Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33589 | 0.944619 | 0.472310 | − | 0.881433i | \(-0.343420\pi\) | ||||
0.472310 | + | 0.881433i | \(0.343420\pi\) | |||||||
\(3\) | 2.00110 | 1.15534 | 0.577668 | − | 0.816272i | \(-0.303963\pi\) | ||||
0.577668 | + | 0.816272i | \(0.303963\pi\) | |||||||
\(4\) | −0.215389 | −0.107695 | ||||||||
\(5\) | −3.88298 | −1.73652 | −0.868262 | − | 0.496106i | \(-0.834763\pi\) | ||||
−0.868262 | + | 0.496106i | \(0.834763\pi\) | |||||||
\(6\) | 2.67326 | 1.09135 | ||||||||
\(7\) | 2.54624 | 0.962387 | 0.481193 | − | 0.876614i | \(-0.340203\pi\) | ||||
0.481193 | + | 0.876614i | \(0.340203\pi\) | |||||||
\(8\) | −2.95952 | −1.04635 | ||||||||
\(9\) | 1.00441 | 0.334803 | ||||||||
\(10\) | −5.18725 | −1.64035 | ||||||||
\(11\) | −3.83983 | −1.15775 | −0.578877 | − | 0.815415i | \(-0.696509\pi\) | ||||
−0.578877 | + | 0.815415i | \(0.696509\pi\) | |||||||
\(12\) | −0.431016 | −0.124424 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.40150 | 0.909089 | ||||||||
\(15\) | −7.77025 | −2.00627 | ||||||||
\(16\) | −3.52283 | −0.880707 | ||||||||
\(17\) | −3.24118 | −0.786102 | −0.393051 | − | 0.919517i | \(-0.628580\pi\) | ||||
−0.393051 | + | 0.919517i | \(0.628580\pi\) | |||||||
\(18\) | 1.34178 | 0.316261 | ||||||||
\(19\) | 1.25285 | 0.287423 | 0.143712 | − | 0.989620i | \(-0.454096\pi\) | ||||
0.143712 | + | 0.989620i | \(0.454096\pi\) | |||||||
\(20\) | 0.836354 | 0.187014 | ||||||||
\(21\) | 5.09528 | 1.11188 | ||||||||
\(22\) | −5.12961 | −1.09364 | ||||||||
\(23\) | −3.59617 | −0.749854 | −0.374927 | − | 0.927054i | \(-0.622332\pi\) | ||||
−0.374927 | + | 0.927054i | \(0.622332\pi\) | |||||||
\(24\) | −5.92231 | −1.20889 | ||||||||
\(25\) | 10.0776 | 2.01551 | ||||||||
\(26\) | −1.33589 | −0.261990 | ||||||||
\(27\) | −3.99338 | −0.768527 | ||||||||
\(28\) | −0.548432 | −0.103644 | ||||||||
\(29\) | −4.68376 | −0.869752 | −0.434876 | − | 0.900490i | \(-0.643208\pi\) | ||||
−0.434876 | + | 0.900490i | \(0.643208\pi\) | |||||||
\(30\) | −10.3802 | −1.89516 | ||||||||
\(31\) | 5.40323 | 0.970449 | 0.485225 | − | 0.874390i | \(-0.338738\pi\) | ||||
0.485225 | + | 0.874390i | \(0.338738\pi\) | |||||||
\(32\) | 1.21292 | 0.214417 | ||||||||
\(33\) | −7.68390 | −1.33759 | ||||||||
\(34\) | −4.32987 | −0.742567 | ||||||||
\(35\) | −9.88700 | −1.67121 | ||||||||
\(36\) | −0.216339 | −0.0360565 | ||||||||
\(37\) | −4.58286 | −0.753417 | −0.376708 | − | 0.926332i | \(-0.622944\pi\) | ||||
−0.376708 | + | 0.926332i | \(0.622944\pi\) | |||||||
\(38\) | 1.67367 | 0.271506 | ||||||||
\(39\) | −2.00110 | −0.320433 | ||||||||
\(40\) | 11.4918 | 1.81701 | ||||||||
\(41\) | −10.5512 | −1.64783 | −0.823913 | − | 0.566716i | \(-0.808214\pi\) | ||||
−0.823913 | + | 0.566716i | \(0.808214\pi\) | |||||||
\(42\) | 6.80675 | 1.05030 | ||||||||
\(43\) | −4.94298 | −0.753798 | −0.376899 | − | 0.926254i | \(-0.623010\pi\) | ||||
−0.376899 | + | 0.926254i | \(0.623010\pi\) | |||||||
\(44\) | 0.827059 | 0.124684 | ||||||||
\(45\) | −3.90010 | −0.581393 | ||||||||
\(46\) | −4.80410 | −0.708326 | ||||||||
\(47\) | 12.8196 | 1.86993 | 0.934963 | − | 0.354744i | \(-0.115432\pi\) | ||||
0.934963 | + | 0.354744i | \(0.115432\pi\) | |||||||
\(48\) | −7.04954 | −1.01751 | ||||||||
\(49\) | −0.516680 | −0.0738115 | ||||||||
\(50\) | 13.4626 | 1.90389 | ||||||||
\(51\) | −6.48593 | −0.908212 | ||||||||
\(52\) | 0.215389 | 0.0298691 | ||||||||
\(53\) | −4.12024 | −0.565958 | −0.282979 | − | 0.959126i | \(-0.591323\pi\) | ||||
−0.282979 | + | 0.959126i | \(0.591323\pi\) | |||||||
\(54\) | −5.33473 | −0.725965 | ||||||||
\(55\) | 14.9100 | 2.01047 | ||||||||
\(56\) | −7.53565 | −1.00699 | ||||||||
\(57\) | 2.50708 | 0.332071 | ||||||||
\(58\) | −6.25700 | −0.821585 | ||||||||
\(59\) | 10.4487 | 1.36030 | 0.680152 | − | 0.733071i | \(-0.261914\pi\) | ||||
0.680152 | + | 0.733071i | \(0.261914\pi\) | |||||||
\(60\) | 1.67363 | 0.216065 | ||||||||
\(61\) | 13.8061 | 1.76769 | 0.883846 | − | 0.467778i | \(-0.154945\pi\) | ||||
0.883846 | + | 0.467778i | \(0.154945\pi\) | |||||||
\(62\) | 7.21814 | 0.916705 | ||||||||
\(63\) | 2.55746 | 0.322210 | ||||||||
\(64\) | 8.66599 | 1.08325 | ||||||||
\(65\) | 3.88298 | 0.481625 | ||||||||
\(66\) | −10.2649 | −1.26352 | ||||||||
\(67\) | −8.63783 | −1.05528 | −0.527639 | − | 0.849469i | \(-0.676923\pi\) | ||||
−0.527639 | + | 0.849469i | \(0.676923\pi\) | |||||||
\(68\) | 0.698116 | 0.0846590 | ||||||||
\(69\) | −7.19631 | −0.866334 | ||||||||
\(70\) | −13.2080 | −1.57865 | ||||||||
\(71\) | −10.1729 | −1.20731 | −0.603653 | − | 0.797247i | \(-0.706289\pi\) | ||||
−0.603653 | + | 0.797247i | \(0.706289\pi\) | |||||||
\(72\) | −2.97257 | −0.350321 | ||||||||
\(73\) | 7.80471 | 0.913473 | 0.456736 | − | 0.889602i | \(-0.349018\pi\) | ||||
0.456736 | + | 0.889602i | \(0.349018\pi\) | |||||||
\(74\) | −6.12221 | −0.711692 | ||||||||
\(75\) | 20.1662 | 2.32860 | ||||||||
\(76\) | −0.269851 | −0.0309540 | ||||||||
\(77\) | −9.77712 | −1.11421 | ||||||||
\(78\) | −2.67326 | −0.302687 | ||||||||
\(79\) | −2.73046 | −0.307201 | −0.153600 | − | 0.988133i | \(-0.549087\pi\) | ||||
−0.153600 | + | 0.988133i | \(0.549087\pi\) | |||||||
\(80\) | 13.6791 | 1.52937 | ||||||||
\(81\) | −11.0044 | −1.22271 | ||||||||
\(82\) | −14.0953 | −1.55657 | ||||||||
\(83\) | 0.267981 | 0.0294148 | 0.0147074 | − | 0.999892i | \(-0.495318\pi\) | ||||
0.0147074 | + | 0.999892i | \(0.495318\pi\) | |||||||
\(84\) | −1.09747 | −0.119744 | ||||||||
\(85\) | 12.5855 | 1.36508 | ||||||||
\(86\) | −6.60330 | −0.712052 | ||||||||
\(87\) | −9.37268 | −1.00486 | ||||||||
\(88\) | 11.3641 | 1.21141 | ||||||||
\(89\) | 5.09593 | 0.540167 | 0.270084 | − | 0.962837i | \(-0.412949\pi\) | ||||
0.270084 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(90\) | −5.21012 | −0.549195 | ||||||||
\(91\) | −2.54624 | −0.266918 | ||||||||
\(92\) | 0.774578 | 0.0807553 | ||||||||
\(93\) | 10.8124 | 1.12120 | ||||||||
\(94\) | 17.1256 | 1.76637 | ||||||||
\(95\) | −4.86480 | −0.499118 | ||||||||
\(96\) | 2.42719 | 0.247724 | ||||||||
\(97\) | −1.27333 | −0.129287 | −0.0646436 | − | 0.997908i | \(-0.520591\pi\) | ||||
−0.0646436 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(98\) | −0.690230 | −0.0697237 | ||||||||
\(99\) | −3.85676 | −0.387619 | ||||||||
\(100\) | −2.17060 | −0.217060 | ||||||||
\(101\) | −16.1375 | −1.60574 | −0.802870 | − | 0.596154i | \(-0.796695\pi\) | ||||
−0.802870 | + | 0.596154i | \(0.796695\pi\) | |||||||
\(102\) | −8.66451 | −0.857915 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 2.95952 | 0.290205 | ||||||||
\(105\) | −19.7849 | −1.93081 | ||||||||
\(106\) | −5.50420 | −0.534615 | ||||||||
\(107\) | 7.59643 | 0.734374 | 0.367187 | − | 0.930147i | \(-0.380321\pi\) | ||||
0.367187 | + | 0.930147i | \(0.380321\pi\) | |||||||
\(108\) | 0.860132 | 0.0827663 | ||||||||
\(109\) | −9.42933 | −0.903166 | −0.451583 | − | 0.892229i | \(-0.649141\pi\) | ||||
−0.451583 | + | 0.892229i | \(0.649141\pi\) | |||||||
\(110\) | 19.9182 | 1.89912 | ||||||||
\(111\) | −9.17076 | −0.870450 | ||||||||
\(112\) | −8.96995 | −0.847581 | ||||||||
\(113\) | 11.2501 | 1.05832 | 0.529159 | − | 0.848523i | \(-0.322508\pi\) | ||||
0.529159 | + | 0.848523i | \(0.322508\pi\) | |||||||
\(114\) | 3.34919 | 0.313680 | ||||||||
\(115\) | 13.9639 | 1.30214 | ||||||||
\(116\) | 1.00883 | 0.0936677 | ||||||||
\(117\) | −1.00441 | −0.0928576 | ||||||||
\(118\) | 13.9583 | 1.28497 | ||||||||
\(119\) | −8.25281 | −0.756534 | ||||||||
\(120\) | 22.9962 | 2.09926 | ||||||||
\(121\) | 3.74432 | 0.340393 | ||||||||
\(122\) | 18.4435 | 1.66980 | ||||||||
\(123\) | −21.1141 | −1.90379 | ||||||||
\(124\) | −1.16380 | −0.104512 | ||||||||
\(125\) | −19.7161 | −1.76346 | ||||||||
\(126\) | 3.41650 | 0.304366 | ||||||||
\(127\) | 4.19682 | 0.372407 | 0.186204 | − | 0.982511i | \(-0.440382\pi\) | ||||
0.186204 | + | 0.982511i | \(0.440382\pi\) | |||||||
\(128\) | 9.15099 | 0.808841 | ||||||||
\(129\) | −9.89141 | −0.870890 | ||||||||
\(130\) | 5.18725 | 0.454952 | ||||||||
\(131\) | −11.6486 | −1.01774 | −0.508872 | − | 0.860842i | \(-0.669937\pi\) | ||||
−0.508872 | + | 0.860842i | \(0.669937\pi\) | |||||||
\(132\) | 1.65503 | 0.144052 | ||||||||
\(133\) | 3.19005 | 0.276613 | ||||||||
\(134\) | −11.5392 | −0.996836 | ||||||||
\(135\) | 15.5062 | 1.33456 | ||||||||
\(136\) | 9.59235 | 0.822537 | ||||||||
\(137\) | 19.0192 | 1.62492 | 0.812461 | − | 0.583016i | \(-0.198127\pi\) | ||||
0.812461 | + | 0.583016i | \(0.198127\pi\) | |||||||
\(138\) | −9.61350 | −0.818355 | ||||||||
\(139\) | 8.74299 | 0.741570 | 0.370785 | − | 0.928719i | \(-0.379089\pi\) | ||||
0.370785 | + | 0.928719i | \(0.379089\pi\) | |||||||
\(140\) | 2.12955 | 0.179980 | ||||||||
\(141\) | 25.6533 | 2.16040 | ||||||||
\(142\) | −13.5900 | −1.14044 | ||||||||
\(143\) | 3.83983 | 0.321103 | ||||||||
\(144\) | −3.53836 | −0.294863 | ||||||||
\(145\) | 18.1870 | 1.51035 | ||||||||
\(146\) | 10.4263 | 0.862884 | ||||||||
\(147\) | −1.03393 | −0.0852771 | ||||||||
\(148\) | 0.987099 | 0.0811390 | ||||||||
\(149\) | 20.2796 | 1.66137 | 0.830685 | − | 0.556743i | \(-0.187949\pi\) | ||||
0.830685 | + | 0.556743i | \(0.187949\pi\) | |||||||
\(150\) | 26.9400 | 2.19964 | ||||||||
\(151\) | −0.148377 | −0.0120748 | −0.00603739 | − | 0.999982i | \(-0.501922\pi\) | ||||
−0.00603739 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(152\) | −3.70784 | −0.300745 | ||||||||
\(153\) | −3.25547 | −0.263189 | ||||||||
\(154\) | −13.0612 | −1.05250 | ||||||||
\(155\) | −20.9807 | −1.68521 | ||||||||
\(156\) | 0.431016 | 0.0345089 | ||||||||
\(157\) | −22.3379 | −1.78276 | −0.891379 | − | 0.453259i | \(-0.850261\pi\) | ||||
−0.891379 | + | 0.453259i | \(0.850261\pi\) | |||||||
\(158\) | −3.64761 | −0.290188 | ||||||||
\(159\) | −8.24502 | −0.653873 | ||||||||
\(160\) | −4.70977 | −0.372340 | ||||||||
\(161\) | −9.15671 | −0.721650 | ||||||||
\(162\) | −14.7007 | −1.15500 | ||||||||
\(163\) | −8.53278 | −0.668339 | −0.334170 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334170 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(164\) | 2.27262 | 0.177462 | ||||||||
\(165\) | 29.8365 | 2.32276 | ||||||||
\(166\) | 0.357994 | 0.0277858 | ||||||||
\(167\) | −9.56498 | −0.740161 | −0.370080 | − | 0.929000i | \(-0.620670\pi\) | ||||
−0.370080 | + | 0.929000i | \(0.620670\pi\) | |||||||
\(168\) | −15.0796 | −1.16342 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 16.8128 | 1.28948 | ||||||||
\(171\) | 1.25837 | 0.0962302 | ||||||||
\(172\) | 1.06467 | 0.0811800 | ||||||||
\(173\) | −21.7385 | −1.65275 | −0.826373 | − | 0.563123i | \(-0.809600\pi\) | ||||
−0.826373 | + | 0.563123i | \(0.809600\pi\) | |||||||
\(174\) | −12.5209 | −0.949207 | ||||||||
\(175\) | 25.6599 | 1.93970 | ||||||||
\(176\) | 13.5271 | 1.01964 | ||||||||
\(177\) | 20.9089 | 1.57161 | ||||||||
\(178\) | 6.80761 | 0.510252 | ||||||||
\(179\) | −23.3080 | −1.74212 | −0.871060 | − | 0.491176i | \(-0.836567\pi\) | ||||
−0.871060 | + | 0.491176i | \(0.836567\pi\) | |||||||
\(180\) | 0.840041 | 0.0626130 | ||||||||
\(181\) | 14.5441 | 1.08105 | 0.540527 | − | 0.841326i | \(-0.318225\pi\) | ||||
0.540527 | + | 0.841326i | \(0.318225\pi\) | |||||||
\(182\) | −3.40150 | −0.252136 | ||||||||
\(183\) | 27.6275 | 2.04228 | ||||||||
\(184\) | 10.6430 | 0.784609 | ||||||||
\(185\) | 17.7952 | 1.30833 | ||||||||
\(186\) | 14.4442 | 1.05910 | ||||||||
\(187\) | 12.4456 | 0.910112 | ||||||||
\(188\) | −2.76120 | −0.201381 | ||||||||
\(189\) | −10.1681 | −0.739620 | ||||||||
\(190\) | −6.49885 | −0.471476 | ||||||||
\(191\) | −2.51192 | −0.181756 | −0.0908781 | − | 0.995862i | \(-0.528967\pi\) | ||||
−0.0908781 | + | 0.995862i | \(0.528967\pi\) | |||||||
\(192\) | 17.3415 | 1.25152 | ||||||||
\(193\) | 26.6131 | 1.91566 | 0.957828 | − | 0.287344i | \(-0.0927722\pi\) | ||||
0.957828 | + | 0.287344i | \(0.0927722\pi\) | |||||||
\(194\) | −1.70103 | −0.122127 | ||||||||
\(195\) | 7.77025 | 0.556439 | ||||||||
\(196\) | 0.111287 | 0.00794910 | ||||||||
\(197\) | −0.417994 | −0.0297808 | −0.0148904 | − | 0.999889i | \(-0.504740\pi\) | ||||
−0.0148904 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(198\) | −5.15222 | −0.366152 | ||||||||
\(199\) | −11.5265 | −0.817094 | −0.408547 | − | 0.912737i | \(-0.633964\pi\) | ||||
−0.408547 | + | 0.912737i | \(0.633964\pi\) | |||||||
\(200\) | −29.8248 | −2.10893 | ||||||||
\(201\) | −17.2852 | −1.21920 | ||||||||
\(202\) | −21.5580 | −1.51681 | ||||||||
\(203\) | −11.9260 | −0.837038 | ||||||||
\(204\) | 1.39700 | 0.0978097 | ||||||||
\(205\) | 40.9703 | 2.86149 | ||||||||
\(206\) | −1.33589 | −0.0930761 | ||||||||
\(207\) | −3.61203 | −0.251053 | ||||||||
\(208\) | 3.52283 | 0.244264 | ||||||||
\(209\) | −4.81073 | −0.332765 | ||||||||
\(210\) | −26.4305 | −1.82388 | ||||||||
\(211\) | 10.4824 | 0.721641 | 0.360821 | − | 0.932635i | \(-0.382497\pi\) | ||||
0.360821 | + | 0.932635i | \(0.382497\pi\) | |||||||
\(212\) | 0.887456 | 0.0609507 | ||||||||
\(213\) | −20.3571 | −1.39485 | ||||||||
\(214\) | 10.1480 | 0.693704 | ||||||||
\(215\) | 19.1935 | 1.30899 | ||||||||
\(216\) | 11.8185 | 0.804148 | ||||||||
\(217\) | 13.7579 | 0.933948 | ||||||||
\(218\) | −12.5966 | −0.853148 | ||||||||
\(219\) | 15.6180 | 1.05537 | ||||||||
\(220\) | −3.21146 | −0.216517 | ||||||||
\(221\) | 3.24118 | 0.218025 | ||||||||
\(222\) | −12.2512 | −0.822244 | ||||||||
\(223\) | −20.7856 | −1.39191 | −0.695954 | − | 0.718086i | \(-0.745018\pi\) | ||||
−0.695954 | + | 0.718086i | \(0.745018\pi\) | |||||||
\(224\) | 3.08839 | 0.206352 | ||||||||
\(225\) | 10.1220 | 0.674800 | ||||||||
\(226\) | 15.0289 | 0.999707 | ||||||||
\(227\) | 14.9523 | 0.992421 | 0.496211 | − | 0.868202i | \(-0.334724\pi\) | ||||
0.496211 | + | 0.868202i | \(0.334724\pi\) | |||||||
\(228\) | −0.539998 | −0.0357623 | ||||||||
\(229\) | 1.95472 | 0.129171 | 0.0645857 | − | 0.997912i | \(-0.479427\pi\) | ||||
0.0645857 | + | 0.997912i | \(0.479427\pi\) | |||||||
\(230\) | 18.6543 | 1.23003 | ||||||||
\(231\) | −19.5650 | −1.28728 | ||||||||
\(232\) | 13.8617 | 0.910065 | ||||||||
\(233\) | 15.6526 | 1.02544 | 0.512719 | − | 0.858556i | \(-0.328638\pi\) | ||||
0.512719 | + | 0.858556i | \(0.328638\pi\) | |||||||
\(234\) | −1.34178 | −0.0877151 | ||||||||
\(235\) | −49.7782 | −3.24717 | ||||||||
\(236\) | −2.25054 | −0.146497 | ||||||||
\(237\) | −5.46393 | −0.354921 | ||||||||
\(238\) | −11.0249 | −0.714637 | ||||||||
\(239\) | −15.6831 | −1.01445 | −0.507226 | − | 0.861813i | \(-0.669329\pi\) | ||||
−0.507226 | + | 0.861813i | \(0.669329\pi\) | |||||||
\(240\) | 27.3733 | 1.76694 | ||||||||
\(241\) | 11.6781 | 0.752251 | 0.376126 | − | 0.926569i | \(-0.377256\pi\) | ||||
0.376126 | + | 0.926569i | \(0.377256\pi\) | |||||||
\(242\) | 5.00201 | 0.321541 | ||||||||
\(243\) | −10.0408 | −0.644115 | ||||||||
\(244\) | −2.97369 | −0.190371 | ||||||||
\(245\) | 2.00626 | 0.128175 | ||||||||
\(246\) | −28.2062 | −1.79836 | ||||||||
\(247\) | −1.25285 | −0.0797169 | ||||||||
\(248\) | −15.9910 | −1.01543 | ||||||||
\(249\) | 0.536258 | 0.0339840 | ||||||||
\(250\) | −26.3386 | −1.66580 | ||||||||
\(251\) | 0.195462 | 0.0123374 | 0.00616871 | − | 0.999981i | \(-0.498036\pi\) | ||||
0.00616871 | + | 0.999981i | \(0.498036\pi\) | |||||||
\(252\) | −0.550850 | −0.0347003 | ||||||||
\(253\) | 13.8087 | 0.868146 | ||||||||
\(254\) | 5.60650 | 0.351783 | ||||||||
\(255\) | 25.1848 | 1.57713 | ||||||||
\(256\) | −5.10724 | −0.319202 | ||||||||
\(257\) | −11.6389 | −0.726016 | −0.363008 | − | 0.931786i | \(-0.618250\pi\) | ||||
−0.363008 | + | 0.931786i | \(0.618250\pi\) | |||||||
\(258\) | −13.2139 | −0.822659 | ||||||||
\(259\) | −11.6690 | −0.725079 | ||||||||
\(260\) | −0.836354 | −0.0518685 | ||||||||
\(261\) | −4.70441 | −0.291196 | ||||||||
\(262\) | −15.5613 | −0.961381 | ||||||||
\(263\) | −14.3288 | −0.883554 | −0.441777 | − | 0.897125i | \(-0.645652\pi\) | ||||
−0.441777 | + | 0.897125i | \(0.645652\pi\) | |||||||
\(264\) | 22.7407 | 1.39959 | ||||||||
\(265\) | 15.9988 | 0.982800 | ||||||||
\(266\) | 4.26157 | 0.261294 | ||||||||
\(267\) | 10.1975 | 0.624075 | ||||||||
\(268\) | 1.86050 | 0.113648 | ||||||||
\(269\) | −11.7742 | −0.717885 | −0.358942 | − | 0.933360i | \(-0.616863\pi\) | ||||
−0.358942 | + | 0.933360i | \(0.616863\pi\) | |||||||
\(270\) | 20.7147 | 1.26066 | ||||||||
\(271\) | −20.4986 | −1.24520 | −0.622601 | − | 0.782540i | \(-0.713924\pi\) | ||||
−0.622601 | + | 0.782540i | \(0.713924\pi\) | |||||||
\(272\) | 11.4181 | 0.692326 | ||||||||
\(273\) | −5.09528 | −0.308380 | ||||||||
\(274\) | 25.4076 | 1.53493 | ||||||||
\(275\) | −38.6962 | −2.33347 | ||||||||
\(276\) | 1.55001 | 0.0932995 | ||||||||
\(277\) | −26.1895 | −1.57357 | −0.786787 | − | 0.617225i | \(-0.788257\pi\) | ||||
−0.786787 | + | 0.617225i | \(0.788257\pi\) | |||||||
\(278\) | 11.6797 | 0.700502 | ||||||||
\(279\) | 5.42705 | 0.324909 | ||||||||
\(280\) | 29.2608 | 1.74867 | ||||||||
\(281\) | −18.5939 | −1.10922 | −0.554609 | − | 0.832111i | \(-0.687132\pi\) | ||||
−0.554609 | + | 0.832111i | \(0.687132\pi\) | |||||||
\(282\) | 34.2700 | 2.04075 | ||||||||
\(283\) | −8.26743 | −0.491448 | −0.245724 | − | 0.969340i | \(-0.579026\pi\) | ||||
−0.245724 | + | 0.969340i | \(0.579026\pi\) | |||||||
\(284\) | 2.19114 | 0.130021 | ||||||||
\(285\) | −9.73495 | −0.576649 | ||||||||
\(286\) | 5.12961 | 0.303320 | ||||||||
\(287\) | −26.8659 | −1.58585 | ||||||||
\(288\) | 1.21827 | 0.0717874 | ||||||||
\(289\) | −6.49474 | −0.382044 | ||||||||
\(290\) | 24.2959 | 1.42670 | ||||||||
\(291\) | −2.54807 | −0.149370 | ||||||||
\(292\) | −1.68105 | −0.0983762 | ||||||||
\(293\) | 26.8458 | 1.56835 | 0.784175 | − | 0.620539i | \(-0.213086\pi\) | ||||
0.784175 | + | 0.620539i | \(0.213086\pi\) | |||||||
\(294\) | −1.38122 | −0.0805544 | ||||||||
\(295\) | −40.5721 | −2.36220 | ||||||||
\(296\) | 13.5631 | 0.788338 | ||||||||
\(297\) | 15.3339 | 0.889764 | ||||||||
\(298\) | 27.0914 | 1.56936 | ||||||||
\(299\) | 3.59617 | 0.207972 | ||||||||
\(300\) | −4.34360 | −0.250778 | ||||||||
\(301\) | −12.5860 | −0.725445 | ||||||||
\(302\) | −0.198216 | −0.0114061 | ||||||||
\(303\) | −32.2928 | −1.85517 | ||||||||
\(304\) | −4.41357 | −0.253136 | ||||||||
\(305\) | −53.6090 | −3.06964 | ||||||||
\(306\) | −4.34896 | −0.248614 | ||||||||
\(307\) | −26.9090 | −1.53578 | −0.767890 | − | 0.640582i | \(-0.778693\pi\) | ||||
−0.767890 | + | 0.640582i | \(0.778693\pi\) | |||||||
\(308\) | 2.10589 | 0.119994 | ||||||||
\(309\) | −2.00110 | −0.113839 | ||||||||
\(310\) | −28.0279 | −1.59188 | ||||||||
\(311\) | 9.84348 | 0.558172 | 0.279086 | − | 0.960266i | \(-0.409968\pi\) | ||||
0.279086 | + | 0.960266i | \(0.409968\pi\) | |||||||
\(312\) | 5.92231 | 0.335285 | ||||||||
\(313\) | −3.13291 | −0.177082 | −0.0885412 | − | 0.996073i | \(-0.528220\pi\) | ||||
−0.0885412 | + | 0.996073i | \(0.528220\pi\) | |||||||
\(314\) | −29.8410 | −1.68403 | ||||||||
\(315\) | −9.93059 | −0.559525 | ||||||||
\(316\) | 0.588113 | 0.0330839 | ||||||||
\(317\) | 10.7317 | 0.602754 | 0.301377 | − | 0.953505i | \(-0.402554\pi\) | ||||
0.301377 | + | 0.953505i | \(0.402554\pi\) | |||||||
\(318\) | −11.0145 | −0.617661 | ||||||||
\(319\) | 17.9849 | 1.00696 | ||||||||
\(320\) | −33.6499 | −1.88109 | ||||||||
\(321\) | 15.2012 | 0.848450 | ||||||||
\(322\) | −12.2324 | −0.681684 | ||||||||
\(323\) | −4.06071 | −0.225944 | ||||||||
\(324\) | 2.37023 | 0.131679 | ||||||||
\(325\) | −10.0776 | −0.559003 | ||||||||
\(326\) | −11.3989 | −0.631326 | ||||||||
\(327\) | −18.8691 | −1.04346 | ||||||||
\(328\) | 31.2266 | 1.72420 | ||||||||
\(329\) | 32.6417 | 1.79959 | ||||||||
\(330\) | 39.8583 | 2.19413 | ||||||||
\(331\) | −20.4312 | −1.12300 | −0.561500 | − | 0.827477i | \(-0.689776\pi\) | ||||
−0.561500 | + | 0.827477i | \(0.689776\pi\) | |||||||
\(332\) | −0.0577203 | −0.00316782 | ||||||||
\(333\) | −4.60306 | −0.252246 | ||||||||
\(334\) | −12.7778 | −0.699170 | ||||||||
\(335\) | 33.5406 | 1.83252 | ||||||||
\(336\) | −17.9498 | −0.979241 | ||||||||
\(337\) | 3.58735 | 0.195415 | 0.0977076 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977076 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(338\) | 1.33589 | 0.0726630 | ||||||||
\(339\) | 22.5125 | 1.22271 | ||||||||
\(340\) | −2.71077 | −0.147012 | ||||||||
\(341\) | −20.7475 | −1.12354 | ||||||||
\(342\) | 1.68105 | 0.0909009 | ||||||||
\(343\) | −19.1392 | −1.03342 | ||||||||
\(344\) | 14.6289 | 0.788736 | ||||||||
\(345\) | 27.9432 | 1.50441 | ||||||||
\(346\) | −29.0403 | −1.56122 | ||||||||
\(347\) | 6.87209 | 0.368913 | 0.184457 | − | 0.982841i | \(-0.440947\pi\) | ||||
0.184457 | + | 0.982841i | \(0.440947\pi\) | |||||||
\(348\) | 2.01878 | 0.108218 | ||||||||
\(349\) | 13.8445 | 0.741077 | 0.370538 | − | 0.928817i | \(-0.379173\pi\) | ||||
0.370538 | + | 0.928817i | \(0.379173\pi\) | |||||||
\(350\) | 34.2789 | 1.83228 | ||||||||
\(351\) | 3.99338 | 0.213151 | ||||||||
\(352\) | −4.65743 | −0.248242 | ||||||||
\(353\) | 10.6017 | 0.564272 | 0.282136 | − | 0.959374i | \(-0.408957\pi\) | ||||
0.282136 | + | 0.959374i | \(0.408957\pi\) | |||||||
\(354\) | 27.9320 | 1.48457 | ||||||||
\(355\) | 39.5014 | 2.09652 | ||||||||
\(356\) | −1.09761 | −0.0581731 | ||||||||
\(357\) | −16.5147 | −0.874052 | ||||||||
\(358\) | −31.1370 | −1.64564 | ||||||||
\(359\) | −10.1497 | −0.535682 | −0.267841 | − | 0.963463i | \(-0.586310\pi\) | ||||
−0.267841 | + | 0.963463i | \(0.586310\pi\) | |||||||
\(360\) | 11.5424 | 0.608340 | ||||||||
\(361\) | −17.4304 | −0.917388 | ||||||||
\(362\) | 19.4294 | 1.02118 | ||||||||
\(363\) | 7.49276 | 0.393268 | ||||||||
\(364\) | 0.548432 | 0.0287457 | ||||||||
\(365\) | −30.3056 | −1.58627 | ||||||||
\(366\) | 36.9073 | 1.92918 | ||||||||
\(367\) | −6.00710 | −0.313568 | −0.156784 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156784 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(368\) | 12.6687 | 0.660402 | ||||||||
\(369\) | −10.5978 | −0.551697 | ||||||||
\(370\) | 23.7724 | 1.23587 | ||||||||
\(371\) | −10.4911 | −0.544671 | ||||||||
\(372\) | −2.32888 | −0.120747 | ||||||||
\(373\) | −23.7751 | −1.23103 | −0.615514 | − | 0.788126i | \(-0.711052\pi\) | ||||
−0.615514 | + | 0.788126i | \(0.711052\pi\) | |||||||
\(374\) | 16.6260 | 0.859709 | ||||||||
\(375\) | −39.4540 | −2.03740 | ||||||||
\(376\) | −37.9398 | −1.95660 | ||||||||
\(377\) | 4.68376 | 0.241226 | ||||||||
\(378\) | −13.5835 | −0.698659 | ||||||||
\(379\) | 18.1574 | 0.932683 | 0.466342 | − | 0.884605i | \(-0.345572\pi\) | ||||
0.466342 | + | 0.884605i | \(0.345572\pi\) | |||||||
\(380\) | 1.04783 | 0.0537523 | ||||||||
\(381\) | 8.39826 | 0.430256 | ||||||||
\(382\) | −3.35566 | −0.171690 | ||||||||
\(383\) | −6.12410 | −0.312927 | −0.156463 | − | 0.987684i | \(-0.550009\pi\) | ||||
−0.156463 | + | 0.987684i | \(0.550009\pi\) | |||||||
\(384\) | 18.3121 | 0.934484 | ||||||||
\(385\) | 37.9644 | 1.93485 | ||||||||
\(386\) | 35.5523 | 1.80956 | ||||||||
\(387\) | −4.96477 | −0.252374 | ||||||||
\(388\) | 0.274262 | 0.0139235 | ||||||||
\(389\) | 24.0692 | 1.22036 | 0.610178 | − | 0.792264i | \(-0.291098\pi\) | ||||
0.610178 | + | 0.792264i | \(0.291098\pi\) | |||||||
\(390\) | 10.3802 | 0.525623 | ||||||||
\(391\) | 11.6558 | 0.589462 | ||||||||
\(392\) | 1.52913 | 0.0772326 | ||||||||
\(393\) | −23.3101 | −1.17584 | ||||||||
\(394\) | −0.558395 | −0.0281316 | ||||||||
\(395\) | 10.6023 | 0.533462 | ||||||||
\(396\) | 0.830706 | 0.0417445 | ||||||||
\(397\) | −29.7844 | −1.49484 | −0.747419 | − | 0.664353i | \(-0.768707\pi\) | ||||
−0.747419 | + | 0.664353i | \(0.768707\pi\) | |||||||
\(398\) | −15.3982 | −0.771843 | ||||||||
\(399\) | 6.38362 | 0.319581 | ||||||||
\(400\) | −35.5016 | −1.77508 | ||||||||
\(401\) | −6.86406 | −0.342775 | −0.171387 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171387 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(402\) | −23.0911 | −1.15168 | ||||||||
\(403\) | −5.40323 | −0.269154 | ||||||||
\(404\) | 3.47585 | 0.172930 | ||||||||
\(405\) | 42.7299 | 2.12326 | ||||||||
\(406\) | −15.9318 | −0.790682 | ||||||||
\(407\) | 17.5974 | 0.872271 | ||||||||
\(408\) | 19.1953 | 0.950308 | ||||||||
\(409\) | 35.7409 | 1.76727 | 0.883637 | − | 0.468172i | \(-0.155087\pi\) | ||||
0.883637 | + | 0.468172i | \(0.155087\pi\) | |||||||
\(410\) | 54.7319 | 2.70302 | ||||||||
\(411\) | 38.0594 | 1.87733 | ||||||||
\(412\) | 0.215389 | 0.0106115 | ||||||||
\(413\) | 26.6048 | 1.30914 | ||||||||
\(414\) | −4.82528 | −0.237150 | ||||||||
\(415\) | −1.04057 | −0.0510794 | ||||||||
\(416\) | −1.21292 | −0.0594685 | ||||||||
\(417\) | 17.4956 | 0.856764 | ||||||||
\(418\) | −6.42663 | −0.314337 | ||||||||
\(419\) | 32.7880 | 1.60180 | 0.800898 | − | 0.598800i | \(-0.204356\pi\) | ||||
0.800898 | + | 0.598800i | \(0.204356\pi\) | |||||||
\(420\) | 4.26146 | 0.207938 | ||||||||
\(421\) | −23.7667 | −1.15832 | −0.579158 | − | 0.815215i | \(-0.696619\pi\) | ||||
−0.579158 | + | 0.815215i | \(0.696619\pi\) | |||||||
\(422\) | 14.0034 | 0.681676 | ||||||||
\(423\) | 12.8761 | 0.626057 | ||||||||
\(424\) | 12.1939 | 0.592190 | ||||||||
\(425\) | −32.6632 | −1.58440 | ||||||||
\(426\) | −27.1949 | −1.31760 | ||||||||
\(427\) | 35.1536 | 1.70120 | ||||||||
\(428\) | −1.63619 | −0.0790882 | ||||||||
\(429\) | 7.68390 | 0.370982 | ||||||||
\(430\) | 25.6405 | 1.23649 | ||||||||
\(431\) | 18.1279 | 0.873189 | 0.436594 | − | 0.899658i | \(-0.356184\pi\) | ||||
0.436594 | + | 0.899658i | \(0.356184\pi\) | |||||||
\(432\) | 14.0680 | 0.676847 | ||||||||
\(433\) | −2.72216 | −0.130819 | −0.0654094 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654094 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(434\) | 18.3791 | 0.882225 | ||||||||
\(435\) | 36.3940 | 1.74496 | ||||||||
\(436\) | 2.03098 | 0.0972662 | ||||||||
\(437\) | −4.50546 | −0.215526 | ||||||||
\(438\) | 20.8640 | 0.996921 | ||||||||
\(439\) | −15.2952 | −0.730001 | −0.365001 | − | 0.931007i | \(-0.618931\pi\) | ||||
−0.365001 | + | 0.931007i | \(0.618931\pi\) | |||||||
\(440\) | −44.1265 | −2.10365 | ||||||||
\(441\) | −0.518958 | −0.0247123 | ||||||||
\(442\) | 4.32987 | 0.205951 | ||||||||
\(443\) | 12.6368 | 0.600395 | 0.300197 | − | 0.953877i | \(-0.402947\pi\) | ||||
0.300197 | + | 0.953877i | \(0.402947\pi\) | |||||||
\(444\) | 1.97529 | 0.0937429 | ||||||||
\(445\) | −19.7874 | −0.938013 | ||||||||
\(446\) | −27.7674 | −1.31482 | ||||||||
\(447\) | 40.5816 | 1.91944 | ||||||||
\(448\) | 22.0657 | 1.04250 | ||||||||
\(449\) | 12.4661 | 0.588311 | 0.294155 | − | 0.955758i | \(-0.404962\pi\) | ||||
0.294155 | + | 0.955758i | \(0.404962\pi\) | |||||||
\(450\) | 13.5219 | 0.637429 | ||||||||
\(451\) | 40.5150 | 1.90778 | ||||||||
\(452\) | −2.42315 | −0.113975 | ||||||||
\(453\) | −0.296918 | −0.0139504 | ||||||||
\(454\) | 19.9747 | 0.937460 | ||||||||
\(455\) | 9.88700 | 0.463510 | ||||||||
\(456\) | −7.41976 | −0.347462 | ||||||||
\(457\) | 12.0044 | 0.561544 | 0.280772 | − | 0.959775i | \(-0.409410\pi\) | ||||
0.280772 | + | 0.959775i | \(0.409410\pi\) | |||||||
\(458\) | 2.61129 | 0.122018 | ||||||||
\(459\) | 12.9433 | 0.604140 | ||||||||
\(460\) | −3.00767 | −0.140233 | ||||||||
\(461\) | −6.78252 | −0.315893 | −0.157947 | − | 0.987448i | \(-0.550487\pi\) | ||||
−0.157947 | + | 0.987448i | \(0.550487\pi\) | |||||||
\(462\) | −26.1368 | −1.21599 | ||||||||
\(463\) | 10.3900 | 0.482864 | 0.241432 | − | 0.970418i | \(-0.422383\pi\) | ||||
0.241432 | + | 0.970418i | \(0.422383\pi\) | |||||||
\(464\) | 16.5001 | 0.765997 | ||||||||
\(465\) | −41.9845 | −1.94698 | ||||||||
\(466\) | 20.9102 | 0.968648 | ||||||||
\(467\) | −25.0483 | −1.15910 | −0.579548 | − | 0.814938i | \(-0.696771\pi\) | ||||
−0.579548 | + | 0.814938i | \(0.696771\pi\) | |||||||
\(468\) | 0.216339 | 0.0100003 | ||||||||
\(469\) | −21.9940 | −1.01559 | ||||||||
\(470\) | −66.4984 | −3.06734 | ||||||||
\(471\) | −44.7004 | −2.05969 | ||||||||
\(472\) | −30.9231 | −1.42335 | ||||||||
\(473\) | 18.9802 | 0.872712 | ||||||||
\(474\) | −7.29923 | −0.335265 | ||||||||
\(475\) | 12.6257 | 0.579306 | ||||||||
\(476\) | 1.77757 | 0.0814747 | ||||||||
\(477\) | −4.13840 | −0.189485 | ||||||||
\(478\) | −20.9509 | −0.958272 | ||||||||
\(479\) | 0.623855 | 0.0285046 | 0.0142523 | − | 0.999898i | \(-0.495463\pi\) | ||||
0.0142523 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(480\) | −9.42473 | −0.430178 | ||||||||
\(481\) | 4.58286 | 0.208960 | ||||||||
\(482\) | 15.6007 | 0.710591 | ||||||||
\(483\) | −18.3235 | −0.833748 | ||||||||
\(484\) | −0.806487 | −0.0366585 | ||||||||
\(485\) | 4.94433 | 0.224510 | ||||||||
\(486\) | −13.4134 | −0.608443 | ||||||||
\(487\) | −41.4598 | −1.87872 | −0.939362 | − | 0.342926i | \(-0.888582\pi\) | ||||
−0.939362 | + | 0.342926i | \(0.888582\pi\) | |||||||
\(488\) | −40.8595 | −1.84962 | ||||||||
\(489\) | −17.0750 | −0.772157 | ||||||||
\(490\) | 2.68015 | 0.121077 | ||||||||
\(491\) | 20.8808 | 0.942338 | 0.471169 | − | 0.882043i | \(-0.343832\pi\) | ||||
0.471169 | + | 0.882043i | \(0.343832\pi\) | |||||||
\(492\) | 4.54775 | 0.205029 | ||||||||
\(493\) | 15.1809 | 0.683714 | ||||||||
\(494\) | −1.67367 | −0.0753021 | ||||||||
\(495\) | 14.9757 | 0.673110 | ||||||||
\(496\) | −19.0347 | −0.854682 | ||||||||
\(497\) | −25.9027 | −1.16190 | ||||||||
\(498\) | 0.716383 | 0.0321019 | ||||||||
\(499\) | −3.68923 | −0.165153 | −0.0825764 | − | 0.996585i | \(-0.526315\pi\) | ||||
−0.0825764 | + | 0.996585i | \(0.526315\pi\) | |||||||
\(500\) | 4.24665 | 0.189916 | ||||||||
\(501\) | −19.1405 | −0.855135 | ||||||||
\(502\) | 0.261116 | 0.0116542 | ||||||||
\(503\) | 19.4452 | 0.867021 | 0.433510 | − | 0.901149i | \(-0.357275\pi\) | ||||
0.433510 | + | 0.901149i | \(0.357275\pi\) | |||||||
\(504\) | −7.56887 | −0.337144 | ||||||||
\(505\) | 62.6617 | 2.78841 | ||||||||
\(506\) | 18.4470 | 0.820067 | ||||||||
\(507\) | 2.00110 | 0.0888721 | ||||||||
\(508\) | −0.903950 | −0.0401063 | ||||||||
\(509\) | 8.32849 | 0.369154 | 0.184577 | − | 0.982818i | \(-0.440908\pi\) | ||||
0.184577 | + | 0.982818i | \(0.440908\pi\) | |||||||
\(510\) | 33.6442 | 1.48979 | ||||||||
\(511\) | 19.8726 | 0.879114 | ||||||||
\(512\) | −25.1247 | −1.11037 | ||||||||
\(513\) | −5.00311 | −0.220893 | ||||||||
\(514\) | −15.5484 | −0.685809 | ||||||||
\(515\) | 3.88298 | 0.171105 | ||||||||
\(516\) | 2.13050 | 0.0937903 | ||||||||
\(517\) | −49.2250 | −2.16491 | ||||||||
\(518\) | −15.5886 | −0.684923 | ||||||||
\(519\) | −43.5009 | −1.90948 | ||||||||
\(520\) | −11.4918 | −0.503948 | ||||||||
\(521\) | 8.48817 | 0.371873 | 0.185937 | − | 0.982562i | \(-0.440468\pi\) | ||||
0.185937 | + | 0.982562i | \(0.440468\pi\) | |||||||
\(522\) | −6.28459 | −0.275069 | ||||||||
\(523\) | −25.5800 | −1.11854 | −0.559268 | − | 0.828987i | \(-0.688918\pi\) | ||||
−0.559268 | + | 0.828987i | \(0.688918\pi\) | |||||||
\(524\) | 2.50899 | 0.109606 | ||||||||
\(525\) | 51.3480 | 2.24101 | ||||||||
\(526\) | −19.1418 | −0.834622 | ||||||||
\(527\) | −17.5129 | −0.762872 | ||||||||
\(528\) | 27.0691 | 1.17803 | ||||||||
\(529\) | −10.0675 | −0.437719 | ||||||||
\(530\) | 21.3727 | 0.928372 | ||||||||
\(531\) | 10.4948 | 0.455433 | ||||||||
\(532\) | −0.687103 | −0.0297897 | ||||||||
\(533\) | 10.5512 | 0.457025 | ||||||||
\(534\) | 13.6227 | 0.589513 | ||||||||
\(535\) | −29.4968 | −1.27526 | ||||||||
\(536\) | 25.5639 | 1.10419 | ||||||||
\(537\) | −46.6417 | −2.01274 | ||||||||
\(538\) | −15.7291 | −0.678128 | ||||||||
\(539\) | 1.98397 | 0.0854555 | ||||||||
\(540\) | −3.33988 | −0.143726 | ||||||||
\(541\) | 4.86264 | 0.209061 | 0.104531 | − | 0.994522i | \(-0.466666\pi\) | ||||
0.104531 | + | 0.994522i | \(0.466666\pi\) | |||||||
\(542\) | −27.3839 | −1.17624 | ||||||||
\(543\) | 29.1042 | 1.24898 | ||||||||
\(544\) | −3.93131 | −0.168553 | ||||||||
\(545\) | 36.6139 | 1.56837 | ||||||||
\(546\) | −6.80675 | −0.291302 | ||||||||
\(547\) | 19.6656 | 0.840839 | 0.420419 | − | 0.907330i | \(-0.361883\pi\) | ||||
0.420419 | + | 0.907330i | \(0.361883\pi\) | |||||||
\(548\) | −4.09654 | −0.174995 | ||||||||
\(549\) | 13.8670 | 0.591828 | ||||||||
\(550\) | −51.6940 | −2.20424 | ||||||||
\(551\) | −5.86805 | −0.249987 | ||||||||
\(552\) | 21.2976 | 0.906488 | ||||||||
\(553\) | −6.95240 | −0.295646 | ||||||||
\(554\) | −34.9864 | −1.48643 | ||||||||
\(555\) | 35.6099 | 1.51156 | ||||||||
\(556\) | −1.88315 | −0.0798632 | ||||||||
\(557\) | −42.6016 | −1.80509 | −0.902543 | − | 0.430599i | \(-0.858302\pi\) | ||||
−0.902543 | + | 0.430599i | \(0.858302\pi\) | |||||||
\(558\) | 7.24996 | 0.306915 | ||||||||
\(559\) | 4.94298 | 0.209066 | ||||||||
\(560\) | 34.8302 | 1.47184 | ||||||||
\(561\) | 24.9049 | 1.05149 | ||||||||
\(562\) | −24.8395 | −1.04779 | ||||||||
\(563\) | −3.22868 | −0.136073 | −0.0680364 | − | 0.997683i | \(-0.521673\pi\) | ||||
−0.0680364 | + | 0.997683i | \(0.521673\pi\) | |||||||
\(564\) | −5.52544 | −0.232663 | ||||||||
\(565\) | −43.6838 | −1.83779 | ||||||||
\(566\) | −11.0444 | −0.464231 | ||||||||
\(567\) | −28.0198 | −1.17672 | ||||||||
\(568\) | 30.1071 | 1.26326 | ||||||||
\(569\) | −31.4540 | −1.31862 | −0.659311 | − | 0.751871i | \(-0.729152\pi\) | ||||
−0.659311 | + | 0.751871i | \(0.729152\pi\) | |||||||
\(570\) | −13.0049 | −0.544714 | ||||||||
\(571\) | −3.09352 | −0.129460 | −0.0647299 | − | 0.997903i | \(-0.520619\pi\) | ||||
−0.0647299 | + | 0.997903i | \(0.520619\pi\) | |||||||
\(572\) | −0.827059 | −0.0345811 | ||||||||
\(573\) | −5.02661 | −0.209990 | ||||||||
\(574\) | −35.8900 | −1.49802 | ||||||||
\(575\) | −36.2407 | −1.51134 | ||||||||
\(576\) | 8.70420 | 0.362675 | ||||||||
\(577\) | 5.72858 | 0.238484 | 0.119242 | − | 0.992865i | \(-0.461954\pi\) | ||||
0.119242 | + | 0.992865i | \(0.461954\pi\) | |||||||
\(578\) | −8.67629 | −0.360886 | ||||||||
\(579\) | 53.2556 | 2.21323 | ||||||||
\(580\) | −3.91728 | −0.162656 | ||||||||
\(581\) | 0.682344 | 0.0283084 | ||||||||
\(582\) | −3.40394 | −0.141098 | ||||||||
\(583\) | 15.8210 | 0.655240 | ||||||||
\(584\) | −23.0982 | −0.955812 | ||||||||
\(585\) | 3.90010 | 0.161249 | ||||||||
\(586\) | 35.8632 | 1.48149 | ||||||||
\(587\) | 0.183700 | 0.00758212 | 0.00379106 | − | 0.999993i | \(-0.498793\pi\) | ||||
0.00379106 | + | 0.999993i | \(0.498793\pi\) | |||||||
\(588\) | 0.222698 | 0.00918389 | ||||||||
\(589\) | 6.76944 | 0.278930 | ||||||||
\(590\) | −54.2000 | −2.23138 | ||||||||
\(591\) | −0.836449 | −0.0344069 | ||||||||
\(592\) | 16.1446 | 0.663540 | ||||||||
\(593\) | 30.0876 | 1.23555 | 0.617776 | − | 0.786354i | \(-0.288034\pi\) | ||||
0.617776 | + | 0.786354i | \(0.288034\pi\) | |||||||
\(594\) | 20.4845 | 0.840488 | ||||||||
\(595\) | 32.0455 | 1.31374 | ||||||||
\(596\) | −4.36801 | −0.178921 | ||||||||
\(597\) | −23.0658 | −0.944019 | ||||||||
\(598\) | 4.80410 | 0.196454 | ||||||||
\(599\) | 0.468431 | 0.0191396 | 0.00956979 | − | 0.999954i | \(-0.496954\pi\) | ||||
0.00956979 | + | 0.999954i | \(0.496954\pi\) | |||||||
\(600\) | −59.6825 | −2.43653 | ||||||||
\(601\) | −33.8936 | −1.38255 | −0.691274 | − | 0.722592i | \(-0.742950\pi\) | ||||
−0.691274 | + | 0.722592i | \(0.742950\pi\) | |||||||
\(602\) | −16.8136 | −0.685269 | ||||||||
\(603\) | −8.67591 | −0.353310 | ||||||||
\(604\) | 0.0319589 | 0.00130039 | ||||||||
\(605\) | −14.5391 | −0.591100 | ||||||||
\(606\) | −43.1397 | −1.75243 | ||||||||
\(607\) | −19.8595 | −0.806071 | −0.403036 | − | 0.915184i | \(-0.632045\pi\) | ||||
−0.403036 | + | 0.915184i | \(0.632045\pi\) | |||||||
\(608\) | 1.51961 | 0.0616284 | ||||||||
\(609\) | −23.8651 | −0.967061 | ||||||||
\(610\) | −71.6158 | −2.89964 | ||||||||
\(611\) | −12.8196 | −0.518624 | ||||||||
\(612\) | 0.701194 | 0.0283441 | ||||||||
\(613\) | 29.4113 | 1.18791 | 0.593955 | − | 0.804498i | \(-0.297566\pi\) | ||||
0.593955 | + | 0.804498i | \(0.297566\pi\) | |||||||
\(614\) | −35.9476 | −1.45073 | ||||||||
\(615\) | 81.9857 | 3.30598 | ||||||||
\(616\) | 28.9356 | 1.16585 | ||||||||
\(617\) | 29.9441 | 1.20550 | 0.602751 | − | 0.797929i | \(-0.294071\pi\) | ||||
0.602751 | + | 0.797929i | \(0.294071\pi\) | |||||||
\(618\) | −2.67326 | −0.107534 | ||||||||
\(619\) | −4.61298 | −0.185411 | −0.0927057 | − | 0.995694i | \(-0.529552\pi\) | ||||
−0.0927057 | + | 0.995694i | \(0.529552\pi\) | |||||||
\(620\) | 4.51901 | 0.181488 | ||||||||
\(621\) | 14.3609 | 0.576283 | ||||||||
\(622\) | 13.1498 | 0.527260 | ||||||||
\(623\) | 12.9754 | 0.519850 | ||||||||
\(624\) | 7.04954 | 0.282207 | ||||||||
\(625\) | 26.1696 | 1.04678 | ||||||||
\(626\) | −4.18523 | −0.167275 | ||||||||
\(627\) | −9.62677 | −0.384456 | ||||||||
\(628\) | 4.81135 | 0.191994 | ||||||||
\(629\) | 14.8539 | 0.592263 | ||||||||
\(630\) | −13.2662 | −0.528538 | ||||||||
\(631\) | −6.31019 | −0.251205 | −0.125602 | − | 0.992081i | \(-0.540086\pi\) | ||||
−0.125602 | + | 0.992081i | \(0.540086\pi\) | |||||||
\(632\) | 8.08087 | 0.321440 | ||||||||
\(633\) | 20.9764 | 0.833739 | ||||||||
\(634\) | 14.3365 | 0.569373 | ||||||||
\(635\) | −16.2962 | −0.646694 | ||||||||
\(636\) | 1.77589 | 0.0704186 | ||||||||
\(637\) | 0.516680 | 0.0204716 | ||||||||
\(638\) | 24.0258 | 0.951192 | ||||||||
\(639\) | −10.2178 | −0.404210 | ||||||||
\(640\) | −35.5332 | −1.40457 | ||||||||
\(641\) | 9.92556 | 0.392036 | 0.196018 | − | 0.980600i | \(-0.437199\pi\) | ||||
0.196018 | + | 0.980600i | \(0.437199\pi\) | |||||||
\(642\) | 20.3072 | 0.801462 | ||||||||
\(643\) | 45.4735 | 1.79330 | 0.896650 | − | 0.442741i | \(-0.145994\pi\) | ||||
0.896650 | + | 0.442741i | \(0.145994\pi\) | |||||||
\(644\) | 1.97226 | 0.0777178 | ||||||||
\(645\) | 38.4082 | 1.51232 | ||||||||
\(646\) | −5.42468 | −0.213431 | ||||||||
\(647\) | −13.3073 | −0.523162 | −0.261581 | − | 0.965182i | \(-0.584244\pi\) | ||||
−0.261581 | + | 0.965182i | \(0.584244\pi\) | |||||||
\(648\) | 32.5677 | 1.27938 | ||||||||
\(649\) | −40.1212 | −1.57490 | ||||||||
\(650\) | −13.4626 | −0.528045 | ||||||||
\(651\) | 27.5310 | 1.07902 | ||||||||
\(652\) | 1.83787 | 0.0719766 | ||||||||
\(653\) | −23.6327 | −0.924817 | −0.462409 | − | 0.886667i | \(-0.653015\pi\) | ||||
−0.462409 | + | 0.886667i | \(0.653015\pi\) | |||||||
\(654\) | −25.2070 | −0.985673 | ||||||||
\(655\) | 45.2314 | 1.76734 | ||||||||
\(656\) | 37.1702 | 1.45125 | ||||||||
\(657\) | 7.83912 | 0.305833 | ||||||||
\(658\) | 43.6058 | 1.69993 | ||||||||
\(659\) | −27.6068 | −1.07541 | −0.537704 | − | 0.843134i | \(-0.680708\pi\) | ||||
−0.537704 | + | 0.843134i | \(0.680708\pi\) | |||||||
\(660\) | −6.42646 | −0.250149 | ||||||||
\(661\) | −27.7878 | −1.08082 | −0.540411 | − | 0.841401i | \(-0.681731\pi\) | ||||
−0.540411 | + | 0.841401i | \(0.681731\pi\) | |||||||
\(662\) | −27.2939 | −1.06081 | ||||||||
\(663\) | 6.48593 | 0.251893 | ||||||||
\(664\) | −0.793097 | −0.0307781 | ||||||||
\(665\) | −12.3869 | −0.480344 | ||||||||
\(666\) | −6.14920 | −0.238277 | ||||||||
\(667\) | 16.8436 | 0.652187 | ||||||||
\(668\) | 2.06020 | 0.0797114 | ||||||||
\(669\) | −41.5942 | −1.60812 | ||||||||
\(670\) | 44.8066 | 1.73103 | ||||||||
\(671\) | −53.0132 | −2.04655 | ||||||||
\(672\) | 6.18019 | 0.238406 | ||||||||
\(673\) | 24.1157 | 0.929590 | 0.464795 | − | 0.885418i | \(-0.346128\pi\) | ||||
0.464795 | + | 0.885418i | \(0.346128\pi\) | |||||||
\(674\) | 4.79231 | 0.184593 | ||||||||
\(675\) | −40.2436 | −1.54898 | ||||||||
\(676\) | −0.215389 | −0.00828421 | ||||||||
\(677\) | −10.4256 | −0.400687 | −0.200343 | − | 0.979726i | \(-0.564206\pi\) | ||||
−0.200343 | + | 0.979726i | \(0.564206\pi\) | |||||||
\(678\) | 30.0743 | 1.15500 | ||||||||
\(679\) | −3.24220 | −0.124424 | ||||||||
\(680\) | −37.2470 | −1.42836 | ||||||||
\(681\) | 29.9211 | 1.14658 | ||||||||
\(682\) | −27.7165 | −1.06132 | ||||||||
\(683\) | −0.771045 | −0.0295032 | −0.0147516 | − | 0.999891i | \(-0.504696\pi\) | ||||
−0.0147516 | + | 0.999891i | \(0.504696\pi\) | |||||||
\(684\) | −0.271040 | −0.0103635 | ||||||||
\(685\) | −73.8513 | −2.82171 | ||||||||
\(686\) | −25.5680 | −0.976190 | ||||||||
\(687\) | 3.91159 | 0.149236 | ||||||||
\(688\) | 17.4133 | 0.663875 | ||||||||
\(689\) | 4.12024 | 0.156969 | ||||||||
\(690\) | 37.3291 | 1.42109 | ||||||||
\(691\) | −44.3328 | −1.68650 | −0.843249 | − | 0.537524i | \(-0.819360\pi\) | ||||
−0.843249 | + | 0.537524i | \(0.819360\pi\) | |||||||
\(692\) | 4.68224 | 0.177992 | ||||||||
\(693\) | −9.82023 | −0.373040 | ||||||||
\(694\) | 9.18038 | 0.348483 | ||||||||
\(695\) | −33.9489 | −1.28775 | ||||||||
\(696\) | 27.7387 | 1.05143 | ||||||||
\(697\) | 34.1985 | 1.29536 | ||||||||
\(698\) | 18.4947 | 0.700035 | ||||||||
\(699\) | 31.3225 | 1.18473 | ||||||||
\(700\) | −5.52687 | −0.208896 | ||||||||
\(701\) | −20.4429 | −0.772118 | −0.386059 | − | 0.922474i | \(-0.626164\pi\) | ||||
−0.386059 | + | 0.922474i | \(0.626164\pi\) | |||||||
\(702\) | 5.33473 | 0.201346 | ||||||||
\(703\) | −5.74163 | −0.216550 | ||||||||
\(704\) | −33.2760 | −1.25414 | ||||||||
\(705\) | −99.6113 | −3.75158 | ||||||||
\(706\) | 14.1628 | 0.533022 | ||||||||
\(707\) | −41.0899 | −1.54534 | ||||||||
\(708\) | −4.50355 | −0.169254 | ||||||||
\(709\) | 22.3465 | 0.839242 | 0.419621 | − | 0.907699i | \(-0.362163\pi\) | ||||
0.419621 | + | 0.907699i | \(0.362163\pi\) | |||||||
\(710\) | 52.7696 | 1.98041 | ||||||||
\(711\) | −2.74250 | −0.102852 | ||||||||
\(712\) | −15.0815 | −0.565204 | ||||||||
\(713\) | −19.4310 | −0.727695 | ||||||||
\(714\) | −22.0619 | −0.825646 | ||||||||
\(715\) | −14.9100 | −0.557603 | ||||||||
\(716\) | 5.02029 | 0.187617 | ||||||||
\(717\) | −31.3834 | −1.17203 | ||||||||
\(718\) | −13.5589 | −0.506015 | ||||||||
\(719\) | 41.8009 | 1.55891 | 0.779455 | − | 0.626458i | \(-0.215496\pi\) | ||||
0.779455 | + | 0.626458i | \(0.215496\pi\) | |||||||
\(720\) | 13.7394 | 0.512037 | ||||||||
\(721\) | −2.54624 | −0.0948268 | ||||||||
\(722\) | −23.2851 | −0.866582 | ||||||||
\(723\) | 23.3690 | 0.869104 | ||||||||
\(724\) | −3.13265 | −0.116424 | ||||||||
\(725\) | −47.2009 | −1.75300 | ||||||||
\(726\) | 10.0095 | 0.371488 | ||||||||
\(727\) | 40.3623 | 1.49696 | 0.748478 | − | 0.663160i | \(-0.230785\pi\) | ||||
0.748478 | + | 0.663160i | \(0.230785\pi\) | |||||||
\(728\) | 7.53565 | 0.279290 | ||||||||
\(729\) | 12.9206 | 0.478540 | ||||||||
\(730\) | −40.4850 | −1.49842 | ||||||||
\(731\) | 16.0211 | 0.592562 | ||||||||
\(732\) | −5.95066 | −0.219943 | ||||||||
\(733\) | −19.5235 | −0.721116 | −0.360558 | − | 0.932737i | \(-0.617414\pi\) | ||||
−0.360558 | + | 0.932737i | \(0.617414\pi\) | |||||||
\(734\) | −8.02485 | −0.296203 | ||||||||
\(735\) | 4.01473 | 0.148086 | ||||||||
\(736\) | −4.36189 | −0.160781 | ||||||||
\(737\) | 33.1678 | 1.22175 | ||||||||
\(738\) | −14.1575 | −0.521143 | ||||||||
\(739\) | 34.2846 | 1.26118 | 0.630590 | − | 0.776116i | \(-0.282813\pi\) | ||||
0.630590 | + | 0.776116i | \(0.282813\pi\) | |||||||
\(740\) | −3.83289 | −0.140900 | ||||||||
\(741\) | −2.50708 | −0.0920999 | ||||||||
\(742\) | −14.0150 | −0.514507 | ||||||||
\(743\) | 9.36580 | 0.343598 | 0.171799 | − | 0.985132i | \(-0.445042\pi\) | ||||
0.171799 | + | 0.985132i | \(0.445042\pi\) | |||||||
\(744\) | −31.9996 | −1.17316 | ||||||||
\(745\) | −78.7454 | −2.88501 | ||||||||
\(746\) | −31.7610 | −1.16285 | ||||||||
\(747\) | 0.269163 | 0.00984815 | ||||||||
\(748\) | −2.68065 | −0.0980142 | ||||||||
\(749\) | 19.3423 | 0.706752 | ||||||||
\(750\) | −52.7063 | −1.92456 | ||||||||
\(751\) | 15.9871 | 0.583376 | 0.291688 | − | 0.956513i | \(-0.405783\pi\) | ||||
0.291688 | + | 0.956513i | \(0.405783\pi\) | |||||||
\(752\) | −45.1612 | −1.64686 | ||||||||
\(753\) | 0.391138 | 0.0142539 | ||||||||
\(754\) | 6.25700 | 0.227867 | ||||||||
\(755\) | 0.576147 | 0.0209681 | ||||||||
\(756\) | 2.19010 | 0.0796532 | ||||||||
\(757\) | −14.7652 | −0.536649 | −0.268325 | − | 0.963329i | \(-0.586470\pi\) | ||||
−0.268325 | + | 0.963329i | \(0.586470\pi\) | |||||||
\(758\) | 24.2564 | 0.881031 | ||||||||
\(759\) | 27.6326 | 1.00300 | ||||||||
\(760\) | 14.3975 | 0.522252 | ||||||||
\(761\) | −24.5755 | −0.890863 | −0.445431 | − | 0.895316i | \(-0.646950\pi\) | ||||
−0.445431 | + | 0.895316i | \(0.646950\pi\) | |||||||
\(762\) | 11.2192 | 0.406428 | ||||||||
\(763\) | −24.0093 | −0.869195 | ||||||||
\(764\) | 0.541041 | 0.0195742 | ||||||||
\(765\) | 12.6409 | 0.457034 | ||||||||
\(766\) | −8.18114 | −0.295597 | ||||||||
\(767\) | −10.4487 | −0.377280 | ||||||||
\(768\) | −10.2201 | −0.368786 | ||||||||
\(769\) | −0.956052 | −0.0344761 | −0.0172381 | − | 0.999851i | \(-0.505487\pi\) | ||||
−0.0172381 | + | 0.999851i | \(0.505487\pi\) | |||||||
\(770\) | 50.7164 | 1.82769 | ||||||||
\(771\) | −23.2907 | −0.838793 | ||||||||
\(772\) | −5.73219 | −0.206306 | ||||||||
\(773\) | −24.2225 | −0.871222 | −0.435611 | − | 0.900135i | \(-0.643468\pi\) | ||||
−0.435611 | + | 0.900135i | \(0.643468\pi\) | |||||||
\(774\) | −6.63241 | −0.238397 | ||||||||
\(775\) | 54.4515 | 1.95595 | ||||||||
\(776\) | 3.76845 | 0.135280 | ||||||||
\(777\) | −23.3509 | −0.837710 | ||||||||
\(778\) | 32.1539 | 1.15277 | ||||||||
\(779\) | −13.2191 | −0.473624 | ||||||||
\(780\) | −1.67363 | −0.0599255 | ||||||||
\(781\) | 39.0624 | 1.39776 | ||||||||
\(782\) | 15.5710 | 0.556817 | ||||||||
\(783\) | 18.7040 | 0.668428 | ||||||||
\(784\) | 1.82018 | 0.0650063 | ||||||||
\(785\) | 86.7377 | 3.09580 | ||||||||
\(786\) | −31.1398 | −1.11072 | ||||||||
\(787\) | −22.7568 | −0.811194 | −0.405597 | − | 0.914052i | \(-0.632936\pi\) | ||||
−0.405597 | + | 0.914052i | \(0.632936\pi\) | |||||||
\(788\) | 0.0900315 | 0.00320724 | ||||||||
\(789\) | −28.6735 | −1.02080 | ||||||||
\(790\) | 14.1636 | 0.503918 | ||||||||
\(791\) | 28.6453 | 1.01851 | ||||||||
\(792\) | 11.4142 | 0.405585 | ||||||||
\(793\) | −13.8061 | −0.490270 | ||||||||
\(794\) | −39.7888 | −1.41205 | ||||||||
\(795\) | 32.0153 | 1.13547 | ||||||||
\(796\) | 2.48269 | 0.0879967 | ||||||||
\(797\) | −19.0731 | −0.675605 | −0.337803 | − | 0.941217i | \(-0.609684\pi\) | ||||
−0.337803 | + | 0.941217i | \(0.609684\pi\) | |||||||
\(798\) | 8.52783 | 0.301882 | ||||||||
\(799\) | −41.5506 | −1.46995 | ||||||||
\(800\) | 12.2233 | 0.432160 | ||||||||
\(801\) | 5.11839 | 0.180849 | ||||||||
\(802\) | −9.16966 | −0.323792 | ||||||||
\(803\) | −29.9688 | −1.05758 | ||||||||
\(804\) | 3.72304 | 0.131302 | ||||||||
\(805\) | 35.5553 | 1.25316 | ||||||||
\(806\) | −7.21814 | −0.254248 | ||||||||
\(807\) | −23.5613 | −0.829399 | ||||||||
\(808\) | 47.7593 | 1.68017 | ||||||||
\(809\) | 11.3422 | 0.398771 | 0.199386 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199386 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(810\) | 57.0826 | 2.00568 | ||||||||
\(811\) | −13.3127 | −0.467473 | −0.233736 | − | 0.972300i | \(-0.575095\pi\) | ||||
−0.233736 | + | 0.972300i | \(0.575095\pi\) | |||||||
\(812\) | 2.56873 | 0.0901446 | ||||||||
\(813\) | −41.0198 | −1.43863 | ||||||||
\(814\) | 23.5083 | 0.823964 | ||||||||
\(815\) | 33.1327 | 1.16059 | ||||||||
\(816\) | 22.8488 | 0.799869 | ||||||||
\(817\) | −6.19281 | −0.216659 | ||||||||
\(818\) | 47.7461 | 1.66940 | ||||||||
\(819\) | −2.55746 | −0.0893649 | ||||||||
\(820\) | −8.82457 | −0.308167 | ||||||||
\(821\) | 30.0747 | 1.04961 | 0.524806 | − | 0.851222i | \(-0.324138\pi\) | ||||
0.524806 | + | 0.851222i | \(0.324138\pi\) | |||||||
\(822\) | 50.8433 | 1.77336 | ||||||||
\(823\) | −16.0204 | −0.558435 | −0.279217 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279217 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(824\) | 2.95952 | 0.103100 | ||||||||
\(825\) | −77.4350 | −2.69594 | ||||||||
\(826\) | 35.5412 | 1.23664 | ||||||||
\(827\) | −20.0489 | −0.697168 | −0.348584 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348584 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(828\) | 0.777992 | 0.0270371 | ||||||||
\(829\) | 40.3768 | 1.40235 | 0.701173 | − | 0.712991i | \(-0.252660\pi\) | ||||
0.701173 | + | 0.712991i | \(0.252660\pi\) | |||||||
\(830\) | −1.39009 | −0.0482506 | ||||||||
\(831\) | −52.4078 | −1.81801 | ||||||||
\(832\) | −8.66599 | −0.300439 | ||||||||
\(833\) | 1.67465 | 0.0580233 | ||||||||
\(834\) | 23.3723 | 0.809315 | ||||||||
\(835\) | 37.1407 | 1.28531 | ||||||||
\(836\) | 1.03618 | 0.0358371 | ||||||||
\(837\) | −21.5772 | −0.745816 | ||||||||
\(838\) | 43.8012 | 1.51309 | ||||||||
\(839\) | 26.9258 | 0.929583 | 0.464791 | − | 0.885420i | \(-0.346129\pi\) | ||||
0.464791 | + | 0.885420i | \(0.346129\pi\) | |||||||
\(840\) | 58.5538 | 2.02030 | ||||||||
\(841\) | −7.06239 | −0.243531 | ||||||||
\(842\) | −31.7497 | −1.09417 | ||||||||
\(843\) | −37.2083 | −1.28152 | ||||||||
\(844\) | −2.25781 | −0.0777169 | ||||||||
\(845\) | −3.88298 | −0.133579 | ||||||||
\(846\) | 17.2011 | 0.591385 | ||||||||
\(847\) | 9.53392 | 0.327589 | ||||||||
\(848\) | 14.5149 | 0.498444 | ||||||||
\(849\) | −16.5440 | −0.567788 | ||||||||
\(850\) | −43.6346 | −1.49665 | ||||||||
\(851\) | 16.4807 | 0.564953 | ||||||||
\(852\) | 4.38470 | 0.150217 | ||||||||
\(853\) | 22.6905 | 0.776907 | 0.388454 | − | 0.921468i | \(-0.373009\pi\) | ||||
0.388454 | + | 0.921468i | \(0.373009\pi\) | |||||||
\(854\) | 46.9615 | 1.60699 | ||||||||
\(855\) | −4.88624 | −0.167106 | ||||||||
\(856\) | −22.4818 | −0.768412 | ||||||||
\(857\) | 20.9947 | 0.717166 | 0.358583 | − | 0.933498i | \(-0.383260\pi\) | ||||
0.358583 | + | 0.933498i | \(0.383260\pi\) | |||||||
\(858\) | 10.2649 | 0.350437 | ||||||||
\(859\) | −2.64911 | −0.0903863 | −0.0451932 | − | 0.998978i | \(-0.514390\pi\) | ||||
−0.0451932 | + | 0.998978i | \(0.514390\pi\) | |||||||
\(860\) | −4.13408 | −0.140971 | ||||||||
\(861\) | −53.7615 | −1.83219 | ||||||||
\(862\) | 24.2169 | 0.824831 | ||||||||
\(863\) | −25.4518 | −0.866389 | −0.433195 | − | 0.901300i | \(-0.642614\pi\) | ||||
−0.433195 | + | 0.901300i | \(0.642614\pi\) | |||||||
\(864\) | −4.84367 | −0.164785 | ||||||||
\(865\) | 84.4102 | 2.87003 | ||||||||
\(866\) | −3.63652 | −0.123574 | ||||||||
\(867\) | −12.9966 | −0.441389 | ||||||||
\(868\) | −2.96331 | −0.100581 | ||||||||
\(869\) | 10.4845 | 0.355663 | ||||||||
\(870\) | 48.6185 | 1.64832 | ||||||||
\(871\) | 8.63783 | 0.292682 | ||||||||
\(872\) | 27.9063 | 0.945027 | ||||||||
\(873\) | −1.27894 | −0.0432857 | ||||||||
\(874\) | −6.01882 | −0.203590 | ||||||||
\(875\) | −50.2019 | −1.69714 | ||||||||
\(876\) | −3.36396 | −0.113658 | ||||||||
\(877\) | 17.2113 | 0.581185 | 0.290593 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290593 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(878\) | −20.4328 | −0.689573 | ||||||||
\(879\) | 53.7213 | 1.81197 | ||||||||
\(880\) | −52.5254 | −1.77063 | ||||||||
\(881\) | 52.0996 | 1.75528 | 0.877640 | − | 0.479320i | \(-0.159117\pi\) | ||||
0.877640 | + | 0.479320i | \(0.159117\pi\) | |||||||
\(882\) | −0.693273 | −0.0233437 | ||||||||
\(883\) | 10.1507 | 0.341597 | 0.170799 | − | 0.985306i | \(-0.445365\pi\) | ||||
0.170799 | + | 0.985306i | \(0.445365\pi\) | |||||||
\(884\) | −0.698116 | −0.0234802 | ||||||||
\(885\) | −81.1889 | −2.72913 | ||||||||
\(886\) | 16.8815 | 0.567144 | ||||||||
\(887\) | 7.68887 | 0.258167 | 0.129083 | − | 0.991634i | \(-0.458796\pi\) | ||||
0.129083 | + | 0.991634i | \(0.458796\pi\) | |||||||
\(888\) | 27.1411 | 0.910795 | ||||||||
\(889\) | 10.6861 | 0.358400 | ||||||||
\(890\) | −26.4339 | −0.886065 | ||||||||
\(891\) | 42.2550 | 1.41560 | ||||||||
\(892\) | 4.47700 | 0.149901 | ||||||||
\(893\) | 16.0610 | 0.537461 | ||||||||
\(894\) | 54.2126 | 1.81314 | ||||||||
\(895\) | 90.5046 | 3.02523 | ||||||||
\(896\) | 23.3006 | 0.778418 | ||||||||
\(897\) | 7.19631 | 0.240278 | ||||||||
\(898\) | 16.6534 | 0.555730 | ||||||||
\(899\) | −25.3075 | −0.844051 | ||||||||
\(900\) | −2.18017 | −0.0726724 | ||||||||
\(901\) | 13.3544 | 0.444901 | ||||||||
\(902\) | 54.1237 | 1.80212 | ||||||||
\(903\) | −25.1859 | −0.838133 | ||||||||
\(904\) | −33.2948 | −1.10737 | ||||||||
\(905\) | −56.4745 | −1.87728 | ||||||||
\(906\) | −0.396651 | −0.0131778 | ||||||||
\(907\) | 27.7770 | 0.922321 | 0.461161 | − | 0.887317i | \(-0.347433\pi\) | ||||
0.461161 | + | 0.887317i | \(0.347433\pi\) | |||||||
\(908\) | −3.22057 | −0.106878 | ||||||||
\(909\) | −16.2086 | −0.537607 | ||||||||
\(910\) | 13.2080 | 0.437840 | ||||||||
\(911\) | 32.9841 | 1.09281 | 0.546406 | − | 0.837521i | \(-0.315996\pi\) | ||||
0.546406 | + | 0.837521i | \(0.315996\pi\) | |||||||
\(912\) | −8.83201 | −0.292457 | ||||||||
\(913\) | −1.02900 | −0.0340550 | ||||||||
\(914\) | 16.0366 | 0.530445 | ||||||||
\(915\) | −107.277 | −3.54647 | ||||||||
\(916\) | −0.421026 | −0.0139111 | ||||||||
\(917\) | −29.6601 | −0.979464 | ||||||||
\(918\) | 17.2908 | 0.570682 | ||||||||
\(919\) | 30.5665 | 1.00830 | 0.504149 | − | 0.863617i | \(-0.331806\pi\) | ||||
0.504149 | + | 0.863617i | \(0.331806\pi\) | |||||||
\(920\) | −41.3264 | −1.36249 | ||||||||
\(921\) | −53.8477 | −1.77434 | ||||||||
\(922\) | −9.06072 | −0.298399 | ||||||||
\(923\) | 10.1729 | 0.334847 | ||||||||
\(924\) | 4.21410 | 0.138634 | ||||||||
\(925\) | −46.1841 | −1.51852 | ||||||||
\(926\) | 13.8799 | 0.456123 | ||||||||
\(927\) | −1.00441 | −0.0329891 | ||||||||
\(928\) | −5.68105 | −0.186490 | ||||||||
\(929\) | −2.83980 | −0.0931709 | −0.0465855 | − | 0.998914i | \(-0.514834\pi\) | ||||
−0.0465855 | + | 0.998914i | \(0.514834\pi\) | |||||||
\(930\) | −56.0868 | −1.83916 | ||||||||
\(931\) | −0.647323 | −0.0212151 | ||||||||
\(932\) | −3.37141 | −0.110434 | ||||||||
\(933\) | 19.6978 | 0.644877 | ||||||||
\(934\) | −33.4618 | −1.09490 | ||||||||
\(935\) | −48.3261 | −1.58043 | ||||||||
\(936\) | 2.97257 | 0.0971615 | ||||||||
\(937\) | −23.1964 | −0.757793 | −0.378897 | − | 0.925439i | \(-0.623696\pi\) | ||||
−0.378897 | + | 0.925439i | \(0.623696\pi\) | |||||||
\(938\) | −29.3816 | −0.959342 | ||||||||
\(939\) | −6.26927 | −0.204590 | ||||||||
\(940\) | 10.7217 | 0.349703 | ||||||||
\(941\) | 19.1725 | 0.625004 | 0.312502 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312502 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(942\) | −59.7150 | −1.94562 | ||||||||
\(943\) | 37.9441 | 1.23563 | ||||||||
\(944\) | −36.8089 | −1.19803 | ||||||||
\(945\) | 39.4826 | 1.28437 | ||||||||
\(946\) | 25.3556 | 0.824380 | ||||||||
\(947\) | −56.6997 | −1.84249 | −0.921246 | − | 0.388980i | \(-0.872827\pi\) | ||||
−0.921246 | + | 0.388980i | \(0.872827\pi\) | |||||||
\(948\) | 1.17687 | 0.0382231 | ||||||||
\(949\) | −7.80471 | −0.253352 | ||||||||
\(950\) | 16.8666 | 0.547224 | ||||||||
\(951\) | 21.4753 | 0.696384 | ||||||||
\(952\) | 24.4244 | 0.791599 | ||||||||
\(953\) | −49.2055 | −1.59392 | −0.796961 | − | 0.604031i | \(-0.793560\pi\) | ||||
−0.796961 | + | 0.604031i | \(0.793560\pi\) | |||||||
\(954\) | −5.52847 | −0.178991 | ||||||||
\(955\) | 9.75375 | 0.315624 | ||||||||
\(956\) | 3.37797 | 0.109251 | ||||||||
\(957\) | 35.9895 | 1.16338 | ||||||||
\(958\) | 0.833403 | 0.0269260 | ||||||||
\(959\) | 48.4274 | 1.56380 | ||||||||
\(960\) | −67.3369 | −2.17329 | ||||||||
\(961\) | −1.80507 | −0.0582281 | ||||||||
\(962\) | 6.12221 | 0.197388 | ||||||||
\(963\) | 7.62992 | 0.245871 | ||||||||
\(964\) | −2.51534 | −0.0810135 | ||||||||
\(965\) | −103.338 | −3.32658 | ||||||||
\(966\) | −24.4782 | −0.787574 | ||||||||
\(967\) | 24.6168 | 0.791621 | 0.395811 | − | 0.918332i | \(-0.370464\pi\) | ||||
0.395811 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(968\) | −11.0814 | −0.356170 | ||||||||
\(969\) | −8.12590 | −0.261042 | ||||||||
\(970\) | 6.60509 | 0.212077 | ||||||||
\(971\) | −43.5571 | −1.39781 | −0.698906 | − | 0.715213i | \(-0.746330\pi\) | ||||
−0.698906 | + | 0.715213i | \(0.746330\pi\) | |||||||
\(972\) | 2.16267 | 0.0693678 | ||||||||
\(973\) | 22.2617 | 0.713678 | ||||||||
\(974\) | −55.3859 | −1.77468 | ||||||||
\(975\) | −20.1662 | −0.645837 | ||||||||
\(976\) | −48.6366 | −1.55682 | ||||||||
\(977\) | 28.7155 | 0.918691 | 0.459346 | − | 0.888258i | \(-0.348084\pi\) | ||||
0.459346 | + | 0.888258i | \(0.348084\pi\) | |||||||
\(978\) | −22.8103 | −0.729394 | ||||||||
\(979\) | −19.5675 | −0.625380 | ||||||||
\(980\) | −0.432128 | −0.0138038 | ||||||||
\(981\) | −9.47090 | −0.302383 | ||||||||
\(982\) | 27.8945 | 0.890151 | ||||||||
\(983\) | −11.7717 | −0.375459 | −0.187730 | − | 0.982221i | \(-0.560113\pi\) | ||||
−0.187730 | + | 0.982221i | \(0.560113\pi\) | |||||||
\(984\) | 62.4877 | 1.99203 | ||||||||
\(985\) | 1.62306 | 0.0517151 | ||||||||
\(986\) | 20.2801 | 0.645849 | ||||||||
\(987\) | 65.3193 | 2.07914 | ||||||||
\(988\) | 0.269851 | 0.00858509 | ||||||||
\(989\) | 17.7758 | 0.565238 | ||||||||
\(990\) | 20.0060 | 0.635832 | ||||||||
\(991\) | 34.6827 | 1.10173 | 0.550866 | − | 0.834594i | \(-0.314298\pi\) | ||||
0.550866 | + | 0.834594i | \(0.314298\pi\) | |||||||
\(992\) | 6.55371 | 0.208081 | ||||||||
\(993\) | −40.8849 | −1.29744 | ||||||||
\(994\) | −34.6033 | −1.09755 | ||||||||
\(995\) | 44.7573 | 1.41890 | ||||||||
\(996\) | −0.115504 | −0.00365989 | ||||||||
\(997\) | 0.688779 | 0.0218138 | 0.0109069 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109069 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(998\) | −4.92842 | −0.156006 | ||||||||
\(999\) | 18.3011 | 0.579021 |
(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 | 1339.2.a.e.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.e.1.15 | ✓ | 21 | 1.1 | even | 1 | trivial |