Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0717307 | −0.0507213 | −0.0253606 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253606 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99485 | −0.997427 | ||||||||
\(5\) | −1.92367 | −0.860293 | −0.430147 | − | 0.902759i | \(-0.641538\pi\) | ||||
−0.430147 | + | 0.902759i | \(0.641538\pi\) | |||||||
\(6\) | 0.0717307 | 0.0292839 | ||||||||
\(7\) | 3.89464 | 1.47204 | 0.736019 | − | 0.676961i | \(-0.236704\pi\) | ||||
0.736019 | + | 0.676961i | \(0.236704\pi\) | |||||||
\(8\) | 0.286554 | 0.101312 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.137987 | 0.0436352 | ||||||||
\(11\) | 0.330322 | 0.0995960 | 0.0497980 | − | 0.998759i | \(-0.484142\pi\) | ||||
0.0497980 | + | 0.998759i | \(0.484142\pi\) | |||||||
\(12\) | 1.99485 | 0.575865 | ||||||||
\(13\) | 1.95585 | 0.542454 | 0.271227 | − | 0.962515i | \(-0.412571\pi\) | ||||
0.271227 | + | 0.962515i | \(0.412571\pi\) | |||||||
\(14\) | −0.279365 | −0.0746636 | ||||||||
\(15\) | 1.92367 | 0.496691 | ||||||||
\(16\) | 3.96915 | 0.992289 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.0717307 | −0.0169071 | ||||||||
\(19\) | 7.45825 | 1.71104 | 0.855520 | − | 0.517770i | \(-0.173238\pi\) | ||||
0.855520 | + | 0.517770i | \(0.173238\pi\) | |||||||
\(20\) | 3.83745 | 0.858080 | ||||||||
\(21\) | −3.89464 | −0.849881 | ||||||||
\(22\) | −0.0236943 | −0.00505163 | ||||||||
\(23\) | −0.344499 | −0.0718330 | −0.0359165 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359165 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(24\) | −0.286554 | −0.0584925 | ||||||||
\(25\) | −1.29948 | −0.259895 | ||||||||
\(26\) | −0.140294 | −0.0275140 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −7.76925 | −1.46825 | ||||||||
\(29\) | −3.99093 | −0.741096 | −0.370548 | − | 0.928813i | \(-0.620830\pi\) | ||||
−0.370548 | + | 0.928813i | \(0.620830\pi\) | |||||||
\(30\) | −0.137987 | −0.0251928 | ||||||||
\(31\) | 6.60369 | 1.18606 | 0.593029 | − | 0.805181i | \(-0.297932\pi\) | ||||
0.593029 | + | 0.805181i | \(0.297932\pi\) | |||||||
\(32\) | −0.857818 | −0.151642 | ||||||||
\(33\) | −0.330322 | −0.0575018 | ||||||||
\(34\) | 0.0717307 | 0.0123017 | ||||||||
\(35\) | −7.49203 | −1.26638 | ||||||||
\(36\) | −1.99485 | −0.332476 | ||||||||
\(37\) | −0.669431 | −0.110054 | −0.0550269 | − | 0.998485i | \(-0.517524\pi\) | ||||
−0.0550269 | + | 0.998485i | \(0.517524\pi\) | |||||||
\(38\) | −0.534985 | −0.0867861 | ||||||||
\(39\) | −1.95585 | −0.313186 | ||||||||
\(40\) | −0.551236 | −0.0871581 | ||||||||
\(41\) | −3.05035 | −0.476385 | −0.238192 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238192 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(42\) | 0.279365 | 0.0431070 | ||||||||
\(43\) | 4.13678 | 0.630854 | 0.315427 | − | 0.948950i | \(-0.397852\pi\) | ||||
0.315427 | + | 0.948950i | \(0.397852\pi\) | |||||||
\(44\) | −0.658945 | −0.0993397 | ||||||||
\(45\) | −1.92367 | −0.286764 | ||||||||
\(46\) | 0.0247111 | 0.00364346 | ||||||||
\(47\) | 3.35605 | 0.489530 | 0.244765 | − | 0.969582i | \(-0.421289\pi\) | ||||
0.244765 | + | 0.969582i | \(0.421289\pi\) | |||||||
\(48\) | −3.96915 | −0.572898 | ||||||||
\(49\) | 8.16825 | 1.16689 | ||||||||
\(50\) | 0.0932123 | 0.0131822 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.90163 | −0.541059 | ||||||||
\(53\) | 10.2366 | 1.40611 | 0.703053 | − | 0.711137i | \(-0.251820\pi\) | ||||
0.703053 | + | 0.711137i | \(0.251820\pi\) | |||||||
\(54\) | 0.0717307 | 0.00976131 | ||||||||
\(55\) | −0.635433 | −0.0856818 | ||||||||
\(56\) | 1.11602 | 0.149135 | ||||||||
\(57\) | −7.45825 | −0.987869 | ||||||||
\(58\) | 0.286272 | 0.0375893 | ||||||||
\(59\) | −14.3338 | −1.86610 | −0.933051 | − | 0.359743i | \(-0.882864\pi\) | ||||
−0.933051 | + | 0.359743i | \(0.882864\pi\) | |||||||
\(60\) | −3.83745 | −0.495413 | ||||||||
\(61\) | 9.85944 | 1.26237 | 0.631186 | − | 0.775632i | \(-0.282569\pi\) | ||||
0.631186 | + | 0.775632i | \(0.282569\pi\) | |||||||
\(62\) | −0.473687 | −0.0601584 | ||||||||
\(63\) | 3.89464 | 0.490679 | ||||||||
\(64\) | −7.87678 | −0.984597 | ||||||||
\(65\) | −3.76241 | −0.466670 | ||||||||
\(66\) | 0.0236943 | 0.00291656 | ||||||||
\(67\) | −7.02759 | −0.858556 | −0.429278 | − | 0.903172i | \(-0.641232\pi\) | ||||
−0.429278 | + | 0.903172i | \(0.641232\pi\) | |||||||
\(68\) | 1.99485 | 0.241912 | ||||||||
\(69\) | 0.344499 | 0.0414728 | ||||||||
\(70\) | 0.537408 | 0.0642326 | ||||||||
\(71\) | −12.3550 | −1.46627 | −0.733137 | − | 0.680081i | \(-0.761944\pi\) | ||||
−0.733137 | + | 0.680081i | \(0.761944\pi\) | |||||||
\(72\) | 0.286554 | 0.0337707 | ||||||||
\(73\) | −13.8133 | −1.61673 | −0.808364 | − | 0.588682i | \(-0.799647\pi\) | ||||
−0.808364 | + | 0.588682i | \(0.799647\pi\) | |||||||
\(74\) | 0.0480187 | 0.00558206 | ||||||||
\(75\) | 1.29948 | 0.150051 | ||||||||
\(76\) | −14.8781 | −1.70664 | ||||||||
\(77\) | 1.28649 | 0.146609 | ||||||||
\(78\) | 0.140294 | 0.0158852 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −7.63536 | −0.853660 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.218804 | 0.0241628 | ||||||||
\(83\) | −13.5470 | −1.48697 | −0.743486 | − | 0.668751i | \(-0.766829\pi\) | ||||
−0.743486 | + | 0.668751i | \(0.766829\pi\) | |||||||
\(84\) | 7.76925 | 0.847695 | ||||||||
\(85\) | 1.92367 | 0.208652 | ||||||||
\(86\) | −0.296734 | −0.0319977 | ||||||||
\(87\) | 3.99093 | 0.427872 | ||||||||
\(88\) | 0.0946551 | 0.0100903 | ||||||||
\(89\) | 14.9069 | 1.58013 | 0.790064 | − | 0.613024i | \(-0.210047\pi\) | ||||
0.790064 | + | 0.613024i | \(0.210047\pi\) | |||||||
\(90\) | 0.137987 | 0.0145451 | ||||||||
\(91\) | 7.61733 | 0.798513 | ||||||||
\(92\) | 0.687225 | 0.0716482 | ||||||||
\(93\) | −6.60369 | −0.684771 | ||||||||
\(94\) | −0.240731 | −0.0248296 | ||||||||
\(95\) | −14.3472 | −1.47200 | ||||||||
\(96\) | 0.857818 | 0.0875506 | ||||||||
\(97\) | −8.01496 | −0.813795 | −0.406898 | − | 0.913474i | \(-0.633389\pi\) | ||||
−0.406898 | + | 0.913474i | \(0.633389\pi\) | |||||||
\(98\) | −0.585914 | −0.0591863 | ||||||||
\(99\) | 0.330322 | 0.0331987 | ||||||||
\(100\) | 2.59226 | 0.259226 | ||||||||
\(101\) | 15.2639 | 1.51882 | 0.759408 | − | 0.650615i | \(-0.225489\pi\) | ||||
0.759408 | + | 0.650615i | \(0.225489\pi\) | |||||||
\(102\) | −0.0717307 | −0.00710240 | ||||||||
\(103\) | 4.93728 | 0.486484 | 0.243242 | − | 0.969966i | \(-0.421789\pi\) | ||||
0.243242 | + | 0.969966i | \(0.421789\pi\) | |||||||
\(104\) | 0.560455 | 0.0549571 | ||||||||
\(105\) | 7.49203 | 0.731147 | ||||||||
\(106\) | −0.734279 | −0.0713195 | ||||||||
\(107\) | −4.27760 | −0.413531 | −0.206766 | − | 0.978390i | \(-0.566294\pi\) | ||||
−0.206766 | + | 0.978390i | \(0.566294\pi\) | |||||||
\(108\) | 1.99485 | 0.191955 | ||||||||
\(109\) | 16.6053 | 1.59050 | 0.795248 | − | 0.606285i | \(-0.207341\pi\) | ||||
0.795248 | + | 0.606285i | \(0.207341\pi\) | |||||||
\(110\) | 0.0455800 | 0.00434589 | ||||||||
\(111\) | 0.669431 | 0.0635395 | ||||||||
\(112\) | 15.4584 | 1.46069 | ||||||||
\(113\) | 9.39687 | 0.883983 | 0.441992 | − | 0.897019i | \(-0.354272\pi\) | ||||
0.441992 | + | 0.897019i | \(0.354272\pi\) | |||||||
\(114\) | 0.534985 | 0.0501060 | ||||||||
\(115\) | 0.662704 | 0.0617974 | ||||||||
\(116\) | 7.96132 | 0.739190 | ||||||||
\(117\) | 1.95585 | 0.180818 | ||||||||
\(118\) | 1.02817 | 0.0946511 | ||||||||
\(119\) | −3.89464 | −0.357021 | ||||||||
\(120\) | 0.551236 | 0.0503207 | ||||||||
\(121\) | −10.8909 | −0.990081 | ||||||||
\(122\) | −0.707224 | −0.0640291 | ||||||||
\(123\) | 3.05035 | 0.275041 | ||||||||
\(124\) | −13.1734 | −1.18301 | ||||||||
\(125\) | 12.1181 | 1.08388 | ||||||||
\(126\) | −0.279365 | −0.0248879 | ||||||||
\(127\) | 10.8463 | 0.962452 | 0.481226 | − | 0.876597i | \(-0.340192\pi\) | ||||
0.481226 | + | 0.876597i | \(0.340192\pi\) | |||||||
\(128\) | 2.28064 | 0.201582 | ||||||||
\(129\) | −4.13678 | −0.364224 | ||||||||
\(130\) | 0.269880 | 0.0236701 | ||||||||
\(131\) | 0.552478 | 0.0482702 | 0.0241351 | − | 0.999709i | \(-0.492317\pi\) | ||||
0.0241351 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(132\) | 0.658945 | 0.0573538 | ||||||||
\(133\) | 29.0472 | 2.51871 | ||||||||
\(134\) | 0.504094 | 0.0435470 | ||||||||
\(135\) | 1.92367 | 0.165564 | ||||||||
\(136\) | −0.286554 | −0.0245718 | ||||||||
\(137\) | 6.96419 | 0.594991 | 0.297495 | − | 0.954723i | \(-0.403849\pi\) | ||||
0.297495 | + | 0.954723i | \(0.403849\pi\) | |||||||
\(138\) | −0.0247111 | −0.00210355 | ||||||||
\(139\) | −4.18547 | −0.355007 | −0.177503 | − | 0.984120i | \(-0.556802\pi\) | ||||
−0.177503 | + | 0.984120i | \(0.556802\pi\) | |||||||
\(140\) | 14.9455 | 1.26313 | ||||||||
\(141\) | −3.35605 | −0.282630 | ||||||||
\(142\) | 0.886235 | 0.0743712 | ||||||||
\(143\) | 0.646060 | 0.0540263 | ||||||||
\(144\) | 3.96915 | 0.330763 | ||||||||
\(145\) | 7.67724 | 0.637560 | ||||||||
\(146\) | 0.990840 | 0.0820025 | ||||||||
\(147\) | −8.16825 | −0.673706 | ||||||||
\(148\) | 1.33542 | 0.109771 | ||||||||
\(149\) | 6.72582 | 0.551000 | 0.275500 | − | 0.961301i | \(-0.411157\pi\) | ||||
0.275500 | + | 0.961301i | \(0.411157\pi\) | |||||||
\(150\) | −0.0932123 | −0.00761075 | ||||||||
\(151\) | 23.2316 | 1.89056 | 0.945279 | − | 0.326263i | \(-0.105790\pi\) | ||||
0.945279 | + | 0.326263i | \(0.105790\pi\) | |||||||
\(152\) | 2.13719 | 0.173349 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.0922807 | −0.00743619 | ||||||||
\(155\) | −12.7034 | −1.02036 | ||||||||
\(156\) | 3.90163 | 0.312380 | ||||||||
\(157\) | −1.91427 | −0.152776 | −0.0763879 | − | 0.997078i | \(-0.524339\pi\) | ||||
−0.0763879 | + | 0.997078i | \(0.524339\pi\) | |||||||
\(158\) | −0.0717307 | −0.00570659 | ||||||||
\(159\) | −10.2366 | −0.811816 | ||||||||
\(160\) | 1.65016 | 0.130457 | ||||||||
\(161\) | −1.34170 | −0.105741 | ||||||||
\(162\) | −0.0717307 | −0.00563570 | ||||||||
\(163\) | −8.09342 | −0.633926 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(164\) | 6.08501 | 0.475159 | ||||||||
\(165\) | 0.635433 | 0.0494684 | ||||||||
\(166\) | 0.971733 | 0.0754211 | ||||||||
\(167\) | −15.3597 | −1.18857 | −0.594284 | − | 0.804256i | \(-0.702564\pi\) | ||||
−0.594284 | + | 0.804256i | \(0.702564\pi\) | |||||||
\(168\) | −1.11602 | −0.0861032 | ||||||||
\(169\) | −9.17466 | −0.705743 | ||||||||
\(170\) | −0.137987 | −0.0105831 | ||||||||
\(171\) | 7.45825 | 0.570346 | ||||||||
\(172\) | −8.25228 | −0.629231 | ||||||||
\(173\) | −8.15160 | −0.619755 | −0.309877 | − | 0.950777i | \(-0.600288\pi\) | ||||
−0.309877 | + | 0.950777i | \(0.600288\pi\) | |||||||
\(174\) | −0.286272 | −0.0217022 | ||||||||
\(175\) | −5.06099 | −0.382575 | ||||||||
\(176\) | 1.31110 | 0.0988279 | ||||||||
\(177\) | 14.3338 | 1.07739 | ||||||||
\(178\) | −1.06928 | −0.0801461 | ||||||||
\(179\) | 12.8997 | 0.964167 | 0.482084 | − | 0.876125i | \(-0.339880\pi\) | ||||
0.482084 | + | 0.876125i | \(0.339880\pi\) | |||||||
\(180\) | 3.83745 | 0.286027 | ||||||||
\(181\) | 15.4930 | 1.15158 | 0.575792 | − | 0.817596i | \(-0.304694\pi\) | ||||
0.575792 | + | 0.817596i | \(0.304694\pi\) | |||||||
\(182\) | −0.546396 | −0.0405016 | ||||||||
\(183\) | −9.85944 | −0.728831 | ||||||||
\(184\) | −0.0987174 | −0.00727754 | ||||||||
\(185\) | 1.28777 | 0.0946785 | ||||||||
\(186\) | 0.473687 | 0.0347325 | ||||||||
\(187\) | −0.330322 | −0.0241556 | ||||||||
\(188\) | −6.69482 | −0.488270 | ||||||||
\(189\) | −3.89464 | −0.283294 | ||||||||
\(190\) | 1.02914 | 0.0746615 | ||||||||
\(191\) | 14.9801 | 1.08392 | 0.541960 | − | 0.840404i | \(-0.317682\pi\) | ||||
0.541960 | + | 0.840404i | \(0.317682\pi\) | |||||||
\(192\) | 7.87678 | 0.568457 | ||||||||
\(193\) | 7.67006 | 0.552103 | 0.276051 | − | 0.961143i | \(-0.410974\pi\) | ||||
0.276051 | + | 0.961143i | \(0.410974\pi\) | |||||||
\(194\) | 0.574918 | 0.0412767 | ||||||||
\(195\) | 3.76241 | 0.269432 | ||||||||
\(196\) | −16.2945 | −1.16389 | ||||||||
\(197\) | 17.8042 | 1.26850 | 0.634249 | − | 0.773129i | \(-0.281309\pi\) | ||||
0.634249 | + | 0.773129i | \(0.281309\pi\) | |||||||
\(198\) | −0.0236943 | −0.00168388 | ||||||||
\(199\) | 5.74954 | 0.407574 | 0.203787 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203787 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(200\) | −0.372369 | −0.0263305 | ||||||||
\(201\) | 7.02759 | 0.495688 | ||||||||
\(202\) | −1.09489 | −0.0770363 | ||||||||
\(203\) | −15.5432 | −1.09092 | ||||||||
\(204\) | −1.99485 | −0.139668 | ||||||||
\(205\) | 5.86788 | 0.409831 | ||||||||
\(206\) | −0.354154 | −0.0246751 | ||||||||
\(207\) | −0.344499 | −0.0239443 | ||||||||
\(208\) | 7.76306 | 0.538271 | ||||||||
\(209\) | 2.46363 | 0.170413 | ||||||||
\(210\) | −0.537408 | −0.0370847 | ||||||||
\(211\) | −7.55785 | −0.520304 | −0.260152 | − | 0.965568i | \(-0.583773\pi\) | ||||
−0.260152 | + | 0.965568i | \(0.583773\pi\) | |||||||
\(212\) | −20.4205 | −1.40249 | ||||||||
\(213\) | 12.3550 | 0.846553 | ||||||||
\(214\) | 0.306835 | 0.0209748 | ||||||||
\(215\) | −7.95783 | −0.542719 | ||||||||
\(216\) | −0.286554 | −0.0194975 | ||||||||
\(217\) | 25.7190 | 1.74592 | ||||||||
\(218\) | −1.19111 | −0.0806719 | ||||||||
\(219\) | 13.8133 | 0.933419 | ||||||||
\(220\) | 1.26760 | 0.0854613 | ||||||||
\(221\) | −1.95585 | −0.131564 | ||||||||
\(222\) | −0.0480187 | −0.00322281 | ||||||||
\(223\) | 25.3149 | 1.69521 | 0.847606 | − | 0.530626i | \(-0.178043\pi\) | ||||
0.847606 | + | 0.530626i | \(0.178043\pi\) | |||||||
\(224\) | −3.34089 | −0.223223 | ||||||||
\(225\) | −1.29948 | −0.0866317 | ||||||||
\(226\) | −0.674044 | −0.0448367 | ||||||||
\(227\) | 13.9165 | 0.923668 | 0.461834 | − | 0.886966i | \(-0.347192\pi\) | ||||
0.461834 | + | 0.886966i | \(0.347192\pi\) | |||||||
\(228\) | 14.8781 | 0.985327 | ||||||||
\(229\) | −17.0794 | −1.12864 | −0.564319 | − | 0.825557i | \(-0.690861\pi\) | ||||
−0.564319 | + | 0.825557i | \(0.690861\pi\) | |||||||
\(230\) | −0.0475362 | −0.00313444 | ||||||||
\(231\) | −1.28649 | −0.0846447 | ||||||||
\(232\) | −1.14361 | −0.0750820 | ||||||||
\(233\) | 13.5356 | 0.886749 | 0.443375 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443375 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(234\) | −0.140294 | −0.00917132 | ||||||||
\(235\) | −6.45594 | −0.421139 | ||||||||
\(236\) | 28.5939 | 1.86130 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0.279365 | 0.0181086 | ||||||||
\(239\) | 3.09713 | 0.200336 | 0.100168 | − | 0.994971i | \(-0.468062\pi\) | ||||
0.100168 | + | 0.994971i | \(0.468062\pi\) | |||||||
\(240\) | 7.63536 | 0.492861 | ||||||||
\(241\) | −12.6937 | −0.817671 | −0.408836 | − | 0.912608i | \(-0.634065\pi\) | ||||
−0.408836 | + | 0.912608i | \(0.634065\pi\) | |||||||
\(242\) | 0.781211 | 0.0502181 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.6681 | −1.25912 | ||||||||
\(245\) | −15.7131 | −1.00387 | ||||||||
\(246\) | −0.218804 | −0.0139504 | ||||||||
\(247\) | 14.5872 | 0.928161 | ||||||||
\(248\) | 1.89231 | 0.120162 | ||||||||
\(249\) | 13.5470 | 0.858504 | ||||||||
\(250\) | −0.869243 | −0.0549757 | ||||||||
\(251\) | 22.2222 | 1.40265 | 0.701327 | − | 0.712840i | \(-0.252591\pi\) | ||||
0.701327 | + | 0.712840i | \(0.252591\pi\) | |||||||
\(252\) | −7.76925 | −0.489417 | ||||||||
\(253\) | −0.113796 | −0.00715427 | ||||||||
\(254\) | −0.778011 | −0.0488168 | ||||||||
\(255\) | −1.92367 | −0.120465 | ||||||||
\(256\) | 15.5900 | 0.974373 | ||||||||
\(257\) | 5.17485 | 0.322798 | 0.161399 | − | 0.986889i | \(-0.448399\pi\) | ||||
0.161399 | + | 0.986889i | \(0.448399\pi\) | |||||||
\(258\) | 0.296734 | 0.0184739 | ||||||||
\(259\) | −2.60719 | −0.162003 | ||||||||
\(260\) | 7.50547 | 0.465469 | ||||||||
\(261\) | −3.99093 | −0.247032 | ||||||||
\(262\) | −0.0396296 | −0.00244833 | ||||||||
\(263\) | 9.97141 | 0.614864 | 0.307432 | − | 0.951570i | \(-0.400530\pi\) | ||||
0.307432 | + | 0.951570i | \(0.400530\pi\) | |||||||
\(264\) | −0.0946551 | −0.00582562 | ||||||||
\(265\) | −19.6919 | −1.20966 | ||||||||
\(266\) | −2.08358 | −0.127752 | ||||||||
\(267\) | −14.9069 | −0.912288 | ||||||||
\(268\) | 14.0190 | 0.856347 | ||||||||
\(269\) | −3.62992 | −0.221320 | −0.110660 | − | 0.993858i | \(-0.535296\pi\) | ||||
−0.110660 | + | 0.993858i | \(0.535296\pi\) | |||||||
\(270\) | −0.137987 | −0.00839759 | ||||||||
\(271\) | −25.8916 | −1.57280 | −0.786401 | − | 0.617717i | \(-0.788058\pi\) | ||||
−0.786401 | + | 0.617717i | \(0.788058\pi\) | |||||||
\(272\) | −3.96915 | −0.240665 | ||||||||
\(273\) | −7.61733 | −0.461022 | ||||||||
\(274\) | −0.499546 | −0.0301787 | ||||||||
\(275\) | −0.429246 | −0.0258845 | ||||||||
\(276\) | −0.687225 | −0.0413661 | ||||||||
\(277\) | 18.4623 | 1.10929 | 0.554645 | − | 0.832087i | \(-0.312854\pi\) | ||||
0.554645 | + | 0.832087i | \(0.312854\pi\) | |||||||
\(278\) | 0.300227 | 0.0180064 | ||||||||
\(279\) | 6.60369 | 0.395353 | ||||||||
\(280\) | −2.14687 | −0.128300 | ||||||||
\(281\) | 8.04062 | 0.479663 | 0.239832 | − | 0.970814i | \(-0.422908\pi\) | ||||
0.239832 | + | 0.970814i | \(0.422908\pi\) | |||||||
\(282\) | 0.240731 | 0.0143354 | ||||||||
\(283\) | 7.20662 | 0.428389 | 0.214195 | − | 0.976791i | \(-0.431287\pi\) | ||||
0.214195 | + | 0.976791i | \(0.431287\pi\) | |||||||
\(284\) | 24.6465 | 1.46250 | ||||||||
\(285\) | 14.3472 | 0.849857 | ||||||||
\(286\) | −0.0463423 | −0.00274028 | ||||||||
\(287\) | −11.8800 | −0.701256 | ||||||||
\(288\) | −0.857818 | −0.0505474 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.550694 | −0.0323379 | ||||||||
\(291\) | 8.01496 | 0.469845 | ||||||||
\(292\) | 27.5556 | 1.61257 | ||||||||
\(293\) | −21.4899 | −1.25545 | −0.627727 | − | 0.778434i | \(-0.716015\pi\) | ||||
−0.627727 | + | 0.778434i | \(0.716015\pi\) | |||||||
\(294\) | 0.585914 | 0.0341712 | ||||||||
\(295\) | 27.5736 | 1.60540 | ||||||||
\(296\) | −0.191828 | −0.0111498 | ||||||||
\(297\) | −0.330322 | −0.0191673 | ||||||||
\(298\) | −0.482448 | −0.0279474 | ||||||||
\(299\) | −0.673787 | −0.0389661 | ||||||||
\(300\) | −2.59226 | −0.149664 | ||||||||
\(301\) | 16.1113 | 0.928640 | ||||||||
\(302\) | −1.66642 | −0.0958915 | ||||||||
\(303\) | −15.2639 | −0.876889 | ||||||||
\(304\) | 29.6029 | 1.69784 | ||||||||
\(305\) | −18.9663 | −1.08601 | ||||||||
\(306\) | 0.0717307 | 0.00410057 | ||||||||
\(307\) | −9.65818 | −0.551221 | −0.275611 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275611 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(308\) | −2.56636 | −0.146232 | ||||||||
\(309\) | −4.93728 | −0.280872 | ||||||||
\(310\) | 0.911221 | 0.0517539 | ||||||||
\(311\) | 27.6205 | 1.56622 | 0.783108 | − | 0.621885i | \(-0.213633\pi\) | ||||
0.783108 | + | 0.621885i | \(0.213633\pi\) | |||||||
\(312\) | −0.560455 | −0.0317295 | ||||||||
\(313\) | −1.18468 | −0.0669623 | −0.0334811 | − | 0.999439i | \(-0.510659\pi\) | ||||
−0.0334811 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(314\) | 0.137312 | 0.00774898 | ||||||||
\(315\) | −7.49203 | −0.422128 | ||||||||
\(316\) | −1.99485 | −0.112219 | ||||||||
\(317\) | 4.56237 | 0.256248 | 0.128124 | − | 0.991758i | \(-0.459104\pi\) | ||||
0.128124 | + | 0.991758i | \(0.459104\pi\) | |||||||
\(318\) | 0.734279 | 0.0411763 | ||||||||
\(319\) | −1.31829 | −0.0738102 | ||||||||
\(320\) | 15.1524 | 0.847043 | ||||||||
\(321\) | 4.27760 | 0.238753 | ||||||||
\(322\) | 0.0962411 | 0.00536331 | ||||||||
\(323\) | −7.45825 | −0.414988 | ||||||||
\(324\) | −1.99485 | −0.110825 | ||||||||
\(325\) | −2.54157 | −0.140981 | ||||||||
\(326\) | 0.580547 | 0.0321535 | ||||||||
\(327\) | −16.6053 | −0.918273 | ||||||||
\(328\) | −0.874089 | −0.0482635 | ||||||||
\(329\) | 13.0706 | 0.720606 | ||||||||
\(330\) | −0.0455800 | −0.00250910 | ||||||||
\(331\) | −14.5436 | −0.799390 | −0.399695 | − | 0.916648i | \(-0.630884\pi\) | ||||
−0.399695 | + | 0.916648i | \(0.630884\pi\) | |||||||
\(332\) | 27.0242 | 1.48315 | ||||||||
\(333\) | −0.669431 | −0.0366846 | ||||||||
\(334\) | 1.10176 | 0.0602856 | ||||||||
\(335\) | 13.5188 | 0.738610 | ||||||||
\(336\) | −15.4584 | −0.843327 | ||||||||
\(337\) | −15.5897 | −0.849225 | −0.424613 | − | 0.905375i | \(-0.639590\pi\) | ||||
−0.424613 | + | 0.905375i | \(0.639590\pi\) | |||||||
\(338\) | 0.658105 | 0.0357962 | ||||||||
\(339\) | −9.39687 | −0.510368 | ||||||||
\(340\) | −3.83745 | −0.208115 | ||||||||
\(341\) | 2.18135 | 0.118127 | ||||||||
\(342\) | −0.534985 | −0.0289287 | ||||||||
\(343\) | 4.54992 | 0.245673 | ||||||||
\(344\) | 1.18541 | 0.0639131 | ||||||||
\(345\) | −0.662704 | −0.0356788 | ||||||||
\(346\) | 0.584720 | 0.0314347 | ||||||||
\(347\) | 0.992376 | 0.0532735 | 0.0266368 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266368 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(348\) | −7.96132 | −0.426771 | ||||||||
\(349\) | 0.260426 | 0.0139403 | 0.00697015 | − | 0.999976i | \(-0.497781\pi\) | ||||
0.00697015 | + | 0.999976i | \(0.497781\pi\) | |||||||
\(350\) | 0.363029 | 0.0194047 | ||||||||
\(351\) | −1.95585 | −0.104395 | ||||||||
\(352\) | −0.283356 | −0.0151029 | ||||||||
\(353\) | −20.0726 | −1.06835 | −0.534177 | − | 0.845373i | \(-0.679378\pi\) | ||||
−0.534177 | + | 0.845373i | \(0.679378\pi\) | |||||||
\(354\) | −1.02817 | −0.0546468 | ||||||||
\(355\) | 23.7671 | 1.26143 | ||||||||
\(356\) | −29.7371 | −1.57606 | ||||||||
\(357\) | 3.89464 | 0.206126 | ||||||||
\(358\) | −0.925303 | −0.0489038 | ||||||||
\(359\) | −26.0056 | −1.37252 | −0.686261 | − | 0.727355i | \(-0.740749\pi\) | ||||
−0.686261 | + | 0.727355i | \(0.740749\pi\) | |||||||
\(360\) | −0.551236 | −0.0290527 | ||||||||
\(361\) | 36.6254 | 1.92766 | ||||||||
\(362\) | −1.11132 | −0.0584098 | ||||||||
\(363\) | 10.8909 | 0.571623 | ||||||||
\(364\) | −15.1955 | −0.796459 | ||||||||
\(365\) | 26.5724 | 1.39086 | ||||||||
\(366\) | 0.707224 | 0.0369672 | ||||||||
\(367\) | −4.22155 | −0.220363 | −0.110182 | − | 0.993911i | \(-0.535143\pi\) | ||||
−0.110182 | + | 0.993911i | \(0.535143\pi\) | |||||||
\(368\) | −1.36737 | −0.0712791 | ||||||||
\(369\) | −3.05035 | −0.158795 | ||||||||
\(370\) | −0.0923724 | −0.00480221 | ||||||||
\(371\) | 39.8679 | 2.06984 | ||||||||
\(372\) | 13.1734 | 0.683009 | ||||||||
\(373\) | 24.6489 | 1.27627 | 0.638137 | − | 0.769923i | \(-0.279705\pi\) | ||||
0.638137 | + | 0.769923i | \(0.279705\pi\) | |||||||
\(374\) | 0.0236943 | 0.00122520 | ||||||||
\(375\) | −12.1181 | −0.625778 | ||||||||
\(376\) | 0.961687 | 0.0495952 | ||||||||
\(377\) | −7.80564 | −0.402011 | ||||||||
\(378\) | 0.279365 | 0.0143690 | ||||||||
\(379\) | −15.3554 | −0.788756 | −0.394378 | − | 0.918948i | \(-0.629040\pi\) | ||||
−0.394378 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(380\) | 28.6207 | 1.46821 | ||||||||
\(381\) | −10.8463 | −0.555672 | ||||||||
\(382\) | −1.07453 | −0.0549778 | ||||||||
\(383\) | 11.2504 | 0.574871 | 0.287435 | − | 0.957800i | \(-0.407197\pi\) | ||||
0.287435 | + | 0.957800i | \(0.407197\pi\) | |||||||
\(384\) | −2.28064 | −0.116384 | ||||||||
\(385\) | −2.47478 | −0.126127 | ||||||||
\(386\) | −0.550178 | −0.0280033 | ||||||||
\(387\) | 4.13678 | 0.210285 | ||||||||
\(388\) | 15.9887 | 0.811702 | ||||||||
\(389\) | −0.427537 | −0.0216770 | −0.0108385 | − | 0.999941i | \(-0.503450\pi\) | ||||
−0.0108385 | + | 0.999941i | \(0.503450\pi\) | |||||||
\(390\) | −0.269880 | −0.0136659 | ||||||||
\(391\) | 0.344499 | 0.0174221 | ||||||||
\(392\) | 2.34064 | 0.118220 | ||||||||
\(393\) | −0.552478 | −0.0278688 | ||||||||
\(394\) | −1.27711 | −0.0643398 | ||||||||
\(395\) | −1.92367 | −0.0967906 | ||||||||
\(396\) | −0.658945 | −0.0331132 | ||||||||
\(397\) | 22.6863 | 1.13859 | 0.569296 | − | 0.822132i | \(-0.307216\pi\) | ||||
0.569296 | + | 0.822132i | \(0.307216\pi\) | |||||||
\(398\) | −0.412419 | −0.0206727 | ||||||||
\(399\) | −29.0472 | −1.45418 | ||||||||
\(400\) | −5.15782 | −0.257891 | ||||||||
\(401\) | 0.432949 | 0.0216204 | 0.0108102 | − | 0.999942i | \(-0.496559\pi\) | ||||
0.0108102 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(402\) | −0.504094 | −0.0251419 | ||||||||
\(403\) | 12.9158 | 0.643382 | ||||||||
\(404\) | −30.4493 | −1.51491 | ||||||||
\(405\) | −1.92367 | −0.0955882 | ||||||||
\(406\) | 1.11493 | 0.0553329 | ||||||||
\(407\) | −0.221128 | −0.0109609 | ||||||||
\(408\) | 0.286554 | 0.0141865 | ||||||||
\(409\) | −23.7771 | −1.17570 | −0.587851 | − | 0.808969i | \(-0.700026\pi\) | ||||
−0.587851 | + | 0.808969i | \(0.700026\pi\) | |||||||
\(410\) | −0.420907 | −0.0207871 | ||||||||
\(411\) | −6.96419 | −0.343518 | ||||||||
\(412\) | −9.84915 | −0.485233 | ||||||||
\(413\) | −55.8251 | −2.74697 | ||||||||
\(414\) | 0.0247111 | 0.00121449 | ||||||||
\(415\) | 26.0600 | 1.27923 | ||||||||
\(416\) | −1.67776 | −0.0822589 | ||||||||
\(417\) | 4.18547 | 0.204963 | ||||||||
\(418\) | −0.176718 | −0.00864354 | ||||||||
\(419\) | −5.21594 | −0.254815 | −0.127408 | − | 0.991850i | \(-0.540666\pi\) | ||||
−0.127408 | + | 0.991850i | \(0.540666\pi\) | |||||||
\(420\) | −14.9455 | −0.729266 | ||||||||
\(421\) | 8.88717 | 0.433134 | 0.216567 | − | 0.976268i | \(-0.430514\pi\) | ||||
0.216567 | + | 0.976268i | \(0.430514\pi\) | |||||||
\(422\) | 0.542130 | 0.0263905 | ||||||||
\(423\) | 3.35605 | 0.163177 | ||||||||
\(424\) | 2.93334 | 0.142455 | ||||||||
\(425\) | 1.29948 | 0.0630338 | ||||||||
\(426\) | −0.886235 | −0.0429382 | ||||||||
\(427\) | 38.3990 | 1.85826 | ||||||||
\(428\) | 8.53320 | 0.412468 | ||||||||
\(429\) | −0.646060 | −0.0311921 | ||||||||
\(430\) | 0.570820 | 0.0275274 | ||||||||
\(431\) | −28.0996 | −1.35351 | −0.676754 | − | 0.736209i | \(-0.736614\pi\) | ||||
−0.676754 | + | 0.736209i | \(0.736614\pi\) | |||||||
\(432\) | −3.96915 | −0.190966 | ||||||||
\(433\) | 35.3210 | 1.69742 | 0.848710 | − | 0.528858i | \(-0.177380\pi\) | ||||
0.848710 | + | 0.528858i | \(0.177380\pi\) | |||||||
\(434\) | −1.84484 | −0.0885553 | ||||||||
\(435\) | −7.67724 | −0.368096 | ||||||||
\(436\) | −33.1251 | −1.58640 | ||||||||
\(437\) | −2.56936 | −0.122909 | ||||||||
\(438\) | −0.990840 | −0.0473442 | ||||||||
\(439\) | −8.16860 | −0.389866 | −0.194933 | − | 0.980817i | \(-0.562449\pi\) | ||||
−0.194933 | + | 0.980817i | \(0.562449\pi\) | |||||||
\(440\) | −0.182086 | −0.00868059 | ||||||||
\(441\) | 8.16825 | 0.388964 | ||||||||
\(442\) | 0.140294 | 0.00667312 | ||||||||
\(443\) | 2.22455 | 0.105692 | 0.0528458 | − | 0.998603i | \(-0.483171\pi\) | ||||
0.0528458 | + | 0.998603i | \(0.483171\pi\) | |||||||
\(444\) | −1.33542 | −0.0633761 | ||||||||
\(445\) | −28.6760 | −1.35937 | ||||||||
\(446\) | −1.81586 | −0.0859833 | ||||||||
\(447\) | −6.72582 | −0.318120 | ||||||||
\(448\) | −30.6772 | −1.44936 | ||||||||
\(449\) | −27.8572 | −1.31466 | −0.657331 | − | 0.753602i | \(-0.728315\pi\) | ||||
−0.657331 | + | 0.753602i | \(0.728315\pi\) | |||||||
\(450\) | 0.0932123 | 0.00439407 | ||||||||
\(451\) | −1.00760 | −0.0474460 | ||||||||
\(452\) | −18.7454 | −0.881709 | ||||||||
\(453\) | −23.2316 | −1.09151 | ||||||||
\(454\) | −0.998238 | −0.0468496 | ||||||||
\(455\) | −14.6533 | −0.686955 | ||||||||
\(456\) | −2.13719 | −0.100083 | ||||||||
\(457\) | 1.14253 | 0.0534455 | 0.0267228 | − | 0.999643i | \(-0.491493\pi\) | ||||
0.0267228 | + | 0.999643i | \(0.491493\pi\) | |||||||
\(458\) | 1.22512 | 0.0572460 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −1.32200 | −0.0616385 | ||||||||
\(461\) | 15.9503 | 0.742879 | 0.371439 | − | 0.928457i | \(-0.378864\pi\) | ||||
0.371439 | + | 0.928457i | \(0.378864\pi\) | |||||||
\(462\) | 0.0922807 | 0.00429329 | ||||||||
\(463\) | −7.73487 | −0.359470 | −0.179735 | − | 0.983715i | \(-0.557524\pi\) | ||||
−0.179735 | + | 0.983715i | \(0.557524\pi\) | |||||||
\(464\) | −15.8406 | −0.735381 | ||||||||
\(465\) | 12.7034 | 0.589104 | ||||||||
\(466\) | −0.970921 | −0.0449770 | ||||||||
\(467\) | −30.8369 | −1.42696 | −0.713480 | − | 0.700675i | \(-0.752882\pi\) | ||||
−0.713480 | + | 0.700675i | \(0.752882\pi\) | |||||||
\(468\) | −3.90163 | −0.180353 | ||||||||
\(469\) | −27.3699 | −1.26383 | ||||||||
\(470\) | 0.463089 | 0.0213607 | ||||||||
\(471\) | 1.91427 | 0.0882051 | ||||||||
\(472\) | −4.10740 | −0.189059 | ||||||||
\(473\) | 1.36647 | 0.0628305 | ||||||||
\(474\) | 0.0717307 | 0.00329470 | ||||||||
\(475\) | −9.69181 | −0.444691 | ||||||||
\(476\) | 7.76925 | 0.356103 | ||||||||
\(477\) | 10.2366 | 0.468702 | ||||||||
\(478\) | −0.222159 | −0.0101613 | ||||||||
\(479\) | 36.0430 | 1.64685 | 0.823424 | − | 0.567426i | \(-0.192061\pi\) | ||||
0.823424 | + | 0.567426i | \(0.192061\pi\) | |||||||
\(480\) | −1.65016 | −0.0753192 | ||||||||
\(481\) | −1.30930 | −0.0596991 | ||||||||
\(482\) | 0.910526 | 0.0414733 | ||||||||
\(483\) | 1.34170 | 0.0610495 | ||||||||
\(484\) | 21.7257 | 0.987534 | ||||||||
\(485\) | 15.4182 | 0.700103 | ||||||||
\(486\) | 0.0717307 | 0.00325377 | ||||||||
\(487\) | −32.4321 | −1.46964 | −0.734820 | − | 0.678262i | \(-0.762733\pi\) | ||||
−0.734820 | + | 0.678262i | \(0.762733\pi\) | |||||||
\(488\) | 2.82526 | 0.127893 | ||||||||
\(489\) | 8.09342 | 0.365997 | ||||||||
\(490\) | 1.12711 | 0.0509176 | ||||||||
\(491\) | 36.7844 | 1.66006 | 0.830028 | − | 0.557722i | \(-0.188325\pi\) | ||||
0.830028 | + | 0.557722i | \(0.188325\pi\) | |||||||
\(492\) | −6.08501 | −0.274333 | ||||||||
\(493\) | 3.99093 | 0.179742 | ||||||||
\(494\) | −1.04635 | −0.0470775 | ||||||||
\(495\) | −0.635433 | −0.0285606 | ||||||||
\(496\) | 26.2111 | 1.17691 | ||||||||
\(497\) | −48.1185 | −2.15841 | ||||||||
\(498\) | −0.971733 | −0.0435444 | ||||||||
\(499\) | 32.0547 | 1.43497 | 0.717484 | − | 0.696575i | \(-0.245294\pi\) | ||||
0.717484 | + | 0.696575i | \(0.245294\pi\) | |||||||
\(500\) | −24.1739 | −1.08109 | ||||||||
\(501\) | 15.3597 | 0.686220 | ||||||||
\(502\) | −1.59402 | −0.0711444 | ||||||||
\(503\) | 21.6955 | 0.967353 | 0.483676 | − | 0.875247i | \(-0.339301\pi\) | ||||
0.483676 | + | 0.875247i | \(0.339301\pi\) | |||||||
\(504\) | 1.11602 | 0.0497117 | ||||||||
\(505\) | −29.3628 | −1.30663 | ||||||||
\(506\) | 0.00816264 | 0.000362874 0 | ||||||||
\(507\) | 9.17466 | 0.407461 | ||||||||
\(508\) | −21.6368 | −0.959976 | ||||||||
\(509\) | −38.5911 | −1.71052 | −0.855261 | − | 0.518197i | \(-0.826603\pi\) | ||||
−0.855261 | + | 0.518197i | \(0.826603\pi\) | |||||||
\(510\) | 0.137987 | 0.00611015 | ||||||||
\(511\) | −53.7980 | −2.37988 | ||||||||
\(512\) | −5.67956 | −0.251004 | ||||||||
\(513\) | −7.45825 | −0.329290 | ||||||||
\(514\) | −0.371196 | −0.0163727 | ||||||||
\(515\) | −9.49771 | −0.418519 | ||||||||
\(516\) | 8.25228 | 0.363287 | ||||||||
\(517\) | 1.10858 | 0.0487552 | ||||||||
\(518\) | 0.187016 | 0.00821700 | ||||||||
\(519\) | 8.15160 | 0.357816 | ||||||||
\(520\) | −1.07813 | −0.0472793 | ||||||||
\(521\) | −3.73243 | −0.163521 | −0.0817604 | − | 0.996652i | \(-0.526054\pi\) | ||||
−0.0817604 | + | 0.996652i | \(0.526054\pi\) | |||||||
\(522\) | 0.286272 | 0.0125298 | ||||||||
\(523\) | 31.7896 | 1.39006 | 0.695031 | − | 0.718979i | \(-0.255390\pi\) | ||||
0.695031 | + | 0.718979i | \(0.255390\pi\) | |||||||
\(524\) | −1.10211 | −0.0481460 | ||||||||
\(525\) | 5.06099 | 0.220880 | ||||||||
\(526\) | −0.715256 | −0.0311867 | ||||||||
\(527\) | −6.60369 | −0.287661 | ||||||||
\(528\) | −1.31110 | −0.0570583 | ||||||||
\(529\) | −22.8813 | −0.994840 | ||||||||
\(530\) | 1.41251 | 0.0613557 | ||||||||
\(531\) | −14.3338 | −0.622034 | ||||||||
\(532\) | −57.9450 | −2.51223 | ||||||||
\(533\) | −5.96602 | −0.258417 | ||||||||
\(534\) | 1.06928 | 0.0462724 | ||||||||
\(535\) | 8.22872 | 0.355758 | ||||||||
\(536\) | −2.01378 | −0.0869821 | ||||||||
\(537\) | −12.8997 | −0.556662 | ||||||||
\(538\) | 0.260377 | 0.0112256 | ||||||||
\(539\) | 2.69816 | 0.116218 | ||||||||
\(540\) | −3.83745 | −0.165138 | ||||||||
\(541\) | 2.37942 | 0.102299 | 0.0511496 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511496 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(542\) | 1.85722 | 0.0797745 | ||||||||
\(543\) | −15.4930 | −0.664867 | ||||||||
\(544\) | 0.857818 | 0.0367786 | ||||||||
\(545\) | −31.9431 | −1.36829 | ||||||||
\(546\) | 0.546396 | 0.0233836 | ||||||||
\(547\) | 39.6860 | 1.69685 | 0.848426 | − | 0.529315i | \(-0.177551\pi\) | ||||
0.848426 | + | 0.529315i | \(0.177551\pi\) | |||||||
\(548\) | −13.8925 | −0.593460 | ||||||||
\(549\) | 9.85944 | 0.420790 | ||||||||
\(550\) | 0.0307901 | 0.00131289 | ||||||||
\(551\) | −29.7653 | −1.26804 | ||||||||
\(552\) | 0.0987174 | 0.00420169 | ||||||||
\(553\) | 3.89464 | 0.165617 | ||||||||
\(554\) | −1.32431 | −0.0562646 | ||||||||
\(555\) | −1.28777 | −0.0546627 | ||||||||
\(556\) | 8.34940 | 0.354094 | ||||||||
\(557\) | 8.96781 | 0.379978 | 0.189989 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(558\) | −0.473687 | −0.0200528 | ||||||||
\(559\) | 8.09092 | 0.342209 | ||||||||
\(560\) | −29.7370 | −1.25662 | ||||||||
\(561\) | 0.330322 | 0.0139462 | ||||||||
\(562\) | −0.576759 | −0.0243291 | ||||||||
\(563\) | 29.1037 | 1.22657 | 0.613286 | − | 0.789861i | \(-0.289847\pi\) | ||||
0.613286 | + | 0.789861i | \(0.289847\pi\) | |||||||
\(564\) | 6.69482 | 0.281903 | ||||||||
\(565\) | −18.0765 | −0.760485 | ||||||||
\(566\) | −0.516936 | −0.0217284 | ||||||||
\(567\) | 3.89464 | 0.163560 | ||||||||
\(568\) | −3.54038 | −0.148551 | ||||||||
\(569\) | 26.7071 | 1.11962 | 0.559809 | − | 0.828621i | \(-0.310874\pi\) | ||||
0.559809 | + | 0.828621i | \(0.310874\pi\) | |||||||
\(570\) | −1.02914 | −0.0431058 | ||||||||
\(571\) | 13.1837 | 0.551720 | 0.275860 | − | 0.961198i | \(-0.411037\pi\) | ||||
0.275860 | + | 0.961198i | \(0.411037\pi\) | |||||||
\(572\) | −1.28880 | −0.0538873 | ||||||||
\(573\) | −14.9801 | −0.625801 | ||||||||
\(574\) | 0.852163 | 0.0355686 | ||||||||
\(575\) | 0.447668 | 0.0186690 | ||||||||
\(576\) | −7.87678 | −0.328199 | ||||||||
\(577\) | −27.2076 | −1.13267 | −0.566334 | − | 0.824176i | \(-0.691639\pi\) | ||||
−0.566334 | + | 0.824176i | \(0.691639\pi\) | |||||||
\(578\) | −0.0717307 | −0.00298360 | ||||||||
\(579\) | −7.67006 | −0.318757 | ||||||||
\(580\) | −15.3150 | −0.635920 | ||||||||
\(581\) | −52.7606 | −2.18888 | ||||||||
\(582\) | −0.574918 | −0.0238311 | ||||||||
\(583\) | 3.38138 | 0.140042 | ||||||||
\(584\) | −3.95826 | −0.163794 | ||||||||
\(585\) | −3.76241 | −0.155557 | ||||||||
\(586\) | 1.54149 | 0.0636782 | ||||||||
\(587\) | −18.9662 | −0.782818 | −0.391409 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391409 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(588\) | 16.2945 | 0.671973 | ||||||||
\(589\) | 49.2520 | 2.02939 | ||||||||
\(590\) | −1.97787 | −0.0814277 | ||||||||
\(591\) | −17.8042 | −0.732368 | ||||||||
\(592\) | −2.65707 | −0.109205 | ||||||||
\(593\) | −43.4843 | −1.78569 | −0.892843 | − | 0.450368i | \(-0.851293\pi\) | ||||
−0.892843 | + | 0.450368i | \(0.851293\pi\) | |||||||
\(594\) | 0.0236943 | 0.000972187 0 | ||||||||
\(595\) | 7.49203 | 0.307143 | ||||||||
\(596\) | −13.4170 | −0.549583 | ||||||||
\(597\) | −5.74954 | −0.235313 | ||||||||
\(598\) | 0.0483312 | 0.00197641 | ||||||||
\(599\) | −22.5081 | −0.919655 | −0.459828 | − | 0.888008i | \(-0.652089\pi\) | ||||
−0.459828 | + | 0.888008i | \(0.652089\pi\) | |||||||
\(600\) | 0.372369 | 0.0152019 | ||||||||
\(601\) | 45.2772 | 1.84690 | 0.923448 | − | 0.383723i | \(-0.125358\pi\) | ||||
0.923448 | + | 0.383723i | \(0.125358\pi\) | |||||||
\(602\) | −1.15567 | −0.0471018 | ||||||||
\(603\) | −7.02759 | −0.286185 | ||||||||
\(604\) | −46.3436 | −1.88569 | ||||||||
\(605\) | 20.9505 | 0.851760 | ||||||||
\(606\) | 1.09489 | 0.0444769 | ||||||||
\(607\) | 6.49095 | 0.263460 | 0.131730 | − | 0.991286i | \(-0.457947\pi\) | ||||
0.131730 | + | 0.991286i | \(0.457947\pi\) | |||||||
\(608\) | −6.39782 | −0.259466 | ||||||||
\(609\) | 15.5432 | 0.629844 | ||||||||
\(610\) | 1.36047 | 0.0550838 | ||||||||
\(611\) | 6.56391 | 0.265547 | ||||||||
\(612\) | 1.99485 | 0.0806372 | ||||||||
\(613\) | 29.4811 | 1.19073 | 0.595365 | − | 0.803456i | \(-0.297008\pi\) | ||||
0.595365 | + | 0.803456i | \(0.297008\pi\) | |||||||
\(614\) | 0.692788 | 0.0279586 | ||||||||
\(615\) | −5.86788 | −0.236616 | ||||||||
\(616\) | 0.368648 | 0.0148532 | ||||||||
\(617\) | −15.9041 | −0.640277 | −0.320138 | − | 0.947371i | \(-0.603729\pi\) | ||||
−0.320138 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(618\) | 0.354154 | 0.0142462 | ||||||||
\(619\) | 36.5940 | 1.47084 | 0.735418 | − | 0.677614i | \(-0.236986\pi\) | ||||
0.735418 | + | 0.677614i | \(0.236986\pi\) | |||||||
\(620\) | 25.3414 | 1.01773 | ||||||||
\(621\) | 0.344499 | 0.0138243 | ||||||||
\(622\) | −1.98124 | −0.0794405 | ||||||||
\(623\) | 58.0571 | 2.32601 | ||||||||
\(624\) | −7.76306 | −0.310771 | ||||||||
\(625\) | −16.8140 | −0.672559 | ||||||||
\(626\) | 0.0849781 | 0.00339641 | ||||||||
\(627\) | −2.46363 | −0.0983878 | ||||||||
\(628\) | 3.81870 | 0.152383 | ||||||||
\(629\) | 0.669431 | 0.0266919 | ||||||||
\(630\) | 0.537408 | 0.0214109 | ||||||||
\(631\) | −8.02315 | −0.319396 | −0.159698 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159698 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(632\) | 0.286554 | 0.0113985 | ||||||||
\(633\) | 7.55785 | 0.300398 | ||||||||
\(634\) | −0.327262 | −0.0129972 | ||||||||
\(635\) | −20.8647 | −0.827991 | ||||||||
\(636\) | 20.4205 | 0.809727 | ||||||||
\(637\) | 15.9758 | 0.632986 | ||||||||
\(638\) | 0.0945620 | 0.00374375 | ||||||||
\(639\) | −12.3550 | −0.488758 | ||||||||
\(640\) | −4.38721 | −0.173420 | ||||||||
\(641\) | 46.0760 | 1.81989 | 0.909947 | − | 0.414726i | \(-0.136122\pi\) | ||||
0.909947 | + | 0.414726i | \(0.136122\pi\) | |||||||
\(642\) | −0.306835 | −0.0121098 | ||||||||
\(643\) | −13.2817 | −0.523779 | −0.261889 | − | 0.965098i | \(-0.584346\pi\) | ||||
−0.261889 | + | 0.965098i | \(0.584346\pi\) | |||||||
\(644\) | 2.67650 | 0.105469 | ||||||||
\(645\) | 7.95783 | 0.313339 | ||||||||
\(646\) | 0.534985 | 0.0210487 | ||||||||
\(647\) | 35.2452 | 1.38563 | 0.692816 | − | 0.721115i | \(-0.256370\pi\) | ||||
0.692816 | + | 0.721115i | \(0.256370\pi\) | |||||||
\(648\) | 0.286554 | 0.0112569 | ||||||||
\(649\) | −4.73478 | −0.185856 | ||||||||
\(650\) | 0.182309 | 0.00715074 | ||||||||
\(651\) | −25.7190 | −1.00801 | ||||||||
\(652\) | 16.1452 | 0.632295 | ||||||||
\(653\) | 18.8204 | 0.736498 | 0.368249 | − | 0.929727i | \(-0.379957\pi\) | ||||
0.368249 | + | 0.929727i | \(0.379957\pi\) | |||||||
\(654\) | 1.19111 | 0.0465759 | ||||||||
\(655\) | −1.06279 | −0.0415266 | ||||||||
\(656\) | −12.1073 | −0.472711 | ||||||||
\(657\) | −13.8133 | −0.538910 | ||||||||
\(658\) | −0.937563 | −0.0365500 | ||||||||
\(659\) | 17.6101 | 0.685994 | 0.342997 | − | 0.939337i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939337i | \(0.388558\pi\) | |||||||
\(660\) | −1.26760 | −0.0493411 | ||||||||
\(661\) | 21.9406 | 0.853389 | 0.426694 | − | 0.904396i | \(-0.359678\pi\) | ||||
0.426694 | + | 0.904396i | \(0.359678\pi\) | |||||||
\(662\) | 1.04322 | 0.0405461 | ||||||||
\(663\) | 1.95585 | 0.0759588 | ||||||||
\(664\) | −3.88193 | −0.150648 | ||||||||
\(665\) | −55.8774 | −2.16683 | ||||||||
\(666\) | 0.0480187 | 0.00186069 | ||||||||
\(667\) | 1.37487 | 0.0532351 | ||||||||
\(668\) | 30.6403 | 1.18551 | ||||||||
\(669\) | −25.3149 | −0.978731 | ||||||||
\(670\) | −0.969712 | −0.0374632 | ||||||||
\(671\) | 3.25679 | 0.125727 | ||||||||
\(672\) | 3.34089 | 0.128878 | ||||||||
\(673\) | −38.5660 | −1.48661 | −0.743305 | − | 0.668953i | \(-0.766743\pi\) | ||||
−0.743305 | + | 0.668953i | \(0.766743\pi\) | |||||||
\(674\) | 1.11826 | 0.0430738 | ||||||||
\(675\) | 1.29948 | 0.0500168 | ||||||||
\(676\) | 18.3021 | 0.703928 | ||||||||
\(677\) | 5.13280 | 0.197270 | 0.0986348 | − | 0.995124i | \(-0.468552\pi\) | ||||
0.0986348 | + | 0.995124i | \(0.468552\pi\) | |||||||
\(678\) | 0.674044 | 0.0258865 | ||||||||
\(679\) | −31.2154 | −1.19794 | ||||||||
\(680\) | 0.551236 | 0.0211389 | ||||||||
\(681\) | −13.9165 | −0.533280 | ||||||||
\(682\) | −0.156470 | −0.00599153 | ||||||||
\(683\) | −29.9446 | −1.14580 | −0.572898 | − | 0.819627i | \(-0.694181\pi\) | ||||
−0.572898 | + | 0.819627i | \(0.694181\pi\) | |||||||
\(684\) | −14.8781 | −0.568879 | ||||||||
\(685\) | −13.3968 | −0.511867 | ||||||||
\(686\) | −0.326369 | −0.0124608 | ||||||||
\(687\) | 17.0794 | 0.651620 | ||||||||
\(688\) | 16.4195 | 0.625989 | ||||||||
\(689\) | 20.0212 | 0.762748 | ||||||||
\(690\) | 0.0475362 | 0.00180967 | ||||||||
\(691\) | −15.8527 | −0.603065 | −0.301533 | − | 0.953456i | \(-0.597498\pi\) | ||||
−0.301533 | + | 0.953456i | \(0.597498\pi\) | |||||||
\(692\) | 16.2613 | 0.618161 | ||||||||
\(693\) | 1.28649 | 0.0488696 | ||||||||
\(694\) | −0.0711838 | −0.00270210 | ||||||||
\(695\) | 8.05148 | 0.305410 | ||||||||
\(696\) | 1.14361 | 0.0433486 | ||||||||
\(697\) | 3.05035 | 0.115540 | ||||||||
\(698\) | −0.0186805 | −0.000707069 0 | ||||||||
\(699\) | −13.5356 | −0.511965 | ||||||||
\(700\) | 10.0959 | 0.381591 | ||||||||
\(701\) | 23.3229 | 0.880894 | 0.440447 | − | 0.897779i | \(-0.354820\pi\) | ||||
0.440447 | + | 0.897779i | \(0.354820\pi\) | |||||||
\(702\) | 0.140294 | 0.00529506 | ||||||||
\(703\) | −4.99278 | −0.188306 | ||||||||
\(704\) | −2.60188 | −0.0980619 | ||||||||
\(705\) | 6.45594 | 0.243145 | ||||||||
\(706\) | 1.43982 | 0.0541883 | ||||||||
\(707\) | 59.4475 | 2.23575 | ||||||||
\(708\) | −28.5939 | −1.07462 | ||||||||
\(709\) | −37.8546 | −1.42166 | −0.710830 | − | 0.703364i | \(-0.751680\pi\) | ||||
−0.710830 | + | 0.703364i | \(0.751680\pi\) | |||||||
\(710\) | −1.70483 | −0.0639811 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 4.27163 | 0.160086 | ||||||||
\(713\) | −2.27496 | −0.0851981 | ||||||||
\(714\) | −0.279365 | −0.0104550 | ||||||||
\(715\) | −1.24281 | −0.0464784 | ||||||||
\(716\) | −25.7330 | −0.961687 | ||||||||
\(717\) | −3.09713 | −0.115664 | ||||||||
\(718\) | 1.86540 | 0.0696161 | ||||||||
\(719\) | −45.6181 | −1.70127 | −0.850634 | − | 0.525758i | \(-0.823782\pi\) | ||||
−0.850634 | + | 0.525758i | \(0.823782\pi\) | |||||||
\(720\) | −7.63536 | −0.284553 | ||||||||
\(721\) | 19.2289 | 0.716123 | ||||||||
\(722\) | −2.62717 | −0.0977731 | ||||||||
\(723\) | 12.6937 | 0.472083 | ||||||||
\(724\) | −30.9062 | −1.14862 | ||||||||
\(725\) | 5.18611 | 0.192607 | ||||||||
\(726\) | −0.781211 | −0.0289935 | ||||||||
\(727\) | 45.5646 | 1.68990 | 0.844949 | − | 0.534846i | \(-0.179631\pi\) | ||||
0.844949 | + | 0.534846i | \(0.179631\pi\) | |||||||
\(728\) | 2.18277 | 0.0808990 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.90605 | −0.0705462 | ||||||||
\(731\) | −4.13678 | −0.153004 | ||||||||
\(732\) | 19.6681 | 0.726955 | ||||||||
\(733\) | −17.0282 | −0.628950 | −0.314475 | − | 0.949266i | \(-0.601828\pi\) | ||||
−0.314475 | + | 0.949266i | \(0.601828\pi\) | |||||||
\(734\) | 0.302815 | 0.0111771 | ||||||||
\(735\) | 15.7131 | 0.579585 | ||||||||
\(736\) | 0.295517 | 0.0108929 | ||||||||
\(737\) | −2.32137 | −0.0855087 | ||||||||
\(738\) | 0.218804 | 0.00805428 | ||||||||
\(739\) | −23.3844 | −0.860210 | −0.430105 | − | 0.902779i | \(-0.641523\pi\) | ||||
−0.430105 | + | 0.902779i | \(0.641523\pi\) | |||||||
\(740\) | −2.56891 | −0.0944349 | ||||||||
\(741\) | −14.5872 | −0.535874 | ||||||||
\(742\) | −2.85975 | −0.104985 | ||||||||
\(743\) | −18.6895 | −0.685652 | −0.342826 | − | 0.939399i | \(-0.611384\pi\) | ||||
−0.342826 | + | 0.939399i | \(0.611384\pi\) | |||||||
\(744\) | −1.89231 | −0.0693755 | ||||||||
\(745\) | −12.9383 | −0.474022 | ||||||||
\(746\) | −1.76809 | −0.0647342 | ||||||||
\(747\) | −13.5470 | −0.495658 | ||||||||
\(748\) | 0.658945 | 0.0240934 | ||||||||
\(749\) | −16.6597 | −0.608734 | ||||||||
\(750\) | 0.869243 | 0.0317403 | ||||||||
\(751\) | −17.5804 | −0.641518 | −0.320759 | − | 0.947161i | \(-0.603938\pi\) | ||||
−0.320759 | + | 0.947161i | \(0.603938\pi\) | |||||||
\(752\) | 13.3207 | 0.485755 | ||||||||
\(753\) | −22.2222 | −0.809823 | ||||||||
\(754\) | 0.559904 | 0.0203905 | ||||||||
\(755\) | −44.6900 | −1.62643 | ||||||||
\(756\) | 7.76925 | 0.282565 | ||||||||
\(757\) | −47.6274 | −1.73105 | −0.865523 | − | 0.500869i | \(-0.833014\pi\) | ||||
−0.865523 | + | 0.500869i | \(0.833014\pi\) | |||||||
\(758\) | 1.10146 | 0.0400067 | ||||||||
\(759\) | 0.113796 | 0.00413052 | ||||||||
\(760\) | −4.11125 | −0.149131 | ||||||||
\(761\) | 32.6918 | 1.18508 | 0.592538 | − | 0.805542i | \(-0.298126\pi\) | ||||
0.592538 | + | 0.805542i | \(0.298126\pi\) | |||||||
\(762\) | 0.778011 | 0.0281844 | ||||||||
\(763\) | 64.6716 | 2.34127 | ||||||||
\(764\) | −29.8831 | −1.08113 | ||||||||
\(765\) | 1.92367 | 0.0695506 | ||||||||
\(766\) | −0.807002 | −0.0291582 | ||||||||
\(767\) | −28.0347 | −1.01228 | ||||||||
\(768\) | −15.5900 | −0.562554 | ||||||||
\(769\) | 13.7155 | 0.494593 | 0.247297 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247297 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(770\) | 0.177518 | 0.00639731 | ||||||||
\(771\) | −5.17485 | −0.186368 | ||||||||
\(772\) | −15.3006 | −0.550682 | ||||||||
\(773\) | −33.0422 | −1.18845 | −0.594223 | − | 0.804300i | \(-0.702540\pi\) | ||||
−0.594223 | + | 0.804300i | \(0.702540\pi\) | |||||||
\(774\) | −0.296734 | −0.0106659 | ||||||||
\(775\) | −8.58134 | −0.308251 | ||||||||
\(776\) | −2.29672 | −0.0824473 | ||||||||
\(777\) | 2.60719 | 0.0935326 | ||||||||
\(778\) | 0.0306675 | 0.00109948 | ||||||||
\(779\) | −22.7503 | −0.815113 | ||||||||
\(780\) | −7.50547 | −0.268739 | ||||||||
\(781\) | −4.08115 | −0.146035 | ||||||||
\(782\) | −0.0247111 | −0.000883669 0 | ||||||||
\(783\) | 3.99093 | 0.142624 | ||||||||
\(784\) | 32.4211 | 1.15789 | ||||||||
\(785\) | 3.68244 | 0.131432 | ||||||||
\(786\) | 0.0396296 | 0.00141354 | ||||||||
\(787\) | 12.9936 | 0.463171 | 0.231585 | − | 0.972815i | \(-0.425609\pi\) | ||||
0.231585 | + | 0.972815i | \(0.425609\pi\) | |||||||
\(788\) | −35.5168 | −1.26523 | ||||||||
\(789\) | −9.97141 | −0.354992 | ||||||||
\(790\) | 0.137987 | 0.00490934 | ||||||||
\(791\) | 36.5975 | 1.30126 | ||||||||
\(792\) | 0.0946551 | 0.00336342 | ||||||||
\(793\) | 19.2835 | 0.684779 | ||||||||
\(794\) | −1.62730 | −0.0577508 | ||||||||
\(795\) | 19.6919 | 0.698400 | ||||||||
\(796\) | −11.4695 | −0.406526 | ||||||||
\(797\) | 12.7179 | 0.450490 | 0.225245 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225245 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(798\) | 2.08358 | 0.0737578 | ||||||||
\(799\) | −3.35605 | −0.118728 | ||||||||
\(800\) | 1.11471 | 0.0394111 | ||||||||
\(801\) | 14.9069 | 0.526709 | ||||||||
\(802\) | −0.0310557 | −0.00109662 | ||||||||
\(803\) | −4.56285 | −0.161020 | ||||||||
\(804\) | −14.0190 | −0.494412 | ||||||||
\(805\) | 2.58100 | 0.0909681 | ||||||||
\(806\) | −0.926460 | −0.0326332 | ||||||||
\(807\) | 3.62992 | 0.127779 | ||||||||
\(808\) | 4.37393 | 0.153874 | ||||||||
\(809\) | −12.0999 | −0.425410 | −0.212705 | − | 0.977116i | \(-0.568227\pi\) | ||||
−0.212705 | + | 0.977116i | \(0.568227\pi\) | |||||||
\(810\) | 0.137987 | 0.00484835 | ||||||||
\(811\) | 36.3321 | 1.27579 | 0.637897 | − | 0.770122i | \(-0.279805\pi\) | ||||
0.637897 | + | 0.770122i | \(0.279805\pi\) | |||||||
\(812\) | 31.0065 | 1.08811 | ||||||||
\(813\) | 25.8916 | 0.908057 | ||||||||
\(814\) | 0.0158617 | 0.000555951 0 | ||||||||
\(815\) | 15.5691 | 0.545362 | ||||||||
\(816\) | 3.96915 | 0.138948 | ||||||||
\(817\) | 30.8532 | 1.07942 | ||||||||
\(818\) | 1.70555 | 0.0596331 | ||||||||
\(819\) | 7.61733 | 0.266171 | ||||||||
\(820\) | −11.7056 | −0.408776 | ||||||||
\(821\) | 10.7638 | 0.375660 | 0.187830 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187830 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(822\) | 0.499546 | 0.0174237 | ||||||||
\(823\) | 21.5152 | 0.749974 | 0.374987 | − | 0.927030i | \(-0.377647\pi\) | ||||
0.374987 | + | 0.927030i | \(0.377647\pi\) | |||||||
\(824\) | 1.41479 | 0.0492867 | ||||||||
\(825\) | 0.429246 | 0.0149444 | ||||||||
\(826\) | 4.00437 | 0.139330 | ||||||||
\(827\) | 43.9232 | 1.52736 | 0.763679 | − | 0.645596i | \(-0.223391\pi\) | ||||
0.763679 | + | 0.645596i | \(0.223391\pi\) | |||||||
\(828\) | 0.687225 | 0.0238827 | ||||||||
\(829\) | −16.9067 | −0.587193 | −0.293596 | − | 0.955930i | \(-0.594852\pi\) | ||||
−0.293596 | + | 0.955930i | \(0.594852\pi\) | |||||||
\(830\) | −1.86930 | −0.0648843 | ||||||||
\(831\) | −18.4623 | −0.640449 | ||||||||
\(832\) | −15.4058 | −0.534099 | ||||||||
\(833\) | −8.16825 | −0.283013 | ||||||||
\(834\) | −0.300227 | −0.0103960 | ||||||||
\(835\) | 29.5470 | 1.02252 | ||||||||
\(836\) | −4.91458 | −0.169974 | ||||||||
\(837\) | −6.60369 | −0.228257 | ||||||||
\(838\) | 0.374143 | 0.0129245 | ||||||||
\(839\) | 36.2251 | 1.25063 | 0.625315 | − | 0.780372i | \(-0.284970\pi\) | ||||
0.625315 | + | 0.780372i | \(0.284970\pi\) | |||||||
\(840\) | 2.14687 | 0.0740740 | ||||||||
\(841\) | −13.0725 | −0.450776 | ||||||||
\(842\) | −0.637483 | −0.0219691 | ||||||||
\(843\) | −8.04062 | −0.276934 | ||||||||
\(844\) | 15.0768 | 0.518966 | ||||||||
\(845\) | 17.6491 | 0.607146 | ||||||||
\(846\) | −0.240731 | −0.00827652 | ||||||||
\(847\) | −42.4161 | −1.45744 | ||||||||
\(848\) | 40.6307 | 1.39526 | ||||||||
\(849\) | −7.20662 | −0.247331 | ||||||||
\(850\) | −0.0932123 | −0.00319715 | ||||||||
\(851\) | 0.230618 | 0.00790549 | ||||||||
\(852\) | −24.6465 | −0.844375 | ||||||||
\(853\) | 32.7287 | 1.12061 | 0.560305 | − | 0.828286i | \(-0.310684\pi\) | ||||
0.560305 | + | 0.828286i | \(0.310684\pi\) | |||||||
\(854\) | −2.75439 | −0.0942532 | ||||||||
\(855\) | −14.3472 | −0.490665 | ||||||||
\(856\) | −1.22576 | −0.0418957 | ||||||||
\(857\) | 8.73749 | 0.298467 | 0.149234 | − | 0.988802i | \(-0.452319\pi\) | ||||
0.149234 | + | 0.988802i | \(0.452319\pi\) | |||||||
\(858\) | 0.0463423 | 0.00158210 | ||||||||
\(859\) | 39.8009 | 1.35799 | 0.678995 | − | 0.734143i | \(-0.262416\pi\) | ||||
0.678995 | + | 0.734143i | \(0.262416\pi\) | |||||||
\(860\) | 15.8747 | 0.541323 | ||||||||
\(861\) | 11.8800 | 0.404870 | ||||||||
\(862\) | 2.01560 | 0.0686516 | ||||||||
\(863\) | −56.2817 | −1.91585 | −0.957925 | − | 0.287018i | \(-0.907336\pi\) | ||||
−0.957925 | + | 0.287018i | \(0.907336\pi\) | |||||||
\(864\) | 0.857818 | 0.0291835 | ||||||||
\(865\) | 15.6810 | 0.533171 | ||||||||
\(866\) | −2.53360 | −0.0860953 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −51.3057 | −1.74143 | ||||||||
\(869\) | 0.330322 | 0.0112054 | ||||||||
\(870\) | 0.550694 | 0.0186703 | ||||||||
\(871\) | −13.7449 | −0.465728 | ||||||||
\(872\) | 4.75830 | 0.161136 | ||||||||
\(873\) | −8.01496 | −0.271265 | ||||||||
\(874\) | 0.184302 | 0.00623410 | ||||||||
\(875\) | 47.1958 | 1.59551 | ||||||||
\(876\) | −27.5556 | −0.931017 | ||||||||
\(877\) | 51.2504 | 1.73060 | 0.865302 | − | 0.501251i | \(-0.167127\pi\) | ||||
0.865302 | + | 0.501251i | \(0.167127\pi\) | |||||||
\(878\) | 0.585939 | 0.0197745 | ||||||||
\(879\) | 21.4899 | 0.724837 | ||||||||
\(880\) | −2.52213 | −0.0850210 | ||||||||
\(881\) | −30.5057 | −1.02776 | −0.513881 | − | 0.857862i | \(-0.671793\pi\) | ||||
−0.513881 | + | 0.857862i | \(0.671793\pi\) | |||||||
\(882\) | −0.585914 | −0.0197288 | ||||||||
\(883\) | 41.2152 | 1.38700 | 0.693501 | − | 0.720456i | \(-0.256067\pi\) | ||||
0.693501 | + | 0.720456i | \(0.256067\pi\) | |||||||
\(884\) | 3.90163 | 0.131226 | ||||||||
\(885\) | −27.5736 | −0.926876 | ||||||||
\(886\) | −0.159569 | −0.00536081 | ||||||||
\(887\) | −4.35717 | −0.146299 | −0.0731497 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731497 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(888\) | 0.191828 | 0.00643732 | ||||||||
\(889\) | 42.2424 | 1.41676 | ||||||||
\(890\) | 2.05695 | 0.0689492 | ||||||||
\(891\) | 0.330322 | 0.0110662 | ||||||||
\(892\) | −50.4996 | −1.69085 | ||||||||
\(893\) | 25.0302 | 0.837604 | ||||||||
\(894\) | 0.482448 | 0.0161355 | ||||||||
\(895\) | −24.8148 | −0.829467 | ||||||||
\(896\) | 8.88229 | 0.296736 | ||||||||
\(897\) | 0.673787 | 0.0224971 | ||||||||
\(898\) | 1.99821 | 0.0666813 | ||||||||
\(899\) | −26.3548 | −0.878983 | ||||||||
\(900\) | 2.59226 | 0.0864088 | ||||||||
\(901\) | −10.2366 | −0.341031 | ||||||||
\(902\) | 0.0722758 | 0.00240652 | ||||||||
\(903\) | −16.1113 | −0.536151 | ||||||||
\(904\) | 2.69271 | 0.0895581 | ||||||||
\(905\) | −29.8034 | −0.990700 | ||||||||
\(906\) | 1.66642 | 0.0553630 | ||||||||
\(907\) | −22.6739 | −0.752874 | −0.376437 | − | 0.926442i | \(-0.622851\pi\) | ||||
−0.376437 | + | 0.926442i | \(0.622851\pi\) | |||||||
\(908\) | −27.7613 | −0.921292 | ||||||||
\(909\) | 15.2639 | 0.506272 | ||||||||
\(910\) | 1.05109 | 0.0348432 | ||||||||
\(911\) | −44.4725 | −1.47344 | −0.736720 | − | 0.676198i | \(-0.763626\pi\) | ||||
−0.736720 | + | 0.676198i | \(0.763626\pi\) | |||||||
\(912\) | −29.6029 | −0.980251 | ||||||||
\(913\) | −4.47487 | −0.148096 | ||||||||
\(914\) | −0.0819548 | −0.00271082 | ||||||||
\(915\) | 18.9663 | 0.627008 | ||||||||
\(916\) | 34.0709 | 1.12574 | ||||||||
\(917\) | 2.15170 | 0.0710556 | ||||||||
\(918\) | −0.0717307 | −0.00236747 | ||||||||
\(919\) | 29.4689 | 0.972088 | 0.486044 | − | 0.873934i | \(-0.338439\pi\) | ||||
0.486044 | + | 0.873934i | \(0.338439\pi\) | |||||||
\(920\) | 0.189900 | 0.00626082 | ||||||||
\(921\) | 9.65818 | 0.318248 | ||||||||
\(922\) | −1.14412 | −0.0376797 | ||||||||
\(923\) | −24.1646 | −0.795386 | ||||||||
\(924\) | 2.56636 | 0.0844270 | ||||||||
\(925\) | 0.869909 | 0.0286024 | ||||||||
\(926\) | 0.554827 | 0.0182328 | ||||||||
\(927\) | 4.93728 | 0.162161 | ||||||||
\(928\) | 3.42349 | 0.112381 | ||||||||
\(929\) | 17.6254 | 0.578269 | 0.289135 | − | 0.957288i | \(-0.406632\pi\) | ||||
0.289135 | + | 0.957288i | \(0.406632\pi\) | |||||||
\(930\) | −0.911221 | −0.0298801 | ||||||||
\(931\) | 60.9208 | 1.99660 | ||||||||
\(932\) | −27.0016 | −0.884468 | ||||||||
\(933\) | −27.6205 | −0.904255 | ||||||||
\(934\) | 2.21195 | 0.0723772 | ||||||||
\(935\) | 0.635433 | 0.0207809 | ||||||||
\(936\) | 0.560455 | 0.0183190 | ||||||||
\(937\) | 52.1125 | 1.70244 | 0.851221 | − | 0.524808i | \(-0.175863\pi\) | ||||
0.851221 | + | 0.524808i | \(0.175863\pi\) | |||||||
\(938\) | 1.96326 | 0.0641029 | ||||||||
\(939\) | 1.18468 | 0.0386607 | ||||||||
\(940\) | 12.8787 | 0.420056 | ||||||||
\(941\) | −51.3286 | −1.67327 | −0.836633 | − | 0.547764i | \(-0.815479\pi\) | ||||
−0.836633 | + | 0.547764i | \(0.815479\pi\) | |||||||
\(942\) | −0.137312 | −0.00447387 | ||||||||
\(943\) | 1.05084 | 0.0342201 | ||||||||
\(944\) | −56.8931 | −1.85171 | ||||||||
\(945\) | 7.49203 | 0.243716 | ||||||||
\(946\) | −0.0980180 | −0.00318684 | ||||||||
\(947\) | 2.43683 | 0.0791863 | 0.0395932 | − | 0.999216i | \(-0.487394\pi\) | ||||
0.0395932 | + | 0.999216i | \(0.487394\pi\) | |||||||
\(948\) | 1.99485 | 0.0647899 | ||||||||
\(949\) | −27.0168 | −0.877001 | ||||||||
\(950\) | 0.695200 | 0.0225553 | ||||||||
\(951\) | −4.56237 | −0.147945 | ||||||||
\(952\) | −1.11602 | −0.0361706 | ||||||||
\(953\) | 31.1967 | 1.01056 | 0.505280 | − | 0.862955i | \(-0.331389\pi\) | ||||
0.505280 | + | 0.862955i | \(0.331389\pi\) | |||||||
\(954\) | −0.734279 | −0.0237732 | ||||||||
\(955\) | −28.8168 | −0.932489 | ||||||||
\(956\) | −6.17832 | −0.199821 | ||||||||
\(957\) | 1.31829 | 0.0426143 | ||||||||
\(958\) | −2.58539 | −0.0835302 | ||||||||
\(959\) | 27.1230 | 0.875848 | ||||||||
\(960\) | −15.1524 | −0.489040 | ||||||||
\(961\) | 12.6088 | 0.406734 | ||||||||
\(962\) | 0.0939173 | 0.00302801 | ||||||||
\(963\) | −4.27760 | −0.137844 | ||||||||
\(964\) | 25.3220 | 0.815568 | ||||||||
\(965\) | −14.7547 | −0.474970 | ||||||||
\(966\) | −0.0962411 | −0.00309651 | ||||||||
\(967\) | 24.4261 | 0.785490 | 0.392745 | − | 0.919647i | \(-0.371525\pi\) | ||||
0.392745 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(968\) | −3.12082 | −0.100307 | ||||||||
\(969\) | 7.45825 | 0.239593 | ||||||||
\(970\) | −1.10596 | −0.0355101 | ||||||||
\(971\) | 24.6118 | 0.789830 | 0.394915 | − | 0.918718i | \(-0.370774\pi\) | ||||
0.394915 | + | 0.918718i | \(0.370774\pi\) | |||||||
\(972\) | 1.99485 | 0.0639850 | ||||||||
\(973\) | −16.3009 | −0.522583 | ||||||||
\(974\) | 2.32638 | 0.0745420 | ||||||||
\(975\) | 2.54157 | 0.0813955 | ||||||||
\(976\) | 39.1336 | 1.25264 | ||||||||
\(977\) | 11.7712 | 0.376595 | 0.188297 | − | 0.982112i | \(-0.439703\pi\) | ||||
0.188297 | + | 0.982112i | \(0.439703\pi\) | |||||||
\(978\) | −0.580547 | −0.0185638 | ||||||||
\(979\) | 4.92408 | 0.157374 | ||||||||
\(980\) | 31.3453 | 1.00129 | ||||||||
\(981\) | 16.6053 | 0.530165 | ||||||||
\(982\) | −2.63857 | −0.0842001 | ||||||||
\(983\) | −31.2321 | −0.996150 | −0.498075 | − | 0.867134i | \(-0.665960\pi\) | ||||
−0.498075 | + | 0.867134i | \(0.665960\pi\) | |||||||
\(984\) | 0.874089 | 0.0278649 | ||||||||
\(985\) | −34.2495 | −1.09128 | ||||||||
\(986\) | −0.286272 | −0.00911675 | ||||||||
\(987\) | −13.0706 | −0.416042 | ||||||||
\(988\) | −29.0993 | −0.925773 | ||||||||
\(989\) | −1.42512 | −0.0453161 | ||||||||
\(990\) | 0.0455800 | 0.00144863 | ||||||||
\(991\) | 28.0232 | 0.890187 | 0.445093 | − | 0.895484i | \(-0.353171\pi\) | ||||
0.445093 | + | 0.895484i | \(0.353171\pi\) | |||||||
\(992\) | −5.66476 | −0.179856 | ||||||||
\(993\) | 14.5436 | 0.461528 | ||||||||
\(994\) | 3.45157 | 0.109477 | ||||||||
\(995\) | −11.0603 | −0.350634 | ||||||||
\(996\) | −27.0242 | −0.856295 | ||||||||
\(997\) | 42.3951 | 1.34267 | 0.671334 | − | 0.741155i | \(-0.265722\pi\) | ||||
0.671334 | + | 0.741155i | \(0.265722\pi\) | |||||||
\(998\) | −2.29931 | −0.0727833 | ||||||||
\(999\) | 0.669431 | 0.0211798 |
(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 | 4029.2.a.l.1.17 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.17 | ✓ | 32 | 1.1 | even | 1 | trivial |