Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(7.84929451869\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64741 | −1.16490 | −0.582448 | − | 0.812868i | \(-0.697905\pi\) | ||||
−0.582448 | + | 0.812868i | \(0.697905\pi\) | |||||||
\(3\) | −0.803598 | −0.463958 | −0.231979 | − | 0.972721i | \(-0.574520\pi\) | ||||
−0.231979 | + | 0.972721i | \(0.574520\pi\) | |||||||
\(4\) | 0.713964 | 0.356982 | ||||||||
\(5\) | 2.48769 | 1.11253 | 0.556263 | − | 0.831006i | \(-0.312235\pi\) | ||||
0.556263 | + | 0.831006i | \(0.312235\pi\) | |||||||
\(6\) | 1.32386 | 0.540462 | ||||||||
\(7\) | 2.09423 | 0.791545 | 0.395772 | − | 0.918349i | \(-0.370477\pi\) | ||||
0.395772 | + | 0.918349i | \(0.370477\pi\) | |||||||
\(8\) | 2.11863 | 0.749049 | ||||||||
\(9\) | −2.35423 | −0.784743 | ||||||||
\(10\) | −4.09824 | −1.29598 | ||||||||
\(11\) | −3.82694 | −1.15387 | −0.576933 | − | 0.816792i | \(-0.695751\pi\) | ||||
−0.576933 | + | 0.816792i | \(0.695751\pi\) | |||||||
\(12\) | −0.573740 | −0.165624 | ||||||||
\(13\) | 1.12633 | 0.312386 | 0.156193 | − | 0.987727i | \(-0.450078\pi\) | ||||
0.156193 | + | 0.987727i | \(0.450078\pi\) | |||||||
\(14\) | −3.45006 | −0.922067 | ||||||||
\(15\) | −1.99910 | −0.516165 | ||||||||
\(16\) | −4.91818 | −1.22955 | ||||||||
\(17\) | −4.62036 | −1.12060 | −0.560301 | − | 0.828289i | \(-0.689315\pi\) | ||||
−0.560301 | + | 0.828289i | \(0.689315\pi\) | |||||||
\(18\) | 3.87838 | 0.914144 | ||||||||
\(19\) | −6.43778 | −1.47693 | −0.738464 | − | 0.674293i | \(-0.764449\pi\) | ||||
−0.738464 | + | 0.674293i | \(0.764449\pi\) | |||||||
\(20\) | 1.77612 | 0.397152 | ||||||||
\(21\) | −1.68292 | −0.367243 | ||||||||
\(22\) | 6.30454 | 1.34413 | ||||||||
\(23\) | 5.61922 | 1.17169 | 0.585844 | − | 0.810424i | \(-0.300763\pi\) | ||||
0.585844 | + | 0.810424i | \(0.300763\pi\) | |||||||
\(24\) | −1.70253 | −0.347527 | ||||||||
\(25\) | 1.18858 | 0.237716 | ||||||||
\(26\) | −1.85552 | −0.363898 | ||||||||
\(27\) | 4.30265 | 0.828045 | ||||||||
\(28\) | 1.49520 | 0.282567 | ||||||||
\(29\) | 0.357349 | 0.0663581 | 0.0331790 | − | 0.999449i | \(-0.489437\pi\) | ||||
0.0331790 | + | 0.999449i | \(0.489437\pi\) | |||||||
\(30\) | 3.29334 | 0.601279 | ||||||||
\(31\) | −1.45175 | −0.260742 | −0.130371 | − | 0.991465i | \(-0.541617\pi\) | ||||
−0.130371 | + | 0.991465i | \(0.541617\pi\) | |||||||
\(32\) | 3.86501 | 0.683244 | ||||||||
\(33\) | 3.07532 | 0.535345 | ||||||||
\(34\) | 7.61163 | 1.30538 | ||||||||
\(35\) | 5.20979 | 0.880615 | ||||||||
\(36\) | −1.68083 | −0.280139 | ||||||||
\(37\) | 3.29798 | 0.542184 | 0.271092 | − | 0.962553i | \(-0.412615\pi\) | ||||
0.271092 | + | 0.962553i | \(0.412615\pi\) | |||||||
\(38\) | 10.6057 | 1.72047 | ||||||||
\(39\) | −0.905113 | −0.144934 | ||||||||
\(40\) | 5.27049 | 0.833337 | ||||||||
\(41\) | −8.09625 | −1.26442 | −0.632211 | − | 0.774796i | \(-0.717853\pi\) | ||||
−0.632211 | + | 0.774796i | \(0.717853\pi\) | |||||||
\(42\) | 2.77246 | 0.427800 | ||||||||
\(43\) | −7.25204 | −1.10593 | −0.552963 | − | 0.833206i | \(-0.686503\pi\) | ||||
−0.552963 | + | 0.833206i | \(0.686503\pi\) | |||||||
\(44\) | −2.73230 | −0.411909 | ||||||||
\(45\) | −5.85658 | −0.873048 | ||||||||
\(46\) | −9.25716 | −1.36489 | ||||||||
\(47\) | 9.45901 | 1.37974 | 0.689870 | − | 0.723934i | \(-0.257668\pi\) | ||||
0.689870 | + | 0.723934i | \(0.257668\pi\) | |||||||
\(48\) | 3.95224 | 0.570457 | ||||||||
\(49\) | −2.61420 | −0.373457 | ||||||||
\(50\) | −1.95808 | −0.276915 | ||||||||
\(51\) | 3.71291 | 0.519912 | ||||||||
\(52\) | 0.804155 | 0.111516 | ||||||||
\(53\) | −9.44411 | −1.29725 | −0.648624 | − | 0.761109i | \(-0.724655\pi\) | ||||
−0.648624 | + | 0.761109i | \(0.724655\pi\) | |||||||
\(54\) | −7.08823 | −0.964586 | ||||||||
\(55\) | −9.52023 | −1.28371 | ||||||||
\(56\) | 4.43690 | 0.592906 | ||||||||
\(57\) | 5.17339 | 0.685232 | ||||||||
\(58\) | −0.588701 | −0.0773002 | ||||||||
\(59\) | 4.05412 | 0.527801 | 0.263901 | − | 0.964550i | \(-0.414991\pi\) | ||||
0.263901 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(60\) | −1.42728 | −0.184262 | ||||||||
\(61\) | −1.85363 | −0.237333 | −0.118667 | − | 0.992934i | \(-0.537862\pi\) | ||||
−0.118667 | + | 0.992934i | \(0.537862\pi\) | |||||||
\(62\) | 2.39163 | 0.303737 | ||||||||
\(63\) | −4.93030 | −0.621159 | ||||||||
\(64\) | 3.46911 | 0.433638 | ||||||||
\(65\) | 2.80194 | 0.347538 | ||||||||
\(66\) | −5.06632 | −0.623621 | ||||||||
\(67\) | 7.83695 | 0.957436 | 0.478718 | − | 0.877969i | \(-0.341102\pi\) | ||||
0.478718 | + | 0.877969i | \(0.341102\pi\) | |||||||
\(68\) | −3.29877 | −0.400035 | ||||||||
\(69\) | −4.51559 | −0.543613 | ||||||||
\(70\) | −8.58266 | −1.02582 | ||||||||
\(71\) | −7.40491 | −0.878801 | −0.439401 | − | 0.898291i | \(-0.644809\pi\) | ||||
−0.439401 | + | 0.898291i | \(0.644809\pi\) | |||||||
\(72\) | −4.98774 | −0.587811 | ||||||||
\(73\) | −6.72027 | −0.786548 | −0.393274 | − | 0.919421i | \(-0.628658\pi\) | ||||
−0.393274 | + | 0.919421i | \(0.628658\pi\) | |||||||
\(74\) | −5.43313 | −0.631588 | ||||||||
\(75\) | −0.955142 | −0.110290 | ||||||||
\(76\) | −4.59634 | −0.527237 | ||||||||
\(77\) | −8.01449 | −0.913336 | ||||||||
\(78\) | 1.49109 | 0.168833 | ||||||||
\(79\) | −10.5786 | −1.19018 | −0.595091 | − | 0.803659i | \(-0.702884\pi\) | ||||
−0.595091 | + | 0.803659i | \(0.702884\pi\) | |||||||
\(80\) | −12.2349 | −1.36790 | ||||||||
\(81\) | 3.60509 | 0.400565 | ||||||||
\(82\) | 13.3379 | 1.47292 | ||||||||
\(83\) | −14.6847 | −1.61185 | −0.805926 | − | 0.592016i | \(-0.798332\pi\) | ||||
−0.805926 | + | 0.592016i | \(0.798332\pi\) | |||||||
\(84\) | −1.20154 | −0.131099 | ||||||||
\(85\) | −11.4940 | −1.24670 | ||||||||
\(86\) | 11.9471 | 1.28829 | ||||||||
\(87\) | −0.287165 | −0.0307873 | ||||||||
\(88\) | −8.10787 | −0.864302 | ||||||||
\(89\) | 0.605361 | 0.0641681 | 0.0320841 | − | 0.999485i | \(-0.489786\pi\) | ||||
0.0320841 | + | 0.999485i | \(0.489786\pi\) | |||||||
\(90\) | 9.64820 | 1.01701 | ||||||||
\(91\) | 2.35878 | 0.247268 | ||||||||
\(92\) | 4.01192 | 0.418271 | ||||||||
\(93\) | 1.16662 | 0.120973 | ||||||||
\(94\) | −15.5829 | −1.60725 | ||||||||
\(95\) | −16.0152 | −1.64312 | ||||||||
\(96\) | −3.10591 | −0.316996 | ||||||||
\(97\) | −18.9734 | −1.92646 | −0.963230 | − | 0.268679i | \(-0.913413\pi\) | ||||
−0.963230 | + | 0.268679i | \(0.913413\pi\) | |||||||
\(98\) | 4.30666 | 0.435039 | ||||||||
\(99\) | 9.00950 | 0.905489 | ||||||||
\(100\) | 0.848604 | 0.0848604 | ||||||||
\(101\) | 10.9486 | 1.08943 | 0.544713 | − | 0.838622i | \(-0.316639\pi\) | ||||
0.544713 | + | 0.838622i | \(0.316639\pi\) | |||||||
\(102\) | −6.11670 | −0.605643 | ||||||||
\(103\) | 19.9941 | 1.97008 | 0.985039 | − | 0.172333i | \(-0.0551304\pi\) | ||||
0.985039 | + | 0.172333i | \(0.0551304\pi\) | |||||||
\(104\) | 2.38627 | 0.233993 | ||||||||
\(105\) | −4.18658 | −0.408568 | ||||||||
\(106\) | 15.5583 | 1.51116 | ||||||||
\(107\) | −1.70199 | −0.164538 | −0.0822690 | − | 0.996610i | \(-0.526217\pi\) | ||||
−0.0822690 | + | 0.996610i | \(0.526217\pi\) | |||||||
\(108\) | 3.07194 | 0.295597 | ||||||||
\(109\) | −13.6117 | −1.30377 | −0.651884 | − | 0.758319i | \(-0.726021\pi\) | ||||
−0.651884 | + | 0.758319i | \(0.726021\pi\) | |||||||
\(110\) | 15.6837 | 1.49538 | ||||||||
\(111\) | −2.65025 | −0.251551 | ||||||||
\(112\) | −10.2998 | −0.973240 | ||||||||
\(113\) | −11.2598 | −1.05923 | −0.529616 | − | 0.848237i | \(-0.677664\pi\) | ||||
−0.529616 | + | 0.848237i | \(0.677664\pi\) | |||||||
\(114\) | −8.52270 | −0.798224 | ||||||||
\(115\) | 13.9788 | 1.30353 | ||||||||
\(116\) | 0.255134 | 0.0236886 | ||||||||
\(117\) | −2.65163 | −0.245143 | ||||||||
\(118\) | −6.67880 | −0.614834 | ||||||||
\(119\) | −9.67610 | −0.887007 | ||||||||
\(120\) | −4.23535 | −0.386633 | ||||||||
\(121\) | 3.64547 | 0.331407 | ||||||||
\(122\) | 3.05370 | 0.276469 | ||||||||
\(123\) | 6.50614 | 0.586638 | ||||||||
\(124\) | −1.03650 | −0.0930802 | ||||||||
\(125\) | −9.48161 | −0.848061 | ||||||||
\(126\) | 8.12223 | 0.723586 | ||||||||
\(127\) | −1.20699 | −0.107103 | −0.0535515 | − | 0.998565i | \(-0.517054\pi\) | ||||
−0.0535515 | + | 0.998565i | \(0.517054\pi\) | |||||||
\(128\) | −13.4451 | −1.18839 | ||||||||
\(129\) | 5.82772 | 0.513102 | ||||||||
\(130\) | −4.61595 | −0.404846 | ||||||||
\(131\) | 22.4280 | 1.95954 | 0.979770 | − | 0.200126i | \(-0.0641352\pi\) | ||||
0.979770 | + | 0.200126i | \(0.0641352\pi\) | |||||||
\(132\) | 2.19567 | 0.191108 | ||||||||
\(133\) | −13.4822 | −1.16905 | ||||||||
\(134\) | −12.9107 | −1.11531 | ||||||||
\(135\) | 10.7036 | 0.921223 | ||||||||
\(136\) | −9.78884 | −0.839386 | ||||||||
\(137\) | 19.1034 | 1.63211 | 0.816056 | − | 0.577973i | \(-0.196156\pi\) | ||||
0.816056 | + | 0.577973i | \(0.196156\pi\) | |||||||
\(138\) | 7.43904 | 0.633253 | ||||||||
\(139\) | −11.5452 | −0.979251 | −0.489626 | − | 0.871933i | \(-0.662867\pi\) | ||||
−0.489626 | + | 0.871933i | \(0.662867\pi\) | |||||||
\(140\) | 3.71960 | 0.314364 | ||||||||
\(141\) | −7.60125 | −0.640140 | ||||||||
\(142\) | 12.1989 | 1.02371 | ||||||||
\(143\) | −4.31038 | −0.360452 | ||||||||
\(144\) | 11.5785 | 0.964878 | ||||||||
\(145\) | 0.888973 | 0.0738252 | ||||||||
\(146\) | 11.0710 | 0.916246 | ||||||||
\(147\) | 2.10077 | 0.173268 | ||||||||
\(148\) | 2.35464 | 0.193550 | ||||||||
\(149\) | 9.25889 | 0.758518 | 0.379259 | − | 0.925291i | \(-0.376179\pi\) | ||||
0.379259 | + | 0.925291i | \(0.376179\pi\) | |||||||
\(150\) | 1.57351 | 0.128477 | ||||||||
\(151\) | −3.42940 | −0.279080 | −0.139540 | − | 0.990216i | \(-0.544562\pi\) | ||||
−0.139540 | + | 0.990216i | \(0.544562\pi\) | |||||||
\(152\) | −13.6393 | −1.10629 | ||||||||
\(153\) | 10.8774 | 0.879385 | ||||||||
\(154\) | 13.2032 | 1.06394 | ||||||||
\(155\) | −3.61150 | −0.290083 | ||||||||
\(156\) | −0.646218 | −0.0517388 | ||||||||
\(157\) | −7.40914 | −0.591313 | −0.295657 | − | 0.955294i | \(-0.595538\pi\) | ||||
−0.295657 | + | 0.955294i | \(0.595538\pi\) | |||||||
\(158\) | 17.4272 | 1.38644 | ||||||||
\(159\) | 7.58927 | 0.601868 | ||||||||
\(160\) | 9.61493 | 0.760127 | ||||||||
\(161\) | 11.7679 | 0.927443 | ||||||||
\(162\) | −5.93906 | −0.466617 | ||||||||
\(163\) | −7.93473 | −0.621496 | −0.310748 | − | 0.950492i | \(-0.600580\pi\) | ||||
−0.310748 | + | 0.950492i | \(0.600580\pi\) | |||||||
\(164\) | −5.78043 | −0.451376 | ||||||||
\(165\) | 7.65044 | 0.595586 | ||||||||
\(166\) | 24.1917 | 1.87764 | ||||||||
\(167\) | −10.9998 | −0.851191 | −0.425596 | − | 0.904913i | \(-0.639935\pi\) | ||||
−0.425596 | + | 0.904913i | \(0.639935\pi\) | |||||||
\(168\) | −3.56549 | −0.275083 | ||||||||
\(169\) | −11.7314 | −0.902415 | ||||||||
\(170\) | 18.9354 | 1.45228 | ||||||||
\(171\) | 15.1560 | 1.15901 | ||||||||
\(172\) | −5.17769 | −0.394795 | ||||||||
\(173\) | 3.41641 | 0.259745 | 0.129872 | − | 0.991531i | \(-0.458543\pi\) | ||||
0.129872 | + | 0.991531i | \(0.458543\pi\) | |||||||
\(174\) | 0.473079 | 0.0358640 | ||||||||
\(175\) | 2.48916 | 0.188163 | ||||||||
\(176\) | 18.8216 | 1.41873 | ||||||||
\(177\) | −3.25788 | −0.244877 | ||||||||
\(178\) | −0.997279 | −0.0747492 | ||||||||
\(179\) | 19.6560 | 1.46916 | 0.734578 | − | 0.678524i | \(-0.237380\pi\) | ||||
0.734578 | + | 0.678524i | \(0.237380\pi\) | |||||||
\(180\) | −4.18139 | −0.311662 | ||||||||
\(181\) | −6.99208 | −0.519717 | −0.259858 | − | 0.965647i | \(-0.583676\pi\) | ||||
−0.259858 | + | 0.965647i | \(0.583676\pi\) | |||||||
\(182\) | −3.88589 | −0.288041 | ||||||||
\(183\) | 1.48958 | 0.110113 | ||||||||
\(184\) | 11.9050 | 0.877652 | ||||||||
\(185\) | 8.20434 | 0.603195 | ||||||||
\(186\) | −1.92191 | −0.140921 | ||||||||
\(187\) | 17.6818 | 1.29302 | ||||||||
\(188\) | 6.75339 | 0.492542 | ||||||||
\(189\) | 9.01074 | 0.655435 | ||||||||
\(190\) | 26.3836 | 1.91407 | ||||||||
\(191\) | −9.58053 | −0.693223 | −0.346611 | − | 0.938009i | \(-0.612668\pi\) | ||||
−0.346611 | + | 0.938009i | \(0.612668\pi\) | |||||||
\(192\) | −2.78777 | −0.201190 | ||||||||
\(193\) | −21.2065 | −1.52648 | −0.763238 | − | 0.646118i | \(-0.776392\pi\) | ||||
−0.763238 | + | 0.646118i | \(0.776392\pi\) | |||||||
\(194\) | 31.2570 | 2.24412 | ||||||||
\(195\) | −2.25164 | −0.161243 | ||||||||
\(196\) | −1.86644 | −0.133317 | ||||||||
\(197\) | 11.2511 | 0.801606 | 0.400803 | − | 0.916164i | \(-0.368731\pi\) | ||||
0.400803 | + | 0.916164i | \(0.368731\pi\) | |||||||
\(198\) | −14.8423 | −1.05480 | ||||||||
\(199\) | −20.5355 | −1.45573 | −0.727863 | − | 0.685723i | \(-0.759486\pi\) | ||||
−0.727863 | + | 0.685723i | \(0.759486\pi\) | |||||||
\(200\) | 2.51816 | 0.178061 | ||||||||
\(201\) | −6.29776 | −0.444210 | ||||||||
\(202\) | −18.0368 | −1.26907 | ||||||||
\(203\) | 0.748372 | 0.0525254 | ||||||||
\(204\) | 2.65089 | 0.185599 | ||||||||
\(205\) | −20.1409 | −1.40670 | ||||||||
\(206\) | −32.9385 | −2.29493 | ||||||||
\(207\) | −13.2289 | −0.919474 | ||||||||
\(208\) | −5.53947 | −0.384093 | ||||||||
\(209\) | 24.6370 | 1.70418 | ||||||||
\(210\) | 6.89701 | 0.475939 | ||||||||
\(211\) | −15.7184 | −1.08210 | −0.541051 | − | 0.840990i | \(-0.681973\pi\) | ||||
−0.541051 | + | 0.840990i | \(0.681973\pi\) | |||||||
\(212\) | −6.74275 | −0.463094 | ||||||||
\(213\) | 5.95057 | 0.407727 | ||||||||
\(214\) | 2.80388 | 0.191670 | ||||||||
\(215\) | −18.0408 | −1.23037 | ||||||||
\(216\) | 9.11572 | 0.620246 | ||||||||
\(217\) | −3.04030 | −0.206389 | ||||||||
\(218\) | 22.4241 | 1.51875 | ||||||||
\(219\) | 5.40040 | 0.364925 | ||||||||
\(220\) | −6.79710 | −0.458260 | ||||||||
\(221\) | −5.20403 | −0.350061 | ||||||||
\(222\) | 4.36605 | 0.293030 | ||||||||
\(223\) | 8.89122 | 0.595400 | 0.297700 | − | 0.954660i | \(-0.403781\pi\) | ||||
0.297700 | + | 0.954660i | \(0.403781\pi\) | |||||||
\(224\) | 8.09422 | 0.540818 | ||||||||
\(225\) | −2.79819 | −0.186546 | ||||||||
\(226\) | 18.5495 | 1.23390 | ||||||||
\(227\) | −16.7819 | −1.11385 | −0.556927 | − | 0.830562i | \(-0.688020\pi\) | ||||
−0.556927 | + | 0.830562i | \(0.688020\pi\) | |||||||
\(228\) | 3.69361 | 0.244615 | ||||||||
\(229\) | −12.5058 | −0.826408 | −0.413204 | − | 0.910639i | \(-0.635590\pi\) | ||||
−0.413204 | + | 0.910639i | \(0.635590\pi\) | |||||||
\(230\) | −23.0289 | −1.51848 | ||||||||
\(231\) | 6.44043 | 0.423749 | ||||||||
\(232\) | 0.757091 | 0.0497055 | ||||||||
\(233\) | −4.70840 | −0.308458 | −0.154229 | − | 0.988035i | \(-0.549289\pi\) | ||||
−0.154229 | + | 0.988035i | \(0.549289\pi\) | |||||||
\(234\) | 4.36832 | 0.285566 | ||||||||
\(235\) | 23.5311 | 1.53500 | ||||||||
\(236\) | 2.89449 | 0.188416 | ||||||||
\(237\) | 8.50091 | 0.552194 | ||||||||
\(238\) | 15.9405 | 1.03327 | ||||||||
\(239\) | 18.3777 | 1.18875 | 0.594377 | − | 0.804187i | \(-0.297399\pi\) | ||||
0.594377 | + | 0.804187i | \(0.297399\pi\) | |||||||
\(240\) | 9.83194 | 0.634649 | ||||||||
\(241\) | 25.3003 | 1.62974 | 0.814868 | − | 0.579647i | \(-0.196809\pi\) | ||||
0.814868 | + | 0.579647i | \(0.196809\pi\) | |||||||
\(242\) | −6.00559 | −0.386054 | ||||||||
\(243\) | −15.8050 | −1.01389 | ||||||||
\(244\) | −1.32343 | −0.0847238 | ||||||||
\(245\) | −6.50331 | −0.415481 | ||||||||
\(246\) | −10.7183 | −0.683373 | ||||||||
\(247\) | −7.25103 | −0.461372 | ||||||||
\(248\) | −3.07572 | −0.195309 | ||||||||
\(249\) | 11.8006 | 0.747831 | ||||||||
\(250\) | 15.6201 | 0.987903 | ||||||||
\(251\) | 12.7355 | 0.803856 | 0.401928 | − | 0.915671i | \(-0.368340\pi\) | ||||
0.401928 | + | 0.915671i | \(0.368340\pi\) | |||||||
\(252\) | −3.52006 | −0.221743 | ||||||||
\(253\) | −21.5044 | −1.35197 | ||||||||
\(254\) | 1.98841 | 0.124764 | ||||||||
\(255\) | 9.23656 | 0.578416 | ||||||||
\(256\) | 15.2113 | 0.950709 | ||||||||
\(257\) | 17.7058 | 1.10446 | 0.552228 | − | 0.833693i | \(-0.313778\pi\) | ||||
0.552228 | + | 0.833693i | \(0.313778\pi\) | |||||||
\(258\) | −9.60066 | −0.597711 | ||||||||
\(259\) | 6.90673 | 0.429163 | ||||||||
\(260\) | 2.00049 | 0.124065 | ||||||||
\(261\) | −0.841282 | −0.0520741 | ||||||||
\(262\) | −36.9481 | −2.28266 | ||||||||
\(263\) | 25.6296 | 1.58039 | 0.790194 | − | 0.612857i | \(-0.209980\pi\) | ||||
0.790194 | + | 0.612857i | \(0.209980\pi\) | |||||||
\(264\) | 6.51547 | 0.401000 | ||||||||
\(265\) | −23.4940 | −1.44322 | ||||||||
\(266\) | 22.2107 | 1.36183 | ||||||||
\(267\) | −0.486467 | −0.0297713 | ||||||||
\(268\) | 5.59530 | 0.341787 | ||||||||
\(269\) | −16.5762 | −1.01067 | −0.505335 | − | 0.862923i | \(-0.668631\pi\) | ||||
−0.505335 | + | 0.862923i | \(0.668631\pi\) | |||||||
\(270\) | −17.6333 | −1.07313 | ||||||||
\(271\) | 3.52683 | 0.214239 | 0.107120 | − | 0.994246i | \(-0.465837\pi\) | ||||
0.107120 | + | 0.994246i | \(0.465837\pi\) | |||||||
\(272\) | 22.7238 | 1.37783 | ||||||||
\(273\) | −1.89551 | −0.114722 | ||||||||
\(274\) | −31.4711 | −1.90124 | ||||||||
\(275\) | −4.54863 | −0.274293 | ||||||||
\(276\) | −3.22397 | −0.194060 | ||||||||
\(277\) | 13.5417 | 0.813644 | 0.406822 | − | 0.913507i | \(-0.366637\pi\) | ||||
0.406822 | + | 0.913507i | \(0.366637\pi\) | |||||||
\(278\) | 19.0197 | 1.14073 | ||||||||
\(279\) | 3.41775 | 0.204616 | ||||||||
\(280\) | 11.0376 | 0.659624 | ||||||||
\(281\) | 9.66925 | 0.576819 | 0.288409 | − | 0.957507i | \(-0.406874\pi\) | ||||
0.288409 | + | 0.957507i | \(0.406874\pi\) | |||||||
\(282\) | 12.5224 | 0.745697 | ||||||||
\(283\) | 26.1422 | 1.55399 | 0.776996 | − | 0.629506i | \(-0.216742\pi\) | ||||
0.776996 | + | 0.629506i | \(0.216742\pi\) | |||||||
\(284\) | −5.28684 | −0.313716 | ||||||||
\(285\) | 12.8698 | 0.762339 | ||||||||
\(286\) | 7.10097 | 0.419889 | ||||||||
\(287\) | −16.9554 | −1.00085 | ||||||||
\(288\) | −9.09912 | −0.536171 | ||||||||
\(289\) | 4.34773 | 0.255749 | ||||||||
\(290\) | −1.46450 | −0.0859986 | ||||||||
\(291\) | 15.2470 | 0.893796 | ||||||||
\(292\) | −4.79803 | −0.280783 | ||||||||
\(293\) | 12.3557 | 0.721827 | 0.360913 | − | 0.932599i | \(-0.382465\pi\) | ||||
0.360913 | + | 0.932599i | \(0.382465\pi\) | |||||||
\(294\) | −3.46083 | −0.201839 | ||||||||
\(295\) | 10.0854 | 0.587193 | ||||||||
\(296\) | 6.98720 | 0.406123 | ||||||||
\(297\) | −16.4660 | −0.955453 | ||||||||
\(298\) | −15.2532 | −0.883594 | ||||||||
\(299\) | 6.32907 | 0.366019 | ||||||||
\(300\) | −0.681937 | −0.0393716 | ||||||||
\(301\) | −15.1874 | −0.875389 | ||||||||
\(302\) | 5.64963 | 0.325099 | ||||||||
\(303\) | −8.79827 | −0.505448 | ||||||||
\(304\) | 31.6622 | 1.81595 | ||||||||
\(305\) | −4.61126 | −0.264040 | ||||||||
\(306\) | −17.9195 | −1.02439 | ||||||||
\(307\) | 28.1026 | 1.60390 | 0.801951 | − | 0.597389i | \(-0.203795\pi\) | ||||
0.801951 | + | 0.597389i | \(0.203795\pi\) | |||||||
\(308\) | −5.72206 | −0.326045 | ||||||||
\(309\) | −16.0672 | −0.914033 | ||||||||
\(310\) | 5.94962 | 0.337916 | ||||||||
\(311\) | −20.9161 | −1.18604 | −0.593020 | − | 0.805188i | \(-0.702065\pi\) | ||||
−0.593020 | + | 0.805188i | \(0.702065\pi\) | |||||||
\(312\) | −1.91760 | −0.108563 | ||||||||
\(313\) | 11.7534 | 0.664341 | 0.332171 | − | 0.943219i | \(-0.392219\pi\) | ||||
0.332171 | + | 0.943219i | \(0.392219\pi\) | |||||||
\(314\) | 12.2059 | 0.688818 | ||||||||
\(315\) | −12.2650 | −0.691057 | ||||||||
\(316\) | −7.55271 | −0.424873 | ||||||||
\(317\) | 7.71046 | 0.433063 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(318\) | −12.5026 | −0.701114 | ||||||||
\(319\) | −1.36755 | −0.0765683 | ||||||||
\(320\) | 8.63005 | 0.482434 | ||||||||
\(321\) | 1.36772 | 0.0763386 | ||||||||
\(322\) | −19.3866 | −1.08037 | ||||||||
\(323\) | 29.7449 | 1.65505 | ||||||||
\(324\) | 2.57390 | 0.142995 | ||||||||
\(325\) | 1.33873 | 0.0742593 | ||||||||
\(326\) | 13.0718 | 0.723978 | ||||||||
\(327\) | 10.9384 | 0.604893 | ||||||||
\(328\) | −17.1530 | −0.947114 | ||||||||
\(329\) | 19.8094 | 1.09213 | ||||||||
\(330\) | −12.6034 | −0.693795 | ||||||||
\(331\) | 17.0722 | 0.938372 | 0.469186 | − | 0.883099i | \(-0.344547\pi\) | ||||
0.469186 | + | 0.883099i | \(0.344547\pi\) | |||||||
\(332\) | −10.4843 | −0.575402 | ||||||||
\(333\) | −7.76420 | −0.425476 | ||||||||
\(334\) | 18.1212 | 0.991549 | ||||||||
\(335\) | 19.4959 | 1.06517 | ||||||||
\(336\) | 8.27691 | 0.451542 | ||||||||
\(337\) | −15.1710 | −0.826418 | −0.413209 | − | 0.910636i | \(-0.635592\pi\) | ||||
−0.413209 | + | 0.910636i | \(0.635592\pi\) | |||||||
\(338\) | 19.3264 | 1.05122 | ||||||||
\(339\) | 9.04835 | 0.491439 | ||||||||
\(340\) | −8.20630 | −0.445049 | ||||||||
\(341\) | 5.55576 | 0.300861 | ||||||||
\(342\) | −24.9682 | −1.35013 | ||||||||
\(343\) | −20.1343 | −1.08715 | ||||||||
\(344\) | −15.3644 | −0.828392 | ||||||||
\(345\) | −11.2334 | −0.604785 | ||||||||
\(346\) | −5.62823 | −0.302575 | ||||||||
\(347\) | −13.7233 | −0.736704 | −0.368352 | − | 0.929686i | \(-0.620078\pi\) | ||||
−0.368352 | + | 0.929686i | \(0.620078\pi\) | |||||||
\(348\) | −0.205026 | −0.0109905 | ||||||||
\(349\) | −10.0767 | −0.539395 | −0.269697 | − | 0.962945i | \(-0.586924\pi\) | ||||
−0.269697 | + | 0.962945i | \(0.586924\pi\) | |||||||
\(350\) | −4.10067 | −0.219190 | ||||||||
\(351\) | 4.84618 | 0.258670 | ||||||||
\(352\) | −14.7912 | −0.788371 | ||||||||
\(353\) | −34.6590 | −1.84471 | −0.922357 | − | 0.386339i | \(-0.873739\pi\) | ||||
−0.922357 | + | 0.386339i | \(0.873739\pi\) | |||||||
\(354\) | 5.36707 | 0.285257 | ||||||||
\(355\) | −18.4211 | −0.977690 | ||||||||
\(356\) | 0.432206 | 0.0229069 | ||||||||
\(357\) | 7.77570 | 0.411533 | ||||||||
\(358\) | −32.3815 | −1.71141 | ||||||||
\(359\) | 13.4631 | 0.710556 | 0.355278 | − | 0.934761i | \(-0.384386\pi\) | ||||
0.355278 | + | 0.934761i | \(0.384386\pi\) | |||||||
\(360\) | −12.4079 | −0.653956 | ||||||||
\(361\) | 22.4450 | 1.18132 | ||||||||
\(362\) | 11.5188 | 0.605416 | ||||||||
\(363\) | −2.92949 | −0.153759 | ||||||||
\(364\) | 1.68409 | 0.0882701 | ||||||||
\(365\) | −16.7179 | −0.875056 | ||||||||
\(366\) | −2.45395 | −0.128270 | ||||||||
\(367\) | −12.9865 | −0.677892 | −0.338946 | − | 0.940806i | \(-0.610070\pi\) | ||||
−0.338946 | + | 0.940806i | \(0.610070\pi\) | |||||||
\(368\) | −27.6363 | −1.44064 | ||||||||
\(369\) | 19.0604 | 0.992247 | ||||||||
\(370\) | −13.5159 | −0.702659 | ||||||||
\(371\) | −19.7781 | −1.02683 | ||||||||
\(372\) | 0.832927 | 0.0431853 | ||||||||
\(373\) | −35.7591 | −1.85154 | −0.925768 | − | 0.378093i | \(-0.876580\pi\) | ||||
−0.925768 | + | 0.378093i | \(0.876580\pi\) | |||||||
\(374\) | −29.1293 | −1.50624 | ||||||||
\(375\) | 7.61941 | 0.393464 | ||||||||
\(376\) | 20.0402 | 1.03349 | ||||||||
\(377\) | 0.402491 | 0.0207294 | ||||||||
\(378\) | −14.8444 | −0.763513 | ||||||||
\(379\) | −2.56674 | −0.131844 | −0.0659222 | − | 0.997825i | \(-0.520999\pi\) | ||||
−0.0659222 | + | 0.997825i | \(0.520999\pi\) | |||||||
\(380\) | −11.4343 | −0.586565 | ||||||||
\(381\) | 0.969934 | 0.0496912 | ||||||||
\(382\) | 15.7831 | 0.807532 | ||||||||
\(383\) | 37.9016 | 1.93668 | 0.968341 | − | 0.249631i | \(-0.0803092\pi\) | ||||
0.968341 | + | 0.249631i | \(0.0803092\pi\) | |||||||
\(384\) | 10.8044 | 0.551361 | ||||||||
\(385\) | −19.9375 | −1.01611 | ||||||||
\(386\) | 34.9358 | 1.77819 | ||||||||
\(387\) | 17.0730 | 0.867867 | ||||||||
\(388\) | −13.5463 | −0.687711 | ||||||||
\(389\) | −6.33221 | −0.321056 | −0.160528 | − | 0.987031i | \(-0.551320\pi\) | ||||
−0.160528 | + | 0.987031i | \(0.551320\pi\) | |||||||
\(390\) | 3.70937 | 0.187831 | ||||||||
\(391\) | −25.9628 | −1.31300 | ||||||||
\(392\) | −5.53852 | −0.279738 | ||||||||
\(393\) | −18.0231 | −0.909144 | ||||||||
\(394\) | −18.5351 | −0.933787 | ||||||||
\(395\) | −26.3161 | −1.32411 | ||||||||
\(396\) | 6.43245 | 0.323243 | ||||||||
\(397\) | 2.05163 | 0.102968 | 0.0514841 | − | 0.998674i | \(-0.483605\pi\) | ||||
0.0514841 | + | 0.998674i | \(0.483605\pi\) | |||||||
\(398\) | 33.8305 | 1.69577 | ||||||||
\(399\) | 10.8343 | 0.542392 | ||||||||
\(400\) | −5.84566 | −0.292283 | ||||||||
\(401\) | 8.17393 | 0.408187 | 0.204093 | − | 0.978951i | \(-0.434575\pi\) | ||||
0.204093 | + | 0.978951i | \(0.434575\pi\) | |||||||
\(402\) | 10.3750 | 0.517458 | ||||||||
\(403\) | −1.63514 | −0.0814523 | ||||||||
\(404\) | 7.81690 | 0.388905 | ||||||||
\(405\) | 8.96833 | 0.445640 | ||||||||
\(406\) | −1.23288 | −0.0611866 | ||||||||
\(407\) | −12.6212 | −0.625608 | ||||||||
\(408\) | 7.86629 | 0.389439 | ||||||||
\(409\) | −22.0069 | −1.08817 | −0.544085 | − | 0.839030i | \(-0.683123\pi\) | ||||
−0.544085 | + | 0.839030i | \(0.683123\pi\) | |||||||
\(410\) | 33.1804 | 1.63866 | ||||||||
\(411\) | −15.3514 | −0.757231 | ||||||||
\(412\) | 14.2751 | 0.703282 | ||||||||
\(413\) | 8.49026 | 0.417778 | ||||||||
\(414\) | 21.7935 | 1.07109 | ||||||||
\(415\) | −36.5309 | −1.79323 | ||||||||
\(416\) | 4.35326 | 0.213436 | ||||||||
\(417\) | 9.27770 | 0.454331 | ||||||||
\(418\) | −40.5873 | −1.98519 | ||||||||
\(419\) | 3.15085 | 0.153929 | 0.0769646 | − | 0.997034i | \(-0.475477\pi\) | ||||
0.0769646 | + | 0.997034i | \(0.475477\pi\) | |||||||
\(420\) | −2.98906 | −0.145851 | ||||||||
\(421\) | 13.1086 | 0.638875 | 0.319438 | − | 0.947607i | \(-0.396506\pi\) | ||||
0.319438 | + | 0.947607i | \(0.396506\pi\) | |||||||
\(422\) | 25.8947 | 1.26053 | ||||||||
\(423\) | −22.2687 | −1.08274 | ||||||||
\(424\) | −20.0086 | −0.971703 | ||||||||
\(425\) | −5.49167 | −0.266385 | ||||||||
\(426\) | −9.80304 | −0.474959 | ||||||||
\(427\) | −3.88194 | −0.187860 | ||||||||
\(428\) | −1.21516 | −0.0587371 | ||||||||
\(429\) | 3.46381 | 0.167234 | ||||||||
\(430\) | 29.7206 | 1.43325 | ||||||||
\(431\) | −11.6037 | −0.558932 | −0.279466 | − | 0.960156i | \(-0.590157\pi\) | ||||
−0.279466 | + | 0.960156i | \(0.590157\pi\) | |||||||
\(432\) | −21.1612 | −1.01812 | ||||||||
\(433\) | −2.01228 | −0.0967038 | −0.0483519 | − | 0.998830i | \(-0.515397\pi\) | ||||
−0.0483519 | + | 0.998830i | \(0.515397\pi\) | |||||||
\(434\) | 5.00862 | 0.240422 | ||||||||
\(435\) | −0.714377 | −0.0342517 | ||||||||
\(436\) | −9.71828 | −0.465421 | ||||||||
\(437\) | −36.1753 | −1.73050 | ||||||||
\(438\) | −8.89667 | −0.425100 | ||||||||
\(439\) | −22.5931 | −1.07831 | −0.539155 | − | 0.842207i | \(-0.681256\pi\) | ||||
−0.539155 | + | 0.842207i | \(0.681256\pi\) | |||||||
\(440\) | −20.1698 | −0.961559 | ||||||||
\(441\) | 6.15443 | 0.293068 | ||||||||
\(442\) | 8.57317 | 0.407784 | ||||||||
\(443\) | −2.75685 | −0.130982 | −0.0654909 | − | 0.997853i | \(-0.520861\pi\) | ||||
−0.0654909 | + | 0.997853i | \(0.520861\pi\) | |||||||
\(444\) | −1.89218 | −0.0897990 | ||||||||
\(445\) | 1.50595 | 0.0713888 | ||||||||
\(446\) | −14.6475 | −0.693579 | ||||||||
\(447\) | −7.44043 | −0.351920 | ||||||||
\(448\) | 7.26511 | 0.343244 | ||||||||
\(449\) | −1.90135 | −0.0897305 | −0.0448652 | − | 0.998993i | \(-0.514286\pi\) | ||||
−0.0448652 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(450\) | 4.60978 | 0.217307 | ||||||||
\(451\) | 30.9839 | 1.45897 | ||||||||
\(452\) | −8.03909 | −0.378127 | ||||||||
\(453\) | 2.75586 | 0.129481 | ||||||||
\(454\) | 27.6467 | 1.29752 | ||||||||
\(455\) | 5.86791 | 0.275092 | ||||||||
\(456\) | 10.9605 | 0.513272 | ||||||||
\(457\) | −14.0492 | −0.657192 | −0.328596 | − | 0.944471i | \(-0.606575\pi\) | ||||
−0.328596 | + | 0.944471i | \(0.606575\pi\) | |||||||
\(458\) | 20.6022 | 0.962679 | ||||||||
\(459\) | −19.8798 | −0.927909 | ||||||||
\(460\) | 9.98039 | 0.465338 | ||||||||
\(461\) | 0.101756 | 0.00473924 | 0.00236962 | − | 0.999997i | \(-0.499246\pi\) | ||||
0.00236962 | + | 0.999997i | \(0.499246\pi\) | |||||||
\(462\) | −10.6100 | −0.493624 | ||||||||
\(463\) | 36.7663 | 1.70867 | 0.854337 | − | 0.519720i | \(-0.173964\pi\) | ||||
0.854337 | + | 0.519720i | \(0.173964\pi\) | |||||||
\(464\) | −1.75751 | −0.0815903 | ||||||||
\(465\) | 2.90219 | 0.134586 | ||||||||
\(466\) | 7.75668 | 0.359321 | ||||||||
\(467\) | −25.9733 | −1.20190 | −0.600951 | − | 0.799286i | \(-0.705211\pi\) | ||||
−0.600951 | + | 0.799286i | \(0.705211\pi\) | |||||||
\(468\) | −1.89317 | −0.0875117 | ||||||||
\(469\) | 16.4124 | 0.757854 | ||||||||
\(470\) | −38.7653 | −1.78811 | ||||||||
\(471\) | 5.95397 | 0.274344 | ||||||||
\(472\) | 8.58918 | 0.395349 | ||||||||
\(473\) | 27.7531 | 1.27609 | ||||||||
\(474\) | −14.0045 | −0.643248 | ||||||||
\(475\) | −7.65183 | −0.351090 | ||||||||
\(476\) | −6.90838 | −0.316645 | ||||||||
\(477\) | 22.2336 | 1.01801 | ||||||||
\(478\) | −30.2756 | −1.38477 | ||||||||
\(479\) | −9.66084 | −0.441415 | −0.220708 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220708 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(480\) | −7.72654 | −0.352667 | ||||||||
\(481\) | 3.71460 | 0.169371 | ||||||||
\(482\) | −41.6800 | −1.89847 | ||||||||
\(483\) | −9.45669 | −0.430294 | ||||||||
\(484\) | 2.60274 | 0.118306 | ||||||||
\(485\) | −47.1999 | −2.14324 | ||||||||
\(486\) | 26.0373 | 1.18108 | ||||||||
\(487\) | 16.6033 | 0.752366 | 0.376183 | − | 0.926545i | \(-0.377236\pi\) | ||||
0.376183 | + | 0.926545i | \(0.377236\pi\) | |||||||
\(488\) | −3.92717 | −0.177774 | ||||||||
\(489\) | 6.37633 | 0.288348 | ||||||||
\(490\) | 10.7136 | 0.483992 | ||||||||
\(491\) | 18.5424 | 0.836805 | 0.418403 | − | 0.908262i | \(-0.362590\pi\) | ||||
0.418403 | + | 0.908262i | \(0.362590\pi\) | |||||||
\(492\) | 4.64514 | 0.209419 | ||||||||
\(493\) | −1.65108 | −0.0743610 | ||||||||
\(494\) | 11.9454 | 0.537451 | ||||||||
\(495\) | 22.4128 | 1.00738 | ||||||||
\(496\) | 7.13997 | 0.320594 | ||||||||
\(497\) | −15.5076 | −0.695610 | ||||||||
\(498\) | −19.4404 | −0.871145 | ||||||||
\(499\) | 28.5148 | 1.27650 | 0.638248 | − | 0.769831i | \(-0.279659\pi\) | ||||
0.638248 | + | 0.769831i | \(0.279659\pi\) | |||||||
\(500\) | −6.76953 | −0.302743 | ||||||||
\(501\) | 8.83943 | 0.394917 | ||||||||
\(502\) | −20.9806 | −0.936408 | ||||||||
\(503\) | 25.0045 | 1.11490 | 0.557448 | − | 0.830212i | \(-0.311781\pi\) | ||||
0.557448 | + | 0.830212i | \(0.311781\pi\) | |||||||
\(504\) | −10.4455 | −0.465279 | ||||||||
\(505\) | 27.2367 | 1.21202 | ||||||||
\(506\) | 35.4266 | 1.57490 | ||||||||
\(507\) | 9.42733 | 0.418682 | ||||||||
\(508\) | −0.861746 | −0.0382338 | ||||||||
\(509\) | 1.78975 | 0.0793291 | 0.0396646 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396646 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(510\) | −15.2164 | −0.673794 | ||||||||
\(511\) | −14.0738 | −0.622588 | ||||||||
\(512\) | 1.83080 | 0.0809108 | ||||||||
\(513\) | −27.6995 | −1.22296 | ||||||||
\(514\) | −29.1687 | −1.28658 | ||||||||
\(515\) | 49.7391 | 2.19176 | ||||||||
\(516\) | 4.16078 | 0.183168 | ||||||||
\(517\) | −36.1991 | −1.59203 | ||||||||
\(518\) | −11.3782 | −0.499930 | ||||||||
\(519\) | −2.74542 | −0.120511 | ||||||||
\(520\) | 5.93628 | 0.260323 | ||||||||
\(521\) | 23.7365 | 1.03991 | 0.519957 | − | 0.854193i | \(-0.325948\pi\) | ||||
0.519957 | + | 0.854193i | \(0.325948\pi\) | |||||||
\(522\) | 1.38594 | 0.0606609 | ||||||||
\(523\) | −15.2695 | −0.667689 | −0.333845 | − | 0.942628i | \(-0.608346\pi\) | ||||
−0.333845 | + | 0.942628i | \(0.608346\pi\) | |||||||
\(524\) | 16.0128 | 0.699520 | ||||||||
\(525\) | −2.00029 | −0.0872997 | ||||||||
\(526\) | −42.2224 | −1.84099 | ||||||||
\(527\) | 6.70761 | 0.292188 | ||||||||
\(528\) | −15.1250 | −0.658231 | ||||||||
\(529\) | 8.57560 | 0.372852 | ||||||||
\(530\) | 38.7042 | 1.68121 | ||||||||
\(531\) | −9.54433 | −0.414189 | ||||||||
\(532\) | −9.62580 | −0.417331 | ||||||||
\(533\) | −9.11901 | −0.394988 | ||||||||
\(534\) | 0.801411 | 0.0346805 | ||||||||
\(535\) | −4.23403 | −0.183053 | ||||||||
\(536\) | 16.6036 | 0.717167 | ||||||||
\(537\) | −15.7955 | −0.681626 | ||||||||
\(538\) | 27.3078 | 1.17732 | ||||||||
\(539\) | 10.0044 | 0.430919 | ||||||||
\(540\) | 7.64201 | 0.328860 | ||||||||
\(541\) | 16.2069 | 0.696791 | 0.348395 | − | 0.937348i | \(-0.386727\pi\) | ||||
0.348395 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(542\) | −5.81013 | −0.249567 | ||||||||
\(543\) | 5.61882 | 0.241127 | ||||||||
\(544\) | −17.8577 | −0.765644 | ||||||||
\(545\) | −33.8617 | −1.45048 | ||||||||
\(546\) | 3.12269 | 0.133639 | ||||||||
\(547\) | 21.6434 | 0.925404 | 0.462702 | − | 0.886514i | \(-0.346880\pi\) | ||||
0.462702 | + | 0.886514i | \(0.346880\pi\) | |||||||
\(548\) | 13.6391 | 0.582635 | ||||||||
\(549\) | 4.36388 | 0.186246 | ||||||||
\(550\) | 7.49346 | 0.319522 | ||||||||
\(551\) | −2.30054 | −0.0980061 | ||||||||
\(552\) | −9.56687 | −0.407193 | ||||||||
\(553\) | −22.1539 | −0.942082 | ||||||||
\(554\) | −22.3088 | −0.947810 | ||||||||
\(555\) | −6.59299 | −0.279857 | ||||||||
\(556\) | −8.24286 | −0.349575 | ||||||||
\(557\) | 8.57423 | 0.363302 | 0.181651 | − | 0.983363i | \(-0.441856\pi\) | ||||
0.181651 | + | 0.983363i | \(0.441856\pi\) | |||||||
\(558\) | −5.63045 | −0.238356 | ||||||||
\(559\) | −8.16815 | −0.345476 | ||||||||
\(560\) | −25.6227 | −1.08276 | ||||||||
\(561\) | −14.2091 | −0.599909 | ||||||||
\(562\) | −15.9292 | −0.671934 | ||||||||
\(563\) | −2.70217 | −0.113883 | −0.0569415 | − | 0.998378i | \(-0.518135\pi\) | ||||
−0.0569415 | + | 0.998378i | \(0.518135\pi\) | |||||||
\(564\) | −5.42701 | −0.228519 | ||||||||
\(565\) | −28.0108 | −1.17842 | ||||||||
\(566\) | −43.0669 | −1.81024 | ||||||||
\(567\) | 7.54989 | 0.317065 | ||||||||
\(568\) | −15.6883 | −0.658265 | ||||||||
\(569\) | −5.31348 | −0.222753 | −0.111376 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111376 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(570\) | −21.2018 | −0.888046 | ||||||||
\(571\) | −16.3022 | −0.682226 | −0.341113 | − | 0.940022i | \(-0.610804\pi\) | ||||
−0.341113 | + | 0.940022i | \(0.610804\pi\) | |||||||
\(572\) | −3.07745 | −0.128675 | ||||||||
\(573\) | 7.69889 | 0.321626 | ||||||||
\(574\) | 27.9326 | 1.16588 | ||||||||
\(575\) | 6.67890 | 0.278529 | ||||||||
\(576\) | −8.16708 | −0.340295 | ||||||||
\(577\) | 12.6109 | 0.524999 | 0.262499 | − | 0.964932i | \(-0.415453\pi\) | ||||
0.262499 | + | 0.964932i | \(0.415453\pi\) | |||||||
\(578\) | −7.16250 | −0.297921 | ||||||||
\(579\) | 17.0415 | 0.708220 | ||||||||
\(580\) | 0.634694 | 0.0263542 | ||||||||
\(581\) | −30.7531 | −1.27585 | ||||||||
\(582\) | −25.1181 | −1.04118 | ||||||||
\(583\) | 36.1420 | 1.49685 | ||||||||
\(584\) | −14.2378 | −0.589163 | ||||||||
\(585\) | −6.59642 | −0.272728 | ||||||||
\(586\) | −20.3549 | −0.840853 | ||||||||
\(587\) | 17.1964 | 0.709770 | 0.354885 | − | 0.934910i | \(-0.384520\pi\) | ||||
0.354885 | + | 0.934910i | \(0.384520\pi\) | |||||||
\(588\) | 1.49987 | 0.0618536 | ||||||||
\(589\) | 9.34605 | 0.385097 | ||||||||
\(590\) | −16.6148 | −0.684019 | ||||||||
\(591\) | −9.04134 | −0.371911 | ||||||||
\(592\) | −16.2201 | −0.666641 | ||||||||
\(593\) | −23.3684 | −0.959625 | −0.479812 | − | 0.877371i | \(-0.659295\pi\) | ||||
−0.479812 | + | 0.877371i | \(0.659295\pi\) | |||||||
\(594\) | 27.1262 | 1.11300 | ||||||||
\(595\) | −24.0711 | −0.986819 | ||||||||
\(596\) | 6.61051 | 0.270777 | ||||||||
\(597\) | 16.5023 | 0.675395 | ||||||||
\(598\) | −10.4266 | −0.426374 | ||||||||
\(599\) | 11.3508 | 0.463782 | 0.231891 | − | 0.972742i | \(-0.425509\pi\) | ||||
0.231891 | + | 0.972742i | \(0.425509\pi\) | |||||||
\(600\) | −2.02359 | −0.0826128 | ||||||||
\(601\) | 37.1783 | 1.51653 | 0.758267 | − | 0.651944i | \(-0.226046\pi\) | ||||
0.758267 | + | 0.651944i | \(0.226046\pi\) | |||||||
\(602\) | 25.0200 | 1.01974 | ||||||||
\(603\) | −18.4500 | −0.751342 | ||||||||
\(604\) | −2.44846 | −0.0996266 | ||||||||
\(605\) | 9.06879 | 0.368699 | ||||||||
\(606\) | 14.4944 | 0.588794 | ||||||||
\(607\) | −1.75515 | −0.0712394 | −0.0356197 | − | 0.999365i | \(-0.511340\pi\) | ||||
−0.0356197 | + | 0.999365i | \(0.511340\pi\) | |||||||
\(608\) | −24.8821 | −1.00910 | ||||||||
\(609\) | −0.601390 | −0.0243696 | ||||||||
\(610\) | 7.59664 | 0.307579 | ||||||||
\(611\) | 10.6539 | 0.431012 | ||||||||
\(612\) | 7.76606 | 0.313925 | ||||||||
\(613\) | 36.2285 | 1.46326 | 0.731628 | − | 0.681704i | \(-0.238761\pi\) | ||||
0.731628 | + | 0.681704i | \(0.238761\pi\) | |||||||
\(614\) | −46.2966 | −1.86838 | ||||||||
\(615\) | 16.1852 | 0.652651 | ||||||||
\(616\) | −16.9798 | −0.684134 | ||||||||
\(617\) | −0.638819 | −0.0257179 | −0.0128589 | − | 0.999917i | \(-0.504093\pi\) | ||||
−0.0128589 | + | 0.999917i | \(0.504093\pi\) | |||||||
\(618\) | 26.4693 | 1.06475 | ||||||||
\(619\) | −7.20840 | −0.289730 | −0.144865 | − | 0.989451i | \(-0.546275\pi\) | ||||
−0.144865 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(620\) | −2.57848 | −0.103554 | ||||||||
\(621\) | 24.1775 | 0.970211 | ||||||||
\(622\) | 34.4573 | 1.38161 | ||||||||
\(623\) | 1.26777 | 0.0507920 | ||||||||
\(624\) | 4.45151 | 0.178203 | ||||||||
\(625\) | −29.5302 | −1.18121 | ||||||||
\(626\) | −19.3627 | −0.773888 | ||||||||
\(627\) | −19.7983 | −0.790666 | ||||||||
\(628\) | −5.28985 | −0.211088 | ||||||||
\(629\) | −15.2379 | −0.607573 | ||||||||
\(630\) | 20.2056 | 0.805009 | ||||||||
\(631\) | 39.3649 | 1.56709 | 0.783547 | − | 0.621333i | \(-0.213408\pi\) | ||||
0.783547 | + | 0.621333i | \(0.213408\pi\) | |||||||
\(632\) | −22.4121 | −0.891504 | ||||||||
\(633\) | 12.6313 | 0.502049 | ||||||||
\(634\) | −12.7023 | −0.504473 | ||||||||
\(635\) | −3.00261 | −0.119155 | ||||||||
\(636\) | 5.41846 | 0.214856 | ||||||||
\(637\) | −2.94444 | −0.116663 | ||||||||
\(638\) | 2.25292 | 0.0891941 | ||||||||
\(639\) | 17.4329 | 0.689633 | ||||||||
\(640\) | −33.4471 | −1.32211 | ||||||||
\(641\) | −6.38766 | −0.252297 | −0.126149 | − | 0.992011i | \(-0.540262\pi\) | ||||
−0.126149 | + | 0.992011i | \(0.540262\pi\) | |||||||
\(642\) | −2.25320 | −0.0889265 | ||||||||
\(643\) | −24.7774 | −0.977126 | −0.488563 | − | 0.872529i | \(-0.662479\pi\) | ||||
−0.488563 | + | 0.872529i | \(0.662479\pi\) | |||||||
\(644\) | 8.40188 | 0.331080 | ||||||||
\(645\) | 14.4975 | 0.570840 | ||||||||
\(646\) | −49.0020 | −1.92796 | ||||||||
\(647\) | −37.2673 | −1.46513 | −0.732565 | − | 0.680697i | \(-0.761677\pi\) | ||||
−0.732565 | + | 0.680697i | \(0.761677\pi\) | |||||||
\(648\) | 7.63785 | 0.300043 | ||||||||
\(649\) | −15.5149 | −0.609012 | ||||||||
\(650\) | −2.20544 | −0.0865043 | ||||||||
\(651\) | 2.44318 | 0.0957557 | ||||||||
\(652\) | −5.66511 | −0.221863 | ||||||||
\(653\) | 0.174941 | 0.00684599 | 0.00342299 | − | 0.999994i | \(-0.498910\pi\) | ||||
0.00342299 | + | 0.999994i | \(0.498910\pi\) | |||||||
\(654\) | −18.0200 | −0.704637 | ||||||||
\(655\) | 55.7937 | 2.18004 | ||||||||
\(656\) | 39.8189 | 1.55467 | ||||||||
\(657\) | 15.8211 | 0.617238 | ||||||||
\(658\) | −32.6342 | −1.27221 | ||||||||
\(659\) | 16.8015 | 0.654494 | 0.327247 | − | 0.944939i | \(-0.393879\pi\) | ||||
0.327247 | + | 0.944939i | \(0.393879\pi\) | |||||||
\(660\) | 5.46213 | 0.212613 | ||||||||
\(661\) | 31.4781 | 1.22436 | 0.612178 | − | 0.790720i | \(-0.290294\pi\) | ||||
0.612178 | + | 0.790720i | \(0.290294\pi\) | |||||||
\(662\) | −28.1249 | −1.09311 | ||||||||
\(663\) | 4.18195 | 0.162413 | ||||||||
\(664\) | −31.1114 | −1.20736 | ||||||||
\(665\) | −33.5395 | −1.30060 | ||||||||
\(666\) | 12.7908 | 0.495635 | ||||||||
\(667\) | 2.00802 | 0.0777510 | ||||||||
\(668\) | −7.85347 | −0.303860 | ||||||||
\(669\) | −7.14496 | −0.276240 | ||||||||
\(670\) | −32.1177 | −1.24082 | ||||||||
\(671\) | 7.09375 | 0.273851 | ||||||||
\(672\) | −6.50450 | −0.250917 | ||||||||
\(673\) | 15.9762 | 0.615837 | 0.307919 | − | 0.951413i | \(-0.400368\pi\) | ||||
0.307919 | + | 0.951413i | \(0.400368\pi\) | |||||||
\(674\) | 24.9929 | 0.962691 | ||||||||
\(675\) | 5.11405 | 0.196840 | ||||||||
\(676\) | −8.37579 | −0.322146 | ||||||||
\(677\) | 18.4699 | 0.709856 | 0.354928 | − | 0.934894i | \(-0.384505\pi\) | ||||
0.354928 | + | 0.934894i | \(0.384505\pi\) | |||||||
\(678\) | −14.9064 | −0.572475 | ||||||||
\(679\) | −39.7347 | −1.52488 | ||||||||
\(680\) | −24.3516 | −0.933839 | ||||||||
\(681\) | 13.4859 | 0.516781 | ||||||||
\(682\) | −9.15262 | −0.350472 | ||||||||
\(683\) | 34.6722 | 1.32670 | 0.663348 | − | 0.748311i | \(-0.269135\pi\) | ||||
0.663348 | + | 0.748311i | \(0.269135\pi\) | |||||||
\(684\) | 10.8208 | 0.413745 | ||||||||
\(685\) | 47.5232 | 1.81577 | ||||||||
\(686\) | 33.1696 | 1.26642 | ||||||||
\(687\) | 10.0497 | 0.383418 | ||||||||
\(688\) | 35.6668 | 1.35979 | ||||||||
\(689\) | −10.6371 | −0.405243 | ||||||||
\(690\) | 18.5060 | 0.704511 | ||||||||
\(691\) | 48.9944 | 1.86383 | 0.931917 | − | 0.362672i | \(-0.118136\pi\) | ||||
0.931917 | + | 0.362672i | \(0.118136\pi\) | |||||||
\(692\) | 2.43919 | 0.0927241 | ||||||||
\(693\) | 18.8680 | 0.716735 | ||||||||
\(694\) | 22.6079 | 0.858183 | ||||||||
\(695\) | −28.7208 | −1.08944 | ||||||||
\(696\) | −0.608397 | −0.0230612 | ||||||||
\(697\) | 37.4076 | 1.41691 | ||||||||
\(698\) | 16.6005 | 0.628339 | ||||||||
\(699\) | 3.78366 | 0.143111 | ||||||||
\(700\) | 1.77717 | 0.0671708 | ||||||||
\(701\) | −28.5131 | −1.07692 | −0.538462 | − | 0.842650i | \(-0.680994\pi\) | ||||
−0.538462 | + | 0.842650i | \(0.680994\pi\) | |||||||
\(702\) | −7.98365 | −0.301324 | ||||||||
\(703\) | −21.2317 | −0.800767 | ||||||||
\(704\) | −13.2761 | −0.500361 | ||||||||
\(705\) | −18.9095 | −0.712174 | ||||||||
\(706\) | 57.0977 | 2.14890 | ||||||||
\(707\) | 22.9289 | 0.862330 | ||||||||
\(708\) | −2.32601 | −0.0874168 | ||||||||
\(709\) | 22.2537 | 0.835754 | 0.417877 | − | 0.908504i | \(-0.362774\pi\) | ||||
0.417877 | + | 0.908504i | \(0.362774\pi\) | |||||||
\(710\) | 30.3471 | 1.13891 | ||||||||
\(711\) | 24.9044 | 0.933987 | ||||||||
\(712\) | 1.28254 | 0.0480651 | ||||||||
\(713\) | −8.15770 | −0.305508 | ||||||||
\(714\) | −12.8098 | −0.479394 | ||||||||
\(715\) | −10.7229 | −0.401013 | ||||||||
\(716\) | 14.0336 | 0.524462 | ||||||||
\(717\) | −14.7683 | −0.551531 | ||||||||
\(718\) | −22.1793 | −0.827723 | ||||||||
\(719\) | −24.7281 | −0.922202 | −0.461101 | − | 0.887348i | \(-0.652545\pi\) | ||||
−0.461101 | + | 0.887348i | \(0.652545\pi\) | |||||||
\(720\) | 28.8038 | 1.07345 | ||||||||
\(721\) | 41.8723 | 1.55940 | ||||||||
\(722\) | −36.9762 | −1.37611 | ||||||||
\(723\) | −20.3313 | −0.756128 | ||||||||
\(724\) | −4.99209 | −0.185530 | ||||||||
\(725\) | 0.424739 | 0.0157744 | ||||||||
\(726\) | 4.82608 | 0.179113 | ||||||||
\(727\) | 19.3636 | 0.718157 | 0.359079 | − | 0.933307i | \(-0.383091\pi\) | ||||
0.359079 | + | 0.933307i | \(0.383091\pi\) | |||||||
\(728\) | 4.99739 | 0.185216 | ||||||||
\(729\) | 1.88560 | 0.0698369 | ||||||||
\(730\) | 27.5413 | 1.01935 | ||||||||
\(731\) | 33.5070 | 1.23930 | ||||||||
\(732\) | 1.06350 | 0.0393082 | ||||||||
\(733\) | −45.2847 | −1.67263 | −0.836315 | − | 0.548250i | \(-0.815294\pi\) | ||||
−0.836315 | + | 0.548250i | \(0.815294\pi\) | |||||||
\(734\) | 21.3942 | 0.789674 | ||||||||
\(735\) | 5.22605 | 0.192766 | ||||||||
\(736\) | 21.7183 | 0.800548 | ||||||||
\(737\) | −29.9916 | −1.10475 | ||||||||
\(738\) | −31.4004 | −1.15586 | ||||||||
\(739\) | 7.91117 | 0.291017 | 0.145509 | − | 0.989357i | \(-0.453518\pi\) | ||||
0.145509 | + | 0.989357i | \(0.453518\pi\) | |||||||
\(740\) | 5.85760 | 0.215330 | ||||||||
\(741\) | 5.82692 | 0.214057 | ||||||||
\(742\) | 32.5827 | 1.19615 | ||||||||
\(743\) | −26.5830 | −0.975234 | −0.487617 | − | 0.873058i | \(-0.662134\pi\) | ||||
−0.487617 | + | 0.873058i | \(0.662134\pi\) | |||||||
\(744\) | 2.47164 | 0.0906149 | ||||||||
\(745\) | 23.0332 | 0.843872 | ||||||||
\(746\) | 58.9099 | 2.15685 | ||||||||
\(747\) | 34.5711 | 1.26489 | ||||||||
\(748\) | 12.6242 | 0.461586 | ||||||||
\(749\) | −3.56437 | −0.130239 | ||||||||
\(750\) | −12.5523 | −0.458345 | ||||||||
\(751\) | 47.1479 | 1.72045 | 0.860225 | − | 0.509915i | \(-0.170323\pi\) | ||||
0.860225 | + | 0.509915i | \(0.170323\pi\) | |||||||
\(752\) | −46.5212 | −1.69645 | ||||||||
\(753\) | −10.2342 | −0.372955 | ||||||||
\(754\) | −0.663069 | −0.0241475 | ||||||||
\(755\) | −8.53126 | −0.310484 | ||||||||
\(756\) | 6.43334 | 0.233978 | ||||||||
\(757\) | 20.1188 | 0.731232 | 0.365616 | − | 0.930766i | \(-0.380858\pi\) | ||||
0.365616 | + | 0.930766i | \(0.380858\pi\) | |||||||
\(758\) | 4.22847 | 0.153585 | ||||||||
\(759\) | 17.2809 | 0.627257 | ||||||||
\(760\) | −33.9302 | −1.23078 | ||||||||
\(761\) | −13.3028 | −0.482227 | −0.241114 | − | 0.970497i | \(-0.577513\pi\) | ||||
−0.241114 | + | 0.970497i | \(0.577513\pi\) | |||||||
\(762\) | −1.59788 | −0.0578851 | ||||||||
\(763\) | −28.5061 | −1.03199 | ||||||||
\(764\) | −6.84015 | −0.247468 | ||||||||
\(765\) | 27.0595 | 0.978339 | ||||||||
\(766\) | −62.4396 | −2.25603 | ||||||||
\(767\) | 4.56626 | 0.164878 | ||||||||
\(768\) | −12.2238 | −0.441088 | ||||||||
\(769\) | −25.4017 | −0.916009 | −0.458005 | − | 0.888950i | \(-0.651436\pi\) | ||||
−0.458005 | + | 0.888950i | \(0.651436\pi\) | |||||||
\(770\) | 32.8453 | 1.18366 | ||||||||
\(771\) | −14.2283 | −0.512421 | ||||||||
\(772\) | −15.1407 | −0.544924 | ||||||||
\(773\) | −38.5881 | −1.38792 | −0.693959 | − | 0.720015i | \(-0.744135\pi\) | ||||
−0.693959 | + | 0.720015i | \(0.744135\pi\) | |||||||
\(774\) | −28.1262 | −1.01098 | ||||||||
\(775\) | −1.72552 | −0.0619826 | ||||||||
\(776\) | −40.1977 | −1.44301 | ||||||||
\(777\) | −5.55023 | −0.199114 | ||||||||
\(778\) | 10.4318 | 0.373997 | ||||||||
\(779\) | 52.1219 | 1.86746 | ||||||||
\(780\) | −1.60759 | −0.0575608 | ||||||||
\(781\) | 28.3382 | 1.01402 | ||||||||
\(782\) | 42.7714 | 1.52950 | ||||||||
\(783\) | 1.53755 | 0.0549475 | ||||||||
\(784\) | 12.8571 | 0.459183 | ||||||||
\(785\) | −18.4316 | −0.657852 | ||||||||
\(786\) | 29.6914 | 1.05906 | ||||||||
\(787\) | −5.58006 | −0.198908 | −0.0994538 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994538 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(788\) | 8.03286 | 0.286159 | ||||||||
\(789\) | −20.5959 | −0.733233 | ||||||||
\(790\) | 43.3535 | 1.54245 | ||||||||
\(791\) | −23.5806 | −0.838430 | ||||||||
\(792\) | 19.0878 | 0.678255 | ||||||||
\(793\) | −2.08779 | −0.0741398 | ||||||||
\(794\) | −3.37988 | −0.119947 | ||||||||
\(795\) | 18.8797 | 0.669595 | ||||||||
\(796\) | −14.6616 | −0.519668 | ||||||||
\(797\) | −18.9854 | −0.672499 | −0.336249 | − | 0.941773i | \(-0.609159\pi\) | ||||
−0.336249 | + | 0.941773i | \(0.609159\pi\) | |||||||
\(798\) | −17.8485 | −0.631830 | ||||||||
\(799\) | −43.7041 | −1.54614 | ||||||||
\(800\) | 4.59388 | 0.162418 | ||||||||
\(801\) | −1.42516 | −0.0503555 | ||||||||
\(802\) | −13.4658 | −0.475495 | ||||||||
\(803\) | 25.7181 | 0.907571 | ||||||||
\(804\) | −4.49637 | −0.158575 | ||||||||
\(805\) | 29.2749 | 1.03181 | ||||||||
\(806\) | 2.69375 | 0.0948834 | ||||||||
\(807\) | 13.3206 | 0.468908 | ||||||||
\(808\) | 23.1960 | 0.816034 | ||||||||
\(809\) | −46.5379 | −1.63618 | −0.818092 | − | 0.575087i | \(-0.804968\pi\) | ||||
−0.818092 | + | 0.575087i | \(0.804968\pi\) | |||||||
\(810\) | −14.7745 | −0.519124 | ||||||||
\(811\) | −28.8818 | −1.01418 | −0.507089 | − | 0.861894i | \(-0.669278\pi\) | ||||
−0.507089 | + | 0.861894i | \(0.669278\pi\) | |||||||
\(812\) | 0.534310 | 0.0187506 | ||||||||
\(813\) | −2.83415 | −0.0993980 | ||||||||
\(814\) | 20.7923 | 0.728768 | ||||||||
\(815\) | −19.7391 | −0.691431 | ||||||||
\(816\) | −18.2608 | −0.639255 | ||||||||
\(817\) | 46.6870 | 1.63337 | ||||||||
\(818\) | 36.2544 | 1.26761 | ||||||||
\(819\) | −5.55312 | −0.194042 | ||||||||
\(820\) | −14.3799 | −0.502168 | ||||||||
\(821\) | −1.48857 | −0.0519514 | −0.0259757 | − | 0.999663i | \(-0.508269\pi\) | ||||
−0.0259757 | + | 0.999663i | \(0.508269\pi\) | |||||||
\(822\) | 25.2901 | 0.882095 | ||||||||
\(823\) | −14.5821 | −0.508299 | −0.254149 | − | 0.967165i | \(-0.581796\pi\) | ||||
−0.254149 | + | 0.967165i | \(0.581796\pi\) | |||||||
\(824\) | 42.3601 | 1.47568 | ||||||||
\(825\) | 3.65527 | 0.127260 | ||||||||
\(826\) | −13.9869 | −0.486668 | ||||||||
\(827\) | 27.6321 | 0.960863 | 0.480431 | − | 0.877032i | \(-0.340480\pi\) | ||||
0.480431 | + | 0.877032i | \(0.340480\pi\) | |||||||
\(828\) | −9.44498 | −0.328236 | ||||||||
\(829\) | 18.9100 | 0.656770 | 0.328385 | − | 0.944544i | \(-0.393496\pi\) | ||||
0.328385 | + | 0.944544i | \(0.393496\pi\) | |||||||
\(830\) | 60.1814 | 2.08893 | ||||||||
\(831\) | −10.8821 | −0.377496 | ||||||||
\(832\) | 3.90734 | 0.135463 | ||||||||
\(833\) | 12.0785 | 0.418497 | ||||||||
\(834\) | −15.2842 | −0.529248 | ||||||||
\(835\) | −27.3641 | −0.946973 | ||||||||
\(836\) | 17.5899 | 0.608360 | ||||||||
\(837\) | −6.24637 | −0.215906 | ||||||||
\(838\) | −5.19075 | −0.179311 | ||||||||
\(839\) | −1.33745 | −0.0461741 | −0.0230870 | − | 0.999733i | \(-0.507349\pi\) | ||||
−0.0230870 | + | 0.999733i | \(0.507349\pi\) | |||||||
\(840\) | −8.86981 | −0.306037 | ||||||||
\(841\) | −28.8723 | −0.995597 | ||||||||
\(842\) | −21.5953 | −0.744223 | ||||||||
\(843\) | −7.77019 | −0.267620 | ||||||||
\(844\) | −11.2224 | −0.386290 | ||||||||
\(845\) | −29.1840 | −1.00396 | ||||||||
\(846\) | 36.6857 | 1.26128 | ||||||||
\(847\) | 7.63446 | 0.262323 | ||||||||
\(848\) | 46.4479 | 1.59503 | ||||||||
\(849\) | −21.0078 | −0.720986 | ||||||||
\(850\) | 9.04704 | 0.310311 | ||||||||
\(851\) | 18.5321 | 0.635271 | ||||||||
\(852\) | 4.24849 | 0.145551 | ||||||||
\(853\) | −30.4764 | −1.04349 | −0.521746 | − | 0.853101i | \(-0.674719\pi\) | ||||
−0.521746 | + | 0.853101i | \(0.674719\pi\) | |||||||
\(854\) | 6.39515 | 0.218837 | ||||||||
\(855\) | 37.7034 | 1.28943 | ||||||||
\(856\) | −3.60590 | −0.123247 | ||||||||
\(857\) | 49.1448 | 1.67876 | 0.839378 | − | 0.543549i | \(-0.182920\pi\) | ||||
0.839378 | + | 0.543549i | \(0.182920\pi\) | |||||||
\(858\) | −5.70632 | −0.194811 | ||||||||
\(859\) | −17.5805 | −0.599839 | −0.299919 | − | 0.953965i | \(-0.596960\pi\) | ||||
−0.299919 | + | 0.953965i | \(0.596960\pi\) | |||||||
\(860\) | −12.8805 | −0.439220 | ||||||||
\(861\) | 13.6253 | 0.464351 | ||||||||
\(862\) | 19.1161 | 0.651097 | ||||||||
\(863\) | −11.8568 | −0.403611 | −0.201805 | − | 0.979426i | \(-0.564681\pi\) | ||||
−0.201805 | + | 0.979426i | \(0.564681\pi\) | |||||||
\(864\) | 16.6298 | 0.565757 | ||||||||
\(865\) | 8.49895 | 0.288973 | ||||||||
\(866\) | 3.31504 | 0.112650 | ||||||||
\(867\) | −3.49383 | −0.118657 | ||||||||
\(868\) | −2.17066 | −0.0736771 | ||||||||
\(869\) | 40.4835 | 1.37331 | ||||||||
\(870\) | 1.17687 | 0.0398997 | ||||||||
\(871\) | 8.82696 | 0.299090 | ||||||||
\(872\) | −28.8382 | −0.976586 | ||||||||
\(873\) | 44.6678 | 1.51178 | ||||||||
\(874\) | 59.5956 | 2.01585 | ||||||||
\(875\) | −19.8567 | −0.671278 | ||||||||
\(876\) | 3.85569 | 0.130272 | ||||||||
\(877\) | 21.1843 | 0.715342 | 0.357671 | − | 0.933848i | \(-0.383571\pi\) | ||||
0.357671 | + | 0.933848i | \(0.383571\pi\) | |||||||
\(878\) | 37.2201 | 1.25612 | ||||||||
\(879\) | −9.92900 | −0.334897 | ||||||||
\(880\) | 46.8222 | 1.57838 | ||||||||
\(881\) | −39.7746 | −1.34004 | −0.670020 | − | 0.742343i | \(-0.733714\pi\) | ||||
−0.670020 | + | 0.742343i | \(0.733714\pi\) | |||||||
\(882\) | −10.1389 | −0.341394 | ||||||||
\(883\) | 4.41111 | 0.148446 | 0.0742228 | − | 0.997242i | \(-0.476352\pi\) | ||||
0.0742228 | + | 0.997242i | \(0.476352\pi\) | |||||||
\(884\) | −3.71549 | −0.124965 | ||||||||
\(885\) | −8.10459 | −0.272433 | ||||||||
\(886\) | 4.54166 | 0.152580 | ||||||||
\(887\) | 19.9120 | 0.668578 | 0.334289 | − | 0.942471i | \(-0.391504\pi\) | ||||
0.334289 | + | 0.942471i | \(0.391504\pi\) | |||||||
\(888\) | −5.61490 | −0.188424 | ||||||||
\(889\) | −2.52771 | −0.0847768 | ||||||||
\(890\) | −2.48092 | −0.0831605 | ||||||||
\(891\) | −13.7965 | −0.462199 | ||||||||
\(892\) | 6.34801 | 0.212547 | ||||||||
\(893\) | −60.8951 | −2.03778 | ||||||||
\(894\) | 12.2574 | 0.409950 | ||||||||
\(895\) | 48.8979 | 1.63448 | ||||||||
\(896\) | −28.1571 | −0.940661 | ||||||||
\(897\) | −5.08603 | −0.169817 | ||||||||
\(898\) | 3.13231 | 0.104527 | ||||||||
\(899\) | −0.518782 | −0.0173023 | ||||||||
\(900\) | −1.99781 | −0.0665936 | ||||||||
\(901\) | 43.6352 | 1.45370 | ||||||||
\(902\) | −51.0432 | −1.69955 | ||||||||
\(903\) | 12.2046 | 0.406144 | ||||||||
\(904\) | −23.8553 | −0.793417 | ||||||||
\(905\) | −17.3941 | −0.578199 | ||||||||
\(906\) | −4.54003 | −0.150832 | ||||||||
\(907\) | 3.05945 | 0.101587 | 0.0507936 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507936 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(908\) | −11.9817 | −0.397626 | ||||||||
\(909\) | −25.7755 | −0.854920 | ||||||||
\(910\) | −9.66687 | −0.320454 | ||||||||
\(911\) | −34.7765 | −1.15220 | −0.576099 | − | 0.817380i | \(-0.695426\pi\) | ||||
−0.576099 | + | 0.817380i | \(0.695426\pi\) | |||||||
\(912\) | −25.4437 | −0.842524 | ||||||||
\(913\) | 56.1974 | 1.85986 | ||||||||
\(914\) | 23.1447 | 0.765560 | ||||||||
\(915\) | 3.70560 | 0.122503 | ||||||||
\(916\) | −8.92870 | −0.295013 | ||||||||
\(917\) | 46.9693 | 1.55106 | ||||||||
\(918\) | 32.7502 | 1.08092 | ||||||||
\(919\) | −56.2686 | −1.85613 | −0.928065 | − | 0.372419i | \(-0.878528\pi\) | ||||
−0.928065 | + | 0.372419i | \(0.878528\pi\) | |||||||
\(920\) | 29.6160 | 0.976411 | ||||||||
\(921\) | −22.5832 | −0.744143 | ||||||||
\(922\) | −0.167634 | −0.00552072 | ||||||||
\(923\) | −8.34034 | −0.274526 | ||||||||
\(924\) | 4.59824 | 0.151271 | ||||||||
\(925\) | 3.91992 | 0.128886 | ||||||||
\(926\) | −60.5692 | −1.99043 | ||||||||
\(927\) | −47.0707 | −1.54601 | ||||||||
\(928\) | 1.38116 | 0.0453387 | ||||||||
\(929\) | 57.0122 | 1.87051 | 0.935255 | − | 0.353974i | \(-0.115170\pi\) | ||||
0.935255 | + | 0.353974i | \(0.115170\pi\) | |||||||
\(930\) | −4.78111 | −0.156779 | ||||||||
\(931\) | 16.8296 | 0.551569 | ||||||||
\(932\) | −3.36163 | −0.110114 | ||||||||
\(933\) | 16.8081 | 0.550273 | ||||||||
\(934\) | 42.7887 | 1.40009 | ||||||||
\(935\) | 43.9869 | 1.43852 | ||||||||
\(936\) | −5.61782 | −0.183624 | ||||||||
\(937\) | 2.07924 | 0.0679257 | 0.0339629 | − | 0.999423i | \(-0.489187\pi\) | ||||
0.0339629 | + | 0.999423i | \(0.489187\pi\) | |||||||
\(938\) | −27.0380 | −0.882820 | ||||||||
\(939\) | −9.44501 | −0.308226 | ||||||||
\(940\) | 16.8003 | 0.547966 | ||||||||
\(941\) | 51.0676 | 1.66476 | 0.832379 | − | 0.554207i | \(-0.186978\pi\) | ||||
0.832379 | + | 0.554207i | \(0.186978\pi\) | |||||||
\(942\) | −9.80863 | −0.319583 | ||||||||
\(943\) | −45.4946 | −1.48151 | ||||||||
\(944\) | −19.9389 | −0.648956 | ||||||||
\(945\) | 22.4159 | 0.729189 | ||||||||
\(946\) | −45.7208 | −1.48651 | ||||||||
\(947\) | −40.2743 | −1.30874 | −0.654370 | − | 0.756175i | \(-0.727066\pi\) | ||||
−0.654370 | + | 0.756175i | \(0.727066\pi\) | |||||||
\(948\) | 6.06935 | 0.197123 | ||||||||
\(949\) | −7.56921 | −0.245707 | ||||||||
\(950\) | 12.6057 | 0.408983 | ||||||||
\(951\) | −6.19611 | −0.200923 | ||||||||
\(952\) | −20.5001 | −0.664411 | ||||||||
\(953\) | 54.4421 | 1.76355 | 0.881777 | − | 0.471667i | \(-0.156348\pi\) | ||||
0.881777 | + | 0.471667i | \(0.156348\pi\) | |||||||
\(954\) | −36.6279 | −1.18587 | ||||||||
\(955\) | −23.8333 | −0.771229 | ||||||||
\(956\) | 13.1210 | 0.424363 | ||||||||
\(957\) | 1.09896 | 0.0355245 | ||||||||
\(958\) | 15.9154 | 0.514203 | ||||||||
\(959\) | 40.0069 | 1.29189 | ||||||||
\(960\) | −6.93509 | −0.223829 | ||||||||
\(961\) | −28.8924 | −0.932014 | ||||||||
\(962\) | −6.11947 | −0.197300 | ||||||||
\(963\) | 4.00688 | 0.129120 | ||||||||
\(964\) | 18.0635 | 0.581786 | ||||||||
\(965\) | −52.7551 | −1.69825 | ||||||||
\(966\) | 15.5791 | 0.501248 | ||||||||
\(967\) | 27.2309 | 0.875686 | 0.437843 | − | 0.899051i | \(-0.355743\pi\) | ||||
0.437843 | + | 0.899051i | \(0.355743\pi\) | |||||||
\(968\) | 7.72341 | 0.248240 | ||||||||
\(969\) | −23.9029 | −0.767873 | ||||||||
\(970\) | 77.7577 | 2.49665 | ||||||||
\(971\) | 36.4762 | 1.17058 | 0.585288 | − | 0.810825i | \(-0.300981\pi\) | ||||
0.585288 | + | 0.810825i | \(0.300981\pi\) | |||||||
\(972\) | −11.2842 | −0.361941 | ||||||||
\(973\) | −24.1783 | −0.775121 | ||||||||
\(974\) | −27.3524 | −0.876428 | ||||||||
\(975\) | −1.07580 | −0.0344532 | ||||||||
\(976\) | 9.11651 | 0.291812 | ||||||||
\(977\) | 5.47206 | 0.175067 | 0.0875333 | − | 0.996162i | \(-0.472102\pi\) | ||||
0.0875333 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(978\) | −10.5044 | −0.335895 | ||||||||
\(979\) | −2.31668 | −0.0740414 | ||||||||
\(980\) | −4.64313 | −0.148319 | ||||||||
\(981\) | 32.0451 | 1.02312 | ||||||||
\(982\) | −30.5469 | −0.974791 | ||||||||
\(983\) | −1.00000 | −0.0318950 | ||||||||
\(984\) | 13.7841 | 0.439421 | ||||||||
\(985\) | 27.9891 | 0.891808 | ||||||||
\(986\) | 2.72001 | 0.0866228 | ||||||||
\(987\) | −15.9188 | −0.506700 | ||||||||
\(988\) | −5.17698 | −0.164702 | ||||||||
\(989\) | −40.7508 | −1.29580 | ||||||||
\(990\) | −36.9231 | −1.17349 | ||||||||
\(991\) | 13.3629 | 0.424488 | 0.212244 | − | 0.977217i | \(-0.431923\pi\) | ||||
0.212244 | + | 0.977217i | \(0.431923\pi\) | |||||||
\(992\) | −5.61103 | −0.178150 | ||||||||
\(993\) | −13.7192 | −0.435365 | ||||||||
\(994\) | 25.5474 | 0.810314 | ||||||||
\(995\) | −51.0860 | −1.61953 | ||||||||
\(996\) | 8.42519 | 0.266962 | ||||||||
\(997\) | 32.2796 | 1.02231 | 0.511153 | − | 0.859490i | \(-0.329218\pi\) | ||||
0.511153 | + | 0.859490i | \(0.329218\pi\) | |||||||
\(998\) | −46.9755 | −1.48698 | ||||||||
\(999\) | 14.1900 | 0.448953 |
(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 | 983.2.a.a.1.9 | ✓ | 28 | |
3.2 | odd | 2 | 8847.2.a.b.1.20 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.a.1.9 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8847.2.a.b.1.20 | 28 | 3.2 | odd | 2 |