −2.49407 | ||||||||
\(795\) | −11.1626 | −0.395898 | ||||||||
\(796\) | 55.2166 | 1.95710 | ||||||||
\(797\) | −5.71963 | −0.202600 | −0.101300 | − | 0.994856i | \(-0.532300\pi\) | ||||
−0.101300 | + | 0.994856i | \(0.532300\pi\) | |||||||
\(798\) | −5.63172 | −0.199361 | ||||||||
\(799\) | −9.34116 | −0.330466 | ||||||||
\(800\) | −26.7145 | −0.944498 | ||||||||
\(801\) | −22.6163 | −0.799109 | ||||||||
\(802\) | −46.1424 | −1.62935 | ||||||||
\(803\) | −25.6134 | −0.903876 | ||||||||
\(804\) | −60.1796 | −2.12237 | ||||||||
\(805\) | 5.12133 | 0.180503 | ||||||||
\(806\) | 57.0301 | 2.00880 | ||||||||
\(807\) | 47.6162 | 1.67617 | ||||||||
\(808\) | −18.7930 | −0.661137 | ||||||||
\(809\) | 53.2172 | 1.87102 | 0.935508 | − | 0.353305i | \(-0.114942\pi\) | ||||
0.935508 | + | 0.353305i | \(0.114942\pi\) | |||||||
\(810\) | 30.3434 | 1.06616 | ||||||||
\(811\) | −17.7778 | −0.624264 | −0.312132 | − | 0.950039i | \(-0.601043\pi\) | ||||
−0.312132 | + | 0.950039i | \(0.601043\pi\) | |||||||
\(812\) | 16.4977 | 0.578955 | ||||||||
\(813\) | −27.9916 | −0.981707 | ||||||||
\(814\) | −46.4467 | −1.62796 | ||||||||
\(815\) | 15.3599 | 0.538032 | ||||||||
\(816\) | −5.21791 | −0.182663 | ||||||||
\(817\) | 10.3274 | 0.361310 | ||||||||
\(818\) | −14.8950 | −0.520792 | ||||||||
\(819\) | −11.4093 | −0.398673 | ||||||||
\(820\) | −4.66440 | −0.162888 | ||||||||
\(821\) | 16.8662 | 0.588635 | 0.294317 | − | 0.955708i | \(-0.404908\pi\) | ||||
0.294317 | + | 0.955708i | \(0.404908\pi\) | |||||||
\(822\) | −12.5974 | −0.439386 | ||||||||
\(823\) | 6.16622 | 0.214941 | 0.107470 | − | 0.994208i | \(-0.465725\pi\) | ||||
0.107470 | + | 0.994208i | \(0.465725\pi\) | |||||||
\(824\) | −10.2892 | −0.358441 | ||||||||
\(825\) | 34.9990 | 1.21851 | ||||||||
\(826\) | 35.8915 | 1.24882 | ||||||||
\(827\) | 0.932231 | 0.0324168 | 0.0162084 | − | 0.999869i | \(-0.494840\pi\) | ||||
0.0162084 | + | 0.999869i | \(0.494840\pi\) | |||||||
\(828\) | 10.6550 | 0.370287 | ||||||||
\(829\) | 8.45248 | 0.293567 | 0.146783 | − | 0.989169i | \(-0.453108\pi\) | ||||
0.146783 | + | 0.989169i | \(0.453108\pi\) | |||||||
\(830\) | 0.0747064 | 0.00259310 | ||||||||
\(831\) | −13.0174 | −0.451568 | ||||||||
\(832\) | 63.7883 | 2.21146 | ||||||||
\(833\) | 4.90900 | 0.170087 | ||||||||
\(834\) | −52.0093 | −1.80094 | ||||||||
\(835\) | −19.5895 | −0.677923 | ||||||||
\(836\) | −10.8159 | −0.374075 | ||||||||
\(837\) | 16.0239 | 0.553868 | ||||||||
\(838\) | −13.8840 | −0.479614 | ||||||||
\(839\) | −7.05848 | −0.243686 | −0.121843 | − | 0.992549i | \(-0.538880\pi\) | ||||
−0.121843 | + | 0.992549i | \(0.538880\pi\) | |||||||
\(840\) | 4.86599 | 0.167893 | ||||||||
\(841\) | −9.60419 | −0.331179 | ||||||||
\(842\) | −31.7301 | −1.09349 | ||||||||
\(843\) | −21.4332 | −0.738199 | ||||||||
\(844\) | −26.1386 | −0.899728 | ||||||||
\(845\) | 20.2944 | 0.698149 | ||||||||
\(846\) | −29.2634 | −1.00610 | ||||||||
\(847\) | 18.1345 | 0.623107 | ||||||||
\(848\) | −10.3677 | −0.356030 | ||||||||
\(849\) | 34.1059 | 1.17051 | ||||||||
\(850\) | −7.31651 | −0.250954 | ||||||||
\(851\) | 12.5685 | 0.430842 | ||||||||
\(852\) | 59.0280 | 2.02227 | ||||||||
\(853\) | −10.4495 | −0.357783 | −0.178891 | − | 0.983869i | \(-0.557251\pi\) | ||||
−0.178891 | + | 0.983869i | \(0.557251\pi\) | |||||||
\(854\) | 36.1391 | 1.23665 | ||||||||
\(855\) | −1.58411 | −0.0541755 | ||||||||
\(856\) | −14.8637 | −0.508032 | ||||||||
\(857\) | −12.6675 | −0.432714 | −0.216357 | − | 0.976314i | \(-0.569418\pi\) | ||||
−0.216357 | + | 0.976314i | \(0.569418\pi\) | |||||||
\(858\) | −118.496 | −4.04540 | ||||||||
\(859\) | −20.0566 | −0.684324 | −0.342162 | − | 0.939641i | \(-0.611159\pi\) | ||||
−0.342162 | + | 0.939641i | \(0.611159\pi\) | |||||||
\(860\) | −39.1434 | −1.33478 | ||||||||
\(861\) | 4.36837 | 0.148873 | ||||||||
\(862\) | −28.2850 | −0.963391 | ||||||||
\(863\) | 21.0799 | 0.717569 | 0.358785 | − | 0.933420i | \(-0.383191\pi\) | ||||
0.358785 | + | 0.933420i | \(0.383191\pi\) | |||||||
\(864\) | 25.4133 | 0.864577 | ||||||||
\(865\) | 5.04042 | 0.171379 | ||||||||
\(866\) | 7.23332 | 0.245798 | ||||||||
\(867\) | −2.11238 | −0.0717402 | ||||||||
\(868\) | 18.4779 | 0.627180 | ||||||||
\(869\) | −58.0613 | −1.96959 | ||||||||
\(870\) | 25.0953 | 0.850812 | ||||||||
\(871\) | −59.3438 | −2.01079 | ||||||||
\(872\) | 9.56487 | 0.323907 | ||||||||
\(873\) | 2.78346 | 0.0942060 | ||||||||
\(874\) | 5.18636 | 0.175431 | ||||||||
\(875\) | −15.3200 | −0.517911 | ||||||||
\(876\) | 28.8881 | 0.976039 | ||||||||
\(877\) | 37.7023 | 1.27311 | 0.636557 | − | 0.771229i | \(-0.280358\pi\) | ||||
0.636557 | + | 0.771229i | \(0.280358\pi\) | |||||||
\(878\) | 3.26912 | 0.110328 | ||||||||
\(879\) | −61.4831 | −2.07378 | ||||||||
\(880\) | −15.0894 | −0.508662 | ||||||||
\(881\) | 44.9407 | 1.51409 | 0.757046 | − | 0.653362i | \(-0.226642\pi\) | ||||
0.757046 | + | 0.653362i | \(0.226642\pi\) | |||||||
\(882\) | 15.3786 | 0.517824 | ||||||||
\(883\) | −38.5616 | −1.29770 | −0.648851 | − | 0.760915i | \(-0.724750\pi\) | ||||
−0.648851 | + | 0.760915i | \(0.724750\pi\) | |||||||
\(884\) | 13.9792 | 0.470170 | ||||||||
\(885\) | 30.8098 | 1.03566 | ||||||||
\(886\) | −21.5244 | −0.723126 | ||||||||
\(887\) | −24.5934 | −0.825765 | −0.412882 | − | 0.910784i | \(-0.635478\pi\) | ||||
−0.412882 | + | 0.910784i | \(0.635478\pi\) | |||||||
\(888\) | 11.9418 | 0.400742 | ||||||||
\(889\) | 29.3880 | 0.985642 | ||||||||
\(890\) | 41.7251 | 1.39863 | ||||||||
\(891\) | −54.5768 | −1.82839 | ||||||||
\(892\) | −27.9294 | −0.935146 | ||||||||
\(893\) | −8.03822 | −0.268989 | ||||||||
\(894\) | −83.0236 | −2.77673 | ||||||||
\(895\) | −26.1078 | −0.872689 | ||||||||
\(896\) | 13.9990 | 0.467674 | ||||||||
\(897\) | 32.0650 | 1.07062 | ||||||||
\(898\) | 57.1818 | 1.90818 | ||||||||
\(899\) | 21.7238 | 0.724531 | ||||||||
\(900\) | −12.9347 | −0.431155 | ||||||||
\(901\) | −4.19720 | −0.139829 | ||||||||
\(902\) | 14.8666 | 0.495005 | ||||||||
\(903\) | 36.6591 | 1.21994 | ||||||||
\(904\) | 10.8976 | 0.362448 | ||||||||
\(905\) | −15.9347 | −0.529687 | ||||||||
\(906\) | 9.61934 | 0.319581 | ||||||||
\(907\) | −29.1769 | −0.968804 | −0.484402 | − | 0.874845i | \(-0.660963\pi\) | ||||
−0.484402 | + | 0.874845i | \(0.660963\pi\) | |||||||
\(908\) | 13.4400 | 0.446022 | ||||||||
\(909\) | 21.7171 | 0.720310 | ||||||||
\(910\) | 21.0491 | 0.697771 | ||||||||
\(911\) | −39.5502 | −1.31036 | −0.655178 | − | 0.755474i | \(-0.727406\pi\) | ||||
−0.655178 | + | 0.755474i | \(0.727406\pi\) | |||||||
\(912\) | −4.49010 | −0.148682 | ||||||||
\(913\) | −0.134370 | −0.00444700 | ||||||||
\(914\) | 12.9291 | 0.427655 | ||||||||
\(915\) | 31.0223 | 1.02557 | ||||||||
\(916\) | −50.9924 | −1.68483 | ||||||||
\(917\) | 9.40518 | 0.310586 | ||||||||
\(918\) | 6.96015 | 0.229719 | ||||||||
\(919\) | −5.00651 | −0.165149 | −0.0825747 | − | 0.996585i | \(-0.526314\pi\) | ||||
−0.0825747 | + | 0.996585i | \(0.526314\pi\) | |||||||
\(920\) | −4.48118 | −0.147740 | ||||||||
\(921\) | 34.7397 | 1.14471 | ||||||||
\(922\) | −32.1880 | −1.06005 | ||||||||
\(923\) | 58.2081 | 1.91594 | ||||||||
\(924\) | −38.3930 | −1.26304 | ||||||||
\(925\) | −15.2575 | −0.501664 | ||||||||
\(926\) | −10.2485 | −0.336788 | ||||||||
\(927\) | 11.8901 | 0.390522 | ||||||||
\(928\) | 34.4531 | 1.13098 | ||||||||
\(929\) | −52.8100 | −1.73264 | −0.866320 | − | 0.499490i | \(-0.833521\pi\) | ||||
−0.866320 | + | 0.499490i | \(0.833521\pi\) | |||||||
\(930\) | 28.1075 | 0.921680 | ||||||||
\(931\) | 4.22427 | 0.138445 | ||||||||
\(932\) | 7.08334 | 0.232022 | ||||||||
\(933\) | −52.6905 | −1.72501 | ||||||||
\(934\) | 36.7079 | 1.20112 | ||||||||
\(935\) | −6.10866 | −0.199775 | ||||||||
\(936\) | 9.98316 | 0.326310 | ||||||||
\(937\) | −25.5732 | −0.835439 | −0.417720 | − | 0.908576i | \(-0.637171\pi\) | ||||
−0.417720 | + | 0.908576i | \(0.637171\pi\) | |||||||
\(938\) | −34.0718 | −1.11248 | ||||||||
\(939\) | 59.6638 | 1.94705 | ||||||||
\(940\) | 30.4668 | 0.993718 | ||||||||
\(941\) | 15.2943 | 0.498581 | 0.249290 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249290 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(942\) | 18.1653 | 0.591858 | ||||||||
\(943\) | −4.02291 | −0.131004 | ||||||||
\(944\) | 28.6158 | 0.931366 | ||||||||
\(945\) | 5.91423 | 0.192390 | ||||||||
\(946\) | 124.760 | 4.05630 | ||||||||
\(947\) | 24.4424 | 0.794273 | 0.397136 | − | 0.917760i | \(-0.370004\pi\) | ||||
0.397136 | + | 0.917760i | \(0.370004\pi\) | |||||||
\(948\) | 65.4846 | 2.12684 | ||||||||
\(949\) | 28.4869 | 0.924723 | ||||||||
\(950\) | −6.29599 | −0.204269 | ||||||||
\(951\) | 58.0108 | 1.88113 | ||||||||
\(952\) | 1.82964 | 0.0592988 | ||||||||
\(953\) | −50.6478 | −1.64064 | −0.820321 | − | 0.571903i | \(-0.806205\pi\) | ||||
−0.820321 | + | 0.571903i | \(0.806205\pi\) | |||||||
\(954\) | −13.1487 | −0.425706 | ||||||||
\(955\) | 28.7437 | 0.930123 | ||||||||
\(956\) | 15.5651 | 0.503411 | ||||||||
\(957\) | −45.1375 | −1.45909 | ||||||||
\(958\) | −49.1175 | −1.58691 | ||||||||
\(959\) | −4.02490 | −0.129971 | ||||||||
\(960\) | 31.4383 | 1.01467 | ||||||||
\(961\) | −6.66869 | −0.215119 | ||||||||
\(962\) | 51.6575 | 1.66550 | ||||||||
\(963\) | 17.1764 | 0.553502 | ||||||||
\(964\) | −11.1257 | −0.358334 | ||||||||
\(965\) | 22.2702 | 0.716904 | ||||||||
\(966\) | 18.4099 | 0.592330 | ||||||||
\(967\) | −26.7278 | −0.859507 | −0.429754 | − | 0.902946i | \(-0.641400\pi\) | ||||
−0.429754 | + | 0.902946i | \(0.641400\pi\) | |||||||
\(968\) | −15.8677 | −0.510008 | ||||||||
\(969\) | −1.81774 | −0.0583942 | ||||||||
\(970\) | −5.13524 | −0.164883 | ||||||||
\(971\) | −20.2491 | −0.649824 | −0.324912 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324912 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(972\) | 36.3083 | 1.16459 | ||||||||
\(973\) | −16.6171 | −0.532719 | ||||||||
\(974\) | 19.3782 | 0.620918 | ||||||||
\(975\) | −38.9254 | −1.24661 | ||||||||
\(976\) | 28.8133 | 0.922290 | ||||||||
\(977\) | −13.0510 | −0.417538 | −0.208769 | − | 0.977965i | \(-0.566946\pi\) | ||||
−0.208769 | + | 0.977965i | \(0.566946\pi\) | |||||||
\(978\) | 55.2149 | 1.76558 | ||||||||
\(979\) | −75.0485 | −2.39856 | ||||||||
\(980\) | −16.0110 | −0.511453 | ||||||||
\(981\) | −11.0531 | −0.352898 | ||||||||
\(982\) | 18.0586 | 0.576275 | ||||||||
\(983\) | −27.7124 | −0.883888 | −0.441944 | − | 0.897043i | \(-0.645711\pi\) | ||||
−0.441944 | + | 0.897043i | \(0.645711\pi\) | |||||||
\(984\) | −3.82233 | −0.121852 | ||||||||
\(985\) | 11.1758 | 0.356089 | ||||||||
\(986\) | 9.43596 | 0.300502 | ||||||||
\(987\) | −28.5332 | −0.908221 | ||||||||
\(988\) | 12.0293 | 0.382703 | ||||||||
\(989\) | −33.7600 | −1.07351 | ||||||||
\(990\) | −19.1368 | −0.608208 | ||||||||
\(991\) | 57.4191 | 1.82398 | 0.911988 | − | 0.410216i | \(-0.134547\pi\) | ||||
0.911988 | + | 0.410216i | \(0.134547\pi\) | |||||||
\(992\) | 38.5884 | 1.22518 | ||||||||
\(993\) | 9.52141 | 0.302153 | ||||||||
\(994\) | 33.4198 | 1.06001 | ||||||||
\(995\) | 26.8357 | 0.850749 | ||||||||
\(996\) | 0.151550 | 0.00480203 | ||||||||
\(997\) | −11.8212 | −0.374380 | −0.187190 | − | 0.982324i | \(-0.559938\pi\) | ||||
−0.187190 | + | 0.982324i | \(0.559938\pi\) | |||||||
\(998\) | −15.9941 | −0.506286 | ||||||||
\(999\) | 14.5144 | 0.459214 |
(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 | 6001.2.a.a.1.19 | ✓ | 113 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.a.1.19 | ✓ | 113 | 1.1 | even | 1 | trivial |