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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) 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 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.58579 | −0.717168 | −0.358584 | − | 0.933497i | \(-0.616740\pi\) | ||||
−0.358584 | + | 0.933497i | \(0.616740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.24264 | −1.43216 | −0.716080 | − | 0.698018i | \(-0.754065\pi\) | ||||
−0.716080 | + | 0.698018i | \(0.754065\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.58579 | −0.507114 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.65685 | −0.307670 | −0.153835 | − | 0.988097i | \(-0.549162\pi\) | ||||
−0.153835 | + | 0.988097i | \(0.549162\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | 2.24264 | 0.402790 | 0.201395 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201395 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.82843 | −0.793789 | −0.396894 | − | 0.917864i | \(-0.629912\pi\) | ||||
−0.396894 | + | 0.917864i | \(0.629912\pi\) | |||||||
\(38\) | −6.24264 | −1.01269 | ||||||||
\(39\) | −2.58579 | −0.414057 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −0.343146 | −0.0535904 | −0.0267952 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267952 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.828427 | 0.126334 | 0.0631670 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631670 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 0.828427 | 0.122145 | ||||||||
\(47\) | −11.8995 | −1.73572 | −0.867860 | − | 0.496809i | \(-0.834505\pi\) | ||||
−0.867860 | + | 0.496809i | \(0.834505\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | −2.58579 | −0.358584 | ||||||||
\(53\) | 6.48528 | 0.890822 | 0.445411 | − | 0.895326i | \(-0.353058\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353058\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.24264 | −0.826858 | ||||||||
\(58\) | −1.65685 | −0.217556 | ||||||||
\(59\) | −1.17157 | −0.152526 | −0.0762629 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762629 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | −5.41421 | −0.693219 | −0.346610 | − | 0.938010i | \(-0.612667\pi\) | ||||
−0.346610 | + | 0.938010i | \(0.612667\pi\) | |||||||
\(62\) | 2.24264 | 0.284816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.17157 | 0.641455 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −6.82843 | −0.834225 | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||||
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −0.343146 | −0.0401622 | −0.0200811 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200811 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(74\) | −4.82843 | −0.561293 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −6.24264 | −0.716080 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.58579 | −0.292783 | ||||||||
\(79\) | 0.485281 | 0.0545984 | 0.0272992 | − | 0.999627i | \(-0.491309\pi\) | ||||
0.0272992 | + | 0.999627i | \(0.491309\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.343146 | −0.0378941 | ||||||||
\(83\) | 9.07107 | 0.995679 | 0.497840 | − | 0.867269i | \(-0.334127\pi\) | ||||
0.497840 | + | 0.867269i | \(0.334127\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0.828427 | 0.0893316 | ||||||||
\(87\) | −1.65685 | −0.177633 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −12.2426 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.828427 | 0.0863695 | ||||||||
\(93\) | 2.24264 | 0.232551 | ||||||||
\(94\) | −11.8995 | −1.22734 | ||||||||
\(95\) | 12.4853 | 1.28096 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −9.89949 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 0.928932 | 0.0924322 | 0.0462161 | − | 0.998931i | \(-0.485284\pi\) | ||||
0.0462161 | + | 0.998931i | \(0.485284\pi\) | |||||||
\(102\) | −2.00000 | −0.198030 | ||||||||
\(103\) | 2.24264 | 0.220974 | 0.110487 | − | 0.993878i | \(-0.464759\pi\) | ||||
0.110487 | + | 0.993878i | \(0.464759\pi\) | |||||||
\(104\) | −2.58579 | −0.253557 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.48528 | 0.629906 | ||||||||
\(107\) | 7.17157 | 0.693302 | 0.346651 | − | 0.937994i | \(-0.387319\pi\) | ||||
0.346651 | + | 0.937994i | \(0.387319\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.6569 | 1.49965 | 0.749827 | − | 0.661634i | \(-0.230137\pi\) | ||||
0.749827 | + | 0.661634i | \(0.230137\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | −4.82843 | −0.458294 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.65685 | −0.532152 | −0.266076 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(114\) | −6.24264 | −0.584677 | ||||||||
\(115\) | −1.65685 | −0.154502 | ||||||||
\(116\) | −1.65685 | −0.153835 | ||||||||
\(117\) | −2.58579 | −0.239056 | ||||||||
\(118\) | −1.17157 | −0.107852 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | −0.182574 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.41421 | −0.490180 | ||||||||
\(123\) | −0.343146 | −0.0309404 | ||||||||
\(124\) | 2.24264 | 0.201395 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.828427 | 0.0729389 | ||||||||
\(130\) | 5.17157 | 0.453577 | ||||||||
\(131\) | 13.5563 | 1.18442 | 0.592212 | − | 0.805782i | \(-0.298255\pi\) | ||||
0.592212 | + | 0.805782i | \(0.298255\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.82843 | −0.589886 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 17.3137 | 1.47921 | 0.739605 | − | 0.673041i | \(-0.235012\pi\) | ||||
0.739605 | + | 0.673041i | \(0.235012\pi\) | |||||||
\(138\) | 0.828427 | 0.0705204 | ||||||||
\(139\) | −19.8995 | −1.68785 | −0.843927 | − | 0.536459i | \(-0.819762\pi\) | ||||
−0.843927 | + | 0.536459i | \(0.819762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8995 | −1.00212 | ||||||||
\(142\) | −5.65685 | −0.474713 | ||||||||
\(143\) | 2.58579 | 0.216234 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.31371 | 0.275189 | ||||||||
\(146\) | −0.343146 | −0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.82843 | −0.396894 | ||||||||
\(149\) | 4.00000 | 0.327693 | 0.163846 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163846 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | −6.24264 | −0.506345 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.48528 | −0.360266 | ||||||||
\(156\) | −2.58579 | −0.207029 | ||||||||
\(157\) | −7.17157 | −0.572354 | −0.286177 | − | 0.958177i | \(-0.592385\pi\) | ||||
−0.286177 | + | 0.958177i | \(0.592385\pi\) | |||||||
\(158\) | 0.485281 | 0.0386069 | ||||||||
\(159\) | 6.48528 | 0.514316 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −13.6569 | −1.06969 | −0.534844 | − | 0.844951i | \(-0.679630\pi\) | ||||
−0.534844 | + | 0.844951i | \(0.679630\pi\) | |||||||
\(164\) | −0.343146 | −0.0267952 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 9.07107 | 0.704051 | ||||||||
\(167\) | 10.8284 | 0.837929 | 0.418964 | − | 0.908003i | \(-0.362393\pi\) | ||||
0.418964 | + | 0.908003i | \(0.362393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31371 | −0.485670 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | −6.24264 | −0.477387 | ||||||||
\(172\) | 0.828427 | 0.0631670 | ||||||||
\(173\) | −13.8995 | −1.05676 | −0.528380 | − | 0.849008i | \(-0.677200\pi\) | ||||
−0.528380 | + | 0.849008i | \(0.677200\pi\) | |||||||
\(174\) | −1.65685 | −0.125606 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −1.17157 | −0.0880608 | ||||||||
\(178\) | −12.2426 | −0.917625 | ||||||||
\(179\) | −3.51472 | −0.262702 | −0.131351 | − | 0.991336i | \(-0.541932\pi\) | ||||
−0.131351 | + | 0.991336i | \(0.541932\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | −13.3137 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.41421 | −0.400230 | ||||||||
\(184\) | 0.828427 | 0.0610725 | ||||||||
\(185\) | 9.65685 | 0.709986 | ||||||||
\(186\) | 2.24264 | 0.164438 | ||||||||
\(187\) | 2.00000 | 0.146254 | ||||||||
\(188\) | −11.8995 | −0.867860 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.4853 | 0.905778 | ||||||||
\(191\) | −17.7990 | −1.28789 | −0.643945 | − | 0.765072i | \(-0.722703\pi\) | ||||
−0.643945 | + | 0.765072i | \(0.722703\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 18.9706 | 1.36553 | 0.682765 | − | 0.730638i | \(-0.260777\pi\) | ||||
0.682765 | + | 0.730638i | \(0.260777\pi\) | |||||||
\(194\) | −9.89949 | −0.710742 | ||||||||
\(195\) | 5.17157 | 0.370344 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.34315 | 0.309436 | 0.154718 | − | 0.987959i | \(-0.450553\pi\) | ||||
0.154718 | + | 0.987959i | \(0.450553\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 27.2132 | 1.92909 | 0.964546 | − | 0.263913i | \(-0.0850133\pi\) | ||||
0.964546 | + | 0.263913i | \(0.0850133\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.82843 | −0.481640 | ||||||||
\(202\) | 0.928932 | 0.0653594 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 0.686292 | 0.0479327 | ||||||||
\(206\) | 2.24264 | 0.156252 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | −2.58579 | −0.179292 | ||||||||
\(209\) | 6.24264 | 0.431812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.8284 | −1.98463 | −0.992315 | − | 0.123734i | \(-0.960513\pi\) | ||||
−0.992315 | + | 0.123734i | \(0.960513\pi\) | |||||||
\(212\) | 6.48528 | 0.445411 | ||||||||
\(213\) | −5.65685 | −0.387601 | ||||||||
\(214\) | 7.17157 | 0.490239 | ||||||||
\(215\) | −1.65685 | −0.112997 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.6569 | 1.06042 | ||||||||
\(219\) | −0.343146 | −0.0231876 | ||||||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 5.17157 | 0.347878 | ||||||||
\(222\) | −4.82843 | −0.324063 | ||||||||
\(223\) | 2.24264 | 0.150178 | 0.0750892 | − | 0.997177i | \(-0.476076\pi\) | ||||
0.0750892 | + | 0.997177i | \(0.476076\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −5.65685 | −0.376288 | ||||||||
\(227\) | −7.89949 | −0.524308 | −0.262154 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262154 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(228\) | −6.24264 | −0.413429 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | −1.65685 | −0.109250 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.65685 | −0.108778 | ||||||||
\(233\) | 3.65685 | 0.239568 | 0.119784 | − | 0.992800i | \(-0.461780\pi\) | ||||
0.119784 | + | 0.992800i | \(0.461780\pi\) | |||||||
\(234\) | −2.58579 | −0.169038 | ||||||||
\(235\) | 23.7990 | 1.55247 | ||||||||
\(236\) | −1.17157 | −0.0762629 | ||||||||
\(237\) | 0.485281 | 0.0315224 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | −2.00000 | −0.129099 | ||||||||
\(241\) | −3.65685 | −0.235559 | −0.117779 | − | 0.993040i | \(-0.537578\pi\) | ||||
−0.117779 | + | 0.993040i | \(0.537578\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.41421 | −0.346610 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.343146 | −0.0218782 | ||||||||
\(247\) | 16.1421 | 1.02710 | ||||||||
\(248\) | 2.24264 | 0.142408 | ||||||||
\(249\) | 9.07107 | 0.574856 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 8.48528 | 0.535586 | 0.267793 | − | 0.963476i | \(-0.413706\pi\) | ||||
0.267793 | + | 0.963476i | \(0.413706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.828427 | −0.0520828 | ||||||||
\(254\) | −14.1421 | −0.887357 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.2132 | −0.824217 | −0.412108 | − | 0.911135i | \(-0.635208\pi\) | ||||
−0.412108 | + | 0.911135i | \(0.635208\pi\) | |||||||
\(258\) | 0.828427 | 0.0515756 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.17157 | 0.320727 | ||||||||
\(261\) | −1.65685 | −0.102557 | ||||||||
\(262\) | 13.5563 | 0.837514 | ||||||||
\(263\) | 14.8284 | 0.914360 | 0.457180 | − | 0.889374i | \(-0.348860\pi\) | ||||
0.457180 | + | 0.889374i | \(0.348860\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −12.9706 | −0.796775 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2426 | −0.749237 | ||||||||
\(268\) | −6.82843 | −0.417113 | ||||||||
\(269\) | 17.3137 | 1.05564 | 0.527818 | − | 0.849358i | \(-0.323010\pi\) | ||||
0.527818 | + | 0.849358i | \(0.323010\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 6.14214 | 0.373108 | 0.186554 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186554 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.3137 | 1.04596 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.828427 | 0.0498655 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −19.8995 | −1.19349 | ||||||||
\(279\) | 2.24264 | 0.134263 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.3137 | 1.27147 | 0.635735 | − | 0.771908i | \(-0.280697\pi\) | ||||
0.635735 | + | 0.771908i | \(0.280697\pi\) | |||||||
\(282\) | −11.8995 | −0.708605 | ||||||||
\(283\) | −6.24264 | −0.371086 | −0.185543 | − | 0.982636i | \(-0.559404\pi\) | ||||
−0.185543 | + | 0.982636i | \(0.559404\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | 12.4853 | 0.739564 | ||||||||
\(286\) | 2.58579 | 0.152901 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 3.31371 | 0.194588 | ||||||||
\(291\) | −9.89949 | −0.580319 | ||||||||
\(292\) | −0.343146 | −0.0200811 | ||||||||
\(293\) | 19.0711 | 1.11414 | 0.557072 | − | 0.830464i | \(-0.311925\pi\) | ||||
0.557072 | + | 0.830464i | \(0.311925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34315 | 0.136423 | ||||||||
\(296\) | −4.82843 | −0.280647 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | −2.14214 | −0.123883 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 0.928932 | 0.0533658 | ||||||||
\(304\) | −6.24264 | −0.358040 | ||||||||
\(305\) | 10.8284 | 0.620034 | ||||||||
\(306\) | −2.00000 | −0.114332 | ||||||||
\(307\) | 10.9289 | 0.623747 | 0.311874 | − | 0.950124i | \(-0.399043\pi\) | ||||
0.311874 | + | 0.950124i | \(0.399043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.24264 | 0.127579 | ||||||||
\(310\) | −4.48528 | −0.254747 | ||||||||
\(311\) | −27.8995 | −1.58204 | −0.791018 | − | 0.611793i | \(-0.790448\pi\) | ||||
−0.791018 | + | 0.611793i | \(0.790448\pi\) | |||||||
\(312\) | −2.58579 | −0.146391 | ||||||||
\(313\) | −0.242641 | −0.0137149 | −0.00685743 | − | 0.999976i | \(-0.502183\pi\) | ||||
−0.00685743 | + | 0.999976i | \(0.502183\pi\) | |||||||
\(314\) | −7.17157 | −0.404715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.485281 | 0.0272992 | ||||||||
\(317\) | 7.17157 | 0.402796 | 0.201398 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201398 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(318\) | 6.48528 | 0.363677 | ||||||||
\(319\) | 1.65685 | 0.0927660 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 7.17157 | 0.400278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4853 | 0.694700 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.58579 | 0.143434 | ||||||||
\(326\) | −13.6569 | −0.756383 | ||||||||
\(327\) | 15.6569 | 0.865826 | ||||||||
\(328\) | −0.343146 | −0.0189471 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.00000 | 0.110096 | ||||||||
\(331\) | 11.7990 | 0.648531 | 0.324266 | − | 0.945966i | \(-0.394883\pi\) | ||||
0.324266 | + | 0.945966i | \(0.394883\pi\) | |||||||
\(332\) | 9.07107 | 0.497840 | ||||||||
\(333\) | −4.82843 | −0.264596 | ||||||||
\(334\) | 10.8284 | 0.592505 | ||||||||
\(335\) | 13.6569 | 0.746154 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.17157 | 0.390660 | 0.195330 | − | 0.980738i | \(-0.437422\pi\) | ||||
0.195330 | + | 0.980738i | \(0.437422\pi\) | |||||||
\(338\) | −6.31371 | −0.343420 | ||||||||
\(339\) | −5.65685 | −0.307238 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | −2.24264 | −0.121446 | ||||||||
\(342\) | −6.24264 | −0.337563 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.828427 | 0.0446658 | ||||||||
\(345\) | −1.65685 | −0.0892020 | ||||||||
\(346\) | −13.8995 | −0.747241 | ||||||||
\(347\) | −31.4558 | −1.68864 | −0.844319 | − | 0.535841i | \(-0.819995\pi\) | ||||
−0.844319 | + | 0.535841i | \(0.819995\pi\) | |||||||
\(348\) | −1.65685 | −0.0888167 | ||||||||
\(349\) | 14.5858 | 0.780759 | 0.390380 | − | 0.920654i | \(-0.372344\pi\) | ||||
0.390380 | + | 0.920654i | \(0.372344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.58579 | −0.138019 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 21.2132 | 1.12906 | 0.564532 | − | 0.825411i | \(-0.309057\pi\) | ||||
0.564532 | + | 0.825411i | \(0.309057\pi\) | |||||||
\(354\) | −1.17157 | −0.0622684 | ||||||||
\(355\) | 11.3137 | 0.600469 | ||||||||
\(356\) | −12.2426 | −0.648859 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.51472 | −0.185759 | ||||||||
\(359\) | 10.8284 | 0.571503 | 0.285751 | − | 0.958304i | \(-0.407757\pi\) | ||||
0.285751 | + | 0.958304i | \(0.407757\pi\) | |||||||
\(360\) | −2.00000 | −0.105409 | ||||||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | −13.3137 | −0.699753 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.686292 | 0.0359221 | ||||||||
\(366\) | −5.41421 | −0.283005 | ||||||||
\(367\) | 35.4142 | 1.84861 | 0.924303 | − | 0.381658i | \(-0.124647\pi\) | ||||
0.924303 | + | 0.381658i | \(0.124647\pi\) | |||||||
\(368\) | 0.828427 | 0.0431847 | ||||||||
\(369\) | −0.343146 | −0.0178635 | ||||||||
\(370\) | 9.65685 | 0.502036 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.24264 | 0.116276 | ||||||||
\(373\) | −31.9411 | −1.65385 | −0.826924 | − | 0.562313i | \(-0.809912\pi\) | ||||
−0.826924 | + | 0.562313i | \(0.809912\pi\) | |||||||
\(374\) | 2.00000 | 0.103418 | ||||||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | −11.8995 | −0.613670 | ||||||||
\(377\) | 4.28427 | 0.220651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.2843 | −1.24740 | −0.623700 | − | 0.781664i | \(-0.714371\pi\) | ||||
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(380\) | 12.4853 | 0.640481 | ||||||||
\(381\) | −14.1421 | −0.724524 | ||||||||
\(382\) | −17.7990 | −0.910676 | ||||||||
\(383\) | −2.72792 | −0.139390 | −0.0696952 | − | 0.997568i | \(-0.522203\pi\) | ||||
−0.0696952 | + | 0.997568i | \(0.522203\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.9706 | 0.965576 | ||||||||
\(387\) | 0.828427 | 0.0421113 | ||||||||
\(388\) | −9.89949 | −0.502571 | ||||||||
\(389\) | 22.2843 | 1.12986 | 0.564929 | − | 0.825140i | \(-0.308904\pi\) | ||||
0.564929 | + | 0.825140i | \(0.308904\pi\) | |||||||
\(390\) | 5.17157 | 0.261873 | ||||||||
\(391\) | −1.65685 | −0.0837907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5563 | 0.683827 | ||||||||
\(394\) | 4.34315 | 0.218805 | ||||||||
\(395\) | −0.970563 | −0.0488343 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 16.8284 | 0.844595 | 0.422297 | − | 0.906457i | \(-0.361224\pi\) | ||||
0.422297 | + | 0.906457i | \(0.361224\pi\) | |||||||
\(398\) | 27.2132 | 1.36407 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 33.3137 | 1.66361 | 0.831804 | − | 0.555070i | \(-0.187309\pi\) | ||||
0.831804 | + | 0.555070i | \(0.187309\pi\) | |||||||
\(402\) | −6.82843 | −0.340571 | ||||||||
\(403\) | −5.79899 | −0.288868 | ||||||||
\(404\) | 0.928932 | 0.0462161 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.82843 | 0.239336 | ||||||||
\(408\) | −2.00000 | −0.0990148 | ||||||||
\(409\) | 18.4853 | 0.914038 | 0.457019 | − | 0.889457i | \(-0.348917\pi\) | ||||
0.457019 | + | 0.889457i | \(0.348917\pi\) | |||||||
\(410\) | 0.686292 | 0.0338935 | ||||||||
\(411\) | 17.3137 | 0.854022 | ||||||||
\(412\) | 2.24264 | 0.110487 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.828427 | 0.0407150 | ||||||||
\(415\) | −18.1421 | −0.890562 | ||||||||
\(416\) | −2.58579 | −0.126779 | ||||||||
\(417\) | −19.8995 | −0.974482 | ||||||||
\(418\) | 6.24264 | 0.305338 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3431 | −0.796516 | −0.398258 | − | 0.917273i | \(-0.630385\pi\) | ||||
−0.398258 | + | 0.917273i | \(0.630385\pi\) | |||||||
\(422\) | −28.8284 | −1.40335 | ||||||||
\(423\) | −11.8995 | −0.578573 | ||||||||
\(424\) | 6.48528 | 0.314953 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | −5.65685 | −0.274075 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.17157 | 0.346651 | ||||||||
\(429\) | 2.58579 | 0.124843 | ||||||||
\(430\) | −1.65685 | −0.0799006 | ||||||||
\(431\) | −26.1421 | −1.25922 | −0.629611 | − | 0.776910i | \(-0.716786\pi\) | ||||
−0.629611 | + | 0.776910i | \(0.716786\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −2.38478 | −0.114605 | −0.0573025 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573025 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.31371 | 0.158880 | ||||||||
\(436\) | 15.6569 | 0.749827 | ||||||||
\(437\) | −5.17157 | −0.247390 | ||||||||
\(438\) | −0.343146 | −0.0163961 | ||||||||
\(439\) | 34.8284 | 1.66227 | 0.831135 | − | 0.556071i | \(-0.187692\pi\) | ||||
0.831135 | + | 0.556071i | \(0.187692\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.17157 | 0.245987 | ||||||||
\(443\) | −4.48528 | −0.213102 | −0.106551 | − | 0.994307i | \(-0.533981\pi\) | ||||
−0.106551 | + | 0.994307i | \(0.533981\pi\) | |||||||
\(444\) | −4.82843 | −0.229147 | ||||||||
\(445\) | 24.4853 | 1.16071 | ||||||||
\(446\) | 2.24264 | 0.106192 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9706 | −0.800890 | −0.400445 | − | 0.916321i | \(-0.631145\pi\) | ||||
−0.400445 | + | 0.916321i | \(0.631145\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0.343146 | 0.0161581 | ||||||||
\(452\) | −5.65685 | −0.266076 | ||||||||
\(453\) | 4.00000 | 0.187936 | ||||||||
\(454\) | −7.89949 | −0.370742 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.24264 | −0.292338 | ||||||||
\(457\) | −6.68629 | −0.312772 | −0.156386 | − | 0.987696i | \(-0.549984\pi\) | ||||
−0.156386 | + | 0.987696i | \(0.549984\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | −1.65685 | −0.0772512 | ||||||||
\(461\) | 33.4142 | 1.55626 | 0.778128 | − | 0.628106i | \(-0.216170\pi\) | ||||
0.778128 | + | 0.628106i | \(0.216170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3137 | 0.897584 | 0.448792 | − | 0.893636i | \(-0.351854\pi\) | ||||
0.448792 | + | 0.893636i | \(0.351854\pi\) | |||||||
\(464\) | −1.65685 | −0.0769175 | ||||||||
\(465\) | −4.48528 | −0.208000 | ||||||||
\(466\) | 3.65685 | 0.169401 | ||||||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −2.58579 | −0.119528 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 23.7990 | 1.09777 | ||||||||
\(471\) | −7.17157 | −0.330449 | ||||||||
\(472\) | −1.17157 | −0.0539260 | ||||||||
\(473\) | −0.828427 | −0.0380911 | ||||||||
\(474\) | 0.485281 | 0.0222897 | ||||||||
\(475\) | 6.24264 | 0.286432 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.48528 | 0.296941 | ||||||||
\(478\) | 23.3137 | 1.06634 | ||||||||
\(479\) | 15.3137 | 0.699701 | 0.349851 | − | 0.936806i | \(-0.386232\pi\) | ||||
0.349851 | + | 0.936806i | \(0.386232\pi\) | |||||||
\(480\) | −2.00000 | −0.0912871 | ||||||||
\(481\) | 12.4853 | 0.569280 | ||||||||
\(482\) | −3.65685 | −0.166565 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 19.7990 | 0.899026 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −28.1421 | −1.27524 | −0.637621 | − | 0.770350i | \(-0.720081\pi\) | ||||
−0.637621 | + | 0.770350i | \(0.720081\pi\) | |||||||
\(488\) | −5.41421 | −0.245090 | ||||||||
\(489\) | −13.6569 | −0.617584 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.62742 | 0.118574 | 0.0592868 | − | 0.998241i | \(-0.481117\pi\) | ||||
0.0592868 | + | 0.998241i | \(0.481117\pi\) | |||||||
\(492\) | −0.343146 | −0.0154702 | ||||||||
\(493\) | 3.31371 | 0.149242 | ||||||||
\(494\) | 16.1421 | 0.726269 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | 2.24264 | 0.100698 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.07107 | 0.406484 | ||||||||
\(499\) | 22.1421 | 0.991218 | 0.495609 | − | 0.868546i | \(-0.334945\pi\) | ||||
0.495609 | + | 0.868546i | \(0.334945\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 10.8284 | 0.483778 | ||||||||
\(502\) | 8.48528 | 0.378717 | ||||||||
\(503\) | −8.48528 | −0.378340 | −0.189170 | − | 0.981944i | \(-0.560580\pi\) | ||||
−0.189170 | + | 0.981944i | \(0.560580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.85786 | −0.0826739 | ||||||||
\(506\) | −0.828427 | −0.0368281 | ||||||||
\(507\) | −6.31371 | −0.280402 | ||||||||
\(508\) | −14.1421 | −0.627456 | ||||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.24264 | −0.275619 | ||||||||
\(514\) | −13.2132 | −0.582809 | ||||||||
\(515\) | −4.48528 | −0.197645 | ||||||||
\(516\) | 0.828427 | 0.0364695 | ||||||||
\(517\) | 11.8995 | 0.523339 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.8995 | −0.610120 | ||||||||
\(520\) | 5.17157 | 0.226788 | ||||||||
\(521\) | 21.2132 | 0.929367 | 0.464684 | − | 0.885477i | \(-0.346168\pi\) | ||||
0.464684 | + | 0.885477i | \(0.346168\pi\) | |||||||
\(522\) | −1.65685 | −0.0725185 | ||||||||
\(523\) | −5.07107 | −0.221742 | −0.110871 | − | 0.993835i | \(-0.535364\pi\) | ||||
−0.110871 | + | 0.993835i | \(0.535364\pi\) | |||||||
\(524\) | 13.5563 | 0.592212 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.8284 | 0.646550 | ||||||||
\(527\) | −4.48528 | −0.195382 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | −12.9706 | −0.563405 | ||||||||
\(531\) | −1.17157 | −0.0508419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.887302 | 0.0384333 | ||||||||
\(534\) | −12.2426 | −0.529791 | ||||||||
\(535\) | −14.3431 | −0.620108 | ||||||||
\(536\) | −6.82843 | −0.294943 | ||||||||
\(537\) | −3.51472 | −0.151671 | ||||||||
\(538\) | 17.3137 | 0.746447 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | −0.0860663 | ||||||||
\(541\) | −22.6863 | −0.975360 | −0.487680 | − | 0.873023i | \(-0.662157\pi\) | ||||
−0.487680 | + | 0.873023i | \(0.662157\pi\) | |||||||
\(542\) | 6.14214 | 0.263827 | ||||||||
\(543\) | −13.3137 | −0.571346 | ||||||||
\(544\) | −2.00000 | −0.0857493 | ||||||||
\(545\) | −31.3137 | −1.34133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.62742 | 0.112340 | 0.0561701 | − | 0.998421i | \(-0.482111\pi\) | ||||
0.0561701 | + | 0.998421i | \(0.482111\pi\) | |||||||
\(548\) | 17.3137 | 0.739605 | ||||||||
\(549\) | −5.41421 | −0.231073 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 10.3431 | 0.440633 | ||||||||
\(552\) | 0.828427 | 0.0352602 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 9.65685 | 0.409911 | ||||||||
\(556\) | −19.8995 | −0.843927 | ||||||||
\(557\) | 8.34315 | 0.353510 | 0.176755 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176755 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(558\) | 2.24264 | 0.0949386 | ||||||||
\(559\) | −2.14214 | −0.0906027 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | 21.3137 | 0.899065 | ||||||||
\(563\) | 6.92893 | 0.292020 | 0.146010 | − | 0.989283i | \(-0.453357\pi\) | ||||
0.146010 | + | 0.989283i | \(0.453357\pi\) | |||||||
\(564\) | −11.8995 | −0.501059 | ||||||||
\(565\) | 11.3137 | 0.475971 | ||||||||
\(566\) | −6.24264 | −0.262398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.65685 | −0.237356 | ||||||||
\(569\) | −33.3137 | −1.39658 | −0.698292 | − | 0.715813i | \(-0.746056\pi\) | ||||
−0.698292 | + | 0.715813i | \(0.746056\pi\) | |||||||
\(570\) | 12.4853 | 0.522951 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 2.58579 | 0.108117 | ||||||||
\(573\) | −17.7990 | −0.743563 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.828427 | −0.0345478 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 35.5563 | 1.48023 | 0.740115 | − | 0.672480i | \(-0.234771\pi\) | ||||
0.740115 | + | 0.672480i | \(0.234771\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 18.9706 | 0.788390 | ||||||||
\(580\) | 3.31371 | 0.137594 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.89949 | −0.410347 | ||||||||
\(583\) | −6.48528 | −0.268593 | ||||||||
\(584\) | −0.343146 | −0.0141995 | ||||||||
\(585\) | 5.17157 | 0.213818 | ||||||||
\(586\) | 19.0711 | 0.787819 | ||||||||
\(587\) | 27.7990 | 1.14739 | 0.573694 | − | 0.819070i | \(-0.305510\pi\) | ||||
0.573694 | + | 0.819070i | \(0.305510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0000 | −0.576860 | ||||||||
\(590\) | 2.34315 | 0.0964658 | ||||||||
\(591\) | 4.34315 | 0.178653 | ||||||||
\(592\) | −4.82843 | −0.198447 | ||||||||
\(593\) | 14.6863 | 0.603094 | 0.301547 | − | 0.953451i | \(-0.402497\pi\) | ||||
0.301547 | + | 0.953451i | \(0.402497\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 27.2132 | 1.11376 | ||||||||
\(598\) | −2.14214 | −0.0875984 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −20.8284 | −0.849609 | −0.424805 | − | 0.905285i | \(-0.639657\pi\) | ||||
−0.424805 | + | 0.905285i | \(0.639657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.82843 | −0.278075 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0.928932 | 0.0377353 | ||||||||
\(607\) | 12.6863 | 0.514921 | 0.257460 | − | 0.966289i | \(-0.417114\pi\) | ||||
0.257460 | + | 0.966289i | \(0.417114\pi\) | |||||||
\(608\) | −6.24264 | −0.253173 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.8284 | 0.438430 | ||||||||
\(611\) | 30.7696 | 1.24480 | ||||||||
\(612\) | −2.00000 | −0.0808452 | ||||||||
\(613\) | −41.6569 | −1.68250 | −0.841252 | − | 0.540643i | \(-0.818181\pi\) | ||||
−0.841252 | + | 0.540643i | \(0.818181\pi\) | |||||||
\(614\) | 10.9289 | 0.441056 | ||||||||
\(615\) | 0.686292 | 0.0276739 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.00000 | −0.322068 | −0.161034 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161034 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(618\) | 2.24264 | 0.0902122 | ||||||||
\(619\) | 10.3431 | 0.415726 | 0.207863 | − | 0.978158i | \(-0.433349\pi\) | ||||
0.207863 | + | 0.978158i | \(0.433349\pi\) | |||||||
\(620\) | −4.48528 | −0.180133 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | −27.8995 | −1.11867 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.58579 | −0.103514 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −0.242641 | −0.00969787 | ||||||||
\(627\) | 6.24264 | 0.249307 | ||||||||
\(628\) | −7.17157 | −0.286177 | ||||||||
\(629\) | 9.65685 | 0.385044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.85786 | 0.312817 | 0.156408 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156408 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(632\) | 0.485281 | 0.0193035 | ||||||||
\(633\) | −28.8284 | −1.14583 | ||||||||
\(634\) | 7.17157 | 0.284820 | ||||||||
\(635\) | 28.2843 | 1.12243 | ||||||||
\(636\) | 6.48528 | 0.257158 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.65685 | 0.0655955 | ||||||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | −2.00000 | −0.0790569 | ||||||||
\(641\) | −12.6863 | −0.501078 | −0.250539 | − | 0.968106i | \(-0.580608\pi\) | ||||
−0.250539 | + | 0.968106i | \(0.580608\pi\) | |||||||
\(642\) | 7.17157 | 0.283039 | ||||||||
\(643\) | 13.4558 | 0.530647 | 0.265323 | − | 0.964159i | \(-0.414521\pi\) | ||||
0.265323 | + | 0.964159i | \(0.414521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.65685 | −0.0652386 | ||||||||
\(646\) | 12.4853 | 0.491227 | ||||||||
\(647\) | 13.0711 | 0.513877 | 0.256938 | − | 0.966428i | \(-0.417286\pi\) | ||||
0.256938 | + | 0.966428i | \(0.417286\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.17157 | 0.0459883 | ||||||||
\(650\) | 2.58579 | 0.101423 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.6569 | −0.534844 | ||||||||
\(653\) | −34.2843 | −1.34165 | −0.670824 | − | 0.741617i | \(-0.734059\pi\) | ||||
−0.670824 | + | 0.741617i | \(0.734059\pi\) | |||||||
\(654\) | 15.6569 | 0.612231 | ||||||||
\(655\) | −27.1127 | −1.05938 | ||||||||
\(656\) | −0.343146 | −0.0133976 | ||||||||
\(657\) | −0.343146 | −0.0133874 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.1127 | 0.510798 | 0.255399 | − | 0.966836i | \(-0.417793\pi\) | ||||
0.255399 | + | 0.966836i | \(0.417793\pi\) | |||||||
\(660\) | 2.00000 | 0.0778499 | ||||||||
\(661\) | −27.9411 | −1.08678 | −0.543392 | − | 0.839479i | \(-0.682860\pi\) | ||||
−0.543392 | + | 0.839479i | \(0.682860\pi\) | |||||||
\(662\) | 11.7990 | 0.458581 | ||||||||
\(663\) | 5.17157 | 0.200847 | ||||||||
\(664\) | 9.07107 | 0.352026 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.82843 | −0.187098 | ||||||||
\(667\) | −1.37258 | −0.0531466 | ||||||||
\(668\) | 10.8284 | 0.418964 | ||||||||
\(669\) | 2.24264 | 0.0867055 | ||||||||
\(670\) | 13.6569 | 0.527610 | ||||||||
\(671\) | 5.41421 | 0.209013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.4853 | −1.32931 | −0.664655 | − | 0.747150i | \(-0.731421\pi\) | ||||
−0.664655 | + | 0.747150i | \(0.731421\pi\) | |||||||
\(674\) | 7.17157 | 0.276239 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −6.31371 | −0.242835 | ||||||||
\(677\) | −12.0416 | −0.462797 | −0.231399 | − | 0.972859i | \(-0.574330\pi\) | ||||
−0.231399 | + | 0.972859i | \(0.574330\pi\) | |||||||
\(678\) | −5.65685 | −0.217250 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −7.89949 | −0.302709 | ||||||||
\(682\) | −2.24264 | −0.0858752 | ||||||||
\(683\) | −44.7696 | −1.71306 | −0.856530 | − | 0.516098i | \(-0.827384\pi\) | ||||
−0.856530 | + | 0.516098i | \(0.827384\pi\) | |||||||
\(684\) | −6.24264 | −0.238693 | ||||||||
\(685\) | −34.6274 | −1.32305 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | 0.828427 | 0.0315835 | ||||||||
\(689\) | −16.7696 | −0.638869 | ||||||||
\(690\) | −1.65685 | −0.0630754 | ||||||||
\(691\) | −14.1421 | −0.537992 | −0.268996 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268996 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(692\) | −13.8995 | −0.528380 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.4558 | −1.19405 | ||||||||
\(695\) | 39.7990 | 1.50966 | ||||||||
\(696\) | −1.65685 | −0.0628029 | ||||||||
\(697\) | 0.686292 | 0.0259951 | ||||||||
\(698\) | 14.5858 | 0.552080 | ||||||||
\(699\) | 3.65685 | 0.138315 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.3137 | −0.502852 | −0.251426 | − | 0.967877i | \(-0.580899\pi\) | ||||
−0.251426 | + | 0.967877i | \(0.580899\pi\) | |||||||
\(702\) | −2.58579 | −0.0975942 | ||||||||
\(703\) | 30.1421 | 1.13683 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 23.7990 | 0.896322 | ||||||||
\(706\) | 21.2132 | 0.798369 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.17157 | −0.0440304 | ||||||||
\(709\) | 38.7696 | 1.45602 | 0.728011 | − | 0.685566i | \(-0.240445\pi\) | ||||
0.728011 | + | 0.685566i | \(0.240445\pi\) | |||||||
\(710\) | 11.3137 | 0.424596 | ||||||||
\(711\) | 0.485281 | 0.0181995 | ||||||||
\(712\) | −12.2426 | −0.458812 | ||||||||
\(713\) | 1.85786 | 0.0695776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.17157 | −0.193406 | ||||||||
\(716\) | −3.51472 | −0.131351 | ||||||||
\(717\) | 23.3137 | 0.870666 | ||||||||
\(718\) | 10.8284 | 0.404113 | ||||||||
\(719\) | −32.1838 | −1.20025 | −0.600126 | − | 0.799906i | \(-0.704883\pi\) | ||||
−0.600126 | + | 0.799906i | \(0.704883\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.9706 | 0.743227 | ||||||||
\(723\) | −3.65685 | −0.136000 | ||||||||
\(724\) | −13.3137 | −0.494800 | ||||||||
\(725\) | 1.65685 | 0.0615340 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 11.2132 | 0.415875 | 0.207937 | − | 0.978142i | \(-0.433325\pi\) | ||||
0.207937 | + | 0.978142i | \(0.433325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.686292 | 0.0254008 | ||||||||
\(731\) | −1.65685 | −0.0612810 | ||||||||
\(732\) | −5.41421 | −0.200115 | ||||||||
\(733\) | 11.5563 | 0.426843 | 0.213422 | − | 0.976960i | \(-0.431539\pi\) | ||||
0.213422 | + | 0.976960i | \(0.431539\pi\) | |||||||
\(734\) | 35.4142 | 1.30716 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.828427 | 0.0305362 | ||||||||
\(737\) | 6.82843 | 0.251528 | ||||||||
\(738\) | −0.343146 | −0.0126314 | ||||||||
\(739\) | −42.6274 | −1.56807 | −0.784037 | − | 0.620714i | \(-0.786843\pi\) | ||||
−0.784037 | + | 0.620714i | \(0.786843\pi\) | |||||||
\(740\) | 9.65685 | 0.354993 | ||||||||
\(741\) | 16.1421 | 0.592996 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.6274 | 0.976865 | 0.488433 | − | 0.872602i | \(-0.337569\pi\) | ||||
0.488433 | + | 0.872602i | \(0.337569\pi\) | |||||||
\(744\) | 2.24264 | 0.0822192 | ||||||||
\(745\) | −8.00000 | −0.293097 | ||||||||
\(746\) | −31.9411 | −1.16945 | ||||||||
\(747\) | 9.07107 | 0.331893 | ||||||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | 16.1421 | 0.589035 | 0.294517 | − | 0.955646i | \(-0.404841\pi\) | ||||
0.294517 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(752\) | −11.8995 | −0.433930 | ||||||||
\(753\) | 8.48528 | 0.309221 | ||||||||
\(754\) | 4.28427 | 0.156024 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8579 | −0.721746 | −0.360873 | − | 0.932615i | \(-0.617521\pi\) | ||||
−0.360873 | + | 0.932615i | \(0.617521\pi\) | |||||||
\(758\) | −24.2843 | −0.882044 | ||||||||
\(759\) | −0.828427 | −0.0300700 | ||||||||
\(760\) | 12.4853 | 0.452889 | ||||||||
\(761\) | 18.4853 | 0.670091 | 0.335045 | − | 0.942202i | \(-0.391248\pi\) | ||||
0.335045 | + | 0.942202i | \(0.391248\pi\) | |||||||
\(762\) | −14.1421 | −0.512316 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.7990 | −0.643945 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | −2.72792 | −0.0985638 | ||||||||
\(767\) | 3.02944 | 0.109387 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 44.1421 | 1.59181 | 0.795903 | − | 0.605424i | \(-0.206996\pi\) | ||||
0.795903 | + | 0.605424i | \(0.206996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2132 | −0.475862 | ||||||||
\(772\) | 18.9706 | 0.682765 | ||||||||
\(773\) | −22.4853 | −0.808739 | −0.404370 | − | 0.914596i | \(-0.632509\pi\) | ||||
−0.404370 | + | 0.914596i | \(0.632509\pi\) | |||||||
\(774\) | 0.828427 | 0.0297772 | ||||||||
\(775\) | −2.24264 | −0.0805580 | ||||||||
\(776\) | −9.89949 | −0.355371 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.2843 | 0.798930 | ||||||||
\(779\) | 2.14214 | 0.0767500 | ||||||||
\(780\) | 5.17157 | 0.185172 | ||||||||
\(781\) | 5.65685 | 0.202418 | ||||||||
\(782\) | −1.65685 | −0.0592490 | ||||||||
\(783\) | −1.65685 | −0.0592111 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3431 | 0.511929 | ||||||||
\(786\) | 13.5563 | 0.483539 | ||||||||
\(787\) | 0.585786 | 0.0208810 | 0.0104405 | − | 0.999945i | \(-0.496677\pi\) | ||||
0.0104405 | + | 0.999945i | \(0.496677\pi\) | |||||||
\(788\) | 4.34315 | 0.154718 | ||||||||
\(789\) | 14.8284 | 0.527906 | ||||||||
\(790\) | −0.970563 | −0.0345311 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 14.0000 | 0.497155 | ||||||||
\(794\) | 16.8284 | 0.597219 | ||||||||
\(795\) | −12.9706 | −0.460018 | ||||||||
\(796\) | 27.2132 | 0.964546 | ||||||||
\(797\) | −34.4853 | −1.22153 | −0.610766 | − | 0.791811i | \(-0.709138\pi\) | ||||
−0.610766 | + | 0.791811i | \(0.709138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7990 | 0.841948 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −12.2426 | −0.432572 | ||||||||
\(802\) | 33.3137 | 1.17635 | ||||||||
\(803\) | 0.343146 | 0.0121094 | ||||||||
\(804\) | −6.82843 | −0.240820 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.79899 | −0.204261 | ||||||||
\(807\) | 17.3137 | 0.609471 | ||||||||
\(808\) | 0.928932 | 0.0326797 | ||||||||
\(809\) | −46.7696 | −1.64433 | −0.822165 | − | 0.569249i | \(-0.807234\pi\) | ||||
−0.822165 | + | 0.569249i | \(0.807234\pi\) | |||||||
\(810\) | −2.00000 | −0.0702728 | ||||||||
\(811\) | 0.384776 | 0.0135113 | 0.00675566 | − | 0.999977i | \(-0.497850\pi\) | ||||
0.00675566 | + | 0.999977i | \(0.497850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.14214 | 0.215414 | ||||||||
\(814\) | 4.82843 | 0.169236 | ||||||||
\(815\) | 27.3137 | 0.956757 | ||||||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | −5.17157 | −0.180930 | ||||||||
\(818\) | 18.4853 | 0.646323 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.686292 | 0.0239663 | ||||||||
\(821\) | 24.6863 | 0.861558 | 0.430779 | − | 0.902458i | \(-0.358239\pi\) | ||||
0.430779 | + | 0.902458i | \(0.358239\pi\) | |||||||
\(822\) | 17.3137 | 0.603885 | ||||||||
\(823\) | 0.142136 | 0.00495454 | 0.00247727 | − | 0.999997i | \(-0.499211\pi\) | ||||
0.00247727 | + | 0.999997i | \(0.499211\pi\) | |||||||
\(824\) | 2.24264 | 0.0781261 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6863 | 0.580239 | 0.290120 | − | 0.956990i | \(-0.406305\pi\) | ||||
0.290120 | + | 0.956990i | \(0.406305\pi\) | |||||||
\(828\) | 0.828427 | 0.0287898 | ||||||||
\(829\) | 6.28427 | 0.218262 | 0.109131 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109131 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(830\) | −18.1421 | −0.629723 | ||||||||
\(831\) | −16.0000 | −0.555034 | ||||||||
\(832\) | −2.58579 | −0.0896460 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.8995 | −0.689063 | ||||||||
\(835\) | −21.6569 | −0.749466 | ||||||||
\(836\) | 6.24264 | 0.215906 | ||||||||
\(837\) | 2.24264 | 0.0775170 | ||||||||
\(838\) | −16.0000 | −0.552711 | ||||||||
\(839\) | 2.92893 | 0.101118 | 0.0505590 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505590 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2548 | −0.905339 | ||||||||
\(842\) | −16.3431 | −0.563222 | ||||||||
\(843\) | 21.3137 | 0.734083 | ||||||||
\(844\) | −28.8284 | −0.992315 | ||||||||
\(845\) | 12.6274 | 0.434396 | ||||||||
\(846\) | −11.8995 | −0.409113 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.48528 | 0.222705 | ||||||||
\(849\) | −6.24264 | −0.214247 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | −5.65685 | −0.193801 | ||||||||
\(853\) | −4.44365 | −0.152148 | −0.0760739 | − | 0.997102i | \(-0.524238\pi\) | ||||
−0.0760739 | + | 0.997102i | \(0.524238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.4853 | 0.426988 | ||||||||
\(856\) | 7.17157 | 0.245119 | ||||||||
\(857\) | 28.1421 | 0.961317 | 0.480659 | − | 0.876908i | \(-0.340398\pi\) | ||||
0.480659 | + | 0.876908i | \(0.340398\pi\) | |||||||
\(858\) | 2.58579 | 0.0882773 | ||||||||
\(859\) | −54.4264 | −1.85701 | −0.928503 | − | 0.371326i | \(-0.878903\pi\) | ||||
−0.928503 | + | 0.371326i | \(0.878903\pi\) | |||||||
\(860\) | −1.65685 | −0.0564983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.1421 | −0.890405 | ||||||||
\(863\) | 34.7696 | 1.18357 | 0.591785 | − | 0.806096i | \(-0.298424\pi\) | ||||
0.591785 | + | 0.806096i | \(0.298424\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 27.7990 | 0.945194 | ||||||||
\(866\) | −2.38478 | −0.0810380 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.485281 | −0.0164620 | ||||||||
\(870\) | 3.31371 | 0.112345 | ||||||||
\(871\) | 17.6569 | 0.598280 | ||||||||
\(872\) | 15.6569 | 0.530208 | ||||||||
\(873\) | −9.89949 | −0.335047 | ||||||||
\(874\) | −5.17157 | −0.174931 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.343146 | −0.0115938 | ||||||||
\(877\) | −29.3137 | −0.989854 | −0.494927 | − | 0.868935i | \(-0.664805\pi\) | ||||
−0.494927 | + | 0.868935i | \(0.664805\pi\) | |||||||
\(878\) | 34.8284 | 1.17540 | ||||||||
\(879\) | 19.0711 | 0.643251 | ||||||||
\(880\) | 2.00000 | 0.0674200 | ||||||||
\(881\) | −18.1005 | −0.609822 | −0.304911 | − | 0.952381i | \(-0.598627\pi\) | ||||
−0.304911 | + | 0.952381i | \(0.598627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.6274 | 1.16531 | 0.582653 | − | 0.812721i | \(-0.302015\pi\) | ||||
0.582653 | + | 0.812721i | \(0.302015\pi\) | |||||||
\(884\) | 5.17157 | 0.173939 | ||||||||
\(885\) | 2.34315 | 0.0787640 | ||||||||
\(886\) | −4.48528 | −0.150686 | ||||||||
\(887\) | 52.2843 | 1.75553 | 0.877767 | − | 0.479088i | \(-0.159032\pi\) | ||||
0.877767 | + | 0.479088i | \(0.159032\pi\) | |||||||
\(888\) | −4.82843 | −0.162031 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.4853 | 0.820748 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 2.24264 | 0.0750892 | ||||||||
\(893\) | 74.2843 | 2.48583 | ||||||||
\(894\) | 4.00000 | 0.133780 | ||||||||
\(895\) | 7.02944 | 0.234968 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.14214 | −0.0715238 | ||||||||
\(898\) | −16.9706 | −0.566315 | ||||||||
\(899\) | −3.71573 | −0.123926 | ||||||||
\(900\) | −1.00000 | −0.0333333 | ||||||||
\(901\) | −12.9706 | −0.432112 | ||||||||
\(902\) | 0.343146 | 0.0114255 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.65685 | −0.188144 | ||||||||
\(905\) | 26.6274 | 0.885125 | ||||||||
\(906\) | 4.00000 | 0.132891 | ||||||||
\(907\) | −47.7990 | −1.58714 | −0.793570 | − | 0.608479i | \(-0.791780\pi\) | ||||
−0.793570 | + | 0.608479i | \(0.791780\pi\) | |||||||
\(908\) | −7.89949 | −0.262154 | ||||||||
\(909\) | 0.928932 | 0.0308107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.4558 | 1.30723 | 0.653615 | − | 0.756827i | \(-0.273251\pi\) | ||||
0.653615 | + | 0.756827i | \(0.273251\pi\) | |||||||
\(912\) | −6.24264 | −0.206714 | ||||||||
\(913\) | −9.07107 | −0.300209 | ||||||||
\(914\) | −6.68629 | −0.221163 | ||||||||
\(915\) | 10.8284 | 0.357977 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | 32.9706 | 1.08760 | 0.543799 | − | 0.839215i | \(-0.316985\pi\) | ||||
0.543799 | + | 0.839215i | \(0.316985\pi\) | |||||||
\(920\) | −1.65685 | −0.0546249 | ||||||||
\(921\) | 10.9289 | 0.360121 | ||||||||
\(922\) | 33.4142 | 1.10044 | ||||||||
\(923\) | 14.6274 | 0.481467 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.82843 | 0.158758 | ||||||||
\(926\) | 19.3137 | 0.634688 | ||||||||
\(927\) | 2.24264 | 0.0736580 | ||||||||
\(928\) | −1.65685 | −0.0543889 | ||||||||
\(929\) | −53.2132 | −1.74587 | −0.872934 | − | 0.487838i | \(-0.837786\pi\) | ||||
−0.872934 | + | 0.487838i | \(0.837786\pi\) | |||||||
\(930\) | −4.48528 | −0.147078 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.65685 | 0.119784 | ||||||||
\(933\) | −27.8995 | −0.913388 | ||||||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | −2.58579 | −0.0845191 | ||||||||
\(937\) | −44.9117 | −1.46720 | −0.733600 | − | 0.679581i | \(-0.762162\pi\) | ||||
−0.733600 | + | 0.679581i | \(0.762162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.242641 | −0.00791828 | ||||||||
\(940\) | 23.7990 | 0.776237 | ||||||||
\(941\) | 3.55635 | 0.115934 | 0.0579668 | − | 0.998319i | \(-0.481538\pi\) | ||||
0.0579668 | + | 0.998319i | \(0.481538\pi\) | |||||||
\(942\) | −7.17157 | −0.233662 | ||||||||
\(943\) | −0.284271 | −0.00925715 | ||||||||
\(944\) | −1.17157 | −0.0381314 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.828427 | −0.0269345 | ||||||||
\(947\) | 60.5685 | 1.96821 | 0.984107 | − | 0.177579i | \(-0.0568265\pi\) | ||||
0.984107 | + | 0.177579i | \(0.0568265\pi\) | |||||||
\(948\) | 0.485281 | 0.0157612 | ||||||||
\(949\) | 0.887302 | 0.0288030 | ||||||||
\(950\) | 6.24264 | 0.202538 | ||||||||
\(951\) | 7.17157 | 0.232554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4853 | 0.857942 | 0.428971 | − | 0.903318i | \(-0.358876\pi\) | ||||
0.428971 | + | 0.903318i | \(0.358876\pi\) | |||||||
\(954\) | 6.48528 | 0.209969 | ||||||||
\(955\) | 35.5980 | 1.15192 | ||||||||
\(956\) | 23.3137 | 0.754019 | ||||||||
\(957\) | 1.65685 | 0.0535585 | ||||||||
\(958\) | 15.3137 | 0.494763 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00000 | −0.0645497 | ||||||||
\(961\) | −25.9706 | −0.837760 | ||||||||
\(962\) | 12.4853 | 0.402542 | ||||||||
\(963\) | 7.17157 | 0.231101 | ||||||||
\(964\) | −3.65685 | −0.117779 | ||||||||
\(965\) | −37.9411 | −1.22137 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.9411 | 1.86326 | 0.931630 | − | 0.363407i | \(-0.118387\pi\) | ||||
0.931630 | + | 0.363407i | \(0.118387\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 12.4853 | 0.401085 | ||||||||
\(970\) | 19.7990 | 0.635707 | ||||||||
\(971\) | −27.3137 | −0.876539 | −0.438269 | − | 0.898844i | \(-0.644408\pi\) | ||||
−0.438269 | + | 0.898844i | \(0.644408\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −28.1421 | −0.901732 | ||||||||
\(975\) | 2.58579 | 0.0828114 | ||||||||
\(976\) | −5.41421 | −0.173305 | ||||||||
\(977\) | −18.6274 | −0.595944 | −0.297972 | − | 0.954575i | \(-0.596310\pi\) | ||||
−0.297972 | + | 0.954575i | \(0.596310\pi\) | |||||||
\(978\) | −13.6569 | −0.436698 | ||||||||
\(979\) | 12.2426 | 0.391276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6569 | 0.499885 | ||||||||
\(982\) | 2.62742 | 0.0838442 | ||||||||
\(983\) | 52.8701 | 1.68629 | 0.843146 | − | 0.537684i | \(-0.180701\pi\) | ||||
0.843146 | + | 0.537684i | \(0.180701\pi\) | |||||||
\(984\) | −0.343146 | −0.0109391 | ||||||||
\(985\) | −8.68629 | −0.276768 | ||||||||
\(986\) | 3.31371 | 0.105530 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.1421 | 0.513550 | ||||||||
\(989\) | 0.686292 | 0.0218228 | ||||||||
\(990\) | 2.00000 | 0.0635642 | ||||||||
\(991\) | −50.9117 | −1.61726 | −0.808632 | − | 0.588315i | \(-0.799791\pi\) | ||||
−0.808632 | + | 0.588315i | \(0.799791\pi\) | |||||||
\(992\) | 2.24264 | 0.0712039 | ||||||||
\(993\) | 11.7990 | 0.374430 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.4264 | −1.72543 | ||||||||
\(996\) | 9.07107 | 0.287428 | ||||||||
\(997\) | −33.4142 | −1.05824 | −0.529119 | − | 0.848547i | \(-0.677478\pi\) | ||||
−0.529119 | + | 0.848547i | \(0.677478\pi\) | |||||||
\(998\) | 22.1421 | 0.700897 | ||||||||
\(999\) | −4.82843 | −0.152765 |
(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.bd.1.2 | yes | 2 | |
3.2 | odd | 2 | 9702.2.a.cy.1.2 | 2 | |||
7.6 | odd | 2 | 3234.2.a.bc.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 9702.2.a.ci.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bc.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
3234.2.a.bd.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9702.2.a.ci.1.1 | 2 | 21.20 | even | 2 | |||
9702.2.a.cy.1.2 | 2 | 3.2 | odd | 2 |