Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(81\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.77693 | −1.60326 | −0.801632 | − | 0.597818i | \(-0.796035\pi\) | ||||
−0.801632 | + | 0.597818i | \(0.796035\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.15661 | 0.964467 | 0.482233 | − | 0.876043i | \(-0.339826\pi\) | ||||
0.482233 | + | 0.876043i | \(0.339826\pi\) | |||||||
\(6\) | 2.77693 | 1.13368 | ||||||||
\(7\) | 3.32117 | 1.25528 | 0.627642 | − | 0.778502i | \(-0.284020\pi\) | ||||
0.627642 | + | 0.778502i | \(0.284020\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.71136 | 1.57045 | ||||||||
\(10\) | −2.15661 | −0.681981 | ||||||||
\(11\) | −1.55320 | −0.468308 | −0.234154 | − | 0.972200i | \(-0.575232\pi\) | ||||
−0.234154 | + | 0.972200i | \(0.575232\pi\) | |||||||
\(12\) | −2.77693 | −0.801632 | ||||||||
\(13\) | −5.45896 | −1.51404 | −0.757021 | − | 0.653391i | \(-0.773346\pi\) | ||||
−0.757021 | + | 0.653391i | \(0.773346\pi\) | |||||||
\(14\) | −3.32117 | −0.887620 | ||||||||
\(15\) | −5.98877 | −1.54629 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.23032 | −0.540933 | −0.270467 | − | 0.962729i | \(-0.587178\pi\) | ||||
−0.270467 | + | 0.962729i | \(0.587178\pi\) | |||||||
\(18\) | −4.71136 | −1.11048 | ||||||||
\(19\) | −4.92047 | −1.12883 | −0.564416 | − | 0.825490i | \(-0.690899\pi\) | ||||
−0.564416 | + | 0.825490i | \(0.690899\pi\) | |||||||
\(20\) | 2.15661 | 0.482233 | ||||||||
\(21\) | −9.22267 | −2.01255 | ||||||||
\(22\) | 1.55320 | 0.331143 | ||||||||
\(23\) | 3.83366 | 0.799374 | 0.399687 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399687 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(24\) | 2.77693 | 0.566839 | ||||||||
\(25\) | −0.349019 | −0.0698038 | ||||||||
\(26\) | 5.45896 | 1.07059 | ||||||||
\(27\) | −4.75234 | −0.914589 | ||||||||
\(28\) | 3.32117 | 0.627642 | ||||||||
\(29\) | −1.49081 | −0.276837 | −0.138418 | − | 0.990374i | \(-0.544202\pi\) | ||||
−0.138418 | + | 0.990374i | \(0.544202\pi\) | |||||||
\(30\) | 5.98877 | 1.09340 | ||||||||
\(31\) | 8.42545 | 1.51326 | 0.756628 | − | 0.653846i | \(-0.226846\pi\) | ||||
0.756628 | + | 0.653846i | \(0.226846\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.31314 | 0.750820 | ||||||||
\(34\) | 2.23032 | 0.382497 | ||||||||
\(35\) | 7.16248 | 1.21068 | ||||||||
\(36\) | 4.71136 | 0.785227 | ||||||||
\(37\) | 6.95298 | 1.14306 | 0.571531 | − | 0.820580i | \(-0.306350\pi\) | ||||
0.571531 | + | 0.820580i | \(0.306350\pi\) | |||||||
\(38\) | 4.92047 | 0.798205 | ||||||||
\(39\) | 15.1592 | 2.42741 | ||||||||
\(40\) | −2.15661 | −0.340991 | ||||||||
\(41\) | 0.843499 | 0.131732 | 0.0658662 | − | 0.997828i | \(-0.479019\pi\) | ||||
0.0658662 | + | 0.997828i | \(0.479019\pi\) | |||||||
\(42\) | 9.22267 | 1.42309 | ||||||||
\(43\) | 2.75008 | 0.419383 | 0.209692 | − | 0.977768i | \(-0.432754\pi\) | ||||
0.209692 | + | 0.977768i | \(0.432754\pi\) | |||||||
\(44\) | −1.55320 | −0.234154 | ||||||||
\(45\) | 10.1606 | 1.51465 | ||||||||
\(46\) | −3.83366 | −0.565243 | ||||||||
\(47\) | −5.54606 | −0.808976 | −0.404488 | − | 0.914543i | \(-0.632550\pi\) | ||||
−0.404488 | + | 0.914543i | \(0.632550\pi\) | |||||||
\(48\) | −2.77693 | −0.400816 | ||||||||
\(49\) | 4.03018 | 0.575740 | ||||||||
\(50\) | 0.349019 | 0.0493588 | ||||||||
\(51\) | 6.19346 | 0.867258 | ||||||||
\(52\) | −5.45896 | −0.757021 | ||||||||
\(53\) | 3.17078 | 0.435540 | 0.217770 | − | 0.976000i | \(-0.430122\pi\) | ||||
0.217770 | + | 0.976000i | \(0.430122\pi\) | |||||||
\(54\) | 4.75234 | 0.646712 | ||||||||
\(55\) | −3.34965 | −0.451667 | ||||||||
\(56\) | −3.32117 | −0.443810 | ||||||||
\(57\) | 13.6638 | 1.80982 | ||||||||
\(58\) | 1.49081 | 0.195753 | ||||||||
\(59\) | −10.8188 | −1.40848 | −0.704241 | − | 0.709961i | \(-0.748713\pi\) | ||||
−0.704241 | + | 0.709961i | \(0.748713\pi\) | |||||||
\(60\) | −5.98877 | −0.773147 | ||||||||
\(61\) | −6.24278 | −0.799306 | −0.399653 | − | 0.916667i | \(-0.630869\pi\) | ||||
−0.399653 | + | 0.916667i | \(0.630869\pi\) | |||||||
\(62\) | −8.42545 | −1.07003 | ||||||||
\(63\) | 15.6472 | 1.97137 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.7729 | −1.46024 | ||||||||
\(66\) | −4.31314 | −0.530910 | ||||||||
\(67\) | −3.87553 | −0.473472 | −0.236736 | − | 0.971574i | \(-0.576078\pi\) | ||||
−0.236736 | + | 0.971574i | \(0.576078\pi\) | |||||||
\(68\) | −2.23032 | −0.270467 | ||||||||
\(69\) | −10.6458 | −1.28161 | ||||||||
\(70\) | −7.16248 | −0.856080 | ||||||||
\(71\) | 10.2541 | 1.21693 | 0.608467 | − | 0.793579i | \(-0.291785\pi\) | ||||
0.608467 | + | 0.793579i | \(0.291785\pi\) | |||||||
\(72\) | −4.71136 | −0.555239 | ||||||||
\(73\) | 15.1668 | 1.77514 | 0.887569 | − | 0.460674i | \(-0.152392\pi\) | ||||
0.887569 | + | 0.460674i | \(0.152392\pi\) | |||||||
\(74\) | −6.95298 | −0.808267 | ||||||||
\(75\) | 0.969203 | 0.111914 | ||||||||
\(76\) | −4.92047 | −0.564416 | ||||||||
\(77\) | −5.15845 | −0.587859 | ||||||||
\(78\) | −15.1592 | −1.71644 | ||||||||
\(79\) | 8.30703 | 0.934614 | 0.467307 | − | 0.884095i | \(-0.345224\pi\) | ||||
0.467307 | + | 0.884095i | \(0.345224\pi\) | |||||||
\(80\) | 2.15661 | 0.241117 | ||||||||
\(81\) | −0.937149 | −0.104128 | ||||||||
\(82\) | −0.843499 | −0.0931489 | ||||||||
\(83\) | −8.98766 | −0.986524 | −0.493262 | − | 0.869881i | \(-0.664196\pi\) | ||||
−0.493262 | + | 0.869881i | \(0.664196\pi\) | |||||||
\(84\) | −9.22267 | −1.00628 | ||||||||
\(85\) | −4.80995 | −0.521712 | ||||||||
\(86\) | −2.75008 | −0.296549 | ||||||||
\(87\) | 4.13988 | 0.443842 | ||||||||
\(88\) | 1.55320 | 0.165572 | ||||||||
\(89\) | −4.24398 | −0.449861 | −0.224931 | − | 0.974375i | \(-0.572216\pi\) | ||||
−0.224931 | + | 0.974375i | \(0.572216\pi\) | |||||||
\(90\) | −10.1606 | −1.07102 | ||||||||
\(91\) | −18.1301 | −1.90055 | ||||||||
\(92\) | 3.83366 | 0.399687 | ||||||||
\(93\) | −23.3969 | −2.42615 | ||||||||
\(94\) | 5.54606 | 0.572033 | ||||||||
\(95\) | −10.6115 | −1.08872 | ||||||||
\(96\) | 2.77693 | 0.283420 | ||||||||
\(97\) | −0.647693 | −0.0657633 | −0.0328816 | − | 0.999459i | \(-0.510468\pi\) | ||||
−0.0328816 | + | 0.999459i | \(0.510468\pi\) | |||||||
\(98\) | −4.03018 | −0.407110 | ||||||||
\(99\) | −7.31769 | −0.735456 | ||||||||
\(100\) | −0.349019 | −0.0349019 | ||||||||
\(101\) | 12.4416 | 1.23799 | 0.618993 | − | 0.785397i | \(-0.287541\pi\) | ||||
0.618993 | + | 0.785397i | \(0.287541\pi\) | |||||||
\(102\) | −6.19346 | −0.613244 | ||||||||
\(103\) | −11.7076 | −1.15358 | −0.576791 | − | 0.816892i | \(-0.695695\pi\) | ||||
−0.576791 | + | 0.816892i | \(0.695695\pi\) | |||||||
\(104\) | 5.45896 | 0.535295 | ||||||||
\(105\) | −19.8897 | −1.94104 | ||||||||
\(106\) | −3.17078 | −0.307973 | ||||||||
\(107\) | 1.29630 | 0.125319 | 0.0626593 | − | 0.998035i | \(-0.480042\pi\) | ||||
0.0626593 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(108\) | −4.75234 | −0.457294 | ||||||||
\(109\) | 5.85943 | 0.561232 | 0.280616 | − | 0.959820i | \(-0.409461\pi\) | ||||
0.280616 | + | 0.959820i | \(0.409461\pi\) | |||||||
\(110\) | 3.34965 | 0.319377 | ||||||||
\(111\) | −19.3080 | −1.83263 | ||||||||
\(112\) | 3.32117 | 0.313821 | ||||||||
\(113\) | 8.38327 | 0.788631 | 0.394316 | − | 0.918975i | \(-0.370982\pi\) | ||||
0.394316 | + | 0.918975i | \(0.370982\pi\) | |||||||
\(114\) | −13.6638 | −1.27973 | ||||||||
\(115\) | 8.26773 | 0.770970 | ||||||||
\(116\) | −1.49081 | −0.138418 | ||||||||
\(117\) | −25.7191 | −2.37773 | ||||||||
\(118\) | 10.8188 | 0.995947 | ||||||||
\(119\) | −7.40729 | −0.679025 | ||||||||
\(120\) | 5.98877 | 0.546698 | ||||||||
\(121\) | −8.58757 | −0.780688 | ||||||||
\(122\) | 6.24278 | 0.565195 | ||||||||
\(123\) | −2.34234 | −0.211202 | ||||||||
\(124\) | 8.42545 | 0.756628 | ||||||||
\(125\) | −11.5358 | −1.03179 | ||||||||
\(126\) | −15.6472 | −1.39397 | ||||||||
\(127\) | 3.86034 | 0.342549 | 0.171275 | − | 0.985223i | \(-0.445211\pi\) | ||||
0.171275 | + | 0.985223i | \(0.445211\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.63679 | −0.672382 | ||||||||
\(130\) | 11.7729 | 1.03255 | ||||||||
\(131\) | −14.4049 | −1.25857 | −0.629283 | − | 0.777176i | \(-0.716651\pi\) | ||||
−0.629283 | + | 0.777176i | \(0.716651\pi\) | |||||||
\(132\) | 4.31314 | 0.375410 | ||||||||
\(133\) | −16.3417 | −1.41701 | ||||||||
\(134\) | 3.87553 | 0.334795 | ||||||||
\(135\) | −10.2490 | −0.882090 | ||||||||
\(136\) | 2.23032 | 0.191249 | ||||||||
\(137\) | −7.40120 | −0.632327 | −0.316164 | − | 0.948705i | \(-0.602395\pi\) | ||||
−0.316164 | + | 0.948705i | \(0.602395\pi\) | |||||||
\(138\) | 10.6458 | 0.906233 | ||||||||
\(139\) | −13.7951 | −1.17008 | −0.585041 | − | 0.811004i | \(-0.698921\pi\) | ||||
−0.585041 | + | 0.811004i | \(0.698921\pi\) | |||||||
\(140\) | 7.16248 | 0.605340 | ||||||||
\(141\) | 15.4011 | 1.29700 | ||||||||
\(142\) | −10.2541 | −0.860503 | ||||||||
\(143\) | 8.47885 | 0.709037 | ||||||||
\(144\) | 4.71136 | 0.392614 | ||||||||
\(145\) | −3.21510 | −0.267000 | ||||||||
\(146\) | −15.1668 | −1.25521 | ||||||||
\(147\) | −11.1915 | −0.923063 | ||||||||
\(148\) | 6.95298 | 0.571531 | ||||||||
\(149\) | 9.88936 | 0.810168 | 0.405084 | − | 0.914279i | \(-0.367242\pi\) | ||||
0.405084 | + | 0.914279i | \(0.367242\pi\) | |||||||
\(150\) | −0.969203 | −0.0791351 | ||||||||
\(151\) | 2.68059 | 0.218143 | 0.109072 | − | 0.994034i | \(-0.465212\pi\) | ||||
0.109072 | + | 0.994034i | \(0.465212\pi\) | |||||||
\(152\) | 4.92047 | 0.399103 | ||||||||
\(153\) | −10.5079 | −0.849511 | ||||||||
\(154\) | 5.15845 | 0.415679 | ||||||||
\(155\) | 18.1704 | 1.45948 | ||||||||
\(156\) | 15.1592 | 1.21370 | ||||||||
\(157\) | −23.3802 | −1.86595 | −0.932973 | − | 0.359946i | \(-0.882795\pi\) | ||||
−0.932973 | + | 0.359946i | \(0.882795\pi\) | |||||||
\(158\) | −8.30703 | −0.660872 | ||||||||
\(159\) | −8.80505 | −0.698286 | ||||||||
\(160\) | −2.15661 | −0.170495 | ||||||||
\(161\) | 12.7323 | 1.00344 | ||||||||
\(162\) | 0.937149 | 0.0736293 | ||||||||
\(163\) | −10.1006 | −0.791137 | −0.395569 | − | 0.918436i | \(-0.629452\pi\) | ||||
−0.395569 | + | 0.918436i | \(0.629452\pi\) | |||||||
\(164\) | 0.843499 | 0.0658662 | ||||||||
\(165\) | 9.30176 | 0.724141 | ||||||||
\(166\) | 8.98766 | 0.697578 | ||||||||
\(167\) | −6.08456 | −0.470837 | −0.235419 | − | 0.971894i | \(-0.575646\pi\) | ||||
−0.235419 | + | 0.971894i | \(0.575646\pi\) | |||||||
\(168\) | 9.22267 | 0.711545 | ||||||||
\(169\) | 16.8002 | 1.29232 | ||||||||
\(170\) | 4.80995 | 0.368906 | ||||||||
\(171\) | −23.1821 | −1.77278 | ||||||||
\(172\) | 2.75008 | 0.209692 | ||||||||
\(173\) | 4.97513 | 0.378252 | 0.189126 | − | 0.981953i | \(-0.439435\pi\) | ||||
0.189126 | + | 0.981953i | \(0.439435\pi\) | |||||||
\(174\) | −4.13988 | −0.313844 | ||||||||
\(175\) | −1.15915 | −0.0876237 | ||||||||
\(176\) | −1.55320 | −0.117077 | ||||||||
\(177\) | 30.0430 | 2.25817 | ||||||||
\(178\) | 4.24398 | 0.318100 | ||||||||
\(179\) | −6.22605 | −0.465357 | −0.232679 | − | 0.972554i | \(-0.574749\pi\) | ||||
−0.232679 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(180\) | 10.1606 | 0.757325 | ||||||||
\(181\) | 13.5566 | 1.00766 | 0.503829 | − | 0.863804i | \(-0.331924\pi\) | ||||
0.503829 | + | 0.863804i | \(0.331924\pi\) | |||||||
\(182\) | 18.1301 | 1.34389 | ||||||||
\(183\) | 17.3358 | 1.28150 | ||||||||
\(184\) | −3.83366 | −0.282621 | ||||||||
\(185\) | 14.9949 | 1.10245 | ||||||||
\(186\) | 23.3969 | 1.71555 | ||||||||
\(187\) | 3.46414 | 0.253323 | ||||||||
\(188\) | −5.54606 | −0.404488 | ||||||||
\(189\) | −15.7833 | −1.14807 | ||||||||
\(190\) | 10.6115 | 0.769843 | ||||||||
\(191\) | −6.67728 | −0.483151 | −0.241575 | − | 0.970382i | \(-0.577664\pi\) | ||||
−0.241575 | + | 0.970382i | \(0.577664\pi\) | |||||||
\(192\) | −2.77693 | −0.200408 | ||||||||
\(193\) | 14.0795 | 1.01346 | 0.506731 | − | 0.862104i | \(-0.330854\pi\) | ||||
0.506731 | + | 0.862104i | \(0.330854\pi\) | |||||||
\(194\) | 0.647693 | 0.0465017 | ||||||||
\(195\) | 32.6924 | 2.34115 | ||||||||
\(196\) | 4.03018 | 0.287870 | ||||||||
\(197\) | 2.22662 | 0.158640 | 0.0793201 | − | 0.996849i | \(-0.474725\pi\) | ||||
0.0793201 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(198\) | 7.31769 | 0.520046 | ||||||||
\(199\) | 3.97736 | 0.281947 | 0.140974 | − | 0.990013i | \(-0.454977\pi\) | ||||
0.140974 | + | 0.990013i | \(0.454977\pi\) | |||||||
\(200\) | 0.349019 | 0.0246794 | ||||||||
\(201\) | 10.7621 | 0.759100 | ||||||||
\(202\) | −12.4416 | −0.875388 | ||||||||
\(203\) | −4.95124 | −0.347509 | ||||||||
\(204\) | 6.19346 | 0.433629 | ||||||||
\(205\) | 1.81910 | 0.127052 | ||||||||
\(206\) | 11.7076 | 0.815706 | ||||||||
\(207\) | 18.0618 | 1.25538 | ||||||||
\(208\) | −5.45896 | −0.378510 | ||||||||
\(209\) | 7.64247 | 0.528641 | ||||||||
\(210\) | 19.8897 | 1.37252 | ||||||||
\(211\) | −20.7908 | −1.43130 | −0.715649 | − | 0.698460i | \(-0.753869\pi\) | ||||
−0.715649 | + | 0.698460i | \(0.753869\pi\) | |||||||
\(212\) | 3.17078 | 0.217770 | ||||||||
\(213\) | −28.4749 | −1.95107 | ||||||||
\(214\) | −1.29630 | −0.0886136 | ||||||||
\(215\) | 5.93086 | 0.404481 | ||||||||
\(216\) | 4.75234 | 0.323356 | ||||||||
\(217\) | 27.9824 | 1.89957 | ||||||||
\(218\) | −5.85943 | −0.396851 | ||||||||
\(219\) | −42.1172 | −2.84601 | ||||||||
\(220\) | −3.34965 | −0.225834 | ||||||||
\(221\) | 12.1752 | 0.818995 | ||||||||
\(222\) | 19.3080 | 1.29587 | ||||||||
\(223\) | −0.185548 | −0.0124252 | −0.00621262 | − | 0.999981i | \(-0.501978\pi\) | ||||
−0.00621262 | + | 0.999981i | \(0.501978\pi\) | |||||||
\(224\) | −3.32117 | −0.221905 | ||||||||
\(225\) | −1.64436 | −0.109624 | ||||||||
\(226\) | −8.38327 | −0.557647 | ||||||||
\(227\) | 19.7975 | 1.31401 | 0.657004 | − | 0.753887i | \(-0.271823\pi\) | ||||
0.657004 | + | 0.753887i | \(0.271823\pi\) | |||||||
\(228\) | 13.6638 | 0.904908 | ||||||||
\(229\) | −0.287303 | −0.0189855 | −0.00949276 | − | 0.999955i | \(-0.503022\pi\) | ||||
−0.00949276 | + | 0.999955i | \(0.503022\pi\) | |||||||
\(230\) | −8.26773 | −0.545158 | ||||||||
\(231\) | 14.3247 | 0.942494 | ||||||||
\(232\) | 1.49081 | 0.0978765 | ||||||||
\(233\) | 17.5813 | 1.15179 | 0.575894 | − | 0.817524i | \(-0.304654\pi\) | ||||
0.575894 | + | 0.817524i | \(0.304654\pi\) | |||||||
\(234\) | 25.7191 | 1.68131 | ||||||||
\(235\) | −11.9607 | −0.780231 | ||||||||
\(236\) | −10.8188 | −0.704241 | ||||||||
\(237\) | −23.0681 | −1.49843 | ||||||||
\(238\) | 7.40729 | 0.480143 | ||||||||
\(239\) | −13.2093 | −0.854437 | −0.427218 | − | 0.904148i | \(-0.640506\pi\) | ||||
−0.427218 | + | 0.904148i | \(0.640506\pi\) | |||||||
\(240\) | −5.98877 | −0.386574 | ||||||||
\(241\) | 4.13484 | 0.266349 | 0.133174 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133174 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(242\) | 8.58757 | 0.552030 | ||||||||
\(243\) | 16.8594 | 1.08153 | ||||||||
\(244\) | −6.24278 | −0.399653 | ||||||||
\(245\) | 8.69154 | 0.555282 | ||||||||
\(246\) | 2.34234 | 0.149342 | ||||||||
\(247\) | 26.8606 | 1.70910 | ||||||||
\(248\) | −8.42545 | −0.535017 | ||||||||
\(249\) | 24.9581 | 1.58166 | ||||||||
\(250\) | 11.5358 | 0.729586 | ||||||||
\(251\) | −7.23351 | −0.456575 | −0.228288 | − | 0.973594i | \(-0.573313\pi\) | ||||
−0.228288 | + | 0.973594i | \(0.573313\pi\) | |||||||
\(252\) | 15.6472 | 0.985684 | ||||||||
\(253\) | −5.95445 | −0.374353 | ||||||||
\(254\) | −3.86034 | −0.242219 | ||||||||
\(255\) | 13.3569 | 0.836442 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8490 | 0.676742 | 0.338371 | − | 0.941013i | \(-0.390124\pi\) | ||||
0.338371 | + | 0.941013i | \(0.390124\pi\) | |||||||
\(258\) | 7.63679 | 0.475446 | ||||||||
\(259\) | 23.0920 | 1.43487 | ||||||||
\(260\) | −11.7729 | −0.730121 | ||||||||
\(261\) | −7.02375 | −0.434759 | ||||||||
\(262\) | 14.4049 | 0.889941 | ||||||||
\(263\) | 7.57649 | 0.467186 | 0.233593 | − | 0.972334i | \(-0.424952\pi\) | ||||
0.233593 | + | 0.972334i | \(0.424952\pi\) | |||||||
\(264\) | −4.31314 | −0.265455 | ||||||||
\(265\) | 6.83815 | 0.420064 | ||||||||
\(266\) | 16.3417 | 1.00198 | ||||||||
\(267\) | 11.7853 | 0.721246 | ||||||||
\(268\) | −3.87553 | −0.236736 | ||||||||
\(269\) | −1.09782 | −0.0669353 | −0.0334677 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334677 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(270\) | 10.2490 | 0.623732 | ||||||||
\(271\) | −18.5265 | −1.12540 | −0.562702 | − | 0.826660i | \(-0.690238\pi\) | ||||
−0.562702 | + | 0.826660i | \(0.690238\pi\) | |||||||
\(272\) | −2.23032 | −0.135233 | ||||||||
\(273\) | 50.3462 | 3.04709 | ||||||||
\(274\) | 7.40120 | 0.447123 | ||||||||
\(275\) | 0.542097 | 0.0326897 | ||||||||
\(276\) | −10.6458 | −0.640804 | ||||||||
\(277\) | −16.7272 | −1.00504 | −0.502521 | − | 0.864565i | \(-0.667594\pi\) | ||||
−0.502521 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(278\) | 13.7951 | 0.827372 | ||||||||
\(279\) | 39.6953 | 2.37650 | ||||||||
\(280\) | −7.16248 | −0.428040 | ||||||||
\(281\) | −20.9778 | −1.25143 | −0.625715 | − | 0.780052i | \(-0.715193\pi\) | ||||
−0.625715 | + | 0.780052i | \(0.715193\pi\) | |||||||
\(282\) | −15.4011 | −0.917119 | ||||||||
\(283\) | 19.6423 | 1.16761 | 0.583807 | − | 0.811892i | \(-0.301562\pi\) | ||||
0.583807 | + | 0.811892i | \(0.301562\pi\) | |||||||
\(284\) | 10.2541 | 0.608467 | ||||||||
\(285\) | 29.4676 | 1.74551 | ||||||||
\(286\) | −8.47885 | −0.501365 | ||||||||
\(287\) | 2.80141 | 0.165362 | ||||||||
\(288\) | −4.71136 | −0.277620 | ||||||||
\(289\) | −12.0257 | −0.707391 | ||||||||
\(290\) | 3.21510 | 0.188797 | ||||||||
\(291\) | 1.79860 | 0.105436 | ||||||||
\(292\) | 15.1668 | 0.887569 | ||||||||
\(293\) | −27.3271 | −1.59646 | −0.798232 | − | 0.602350i | \(-0.794231\pi\) | ||||
−0.798232 | + | 0.602350i | \(0.794231\pi\) | |||||||
\(294\) | 11.1915 | 0.652704 | ||||||||
\(295\) | −23.3319 | −1.35843 | ||||||||
\(296\) | −6.95298 | −0.404134 | ||||||||
\(297\) | 7.38134 | 0.428309 | ||||||||
\(298\) | −9.88936 | −0.572876 | ||||||||
\(299\) | −20.9278 | −1.21029 | ||||||||
\(300\) | 0.969203 | 0.0559570 | ||||||||
\(301\) | 9.13348 | 0.526445 | ||||||||
\(302\) | −2.68059 | −0.154250 | ||||||||
\(303\) | −34.5495 | −1.98482 | ||||||||
\(304\) | −4.92047 | −0.282208 | ||||||||
\(305\) | −13.4633 | −0.770904 | ||||||||
\(306\) | 10.5079 | 0.600695 | ||||||||
\(307\) | −23.8300 | −1.36005 | −0.680024 | − | 0.733190i | \(-0.738031\pi\) | ||||
−0.680024 | + | 0.733190i | \(0.738031\pi\) | |||||||
\(308\) | −5.15845 | −0.293930 | ||||||||
\(309\) | 32.5112 | 1.84950 | ||||||||
\(310\) | −18.1704 | −1.03201 | ||||||||
\(311\) | −20.8363 | −1.18152 | −0.590760 | − | 0.806848i | \(-0.701172\pi\) | ||||
−0.590760 | + | 0.806848i | \(0.701172\pi\) | |||||||
\(312\) | −15.1592 | −0.858218 | ||||||||
\(313\) | −27.1987 | −1.53736 | −0.768681 | − | 0.639632i | \(-0.779087\pi\) | ||||
−0.768681 | + | 0.639632i | \(0.779087\pi\) | |||||||
\(314\) | 23.3802 | 1.31942 | ||||||||
\(315\) | 33.7451 | 1.90132 | ||||||||
\(316\) | 8.30703 | 0.467307 | ||||||||
\(317\) | 25.7323 | 1.44527 | 0.722636 | − | 0.691229i | \(-0.242930\pi\) | ||||
0.722636 | + | 0.691229i | \(0.242930\pi\) | |||||||
\(318\) | 8.80505 | 0.493763 | ||||||||
\(319\) | 2.31553 | 0.129645 | ||||||||
\(320\) | 2.15661 | 0.120558 | ||||||||
\(321\) | −3.59975 | −0.200919 | ||||||||
\(322\) | −12.7323 | −0.709541 | ||||||||
\(323\) | 10.9742 | 0.610623 | ||||||||
\(324\) | −0.937149 | −0.0520638 | ||||||||
\(325\) | 1.90528 | 0.105686 | ||||||||
\(326\) | 10.1006 | 0.559419 | ||||||||
\(327\) | −16.2713 | −0.899803 | ||||||||
\(328\) | −0.843499 | −0.0465745 | ||||||||
\(329\) | −18.4194 | −1.01550 | ||||||||
\(330\) | −9.30176 | −0.512045 | ||||||||
\(331\) | −0.417145 | −0.0229283 | −0.0114642 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114642 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(332\) | −8.98766 | −0.493262 | ||||||||
\(333\) | 32.7580 | 1.79513 | ||||||||
\(334\) | 6.08456 | 0.332932 | ||||||||
\(335\) | −8.35803 | −0.456648 | ||||||||
\(336\) | −9.22267 | −0.503138 | ||||||||
\(337\) | −7.25189 | −0.395036 | −0.197518 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197518 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(338\) | −16.8002 | −0.913810 | ||||||||
\(339\) | −23.2798 | −1.26438 | ||||||||
\(340\) | −4.80995 | −0.260856 | ||||||||
\(341\) | −13.0864 | −0.708669 | ||||||||
\(342\) | 23.1821 | 1.25354 | ||||||||
\(343\) | −9.86328 | −0.532567 | ||||||||
\(344\) | −2.75008 | −0.148274 | ||||||||
\(345\) | −22.9589 | −1.23607 | ||||||||
\(346\) | −4.97513 | −0.267465 | ||||||||
\(347\) | −13.4874 | −0.724044 | −0.362022 | − | 0.932170i | \(-0.617913\pi\) | ||||
−0.362022 | + | 0.932170i | \(0.617913\pi\) | |||||||
\(348\) | 4.13988 | 0.221921 | ||||||||
\(349\) | −2.96719 | −0.158830 | −0.0794151 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794151 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(350\) | 1.15915 | 0.0619593 | ||||||||
\(351\) | 25.9428 | 1.38473 | ||||||||
\(352\) | 1.55320 | 0.0827859 | ||||||||
\(353\) | 13.0493 | 0.694546 | 0.347273 | − | 0.937764i | \(-0.387108\pi\) | ||||
0.347273 | + | 0.937764i | \(0.387108\pi\) | |||||||
\(354\) | −30.0430 | −1.59677 | ||||||||
\(355\) | 22.1141 | 1.17369 | ||||||||
\(356\) | −4.24398 | −0.224931 | ||||||||
\(357\) | 20.5696 | 1.08866 | ||||||||
\(358\) | 6.22605 | 0.329057 | ||||||||
\(359\) | −12.0619 | −0.636603 | −0.318301 | − | 0.947990i | \(-0.603112\pi\) | ||||
−0.318301 | + | 0.947990i | \(0.603112\pi\) | |||||||
\(360\) | −10.1606 | −0.535510 | ||||||||
\(361\) | 5.21101 | 0.274263 | ||||||||
\(362\) | −13.5566 | −0.712521 | ||||||||
\(363\) | 23.8471 | 1.25165 | ||||||||
\(364\) | −18.1301 | −0.950277 | ||||||||
\(365\) | 32.7089 | 1.71206 | ||||||||
\(366\) | −17.3358 | −0.906156 | ||||||||
\(367\) | −37.3889 | −1.95168 | −0.975842 | − | 0.218480i | \(-0.929890\pi\) | ||||
−0.975842 | + | 0.218480i | \(0.929890\pi\) | |||||||
\(368\) | 3.83366 | 0.199844 | ||||||||
\(369\) | 3.97403 | 0.206880 | ||||||||
\(370\) | −14.9949 | −0.779547 | ||||||||
\(371\) | 10.5307 | 0.546727 | ||||||||
\(372\) | −23.3969 | −1.21307 | ||||||||
\(373\) | 35.4078 | 1.83335 | 0.916674 | − | 0.399636i | \(-0.130864\pi\) | ||||
0.916674 | + | 0.399636i | \(0.130864\pi\) | |||||||
\(374\) | −3.46414 | −0.179126 | ||||||||
\(375\) | 32.0341 | 1.65423 | ||||||||
\(376\) | 5.54606 | 0.286016 | ||||||||
\(377\) | 8.13827 | 0.419142 | ||||||||
\(378\) | 15.7833 | 0.811808 | ||||||||
\(379\) | 36.1932 | 1.85912 | 0.929560 | − | 0.368672i | \(-0.120187\pi\) | ||||
0.929560 | + | 0.368672i | \(0.120187\pi\) | |||||||
\(380\) | −10.6115 | −0.544361 | ||||||||
\(381\) | −10.7199 | −0.549197 | ||||||||
\(382\) | 6.67728 | 0.341639 | ||||||||
\(383\) | −11.7935 | −0.602621 | −0.301311 | − | 0.953526i | \(-0.597424\pi\) | ||||
−0.301311 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(384\) | 2.77693 | 0.141710 | ||||||||
\(385\) | −11.1248 | −0.566971 | ||||||||
\(386\) | −14.0795 | −0.716626 | ||||||||
\(387\) | 12.9566 | 0.658622 | ||||||||
\(388\) | −0.647693 | −0.0328816 | ||||||||
\(389\) | −22.5729 | −1.14449 | −0.572245 | − | 0.820083i | \(-0.693927\pi\) | ||||
−0.572245 | + | 0.820083i | \(0.693927\pi\) | |||||||
\(390\) | −32.6924 | −1.65545 | ||||||||
\(391\) | −8.55031 | −0.432408 | ||||||||
\(392\) | −4.03018 | −0.203555 | ||||||||
\(393\) | 40.0016 | 2.01781 | ||||||||
\(394\) | −2.22662 | −0.112176 | ||||||||
\(395\) | 17.9151 | 0.901404 | ||||||||
\(396\) | −7.31769 | −0.367728 | ||||||||
\(397\) | 1.11349 | 0.0558844 | 0.0279422 | − | 0.999610i | \(-0.491105\pi\) | ||||
0.0279422 | + | 0.999610i | \(0.491105\pi\) | |||||||
\(398\) | −3.97736 | −0.199367 | ||||||||
\(399\) | 45.3799 | 2.27184 | ||||||||
\(400\) | −0.349019 | −0.0174510 | ||||||||
\(401\) | −28.4318 | −1.41982 | −0.709908 | − | 0.704294i | \(-0.751264\pi\) | ||||
−0.709908 | + | 0.704294i | \(0.751264\pi\) | |||||||
\(402\) | −10.7621 | −0.536765 | ||||||||
\(403\) | −45.9941 | −2.29113 | ||||||||
\(404\) | 12.4416 | 0.618993 | ||||||||
\(405\) | −2.02107 | −0.100428 | ||||||||
\(406\) | 4.95124 | 0.245726 | ||||||||
\(407\) | −10.7994 | −0.535305 | ||||||||
\(408\) | −6.19346 | −0.306622 | ||||||||
\(409\) | −3.33936 | −0.165121 | −0.0825603 | − | 0.996586i | \(-0.526310\pi\) | ||||
−0.0825603 | + | 0.996586i | \(0.526310\pi\) | |||||||
\(410\) | −1.81910 | −0.0898390 | ||||||||
\(411\) | 20.5526 | 1.01379 | ||||||||
\(412\) | −11.7076 | −0.576791 | ||||||||
\(413\) | −35.9309 | −1.76805 | ||||||||
\(414\) | −18.0618 | −0.887688 | ||||||||
\(415\) | −19.3829 | −0.951469 | ||||||||
\(416\) | 5.45896 | 0.267647 | ||||||||
\(417\) | 38.3080 | 1.87595 | ||||||||
\(418\) | −7.64247 | −0.373806 | ||||||||
\(419\) | −30.4571 | −1.48793 | −0.743963 | − | 0.668221i | \(-0.767056\pi\) | ||||
−0.743963 | + | 0.668221i | \(0.767056\pi\) | |||||||
\(420\) | −19.8897 | −0.970520 | ||||||||
\(421\) | 29.2355 | 1.42485 | 0.712425 | − | 0.701748i | \(-0.247597\pi\) | ||||
0.712425 | + | 0.701748i | \(0.247597\pi\) | |||||||
\(422\) | 20.7908 | 1.01208 | ||||||||
\(423\) | −26.1295 | −1.27046 | ||||||||
\(424\) | −3.17078 | −0.153987 | ||||||||
\(425\) | 0.778426 | 0.0377592 | ||||||||
\(426\) | 28.4749 | 1.37961 | ||||||||
\(427\) | −20.7333 | −1.00336 | ||||||||
\(428\) | 1.29630 | 0.0626593 | ||||||||
\(429\) | −23.5452 | −1.13677 | ||||||||
\(430\) | −5.93086 | −0.286011 | ||||||||
\(431\) | −21.5252 | −1.03683 | −0.518415 | − | 0.855129i | \(-0.673478\pi\) | ||||
−0.518415 | + | 0.855129i | \(0.673478\pi\) | |||||||
\(432\) | −4.75234 | −0.228647 | ||||||||
\(433\) | 25.2201 | 1.21200 | 0.606002 | − | 0.795463i | \(-0.292773\pi\) | ||||
0.606002 | + | 0.795463i | \(0.292773\pi\) | |||||||
\(434\) | −27.9824 | −1.34320 | ||||||||
\(435\) | 8.92813 | 0.428071 | ||||||||
\(436\) | 5.85943 | 0.280616 | ||||||||
\(437\) | −18.8634 | −0.902360 | ||||||||
\(438\) | 42.1172 | 2.01244 | ||||||||
\(439\) | 27.0325 | 1.29019 | 0.645095 | − | 0.764102i | \(-0.276818\pi\) | ||||
0.645095 | + | 0.764102i | \(0.276818\pi\) | |||||||
\(440\) | 3.34965 | 0.159688 | ||||||||
\(441\) | 18.9876 | 0.904174 | ||||||||
\(442\) | −12.1752 | −0.579117 | ||||||||
\(443\) | 7.51560 | 0.357077 | 0.178538 | − | 0.983933i | \(-0.442863\pi\) | ||||
0.178538 | + | 0.983933i | \(0.442863\pi\) | |||||||
\(444\) | −19.3080 | −0.916315 | ||||||||
\(445\) | −9.15263 | −0.433876 | ||||||||
\(446\) | 0.185548 | 0.00878597 | ||||||||
\(447\) | −27.4621 | −1.29891 | ||||||||
\(448\) | 3.32117 | 0.156911 | ||||||||
\(449\) | −7.51061 | −0.354448 | −0.177224 | − | 0.984171i | \(-0.556712\pi\) | ||||
−0.177224 | + | 0.984171i | \(0.556712\pi\) | |||||||
\(450\) | 1.64436 | 0.0775157 | ||||||||
\(451\) | −1.31012 | −0.0616913 | ||||||||
\(452\) | 8.38327 | 0.394316 | ||||||||
\(453\) | −7.44381 | −0.349741 | ||||||||
\(454\) | −19.7975 | −0.929145 | ||||||||
\(455\) | −39.0997 | −1.83302 | ||||||||
\(456\) | −13.6638 | −0.639867 | ||||||||
\(457\) | 3.83154 | 0.179232 | 0.0896159 | − | 0.995976i | \(-0.471436\pi\) | ||||
0.0896159 | + | 0.995976i | \(0.471436\pi\) | |||||||
\(458\) | 0.287303 | 0.0134248 | ||||||||
\(459\) | 10.5993 | 0.494731 | ||||||||
\(460\) | 8.26773 | 0.385485 | ||||||||
\(461\) | 12.2934 | 0.572560 | 0.286280 | − | 0.958146i | \(-0.407581\pi\) | ||||
0.286280 | + | 0.958146i | \(0.407581\pi\) | |||||||
\(462\) | −14.3247 | −0.666444 | ||||||||
\(463\) | 17.1507 | 0.797062 | 0.398531 | − | 0.917155i | \(-0.369520\pi\) | ||||
0.398531 | + | 0.917155i | \(0.369520\pi\) | |||||||
\(464\) | −1.49081 | −0.0692092 | ||||||||
\(465\) | −50.4581 | −2.33994 | ||||||||
\(466\) | −17.5813 | −0.814438 | ||||||||
\(467\) | −36.4013 | −1.68445 | −0.842226 | − | 0.539124i | \(-0.818755\pi\) | ||||
−0.842226 | + | 0.539124i | \(0.818755\pi\) | |||||||
\(468\) | −25.7191 | −1.18887 | ||||||||
\(469\) | −12.8713 | −0.594342 | ||||||||
\(470\) | 11.9607 | 0.551707 | ||||||||
\(471\) | 64.9254 | 2.99160 | ||||||||
\(472\) | 10.8188 | 0.497974 | ||||||||
\(473\) | −4.27142 | −0.196400 | ||||||||
\(474\) | 23.0681 | 1.05955 | ||||||||
\(475\) | 1.71734 | 0.0787969 | ||||||||
\(476\) | −7.40729 | −0.339513 | ||||||||
\(477\) | 14.9387 | 0.683996 | ||||||||
\(478\) | 13.2093 | 0.604178 | ||||||||
\(479\) | −11.2479 | −0.513932 | −0.256966 | − | 0.966420i | \(-0.582723\pi\) | ||||
−0.256966 | + | 0.966420i | \(0.582723\pi\) | |||||||
\(480\) | 5.98877 | 0.273349 | ||||||||
\(481\) | −37.9560 | −1.73064 | ||||||||
\(482\) | −4.13484 | −0.188337 | ||||||||
\(483\) | −35.3566 | −1.60878 | ||||||||
\(484\) | −8.58757 | −0.390344 | ||||||||
\(485\) | −1.39682 | −0.0634265 | ||||||||
\(486\) | −16.8594 | −0.764759 | ||||||||
\(487\) | −3.94271 | −0.178661 | −0.0893306 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893306 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(488\) | 6.24278 | 0.282597 | ||||||||
\(489\) | 28.0486 | 1.26840 | ||||||||
\(490\) | −8.69154 | −0.392644 | ||||||||
\(491\) | 16.8873 | 0.762114 | 0.381057 | − | 0.924551i | \(-0.375560\pi\) | ||||
0.381057 | + | 0.924551i | \(0.375560\pi\) | |||||||
\(492\) | −2.34234 | −0.105601 | ||||||||
\(493\) | 3.32499 | 0.149750 | ||||||||
\(494\) | −26.8606 | −1.20852 | ||||||||
\(495\) | −15.7814 | −0.709323 | ||||||||
\(496\) | 8.42545 | 0.378314 | ||||||||
\(497\) | 34.0555 | 1.52760 | ||||||||
\(498\) | −24.9581 | −1.11840 | ||||||||
\(499\) | −34.6841 | −1.55267 | −0.776336 | − | 0.630319i | \(-0.782924\pi\) | ||||
−0.776336 | + | 0.630319i | \(0.782924\pi\) | |||||||
\(500\) | −11.5358 | −0.515895 | ||||||||
\(501\) | 16.8964 | 0.754876 | ||||||||
\(502\) | 7.23351 | 0.322847 | ||||||||
\(503\) | 39.3625 | 1.75509 | 0.877543 | − | 0.479499i | \(-0.159181\pi\) | ||||
0.877543 | + | 0.479499i | \(0.159181\pi\) | |||||||
\(504\) | −15.6472 | −0.696984 | ||||||||
\(505\) | 26.8317 | 1.19400 | ||||||||
\(506\) | 5.95445 | 0.264708 | ||||||||
\(507\) | −46.6530 | −2.07193 | ||||||||
\(508\) | 3.86034 | 0.171275 | ||||||||
\(509\) | −7.60205 | −0.336955 | −0.168477 | − | 0.985706i | \(-0.553885\pi\) | ||||
−0.168477 | + | 0.985706i | \(0.553885\pi\) | |||||||
\(510\) | −13.3569 | −0.591454 | ||||||||
\(511\) | 50.3715 | 2.22830 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 23.3837 | 1.03242 | ||||||||
\(514\) | −10.8490 | −0.478529 | ||||||||
\(515\) | −25.2487 | −1.11259 | ||||||||
\(516\) | −7.63679 | −0.336191 | ||||||||
\(517\) | 8.61415 | 0.378850 | ||||||||
\(518\) | −23.0920 | −1.01461 | ||||||||
\(519\) | −13.8156 | −0.606438 | ||||||||
\(520\) | 11.7729 | 0.516274 | ||||||||
\(521\) | −27.6783 | −1.21261 | −0.606305 | − | 0.795232i | \(-0.707349\pi\) | ||||
−0.606305 | + | 0.795232i | \(0.707349\pi\) | |||||||
\(522\) | 7.02375 | 0.307421 | ||||||||
\(523\) | 3.76553 | 0.164655 | 0.0823275 | − | 0.996605i | \(-0.473765\pi\) | ||||
0.0823275 | + | 0.996605i | \(0.473765\pi\) | |||||||
\(524\) | −14.4049 | −0.629283 | ||||||||
\(525\) | 3.21889 | 0.140484 | ||||||||
\(526\) | −7.57649 | −0.330351 | ||||||||
\(527\) | −18.7915 | −0.818570 | ||||||||
\(528\) | 4.31314 | 0.187705 | ||||||||
\(529\) | −8.30302 | −0.361001 | ||||||||
\(530\) | −6.83815 | −0.297030 | ||||||||
\(531\) | −50.9711 | −2.21196 | ||||||||
\(532\) | −16.3417 | −0.708503 | ||||||||
\(533\) | −4.60462 | −0.199448 | ||||||||
\(534\) | −11.7853 | −0.509998 | ||||||||
\(535\) | 2.79563 | 0.120866 | ||||||||
\(536\) | 3.87553 | 0.167398 | ||||||||
\(537\) | 17.2893 | 0.746090 | ||||||||
\(538\) | 1.09782 | 0.0473304 | ||||||||
\(539\) | −6.25968 | −0.269623 | ||||||||
\(540\) | −10.2490 | −0.441045 | ||||||||
\(541\) | 21.6076 | 0.928983 | 0.464491 | − | 0.885578i | \(-0.346237\pi\) | ||||
0.464491 | + | 0.885578i | \(0.346237\pi\) | |||||||
\(542\) | 18.5265 | 0.795781 | ||||||||
\(543\) | −37.6459 | −1.61554 | ||||||||
\(544\) | 2.23032 | 0.0956243 | ||||||||
\(545\) | 12.6365 | 0.541290 | ||||||||
\(546\) | −50.3462 | −2.15462 | ||||||||
\(547\) | −13.5169 | −0.577943 | −0.288971 | − | 0.957338i | \(-0.593313\pi\) | ||||
−0.288971 | + | 0.957338i | \(0.593313\pi\) | |||||||
\(548\) | −7.40120 | −0.316164 | ||||||||
\(549\) | −29.4120 | −1.25527 | ||||||||
\(550\) | −0.542097 | −0.0231151 | ||||||||
\(551\) | 7.33549 | 0.312502 | ||||||||
\(552\) | 10.6458 | 0.453117 | ||||||||
\(553\) | 27.5891 | 1.17321 | ||||||||
\(554\) | 16.7272 | 0.710672 | ||||||||
\(555\) | −41.6398 | −1.76751 | ||||||||
\(556\) | −13.7951 | −0.585041 | ||||||||
\(557\) | 27.1872 | 1.15196 | 0.575980 | − | 0.817464i | \(-0.304620\pi\) | ||||
0.575980 | + | 0.817464i | \(0.304620\pi\) | |||||||
\(558\) | −39.6953 | −1.68044 | ||||||||
\(559\) | −15.0126 | −0.634963 | ||||||||
\(560\) | 7.16248 | 0.302670 | ||||||||
\(561\) | −9.61969 | −0.406144 | ||||||||
\(562\) | 20.9778 | 0.884894 | ||||||||
\(563\) | −14.2164 | −0.599149 | −0.299574 | − | 0.954073i | \(-0.596845\pi\) | ||||
−0.299574 | + | 0.954073i | \(0.596845\pi\) | |||||||
\(564\) | 15.4011 | 0.648501 | ||||||||
\(565\) | 18.0795 | 0.760609 | ||||||||
\(566\) | −19.6423 | −0.825628 | ||||||||
\(567\) | −3.11243 | −0.130710 | ||||||||
\(568\) | −10.2541 | −0.430251 | ||||||||
\(569\) | −32.3805 | −1.35746 | −0.678731 | − | 0.734387i | \(-0.737470\pi\) | ||||
−0.678731 | + | 0.734387i | \(0.737470\pi\) | |||||||
\(570\) | −29.4676 | −1.23426 | ||||||||
\(571\) | 13.9112 | 0.582167 | 0.291083 | − | 0.956698i | \(-0.405984\pi\) | ||||
0.291083 | + | 0.956698i | \(0.405984\pi\) | |||||||
\(572\) | 8.47885 | 0.354519 | ||||||||
\(573\) | 18.5424 | 0.774618 | ||||||||
\(574\) | −2.80141 | −0.116928 | ||||||||
\(575\) | −1.33802 | −0.0557994 | ||||||||
\(576\) | 4.71136 | 0.196307 | ||||||||
\(577\) | 21.9646 | 0.914397 | 0.457198 | − | 0.889365i | \(-0.348853\pi\) | ||||
0.457198 | + | 0.889365i | \(0.348853\pi\) | |||||||
\(578\) | 12.0257 | 0.500201 | ||||||||
\(579\) | −39.0977 | −1.62485 | ||||||||
\(580\) | −3.21510 | −0.133500 | ||||||||
\(581\) | −29.8496 | −1.23837 | ||||||||
\(582\) | −1.79860 | −0.0745544 | ||||||||
\(583\) | −4.92486 | −0.203967 | ||||||||
\(584\) | −15.1668 | −0.627606 | ||||||||
\(585\) | −55.4662 | −2.29324 | ||||||||
\(586\) | 27.3271 | 1.12887 | ||||||||
\(587\) | −18.4813 | −0.762806 | −0.381403 | − | 0.924409i | \(-0.624559\pi\) | ||||
−0.381403 | + | 0.924409i | \(0.624559\pi\) | |||||||
\(588\) | −11.1915 | −0.461532 | ||||||||
\(589\) | −41.4572 | −1.70821 | ||||||||
\(590\) | 23.3319 | 0.960558 | ||||||||
\(591\) | −6.18318 | −0.254342 | ||||||||
\(592\) | 6.95298 | 0.285766 | ||||||||
\(593\) | −7.19591 | −0.295501 | −0.147750 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147750 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(594\) | −7.38134 | −0.302860 | ||||||||
\(595\) | −15.9747 | −0.654897 | ||||||||
\(596\) | 9.88936 | 0.405084 | ||||||||
\(597\) | −11.0449 | −0.452036 | ||||||||
\(598\) | 20.9278 | 0.855801 | ||||||||
\(599\) | −26.6900 | −1.09052 | −0.545261 | − | 0.838266i | \(-0.683570\pi\) | ||||
−0.545261 | + | 0.838266i | \(0.683570\pi\) | |||||||
\(600\) | −0.969203 | −0.0395676 | ||||||||
\(601\) | 24.8539 | 1.01381 | 0.506905 | − | 0.862002i | \(-0.330789\pi\) | ||||
0.506905 | + | 0.862002i | \(0.330789\pi\) | |||||||
\(602\) | −9.13348 | −0.372253 | ||||||||
\(603\) | −18.2591 | −0.743566 | ||||||||
\(604\) | 2.68059 | 0.109072 | ||||||||
\(605\) | −18.5201 | −0.752948 | ||||||||
\(606\) | 34.5495 | 1.40348 | ||||||||
\(607\) | −33.6778 | −1.36694 | −0.683471 | − | 0.729978i | \(-0.739530\pi\) | ||||
−0.683471 | + | 0.729978i | \(0.739530\pi\) | |||||||
\(608\) | 4.92047 | 0.199551 | ||||||||
\(609\) | 13.7493 | 0.557148 | ||||||||
\(610\) | 13.4633 | 0.545111 | ||||||||
\(611\) | 30.2757 | 1.22482 | ||||||||
\(612\) | −10.5079 | −0.424755 | ||||||||
\(613\) | −37.5018 | −1.51468 | −0.757341 | − | 0.653020i | \(-0.773502\pi\) | ||||
−0.757341 | + | 0.653020i | \(0.773502\pi\) | |||||||
\(614\) | 23.8300 | 0.961699 | ||||||||
\(615\) | −5.05153 | −0.203697 | ||||||||
\(616\) | 5.15845 | 0.207840 | ||||||||
\(617\) | 22.2961 | 0.897608 | 0.448804 | − | 0.893630i | \(-0.351850\pi\) | ||||
0.448804 | + | 0.893630i | \(0.351850\pi\) | |||||||
\(618\) | −32.5112 | −1.30779 | ||||||||
\(619\) | −32.7285 | −1.31547 | −0.657734 | − | 0.753250i | \(-0.728485\pi\) | ||||
−0.657734 | + | 0.753250i | \(0.728485\pi\) | |||||||
\(620\) | 18.1704 | 0.729742 | ||||||||
\(621\) | −18.2189 | −0.731098 | ||||||||
\(622\) | 20.8363 | 0.835460 | ||||||||
\(623\) | −14.0950 | −0.564704 | ||||||||
\(624\) | 15.1592 | 0.606852 | ||||||||
\(625\) | −23.1331 | −0.925324 | ||||||||
\(626\) | 27.1987 | 1.08708 | ||||||||
\(627\) | −21.2226 | −0.847551 | ||||||||
\(628\) | −23.3802 | −0.932973 | ||||||||
\(629\) | −15.5074 | −0.618320 | ||||||||
\(630\) | −33.7451 | −1.34444 | ||||||||
\(631\) | 18.2998 | 0.728504 | 0.364252 | − | 0.931300i | \(-0.381325\pi\) | ||||
0.364252 | + | 0.931300i | \(0.381325\pi\) | |||||||
\(632\) | −8.30703 | −0.330436 | ||||||||
\(633\) | 57.7347 | 2.29475 | ||||||||
\(634\) | −25.7323 | −1.02196 | ||||||||
\(635\) | 8.32525 | 0.330378 | ||||||||
\(636\) | −8.80505 | −0.349143 | ||||||||
\(637\) | −22.0006 | −0.871695 | ||||||||
\(638\) | −2.31553 | −0.0916726 | ||||||||
\(639\) | 48.3107 | 1.91114 | ||||||||
\(640\) | −2.15661 | −0.0852476 | ||||||||
\(641\) | 2.21361 | 0.0874322 | 0.0437161 | − | 0.999044i | \(-0.486080\pi\) | ||||
0.0437161 | + | 0.999044i | \(0.486080\pi\) | |||||||
\(642\) | 3.59975 | 0.142071 | ||||||||
\(643\) | 41.9377 | 1.65386 | 0.826930 | − | 0.562304i | \(-0.190085\pi\) | ||||
0.826930 | + | 0.562304i | \(0.190085\pi\) | |||||||
\(644\) | 12.7323 | 0.501721 | ||||||||
\(645\) | −16.4696 | −0.648490 | ||||||||
\(646\) | −10.9742 | −0.431776 | ||||||||
\(647\) | 6.31833 | 0.248399 | 0.124200 | − | 0.992257i | \(-0.460364\pi\) | ||||
0.124200 | + | 0.992257i | \(0.460364\pi\) | |||||||
\(648\) | 0.937149 | 0.0368147 | ||||||||
\(649\) | 16.8037 | 0.659603 | ||||||||
\(650\) | −1.90528 | −0.0747312 | ||||||||
\(651\) | −77.7052 | −3.04551 | ||||||||
\(652\) | −10.1006 | −0.395569 | ||||||||
\(653\) | −27.1677 | −1.06315 | −0.531577 | − | 0.847010i | \(-0.678400\pi\) | ||||
−0.531577 | + | 0.847010i | \(0.678400\pi\) | |||||||
\(654\) | 16.2713 | 0.636257 | ||||||||
\(655\) | −31.0659 | −1.21385 | ||||||||
\(656\) | 0.843499 | 0.0329331 | ||||||||
\(657\) | 71.4562 | 2.78777 | ||||||||
\(658\) | 18.4194 | 0.718064 | ||||||||
\(659\) | −24.9384 | −0.971463 | −0.485732 | − | 0.874108i | \(-0.661447\pi\) | ||||
−0.485732 | + | 0.874108i | \(0.661447\pi\) | |||||||
\(660\) | 9.30176 | 0.362071 | ||||||||
\(661\) | 32.7065 | 1.27214 | 0.636068 | − | 0.771633i | \(-0.280560\pi\) | ||||
0.636068 | + | 0.771633i | \(0.280560\pi\) | |||||||
\(662\) | 0.417145 | 0.0162128 | ||||||||
\(663\) | −33.8098 | −1.31307 | ||||||||
\(664\) | 8.98766 | 0.348789 | ||||||||
\(665\) | −35.2428 | −1.36666 | ||||||||
\(666\) | −32.7580 | −1.26935 | ||||||||
\(667\) | −5.71527 | −0.221296 | ||||||||
\(668\) | −6.08456 | −0.235419 | ||||||||
\(669\) | 0.515256 | 0.0199209 | ||||||||
\(670\) | 8.35803 | 0.322899 | ||||||||
\(671\) | 9.69629 | 0.374321 | ||||||||
\(672\) | 9.22267 | 0.355772 | ||||||||
\(673\) | 13.2434 | 0.510494 | 0.255247 | − | 0.966876i | \(-0.417843\pi\) | ||||
0.255247 | + | 0.966876i | \(0.417843\pi\) | |||||||
\(674\) | 7.25189 | 0.279333 | ||||||||
\(675\) | 1.65866 | 0.0638418 | ||||||||
\(676\) | 16.8002 | 0.646161 | ||||||||
\(677\) | −11.1951 | −0.430263 | −0.215131 | − | 0.976585i | \(-0.569018\pi\) | ||||
−0.215131 | + | 0.976585i | \(0.569018\pi\) | |||||||
\(678\) | 23.2798 | 0.894054 | ||||||||
\(679\) | −2.15110 | −0.0825517 | ||||||||
\(680\) | 4.80995 | 0.184453 | ||||||||
\(681\) | −54.9765 | −2.10670 | ||||||||
\(682\) | 13.0864 | 0.501105 | ||||||||
\(683\) | −25.9023 | −0.991125 | −0.495563 | − | 0.868572i | \(-0.665038\pi\) | ||||
−0.495563 | + | 0.868572i | \(0.665038\pi\) | |||||||
\(684\) | −23.1821 | −0.886390 | ||||||||
\(685\) | −15.9615 | −0.609859 | ||||||||
\(686\) | 9.86328 | 0.376582 | ||||||||
\(687\) | 0.797821 | 0.0304388 | ||||||||
\(688\) | 2.75008 | 0.104846 | ||||||||
\(689\) | −17.3091 | −0.659426 | ||||||||
\(690\) | 22.9589 | 0.874032 | ||||||||
\(691\) | 0.451380 | 0.0171713 | 0.00858566 | − | 0.999963i | \(-0.497267\pi\) | ||||
0.00858566 | + | 0.999963i | \(0.497267\pi\) | |||||||
\(692\) | 4.97513 | 0.189126 | ||||||||
\(693\) | −24.3033 | −0.923206 | ||||||||
\(694\) | 13.4874 | 0.511976 | ||||||||
\(695\) | −29.7506 | −1.12850 | ||||||||
\(696\) | −4.13988 | −0.156922 | ||||||||
\(697\) | −1.88128 | −0.0712584 | ||||||||
\(698\) | 2.96719 | 0.112310 | ||||||||
\(699\) | −48.8221 | −1.84662 | ||||||||
\(700\) | −1.15915 | −0.0438118 | ||||||||
\(701\) | −24.2695 | −0.916645 | −0.458322 | − | 0.888786i | \(-0.651549\pi\) | ||||
−0.458322 | + | 0.888786i | \(0.651549\pi\) | |||||||
\(702\) | −25.9428 | −0.979149 | ||||||||
\(703\) | −34.2119 | −1.29033 | ||||||||
\(704\) | −1.55320 | −0.0585384 | ||||||||
\(705\) | 33.2141 | 1.25092 | ||||||||
\(706\) | −13.0493 | −0.491118 | ||||||||
\(707\) | 41.3207 | 1.55402 | ||||||||
\(708\) | 30.0430 | 1.12908 | ||||||||
\(709\) | −1.61409 | −0.0606185 | −0.0303092 | − | 0.999541i | \(-0.509649\pi\) | ||||
−0.0303092 | + | 0.999541i | \(0.509649\pi\) | |||||||
\(710\) | −22.1141 | −0.829926 | ||||||||
\(711\) | 39.1374 | 1.46777 | ||||||||
\(712\) | 4.24398 | 0.159050 | ||||||||
\(713\) | 32.3003 | 1.20966 | ||||||||
\(714\) | −20.5696 | −0.769796 | ||||||||
\(715\) | 18.2856 | 0.683843 | ||||||||
\(716\) | −6.22605 | −0.232679 | ||||||||
\(717\) | 36.6813 | 1.36989 | ||||||||
\(718\) | 12.0619 | 0.450146 | ||||||||
\(719\) | −21.5975 | −0.805449 | −0.402725 | − | 0.915321i | \(-0.631937\pi\) | ||||
−0.402725 | + | 0.915321i | \(0.631937\pi\) | |||||||
\(720\) | 10.1606 | 0.378663 | ||||||||
\(721\) | −38.8829 | −1.44807 | ||||||||
\(722\) | −5.21101 | −0.193934 | ||||||||
\(723\) | −11.4822 | −0.427027 | ||||||||
\(724\) | 13.5566 | 0.503829 | ||||||||
\(725\) | 0.520322 | 0.0193243 | ||||||||
\(726\) | −23.8471 | −0.885049 | ||||||||
\(727\) | 37.5227 | 1.39164 | 0.695820 | − | 0.718216i | \(-0.255041\pi\) | ||||
0.695820 | + | 0.718216i | \(0.255041\pi\) | |||||||
\(728\) | 18.1301 | 0.671947 | ||||||||
\(729\) | −44.0061 | −1.62985 | ||||||||
\(730\) | −32.7089 | −1.21061 | ||||||||
\(731\) | −6.13357 | −0.226858 | ||||||||
\(732\) | 17.3358 | 0.640749 | ||||||||
\(733\) | 10.6844 | 0.394639 | 0.197319 | − | 0.980339i | \(-0.436776\pi\) | ||||
0.197319 | + | 0.980339i | \(0.436776\pi\) | |||||||
\(734\) | 37.3889 | 1.38005 | ||||||||
\(735\) | −24.1358 | −0.890264 | ||||||||
\(736\) | −3.83366 | −0.141311 | ||||||||
\(737\) | 6.01948 | 0.221730 | ||||||||
\(738\) | −3.97403 | −0.146286 | ||||||||
\(739\) | −2.81189 | −0.103437 | −0.0517185 | − | 0.998662i | \(-0.516470\pi\) | ||||
−0.0517185 | + | 0.998662i | \(0.516470\pi\) | |||||||
\(740\) | 14.9949 | 0.551223 | ||||||||
\(741\) | −74.5902 | −2.74014 | ||||||||
\(742\) | −10.5307 | −0.386594 | ||||||||
\(743\) | −48.0123 | −1.76140 | −0.880701 | − | 0.473673i | \(-0.842928\pi\) | ||||
−0.880701 | + | 0.473673i | \(0.842928\pi\) | |||||||
\(744\) | 23.3969 | 0.857773 | ||||||||
\(745\) | 21.3275 | 0.781380 | ||||||||
\(746\) | −35.4078 | −1.29637 | ||||||||
\(747\) | −42.3441 | −1.54929 | ||||||||
\(748\) | 3.46414 | 0.126662 | ||||||||
\(749\) | 4.30525 | 0.157310 | ||||||||
\(750\) | −32.0341 | −1.16972 | ||||||||
\(751\) | 16.6751 | 0.608484 | 0.304242 | − | 0.952595i | \(-0.401597\pi\) | ||||
0.304242 | + | 0.952595i | \(0.401597\pi\) | |||||||
\(752\) | −5.54606 | −0.202244 | ||||||||
\(753\) | 20.0870 | 0.732010 | ||||||||
\(754\) | −8.13827 | −0.296378 | ||||||||
\(755\) | 5.78099 | 0.210392 | ||||||||
\(756\) | −15.7833 | −0.574035 | ||||||||
\(757\) | 25.0656 | 0.911023 | 0.455512 | − | 0.890230i | \(-0.349456\pi\) | ||||
0.455512 | + | 0.890230i | \(0.349456\pi\) | |||||||
\(758\) | −36.1932 | −1.31460 | ||||||||
\(759\) | 16.5351 | 0.600186 | ||||||||
\(760\) | 10.6115 | 0.384921 | ||||||||
\(761\) | 18.7490 | 0.679652 | 0.339826 | − | 0.940488i | \(-0.389632\pi\) | ||||
0.339826 | + | 0.940488i | \(0.389632\pi\) | |||||||
\(762\) | 10.7199 | 0.388341 | ||||||||
\(763\) | 19.4602 | 0.704506 | ||||||||
\(764\) | −6.67728 | −0.241575 | ||||||||
\(765\) | −22.6614 | −0.819325 | ||||||||
\(766\) | 11.7935 | 0.426118 | ||||||||
\(767\) | 59.0591 | 2.13250 | ||||||||
\(768\) | −2.77693 | −0.100204 | ||||||||
\(769\) | 41.2480 | 1.48744 | 0.743721 | − | 0.668490i | \(-0.233059\pi\) | ||||
0.743721 | + | 0.668490i | \(0.233059\pi\) | |||||||
\(770\) | 11.1248 | 0.400909 | ||||||||
\(771\) | −30.1269 | −1.08500 | ||||||||
\(772\) | 14.0795 | 0.506731 | ||||||||
\(773\) | 17.5037 | 0.629563 | 0.314782 | − | 0.949164i | \(-0.398069\pi\) | ||||
0.314782 | + | 0.949164i | \(0.398069\pi\) | |||||||
\(774\) | −12.9566 | −0.465716 | ||||||||
\(775\) | −2.94064 | −0.105631 | ||||||||
\(776\) | 0.647693 | 0.0232508 | ||||||||
\(777\) | −64.1251 | −2.30047 | ||||||||
\(778\) | 22.5729 | 0.809276 | ||||||||
\(779\) | −4.15041 | −0.148704 | ||||||||
\(780\) | 32.6924 | 1.17058 | ||||||||
\(781\) | −15.9266 | −0.569900 | ||||||||
\(782\) | 8.55031 | 0.305759 | ||||||||
\(783\) | 7.08484 | 0.253192 | ||||||||
\(784\) | 4.03018 | 0.143935 | ||||||||
\(785\) | −50.4221 | −1.79964 | ||||||||
\(786\) | −40.0016 | −1.42681 | ||||||||
\(787\) | −6.02118 | −0.214632 | −0.107316 | − | 0.994225i | \(-0.534226\pi\) | ||||
−0.107316 | + | 0.994225i | \(0.534226\pi\) | |||||||
\(788\) | 2.22662 | 0.0793201 | ||||||||
\(789\) | −21.0394 | −0.749023 | ||||||||
\(790\) | −17.9151 | −0.637389 | ||||||||
\(791\) | 27.8423 | 0.989957 | ||||||||
\(792\) | 7.31769 | 0.260023 | ||||||||
\(793\) | 34.0790 | 1.21018 | ||||||||
\(794\) | −1.11349 | −0.0395162 | ||||||||
\(795\) | −18.9891 | −0.673473 | ||||||||
\(796\) | 3.97736 | 0.140974 | ||||||||
\(797\) | −7.00739 | −0.248214 | −0.124107 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124107 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(798\) | −45.3799 | −1.60643 | ||||||||
\(799\) | 12.3695 | 0.437602 | ||||||||
\(800\) | 0.349019 | 0.0123397 | ||||||||
\(801\) | −19.9949 | −0.706486 | ||||||||
\(802\) | 28.4318 | 1.00396 | ||||||||
\(803\) | −23.5571 | −0.831311 | ||||||||
\(804\) | 10.7621 | 0.379550 | ||||||||
\(805\) | 27.4585 | 0.967787 | ||||||||
\(806\) | 45.9941 | 1.62007 | ||||||||
\(807\) | 3.04858 | 0.107315 | ||||||||
\(808\) | −12.4416 | −0.437694 | ||||||||
\(809\) | −3.43766 | −0.120862 | −0.0604308 | − | 0.998172i | \(-0.519247\pi\) | ||||
−0.0604308 | + | 0.998172i | \(0.519247\pi\) | |||||||
\(810\) | 2.02107 | 0.0710131 | ||||||||
\(811\) | −30.9964 | −1.08843 | −0.544215 | − | 0.838946i | \(-0.683172\pi\) | ||||
−0.544215 | + | 0.838946i | \(0.683172\pi\) | |||||||
\(812\) | −4.95124 | −0.173754 | ||||||||
\(813\) | 51.4468 | 1.80432 | ||||||||
\(814\) | 10.7994 | 0.378518 | ||||||||
\(815\) | −21.7830 | −0.763026 | ||||||||
\(816\) | 6.19346 | 0.216815 | ||||||||
\(817\) | −13.5317 | −0.473413 | ||||||||
\(818\) | 3.33936 | 0.116758 | ||||||||
\(819\) | −85.4176 | −2.98473 | ||||||||
\(820\) | 1.81910 | 0.0635258 | ||||||||
\(821\) | 2.67824 | 0.0934711 | 0.0467356 | − | 0.998907i | \(-0.485118\pi\) | ||||
0.0467356 | + | 0.998907i | \(0.485118\pi\) | |||||||
\(822\) | −20.5526 | −0.716856 | ||||||||
\(823\) | 34.7444 | 1.21111 | 0.605556 | − | 0.795802i | \(-0.292951\pi\) | ||||
0.605556 | + | 0.795802i | \(0.292951\pi\) | |||||||
\(824\) | 11.7076 | 0.407853 | ||||||||
\(825\) | −1.50537 | −0.0524101 | ||||||||
\(826\) | 35.9309 | 1.25020 | ||||||||
\(827\) | −0.990216 | −0.0344332 | −0.0172166 | − | 0.999852i | \(-0.505480\pi\) | ||||
−0.0172166 | + | 0.999852i | \(0.505480\pi\) | |||||||
\(828\) | 18.0618 | 0.627690 | ||||||||
\(829\) | −34.1111 | −1.18473 | −0.592365 | − | 0.805670i | \(-0.701805\pi\) | ||||
−0.592365 | + | 0.805670i | \(0.701805\pi\) | |||||||
\(830\) | 19.3829 | 0.672790 | ||||||||
\(831\) | 46.4504 | 1.61135 | ||||||||
\(832\) | −5.45896 | −0.189255 | ||||||||
\(833\) | −8.98861 | −0.311437 | ||||||||
\(834\) | −38.3080 | −1.32650 | ||||||||
\(835\) | −13.1220 | −0.454107 | ||||||||
\(836\) | 7.64247 | 0.264320 | ||||||||
\(837\) | −40.0406 | −1.38401 | ||||||||
\(838\) | 30.4571 | 1.05212 | ||||||||
\(839\) | 2.73855 | 0.0945452 | 0.0472726 | − | 0.998882i | \(-0.484947\pi\) | ||||
0.0472726 | + | 0.998882i | \(0.484947\pi\) | |||||||
\(840\) | 19.8897 | 0.686261 | ||||||||
\(841\) | −26.7775 | −0.923361 | ||||||||
\(842\) | −29.2355 | −1.00752 | ||||||||
\(843\) | 58.2539 | 2.00637 | ||||||||
\(844\) | −20.7908 | −0.715649 | ||||||||
\(845\) | 36.2315 | 1.24640 | ||||||||
\(846\) | 26.1295 | 0.898351 | ||||||||
\(847\) | −28.5208 | −0.979986 | ||||||||
\(848\) | 3.17078 | 0.108885 | ||||||||
\(849\) | −54.5454 | −1.87199 | ||||||||
\(850\) | −0.778426 | −0.0266998 | ||||||||
\(851\) | 26.6554 | 0.913735 | ||||||||
\(852\) | −28.4749 | −0.975534 | ||||||||
\(853\) | 38.4126 | 1.31522 | 0.657611 | − | 0.753358i | \(-0.271567\pi\) | ||||
0.657611 | + | 0.753358i | \(0.271567\pi\) | |||||||
\(854\) | 20.7333 | 0.709480 | ||||||||
\(855\) | −49.9948 | −1.70979 | ||||||||
\(856\) | −1.29630 | −0.0443068 | ||||||||
\(857\) | 33.2560 | 1.13600 | 0.568001 | − | 0.823028i | \(-0.307717\pi\) | ||||
0.568001 | + | 0.823028i | \(0.307717\pi\) | |||||||
\(858\) | 23.5452 | 0.803820 | ||||||||
\(859\) | −38.0499 | −1.29824 | −0.649122 | − | 0.760684i | \(-0.724864\pi\) | ||||
−0.649122 | + | 0.760684i | \(0.724864\pi\) | |||||||
\(860\) | 5.93086 | 0.202241 | ||||||||
\(861\) | −7.77932 | −0.265118 | ||||||||
\(862\) | 21.5252 | 0.733150 | ||||||||
\(863\) | 23.0316 | 0.784006 | 0.392003 | − | 0.919964i | \(-0.371782\pi\) | ||||
0.392003 | + | 0.919964i | \(0.371782\pi\) | |||||||
\(864\) | 4.75234 | 0.161678 | ||||||||
\(865\) | 10.7294 | 0.364812 | ||||||||
\(866\) | −25.2201 | −0.857016 | ||||||||
\(867\) | 33.3945 | 1.13414 | ||||||||
\(868\) | 27.9824 | 0.949783 | ||||||||
\(869\) | −12.9025 | −0.437687 | ||||||||
\(870\) | −8.92813 | −0.302692 | ||||||||
\(871\) | 21.1564 | 0.716856 | ||||||||
\(872\) | −5.85943 | −0.198425 | ||||||||
\(873\) | −3.05152 | −0.103278 | ||||||||
\(874\) | 18.8634 | 0.638065 | ||||||||
\(875\) | −38.3123 | −1.29519 | ||||||||
\(876\) | −42.1172 | −1.42301 | ||||||||
\(877\) | 5.92251 | 0.199989 | 0.0999945 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999945 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(878\) | −27.0325 | −0.912302 | ||||||||
\(879\) | 75.8855 | 2.55955 | ||||||||
\(880\) | −3.34965 | −0.112917 | ||||||||
\(881\) | 49.0165 | 1.65141 | 0.825704 | − | 0.564103i | \(-0.190778\pi\) | ||||
0.825704 | + | 0.564103i | \(0.190778\pi\) | |||||||
\(882\) | −18.9876 | −0.639347 | ||||||||
\(883\) | 2.84114 | 0.0956121 | 0.0478061 | − | 0.998857i | \(-0.484777\pi\) | ||||
0.0478061 | + | 0.998857i | \(0.484777\pi\) | |||||||
\(884\) | 12.1752 | 0.409498 | ||||||||
\(885\) | 64.7911 | 2.17793 | ||||||||
\(886\) | −7.51560 | −0.252491 | ||||||||
\(887\) | −36.8994 | −1.23896 | −0.619480 | − | 0.785013i | \(-0.712656\pi\) | ||||
−0.619480 | + | 0.785013i | \(0.712656\pi\) | |||||||
\(888\) | 19.3080 | 0.647933 | ||||||||
\(889\) | 12.8208 | 0.429997 | ||||||||
\(890\) | 9.15263 | 0.306797 | ||||||||
\(891\) | 1.45558 | 0.0487638 | ||||||||
\(892\) | −0.185548 | −0.00621262 | ||||||||
\(893\) | 27.2892 | 0.913199 | ||||||||
\(894\) | 27.4621 | 0.918471 | ||||||||
\(895\) | −13.4272 | −0.448821 | ||||||||
\(896\) | −3.32117 | −0.110953 | ||||||||
\(897\) | 58.1151 | 1.94041 | ||||||||
\(898\) | 7.51061 | 0.250632 | ||||||||
\(899\) | −12.5607 | −0.418924 | ||||||||
\(900\) | −1.64436 | −0.0548119 | ||||||||
\(901\) | −7.07187 | −0.235598 | ||||||||
\(902\) | 1.31012 | 0.0436223 | ||||||||
\(903\) | −25.3631 | −0.844031 | ||||||||
\(904\) | −8.38327 | −0.278823 | ||||||||
\(905\) | 29.2364 | 0.971852 | ||||||||
\(906\) | 7.44381 | 0.247304 | ||||||||
\(907\) | 16.5696 | 0.550185 | 0.275092 | − | 0.961418i | \(-0.411292\pi\) | ||||
0.275092 | + | 0.961418i | \(0.411292\pi\) | |||||||
\(908\) | 19.7975 | 0.657004 | ||||||||
\(909\) | 58.6169 | 1.94420 | ||||||||
\(910\) | 39.0997 | 1.29614 | ||||||||
\(911\) | −27.4801 | −0.910457 | −0.455229 | − | 0.890375i | \(-0.650442\pi\) | ||||
−0.455229 | + | 0.890375i | \(0.650442\pi\) | |||||||
\(912\) | 13.6638 | 0.452454 | ||||||||
\(913\) | 13.9596 | 0.461996 | ||||||||
\(914\) | −3.83154 | −0.126736 | ||||||||
\(915\) | 37.3866 | 1.23596 | ||||||||
\(916\) | −0.287303 | −0.00949276 | ||||||||
\(917\) | −47.8413 | −1.57986 | ||||||||
\(918\) | −10.5993 | −0.349828 | ||||||||
\(919\) | 5.29874 | 0.174789 | 0.0873947 | − | 0.996174i | \(-0.472146\pi\) | ||||
0.0873947 | + | 0.996174i | \(0.472146\pi\) | |||||||
\(920\) | −8.26773 | −0.272579 | ||||||||
\(921\) | 66.1743 | 2.18052 | ||||||||
\(922\) | −12.2934 | −0.404861 | ||||||||
\(923\) | −55.9765 | −1.84249 | ||||||||
\(924\) | 14.3247 | 0.471247 | ||||||||
\(925\) | −2.42672 | −0.0797902 | ||||||||
\(926\) | −17.1507 | −0.563608 | ||||||||
\(927\) | −55.1586 | −1.81165 | ||||||||
\(928\) | 1.49081 | 0.0489383 | ||||||||
\(929\) | −30.3046 | −0.994263 | −0.497132 | − | 0.867675i | \(-0.665613\pi\) | ||||
−0.497132 | + | 0.867675i | \(0.665613\pi\) | |||||||
\(930\) | 50.4581 | 1.65459 | ||||||||
\(931\) | −19.8304 | −0.649914 | ||||||||
\(932\) | 17.5813 | 0.575894 | ||||||||
\(933\) | 57.8611 | 1.89429 | ||||||||
\(934\) | 36.4013 | 1.19109 | ||||||||
\(935\) | 7.47081 | 0.244322 | ||||||||
\(936\) | 25.7191 | 0.840656 | ||||||||
\(937\) | −32.1459 | −1.05016 | −0.525080 | − | 0.851053i | \(-0.675965\pi\) | ||||
−0.525080 | + | 0.851053i | \(0.675965\pi\) | |||||||
\(938\) | 12.8713 | 0.420263 | ||||||||
\(939\) | 75.5290 | 2.46480 | ||||||||
\(940\) | −11.9607 | −0.390115 | ||||||||
\(941\) | −51.0743 | −1.66497 | −0.832487 | − | 0.554045i | \(-0.813083\pi\) | ||||
−0.832487 | + | 0.554045i | \(0.813083\pi\) | |||||||
\(942\) | −64.9254 | −2.11538 | ||||||||
\(943\) | 3.23369 | 0.105304 | ||||||||
\(944\) | −10.8188 | −0.352120 | ||||||||
\(945\) | −34.0386 | −1.10727 | ||||||||
\(946\) | 4.27142 | 0.138876 | ||||||||
\(947\) | 8.69091 | 0.282417 | 0.141208 | − | 0.989980i | \(-0.454901\pi\) | ||||
0.141208 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(948\) | −23.0681 | −0.749216 | ||||||||
\(949\) | −82.7948 | −2.68763 | ||||||||
\(950\) | −1.71734 | −0.0557178 | ||||||||
\(951\) | −71.4570 | −2.31715 | ||||||||
\(952\) | 7.40729 | 0.240072 | ||||||||
\(953\) | −32.0021 | −1.03665 | −0.518325 | − | 0.855184i | \(-0.673444\pi\) | ||||
−0.518325 | + | 0.855184i | \(0.673444\pi\) | |||||||
\(954\) | −14.9387 | −0.483658 | ||||||||
\(955\) | −14.4003 | −0.465983 | ||||||||
\(956\) | −13.2093 | −0.427218 | ||||||||
\(957\) | −6.43007 | −0.207855 | ||||||||
\(958\) | 11.2479 | 0.363405 | ||||||||
\(959\) | −24.5807 | −0.793751 | ||||||||
\(960\) | −5.98877 | −0.193287 | ||||||||
\(961\) | 39.9882 | 1.28994 | ||||||||
\(962\) | 37.9560 | 1.22375 | ||||||||
\(963\) | 6.10736 | 0.196807 | ||||||||
\(964\) | 4.13484 | 0.133174 | ||||||||
\(965\) | 30.3640 | 0.977450 | ||||||||
\(966\) | 35.3566 | 1.13758 | ||||||||
\(967\) | 10.4638 | 0.336495 | 0.168247 | − | 0.985745i | \(-0.446189\pi\) | ||||
0.168247 | + | 0.985745i | \(0.446189\pi\) | |||||||
\(968\) | 8.58757 | 0.276015 | ||||||||
\(969\) | −30.4747 | −0.978990 | ||||||||
\(970\) | 1.39682 | 0.0448493 | ||||||||
\(971\) | 21.4573 | 0.688597 | 0.344298 | − | 0.938860i | \(-0.388117\pi\) | ||||
0.344298 | + | 0.938860i | \(0.388117\pi\) | |||||||
\(972\) | 16.8594 | 0.540766 | ||||||||
\(973\) | −45.8157 | −1.46879 | ||||||||
\(974\) | 3.94271 | 0.126332 | ||||||||
\(975\) | −5.29084 | −0.169442 | ||||||||
\(976\) | −6.24278 | −0.199826 | ||||||||
\(977\) | −20.1359 | −0.644204 | −0.322102 | − | 0.946705i | \(-0.604389\pi\) | ||||
−0.322102 | + | 0.946705i | \(0.604389\pi\) | |||||||
\(978\) | −28.0486 | −0.896896 | ||||||||
\(979\) | 6.59175 | 0.210673 | ||||||||
\(980\) | 8.69154 | 0.277641 | ||||||||
\(981\) | 27.6059 | 0.881389 | ||||||||
\(982\) | −16.8873 | −0.538896 | ||||||||
\(983\) | −52.0734 | −1.66088 | −0.830441 | − | 0.557106i | \(-0.811912\pi\) | ||||
−0.830441 | + | 0.557106i | \(0.811912\pi\) | |||||||
\(984\) | 2.34234 | 0.0746711 | ||||||||
\(985\) | 4.80196 | 0.153003 | ||||||||
\(986\) | −3.32499 | −0.105889 | ||||||||
\(987\) | 51.1495 | 1.62811 | ||||||||
\(988\) | 26.8606 | 0.854550 | ||||||||
\(989\) | 10.5429 | 0.335244 | ||||||||
\(990\) | 15.7814 | 0.501567 | ||||||||
\(991\) | −23.4351 | −0.744440 | −0.372220 | − | 0.928144i | \(-0.621403\pi\) | ||||
−0.372220 | + | 0.928144i | \(0.621403\pi\) | |||||||
\(992\) | −8.42545 | −0.267508 | ||||||||
\(993\) | 1.15838 | 0.0367602 | ||||||||
\(994\) | −34.0555 | −1.08018 | ||||||||
\(995\) | 8.57762 | 0.271929 | ||||||||
\(996\) | 24.9581 | 0.790829 | ||||||||
\(997\) | −26.0215 | −0.824109 | −0.412055 | − | 0.911159i | \(-0.635189\pi\) | ||||
−0.412055 | + | 0.911159i | \(0.635189\pi\) | |||||||
\(998\) | 34.6841 | 1.09791 | ||||||||
\(999\) | −33.0429 | −1.04543 |
(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 | 8026.2.a.b.1.8 | ✓ | 81 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.b.1.8 | ✓ | 81 | 1.1 | even | 1 | trivial |