Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26x^{14} + 269x^{12} - 1408x^{10} + 3924x^{8} - 5655x^{6} + 3886x^{4} - 1107x^{2} + 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.36017\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36017 | −0.961786 | −0.480893 | − | 0.876779i | \(-0.659687\pi\) | ||||
−0.480893 | + | 0.876779i | \(0.659687\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.149936 | −0.0749679 | ||||||||
\(5\) | −3.81085 | −1.70427 | −0.852133 | − | 0.523326i | \(-0.824691\pi\) | ||||
−0.852133 | + | 0.523326i | \(0.824691\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.20131 | 1.58795 | 0.793974 | − | 0.607952i | \(-0.208009\pi\) | ||||
0.793974 | + | 0.607952i | \(0.208009\pi\) | |||||||
\(8\) | 2.92428 | 1.03389 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.18341 | 1.63914 | ||||||||
\(11\) | −5.13086 | −1.54701 | −0.773506 | − | 0.633789i | \(-0.781499\pi\) | ||||
−0.773506 | + | 0.633789i | \(0.781499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.63599 | −0.731093 | −0.365547 | − | 0.930793i | \(-0.619118\pi\) | ||||
−0.365547 | + | 0.930793i | \(0.619118\pi\) | |||||||
\(14\) | −5.71450 | −1.52727 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.67765 | −0.919412 | ||||||||
\(17\) | 5.08847 | 1.23414 | 0.617068 | − | 0.786910i | \(-0.288320\pi\) | ||||
0.617068 | + | 0.786910i | \(0.288320\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.48160 | −0.798733 | −0.399367 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399367 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(20\) | 0.571383 | 0.127765 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.97885 | 1.48789 | ||||||||
\(23\) | −6.87803 | −1.43417 | −0.717084 | − | 0.696986i | \(-0.754524\pi\) | ||||
−0.717084 | + | 0.696986i | \(0.754524\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.52260 | 1.90452 | ||||||||
\(26\) | 3.58540 | 0.703155 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.629927 | −0.119045 | ||||||||
\(29\) | 8.87365 | 1.64779 | 0.823897 | − | 0.566739i | \(-0.191795\pi\) | ||||
0.823897 | + | 0.566739i | \(0.191795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.71827 | 0.488215 | 0.244108 | − | 0.969748i | \(-0.421505\pi\) | ||||
0.244108 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(32\) | −0.846330 | −0.149611 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.92119 | −1.18697 | ||||||||
\(35\) | −16.0106 | −2.70628 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.12586 | −1.00709 | −0.503543 | − | 0.863970i | \(-0.667970\pi\) | ||||
−0.503543 | + | 0.863970i | \(0.667970\pi\) | |||||||
\(38\) | 4.73557 | 0.768210 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.1440 | −1.76202 | ||||||||
\(41\) | −2.10756 | −0.329146 | −0.164573 | − | 0.986365i | \(-0.552625\pi\) | ||||
−0.164573 | + | 0.986365i | \(0.552625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.74037 | −1.48539 | −0.742696 | − | 0.669628i | \(-0.766453\pi\) | ||||
−0.742696 | + | 0.669628i | \(0.766453\pi\) | |||||||
\(44\) | 0.769299 | 0.115976 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.35530 | 1.37936 | ||||||||
\(47\) | 3.39416 | 0.495089 | 0.247545 | − | 0.968877i | \(-0.420376\pi\) | ||||
0.247545 | + | 0.968877i | \(0.420376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6510 | 1.52158 | ||||||||
\(50\) | −12.9524 | −1.83174 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.395230 | 0.0548085 | ||||||||
\(53\) | 3.88387 | 0.533490 | 0.266745 | − | 0.963767i | \(-0.414052\pi\) | ||||
0.266745 | + | 0.963767i | \(0.414052\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.5530 | 2.63652 | ||||||||
\(56\) | 12.2858 | 1.64176 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.0697 | −1.58483 | ||||||||
\(59\) | 0.860571 | 0.112037 | 0.0560184 | − | 0.998430i | \(-0.482159\pi\) | ||||
0.0560184 | + | 0.998430i | \(0.482159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.91166 | 0.500837 | 0.250418 | − | 0.968138i | \(-0.419432\pi\) | ||||
0.250418 | + | 0.968138i | \(0.419432\pi\) | |||||||
\(62\) | −3.69731 | −0.469559 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.50645 | 1.06331 | ||||||||
\(65\) | 10.0454 | 1.24598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1440 | 1.60580 | 0.802898 | − | 0.596117i | \(-0.203291\pi\) | ||||
0.802898 | + | 0.596117i | \(0.203291\pi\) | |||||||
\(68\) | −0.762944 | −0.0925205 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 21.7771 | 2.60287 | ||||||||
\(71\) | 10.5463 | 1.25162 | 0.625809 | − | 0.779977i | \(-0.284769\pi\) | ||||
0.625809 | + | 0.779977i | \(0.284769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.5787 | 1.82335 | 0.911673 | − | 0.410916i | \(-0.134791\pi\) | ||||
0.911673 | + | 0.410916i | \(0.134791\pi\) | |||||||
\(74\) | 8.33222 | 0.968601 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.522016 | 0.0598793 | ||||||||
\(77\) | −21.5564 | −2.45657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9184 | 1.45343 | 0.726717 | − | 0.686936i | \(-0.241045\pi\) | ||||
0.726717 | + | 0.686936i | \(0.241045\pi\) | |||||||
\(80\) | 14.0150 | 1.56692 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.86665 | 0.316568 | ||||||||
\(83\) | −3.13017 | −0.343581 | −0.171790 | − | 0.985134i | \(-0.554955\pi\) | ||||
−0.171790 | + | 0.985134i | \(0.554955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.3914 | −2.10329 | ||||||||
\(86\) | 13.2486 | 1.42863 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.0041 | −1.59944 | ||||||||
\(89\) | −1.06384 | −0.112767 | −0.0563834 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563834 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0746 | −1.16094 | ||||||||
\(92\) | 1.03126 | 0.107517 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.61664 | −0.476170 | ||||||||
\(95\) | 13.2679 | 1.36125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.56949 | 0.463961 | 0.231981 | − | 0.972720i | \(-0.425479\pi\) | ||||
0.231981 | + | 0.972720i | \(0.425479\pi\) | |||||||
\(98\) | −14.4872 | −1.46343 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.42778 | −0.142778 | ||||||||
\(101\) | 6.22093 | 0.619005 | 0.309503 | − | 0.950899i | \(-0.399837\pi\) | ||||
0.309503 | + | 0.950899i | \(0.399837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.45078 | −0.635614 | −0.317807 | − | 0.948155i | \(-0.602946\pi\) | ||||
−0.317807 | + | 0.948155i | \(0.602946\pi\) | |||||||
\(104\) | −7.70838 | −0.755869 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.28272 | −0.513103 | ||||||||
\(107\) | 17.2746 | 1.67000 | 0.834999 | − | 0.550251i | \(-0.185468\pi\) | ||||
0.834999 | + | 0.550251i | \(0.185468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.97212 | −0.476242 | −0.238121 | − | 0.971235i | \(-0.576532\pi\) | ||||
−0.238121 | + | 0.971235i | \(0.576532\pi\) | |||||||
\(110\) | −26.5954 | −2.53577 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.4510 | −1.45998 | ||||||||
\(113\) | 7.01139 | 0.659576 | 0.329788 | − | 0.944055i | \(-0.393023\pi\) | ||||
0.329788 | + | 0.944055i | \(0.393023\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.2112 | 2.44420 | ||||||||
\(116\) | −1.33048 | −0.123532 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.17052 | −0.107755 | ||||||||
\(119\) | 21.3783 | 1.95974 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3257 | 1.39325 | ||||||||
\(122\) | −5.32052 | −0.481698 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.407565 | −0.0366005 | ||||||||
\(125\) | −17.2350 | −1.54154 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −9.87756 | −0.873061 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.6634 | −1.19836 | ||||||||
\(131\) | 13.0678 | 1.14174 | 0.570869 | − | 0.821041i | \(-0.306606\pi\) | ||||
0.570869 | + | 0.821041i | \(0.306606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6273 | −1.26835 | ||||||||
\(134\) | −17.8781 | −1.54443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.8801 | 1.27596 | ||||||||
\(137\) | −8.66626 | −0.740409 | −0.370204 | − | 0.928950i | \(-0.620712\pi\) | ||||
−0.370204 | + | 0.928950i | \(0.620712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7918 | −1.25463 | −0.627313 | − | 0.778767i | \(-0.715845\pi\) | ||||
−0.627313 | + | 0.778767i | \(0.715845\pi\) | |||||||
\(140\) | 2.40056 | 0.202884 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3448 | −1.20379 | ||||||||
\(143\) | 13.5249 | 1.13101 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8162 | −2.80828 | ||||||||
\(146\) | −21.1897 | −1.75367 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.918486 | 0.0754991 | ||||||||
\(149\) | 12.4749 | 1.02198 | 0.510992 | − | 0.859586i | \(-0.329278\pi\) | ||||
0.510992 | + | 0.859586i | \(0.329278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.99628 | 0.243834 | 0.121917 | − | 0.992540i | \(-0.461096\pi\) | ||||
0.121917 | + | 0.992540i | \(0.461096\pi\) | |||||||
\(152\) | −10.1812 | −0.825801 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 29.3203 | 2.36270 | ||||||||
\(155\) | −10.3589 | −0.832049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6474 | 1.16899 | 0.584496 | − | 0.811396i | \(-0.301292\pi\) | ||||
0.584496 | + | 0.811396i | \(0.301292\pi\) | |||||||
\(158\) | −17.5712 | −1.39789 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.22524 | 0.254978 | ||||||||
\(161\) | −28.8968 | −2.27738 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5686 | −1.37608 | −0.688039 | − | 0.725674i | \(-0.741528\pi\) | ||||
−0.688039 | + | 0.725674i | \(0.741528\pi\) | |||||||
\(164\) | 0.315999 | 0.0246754 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.25756 | 0.330451 | ||||||||
\(167\) | −6.96465 | −0.538941 | −0.269471 | − | 0.963009i | \(-0.586849\pi\) | ||||
−0.269471 | + | 0.963009i | \(0.586849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.05154 | −0.465503 | ||||||||
\(170\) | 26.3756 | 2.02292 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.46043 | 0.111357 | ||||||||
\(173\) | 12.0852 | 0.918819 | 0.459409 | − | 0.888225i | \(-0.348061\pi\) | ||||
0.459409 | + | 0.888225i | \(0.348061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.0075 | 3.02428 | ||||||||
\(176\) | 18.8695 | 1.42234 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.44700 | 0.108458 | ||||||||
\(179\) | 21.7044 | 1.62227 | 0.811133 | − | 0.584862i | \(-0.198851\pi\) | ||||
0.811133 | + | 0.584862i | \(0.198851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2247 | −0.908651 | −0.454326 | − | 0.890836i | \(-0.650120\pi\) | ||||
−0.454326 | + | 0.890836i | \(0.650120\pi\) | |||||||
\(182\) | 15.0634 | 1.11657 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.1133 | −1.48277 | ||||||||
\(185\) | 23.3448 | 1.71634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.1082 | −1.90922 | ||||||||
\(188\) | −0.508906 | −0.0371158 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0465 | −1.30923 | ||||||||
\(191\) | −13.7276 | −0.993293 | −0.496646 | − | 0.867953i | \(-0.665435\pi\) | ||||
−0.496646 | + | 0.867953i | \(0.665435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.39341 | −0.532190 | −0.266095 | − | 0.963947i | \(-0.585733\pi\) | ||||
−0.266095 | + | 0.963947i | \(0.585733\pi\) | |||||||
\(194\) | −6.21528 | −0.446231 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.59697 | −0.114069 | ||||||||
\(197\) | −4.90823 | −0.349697 | −0.174849 | − | 0.984595i | \(-0.555944\pi\) | ||||
−0.174849 | + | 0.984595i | \(0.555944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.42470 | −0.313659 | −0.156829 | − | 0.987626i | \(-0.550127\pi\) | ||||
−0.156829 | + | 0.987626i | \(0.550127\pi\) | |||||||
\(200\) | 27.8468 | 1.96906 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.46152 | −0.595350 | ||||||||
\(203\) | 37.2810 | 2.61661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.03162 | 0.560952 | ||||||||
\(206\) | 8.77416 | 0.611325 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.69426 | 0.672176 | ||||||||
\(209\) | 17.8636 | 1.23565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6596 | 1.07805 | 0.539025 | − | 0.842290i | \(-0.318793\pi\) | ||||
0.539025 | + | 0.842290i | \(0.318793\pi\) | |||||||
\(212\) | −0.582331 | −0.0399946 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.4964 | −1.60618 | ||||||||
\(215\) | 37.1191 | 2.53150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4203 | 0.775260 | ||||||||
\(218\) | 6.76293 | 0.458043 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.93169 | −0.197654 | ||||||||
\(221\) | −13.4132 | −0.902268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4439 | −0.766338 | −0.383169 | − | 0.923678i | \(-0.625167\pi\) | ||||
−0.383169 | + | 0.923678i | \(0.625167\pi\) | |||||||
\(224\) | −3.55570 | −0.237575 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.53669 | −0.634371 | ||||||||
\(227\) | −2.94281 | −0.195321 | −0.0976606 | − | 0.995220i | \(-0.531136\pi\) | ||||
−0.0976606 | + | 0.995220i | \(0.531136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.17845 | 0.276119 | 0.138060 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138060 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(230\) | −35.6517 | −2.35080 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.9490 | 1.70364 | ||||||||
\(233\) | −6.10927 | −0.400231 | −0.200116 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200116 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9346 | −0.843763 | ||||||||
\(236\) | −0.129030 | −0.00839916 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −29.0781 | −1.88485 | ||||||||
\(239\) | 4.43788 | 0.287063 | 0.143531 | − | 0.989646i | \(-0.454154\pi\) | ||||
0.143531 | + | 0.989646i | \(0.454154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.60706 | 0.296767 | 0.148383 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148383 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(242\) | −20.8456 | −1.34001 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.586498 | −0.0375467 | ||||||||
\(245\) | −40.5896 | −2.59317 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.17747 | 0.583948 | ||||||||
\(248\) | 7.94897 | 0.504760 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.4425 | 1.48264 | ||||||||
\(251\) | −8.87230 | −0.560015 | −0.280007 | − | 0.959998i | \(-0.590337\pi\) | ||||
−0.280007 | + | 0.959998i | \(0.590337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.2902 | 2.21868 | ||||||||
\(254\) | −1.36017 | −0.0853447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.57773 | −0.223608 | ||||||||
\(257\) | −20.5081 | −1.27926 | −0.639631 | − | 0.768682i | \(-0.720913\pi\) | ||||
−0.639631 | + | 0.768682i | \(0.720913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.7367 | −1.59920 | ||||||||
\(260\) | −1.50616 | −0.0934082 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.7744 | −1.09811 | ||||||||
\(263\) | −7.23530 | −0.446148 | −0.223074 | − | 0.974802i | \(-0.571609\pi\) | ||||
−0.223074 | + | 0.974802i | \(0.571609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.8009 | −0.909209 | ||||||||
\(266\) | 19.8956 | 1.21988 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.97076 | −0.120383 | ||||||||
\(269\) | −4.48256 | −0.273306 | −0.136653 | − | 0.990619i | \(-0.543635\pi\) | ||||
−0.136653 | + | 0.990619i | \(0.543635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3960 | −0.935239 | −0.467620 | − | 0.883930i | \(-0.654888\pi\) | ||||
−0.467620 | + | 0.883930i | \(0.654888\pi\) | |||||||
\(272\) | −18.7136 | −1.13468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.7876 | 0.712115 | ||||||||
\(275\) | −48.8592 | −2.94632 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7500 | 0.886242 | 0.443121 | − | 0.896462i | \(-0.353871\pi\) | ||||
0.443121 | + | 0.896462i | \(0.353871\pi\) | |||||||
\(278\) | 20.1194 | 1.20668 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −46.8195 | −2.79800 | ||||||||
\(281\) | −0.941799 | −0.0561830 | −0.0280915 | − | 0.999605i | \(-0.508943\pi\) | ||||
−0.0280915 | + | 0.999605i | \(0.508943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8299 | 1.29765 | 0.648827 | − | 0.760936i | \(-0.275260\pi\) | ||||
0.648827 | + | 0.760936i | \(0.275260\pi\) | |||||||
\(284\) | −1.58127 | −0.0938311 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.3962 | −1.08779 | ||||||||
\(287\) | −8.85454 | −0.522667 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.89253 | 0.523090 | ||||||||
\(290\) | 45.9958 | 2.70096 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.33580 | −0.136692 | ||||||||
\(293\) | 25.7330 | 1.50334 | 0.751670 | − | 0.659539i | \(-0.229249\pi\) | ||||
0.751670 | + | 0.659539i | \(0.229249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.27951 | −0.190940 | ||||||||
\(296\) | −17.9137 | −1.04121 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.9680 | −0.982929 | ||||||||
\(299\) | 18.1304 | 1.04851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.9224 | −2.35873 | ||||||||
\(302\) | −4.07545 | −0.234516 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.8041 | 0.734365 | ||||||||
\(305\) | −14.9068 | −0.853559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.98285 | 0.284386 | 0.142193 | − | 0.989839i | \(-0.454585\pi\) | ||||
0.142193 | + | 0.989839i | \(0.454585\pi\) | |||||||
\(308\) | 3.23207 | 0.184164 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.0899 | 0.800253 | ||||||||
\(311\) | −24.1803 | −1.37114 | −0.685569 | − | 0.728008i | \(-0.740446\pi\) | ||||
−0.685569 | + | 0.728008i | \(0.740446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.5529 | 1.78348 | 0.891738 | − | 0.452552i | \(-0.149486\pi\) | ||||
0.891738 | + | 0.452552i | \(0.149486\pi\) | |||||||
\(314\) | −19.9230 | −1.12432 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.93693 | −0.108961 | ||||||||
\(317\) | −8.71577 | −0.489526 | −0.244763 | − | 0.969583i | \(-0.578710\pi\) | ||||
−0.244763 | + | 0.969583i | \(0.578710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.5294 | −2.54916 | ||||||||
\(320\) | −32.4168 | −1.81216 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 39.3045 | 2.19036 | ||||||||
\(323\) | −17.7160 | −0.985745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.1015 | −1.39238 | ||||||||
\(326\) | 23.8963 | 1.32349 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.16310 | −0.340301 | ||||||||
\(329\) | 14.2599 | 0.786176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.75225 | 0.371137 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(332\) | 0.469324 | 0.0257575 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.47312 | 0.518346 | ||||||||
\(335\) | −50.0899 | −2.73670 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7820 | 0.696279 | 0.348139 | − | 0.937443i | \(-0.386814\pi\) | ||||
0.348139 | + | 0.937443i | \(0.386814\pi\) | |||||||
\(338\) | 8.23112 | 0.447714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.90747 | 0.157679 | ||||||||
\(341\) | −13.9471 | −0.755275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.3392 | 0.828238 | ||||||||
\(344\) | −28.4836 | −1.53573 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.4379 | −0.883707 | ||||||||
\(347\) | 11.9717 | 0.642676 | 0.321338 | − | 0.946965i | \(-0.395867\pi\) | ||||
0.321338 | + | 0.946965i | \(0.395867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5092 | 1.31195 | 0.655974 | − | 0.754783i | \(-0.272258\pi\) | ||||
0.655974 | + | 0.754783i | \(0.272258\pi\) | |||||||
\(350\) | −54.4170 | −2.90871 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.34240 | 0.231451 | ||||||||
\(353\) | 25.6594 | 1.36571 | 0.682855 | − | 0.730554i | \(-0.260738\pi\) | ||||
0.682855 | + | 0.730554i | \(0.260738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.1905 | −2.13309 | ||||||||
\(356\) | 0.159508 | 0.00845389 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.5217 | −1.56027 | ||||||||
\(359\) | 19.3783 | 1.02275 | 0.511373 | − | 0.859359i | \(-0.329137\pi\) | ||||
0.511373 | + | 0.859359i | \(0.329137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.87848 | −0.362025 | ||||||||
\(362\) | 16.6276 | 0.873928 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.66048 | 0.0870330 | ||||||||
\(365\) | −59.3681 | −3.10747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.68336 | −0.348869 | −0.174434 | − | 0.984669i | \(-0.555810\pi\) | ||||
−0.174434 | + | 0.984669i | \(0.555810\pi\) | |||||||
\(368\) | 25.2950 | 1.31859 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −31.7529 | −1.65075 | ||||||||
\(371\) | 16.3173 | 0.847155 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.1247 | 1.35269 | 0.676344 | − | 0.736586i | \(-0.263563\pi\) | ||||
0.676344 | + | 0.736586i | \(0.263563\pi\) | |||||||
\(374\) | 35.5116 | 1.83626 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.92547 | 0.511867 | ||||||||
\(377\) | −23.3909 | −1.20469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.3991 | 1.81833 | 0.909165 | − | 0.416436i | \(-0.136721\pi\) | ||||
0.909165 | + | 0.416436i | \(0.136721\pi\) | |||||||
\(380\) | −1.98933 | −0.102050 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.6719 | 0.955335 | ||||||||
\(383\) | 9.81290 | 0.501416 | 0.250708 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250708 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 82.1481 | 4.18666 | ||||||||
\(386\) | 10.0563 | 0.511852 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.685130 | −0.0347822 | ||||||||
\(389\) | −31.6881 | −1.60665 | −0.803325 | − | 0.595540i | \(-0.796938\pi\) | ||||
−0.803325 | + | 0.595540i | \(0.796938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.9987 | −1.76996 | ||||||||
\(392\) | 31.1466 | 1.57314 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.67603 | 0.336334 | ||||||||
\(395\) | −49.2302 | −2.47704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.6152 | −0.582949 | −0.291474 | − | 0.956579i | \(-0.594146\pi\) | ||||
−0.291474 | + | 0.956579i | \(0.594146\pi\) | |||||||
\(398\) | 6.01835 | 0.301672 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −35.0208 | −1.75104 | ||||||||
\(401\) | 6.50746 | 0.324967 | 0.162483 | − | 0.986711i | \(-0.448050\pi\) | ||||
0.162483 | + | 0.986711i | \(0.448050\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.16534 | −0.356931 | ||||||||
\(404\) | −0.932739 | −0.0464055 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.7085 | −2.51662 | ||||||||
\(407\) | 31.4309 | 1.55797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.3726 | −0.957915 | −0.478957 | − | 0.877838i | \(-0.658985\pi\) | ||||
−0.478957 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(410\) | −10.9244 | −0.539516 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.967203 | 0.0476507 | ||||||||
\(413\) | 3.61553 | 0.177909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.9286 | 0.585553 | ||||||||
\(416\) | 2.23092 | 0.109380 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −24.2975 | −1.18843 | ||||||||
\(419\) | 20.4226 | 0.997707 | 0.498853 | − | 0.866686i | \(-0.333755\pi\) | ||||
0.498853 | + | 0.866686i | \(0.333755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.88195 | −0.0917204 | −0.0458602 | − | 0.998948i | \(-0.514603\pi\) | ||||
−0.0458602 | + | 0.998948i | \(0.514603\pi\) | |||||||
\(422\) | −21.2997 | −1.03685 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.3575 | 0.551570 | ||||||||
\(425\) | 48.4555 | 2.35044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.4341 | 0.795302 | ||||||||
\(428\) | −2.59008 | −0.125196 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −50.4884 | −2.43476 | ||||||||
\(431\) | −7.73832 | −0.372742 | −0.186371 | − | 0.982479i | \(-0.559673\pi\) | ||||
−0.186371 | + | 0.982479i | \(0.559673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.1363 | 1.68854 | 0.844271 | − | 0.535916i | \(-0.180034\pi\) | ||||
0.844271 | + | 0.535916i | \(0.180034\pi\) | |||||||
\(434\) | −15.5336 | −0.745634 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.745498 | 0.0357029 | ||||||||
\(437\) | 23.9465 | 1.14552 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.1890 | 1.15448 | 0.577239 | − | 0.816575i | \(-0.304130\pi\) | ||||
0.577239 | + | 0.816575i | \(0.304130\pi\) | |||||||
\(440\) | 57.1783 | 2.72587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.2442 | 0.867789 | ||||||||
\(443\) | −1.17625 | −0.0558852 | −0.0279426 | − | 0.999610i | \(-0.508896\pi\) | ||||
−0.0279426 | + | 0.999610i | \(0.508896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.05414 | 0.192185 | ||||||||
\(446\) | 15.5656 | 0.737053 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 35.7383 | 1.68847 | ||||||||
\(449\) | 24.8321 | 1.17190 | 0.585949 | − | 0.810348i | \(-0.300722\pi\) | ||||
0.585949 | + | 0.810348i | \(0.300722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8136 | 0.509193 | ||||||||
\(452\) | −1.05126 | −0.0494470 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00272 | 0.187857 | ||||||||
\(455\) | 42.2038 | 1.97855 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.1604 | −1.73829 | −0.869146 | − | 0.494556i | \(-0.835331\pi\) | ||||
−0.869146 | + | 0.494556i | \(0.835331\pi\) | |||||||
\(458\) | −5.68340 | −0.265568 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.92999 | −0.183237 | ||||||||
\(461\) | −13.5898 | −0.632939 | −0.316470 | − | 0.948603i | \(-0.602498\pi\) | ||||
−0.316470 | + | 0.948603i | \(0.602498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.0821 | −1.67688 | −0.838438 | − | 0.544996i | \(-0.816531\pi\) | ||||
−0.838438 | + | 0.544996i | \(0.816531\pi\) | |||||||
\(464\) | −32.6341 | −1.51500 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.30964 | 0.384937 | ||||||||
\(467\) | −9.39217 | −0.434618 | −0.217309 | − | 0.976103i | \(-0.569728\pi\) | ||||
−0.217309 | + | 0.976103i | \(0.569728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.2221 | 2.54992 | ||||||||
\(470\) | 17.5933 | 0.811520 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.51655 | 0.115834 | ||||||||
\(473\) | 49.9765 | 2.29792 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.1539 | −1.52120 | ||||||||
\(476\) | −3.20537 | −0.146918 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.03628 | −0.276093 | ||||||||
\(479\) | −16.8408 | −0.769478 | −0.384739 | − | 0.923025i | \(-0.625708\pi\) | ||||
−0.384739 | + | 0.923025i | \(0.625708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.1477 | 0.736273 | ||||||||
\(482\) | −6.26639 | −0.285426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.29787 | −0.104449 | ||||||||
\(485\) | −17.4137 | −0.790713 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.74688 | −0.0791585 | −0.0395792 | − | 0.999216i | \(-0.512602\pi\) | ||||
−0.0395792 | + | 0.999216i | \(0.512602\pi\) | |||||||
\(488\) | 11.4388 | 0.517809 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 55.2087 | 2.49408 | ||||||||
\(491\) | 1.83853 | 0.0829717 | 0.0414858 | − | 0.999139i | \(-0.486791\pi\) | ||||
0.0414858 | + | 0.999139i | \(0.486791\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.1533 | 2.03360 | ||||||||
\(494\) | −12.4829 | −0.561633 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.99683 | −0.448871 | ||||||||
\(497\) | 44.3084 | 1.98750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.9253 | −1.29488 | −0.647438 | − | 0.762118i | \(-0.724159\pi\) | ||||
−0.647438 | + | 0.762118i | \(0.724159\pi\) | |||||||
\(500\) | 2.58414 | 0.115566 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0678 | 0.538614 | ||||||||
\(503\) | 28.3575 | 1.26440 | 0.632199 | − | 0.774806i | \(-0.282153\pi\) | ||||
0.632199 | + | 0.774806i | \(0.282153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.7070 | −1.05495 | ||||||||
\(506\) | −48.0007 | −2.13389 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.149936 | −0.00665232 | ||||||||
\(509\) | −21.7242 | −0.962906 | −0.481453 | − | 0.876472i | \(-0.659891\pi\) | ||||
−0.481453 | + | 0.876472i | \(0.659891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65.4509 | 2.89538 | ||||||||
\(512\) | 24.6214 | 1.08812 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27.8945 | 1.23038 | ||||||||
\(515\) | 24.5830 | 1.08326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4150 | −0.765909 | ||||||||
\(518\) | 35.0063 | 1.53809 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 29.3755 | 1.28820 | ||||||||
\(521\) | −35.3198 | −1.54739 | −0.773694 | − | 0.633560i | \(-0.781593\pi\) | ||||
−0.773694 | + | 0.633560i | \(0.781593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0682 | −0.833793 | −0.416897 | − | 0.908954i | \(-0.636882\pi\) | ||||
−0.416897 | + | 0.908954i | \(0.636882\pi\) | |||||||
\(524\) | −1.95933 | −0.0855936 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.84124 | 0.429099 | ||||||||
\(527\) | 13.8318 | 0.602524 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.3073 | 1.05684 | ||||||||
\(530\) | 20.1317 | 0.874464 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.19315 | 0.0950852 | ||||||||
\(533\) | 5.55552 | 0.240636 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −65.8310 | −2.84612 | ||||||||
\(536\) | 38.4367 | 1.66021 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.09705 | 0.262862 | ||||||||
\(539\) | −54.6490 | −2.35390 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3314 | 1.60500 | 0.802501 | − | 0.596651i | \(-0.203502\pi\) | ||||
0.802501 | + | 0.596651i | \(0.203502\pi\) | |||||||
\(542\) | 20.9412 | 0.899500 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.30653 | −0.184641 | ||||||||
\(545\) | 18.9480 | 0.811644 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.81943 | −0.163307 | −0.0816535 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816535 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(548\) | 1.29938 | 0.0555069 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 66.4568 | 2.83373 | ||||||||
\(551\) | −30.8945 | −1.31615 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.2743 | 2.30798 | ||||||||
\(554\) | −20.0625 | −0.852375 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.21782 | 0.0940567 | ||||||||
\(557\) | −6.50616 | −0.275675 | −0.137837 | − | 0.990455i | \(-0.544015\pi\) | ||||
−0.137837 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.6756 | 1.08596 | ||||||||
\(560\) | 58.8813 | 2.48819 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.28101 | 0.0540360 | ||||||||
\(563\) | 30.3002 | 1.27700 | 0.638500 | − | 0.769621i | \(-0.279555\pi\) | ||||
0.638500 | + | 0.769621i | \(0.279555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.7194 | −1.12409 | ||||||||
\(566\) | −29.6924 | −1.24806 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.8404 | 1.29403 | ||||||||
\(569\) | 28.3544 | 1.18868 | 0.594340 | − | 0.804214i | \(-0.297413\pi\) | ||||
0.594340 | + | 0.804214i | \(0.297413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4841 | −0.480595 | −0.240297 | − | 0.970699i | \(-0.577245\pi\) | ||||
−0.240297 | + | 0.970699i | \(0.577245\pi\) | |||||||
\(572\) | −2.02787 | −0.0847894 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0437 | 0.502694 | ||||||||
\(575\) | −65.4968 | −2.73140 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8969 | 1.41115 | 0.705573 | − | 0.708637i | \(-0.250690\pi\) | ||||
0.705573 | + | 0.708637i | \(0.250690\pi\) | |||||||
\(578\) | −12.0954 | −0.503100 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.07025 | 0.210531 | ||||||||
\(581\) | −13.1508 | −0.545588 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.9276 | −0.825316 | ||||||||
\(584\) | 45.5564 | 1.88514 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.0013 | −1.44589 | ||||||||
\(587\) | −31.6046 | −1.30446 | −0.652231 | − | 0.758020i | \(-0.726167\pi\) | ||||
−0.652231 | + | 0.758020i | \(0.726167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.46391 | −0.389954 | ||||||||
\(590\) | 4.46069 | 0.183644 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.5288 | 0.925926 | ||||||||
\(593\) | −2.45836 | −0.100953 | −0.0504765 | − | 0.998725i | \(-0.516074\pi\) | ||||
−0.0504765 | + | 0.998725i | \(0.516074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −81.4694 | −3.33992 | ||||||||
\(596\) | −1.87043 | −0.0766159 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.6605 | −1.00844 | ||||||||
\(599\) | −32.4195 | −1.32462 | −0.662312 | − | 0.749228i | \(-0.730425\pi\) | ||||
−0.662312 | + | 0.749228i | \(0.730425\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9869 | −1.26398 | −0.631992 | − | 0.774975i | \(-0.717762\pi\) | ||||
−0.631992 | + | 0.774975i | \(0.717762\pi\) | |||||||
\(602\) | 55.6614 | 2.26859 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.449249 | −0.0182797 | ||||||||
\(605\) | −58.4041 | −2.37446 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8833 | 1.29410 | 0.647052 | − | 0.762446i | \(-0.276002\pi\) | ||||
0.647052 | + | 0.762446i | \(0.276002\pi\) | |||||||
\(608\) | 2.94658 | 0.119500 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.2757 | 0.820941 | ||||||||
\(611\) | −8.94699 | −0.361956 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.3436 | −0.417774 | −0.208887 | − | 0.977940i | \(-0.566984\pi\) | ||||
−0.208887 | + | 0.977940i | \(0.566984\pi\) | |||||||
\(614\) | −6.77753 | −0.273519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −63.0368 | −2.53983 | ||||||||
\(617\) | −45.6478 | −1.83771 | −0.918856 | − | 0.394593i | \(-0.870886\pi\) | ||||
−0.918856 | + | 0.394593i | \(0.870886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0010 | 1.04507 | 0.522535 | − | 0.852618i | \(-0.324986\pi\) | ||||
0.522535 | + | 0.852618i | \(0.324986\pi\) | |||||||
\(620\) | 1.55317 | 0.0623769 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.8893 | 1.31874 | ||||||||
\(623\) | −4.46953 | −0.179068 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0670 | 0.722679 | ||||||||
\(626\) | −42.9173 | −1.71532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.19617 | −0.0876369 | ||||||||
\(629\) | −31.1713 | −1.24288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2177 | 0.924282 | 0.462141 | − | 0.886807i | \(-0.347081\pi\) | ||||
0.462141 | + | 0.886807i | \(0.347081\pi\) | |||||||
\(632\) | 37.7770 | 1.50269 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.8549 | 0.470820 | ||||||||
\(635\) | −3.81085 | −0.151229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.0761 | −1.11241 | ||||||||
\(638\) | 61.9278 | 2.45175 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37.6419 | 1.48793 | ||||||||
\(641\) | 3.46335 | 0.136794 | 0.0683971 | − | 0.997658i | \(-0.478212\pi\) | ||||
0.0683971 | + | 0.997658i | \(0.478212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.3858 | −0.803937 | −0.401968 | − | 0.915654i | \(-0.631674\pi\) | ||||
−0.401968 | + | 0.915654i | \(0.631674\pi\) | |||||||
\(644\) | 4.33266 | 0.170731 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0968 | 0.948075 | ||||||||
\(647\) | 15.1587 | 0.595949 | 0.297974 | − | 0.954574i | \(-0.403689\pi\) | ||||
0.297974 | + | 0.954574i | \(0.403689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.41547 | −0.173322 | ||||||||
\(650\) | 34.1424 | 1.33917 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.63416 | 0.103162 | ||||||||
\(653\) | −18.5147 | −0.724536 | −0.362268 | − | 0.932074i | \(-0.617997\pi\) | ||||
−0.362268 | + | 0.932074i | \(0.617997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.7994 | −1.94582 | ||||||||
\(656\) | 7.75088 | 0.302621 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.3959 | −0.756133 | ||||||||
\(659\) | 20.0515 | 0.781094 | 0.390547 | − | 0.920583i | \(-0.372286\pi\) | ||||
0.390547 | + | 0.920583i | \(0.372286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.67512 | 0.337423 | 0.168711 | − | 0.985665i | \(-0.446039\pi\) | ||||
0.168711 | + | 0.985665i | \(0.446039\pi\) | |||||||
\(662\) | −9.18422 | −0.356955 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.15349 | −0.355224 | ||||||||
\(665\) | 55.7424 | 2.16160 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61.0332 | −2.36322 | ||||||||
\(668\) | 1.04425 | 0.0404033 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 68.1308 | 2.63212 | ||||||||
\(671\) | −20.0702 | −0.774801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9367 | −1.23107 | −0.615535 | − | 0.788109i | \(-0.711060\pi\) | ||||
−0.615535 | + | 0.788109i | \(0.711060\pi\) | |||||||
\(674\) | −17.3857 | −0.669671 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.907341 | 0.0348977 | ||||||||
\(677\) | 36.6170 | 1.40731 | 0.703653 | − | 0.710543i | \(-0.251551\pi\) | ||||
0.703653 | + | 0.710543i | \(0.251551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1979 | 0.736746 | ||||||||
\(680\) | −56.7059 | −2.17457 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.9704 | 0.726413 | ||||||||
\(683\) | 5.47798 | 0.209609 | 0.104805 | − | 0.994493i | \(-0.466578\pi\) | ||||
0.104805 | + | 0.994493i | \(0.466578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.0258 | 1.26185 | ||||||||
\(686\) | −20.8639 | −0.796587 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 35.8217 | 1.36569 | ||||||||
\(689\) | −10.2379 | −0.390031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.38430 | 0.356996 | 0.178498 | − | 0.983940i | \(-0.442876\pi\) | ||||
0.178498 | + | 0.983940i | \(0.442876\pi\) | |||||||
\(692\) | −1.81200 | −0.0688819 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.2836 | −0.618116 | ||||||||
\(695\) | 56.3695 | 2.13822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.7243 | −0.406211 | ||||||||
\(698\) | −33.3367 | −1.26181 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.99855 | −0.226724 | ||||||||
\(701\) | 11.5491 | 0.436203 | 0.218101 | − | 0.975926i | \(-0.430014\pi\) | ||||
0.218101 | + | 0.975926i | \(0.430014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.3278 | 0.804393 | ||||||||
\(704\) | −43.6454 | −1.64495 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.9011 | −1.31352 | ||||||||
\(707\) | 26.1361 | 0.982948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4046 | −0.766311 | −0.383155 | − | 0.923684i | \(-0.625163\pi\) | ||||
−0.383155 | + | 0.923684i | \(0.625163\pi\) | |||||||
\(710\) | 54.6659 | 2.05157 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.11097 | −0.116588 | ||||||||
\(713\) | −18.6963 | −0.700183 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −51.5415 | −1.92754 | ||||||||
\(716\) | −3.25427 | −0.121618 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26.3577 | −0.983662 | ||||||||
\(719\) | −41.2162 | −1.53710 | −0.768552 | − | 0.639787i | \(-0.779023\pi\) | ||||
−0.768552 | + | 0.639787i | \(0.779023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.1018 | −1.00932 | ||||||||
\(722\) | 9.35591 | 0.348191 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.83291 | 0.0681197 | ||||||||
\(725\) | 84.5002 | 3.13826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.381582 | 0.0141521 | 0.00707605 | − | 0.999975i | \(-0.497748\pi\) | ||||
0.00707605 | + | 0.999975i | \(0.497748\pi\) | |||||||
\(728\) | −32.3853 | −1.20028 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 80.7507 | 2.98872 | ||||||||
\(731\) | −49.5636 | −1.83318 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7194 | 1.13465 | 0.567324 | − | 0.823495i | \(-0.307979\pi\) | ||||
0.567324 | + | 0.823495i | \(0.307979\pi\) | |||||||
\(734\) | 9.09051 | 0.335537 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.82109 | 0.214568 | ||||||||
\(737\) | −67.4400 | −2.48419 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8373 | 0.692940 | 0.346470 | − | 0.938061i | \(-0.387380\pi\) | ||||
0.346470 | + | 0.938061i | \(0.387380\pi\) | |||||||
\(740\) | −3.50021 | −0.128670 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.1944 | −0.814781 | ||||||||
\(743\) | −17.3527 | −0.636609 | −0.318305 | − | 0.947989i | \(-0.603113\pi\) | ||||
−0.318305 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.5400 | −1.74173 | ||||||||
\(746\) | −35.5341 | −1.30100 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.91456 | 0.143130 | ||||||||
\(749\) | 72.5760 | 2.65187 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.3700 | −1.69206 | −0.846032 | − | 0.533132i | \(-0.821015\pi\) | ||||
−0.846032 | + | 0.533132i | \(0.821015\pi\) | |||||||
\(752\) | −12.4825 | −0.455191 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 31.8156 | 1.15866 | ||||||||
\(755\) | −11.4184 | −0.415557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0648 | −0.402156 | −0.201078 | − | 0.979575i | \(-0.564444\pi\) | ||||
−0.201078 | + | 0.979575i | \(0.564444\pi\) | |||||||
\(758\) | −48.1488 | −1.74884 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38.7989 | 1.40738 | ||||||||
\(761\) | 27.8839 | 1.01079 | 0.505395 | − | 0.862888i | \(-0.331347\pi\) | ||||
0.505395 | + | 0.862888i | \(0.331347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.8894 | −0.756248 | ||||||||
\(764\) | 2.05825 | 0.0744650 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.3472 | −0.482254 | ||||||||
\(767\) | −2.26846 | −0.0819093 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.33132 | −0.120130 | −0.0600652 | − | 0.998194i | \(-0.519131\pi\) | ||||
−0.0600652 | + | 0.998194i | \(0.519131\pi\) | |||||||
\(770\) | −111.735 | −4.02667 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.10854 | 0.0398971 | ||||||||
\(773\) | −11.8837 | −0.427426 | −0.213713 | − | 0.976896i | \(-0.568556\pi\) | ||||
−0.213713 | + | 0.976896i | \(0.568556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.8850 | 0.929816 | ||||||||
\(776\) | 13.3625 | 0.479684 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 43.1012 | 1.54525 | ||||||||
\(779\) | 7.33769 | 0.262900 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1117 | −1.93627 | ||||||||
\(782\) | 47.6041 | 1.70232 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39.1708 | −1.39896 | ||||||||
\(785\) | −55.8192 | −1.99227 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.4099 | 1.40481 | 0.702406 | − | 0.711776i | \(-0.252109\pi\) | ||||
0.702406 | + | 0.711776i | \(0.252109\pi\) | |||||||
\(788\) | 0.735919 | 0.0262160 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 66.9614 | 2.38238 | ||||||||
\(791\) | 29.4571 | 1.04737 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3111 | −0.366158 | ||||||||
\(794\) | 15.7986 | 0.560672 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.663421 | 0.0235143 | ||||||||
\(797\) | 55.4958 | 1.96576 | 0.982881 | − | 0.184241i | \(-0.0589827\pi\) | ||||
0.982881 | + | 0.184241i | \(0.0589827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.2711 | 0.611007 | ||||||||
\(800\) | −8.05927 | −0.284938 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.85125 | −0.312549 | ||||||||
\(803\) | −79.9320 | −2.82074 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 110.121 | 3.88127 | ||||||||
\(806\) | 9.74608 | 0.343291 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.1917 | 0.639983 | ||||||||
\(809\) | 31.3721 | 1.10298 | 0.551491 | − | 0.834181i | \(-0.314059\pi\) | ||||
0.551491 | + | 0.834181i | \(0.314059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.7537 | 0.798991 | 0.399496 | − | 0.916735i | \(-0.369185\pi\) | ||||
0.399496 | + | 0.916735i | \(0.369185\pi\) | |||||||
\(812\) | −5.58975 | −0.196162 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42.7514 | −1.49844 | ||||||||
\(815\) | 66.9513 | 2.34520 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.9121 | 1.18643 | ||||||||
\(818\) | 26.3501 | 0.921309 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.20423 | −0.0420534 | ||||||||
\(821\) | −34.8957 | −1.21787 | −0.608934 | − | 0.793221i | \(-0.708403\pi\) | ||||
−0.608934 | + | 0.793221i | \(0.708403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.3189 | 0.568840 | 0.284420 | − | 0.958700i | \(-0.408199\pi\) | ||||
0.284420 | + | 0.958700i | \(0.408199\pi\) | |||||||
\(824\) | −18.8639 | −0.657155 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.91774 | −0.171110 | ||||||||
\(827\) | −39.3623 | −1.36876 | −0.684380 | − | 0.729126i | \(-0.739927\pi\) | ||||
−0.684380 | + | 0.729126i | \(0.739927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.0024 | −1.45880 | −0.729402 | − | 0.684086i | \(-0.760201\pi\) | ||||
−0.729402 | + | 0.684086i | \(0.760201\pi\) | |||||||
\(830\) | −16.2249 | −0.563176 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.4230 | −0.777376 | ||||||||
\(833\) | 54.1975 | 1.87783 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.5413 | 0.918499 | ||||||||
\(836\) | −2.67839 | −0.0926341 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.7782 | −0.959581 | ||||||||
\(839\) | −8.89866 | −0.307216 | −0.153608 | − | 0.988132i | \(-0.549089\pi\) | ||||
−0.153608 | + | 0.988132i | \(0.549089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.7416 | 1.71523 | ||||||||
\(842\) | 2.55977 | 0.0882154 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.34793 | −0.0808191 | ||||||||
\(845\) | 23.0615 | 0.793340 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 64.3882 | 2.21240 | ||||||||
\(848\) | −14.2835 | −0.490497 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −65.9077 | −2.26062 | ||||||||
\(851\) | 42.1339 | 1.44433 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.2679 | 1.48146 | 0.740732 | − | 0.671801i | \(-0.234479\pi\) | ||||
0.740732 | + | 0.671801i | \(0.234479\pi\) | |||||||
\(854\) | −22.3532 | −0.764911 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 50.5158 | 1.72659 | ||||||||
\(857\) | 36.6021 | 1.25031 | 0.625153 | − | 0.780502i | \(-0.285037\pi\) | ||||
0.625153 | + | 0.780502i | \(0.285037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.50827 | 0.324418 | 0.162209 | − | 0.986756i | \(-0.448138\pi\) | ||||
0.162209 | + | 0.986756i | \(0.448138\pi\) | |||||||
\(860\) | −5.56548 | −0.189781 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.5254 | 0.358498 | ||||||||
\(863\) | −46.1979 | −1.57260 | −0.786298 | − | 0.617848i | \(-0.788005\pi\) | ||||
−0.786298 | + | 0.617848i | \(0.788005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.0548 | −1.56591 | ||||||||
\(866\) | −47.7914 | −1.62402 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.71231 | −0.0581196 | ||||||||
\(869\) | −66.2826 | −2.24848 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.6475 | −1.17399 | ||||||||
\(872\) | −14.5399 | −0.492382 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.5714 | −1.10174 | ||||||||
\(875\) | −72.4096 | −2.44789 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.81661 | 0.162645 | 0.0813227 | − | 0.996688i | \(-0.474086\pi\) | ||||
0.0813227 | + | 0.996688i | \(0.474086\pi\) | |||||||
\(878\) | −32.9012 | −1.11036 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −71.9089 | −2.42405 | ||||||||
\(881\) | 26.8459 | 0.904462 | 0.452231 | − | 0.891901i | \(-0.350628\pi\) | ||||
0.452231 | + | 0.891901i | \(0.350628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.05018 | 0.304563 | 0.152281 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152281 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(884\) | 2.01111 | 0.0676411 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.59990 | 0.0537496 | ||||||||
\(887\) | −21.0242 | −0.705925 | −0.352962 | − | 0.935637i | \(-0.614826\pi\) | ||||
−0.352962 | + | 0.935637i | \(0.614826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.20131 | 0.140908 | ||||||||
\(890\) | −5.51432 | −0.184840 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.71585 | 0.0574508 | ||||||||
\(893\) | −11.8171 | −0.395444 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −82.7124 | −2.76477 | ||||||||
\(896\) | −41.4987 | −1.38638 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.7759 | −1.12712 | ||||||||
\(899\) | 24.1209 | 0.804479 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7629 | 0.658399 | ||||||||
\(902\) | −14.7084 | −0.489735 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.5033 | 0.681929 | ||||||||
\(905\) | 46.5864 | 1.54858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.49947 | −0.315425 | −0.157712 | − | 0.987485i | \(-0.550412\pi\) | ||||
−0.157712 | + | 0.987485i | \(0.550412\pi\) | |||||||
\(908\) | 0.441232 | 0.0146428 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −57.4044 | −1.90294 | ||||||||
\(911\) | −7.22549 | −0.239391 | −0.119696 | − | 0.992811i | \(-0.538192\pi\) | ||||
−0.119696 | + | 0.992811i | \(0.538192\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0605 | 0.531523 | ||||||||
\(914\) | 50.5445 | 1.67186 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.626498 | −0.0207001 | ||||||||
\(917\) | 54.9019 | 1.81302 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6819 | 0.847169 | 0.423584 | − | 0.905857i | \(-0.360772\pi\) | ||||
0.423584 | + | 0.905857i | \(0.360772\pi\) | |||||||
\(920\) | 76.6488 | 2.52704 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.4844 | 0.608752 | ||||||||
\(923\) | −27.8000 | −0.915049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.3342 | −1.91802 | ||||||||
\(926\) | 49.0778 | 1.61280 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.51004 | −0.246529 | ||||||||
\(929\) | 29.8044 | 0.977850 | 0.488925 | − | 0.872326i | \(-0.337389\pi\) | ||||
0.488925 | + | 0.872326i | \(0.337389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.0826 | −1.21533 | ||||||||
\(932\) | 0.915997 | 0.0300045 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.7750 | 0.418009 | ||||||||
\(935\) | 99.4946 | 3.25382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.1050 | 1.47352 | 0.736759 | − | 0.676156i | \(-0.236355\pi\) | ||||
0.736759 | + | 0.676156i | \(0.236355\pi\) | |||||||
\(938\) | −75.1115 | −2.45248 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.93937 | 0.0632551 | ||||||||
\(941\) | 46.2269 | 1.50695 | 0.753477 | − | 0.657474i | \(-0.228375\pi\) | ||||
0.753477 | + | 0.657474i | \(0.228375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4959 | 0.472051 | ||||||||
\(944\) | −3.16488 | −0.103008 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −67.9766 | −2.21011 | ||||||||
\(947\) | −30.4501 | −0.989494 | −0.494747 | − | 0.869037i | \(-0.664739\pi\) | ||||
−0.494747 | + | 0.869037i | \(0.664739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.0653 | −1.33304 | ||||||||
\(950\) | 45.0949 | 1.46307 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 62.5160 | 2.02616 | ||||||||
\(953\) | 4.84074 | 0.156807 | 0.0784035 | − | 0.996922i | \(-0.475018\pi\) | ||||
0.0784035 | + | 0.996922i | \(0.475018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.3138 | 1.69283 | ||||||||
\(956\) | −0.665397 | −0.0215205 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.9064 | 0.740073 | ||||||||
\(959\) | −36.4097 | −1.17573 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.6110 | −0.761646 | ||||||||
\(962\) | −21.9637 | −0.708137 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.690763 | −0.0222480 | ||||||||
\(965\) | 28.1752 | 0.906992 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.2445 | −1.29417 | −0.647087 | − | 0.762416i | \(-0.724013\pi\) | ||||
−0.647087 | + | 0.762416i | \(0.724013\pi\) | |||||||
\(968\) | 44.8167 | 1.44046 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.6855 | 0.760497 | ||||||||
\(971\) | 11.2966 | 0.362525 | 0.181262 | − | 0.983435i | \(-0.441982\pi\) | ||||
0.181262 | + | 0.983435i | \(0.441982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.1451 | −1.99228 | ||||||||
\(974\) | 2.37605 | 0.0761335 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.3857 | −0.460475 | ||||||||
\(977\) | −37.4195 | −1.19716 | −0.598578 | − | 0.801064i | \(-0.704267\pi\) | ||||
−0.598578 | + | 0.801064i | \(0.704267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.45841 | 0.174452 | ||||||||
\(980\) | 6.08583 | 0.194405 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.50071 | −0.0798010 | ||||||||
\(983\) | 7.98240 | 0.254599 | 0.127299 | − | 0.991864i | \(-0.459369\pi\) | ||||
0.127299 | + | 0.991864i | \(0.459369\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7046 | 0.595977 | ||||||||
\(986\) | −61.4162 | −1.95589 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.37603 | −0.0437774 | ||||||||
\(989\) | 66.9946 | 2.13030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3554 | 0.583080 | 0.291540 | − | 0.956559i | \(-0.405832\pi\) | ||||
0.291540 | + | 0.956559i | \(0.405832\pi\) | |||||||
\(992\) | −2.30055 | −0.0730426 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −60.2670 | −1.91155 | ||||||||
\(995\) | 16.8619 | 0.534558 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.2142 | −1.21026 | −0.605128 | − | 0.796128i | \(-0.706878\pi\) | ||||
−0.605128 | + | 0.796128i | \(0.706878\pi\) | |||||||
\(998\) | 39.3434 | 1.24539 | ||||||||
\(999\) | 0 | 0 |
(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 | 1143.2.a.k.1.5 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1143.2.a.k.1.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.2.a.k.1.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1143.2.a.k.1.12 | yes | 16 | 3.2 | odd | 2 | inner |