Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51520 | −1.77852 | −0.889258 | − | 0.457405i | \(-0.848779\pi\) | ||||
−0.889258 | + | 0.457405i | \(0.848779\pi\) | |||||||
\(3\) | 3.16825 | 1.82919 | 0.914596 | − | 0.404369i | \(-0.132509\pi\) | ||||
0.914596 | + | 0.404369i | \(0.132509\pi\) | |||||||
\(4\) | 4.32624 | 2.16312 | ||||||||
\(5\) | 1.81160 | 0.810172 | 0.405086 | − | 0.914279i | \(-0.367242\pi\) | ||||
0.405086 | + | 0.914279i | \(0.367242\pi\) | |||||||
\(6\) | −7.96880 | −3.25325 | ||||||||
\(7\) | 1.29182 | 0.488262 | 0.244131 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244131 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(8\) | −5.85097 | −2.06863 | ||||||||
\(9\) | 7.03782 | 2.34594 | ||||||||
\(10\) | −4.55654 | −1.44090 | ||||||||
\(11\) | 1.52442 | 0.459629 | 0.229814 | − | 0.973234i | \(-0.426188\pi\) | ||||
0.229814 | + | 0.973234i | \(0.426188\pi\) | |||||||
\(12\) | 13.7066 | 3.95676 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.24919 | −0.868382 | ||||||||
\(15\) | 5.73961 | 1.48196 | ||||||||
\(16\) | 6.06389 | 1.51597 | ||||||||
\(17\) | −5.34451 | −1.29623 | −0.648117 | − | 0.761541i | \(-0.724443\pi\) | ||||
−0.648117 | + | 0.761541i | \(0.724443\pi\) | |||||||
\(18\) | −17.7016 | −4.17230 | ||||||||
\(19\) | −0.154094 | −0.0353516 | −0.0176758 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176758 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(20\) | 7.83742 | 1.75250 | ||||||||
\(21\) | 4.09281 | 0.893125 | ||||||||
\(22\) | −3.83422 | −0.817457 | ||||||||
\(23\) | 2.71756 | 0.566649 | 0.283325 | − | 0.959024i | \(-0.408563\pi\) | ||||
0.283325 | + | 0.959024i | \(0.408563\pi\) | |||||||
\(24\) | −18.5373 | −3.78392 | ||||||||
\(25\) | −1.71810 | −0.343621 | ||||||||
\(26\) | 2.51520 | 0.493272 | ||||||||
\(27\) | 12.7928 | 2.46198 | ||||||||
\(28\) | 5.58873 | 1.05617 | ||||||||
\(29\) | 3.59950 | 0.668410 | 0.334205 | − | 0.942500i | \(-0.391532\pi\) | ||||
0.334205 | + | 0.942500i | \(0.391532\pi\) | |||||||
\(30\) | −14.4363 | −2.63569 | ||||||||
\(31\) | 5.80825 | 1.04319 | 0.521596 | − | 0.853193i | \(-0.325337\pi\) | ||||
0.521596 | + | 0.853193i | \(0.325337\pi\) | |||||||
\(32\) | −3.54996 | −0.627551 | ||||||||
\(33\) | 4.82974 | 0.840749 | ||||||||
\(34\) | 13.4425 | 2.30537 | ||||||||
\(35\) | 2.34026 | 0.395577 | ||||||||
\(36\) | 30.4473 | 5.07456 | ||||||||
\(37\) | 8.44083 | 1.38766 | 0.693832 | − | 0.720137i | \(-0.255921\pi\) | ||||
0.693832 | + | 0.720137i | \(0.255921\pi\) | |||||||
\(38\) | 0.387577 | 0.0628734 | ||||||||
\(39\) | −3.16825 | −0.507326 | ||||||||
\(40\) | −10.5996 | −1.67595 | ||||||||
\(41\) | −5.21842 | −0.814981 | −0.407490 | − | 0.913210i | \(-0.633596\pi\) | ||||
−0.407490 | + | 0.913210i | \(0.633596\pi\) | |||||||
\(42\) | −10.2943 | −1.58844 | ||||||||
\(43\) | −3.99011 | −0.608486 | −0.304243 | − | 0.952595i | \(-0.598403\pi\) | ||||
−0.304243 | + | 0.952595i | \(0.598403\pi\) | |||||||
\(44\) | 6.59499 | 0.994233 | ||||||||
\(45\) | 12.7497 | 1.90062 | ||||||||
\(46\) | −6.83520 | −1.00780 | ||||||||
\(47\) | 2.88958 | 0.421488 | 0.210744 | − | 0.977541i | \(-0.432411\pi\) | ||||
0.210744 | + | 0.977541i | \(0.432411\pi\) | |||||||
\(48\) | 19.2119 | 2.77300 | ||||||||
\(49\) | −5.33120 | −0.761600 | ||||||||
\(50\) | 4.32138 | 0.611135 | ||||||||
\(51\) | −16.9328 | −2.37106 | ||||||||
\(52\) | −4.32624 | −0.599942 | ||||||||
\(53\) | 8.74376 | 1.20105 | 0.600524 | − | 0.799607i | \(-0.294959\pi\) | ||||
0.600524 | + | 0.799607i | \(0.294959\pi\) | |||||||
\(54\) | −32.1766 | −4.37868 | ||||||||
\(55\) | 2.76163 | 0.372379 | ||||||||
\(56\) | −7.55840 | −1.01003 | ||||||||
\(57\) | −0.488209 | −0.0646648 | ||||||||
\(58\) | −9.05347 | −1.18878 | ||||||||
\(59\) | −1.18271 | −0.153975 | −0.0769876 | − | 0.997032i | \(-0.524530\pi\) | ||||
−0.0769876 | + | 0.997032i | \(0.524530\pi\) | |||||||
\(60\) | 24.8309 | 3.20566 | ||||||||
\(61\) | 4.63924 | 0.593994 | 0.296997 | − | 0.954878i | \(-0.404015\pi\) | ||||
0.296997 | + | 0.954878i | \(0.404015\pi\) | |||||||
\(62\) | −14.6089 | −1.85533 | ||||||||
\(63\) | 9.09160 | 1.14543 | ||||||||
\(64\) | −3.19890 | −0.399863 | ||||||||
\(65\) | −1.81160 | −0.224701 | ||||||||
\(66\) | −12.1478 | −1.49529 | ||||||||
\(67\) | 1.26948 | 0.155092 | 0.0775458 | − | 0.996989i | \(-0.475292\pi\) | ||||
0.0775458 | + | 0.996989i | \(0.475292\pi\) | |||||||
\(68\) | −23.1216 | −2.80391 | ||||||||
\(69\) | 8.60990 | 1.03651 | ||||||||
\(70\) | −5.88623 | −0.703539 | ||||||||
\(71\) | 10.4525 | 1.24049 | 0.620243 | − | 0.784410i | \(-0.287034\pi\) | ||||
0.620243 | + | 0.784410i | \(0.287034\pi\) | |||||||
\(72\) | −41.1781 | −4.85289 | ||||||||
\(73\) | −16.2062 | −1.89680 | −0.948398 | − | 0.317082i | \(-0.897297\pi\) | ||||
−0.948398 | + | 0.317082i | \(0.897297\pi\) | |||||||
\(74\) | −21.2304 | −2.46798 | ||||||||
\(75\) | −5.44339 | −0.628548 | ||||||||
\(76\) | −0.666648 | −0.0764697 | ||||||||
\(77\) | 1.96927 | 0.224419 | ||||||||
\(78\) | 7.96880 | 0.902288 | ||||||||
\(79\) | 9.18208 | 1.03306 | 0.516532 | − | 0.856268i | \(-0.327223\pi\) | ||||
0.516532 | + | 0.856268i | \(0.327223\pi\) | |||||||
\(80\) | 10.9853 | 1.22820 | ||||||||
\(81\) | 19.4175 | 2.15750 | ||||||||
\(82\) | 13.1254 | 1.44946 | ||||||||
\(83\) | 3.11669 | 0.342101 | 0.171050 | − | 0.985262i | \(-0.445284\pi\) | ||||
0.171050 | + | 0.985262i | \(0.445284\pi\) | |||||||
\(84\) | 17.7065 | 1.93194 | ||||||||
\(85\) | −9.68211 | −1.05017 | ||||||||
\(86\) | 10.0359 | 1.08220 | ||||||||
\(87\) | 11.4041 | 1.22265 | ||||||||
\(88\) | −8.91931 | −0.950802 | ||||||||
\(89\) | 14.9351 | 1.58312 | 0.791559 | − | 0.611093i | \(-0.209270\pi\) | ||||
0.791559 | + | 0.611093i | \(0.209270\pi\) | |||||||
\(90\) | −32.0681 | −3.38028 | ||||||||
\(91\) | −1.29182 | −0.135420 | ||||||||
\(92\) | 11.7568 | 1.22573 | ||||||||
\(93\) | 18.4020 | 1.90820 | ||||||||
\(94\) | −7.26787 | −0.749623 | ||||||||
\(95\) | −0.279157 | −0.0286409 | ||||||||
\(96\) | −11.2472 | −1.14791 | ||||||||
\(97\) | 6.06605 | 0.615914 | 0.307957 | − | 0.951400i | \(-0.400355\pi\) | ||||
0.307957 | + | 0.951400i | \(0.400355\pi\) | |||||||
\(98\) | 13.4090 | 1.35452 | ||||||||
\(99\) | 10.7286 | 1.07826 | ||||||||
\(100\) | −7.43293 | −0.743293 | ||||||||
\(101\) | 3.25959 | 0.324342 | 0.162171 | − | 0.986763i | \(-0.448150\pi\) | ||||
0.162171 | + | 0.986763i | \(0.448150\pi\) | |||||||
\(102\) | 42.5893 | 4.21697 | ||||||||
\(103\) | 3.85654 | 0.379996 | 0.189998 | − | 0.981784i | \(-0.439152\pi\) | ||||
0.189998 | + | 0.981784i | \(0.439152\pi\) | |||||||
\(104\) | 5.85097 | 0.573735 | ||||||||
\(105\) | 7.41454 | 0.723585 | ||||||||
\(106\) | −21.9923 | −2.13608 | ||||||||
\(107\) | −4.89182 | −0.472911 | −0.236455 | − | 0.971642i | \(-0.575986\pi\) | ||||
−0.236455 | + | 0.971642i | \(0.575986\pi\) | |||||||
\(108\) | 55.3450 | 5.32557 | ||||||||
\(109\) | −9.36239 | −0.896755 | −0.448377 | − | 0.893844i | \(-0.647998\pi\) | ||||
−0.448377 | + | 0.893844i | \(0.647998\pi\) | |||||||
\(110\) | −6.94607 | −0.662281 | ||||||||
\(111\) | 26.7427 | 2.53830 | ||||||||
\(112\) | 7.83345 | 0.740192 | ||||||||
\(113\) | 8.32097 | 0.782771 | 0.391386 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391386 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(114\) | 1.22794 | 0.115007 | ||||||||
\(115\) | 4.92312 | 0.459084 | ||||||||
\(116\) | 15.5723 | 1.44585 | ||||||||
\(117\) | −7.03782 | −0.650647 | ||||||||
\(118\) | 2.97474 | 0.273847 | ||||||||
\(119\) | −6.90414 | −0.632902 | ||||||||
\(120\) | −33.5823 | −3.06563 | ||||||||
\(121\) | −8.67615 | −0.788741 | ||||||||
\(122\) | −11.6686 | −1.05643 | ||||||||
\(123\) | −16.5333 | −1.49076 | ||||||||
\(124\) | 25.1279 | 2.25655 | ||||||||
\(125\) | −12.1705 | −1.08856 | ||||||||
\(126\) | −22.8672 | −2.03717 | ||||||||
\(127\) | 6.18414 | 0.548754 | 0.274377 | − | 0.961622i | \(-0.411528\pi\) | ||||
0.274377 | + | 0.961622i | \(0.411528\pi\) | |||||||
\(128\) | 15.1458 | 1.33871 | ||||||||
\(129\) | −12.6417 | −1.11304 | ||||||||
\(130\) | 4.55654 | 0.399635 | ||||||||
\(131\) | −22.0939 | −1.93035 | −0.965175 | − | 0.261606i | \(-0.915748\pi\) | ||||
−0.965175 | + | 0.261606i | \(0.915748\pi\) | |||||||
\(132\) | 20.8946 | 1.81864 | ||||||||
\(133\) | −0.199062 | −0.0172608 | ||||||||
\(134\) | −3.19300 | −0.275833 | ||||||||
\(135\) | 23.1755 | 1.99463 | ||||||||
\(136\) | 31.2706 | 2.68143 | ||||||||
\(137\) | −0.808644 | −0.0690872 | −0.0345436 | − | 0.999403i | \(-0.510998\pi\) | ||||
−0.0345436 | + | 0.999403i | \(0.510998\pi\) | |||||||
\(138\) | −21.6556 | −1.84345 | ||||||||
\(139\) | −4.66427 | −0.395618 | −0.197809 | − | 0.980241i | \(-0.563383\pi\) | ||||
−0.197809 | + | 0.980241i | \(0.563383\pi\) | |||||||
\(140\) | 10.1245 | 0.855680 | ||||||||
\(141\) | 9.15490 | 0.770982 | ||||||||
\(142\) | −26.2902 | −2.20623 | ||||||||
\(143\) | −1.52442 | −0.127478 | ||||||||
\(144\) | 42.6766 | 3.55638 | ||||||||
\(145\) | 6.52085 | 0.541528 | ||||||||
\(146\) | 40.7620 | 3.37348 | ||||||||
\(147\) | −16.8906 | −1.39311 | ||||||||
\(148\) | 36.5171 | 3.00169 | ||||||||
\(149\) | 4.21510 | 0.345315 | 0.172657 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172657 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(150\) | 13.6912 | 1.11788 | ||||||||
\(151\) | 6.61129 | 0.538019 | 0.269010 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269010 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(152\) | 0.901599 | 0.0731293 | ||||||||
\(153\) | −37.6137 | −3.04089 | ||||||||
\(154\) | −4.95312 | −0.399134 | ||||||||
\(155\) | 10.5222 | 0.845165 | ||||||||
\(156\) | −13.7066 | −1.09741 | ||||||||
\(157\) | −4.53111 | −0.361622 | −0.180811 | − | 0.983518i | \(-0.557872\pi\) | ||||
−0.180811 | + | 0.983518i | \(0.557872\pi\) | |||||||
\(158\) | −23.0948 | −1.83732 | ||||||||
\(159\) | 27.7025 | 2.19695 | ||||||||
\(160\) | −6.43111 | −0.508424 | ||||||||
\(161\) | 3.51059 | 0.276673 | ||||||||
\(162\) | −48.8389 | −3.83715 | ||||||||
\(163\) | −6.63172 | −0.519437 | −0.259718 | − | 0.965684i | \(-0.583630\pi\) | ||||
−0.259718 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(164\) | −22.5762 | −1.76290 | ||||||||
\(165\) | 8.74955 | 0.681152 | ||||||||
\(166\) | −7.83909 | −0.608432 | ||||||||
\(167\) | 19.4998 | 1.50894 | 0.754471 | − | 0.656334i | \(-0.227894\pi\) | ||||
0.754471 | + | 0.656334i | \(0.227894\pi\) | |||||||
\(168\) | −23.9469 | −1.84755 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 24.3525 | 1.86775 | ||||||||
\(171\) | −1.08449 | −0.0829327 | ||||||||
\(172\) | −17.2622 | −1.31623 | ||||||||
\(173\) | 1.88315 | 0.143173 | 0.0715864 | − | 0.997434i | \(-0.477194\pi\) | ||||
0.0715864 | + | 0.997434i | \(0.477194\pi\) | |||||||
\(174\) | −28.6837 | −2.17450 | ||||||||
\(175\) | −2.21948 | −0.167777 | ||||||||
\(176\) | 9.24389 | 0.696784 | ||||||||
\(177\) | −3.74711 | −0.281650 | ||||||||
\(178\) | −37.5648 | −2.81560 | ||||||||
\(179\) | −21.1034 | −1.57734 | −0.788670 | − | 0.614817i | \(-0.789230\pi\) | ||||
−0.788670 | + | 0.614817i | \(0.789230\pi\) | |||||||
\(180\) | 55.1584 | 4.11126 | ||||||||
\(181\) | 5.66260 | 0.420897 | 0.210449 | − | 0.977605i | \(-0.432508\pi\) | ||||
0.210449 | + | 0.977605i | \(0.432508\pi\) | |||||||
\(182\) | 3.24919 | 0.240846 | ||||||||
\(183\) | 14.6983 | 1.08653 | ||||||||
\(184\) | −15.9003 | −1.17219 | ||||||||
\(185\) | 15.2914 | 1.12425 | ||||||||
\(186\) | −46.2847 | −3.39376 | ||||||||
\(187\) | −8.14726 | −0.595786 | ||||||||
\(188\) | 12.5010 | 0.911729 | ||||||||
\(189\) | 16.5261 | 1.20209 | ||||||||
\(190\) | 0.702135 | 0.0509383 | ||||||||
\(191\) | −3.77610 | −0.273229 | −0.136615 | − | 0.990624i | \(-0.543622\pi\) | ||||
−0.136615 | + | 0.990624i | \(0.543622\pi\) | |||||||
\(192\) | −10.1349 | −0.731425 | ||||||||
\(193\) | 1.72532 | 0.124192 | 0.0620958 | − | 0.998070i | \(-0.480222\pi\) | ||||
0.0620958 | + | 0.998070i | \(0.480222\pi\) | |||||||
\(194\) | −15.2574 | −1.09541 | ||||||||
\(195\) | −5.73961 | −0.411022 | ||||||||
\(196\) | −23.0641 | −1.64743 | ||||||||
\(197\) | 16.5950 | 1.18235 | 0.591173 | − | 0.806545i | \(-0.298665\pi\) | ||||
0.591173 | + | 0.806545i | \(0.298665\pi\) | |||||||
\(198\) | −26.9845 | −1.91771 | ||||||||
\(199\) | −8.30463 | −0.588700 | −0.294350 | − | 0.955698i | \(-0.595103\pi\) | ||||
−0.294350 | + | 0.955698i | \(0.595103\pi\) | |||||||
\(200\) | 10.0526 | 0.710824 | ||||||||
\(201\) | 4.02203 | 0.283692 | ||||||||
\(202\) | −8.19854 | −0.576847 | ||||||||
\(203\) | 4.64991 | 0.326359 | ||||||||
\(204\) | −73.2552 | −5.12889 | ||||||||
\(205\) | −9.45370 | −0.660275 | ||||||||
\(206\) | −9.69997 | −0.675829 | ||||||||
\(207\) | 19.1257 | 1.32933 | ||||||||
\(208\) | −6.06389 | −0.420455 | ||||||||
\(209\) | −0.234903 | −0.0162486 | ||||||||
\(210\) | −18.6491 | −1.28691 | ||||||||
\(211\) | 7.80322 | 0.537196 | 0.268598 | − | 0.963252i | \(-0.413440\pi\) | ||||
0.268598 | + | 0.963252i | \(0.413440\pi\) | |||||||
\(212\) | 37.8276 | 2.59801 | ||||||||
\(213\) | 33.1162 | 2.26909 | ||||||||
\(214\) | 12.3039 | 0.841079 | ||||||||
\(215\) | −7.22848 | −0.492978 | ||||||||
\(216\) | −74.8506 | −5.09294 | ||||||||
\(217\) | 7.50321 | 0.509351 | ||||||||
\(218\) | 23.5483 | 1.59489 | ||||||||
\(219\) | −51.3454 | −3.46960 | ||||||||
\(220\) | 11.9475 | 0.805500 | ||||||||
\(221\) | 5.34451 | 0.359511 | ||||||||
\(222\) | −67.2633 | −4.51442 | ||||||||
\(223\) | 16.1102 | 1.07882 | 0.539411 | − | 0.842043i | \(-0.318647\pi\) | ||||
0.539411 | + | 0.842043i | \(0.318647\pi\) | |||||||
\(224\) | −4.58591 | −0.306409 | ||||||||
\(225\) | −12.0917 | −0.806114 | ||||||||
\(226\) | −20.9289 | −1.39217 | ||||||||
\(227\) | 20.8647 | 1.38484 | 0.692420 | − | 0.721495i | \(-0.256545\pi\) | ||||
0.692420 | + | 0.721495i | \(0.256545\pi\) | |||||||
\(228\) | −2.11211 | −0.139878 | ||||||||
\(229\) | −8.68362 | −0.573830 | −0.286915 | − | 0.957956i | \(-0.592630\pi\) | ||||
−0.286915 | + | 0.957956i | \(0.592630\pi\) | |||||||
\(230\) | −12.3827 | −0.816488 | ||||||||
\(231\) | 6.23915 | 0.410506 | ||||||||
\(232\) | −21.0606 | −1.38269 | ||||||||
\(233\) | 10.4478 | 0.684459 | 0.342230 | − | 0.939616i | \(-0.388818\pi\) | ||||
0.342230 | + | 0.939616i | \(0.388818\pi\) | |||||||
\(234\) | 17.7016 | 1.15719 | ||||||||
\(235\) | 5.23476 | 0.341478 | ||||||||
\(236\) | −5.11667 | −0.333067 | ||||||||
\(237\) | 29.0911 | 1.88967 | ||||||||
\(238\) | 17.3653 | 1.12563 | ||||||||
\(239\) | 27.5854 | 1.78435 | 0.892177 | − | 0.451686i | \(-0.149177\pi\) | ||||
0.892177 | + | 0.451686i | \(0.149177\pi\) | |||||||
\(240\) | 34.8043 | 2.24661 | ||||||||
\(241\) | 30.4299 | 1.96016 | 0.980081 | − | 0.198597i | \(-0.0636386\pi\) | ||||
0.980081 | + | 0.198597i | \(0.0636386\pi\) | |||||||
\(242\) | 21.8223 | 1.40279 | ||||||||
\(243\) | 23.1410 | 1.48450 | ||||||||
\(244\) | 20.0705 | 1.28488 | ||||||||
\(245\) | −9.65800 | −0.617027 | ||||||||
\(246\) | 41.5845 | 2.65133 | ||||||||
\(247\) | 0.154094 | 0.00980476 | ||||||||
\(248\) | −33.9839 | −2.15798 | ||||||||
\(249\) | 9.87445 | 0.625768 | ||||||||
\(250\) | 30.6113 | 1.93603 | ||||||||
\(251\) | 11.6483 | 0.735236 | 0.367618 | − | 0.929977i | \(-0.380173\pi\) | ||||
0.367618 | + | 0.929977i | \(0.380173\pi\) | |||||||
\(252\) | 39.3325 | 2.47771 | ||||||||
\(253\) | 4.14269 | 0.260448 | ||||||||
\(254\) | −15.5544 | −0.975968 | ||||||||
\(255\) | −30.6754 | −1.92097 | ||||||||
\(256\) | −31.6970 | −1.98106 | ||||||||
\(257\) | −9.34468 | −0.582905 | −0.291453 | − | 0.956585i | \(-0.594139\pi\) | ||||
−0.291453 | + | 0.956585i | \(0.594139\pi\) | |||||||
\(258\) | 31.7963 | 1.97955 | ||||||||
\(259\) | 10.9040 | 0.677544 | ||||||||
\(260\) | −7.83742 | −0.486056 | ||||||||
\(261\) | 25.3326 | 1.56805 | ||||||||
\(262\) | 55.5705 | 3.43316 | ||||||||
\(263\) | 21.9842 | 1.35560 | 0.677801 | − | 0.735246i | \(-0.262933\pi\) | ||||
0.677801 | + | 0.735246i | \(0.262933\pi\) | |||||||
\(264\) | −28.2586 | −1.73920 | ||||||||
\(265\) | 15.8402 | 0.973056 | ||||||||
\(266\) | 0.500680 | 0.0306987 | ||||||||
\(267\) | 47.3182 | 2.89583 | ||||||||
\(268\) | 5.49207 | 0.335482 | ||||||||
\(269\) | −32.0310 | −1.95296 | −0.976481 | − | 0.215603i | \(-0.930828\pi\) | ||||
−0.976481 | + | 0.215603i | \(0.930828\pi\) | |||||||
\(270\) | −58.2911 | −3.54749 | ||||||||
\(271\) | 11.7164 | 0.711724 | 0.355862 | − | 0.934539i | \(-0.384187\pi\) | ||||
0.355862 | + | 0.934539i | \(0.384187\pi\) | |||||||
\(272\) | −32.4085 | −1.96505 | ||||||||
\(273\) | −4.09281 | −0.247708 | ||||||||
\(274\) | 2.03390 | 0.122873 | ||||||||
\(275\) | −2.61911 | −0.157938 | ||||||||
\(276\) | 37.2485 | 2.24210 | ||||||||
\(277\) | −29.5894 | −1.77785 | −0.888927 | − | 0.458049i | \(-0.848548\pi\) | ||||
−0.888927 | + | 0.458049i | \(0.848548\pi\) | |||||||
\(278\) | 11.7316 | 0.703614 | ||||||||
\(279\) | 40.8774 | 2.44727 | ||||||||
\(280\) | −13.6928 | −0.818301 | ||||||||
\(281\) | −0.626570 | −0.0373780 | −0.0186890 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186890 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(282\) | −23.0264 | −1.37120 | ||||||||
\(283\) | −17.1781 | −1.02113 | −0.510565 | − | 0.859839i | \(-0.670564\pi\) | ||||
−0.510565 | + | 0.859839i | \(0.670564\pi\) | |||||||
\(284\) | 45.2202 | 2.68332 | ||||||||
\(285\) | −0.884439 | −0.0523896 | ||||||||
\(286\) | 3.83422 | 0.226722 | ||||||||
\(287\) | −6.74126 | −0.397924 | ||||||||
\(288\) | −24.9840 | −1.47220 | ||||||||
\(289\) | 11.5638 | 0.680222 | ||||||||
\(290\) | −16.4013 | −0.963116 | ||||||||
\(291\) | 19.2188 | 1.12663 | ||||||||
\(292\) | −70.1121 | −4.10300 | ||||||||
\(293\) | −17.6481 | −1.03101 | −0.515505 | − | 0.856886i | \(-0.672396\pi\) | ||||
−0.515505 | + | 0.856886i | \(0.672396\pi\) | |||||||
\(294\) | 42.4832 | 2.47767 | ||||||||
\(295\) | −2.14259 | −0.124746 | ||||||||
\(296\) | −49.3871 | −2.87056 | ||||||||
\(297\) | 19.5016 | 1.13160 | ||||||||
\(298\) | −10.6018 | −0.614148 | ||||||||
\(299\) | −2.71756 | −0.157160 | ||||||||
\(300\) | −23.5494 | −1.35963 | ||||||||
\(301\) | −5.15450 | −0.297101 | ||||||||
\(302\) | −16.6287 | −0.956876 | ||||||||
\(303\) | 10.3272 | 0.593283 | ||||||||
\(304\) | −0.934408 | −0.0535920 | ||||||||
\(305\) | 8.40446 | 0.481238 | ||||||||
\(306\) | 94.6061 | 5.40827 | ||||||||
\(307\) | −18.5188 | −1.05692 | −0.528462 | − | 0.848957i | \(-0.677231\pi\) | ||||
−0.528462 | + | 0.848957i | \(0.677231\pi\) | |||||||
\(308\) | 8.51955 | 0.485446 | ||||||||
\(309\) | 12.2185 | 0.695085 | ||||||||
\(310\) | −26.4655 | −1.50314 | ||||||||
\(311\) | −12.2395 | −0.694037 | −0.347019 | − | 0.937858i | \(-0.612806\pi\) | ||||
−0.347019 | + | 0.937858i | \(0.612806\pi\) | |||||||
\(312\) | 18.5373 | 1.04947 | ||||||||
\(313\) | 17.5378 | 0.991295 | 0.495647 | − | 0.868524i | \(-0.334931\pi\) | ||||
0.495647 | + | 0.868524i | \(0.334931\pi\) | |||||||
\(314\) | 11.3967 | 0.643150 | ||||||||
\(315\) | 16.4704 | 0.927999 | ||||||||
\(316\) | 39.7239 | 2.23464 | ||||||||
\(317\) | −3.77029 | −0.211760 | −0.105880 | − | 0.994379i | \(-0.533766\pi\) | ||||
−0.105880 | + | 0.994379i | \(0.533766\pi\) | |||||||
\(318\) | −69.6773 | −3.90731 | ||||||||
\(319\) | 5.48714 | 0.307221 | ||||||||
\(320\) | −5.79513 | −0.323958 | ||||||||
\(321\) | −15.4985 | −0.865044 | ||||||||
\(322\) | −8.82985 | −0.492068 | ||||||||
\(323\) | 0.823556 | 0.0458239 | ||||||||
\(324\) | 84.0048 | 4.66693 | ||||||||
\(325\) | 1.71810 | 0.0953033 | ||||||||
\(326\) | 16.6801 | 0.923827 | ||||||||
\(327\) | −29.6624 | −1.64034 | ||||||||
\(328\) | 30.5328 | 1.68589 | ||||||||
\(329\) | 3.73281 | 0.205797 | ||||||||
\(330\) | −22.0069 | −1.21144 | ||||||||
\(331\) | −2.58474 | −0.142070 | −0.0710352 | − | 0.997474i | \(-0.522630\pi\) | ||||
−0.0710352 | + | 0.997474i | \(0.522630\pi\) | |||||||
\(332\) | 13.4835 | 0.740005 | ||||||||
\(333\) | 59.4051 | 3.25538 | ||||||||
\(334\) | −49.0460 | −2.68368 | ||||||||
\(335\) | 2.29979 | 0.125651 | ||||||||
\(336\) | 24.8184 | 1.35395 | ||||||||
\(337\) | 12.4844 | 0.680069 | 0.340034 | − | 0.940413i | \(-0.389561\pi\) | ||||
0.340034 | + | 0.940413i | \(0.389561\pi\) | |||||||
\(338\) | −2.51520 | −0.136809 | ||||||||
\(339\) | 26.3629 | 1.43184 | ||||||||
\(340\) | −41.8872 | −2.27165 | ||||||||
\(341\) | 8.85419 | 0.479481 | ||||||||
\(342\) | 2.72770 | 0.147497 | ||||||||
\(343\) | −15.9297 | −0.860123 | ||||||||
\(344\) | 23.3460 | 1.25873 | ||||||||
\(345\) | 15.5977 | 0.839752 | ||||||||
\(346\) | −4.73649 | −0.254635 | ||||||||
\(347\) | −9.30942 | −0.499756 | −0.249878 | − | 0.968277i | \(-0.580391\pi\) | ||||
−0.249878 | + | 0.968277i | \(0.580391\pi\) | |||||||
\(348\) | 49.3370 | 2.64474 | ||||||||
\(349\) | −0.885935 | −0.0474230 | −0.0237115 | − | 0.999719i | \(-0.507548\pi\) | ||||
−0.0237115 | + | 0.999719i | \(0.507548\pi\) | |||||||
\(350\) | 5.58244 | 0.298394 | ||||||||
\(351\) | −12.7928 | −0.682832 | ||||||||
\(352\) | −5.41162 | −0.288440 | ||||||||
\(353\) | 8.16467 | 0.434561 | 0.217281 | − | 0.976109i | \(-0.430281\pi\) | ||||
0.217281 | + | 0.976109i | \(0.430281\pi\) | |||||||
\(354\) | 9.42474 | 0.500919 | ||||||||
\(355\) | 18.9358 | 1.00501 | ||||||||
\(356\) | 64.6129 | 3.42448 | ||||||||
\(357\) | −21.8741 | −1.15770 | ||||||||
\(358\) | 53.0792 | 2.80532 | ||||||||
\(359\) | 33.4590 | 1.76590 | 0.882949 | − | 0.469469i | \(-0.155555\pi\) | ||||
0.882949 | + | 0.469469i | \(0.155555\pi\) | |||||||
\(360\) | −74.5983 | −3.93167 | ||||||||
\(361\) | −18.9763 | −0.998750 | ||||||||
\(362\) | −14.2426 | −0.748573 | ||||||||
\(363\) | −27.4882 | −1.44276 | ||||||||
\(364\) | −5.58873 | −0.292929 | ||||||||
\(365\) | −29.3592 | −1.53673 | ||||||||
\(366\) | −36.9692 | −1.93241 | ||||||||
\(367\) | 0.467043 | 0.0243794 | 0.0121897 | − | 0.999926i | \(-0.496120\pi\) | ||||
0.0121897 | + | 0.999926i | \(0.496120\pi\) | |||||||
\(368\) | 16.4789 | 0.859024 | ||||||||
\(369\) | −36.7263 | −1.91190 | ||||||||
\(370\) | −38.4610 | −1.99949 | ||||||||
\(371\) | 11.2954 | 0.586426 | ||||||||
\(372\) | 79.6115 | 4.12766 | ||||||||
\(373\) | −12.8782 | −0.666809 | −0.333405 | − | 0.942784i | \(-0.608198\pi\) | ||||
−0.333405 | + | 0.942784i | \(0.608198\pi\) | |||||||
\(374\) | 20.4920 | 1.05962 | ||||||||
\(375\) | −38.5593 | −1.99119 | ||||||||
\(376\) | −16.9068 | −0.871902 | ||||||||
\(377\) | −3.59950 | −0.185384 | ||||||||
\(378\) | −41.5664 | −2.13794 | ||||||||
\(379\) | −9.49097 | −0.487518 | −0.243759 | − | 0.969836i | \(-0.578381\pi\) | ||||
−0.243759 | + | 0.969836i | \(0.578381\pi\) | |||||||
\(380\) | −1.20770 | −0.0619537 | ||||||||
\(381\) | 19.5929 | 1.00378 | ||||||||
\(382\) | 9.49766 | 0.485942 | ||||||||
\(383\) | 26.9402 | 1.37658 | 0.688291 | − | 0.725435i | \(-0.258361\pi\) | ||||
0.688291 | + | 0.725435i | \(0.258361\pi\) | |||||||
\(384\) | 47.9857 | 2.44876 | ||||||||
\(385\) | 3.56753 | 0.181818 | ||||||||
\(386\) | −4.33954 | −0.220877 | ||||||||
\(387\) | −28.0817 | −1.42747 | ||||||||
\(388\) | 26.2432 | 1.33230 | ||||||||
\(389\) | −22.5183 | −1.14172 | −0.570862 | − | 0.821046i | \(-0.693391\pi\) | ||||
−0.570862 | + | 0.821046i | \(0.693391\pi\) | |||||||
\(390\) | 14.4363 | 0.731009 | ||||||||
\(391\) | −14.5240 | −0.734510 | ||||||||
\(392\) | 31.1927 | 1.57547 | ||||||||
\(393\) | −69.9989 | −3.53098 | ||||||||
\(394\) | −41.7398 | −2.10282 | ||||||||
\(395\) | 16.6343 | 0.836960 | ||||||||
\(396\) | 46.4144 | 2.33241 | ||||||||
\(397\) | 2.69215 | 0.135115 | 0.0675577 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675577 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(398\) | 20.8878 | 1.04701 | ||||||||
\(399\) | −0.630678 | −0.0315734 | ||||||||
\(400\) | −10.4184 | −0.520919 | ||||||||
\(401\) | −20.7771 | −1.03756 | −0.518778 | − | 0.854909i | \(-0.673613\pi\) | ||||
−0.518778 | + | 0.854909i | \(0.673613\pi\) | |||||||
\(402\) | −10.1162 | −0.504551 | ||||||||
\(403\) | −5.80825 | −0.289329 | ||||||||
\(404\) | 14.1018 | 0.701590 | ||||||||
\(405\) | 35.1768 | 1.74795 | ||||||||
\(406\) | −11.6955 | −0.580436 | ||||||||
\(407\) | 12.8673 | 0.637811 | ||||||||
\(408\) | 99.0730 | 4.90485 | ||||||||
\(409\) | −23.5214 | −1.16306 | −0.581529 | − | 0.813526i | \(-0.697545\pi\) | ||||
−0.581529 | + | 0.813526i | \(0.697545\pi\) | |||||||
\(410\) | 23.7780 | 1.17431 | ||||||||
\(411\) | −2.56199 | −0.126374 | ||||||||
\(412\) | 16.6843 | 0.821977 | ||||||||
\(413\) | −1.52784 | −0.0751802 | ||||||||
\(414\) | −48.1049 | −2.36423 | ||||||||
\(415\) | 5.64619 | 0.277161 | ||||||||
\(416\) | 3.54996 | 0.174051 | ||||||||
\(417\) | −14.7776 | −0.723662 | ||||||||
\(418\) | 0.590829 | 0.0288984 | ||||||||
\(419\) | 22.5009 | 1.09924 | 0.549621 | − | 0.835414i | \(-0.314772\pi\) | ||||
0.549621 | + | 0.835414i | \(0.314772\pi\) | |||||||
\(420\) | 32.0771 | 1.56520 | ||||||||
\(421\) | −11.0320 | −0.537666 | −0.268833 | − | 0.963187i | \(-0.586638\pi\) | ||||
−0.268833 | + | 0.963187i | \(0.586638\pi\) | |||||||
\(422\) | −19.6267 | −0.955412 | ||||||||
\(423\) | 20.3363 | 0.988786 | ||||||||
\(424\) | −51.1595 | −2.48452 | ||||||||
\(425\) | 9.18242 | 0.445413 | ||||||||
\(426\) | −83.2940 | −4.03561 | ||||||||
\(427\) | 5.99307 | 0.290025 | ||||||||
\(428\) | −21.1632 | −1.02296 | ||||||||
\(429\) | −4.82974 | −0.233182 | ||||||||
\(430\) | 18.1811 | 0.876770 | ||||||||
\(431\) | 7.05294 | 0.339728 | 0.169864 | − | 0.985467i | \(-0.445667\pi\) | ||||
0.169864 | + | 0.985467i | \(0.445667\pi\) | |||||||
\(432\) | 77.5744 | 3.73230 | ||||||||
\(433\) | 28.8346 | 1.38570 | 0.692850 | − | 0.721081i | \(-0.256355\pi\) | ||||
0.692850 | + | 0.721081i | \(0.256355\pi\) | |||||||
\(434\) | −18.8721 | −0.905890 | ||||||||
\(435\) | 20.6597 | 0.990558 | ||||||||
\(436\) | −40.5040 | −1.93979 | ||||||||
\(437\) | −0.418759 | −0.0200319 | ||||||||
\(438\) | 129.144 | 6.17075 | ||||||||
\(439\) | −5.17222 | −0.246857 | −0.123428 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123428 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(440\) | −16.1582 | −0.770313 | ||||||||
\(441\) | −37.5201 | −1.78667 | ||||||||
\(442\) | −13.4425 | −0.639395 | ||||||||
\(443\) | 8.28359 | 0.393565 | 0.196783 | − | 0.980447i | \(-0.436951\pi\) | ||||
0.196783 | + | 0.980447i | \(0.436951\pi\) | |||||||
\(444\) | 115.695 | 5.49066 | ||||||||
\(445\) | 27.0564 | 1.28260 | ||||||||
\(446\) | −40.5205 | −1.91870 | ||||||||
\(447\) | 13.3545 | 0.631647 | ||||||||
\(448\) | −4.13240 | −0.195238 | ||||||||
\(449\) | −13.6724 | −0.645240 | −0.322620 | − | 0.946529i | \(-0.604564\pi\) | ||||
−0.322620 | + | 0.946529i | \(0.604564\pi\) | |||||||
\(450\) | 30.4131 | 1.43369 | ||||||||
\(451\) | −7.95505 | −0.374589 | ||||||||
\(452\) | 35.9986 | 1.69323 | ||||||||
\(453\) | 20.9462 | 0.984140 | ||||||||
\(454\) | −52.4790 | −2.46296 | ||||||||
\(455\) | −2.34026 | −0.109713 | ||||||||
\(456\) | 2.85649 | 0.133768 | ||||||||
\(457\) | −21.6195 | −1.01132 | −0.505659 | − | 0.862734i | \(-0.668751\pi\) | ||||
−0.505659 | + | 0.862734i | \(0.668751\pi\) | |||||||
\(458\) | 21.8411 | 1.02057 | ||||||||
\(459\) | −68.3715 | −3.19131 | ||||||||
\(460\) | 21.2986 | 0.993054 | ||||||||
\(461\) | −6.07529 | −0.282954 | −0.141477 | − | 0.989942i | \(-0.545185\pi\) | ||||
−0.141477 | + | 0.989942i | \(0.545185\pi\) | |||||||
\(462\) | −15.6927 | −0.730092 | ||||||||
\(463\) | −16.1244 | −0.749365 | −0.374683 | − | 0.927153i | \(-0.622248\pi\) | ||||
−0.374683 | + | 0.927153i | \(0.622248\pi\) | |||||||
\(464\) | 21.8270 | 1.01329 | ||||||||
\(465\) | 33.3371 | 1.54597 | ||||||||
\(466\) | −26.2784 | −1.21732 | ||||||||
\(467\) | −1.15849 | −0.0536085 | −0.0268043 | − | 0.999641i | \(-0.508533\pi\) | ||||
−0.0268043 | + | 0.999641i | \(0.508533\pi\) | |||||||
\(468\) | −30.4473 | −1.40743 | ||||||||
\(469\) | 1.63994 | 0.0757253 | ||||||||
\(470\) | −13.1665 | −0.607324 | ||||||||
\(471\) | −14.3557 | −0.661476 | ||||||||
\(472\) | 6.91997 | 0.318518 | ||||||||
\(473\) | −6.08258 | −0.279678 | ||||||||
\(474\) | −73.1701 | −3.36081 | ||||||||
\(475\) | 0.264749 | 0.0121475 | ||||||||
\(476\) | −29.8690 | −1.36904 | ||||||||
\(477\) | 61.5371 | 2.81759 | ||||||||
\(478\) | −69.3830 | −3.17350 | ||||||||
\(479\) | −15.7352 | −0.718960 | −0.359480 | − | 0.933153i | \(-0.617046\pi\) | ||||
−0.359480 | + | 0.933153i | \(0.617046\pi\) | |||||||
\(480\) | −20.3754 | −0.930005 | ||||||||
\(481\) | −8.44083 | −0.384869 | ||||||||
\(482\) | −76.5374 | −3.48618 | ||||||||
\(483\) | 11.1224 | 0.506089 | ||||||||
\(484\) | −37.5351 | −1.70614 | ||||||||
\(485\) | 10.9893 | 0.498997 | ||||||||
\(486\) | −58.2043 | −2.64020 | ||||||||
\(487\) | 20.9871 | 0.951016 | 0.475508 | − | 0.879711i | \(-0.342264\pi\) | ||||
0.475508 | + | 0.879711i | \(0.342264\pi\) | |||||||
\(488\) | −27.1441 | −1.22875 | ||||||||
\(489\) | −21.0110 | −0.950149 | ||||||||
\(490\) | 24.2918 | 1.09739 | ||||||||
\(491\) | −17.0231 | −0.768240 | −0.384120 | − | 0.923283i | \(-0.625495\pi\) | ||||
−0.384120 | + | 0.923283i | \(0.625495\pi\) | |||||||
\(492\) | −71.5270 | −3.22468 | ||||||||
\(493\) | −19.2376 | −0.866416 | ||||||||
\(494\) | −0.387577 | −0.0174379 | ||||||||
\(495\) | 19.4359 | 0.873578 | ||||||||
\(496\) | 35.2206 | 1.58145 | ||||||||
\(497\) | 13.5028 | 0.605683 | ||||||||
\(498\) | −24.8362 | −1.11294 | ||||||||
\(499\) | 3.61170 | 0.161682 | 0.0808408 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808408 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(500\) | −52.6526 | −2.35470 | ||||||||
\(501\) | 61.7804 | 2.76014 | ||||||||
\(502\) | −29.2979 | −1.30763 | ||||||||
\(503\) | 26.9491 | 1.20160 | 0.600800 | − | 0.799399i | \(-0.294849\pi\) | ||||
0.600800 | + | 0.799399i | \(0.294849\pi\) | |||||||
\(504\) | −53.1947 | −2.36948 | ||||||||
\(505\) | 5.90508 | 0.262773 | ||||||||
\(506\) | −10.4197 | −0.463212 | ||||||||
\(507\) | 3.16825 | 0.140707 | ||||||||
\(508\) | 26.7541 | 1.18702 | ||||||||
\(509\) | −19.4193 | −0.860747 | −0.430373 | − | 0.902651i | \(-0.641618\pi\) | ||||
−0.430373 | + | 0.902651i | \(0.641618\pi\) | |||||||
\(510\) | 77.1548 | 3.41647 | ||||||||
\(511\) | −20.9355 | −0.926134 | ||||||||
\(512\) | 49.4327 | 2.18464 | ||||||||
\(513\) | −1.97130 | −0.0870350 | ||||||||
\(514\) | 23.5038 | 1.03671 | ||||||||
\(515\) | 6.98650 | 0.307862 | ||||||||
\(516\) | −54.6909 | −2.40763 | ||||||||
\(517\) | 4.40492 | 0.193728 | ||||||||
\(518\) | −27.4259 | −1.20502 | ||||||||
\(519\) | 5.96628 | 0.261891 | ||||||||
\(520\) | 10.5996 | 0.464824 | ||||||||
\(521\) | −16.6332 | −0.728713 | −0.364357 | − | 0.931259i | \(-0.618711\pi\) | ||||
−0.364357 | + | 0.931259i | \(0.618711\pi\) | |||||||
\(522\) | −63.7167 | −2.78881 | ||||||||
\(523\) | −29.6498 | −1.29650 | −0.648248 | − | 0.761429i | \(-0.724498\pi\) | ||||
−0.648248 | + | 0.761429i | \(0.724498\pi\) | |||||||
\(524\) | −95.5834 | −4.17558 | ||||||||
\(525\) | −7.03188 | −0.306896 | ||||||||
\(526\) | −55.2946 | −2.41096 | ||||||||
\(527\) | −31.0422 | −1.35222 | ||||||||
\(528\) | 29.2870 | 1.27455 | ||||||||
\(529\) | −15.6149 | −0.678908 | ||||||||
\(530\) | −39.8413 | −1.73060 | ||||||||
\(531\) | −8.32367 | −0.361217 | ||||||||
\(532\) | −0.861189 | −0.0373373 | ||||||||
\(533\) | 5.21842 | 0.226035 | ||||||||
\(534\) | −119.015 | −5.15028 | ||||||||
\(535\) | −8.86203 | −0.383139 | ||||||||
\(536\) | −7.42768 | −0.320827 | ||||||||
\(537\) | −66.8608 | −2.88526 | ||||||||
\(538\) | 80.5644 | 3.47338 | ||||||||
\(539\) | −8.12697 | −0.350053 | ||||||||
\(540\) | 100.263 | 4.31463 | ||||||||
\(541\) | −30.5356 | −1.31283 | −0.656414 | − | 0.754401i | \(-0.727927\pi\) | ||||
−0.656414 | + | 0.754401i | \(0.727927\pi\) | |||||||
\(542\) | −29.4692 | −1.26581 | ||||||||
\(543\) | 17.9405 | 0.769902 | ||||||||
\(544\) | 18.9728 | 0.813452 | ||||||||
\(545\) | −16.9609 | −0.726526 | ||||||||
\(546\) | 10.2943 | 0.440553 | ||||||||
\(547\) | −11.9059 | −0.509060 | −0.254530 | − | 0.967065i | \(-0.581921\pi\) | ||||
−0.254530 | + | 0.967065i | \(0.581921\pi\) | |||||||
\(548\) | −3.49839 | −0.149444 | ||||||||
\(549\) | 32.6502 | 1.39348 | ||||||||
\(550\) | 6.58758 | 0.280895 | ||||||||
\(551\) | −0.554661 | −0.0236294 | ||||||||
\(552\) | −50.3763 | −2.14416 | ||||||||
\(553\) | 11.8616 | 0.504406 | ||||||||
\(554\) | 74.4233 | 3.16194 | ||||||||
\(555\) | 48.4471 | 2.05646 | ||||||||
\(556\) | −20.1788 | −0.855770 | ||||||||
\(557\) | −0.111954 | −0.00474364 | −0.00237182 | − | 0.999997i | \(-0.500755\pi\) | ||||
−0.00237182 | + | 0.999997i | \(0.500755\pi\) | |||||||
\(558\) | −102.815 | −4.35251 | ||||||||
\(559\) | 3.99011 | 0.168764 | ||||||||
\(560\) | 14.1911 | 0.599683 | ||||||||
\(561\) | −25.8126 | −1.08981 | ||||||||
\(562\) | 1.57595 | 0.0664774 | ||||||||
\(563\) | 21.8132 | 0.919315 | 0.459658 | − | 0.888096i | \(-0.347972\pi\) | ||||
0.459658 | + | 0.888096i | \(0.347972\pi\) | |||||||
\(564\) | 39.6063 | 1.66773 | ||||||||
\(565\) | 15.0743 | 0.634180 | ||||||||
\(566\) | 43.2063 | 1.81610 | ||||||||
\(567\) | 25.0839 | 1.05343 | ||||||||
\(568\) | −61.1574 | −2.56611 | ||||||||
\(569\) | 0.243757 | 0.0102188 | 0.00510941 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510941 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(570\) | 2.22454 | 0.0931758 | ||||||||
\(571\) | 35.9084 | 1.50272 | 0.751360 | − | 0.659892i | \(-0.229398\pi\) | ||||
0.751360 | + | 0.659892i | \(0.229398\pi\) | |||||||
\(572\) | −6.59499 | −0.275751 | ||||||||
\(573\) | −11.9636 | −0.499788 | ||||||||
\(574\) | 16.9556 | 0.707715 | ||||||||
\(575\) | −4.66904 | −0.194713 | ||||||||
\(576\) | −22.5133 | −0.938054 | ||||||||
\(577\) | 12.8710 | 0.535827 | 0.267914 | − | 0.963443i | \(-0.413666\pi\) | ||||
0.267914 | + | 0.963443i | \(0.413666\pi\) | |||||||
\(578\) | −29.0852 | −1.20979 | ||||||||
\(579\) | 5.46626 | 0.227170 | ||||||||
\(580\) | 28.2108 | 1.17139 | ||||||||
\(581\) | 4.02620 | 0.167035 | ||||||||
\(582\) | −48.3391 | −2.00372 | ||||||||
\(583\) | 13.3291 | 0.552036 | ||||||||
\(584\) | 94.8222 | 3.92377 | ||||||||
\(585\) | −12.7497 | −0.527136 | ||||||||
\(586\) | 44.3884 | 1.83367 | ||||||||
\(587\) | −38.9782 | −1.60880 | −0.804401 | − | 0.594087i | \(-0.797513\pi\) | ||||
−0.804401 | + | 0.594087i | \(0.797513\pi\) | |||||||
\(588\) | −73.0728 | −3.01347 | ||||||||
\(589\) | −0.895016 | −0.0368785 | ||||||||
\(590\) | 5.38905 | 0.221863 | ||||||||
\(591\) | 52.5772 | 2.16274 | ||||||||
\(592\) | 51.1843 | 2.10366 | ||||||||
\(593\) | 28.8651 | 1.18535 | 0.592674 | − | 0.805442i | \(-0.298072\pi\) | ||||
0.592674 | + | 0.805442i | \(0.298072\pi\) | |||||||
\(594\) | −49.0505 | −2.01257 | ||||||||
\(595\) | −12.5076 | −0.512760 | ||||||||
\(596\) | 18.2356 | 0.746957 | ||||||||
\(597\) | −26.3112 | −1.07684 | ||||||||
\(598\) | 6.83520 | 0.279512 | ||||||||
\(599\) | −27.4911 | −1.12326 | −0.561628 | − | 0.827390i | \(-0.689825\pi\) | ||||
−0.561628 | + | 0.827390i | \(0.689825\pi\) | |||||||
\(600\) | 31.8491 | 1.30023 | ||||||||
\(601\) | −43.2111 | −1.76262 | −0.881309 | − | 0.472541i | \(-0.843337\pi\) | ||||
−0.881309 | + | 0.472541i | \(0.843337\pi\) | |||||||
\(602\) | 12.9646 | 0.528398 | ||||||||
\(603\) | 8.93437 | 0.363836 | ||||||||
\(604\) | 28.6020 | 1.16380 | ||||||||
\(605\) | −15.7177 | −0.639016 | ||||||||
\(606\) | −25.9750 | −1.05516 | ||||||||
\(607\) | 13.7527 | 0.558206 | 0.279103 | − | 0.960261i | \(-0.409963\pi\) | ||||
0.279103 | + | 0.960261i | \(0.409963\pi\) | |||||||
\(608\) | 0.547028 | 0.0221849 | ||||||||
\(609\) | 14.7321 | 0.596974 | ||||||||
\(610\) | −21.1389 | −0.855889 | ||||||||
\(611\) | −2.88958 | −0.116900 | ||||||||
\(612\) | −162.726 | −6.57781 | ||||||||
\(613\) | −5.82538 | −0.235285 | −0.117642 | − | 0.993056i | \(-0.537534\pi\) | ||||
−0.117642 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(614\) | 46.5786 | 1.87976 | ||||||||
\(615\) | −29.9517 | −1.20777 | ||||||||
\(616\) | −11.5221 | −0.464241 | ||||||||
\(617\) | −45.1072 | −1.81595 | −0.907974 | − | 0.419026i | \(-0.862372\pi\) | ||||
−0.907974 | + | 0.419026i | \(0.862372\pi\) | |||||||
\(618\) | −30.7320 | −1.23622 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 45.5217 | 1.82820 | ||||||||
\(621\) | 34.7653 | 1.39508 | ||||||||
\(622\) | 30.7848 | 1.23436 | ||||||||
\(623\) | 19.2935 | 0.772977 | ||||||||
\(624\) | −19.2119 | −0.769092 | ||||||||
\(625\) | −13.4576 | −0.538304 | ||||||||
\(626\) | −44.1111 | −1.76303 | ||||||||
\(627\) | −0.744233 | −0.0297218 | ||||||||
\(628\) | −19.6027 | −0.782232 | ||||||||
\(629\) | −45.1121 | −1.79874 | ||||||||
\(630\) | −41.4263 | −1.65046 | ||||||||
\(631\) | −10.1925 | −0.405758 | −0.202879 | − | 0.979204i | \(-0.565030\pi\) | ||||
−0.202879 | + | 0.979204i | \(0.565030\pi\) | |||||||
\(632\) | −53.7240 | −2.13703 | ||||||||
\(633\) | 24.7226 | 0.982634 | ||||||||
\(634\) | 9.48303 | 0.376619 | ||||||||
\(635\) | 11.2032 | 0.444585 | ||||||||
\(636\) | 119.848 | 4.75226 | ||||||||
\(637\) | 5.33120 | 0.211230 | ||||||||
\(638\) | −13.8013 | −0.546397 | ||||||||
\(639\) | 73.5630 | 2.91011 | ||||||||
\(640\) | 27.4381 | 1.08459 | ||||||||
\(641\) | 36.0744 | 1.42485 | 0.712426 | − | 0.701747i | \(-0.247596\pi\) | ||||
0.712426 | + | 0.701747i | \(0.247596\pi\) | |||||||
\(642\) | 38.9820 | 1.53849 | ||||||||
\(643\) | −9.53401 | −0.375985 | −0.187992 | − | 0.982170i | \(-0.560198\pi\) | ||||
−0.187992 | + | 0.982170i | \(0.560198\pi\) | |||||||
\(644\) | 15.1877 | 0.598478 | ||||||||
\(645\) | −22.9017 | −0.901752 | ||||||||
\(646\) | −2.07141 | −0.0814986 | ||||||||
\(647\) | −10.9390 | −0.430058 | −0.215029 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215029 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(648\) | −113.611 | −4.46307 | ||||||||
\(649\) | −1.80294 | −0.0707714 | ||||||||
\(650\) | −4.32138 | −0.169498 | ||||||||
\(651\) | 23.7721 | 0.931701 | ||||||||
\(652\) | −28.6904 | −1.12360 | ||||||||
\(653\) | −26.1304 | −1.02256 | −0.511281 | − | 0.859414i | \(-0.670829\pi\) | ||||
−0.511281 | + | 0.859414i | \(0.670829\pi\) | |||||||
\(654\) | 74.6070 | 2.91736 | ||||||||
\(655\) | −40.0252 | −1.56392 | ||||||||
\(656\) | −31.6439 | −1.23549 | ||||||||
\(657\) | −114.057 | −4.44977 | ||||||||
\(658\) | −9.38878 | −0.366013 | ||||||||
\(659\) | 26.8823 | 1.04719 | 0.523593 | − | 0.851969i | \(-0.324591\pi\) | ||||
0.523593 | + | 0.851969i | \(0.324591\pi\) | |||||||
\(660\) | 37.8527 | 1.47341 | ||||||||
\(661\) | −28.8913 | −1.12374 | −0.561870 | − | 0.827226i | \(-0.689918\pi\) | ||||
−0.561870 | + | 0.827226i | \(0.689918\pi\) | |||||||
\(662\) | 6.50115 | 0.252675 | ||||||||
\(663\) | 16.9328 | 0.657614 | ||||||||
\(664\) | −18.2356 | −0.707680 | ||||||||
\(665\) | −0.360620 | −0.0139843 | ||||||||
\(666\) | −149.416 | −5.78975 | ||||||||
\(667\) | 9.78184 | 0.378754 | ||||||||
\(668\) | 84.3610 | 3.26402 | ||||||||
\(669\) | 51.0413 | 1.97337 | ||||||||
\(670\) | −5.78443 | −0.223472 | ||||||||
\(671\) | 7.07214 | 0.273017 | ||||||||
\(672\) | −14.5293 | −0.560481 | ||||||||
\(673\) | −28.1500 | −1.08510 | −0.542551 | − | 0.840023i | \(-0.682541\pi\) | ||||
−0.542551 | + | 0.840023i | \(0.682541\pi\) | |||||||
\(674\) | −31.4008 | −1.20951 | ||||||||
\(675\) | −21.9794 | −0.845989 | ||||||||
\(676\) | 4.32624 | 0.166394 | ||||||||
\(677\) | −13.5286 | −0.519945 | −0.259972 | − | 0.965616i | \(-0.583713\pi\) | ||||
−0.259972 | + | 0.965616i | \(0.583713\pi\) | |||||||
\(678\) | −66.3081 | −2.54655 | ||||||||
\(679\) | 7.83625 | 0.300728 | ||||||||
\(680\) | 56.6498 | 2.17242 | ||||||||
\(681\) | 66.1047 | 2.53314 | ||||||||
\(682\) | −22.2701 | −0.852765 | ||||||||
\(683\) | 18.7037 | 0.715677 | 0.357838 | − | 0.933784i | \(-0.383514\pi\) | ||||
0.357838 | + | 0.933784i | \(0.383514\pi\) | |||||||
\(684\) | −4.69175 | −0.179394 | ||||||||
\(685\) | −1.46494 | −0.0559725 | ||||||||
\(686\) | 40.0664 | 1.52974 | ||||||||
\(687\) | −27.5119 | −1.04964 | ||||||||
\(688\) | −24.1956 | −0.922447 | ||||||||
\(689\) | −8.74376 | −0.333111 | ||||||||
\(690\) | −39.2314 | −1.49351 | ||||||||
\(691\) | −47.0623 | −1.79034 | −0.895168 | − | 0.445729i | \(-0.852944\pi\) | ||||
−0.895168 | + | 0.445729i | \(0.852944\pi\) | |||||||
\(692\) | 8.14694 | 0.309700 | ||||||||
\(693\) | 13.8594 | 0.526475 | ||||||||
\(694\) | 23.4151 | 0.888824 | ||||||||
\(695\) | −8.44979 | −0.320519 | ||||||||
\(696\) | −66.7252 | −2.52921 | ||||||||
\(697\) | 27.8899 | 1.05641 | ||||||||
\(698\) | 2.22831 | 0.0843426 | ||||||||
\(699\) | 33.1013 | 1.25201 | ||||||||
\(700\) | −9.60201 | −0.362922 | ||||||||
\(701\) | −26.6066 | −1.00492 | −0.502459 | − | 0.864601i | \(-0.667571\pi\) | ||||
−0.502459 | + | 0.864601i | \(0.667571\pi\) | |||||||
\(702\) | 32.1766 | 1.21443 | ||||||||
\(703\) | −1.30068 | −0.0490561 | ||||||||
\(704\) | −4.87646 | −0.183788 | ||||||||
\(705\) | 16.5850 | 0.624628 | ||||||||
\(706\) | −20.5358 | −0.772875 | ||||||||
\(707\) | 4.21081 | 0.158364 | ||||||||
\(708\) | −16.2109 | −0.609243 | ||||||||
\(709\) | −15.1224 | −0.567935 | −0.283967 | − | 0.958834i | \(-0.591651\pi\) | ||||
−0.283967 | + | 0.958834i | \(0.591651\pi\) | |||||||
\(710\) | −47.6274 | −1.78742 | ||||||||
\(711\) | 64.6218 | 2.42351 | ||||||||
\(712\) | −87.3849 | −3.27489 | ||||||||
\(713\) | 15.7842 | 0.591124 | ||||||||
\(714\) | 55.0177 | 2.05899 | ||||||||
\(715\) | −2.76163 | −0.103279 | ||||||||
\(716\) | −91.2983 | −3.41198 | ||||||||
\(717\) | 87.3977 | 3.26393 | ||||||||
\(718\) | −84.1561 | −3.14068 | ||||||||
\(719\) | 6.01264 | 0.224234 | 0.112117 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112117 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(720\) | 77.3129 | 2.88128 | ||||||||
\(721\) | 4.98195 | 0.185538 | ||||||||
\(722\) | 47.7291 | 1.77629 | ||||||||
\(723\) | 96.4096 | 3.58551 | ||||||||
\(724\) | 24.4978 | 0.910452 | ||||||||
\(725\) | −6.18431 | −0.229680 | ||||||||
\(726\) | 69.1385 | 2.56597 | ||||||||
\(727\) | −28.3834 | −1.05268 | −0.526341 | − | 0.850273i | \(-0.676437\pi\) | ||||
−0.526341 | + | 0.850273i | \(0.676437\pi\) | |||||||
\(728\) | 7.55840 | 0.280133 | ||||||||
\(729\) | 15.0641 | 0.557928 | ||||||||
\(730\) | 73.8444 | 2.73310 | ||||||||
\(731\) | 21.3252 | 0.788740 | ||||||||
\(732\) | 63.5884 | 2.35029 | ||||||||
\(733\) | 21.9308 | 0.810032 | 0.405016 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405016 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(734\) | −1.17471 | −0.0433592 | ||||||||
\(735\) | −30.5990 | −1.12866 | ||||||||
\(736\) | −9.64722 | −0.355601 | ||||||||
\(737\) | 1.93521 | 0.0712846 | ||||||||
\(738\) | 92.3742 | 3.40034 | ||||||||
\(739\) | 25.2878 | 0.930227 | 0.465114 | − | 0.885251i | \(-0.346013\pi\) | ||||
0.465114 | + | 0.885251i | \(0.346013\pi\) | |||||||
\(740\) | 66.1544 | 2.43188 | ||||||||
\(741\) | 0.488209 | 0.0179348 | ||||||||
\(742\) | −28.4101 | −1.04297 | ||||||||
\(743\) | 6.33037 | 0.232239 | 0.116119 | − | 0.993235i | \(-0.462954\pi\) | ||||
0.116119 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(744\) | −107.670 | −3.94736 | ||||||||
\(745\) | 7.63608 | 0.279764 | ||||||||
\(746\) | 32.3913 | 1.18593 | ||||||||
\(747\) | 21.9347 | 0.802548 | ||||||||
\(748\) | −35.2470 | −1.28876 | ||||||||
\(749\) | −6.31936 | −0.230904 | ||||||||
\(750\) | 96.9844 | 3.54137 | ||||||||
\(751\) | −50.2341 | −1.83307 | −0.916534 | − | 0.399957i | \(-0.869025\pi\) | ||||
−0.916534 | + | 0.399957i | \(0.869025\pi\) | |||||||
\(752\) | 17.5221 | 0.638964 | ||||||||
\(753\) | 36.9049 | 1.34489 | ||||||||
\(754\) | 9.05347 | 0.329708 | ||||||||
\(755\) | 11.9770 | 0.435888 | ||||||||
\(756\) | 71.4957 | 2.60028 | ||||||||
\(757\) | −35.0953 | −1.27556 | −0.637779 | − | 0.770219i | \(-0.720147\pi\) | ||||
−0.637779 | + | 0.770219i | \(0.720147\pi\) | |||||||
\(758\) | 23.8717 | 0.867060 | ||||||||
\(759\) | 13.1251 | 0.476410 | ||||||||
\(760\) | 1.63334 | 0.0592474 | ||||||||
\(761\) | −28.1134 | −1.01911 | −0.509556 | − | 0.860438i | \(-0.670190\pi\) | ||||
−0.509556 | + | 0.860438i | \(0.670190\pi\) | |||||||
\(762\) | −49.2802 | −1.78523 | ||||||||
\(763\) | −12.0945 | −0.437851 | ||||||||
\(764\) | −16.3363 | −0.591027 | ||||||||
\(765\) | −68.1410 | −2.46364 | ||||||||
\(766\) | −67.7602 | −2.44827 | ||||||||
\(767\) | 1.18271 | 0.0427050 | ||||||||
\(768\) | −100.424 | −3.62374 | ||||||||
\(769\) | 18.3039 | 0.660055 | 0.330028 | − | 0.943971i | \(-0.392942\pi\) | ||||
0.330028 | + | 0.943971i | \(0.392942\pi\) | |||||||
\(770\) | −8.97307 | −0.323367 | ||||||||
\(771\) | −29.6063 | −1.06625 | ||||||||
\(772\) | 7.46417 | 0.268641 | ||||||||
\(773\) | 13.1012 | 0.471218 | 0.235609 | − | 0.971848i | \(-0.424292\pi\) | ||||
0.235609 | + | 0.971848i | \(0.424292\pi\) | |||||||
\(774\) | 70.6311 | 2.53878 | ||||||||
\(775\) | −9.97917 | −0.358463 | ||||||||
\(776\) | −35.4923 | −1.27410 | ||||||||
\(777\) | 34.5468 | 1.23936 | ||||||||
\(778\) | 56.6381 | 2.03058 | ||||||||
\(779\) | 0.804127 | 0.0288108 | ||||||||
\(780\) | −24.8309 | −0.889090 | ||||||||
\(781\) | 15.9340 | 0.570163 | ||||||||
\(782\) | 36.5308 | 1.30634 | ||||||||
\(783\) | 46.0479 | 1.64562 | ||||||||
\(784\) | −32.3278 | −1.15456 | ||||||||
\(785\) | −8.20856 | −0.292976 | ||||||||
\(786\) | 176.061 | 6.27990 | ||||||||
\(787\) | −38.2585 | −1.36377 | −0.681885 | − | 0.731460i | \(-0.738839\pi\) | ||||
−0.681885 | + | 0.731460i | \(0.738839\pi\) | |||||||
\(788\) | 71.7941 | 2.55756 | ||||||||
\(789\) | 69.6514 | 2.47965 | ||||||||
\(790\) | −41.8385 | −1.48855 | ||||||||
\(791\) | 10.7492 | 0.382198 | ||||||||
\(792\) | −62.7726 | −2.23053 | ||||||||
\(793\) | −4.63924 | −0.164744 | ||||||||
\(794\) | −6.77131 | −0.240305 | ||||||||
\(795\) | 50.1858 | 1.77991 | ||||||||
\(796\) | −35.9278 | −1.27343 | ||||||||
\(797\) | 49.2804 | 1.74560 | 0.872801 | − | 0.488077i | \(-0.162301\pi\) | ||||
0.872801 | + | 0.488077i | \(0.162301\pi\) | |||||||
\(798\) | 1.58628 | 0.0561538 | ||||||||
\(799\) | −15.4434 | −0.546347 | ||||||||
\(800\) | 6.09920 | 0.215639 | ||||||||
\(801\) | 105.111 | 3.71390 | ||||||||
\(802\) | 52.2585 | 1.84531 | ||||||||
\(803\) | −24.7050 | −0.871822 | ||||||||
\(804\) | 17.4003 | 0.613661 | ||||||||
\(805\) | 6.35979 | 0.224153 | ||||||||
\(806\) | 14.6089 | 0.514577 | ||||||||
\(807\) | −101.482 | −3.57234 | ||||||||
\(808\) | −19.0718 | −0.670943 | ||||||||
\(809\) | −24.0104 | −0.844161 | −0.422081 | − | 0.906558i | \(-0.638700\pi\) | ||||
−0.422081 | + | 0.906558i | \(0.638700\pi\) | |||||||
\(810\) | −88.4767 | −3.10875 | ||||||||
\(811\) | −0.408788 | −0.0143545 | −0.00717724 | − | 0.999974i | \(-0.502285\pi\) | ||||
−0.00717724 | + | 0.999974i | \(0.502285\pi\) | |||||||
\(812\) | 20.1166 | 0.705955 | ||||||||
\(813\) | 37.1207 | 1.30188 | ||||||||
\(814\) | −32.3640 | −1.13436 | ||||||||
\(815\) | −12.0140 | −0.420833 | ||||||||
\(816\) | −102.678 | −3.59446 | ||||||||
\(817\) | 0.614851 | 0.0215109 | ||||||||
\(818\) | 59.1610 | 2.06852 | ||||||||
\(819\) | −9.09160 | −0.317686 | ||||||||
\(820\) | −40.8990 | −1.42825 | ||||||||
\(821\) | 5.55179 | 0.193759 | 0.0968795 | − | 0.995296i | \(-0.469114\pi\) | ||||
0.0968795 | + | 0.995296i | \(0.469114\pi\) | |||||||
\(822\) | 6.44392 | 0.224758 | ||||||||
\(823\) | −41.0826 | −1.43205 | −0.716025 | − | 0.698075i | \(-0.754040\pi\) | ||||
−0.716025 | + | 0.698075i | \(0.754040\pi\) | |||||||
\(824\) | −22.5645 | −0.786071 | ||||||||
\(825\) | −8.29799 | −0.288899 | ||||||||
\(826\) | 3.84283 | 0.133709 | ||||||||
\(827\) | 14.5760 | 0.506858 | 0.253429 | − | 0.967354i | \(-0.418442\pi\) | ||||
0.253429 | + | 0.967354i | \(0.418442\pi\) | |||||||
\(828\) | 82.7423 | 2.87549 | ||||||||
\(829\) | 40.9233 | 1.42132 | 0.710662 | − | 0.703533i | \(-0.248395\pi\) | ||||
0.710662 | + | 0.703533i | \(0.248395\pi\) | |||||||
\(830\) | −14.2013 | −0.492935 | ||||||||
\(831\) | −93.7466 | −3.25204 | ||||||||
\(832\) | 3.19890 | 0.110902 | ||||||||
\(833\) | 28.4926 | 0.987212 | ||||||||
\(834\) | 37.1686 | 1.28704 | ||||||||
\(835\) | 35.3259 | 1.22250 | ||||||||
\(836\) | −1.01625 | −0.0351477 | ||||||||
\(837\) | 74.3040 | 2.56832 | ||||||||
\(838\) | −56.5943 | −1.95502 | ||||||||
\(839\) | −19.0051 | −0.656127 | −0.328064 | − | 0.944656i | \(-0.606396\pi\) | ||||
−0.328064 | + | 0.944656i | \(0.606396\pi\) | |||||||
\(840\) | −43.3823 | −1.49683 | ||||||||
\(841\) | −16.0436 | −0.553228 | ||||||||
\(842\) | 27.7477 | 0.956247 | ||||||||
\(843\) | −1.98513 | −0.0683716 | ||||||||
\(844\) | 33.7586 | 1.16202 | ||||||||
\(845\) | 1.81160 | 0.0623209 | ||||||||
\(846\) | −51.1500 | −1.75857 | ||||||||
\(847\) | −11.2080 | −0.385113 | ||||||||
\(848\) | 53.0212 | 1.82076 | ||||||||
\(849\) | −54.4244 | −1.86784 | ||||||||
\(850\) | −23.0956 | −0.792174 | ||||||||
\(851\) | 22.9384 | 0.786319 | ||||||||
\(852\) | 143.269 | 4.90831 | ||||||||
\(853\) | 8.64295 | 0.295929 | 0.147964 | − | 0.988993i | \(-0.452728\pi\) | ||||
0.147964 | + | 0.988993i | \(0.452728\pi\) | |||||||
\(854\) | −15.0738 | −0.515814 | ||||||||
\(855\) | −1.96466 | −0.0671898 | ||||||||
\(856\) | 28.6219 | 0.978277 | ||||||||
\(857\) | 15.4885 | 0.529077 | 0.264539 | − | 0.964375i | \(-0.414780\pi\) | ||||
0.264539 | + | 0.964375i | \(0.414780\pi\) | |||||||
\(858\) | 12.1478 | 0.414718 | ||||||||
\(859\) | 34.7575 | 1.18591 | 0.592956 | − | 0.805235i | \(-0.297961\pi\) | ||||
0.592956 | + | 0.805235i | \(0.297961\pi\) | |||||||
\(860\) | −31.2722 | −1.06637 | ||||||||
\(861\) | −21.3580 | −0.727880 | ||||||||
\(862\) | −17.7396 | −0.604212 | ||||||||
\(863\) | −33.6611 | −1.14584 | −0.572919 | − | 0.819612i | \(-0.694189\pi\) | ||||
−0.572919 | + | 0.819612i | \(0.694189\pi\) | |||||||
\(864\) | −45.4141 | −1.54502 | ||||||||
\(865\) | 3.41151 | 0.115995 | ||||||||
\(866\) | −72.5248 | −2.46449 | ||||||||
\(867\) | 36.6369 | 1.24426 | ||||||||
\(868\) | 32.4607 | 1.10179 | ||||||||
\(869\) | 13.9973 | 0.474826 | ||||||||
\(870\) | −51.9634 | −1.76172 | ||||||||
\(871\) | −1.26948 | −0.0430147 | ||||||||
\(872\) | 54.7791 | 1.85505 | ||||||||
\(873\) | 42.6918 | 1.44490 | ||||||||
\(874\) | 1.05326 | 0.0356272 | ||||||||
\(875\) | −15.7221 | −0.531505 | ||||||||
\(876\) | −222.133 | −7.50517 | ||||||||
\(877\) | −30.0011 | −1.01306 | −0.506532 | − | 0.862221i | \(-0.669073\pi\) | ||||
−0.506532 | + | 0.862221i | \(0.669073\pi\) | |||||||
\(878\) | 13.0092 | 0.439038 | ||||||||
\(879\) | −55.9135 | −1.88592 | ||||||||
\(880\) | 16.7462 | 0.564515 | ||||||||
\(881\) | −33.5342 | −1.12979 | −0.564897 | − | 0.825161i | \(-0.691084\pi\) | ||||
−0.564897 | + | 0.825161i | \(0.691084\pi\) | |||||||
\(882\) | 94.3705 | 3.17762 | ||||||||
\(883\) | −15.3852 | −0.517752 | −0.258876 | − | 0.965911i | \(-0.583352\pi\) | ||||
−0.258876 | + | 0.965911i | \(0.583352\pi\) | |||||||
\(884\) | 23.1216 | 0.777665 | ||||||||
\(885\) | −6.78826 | −0.228185 | ||||||||
\(886\) | −20.8349 | −0.699962 | ||||||||
\(887\) | 57.8564 | 1.94263 | 0.971314 | − | 0.237800i | \(-0.0764263\pi\) | ||||
0.971314 | + | 0.237800i | \(0.0764263\pi\) | |||||||
\(888\) | −156.471 | −5.25081 | ||||||||
\(889\) | 7.98880 | 0.267936 | ||||||||
\(890\) | −68.0524 | −2.28112 | ||||||||
\(891\) | 29.6004 | 0.991649 | ||||||||
\(892\) | 69.6968 | 2.33362 | ||||||||
\(893\) | −0.445266 | −0.0149003 | ||||||||
\(894\) | −33.5893 | −1.12339 | ||||||||
\(895\) | −38.2309 | −1.27792 | ||||||||
\(896\) | 19.5657 | 0.653643 | ||||||||
\(897\) | −8.60990 | −0.287476 | ||||||||
\(898\) | 34.3888 | 1.14757 | ||||||||
\(899\) | 20.9068 | 0.697280 | ||||||||
\(900\) | −52.3117 | −1.74372 | ||||||||
\(901\) | −46.7311 | −1.55684 | ||||||||
\(902\) | 20.0086 | 0.666212 | ||||||||
\(903\) | −16.3308 | −0.543454 | ||||||||
\(904\) | −48.6858 | −1.61926 | ||||||||
\(905\) | 10.2584 | 0.340999 | ||||||||
\(906\) | −52.6840 | −1.75031 | ||||||||
\(907\) | 1.12126 | 0.0372307 | 0.0186154 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186154 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(908\) | 90.2658 | 2.99558 | ||||||||
\(909\) | 22.9404 | 0.760887 | ||||||||
\(910\) | 5.88623 | 0.195127 | ||||||||
\(911\) | −11.3938 | −0.377494 | −0.188747 | − | 0.982026i | \(-0.560443\pi\) | ||||
−0.188747 | + | 0.982026i | \(0.560443\pi\) | |||||||
\(912\) | −2.96044 | −0.0980300 | ||||||||
\(913\) | 4.75113 | 0.157239 | ||||||||
\(914\) | 54.3774 | 1.79864 | ||||||||
\(915\) | 26.6274 | 0.880276 | ||||||||
\(916\) | −37.5674 | −1.24126 | ||||||||
\(917\) | −28.5413 | −0.942517 | ||||||||
\(918\) | 171.968 | 5.67579 | ||||||||
\(919\) | 38.9525 | 1.28493 | 0.642463 | − | 0.766317i | \(-0.277913\pi\) | ||||
0.642463 | + | 0.766317i | \(0.277913\pi\) | |||||||
\(920\) | −28.8050 | −0.949674 | ||||||||
\(921\) | −58.6723 | −1.93332 | ||||||||
\(922\) | 15.2806 | 0.503239 | ||||||||
\(923\) | −10.4525 | −0.344049 | ||||||||
\(924\) | 26.9921 | 0.887974 | ||||||||
\(925\) | −14.5022 | −0.476830 | ||||||||
\(926\) | 40.5562 | 1.33276 | ||||||||
\(927\) | 27.1416 | 0.891448 | ||||||||
\(928\) | −12.7781 | −0.419461 | ||||||||
\(929\) | 28.8405 | 0.946228 | 0.473114 | − | 0.881001i | \(-0.343130\pi\) | ||||
0.473114 | + | 0.881001i | \(0.343130\pi\) | |||||||
\(930\) | −83.8495 | −2.74953 | ||||||||
\(931\) | 0.821506 | 0.0269238 | ||||||||
\(932\) | 45.1998 | 1.48057 | ||||||||
\(933\) | −38.7778 | −1.26953 | ||||||||
\(934\) | 2.91384 | 0.0953437 | ||||||||
\(935\) | −14.7596 | −0.482690 | ||||||||
\(936\) | 41.1781 | 1.34595 | ||||||||
\(937\) | 0.671854 | 0.0219485 | 0.0109743 | − | 0.999940i | \(-0.496507\pi\) | ||||
0.0109743 | + | 0.999940i | \(0.496507\pi\) | |||||||
\(938\) | −4.12478 | −0.134679 | ||||||||
\(939\) | 55.5642 | 1.81327 | ||||||||
\(940\) | 22.6468 | 0.738658 | ||||||||
\(941\) | −12.8587 | −0.419180 | −0.209590 | − | 0.977789i | \(-0.567213\pi\) | ||||
−0.209590 | + | 0.977789i | \(0.567213\pi\) | |||||||
\(942\) | 36.1075 | 1.17645 | ||||||||
\(943\) | −14.1814 | −0.461808 | ||||||||
\(944\) | −7.17179 | −0.233422 | ||||||||
\(945\) | 29.9386 | 0.973903 | ||||||||
\(946\) | 15.2989 | 0.497411 | ||||||||
\(947\) | 36.1853 | 1.17587 | 0.587933 | − | 0.808910i | \(-0.299942\pi\) | ||||
0.587933 | + | 0.808910i | \(0.299942\pi\) | |||||||
\(948\) | 125.855 | 4.08759 | ||||||||
\(949\) | 16.2062 | 0.526077 | ||||||||
\(950\) | −0.665898 | −0.0216046 | ||||||||
\(951\) | −11.9452 | −0.387350 | ||||||||
\(952\) | 40.3959 | 1.30924 | ||||||||
\(953\) | 26.0118 | 0.842606 | 0.421303 | − | 0.906920i | \(-0.361573\pi\) | ||||
0.421303 | + | 0.906920i | \(0.361573\pi\) | |||||||
\(954\) | −154.778 | −5.01113 | ||||||||
\(955\) | −6.84078 | −0.221363 | ||||||||
\(956\) | 119.341 | 3.85977 | ||||||||
\(957\) | 17.3846 | 0.561965 | ||||||||
\(958\) | 39.5772 | 1.27868 | ||||||||
\(959\) | −1.04462 | −0.0337326 | ||||||||
\(960\) | −18.3604 | −0.592581 | ||||||||
\(961\) | 2.73575 | 0.0882500 | ||||||||
\(962\) | 21.2304 | 0.684496 | ||||||||
\(963\) | −34.4278 | −1.10942 | ||||||||
\(964\) | 131.647 | 4.24007 | ||||||||
\(965\) | 3.12560 | 0.100617 | ||||||||
\(966\) | −27.9752 | −0.900087 | ||||||||
\(967\) | −39.5850 | −1.27297 | −0.636484 | − | 0.771290i | \(-0.719612\pi\) | ||||
−0.636484 | + | 0.771290i | \(0.719612\pi\) | |||||||
\(968\) | 50.7639 | 1.63161 | ||||||||
\(969\) | 2.60923 | 0.0838207 | ||||||||
\(970\) | −27.6402 | −0.887474 | ||||||||
\(971\) | 30.0445 | 0.964174 | 0.482087 | − | 0.876123i | \(-0.339879\pi\) | ||||
0.482087 | + | 0.876123i | \(0.339879\pi\) | |||||||
\(972\) | 100.114 | 3.21115 | ||||||||
\(973\) | −6.02540 | −0.193165 | ||||||||
\(974\) | −52.7868 | −1.69140 | ||||||||
\(975\) | 5.44339 | 0.174328 | ||||||||
\(976\) | 28.1318 | 0.900479 | ||||||||
\(977\) | 52.0746 | 1.66601 | 0.833007 | − | 0.553262i | \(-0.186617\pi\) | ||||
0.833007 | + | 0.553262i | \(0.186617\pi\) | |||||||
\(978\) | 52.8469 | 1.68986 | ||||||||
\(979\) | 22.7673 | 0.727647 | ||||||||
\(980\) | −41.7829 | −1.33470 | ||||||||
\(981\) | −65.8909 | −2.10373 | ||||||||
\(982\) | 42.8165 | 1.36633 | ||||||||
\(983\) | −44.0826 | −1.40602 | −0.703008 | − | 0.711182i | \(-0.748160\pi\) | ||||
−0.703008 | + | 0.711182i | \(0.748160\pi\) | |||||||
\(984\) | 96.7357 | 3.08382 | ||||||||
\(985\) | 30.0636 | 0.957905 | ||||||||
\(986\) | 48.3863 | 1.54094 | ||||||||
\(987\) | 11.8265 | 0.376441 | ||||||||
\(988\) | 0.666648 | 0.0212089 | ||||||||
\(989\) | −10.8433 | −0.344798 | ||||||||
\(990\) | −48.8852 | −1.55367 | ||||||||
\(991\) | 55.4111 | 1.76019 | 0.880095 | − | 0.474797i | \(-0.157479\pi\) | ||||
0.880095 | + | 0.474797i | \(0.157479\pi\) | |||||||
\(992\) | −20.6191 | −0.654656 | ||||||||
\(993\) | −8.18912 | −0.259874 | ||||||||
\(994\) | −33.9622 | −1.07722 | ||||||||
\(995\) | −15.0447 | −0.476948 | ||||||||
\(996\) | 42.7192 | 1.35361 | ||||||||
\(997\) | 30.1161 | 0.953785 | 0.476893 | − | 0.878962i | \(-0.341763\pi\) | ||||
0.476893 | + | 0.878962i | \(0.341763\pi\) | |||||||
\(998\) | −9.08414 | −0.287554 | ||||||||
\(999\) | 107.982 | 3.41641 |
(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 | 8047.2.a.d.1.8 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.8 | ✓ | 156 | 1.1 | even | 1 | trivial |