Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62641 | −1.85715 | −0.928577 | − | 0.371141i | \(-0.878967\pi\) | ||||
−0.928577 | + | 0.371141i | \(0.878967\pi\) | |||||||
\(3\) | −3.35140 | −1.93493 | −0.967466 | − | 0.253003i | \(-0.918582\pi\) | ||||
−0.967466 | + | 0.253003i | \(0.918582\pi\) | |||||||
\(4\) | 4.89803 | 2.44902 | ||||||||
\(5\) | −4.35294 | −1.94669 | −0.973346 | − | 0.229341i | \(-0.926343\pi\) | ||||
−0.973346 | + | 0.229341i | \(0.926343\pi\) | |||||||
\(6\) | 8.80215 | 3.59346 | ||||||||
\(7\) | 2.67168 | 1.00980 | 0.504901 | − | 0.863177i | \(-0.331529\pi\) | ||||
0.504901 | + | 0.863177i | \(0.331529\pi\) | |||||||
\(8\) | −7.61143 | −2.69105 | ||||||||
\(9\) | 8.23188 | 2.74396 | ||||||||
\(10\) | 11.4326 | 3.61531 | ||||||||
\(11\) | −0.768445 | −0.231695 | −0.115847 | − | 0.993267i | \(-0.536958\pi\) | ||||
−0.115847 | + | 0.993267i | \(0.536958\pi\) | |||||||
\(12\) | −16.4153 | −4.73868 | ||||||||
\(13\) | 6.00805 | 1.66633 | 0.833167 | − | 0.553022i | \(-0.186525\pi\) | ||||
0.833167 | + | 0.553022i | \(0.186525\pi\) | |||||||
\(14\) | −7.01694 | −1.87536 | ||||||||
\(15\) | 14.5884 | 3.76672 | ||||||||
\(16\) | 10.1947 | 2.54867 | ||||||||
\(17\) | 4.35173 | 1.05545 | 0.527725 | − | 0.849415i | \(-0.323045\pi\) | ||||
0.527725 | + | 0.849415i | \(0.323045\pi\) | |||||||
\(18\) | −21.6203 | −5.09595 | ||||||||
\(19\) | −3.91306 | −0.897718 | −0.448859 | − | 0.893603i | \(-0.648169\pi\) | ||||
−0.448859 | + | 0.893603i | \(0.648169\pi\) | |||||||
\(20\) | −21.3208 | −4.76748 | ||||||||
\(21\) | −8.95388 | −1.95390 | ||||||||
\(22\) | 2.01825 | 0.430293 | ||||||||
\(23\) | 2.20940 | 0.460692 | 0.230346 | − | 0.973109i | \(-0.426014\pi\) | ||||
0.230346 | + | 0.973109i | \(0.426014\pi\) | |||||||
\(24\) | 25.5089 | 5.20699 | ||||||||
\(25\) | 13.9481 | 2.78961 | ||||||||
\(26\) | −15.7796 | −3.09464 | ||||||||
\(27\) | −17.5341 | −3.37444 | ||||||||
\(28\) | 13.0860 | 2.47302 | ||||||||
\(29\) | 6.03569 | 1.12080 | 0.560400 | − | 0.828222i | \(-0.310647\pi\) | ||||
0.560400 | + | 0.828222i | \(0.310647\pi\) | |||||||
\(30\) | −38.3152 | −6.99537 | ||||||||
\(31\) | 5.87842 | 1.05580 | 0.527898 | − | 0.849308i | \(-0.322980\pi\) | ||||
0.527898 | + | 0.849308i | \(0.322980\pi\) | |||||||
\(32\) | −11.5525 | −2.04222 | ||||||||
\(33\) | 2.57537 | 0.448314 | ||||||||
\(34\) | −11.4294 | −1.96013 | ||||||||
\(35\) | −11.6297 | −1.96577 | ||||||||
\(36\) | 40.3200 | 6.72000 | ||||||||
\(37\) | 3.95604 | 0.650368 | 0.325184 | − | 0.945651i | \(-0.394574\pi\) | ||||
0.325184 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(38\) | 10.2773 | 1.66720 | ||||||||
\(39\) | −20.1354 | −3.22424 | ||||||||
\(40\) | 33.1321 | 5.23864 | ||||||||
\(41\) | 8.23293 | 1.28577 | 0.642884 | − | 0.765964i | \(-0.277738\pi\) | ||||
0.642884 | + | 0.765964i | \(0.277738\pi\) | |||||||
\(42\) | 23.5166 | 3.62869 | ||||||||
\(43\) | −7.07844 | −1.07945 | −0.539726 | − | 0.841841i | \(-0.681472\pi\) | ||||
−0.539726 | + | 0.841841i | \(0.681472\pi\) | |||||||
\(44\) | −3.76387 | −0.567425 | ||||||||
\(45\) | −35.8328 | −5.34164 | ||||||||
\(46\) | −5.80279 | −0.855575 | ||||||||
\(47\) | −6.17473 | −0.900677 | −0.450338 | − | 0.892858i | \(-0.648697\pi\) | ||||
−0.450338 | + | 0.892858i | \(0.648697\pi\) | |||||||
\(48\) | −34.1664 | −4.93150 | ||||||||
\(49\) | 0.137897 | 0.0196995 | ||||||||
\(50\) | −36.6333 | −5.18073 | ||||||||
\(51\) | −14.5844 | −2.04222 | ||||||||
\(52\) | 29.4276 | 4.08088 | ||||||||
\(53\) | −6.77161 | −0.930152 | −0.465076 | − | 0.885271i | \(-0.653973\pi\) | ||||
−0.465076 | + | 0.885271i | \(0.653973\pi\) | |||||||
\(54\) | 46.0518 | 6.26685 | ||||||||
\(55\) | 3.34499 | 0.451039 | ||||||||
\(56\) | −20.3353 | −2.71742 | ||||||||
\(57\) | 13.1142 | 1.73702 | ||||||||
\(58\) | −15.8522 | −2.08150 | ||||||||
\(59\) | 1.70484 | 0.221952 | 0.110976 | − | 0.993823i | \(-0.464602\pi\) | ||||
0.110976 | + | 0.993823i | \(0.464602\pi\) | |||||||
\(60\) | 71.4546 | 9.22475 | ||||||||
\(61\) | 0.753420 | 0.0964655 | 0.0482328 | − | 0.998836i | \(-0.484641\pi\) | ||||
0.0482328 | + | 0.998836i | \(0.484641\pi\) | |||||||
\(62\) | −15.4392 | −1.96077 | ||||||||
\(63\) | 21.9930 | 2.77085 | ||||||||
\(64\) | 9.95238 | 1.24405 | ||||||||
\(65\) | −26.1527 | −3.24384 | ||||||||
\(66\) | −6.76397 | −0.832587 | ||||||||
\(67\) | −12.2660 | −1.49853 | −0.749264 | − | 0.662271i | \(-0.769593\pi\) | ||||
−0.749264 | + | 0.662271i | \(0.769593\pi\) | |||||||
\(68\) | 21.3149 | 2.58482 | ||||||||
\(69\) | −7.40458 | −0.891406 | ||||||||
\(70\) | 30.5443 | 3.65074 | ||||||||
\(71\) | −14.3058 | −1.69779 | −0.848895 | − | 0.528562i | \(-0.822731\pi\) | ||||
−0.848895 | + | 0.528562i | \(0.822731\pi\) | |||||||
\(72\) | −62.6563 | −7.38412 | ||||||||
\(73\) | −0.962519 | −0.112654 | −0.0563271 | − | 0.998412i | \(-0.517939\pi\) | ||||
−0.0563271 | + | 0.998412i | \(0.517939\pi\) | |||||||
\(74\) | −10.3902 | −1.20783 | ||||||||
\(75\) | −46.7455 | −5.39770 | ||||||||
\(76\) | −19.1663 | −2.19853 | ||||||||
\(77\) | −2.05304 | −0.233966 | ||||||||
\(78\) | 52.8838 | 5.98791 | ||||||||
\(79\) | −4.69274 | −0.527975 | −0.263987 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263987 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(80\) | −44.3768 | −4.96147 | ||||||||
\(81\) | 34.0681 | 3.78535 | ||||||||
\(82\) | −21.6231 | −2.38787 | ||||||||
\(83\) | −10.6501 | −1.16900 | −0.584499 | − | 0.811394i | \(-0.698709\pi\) | ||||
−0.584499 | + | 0.811394i | \(0.698709\pi\) | |||||||
\(84\) | −43.8564 | −4.78513 | ||||||||
\(85\) | −18.9428 | −2.05464 | ||||||||
\(86\) | 18.5909 | 2.00471 | ||||||||
\(87\) | −20.2280 | −2.16867 | ||||||||
\(88\) | 5.84896 | 0.623502 | ||||||||
\(89\) | 4.47991 | 0.474870 | 0.237435 | − | 0.971403i | \(-0.423693\pi\) | ||||
0.237435 | + | 0.971403i | \(0.423693\pi\) | |||||||
\(90\) | 94.1117 | 9.92025 | ||||||||
\(91\) | 16.0516 | 1.68267 | ||||||||
\(92\) | 10.8217 | 1.12824 | ||||||||
\(93\) | −19.7009 | −2.04289 | ||||||||
\(94\) | 16.2174 | 1.67269 | ||||||||
\(95\) | 17.0333 | 1.74758 | ||||||||
\(96\) | 38.7172 | 3.95156 | ||||||||
\(97\) | −7.80956 | −0.792941 | −0.396470 | − | 0.918048i | \(-0.629765\pi\) | ||||
−0.396470 | + | 0.918048i | \(0.629765\pi\) | |||||||
\(98\) | −0.362173 | −0.0365850 | ||||||||
\(99\) | −6.32574 | −0.635761 | ||||||||
\(100\) | 68.3180 | 6.83180 | ||||||||
\(101\) | 9.68037 | 0.963233 | 0.481616 | − | 0.876382i | \(-0.340050\pi\) | ||||
0.481616 | + | 0.876382i | \(0.340050\pi\) | |||||||
\(102\) | 38.3046 | 3.79272 | ||||||||
\(103\) | 17.5659 | 1.73082 | 0.865412 | − | 0.501061i | \(-0.167057\pi\) | ||||
0.865412 | + | 0.501061i | \(0.167057\pi\) | |||||||
\(104\) | −45.7299 | −4.48418 | ||||||||
\(105\) | 38.9757 | 3.80364 | ||||||||
\(106\) | 17.7850 | 1.72744 | ||||||||
\(107\) | −16.6215 | −1.60686 | −0.803430 | − | 0.595399i | \(-0.796994\pi\) | ||||
−0.803430 | + | 0.595399i | \(0.796994\pi\) | |||||||
\(108\) | −85.8826 | −8.26406 | ||||||||
\(109\) | 4.94978 | 0.474103 | 0.237051 | − | 0.971497i | \(-0.423819\pi\) | ||||
0.237051 | + | 0.971497i | \(0.423819\pi\) | |||||||
\(110\) | −8.78532 | −0.837648 | ||||||||
\(111\) | −13.2583 | −1.25842 | ||||||||
\(112\) | 27.2369 | 2.57365 | ||||||||
\(113\) | 5.04932 | 0.475000 | 0.237500 | − | 0.971388i | \(-0.423672\pi\) | ||||
0.237500 | + | 0.971388i | \(0.423672\pi\) | |||||||
\(114\) | −34.4434 | −3.22592 | ||||||||
\(115\) | −9.61737 | −0.896825 | ||||||||
\(116\) | 29.5630 | 2.74486 | ||||||||
\(117\) | 49.4575 | 4.57235 | ||||||||
\(118\) | −4.47762 | −0.412198 | ||||||||
\(119\) | 11.6265 | 1.06580 | ||||||||
\(120\) | −111.039 | −10.1364 | ||||||||
\(121\) | −10.4095 | −0.946317 | ||||||||
\(122\) | −1.97879 | −0.179151 | ||||||||
\(123\) | −27.5918 | −2.48787 | ||||||||
\(124\) | 28.7927 | 2.58566 | ||||||||
\(125\) | −38.9503 | −3.48382 | ||||||||
\(126\) | −57.7626 | −5.14590 | ||||||||
\(127\) | −5.62832 | −0.499432 | −0.249716 | − | 0.968319i | \(-0.580337\pi\) | ||||
−0.249716 | + | 0.968319i | \(0.580337\pi\) | |||||||
\(128\) | −3.03395 | −0.268166 | ||||||||
\(129\) | 23.7227 | 2.08867 | ||||||||
\(130\) | 68.6876 | 6.02431 | ||||||||
\(131\) | 8.28231 | 0.723628 | 0.361814 | − | 0.932250i | \(-0.382157\pi\) | ||||
0.361814 | + | 0.932250i | \(0.382157\pi\) | |||||||
\(132\) | 12.6142 | 1.09793 | ||||||||
\(133\) | −10.4545 | −0.906517 | ||||||||
\(134\) | 32.2155 | 2.78300 | ||||||||
\(135\) | 76.3248 | 6.56899 | ||||||||
\(136\) | −33.1229 | −2.84027 | ||||||||
\(137\) | −4.25629 | −0.363639 | −0.181820 | − | 0.983332i | \(-0.558199\pi\) | ||||
−0.181820 | + | 0.983332i | \(0.558199\pi\) | |||||||
\(138\) | 19.4475 | 1.65548 | ||||||||
\(139\) | 2.95510 | 0.250648 | 0.125324 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125324 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(140\) | −56.9625 | −4.81421 | ||||||||
\(141\) | 20.6940 | 1.74275 | ||||||||
\(142\) | 37.5730 | 3.15305 | ||||||||
\(143\) | −4.61686 | −0.386081 | ||||||||
\(144\) | 83.9213 | 6.99344 | ||||||||
\(145\) | −26.2730 | −2.18185 | ||||||||
\(146\) | 2.52797 | 0.209216 | ||||||||
\(147\) | −0.462147 | −0.0381172 | ||||||||
\(148\) | 19.3768 | 1.59276 | ||||||||
\(149\) | 6.12290 | 0.501608 | 0.250804 | − | 0.968038i | \(-0.419305\pi\) | ||||
0.250804 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(150\) | 122.773 | 10.0244 | ||||||||
\(151\) | −14.4111 | −1.17276 | −0.586379 | − | 0.810036i | \(-0.699447\pi\) | ||||
−0.586379 | + | 0.810036i | \(0.699447\pi\) | |||||||
\(152\) | 29.7840 | 2.41580 | ||||||||
\(153\) | 35.8229 | 2.89611 | ||||||||
\(154\) | 5.39213 | 0.434510 | ||||||||
\(155\) | −25.5884 | −2.05531 | ||||||||
\(156\) | −98.6238 | −7.89622 | ||||||||
\(157\) | 7.51763 | 0.599972 | 0.299986 | − | 0.953944i | \(-0.403018\pi\) | ||||
0.299986 | + | 0.953944i | \(0.403018\pi\) | |||||||
\(158\) | 12.3251 | 0.980530 | ||||||||
\(159\) | 22.6944 | 1.79978 | ||||||||
\(160\) | 50.2875 | 3.97557 | ||||||||
\(161\) | 5.90282 | 0.465207 | ||||||||
\(162\) | −89.4770 | −7.02997 | ||||||||
\(163\) | −18.1477 | −1.42143 | −0.710717 | − | 0.703478i | \(-0.751629\pi\) | ||||
−0.710717 | + | 0.703478i | \(0.751629\pi\) | |||||||
\(164\) | 40.3252 | 3.14887 | ||||||||
\(165\) | −11.2104 | −0.872729 | ||||||||
\(166\) | 27.9715 | 2.17101 | ||||||||
\(167\) | −14.5543 | −1.12625 | −0.563123 | − | 0.826373i | \(-0.690400\pi\) | ||||
−0.563123 | + | 0.826373i | \(0.690400\pi\) | |||||||
\(168\) | 68.1518 | 5.25803 | ||||||||
\(169\) | 23.0967 | 1.77667 | ||||||||
\(170\) | 49.7516 | 3.81577 | ||||||||
\(171\) | −32.2118 | −2.46330 | ||||||||
\(172\) | −34.6705 | −2.64360 | ||||||||
\(173\) | −10.9106 | −0.829516 | −0.414758 | − | 0.909932i | \(-0.636134\pi\) | ||||
−0.414758 | + | 0.909932i | \(0.636134\pi\) | |||||||
\(174\) | 53.1271 | 4.02755 | ||||||||
\(175\) | 37.2648 | 2.81695 | ||||||||
\(176\) | −7.83405 | −0.590513 | ||||||||
\(177\) | −5.71361 | −0.429461 | ||||||||
\(178\) | −11.7661 | −0.881905 | ||||||||
\(179\) | 20.2568 | 1.51407 | 0.757033 | − | 0.653377i | \(-0.226648\pi\) | ||||
0.757033 | + | 0.653377i | \(0.226648\pi\) | |||||||
\(180\) | −175.510 | −13.0818 | ||||||||
\(181\) | 2.23232 | 0.165927 | 0.0829635 | − | 0.996553i | \(-0.473562\pi\) | ||||
0.0829635 | + | 0.996553i | \(0.473562\pi\) | |||||||
\(182\) | −42.1581 | −3.12497 | ||||||||
\(183\) | −2.52501 | −0.186654 | ||||||||
\(184\) | −16.8167 | −1.23974 | ||||||||
\(185\) | −17.2204 | −1.26607 | ||||||||
\(186\) | 51.7428 | 3.79396 | ||||||||
\(187\) | −3.34407 | −0.244542 | ||||||||
\(188\) | −30.2440 | −2.20577 | ||||||||
\(189\) | −46.8456 | −3.40751 | ||||||||
\(190\) | −44.7365 | −3.24552 | ||||||||
\(191\) | 2.74977 | 0.198966 | 0.0994831 | − | 0.995039i | \(-0.468281\pi\) | ||||
0.0994831 | + | 0.995039i | \(0.468281\pi\) | |||||||
\(192\) | −33.3544 | −2.40715 | ||||||||
\(193\) | 15.0977 | 1.08676 | 0.543379 | − | 0.839488i | \(-0.317145\pi\) | ||||
0.543379 | + | 0.839488i | \(0.317145\pi\) | |||||||
\(194\) | 20.5111 | 1.47261 | ||||||||
\(195\) | 87.6480 | 6.27661 | ||||||||
\(196\) | 0.675423 | 0.0482445 | ||||||||
\(197\) | −0.182597 | −0.0130095 | −0.00650475 | − | 0.999979i | \(-0.502071\pi\) | ||||
−0.00650475 | + | 0.999979i | \(0.502071\pi\) | |||||||
\(198\) | 16.6140 | 1.18071 | ||||||||
\(199\) | −13.4157 | −0.951015 | −0.475508 | − | 0.879712i | \(-0.657736\pi\) | ||||
−0.475508 | + | 0.879712i | \(0.657736\pi\) | |||||||
\(200\) | −106.165 | −7.50697 | ||||||||
\(201\) | 41.1082 | 2.89955 | ||||||||
\(202\) | −25.4246 | −1.78887 | ||||||||
\(203\) | 16.1255 | 1.13179 | ||||||||
\(204\) | −71.4348 | −5.00144 | ||||||||
\(205\) | −35.8374 | −2.50299 | ||||||||
\(206\) | −46.1354 | −3.21440 | ||||||||
\(207\) | 18.1875 | 1.26412 | ||||||||
\(208\) | 61.2501 | 4.24693 | ||||||||
\(209\) | 3.00697 | 0.207997 | ||||||||
\(210\) | −102.366 | −7.06393 | ||||||||
\(211\) | 6.99188 | 0.481341 | 0.240670 | − | 0.970607i | \(-0.422633\pi\) | ||||
0.240670 | + | 0.970607i | \(0.422633\pi\) | |||||||
\(212\) | −33.1676 | −2.27796 | ||||||||
\(213\) | 47.9445 | 3.28511 | ||||||||
\(214\) | 43.6549 | 2.98419 | ||||||||
\(215\) | 30.8120 | 2.10136 | ||||||||
\(216\) | 133.460 | 9.08077 | ||||||||
\(217\) | 15.7053 | 1.06614 | ||||||||
\(218\) | −13.0001 | −0.880481 | ||||||||
\(219\) | 3.22578 | 0.217978 | ||||||||
\(220\) | 16.3839 | 1.10460 | ||||||||
\(221\) | 26.1454 | 1.75873 | ||||||||
\(222\) | 34.8216 | 2.33707 | ||||||||
\(223\) | −27.1657 | −1.81915 | −0.909575 | − | 0.415540i | \(-0.863593\pi\) | ||||
−0.909575 | + | 0.415540i | \(0.863593\pi\) | |||||||
\(224\) | −30.8647 | −2.06224 | ||||||||
\(225\) | 114.819 | 7.65457 | ||||||||
\(226\) | −13.2616 | −0.882148 | ||||||||
\(227\) | −10.4799 | −0.695573 | −0.347787 | − | 0.937574i | \(-0.613067\pi\) | ||||
−0.347787 | + | 0.937574i | \(0.613067\pi\) | |||||||
\(228\) | 64.2340 | 4.25400 | ||||||||
\(229\) | −22.9583 | −1.51713 | −0.758565 | − | 0.651597i | \(-0.774099\pi\) | ||||
−0.758565 | + | 0.651597i | \(0.774099\pi\) | |||||||
\(230\) | 25.2592 | 1.66554 | ||||||||
\(231\) | 6.88056 | 0.452708 | ||||||||
\(232\) | −45.9403 | −3.01613 | ||||||||
\(233\) | −4.61222 | −0.302157 | −0.151078 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(234\) | −129.896 | −8.49156 | ||||||||
\(235\) | 26.8782 | 1.75334 | ||||||||
\(236\) | 8.35038 | 0.543563 | ||||||||
\(237\) | 15.7273 | 1.02160 | ||||||||
\(238\) | −30.5358 | −1.97934 | ||||||||
\(239\) | 1.38394 | 0.0895198 | 0.0447599 | − | 0.998998i | \(-0.485748\pi\) | ||||
0.0447599 | + | 0.998998i | \(0.485748\pi\) | |||||||
\(240\) | 148.724 | 9.60011 | ||||||||
\(241\) | 20.1105 | 1.29543 | 0.647715 | − | 0.761883i | \(-0.275725\pi\) | ||||
0.647715 | + | 0.761883i | \(0.275725\pi\) | |||||||
\(242\) | 27.3396 | 1.75746 | ||||||||
\(243\) | −61.5736 | −3.94995 | ||||||||
\(244\) | 3.69028 | 0.236246 | ||||||||
\(245\) | −0.600255 | −0.0383489 | ||||||||
\(246\) | 72.4675 | 4.62036 | ||||||||
\(247\) | −23.5099 | −1.49590 | ||||||||
\(248\) | −44.7432 | −2.84120 | ||||||||
\(249\) | 35.6927 | 2.26193 | ||||||||
\(250\) | 102.299 | 6.46999 | ||||||||
\(251\) | 11.3916 | 0.719031 | 0.359516 | − | 0.933139i | \(-0.382942\pi\) | ||||
0.359516 | + | 0.933139i | \(0.382942\pi\) | |||||||
\(252\) | 107.722 | 6.78587 | ||||||||
\(253\) | −1.69780 | −0.106740 | ||||||||
\(254\) | 14.7823 | 0.927523 | ||||||||
\(255\) | 63.4849 | 3.97558 | ||||||||
\(256\) | −11.9364 | −0.746022 | ||||||||
\(257\) | −24.4972 | −1.52809 | −0.764046 | − | 0.645162i | \(-0.776790\pi\) | ||||
−0.764046 | + | 0.645162i | \(0.776790\pi\) | |||||||
\(258\) | −62.3055 | −3.87897 | ||||||||
\(259\) | 10.5693 | 0.656743 | ||||||||
\(260\) | −128.097 | −7.94422 | ||||||||
\(261\) | 49.6851 | 3.07543 | ||||||||
\(262\) | −21.7527 | −1.34389 | ||||||||
\(263\) | 3.30243 | 0.203637 | 0.101818 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101818 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(264\) | −19.6022 | −1.20643 | ||||||||
\(265\) | 29.4764 | 1.81072 | ||||||||
\(266\) | 27.4577 | 1.68354 | ||||||||
\(267\) | −15.0140 | −0.918840 | ||||||||
\(268\) | −60.0792 | −3.66992 | ||||||||
\(269\) | −11.1185 | −0.677906 | −0.338953 | − | 0.940803i | \(-0.610073\pi\) | ||||
−0.338953 | + | 0.940803i | \(0.610073\pi\) | |||||||
\(270\) | −200.460 | −12.1996 | ||||||||
\(271\) | 27.5718 | 1.67487 | 0.837433 | − | 0.546541i | \(-0.184056\pi\) | ||||
0.837433 | + | 0.546541i | \(0.184056\pi\) | |||||||
\(272\) | 44.3645 | 2.68999 | ||||||||
\(273\) | −53.7954 | −3.25584 | ||||||||
\(274\) | 11.1788 | 0.675333 | ||||||||
\(275\) | −10.7183 | −0.646338 | ||||||||
\(276\) | −36.2679 | −2.18307 | ||||||||
\(277\) | −20.0060 | −1.20204 | −0.601022 | − | 0.799233i | \(-0.705240\pi\) | ||||
−0.601022 | + | 0.799233i | \(0.705240\pi\) | |||||||
\(278\) | −7.76131 | −0.465493 | ||||||||
\(279\) | 48.3904 | 2.89706 | ||||||||
\(280\) | 88.5184 | 5.28999 | ||||||||
\(281\) | −24.8991 | −1.48536 | −0.742678 | − | 0.669649i | \(-0.766445\pi\) | ||||
−0.742678 | + | 0.669649i | \(0.766445\pi\) | |||||||
\(282\) | −54.3509 | −3.23655 | ||||||||
\(283\) | 13.3152 | 0.791505 | 0.395753 | − | 0.918357i | \(-0.370484\pi\) | ||||
0.395753 | + | 0.918357i | \(0.370484\pi\) | |||||||
\(284\) | −70.0704 | −4.15792 | ||||||||
\(285\) | −57.0854 | −3.38145 | ||||||||
\(286\) | 12.1258 | 0.717011 | ||||||||
\(287\) | 21.9958 | 1.29837 | ||||||||
\(288\) | −95.0991 | −5.60377 | ||||||||
\(289\) | 1.93757 | 0.113975 | ||||||||
\(290\) | 69.0037 | 4.05203 | ||||||||
\(291\) | 26.1730 | 1.53429 | ||||||||
\(292\) | −4.71445 | −0.275892 | ||||||||
\(293\) | −10.0223 | −0.585510 | −0.292755 | − | 0.956188i | \(-0.594572\pi\) | ||||
−0.292755 | + | 0.956188i | \(0.594572\pi\) | |||||||
\(294\) | 1.21379 | 0.0707895 | ||||||||
\(295\) | −7.42107 | −0.432071 | ||||||||
\(296\) | −30.1111 | −1.75017 | ||||||||
\(297\) | 13.4740 | 0.781840 | ||||||||
\(298\) | −16.0813 | −0.931562 | ||||||||
\(299\) | 13.2742 | 0.767666 | ||||||||
\(300\) | −228.961 | −13.2191 | ||||||||
\(301\) | −18.9114 | −1.09003 | ||||||||
\(302\) | 37.8495 | 2.17799 | ||||||||
\(303\) | −32.4428 | −1.86379 | ||||||||
\(304\) | −39.8924 | −2.28799 | ||||||||
\(305\) | −3.27959 | −0.187789 | ||||||||
\(306\) | −94.0857 | −5.37852 | ||||||||
\(307\) | 14.3416 | 0.818519 | 0.409259 | − | 0.912418i | \(-0.365787\pi\) | ||||
0.409259 | + | 0.912418i | \(0.365787\pi\) | |||||||
\(308\) | −10.0559 | −0.572986 | ||||||||
\(309\) | −58.8705 | −3.34902 | ||||||||
\(310\) | 67.2057 | 3.81702 | ||||||||
\(311\) | −2.70719 | −0.153511 | −0.0767555 | − | 0.997050i | \(-0.524456\pi\) | ||||
−0.0767555 | + | 0.997050i | \(0.524456\pi\) | |||||||
\(312\) | 153.259 | 8.67658 | ||||||||
\(313\) | −17.3533 | −0.980868 | −0.490434 | − | 0.871478i | \(-0.663162\pi\) | ||||
−0.490434 | + | 0.871478i | \(0.663162\pi\) | |||||||
\(314\) | −19.7444 | −1.11424 | ||||||||
\(315\) | −95.7340 | −5.39400 | ||||||||
\(316\) | −22.9852 | −1.29302 | ||||||||
\(317\) | 5.28477 | 0.296822 | 0.148411 | − | 0.988926i | \(-0.452584\pi\) | ||||
0.148411 | + | 0.988926i | \(0.452584\pi\) | |||||||
\(318\) | −59.6047 | −3.34247 | ||||||||
\(319\) | −4.63810 | −0.259684 | ||||||||
\(320\) | −43.3221 | −2.42178 | ||||||||
\(321\) | 55.7053 | 3.10916 | ||||||||
\(322\) | −15.5032 | −0.863961 | ||||||||
\(323\) | −17.0286 | −0.947497 | ||||||||
\(324\) | 166.867 | 9.27039 | ||||||||
\(325\) | 83.8006 | 4.64842 | ||||||||
\(326\) | 47.6632 | 2.63982 | ||||||||
\(327\) | −16.5887 | −0.917356 | ||||||||
\(328\) | −62.6644 | −3.46006 | ||||||||
\(329\) | −16.4969 | −0.909505 | ||||||||
\(330\) | 29.4431 | 1.62079 | ||||||||
\(331\) | 17.8100 | 0.978923 | 0.489462 | − | 0.872025i | \(-0.337193\pi\) | ||||
0.489462 | + | 0.872025i | \(0.337193\pi\) | |||||||
\(332\) | −52.1645 | −2.86290 | ||||||||
\(333\) | 32.5656 | 1.78458 | ||||||||
\(334\) | 38.2256 | 2.09161 | ||||||||
\(335\) | 53.3930 | 2.91717 | ||||||||
\(336\) | −91.2819 | −4.97984 | ||||||||
\(337\) | −19.6449 | −1.07013 | −0.535063 | − | 0.844812i | \(-0.679712\pi\) | ||||
−0.535063 | + | 0.844812i | \(0.679712\pi\) | |||||||
\(338\) | −60.6614 | −3.29955 | ||||||||
\(339\) | −16.9223 | −0.919092 | ||||||||
\(340\) | −92.7825 | −5.03184 | ||||||||
\(341\) | −4.51724 | −0.244623 | ||||||||
\(342\) | 84.6015 | 4.57473 | ||||||||
\(343\) | −18.3334 | −0.989909 | ||||||||
\(344\) | 53.8771 | 2.90486 | ||||||||
\(345\) | 32.2317 | 1.73529 | ||||||||
\(346\) | 28.6557 | 1.54054 | ||||||||
\(347\) | −21.4519 | −1.15160 | −0.575799 | − | 0.817591i | \(-0.695309\pi\) | ||||
−0.575799 | + | 0.817591i | \(0.695309\pi\) | |||||||
\(348\) | −99.0775 | −5.31111 | ||||||||
\(349\) | −25.3586 | −1.35742 | −0.678708 | − | 0.734408i | \(-0.737460\pi\) | ||||
−0.678708 | + | 0.734408i | \(0.737460\pi\) | |||||||
\(350\) | −97.8727 | −5.23151 | ||||||||
\(351\) | −105.346 | −5.62294 | ||||||||
\(352\) | 8.87749 | 0.473172 | ||||||||
\(353\) | 8.62680 | 0.459158 | 0.229579 | − | 0.973290i | \(-0.426265\pi\) | ||||
0.229579 | + | 0.973290i | \(0.426265\pi\) | |||||||
\(354\) | 15.0063 | 0.797575 | ||||||||
\(355\) | 62.2723 | 3.30507 | ||||||||
\(356\) | 21.9428 | 1.16296 | ||||||||
\(357\) | −38.9649 | −2.06224 | ||||||||
\(358\) | −53.2027 | −2.81185 | ||||||||
\(359\) | 3.48837 | 0.184109 | 0.0920545 | − | 0.995754i | \(-0.470657\pi\) | ||||
0.0920545 | + | 0.995754i | \(0.470657\pi\) | |||||||
\(360\) | 272.739 | 14.3746 | ||||||||
\(361\) | −3.68794 | −0.194102 | ||||||||
\(362\) | −5.86299 | −0.308152 | ||||||||
\(363\) | 34.8864 | 1.83106 | ||||||||
\(364\) | 78.6214 | 4.12088 | ||||||||
\(365\) | 4.18978 | 0.219303 | ||||||||
\(366\) | 6.63172 | 0.346645 | ||||||||
\(367\) | 16.2841 | 0.850024 | 0.425012 | − | 0.905188i | \(-0.360270\pi\) | ||||
0.425012 | + | 0.905188i | \(0.360270\pi\) | |||||||
\(368\) | 22.5241 | 1.17415 | ||||||||
\(369\) | 67.7725 | 3.52809 | ||||||||
\(370\) | 45.2278 | 2.35128 | ||||||||
\(371\) | −18.0916 | −0.939269 | ||||||||
\(372\) | −96.4959 | −5.00308 | ||||||||
\(373\) | 19.4325 | 1.00617 | 0.503087 | − | 0.864235i | \(-0.332197\pi\) | ||||
0.503087 | + | 0.864235i | \(0.332197\pi\) | |||||||
\(374\) | 8.78289 | 0.454153 | ||||||||
\(375\) | 130.538 | 6.74095 | ||||||||
\(376\) | 46.9985 | 2.42376 | ||||||||
\(377\) | 36.2628 | 1.86763 | ||||||||
\(378\) | 123.036 | 6.32828 | ||||||||
\(379\) | −4.56565 | −0.234522 | −0.117261 | − | 0.993101i | \(-0.537411\pi\) | ||||
−0.117261 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(380\) | 83.4297 | 4.27986 | ||||||||
\(381\) | 18.8627 | 0.966367 | ||||||||
\(382\) | −7.22202 | −0.369511 | ||||||||
\(383\) | −9.37637 | −0.479110 | −0.239555 | − | 0.970883i | \(-0.577002\pi\) | ||||
−0.239555 | + | 0.970883i | \(0.577002\pi\) | |||||||
\(384\) | 10.1680 | 0.518883 | ||||||||
\(385\) | 8.93676 | 0.455460 | ||||||||
\(386\) | −39.6528 | −2.01827 | ||||||||
\(387\) | −58.2689 | −2.96197 | ||||||||
\(388\) | −38.2515 | −1.94193 | ||||||||
\(389\) | 29.9200 | 1.51700 | 0.758502 | − | 0.651671i | \(-0.225932\pi\) | ||||
0.758502 | + | 0.651671i | \(0.225932\pi\) | |||||||
\(390\) | −230.200 | −11.6566 | ||||||||
\(391\) | 9.61471 | 0.486237 | ||||||||
\(392\) | −1.04959 | −0.0530123 | ||||||||
\(393\) | −27.7573 | −1.40017 | ||||||||
\(394\) | 0.479575 | 0.0241606 | ||||||||
\(395\) | 20.4272 | 1.02780 | ||||||||
\(396\) | −30.9837 | −1.55699 | ||||||||
\(397\) | 12.7544 | 0.640126 | 0.320063 | − | 0.947396i | \(-0.396296\pi\) | ||||
0.320063 | + | 0.947396i | \(0.396296\pi\) | |||||||
\(398\) | 35.2352 | 1.76618 | ||||||||
\(399\) | 35.0371 | 1.75405 | ||||||||
\(400\) | 142.196 | 7.10979 | ||||||||
\(401\) | 22.9930 | 1.14821 | 0.574107 | − | 0.818780i | \(-0.305349\pi\) | ||||
0.574107 | + | 0.818780i | \(0.305349\pi\) | |||||||
\(402\) | −107.967 | −5.38490 | ||||||||
\(403\) | 35.3179 | 1.75931 | ||||||||
\(404\) | 47.4148 | 2.35897 | ||||||||
\(405\) | −148.296 | −7.36891 | ||||||||
\(406\) | −42.3521 | −2.10190 | ||||||||
\(407\) | −3.04000 | −0.150687 | ||||||||
\(408\) | 111.008 | 5.49572 | ||||||||
\(409\) | 19.3603 | 0.957303 | 0.478652 | − | 0.878005i | \(-0.341126\pi\) | ||||
0.478652 | + | 0.878005i | \(0.341126\pi\) | |||||||
\(410\) | 94.1238 | 4.64844 | ||||||||
\(411\) | 14.2645 | 0.703616 | ||||||||
\(412\) | 86.0386 | 4.23882 | ||||||||
\(413\) | 4.55480 | 0.224127 | ||||||||
\(414\) | −47.7678 | −2.34766 | ||||||||
\(415\) | 46.3591 | 2.27568 | ||||||||
\(416\) | −69.4083 | −3.40302 | ||||||||
\(417\) | −9.90372 | −0.484987 | ||||||||
\(418\) | −7.89755 | −0.386282 | ||||||||
\(419\) | 13.9730 | 0.682626 | 0.341313 | − | 0.939950i | \(-0.389128\pi\) | ||||
0.341313 | + | 0.939950i | \(0.389128\pi\) | |||||||
\(420\) | 190.904 | 9.31517 | ||||||||
\(421\) | −32.9556 | −1.60616 | −0.803079 | − | 0.595873i | \(-0.796806\pi\) | ||||
−0.803079 | + | 0.595873i | \(0.796806\pi\) | |||||||
\(422\) | −18.3635 | −0.893923 | ||||||||
\(423\) | −50.8296 | −2.47142 | ||||||||
\(424\) | 51.5416 | 2.50308 | ||||||||
\(425\) | 60.6982 | 2.94429 | ||||||||
\(426\) | −125.922 | −6.10094 | ||||||||
\(427\) | 2.01290 | 0.0974111 | ||||||||
\(428\) | −81.4127 | −3.93523 | ||||||||
\(429\) | 15.4729 | 0.747040 | ||||||||
\(430\) | −80.9250 | −3.90255 | ||||||||
\(431\) | −25.4184 | −1.22436 | −0.612182 | − | 0.790717i | \(-0.709708\pi\) | ||||
−0.612182 | + | 0.790717i | \(0.709708\pi\) | |||||||
\(432\) | −178.754 | −8.60033 | ||||||||
\(433\) | −21.6478 | −1.04033 | −0.520163 | − | 0.854067i | \(-0.674129\pi\) | ||||
−0.520163 | + | 0.854067i | \(0.674129\pi\) | |||||||
\(434\) | −41.2485 | −1.97999 | ||||||||
\(435\) | 88.0513 | 4.22174 | ||||||||
\(436\) | 24.2442 | 1.16109 | ||||||||
\(437\) | −8.64552 | −0.413571 | ||||||||
\(438\) | −8.47223 | −0.404819 | ||||||||
\(439\) | −26.8861 | −1.28320 | −0.641602 | − | 0.767038i | \(-0.721730\pi\) | ||||
−0.641602 | + | 0.767038i | \(0.721730\pi\) | |||||||
\(440\) | −25.4602 | −1.21377 | ||||||||
\(441\) | 1.13515 | 0.0540547 | ||||||||
\(442\) | −68.6686 | −3.26623 | ||||||||
\(443\) | −2.33514 | −0.110946 | −0.0554730 | − | 0.998460i | \(-0.517667\pi\) | ||||
−0.0554730 | + | 0.998460i | \(0.517667\pi\) | |||||||
\(444\) | −64.9394 | −3.08189 | ||||||||
\(445\) | −19.5008 | −0.924425 | ||||||||
\(446\) | 71.3483 | 3.37844 | ||||||||
\(447\) | −20.5203 | −0.970576 | ||||||||
\(448\) | 26.5896 | 1.25624 | ||||||||
\(449\) | −37.8827 | −1.78780 | −0.893898 | − | 0.448271i | \(-0.852040\pi\) | ||||
−0.893898 | + | 0.448271i | \(0.852040\pi\) | |||||||
\(450\) | −301.561 | −14.2157 | ||||||||
\(451\) | −6.32655 | −0.297906 | ||||||||
\(452\) | 24.7317 | 1.16328 | ||||||||
\(453\) | 48.2974 | 2.26921 | ||||||||
\(454\) | 27.5244 | 1.29179 | ||||||||
\(455\) | −69.8717 | −3.27563 | ||||||||
\(456\) | −99.8181 | −4.67441 | ||||||||
\(457\) | −32.6601 | −1.52777 | −0.763887 | − | 0.645350i | \(-0.776711\pi\) | ||||
−0.763887 | + | 0.645350i | \(0.776711\pi\) | |||||||
\(458\) | 60.2980 | 2.81754 | ||||||||
\(459\) | −76.3037 | −3.56155 | ||||||||
\(460\) | −47.1062 | −2.19634 | ||||||||
\(461\) | −32.1309 | −1.49648 | −0.748242 | − | 0.663426i | \(-0.769102\pi\) | ||||
−0.748242 | + | 0.663426i | \(0.769102\pi\) | |||||||
\(462\) | −18.0712 | −0.840748 | ||||||||
\(463\) | −17.1377 | −0.796455 | −0.398227 | − | 0.917287i | \(-0.630375\pi\) | ||||
−0.398227 | + | 0.917287i | \(0.630375\pi\) | |||||||
\(464\) | 61.5319 | 2.85655 | ||||||||
\(465\) | 85.7569 | 3.97688 | ||||||||
\(466\) | 12.1136 | 0.561151 | ||||||||
\(467\) | 17.9473 | 0.830503 | 0.415251 | − | 0.909707i | \(-0.363694\pi\) | ||||
0.415251 | + | 0.909707i | \(0.363694\pi\) | |||||||
\(468\) | 242.245 | 11.1978 | ||||||||
\(469\) | −32.7708 | −1.51322 | ||||||||
\(470\) | −70.5932 | −3.25622 | ||||||||
\(471\) | −25.1946 | −1.16090 | ||||||||
\(472\) | −12.9763 | −0.597282 | ||||||||
\(473\) | 5.43939 | 0.250104 | ||||||||
\(474\) | −41.3062 | −1.89726 | ||||||||
\(475\) | −54.5796 | −2.50428 | ||||||||
\(476\) | 56.9468 | 2.61015 | ||||||||
\(477\) | −55.7431 | −2.55230 | ||||||||
\(478\) | −3.63480 | −0.166252 | ||||||||
\(479\) | 9.25808 | 0.423013 | 0.211506 | − | 0.977377i | \(-0.432163\pi\) | ||||
0.211506 | + | 0.977377i | \(0.432163\pi\) | |||||||
\(480\) | −168.533 | −7.69246 | ||||||||
\(481\) | 23.7681 | 1.08373 | ||||||||
\(482\) | −52.8184 | −2.40581 | ||||||||
\(483\) | −19.7827 | −0.900144 | ||||||||
\(484\) | −50.9861 | −2.31755 | ||||||||
\(485\) | 33.9945 | 1.54361 | ||||||||
\(486\) | 161.718 | 7.33566 | ||||||||
\(487\) | 1.99111 | 0.0902260 | 0.0451130 | − | 0.998982i | \(-0.485635\pi\) | ||||
0.0451130 | + | 0.998982i | \(0.485635\pi\) | |||||||
\(488\) | −5.73460 | −0.259593 | ||||||||
\(489\) | 60.8200 | 2.75038 | ||||||||
\(490\) | 1.57652 | 0.0712198 | ||||||||
\(491\) | −20.9652 | −0.946145 | −0.473073 | − | 0.881023i | \(-0.656855\pi\) | ||||
−0.473073 | + | 0.881023i | \(0.656855\pi\) | |||||||
\(492\) | −135.146 | −6.09284 | ||||||||
\(493\) | 26.2657 | 1.18295 | ||||||||
\(494\) | 61.7466 | 2.77811 | ||||||||
\(495\) | 27.5356 | 1.23763 | ||||||||
\(496\) | 59.9286 | 2.69087 | ||||||||
\(497\) | −38.2206 | −1.71443 | ||||||||
\(498\) | −93.7436 | −4.20075 | ||||||||
\(499\) | −26.5168 | −1.18705 | −0.593527 | − | 0.804814i | \(-0.702265\pi\) | ||||
−0.593527 | + | 0.804814i | \(0.702265\pi\) | |||||||
\(500\) | −190.780 | −8.53194 | ||||||||
\(501\) | 48.7773 | 2.17921 | ||||||||
\(502\) | −29.9190 | −1.33535 | ||||||||
\(503\) | 21.2881 | 0.949190 | 0.474595 | − | 0.880204i | \(-0.342594\pi\) | ||||
0.474595 | + | 0.880204i | \(0.342594\pi\) | |||||||
\(504\) | −167.398 | −7.45650 | ||||||||
\(505\) | −42.1380 | −1.87512 | ||||||||
\(506\) | 4.45912 | 0.198232 | ||||||||
\(507\) | −77.4062 | −3.43773 | ||||||||
\(508\) | −27.5677 | −1.22312 | ||||||||
\(509\) | 6.45756 | 0.286226 | 0.143113 | − | 0.989706i | \(-0.454289\pi\) | ||||
0.143113 | + | 0.989706i | \(0.454289\pi\) | |||||||
\(510\) | −166.737 | −7.38326 | ||||||||
\(511\) | −2.57155 | −0.113758 | ||||||||
\(512\) | 37.4177 | 1.65364 | ||||||||
\(513\) | 68.6120 | 3.02930 | ||||||||
\(514\) | 64.3396 | 2.83790 | ||||||||
\(515\) | −76.4634 | −3.36938 | ||||||||
\(516\) | 116.195 | 5.11518 | ||||||||
\(517\) | 4.74494 | 0.208682 | ||||||||
\(518\) | −27.7593 | −1.21967 | ||||||||
\(519\) | 36.5657 | 1.60506 | ||||||||
\(520\) | 199.059 | 8.72932 | ||||||||
\(521\) | −22.7340 | −0.995994 | −0.497997 | − | 0.867179i | \(-0.665931\pi\) | ||||
−0.497997 | + | 0.867179i | \(0.665931\pi\) | |||||||
\(522\) | −130.493 | −5.71154 | ||||||||
\(523\) | −16.8033 | −0.734756 | −0.367378 | − | 0.930072i | \(-0.619744\pi\) | ||||
−0.367378 | + | 0.930072i | \(0.619744\pi\) | |||||||
\(524\) | 40.5670 | 1.77218 | ||||||||
\(525\) | −124.889 | −5.45061 | ||||||||
\(526\) | −8.67354 | −0.378184 | ||||||||
\(527\) | 25.5813 | 1.11434 | ||||||||
\(528\) | 26.2550 | 1.14260 | ||||||||
\(529\) | −18.1186 | −0.787763 | ||||||||
\(530\) | −77.4171 | −3.36278 | ||||||||
\(531\) | 14.0340 | 0.609026 | ||||||||
\(532\) | −51.2063 | −2.22008 | ||||||||
\(533\) | 49.4639 | 2.14252 | ||||||||
\(534\) | 39.4329 | 1.70643 | ||||||||
\(535\) | 72.3523 | 3.12806 | ||||||||
\(536\) | 93.3616 | 4.03261 | ||||||||
\(537\) | −67.8887 | −2.92961 | ||||||||
\(538\) | 29.2017 | 1.25898 | ||||||||
\(539\) | −0.105966 | −0.00456428 | ||||||||
\(540\) | 373.842 | 16.0876 | ||||||||
\(541\) | −17.9150 | −0.770227 | −0.385114 | − | 0.922869i | \(-0.625838\pi\) | ||||
−0.385114 | + | 0.922869i | \(0.625838\pi\) | |||||||
\(542\) | −72.4148 | −3.11048 | ||||||||
\(543\) | −7.48139 | −0.321057 | ||||||||
\(544\) | −50.2736 | −2.15546 | ||||||||
\(545\) | −21.5461 | −0.922932 | ||||||||
\(546\) | 141.289 | 6.04660 | ||||||||
\(547\) | 37.1556 | 1.58866 | 0.794330 | − | 0.607487i | \(-0.207822\pi\) | ||||
0.794330 | + | 0.607487i | \(0.207822\pi\) | |||||||
\(548\) | −20.8474 | −0.890558 | ||||||||
\(549\) | 6.20206 | 0.264697 | ||||||||
\(550\) | 28.1507 | 1.20035 | ||||||||
\(551\) | −23.6180 | −1.00616 | ||||||||
\(552\) | 56.3594 | 2.39882 | ||||||||
\(553\) | −12.5375 | −0.533150 | ||||||||
\(554\) | 52.5440 | 2.23238 | ||||||||
\(555\) | 57.7123 | 2.44975 | ||||||||
\(556\) | 14.4742 | 0.613842 | ||||||||
\(557\) | −7.10504 | −0.301050 | −0.150525 | − | 0.988606i | \(-0.548096\pi\) | ||||
−0.150525 | + | 0.988606i | \(0.548096\pi\) | |||||||
\(558\) | −127.093 | −5.38028 | ||||||||
\(559\) | −42.5277 | −1.79873 | ||||||||
\(560\) | −118.561 | −5.01010 | ||||||||
\(561\) | 11.2073 | 0.473173 | ||||||||
\(562\) | 65.3953 | 2.75853 | ||||||||
\(563\) | 40.6571 | 1.71349 | 0.856746 | − | 0.515739i | \(-0.172483\pi\) | ||||
0.856746 | + | 0.515739i | \(0.172483\pi\) | |||||||
\(564\) | 101.360 | 4.26802 | ||||||||
\(565\) | −21.9794 | −0.924679 | ||||||||
\(566\) | −34.9711 | −1.46995 | ||||||||
\(567\) | 91.0193 | 3.82245 | ||||||||
\(568\) | 108.888 | 4.56883 | ||||||||
\(569\) | 24.3221 | 1.01964 | 0.509819 | − | 0.860282i | \(-0.329713\pi\) | ||||
0.509819 | + | 0.860282i | \(0.329713\pi\) | |||||||
\(570\) | 149.930 | 6.27987 | ||||||||
\(571\) | −3.25266 | −0.136120 | −0.0680599 | − | 0.997681i | \(-0.521681\pi\) | ||||
−0.0680599 | + | 0.997681i | \(0.521681\pi\) | |||||||
\(572\) | −22.6135 | −0.945519 | ||||||||
\(573\) | −9.21557 | −0.384986 | ||||||||
\(574\) | −57.7700 | −2.41127 | ||||||||
\(575\) | 30.8168 | 1.28515 | ||||||||
\(576\) | 81.9267 | 3.41361 | ||||||||
\(577\) | 7.35010 | 0.305989 | 0.152994 | − | 0.988227i | \(-0.451108\pi\) | ||||
0.152994 | + | 0.988227i | \(0.451108\pi\) | |||||||
\(578\) | −5.08885 | −0.211668 | ||||||||
\(579\) | −50.5985 | −2.10280 | ||||||||
\(580\) | −128.686 | −5.34340 | ||||||||
\(581\) | −28.4537 | −1.18046 | ||||||||
\(582\) | −68.7409 | −2.84940 | ||||||||
\(583\) | 5.20361 | 0.215512 | ||||||||
\(584\) | 7.32614 | 0.303158 | ||||||||
\(585\) | −215.285 | −8.90096 | ||||||||
\(586\) | 26.3227 | 1.08738 | ||||||||
\(587\) | 40.7603 | 1.68236 | 0.841178 | − | 0.540759i | \(-0.181863\pi\) | ||||
0.841178 | + | 0.540759i | \(0.181863\pi\) | |||||||
\(588\) | −2.26361 | −0.0933497 | ||||||||
\(589\) | −23.0026 | −0.947807 | ||||||||
\(590\) | 19.4908 | 0.802423 | ||||||||
\(591\) | 0.611955 | 0.0251725 | ||||||||
\(592\) | 40.3305 | 1.65757 | ||||||||
\(593\) | −26.3182 | −1.08076 | −0.540379 | − | 0.841422i | \(-0.681719\pi\) | ||||
−0.540379 | + | 0.841422i | \(0.681719\pi\) | |||||||
\(594\) | −35.3882 | −1.45200 | ||||||||
\(595\) | −50.6092 | −2.07478 | ||||||||
\(596\) | 29.9902 | 1.22845 | ||||||||
\(597\) | 44.9614 | 1.84015 | ||||||||
\(598\) | −34.8635 | −1.42567 | ||||||||
\(599\) | −25.3650 | −1.03639 | −0.518194 | − | 0.855263i | \(-0.673395\pi\) | ||||
−0.518194 | + | 0.855263i | \(0.673395\pi\) | |||||||
\(600\) | 355.800 | 14.5255 | ||||||||
\(601\) | −13.9348 | −0.568413 | −0.284206 | − | 0.958763i | \(-0.591730\pi\) | ||||
−0.284206 | + | 0.958763i | \(0.591730\pi\) | |||||||
\(602\) | 49.6690 | 2.02436 | ||||||||
\(603\) | −100.972 | −4.11190 | ||||||||
\(604\) | −70.5861 | −2.87211 | ||||||||
\(605\) | 45.3119 | 1.84219 | ||||||||
\(606\) | 85.2081 | 3.46134 | ||||||||
\(607\) | −17.7557 | −0.720682 | −0.360341 | − | 0.932821i | \(-0.617340\pi\) | ||||
−0.360341 | + | 0.932821i | \(0.617340\pi\) | |||||||
\(608\) | 45.2058 | 1.83334 | ||||||||
\(609\) | −54.0429 | −2.18993 | ||||||||
\(610\) | 8.61355 | 0.348752 | ||||||||
\(611\) | −37.0981 | −1.50083 | ||||||||
\(612\) | 175.462 | 7.09263 | ||||||||
\(613\) | −12.4015 | −0.500890 | −0.250445 | − | 0.968131i | \(-0.580577\pi\) | ||||
−0.250445 | + | 0.968131i | \(0.580577\pi\) | |||||||
\(614\) | −37.6669 | −1.52011 | ||||||||
\(615\) | 120.106 | 4.84312 | ||||||||
\(616\) | 15.6266 | 0.629613 | ||||||||
\(617\) | −21.6689 | −0.872355 | −0.436178 | − | 0.899861i | \(-0.643668\pi\) | ||||
−0.436178 | + | 0.899861i | \(0.643668\pi\) | |||||||
\(618\) | 154.618 | 6.21965 | ||||||||
\(619\) | −20.1804 | −0.811117 | −0.405559 | − | 0.914069i | \(-0.632923\pi\) | ||||
−0.405559 | + | 0.914069i | \(0.632923\pi\) | |||||||
\(620\) | −125.333 | −5.03349 | ||||||||
\(621\) | −38.7398 | −1.55458 | ||||||||
\(622\) | 7.11021 | 0.285093 | ||||||||
\(623\) | 11.9689 | 0.479524 | ||||||||
\(624\) | −205.274 | −8.21752 | ||||||||
\(625\) | 99.8079 | 3.99232 | ||||||||
\(626\) | 45.5770 | 1.82162 | ||||||||
\(627\) | −10.0776 | −0.402459 | ||||||||
\(628\) | 36.8216 | 1.46934 | ||||||||
\(629\) | 17.2156 | 0.686431 | ||||||||
\(630\) | 251.437 | 10.0175 | ||||||||
\(631\) | 0.668608 | 0.0266169 | 0.0133084 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133084 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(632\) | 35.7185 | 1.42081 | ||||||||
\(633\) | −23.4326 | −0.931361 | ||||||||
\(634\) | −13.8800 | −0.551244 | ||||||||
\(635\) | 24.4997 | 0.972241 | ||||||||
\(636\) | 111.158 | 4.40769 | ||||||||
\(637\) | 0.828490 | 0.0328260 | ||||||||
\(638\) | 12.1816 | 0.482272 | ||||||||
\(639\) | −117.764 | −4.65866 | ||||||||
\(640\) | 13.2066 | 0.522036 | ||||||||
\(641\) | −24.3927 | −0.963453 | −0.481727 | − | 0.876322i | \(-0.659990\pi\) | ||||
−0.481727 | + | 0.876322i | \(0.659990\pi\) | |||||||
\(642\) | −146.305 | −5.77419 | ||||||||
\(643\) | −9.64985 | −0.380553 | −0.190277 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190277 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(644\) | 28.9122 | 1.13930 | ||||||||
\(645\) | −103.263 | −4.06599 | ||||||||
\(646\) | 44.7241 | 1.75965 | ||||||||
\(647\) | −2.54788 | −0.100167 | −0.0500837 | − | 0.998745i | \(-0.515949\pi\) | ||||
−0.0500837 | + | 0.998745i | \(0.515949\pi\) | |||||||
\(648\) | −259.307 | −10.1866 | ||||||||
\(649\) | −1.31008 | −0.0514250 | ||||||||
\(650\) | −220.095 | −8.63283 | ||||||||
\(651\) | −52.6347 | −2.06292 | ||||||||
\(652\) | −88.8878 | −3.48112 | ||||||||
\(653\) | −27.5261 | −1.07718 | −0.538590 | − | 0.842568i | \(-0.681043\pi\) | ||||
−0.538590 | + | 0.842568i | \(0.681043\pi\) | |||||||
\(654\) | 43.5687 | 1.70367 | ||||||||
\(655\) | −36.0523 | −1.40868 | ||||||||
\(656\) | 83.9321 | 3.27700 | ||||||||
\(657\) | −7.92333 | −0.309119 | ||||||||
\(658\) | 43.3277 | 1.68909 | ||||||||
\(659\) | 23.5063 | 0.915676 | 0.457838 | − | 0.889036i | \(-0.348624\pi\) | ||||
0.457838 | + | 0.889036i | \(0.348624\pi\) | |||||||
\(660\) | −54.9089 | −2.13733 | ||||||||
\(661\) | 3.89497 | 0.151497 | 0.0757484 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757484 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(662\) | −46.7763 | −1.81801 | ||||||||
\(663\) | −87.6238 | −3.40303 | ||||||||
\(664\) | 81.0623 | 3.14583 | ||||||||
\(665\) | 45.5076 | 1.76471 | ||||||||
\(666\) | −85.5306 | −3.31424 | ||||||||
\(667\) | 13.3353 | 0.516343 | ||||||||
\(668\) | −71.2875 | −2.75820 | ||||||||
\(669\) | 91.0431 | 3.51993 | ||||||||
\(670\) | −140.232 | −5.41764 | ||||||||
\(671\) | −0.578962 | −0.0223506 | ||||||||
\(672\) | 103.440 | 3.99029 | ||||||||
\(673\) | 4.02640 | 0.155206 | 0.0776031 | − | 0.996984i | \(-0.475273\pi\) | ||||
0.0776031 | + | 0.996984i | \(0.475273\pi\) | |||||||
\(674\) | 51.5956 | 1.98739 | ||||||||
\(675\) | −244.567 | −9.41337 | ||||||||
\(676\) | 113.128 | 4.35109 | ||||||||
\(677\) | 24.1497 | 0.928148 | 0.464074 | − | 0.885796i | \(-0.346387\pi\) | ||||
0.464074 | + | 0.885796i | \(0.346387\pi\) | |||||||
\(678\) | 44.4449 | 1.70690 | ||||||||
\(679\) | −20.8647 | −0.800713 | ||||||||
\(680\) | 144.182 | 5.52912 | ||||||||
\(681\) | 35.1222 | 1.34589 | ||||||||
\(682\) | 11.8641 | 0.454301 | ||||||||
\(683\) | −14.8389 | −0.567793 | −0.283897 | − | 0.958855i | \(-0.591627\pi\) | ||||
−0.283897 | + | 0.958855i | \(0.591627\pi\) | |||||||
\(684\) | −157.775 | −6.03267 | ||||||||
\(685\) | 18.5273 | 0.707893 | ||||||||
\(686\) | 48.1510 | 1.83841 | ||||||||
\(687\) | 76.9426 | 2.93554 | ||||||||
\(688\) | −72.1624 | −2.75117 | ||||||||
\(689\) | −40.6842 | −1.54994 | ||||||||
\(690\) | −84.6536 | −3.22271 | ||||||||
\(691\) | 4.14764 | 0.157784 | 0.0788918 | − | 0.996883i | \(-0.474862\pi\) | ||||
0.0788918 | + | 0.996883i | \(0.474862\pi\) | |||||||
\(692\) | −53.4404 | −2.03150 | ||||||||
\(693\) | −16.9004 | −0.641993 | ||||||||
\(694\) | 56.3415 | 2.13869 | ||||||||
\(695\) | −12.8634 | −0.487935 | ||||||||
\(696\) | 153.964 | 5.83600 | ||||||||
\(697\) | 35.8275 | 1.35706 | ||||||||
\(698\) | 66.6022 | 2.52093 | ||||||||
\(699\) | 15.4574 | 0.584652 | ||||||||
\(700\) | 182.524 | 6.89877 | ||||||||
\(701\) | −45.3272 | −1.71199 | −0.855993 | − | 0.516987i | \(-0.827053\pi\) | ||||
−0.855993 | + | 0.516987i | \(0.827053\pi\) | |||||||
\(702\) | 276.681 | 10.4427 | ||||||||
\(703\) | −15.4802 | −0.583847 | ||||||||
\(704\) | −7.64786 | −0.288239 | ||||||||
\(705\) | −90.0796 | −3.39259 | ||||||||
\(706\) | −22.6575 | −0.852727 | ||||||||
\(707\) | 25.8629 | 0.972674 | ||||||||
\(708\) | −27.9854 | −1.05176 | ||||||||
\(709\) | 15.5043 | 0.582277 | 0.291139 | − | 0.956681i | \(-0.405966\pi\) | ||||
0.291139 | + | 0.956681i | \(0.405966\pi\) | |||||||
\(710\) | −163.553 | −6.13803 | ||||||||
\(711\) | −38.6301 | −1.44874 | ||||||||
\(712\) | −34.0985 | −1.27790 | ||||||||
\(713\) | 12.9878 | 0.486396 | ||||||||
\(714\) | 102.338 | 3.82990 | ||||||||
\(715\) | 20.0969 | 0.751581 | ||||||||
\(716\) | 99.2186 | 3.70797 | ||||||||
\(717\) | −4.63814 | −0.173215 | ||||||||
\(718\) | −9.16189 | −0.341919 | ||||||||
\(719\) | −1.49333 | −0.0556917 | −0.0278458 | − | 0.999612i | \(-0.508865\pi\) | ||||
−0.0278458 | + | 0.999612i | \(0.508865\pi\) | |||||||
\(720\) | −365.304 | −13.6141 | ||||||||
\(721\) | 46.9307 | 1.74779 | ||||||||
\(722\) | 9.68605 | 0.360478 | ||||||||
\(723\) | −67.3982 | −2.50657 | ||||||||
\(724\) | 10.9340 | 0.406358 | ||||||||
\(725\) | 84.1862 | 3.12660 | ||||||||
\(726\) | −91.6259 | −3.40056 | ||||||||
\(727\) | 44.2205 | 1.64005 | 0.820024 | − | 0.572329i | \(-0.193960\pi\) | ||||
0.820024 | + | 0.572329i | \(0.193960\pi\) | |||||||
\(728\) | −122.176 | −4.52814 | ||||||||
\(729\) | 104.153 | 3.85753 | ||||||||
\(730\) | −11.0041 | −0.407280 | ||||||||
\(731\) | −30.8035 | −1.13931 | ||||||||
\(732\) | −12.3676 | −0.457119 | ||||||||
\(733\) | −12.2263 | −0.451587 | −0.225794 | − | 0.974175i | \(-0.572497\pi\) | ||||
−0.225794 | + | 0.974175i | \(0.572497\pi\) | |||||||
\(734\) | −42.7688 | −1.57862 | ||||||||
\(735\) | 2.01170 | 0.0742025 | ||||||||
\(736\) | −25.5242 | −0.940834 | ||||||||
\(737\) | 9.42573 | 0.347201 | ||||||||
\(738\) | −177.998 | −6.55221 | ||||||||
\(739\) | 31.2875 | 1.15093 | 0.575464 | − | 0.817827i | \(-0.304821\pi\) | ||||
0.575464 | + | 0.817827i | \(0.304821\pi\) | |||||||
\(740\) | −84.3460 | −3.10062 | ||||||||
\(741\) | 78.7910 | 2.89446 | ||||||||
\(742\) | 47.5160 | 1.74437 | ||||||||
\(743\) | −0.0431752 | −0.00158394 | −0.000791972 | − | 1.00000i | \(-0.500252\pi\) | ||||
−0.000791972 | 1.00000i | \(0.500252\pi\) | ||||||||
\(744\) | 149.952 | 5.49752 | ||||||||
\(745\) | −26.6526 | −0.976476 | ||||||||
\(746\) | −51.0376 | −1.86862 | ||||||||
\(747\) | −87.6701 | −3.20768 | ||||||||
\(748\) | −16.3794 | −0.598888 | ||||||||
\(749\) | −44.4074 | −1.62261 | ||||||||
\(750\) | −342.846 | −12.5190 | ||||||||
\(751\) | 4.81612 | 0.175743 | 0.0878714 | − | 0.996132i | \(-0.471994\pi\) | ||||
0.0878714 | + | 0.996132i | \(0.471994\pi\) | |||||||
\(752\) | −62.9493 | −2.29553 | ||||||||
\(753\) | −38.1778 | −1.39128 | ||||||||
\(754\) | −95.2409 | −3.46847 | ||||||||
\(755\) | 62.7306 | 2.28300 | ||||||||
\(756\) | −229.451 | −8.34506 | ||||||||
\(757\) | −34.8383 | −1.26622 | −0.633110 | − | 0.774062i | \(-0.718222\pi\) | ||||
−0.633110 | + | 0.774062i | \(0.718222\pi\) | |||||||
\(758\) | 11.9913 | 0.435542 | ||||||||
\(759\) | 5.69001 | 0.206534 | ||||||||
\(760\) | −129.648 | −4.70282 | ||||||||
\(761\) | 2.21871 | 0.0804280 | 0.0402140 | − | 0.999191i | \(-0.487196\pi\) | ||||
0.0402140 | + | 0.999191i | \(0.487196\pi\) | |||||||
\(762\) | −49.5413 | −1.79469 | ||||||||
\(763\) | 13.2242 | 0.478750 | ||||||||
\(764\) | 13.4685 | 0.487272 | ||||||||
\(765\) | −155.935 | −5.63784 | ||||||||
\(766\) | 24.6262 | 0.889780 | ||||||||
\(767\) | 10.2428 | 0.369845 | ||||||||
\(768\) | 40.0035 | 1.44350 | ||||||||
\(769\) | −27.7572 | −1.00095 | −0.500474 | − | 0.865751i | \(-0.666841\pi\) | ||||
−0.500474 | + | 0.865751i | \(0.666841\pi\) | |||||||
\(770\) | −23.4716 | −0.845858 | ||||||||
\(771\) | 82.0998 | 2.95675 | ||||||||
\(772\) | 73.9491 | 2.66149 | ||||||||
\(773\) | 35.4441 | 1.27484 | 0.637418 | − | 0.770518i | \(-0.280002\pi\) | ||||
0.637418 | + | 0.770518i | \(0.280002\pi\) | |||||||
\(774\) | 153.038 | 5.50084 | ||||||||
\(775\) | 81.9926 | 2.94526 | ||||||||
\(776\) | 59.4419 | 2.13384 | ||||||||
\(777\) | −35.4219 | −1.27075 | ||||||||
\(778\) | −78.5822 | −2.81731 | ||||||||
\(779\) | −32.2160 | −1.15426 | ||||||||
\(780\) | 429.303 | 15.3715 | ||||||||
\(781\) | 10.9932 | 0.393369 | ||||||||
\(782\) | −25.2522 | −0.903016 | ||||||||
\(783\) | −105.830 | −3.78207 | ||||||||
\(784\) | 1.40581 | 0.0502076 | ||||||||
\(785\) | −32.7238 | −1.16796 | ||||||||
\(786\) | 72.9021 | 2.60033 | ||||||||
\(787\) | 38.5862 | 1.37545 | 0.687724 | − | 0.725972i | \(-0.258610\pi\) | ||||
0.687724 | + | 0.725972i | \(0.258610\pi\) | |||||||
\(788\) | −0.894367 | −0.0318605 | ||||||||
\(789\) | −11.0678 | −0.394023 | ||||||||
\(790\) | −53.6503 | −1.90879 | ||||||||
\(791\) | 13.4902 | 0.479656 | ||||||||
\(792\) | 48.1479 | 1.71086 | ||||||||
\(793\) | 4.52659 | 0.160744 | ||||||||
\(794\) | −33.4983 | −1.18881 | ||||||||
\(795\) | −98.7871 | −3.50362 | ||||||||
\(796\) | −65.7107 | −2.32905 | ||||||||
\(797\) | 30.9733 | 1.09713 | 0.548565 | − | 0.836108i | \(-0.315174\pi\) | ||||
0.548565 | + | 0.836108i | \(0.315174\pi\) | |||||||
\(798\) | −92.0218 | −3.25754 | ||||||||
\(799\) | −26.8708 | −0.950619 | ||||||||
\(800\) | −161.135 | −5.69700 | ||||||||
\(801\) | 36.8781 | 1.30302 | ||||||||
\(802\) | −60.3890 | −2.13241 | ||||||||
\(803\) | 0.739643 | 0.0261014 | ||||||||
\(804\) | 201.349 | 7.10104 | ||||||||
\(805\) | −25.6946 | −0.905615 | ||||||||
\(806\) | −92.7593 | −3.26731 | ||||||||
\(807\) | 37.2625 | 1.31170 | ||||||||
\(808\) | −73.6815 | −2.59210 | ||||||||
\(809\) | 18.4802 | 0.649729 | 0.324865 | − | 0.945761i | \(-0.394681\pi\) | ||||
0.324865 | + | 0.945761i | \(0.394681\pi\) | |||||||
\(810\) | 389.487 | 13.6852 | ||||||||
\(811\) | 17.0647 | 0.599223 | 0.299611 | − | 0.954061i | \(-0.403143\pi\) | ||||
0.299611 | + | 0.954061i | \(0.403143\pi\) | |||||||
\(812\) | 78.9831 | 2.77176 | ||||||||
\(813\) | −92.4040 | −3.24075 | ||||||||
\(814\) | 7.98428 | 0.279849 | ||||||||
\(815\) | 78.9956 | 2.76709 | ||||||||
\(816\) | −148.683 | −5.20495 | ||||||||
\(817\) | 27.6984 | 0.969044 | ||||||||
\(818\) | −50.8480 | −1.77786 | ||||||||
\(819\) | 132.135 | 4.61717 | ||||||||
\(820\) | −175.533 | −6.12988 | ||||||||
\(821\) | 0.0310372 | 0.00108321 | 0.000541603 | − | 1.00000i | \(-0.499828\pi\) | ||||
0.000541603 | 1.00000i | \(0.499828\pi\) | ||||||||
\(822\) | −37.4645 | −1.30672 | ||||||||
\(823\) | −25.9165 | −0.903391 | −0.451696 | − | 0.892172i | \(-0.649181\pi\) | ||||
−0.451696 | + | 0.892172i | \(0.649181\pi\) | |||||||
\(824\) | −133.702 | −4.65773 | ||||||||
\(825\) | 35.9213 | 1.25062 | ||||||||
\(826\) | −11.9628 | −0.416238 | ||||||||
\(827\) | 48.3252 | 1.68043 | 0.840216 | − | 0.542251i | \(-0.182428\pi\) | ||||
0.840216 | + | 0.542251i | \(0.182428\pi\) | |||||||
\(828\) | 89.0830 | 3.09585 | ||||||||
\(829\) | −30.1488 | −1.04711 | −0.523555 | − | 0.851992i | \(-0.675394\pi\) | ||||
−0.523555 | + | 0.851992i | \(0.675394\pi\) | |||||||
\(830\) | −121.758 | −4.22629 | ||||||||
\(831\) | 67.0481 | 2.32587 | ||||||||
\(832\) | 59.7944 | 2.07300 | ||||||||
\(833\) | 0.600089 | 0.0207919 | ||||||||
\(834\) | 26.0113 | 0.900696 | ||||||||
\(835\) | 63.3540 | 2.19246 | ||||||||
\(836\) | 14.7283 | 0.509387 | ||||||||
\(837\) | −103.073 | −3.56272 | ||||||||
\(838\) | −36.6989 | −1.26774 | ||||||||
\(839\) | −14.1237 | −0.487603 | −0.243802 | − | 0.969825i | \(-0.578395\pi\) | ||||
−0.243802 | + | 0.969825i | \(0.578395\pi\) | |||||||
\(840\) | −296.661 | −10.2358 | ||||||||
\(841\) | 7.42960 | 0.256193 | ||||||||
\(842\) | 86.5550 | 2.98288 | ||||||||
\(843\) | 83.4468 | 2.87406 | ||||||||
\(844\) | 34.2464 | 1.17881 | ||||||||
\(845\) | −100.538 | −3.45863 | ||||||||
\(846\) | 133.499 | 4.58980 | ||||||||
\(847\) | −27.8109 | −0.955593 | ||||||||
\(848\) | −69.0344 | −2.37065 | ||||||||
\(849\) | −44.6245 | −1.53151 | ||||||||
\(850\) | −159.418 | −5.46800 | ||||||||
\(851\) | 8.74046 | 0.299619 | ||||||||
\(852\) | 234.834 | 8.04528 | ||||||||
\(853\) | 8.82232 | 0.302071 | 0.151035 | − | 0.988528i | \(-0.451739\pi\) | ||||
0.151035 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(854\) | −5.28670 | −0.180907 | ||||||||
\(855\) | 140.216 | 4.79529 | ||||||||
\(856\) | 126.513 | 4.32414 | ||||||||
\(857\) | −6.95385 | −0.237539 | −0.118769 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118769 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(858\) | −40.6383 | −1.38737 | ||||||||
\(859\) | 6.33425 | 0.216122 | 0.108061 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108061 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(860\) | 150.918 | 5.14627 | ||||||||
\(861\) | −73.7167 | −2.51226 | ||||||||
\(862\) | 66.7593 | 2.27383 | ||||||||
\(863\) | −11.8354 | −0.402883 | −0.201441 | − | 0.979501i | \(-0.564563\pi\) | ||||
−0.201441 | + | 0.979501i | \(0.564563\pi\) | |||||||
\(864\) | 202.563 | 6.89135 | ||||||||
\(865\) | 47.4930 | 1.61481 | ||||||||
\(866\) | 56.8560 | 1.93204 | ||||||||
\(867\) | −6.49357 | −0.220533 | ||||||||
\(868\) | 76.9251 | 2.61101 | ||||||||
\(869\) | 3.60612 | 0.122329 | ||||||||
\(870\) | −231.259 | −7.84041 | ||||||||
\(871\) | −73.6946 | −2.49705 | ||||||||
\(872\) | −37.6749 | −1.27583 | ||||||||
\(873\) | −64.2873 | −2.17580 | ||||||||
\(874\) | 22.7067 | 0.768065 | ||||||||
\(875\) | −104.063 | −3.51797 | ||||||||
\(876\) | 15.8000 | 0.533833 | ||||||||
\(877\) | 0.952410 | 0.0321606 | 0.0160803 | − | 0.999871i | \(-0.494881\pi\) | ||||
0.0160803 | + | 0.999871i | \(0.494881\pi\) | |||||||
\(878\) | 70.6140 | 2.38311 | ||||||||
\(879\) | 33.5888 | 1.13292 | ||||||||
\(880\) | 34.1011 | 1.14955 | ||||||||
\(881\) | −16.1826 | −0.545204 | −0.272602 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272602 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(882\) | −2.98137 | −0.100388 | ||||||||
\(883\) | −3.21186 | −0.108088 | −0.0540438 | − | 0.998539i | \(-0.517211\pi\) | ||||
−0.0540438 | + | 0.998539i | \(0.517211\pi\) | |||||||
\(884\) | 128.061 | 4.30717 | ||||||||
\(885\) | 24.8710 | 0.836028 | ||||||||
\(886\) | 6.13304 | 0.206044 | ||||||||
\(887\) | 44.4044 | 1.49095 | 0.745477 | − | 0.666531i | \(-0.232222\pi\) | ||||
0.745477 | + | 0.666531i | \(0.232222\pi\) | |||||||
\(888\) | 100.914 | 3.38646 | ||||||||
\(889\) | −15.0371 | −0.504328 | ||||||||
\(890\) | 51.2170 | 1.71680 | ||||||||
\(891\) | −26.1795 | −0.877046 | ||||||||
\(892\) | −133.059 | −4.45513 | ||||||||
\(893\) | 24.1621 | 0.808554 | ||||||||
\(894\) | 53.8947 | 1.80251 | ||||||||
\(895\) | −88.1766 | −2.94742 | ||||||||
\(896\) | −8.10576 | −0.270794 | ||||||||
\(897\) | −44.4871 | −1.48538 | ||||||||
\(898\) | 99.4956 | 3.32021 | ||||||||
\(899\) | 35.4804 | 1.18334 | ||||||||
\(900\) | 562.386 | 18.7462 | ||||||||
\(901\) | −29.4682 | −0.981729 | ||||||||
\(902\) | 16.6161 | 0.553257 | ||||||||
\(903\) | 63.3795 | 2.10914 | ||||||||
\(904\) | −38.4325 | −1.27825 | ||||||||
\(905\) | −9.71714 | −0.323009 | ||||||||
\(906\) | −126.849 | −4.21427 | ||||||||
\(907\) | 32.5162 | 1.07968 | 0.539842 | − | 0.841767i | \(-0.318484\pi\) | ||||
0.539842 | + | 0.841767i | \(0.318484\pi\) | |||||||
\(908\) | −51.3308 | −1.70347 | ||||||||
\(909\) | 79.6876 | 2.64307 | ||||||||
\(910\) | 183.512 | 6.08335 | ||||||||
\(911\) | 0.200172 | 0.00663199 | 0.00331599 | − | 0.999995i | \(-0.498944\pi\) | ||||
0.00331599 | + | 0.999995i | \(0.498944\pi\) | |||||||
\(912\) | 133.695 | 4.42709 | ||||||||
\(913\) | 8.18400 | 0.270851 | ||||||||
\(914\) | 85.7788 | 2.83731 | ||||||||
\(915\) | 10.9912 | 0.363358 | ||||||||
\(916\) | −112.451 | −3.71548 | ||||||||
\(917\) | 22.1277 | 0.730721 | ||||||||
\(918\) | 200.405 | 6.61435 | ||||||||
\(919\) | −16.0897 | −0.530750 | −0.265375 | − | 0.964145i | \(-0.585496\pi\) | ||||
−0.265375 | + | 0.964145i | \(0.585496\pi\) | |||||||
\(920\) | 73.2020 | 2.41340 | ||||||||
\(921\) | −48.0644 | −1.58378 | ||||||||
\(922\) | 84.3889 | 2.77920 | ||||||||
\(923\) | −85.9501 | −2.82908 | ||||||||
\(924\) | 33.7012 | 1.10869 | ||||||||
\(925\) | 55.1790 | 1.81427 | ||||||||
\(926\) | 45.0105 | 1.47914 | ||||||||
\(927\) | 144.601 | 4.74931 | ||||||||
\(928\) | −69.7276 | −2.28892 | ||||||||
\(929\) | −2.71569 | −0.0890988 | −0.0445494 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445494 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(930\) | −225.233 | −7.38568 | ||||||||
\(931\) | −0.539598 | −0.0176846 | ||||||||
\(932\) | −22.5908 | −0.739987 | ||||||||
\(933\) | 9.07289 | 0.297033 | ||||||||
\(934\) | −47.1370 | −1.54237 | ||||||||
\(935\) | 14.5565 | 0.476049 | ||||||||
\(936\) | −376.443 | −12.3044 | ||||||||
\(937\) | −47.6535 | −1.55677 | −0.778386 | − | 0.627787i | \(-0.783961\pi\) | ||||
−0.778386 | + | 0.627787i | \(0.783961\pi\) | |||||||
\(938\) | 86.0697 | 2.81027 | ||||||||
\(939\) | 58.1579 | 1.89791 | ||||||||
\(940\) | 131.650 | 4.29396 | ||||||||
\(941\) | −18.6270 | −0.607222 | −0.303611 | − | 0.952796i | \(-0.598192\pi\) | ||||
−0.303611 | + | 0.952796i | \(0.598192\pi\) | |||||||
\(942\) | 66.1713 | 2.15598 | ||||||||
\(943\) | 18.1898 | 0.592342 | ||||||||
\(944\) | 17.3803 | 0.565681 | ||||||||
\(945\) | 203.916 | 6.63338 | ||||||||
\(946\) | −14.2861 | −0.464481 | ||||||||
\(947\) | 19.5673 | 0.635853 | 0.317926 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317926 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(948\) | 77.0326 | 2.50190 | ||||||||
\(949\) | −5.78286 | −0.187720 | ||||||||
\(950\) | 143.348 | 4.65084 | ||||||||
\(951\) | −17.7114 | −0.574331 | ||||||||
\(952\) | −88.4939 | −2.86810 | ||||||||
\(953\) | 35.7342 | 1.15754 | 0.578772 | − | 0.815490i | \(-0.303532\pi\) | ||||
0.578772 | + | 0.815490i | \(0.303532\pi\) | |||||||
\(954\) | 146.404 | 4.74001 | ||||||||
\(955\) | −11.9696 | −0.387326 | ||||||||
\(956\) | 6.77860 | 0.219235 | ||||||||
\(957\) | 15.5441 | 0.502470 | ||||||||
\(958\) | −24.3155 | −0.785599 | ||||||||
\(959\) | −11.3715 | −0.367203 | ||||||||
\(960\) | 145.190 | 4.68597 | ||||||||
\(961\) | 3.55586 | 0.114705 | ||||||||
\(962\) | −62.4247 | −2.01265 | ||||||||
\(963\) | −136.826 | −4.40916 | ||||||||
\(964\) | 98.5018 | 3.17253 | ||||||||
\(965\) | −65.7194 | −2.11558 | ||||||||
\(966\) | 51.9575 | 1.67170 | ||||||||
\(967\) | −56.2320 | −1.80830 | −0.904149 | − | 0.427217i | \(-0.859494\pi\) | ||||
−0.904149 | + | 0.427217i | \(0.859494\pi\) | |||||||
\(968\) | 79.2311 | 2.54658 | ||||||||
\(969\) | 57.0696 | 1.83334 | ||||||||
\(970\) | −89.2836 | −2.86672 | ||||||||
\(971\) | −19.9665 | −0.640756 | −0.320378 | − | 0.947290i | \(-0.603810\pi\) | ||||
−0.320378 | + | 0.947290i | \(0.603810\pi\) | |||||||
\(972\) | −301.590 | −9.67350 | ||||||||
\(973\) | 7.89510 | 0.253105 | ||||||||
\(974\) | −5.22949 | −0.167564 | ||||||||
\(975\) | −280.849 | −8.99438 | ||||||||
\(976\) | 7.68087 | 0.245859 | ||||||||
\(977\) | 40.3805 | 1.29189 | 0.645943 | − | 0.763386i | \(-0.276465\pi\) | ||||
0.645943 | + | 0.763386i | \(0.276465\pi\) | |||||||
\(978\) | −159.738 | −5.10787 | ||||||||
\(979\) | −3.44256 | −0.110025 | ||||||||
\(980\) | −2.94007 | −0.0939171 | ||||||||
\(981\) | 40.7460 | 1.30092 | ||||||||
\(982\) | 55.0632 | 1.75714 | ||||||||
\(983\) | 59.0630 | 1.88382 | 0.941909 | − | 0.335868i | \(-0.109030\pi\) | ||||
0.941909 | + | 0.335868i | \(0.109030\pi\) | |||||||
\(984\) | 210.013 | 6.69498 | ||||||||
\(985\) | 0.794833 | 0.0253255 | ||||||||
\(986\) | −68.9846 | −2.19692 | ||||||||
\(987\) | 55.2878 | 1.75983 | ||||||||
\(988\) | −115.152 | −3.66348 | ||||||||
\(989\) | −15.6391 | −0.497295 | ||||||||
\(990\) | −72.3197 | −2.29847 | ||||||||
\(991\) | 34.6694 | 1.10131 | 0.550655 | − | 0.834733i | \(-0.314378\pi\) | ||||
0.550655 | + | 0.834733i | \(0.314378\pi\) | |||||||
\(992\) | −67.9107 | −2.15617 | ||||||||
\(993\) | −59.6883 | −1.89415 | ||||||||
\(994\) | 100.383 | 3.18396 | ||||||||
\(995\) | 58.3978 | 1.85133 | ||||||||
\(996\) | 174.824 | 5.53951 | ||||||||
\(997\) | −46.2891 | −1.46599 | −0.732996 | − | 0.680233i | \(-0.761879\pi\) | ||||
−0.732996 | + | 0.680233i | \(0.761879\pi\) | |||||||
\(998\) | 69.6439 | 2.20454 | ||||||||
\(999\) | −69.3655 | −2.19463 |
(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 | 6037.2.a.a.1.19 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.19 | ✓ | 243 | 1.1 | even | 1 | trivial |