Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43441 | −1.72138 | −0.860692 | − | 0.509126i | \(-0.829969\pi\) | ||||
−0.860692 | + | 0.509126i | \(0.829969\pi\) | |||||||
\(3\) | 1.77953 | 1.02741 | 0.513705 | − | 0.857967i | \(-0.328273\pi\) | ||||
0.513705 | + | 0.857967i | \(0.328273\pi\) | |||||||
\(4\) | 3.92633 | 1.96316 | ||||||||
\(5\) | −0.360928 | −0.161412 | −0.0807060 | − | 0.996738i | \(-0.525717\pi\) | ||||
−0.0807060 | + | 0.996738i | \(0.525717\pi\) | |||||||
\(6\) | −4.33209 | −1.76857 | ||||||||
\(7\) | −1.53438 | −0.579940 | −0.289970 | − | 0.957036i | \(-0.593645\pi\) | ||||
−0.289970 | + | 0.957036i | \(0.593645\pi\) | |||||||
\(8\) | −4.68946 | −1.65798 | ||||||||
\(9\) | 0.166714 | 0.0555712 | ||||||||
\(10\) | 0.878646 | 0.277852 | ||||||||
\(11\) | −2.71903 | −0.819818 | −0.409909 | − | 0.912126i | \(-0.634440\pi\) | ||||
−0.409909 | + | 0.912126i | \(0.634440\pi\) | |||||||
\(12\) | 6.98700 | 2.01697 | ||||||||
\(13\) | 5.42134 | 1.50361 | 0.751804 | − | 0.659386i | \(-0.229184\pi\) | ||||
0.751804 | + | 0.659386i | \(0.229184\pi\) | |||||||
\(14\) | 3.73530 | 0.998300 | ||||||||
\(15\) | −0.642281 | −0.165836 | ||||||||
\(16\) | 3.56340 | 0.890849 | ||||||||
\(17\) | 1.82952 | 0.443724 | 0.221862 | − | 0.975078i | \(-0.428787\pi\) | ||||
0.221862 | + | 0.975078i | \(0.428787\pi\) | |||||||
\(18\) | −0.405849 | −0.0956594 | ||||||||
\(19\) | −1.34221 | −0.307924 | −0.153962 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153962 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(20\) | −1.41712 | −0.316878 | ||||||||
\(21\) | −2.73047 | −0.595837 | ||||||||
\(22\) | 6.61922 | 1.41122 | ||||||||
\(23\) | 6.95468 | 1.45015 | 0.725076 | − | 0.688669i | \(-0.241805\pi\) | ||||
0.725076 | + | 0.688669i | \(0.241805\pi\) | |||||||
\(24\) | −8.34502 | −1.70342 | ||||||||
\(25\) | −4.86973 | −0.973946 | ||||||||
\(26\) | −13.1977 | −2.58829 | ||||||||
\(27\) | −5.04191 | −0.970316 | ||||||||
\(28\) | −6.02447 | −1.13852 | ||||||||
\(29\) | −6.05028 | −1.12351 | −0.561755 | − | 0.827304i | \(-0.689874\pi\) | ||||
−0.561755 | + | 0.827304i | \(0.689874\pi\) | |||||||
\(30\) | 1.56357 | 0.285468 | ||||||||
\(31\) | 3.54754 | 0.637157 | 0.318579 | − | 0.947896i | \(-0.396794\pi\) | ||||
0.318579 | + | 0.947896i | \(0.396794\pi\) | |||||||
\(32\) | 0.704175 | 0.124482 | ||||||||
\(33\) | −4.83859 | −0.842290 | ||||||||
\(34\) | −4.45379 | −0.763819 | ||||||||
\(35\) | 0.553801 | 0.0936094 | ||||||||
\(36\) | 0.654572 | 0.109095 | ||||||||
\(37\) | −1.69847 | −0.279227 | −0.139613 | − | 0.990206i | \(-0.544586\pi\) | ||||
−0.139613 | + | 0.990206i | \(0.544586\pi\) | |||||||
\(38\) | 3.26748 | 0.530055 | ||||||||
\(39\) | 9.64741 | 1.54482 | ||||||||
\(40\) | 1.69256 | 0.267617 | ||||||||
\(41\) | −5.25484 | −0.820668 | −0.410334 | − | 0.911935i | \(-0.634588\pi\) | ||||
−0.410334 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(42\) | 6.64706 | 1.02566 | ||||||||
\(43\) | −3.53428 | −0.538972 | −0.269486 | − | 0.963004i | \(-0.586854\pi\) | ||||
−0.269486 | + | 0.963004i | \(0.586854\pi\) | |||||||
\(44\) | −10.6758 | −1.60944 | ||||||||
\(45\) | −0.0601717 | −0.00896986 | ||||||||
\(46\) | −16.9305 | −2.49627 | ||||||||
\(47\) | 0.427352 | 0.0623357 | 0.0311679 | − | 0.999514i | \(-0.490077\pi\) | ||||
0.0311679 | + | 0.999514i | \(0.490077\pi\) | |||||||
\(48\) | 6.34116 | 0.915267 | ||||||||
\(49\) | −4.64568 | −0.663669 | ||||||||
\(50\) | 11.8549 | 1.67654 | ||||||||
\(51\) | 3.25568 | 0.455886 | ||||||||
\(52\) | 21.2860 | 2.95183 | ||||||||
\(53\) | 2.88425 | 0.396182 | 0.198091 | − | 0.980184i | \(-0.436526\pi\) | ||||
0.198091 | + | 0.980184i | \(0.436526\pi\) | |||||||
\(54\) | 12.2740 | 1.67029 | ||||||||
\(55\) | 0.981375 | 0.132329 | ||||||||
\(56\) | 7.19541 | 0.961527 | ||||||||
\(57\) | −2.38850 | −0.316364 | ||||||||
\(58\) | 14.7288 | 1.93399 | ||||||||
\(59\) | −13.7321 | −1.78777 | −0.893886 | − | 0.448295i | \(-0.852032\pi\) | ||||
−0.893886 | + | 0.448295i | \(0.852032\pi\) | |||||||
\(60\) | −2.52181 | −0.325564 | ||||||||
\(61\) | 8.87911 | 1.13685 | 0.568427 | − | 0.822734i | \(-0.307552\pi\) | ||||
0.568427 | + | 0.822734i | \(0.307552\pi\) | |||||||
\(62\) | −8.63616 | −1.09679 | ||||||||
\(63\) | −0.255802 | −0.0322280 | ||||||||
\(64\) | −8.84104 | −1.10513 | ||||||||
\(65\) | −1.95671 | −0.242701 | ||||||||
\(66\) | 11.7791 | 1.44990 | ||||||||
\(67\) | 9.16717 | 1.11995 | 0.559974 | − | 0.828510i | \(-0.310811\pi\) | ||||
0.559974 | + | 0.828510i | \(0.310811\pi\) | |||||||
\(68\) | 7.18330 | 0.871103 | ||||||||
\(69\) | 12.3760 | 1.48990 | ||||||||
\(70\) | −1.34817 | −0.161138 | ||||||||
\(71\) | 5.39556 | 0.640335 | 0.320168 | − | 0.947361i | \(-0.396261\pi\) | ||||
0.320168 | + | 0.947361i | \(0.396261\pi\) | |||||||
\(72\) | −0.781797 | −0.0921357 | ||||||||
\(73\) | 11.6556 | 1.36419 | 0.682093 | − | 0.731266i | \(-0.261070\pi\) | ||||
0.682093 | + | 0.731266i | \(0.261070\pi\) | |||||||
\(74\) | 4.13476 | 0.480656 | ||||||||
\(75\) | −8.66581 | −1.00064 | ||||||||
\(76\) | −5.26995 | −0.604505 | ||||||||
\(77\) | 4.17202 | 0.475446 | ||||||||
\(78\) | −23.4857 | −2.65923 | ||||||||
\(79\) | −2.01441 | −0.226639 | −0.113320 | − | 0.993559i | \(-0.536148\pi\) | ||||
−0.113320 | + | 0.993559i | \(0.536148\pi\) | |||||||
\(80\) | −1.28613 | −0.143794 | ||||||||
\(81\) | −9.47235 | −1.05248 | ||||||||
\(82\) | 12.7924 | 1.41268 | ||||||||
\(83\) | −6.98293 | −0.766477 | −0.383238 | − | 0.923650i | \(-0.625191\pi\) | ||||
−0.383238 | + | 0.923650i | \(0.625191\pi\) | |||||||
\(84\) | −10.7207 | −1.16972 | ||||||||
\(85\) | −0.660326 | −0.0716224 | ||||||||
\(86\) | 8.60386 | 0.927778 | ||||||||
\(87\) | −10.7666 | −1.15430 | ||||||||
\(88\) | 12.7508 | 1.35924 | ||||||||
\(89\) | 1.05385 | 0.111708 | 0.0558540 | − | 0.998439i | \(-0.482212\pi\) | ||||
0.0558540 | + | 0.998439i | \(0.482212\pi\) | |||||||
\(90\) | 0.146482 | 0.0154406 | ||||||||
\(91\) | −8.31838 | −0.872003 | ||||||||
\(92\) | 27.3064 | 2.84689 | ||||||||
\(93\) | 6.31295 | 0.654622 | ||||||||
\(94\) | −1.04035 | −0.107304 | ||||||||
\(95\) | 0.484441 | 0.0497026 | ||||||||
\(96\) | 1.25310 | 0.127894 | ||||||||
\(97\) | −0.00171825 | −0.000174462 0 | −8.72309e−5 | − | 1.00000i | \(-0.500028\pi\) | ||||
−8.72309e−5 | 1.00000i | \(0.500028\pi\) | ||||||||
\(98\) | 11.3095 | 1.14243 | ||||||||
\(99\) | −0.453299 | −0.0455583 | ||||||||
\(100\) | −19.1202 | −1.91202 | ||||||||
\(101\) | −10.8815 | −1.08275 | −0.541373 | − | 0.840783i | \(-0.682095\pi\) | ||||
−0.541373 | + | 0.840783i | \(0.682095\pi\) | |||||||
\(102\) | −7.92564 | −0.784756 | ||||||||
\(103\) | 9.23290 | 0.909745 | 0.454872 | − | 0.890557i | \(-0.349685\pi\) | ||||
0.454872 | + | 0.890557i | \(0.349685\pi\) | |||||||
\(104\) | −25.4232 | −2.49295 | ||||||||
\(105\) | 0.985503 | 0.0961752 | ||||||||
\(106\) | −7.02144 | −0.681982 | ||||||||
\(107\) | −18.9603 | −1.83296 | −0.916481 | − | 0.400078i | \(-0.868983\pi\) | ||||
−0.916481 | + | 0.400078i | \(0.868983\pi\) | |||||||
\(108\) | −19.7962 | −1.90489 | ||||||||
\(109\) | 2.88088 | 0.275938 | 0.137969 | − | 0.990437i | \(-0.455943\pi\) | ||||
0.137969 | + | 0.990437i | \(0.455943\pi\) | |||||||
\(110\) | −2.38906 | −0.227788 | ||||||||
\(111\) | −3.02247 | −0.286880 | ||||||||
\(112\) | −5.46760 | −0.516639 | ||||||||
\(113\) | −10.4326 | −0.981417 | −0.490709 | − | 0.871324i | \(-0.663262\pi\) | ||||
−0.490709 | + | 0.871324i | \(0.663262\pi\) | |||||||
\(114\) | 5.81457 | 0.544584 | ||||||||
\(115\) | −2.51014 | −0.234072 | ||||||||
\(116\) | −23.7554 | −2.20563 | ||||||||
\(117\) | 0.903811 | 0.0835574 | ||||||||
\(118\) | 33.4296 | 3.07744 | ||||||||
\(119\) | −2.80718 | −0.257333 | ||||||||
\(120\) | 3.01196 | 0.274953 | ||||||||
\(121\) | −3.60688 | −0.327898 | ||||||||
\(122\) | −21.6153 | −1.95696 | ||||||||
\(123\) | −9.35112 | −0.843162 | ||||||||
\(124\) | 13.9288 | 1.25084 | ||||||||
\(125\) | 3.56227 | 0.318619 | ||||||||
\(126\) | 0.622725 | 0.0554768 | ||||||||
\(127\) | 1.76375 | 0.156507 | 0.0782537 | − | 0.996933i | \(-0.475066\pi\) | ||||
0.0782537 | + | 0.996933i | \(0.475066\pi\) | |||||||
\(128\) | 20.1143 | 1.77787 | ||||||||
\(129\) | −6.28934 | −0.553745 | ||||||||
\(130\) | 4.76344 | 0.417781 | ||||||||
\(131\) | −11.3760 | −0.993928 | −0.496964 | − | 0.867771i | \(-0.665552\pi\) | ||||
−0.496964 | + | 0.867771i | \(0.665552\pi\) | |||||||
\(132\) | −18.9979 | −1.65355 | ||||||||
\(133\) | 2.05946 | 0.178578 | ||||||||
\(134\) | −22.3166 | −1.92786 | ||||||||
\(135\) | 1.81977 | 0.156621 | ||||||||
\(136\) | −8.57947 | −0.735683 | ||||||||
\(137\) | −7.11757 | −0.608095 | −0.304047 | − | 0.952657i | \(-0.598338\pi\) | ||||
−0.304047 | + | 0.952657i | \(0.598338\pi\) | |||||||
\(138\) | −30.1283 | −2.56469 | ||||||||
\(139\) | 0.279750 | 0.0237281 | 0.0118640 | − | 0.999930i | \(-0.496223\pi\) | ||||
0.0118640 | + | 0.999930i | \(0.496223\pi\) | |||||||
\(140\) | 2.17440 | 0.183771 | ||||||||
\(141\) | 0.760485 | 0.0640444 | ||||||||
\(142\) | −13.1350 | −1.10226 | ||||||||
\(143\) | −14.7408 | −1.23269 | ||||||||
\(144\) | 0.594067 | 0.0495056 | ||||||||
\(145\) | 2.18372 | 0.181348 | ||||||||
\(146\) | −28.3745 | −2.34829 | ||||||||
\(147\) | −8.26712 | −0.681860 | ||||||||
\(148\) | −6.66875 | −0.548168 | ||||||||
\(149\) | 0.431693 | 0.0353656 | 0.0176828 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176828 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(150\) | 21.0961 | 1.72249 | ||||||||
\(151\) | −0.974531 | −0.0793062 | −0.0396531 | − | 0.999214i | \(-0.512625\pi\) | ||||
−0.0396531 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(152\) | 6.29424 | 0.510530 | ||||||||
\(153\) | 0.305006 | 0.0246583 | ||||||||
\(154\) | −10.1564 | −0.818425 | ||||||||
\(155\) | −1.28041 | −0.102845 | ||||||||
\(156\) | 37.8789 | 3.03274 | ||||||||
\(157\) | 2.38774 | 0.190563 | 0.0952813 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952813 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(158\) | 4.90390 | 0.390133 | ||||||||
\(159\) | 5.13260 | 0.407042 | ||||||||
\(160\) | −0.254157 | −0.0200929 | ||||||||
\(161\) | −10.6711 | −0.841001 | ||||||||
\(162\) | 23.0595 | 1.81173 | ||||||||
\(163\) | −1.77098 | −0.138714 | −0.0693571 | − | 0.997592i | \(-0.522095\pi\) | ||||
−0.0693571 | + | 0.997592i | \(0.522095\pi\) | |||||||
\(164\) | −20.6322 | −1.61111 | ||||||||
\(165\) | 1.74638 | 0.135956 | ||||||||
\(166\) | 16.9993 | 1.31940 | ||||||||
\(167\) | 16.4248 | 1.27099 | 0.635496 | − | 0.772104i | \(-0.280795\pi\) | ||||
0.635496 | + | 0.772104i | \(0.280795\pi\) | |||||||
\(168\) | 12.8044 | 0.987882 | ||||||||
\(169\) | 16.3909 | 1.26084 | ||||||||
\(170\) | 1.60750 | 0.123290 | ||||||||
\(171\) | −0.223765 | −0.0171117 | ||||||||
\(172\) | −13.8767 | −1.05809 | ||||||||
\(173\) | −17.3309 | −1.31765 | −0.658823 | − | 0.752298i | \(-0.728945\pi\) | ||||
−0.658823 | + | 0.752298i | \(0.728945\pi\) | |||||||
\(174\) | 26.2104 | 1.98700 | ||||||||
\(175\) | 7.47201 | 0.564831 | ||||||||
\(176\) | −9.68898 | −0.730335 | ||||||||
\(177\) | −24.4367 | −1.83677 | ||||||||
\(178\) | −2.56550 | −0.192292 | ||||||||
\(179\) | −13.4213 | −1.00315 | −0.501577 | − | 0.865113i | \(-0.667247\pi\) | ||||
−0.501577 | + | 0.865113i | \(0.667247\pi\) | |||||||
\(180\) | −0.236254 | −0.0176093 | ||||||||
\(181\) | −11.0756 | −0.823241 | −0.411620 | − | 0.911355i | \(-0.635037\pi\) | ||||
−0.411620 | + | 0.911355i | \(0.635037\pi\) | |||||||
\(182\) | 20.2503 | 1.50105 | ||||||||
\(183\) | 15.8006 | 1.16801 | ||||||||
\(184\) | −32.6137 | −2.40432 | ||||||||
\(185\) | 0.613026 | 0.0450705 | ||||||||
\(186\) | −15.3683 | −1.12686 | ||||||||
\(187\) | −4.97452 | −0.363773 | ||||||||
\(188\) | 1.67793 | 0.122375 | ||||||||
\(189\) | 7.73619 | 0.562725 | ||||||||
\(190\) | −1.17933 | −0.0855574 | ||||||||
\(191\) | −25.9102 | −1.87480 | −0.937398 | − | 0.348259i | \(-0.886773\pi\) | ||||
−0.937398 | + | 0.348259i | \(0.886773\pi\) | |||||||
\(192\) | −15.7329 | −1.13542 | ||||||||
\(193\) | −7.76187 | −0.558711 | −0.279356 | − | 0.960188i | \(-0.590121\pi\) | ||||
−0.279356 | + | 0.960188i | \(0.590121\pi\) | |||||||
\(194\) | 0.00418291 | 0.000300316 0 | ||||||||
\(195\) | −3.48203 | −0.249353 | ||||||||
\(196\) | −18.2405 | −1.30289 | ||||||||
\(197\) | −7.21440 | −0.514005 | −0.257002 | − | 0.966411i | \(-0.582735\pi\) | ||||
−0.257002 | + | 0.966411i | \(0.582735\pi\) | |||||||
\(198\) | 1.10351 | 0.0784234 | ||||||||
\(199\) | −8.30703 | −0.588870 | −0.294435 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294435 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(200\) | 22.8364 | 1.61478 | ||||||||
\(201\) | 16.3132 | 1.15065 | ||||||||
\(202\) | 26.4899 | 1.86382 | ||||||||
\(203\) | 9.28342 | 0.651569 | ||||||||
\(204\) | 12.7829 | 0.894980 | ||||||||
\(205\) | 1.89662 | 0.132466 | ||||||||
\(206\) | −22.4766 | −1.56602 | ||||||||
\(207\) | 1.15944 | 0.0805867 | ||||||||
\(208\) | 19.3184 | 1.33949 | ||||||||
\(209\) | 3.64951 | 0.252442 | ||||||||
\(210\) | −2.39911 | −0.165554 | ||||||||
\(211\) | 2.41851 | 0.166497 | 0.0832485 | − | 0.996529i | \(-0.473470\pi\) | ||||
0.0832485 | + | 0.996529i | \(0.473470\pi\) | |||||||
\(212\) | 11.3245 | 0.777771 | ||||||||
\(213\) | 9.60154 | 0.657887 | ||||||||
\(214\) | 46.1571 | 3.15523 | ||||||||
\(215\) | 1.27562 | 0.0869966 | ||||||||
\(216\) | 23.6438 | 1.60876 | ||||||||
\(217\) | −5.44327 | −0.369513 | ||||||||
\(218\) | −7.01322 | −0.474995 | ||||||||
\(219\) | 20.7415 | 1.40158 | ||||||||
\(220\) | 3.85320 | 0.259783 | ||||||||
\(221\) | 9.91845 | 0.667187 | ||||||||
\(222\) | 7.35792 | 0.493831 | ||||||||
\(223\) | 1.47657 | 0.0988787 | 0.0494394 | − | 0.998777i | \(-0.484257\pi\) | ||||
0.0494394 | + | 0.998777i | \(0.484257\pi\) | |||||||
\(224\) | −1.08047 | −0.0721920 | ||||||||
\(225\) | −0.811851 | −0.0541234 | ||||||||
\(226\) | 25.3972 | 1.68940 | ||||||||
\(227\) | −6.29268 | −0.417660 | −0.208830 | − | 0.977952i | \(-0.566965\pi\) | ||||
−0.208830 | + | 0.977952i | \(0.566965\pi\) | |||||||
\(228\) | −9.37802 | −0.621075 | ||||||||
\(229\) | 10.3797 | 0.685908 | 0.342954 | − | 0.939352i | \(-0.388572\pi\) | ||||
0.342954 | + | 0.939352i | \(0.388572\pi\) | |||||||
\(230\) | 6.11070 | 0.402928 | ||||||||
\(231\) | 7.42422 | 0.488478 | ||||||||
\(232\) | 28.3726 | 1.86275 | ||||||||
\(233\) | 6.96882 | 0.456543 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(234\) | −2.20024 | −0.143834 | ||||||||
\(235\) | −0.154244 | −0.0100617 | ||||||||
\(236\) | −53.9169 | −3.50969 | ||||||||
\(237\) | −3.58470 | −0.232851 | ||||||||
\(238\) | 6.83380 | 0.442970 | ||||||||
\(239\) | 3.81790 | 0.246959 | 0.123480 | − | 0.992347i | \(-0.460595\pi\) | ||||
0.123480 | + | 0.992347i | \(0.460595\pi\) | |||||||
\(240\) | −2.28870 | −0.147735 | ||||||||
\(241\) | 3.58227 | 0.230754 | 0.115377 | − | 0.993322i | \(-0.463192\pi\) | ||||
0.115377 | + | 0.993322i | \(0.463192\pi\) | |||||||
\(242\) | 8.78060 | 0.564438 | ||||||||
\(243\) | −1.73057 | −0.111016 | ||||||||
\(244\) | 34.8623 | 2.23183 | ||||||||
\(245\) | 1.67676 | 0.107124 | ||||||||
\(246\) | 22.7644 | 1.45141 | ||||||||
\(247\) | −7.27657 | −0.462997 | ||||||||
\(248\) | −16.6361 | −1.05639 | ||||||||
\(249\) | −12.4263 | −0.787486 | ||||||||
\(250\) | −8.67200 | −0.548465 | ||||||||
\(251\) | −8.55140 | −0.539759 | −0.269880 | − | 0.962894i | \(-0.586984\pi\) | ||||
−0.269880 | + | 0.962894i | \(0.586984\pi\) | |||||||
\(252\) | −1.00436 | −0.0632688 | ||||||||
\(253\) | −18.9100 | −1.18886 | ||||||||
\(254\) | −4.29368 | −0.269409 | ||||||||
\(255\) | −1.17507 | −0.0735856 | ||||||||
\(256\) | −31.2843 | −1.95527 | ||||||||
\(257\) | 6.56368 | 0.409431 | 0.204716 | − | 0.978821i | \(-0.434373\pi\) | ||||
0.204716 | + | 0.978821i | \(0.434373\pi\) | |||||||
\(258\) | 15.3108 | 0.953208 | ||||||||
\(259\) | 2.60609 | 0.161935 | ||||||||
\(260\) | −7.68270 | −0.476461 | ||||||||
\(261\) | −1.00866 | −0.0624348 | ||||||||
\(262\) | 27.6938 | 1.71093 | ||||||||
\(263\) | 29.7712 | 1.83577 | 0.917884 | − | 0.396849i | \(-0.129896\pi\) | ||||
0.917884 | + | 0.396849i | \(0.129896\pi\) | |||||||
\(264\) | 22.6904 | 1.39650 | ||||||||
\(265\) | −1.04101 | −0.0639486 | ||||||||
\(266\) | −5.01355 | −0.307401 | ||||||||
\(267\) | 1.87536 | 0.114770 | ||||||||
\(268\) | 35.9933 | 2.19864 | ||||||||
\(269\) | −8.69549 | −0.530173 | −0.265087 | − | 0.964225i | \(-0.585401\pi\) | ||||
−0.265087 | + | 0.964225i | \(0.585401\pi\) | |||||||
\(270\) | −4.43005 | −0.269604 | ||||||||
\(271\) | −2.99039 | −0.181653 | −0.0908266 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908266 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(272\) | 6.51931 | 0.395291 | ||||||||
\(273\) | −14.8028 | −0.895905 | ||||||||
\(274\) | 17.3270 | 1.04676 | ||||||||
\(275\) | 13.2409 | 0.798459 | ||||||||
\(276\) | 48.5924 | 2.92492 | ||||||||
\(277\) | −9.40388 | −0.565025 | −0.282512 | − | 0.959264i | \(-0.591168\pi\) | ||||
−0.282512 | + | 0.959264i | \(0.591168\pi\) | |||||||
\(278\) | −0.681025 | −0.0408451 | ||||||||
\(279\) | 0.591424 | 0.0354076 | ||||||||
\(280\) | −2.59703 | −0.155202 | ||||||||
\(281\) | 23.4111 | 1.39659 | 0.698294 | − | 0.715811i | \(-0.253943\pi\) | ||||
0.698294 | + | 0.715811i | \(0.253943\pi\) | |||||||
\(282\) | −1.85133 | −0.110245 | ||||||||
\(283\) | −26.0157 | −1.54647 | −0.773235 | − | 0.634119i | \(-0.781363\pi\) | ||||
−0.773235 | + | 0.634119i | \(0.781363\pi\) | |||||||
\(284\) | 21.1847 | 1.25708 | ||||||||
\(285\) | 0.862076 | 0.0510650 | ||||||||
\(286\) | 35.8850 | 2.12193 | ||||||||
\(287\) | 8.06291 | 0.475938 | ||||||||
\(288\) | 0.117396 | 0.00691760 | ||||||||
\(289\) | −13.6529 | −0.803109 | ||||||||
\(290\) | −5.31606 | −0.312170 | ||||||||
\(291\) | −0.00305767 | −0.000179244 0 | ||||||||
\(292\) | 45.7637 | 2.67812 | ||||||||
\(293\) | 0.0159037 | 0.000929102 0 | 0.000464551 | − | 1.00000i | \(-0.499852\pi\) | ||||
0.000464551 | 1.00000i | \(0.499852\pi\) | ||||||||
\(294\) | 20.1255 | 1.17374 | ||||||||
\(295\) | 4.95632 | 0.288568 | ||||||||
\(296\) | 7.96491 | 0.462951 | ||||||||
\(297\) | 13.7091 | 0.795483 | ||||||||
\(298\) | −1.05091 | −0.0608779 | ||||||||
\(299\) | 37.7037 | 2.18046 | ||||||||
\(300\) | −34.0248 | −1.96442 | ||||||||
\(301\) | 5.42292 | 0.312572 | ||||||||
\(302\) | 2.37240 | 0.136517 | ||||||||
\(303\) | −19.3638 | −1.11242 | ||||||||
\(304\) | −4.78282 | −0.274314 | ||||||||
\(305\) | −3.20472 | −0.183502 | ||||||||
\(306\) | −0.742508 | −0.0424464 | ||||||||
\(307\) | 3.89875 | 0.222514 | 0.111257 | − | 0.993792i | \(-0.464512\pi\) | ||||
0.111257 | + | 0.993792i | \(0.464512\pi\) | |||||||
\(308\) | 16.3807 | 0.933378 | ||||||||
\(309\) | 16.4302 | 0.934681 | ||||||||
\(310\) | 3.11703 | 0.177036 | ||||||||
\(311\) | −6.30304 | −0.357413 | −0.178706 | − | 0.983902i | \(-0.557191\pi\) | ||||
−0.178706 | + | 0.983902i | \(0.557191\pi\) | |||||||
\(312\) | −45.2412 | −2.56128 | ||||||||
\(313\) | −9.76144 | −0.551749 | −0.275874 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275874 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(314\) | −5.81273 | −0.328031 | ||||||||
\(315\) | 0.0923261 | 0.00520199 | ||||||||
\(316\) | −7.90925 | −0.444930 | ||||||||
\(317\) | −9.23281 | −0.518566 | −0.259283 | − | 0.965801i | \(-0.583486\pi\) | ||||
−0.259283 | + | 0.965801i | \(0.583486\pi\) | |||||||
\(318\) | −12.4948 | −0.700675 | ||||||||
\(319\) | 16.4509 | 0.921074 | ||||||||
\(320\) | 3.19098 | 0.178381 | ||||||||
\(321\) | −33.7404 | −1.88320 | ||||||||
\(322\) | 25.9778 | 1.44769 | ||||||||
\(323\) | −2.45560 | −0.136633 | ||||||||
\(324\) | −37.1915 | −2.06620 | ||||||||
\(325\) | −26.4005 | −1.46443 | ||||||||
\(326\) | 4.31129 | 0.238780 | ||||||||
\(327\) | 5.12660 | 0.283501 | ||||||||
\(328\) | 24.6424 | 1.36065 | ||||||||
\(329\) | −0.655720 | −0.0361510 | ||||||||
\(330\) | −4.25140 | −0.234032 | ||||||||
\(331\) | −9.86665 | −0.542320 | −0.271160 | − | 0.962534i | \(-0.587407\pi\) | ||||
−0.271160 | + | 0.962534i | \(0.587407\pi\) | |||||||
\(332\) | −27.4173 | −1.50472 | ||||||||
\(333\) | −0.283158 | −0.0155170 | ||||||||
\(334\) | −39.9847 | −2.18787 | ||||||||
\(335\) | −3.30869 | −0.180773 | ||||||||
\(336\) | −9.72973 | −0.530801 | ||||||||
\(337\) | −29.9516 | −1.63157 | −0.815785 | − | 0.578356i | \(-0.803695\pi\) | ||||
−0.815785 | + | 0.578356i | \(0.803695\pi\) | |||||||
\(338\) | −39.9021 | −2.17039 | ||||||||
\(339\) | −18.5651 | −1.00832 | ||||||||
\(340\) | −2.59266 | −0.140607 | ||||||||
\(341\) | −9.64588 | −0.522353 | ||||||||
\(342\) | 0.544734 | 0.0294558 | ||||||||
\(343\) | 17.8689 | 0.964829 | ||||||||
\(344\) | 16.5739 | 0.893603 | ||||||||
\(345\) | −4.46686 | −0.240488 | ||||||||
\(346\) | 42.1905 | 2.26818 | ||||||||
\(347\) | −17.2299 | −0.924951 | −0.462475 | − | 0.886632i | \(-0.653039\pi\) | ||||
−0.462475 | + | 0.886632i | \(0.653039\pi\) | |||||||
\(348\) | −42.2734 | −2.26609 | ||||||||
\(349\) | −21.5405 | −1.15304 | −0.576519 | − | 0.817084i | \(-0.695589\pi\) | ||||
−0.576519 | + | 0.817084i | \(0.695589\pi\) | |||||||
\(350\) | −18.1899 | −0.972291 | ||||||||
\(351\) | −27.3339 | −1.45898 | ||||||||
\(352\) | −1.91467 | −0.102052 | ||||||||
\(353\) | −28.0720 | −1.49412 | −0.747060 | − | 0.664757i | \(-0.768535\pi\) | ||||
−0.747060 | + | 0.664757i | \(0.768535\pi\) | |||||||
\(354\) | 59.4888 | 3.16179 | ||||||||
\(355\) | −1.94741 | −0.103358 | ||||||||
\(356\) | 4.13777 | 0.219301 | ||||||||
\(357\) | −4.99544 | −0.264387 | ||||||||
\(358\) | 32.6729 | 1.72681 | ||||||||
\(359\) | 14.6434 | 0.772851 | 0.386426 | − | 0.922321i | \(-0.373710\pi\) | ||||
0.386426 | + | 0.922321i | \(0.373710\pi\) | |||||||
\(360\) | 0.282173 | 0.0148718 | ||||||||
\(361\) | −17.1985 | −0.905183 | ||||||||
\(362\) | 26.9624 | 1.41711 | ||||||||
\(363\) | −6.41853 | −0.336885 | ||||||||
\(364\) | −32.6607 | −1.71189 | ||||||||
\(365\) | −4.20684 | −0.220196 | ||||||||
\(366\) | −38.4651 | −2.01060 | ||||||||
\(367\) | 19.7503 | 1.03096 | 0.515479 | − | 0.856902i | \(-0.327614\pi\) | ||||
0.515479 | + | 0.856902i | \(0.327614\pi\) | |||||||
\(368\) | 24.7823 | 1.29187 | ||||||||
\(369\) | −0.876053 | −0.0456055 | ||||||||
\(370\) | −1.49235 | −0.0775837 | ||||||||
\(371\) | −4.42553 | −0.229762 | ||||||||
\(372\) | 24.7867 | 1.28513 | ||||||||
\(373\) | 26.4196 | 1.36796 | 0.683978 | − | 0.729503i | \(-0.260248\pi\) | ||||
0.683978 | + | 0.729503i | \(0.260248\pi\) | |||||||
\(374\) | 12.1100 | 0.626193 | ||||||||
\(375\) | 6.33915 | 0.327352 | ||||||||
\(376\) | −2.00405 | −0.103351 | ||||||||
\(377\) | −32.8006 | −1.68932 | ||||||||
\(378\) | −18.8330 | −0.968666 | ||||||||
\(379\) | −5.76350 | −0.296051 | −0.148026 | − | 0.988984i | \(-0.547292\pi\) | ||||
−0.148026 | + | 0.988984i | \(0.547292\pi\) | |||||||
\(380\) | 1.90208 | 0.0975744 | ||||||||
\(381\) | 3.13864 | 0.160797 | ||||||||
\(382\) | 63.0759 | 3.22725 | ||||||||
\(383\) | −8.45821 | −0.432194 | −0.216097 | − | 0.976372i | \(-0.569333\pi\) | ||||
−0.216097 | + | 0.976372i | \(0.569333\pi\) | |||||||
\(384\) | 35.7940 | 1.82660 | ||||||||
\(385\) | −1.50580 | −0.0767427 | ||||||||
\(386\) | 18.8955 | 0.961757 | ||||||||
\(387\) | −0.589212 | −0.0299513 | ||||||||
\(388\) | −0.00674641 | −0.000342497 0 | ||||||||
\(389\) | −33.0117 | −1.67376 | −0.836880 | − | 0.547387i | \(-0.815623\pi\) | ||||
−0.836880 | + | 0.547387i | \(0.815623\pi\) | |||||||
\(390\) | 8.47666 | 0.429232 | ||||||||
\(391\) | 12.7237 | 0.643467 | ||||||||
\(392\) | 21.7858 | 1.10035 | ||||||||
\(393\) | −20.2439 | −1.02117 | ||||||||
\(394\) | 17.5628 | 0.884800 | ||||||||
\(395\) | 0.727059 | 0.0365823 | ||||||||
\(396\) | −1.77980 | −0.0894384 | ||||||||
\(397\) | 13.4482 | 0.674944 | 0.337472 | − | 0.941336i | \(-0.390428\pi\) | ||||
0.337472 | + | 0.941336i | \(0.390428\pi\) | |||||||
\(398\) | 20.2227 | 1.01367 | ||||||||
\(399\) | 3.66486 | 0.183472 | ||||||||
\(400\) | −17.3528 | −0.867639 | ||||||||
\(401\) | −7.22760 | −0.360929 | −0.180465 | − | 0.983581i | \(-0.557760\pi\) | ||||
−0.180465 | + | 0.983581i | \(0.557760\pi\) | |||||||
\(402\) | −39.7130 | −1.98070 | ||||||||
\(403\) | 19.2324 | 0.958036 | ||||||||
\(404\) | −42.7242 | −2.12561 | ||||||||
\(405\) | 3.41884 | 0.169883 | ||||||||
\(406\) | −22.5996 | −1.12160 | ||||||||
\(407\) | 4.61819 | 0.228915 | ||||||||
\(408\) | −15.2674 | −0.755848 | ||||||||
\(409\) | 17.1033 | 0.845704 | 0.422852 | − | 0.906199i | \(-0.361029\pi\) | ||||
0.422852 | + | 0.906199i | \(0.361029\pi\) | |||||||
\(410\) | −4.61714 | −0.228024 | ||||||||
\(411\) | −12.6659 | −0.624763 | ||||||||
\(412\) | 36.2514 | 1.78598 | ||||||||
\(413\) | 21.0703 | 1.03680 | ||||||||
\(414\) | −2.82255 | −0.138721 | ||||||||
\(415\) | 2.52034 | 0.123719 | ||||||||
\(416\) | 3.81757 | 0.187172 | ||||||||
\(417\) | 0.497822 | 0.0243785 | ||||||||
\(418\) | −8.88438 | −0.434549 | ||||||||
\(419\) | 15.8437 | 0.774015 | 0.387008 | − | 0.922077i | \(-0.373509\pi\) | ||||
0.387008 | + | 0.922077i | \(0.373509\pi\) | |||||||
\(420\) | 3.86941 | 0.188808 | ||||||||
\(421\) | −12.9353 | −0.630430 | −0.315215 | − | 0.949020i | \(-0.602077\pi\) | ||||
−0.315215 | + | 0.949020i | \(0.602077\pi\) | |||||||
\(422\) | −5.88763 | −0.286605 | ||||||||
\(423\) | 0.0712455 | 0.00346407 | ||||||||
\(424\) | −13.5256 | −0.656861 | ||||||||
\(425\) | −8.90927 | −0.432163 | ||||||||
\(426\) | −23.3740 | −1.13248 | ||||||||
\(427\) | −13.6239 | −0.659307 | ||||||||
\(428\) | −74.4444 | −3.59841 | ||||||||
\(429\) | −26.2316 | −1.26647 | ||||||||
\(430\) | −3.10538 | −0.149755 | ||||||||
\(431\) | 7.16212 | 0.344987 | 0.172494 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172494 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(432\) | −17.9663 | −0.864405 | ||||||||
\(433\) | −18.9370 | −0.910052 | −0.455026 | − | 0.890478i | \(-0.650370\pi\) | ||||
−0.455026 | + | 0.890478i | \(0.650370\pi\) | |||||||
\(434\) | 13.2511 | 0.636075 | ||||||||
\(435\) | 3.88599 | 0.186319 | ||||||||
\(436\) | 11.3113 | 0.541712 | ||||||||
\(437\) | −9.33464 | −0.446536 | ||||||||
\(438\) | −50.4931 | −2.41265 | ||||||||
\(439\) | 35.9615 | 1.71635 | 0.858173 | − | 0.513360i | \(-0.171599\pi\) | ||||
0.858173 | + | 0.513360i | \(0.171599\pi\) | |||||||
\(440\) | −4.60212 | −0.219398 | ||||||||
\(441\) | −0.774499 | −0.0368809 | ||||||||
\(442\) | −24.1455 | −1.14849 | ||||||||
\(443\) | −6.42771 | −0.305390 | −0.152695 | − | 0.988273i | \(-0.548795\pi\) | ||||
−0.152695 | + | 0.988273i | \(0.548795\pi\) | |||||||
\(444\) | −11.8672 | −0.563193 | ||||||||
\(445\) | −0.380365 | −0.0180310 | ||||||||
\(446\) | −3.59458 | −0.170208 | ||||||||
\(447\) | 0.768209 | 0.0363350 | ||||||||
\(448\) | 13.5655 | 0.640910 | ||||||||
\(449\) | −13.8258 | −0.652482 | −0.326241 | − | 0.945287i | \(-0.605782\pi\) | ||||
−0.326241 | + | 0.945287i | \(0.605782\pi\) | |||||||
\(450\) | 1.97637 | 0.0931671 | ||||||||
\(451\) | 14.2881 | 0.672799 | ||||||||
\(452\) | −40.9618 | −1.92668 | ||||||||
\(453\) | −1.73420 | −0.0814800 | ||||||||
\(454\) | 15.3189 | 0.718953 | ||||||||
\(455\) | 3.00234 | 0.140752 | ||||||||
\(456\) | 11.2008 | 0.524524 | ||||||||
\(457\) | 29.4748 | 1.37878 | 0.689388 | − | 0.724393i | \(-0.257880\pi\) | ||||
0.689388 | + | 0.724393i | \(0.257880\pi\) | |||||||
\(458\) | −25.2683 | −1.18071 | ||||||||
\(459\) | −9.22427 | −0.430552 | ||||||||
\(460\) | −9.85564 | −0.459522 | ||||||||
\(461\) | −24.8082 | −1.15543 | −0.577716 | − | 0.816238i | \(-0.696056\pi\) | ||||
−0.577716 | + | 0.816238i | \(0.696056\pi\) | |||||||
\(462\) | −18.0736 | −0.840858 | ||||||||
\(463\) | 5.79512 | 0.269322 | 0.134661 | − | 0.990892i | \(-0.457005\pi\) | ||||
0.134661 | + | 0.990892i | \(0.457005\pi\) | |||||||
\(464\) | −21.5596 | −1.00088 | ||||||||
\(465\) | −2.27852 | −0.105664 | ||||||||
\(466\) | −16.9649 | −0.785885 | ||||||||
\(467\) | −4.45534 | −0.206169 | −0.103084 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103084 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(468\) | 3.54866 | 0.164037 | ||||||||
\(469\) | −14.0659 | −0.649503 | ||||||||
\(470\) | 0.375491 | 0.0173201 | ||||||||
\(471\) | 4.24905 | 0.195786 | ||||||||
\(472\) | 64.3963 | 2.96408 | ||||||||
\(473\) | 9.60980 | 0.441859 | ||||||||
\(474\) | 8.72661 | 0.400827 | ||||||||
\(475\) | 6.53620 | 0.299901 | ||||||||
\(476\) | −11.0219 | −0.505188 | ||||||||
\(477\) | 0.480844 | 0.0220163 | ||||||||
\(478\) | −9.29431 | −0.425112 | ||||||||
\(479\) | 27.5003 | 1.25652 | 0.628260 | − | 0.778003i | \(-0.283767\pi\) | ||||
0.628260 | + | 0.778003i | \(0.283767\pi\) | |||||||
\(480\) | −0.452279 | −0.0206436 | ||||||||
\(481\) | −9.20798 | −0.419848 | ||||||||
\(482\) | −8.72069 | −0.397217 | ||||||||
\(483\) | −18.9895 | −0.864053 | ||||||||
\(484\) | −14.1618 | −0.643717 | ||||||||
\(485\) | 0.000620165 0 | 2.81602e−5 0 | ||||||||
\(486\) | 4.21291 | 0.191101 | ||||||||
\(487\) | −43.9550 | −1.99179 | −0.995895 | − | 0.0905110i | \(-0.971150\pi\) | ||||
−0.995895 | + | 0.0905110i | \(0.971150\pi\) | |||||||
\(488\) | −41.6382 | −1.88487 | ||||||||
\(489\) | −3.15151 | −0.142516 | ||||||||
\(490\) | −4.08191 | −0.184402 | ||||||||
\(491\) | 18.6143 | 0.840051 | 0.420026 | − | 0.907512i | \(-0.362021\pi\) | ||||
0.420026 | + | 0.907512i | \(0.362021\pi\) | |||||||
\(492\) | −36.7156 | −1.65527 | ||||||||
\(493\) | −11.0691 | −0.498528 | ||||||||
\(494\) | 17.7141 | 0.796996 | ||||||||
\(495\) | 0.163609 | 0.00735366 | ||||||||
\(496\) | 12.6413 | 0.567611 | ||||||||
\(497\) | −8.27883 | −0.371356 | ||||||||
\(498\) | 30.2507 | 1.35557 | ||||||||
\(499\) | 14.9742 | 0.670339 | 0.335170 | − | 0.942158i | \(-0.391206\pi\) | ||||
0.335170 | + | 0.942158i | \(0.391206\pi\) | |||||||
\(500\) | 13.9866 | 0.625501 | ||||||||
\(501\) | 29.2284 | 1.30583 | ||||||||
\(502\) | 20.8176 | 0.929133 | ||||||||
\(503\) | −35.6500 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(504\) | 1.19957 | 0.0534332 | ||||||||
\(505\) | 3.92743 | 0.174768 | ||||||||
\(506\) | 46.0346 | 2.04649 | ||||||||
\(507\) | 29.1681 | 1.29540 | ||||||||
\(508\) | 6.92505 | 0.307250 | ||||||||
\(509\) | 14.4290 | 0.639554 | 0.319777 | − | 0.947493i | \(-0.396392\pi\) | ||||
0.319777 | + | 0.947493i | \(0.396392\pi\) | |||||||
\(510\) | 2.86059 | 0.126669 | ||||||||
\(511\) | −17.8841 | −0.791146 | ||||||||
\(512\) | 35.9301 | 1.58790 | ||||||||
\(513\) | 6.76730 | 0.298783 | ||||||||
\(514\) | −15.9787 | −0.704789 | ||||||||
\(515\) | −3.33242 | −0.146844 | ||||||||
\(516\) | −24.6940 | −1.08709 | ||||||||
\(517\) | −1.16198 | −0.0511040 | ||||||||
\(518\) | −6.34429 | −0.278752 | ||||||||
\(519\) | −30.8408 | −1.35376 | ||||||||
\(520\) | 9.17594 | 0.402392 | ||||||||
\(521\) | −38.7147 | −1.69612 | −0.848062 | − | 0.529898i | \(-0.822230\pi\) | ||||
−0.848062 | + | 0.529898i | \(0.822230\pi\) | |||||||
\(522\) | 2.45550 | 0.107474 | ||||||||
\(523\) | 9.85415 | 0.430892 | 0.215446 | − | 0.976516i | \(-0.430879\pi\) | ||||
0.215446 | + | 0.976516i | \(0.430879\pi\) | |||||||
\(524\) | −44.6660 | −1.95124 | ||||||||
\(525\) | 13.2966 | 0.580313 | ||||||||
\(526\) | −72.4750 | −3.16006 | ||||||||
\(527\) | 6.49030 | 0.282722 | ||||||||
\(528\) | −17.2418 | −0.750353 | ||||||||
\(529\) | 25.3676 | 1.10294 | ||||||||
\(530\) | 2.53424 | 0.110080 | ||||||||
\(531\) | −2.28933 | −0.0993486 | ||||||||
\(532\) | 8.08610 | 0.350577 | ||||||||
\(533\) | −28.4883 | −1.23396 | ||||||||
\(534\) | −4.56538 | −0.197563 | ||||||||
\(535\) | 6.84331 | 0.295862 | ||||||||
\(536\) | −42.9891 | −1.85685 | ||||||||
\(537\) | −23.8835 | −1.03065 | ||||||||
\(538\) | 21.1683 | 0.912632 | ||||||||
\(539\) | 12.6318 | 0.544088 | ||||||||
\(540\) | 7.14500 | 0.307472 | ||||||||
\(541\) | −19.9504 | −0.857737 | −0.428868 | − | 0.903367i | \(-0.641088\pi\) | ||||
−0.428868 | + | 0.903367i | \(0.641088\pi\) | |||||||
\(542\) | 7.27982 | 0.312695 | ||||||||
\(543\) | −19.7093 | −0.845806 | ||||||||
\(544\) | 1.28830 | 0.0552355 | ||||||||
\(545\) | −1.03979 | −0.0445397 | ||||||||
\(546\) | 36.0360 | 1.54220 | ||||||||
\(547\) | −29.7185 | −1.27067 | −0.635337 | − | 0.772235i | \(-0.719139\pi\) | ||||
−0.635337 | + | 0.772235i | \(0.719139\pi\) | |||||||
\(548\) | −27.9459 | −1.19379 | ||||||||
\(549\) | 1.48027 | 0.0631763 | ||||||||
\(550\) | −32.2338 | −1.37445 | ||||||||
\(551\) | 8.12075 | 0.345955 | ||||||||
\(552\) | −58.0370 | −2.47022 | ||||||||
\(553\) | 3.09087 | 0.131437 | ||||||||
\(554\) | 22.8929 | 0.972624 | ||||||||
\(555\) | 1.09090 | 0.0463059 | ||||||||
\(556\) | 1.09839 | 0.0465821 | ||||||||
\(557\) | −34.6065 | −1.46632 | −0.733161 | − | 0.680055i | \(-0.761956\pi\) | ||||
−0.733161 | + | 0.680055i | \(0.761956\pi\) | |||||||
\(558\) | −1.43977 | −0.0609501 | ||||||||
\(559\) | −19.1605 | −0.810403 | ||||||||
\(560\) | 1.97341 | 0.0833918 | ||||||||
\(561\) | −8.85229 | −0.373744 | ||||||||
\(562\) | −56.9920 | −2.40406 | ||||||||
\(563\) | −8.96186 | −0.377697 | −0.188849 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188849 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(564\) | 2.98591 | 0.125730 | ||||||||
\(565\) | 3.76542 | 0.158413 | ||||||||
\(566\) | 63.3326 | 2.66207 | ||||||||
\(567\) | 14.5342 | 0.610377 | ||||||||
\(568\) | −25.3023 | −1.06166 | ||||||||
\(569\) | 23.1417 | 0.970151 | 0.485075 | − | 0.874472i | \(-0.338792\pi\) | ||||
0.485075 | + | 0.874472i | \(0.338792\pi\) | |||||||
\(570\) | −2.09864 | −0.0879025 | ||||||||
\(571\) | −37.6945 | −1.57746 | −0.788732 | − | 0.614737i | \(-0.789262\pi\) | ||||
−0.788732 | + | 0.614737i | \(0.789262\pi\) | |||||||
\(572\) | −57.8772 | −2.41997 | ||||||||
\(573\) | −46.1079 | −1.92618 | ||||||||
\(574\) | −19.6284 | −0.819273 | ||||||||
\(575\) | −33.8674 | −1.41237 | ||||||||
\(576\) | −1.47392 | −0.0614134 | ||||||||
\(577\) | −9.43782 | −0.392902 | −0.196451 | − | 0.980514i | \(-0.562942\pi\) | ||||
−0.196451 | + | 0.980514i | \(0.562942\pi\) | |||||||
\(578\) | 33.2366 | 1.38246 | ||||||||
\(579\) | −13.8124 | −0.574026 | ||||||||
\(580\) | 8.57400 | 0.356016 | ||||||||
\(581\) | 10.7145 | 0.444511 | ||||||||
\(582\) | 0.00744360 | 0.000308547 0 | ||||||||
\(583\) | −7.84237 | −0.324798 | ||||||||
\(584\) | −54.6585 | −2.26179 | ||||||||
\(585\) | −0.326211 | −0.0134872 | ||||||||
\(586\) | −0.0387159 | −0.00159934 | ||||||||
\(587\) | 4.20125 | 0.173404 | 0.0867020 | − | 0.996234i | \(-0.472367\pi\) | ||||
0.0867020 | + | 0.996234i | \(0.472367\pi\) | |||||||
\(588\) | −32.4594 | −1.33860 | ||||||||
\(589\) | −4.76155 | −0.196196 | ||||||||
\(590\) | −12.0657 | −0.496736 | ||||||||
\(591\) | −12.8382 | −0.528094 | ||||||||
\(592\) | −6.05232 | −0.248749 | ||||||||
\(593\) | −14.2869 | −0.586694 | −0.293347 | − | 0.956006i | \(-0.594769\pi\) | ||||
−0.293347 | + | 0.956006i | \(0.594769\pi\) | |||||||
\(594\) | −33.3735 | −1.36933 | ||||||||
\(595\) | 1.01319 | 0.0415367 | ||||||||
\(596\) | 1.69497 | 0.0694286 | ||||||||
\(597\) | −14.7826 | −0.605010 | ||||||||
\(598\) | −91.7860 | −3.75341 | ||||||||
\(599\) | −8.45517 | −0.345469 | −0.172734 | − | 0.984968i | \(-0.555260\pi\) | ||||
−0.172734 | + | 0.984968i | \(0.555260\pi\) | |||||||
\(600\) | 40.6380 | 1.65904 | ||||||||
\(601\) | −10.3852 | −0.423623 | −0.211811 | − | 0.977311i | \(-0.567936\pi\) | ||||
−0.211811 | + | 0.977311i | \(0.567936\pi\) | |||||||
\(602\) | −13.2016 | −0.538056 | ||||||||
\(603\) | 1.52829 | 0.0622369 | ||||||||
\(604\) | −3.82633 | −0.155691 | ||||||||
\(605\) | 1.30182 | 0.0529267 | ||||||||
\(606\) | 47.1394 | 1.91491 | ||||||||
\(607\) | 9.68019 | 0.392907 | 0.196453 | − | 0.980513i | \(-0.437058\pi\) | ||||
0.196453 | + | 0.980513i | \(0.437058\pi\) | |||||||
\(608\) | −0.945150 | −0.0383309 | ||||||||
\(609\) | 16.5201 | 0.669428 | ||||||||
\(610\) | 7.80159 | 0.315877 | ||||||||
\(611\) | 2.31682 | 0.0937286 | ||||||||
\(612\) | 1.19755 | 0.0484082 | ||||||||
\(613\) | −9.12829 | −0.368688 | −0.184344 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184344 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(614\) | −9.49114 | −0.383031 | ||||||||
\(615\) | 3.37509 | 0.136097 | ||||||||
\(616\) | −19.5645 | −0.788278 | ||||||||
\(617\) | 38.2907 | 1.54153 | 0.770763 | − | 0.637122i | \(-0.219875\pi\) | ||||
0.770763 | + | 0.637122i | \(0.219875\pi\) | |||||||
\(618\) | −39.9977 | −1.60894 | ||||||||
\(619\) | 16.1469 | 0.648997 | 0.324499 | − | 0.945886i | \(-0.394804\pi\) | ||||
0.324499 | + | 0.945886i | \(0.394804\pi\) | |||||||
\(620\) | −5.02731 | −0.201901 | ||||||||
\(621\) | −35.0649 | −1.40710 | ||||||||
\(622\) | 15.3442 | 0.615245 | ||||||||
\(623\) | −1.61701 | −0.0647840 | ||||||||
\(624\) | 34.3776 | 1.37620 | ||||||||
\(625\) | 23.0629 | 0.922517 | ||||||||
\(626\) | 23.7633 | 0.949772 | ||||||||
\(627\) | 6.49439 | 0.259361 | ||||||||
\(628\) | 9.37506 | 0.374106 | ||||||||
\(629\) | −3.10738 | −0.123900 | ||||||||
\(630\) | −0.224759 | −0.00895462 | ||||||||
\(631\) | −9.21589 | −0.366879 | −0.183439 | − | 0.983031i | \(-0.558723\pi\) | ||||
−0.183439 | + | 0.983031i | \(0.558723\pi\) | |||||||
\(632\) | 9.44652 | 0.375762 | ||||||||
\(633\) | 4.30380 | 0.171061 | ||||||||
\(634\) | 22.4764 | 0.892652 | ||||||||
\(635\) | −0.636587 | −0.0252622 | ||||||||
\(636\) | 20.1523 | 0.799090 | ||||||||
\(637\) | −25.1858 | −0.997899 | ||||||||
\(638\) | −40.0482 | −1.58552 | ||||||||
\(639\) | 0.899514 | 0.0355842 | ||||||||
\(640\) | −7.25983 | −0.286970 | ||||||||
\(641\) | 9.68779 | 0.382645 | 0.191322 | − | 0.981527i | \(-0.438722\pi\) | ||||
0.191322 | + | 0.981527i | \(0.438722\pi\) | |||||||
\(642\) | 82.1377 | 3.24172 | ||||||||
\(643\) | 24.8826 | 0.981272 | 0.490636 | − | 0.871365i | \(-0.336764\pi\) | ||||
0.490636 | + | 0.871365i | \(0.336764\pi\) | |||||||
\(644\) | −41.8983 | −1.65102 | ||||||||
\(645\) | 2.27000 | 0.0893812 | ||||||||
\(646\) | 5.97792 | 0.235198 | ||||||||
\(647\) | 21.0575 | 0.827855 | 0.413928 | − | 0.910310i | \(-0.364157\pi\) | ||||
0.413928 | + | 0.910310i | \(0.364157\pi\) | |||||||
\(648\) | 44.4202 | 1.74499 | ||||||||
\(649\) | 37.3381 | 1.46565 | ||||||||
\(650\) | 64.2694 | 2.52085 | ||||||||
\(651\) | −9.68644 | −0.379642 | ||||||||
\(652\) | −6.95346 | −0.272319 | ||||||||
\(653\) | 25.7195 | 1.00648 | 0.503240 | − | 0.864146i | \(-0.332141\pi\) | ||||
0.503240 | + | 0.864146i | \(0.332141\pi\) | |||||||
\(654\) | −12.4802 | −0.488015 | ||||||||
\(655\) | 4.10593 | 0.160432 | ||||||||
\(656\) | −18.7251 | −0.731091 | ||||||||
\(657\) | 1.94315 | 0.0758094 | ||||||||
\(658\) | 1.59629 | 0.0622298 | ||||||||
\(659\) | 23.2097 | 0.904122 | 0.452061 | − | 0.891987i | \(-0.350689\pi\) | ||||
0.452061 | + | 0.891987i | \(0.350689\pi\) | |||||||
\(660\) | 6.85687 | 0.266903 | ||||||||
\(661\) | −23.1703 | −0.901222 | −0.450611 | − | 0.892720i | \(-0.648794\pi\) | ||||
−0.450611 | + | 0.892720i | \(0.648794\pi\) | |||||||
\(662\) | 24.0194 | 0.933542 | ||||||||
\(663\) | 17.6501 | 0.685475 | ||||||||
\(664\) | 32.7462 | 1.27080 | ||||||||
\(665\) | −0.743316 | −0.0288246 | ||||||||
\(666\) | 0.689321 | 0.0267107 | ||||||||
\(667\) | −42.0778 | −1.62926 | ||||||||
\(668\) | 64.4893 | 2.49517 | ||||||||
\(669\) | 2.62760 | 0.101589 | ||||||||
\(670\) | 8.05470 | 0.311180 | ||||||||
\(671\) | −24.1426 | −0.932013 | ||||||||
\(672\) | −1.92273 | −0.0741708 | ||||||||
\(673\) | 29.2139 | 1.12611 | 0.563056 | − | 0.826419i | \(-0.309626\pi\) | ||||
0.563056 | + | 0.826419i | \(0.309626\pi\) | |||||||
\(674\) | 72.9144 | 2.80856 | ||||||||
\(675\) | 24.5527 | 0.945035 | ||||||||
\(676\) | 64.3561 | 2.47523 | ||||||||
\(677\) | −20.5320 | −0.789108 | −0.394554 | − | 0.918873i | \(-0.629101\pi\) | ||||
−0.394554 | + | 0.918873i | \(0.629101\pi\) | |||||||
\(678\) | 45.1950 | 1.73570 | ||||||||
\(679\) | 0.00263644 | 0.000101177 0 | ||||||||
\(680\) | 3.09657 | 0.118748 | ||||||||
\(681\) | −11.1980 | −0.429108 | ||||||||
\(682\) | 23.4820 | 0.899171 | ||||||||
\(683\) | −1.82937 | −0.0699990 | −0.0349995 | − | 0.999387i | \(-0.511143\pi\) | ||||
−0.0349995 | + | 0.999387i | \(0.511143\pi\) | |||||||
\(684\) | −0.878573 | −0.0335931 | ||||||||
\(685\) | 2.56893 | 0.0981538 | ||||||||
\(686\) | −43.5001 | −1.66084 | ||||||||
\(687\) | 18.4709 | 0.704709 | ||||||||
\(688\) | −12.5940 | −0.480143 | ||||||||
\(689\) | 15.6365 | 0.595703 | ||||||||
\(690\) | 10.8742 | 0.413972 | ||||||||
\(691\) | −37.7553 | −1.43628 | −0.718139 | − | 0.695900i | \(-0.755006\pi\) | ||||
−0.718139 | + | 0.695900i | \(0.755006\pi\) | |||||||
\(692\) | −68.0469 | −2.58676 | ||||||||
\(693\) | 0.695533 | 0.0264211 | ||||||||
\(694\) | 41.9446 | 1.59220 | ||||||||
\(695\) | −0.100970 | −0.00383000 | ||||||||
\(696\) | 50.4898 | 1.91381 | ||||||||
\(697\) | −9.61383 | −0.364150 | ||||||||
\(698\) | 52.4383 | 1.98482 | ||||||||
\(699\) | 12.4012 | 0.469056 | ||||||||
\(700\) | 29.3376 | 1.10886 | ||||||||
\(701\) | 22.9884 | 0.868260 | 0.434130 | − | 0.900850i | \(-0.357056\pi\) | ||||
0.434130 | + | 0.900850i | \(0.357056\pi\) | |||||||
\(702\) | 66.5418 | 2.51146 | ||||||||
\(703\) | 2.27970 | 0.0859806 | ||||||||
\(704\) | 24.0391 | 0.906006 | ||||||||
\(705\) | −0.274480 | −0.0103375 | ||||||||
\(706\) | 68.3385 | 2.57195 | ||||||||
\(707\) | 16.6963 | 0.627928 | ||||||||
\(708\) | −95.9465 | −3.60589 | ||||||||
\(709\) | 23.9602 | 0.899844 | 0.449922 | − | 0.893068i | \(-0.351452\pi\) | ||||
0.449922 | + | 0.893068i | \(0.351452\pi\) | |||||||
\(710\) | 4.74079 | 0.177919 | ||||||||
\(711\) | −0.335830 | −0.0125946 | ||||||||
\(712\) | −4.94200 | −0.185209 | ||||||||
\(713\) | 24.6720 | 0.923975 | ||||||||
\(714\) | 12.1609 | 0.455111 | ||||||||
\(715\) | 5.32037 | 0.198970 | ||||||||
\(716\) | −52.6964 | −1.96936 | ||||||||
\(717\) | 6.79405 | 0.253728 | ||||||||
\(718\) | −35.6481 | −1.33037 | ||||||||
\(719\) | 31.4605 | 1.17328 | 0.586639 | − | 0.809848i | \(-0.300451\pi\) | ||||
0.586639 | + | 0.809848i | \(0.300451\pi\) | |||||||
\(720\) | −0.214416 | −0.00799080 | ||||||||
\(721\) | −14.1668 | −0.527598 | ||||||||
\(722\) | 41.8681 | 1.55817 | ||||||||
\(723\) | 6.37474 | 0.237079 | ||||||||
\(724\) | −43.4863 | −1.61616 | ||||||||
\(725\) | 29.4633 | 1.09424 | ||||||||
\(726\) | 15.6253 | 0.579909 | ||||||||
\(727\) | −1.16498 | −0.0432068 | −0.0216034 | − | 0.999767i | \(-0.506877\pi\) | ||||
−0.0216034 | + | 0.999767i | \(0.506877\pi\) | |||||||
\(728\) | 39.0088 | 1.44576 | ||||||||
\(729\) | 25.3375 | 0.938424 | ||||||||
\(730\) | 10.2411 | 0.379042 | ||||||||
\(731\) | −6.46603 | −0.239155 | ||||||||
\(732\) | 62.0384 | 2.29300 | ||||||||
\(733\) | −22.0307 | −0.813721 | −0.406860 | − | 0.913490i | \(-0.633376\pi\) | ||||
−0.406860 | + | 0.913490i | \(0.633376\pi\) | |||||||
\(734\) | −48.0803 | −1.77468 | ||||||||
\(735\) | 2.98384 | 0.110060 | ||||||||
\(736\) | 4.89731 | 0.180517 | ||||||||
\(737\) | −24.9258 | −0.918155 | ||||||||
\(738\) | 2.13267 | 0.0785046 | ||||||||
\(739\) | −31.9974 | −1.17704 | −0.588521 | − | 0.808482i | \(-0.700290\pi\) | ||||
−0.588521 | + | 0.808482i | \(0.700290\pi\) | |||||||
\(740\) | 2.40694 | 0.0884809 | ||||||||
\(741\) | −12.9489 | −0.475688 | ||||||||
\(742\) | 10.7735 | 0.395509 | ||||||||
\(743\) | −47.2497 | −1.73342 | −0.866711 | − | 0.498810i | \(-0.833771\pi\) | ||||
−0.866711 | + | 0.498810i | \(0.833771\pi\) | |||||||
\(744\) | −29.6043 | −1.08535 | ||||||||
\(745\) | −0.155810 | −0.00570844 | ||||||||
\(746\) | −64.3160 | −2.35478 | ||||||||
\(747\) | −1.16415 | −0.0425940 | ||||||||
\(748\) | −19.5316 | −0.714146 | ||||||||
\(749\) | 29.0923 | 1.06301 | ||||||||
\(750\) | −15.4320 | −0.563499 | ||||||||
\(751\) | 18.0746 | 0.659551 | 0.329775 | − | 0.944059i | \(-0.393027\pi\) | ||||
0.329775 | + | 0.944059i | \(0.393027\pi\) | |||||||
\(752\) | 1.52283 | 0.0555317 | ||||||||
\(753\) | −15.2174 | −0.554554 | ||||||||
\(754\) | 79.8500 | 2.90797 | ||||||||
\(755\) | 0.351736 | 0.0128010 | ||||||||
\(756\) | 30.3748 | 1.10472 | ||||||||
\(757\) | 42.5737 | 1.54737 | 0.773683 | − | 0.633573i | \(-0.218412\pi\) | ||||
0.773683 | + | 0.633573i | \(0.218412\pi\) | |||||||
\(758\) | 14.0307 | 0.509618 | ||||||||
\(759\) | −33.6508 | −1.22145 | ||||||||
\(760\) | −2.27177 | −0.0824058 | ||||||||
\(761\) | −3.79319 | −0.137503 | −0.0687515 | − | 0.997634i | \(-0.521902\pi\) | ||||
−0.0687515 | + | 0.997634i | \(0.521902\pi\) | |||||||
\(762\) | −7.64071 | −0.276794 | ||||||||
\(763\) | −4.42036 | −0.160028 | ||||||||
\(764\) | −101.732 | −3.68053 | ||||||||
\(765\) | −0.110085 | −0.00398014 | ||||||||
\(766\) | 20.5907 | 0.743973 | ||||||||
\(767\) | −74.4466 | −2.68811 | ||||||||
\(768\) | −55.6713 | −2.00886 | ||||||||
\(769\) | 25.9928 | 0.937324 | 0.468662 | − | 0.883378i | \(-0.344736\pi\) | ||||
0.468662 | + | 0.883378i | \(0.344736\pi\) | |||||||
\(770\) | 3.66573 | 0.132104 | ||||||||
\(771\) | 11.6802 | 0.420654 | ||||||||
\(772\) | −30.4756 | −1.09684 | ||||||||
\(773\) | −17.9650 | −0.646154 | −0.323077 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323077 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(774\) | 1.43438 | 0.0515578 | ||||||||
\(775\) | −17.2756 | −0.620557 | ||||||||
\(776\) | 0.00805766 | 0.000289253 0 | ||||||||
\(777\) | 4.63761 | 0.166373 | ||||||||
\(778\) | 80.3638 | 2.88118 | ||||||||
\(779\) | 7.05309 | 0.252703 | ||||||||
\(780\) | −13.6716 | −0.489521 | ||||||||
\(781\) | −14.6707 | −0.524959 | ||||||||
\(782\) | −30.9747 | −1.10765 | ||||||||
\(783\) | 30.5050 | 1.09016 | ||||||||
\(784\) | −16.5544 | −0.591229 | ||||||||
\(785\) | −0.861804 | −0.0307591 | ||||||||
\(786\) | 49.2819 | 1.75783 | ||||||||
\(787\) | 21.3822 | 0.762193 | 0.381096 | − | 0.924535i | \(-0.375547\pi\) | ||||
0.381096 | + | 0.924535i | \(0.375547\pi\) | |||||||
\(788\) | −28.3261 | −1.00908 | ||||||||
\(789\) | 52.9785 | 1.88609 | ||||||||
\(790\) | −1.76996 | −0.0629722 | ||||||||
\(791\) | 16.0076 | 0.569164 | ||||||||
\(792\) | 2.12573 | 0.0755346 | ||||||||
\(793\) | 48.1366 | 1.70938 | ||||||||
\(794\) | −32.7383 | −1.16184 | ||||||||
\(795\) | −1.85250 | −0.0657014 | ||||||||
\(796\) | −32.6161 | −1.15605 | ||||||||
\(797\) | −11.1237 | −0.394023 | −0.197012 | − | 0.980401i | \(-0.563124\pi\) | ||||
−0.197012 | + | 0.980401i | \(0.563124\pi\) | |||||||
\(798\) | −8.92175 | −0.315826 | ||||||||
\(799\) | 0.781850 | 0.0276599 | ||||||||
\(800\) | −3.42914 | −0.121239 | ||||||||
\(801\) | 0.175691 | 0.00620775 | ||||||||
\(802\) | 17.5949 | 0.621298 | ||||||||
\(803\) | −31.6919 | −1.11838 | ||||||||
\(804\) | 64.0511 | 2.25891 | ||||||||
\(805\) | 3.85151 | 0.135748 | ||||||||
\(806\) | −46.8195 | −1.64915 | ||||||||
\(807\) | −15.4739 | −0.544705 | ||||||||
\(808\) | 51.0282 | 1.79517 | ||||||||
\(809\) | −14.7939 | −0.520127 | −0.260063 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260063 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(810\) | −8.32284 | −0.292435 | ||||||||
\(811\) | 17.8191 | 0.625713 | 0.312857 | − | 0.949800i | \(-0.398714\pi\) | ||||
0.312857 | + | 0.949800i | \(0.398714\pi\) | |||||||
\(812\) | 36.4498 | 1.27914 | ||||||||
\(813\) | −5.32148 | −0.186632 | ||||||||
\(814\) | −11.2425 | −0.394051 | ||||||||
\(815\) | 0.639198 | 0.0223901 | ||||||||
\(816\) | 11.6013 | 0.406126 | ||||||||
\(817\) | 4.74374 | 0.165962 | ||||||||
\(818\) | −41.6364 | −1.45578 | ||||||||
\(819\) | −1.38679 | −0.0484583 | ||||||||
\(820\) | 7.44675 | 0.260052 | ||||||||
\(821\) | 3.65192 | 0.127453 | 0.0637265 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637265 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(822\) | 30.8339 | 1.07546 | ||||||||
\(823\) | −41.6032 | −1.45020 | −0.725098 | − | 0.688646i | \(-0.758206\pi\) | ||||
−0.725098 | + | 0.688646i | \(0.758206\pi\) | |||||||
\(824\) | −43.2973 | −1.50833 | ||||||||
\(825\) | 23.5626 | 0.820345 | ||||||||
\(826\) | −51.2936 | −1.78473 | ||||||||
\(827\) | 6.24366 | 0.217113 | 0.108557 | − | 0.994090i | \(-0.465377\pi\) | ||||
0.108557 | + | 0.994090i | \(0.465377\pi\) | |||||||
\(828\) | 4.55234 | 0.158205 | ||||||||
\(829\) | 28.0990 | 0.975920 | 0.487960 | − | 0.872866i | \(-0.337741\pi\) | ||||
0.487960 | + | 0.872866i | \(0.337741\pi\) | |||||||
\(830\) | −6.13553 | −0.212967 | ||||||||
\(831\) | −16.7345 | −0.580512 | ||||||||
\(832\) | −47.9303 | −1.66168 | ||||||||
\(833\) | −8.49937 | −0.294486 | ||||||||
\(834\) | −1.21190 | −0.0419647 | ||||||||
\(835\) | −5.92819 | −0.205154 | ||||||||
\(836\) | 14.3292 | 0.495585 | ||||||||
\(837\) | −17.8864 | −0.618244 | ||||||||
\(838\) | −38.5700 | −1.33238 | ||||||||
\(839\) | 33.8225 | 1.16768 | 0.583842 | − | 0.811868i | \(-0.301549\pi\) | ||||
0.583842 | + | 0.811868i | \(0.301549\pi\) | |||||||
\(840\) | −4.62148 | −0.159456 | ||||||||
\(841\) | 7.60594 | 0.262274 | ||||||||
\(842\) | 31.4899 | 1.08521 | ||||||||
\(843\) | 41.6606 | 1.43487 | ||||||||
\(844\) | 9.49586 | 0.326861 | ||||||||
\(845\) | −5.91595 | −0.203515 | ||||||||
\(846\) | −0.173440 | −0.00596300 | ||||||||
\(847\) | 5.53431 | 0.190161 | ||||||||
\(848\) | 10.2777 | 0.352939 | ||||||||
\(849\) | −46.2955 | −1.58886 | ||||||||
\(850\) | 21.6888 | 0.743919 | ||||||||
\(851\) | −11.8123 | −0.404921 | ||||||||
\(852\) | 37.6988 | 1.29154 | ||||||||
\(853\) | 22.7291 | 0.778229 | 0.389114 | − | 0.921189i | \(-0.372781\pi\) | ||||
0.389114 | + | 0.921189i | \(0.372781\pi\) | |||||||
\(854\) | 33.1661 | 1.13492 | ||||||||
\(855\) | 0.0807630 | 0.00276204 | ||||||||
\(856\) | 88.9137 | 3.03901 | ||||||||
\(857\) | 33.6001 | 1.14776 | 0.573878 | − | 0.818941i | \(-0.305438\pi\) | ||||
0.573878 | + | 0.818941i | \(0.305438\pi\) | |||||||
\(858\) | 63.8584 | 2.18009 | ||||||||
\(859\) | 5.67293 | 0.193558 | 0.0967790 | − | 0.995306i | \(-0.469146\pi\) | ||||
0.0967790 | + | 0.995306i | \(0.469146\pi\) | |||||||
\(860\) | 5.00850 | 0.170789 | ||||||||
\(861\) | 14.3482 | 0.488984 | ||||||||
\(862\) | −17.4355 | −0.593855 | ||||||||
\(863\) | 25.2822 | 0.860616 | 0.430308 | − | 0.902682i | \(-0.358405\pi\) | ||||
0.430308 | + | 0.902682i | \(0.358405\pi\) | |||||||
\(864\) | −3.55039 | −0.120787 | ||||||||
\(865\) | 6.25522 | 0.212684 | ||||||||
\(866\) | 46.1002 | 1.56655 | ||||||||
\(867\) | −24.2956 | −0.825122 | ||||||||
\(868\) | −21.3721 | −0.725415 | ||||||||
\(869\) | 5.47725 | 0.185803 | ||||||||
\(870\) | −9.46006 | −0.320726 | ||||||||
\(871\) | 49.6984 | 1.68396 | ||||||||
\(872\) | −13.5098 | −0.457499 | ||||||||
\(873\) | −0.000286456 0 | −9.69505e−6 0 | ||||||||
\(874\) | 22.7243 | 0.768661 | ||||||||
\(875\) | −5.46586 | −0.184780 | ||||||||
\(876\) | 81.4378 | 2.75153 | ||||||||
\(877\) | −38.7794 | −1.30949 | −0.654744 | − | 0.755851i | \(-0.727224\pi\) | ||||
−0.654744 | + | 0.755851i | \(0.727224\pi\) | |||||||
\(878\) | −87.5447 | −2.95449 | ||||||||
\(879\) | 0.0283010 | 0.000954568 0 | ||||||||
\(880\) | 3.49703 | 0.117885 | ||||||||
\(881\) | −25.7886 | −0.868838 | −0.434419 | − | 0.900711i | \(-0.643046\pi\) | ||||
−0.434419 | + | 0.900711i | \(0.643046\pi\) | |||||||
\(882\) | 1.88544 | 0.0634862 | ||||||||
\(883\) | −24.1823 | −0.813799 | −0.406899 | − | 0.913473i | \(-0.633390\pi\) | ||||
−0.406899 | + | 0.913473i | \(0.633390\pi\) | |||||||
\(884\) | 38.9431 | 1.30980 | ||||||||
\(885\) | 8.81990 | 0.296478 | ||||||||
\(886\) | 15.6477 | 0.525693 | ||||||||
\(887\) | −7.03011 | −0.236048 | −0.118024 | − | 0.993011i | \(-0.537656\pi\) | ||||
−0.118024 | + | 0.993011i | \(0.537656\pi\) | |||||||
\(888\) | 14.1738 | 0.475640 | ||||||||
\(889\) | −2.70626 | −0.0907649 | ||||||||
\(890\) | 0.925962 | 0.0310383 | ||||||||
\(891\) | 25.7556 | 0.862845 | ||||||||
\(892\) | 5.79752 | 0.194115 | ||||||||
\(893\) | −0.573596 | −0.0191947 | ||||||||
\(894\) | −1.87013 | −0.0625465 | ||||||||
\(895\) | 4.84412 | 0.161921 | ||||||||
\(896\) | −30.8630 | −1.03106 | ||||||||
\(897\) | 67.0947 | 2.24023 | ||||||||
\(898\) | 33.6577 | 1.12317 | ||||||||
\(899\) | −21.4636 | −0.715852 | ||||||||
\(900\) | −3.18759 | −0.106253 | ||||||||
\(901\) | 5.27680 | 0.175796 | ||||||||
\(902\) | −34.7829 | −1.15815 | ||||||||
\(903\) | 9.65022 | 0.321139 | ||||||||
\(904\) | 48.9233 | 1.62717 | ||||||||
\(905\) | 3.99749 | 0.132881 | ||||||||
\(906\) | 4.22176 | 0.140258 | ||||||||
\(907\) | 5.32177 | 0.176707 | 0.0883533 | − | 0.996089i | \(-0.471840\pi\) | ||||
0.0883533 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(908\) | −24.7071 | −0.819935 | ||||||||
\(909\) | −1.81409 | −0.0601695 | ||||||||
\(910\) | −7.30891 | −0.242288 | ||||||||
\(911\) | 40.6208 | 1.34583 | 0.672913 | − | 0.739722i | \(-0.265043\pi\) | ||||
0.672913 | + | 0.739722i | \(0.265043\pi\) | |||||||
\(912\) | −8.51116 | −0.281833 | ||||||||
\(913\) | 18.9868 | 0.628372 | ||||||||
\(914\) | −71.7537 | −2.37340 | ||||||||
\(915\) | −5.70289 | −0.188532 | ||||||||
\(916\) | 40.7540 | 1.34655 | ||||||||
\(917\) | 17.4551 | 0.576419 | ||||||||
\(918\) | 22.4556 | 0.741146 | ||||||||
\(919\) | 39.1305 | 1.29080 | 0.645398 | − | 0.763847i | \(-0.276692\pi\) | ||||
0.645398 | + | 0.763847i | \(0.276692\pi\) | |||||||
\(920\) | 11.7712 | 0.388086 | ||||||||
\(921\) | 6.93793 | 0.228613 | ||||||||
\(922\) | 60.3932 | 1.98894 | ||||||||
\(923\) | 29.2512 | 0.962814 | ||||||||
\(924\) | 29.1499 | 0.958962 | ||||||||
\(925\) | 8.27109 | 0.271952 | ||||||||
\(926\) | −14.1077 | −0.463607 | ||||||||
\(927\) | 1.53925 | 0.0505556 | ||||||||
\(928\) | −4.26046 | −0.139856 | ||||||||
\(929\) | 41.7517 | 1.36983 | 0.684914 | − | 0.728623i | \(-0.259840\pi\) | ||||
0.684914 | + | 0.728623i | \(0.259840\pi\) | |||||||
\(930\) | 5.54684 | 0.181888 | ||||||||
\(931\) | 6.23548 | 0.204360 | ||||||||
\(932\) | 27.3619 | 0.896268 | ||||||||
\(933\) | −11.2164 | −0.367209 | ||||||||
\(934\) | 10.8461 | 0.354896 | ||||||||
\(935\) | 1.79545 | 0.0587174 | ||||||||
\(936\) | −4.23839 | −0.138536 | ||||||||
\(937\) | −14.1376 | −0.461854 | −0.230927 | − | 0.972971i | \(-0.574176\pi\) | ||||
−0.230927 | + | 0.972971i | \(0.574176\pi\) | |||||||
\(938\) | 34.2421 | 1.11805 | ||||||||
\(939\) | −17.3707 | −0.566872 | ||||||||
\(940\) | −0.605611 | −0.0197528 | ||||||||
\(941\) | 47.9322 | 1.56254 | 0.781272 | − | 0.624191i | \(-0.214571\pi\) | ||||
0.781272 | + | 0.624191i | \(0.214571\pi\) | |||||||
\(942\) | −10.3439 | −0.337023 | ||||||||
\(943\) | −36.5457 | −1.19009 | ||||||||
\(944\) | −48.9330 | −1.59263 | ||||||||
\(945\) | −2.79221 | −0.0908306 | ||||||||
\(946\) | −23.3942 | −0.760610 | ||||||||
\(947\) | −10.5619 | −0.343215 | −0.171607 | − | 0.985165i | \(-0.554896\pi\) | ||||
−0.171607 | + | 0.985165i | \(0.554896\pi\) | |||||||
\(948\) | −14.0747 | −0.457125 | ||||||||
\(949\) | 63.1890 | 2.05120 | ||||||||
\(950\) | −15.9118 | −0.516245 | ||||||||
\(951\) | −16.4300 | −0.532780 | ||||||||
\(952\) | 13.1641 | 0.426653 | ||||||||
\(953\) | 37.2634 | 1.20708 | 0.603540 | − | 0.797333i | \(-0.293756\pi\) | ||||
0.603540 | + | 0.797333i | \(0.293756\pi\) | |||||||
\(954\) | −1.17057 | −0.0378986 | ||||||||
\(955\) | 9.35173 | 0.302615 | ||||||||
\(956\) | 14.9903 | 0.484821 | ||||||||
\(957\) | 29.2748 | 0.946320 | ||||||||
\(958\) | −66.9469 | −2.16296 | ||||||||
\(959\) | 10.9210 | 0.352659 | ||||||||
\(960\) | 5.67844 | 0.183271 | ||||||||
\(961\) | −18.4149 | −0.594030 | ||||||||
\(962\) | 22.4159 | 0.722719 | ||||||||
\(963\) | −3.16094 | −0.101860 | ||||||||
\(964\) | 14.0652 | 0.453008 | ||||||||
\(965\) | 2.80148 | 0.0901828 | ||||||||
\(966\) | 46.2282 | 1.48737 | ||||||||
\(967\) | −24.1777 | −0.777501 | −0.388751 | − | 0.921343i | \(-0.627093\pi\) | ||||
−0.388751 | + | 0.921343i | \(0.627093\pi\) | |||||||
\(968\) | 16.9143 | 0.543646 | ||||||||
\(969\) | −4.36980 | −0.140378 | ||||||||
\(970\) | −0.00150973 | −4.84746e−5 0 | ||||||||
\(971\) | 56.3468 | 1.80825 | 0.904127 | − | 0.427264i | \(-0.140522\pi\) | ||||
0.904127 | + | 0.427264i | \(0.140522\pi\) | |||||||
\(972\) | −6.79478 | −0.217943 | ||||||||
\(973\) | −0.429242 | −0.0137609 | ||||||||
\(974\) | 107.004 | 3.42864 | ||||||||
\(975\) | −46.9803 | −1.50457 | ||||||||
\(976\) | 31.6398 | 1.01276 | ||||||||
\(977\) | −49.4353 | −1.58157 | −0.790787 | − | 0.612091i | \(-0.790329\pi\) | ||||
−0.790787 | + | 0.612091i | \(0.790329\pi\) | |||||||
\(978\) | 7.67206 | 0.245325 | ||||||||
\(979\) | −2.86545 | −0.0915803 | ||||||||
\(980\) | 6.58351 | 0.210302 | ||||||||
\(981\) | 0.480282 | 0.0153342 | ||||||||
\(982\) | −45.3147 | −1.44605 | ||||||||
\(983\) | −21.5557 | −0.687519 | −0.343760 | − | 0.939058i | \(-0.611701\pi\) | ||||
−0.343760 | + | 0.939058i | \(0.611701\pi\) | |||||||
\(984\) | 43.8517 | 1.39794 | ||||||||
\(985\) | 2.60388 | 0.0829666 | ||||||||
\(986\) | 26.9467 | 0.858158 | ||||||||
\(987\) | −1.16687 | −0.0371419 | ||||||||
\(988\) | −28.5702 | −0.908939 | ||||||||
\(989\) | −24.5798 | −0.781591 | ||||||||
\(990\) | −0.398290 | −0.0126585 | ||||||||
\(991\) | −10.9082 | −0.346509 | −0.173255 | − | 0.984877i | \(-0.555428\pi\) | ||||
−0.173255 | + | 0.984877i | \(0.555428\pi\) | |||||||
\(992\) | 2.49809 | 0.0793145 | ||||||||
\(993\) | −17.5580 | −0.557185 | ||||||||
\(994\) | 20.1540 | 0.639247 | ||||||||
\(995\) | 2.99824 | 0.0950507 | ||||||||
\(996\) | −48.7898 | −1.54596 | ||||||||
\(997\) | 55.3657 | 1.75345 | 0.876725 | − | 0.480993i | \(-0.159724\pi\) | ||||
0.876725 | + | 0.480993i | \(0.159724\pi\) | |||||||
\(998\) | −36.4534 | −1.15391 | ||||||||
\(999\) | 8.56352 | 0.270938 |
(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 | 4003.2.a.b.1.15 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.15 | ✓ | 152 | 1.1 | even | 1 | trivial |