Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.523976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(5\) | 3.20147 | 1.43174 | 0.715871 | − | 0.698233i | \(-0.246030\pi\) | ||||
0.715871 | + | 0.698233i | \(0.246030\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.20147 | 1.01239 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.40294 | 1.77586 | 0.887929 | − | 0.459981i | \(-0.152144\pi\) | ||||
0.887929 | + | 0.459981i | \(0.152144\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.20147 | −0.826617 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.15352 | −0.264636 | −0.132318 | − | 0.991207i | \(-0.542242\pi\) | ||||
−0.132318 | + | 0.991207i | \(0.542242\pi\) | |||||||
\(20\) | 3.20147 | 0.715871 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.95205 | 0.407030 | 0.203515 | − | 0.979072i | \(-0.434763\pi\) | ||||
0.203515 | + | 0.979072i | \(0.434763\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 5.24943 | 1.04989 | ||||||||
\(26\) | 6.40294 | 1.25572 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.24943 | 1.34618 | 0.673092 | − | 0.739559i | \(-0.264966\pi\) | ||||
0.673092 | + | 0.739559i | \(0.264966\pi\) | |||||||
\(30\) | −3.20147 | −0.584506 | ||||||||
\(31\) | −10.4989 | −1.88565 | −0.942825 | − | 0.333289i | \(-0.891841\pi\) | ||||
−0.942825 | + | 0.333289i | \(0.891841\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.15352 | 0.847233 | 0.423617 | − | 0.905842i | \(-0.360760\pi\) | ||||
0.423617 | + | 0.905842i | \(0.360760\pi\) | |||||||
\(38\) | −1.15352 | −0.187126 | ||||||||
\(39\) | −6.40294 | −1.02529 | ||||||||
\(40\) | 3.20147 | 0.506197 | ||||||||
\(41\) | −8.24943 | −1.28834 | −0.644172 | − | 0.764881i | \(-0.722798\pi\) | ||||
−0.644172 | + | 0.764881i | \(0.722798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.15352 | 0.785904 | 0.392952 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392952 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 3.20147 | 0.477247 | ||||||||
\(46\) | 1.95205 | 0.287814 | ||||||||
\(47\) | 6.04795 | 0.882185 | 0.441092 | − | 0.897462i | \(-0.354591\pi\) | ||||
0.441092 | + | 0.897462i | \(0.354591\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.24943 | 0.742381 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 6.40294 | 0.887929 | ||||||||
\(53\) | −6.40294 | −0.879512 | −0.439756 | − | 0.898117i | \(-0.644935\pi\) | ||||
−0.439756 | + | 0.898117i | \(0.644935\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.20147 | 0.431686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.15352 | 0.152787 | ||||||||
\(58\) | 7.24943 | 0.951896 | ||||||||
\(59\) | −11.5565 | −1.50452 | −0.752262 | − | 0.658864i | \(-0.771037\pi\) | ||||
−0.752262 | + | 0.658864i | \(0.771037\pi\) | |||||||
\(60\) | −3.20147 | −0.413308 | ||||||||
\(61\) | −9.70032 | −1.24200 | −0.621000 | − | 0.783811i | \(-0.713273\pi\) | ||||
−0.621000 | + | 0.783811i | \(0.713273\pi\) | |||||||
\(62\) | −10.4989 | −1.33336 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 20.4989 | 2.54257 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 6.24943 | 0.763489 | 0.381744 | − | 0.924268i | \(-0.375323\pi\) | ||||
0.381744 | + | 0.924268i | \(0.375323\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −1.95205 | −0.234999 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.24943 | 0.622992 | 0.311496 | − | 0.950247i | \(-0.399170\pi\) | ||||
0.311496 | + | 0.950247i | \(0.399170\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.09591 | 0.245307 | 0.122654 | − | 0.992450i | \(-0.460860\pi\) | ||||
0.122654 | + | 0.992450i | \(0.460860\pi\) | |||||||
\(74\) | 5.15352 | 0.599084 | ||||||||
\(75\) | −5.24943 | −0.606151 | ||||||||
\(76\) | −1.15352 | −0.132318 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.40294 | −0.724991 | ||||||||
\(79\) | −5.60442 | −0.630546 | −0.315273 | − | 0.949001i | \(-0.602096\pi\) | ||||
−0.315273 | + | 0.949001i | \(0.602096\pi\) | |||||||
\(80\) | 3.20147 | 0.357935 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.24943 | −0.910997 | ||||||||
\(83\) | −6.55646 | −0.719665 | −0.359833 | − | 0.933017i | \(-0.617166\pi\) | ||||
−0.359833 | + | 0.933017i | \(0.617166\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20147 | −0.347248 | ||||||||
\(86\) | 5.15352 | 0.555718 | ||||||||
\(87\) | −7.24943 | −0.777220 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 18.4029 | 1.95071 | 0.975354 | − | 0.220645i | \(-0.0708163\pi\) | ||||
0.975354 | + | 0.220645i | \(0.0708163\pi\) | |||||||
\(90\) | 3.20147 | 0.337465 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.95205 | 0.203515 | ||||||||
\(93\) | 10.4989 | 1.08868 | ||||||||
\(94\) | 6.04795 | 0.623799 | ||||||||
\(95\) | −3.69296 | −0.378890 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.49885 | 0.558324 | 0.279162 | − | 0.960244i | \(-0.409943\pi\) | ||||
0.279162 | + | 0.960244i | \(0.409943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 5.24943 | 0.524943 | ||||||||
\(101\) | 19.9594 | 1.98604 | 0.993018 | − | 0.117965i | \(-0.0376372\pi\) | ||||
0.993018 | + | 0.117965i | \(0.0376372\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −0.307039 | −0.0302535 | −0.0151267 | − | 0.999886i | \(-0.504815\pi\) | ||||
−0.0151267 | + | 0.999886i | \(0.504815\pi\) | |||||||
\(104\) | 6.40294 | 0.627860 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.40294 | −0.621909 | ||||||||
\(107\) | −9.05531 | −0.875410 | −0.437705 | − | 0.899119i | \(-0.644209\pi\) | ||||
−0.437705 | + | 0.899119i | \(0.644209\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.70032 | −0.929122 | −0.464561 | − | 0.885541i | \(-0.653788\pi\) | ||||
−0.464561 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(110\) | 3.20147 | 0.305248 | ||||||||
\(111\) | −5.15352 | −0.489150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.4989 | −1.17579 | −0.587896 | − | 0.808936i | \(-0.700044\pi\) | ||||
−0.587896 | + | 0.808936i | \(0.700044\pi\) | |||||||
\(114\) | 1.15352 | 0.108037 | ||||||||
\(115\) | 6.24943 | 0.582762 | ||||||||
\(116\) | 7.24943 | 0.673092 | ||||||||
\(117\) | 6.40294 | 0.591952 | ||||||||
\(118\) | −11.5565 | −1.06386 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.20147 | −0.292253 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −9.70032 | −0.878226 | ||||||||
\(123\) | 8.24943 | 0.743826 | ||||||||
\(124\) | −10.4989 | −0.942825 | ||||||||
\(125\) | 0.798528 | 0.0714225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.35499 | 0.741386 | 0.370693 | − | 0.928756i | \(-0.379120\pi\) | ||||
0.370693 | + | 0.928756i | \(0.379120\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.15352 | −0.453742 | ||||||||
\(130\) | 20.4989 | 1.79787 | ||||||||
\(131\) | −15.3047 | −1.33718 | −0.668591 | − | 0.743631i | \(-0.733102\pi\) | ||||
−0.668591 | + | 0.743631i | \(0.733102\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.24943 | 0.539868 | ||||||||
\(135\) | −3.20147 | −0.275539 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −6.40294 | −0.547040 | −0.273520 | − | 0.961866i | \(-0.588188\pi\) | ||||
−0.273520 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(138\) | −1.95205 | −0.166169 | ||||||||
\(139\) | −21.7483 | −1.84466 | −0.922332 | − | 0.386398i | \(-0.873719\pi\) | ||||
−0.922332 | + | 0.386398i | \(0.873719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.04795 | −0.509330 | ||||||||
\(142\) | 5.24943 | 0.440522 | ||||||||
\(143\) | 6.40294 | 0.535441 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 23.2088 | 1.92739 | ||||||||
\(146\) | 2.09591 | 0.173458 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.15352 | 0.423617 | ||||||||
\(149\) | 6.84648 | 0.560886 | 0.280443 | − | 0.959871i | \(-0.409519\pi\) | ||||
0.280443 | + | 0.959871i | \(0.409519\pi\) | |||||||
\(150\) | −5.24943 | −0.428614 | ||||||||
\(151\) | 14.8538 | 1.20879 | 0.604394 | − | 0.796685i | \(-0.293415\pi\) | ||||
0.604394 | + | 0.796685i | \(0.293415\pi\) | |||||||
\(152\) | −1.15352 | −0.0935628 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.6118 | −2.69976 | ||||||||
\(156\) | −6.40294 | −0.512646 | ||||||||
\(157\) | 9.46056 | 0.755035 | 0.377517 | − | 0.926002i | \(-0.376778\pi\) | ||||
0.377517 | + | 0.926002i | \(0.376778\pi\) | |||||||
\(158\) | −5.60442 | −0.445863 | ||||||||
\(159\) | 6.40294 | 0.507787 | ||||||||
\(160\) | 3.20147 | 0.253099 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 13.0553 | 1.02257 | 0.511286 | − | 0.859411i | \(-0.329169\pi\) | ||||
0.511286 | + | 0.859411i | \(0.329169\pi\) | |||||||
\(164\) | −8.24943 | −0.644172 | ||||||||
\(165\) | −3.20147 | −0.249234 | ||||||||
\(166\) | −6.55646 | −0.508880 | ||||||||
\(167\) | 6.70998 | 0.519234 | 0.259617 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259617 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.9977 | 2.15367 | ||||||||
\(170\) | −3.20147 | −0.245542 | ||||||||
\(171\) | −1.15352 | −0.0882118 | ||||||||
\(172\) | 5.15352 | 0.392952 | ||||||||
\(173\) | 5.50115 | 0.418245 | 0.209122 | − | 0.977889i | \(-0.432939\pi\) | ||||
0.209122 | + | 0.977889i | \(0.432939\pi\) | |||||||
\(174\) | −7.24943 | −0.549578 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 11.5565 | 0.868637 | ||||||||
\(178\) | 18.4029 | 1.37936 | ||||||||
\(179\) | 1.65237 | 0.123504 | 0.0617520 | − | 0.998092i | \(-0.480331\pi\) | ||||
0.0617520 | + | 0.998092i | \(0.480331\pi\) | |||||||
\(180\) | 3.20147 | 0.238624 | ||||||||
\(181\) | −24.9018 | −1.85094 | −0.925468 | − | 0.378826i | \(-0.876328\pi\) | ||||
−0.925468 | + | 0.378826i | \(0.876328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.70032 | 0.717068 | ||||||||
\(184\) | 1.95205 | 0.143907 | ||||||||
\(185\) | 16.4989 | 1.21302 | ||||||||
\(186\) | 10.4989 | 0.769813 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 6.04795 | 0.441092 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.69296 | −0.267916 | ||||||||
\(191\) | −4.80589 | −0.347742 | −0.173871 | − | 0.984768i | \(-0.555628\pi\) | ||||
−0.173871 | + | 0.984768i | \(0.555628\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.70998 | 0.626958 | 0.313479 | − | 0.949595i | \(-0.398505\pi\) | ||||
0.313479 | + | 0.949595i | \(0.398505\pi\) | |||||||
\(194\) | 5.49885 | 0.394794 | ||||||||
\(195\) | −20.4989 | −1.46795 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.654669 | 0.0466433 | 0.0233216 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233216 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 7.69296 | 0.545340 | 0.272670 | − | 0.962108i | \(-0.412093\pi\) | ||||
0.272670 | + | 0.962108i | \(0.412093\pi\) | |||||||
\(200\) | 5.24943 | 0.371190 | ||||||||
\(201\) | −6.24943 | −0.440800 | ||||||||
\(202\) | 19.9594 | 1.40434 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −26.4103 | −1.84458 | ||||||||
\(206\) | −0.307039 | −0.0213924 | ||||||||
\(207\) | 1.95205 | 0.135677 | ||||||||
\(208\) | 6.40294 | 0.443964 | ||||||||
\(209\) | −1.15352 | −0.0797906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5948 | 1.00474 | 0.502372 | − | 0.864651i | \(-0.332461\pi\) | ||||
0.502372 | + | 0.864651i | \(0.332461\pi\) | |||||||
\(212\) | −6.40294 | −0.439756 | ||||||||
\(213\) | −5.24943 | −0.359685 | ||||||||
\(214\) | −9.05531 | −0.619009 | ||||||||
\(215\) | 16.4989 | 1.12521 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.70032 | −0.656989 | ||||||||
\(219\) | −2.09591 | −0.141628 | ||||||||
\(220\) | 3.20147 | 0.215843 | ||||||||
\(221\) | −6.40294 | −0.430709 | ||||||||
\(222\) | −5.15352 | −0.345882 | ||||||||
\(223\) | 14.9018 | 0.997898 | 0.498949 | − | 0.866631i | \(-0.333719\pi\) | ||||
0.498949 | + | 0.866631i | \(0.333719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.24943 | 0.349962 | ||||||||
\(226\) | −12.4989 | −0.831411 | ||||||||
\(227\) | 0.249425 | 0.0165549 | 0.00827746 | − | 0.999966i | \(-0.497365\pi\) | ||||
0.00827746 | + | 0.999966i | \(0.497365\pi\) | |||||||
\(228\) | 1.15352 | 0.0763937 | ||||||||
\(229\) | 4.09591 | 0.270665 | 0.135333 | − | 0.990800i | \(-0.456790\pi\) | ||||
0.135333 | + | 0.990800i | \(0.456790\pi\) | |||||||
\(230\) | 6.24943 | 0.412075 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.24943 | 0.475948 | ||||||||
\(233\) | 11.3070 | 0.740749 | 0.370374 | − | 0.928883i | \(-0.379229\pi\) | ||||
0.370374 | + | 0.928883i | \(0.379229\pi\) | |||||||
\(234\) | 6.40294 | 0.418574 | ||||||||
\(235\) | 19.3624 | 1.26306 | ||||||||
\(236\) | −11.5565 | −0.752262 | ||||||||
\(237\) | 5.60442 | 0.364046 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.59476 | 0.426579 | 0.213290 | − | 0.976989i | \(-0.431582\pi\) | ||||
0.213290 | + | 0.976989i | \(0.431582\pi\) | |||||||
\(240\) | −3.20147 | −0.206654 | ||||||||
\(241\) | −17.1129 | −1.10234 | −0.551170 | − | 0.834393i | \(-0.685819\pi\) | ||||
−0.551170 | + | 0.834393i | \(0.685819\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.70032 | −0.621000 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.24943 | 0.525964 | ||||||||
\(247\) | −7.38592 | −0.469955 | ||||||||
\(248\) | −10.4989 | −0.666678 | ||||||||
\(249\) | 6.55646 | 0.415499 | ||||||||
\(250\) | 0.798528 | 0.0505033 | ||||||||
\(251\) | −7.95941 | −0.502393 | −0.251197 | − | 0.967936i | \(-0.580824\pi\) | ||||
−0.251197 | + | 0.967936i | \(0.580824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.95205 | 0.122724 | ||||||||
\(254\) | 8.35499 | 0.524239 | ||||||||
\(255\) | 3.20147 | 0.200484 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.4029 | 1.39746 | 0.698729 | − | 0.715387i | \(-0.253749\pi\) | ||||
0.698729 | + | 0.715387i | \(0.253749\pi\) | |||||||
\(258\) | −5.15352 | −0.320844 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 20.4989 | 1.27128 | ||||||||
\(261\) | 7.24943 | 0.448728 | ||||||||
\(262\) | −15.3047 | −0.945530 | ||||||||
\(263\) | −25.0170 | −1.54262 | −0.771308 | − | 0.636462i | \(-0.780397\pi\) | ||||
−0.771308 | + | 0.636462i | \(0.780397\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −20.4989 | −1.25923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.4029 | −1.12624 | ||||||||
\(268\) | 6.24943 | 0.381744 | ||||||||
\(269\) | −8.10327 | −0.494065 | −0.247032 | − | 0.969007i | \(-0.579455\pi\) | ||||
−0.247032 | + | 0.969007i | \(0.579455\pi\) | |||||||
\(270\) | −3.20147 | −0.194835 | ||||||||
\(271\) | 4.80589 | 0.291937 | 0.145968 | − | 0.989289i | \(-0.453370\pi\) | ||||
0.145968 | + | 0.989289i | \(0.453370\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.40294 | −0.386816 | ||||||||
\(275\) | 5.24943 | 0.316552 | ||||||||
\(276\) | −1.95205 | −0.117499 | ||||||||
\(277\) | −11.2088 | −0.673474 | −0.336737 | − | 0.941599i | \(-0.609323\pi\) | ||||
−0.336737 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(278\) | −21.7483 | −1.30437 | ||||||||
\(279\) | −10.4989 | −0.628550 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4989 | −1.04389 | −0.521947 | − | 0.852978i | \(-0.674794\pi\) | ||||
−0.521947 | + | 0.852978i | \(0.674794\pi\) | |||||||
\(282\) | −6.04795 | −0.360150 | ||||||||
\(283\) | −27.4006 | −1.62880 | −0.814400 | − | 0.580304i | \(-0.802934\pi\) | ||||
−0.814400 | + | 0.580304i | \(0.802934\pi\) | |||||||
\(284\) | 5.24943 | 0.311496 | ||||||||
\(285\) | 3.69296 | 0.218752 | ||||||||
\(286\) | 6.40294 | 0.378614 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 23.2088 | 1.36287 | ||||||||
\(291\) | −5.49885 | −0.322348 | ||||||||
\(292\) | 2.09591 | 0.122654 | ||||||||
\(293\) | 19.7483 | 1.15371 | 0.576853 | − | 0.816848i | \(-0.304280\pi\) | ||||
0.576853 | + | 0.816848i | \(0.304280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.9977 | −2.15409 | ||||||||
\(296\) | 5.15352 | 0.299542 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 6.84648 | 0.396606 | ||||||||
\(299\) | 12.4989 | 0.722827 | ||||||||
\(300\) | −5.24943 | −0.303076 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.8538 | 0.854743 | ||||||||
\(303\) | −19.9594 | −1.14664 | ||||||||
\(304\) | −1.15352 | −0.0661589 | ||||||||
\(305\) | −31.0553 | −1.77822 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −4.30704 | −0.245816 | −0.122908 | − | 0.992418i | \(-0.539222\pi\) | ||||
−0.122908 | + | 0.992418i | \(0.539222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.307039 | 0.0174668 | ||||||||
\(310\) | −33.6118 | −1.90902 | ||||||||
\(311\) | 14.7579 | 0.836846 | 0.418423 | − | 0.908252i | \(-0.362583\pi\) | ||||
0.418423 | + | 0.908252i | \(0.362583\pi\) | |||||||
\(312\) | −6.40294 | −0.362495 | ||||||||
\(313\) | −20.7506 | −1.17289 | −0.586446 | − | 0.809988i | \(-0.699473\pi\) | ||||
−0.586446 | + | 0.809988i | \(0.699473\pi\) | |||||||
\(314\) | 9.46056 | 0.533890 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.60442 | −0.315273 | ||||||||
\(317\) | 16.1992 | 0.909836 | 0.454918 | − | 0.890533i | \(-0.349669\pi\) | ||||
0.454918 | + | 0.890533i | \(0.349669\pi\) | |||||||
\(318\) | 6.40294 | 0.359059 | ||||||||
\(319\) | 7.24943 | 0.405890 | ||||||||
\(320\) | 3.20147 | 0.178968 | ||||||||
\(321\) | 9.05531 | 0.505418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.15352 | 0.0641835 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 33.6118 | 1.86445 | ||||||||
\(326\) | 13.0553 | 0.723067 | ||||||||
\(327\) | 9.70032 | 0.536429 | ||||||||
\(328\) | −8.24943 | −0.455498 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.20147 | −0.176235 | ||||||||
\(331\) | 21.2471 | 1.16785 | 0.583924 | − | 0.811808i | \(-0.301517\pi\) | ||||
0.583924 | + | 0.811808i | \(0.301517\pi\) | |||||||
\(332\) | −6.55646 | −0.359833 | ||||||||
\(333\) | 5.15352 | 0.282411 | ||||||||
\(334\) | 6.70998 | 0.367154 | ||||||||
\(335\) | 20.0074 | 1.09312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.5159 | −1.38994 | −0.694969 | − | 0.719040i | \(-0.744582\pi\) | ||||
−0.694969 | + | 0.719040i | \(0.744582\pi\) | |||||||
\(338\) | 27.9977 | 1.52287 | ||||||||
\(339\) | 12.4989 | 0.678844 | ||||||||
\(340\) | −3.20147 | −0.173624 | ||||||||
\(341\) | −10.4989 | −0.568545 | ||||||||
\(342\) | −1.15352 | −0.0623752 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.15352 | 0.277859 | ||||||||
\(345\) | −6.24943 | −0.336458 | ||||||||
\(346\) | 5.50115 | 0.295744 | ||||||||
\(347\) | 3.05531 | 0.164018 | 0.0820089 | − | 0.996632i | \(-0.473866\pi\) | ||||
0.0820089 | + | 0.996632i | \(0.473866\pi\) | |||||||
\(348\) | −7.24943 | −0.388610 | ||||||||
\(349\) | 4.00736 | 0.214509 | 0.107255 | − | 0.994232i | \(-0.465794\pi\) | ||||
0.107255 | + | 0.994232i | \(0.465794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.40294 | −0.341764 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 1.09821 | 0.0584516 | 0.0292258 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292258 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(354\) | 11.5565 | 0.614219 | ||||||||
\(355\) | 16.8059 | 0.891964 | ||||||||
\(356\) | 18.4029 | 0.975354 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.65237 | 0.0873305 | ||||||||
\(359\) | 15.6118 | 0.823958 | 0.411979 | − | 0.911193i | \(-0.364838\pi\) | ||||
0.411979 | + | 0.911193i | \(0.364838\pi\) | |||||||
\(360\) | 3.20147 | 0.168732 | ||||||||
\(361\) | −17.6694 | −0.929968 | ||||||||
\(362\) | −24.9018 | −1.30881 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.70998 | 0.351217 | ||||||||
\(366\) | 9.70032 | 0.507044 | ||||||||
\(367\) | −0.791166 | −0.0412985 | −0.0206493 | − | 0.999787i | \(-0.506573\pi\) | ||||
−0.0206493 | + | 0.999787i | \(0.506573\pi\) | |||||||
\(368\) | 1.95205 | 0.101757 | ||||||||
\(369\) | −8.24943 | −0.429448 | ||||||||
\(370\) | 16.4989 | 0.857734 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.4989 | 0.544340 | ||||||||
\(373\) | 15.9115 | 0.823864 | 0.411932 | − | 0.911215i | \(-0.364854\pi\) | ||||
0.411932 | + | 0.911215i | \(0.364854\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | −0.798528 | −0.0412358 | ||||||||
\(376\) | 6.04795 | 0.311899 | ||||||||
\(377\) | 46.4177 | 2.39063 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0553 | −0.876073 | −0.438036 | − | 0.898957i | \(-0.644326\pi\) | ||||
−0.438036 | + | 0.898957i | \(0.644326\pi\) | |||||||
\(380\) | −3.69296 | −0.189445 | ||||||||
\(381\) | −8.35499 | −0.428039 | ||||||||
\(382\) | −4.80589 | −0.245891 | ||||||||
\(383\) | −13.4412 | −0.686815 | −0.343408 | − | 0.939186i | \(-0.611581\pi\) | ||||
−0.343408 | + | 0.939186i | \(0.611581\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.70998 | 0.443327 | ||||||||
\(387\) | 5.15352 | 0.261968 | ||||||||
\(388\) | 5.49885 | 0.279162 | ||||||||
\(389\) | −7.20147 | −0.365129 | −0.182565 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182565 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(390\) | −20.4989 | −1.03800 | ||||||||
\(391\) | −1.95205 | −0.0987193 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3047 | 0.772022 | ||||||||
\(394\) | 0.654669 | 0.0329818 | ||||||||
\(395\) | −17.9424 | −0.902779 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −12.9424 | −0.649560 | −0.324780 | − | 0.945790i | \(-0.605290\pi\) | ||||
−0.324780 | + | 0.945790i | \(0.605290\pi\) | |||||||
\(398\) | 7.69296 | 0.385613 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.24943 | 0.262471 | ||||||||
\(401\) | −16.9018 | −0.844035 | −0.422018 | − | 0.906588i | \(-0.638678\pi\) | ||||
−0.422018 | + | 0.906588i | \(0.638678\pi\) | |||||||
\(402\) | −6.24943 | −0.311693 | ||||||||
\(403\) | −67.2236 | −3.34864 | ||||||||
\(404\) | 19.9594 | 0.993018 | ||||||||
\(405\) | 3.20147 | 0.159082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.15352 | 0.255450 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 37.0936 | 1.83416 | 0.917080 | − | 0.398702i | \(-0.130539\pi\) | ||||
0.917080 | + | 0.398702i | \(0.130539\pi\) | |||||||
\(410\) | −26.4103 | −1.30431 | ||||||||
\(411\) | 6.40294 | 0.315834 | ||||||||
\(412\) | −0.307039 | −0.0151267 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.95205 | 0.0959379 | ||||||||
\(415\) | −20.9903 | −1.03038 | ||||||||
\(416\) | 6.40294 | 0.313930 | ||||||||
\(417\) | 21.7483 | 1.06502 | ||||||||
\(418\) | −1.15352 | −0.0564205 | ||||||||
\(419\) | −22.4583 | −1.09716 | −0.548579 | − | 0.836099i | \(-0.684831\pi\) | ||||
−0.548579 | + | 0.836099i | \(0.684831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3453 | −1.13778 | −0.568891 | − | 0.822413i | \(-0.692627\pi\) | ||||
−0.568891 | + | 0.822413i | \(0.692627\pi\) | |||||||
\(422\) | 14.5948 | 0.710462 | ||||||||
\(423\) | 6.04795 | 0.294062 | ||||||||
\(424\) | −6.40294 | −0.310954 | ||||||||
\(425\) | −5.24943 | −0.254635 | ||||||||
\(426\) | −5.24943 | −0.254335 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.05531 | −0.437705 | ||||||||
\(429\) | −6.40294 | −0.309137 | ||||||||
\(430\) | 16.4989 | 0.795645 | ||||||||
\(431\) | 31.8229 | 1.53286 | 0.766428 | − | 0.642330i | \(-0.222032\pi\) | ||||
0.766428 | + | 0.642330i | \(0.222032\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −30.3047 | −1.45635 | −0.728176 | − | 0.685390i | \(-0.759632\pi\) | ||||
−0.728176 | + | 0.685390i | \(0.759632\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.2088 | −1.11278 | ||||||||
\(436\) | −9.70032 | −0.464561 | ||||||||
\(437\) | −2.25172 | −0.107715 | ||||||||
\(438\) | −2.09591 | −0.100146 | ||||||||
\(439\) | 10.6620 | 0.508871 | 0.254435 | − | 0.967090i | \(-0.418110\pi\) | ||||
0.254435 | + | 0.967090i | \(0.418110\pi\) | |||||||
\(440\) | 3.20147 | 0.152624 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.40294 | −0.304557 | ||||||||
\(443\) | −36.0553 | −1.71304 | −0.856520 | − | 0.516114i | \(-0.827378\pi\) | ||||
−0.856520 | + | 0.516114i | \(0.827378\pi\) | |||||||
\(444\) | −5.15352 | −0.244575 | ||||||||
\(445\) | 58.9165 | 2.79291 | ||||||||
\(446\) | 14.9018 | 0.705620 | ||||||||
\(447\) | −6.84648 | −0.323827 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4006 | 1.10434 | 0.552172 | − | 0.833730i | \(-0.313799\pi\) | ||||
0.552172 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(450\) | 5.24943 | 0.247460 | ||||||||
\(451\) | −8.24943 | −0.388450 | ||||||||
\(452\) | −12.4989 | −0.587896 | ||||||||
\(453\) | −14.8538 | −0.697894 | ||||||||
\(454\) | 0.249425 | 0.0117061 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.15352 | 0.0540185 | ||||||||
\(457\) | −18.6141 | −0.870730 | −0.435365 | − | 0.900254i | \(-0.643381\pi\) | ||||
−0.435365 | + | 0.900254i | \(0.643381\pi\) | |||||||
\(458\) | 4.09591 | 0.191389 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 6.24943 | 0.291381 | ||||||||
\(461\) | 31.4412 | 1.46436 | 0.732182 | − | 0.681109i | \(-0.238502\pi\) | ||||
0.732182 | + | 0.681109i | \(0.238502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0959 | −1.02688 | −0.513442 | − | 0.858124i | \(-0.671630\pi\) | ||||
−0.513442 | + | 0.858124i | \(0.671630\pi\) | |||||||
\(464\) | 7.24943 | 0.336546 | ||||||||
\(465\) | 33.6118 | 1.55871 | ||||||||
\(466\) | 11.3070 | 0.523788 | ||||||||
\(467\) | −21.0576 | −0.974430 | −0.487215 | − | 0.873282i | \(-0.661987\pi\) | ||||
−0.487215 | + | 0.873282i | \(0.661987\pi\) | |||||||
\(468\) | 6.40294 | 0.295976 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.3624 | 0.893119 | ||||||||
\(471\) | −9.46056 | −0.435920 | ||||||||
\(472\) | −11.5565 | −0.531929 | ||||||||
\(473\) | 5.15352 | 0.236959 | ||||||||
\(474\) | 5.60442 | 0.257419 | ||||||||
\(475\) | −6.05531 | −0.277837 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.40294 | −0.293171 | ||||||||
\(478\) | 6.59476 | 0.301637 | ||||||||
\(479\) | 21.2088 | 0.969056 | 0.484528 | − | 0.874776i | \(-0.338991\pi\) | ||||
0.484528 | + | 0.874776i | \(0.338991\pi\) | |||||||
\(480\) | −3.20147 | −0.146127 | ||||||||
\(481\) | 32.9977 | 1.50457 | ||||||||
\(482\) | −17.1129 | −0.779473 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 17.6044 | 0.799375 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −38.7100 | −1.75412 | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(488\) | −9.70032 | −0.439113 | ||||||||
\(489\) | −13.0553 | −0.590382 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1705 | 0.865154 | 0.432577 | − | 0.901597i | \(-0.357604\pi\) | ||||
0.432577 | + | 0.901597i | \(0.357604\pi\) | |||||||
\(492\) | 8.24943 | 0.371913 | ||||||||
\(493\) | −7.24943 | −0.326498 | ||||||||
\(494\) | −7.38592 | −0.332308 | ||||||||
\(495\) | 3.20147 | 0.143895 | ||||||||
\(496\) | −10.4989 | −0.471412 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.55646 | 0.293802 | ||||||||
\(499\) | −27.9188 | −1.24982 | −0.624909 | − | 0.780698i | \(-0.714864\pi\) | ||||
−0.624909 | + | 0.780698i | \(0.714864\pi\) | |||||||
\(500\) | 0.798528 | 0.0357112 | ||||||||
\(501\) | −6.70998 | −0.299780 | ||||||||
\(502\) | −7.95941 | −0.355246 | ||||||||
\(503\) | 8.70998 | 0.388359 | 0.194179 | − | 0.980966i | \(-0.437796\pi\) | ||||
0.194179 | + | 0.980966i | \(0.437796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 63.8995 | 2.84349 | ||||||||
\(506\) | 1.95205 | 0.0867791 | ||||||||
\(507\) | −27.9977 | −1.24342 | ||||||||
\(508\) | 8.35499 | 0.370693 | ||||||||
\(509\) | 1.78887 | 0.0792901 | 0.0396451 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396451 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(510\) | 3.20147 | 0.141764 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.15352 | 0.0509291 | ||||||||
\(514\) | 22.4029 | 0.988152 | ||||||||
\(515\) | −0.982977 | −0.0433151 | ||||||||
\(516\) | −5.15352 | −0.226871 | ||||||||
\(517\) | 6.04795 | 0.265989 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.50115 | −0.241474 | ||||||||
\(520\) | 20.4989 | 0.898934 | ||||||||
\(521\) | −23.6118 | −1.03445 | −0.517225 | − | 0.855849i | \(-0.673035\pi\) | ||||
−0.517225 | + | 0.855849i | \(0.673035\pi\) | |||||||
\(522\) | 7.24943 | 0.317299 | ||||||||
\(523\) | −43.4006 | −1.89778 | −0.948889 | − | 0.315610i | \(-0.897791\pi\) | ||||
−0.948889 | + | 0.315610i | \(0.897791\pi\) | |||||||
\(524\) | −15.3047 | −0.668591 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.0170 | −1.09079 | ||||||||
\(527\) | 10.4989 | 0.457337 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −19.1895 | −0.834327 | ||||||||
\(530\) | −20.4989 | −0.890413 | ||||||||
\(531\) | −11.5565 | −0.501508 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.8206 | −2.28791 | ||||||||
\(534\) | −18.4029 | −0.796373 | ||||||||
\(535\) | −28.9903 | −1.25336 | ||||||||
\(536\) | 6.24943 | 0.269934 | ||||||||
\(537\) | −1.65237 | −0.0713050 | ||||||||
\(538\) | −8.10327 | −0.349357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.20147 | −0.137769 | ||||||||
\(541\) | 16.9903 | 0.730472 | 0.365236 | − | 0.930915i | \(-0.380988\pi\) | ||||
0.365236 | + | 0.930915i | \(0.380988\pi\) | |||||||
\(542\) | 4.80589 | 0.206431 | ||||||||
\(543\) | 24.9018 | 1.06864 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −31.0553 | −1.33026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.34533 | −0.0575222 | −0.0287611 | − | 0.999586i | \(-0.509156\pi\) | ||||
−0.0287611 | + | 0.999586i | \(0.509156\pi\) | |||||||
\(548\) | −6.40294 | −0.273520 | ||||||||
\(549\) | −9.70032 | −0.414000 | ||||||||
\(550\) | 5.24943 | 0.223836 | ||||||||
\(551\) | −8.36235 | −0.356248 | ||||||||
\(552\) | −1.95205 | −0.0830846 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.2088 | −0.476218 | ||||||||
\(555\) | −16.4989 | −0.700337 | ||||||||
\(556\) | −21.7483 | −0.922332 | ||||||||
\(557\) | −16.6547 | −0.705681 | −0.352840 | − | 0.935683i | \(-0.614784\pi\) | ||||
−0.352840 | + | 0.935683i | \(0.614784\pi\) | |||||||
\(558\) | −10.4989 | −0.444452 | ||||||||
\(559\) | 32.9977 | 1.39565 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −17.4989 | −0.738144 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | −6.04795 | −0.254665 | ||||||||
\(565\) | −40.0147 | −1.68343 | ||||||||
\(566\) | −27.4006 | −1.15174 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.24943 | 0.220261 | ||||||||
\(569\) | −10.5542 | −0.442454 | −0.221227 | − | 0.975222i | \(-0.571006\pi\) | ||||
−0.221227 | + | 0.975222i | \(0.571006\pi\) | |||||||
\(570\) | 3.69296 | 0.154681 | ||||||||
\(571\) | 4.75057 | 0.198805 | 0.0994027 | − | 0.995047i | \(-0.468307\pi\) | ||||
0.0994027 | + | 0.995047i | \(0.468307\pi\) | |||||||
\(572\) | 6.40294 | 0.267721 | ||||||||
\(573\) | 4.80589 | 0.200769 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2471 | 0.427335 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −37.5542 | −1.56340 | −0.781700 | − | 0.623654i | \(-0.785647\pi\) | ||||
−0.781700 | + | 0.623654i | \(0.785647\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | −8.70998 | −0.361975 | ||||||||
\(580\) | 23.2088 | 0.963694 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.49885 | −0.227935 | ||||||||
\(583\) | −6.40294 | −0.265183 | ||||||||
\(584\) | 2.09591 | 0.0867292 | ||||||||
\(585\) | 20.4989 | 0.847523 | ||||||||
\(586\) | 19.7483 | 0.815794 | ||||||||
\(587\) | 17.0982 | 0.705718 | 0.352859 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352859 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.1106 | 0.499010 | ||||||||
\(590\) | −36.9977 | −1.52317 | ||||||||
\(591\) | −0.654669 | −0.0269295 | ||||||||
\(592\) | 5.15352 | 0.211808 | ||||||||
\(593\) | 32.2471 | 1.32423 | 0.662115 | − | 0.749402i | \(-0.269659\pi\) | ||||
0.662115 | + | 0.749402i | \(0.269659\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.84648 | 0.280443 | ||||||||
\(597\) | −7.69296 | −0.314852 | ||||||||
\(598\) | 12.4989 | 0.511116 | ||||||||
\(599\) | 3.39328 | 0.138646 | 0.0693229 | − | 0.997594i | \(-0.477916\pi\) | ||||
0.0693229 | + | 0.997594i | \(0.477916\pi\) | |||||||
\(600\) | −5.24943 | −0.214307 | ||||||||
\(601\) | −30.4989 | −1.24407 | −0.622037 | − | 0.782988i | \(-0.713695\pi\) | ||||
−0.622037 | + | 0.782988i | \(0.713695\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.24943 | 0.254496 | ||||||||
\(604\) | 14.8538 | 0.604394 | ||||||||
\(605\) | 3.20147 | 0.130158 | ||||||||
\(606\) | −19.9594 | −0.810796 | ||||||||
\(607\) | −12.9903 | −0.527262 | −0.263631 | − | 0.964624i | \(-0.584920\pi\) | ||||
−0.263631 | + | 0.964624i | \(0.584920\pi\) | |||||||
\(608\) | −1.15352 | −0.0467814 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.0553 | −1.25739 | ||||||||
\(611\) | 38.7247 | 1.56663 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 20.1992 | 0.815837 | 0.407918 | − | 0.913018i | \(-0.366255\pi\) | ||||
0.407918 | + | 0.913018i | \(0.366255\pi\) | |||||||
\(614\) | −4.30704 | −0.173818 | ||||||||
\(615\) | 26.4103 | 1.06497 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0936 | 0.688163 | 0.344081 | − | 0.938940i | \(-0.388190\pi\) | ||||
0.344081 | + | 0.938940i | \(0.388190\pi\) | |||||||
\(618\) | 0.307039 | 0.0123509 | ||||||||
\(619\) | −41.6694 | −1.67483 | −0.837417 | − | 0.546564i | \(-0.815935\pi\) | ||||
−0.837417 | + | 0.546564i | \(0.815935\pi\) | |||||||
\(620\) | −33.6118 | −1.34988 | ||||||||
\(621\) | −1.95205 | −0.0783330 | ||||||||
\(622\) | 14.7579 | 0.591739 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.40294 | −0.256323 | ||||||||
\(625\) | −23.6907 | −0.947626 | ||||||||
\(626\) | −20.7506 | −0.829360 | ||||||||
\(627\) | 1.15352 | 0.0460671 | ||||||||
\(628\) | 9.46056 | 0.377517 | ||||||||
\(629\) | −5.15352 | −0.205484 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8995 | −0.951424 | −0.475712 | − | 0.879601i | \(-0.657810\pi\) | ||||
−0.475712 | + | 0.879601i | \(0.657810\pi\) | |||||||
\(632\) | −5.60442 | −0.222932 | ||||||||
\(633\) | −14.5948 | −0.580089 | ||||||||
\(634\) | 16.1992 | 0.643351 | ||||||||
\(635\) | 26.7483 | 1.06147 | ||||||||
\(636\) | 6.40294 | 0.253893 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.24943 | 0.287007 | ||||||||
\(639\) | 5.24943 | 0.207664 | ||||||||
\(640\) | 3.20147 | 0.126549 | ||||||||
\(641\) | −14.3070 | −0.565094 | −0.282547 | − | 0.959253i | \(-0.591179\pi\) | ||||
−0.282547 | + | 0.959253i | \(0.591179\pi\) | |||||||
\(642\) | 9.05531 | 0.357385 | ||||||||
\(643\) | 35.4966 | 1.39985 | 0.699924 | − | 0.714218i | \(-0.253217\pi\) | ||||
0.699924 | + | 0.714218i | \(0.253217\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4989 | −0.649642 | ||||||||
\(646\) | 1.15352 | 0.0453846 | ||||||||
\(647\) | −23.8156 | −0.936286 | −0.468143 | − | 0.883653i | \(-0.655077\pi\) | ||||
−0.468143 | + | 0.883653i | \(0.655077\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −11.5565 | −0.453631 | ||||||||
\(650\) | 33.6118 | 1.31836 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0553 | 0.511286 | ||||||||
\(653\) | −13.7962 | −0.539888 | −0.269944 | − | 0.962876i | \(-0.587005\pi\) | ||||
−0.269944 | + | 0.962876i | \(0.587005\pi\) | |||||||
\(654\) | 9.70032 | 0.379313 | ||||||||
\(655\) | −48.9977 | −1.91450 | ||||||||
\(656\) | −8.24943 | −0.322086 | ||||||||
\(657\) | 2.09591 | 0.0817691 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.9447 | 0.737980 | 0.368990 | − | 0.929433i | \(-0.379704\pi\) | ||||
0.368990 | + | 0.929433i | \(0.379704\pi\) | |||||||
\(660\) | −3.20147 | −0.124617 | ||||||||
\(661\) | −3.95941 | −0.154003 | −0.0770016 | − | 0.997031i | \(-0.524535\pi\) | ||||
−0.0770016 | + | 0.997031i | \(0.524535\pi\) | |||||||
\(662\) | 21.2471 | 0.825793 | ||||||||
\(663\) | 6.40294 | 0.248670 | ||||||||
\(664\) | −6.55646 | −0.254440 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.15352 | 0.199695 | ||||||||
\(667\) | 14.1512 | 0.547937 | ||||||||
\(668\) | 6.70998 | 0.259617 | ||||||||
\(669\) | −14.9018 | −0.576137 | ||||||||
\(670\) | 20.0074 | 0.772952 | ||||||||
\(671\) | −9.70032 | −0.374477 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.69066 | −0.335000 | −0.167500 | − | 0.985872i | \(-0.553569\pi\) | ||||
−0.167500 | + | 0.985872i | \(0.553569\pi\) | |||||||
\(674\) | −25.5159 | −0.982835 | ||||||||
\(675\) | −5.24943 | −0.202050 | ||||||||
\(676\) | 27.9977 | 1.07683 | ||||||||
\(677\) | 31.4606 | 1.20913 | 0.604564 | − | 0.796557i | \(-0.293347\pi\) | ||||
0.604564 | + | 0.796557i | \(0.293347\pi\) | |||||||
\(678\) | 12.4989 | 0.480015 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.20147 | −0.122771 | ||||||||
\(681\) | −0.249425 | −0.00955799 | ||||||||
\(682\) | −10.4989 | −0.402022 | ||||||||
\(683\) | 24.7460 | 0.946878 | 0.473439 | − | 0.880826i | \(-0.343012\pi\) | ||||
0.473439 | + | 0.880826i | \(0.343012\pi\) | |||||||
\(684\) | −1.15352 | −0.0441059 | ||||||||
\(685\) | −20.4989 | −0.783221 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.09591 | −0.156269 | ||||||||
\(688\) | 5.15352 | 0.196476 | ||||||||
\(689\) | −40.9977 | −1.56189 | ||||||||
\(690\) | −6.24943 | −0.237912 | ||||||||
\(691\) | −25.5542 | −0.972126 | −0.486063 | − | 0.873924i | \(-0.661567\pi\) | ||||
−0.486063 | + | 0.873924i | \(0.661567\pi\) | |||||||
\(692\) | 5.50115 | 0.209122 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.05531 | 0.115978 | ||||||||
\(695\) | −69.6265 | −2.64108 | ||||||||
\(696\) | −7.24943 | −0.274789 | ||||||||
\(697\) | 8.24943 | 0.312469 | ||||||||
\(698\) | 4.00736 | 0.151681 | ||||||||
\(699\) | −11.3070 | −0.427671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1512 | −0.534484 | −0.267242 | − | 0.963629i | \(-0.586112\pi\) | ||||
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(702\) | −6.40294 | −0.241664 | ||||||||
\(703\) | −5.94469 | −0.224208 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −19.3624 | −0.729228 | ||||||||
\(706\) | 1.09821 | 0.0413315 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11.5565 | 0.434319 | ||||||||
\(709\) | −10.7506 | −0.403746 | −0.201873 | − | 0.979412i | \(-0.564703\pi\) | ||||
−0.201873 | + | 0.979412i | \(0.564703\pi\) | |||||||
\(710\) | 16.8059 | 0.630714 | ||||||||
\(711\) | −5.60442 | −0.210182 | ||||||||
\(712\) | 18.4029 | 0.689680 | ||||||||
\(713\) | −20.4943 | −0.767516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4989 | 0.766614 | ||||||||
\(716\) | 1.65237 | 0.0617520 | ||||||||
\(717\) | −6.59476 | −0.246286 | ||||||||
\(718\) | 15.6118 | 0.582626 | ||||||||
\(719\) | −2.75794 | −0.102854 | −0.0514268 | − | 0.998677i | \(-0.516377\pi\) | ||||
−0.0514268 | + | 0.998677i | \(0.516377\pi\) | |||||||
\(720\) | 3.20147 | 0.119312 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.6694 | −0.657587 | ||||||||
\(723\) | 17.1129 | 0.636437 | ||||||||
\(724\) | −24.9018 | −0.925468 | ||||||||
\(725\) | 38.0553 | 1.41334 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −14.6141 | −0.542006 | −0.271003 | − | 0.962578i | \(-0.587355\pi\) | ||||
−0.271003 | + | 0.962578i | \(0.587355\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.70998 | 0.248348 | ||||||||
\(731\) | −5.15352 | −0.190610 | ||||||||
\(732\) | 9.70032 | 0.358534 | ||||||||
\(733\) | −7.10557 | −0.262450 | −0.131225 | − | 0.991353i | \(-0.541891\pi\) | ||||
−0.131225 | + | 0.991353i | \(0.541891\pi\) | |||||||
\(734\) | −0.791166 | −0.0292025 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.95205 | 0.0719534 | ||||||||
\(737\) | 6.24943 | 0.230201 | ||||||||
\(738\) | −8.24943 | −0.303666 | ||||||||
\(739\) | −41.4966 | −1.52648 | −0.763238 | − | 0.646118i | \(-0.776391\pi\) | ||||
−0.763238 | + | 0.646118i | \(0.776391\pi\) | |||||||
\(740\) | 16.4989 | 0.606510 | ||||||||
\(741\) | 7.38592 | 0.271329 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.9041 | −1.17045 | −0.585224 | − | 0.810872i | \(-0.698993\pi\) | ||||
−0.585224 | + | 0.810872i | \(0.698993\pi\) | |||||||
\(744\) | 10.4989 | 0.384907 | ||||||||
\(745\) | 21.9188 | 0.803043 | ||||||||
\(746\) | 15.9115 | 0.582560 | ||||||||
\(747\) | −6.55646 | −0.239888 | ||||||||
\(748\) | −1.00000 | −0.0365636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.798528 | −0.0291581 | ||||||||
\(751\) | 13.5159 | 0.493201 | 0.246601 | − | 0.969117i | \(-0.420686\pi\) | ||||
0.246601 | + | 0.969117i | \(0.420686\pi\) | |||||||
\(752\) | 6.04795 | 0.220546 | ||||||||
\(753\) | 7.95941 | 0.290057 | ||||||||
\(754\) | 46.4177 | 1.69043 | ||||||||
\(755\) | 47.5542 | 1.73067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.5542 | −0.674363 | −0.337181 | − | 0.941440i | \(-0.609474\pi\) | ||||
−0.337181 | + | 0.941440i | \(0.609474\pi\) | |||||||
\(758\) | −17.0553 | −0.619477 | ||||||||
\(759\) | −1.95205 | −0.0708548 | ||||||||
\(760\) | −3.69296 | −0.133958 | ||||||||
\(761\) | −15.7506 | −0.570958 | −0.285479 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285479 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(762\) | −8.35499 | −0.302669 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.80589 | −0.173871 | ||||||||
\(765\) | −3.20147 | −0.115749 | ||||||||
\(766\) | −13.4412 | −0.485652 | ||||||||
\(767\) | −73.9954 | −2.67182 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −41.2854 | −1.48879 | −0.744395 | − | 0.667739i | \(-0.767262\pi\) | ||||
−0.744395 | + | 0.667739i | \(0.767262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4029 | −0.806822 | ||||||||
\(772\) | 8.70998 | 0.313479 | ||||||||
\(773\) | −4.90916 | −0.176570 | −0.0882850 | − | 0.996095i | \(-0.528139\pi\) | ||||
−0.0882850 | + | 0.996095i | \(0.528139\pi\) | |||||||
\(774\) | 5.15352 | 0.185239 | ||||||||
\(775\) | −55.1129 | −1.97971 | ||||||||
\(776\) | 5.49885 | 0.197397 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.20147 | −0.258185 | ||||||||
\(779\) | 9.51587 | 0.340942 | ||||||||
\(780\) | −20.4989 | −0.733977 | ||||||||
\(781\) | 5.24943 | 0.187839 | ||||||||
\(782\) | −1.95205 | −0.0698051 | ||||||||
\(783\) | −7.24943 | −0.259073 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.2877 | 1.08101 | ||||||||
\(786\) | 15.3047 | 0.545902 | ||||||||
\(787\) | −0.769897 | −0.0274439 | −0.0137219 | − | 0.999906i | \(-0.504368\pi\) | ||||
−0.0137219 | + | 0.999906i | \(0.504368\pi\) | |||||||
\(788\) | 0.654669 | 0.0233216 | ||||||||
\(789\) | 25.0170 | 0.890630 | ||||||||
\(790\) | −17.9424 | −0.638361 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −62.1106 | −2.20561 | ||||||||
\(794\) | −12.9424 | −0.459308 | ||||||||
\(795\) | 20.4989 | 0.727019 | ||||||||
\(796\) | 7.69296 | 0.272670 | ||||||||
\(797\) | −28.9092 | −1.02401 | −0.512007 | − | 0.858981i | \(-0.671098\pi\) | ||||
−0.512007 | + | 0.858981i | \(0.671098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.04795 | −0.213961 | ||||||||
\(800\) | 5.24943 | 0.185595 | ||||||||
\(801\) | 18.4029 | 0.650236 | ||||||||
\(802\) | −16.9018 | −0.596823 | ||||||||
\(803\) | 2.09591 | 0.0739629 | ||||||||
\(804\) | −6.24943 | −0.220400 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −67.2236 | −2.36785 | ||||||||
\(807\) | 8.10327 | 0.285249 | ||||||||
\(808\) | 19.9594 | 0.702170 | ||||||||
\(809\) | −20.2494 | −0.711932 | −0.355966 | − | 0.934499i | \(-0.615848\pi\) | ||||
−0.355966 | + | 0.934499i | \(0.615848\pi\) | |||||||
\(810\) | 3.20147 | 0.112488 | ||||||||
\(811\) | 48.4989 | 1.70302 | 0.851512 | − | 0.524334i | \(-0.175686\pi\) | ||||
0.851512 | + | 0.524334i | \(0.175686\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.80589 | −0.168550 | ||||||||
\(814\) | 5.15352 | 0.180631 | ||||||||
\(815\) | 41.7962 | 1.46406 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −5.94469 | −0.207978 | ||||||||
\(818\) | 37.0936 | 1.29695 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.4103 | −0.922288 | ||||||||
\(821\) | 31.3047 | 1.09254 | 0.546271 | − | 0.837608i | \(-0.316047\pi\) | ||||
0.546271 | + | 0.837608i | \(0.316047\pi\) | |||||||
\(822\) | 6.40294 | 0.223328 | ||||||||
\(823\) | 0.287717 | 0.0100292 | 0.00501459 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501459 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(824\) | −0.307039 | −0.0106962 | ||||||||
\(825\) | −5.24943 | −0.182762 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2471 | 1.29521 | 0.647605 | − | 0.761976i | \(-0.275771\pi\) | ||||
0.647605 | + | 0.761976i | \(0.275771\pi\) | |||||||
\(828\) | 1.95205 | 0.0678383 | ||||||||
\(829\) | −49.1535 | −1.70717 | −0.853586 | − | 0.520952i | \(-0.825577\pi\) | ||||
−0.853586 | + | 0.520952i | \(0.825577\pi\) | |||||||
\(830\) | −20.9903 | −0.728585 | ||||||||
\(831\) | 11.2088 | 0.388830 | ||||||||
\(832\) | 6.40294 | 0.221982 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.7483 | 0.753081 | ||||||||
\(835\) | 21.4818 | 0.743409 | ||||||||
\(836\) | −1.15352 | −0.0398953 | ||||||||
\(837\) | 10.4989 | 0.362893 | ||||||||
\(838\) | −22.4583 | −0.775808 | ||||||||
\(839\) | 2.81785 | 0.0972830 | 0.0486415 | − | 0.998816i | \(-0.484511\pi\) | ||||
0.0486415 | + | 0.998816i | \(0.484511\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.5542 | 0.812213 | ||||||||
\(842\) | −23.3453 | −0.804533 | ||||||||
\(843\) | 17.4989 | 0.602692 | ||||||||
\(844\) | 14.5948 | 0.502372 | ||||||||
\(845\) | 89.6339 | 3.08350 | ||||||||
\(846\) | 6.04795 | 0.207933 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.40294 | −0.219878 | ||||||||
\(849\) | 27.4006 | 0.940388 | ||||||||
\(850\) | −5.24943 | −0.180054 | ||||||||
\(851\) | 10.0599 | 0.344849 | ||||||||
\(852\) | −5.24943 | −0.179842 | ||||||||
\(853\) | −2.39558 | −0.0820232 | −0.0410116 | − | 0.999159i | \(-0.513058\pi\) | ||||
−0.0410116 | + | 0.999159i | \(0.513058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.69296 | −0.126297 | ||||||||
\(856\) | −9.05531 | −0.309504 | ||||||||
\(857\) | −0.808189 | −0.0276072 | −0.0138036 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138036 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(858\) | −6.40294 | −0.218593 | ||||||||
\(859\) | −6.55646 | −0.223704 | −0.111852 | − | 0.993725i | \(-0.535678\pi\) | ||||
−0.111852 | + | 0.993725i | \(0.535678\pi\) | |||||||
\(860\) | 16.4989 | 0.562606 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.8229 | 1.08389 | ||||||||
\(863\) | −20.6067 | −0.701461 | −0.350730 | − | 0.936476i | \(-0.614067\pi\) | ||||
−0.350730 | + | 0.936476i | \(0.614067\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 17.6118 | 0.598818 | ||||||||
\(866\) | −30.3047 | −1.02980 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.60442 | −0.190117 | ||||||||
\(870\) | −23.2088 | −0.786853 | ||||||||
\(871\) | 40.0147 | 1.35585 | ||||||||
\(872\) | −9.70032 | −0.328494 | ||||||||
\(873\) | 5.49885 | 0.186108 | ||||||||
\(874\) | −2.25172 | −0.0761657 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.09591 | −0.0708141 | ||||||||
\(877\) | 26.6021 | 0.898290 | 0.449145 | − | 0.893459i | \(-0.351729\pi\) | ||||
0.449145 | + | 0.893459i | \(0.351729\pi\) | |||||||
\(878\) | 10.6620 | 0.359826 | ||||||||
\(879\) | −19.7483 | −0.666093 | ||||||||
\(880\) | 3.20147 | 0.107922 | ||||||||
\(881\) | 8.49885 | 0.286334 | 0.143167 | − | 0.989699i | \(-0.454271\pi\) | ||||
0.143167 | + | 0.989699i | \(0.454271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.2448 | 1.55626 | 0.778131 | − | 0.628102i | \(-0.216168\pi\) | ||||
0.778131 | + | 0.628102i | \(0.216168\pi\) | |||||||
\(884\) | −6.40294 | −0.215354 | ||||||||
\(885\) | 36.9977 | 1.24366 | ||||||||
\(886\) | −36.0553 | −1.21130 | ||||||||
\(887\) | −18.2877 | −0.614041 | −0.307021 | − | 0.951703i | \(-0.599332\pi\) | ||||
−0.307021 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(888\) | −5.15352 | −0.172941 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 58.9165 | 1.97489 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 14.9018 | 0.498949 | ||||||||
\(893\) | −6.97643 | −0.233457 | ||||||||
\(894\) | −6.84648 | −0.228981 | ||||||||
\(895\) | 5.29002 | 0.176826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.4989 | −0.417324 | ||||||||
\(898\) | 23.4006 | 0.780890 | ||||||||
\(899\) | −76.1106 | −2.53843 | ||||||||
\(900\) | 5.24943 | 0.174981 | ||||||||
\(901\) | 6.40294 | 0.213313 | ||||||||
\(902\) | −8.24943 | −0.274676 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.4989 | −0.415706 | ||||||||
\(905\) | −79.7224 | −2.65006 | ||||||||
\(906\) | −14.8538 | −0.493486 | ||||||||
\(907\) | −31.6694 | −1.05156 | −0.525782 | − | 0.850619i | \(-0.676227\pi\) | ||||
−0.525782 | + | 0.850619i | \(0.676227\pi\) | |||||||
\(908\) | 0.249425 | 0.00827746 | ||||||||
\(909\) | 19.9594 | 0.662012 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.7727 | 1.94723 | 0.973613 | − | 0.228207i | \(-0.0732864\pi\) | ||||
0.973613 | + | 0.228207i | \(0.0732864\pi\) | |||||||
\(912\) | 1.15352 | 0.0381968 | ||||||||
\(913\) | −6.55646 | −0.216987 | ||||||||
\(914\) | −18.6141 | −0.615699 | ||||||||
\(915\) | 31.0553 | 1.02666 | ||||||||
\(916\) | 4.09591 | 0.135333 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −32.9691 | −1.08755 | −0.543775 | − | 0.839231i | \(-0.683005\pi\) | ||||
−0.543775 | + | 0.839231i | \(0.683005\pi\) | |||||||
\(920\) | 6.24943 | 0.206037 | ||||||||
\(921\) | 4.30704 | 0.141922 | ||||||||
\(922\) | 31.4412 | 1.03546 | ||||||||
\(923\) | 33.6118 | 1.10635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.0530 | 0.889498 | ||||||||
\(926\) | −22.0959 | −0.726117 | ||||||||
\(927\) | −0.307039 | −0.0100845 | ||||||||
\(928\) | 7.24943 | 0.237974 | ||||||||
\(929\) | −41.8995 | −1.37468 | −0.687339 | − | 0.726337i | \(-0.741221\pi\) | ||||
−0.687339 | + | 0.726337i | \(0.741221\pi\) | |||||||
\(930\) | 33.6118 | 1.10217 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.3070 | 0.370374 | ||||||||
\(933\) | −14.7579 | −0.483153 | ||||||||
\(934\) | −21.0576 | −0.689026 | ||||||||
\(935\) | −3.20147 | −0.104699 | ||||||||
\(936\) | 6.40294 | 0.209287 | ||||||||
\(937\) | 33.4966 | 1.09428 | 0.547142 | − | 0.837040i | \(-0.315716\pi\) | ||||
0.547142 | + | 0.837040i | \(0.315716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7506 | 0.677169 | ||||||||
\(940\) | 19.3624 | 0.631530 | ||||||||
\(941\) | 45.7483 | 1.49135 | 0.745676 | − | 0.666309i | \(-0.232127\pi\) | ||||
0.745676 | + | 0.666309i | \(0.232127\pi\) | |||||||
\(942\) | −9.46056 | −0.308242 | ||||||||
\(943\) | −16.1033 | −0.524395 | ||||||||
\(944\) | −11.5565 | −0.376131 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.15352 | 0.167555 | ||||||||
\(947\) | −45.0530 | −1.46403 | −0.732013 | − | 0.681291i | \(-0.761419\pi\) | ||||
−0.732013 | + | 0.681291i | \(0.761419\pi\) | |||||||
\(948\) | 5.60442 | 0.182023 | ||||||||
\(949\) | 13.4200 | 0.435631 | ||||||||
\(950\) | −6.05531 | −0.196460 | ||||||||
\(951\) | −16.1992 | −0.525294 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1705 | 1.20407 | 0.602036 | − | 0.798469i | \(-0.294356\pi\) | ||||
0.602036 | + | 0.798469i | \(0.294356\pi\) | |||||||
\(954\) | −6.40294 | −0.207303 | ||||||||
\(955\) | −15.3859 | −0.497877 | ||||||||
\(956\) | 6.59476 | 0.213290 | ||||||||
\(957\) | −7.24943 | −0.234341 | ||||||||
\(958\) | 21.2088 | 0.685226 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.20147 | −0.103327 | ||||||||
\(961\) | 79.2259 | 2.55567 | ||||||||
\(962\) | 32.9977 | 1.06389 | ||||||||
\(963\) | −9.05531 | −0.291803 | ||||||||
\(964\) | −17.1129 | −0.551170 | ||||||||
\(965\) | 27.8848 | 0.897643 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.7579 | 1.37500 | 0.687501 | − | 0.726183i | \(-0.258708\pi\) | ||||
0.687501 | + | 0.726183i | \(0.258708\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −1.15352 | −0.0370564 | ||||||||
\(970\) | 17.6044 | 0.565244 | ||||||||
\(971\) | −0.690661 | −0.0221644 | −0.0110822 | − | 0.999939i | \(-0.503528\pi\) | ||||
−0.0110822 | + | 0.999939i | \(0.503528\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −38.7100 | −1.24035 | ||||||||
\(975\) | −33.6118 | −1.07644 | ||||||||
\(976\) | −9.70032 | −0.310500 | ||||||||
\(977\) | −33.1895 | −1.06183 | −0.530913 | − | 0.847426i | \(-0.678151\pi\) | ||||
−0.530913 | + | 0.847426i | \(0.678151\pi\) | |||||||
\(978\) | −13.0553 | −0.417463 | ||||||||
\(979\) | 18.4029 | 0.588161 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.70032 | −0.309707 | ||||||||
\(982\) | 19.1705 | 0.611757 | ||||||||
\(983\) | 42.6620 | 1.36071 | 0.680354 | − | 0.732884i | \(-0.261826\pi\) | ||||
0.680354 | + | 0.732884i | \(0.261826\pi\) | |||||||
\(984\) | 8.24943 | 0.262982 | ||||||||
\(985\) | 2.09591 | 0.0667811 | ||||||||
\(986\) | −7.24943 | −0.230869 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.38592 | −0.234977 | ||||||||
\(989\) | 10.0599 | 0.319887 | ||||||||
\(990\) | 3.20147 | 0.101749 | ||||||||
\(991\) | −24.0147 | −0.762853 | −0.381426 | − | 0.924399i | \(-0.624567\pi\) | ||||
−0.381426 | + | 0.924399i | \(0.624567\pi\) | |||||||
\(992\) | −10.4989 | −0.333339 | ||||||||
\(993\) | −21.2471 | −0.674257 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.6288 | 0.780785 | ||||||||
\(996\) | 6.55646 | 0.207750 | ||||||||
\(997\) | −33.5971 | −1.06403 | −0.532015 | − | 0.846735i | \(-0.678565\pi\) | ||||
−0.532015 | + | 0.846735i | \(0.678565\pi\) | |||||||
\(998\) | −27.9188 | −0.883755 | ||||||||
\(999\) | −5.15352 | −0.163050 |
(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 | 3234.2.a.bg.1.3 | 3 | ||
3.2 | odd | 2 | 9702.2.a.du.1.1 | 3 | |||
7.3 | odd | 6 | 462.2.i.f.331.3 | yes | 6 | ||
7.5 | odd | 6 | 462.2.i.f.67.3 | ✓ | 6 | ||
7.6 | odd | 2 | 3234.2.a.bi.1.1 | 3 | |||
21.5 | even | 6 | 1386.2.k.w.991.1 | 6 | |||
21.17 | even | 6 | 1386.2.k.w.793.1 | 6 | |||
21.20 | even | 2 | 9702.2.a.dt.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.3 | ✓ | 6 | 7.5 | odd | 6 | ||
462.2.i.f.331.3 | yes | 6 | 7.3 | odd | 6 | ||
1386.2.k.w.793.1 | 6 | 21.17 | even | 6 | |||
1386.2.k.w.991.1 | 6 | 21.5 | even | 6 | |||
3234.2.a.bg.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3234.2.a.bi.1.1 | 3 | 7.6 | odd | 2 | |||
9702.2.a.dt.1.3 | 3 | 21.20 | even | 2 | |||
9702.2.a.du.1.1 | 3 | 3.2 | odd | 2 |