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 | 1.1 | ||
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 | \(-0.753970\pi\) | ||||
−0.715871 | + | 0.698233i | \(0.753970\pi\) | |||||||
\(6\) | 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 | \(-0.847856\pi\) | ||||
−0.887929 | + | 0.459981i | \(0.847856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.20147 | −0.826617 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.15352 | 0.264636 | 0.132318 | − | 0.991207i | \(-0.457758\pi\) | ||||
0.132318 | + | 0.991207i | \(0.457758\pi\) | |||||||
\(20\) | −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 | \(-0.108159\pi\) | ||||
0.942825 | + | 0.333289i | \(0.108159\pi\) | |||||||
\(32\) | 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 | \(-0.277202\pi\) | ||||
0.644172 | + | 0.764881i | \(0.277202\pi\) | |||||||
\(42\) | 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 | \(-0.645409\pi\) | ||||
−0.441092 | + | 0.897462i | \(0.645409\pi\) | |||||||
\(48\) | 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 | \(-0.228963\pi\) | ||||
0.752262 | + | 0.658864i | \(0.228963\pi\) | |||||||
\(60\) | −3.20147 | −0.413308 | ||||||||
\(61\) | 9.70032 | 1.24200 | 0.621000 | − | 0.783811i | \(-0.286727\pi\) | ||||
0.621000 | + | 0.783811i | \(0.286727\pi\) | |||||||
\(62\) | 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 | \(-0.539140\pi\) | ||||
−0.122654 | + | 0.992450i | \(0.539140\pi\) | |||||||
\(74\) | 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 | \(-0.382834\pi\) | ||||
0.359833 | + | 0.933017i | \(0.382834\pi\) | |||||||
\(84\) | 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 | \(-0.929184\pi\) | ||||
−0.975354 | + | 0.220645i | \(0.929184\pi\) | |||||||
\(90\) | −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 | \(-0.590057\pi\) | ||||
−0.279162 | + | 0.960244i | \(0.590057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 5.24943 | 0.524943 | ||||||||
\(101\) | −19.9594 | −1.98604 | −0.993018 | − | 0.117965i | \(-0.962363\pi\) | ||||
−0.993018 | + | 0.117965i | \(0.962363\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 0.307039 | 0.0302535 | 0.0151267 | − | 0.999886i | \(-0.495185\pi\) | ||||
0.0151267 | + | 0.999886i | \(0.495185\pi\) | |||||||
\(104\) | −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 | \(-0.266898\pi\) | ||||
0.668591 | + | 0.743631i | \(0.266898\pi\) | |||||||
\(132\) | 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 | \(-0.126281\pi\) | ||||
0.922332 | + | 0.386398i | \(0.126281\pi\) | |||||||
\(140\) | 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 | \(-0.623222\pi\) | ||||
−0.377517 | + | 0.926002i | \(0.623222\pi\) | |||||||
\(158\) | −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 | \(-0.583596\pi\) | ||||
−0.259617 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(168\) | 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 | \(-0.567061\pi\) | ||||
−0.209122 | + | 0.977889i | \(0.567061\pi\) | |||||||
\(174\) | 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 | \(-0.123672\pi\) | ||||
0.925468 | + | 0.378826i | \(0.123672\pi\) | |||||||
\(182\) | 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 | \(-0.587907\pi\) | ||||
−0.272670 | + | 0.962108i | \(0.587907\pi\) | |||||||
\(200\) | 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 | \(-0.666281\pi\) | ||||
−0.498949 | + | 0.866631i | \(0.666281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.24943 | 0.349962 | ||||||||
\(226\) | −12.4989 | −0.831411 | ||||||||
\(227\) | −0.249425 | −0.0165549 | −0.00827746 | − | 0.999966i | \(-0.502635\pi\) | ||||
−0.00827746 | + | 0.999966i | \(0.502635\pi\) | |||||||
\(228\) | 1.15352 | 0.0763937 | ||||||||
\(229\) | −4.09591 | −0.270665 | −0.135333 | − | 0.990800i | \(-0.543210\pi\) | ||||
−0.135333 | + | 0.990800i | \(0.543210\pi\) | |||||||
\(230\) | −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 | \(-0.314181\pi\) | ||||
0.551170 | + | 0.834393i | \(0.314181\pi\) | |||||||
\(242\) | 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 | \(-0.419176\pi\) | ||||
0.251197 | + | 0.967936i | \(0.419176\pi\) | |||||||
\(252\) | 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 | \(-0.746251\pi\) | ||||
−0.698729 | + | 0.715387i | \(0.746251\pi\) | |||||||
\(258\) | 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 | \(-0.420545\pi\) | ||||
0.247032 | + | 0.969007i | \(0.420545\pi\) | |||||||
\(270\) | −3.20147 | −0.194835 | ||||||||
\(271\) | −4.80589 | −0.291937 | −0.145968 | − | 0.989289i | \(-0.546630\pi\) | ||||
−0.145968 | + | 0.989289i | \(0.546630\pi\) | |||||||
\(272\) | 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 | \(-0.197066\pi\) | ||||
0.814400 | + | 0.580304i | \(0.197066\pi\) | |||||||
\(284\) | 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 | \(-0.695720\pi\) | ||||
−0.576853 | + | 0.816848i | \(0.695720\pi\) | |||||||
\(294\) | 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 | \(-0.460778\pi\) | ||||
0.122908 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.307039 | 0.0174668 | ||||||||
\(310\) | −33.6118 | −1.90902 | ||||||||
\(311\) | −14.7579 | −0.836846 | −0.418423 | − | 0.908252i | \(-0.637417\pi\) | ||||
−0.418423 | + | 0.908252i | \(0.637417\pi\) | |||||||
\(312\) | −6.40294 | −0.362495 | ||||||||
\(313\) | 20.7506 | 1.17289 | 0.586446 | − | 0.809988i | \(-0.300527\pi\) | ||||
0.586446 | + | 0.809988i | \(0.300527\pi\) | |||||||
\(314\) | −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 | \(-0.534206\pi\) | ||||
−0.107255 | + | 0.994232i | \(0.534206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.40294 | −0.341764 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −1.09821 | −0.0584516 | −0.0292258 | − | 0.999573i | \(-0.509304\pi\) | ||||
−0.0292258 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(354\) | 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 | \(-0.493427\pi\) | ||||
0.0206493 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(368\) | 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 | \(-0.388419\pi\) | ||||
0.343408 | + | 0.939186i | \(0.388419\pi\) | |||||||
\(384\) | 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 | \(-0.394710\pi\) | ||||
0.324780 | + | 0.945790i | \(0.394710\pi\) | |||||||
\(398\) | −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 | \(-0.869461\pi\) | ||||
−0.917080 | + | 0.398702i | \(0.869461\pi\) | |||||||
\(410\) | −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 | \(-0.315169\pi\) | ||||
0.548579 | + | 0.836099i | \(0.315169\pi\) | |||||||
\(420\) | 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 | \(-0.240368\pi\) | ||||
0.728176 | + | 0.685390i | \(0.240368\pi\) | |||||||
\(434\) | 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 | \(-0.581890\pi\) | ||||
−0.254435 | + | 0.967090i | \(0.581890\pi\) | |||||||
\(440\) | −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 | \(-0.761498\pi\) | ||||
−0.732182 | + | 0.681109i | \(0.761498\pi\) | |||||||
\(462\) | 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 | \(-0.338013\pi\) | ||||
0.487215 | + | 0.873282i | \(0.338013\pi\) | |||||||
\(468\) | −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 | \(-0.661009\pi\) | ||||
−0.484528 | + | 0.874776i | \(0.661009\pi\) | |||||||
\(480\) | −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 | \(-0.562204\pi\) | ||||
−0.194179 | + | 0.980966i | \(0.562204\pi\) | |||||||
\(504\) | 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 | \(-0.512623\pi\) | ||||
−0.0396451 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(510\) | −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 | \(-0.326965\pi\) | ||||
0.517225 | + | 0.855849i | \(0.326965\pi\) | |||||||
\(522\) | 7.24943 | 0.317299 | ||||||||
\(523\) | 43.4006 | 1.89778 | 0.948889 | − | 0.315610i | \(-0.102209\pi\) | ||||
0.948889 | + | 0.315610i | \(0.102209\pi\) | |||||||
\(524\) | 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 | \(-0.214353\pi\) | ||||
0.781700 | + | 0.623654i | \(0.214353\pi\) | |||||||
\(578\) | −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 | \(-0.614791\pi\) | ||||
−0.352859 | + | 0.935676i | \(0.614791\pi\) | |||||||
\(588\) | 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 | \(-0.730341\pi\) | ||||
−0.662115 | + | 0.749402i | \(0.730341\pi\) | |||||||
\(594\) | 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 | \(-0.286305\pi\) | ||||
0.622037 | + | 0.782988i | \(0.286305\pi\) | |||||||
\(602\) | 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 | \(-0.415080\pi\) | ||||
0.263631 | + | 0.964624i | \(0.415080\pi\) | |||||||
\(608\) | 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 | \(-0.184065\pi\) | ||||
0.837417 | + | 0.546564i | \(0.184065\pi\) | |||||||
\(620\) | −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 | \(-0.746783\pi\) | ||||
−0.699924 | + | 0.714218i | \(0.746783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4989 | −0.649642 | ||||||||
\(646\) | 1.15352 | 0.0453846 | ||||||||
\(647\) | 23.8156 | 0.936286 | 0.468143 | − | 0.883653i | \(-0.344923\pi\) | ||||
0.468143 | + | 0.883653i | \(0.344923\pi\) | |||||||
\(648\) | 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 | \(-0.475465\pi\) | ||||
0.0770016 | + | 0.997031i | \(0.475465\pi\) | |||||||
\(662\) | 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 | \(-0.706653\pi\) | ||||
−0.604564 | + | 0.796557i | \(0.706653\pi\) | |||||||
\(678\) | −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 | \(-0.338433\pi\) | ||||
0.486063 | + | 0.873924i | \(0.338433\pi\) | |||||||
\(692\) | −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 | \(-0.483623\pi\) | ||||
0.0514268 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(720\) | −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 | \(-0.412645\pi\) | ||||
0.271003 | + | 0.962578i | \(0.412645\pi\) | |||||||
\(728\) | 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 | \(-0.458109\pi\) | ||||
0.131225 | + | 0.991353i | \(0.458109\pi\) | |||||||
\(734\) | 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 | \(-0.407847\pi\) | ||||
0.285479 | + | 0.958385i | \(0.407847\pi\) | |||||||
\(762\) | 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 | \(-0.232738\pi\) | ||||
0.744395 | + | 0.667739i | \(0.232738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4029 | −0.806822 | ||||||||
\(772\) | 8.70998 | 0.313479 | ||||||||
\(773\) | 4.90916 | 0.176570 | 0.0882850 | − | 0.996095i | \(-0.471861\pi\) | ||||
0.0882850 | + | 0.996095i | \(0.471861\pi\) | |||||||
\(774\) | 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 | \(-0.495632\pi\) | ||||
0.0137219 | + | 0.999906i | \(0.495632\pi\) | |||||||
\(788\) | 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 | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(798\) | 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 | \(-0.824314\pi\) | ||||
−0.851512 | + | 0.524334i | \(0.824314\pi\) | |||||||
\(812\) | 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 | \(-0.174423\pi\) | ||||
0.853586 | + | 0.520952i | \(0.174423\pi\) | |||||||
\(830\) | −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 | \(-0.515489\pi\) | ||||
−0.0486415 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(840\) | 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 | \(-0.486942\pi\) | ||||
0.0410116 | + | 0.999159i | \(0.486942\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.69296 | −0.126297 | ||||||||
\(856\) | −9.05531 | −0.309504 | ||||||||
\(857\) | 0.808189 | 0.0276072 | 0.0138036 | − | 0.999905i | \(-0.495606\pi\) | ||||
0.0138036 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(858\) | −6.40294 | −0.218593 | ||||||||
\(859\) | 6.55646 | 0.223704 | 0.111852 | − | 0.993725i | \(-0.464322\pi\) | ||||
0.111852 | + | 0.993725i | \(0.464322\pi\) | |||||||
\(860\) | −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 | \(-0.545729\pi\) | ||||
−0.143167 | + | 0.989699i | \(0.545729\pi\) | |||||||
\(882\) | 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 | \(-0.400668\pi\) | ||||
0.307021 | + | 0.951703i | \(0.400668\pi\) | |||||||
\(888\) | 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 | \(-0.258779\pi\) | ||||
0.687339 | + | 0.726337i | \(0.258779\pi\) | |||||||
\(930\) | −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 | \(-0.684284\pi\) | ||||
−0.547142 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7506 | 0.677169 | ||||||||
\(940\) | 19.3624 | 0.631530 | ||||||||
\(941\) | −45.7483 | −1.49135 | −0.745676 | − | 0.666309i | \(-0.767873\pi\) | ||||
−0.745676 | + | 0.666309i | \(0.767873\pi\) | |||||||
\(942\) | −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 | \(-0.496472\pi\) | ||||
0.0110822 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(972\) | 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 | \(-0.738174\pi\) | ||||
−0.680354 | + | 0.732884i | \(0.738174\pi\) | |||||||
\(984\) | 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 | \(-0.321435\pi\) | ||||
0.532015 | + | 0.846735i | \(0.321435\pi\) | |||||||
\(998\) | −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.bi.1.1 | 3 | ||
3.2 | odd | 2 | 9702.2.a.dt.1.3 | 3 | |||
7.2 | even | 3 | 462.2.i.f.67.3 | ✓ | 6 | ||
7.4 | even | 3 | 462.2.i.f.331.3 | yes | 6 | ||
7.6 | odd | 2 | 3234.2.a.bg.1.3 | 3 | |||
21.2 | odd | 6 | 1386.2.k.w.991.1 | 6 | |||
21.11 | odd | 6 | 1386.2.k.w.793.1 | 6 | |||
21.20 | even | 2 | 9702.2.a.du.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.3 | ✓ | 6 | 7.2 | even | 3 | ||
462.2.i.f.331.3 | yes | 6 | 7.4 | even | 3 | ||
1386.2.k.w.793.1 | 6 | 21.11 | odd | 6 | |||
1386.2.k.w.991.1 | 6 | 21.2 | odd | 6 | |||
3234.2.a.bg.1.3 | 3 | 7.6 | odd | 2 | |||
3234.2.a.bi.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9702.2.a.dt.1.3 | 3 | 3.2 | odd | 2 | |||
9702.2.a.du.1.1 | 3 | 21.20 | even | 2 |