Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.664239\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.664239 | −0.297057 | −0.148528 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148528 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.36162 | 0.892607 | 0.446304 | − | 0.894882i | \(-0.352740\pi\) | ||||
0.446304 | + | 0.894882i | \(0.352740\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.664239 | 0.210051 | ||||||||
\(11\) | −3.14397 | −0.947941 | −0.473971 | − | 0.880541i | \(-0.657180\pi\) | ||||
−0.473971 | + | 0.880541i | \(0.657180\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.36162 | −0.631169 | ||||||||
\(15\) | 0.664239 | 0.171506 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.53535 | −1.82759 | −0.913796 | − | 0.406174i | \(-0.866863\pi\) | ||||
−0.913796 | + | 0.406174i | \(0.866863\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.47817 | 1.25678 | 0.628389 | − | 0.777899i | \(-0.283714\pi\) | ||||
0.628389 | + | 0.777899i | \(0.283714\pi\) | |||||||
\(20\) | −0.664239 | −0.148528 | ||||||||
\(21\) | −2.36162 | −0.515347 | ||||||||
\(22\) | 3.14397 | 0.670296 | ||||||||
\(23\) | 1.27876 | 0.266641 | 0.133320 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133320 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.55879 | −0.911757 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.36162 | 0.446304 | ||||||||
\(29\) | −5.06863 | −0.941221 | −0.470610 | − | 0.882341i | \(-0.655966\pi\) | ||||
−0.470610 | + | 0.882341i | \(0.655966\pi\) | |||||||
\(30\) | −0.664239 | −0.121273 | ||||||||
\(31\) | 6.27777 | 1.12752 | 0.563760 | − | 0.825938i | \(-0.309354\pi\) | ||||
0.563760 | + | 0.825938i | \(0.309354\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.14397 | 0.547294 | ||||||||
\(34\) | 7.53535 | 1.29230 | ||||||||
\(35\) | −1.56868 | −0.265155 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.8042 | 1.77620 | 0.888102 | − | 0.459647i | \(-0.152024\pi\) | ||||
0.888102 | + | 0.459647i | \(0.152024\pi\) | |||||||
\(38\) | −5.47817 | −0.888677 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.664239 | 0.105025 | ||||||||
\(41\) | 11.1801 | 1.74604 | 0.873022 | − | 0.487681i | \(-0.162157\pi\) | ||||
0.873022 | + | 0.487681i | \(0.162157\pi\) | |||||||
\(42\) | 2.36162 | 0.364405 | ||||||||
\(43\) | −6.25237 | −0.953478 | −0.476739 | − | 0.879045i | \(-0.658181\pi\) | ||||
−0.476739 | + | 0.879045i | \(0.658181\pi\) | |||||||
\(44\) | −3.14397 | −0.473971 | ||||||||
\(45\) | −0.664239 | −0.0990189 | ||||||||
\(46\) | −1.27876 | −0.188543 | ||||||||
\(47\) | −8.67811 | −1.26583 | −0.632916 | − | 0.774220i | \(-0.718142\pi\) | ||||
−0.632916 | + | 0.774220i | \(0.718142\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.42277 | −0.203252 | ||||||||
\(50\) | 4.55879 | 0.644710 | ||||||||
\(51\) | 7.53535 | 1.05516 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −9.70904 | −1.33364 | −0.666819 | − | 0.745219i | \(-0.732345\pi\) | ||||
−0.666819 | + | 0.745219i | \(0.732345\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.08835 | 0.281592 | ||||||||
\(56\) | −2.36162 | −0.315584 | ||||||||
\(57\) | −5.47817 | −0.725602 | ||||||||
\(58\) | 5.06863 | 0.665543 | ||||||||
\(59\) | −10.6905 | −1.39179 | −0.695893 | − | 0.718145i | \(-0.744991\pi\) | ||||
−0.695893 | + | 0.718145i | \(0.744991\pi\) | |||||||
\(60\) | 0.664239 | 0.0857529 | ||||||||
\(61\) | −2.60711 | −0.333807 | −0.166903 | − | 0.985973i | \(-0.553377\pi\) | ||||
−0.166903 | + | 0.985973i | \(0.553377\pi\) | |||||||
\(62\) | −6.27777 | −0.797277 | ||||||||
\(63\) | 2.36162 | 0.297536 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.664239 | −0.0823887 | ||||||||
\(66\) | −3.14397 | −0.386995 | ||||||||
\(67\) | −6.78514 | −0.828937 | −0.414469 | − | 0.910064i | \(-0.636033\pi\) | ||||
−0.414469 | + | 0.910064i | \(0.636033\pi\) | |||||||
\(68\) | −7.53535 | −0.913796 | ||||||||
\(69\) | −1.27876 | −0.153945 | ||||||||
\(70\) | 1.56868 | 0.187493 | ||||||||
\(71\) | 1.70711 | 0.202596 | 0.101298 | − | 0.994856i | \(-0.467700\pi\) | ||||
0.101298 | + | 0.994856i | \(0.467700\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.395522 | 0.0462923 | 0.0231462 | − | 0.999732i | \(-0.492632\pi\) | ||||
0.0231462 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(74\) | −10.8042 | −1.25597 | ||||||||
\(75\) | 4.55879 | 0.526403 | ||||||||
\(76\) | 5.47817 | 0.628389 | ||||||||
\(77\) | −7.42484 | −0.846139 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 2.79959 | 0.314979 | 0.157489 | − | 0.987521i | \(-0.449660\pi\) | ||||
0.157489 | + | 0.987521i | \(0.449660\pi\) | |||||||
\(80\) | −0.664239 | −0.0742642 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.1801 | −1.23464 | ||||||||
\(83\) | 11.4961 | 1.26186 | 0.630929 | − | 0.775841i | \(-0.282674\pi\) | ||||
0.630929 | + | 0.775841i | \(0.282674\pi\) | |||||||
\(84\) | −2.36162 | −0.257674 | ||||||||
\(85\) | 5.00528 | 0.542899 | ||||||||
\(86\) | 6.25237 | 0.674211 | ||||||||
\(87\) | 5.06863 | 0.543414 | ||||||||
\(88\) | 3.14397 | 0.335148 | ||||||||
\(89\) | 17.4900 | 1.85393 | 0.926967 | − | 0.375142i | \(-0.122406\pi\) | ||||
0.926967 | + | 0.375142i | \(0.122406\pi\) | |||||||
\(90\) | 0.664239 | 0.0700170 | ||||||||
\(91\) | 2.36162 | 0.247565 | ||||||||
\(92\) | 1.27876 | 0.133320 | ||||||||
\(93\) | −6.27777 | −0.650974 | ||||||||
\(94\) | 8.67811 | 0.895079 | ||||||||
\(95\) | −3.63882 | −0.373335 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.21361 | 0.935501 | 0.467750 | − | 0.883861i | \(-0.345065\pi\) | ||||
0.467750 | + | 0.883861i | \(0.345065\pi\) | |||||||
\(98\) | 1.42277 | 0.143721 | ||||||||
\(99\) | −3.14397 | −0.315980 | ||||||||
\(100\) | −4.55879 | −0.455879 | ||||||||
\(101\) | 14.3771 | 1.43057 | 0.715285 | − | 0.698832i | \(-0.246297\pi\) | ||||
0.715285 | + | 0.698832i | \(0.246297\pi\) | |||||||
\(102\) | −7.53535 | −0.746111 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 1.56868 | 0.153087 | ||||||||
\(106\) | 9.70904 | 0.943025 | ||||||||
\(107\) | 12.2751 | 1.18668 | 0.593341 | − | 0.804952i | \(-0.297809\pi\) | ||||
0.593341 | + | 0.804952i | \(0.297809\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 19.6836 | 1.88534 | 0.942672 | − | 0.333721i | \(-0.108304\pi\) | ||||
0.942672 | + | 0.333721i | \(0.108304\pi\) | |||||||
\(110\) | −2.08835 | −0.199116 | ||||||||
\(111\) | −10.8042 | −1.02549 | ||||||||
\(112\) | 2.36162 | 0.223152 | ||||||||
\(113\) | −12.4526 | −1.17144 | −0.585721 | − | 0.810513i | \(-0.699188\pi\) | ||||
−0.585721 | + | 0.810513i | \(0.699188\pi\) | |||||||
\(114\) | 5.47817 | 0.513078 | ||||||||
\(115\) | −0.849405 | −0.0792074 | ||||||||
\(116\) | −5.06863 | −0.470610 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 10.6905 | 0.984142 | ||||||||
\(119\) | −17.7956 | −1.63132 | ||||||||
\(120\) | −0.664239 | −0.0606365 | ||||||||
\(121\) | −1.11548 | −0.101407 | ||||||||
\(122\) | 2.60711 | 0.236037 | ||||||||
\(123\) | −11.1801 | −1.00808 | ||||||||
\(124\) | 6.27777 | 0.563760 | ||||||||
\(125\) | 6.34932 | 0.567901 | ||||||||
\(126\) | −2.36162 | −0.210390 | ||||||||
\(127\) | −12.7497 | −1.13135 | −0.565676 | − | 0.824627i | \(-0.691385\pi\) | ||||
−0.565676 | + | 0.824627i | \(0.691385\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.25237 | 0.550491 | ||||||||
\(130\) | 0.664239 | 0.0582576 | ||||||||
\(131\) | −6.54233 | −0.571606 | −0.285803 | − | 0.958288i | \(-0.592260\pi\) | ||||
−0.285803 | + | 0.958288i | \(0.592260\pi\) | |||||||
\(132\) | 3.14397 | 0.273647 | ||||||||
\(133\) | 12.9373 | 1.12181 | ||||||||
\(134\) | 6.78514 | 0.586147 | ||||||||
\(135\) | 0.664239 | 0.0571686 | ||||||||
\(136\) | 7.53535 | 0.646151 | ||||||||
\(137\) | 18.3434 | 1.56718 | 0.783592 | − | 0.621276i | \(-0.213386\pi\) | ||||
0.783592 | + | 0.621276i | \(0.213386\pi\) | |||||||
\(138\) | 1.27876 | 0.108856 | ||||||||
\(139\) | 4.49746 | 0.381470 | 0.190735 | − | 0.981642i | \(-0.438913\pi\) | ||||
0.190735 | + | 0.981642i | \(0.438913\pi\) | |||||||
\(140\) | −1.56868 | −0.132578 | ||||||||
\(141\) | 8.67811 | 0.730829 | ||||||||
\(142\) | −1.70711 | −0.143257 | ||||||||
\(143\) | −3.14397 | −0.262912 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.36678 | 0.279596 | ||||||||
\(146\) | −0.395522 | −0.0327336 | ||||||||
\(147\) | 1.42277 | 0.117348 | ||||||||
\(148\) | 10.8042 | 0.888102 | ||||||||
\(149\) | 10.5024 | 0.860392 | 0.430196 | − | 0.902736i | \(-0.358444\pi\) | ||||
0.430196 | + | 0.902736i | \(0.358444\pi\) | |||||||
\(150\) | −4.55879 | −0.372223 | ||||||||
\(151\) | −0.330883 | −0.0269269 | −0.0134635 | − | 0.999909i | \(-0.504286\pi\) | ||||
−0.0134635 | + | 0.999909i | \(0.504286\pi\) | |||||||
\(152\) | −5.47817 | −0.444338 | ||||||||
\(153\) | −7.53535 | −0.609197 | ||||||||
\(154\) | 7.42484 | 0.598311 | ||||||||
\(155\) | −4.16994 | −0.334938 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 6.48802 | 0.517800 | 0.258900 | − | 0.965904i | \(-0.416640\pi\) | ||||
0.258900 | + | 0.965904i | \(0.416640\pi\) | |||||||
\(158\) | −2.79959 | −0.222724 | ||||||||
\(159\) | 9.70904 | 0.769977 | ||||||||
\(160\) | 0.664239 | 0.0525127 | ||||||||
\(161\) | 3.01995 | 0.238005 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −10.2456 | −0.802499 | −0.401249 | − | 0.915969i | \(-0.631424\pi\) | ||||
−0.401249 | + | 0.915969i | \(0.631424\pi\) | |||||||
\(164\) | 11.1801 | 0.873022 | ||||||||
\(165\) | −2.08835 | −0.162577 | ||||||||
\(166\) | −11.4961 | −0.892268 | ||||||||
\(167\) | 1.93544 | 0.149769 | 0.0748846 | − | 0.997192i | \(-0.476141\pi\) | ||||
0.0748846 | + | 0.997192i | \(0.476141\pi\) | |||||||
\(168\) | 2.36162 | 0.182203 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −5.00528 | −0.383887 | ||||||||
\(171\) | 5.47817 | 0.418926 | ||||||||
\(172\) | −6.25237 | −0.476739 | ||||||||
\(173\) | −2.22848 | −0.169428 | −0.0847142 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847142 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(174\) | −5.06863 | −0.384252 | ||||||||
\(175\) | −10.7661 | −0.813841 | ||||||||
\(176\) | −3.14397 | −0.236985 | ||||||||
\(177\) | 10.6905 | 0.803548 | ||||||||
\(178\) | −17.4900 | −1.31093 | ||||||||
\(179\) | −5.40080 | −0.403675 | −0.201838 | − | 0.979419i | \(-0.564691\pi\) | ||||
−0.201838 | + | 0.979419i | \(0.564691\pi\) | |||||||
\(180\) | −0.664239 | −0.0495095 | ||||||||
\(181\) | −14.4182 | −1.07170 | −0.535848 | − | 0.844314i | \(-0.680008\pi\) | ||||
−0.535848 | + | 0.844314i | \(0.680008\pi\) | |||||||
\(182\) | −2.36162 | −0.175055 | ||||||||
\(183\) | 2.60711 | 0.192723 | ||||||||
\(184\) | −1.27876 | −0.0942717 | ||||||||
\(185\) | −7.17659 | −0.527633 | ||||||||
\(186\) | 6.27777 | 0.460308 | ||||||||
\(187\) | 23.6909 | 1.73245 | ||||||||
\(188\) | −8.67811 | −0.632916 | ||||||||
\(189\) | −2.36162 | −0.171782 | ||||||||
\(190\) | 3.63882 | 0.263988 | ||||||||
\(191\) | 10.8810 | 0.787324 | 0.393662 | − | 0.919255i | \(-0.371208\pi\) | ||||
0.393662 | + | 0.919255i | \(0.371208\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −27.6749 | −1.99209 | −0.996043 | − | 0.0888700i | \(-0.971674\pi\) | ||||
−0.996043 | + | 0.0888700i | \(0.971674\pi\) | |||||||
\(194\) | −9.21361 | −0.661499 | ||||||||
\(195\) | 0.664239 | 0.0475672 | ||||||||
\(196\) | −1.42277 | −0.101626 | ||||||||
\(197\) | −22.7122 | −1.61817 | −0.809087 | − | 0.587689i | \(-0.800038\pi\) | ||||
−0.809087 | + | 0.587689i | \(0.800038\pi\) | |||||||
\(198\) | 3.14397 | 0.223432 | ||||||||
\(199\) | −10.5958 | −0.751118 | −0.375559 | − | 0.926799i | \(-0.622549\pi\) | ||||
−0.375559 | + | 0.926799i | \(0.622549\pi\) | |||||||
\(200\) | 4.55879 | 0.322355 | ||||||||
\(201\) | 6.78514 | 0.478587 | ||||||||
\(202\) | −14.3771 | −1.01157 | ||||||||
\(203\) | −11.9702 | −0.840140 | ||||||||
\(204\) | 7.53535 | 0.527580 | ||||||||
\(205\) | −7.42629 | −0.518674 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 1.27876 | 0.0888802 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −17.2232 | −1.19135 | ||||||||
\(210\) | −1.56868 | −0.108249 | ||||||||
\(211\) | −23.9450 | −1.64844 | −0.824220 | − | 0.566269i | \(-0.808386\pi\) | ||||
−0.824220 | + | 0.566269i | \(0.808386\pi\) | |||||||
\(212\) | −9.70904 | −0.666819 | ||||||||
\(213\) | −1.70711 | −0.116969 | ||||||||
\(214\) | −12.2751 | −0.839110 | ||||||||
\(215\) | 4.15307 | 0.283237 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 14.8257 | 1.00643 | ||||||||
\(218\) | −19.6836 | −1.33314 | ||||||||
\(219\) | −0.395522 | −0.0267269 | ||||||||
\(220\) | 2.08835 | 0.140796 | ||||||||
\(221\) | −7.53535 | −0.506883 | ||||||||
\(222\) | 10.8042 | 0.725132 | ||||||||
\(223\) | 9.14462 | 0.612369 | 0.306185 | − | 0.951972i | \(-0.400948\pi\) | ||||
0.306185 | + | 0.951972i | \(0.400948\pi\) | |||||||
\(224\) | −2.36162 | −0.157792 | ||||||||
\(225\) | −4.55879 | −0.303919 | ||||||||
\(226\) | 12.4526 | 0.828334 | ||||||||
\(227\) | −0.990850 | −0.0657650 | −0.0328825 | − | 0.999459i | \(-0.510469\pi\) | ||||
−0.0328825 | + | 0.999459i | \(0.510469\pi\) | |||||||
\(228\) | −5.47817 | −0.362801 | ||||||||
\(229\) | −0.230645 | −0.0152414 | −0.00762072 | − | 0.999971i | \(-0.502426\pi\) | ||||
−0.00762072 | + | 0.999971i | \(0.502426\pi\) | |||||||
\(230\) | 0.849405 | 0.0560081 | ||||||||
\(231\) | 7.42484 | 0.488519 | ||||||||
\(232\) | 5.06863 | 0.332772 | ||||||||
\(233\) | 29.6243 | 1.94075 | 0.970377 | − | 0.241598i | \(-0.0776714\pi\) | ||||
0.970377 | + | 0.241598i | \(0.0776714\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 5.76434 | 0.376024 | ||||||||
\(236\) | −10.6905 | −0.695893 | ||||||||
\(237\) | −2.79959 | −0.181853 | ||||||||
\(238\) | 17.7956 | 1.15352 | ||||||||
\(239\) | −12.1630 | −0.786760 | −0.393380 | − | 0.919376i | \(-0.628694\pi\) | ||||
−0.393380 | + | 0.919376i | \(0.628694\pi\) | |||||||
\(240\) | 0.664239 | 0.0428765 | ||||||||
\(241\) | −9.36359 | −0.603162 | −0.301581 | − | 0.953441i | \(-0.597514\pi\) | ||||
−0.301581 | + | 0.953441i | \(0.597514\pi\) | |||||||
\(242\) | 1.11548 | 0.0717057 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.60711 | −0.166903 | ||||||||
\(245\) | 0.945057 | 0.0603775 | ||||||||
\(246\) | 11.1801 | 0.712820 | ||||||||
\(247\) | 5.47817 | 0.348568 | ||||||||
\(248\) | −6.27777 | −0.398639 | ||||||||
\(249\) | −11.4961 | −0.728534 | ||||||||
\(250\) | −6.34932 | −0.401566 | ||||||||
\(251\) | 24.7530 | 1.56239 | 0.781196 | − | 0.624286i | \(-0.214610\pi\) | ||||
0.781196 | + | 0.624286i | \(0.214610\pi\) | |||||||
\(252\) | 2.36162 | 0.148768 | ||||||||
\(253\) | −4.02039 | −0.252760 | ||||||||
\(254\) | 12.7497 | 0.799987 | ||||||||
\(255\) | −5.00528 | −0.313443 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.92601 | −0.619167 | −0.309584 | − | 0.950872i | \(-0.600190\pi\) | ||||
−0.309584 | + | 0.950872i | \(0.600190\pi\) | |||||||
\(258\) | −6.25237 | −0.389256 | ||||||||
\(259\) | 25.5154 | 1.58545 | ||||||||
\(260\) | −0.664239 | −0.0411944 | ||||||||
\(261\) | −5.06863 | −0.313740 | ||||||||
\(262\) | 6.54233 | 0.404186 | ||||||||
\(263\) | 23.0280 | 1.41997 | 0.709983 | − | 0.704219i | \(-0.248703\pi\) | ||||
0.709983 | + | 0.704219i | \(0.248703\pi\) | |||||||
\(264\) | −3.14397 | −0.193498 | ||||||||
\(265\) | 6.44912 | 0.396166 | ||||||||
\(266\) | −12.9373 | −0.793239 | ||||||||
\(267\) | −17.4900 | −1.07037 | ||||||||
\(268\) | −6.78514 | −0.414469 | ||||||||
\(269\) | 11.0757 | 0.675296 | 0.337648 | − | 0.941273i | \(-0.390369\pi\) | ||||
0.337648 | + | 0.941273i | \(0.390369\pi\) | |||||||
\(270\) | −0.664239 | −0.0404243 | ||||||||
\(271\) | 13.7124 | 0.832970 | 0.416485 | − | 0.909143i | \(-0.363262\pi\) | ||||
0.416485 | + | 0.909143i | \(0.363262\pi\) | |||||||
\(272\) | −7.53535 | −0.456898 | ||||||||
\(273\) | −2.36162 | −0.142932 | ||||||||
\(274\) | −18.3434 | −1.10817 | ||||||||
\(275\) | 14.3327 | 0.864292 | ||||||||
\(276\) | −1.27876 | −0.0769725 | ||||||||
\(277\) | 25.1561 | 1.51148 | 0.755742 | − | 0.654869i | \(-0.227276\pi\) | ||||
0.755742 | + | 0.654869i | \(0.227276\pi\) | |||||||
\(278\) | −4.49746 | −0.269740 | ||||||||
\(279\) | 6.27777 | 0.375840 | ||||||||
\(280\) | 1.56868 | 0.0937465 | ||||||||
\(281\) | −19.4460 | −1.16005 | −0.580026 | − | 0.814598i | \(-0.696957\pi\) | ||||
−0.580026 | + | 0.814598i | \(0.696957\pi\) | |||||||
\(282\) | −8.67811 | −0.516774 | ||||||||
\(283\) | −16.6056 | −0.987100 | −0.493550 | − | 0.869717i | \(-0.664301\pi\) | ||||
−0.493550 | + | 0.869717i | \(0.664301\pi\) | |||||||
\(284\) | 1.70711 | 0.101298 | ||||||||
\(285\) | 3.63882 | 0.215545 | ||||||||
\(286\) | 3.14397 | 0.185907 | ||||||||
\(287\) | 26.4032 | 1.55853 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 39.7815 | 2.34009 | ||||||||
\(290\) | −3.36678 | −0.197704 | ||||||||
\(291\) | −9.21361 | −0.540112 | ||||||||
\(292\) | 0.395522 | 0.0231462 | ||||||||
\(293\) | 22.3887 | 1.30796 | 0.653982 | − | 0.756511i | \(-0.273097\pi\) | ||||
0.653982 | + | 0.756511i | \(0.273097\pi\) | |||||||
\(294\) | −1.42277 | −0.0829774 | ||||||||
\(295\) | 7.10106 | 0.413440 | ||||||||
\(296\) | −10.8042 | −0.627983 | ||||||||
\(297\) | 3.14397 | 0.182431 | ||||||||
\(298\) | −10.5024 | −0.608389 | ||||||||
\(299\) | 1.27876 | 0.0739528 | ||||||||
\(300\) | 4.55879 | 0.263202 | ||||||||
\(301\) | −14.7657 | −0.851081 | ||||||||
\(302\) | 0.330883 | 0.0190402 | ||||||||
\(303\) | −14.3771 | −0.825940 | ||||||||
\(304\) | 5.47817 | 0.314195 | ||||||||
\(305\) | 1.73175 | 0.0991596 | ||||||||
\(306\) | 7.53535 | 0.430767 | ||||||||
\(307\) | 8.75392 | 0.499612 | 0.249806 | − | 0.968296i | \(-0.419633\pi\) | ||||
0.249806 | + | 0.968296i | \(0.419633\pi\) | |||||||
\(308\) | −7.42484 | −0.423070 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 4.16994 | 0.236837 | ||||||||
\(311\) | 3.32236 | 0.188394 | 0.0941968 | − | 0.995554i | \(-0.469972\pi\) | ||||
0.0941968 | + | 0.995554i | \(0.469972\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 13.9039 | 0.785894 | 0.392947 | − | 0.919561i | \(-0.371456\pi\) | ||||
0.392947 | + | 0.919561i | \(0.371456\pi\) | |||||||
\(314\) | −6.48802 | −0.366140 | ||||||||
\(315\) | −1.56868 | −0.0883850 | ||||||||
\(316\) | 2.79959 | 0.157489 | ||||||||
\(317\) | −12.9648 | −0.728177 | −0.364089 | − | 0.931364i | \(-0.618619\pi\) | ||||
−0.364089 | + | 0.931364i | \(0.618619\pi\) | |||||||
\(318\) | −9.70904 | −0.544456 | ||||||||
\(319\) | 15.9356 | 0.892222 | ||||||||
\(320\) | −0.664239 | −0.0371321 | ||||||||
\(321\) | −12.2751 | −0.685131 | ||||||||
\(322\) | −3.01995 | −0.168295 | ||||||||
\(323\) | −41.2800 | −2.29688 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.55879 | −0.252876 | ||||||||
\(326\) | 10.2456 | 0.567452 | ||||||||
\(327\) | −19.6836 | −1.08850 | ||||||||
\(328\) | −11.1801 | −0.617320 | ||||||||
\(329\) | −20.4944 | −1.12989 | ||||||||
\(330\) | 2.08835 | 0.114960 | ||||||||
\(331\) | 28.9193 | 1.58955 | 0.794773 | − | 0.606906i | \(-0.207590\pi\) | ||||
0.794773 | + | 0.606906i | \(0.207590\pi\) | |||||||
\(332\) | 11.4961 | 0.630929 | ||||||||
\(333\) | 10.8042 | 0.592068 | ||||||||
\(334\) | −1.93544 | −0.105903 | ||||||||
\(335\) | 4.50696 | 0.246242 | ||||||||
\(336\) | −2.36162 | −0.128837 | ||||||||
\(337\) | −24.6699 | −1.34386 | −0.671929 | − | 0.740616i | \(-0.734534\pi\) | ||||
−0.671929 | + | 0.740616i | \(0.734534\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 12.4526 | 0.676332 | ||||||||
\(340\) | 5.00528 | 0.271449 | ||||||||
\(341\) | −19.7371 | −1.06882 | ||||||||
\(342\) | −5.47817 | −0.296226 | ||||||||
\(343\) | −19.8913 | −1.07403 | ||||||||
\(344\) | 6.25237 | 0.337105 | ||||||||
\(345\) | 0.849405 | 0.0457304 | ||||||||
\(346\) | 2.22848 | 0.119804 | ||||||||
\(347\) | −3.17151 | −0.170255 | −0.0851277 | − | 0.996370i | \(-0.527130\pi\) | ||||
−0.0851277 | + | 0.996370i | \(0.527130\pi\) | |||||||
\(348\) | 5.06863 | 0.271707 | ||||||||
\(349\) | −31.3835 | −1.67992 | −0.839961 | − | 0.542646i | \(-0.817422\pi\) | ||||
−0.839961 | + | 0.542646i | \(0.817422\pi\) | |||||||
\(350\) | 10.7661 | 0.575473 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.14397 | 0.167574 | ||||||||
\(353\) | 17.0417 | 0.907037 | 0.453519 | − | 0.891247i | \(-0.350169\pi\) | ||||
0.453519 | + | 0.891247i | \(0.350169\pi\) | |||||||
\(354\) | −10.6905 | −0.568194 | ||||||||
\(355\) | −1.13393 | −0.0601826 | ||||||||
\(356\) | 17.4900 | 0.926967 | ||||||||
\(357\) | 17.7956 | 0.941844 | ||||||||
\(358\) | 5.40080 | 0.285441 | ||||||||
\(359\) | 25.2917 | 1.33484 | 0.667422 | − | 0.744680i | \(-0.267398\pi\) | ||||
0.667422 | + | 0.744680i | \(0.267398\pi\) | |||||||
\(360\) | 0.664239 | 0.0350085 | ||||||||
\(361\) | 11.0104 | 0.579493 | ||||||||
\(362\) | 14.4182 | 0.757804 | ||||||||
\(363\) | 1.11548 | 0.0585475 | ||||||||
\(364\) | 2.36162 | 0.123782 | ||||||||
\(365\) | −0.262721 | −0.0137515 | ||||||||
\(366\) | −2.60711 | −0.136276 | ||||||||
\(367\) | 13.0779 | 0.682662 | 0.341331 | − | 0.939943i | \(-0.389122\pi\) | ||||
0.341331 | + | 0.939943i | \(0.389122\pi\) | |||||||
\(368\) | 1.27876 | 0.0666601 | ||||||||
\(369\) | 11.1801 | 0.582015 | ||||||||
\(370\) | 7.17659 | 0.373093 | ||||||||
\(371\) | −22.9290 | −1.19042 | ||||||||
\(372\) | −6.27777 | −0.325487 | ||||||||
\(373\) | −25.9846 | −1.34543 | −0.672717 | − | 0.739900i | \(-0.734873\pi\) | ||||
−0.672717 | + | 0.739900i | \(0.734873\pi\) | |||||||
\(374\) | −23.6909 | −1.22503 | ||||||||
\(375\) | −6.34932 | −0.327878 | ||||||||
\(376\) | 8.67811 | 0.447539 | ||||||||
\(377\) | −5.06863 | −0.261048 | ||||||||
\(378\) | 2.36162 | 0.121468 | ||||||||
\(379\) | −14.4762 | −0.743590 | −0.371795 | − | 0.928315i | \(-0.621258\pi\) | ||||
−0.371795 | + | 0.928315i | \(0.621258\pi\) | |||||||
\(380\) | −3.63882 | −0.186667 | ||||||||
\(381\) | 12.7497 | 0.653187 | ||||||||
\(382\) | −10.8810 | −0.556722 | ||||||||
\(383\) | 29.6314 | 1.51409 | 0.757046 | − | 0.653362i | \(-0.226642\pi\) | ||||
0.757046 | + | 0.653362i | \(0.226642\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.93187 | 0.251351 | ||||||||
\(386\) | 27.6749 | 1.40862 | ||||||||
\(387\) | −6.25237 | −0.317826 | ||||||||
\(388\) | 9.21361 | 0.467750 | ||||||||
\(389\) | −31.9402 | −1.61943 | −0.809716 | − | 0.586822i | \(-0.800379\pi\) | ||||
−0.809716 | + | 0.586822i | \(0.800379\pi\) | |||||||
\(390\) | −0.664239 | −0.0336351 | ||||||||
\(391\) | −9.63593 | −0.487310 | ||||||||
\(392\) | 1.42277 | 0.0718605 | ||||||||
\(393\) | 6.54233 | 0.330017 | ||||||||
\(394\) | 22.7122 | 1.14422 | ||||||||
\(395\) | −1.85960 | −0.0935666 | ||||||||
\(396\) | −3.14397 | −0.157990 | ||||||||
\(397\) | −1.91074 | −0.0958973 | −0.0479486 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479486 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(398\) | 10.5958 | 0.531120 | ||||||||
\(399\) | −12.9373 | −0.647677 | ||||||||
\(400\) | −4.55879 | −0.227939 | ||||||||
\(401\) | 24.2814 | 1.21255 | 0.606277 | − | 0.795254i | \(-0.292662\pi\) | ||||
0.606277 | + | 0.795254i | \(0.292662\pi\) | |||||||
\(402\) | −6.78514 | −0.338412 | ||||||||
\(403\) | 6.27777 | 0.312718 | ||||||||
\(404\) | 14.3771 | 0.715285 | ||||||||
\(405\) | −0.664239 | −0.0330063 | ||||||||
\(406\) | 11.9702 | 0.594069 | ||||||||
\(407\) | −33.9681 | −1.68374 | ||||||||
\(408\) | −7.53535 | −0.373056 | ||||||||
\(409\) | 8.85686 | 0.437944 | 0.218972 | − | 0.975731i | \(-0.429730\pi\) | ||||
0.218972 | + | 0.975731i | \(0.429730\pi\) | |||||||
\(410\) | 7.42629 | 0.366758 | ||||||||
\(411\) | −18.3434 | −0.904814 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −25.2469 | −1.24232 | ||||||||
\(414\) | −1.27876 | −0.0628478 | ||||||||
\(415\) | −7.63614 | −0.374844 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −4.49746 | −0.220242 | ||||||||
\(418\) | 17.2232 | 0.842414 | ||||||||
\(419\) | 24.4543 | 1.19467 | 0.597334 | − | 0.801992i | \(-0.296227\pi\) | ||||
0.597334 | + | 0.801992i | \(0.296227\pi\) | |||||||
\(420\) | 1.56868 | 0.0765437 | ||||||||
\(421\) | 28.6102 | 1.39437 | 0.697187 | − | 0.716889i | \(-0.254435\pi\) | ||||
0.697187 | + | 0.716889i | \(0.254435\pi\) | |||||||
\(422\) | 23.9450 | 1.16562 | ||||||||
\(423\) | −8.67811 | −0.421944 | ||||||||
\(424\) | 9.70904 | 0.471512 | ||||||||
\(425\) | 34.3521 | 1.66632 | ||||||||
\(426\) | 1.70711 | 0.0827095 | ||||||||
\(427\) | −6.15701 | −0.297958 | ||||||||
\(428\) | 12.2751 | 0.593341 | ||||||||
\(429\) | 3.14397 | 0.151792 | ||||||||
\(430\) | −4.15307 | −0.200279 | ||||||||
\(431\) | −0.310658 | −0.0149639 | −0.00748193 | − | 0.999972i | \(-0.502382\pi\) | ||||
−0.00748193 | + | 0.999972i | \(0.502382\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.72676 | −0.371324 | −0.185662 | − | 0.982614i | \(-0.559443\pi\) | ||||
−0.185662 | + | 0.982614i | \(0.559443\pi\) | |||||||
\(434\) | −14.8257 | −0.711656 | ||||||||
\(435\) | −3.36678 | −0.161425 | ||||||||
\(436\) | 19.6836 | 0.942672 | ||||||||
\(437\) | 7.00528 | 0.335108 | ||||||||
\(438\) | 0.395522 | 0.0188988 | ||||||||
\(439\) | 22.7682 | 1.08667 | 0.543333 | − | 0.839517i | \(-0.317162\pi\) | ||||
0.543333 | + | 0.839517i | \(0.317162\pi\) | |||||||
\(440\) | −2.08835 | −0.0995580 | ||||||||
\(441\) | −1.42277 | −0.0677508 | ||||||||
\(442\) | 7.53535 | 0.358420 | ||||||||
\(443\) | 16.7094 | 0.793888 | 0.396944 | − | 0.917843i | \(-0.370071\pi\) | ||||
0.396944 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(444\) | −10.8042 | −0.512746 | ||||||||
\(445\) | −11.6175 | −0.550724 | ||||||||
\(446\) | −9.14462 | −0.433010 | ||||||||
\(447\) | −10.5024 | −0.496748 | ||||||||
\(448\) | 2.36162 | 0.111576 | ||||||||
\(449\) | 28.7189 | 1.35533 | 0.677664 | − | 0.735372i | \(-0.262992\pi\) | ||||
0.677664 | + | 0.735372i | \(0.262992\pi\) | |||||||
\(450\) | 4.55879 | 0.214903 | ||||||||
\(451\) | −35.1500 | −1.65515 | ||||||||
\(452\) | −12.4526 | −0.585721 | ||||||||
\(453\) | 0.330883 | 0.0155463 | ||||||||
\(454\) | 0.990850 | 0.0465029 | ||||||||
\(455\) | −1.56868 | −0.0735408 | ||||||||
\(456\) | 5.47817 | 0.256539 | ||||||||
\(457\) | 1.32877 | 0.0621571 | 0.0310786 | − | 0.999517i | \(-0.490106\pi\) | ||||
0.0310786 | + | 0.999517i | \(0.490106\pi\) | |||||||
\(458\) | 0.230645 | 0.0107773 | ||||||||
\(459\) | 7.53535 | 0.351720 | ||||||||
\(460\) | −0.849405 | −0.0396037 | ||||||||
\(461\) | 7.92563 | 0.369133 | 0.184567 | − | 0.982820i | \(-0.440912\pi\) | ||||
0.184567 | + | 0.982820i | \(0.440912\pi\) | |||||||
\(462\) | −7.42484 | −0.345435 | ||||||||
\(463\) | 13.7247 | 0.637840 | 0.318920 | − | 0.947782i | \(-0.396680\pi\) | ||||
0.318920 | + | 0.947782i | \(0.396680\pi\) | |||||||
\(464\) | −5.06863 | −0.235305 | ||||||||
\(465\) | 4.16994 | 0.193376 | ||||||||
\(466\) | −29.6243 | −1.37232 | ||||||||
\(467\) | 23.7417 | 1.09863 | 0.549317 | − | 0.835614i | \(-0.314888\pi\) | ||||
0.549317 | + | 0.835614i | \(0.314888\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −16.0239 | −0.739915 | ||||||||
\(470\) | −5.76434 | −0.265889 | ||||||||
\(471\) | −6.48802 | −0.298952 | ||||||||
\(472\) | 10.6905 | 0.492071 | ||||||||
\(473\) | 19.6572 | 0.903841 | ||||||||
\(474\) | 2.79959 | 0.128589 | ||||||||
\(475\) | −24.9738 | −1.14588 | ||||||||
\(476\) | −17.7956 | −0.815661 | ||||||||
\(477\) | −9.70904 | −0.444546 | ||||||||
\(478\) | 12.1630 | 0.556323 | ||||||||
\(479\) | −37.4668 | −1.71190 | −0.855951 | − | 0.517057i | \(-0.827028\pi\) | ||||
−0.855951 | + | 0.517057i | \(0.827028\pi\) | |||||||
\(480\) | −0.664239 | −0.0303182 | ||||||||
\(481\) | 10.8042 | 0.492630 | ||||||||
\(482\) | 9.36359 | 0.426500 | ||||||||
\(483\) | −3.01995 | −0.137412 | ||||||||
\(484\) | −1.11548 | −0.0507036 | ||||||||
\(485\) | −6.12004 | −0.277897 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 38.2613 | 1.73379 | 0.866893 | − | 0.498494i | \(-0.166113\pi\) | ||||
0.866893 | + | 0.498494i | \(0.166113\pi\) | |||||||
\(488\) | 2.60711 | 0.118019 | ||||||||
\(489\) | 10.2456 | 0.463323 | ||||||||
\(490\) | −0.945057 | −0.0426933 | ||||||||
\(491\) | 33.2072 | 1.49862 | 0.749311 | − | 0.662218i | \(-0.230385\pi\) | ||||
0.749311 | + | 0.662218i | \(0.230385\pi\) | |||||||
\(492\) | −11.1801 | −0.504040 | ||||||||
\(493\) | 38.1939 | 1.72017 | ||||||||
\(494\) | −5.47817 | −0.246475 | ||||||||
\(495\) | 2.08835 | 0.0938642 | ||||||||
\(496\) | 6.27777 | 0.281880 | ||||||||
\(497\) | 4.03153 | 0.180839 | ||||||||
\(498\) | 11.4961 | 0.515151 | ||||||||
\(499\) | 17.9832 | 0.805039 | 0.402520 | − | 0.915411i | \(-0.368135\pi\) | ||||
0.402520 | + | 0.915411i | \(0.368135\pi\) | |||||||
\(500\) | 6.34932 | 0.283950 | ||||||||
\(501\) | −1.93544 | −0.0864693 | ||||||||
\(502\) | −24.7530 | −1.10478 | ||||||||
\(503\) | 10.8923 | 0.485663 | 0.242832 | − | 0.970068i | \(-0.421924\pi\) | ||||
0.242832 | + | 0.970068i | \(0.421924\pi\) | |||||||
\(504\) | −2.36162 | −0.105195 | ||||||||
\(505\) | −9.54981 | −0.424961 | ||||||||
\(506\) | 4.02039 | 0.178728 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −12.7497 | −0.565676 | ||||||||
\(509\) | −44.1708 | −1.95784 | −0.978918 | − | 0.204256i | \(-0.934523\pi\) | ||||
−0.978918 | + | 0.204256i | \(0.934523\pi\) | |||||||
\(510\) | 5.00528 | 0.221637 | ||||||||
\(511\) | 0.934071 | 0.0413209 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.47817 | −0.241867 | ||||||||
\(514\) | 9.92601 | 0.437817 | ||||||||
\(515\) | 0.664239 | 0.0292699 | ||||||||
\(516\) | 6.25237 | 0.275245 | ||||||||
\(517\) | 27.2837 | 1.19993 | ||||||||
\(518\) | −25.5154 | −1.12108 | ||||||||
\(519\) | 2.22848 | 0.0978195 | ||||||||
\(520\) | 0.664239 | 0.0291288 | ||||||||
\(521\) | 15.4635 | 0.677470 | 0.338735 | − | 0.940882i | \(-0.390001\pi\) | ||||
0.338735 | + | 0.940882i | \(0.390001\pi\) | |||||||
\(522\) | 5.06863 | 0.221848 | ||||||||
\(523\) | 24.4856 | 1.07068 | 0.535341 | − | 0.844636i | \(-0.320183\pi\) | ||||
0.535341 | + | 0.844636i | \(0.320183\pi\) | |||||||
\(524\) | −6.54233 | −0.285803 | ||||||||
\(525\) | 10.7661 | 0.469871 | ||||||||
\(526\) | −23.0280 | −1.00407 | ||||||||
\(527\) | −47.3052 | −2.06065 | ||||||||
\(528\) | 3.14397 | 0.136824 | ||||||||
\(529\) | −21.3648 | −0.928903 | ||||||||
\(530\) | −6.44912 | −0.280132 | ||||||||
\(531\) | −10.6905 | −0.463929 | ||||||||
\(532\) | 12.9373 | 0.560905 | ||||||||
\(533\) | 11.1801 | 0.484266 | ||||||||
\(534\) | 17.4900 | 0.756866 | ||||||||
\(535\) | −8.15362 | −0.352512 | ||||||||
\(536\) | 6.78514 | 0.293074 | ||||||||
\(537\) | 5.40080 | 0.233062 | ||||||||
\(538\) | −11.0757 | −0.477506 | ||||||||
\(539\) | 4.47313 | 0.192671 | ||||||||
\(540\) | 0.664239 | 0.0285843 | ||||||||
\(541\) | 12.8639 | 0.553063 | 0.276531 | − | 0.961005i | \(-0.410815\pi\) | ||||
0.276531 | + | 0.961005i | \(0.410815\pi\) | |||||||
\(542\) | −13.7124 | −0.588999 | ||||||||
\(543\) | 14.4182 | 0.618744 | ||||||||
\(544\) | 7.53535 | 0.323076 | ||||||||
\(545\) | −13.0746 | −0.560054 | ||||||||
\(546\) | 2.36162 | 0.101068 | ||||||||
\(547\) | 31.9973 | 1.36810 | 0.684052 | − | 0.729433i | \(-0.260216\pi\) | ||||
0.684052 | + | 0.729433i | \(0.260216\pi\) | |||||||
\(548\) | 18.3434 | 0.783592 | ||||||||
\(549\) | −2.60711 | −0.111269 | ||||||||
\(550\) | −14.3327 | −0.611147 | ||||||||
\(551\) | −27.7668 | −1.18291 | ||||||||
\(552\) | 1.27876 | 0.0544278 | ||||||||
\(553\) | 6.61156 | 0.281152 | ||||||||
\(554\) | −25.1561 | −1.06878 | ||||||||
\(555\) | 7.17659 | 0.304629 | ||||||||
\(556\) | 4.49746 | 0.190735 | ||||||||
\(557\) | −33.3350 | −1.41245 | −0.706225 | − | 0.707987i | \(-0.749603\pi\) | ||||
−0.706225 | + | 0.707987i | \(0.749603\pi\) | |||||||
\(558\) | −6.27777 | −0.265759 | ||||||||
\(559\) | −6.25237 | −0.264447 | ||||||||
\(560\) | −1.56868 | −0.0662888 | ||||||||
\(561\) | −23.6909 | −1.00023 | ||||||||
\(562\) | 19.4460 | 0.820280 | ||||||||
\(563\) | 13.5663 | 0.571753 | 0.285877 | − | 0.958266i | \(-0.407715\pi\) | ||||
0.285877 | + | 0.958266i | \(0.407715\pi\) | |||||||
\(564\) | 8.67811 | 0.365414 | ||||||||
\(565\) | 8.27150 | 0.347985 | ||||||||
\(566\) | 16.6056 | 0.697985 | ||||||||
\(567\) | 2.36162 | 0.0991786 | ||||||||
\(568\) | −1.70711 | −0.0716286 | ||||||||
\(569\) | 8.42617 | 0.353244 | 0.176622 | − | 0.984279i | \(-0.443483\pi\) | ||||
0.176622 | + | 0.984279i | \(0.443483\pi\) | |||||||
\(570\) | −3.63882 | −0.152413 | ||||||||
\(571\) | 2.49998 | 0.104621 | 0.0523105 | − | 0.998631i | \(-0.483341\pi\) | ||||
0.0523105 | + | 0.998631i | \(0.483341\pi\) | |||||||
\(572\) | −3.14397 | −0.131456 | ||||||||
\(573\) | −10.8810 | −0.454561 | ||||||||
\(574\) | −26.4032 | −1.10205 | ||||||||
\(575\) | −5.82961 | −0.243111 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.45831 | −0.352124 | −0.176062 | − | 0.984379i | \(-0.556336\pi\) | ||||
−0.176062 | + | 0.984379i | \(0.556336\pi\) | |||||||
\(578\) | −39.7815 | −1.65469 | ||||||||
\(579\) | 27.6749 | 1.15013 | ||||||||
\(580\) | 3.36678 | 0.139798 | ||||||||
\(581\) | 27.1493 | 1.12634 | ||||||||
\(582\) | 9.21361 | 0.381917 | ||||||||
\(583\) | 30.5249 | 1.26421 | ||||||||
\(584\) | −0.395522 | −0.0163668 | ||||||||
\(585\) | −0.664239 | −0.0274629 | ||||||||
\(586\) | −22.3887 | −0.924870 | ||||||||
\(587\) | 12.8004 | 0.528327 | 0.264164 | − | 0.964478i | \(-0.414904\pi\) | ||||
0.264164 | + | 0.964478i | \(0.414904\pi\) | |||||||
\(588\) | 1.42277 | 0.0586739 | ||||||||
\(589\) | 34.3907 | 1.41704 | ||||||||
\(590\) | −7.10106 | −0.292346 | ||||||||
\(591\) | 22.7122 | 0.934253 | ||||||||
\(592\) | 10.8042 | 0.444051 | ||||||||
\(593\) | 45.6065 | 1.87284 | 0.936418 | − | 0.350887i | \(-0.114120\pi\) | ||||
0.936418 | + | 0.350887i | \(0.114120\pi\) | |||||||
\(594\) | −3.14397 | −0.128998 | ||||||||
\(595\) | 11.8205 | 0.484595 | ||||||||
\(596\) | 10.5024 | 0.430196 | ||||||||
\(597\) | 10.5958 | 0.433658 | ||||||||
\(598\) | −1.27876 | −0.0522925 | ||||||||
\(599\) | 20.6359 | 0.843162 | 0.421581 | − | 0.906791i | \(-0.361475\pi\) | ||||
0.421581 | + | 0.906791i | \(0.361475\pi\) | |||||||
\(600\) | −4.55879 | −0.186112 | ||||||||
\(601\) | 42.0920 | 1.71697 | 0.858483 | − | 0.512842i | \(-0.171407\pi\) | ||||
0.858483 | + | 0.512842i | \(0.171407\pi\) | |||||||
\(602\) | 14.7657 | 0.601805 | ||||||||
\(603\) | −6.78514 | −0.276312 | ||||||||
\(604\) | −0.330883 | −0.0134635 | ||||||||
\(605\) | 0.740945 | 0.0301237 | ||||||||
\(606\) | 14.3771 | 0.584028 | ||||||||
\(607\) | 5.21766 | 0.211778 | 0.105889 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105889 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(608\) | −5.47817 | −0.222169 | ||||||||
\(609\) | 11.9702 | 0.485055 | ||||||||
\(610\) | −1.73175 | −0.0701164 | ||||||||
\(611\) | −8.67811 | −0.351079 | ||||||||
\(612\) | −7.53535 | −0.304599 | ||||||||
\(613\) | 7.11873 | 0.287523 | 0.143761 | − | 0.989612i | \(-0.454080\pi\) | ||||
0.143761 | + | 0.989612i | \(0.454080\pi\) | |||||||
\(614\) | −8.75392 | −0.353279 | ||||||||
\(615\) | 7.42629 | 0.299457 | ||||||||
\(616\) | 7.42484 | 0.299155 | ||||||||
\(617\) | 20.5398 | 0.826900 | 0.413450 | − | 0.910527i | \(-0.364324\pi\) | ||||
0.413450 | + | 0.910527i | \(0.364324\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 14.3158 | 0.575400 | 0.287700 | − | 0.957721i | \(-0.407109\pi\) | ||||
0.287700 | + | 0.957721i | \(0.407109\pi\) | |||||||
\(620\) | −4.16994 | −0.167469 | ||||||||
\(621\) | −1.27876 | −0.0513150 | ||||||||
\(622\) | −3.32236 | −0.133214 | ||||||||
\(623\) | 41.3046 | 1.65484 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 18.5765 | 0.743058 | ||||||||
\(626\) | −13.9039 | −0.555711 | ||||||||
\(627\) | 17.2232 | 0.687828 | ||||||||
\(628\) | 6.48802 | 0.258900 | ||||||||
\(629\) | −81.4136 | −3.24617 | ||||||||
\(630\) | 1.56868 | 0.0624977 | ||||||||
\(631\) | −3.55289 | −0.141438 | −0.0707191 | − | 0.997496i | \(-0.522529\pi\) | ||||
−0.0707191 | + | 0.997496i | \(0.522529\pi\) | |||||||
\(632\) | −2.79959 | −0.111362 | ||||||||
\(633\) | 23.9450 | 0.951728 | ||||||||
\(634\) | 12.9648 | 0.514899 | ||||||||
\(635\) | 8.46885 | 0.336076 | ||||||||
\(636\) | 9.70904 | 0.384988 | ||||||||
\(637\) | −1.42277 | −0.0563720 | ||||||||
\(638\) | −15.9356 | −0.630896 | ||||||||
\(639\) | 1.70711 | 0.0675321 | ||||||||
\(640\) | 0.664239 | 0.0262564 | ||||||||
\(641\) | −3.75222 | −0.148204 | −0.0741018 | − | 0.997251i | \(-0.523609\pi\) | ||||
−0.0741018 | + | 0.997251i | \(0.523609\pi\) | |||||||
\(642\) | 12.2751 | 0.484461 | ||||||||
\(643\) | −8.72343 | −0.344018 | −0.172009 | − | 0.985095i | \(-0.555026\pi\) | ||||
−0.172009 | + | 0.985095i | \(0.555026\pi\) | |||||||
\(644\) | 3.01995 | 0.119003 | ||||||||
\(645\) | −4.15307 | −0.163527 | ||||||||
\(646\) | 41.2800 | 1.62414 | ||||||||
\(647\) | 45.6646 | 1.79526 | 0.897630 | − | 0.440749i | \(-0.145287\pi\) | ||||
0.897630 | + | 0.440749i | \(0.145287\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 33.6106 | 1.31933 | ||||||||
\(650\) | 4.55879 | 0.178810 | ||||||||
\(651\) | −14.8257 | −0.581064 | ||||||||
\(652\) | −10.2456 | −0.401249 | ||||||||
\(653\) | −41.8437 | −1.63747 | −0.818734 | − | 0.574173i | \(-0.805324\pi\) | ||||
−0.818734 | + | 0.574173i | \(0.805324\pi\) | |||||||
\(654\) | 19.6836 | 0.769689 | ||||||||
\(655\) | 4.34567 | 0.169799 | ||||||||
\(656\) | 11.1801 | 0.436511 | ||||||||
\(657\) | 0.395522 | 0.0154308 | ||||||||
\(658\) | 20.4944 | 0.798954 | ||||||||
\(659\) | 27.0576 | 1.05402 | 0.527008 | − | 0.849860i | \(-0.323314\pi\) | ||||
0.527008 | + | 0.849860i | \(0.323314\pi\) | |||||||
\(660\) | −2.08835 | −0.0812887 | ||||||||
\(661\) | −22.9241 | −0.891643 | −0.445822 | − | 0.895122i | \(-0.647088\pi\) | ||||
−0.445822 | + | 0.895122i | \(0.647088\pi\) | |||||||
\(662\) | −28.9193 | −1.12398 | ||||||||
\(663\) | 7.53535 | 0.292649 | ||||||||
\(664\) | −11.4961 | −0.446134 | ||||||||
\(665\) | −8.59349 | −0.333241 | ||||||||
\(666\) | −10.8042 | −0.418655 | ||||||||
\(667\) | −6.48157 | −0.250968 | ||||||||
\(668\) | 1.93544 | 0.0748846 | ||||||||
\(669\) | −9.14462 | −0.353552 | ||||||||
\(670\) | −4.50696 | −0.174119 | ||||||||
\(671\) | 8.19668 | 0.316429 | ||||||||
\(672\) | 2.36162 | 0.0911013 | ||||||||
\(673\) | −20.6263 | −0.795084 | −0.397542 | − | 0.917584i | \(-0.630137\pi\) | ||||
−0.397542 | + | 0.917584i | \(0.630137\pi\) | |||||||
\(674\) | 24.6699 | 0.950251 | ||||||||
\(675\) | 4.55879 | 0.175468 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −32.8317 | −1.26183 | −0.630913 | − | 0.775854i | \(-0.717320\pi\) | ||||
−0.630913 | + | 0.775854i | \(0.717320\pi\) | |||||||
\(678\) | −12.4526 | −0.478239 | ||||||||
\(679\) | 21.7590 | 0.835035 | ||||||||
\(680\) | −5.00528 | −0.191944 | ||||||||
\(681\) | 0.990850 | 0.0379694 | ||||||||
\(682\) | 19.7371 | 0.755772 | ||||||||
\(683\) | 9.15816 | 0.350427 | 0.175214 | − | 0.984530i | \(-0.443938\pi\) | ||||
0.175214 | + | 0.984530i | \(0.443938\pi\) | |||||||
\(684\) | 5.47817 | 0.209463 | ||||||||
\(685\) | −12.1844 | −0.465543 | ||||||||
\(686\) | 19.8913 | 0.759455 | ||||||||
\(687\) | 0.230645 | 0.00879965 | ||||||||
\(688\) | −6.25237 | −0.238370 | ||||||||
\(689\) | −9.70904 | −0.369885 | ||||||||
\(690\) | −0.849405 | −0.0323363 | ||||||||
\(691\) | −38.4791 | −1.46381 | −0.731907 | − | 0.681404i | \(-0.761370\pi\) | ||||
−0.731907 | + | 0.681404i | \(0.761370\pi\) | |||||||
\(692\) | −2.22848 | −0.0847142 | ||||||||
\(693\) | −7.42484 | −0.282046 | ||||||||
\(694\) | 3.17151 | 0.120389 | ||||||||
\(695\) | −2.98739 | −0.113318 | ||||||||
\(696\) | −5.06863 | −0.192126 | ||||||||
\(697\) | −84.2463 | −3.19106 | ||||||||
\(698\) | 31.3835 | 1.18788 | ||||||||
\(699\) | −29.6243 | −1.12049 | ||||||||
\(700\) | −10.7661 | −0.406921 | ||||||||
\(701\) | 13.1508 | 0.496699 | 0.248350 | − | 0.968670i | \(-0.420112\pi\) | ||||
0.248350 | + | 0.968670i | \(0.420112\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 59.1874 | 2.23229 | ||||||||
\(704\) | −3.14397 | −0.118493 | ||||||||
\(705\) | −5.76434 | −0.217098 | ||||||||
\(706\) | −17.0417 | −0.641372 | ||||||||
\(707\) | 33.9531 | 1.27694 | ||||||||
\(708\) | 10.6905 | 0.401774 | ||||||||
\(709\) | 25.9875 | 0.975981 | 0.487991 | − | 0.872849i | \(-0.337730\pi\) | ||||
0.487991 | + | 0.872849i | \(0.337730\pi\) | |||||||
\(710\) | 1.13393 | 0.0425555 | ||||||||
\(711\) | 2.79959 | 0.104993 | ||||||||
\(712\) | −17.4900 | −0.655465 | ||||||||
\(713\) | 8.02778 | 0.300643 | ||||||||
\(714\) | −17.7956 | −0.665984 | ||||||||
\(715\) | 2.08835 | 0.0780997 | ||||||||
\(716\) | −5.40080 | −0.201838 | ||||||||
\(717\) | 12.1630 | 0.454236 | ||||||||
\(718\) | −25.2917 | −0.943877 | ||||||||
\(719\) | 19.2146 | 0.716585 | 0.358293 | − | 0.933609i | \(-0.383359\pi\) | ||||
0.358293 | + | 0.933609i | \(0.383359\pi\) | |||||||
\(720\) | −0.664239 | −0.0247547 | ||||||||
\(721\) | −2.36162 | −0.0879512 | ||||||||
\(722\) | −11.0104 | −0.409763 | ||||||||
\(723\) | 9.36359 | 0.348236 | ||||||||
\(724\) | −14.4182 | −0.535848 | ||||||||
\(725\) | 23.1068 | 0.858165 | ||||||||
\(726\) | −1.11548 | −0.0413993 | ||||||||
\(727\) | 45.1083 | 1.67297 | 0.836487 | − | 0.547986i | \(-0.184605\pi\) | ||||
0.836487 | + | 0.547986i | \(0.184605\pi\) | |||||||
\(728\) | −2.36162 | −0.0875273 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.262721 | 0.00972375 | ||||||||
\(731\) | 47.1138 | 1.74257 | ||||||||
\(732\) | 2.60711 | 0.0963617 | ||||||||
\(733\) | 39.0830 | 1.44356 | 0.721782 | − | 0.692120i | \(-0.243323\pi\) | ||||
0.721782 | + | 0.692120i | \(0.243323\pi\) | |||||||
\(734\) | −13.0779 | −0.482715 | ||||||||
\(735\) | −0.945057 | −0.0348590 | ||||||||
\(736\) | −1.27876 | −0.0471358 | ||||||||
\(737\) | 21.3323 | 0.785784 | ||||||||
\(738\) | −11.1801 | −0.411547 | ||||||||
\(739\) | 38.5615 | 1.41851 | 0.709254 | − | 0.704954i | \(-0.249032\pi\) | ||||
0.709254 | + | 0.704954i | \(0.249032\pi\) | |||||||
\(740\) | −7.17659 | −0.263817 | ||||||||
\(741\) | −5.47817 | −0.201246 | ||||||||
\(742\) | 22.9290 | 0.841751 | ||||||||
\(743\) | −11.8727 | −0.435568 | −0.217784 | − | 0.975997i | \(-0.569883\pi\) | ||||
−0.217784 | + | 0.975997i | \(0.569883\pi\) | |||||||
\(744\) | 6.27777 | 0.230154 | ||||||||
\(745\) | −6.97612 | −0.255585 | ||||||||
\(746\) | 25.9846 | 0.951365 | ||||||||
\(747\) | 11.4961 | 0.420619 | ||||||||
\(748\) | 23.6909 | 0.866225 | ||||||||
\(749\) | 28.9891 | 1.05924 | ||||||||
\(750\) | 6.34932 | 0.231844 | ||||||||
\(751\) | 12.6541 | 0.461755 | 0.230878 | − | 0.972983i | \(-0.425840\pi\) | ||||
0.230878 | + | 0.972983i | \(0.425840\pi\) | |||||||
\(752\) | −8.67811 | −0.316458 | ||||||||
\(753\) | −24.7530 | −0.902048 | ||||||||
\(754\) | 5.06863 | 0.184589 | ||||||||
\(755\) | 0.219786 | 0.00799882 | ||||||||
\(756\) | −2.36162 | −0.0858912 | ||||||||
\(757\) | −38.6113 | −1.40335 | −0.701675 | − | 0.712497i | \(-0.747564\pi\) | ||||
−0.701675 | + | 0.712497i | \(0.747564\pi\) | |||||||
\(758\) | 14.4762 | 0.525798 | ||||||||
\(759\) | 4.02039 | 0.145931 | ||||||||
\(760\) | 3.63882 | 0.131994 | ||||||||
\(761\) | −27.9940 | −1.01478 | −0.507392 | − | 0.861716i | \(-0.669390\pi\) | ||||
−0.507392 | + | 0.861716i | \(0.669390\pi\) | |||||||
\(762\) | −12.7497 | −0.461873 | ||||||||
\(763\) | 46.4851 | 1.68287 | ||||||||
\(764\) | 10.8810 | 0.393662 | ||||||||
\(765\) | 5.00528 | 0.180966 | ||||||||
\(766\) | −29.6314 | −1.07062 | ||||||||
\(767\) | −10.6905 | −0.386012 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 0.756287 | 0.0272724 | 0.0136362 | − | 0.999907i | \(-0.495659\pi\) | ||||
0.0136362 | + | 0.999907i | \(0.495659\pi\) | |||||||
\(770\) | −4.93187 | −0.177732 | ||||||||
\(771\) | 9.92601 | 0.357476 | ||||||||
\(772\) | −27.6749 | −0.996043 | ||||||||
\(773\) | −47.1362 | −1.69537 | −0.847686 | − | 0.530498i | \(-0.822005\pi\) | ||||
−0.847686 | + | 0.530498i | \(0.822005\pi\) | |||||||
\(774\) | 6.25237 | 0.224737 | ||||||||
\(775\) | −28.6190 | −1.02802 | ||||||||
\(776\) | −9.21361 | −0.330749 | ||||||||
\(777\) | −25.5154 | −0.915361 | ||||||||
\(778\) | 31.9402 | 1.14511 | ||||||||
\(779\) | 61.2467 | 2.19439 | ||||||||
\(780\) | 0.664239 | 0.0237836 | ||||||||
\(781\) | −5.36708 | −0.192049 | ||||||||
\(782\) | 9.63593 | 0.344580 | ||||||||
\(783\) | 5.06863 | 0.181138 | ||||||||
\(784\) | −1.42277 | −0.0508131 | ||||||||
\(785\) | −4.30960 | −0.153816 | ||||||||
\(786\) | −6.54233 | −0.233357 | ||||||||
\(787\) | −32.8581 | −1.17127 | −0.585633 | − | 0.810577i | \(-0.699154\pi\) | ||||
−0.585633 | + | 0.810577i | \(0.699154\pi\) | |||||||
\(788\) | −22.7122 | −0.809087 | ||||||||
\(789\) | −23.0280 | −0.819818 | ||||||||
\(790\) | 1.85960 | 0.0661615 | ||||||||
\(791\) | −29.4083 | −1.04564 | ||||||||
\(792\) | 3.14397 | 0.111716 | ||||||||
\(793\) | −2.60711 | −0.0925814 | ||||||||
\(794\) | 1.91074 | 0.0678096 | ||||||||
\(795\) | −6.44912 | −0.228727 | ||||||||
\(796\) | −10.5958 | −0.375559 | ||||||||
\(797\) | 30.1082 | 1.06649 | 0.533243 | − | 0.845962i | \(-0.320973\pi\) | ||||
0.533243 | + | 0.845962i | \(0.320973\pi\) | |||||||
\(798\) | 12.9373 | 0.457977 | ||||||||
\(799\) | 65.3926 | 2.31342 | ||||||||
\(800\) | 4.55879 | 0.161177 | ||||||||
\(801\) | 17.4900 | 0.617978 | ||||||||
\(802\) | −24.2814 | −0.857405 | ||||||||
\(803\) | −1.24351 | −0.0438824 | ||||||||
\(804\) | 6.78514 | 0.239294 | ||||||||
\(805\) | −2.00597 | −0.0707011 | ||||||||
\(806\) | −6.27777 | −0.221125 | ||||||||
\(807\) | −11.0757 | −0.389882 | ||||||||
\(808\) | −14.3771 | −0.505783 | ||||||||
\(809\) | −42.1891 | −1.48329 | −0.741645 | − | 0.670792i | \(-0.765954\pi\) | ||||
−0.741645 | + | 0.670792i | \(0.765954\pi\) | |||||||
\(810\) | 0.664239 | 0.0233390 | ||||||||
\(811\) | 49.6828 | 1.74460 | 0.872300 | − | 0.488971i | \(-0.162628\pi\) | ||||
0.872300 | + | 0.488971i | \(0.162628\pi\) | |||||||
\(812\) | −11.9702 | −0.420070 | ||||||||
\(813\) | −13.7124 | −0.480915 | ||||||||
\(814\) | 33.9681 | 1.19058 | ||||||||
\(815\) | 6.80554 | 0.238388 | ||||||||
\(816\) | 7.53535 | 0.263790 | ||||||||
\(817\) | −34.2516 | −1.19831 | ||||||||
\(818\) | −8.85686 | −0.309673 | ||||||||
\(819\) | 2.36162 | 0.0825216 | ||||||||
\(820\) | −7.42629 | −0.259337 | ||||||||
\(821\) | 7.94747 | 0.277369 | 0.138684 | − | 0.990337i | \(-0.455713\pi\) | ||||
0.138684 | + | 0.990337i | \(0.455713\pi\) | |||||||
\(822\) | 18.3434 | 0.639800 | ||||||||
\(823\) | −4.62944 | −0.161372 | −0.0806860 | − | 0.996740i | \(-0.525711\pi\) | ||||
−0.0806860 | + | 0.996740i | \(0.525711\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −14.3327 | −0.498999 | ||||||||
\(826\) | 25.2469 | 0.878452 | ||||||||
\(827\) | 5.49732 | 0.191161 | 0.0955804 | − | 0.995422i | \(-0.469529\pi\) | ||||
0.0955804 | + | 0.995422i | \(0.469529\pi\) | |||||||
\(828\) | 1.27876 | 0.0444401 | ||||||||
\(829\) | −19.6703 | −0.683179 | −0.341589 | − | 0.939849i | \(-0.610965\pi\) | ||||
−0.341589 | + | 0.939849i | \(0.610965\pi\) | |||||||
\(830\) | 7.63614 | 0.265054 | ||||||||
\(831\) | −25.1561 | −0.872656 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 10.7210 | 0.371462 | ||||||||
\(834\) | 4.49746 | 0.155734 | ||||||||
\(835\) | −1.28560 | −0.0444900 | ||||||||
\(836\) | −17.2232 | −0.595676 | ||||||||
\(837\) | −6.27777 | −0.216991 | ||||||||
\(838\) | −24.4543 | −0.844758 | ||||||||
\(839\) | 8.90073 | 0.307287 | 0.153644 | − | 0.988126i | \(-0.450899\pi\) | ||||
0.153644 | + | 0.988126i | \(0.450899\pi\) | |||||||
\(840\) | −1.56868 | −0.0541246 | ||||||||
\(841\) | −3.30901 | −0.114104 | ||||||||
\(842\) | −28.6102 | −0.985972 | ||||||||
\(843\) | 19.4460 | 0.669756 | ||||||||
\(844\) | −23.9450 | −0.824220 | ||||||||
\(845\) | −0.664239 | −0.0228505 | ||||||||
\(846\) | 8.67811 | 0.298360 | ||||||||
\(847\) | −2.63433 | −0.0905168 | ||||||||
\(848\) | −9.70904 | −0.333410 | ||||||||
\(849\) | 16.6056 | 0.569903 | ||||||||
\(850\) | −34.3521 | −1.17827 | ||||||||
\(851\) | 13.8160 | 0.473608 | ||||||||
\(852\) | −1.70711 | −0.0584845 | ||||||||
\(853\) | 36.4129 | 1.24675 | 0.623376 | − | 0.781922i | \(-0.285760\pi\) | ||||
0.623376 | + | 0.781922i | \(0.285760\pi\) | |||||||
\(854\) | 6.15701 | 0.210688 | ||||||||
\(855\) | −3.63882 | −0.124445 | ||||||||
\(856\) | −12.2751 | −0.419555 | ||||||||
\(857\) | −24.7991 | −0.847121 | −0.423561 | − | 0.905868i | \(-0.639220\pi\) | ||||
−0.423561 | + | 0.905868i | \(0.639220\pi\) | |||||||
\(858\) | −3.14397 | −0.107333 | ||||||||
\(859\) | 36.7409 | 1.25358 | 0.626792 | − | 0.779187i | \(-0.284368\pi\) | ||||
0.626792 | + | 0.779187i | \(0.284368\pi\) | |||||||
\(860\) | 4.15307 | 0.141619 | ||||||||
\(861\) | −26.4032 | −0.899819 | ||||||||
\(862\) | 0.310658 | 0.0105810 | ||||||||
\(863\) | −15.9874 | −0.544217 | −0.272109 | − | 0.962267i | \(-0.587721\pi\) | ||||
−0.272109 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.48025 | 0.0503299 | ||||||||
\(866\) | 7.72676 | 0.262566 | ||||||||
\(867\) | −39.7815 | −1.35105 | ||||||||
\(868\) | 14.8257 | 0.503216 | ||||||||
\(869\) | −8.80182 | −0.298581 | ||||||||
\(870\) | 3.36678 | 0.114145 | ||||||||
\(871\) | −6.78514 | −0.229906 | ||||||||
\(872\) | −19.6836 | −0.666570 | ||||||||
\(873\) | 9.21361 | 0.311834 | ||||||||
\(874\) | −7.00528 | −0.236957 | ||||||||
\(875\) | 14.9947 | 0.506912 | ||||||||
\(876\) | −0.395522 | −0.0133634 | ||||||||
\(877\) | 6.44711 | 0.217703 | 0.108852 | − | 0.994058i | \(-0.465283\pi\) | ||||
0.108852 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(878\) | −22.7682 | −0.768389 | ||||||||
\(879\) | −22.3887 | −0.755153 | ||||||||
\(880\) | 2.08835 | 0.0703981 | ||||||||
\(881\) | −0.521288 | −0.0175627 | −0.00878133 | − | 0.999961i | \(-0.502795\pi\) | ||||
−0.00878133 | + | 0.999961i | \(0.502795\pi\) | |||||||
\(882\) | 1.42277 | 0.0479070 | ||||||||
\(883\) | −5.73123 | −0.192871 | −0.0964355 | − | 0.995339i | \(-0.530744\pi\) | ||||
−0.0964355 | + | 0.995339i | \(0.530744\pi\) | |||||||
\(884\) | −7.53535 | −0.253441 | ||||||||
\(885\) | −7.10106 | −0.238700 | ||||||||
\(886\) | −16.7094 | −0.561363 | ||||||||
\(887\) | −21.9178 | −0.735927 | −0.367963 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367963 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(888\) | 10.8042 | 0.362566 | ||||||||
\(889\) | −30.1099 | −1.00985 | ||||||||
\(890\) | 11.6175 | 0.389421 | ||||||||
\(891\) | −3.14397 | −0.105327 | ||||||||
\(892\) | 9.14462 | 0.306185 | ||||||||
\(893\) | −47.5402 | −1.59087 | ||||||||
\(894\) | 10.5024 | 0.351254 | ||||||||
\(895\) | 3.58743 | 0.119914 | ||||||||
\(896\) | −2.36162 | −0.0788961 | ||||||||
\(897\) | −1.27876 | −0.0426967 | ||||||||
\(898\) | −28.7189 | −0.958362 | ||||||||
\(899\) | −31.8197 | −1.06125 | ||||||||
\(900\) | −4.55879 | −0.151960 | ||||||||
\(901\) | 73.1610 | 2.43735 | ||||||||
\(902\) | 35.1500 | 1.17037 | ||||||||
\(903\) | 14.7657 | 0.491372 | ||||||||
\(904\) | 12.4526 | 0.414167 | ||||||||
\(905\) | 9.57714 | 0.318355 | ||||||||
\(906\) | −0.330883 | −0.0109929 | ||||||||
\(907\) | 28.4556 | 0.944851 | 0.472426 | − | 0.881370i | \(-0.343378\pi\) | ||||
0.472426 | + | 0.881370i | \(0.343378\pi\) | |||||||
\(908\) | −0.990850 | −0.0328825 | ||||||||
\(909\) | 14.3771 | 0.476857 | ||||||||
\(910\) | 1.56868 | 0.0520012 | ||||||||
\(911\) | 18.7391 | 0.620853 | 0.310427 | − | 0.950597i | \(-0.399528\pi\) | ||||
0.310427 | + | 0.950597i | \(0.399528\pi\) | |||||||
\(912\) | −5.47817 | −0.181400 | ||||||||
\(913\) | −36.1433 | −1.19617 | ||||||||
\(914\) | −1.32877 | −0.0439517 | ||||||||
\(915\) | −1.73175 | −0.0572498 | ||||||||
\(916\) | −0.230645 | −0.00762072 | ||||||||
\(917\) | −15.4505 | −0.510220 | ||||||||
\(918\) | −7.53535 | −0.248704 | ||||||||
\(919\) | −47.2334 | −1.55809 | −0.779044 | − | 0.626970i | \(-0.784295\pi\) | ||||
−0.779044 | + | 0.626970i | \(0.784295\pi\) | |||||||
\(920\) | 0.849405 | 0.0280040 | ||||||||
\(921\) | −8.75392 | −0.288451 | ||||||||
\(922\) | −7.92563 | −0.261017 | ||||||||
\(923\) | 1.70711 | 0.0561901 | ||||||||
\(924\) | 7.42484 | 0.244259 | ||||||||
\(925\) | −49.2541 | −1.61947 | ||||||||
\(926\) | −13.7247 | −0.451021 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 5.06863 | 0.166386 | ||||||||
\(929\) | −10.0189 | −0.328709 | −0.164354 | − | 0.986401i | \(-0.552554\pi\) | ||||
−0.164354 | + | 0.986401i | \(0.552554\pi\) | |||||||
\(930\) | −4.16994 | −0.136738 | ||||||||
\(931\) | −7.79416 | −0.255443 | ||||||||
\(932\) | 29.6243 | 0.970377 | ||||||||
\(933\) | −3.32236 | −0.108769 | ||||||||
\(934\) | −23.7417 | −0.776851 | ||||||||
\(935\) | −15.7364 | −0.514636 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −43.2306 | −1.41228 | −0.706140 | − | 0.708072i | \(-0.749565\pi\) | ||||
−0.706140 | + | 0.708072i | \(0.749565\pi\) | |||||||
\(938\) | 16.0239 | 0.523199 | ||||||||
\(939\) | −13.9039 | −0.453736 | ||||||||
\(940\) | 5.76434 | 0.188012 | ||||||||
\(941\) | 6.82721 | 0.222561 | 0.111280 | − | 0.993789i | \(-0.464505\pi\) | ||||
0.111280 | + | 0.993789i | \(0.464505\pi\) | |||||||
\(942\) | 6.48802 | 0.211391 | ||||||||
\(943\) | 14.2967 | 0.465566 | ||||||||
\(944\) | −10.6905 | −0.347947 | ||||||||
\(945\) | 1.56868 | 0.0510291 | ||||||||
\(946\) | −19.6572 | −0.639112 | ||||||||
\(947\) | −26.7614 | −0.869630 | −0.434815 | − | 0.900520i | \(-0.643186\pi\) | ||||
−0.434815 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(948\) | −2.79959 | −0.0909265 | ||||||||
\(949\) | 0.395522 | 0.0128392 | ||||||||
\(950\) | 24.9738 | 0.810258 | ||||||||
\(951\) | 12.9648 | 0.420413 | ||||||||
\(952\) | 17.7956 | 0.576759 | ||||||||
\(953\) | 38.6543 | 1.25213 | 0.626067 | − | 0.779769i | \(-0.284663\pi\) | ||||
0.626067 | + | 0.779769i | \(0.284663\pi\) | |||||||
\(954\) | 9.70904 | 0.314342 | ||||||||
\(955\) | −7.22761 | −0.233880 | ||||||||
\(956\) | −12.1630 | −0.393380 | ||||||||
\(957\) | −15.9356 | −0.515125 | ||||||||
\(958\) | 37.4668 | 1.21050 | ||||||||
\(959\) | 43.3201 | 1.39888 | ||||||||
\(960\) | 0.664239 | 0.0214382 | ||||||||
\(961\) | 8.41038 | 0.271302 | ||||||||
\(962\) | −10.8042 | −0.348342 | ||||||||
\(963\) | 12.2751 | 0.395560 | ||||||||
\(964\) | −9.36359 | −0.301581 | ||||||||
\(965\) | 18.3828 | 0.591763 | ||||||||
\(966\) | 3.01995 | 0.0971653 | ||||||||
\(967\) | −4.22906 | −0.135997 | −0.0679986 | − | 0.997685i | \(-0.521661\pi\) | ||||
−0.0679986 | + | 0.997685i | \(0.521661\pi\) | |||||||
\(968\) | 1.11548 | 0.0358529 | ||||||||
\(969\) | 41.2800 | 1.32610 | ||||||||
\(970\) | 6.12004 | 0.196503 | ||||||||
\(971\) | −17.2273 | −0.552851 | −0.276426 | − | 0.961035i | \(-0.589150\pi\) | ||||
−0.276426 | + | 0.961035i | \(0.589150\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 10.6213 | 0.340503 | ||||||||
\(974\) | −38.2613 | −1.22597 | ||||||||
\(975\) | 4.55879 | 0.145998 | ||||||||
\(976\) | −2.60711 | −0.0834517 | ||||||||
\(977\) | 25.4933 | 0.815604 | 0.407802 | − | 0.913070i | \(-0.366295\pi\) | ||||
0.407802 | + | 0.913070i | \(0.366295\pi\) | |||||||
\(978\) | −10.2456 | −0.327619 | ||||||||
\(979\) | −54.9879 | −1.75742 | ||||||||
\(980\) | 0.945057 | 0.0301887 | ||||||||
\(981\) | 19.6836 | 0.628448 | ||||||||
\(982\) | −33.2072 | −1.05969 | ||||||||
\(983\) | 13.7769 | 0.439414 | 0.219707 | − | 0.975566i | \(-0.429490\pi\) | ||||
0.219707 | + | 0.975566i | \(0.429490\pi\) | |||||||
\(984\) | 11.1801 | 0.356410 | ||||||||
\(985\) | 15.0863 | 0.480690 | ||||||||
\(986\) | −38.1939 | −1.21634 | ||||||||
\(987\) | 20.4944 | 0.652343 | ||||||||
\(988\) | 5.47817 | 0.174284 | ||||||||
\(989\) | −7.99531 | −0.254236 | ||||||||
\(990\) | −2.08835 | −0.0663720 | ||||||||
\(991\) | 14.8256 | 0.470952 | 0.235476 | − | 0.971880i | \(-0.424335\pi\) | ||||
0.235476 | + | 0.971880i | \(0.424335\pi\) | |||||||
\(992\) | −6.27777 | −0.199319 | ||||||||
\(993\) | −28.9193 | −0.917725 | ||||||||
\(994\) | −4.03153 | −0.127872 | ||||||||
\(995\) | 7.03816 | 0.223125 | ||||||||
\(996\) | −11.4961 | −0.364267 | ||||||||
\(997\) | −18.5990 | −0.589036 | −0.294518 | − | 0.955646i | \(-0.595159\pi\) | ||||
−0.294518 | + | 0.955646i | \(0.595159\pi\) | |||||||
\(998\) | −17.9832 | −0.569249 | ||||||||
\(999\) | −10.8042 | −0.341830 |
(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 | 8034.2.a.z.1.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.7 | ✓ | 14 | 1.1 | even | 1 | trivial |