Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, 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("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1418073786\) |
Analytic rank: | \(0\) |
Dimension: | \(268\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76187 | −1.95294 | −0.976468 | − | 0.215661i | \(-0.930809\pi\) | ||||
−0.976468 | + | 0.215661i | \(0.930809\pi\) | |||||||
\(3\) | −2.45998 | −1.42027 | −0.710136 | − | 0.704065i | \(-0.751366\pi\) | ||||
−0.710136 | + | 0.704065i | \(0.751366\pi\) | |||||||
\(4\) | 5.62792 | 2.81396 | ||||||||
\(5\) | 2.94480 | 1.31695 | 0.658477 | − | 0.752601i | \(-0.271201\pi\) | ||||
0.658477 | + | 0.752601i | \(0.271201\pi\) | |||||||
\(6\) | 6.79415 | 2.77370 | ||||||||
\(7\) | 1.83308 | 0.692841 | 0.346420 | − | 0.938079i | \(-0.387397\pi\) | ||||
0.346420 | + | 0.938079i | \(0.387397\pi\) | |||||||
\(8\) | −10.0198 | −3.54255 | ||||||||
\(9\) | 3.05151 | 1.01717 | ||||||||
\(10\) | −8.13315 | −2.57193 | ||||||||
\(11\) | −1.81301 | −0.546642 | −0.273321 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273321 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(12\) | −13.8446 | −3.99659 | ||||||||
\(13\) | 1.02382 | 0.283958 | 0.141979 | − | 0.989870i | \(-0.454653\pi\) | ||||
0.141979 | + | 0.989870i | \(0.454653\pi\) | |||||||
\(14\) | −5.06274 | −1.35307 | ||||||||
\(15\) | −7.24415 | −1.87043 | ||||||||
\(16\) | 16.4177 | 4.10442 | ||||||||
\(17\) | 0.386297 | 0.0936907 | 0.0468453 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468453 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(18\) | −8.42787 | −1.98647 | ||||||||
\(19\) | 7.64280 | 1.75338 | 0.876689 | − | 0.481057i | \(-0.159747\pi\) | ||||
0.876689 | + | 0.481057i | \(0.159747\pi\) | |||||||
\(20\) | 16.5731 | 3.70586 | ||||||||
\(21\) | −4.50936 | −0.984022 | ||||||||
\(22\) | 5.00729 | 1.06756 | ||||||||
\(23\) | −8.13701 | −1.69668 | −0.848342 | − | 0.529449i | \(-0.822399\pi\) | ||||
−0.848342 | + | 0.529449i | \(0.822399\pi\) | |||||||
\(24\) | 24.6486 | 5.03138 | ||||||||
\(25\) | 3.67184 | 0.734369 | ||||||||
\(26\) | −2.82767 | −0.554552 | ||||||||
\(27\) | −0.126714 | −0.0243860 | ||||||||
\(28\) | 10.3165 | 1.94963 | ||||||||
\(29\) | −2.16417 | −0.401877 | −0.200938 | − | 0.979604i | \(-0.564399\pi\) | ||||
−0.200938 | + | 0.979604i | \(0.564399\pi\) | |||||||
\(30\) | 20.0074 | 3.65284 | ||||||||
\(31\) | 6.43282 | 1.15537 | 0.577684 | − | 0.816260i | \(-0.303957\pi\) | ||||
0.577684 | + | 0.816260i | \(0.303957\pi\) | |||||||
\(32\) | −25.3037 | −4.47311 | ||||||||
\(33\) | 4.45996 | 0.776380 | ||||||||
\(34\) | −1.06690 | −0.182972 | ||||||||
\(35\) | 5.39807 | 0.912440 | ||||||||
\(36\) | 17.1737 | 2.86228 | ||||||||
\(37\) | −0.190632 | −0.0313396 | −0.0156698 | − | 0.999877i | \(-0.504988\pi\) | ||||
−0.0156698 | + | 0.999877i | \(0.504988\pi\) | |||||||
\(38\) | −21.1084 | −3.42424 | ||||||||
\(39\) | −2.51859 | −0.403297 | ||||||||
\(40\) | −29.5064 | −4.66538 | ||||||||
\(41\) | −3.89847 | −0.608839 | −0.304419 | − | 0.952538i | \(-0.598462\pi\) | ||||
−0.304419 | + | 0.952538i | \(0.598462\pi\) | |||||||
\(42\) | 12.4542 | 1.92173 | ||||||||
\(43\) | −2.13094 | −0.324965 | −0.162483 | − | 0.986711i | \(-0.551950\pi\) | ||||
−0.162483 | + | 0.986711i | \(0.551950\pi\) | |||||||
\(44\) | −10.2035 | −1.53823 | ||||||||
\(45\) | 8.98608 | 1.33957 | ||||||||
\(46\) | 22.4734 | 3.31352 | ||||||||
\(47\) | −4.51809 | −0.659031 | −0.329516 | − | 0.944150i | \(-0.606885\pi\) | ||||
−0.329516 | + | 0.944150i | \(0.606885\pi\) | |||||||
\(48\) | −40.3872 | −5.82938 | ||||||||
\(49\) | −3.63980 | −0.519971 | ||||||||
\(50\) | −10.1412 | −1.43418 | ||||||||
\(51\) | −0.950283 | −0.133066 | ||||||||
\(52\) | 5.76201 | 0.799047 | ||||||||
\(53\) | −6.91539 | −0.949902 | −0.474951 | − | 0.880012i | \(-0.657534\pi\) | ||||
−0.474951 | + | 0.880012i | \(0.657534\pi\) | |||||||
\(54\) | 0.349966 | 0.0476244 | ||||||||
\(55\) | −5.33894 | −0.719903 | ||||||||
\(56\) | −18.3672 | −2.45442 | ||||||||
\(57\) | −18.8011 | −2.49027 | ||||||||
\(58\) | 5.97716 | 0.784839 | ||||||||
\(59\) | 4.87745 | 0.634990 | 0.317495 | − | 0.948260i | \(-0.397158\pi\) | ||||
0.317495 | + | 0.948260i | \(0.397158\pi\) | |||||||
\(60\) | −40.7695 | −5.26332 | ||||||||
\(61\) | 2.72175 | 0.348484 | 0.174242 | − | 0.984703i | \(-0.444252\pi\) | ||||
0.174242 | + | 0.984703i | \(0.444252\pi\) | |||||||
\(62\) | −17.7666 | −2.25636 | ||||||||
\(63\) | 5.59368 | 0.704737 | ||||||||
\(64\) | 37.0503 | 4.63129 | ||||||||
\(65\) | 3.01496 | 0.373960 | ||||||||
\(66\) | −12.3178 | −1.51622 | ||||||||
\(67\) | 1.23528 | 0.150914 | 0.0754569 | − | 0.997149i | \(-0.475958\pi\) | ||||
0.0754569 | + | 0.997149i | \(0.475958\pi\) | |||||||
\(68\) | 2.17405 | 0.263642 | ||||||||
\(69\) | 20.0169 | 2.40975 | ||||||||
\(70\) | −14.9088 | −1.78194 | ||||||||
\(71\) | 3.41889 | 0.405748 | 0.202874 | − | 0.979205i | \(-0.434972\pi\) | ||||
0.202874 | + | 0.979205i | \(0.434972\pi\) | |||||||
\(72\) | −30.5757 | −3.60338 | ||||||||
\(73\) | −8.92070 | −1.04409 | −0.522044 | − | 0.852918i | \(-0.674830\pi\) | ||||
−0.522044 | + | 0.852918i | \(0.674830\pi\) | |||||||
\(74\) | 0.526500 | 0.0612043 | ||||||||
\(75\) | −9.03267 | −1.04300 | ||||||||
\(76\) | 43.0131 | 4.93394 | ||||||||
\(77\) | −3.32339 | −0.378736 | ||||||||
\(78\) | 6.95602 | 0.787614 | ||||||||
\(79\) | 8.79434 | 0.989441 | 0.494720 | − | 0.869052i | \(-0.335270\pi\) | ||||
0.494720 | + | 0.869052i | \(0.335270\pi\) | |||||||
\(80\) | 48.3467 | 5.40533 | ||||||||
\(81\) | −8.84282 | −0.982535 | ||||||||
\(82\) | 10.7671 | 1.18902 | ||||||||
\(83\) | 3.31980 | 0.364396 | 0.182198 | − | 0.983262i | \(-0.441679\pi\) | ||||
0.182198 | + | 0.983262i | \(0.441679\pi\) | |||||||
\(84\) | −25.3783 | −2.76900 | ||||||||
\(85\) | 1.13757 | 0.123386 | ||||||||
\(86\) | 5.88537 | 0.634636 | ||||||||
\(87\) | 5.32382 | 0.570774 | ||||||||
\(88\) | 18.1660 | 1.93651 | ||||||||
\(89\) | 9.66287 | 1.02426 | 0.512131 | − | 0.858907i | \(-0.328856\pi\) | ||||
0.512131 | + | 0.858907i | \(0.328856\pi\) | |||||||
\(90\) | −24.8184 | −2.61609 | ||||||||
\(91\) | 1.87676 | 0.196738 | ||||||||
\(92\) | −45.7945 | −4.77440 | ||||||||
\(93\) | −15.8246 | −1.64094 | ||||||||
\(94\) | 12.4784 | 1.28705 | ||||||||
\(95\) | 22.5065 | 2.30912 | ||||||||
\(96\) | 62.2468 | 6.35303 | ||||||||
\(97\) | 6.75489 | 0.685855 | 0.342927 | − | 0.939362i | \(-0.388581\pi\) | ||||
0.342927 | + | 0.939362i | \(0.388581\pi\) | |||||||
\(98\) | 10.0527 | 1.01547 | ||||||||
\(99\) | −5.53241 | −0.556028 | ||||||||
\(100\) | 20.6649 | 2.06649 | ||||||||
\(101\) | 17.7832 | 1.76950 | 0.884749 | − | 0.466068i | \(-0.154330\pi\) | ||||
0.884749 | + | 0.466068i | \(0.154330\pi\) | |||||||
\(102\) | 2.62456 | 0.259870 | ||||||||
\(103\) | 13.4400 | 1.32429 | 0.662143 | − | 0.749377i | \(-0.269647\pi\) | ||||
0.662143 | + | 0.749377i | \(0.269647\pi\) | |||||||
\(104\) | −10.2586 | −1.00594 | ||||||||
\(105\) | −13.2791 | −1.29591 | ||||||||
\(106\) | 19.0994 | 1.85510 | ||||||||
\(107\) | 12.8963 | 1.24673 | 0.623366 | − | 0.781930i | \(-0.285765\pi\) | ||||
0.623366 | + | 0.781930i | \(0.285765\pi\) | |||||||
\(108\) | −0.713134 | −0.0686213 | ||||||||
\(109\) | −18.6677 | −1.78805 | −0.894023 | − | 0.448022i | \(-0.852129\pi\) | ||||
−0.894023 | + | 0.448022i | \(0.852129\pi\) | |||||||
\(110\) | 14.7455 | 1.40592 | ||||||||
\(111\) | 0.468950 | 0.0445108 | ||||||||
\(112\) | 30.0950 | 2.84371 | ||||||||
\(113\) | 14.7744 | 1.38986 | 0.694930 | − | 0.719077i | \(-0.255435\pi\) | ||||
0.694930 | + | 0.719077i | \(0.255435\pi\) | |||||||
\(114\) | 51.9263 | 4.86335 | ||||||||
\(115\) | −23.9619 | −2.23445 | ||||||||
\(116\) | −12.1798 | −1.13086 | ||||||||
\(117\) | 3.12421 | 0.288833 | ||||||||
\(118\) | −13.4709 | −1.24009 | ||||||||
\(119\) | 0.708114 | 0.0649127 | ||||||||
\(120\) | 72.5853 | 6.62610 | ||||||||
\(121\) | −7.71301 | −0.701182 | ||||||||
\(122\) | −7.51711 | −0.680567 | ||||||||
\(123\) | 9.59017 | 0.864716 | ||||||||
\(124\) | 36.2034 | 3.25116 | ||||||||
\(125\) | −3.91115 | −0.349824 | ||||||||
\(126\) | −15.4490 | −1.37631 | ||||||||
\(127\) | 11.5885 | 1.02831 | 0.514156 | − | 0.857697i | \(-0.328105\pi\) | ||||
0.514156 | + | 0.857697i | \(0.328105\pi\) | |||||||
\(128\) | −51.7206 | −4.57150 | ||||||||
\(129\) | 5.24207 | 0.461538 | ||||||||
\(130\) | −8.32692 | −0.730319 | ||||||||
\(131\) | −19.3883 | −1.69396 | −0.846981 | − | 0.531623i | \(-0.821582\pi\) | ||||
−0.846981 | + | 0.531623i | \(0.821582\pi\) | |||||||
\(132\) | 25.1003 | 2.18470 | ||||||||
\(133\) | 14.0099 | 1.21481 | ||||||||
\(134\) | −3.41169 | −0.294725 | ||||||||
\(135\) | −0.373146 | −0.0321153 | ||||||||
\(136\) | −3.87063 | −0.331904 | ||||||||
\(137\) | 8.52540 | 0.728374 | 0.364187 | − | 0.931326i | \(-0.381347\pi\) | ||||
0.364187 | + | 0.931326i | \(0.381347\pi\) | |||||||
\(138\) | −55.2840 | −4.70609 | ||||||||
\(139\) | −15.7870 | −1.33903 | −0.669517 | − | 0.742797i | \(-0.733499\pi\) | ||||
−0.669517 | + | 0.742797i | \(0.733499\pi\) | |||||||
\(140\) | 30.3799 | 2.56757 | ||||||||
\(141\) | 11.1144 | 0.936003 | ||||||||
\(142\) | −9.44253 | −0.792399 | ||||||||
\(143\) | −1.85620 | −0.155223 | ||||||||
\(144\) | 50.0987 | 4.17489 | ||||||||
\(145\) | −6.37305 | −0.529253 | ||||||||
\(146\) | 24.6378 | 2.03904 | ||||||||
\(147\) | 8.95384 | 0.738500 | ||||||||
\(148\) | −1.07286 | −0.0881885 | ||||||||
\(149\) | 13.6573 | 1.11885 | 0.559424 | − | 0.828882i | \(-0.311022\pi\) | ||||
0.559424 | + | 0.828882i | \(0.311022\pi\) | |||||||
\(150\) | 24.9470 | 2.03692 | ||||||||
\(151\) | 11.9194 | 0.969990 | 0.484995 | − | 0.874517i | \(-0.338821\pi\) | ||||
0.484995 | + | 0.874517i | \(0.338821\pi\) | |||||||
\(152\) | −76.5797 | −6.21143 | ||||||||
\(153\) | 1.17879 | 0.0952994 | ||||||||
\(154\) | 9.17878 | 0.739647 | ||||||||
\(155\) | 18.9434 | 1.52157 | ||||||||
\(156\) | −14.1744 | −1.13486 | ||||||||
\(157\) | 13.3557 | 1.06590 | 0.532952 | − | 0.846145i | \(-0.321083\pi\) | ||||
0.532952 | + | 0.846145i | \(0.321083\pi\) | |||||||
\(158\) | −24.2888 | −1.93231 | ||||||||
\(159\) | 17.0117 | 1.34912 | ||||||||
\(160\) | −74.5145 | −5.89089 | ||||||||
\(161\) | −14.9158 | −1.17553 | ||||||||
\(162\) | 24.4227 | 1.91883 | ||||||||
\(163\) | −12.6872 | −0.993735 | −0.496867 | − | 0.867827i | \(-0.665516\pi\) | ||||
−0.496867 | + | 0.867827i | \(0.665516\pi\) | |||||||
\(164\) | −21.9403 | −1.71325 | ||||||||
\(165\) | 13.1337 | 1.02246 | ||||||||
\(166\) | −9.16886 | −0.711642 | ||||||||
\(167\) | −6.11737 | −0.473376 | −0.236688 | − | 0.971586i | \(-0.576062\pi\) | ||||
−0.236688 | + | 0.971586i | \(0.576062\pi\) | |||||||
\(168\) | 45.1830 | 3.48595 | ||||||||
\(169\) | −11.9518 | −0.919368 | ||||||||
\(170\) | −3.14181 | −0.240966 | ||||||||
\(171\) | 23.3221 | 1.78348 | ||||||||
\(172\) | −11.9928 | −0.914439 | ||||||||
\(173\) | 13.3940 | 1.01833 | 0.509164 | − | 0.860670i | \(-0.329955\pi\) | ||||
0.509164 | + | 0.860670i | \(0.329955\pi\) | |||||||
\(174\) | −14.7037 | −1.11468 | ||||||||
\(175\) | 6.73080 | 0.508801 | ||||||||
\(176\) | −29.7653 | −2.24365 | ||||||||
\(177\) | −11.9984 | −0.901858 | ||||||||
\(178\) | −26.6876 | −2.00032 | ||||||||
\(179\) | −14.8146 | −1.10730 | −0.553648 | − | 0.832751i | \(-0.686765\pi\) | ||||
−0.553648 | + | 0.832751i | \(0.686765\pi\) | |||||||
\(180\) | 50.5730 | 3.76949 | ||||||||
\(181\) | 20.4160 | 1.51751 | 0.758754 | − | 0.651377i | \(-0.225808\pi\) | ||||
0.758754 | + | 0.651377i | \(0.225808\pi\) | |||||||
\(182\) | −5.18336 | −0.384216 | ||||||||
\(183\) | −6.69545 | −0.494942 | ||||||||
\(184\) | 81.5316 | 6.01059 | ||||||||
\(185\) | −0.561372 | −0.0412729 | ||||||||
\(186\) | 43.7055 | 3.20464 | ||||||||
\(187\) | −0.700358 | −0.0512153 | ||||||||
\(188\) | −25.4275 | −1.85449 | ||||||||
\(189\) | −0.232277 | −0.0168956 | ||||||||
\(190\) | −62.1600 | −4.50956 | ||||||||
\(191\) | 24.6524 | 1.78379 | 0.891894 | − | 0.452245i | \(-0.149377\pi\) | ||||
0.891894 | + | 0.452245i | \(0.149377\pi\) | |||||||
\(192\) | −91.1431 | −6.57769 | ||||||||
\(193\) | −4.74669 | −0.341674 | −0.170837 | − | 0.985299i | \(-0.554647\pi\) | ||||
−0.170837 | + | 0.985299i | \(0.554647\pi\) | |||||||
\(194\) | −18.6561 | −1.33943 | ||||||||
\(195\) | −7.41674 | −0.531124 | ||||||||
\(196\) | −20.4845 | −1.46318 | ||||||||
\(197\) | 11.1113 | 0.791650 | 0.395825 | − | 0.918326i | \(-0.370459\pi\) | ||||
0.395825 | + | 0.918326i | \(0.370459\pi\) | |||||||
\(198\) | 15.2798 | 1.08589 | ||||||||
\(199\) | 11.8476 | 0.839852 | 0.419926 | − | 0.907558i | \(-0.362056\pi\) | ||||
0.419926 | + | 0.907558i | \(0.362056\pi\) | |||||||
\(200\) | −36.7913 | −2.60154 | ||||||||
\(201\) | −3.03877 | −0.214338 | ||||||||
\(202\) | −49.1150 | −3.45572 | ||||||||
\(203\) | −3.96711 | −0.278437 | ||||||||
\(204\) | −5.34812 | −0.374443 | ||||||||
\(205\) | −11.4802 | −0.801813 | ||||||||
\(206\) | −37.1196 | −2.58625 | ||||||||
\(207\) | −24.8302 | −1.72582 | ||||||||
\(208\) | 16.8088 | 1.16548 | ||||||||
\(209\) | −13.8564 | −0.958471 | ||||||||
\(210\) | 36.6753 | 2.53083 | ||||||||
\(211\) | 7.34636 | 0.505744 | 0.252872 | − | 0.967500i | \(-0.418625\pi\) | ||||
0.252872 | + | 0.967500i | \(0.418625\pi\) | |||||||
\(212\) | −38.9193 | −2.67299 | ||||||||
\(213\) | −8.41041 | −0.576272 | ||||||||
\(214\) | −35.6179 | −2.43479 | ||||||||
\(215\) | −6.27519 | −0.427964 | ||||||||
\(216\) | 1.26965 | 0.0863887 | ||||||||
\(217\) | 11.7919 | 0.800486 | ||||||||
\(218\) | 51.5579 | 3.49194 | ||||||||
\(219\) | 21.9448 | 1.48289 | ||||||||
\(220\) | −30.0471 | −2.02578 | ||||||||
\(221\) | 0.395500 | 0.0266042 | ||||||||
\(222\) | −1.29518 | −0.0869267 | ||||||||
\(223\) | −1.75697 | −0.117656 | −0.0588278 | − | 0.998268i | \(-0.518736\pi\) | ||||
−0.0588278 | + | 0.998268i | \(0.518736\pi\) | |||||||
\(224\) | −46.3839 | −3.09916 | ||||||||
\(225\) | 11.2047 | 0.746978 | ||||||||
\(226\) | −40.8050 | −2.71431 | ||||||||
\(227\) | −3.50337 | −0.232527 | −0.116263 | − | 0.993218i | \(-0.537092\pi\) | ||||
−0.116263 | + | 0.993218i | \(0.537092\pi\) | |||||||
\(228\) | −105.811 | −7.00753 | ||||||||
\(229\) | −5.41895 | −0.358095 | −0.179047 | − | 0.983840i | \(-0.557302\pi\) | ||||
−0.179047 | + | 0.983840i | \(0.557302\pi\) | |||||||
\(230\) | 66.1795 | 4.36375 | ||||||||
\(231\) | 8.17549 | 0.537908 | ||||||||
\(232\) | 21.6847 | 1.42367 | ||||||||
\(233\) | −3.32322 | −0.217711 | −0.108856 | − | 0.994058i | \(-0.534719\pi\) | ||||
−0.108856 | + | 0.994058i | \(0.534719\pi\) | |||||||
\(234\) | −8.62866 | −0.564073 | ||||||||
\(235\) | −13.3049 | −0.867914 | ||||||||
\(236\) | 27.4499 | 1.78684 | ||||||||
\(237\) | −21.6339 | −1.40527 | ||||||||
\(238\) | −1.95572 | −0.126770 | ||||||||
\(239\) | 11.7022 | 0.756951 | 0.378476 | − | 0.925611i | \(-0.376448\pi\) | ||||
0.378476 | + | 0.925611i | \(0.376448\pi\) | |||||||
\(240\) | −118.932 | −7.67703 | ||||||||
\(241\) | 20.8848 | 1.34531 | 0.672655 | − | 0.739956i | \(-0.265154\pi\) | ||||
0.672655 | + | 0.739956i | \(0.265154\pi\) | |||||||
\(242\) | 21.3023 | 1.36936 | ||||||||
\(243\) | 22.1333 | 1.41985 | ||||||||
\(244\) | 15.3178 | 0.980621 | ||||||||
\(245\) | −10.7185 | −0.684779 | ||||||||
\(246\) | −26.4868 | −1.68874 | ||||||||
\(247\) | 7.82489 | 0.497886 | ||||||||
\(248\) | −64.4558 | −4.09295 | ||||||||
\(249\) | −8.16665 | −0.517541 | ||||||||
\(250\) | 10.8021 | 0.683185 | ||||||||
\(251\) | 9.50454 | 0.599921 | 0.299961 | − | 0.953952i | \(-0.403026\pi\) | ||||
0.299961 | + | 0.953952i | \(0.403026\pi\) | |||||||
\(252\) | 31.4808 | 1.98310 | ||||||||
\(253\) | 14.7525 | 0.927479 | ||||||||
\(254\) | −32.0059 | −2.00823 | ||||||||
\(255\) | −2.79839 | −0.175242 | ||||||||
\(256\) | 68.7450 | 4.29656 | ||||||||
\(257\) | −7.58262 | −0.472991 | −0.236496 | − | 0.971633i | \(-0.575999\pi\) | ||||
−0.236496 | + | 0.971633i | \(0.575999\pi\) | |||||||
\(258\) | −14.4779 | −0.901355 | ||||||||
\(259\) | −0.349444 | −0.0217134 | ||||||||
\(260\) | 16.9680 | 1.05231 | ||||||||
\(261\) | −6.60399 | −0.408777 | ||||||||
\(262\) | 53.5479 | 3.30820 | ||||||||
\(263\) | 19.0591 | 1.17523 | 0.587617 | − | 0.809139i | \(-0.300066\pi\) | ||||
0.587617 | + | 0.809139i | \(0.300066\pi\) | |||||||
\(264\) | −44.6881 | −2.75037 | ||||||||
\(265\) | −20.3644 | −1.25098 | ||||||||
\(266\) | −38.6935 | −2.37245 | ||||||||
\(267\) | −23.7705 | −1.45473 | ||||||||
\(268\) | 6.95207 | 0.424665 | ||||||||
\(269\) | −13.1532 | −0.801965 | −0.400983 | − | 0.916086i | \(-0.631331\pi\) | ||||
−0.400983 | + | 0.916086i | \(0.631331\pi\) | |||||||
\(270\) | 1.03058 | 0.0627191 | ||||||||
\(271\) | 8.42874 | 0.512009 | 0.256005 | − | 0.966676i | \(-0.417594\pi\) | ||||
0.256005 | + | 0.966676i | \(0.417594\pi\) | |||||||
\(272\) | 6.34209 | 0.384546 | ||||||||
\(273\) | −4.61679 | −0.279421 | ||||||||
\(274\) | −23.5460 | −1.42247 | ||||||||
\(275\) | −6.65708 | −0.401437 | ||||||||
\(276\) | 112.654 | 6.78094 | ||||||||
\(277\) | −30.5960 | −1.83834 | −0.919169 | − | 0.393864i | \(-0.871138\pi\) | ||||
−0.919169 | + | 0.393864i | \(0.871138\pi\) | |||||||
\(278\) | 43.6015 | 2.61505 | ||||||||
\(279\) | 19.6298 | 1.17521 | ||||||||
\(280\) | −54.0878 | −3.23236 | ||||||||
\(281\) | 0.107479 | 0.00641168 | 0.00320584 | − | 0.999995i | \(-0.498980\pi\) | ||||
0.00320584 | + | 0.999995i | \(0.498980\pi\) | |||||||
\(282\) | −30.6966 | −1.82795 | ||||||||
\(283\) | −2.69680 | −0.160308 | −0.0801542 | − | 0.996782i | \(-0.525541\pi\) | ||||
−0.0801542 | + | 0.996782i | \(0.525541\pi\) | |||||||
\(284\) | 19.2412 | 1.14176 | ||||||||
\(285\) | −55.3656 | −3.27958 | ||||||||
\(286\) | 5.12659 | 0.303141 | ||||||||
\(287\) | −7.14623 | −0.421828 | ||||||||
\(288\) | −77.2146 | −4.54992 | ||||||||
\(289\) | −16.8508 | −0.991222 | ||||||||
\(290\) | 17.6015 | 1.03360 | ||||||||
\(291\) | −16.6169 | −0.974100 | ||||||||
\(292\) | −50.2050 | −2.93803 | ||||||||
\(293\) | −19.1515 | −1.11884 | −0.559421 | − | 0.828884i | \(-0.688976\pi\) | ||||
−0.559421 | + | 0.828884i | \(0.688976\pi\) | |||||||
\(294\) | −24.7293 | −1.44224 | ||||||||
\(295\) | 14.3631 | 0.836253 | ||||||||
\(296\) | 1.91010 | 0.111022 | ||||||||
\(297\) | 0.229732 | 0.0133304 | ||||||||
\(298\) | −37.7196 | −2.18504 | ||||||||
\(299\) | −8.33087 | −0.481787 | ||||||||
\(300\) | −50.8352 | −2.93497 | ||||||||
\(301\) | −3.90619 | −0.225149 | ||||||||
\(302\) | −32.9199 | −1.89433 | ||||||||
\(303\) | −43.7464 | −2.51317 | ||||||||
\(304\) | 125.477 | 7.19659 | ||||||||
\(305\) | 8.01500 | 0.458938 | ||||||||
\(306\) | −3.25566 | −0.186114 | ||||||||
\(307\) | −4.68317 | −0.267283 | −0.133641 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133641 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(308\) | −18.7038 | −1.06575 | ||||||||
\(309\) | −33.0623 | −1.88085 | ||||||||
\(310\) | −52.3191 | −2.97152 | ||||||||
\(311\) | 17.4852 | 0.991496 | 0.495748 | − | 0.868466i | \(-0.334894\pi\) | ||||
0.495748 | + | 0.868466i | \(0.334894\pi\) | |||||||
\(312\) | 25.2359 | 1.42870 | ||||||||
\(313\) | −21.1255 | −1.19409 | −0.597043 | − | 0.802209i | \(-0.703658\pi\) | ||||
−0.597043 | + | 0.802209i | \(0.703658\pi\) | |||||||
\(314\) | −36.8868 | −2.08164 | ||||||||
\(315\) | 16.4723 | 0.928106 | ||||||||
\(316\) | 49.4939 | 2.78425 | ||||||||
\(317\) | 13.5889 | 0.763228 | 0.381614 | − | 0.924322i | \(-0.375368\pi\) | ||||
0.381614 | + | 0.924322i | \(0.375368\pi\) | |||||||
\(318\) | −46.9842 | −2.63474 | ||||||||
\(319\) | 3.92366 | 0.219683 | ||||||||
\(320\) | 109.106 | 6.09920 | ||||||||
\(321\) | −31.7246 | −1.77070 | ||||||||
\(322\) | 41.1956 | 2.29574 | ||||||||
\(323\) | 2.95239 | 0.164275 | ||||||||
\(324\) | −49.7667 | −2.76482 | ||||||||
\(325\) | 3.75932 | 0.208530 | ||||||||
\(326\) | 35.0403 | 1.94070 | ||||||||
\(327\) | 45.9223 | 2.53951 | ||||||||
\(328\) | 39.0621 | 2.15684 | ||||||||
\(329\) | −8.28204 | −0.456604 | ||||||||
\(330\) | −36.2736 | −1.99679 | ||||||||
\(331\) | 8.58074 | 0.471640 | 0.235820 | − | 0.971797i | \(-0.424222\pi\) | ||||
0.235820 | + | 0.971797i | \(0.424222\pi\) | |||||||
\(332\) | 18.6836 | 1.02540 | ||||||||
\(333\) | −0.581714 | −0.0318777 | ||||||||
\(334\) | 16.8954 | 0.924474 | ||||||||
\(335\) | 3.63766 | 0.198747 | ||||||||
\(336\) | −74.0331 | −4.03884 | ||||||||
\(337\) | −0.139185 | −0.00758190 | −0.00379095 | − | 0.999993i | \(-0.501207\pi\) | ||||
−0.00379095 | + | 0.999993i | \(0.501207\pi\) | |||||||
\(338\) | 33.0093 | 1.79547 | ||||||||
\(339\) | −36.3448 | −1.97398 | ||||||||
\(340\) | 6.40213 | 0.347204 | ||||||||
\(341\) | −11.6627 | −0.631573 | ||||||||
\(342\) | −64.4125 | −3.48303 | ||||||||
\(343\) | −19.5037 | −1.05310 | ||||||||
\(344\) | 21.3517 | 1.15121 | ||||||||
\(345\) | 58.9457 | 3.17353 | ||||||||
\(346\) | −36.9925 | −1.98873 | ||||||||
\(347\) | 16.4244 | 0.881710 | 0.440855 | − | 0.897578i | \(-0.354675\pi\) | ||||
0.440855 | + | 0.897578i | \(0.354675\pi\) | |||||||
\(348\) | 29.9621 | 1.60613 | ||||||||
\(349\) | −12.2741 | −0.657015 | −0.328507 | − | 0.944501i | \(-0.606546\pi\) | ||||
−0.328507 | + | 0.944501i | \(0.606546\pi\) | |||||||
\(350\) | −18.5896 | −0.993655 | ||||||||
\(351\) | −0.129732 | −0.00692461 | ||||||||
\(352\) | 45.8759 | 2.44519 | ||||||||
\(353\) | −25.6029 | −1.36270 | −0.681352 | − | 0.731956i | \(-0.738608\pi\) | ||||
−0.681352 | + | 0.731956i | \(0.738608\pi\) | |||||||
\(354\) | 33.1381 | 1.76127 | ||||||||
\(355\) | 10.0679 | 0.534351 | ||||||||
\(356\) | 54.3819 | 2.88223 | ||||||||
\(357\) | −1.74195 | −0.0921937 | ||||||||
\(358\) | 40.9160 | 2.16248 | ||||||||
\(359\) | 23.4877 | 1.23963 | 0.619816 | − | 0.784747i | \(-0.287207\pi\) | ||||
0.619816 | + | 0.784747i | \(0.287207\pi\) | |||||||
\(360\) | −90.0392 | −4.74548 | ||||||||
\(361\) | 39.4124 | 2.07434 | ||||||||
\(362\) | −56.3863 | −2.96360 | ||||||||
\(363\) | 18.9739 | 0.995869 | ||||||||
\(364\) | 10.5622 | 0.553612 | ||||||||
\(365\) | −26.2697 | −1.37502 | ||||||||
\(366\) | 18.4920 | 0.966590 | ||||||||
\(367\) | −4.70148 | −0.245415 | −0.122708 | − | 0.992443i | \(-0.539158\pi\) | ||||
−0.122708 | + | 0.992443i | \(0.539158\pi\) | |||||||
\(368\) | −133.591 | −6.96389 | ||||||||
\(369\) | −11.8962 | −0.619293 | ||||||||
\(370\) | 1.55044 | 0.0806033 | ||||||||
\(371\) | −12.6765 | −0.658131 | ||||||||
\(372\) | −89.0597 | −4.61753 | ||||||||
\(373\) | −4.91089 | −0.254276 | −0.127138 | − | 0.991885i | \(-0.540579\pi\) | ||||
−0.127138 | + | 0.991885i | \(0.540579\pi\) | |||||||
\(374\) | 1.93430 | 0.100020 | ||||||||
\(375\) | 9.62137 | 0.496845 | ||||||||
\(376\) | 45.2706 | 2.33465 | ||||||||
\(377\) | −2.21573 | −0.114116 | ||||||||
\(378\) | 0.641518 | 0.0329961 | ||||||||
\(379\) | 13.4160 | 0.689133 | 0.344566 | − | 0.938762i | \(-0.388026\pi\) | ||||
0.344566 | + | 0.938762i | \(0.388026\pi\) | |||||||
\(380\) | 126.665 | 6.49777 | ||||||||
\(381\) | −28.5075 | −1.46048 | ||||||||
\(382\) | −68.0868 | −3.48362 | ||||||||
\(383\) | −7.51654 | −0.384077 | −0.192039 | − | 0.981387i | \(-0.561510\pi\) | ||||
−0.192039 | + | 0.981387i | \(0.561510\pi\) | |||||||
\(384\) | 127.232 | 6.49277 | ||||||||
\(385\) | −9.78673 | −0.498778 | ||||||||
\(386\) | 13.1097 | 0.667268 | ||||||||
\(387\) | −6.50258 | −0.330545 | ||||||||
\(388\) | 38.0160 | 1.92997 | ||||||||
\(389\) | −23.5109 | −1.19205 | −0.596025 | − | 0.802966i | \(-0.703254\pi\) | ||||
−0.596025 | + | 0.802966i | \(0.703254\pi\) | |||||||
\(390\) | 20.4841 | 1.03725 | ||||||||
\(391\) | −3.14330 | −0.158963 | ||||||||
\(392\) | 36.4702 | 1.84203 | ||||||||
\(393\) | 47.6948 | 2.40589 | ||||||||
\(394\) | −30.6881 | −1.54604 | ||||||||
\(395\) | 25.8976 | 1.30305 | ||||||||
\(396\) | −31.1360 | −1.56464 | ||||||||
\(397\) | 22.6065 | 1.13459 | 0.567295 | − | 0.823515i | \(-0.307990\pi\) | ||||
0.567295 | + | 0.823515i | \(0.307990\pi\) | |||||||
\(398\) | −32.7215 | −1.64018 | ||||||||
\(399\) | −34.4641 | −1.72536 | ||||||||
\(400\) | 60.2831 | 3.01415 | ||||||||
\(401\) | 3.13021 | 0.156315 | 0.0781575 | − | 0.996941i | \(-0.475096\pi\) | ||||
0.0781575 | + | 0.996941i | \(0.475096\pi\) | |||||||
\(402\) | 8.39269 | 0.418589 | ||||||||
\(403\) | 6.58608 | 0.328076 | ||||||||
\(404\) | 100.083 | 4.97930 | ||||||||
\(405\) | −26.0403 | −1.29395 | ||||||||
\(406\) | 10.9566 | 0.543769 | ||||||||
\(407\) | 0.345616 | 0.0171316 | ||||||||
\(408\) | 9.52169 | 0.471394 | ||||||||
\(409\) | −9.96785 | −0.492878 | −0.246439 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246439 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(410\) | 31.7068 | 1.56589 | ||||||||
\(411\) | −20.9723 | −1.03449 | ||||||||
\(412\) | 75.6395 | 3.72649 | ||||||||
\(413\) | 8.94078 | 0.439947 | ||||||||
\(414\) | 68.5777 | 3.37041 | ||||||||
\(415\) | 9.77615 | 0.479892 | ||||||||
\(416\) | −25.9066 | −1.27018 | ||||||||
\(417\) | 38.8357 | 1.90179 | ||||||||
\(418\) | 38.2697 | 1.87183 | ||||||||
\(419\) | −34.0577 | −1.66383 | −0.831913 | − | 0.554906i | \(-0.812754\pi\) | ||||
−0.831913 | + | 0.554906i | \(0.812754\pi\) | |||||||
\(420\) | −74.7340 | −3.64665 | ||||||||
\(421\) | 26.5540 | 1.29416 | 0.647082 | − | 0.762421i | \(-0.275989\pi\) | ||||
0.647082 | + | 0.762421i | \(0.275989\pi\) | |||||||
\(422\) | −20.2897 | −0.987687 | ||||||||
\(423\) | −13.7870 | −0.670347 | ||||||||
\(424\) | 69.2912 | 3.36508 | ||||||||
\(425\) | 1.41842 | 0.0688035 | ||||||||
\(426\) | 23.2284 | 1.12542 | ||||||||
\(427\) | 4.98919 | 0.241444 | ||||||||
\(428\) | 72.5793 | 3.50825 | ||||||||
\(429\) | 4.56622 | 0.220459 | ||||||||
\(430\) | 17.3312 | 0.835787 | ||||||||
\(431\) | 40.6580 | 1.95843 | 0.979214 | − | 0.202829i | \(-0.0650135\pi\) | ||||
0.979214 | + | 0.202829i | \(0.0650135\pi\) | |||||||
\(432\) | −2.08034 | −0.100090 | ||||||||
\(433\) | −34.8815 | −1.67630 | −0.838149 | − | 0.545441i | \(-0.816362\pi\) | ||||
−0.838149 | + | 0.545441i | \(0.816362\pi\) | |||||||
\(434\) | −32.5677 | −1.56330 | ||||||||
\(435\) | 15.6776 | 0.751683 | ||||||||
\(436\) | −105.061 | −5.03149 | ||||||||
\(437\) | −62.1895 | −2.97493 | ||||||||
\(438\) | −60.6085 | −2.89599 | ||||||||
\(439\) | 17.2156 | 0.821654 | 0.410827 | − | 0.911713i | \(-0.365240\pi\) | ||||
0.410827 | + | 0.911713i | \(0.365240\pi\) | |||||||
\(440\) | 53.4954 | 2.55029 | ||||||||
\(441\) | −11.1069 | −0.528899 | ||||||||
\(442\) | −1.09232 | −0.0519563 | ||||||||
\(443\) | 3.24573 | 0.154209 | 0.0771046 | − | 0.997023i | \(-0.475432\pi\) | ||||
0.0771046 | + | 0.997023i | \(0.475432\pi\) | |||||||
\(444\) | 2.63922 | 0.125252 | ||||||||
\(445\) | 28.4552 | 1.34891 | ||||||||
\(446\) | 4.85253 | 0.229774 | ||||||||
\(447\) | −33.5967 | −1.58907 | ||||||||
\(448\) | 67.9164 | 3.20875 | ||||||||
\(449\) | 16.8128 | 0.793447 | 0.396724 | − | 0.917938i | \(-0.370147\pi\) | ||||
0.396724 | + | 0.917938i | \(0.370147\pi\) | |||||||
\(450\) | −30.9458 | −1.45880 | ||||||||
\(451\) | 7.06795 | 0.332817 | ||||||||
\(452\) | 83.1493 | 3.91101 | ||||||||
\(453\) | −29.3216 | −1.37765 | ||||||||
\(454\) | 9.67585 | 0.454110 | ||||||||
\(455\) | 5.52668 | 0.259095 | ||||||||
\(456\) | 188.385 | 8.82192 | ||||||||
\(457\) | 12.6947 | 0.593834 | 0.296917 | − | 0.954903i | \(-0.404042\pi\) | ||||
0.296917 | + | 0.954903i | \(0.404042\pi\) | |||||||
\(458\) | 14.9664 | 0.699336 | ||||||||
\(459\) | −0.0489490 | −0.00228474 | ||||||||
\(460\) | −134.855 | −6.28767 | ||||||||
\(461\) | −22.0799 | −1.02836 | −0.514181 | − | 0.857682i | \(-0.671904\pi\) | ||||
−0.514181 | + | 0.857682i | \(0.671904\pi\) | |||||||
\(462\) | −22.5796 | −1.05050 | ||||||||
\(463\) | −20.5139 | −0.953363 | −0.476681 | − | 0.879076i | \(-0.658160\pi\) | ||||
−0.476681 | + | 0.879076i | \(0.658160\pi\) | |||||||
\(464\) | −35.5306 | −1.64947 | ||||||||
\(465\) | −46.6003 | −2.16104 | ||||||||
\(466\) | 9.17830 | 0.425177 | ||||||||
\(467\) | 22.6108 | 1.04631 | 0.523153 | − | 0.852239i | \(-0.324756\pi\) | ||||
0.523153 | + | 0.852239i | \(0.324756\pi\) | |||||||
\(468\) | 17.5828 | 0.812766 | ||||||||
\(469\) | 2.26438 | 0.104559 | ||||||||
\(470\) | 36.7463 | 1.69498 | ||||||||
\(471\) | −32.8549 | −1.51387 | ||||||||
\(472\) | −48.8713 | −2.24948 | ||||||||
\(473\) | 3.86340 | 0.177640 | ||||||||
\(474\) | 59.7501 | 2.74441 | ||||||||
\(475\) | 28.0632 | 1.28763 | ||||||||
\(476\) | 3.98521 | 0.182662 | ||||||||
\(477\) | −21.1024 | −0.966212 | ||||||||
\(478\) | −32.3199 | −1.47828 | ||||||||
\(479\) | 26.3057 | 1.20194 | 0.600969 | − | 0.799272i | \(-0.294781\pi\) | ||||
0.600969 | + | 0.799272i | \(0.294781\pi\) | |||||||
\(480\) | 183.304 | 8.36665 | ||||||||
\(481\) | −0.195173 | −0.00889914 | ||||||||
\(482\) | −57.6811 | −2.62730 | ||||||||
\(483\) | 36.6927 | 1.66957 | ||||||||
\(484\) | −43.4082 | −1.97310 | ||||||||
\(485\) | 19.8918 | 0.903240 | ||||||||
\(486\) | −61.1293 | −2.77288 | ||||||||
\(487\) | 23.1266 | 1.04797 | 0.523983 | − | 0.851729i | \(-0.324446\pi\) | ||||
0.523983 | + | 0.851729i | \(0.324446\pi\) | |||||||
\(488\) | −27.2715 | −1.23452 | ||||||||
\(489\) | 31.2102 | 1.41137 | ||||||||
\(490\) | 29.6030 | 1.33733 | ||||||||
\(491\) | −21.3535 | −0.963672 | −0.481836 | − | 0.876262i | \(-0.660030\pi\) | ||||
−0.481836 | + | 0.876262i | \(0.660030\pi\) | |||||||
\(492\) | 53.9727 | 2.43328 | ||||||||
\(493\) | −0.836012 | −0.0376521 | ||||||||
\(494\) | −21.6113 | −0.972339 | ||||||||
\(495\) | −16.2918 | −0.732263 | ||||||||
\(496\) | 105.612 | 4.74211 | ||||||||
\(497\) | 6.26712 | 0.281119 | ||||||||
\(498\) | 22.5552 | 1.01072 | ||||||||
\(499\) | 20.0004 | 0.895342 | 0.447671 | − | 0.894198i | \(-0.352254\pi\) | ||||
0.447671 | + | 0.894198i | \(0.352254\pi\) | |||||||
\(500\) | −22.0117 | −0.984392 | ||||||||
\(501\) | 15.0486 | 0.672322 | ||||||||
\(502\) | −26.2503 | −1.17161 | ||||||||
\(503\) | −13.2405 | −0.590365 | −0.295182 | − | 0.955441i | \(-0.595380\pi\) | ||||
−0.295182 | + | 0.955441i | \(0.595380\pi\) | |||||||
\(504\) | −56.0478 | −2.49657 | ||||||||
\(505\) | 52.3681 | 2.33035 | ||||||||
\(506\) | −40.7443 | −1.81131 | ||||||||
\(507\) | 29.4012 | 1.30575 | ||||||||
\(508\) | 65.2191 | 2.89363 | ||||||||
\(509\) | 0.401532 | 0.0177976 | 0.00889881 | − | 0.999960i | \(-0.497167\pi\) | ||||
0.00889881 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(510\) | 7.72879 | 0.342237 | ||||||||
\(511\) | −16.3524 | −0.723387 | ||||||||
\(512\) | −86.4235 | −3.81941 | ||||||||
\(513\) | −0.968446 | −0.0427579 | ||||||||
\(514\) | 20.9422 | 0.923722 | ||||||||
\(515\) | 39.5782 | 1.74402 | ||||||||
\(516\) | 29.5020 | 1.29875 | ||||||||
\(517\) | 8.19133 | 0.360254 | ||||||||
\(518\) | 0.965118 | 0.0424049 | ||||||||
\(519\) | −32.9490 | −1.44630 | ||||||||
\(520\) | −30.2094 | −1.32477 | ||||||||
\(521\) | 11.4530 | 0.501767 | 0.250884 | − | 0.968017i | \(-0.419279\pi\) | ||||
0.250884 | + | 0.968017i | \(0.419279\pi\) | |||||||
\(522\) | 18.2394 | 0.798315 | ||||||||
\(523\) | 1.66959 | 0.0730060 | 0.0365030 | − | 0.999334i | \(-0.488378\pi\) | ||||
0.0365030 | + | 0.999334i | \(0.488378\pi\) | |||||||
\(524\) | −109.116 | −4.76674 | ||||||||
\(525\) | −16.5576 | −0.722635 | ||||||||
\(526\) | −52.6387 | −2.29516 | ||||||||
\(527\) | 2.48498 | 0.108247 | ||||||||
\(528\) | 73.2222 | 3.18659 | ||||||||
\(529\) | 43.2109 | 1.87874 | ||||||||
\(530\) | 56.2439 | 2.44308 | ||||||||
\(531\) | 14.8836 | 0.645893 | ||||||||
\(532\) | 78.8466 | 3.41843 | ||||||||
\(533\) | −3.99135 | −0.172885 | ||||||||
\(534\) | 65.6509 | 2.84099 | ||||||||
\(535\) | 37.9770 | 1.64189 | ||||||||
\(536\) | −12.3773 | −0.534620 | ||||||||
\(537\) | 36.4437 | 1.57266 | ||||||||
\(538\) | 36.3275 | 1.56619 | ||||||||
\(539\) | 6.59898 | 0.284238 | ||||||||
\(540\) | −2.10004 | −0.0903712 | ||||||||
\(541\) | 10.1682 | 0.437166 | 0.218583 | − | 0.975818i | \(-0.429857\pi\) | ||||
0.218583 | + | 0.975818i | \(0.429857\pi\) | |||||||
\(542\) | −23.2791 | −0.999921 | ||||||||
\(543\) | −50.2230 | −2.15527 | ||||||||
\(544\) | −9.77475 | −0.419089 | ||||||||
\(545\) | −54.9727 | −2.35477 | ||||||||
\(546\) | 12.7510 | 0.545691 | ||||||||
\(547\) | −21.0758 | −0.901136 | −0.450568 | − | 0.892742i | \(-0.648778\pi\) | ||||
−0.450568 | + | 0.892742i | \(0.648778\pi\) | |||||||
\(548\) | 47.9803 | 2.04962 | ||||||||
\(549\) | 8.30544 | 0.354468 | ||||||||
\(550\) | 18.3860 | 0.783981 | ||||||||
\(551\) | −16.5403 | −0.704642 | ||||||||
\(552\) | −200.566 | −8.53666 | ||||||||
\(553\) | 16.1208 | 0.685525 | ||||||||
\(554\) | 84.5023 | 3.59016 | ||||||||
\(555\) | 1.38096 | 0.0586187 | ||||||||
\(556\) | −88.8478 | −3.76799 | ||||||||
\(557\) | −10.5110 | −0.445365 | −0.222682 | − | 0.974891i | \(-0.571481\pi\) | ||||
−0.222682 | + | 0.974891i | \(0.571481\pi\) | |||||||
\(558\) | −54.2150 | −2.29510 | ||||||||
\(559\) | −2.18171 | −0.0922764 | ||||||||
\(560\) | 88.6236 | 3.74503 | ||||||||
\(561\) | 1.72287 | 0.0727396 | ||||||||
\(562\) | −0.296844 | −0.0125216 | ||||||||
\(563\) | 31.6828 | 1.33527 | 0.667636 | − | 0.744488i | \(-0.267306\pi\) | ||||
0.667636 | + | 0.744488i | \(0.267306\pi\) | |||||||
\(564\) | 62.5511 | 2.63388 | ||||||||
\(565\) | 43.5077 | 1.83038 | ||||||||
\(566\) | 7.44822 | 0.313072 | ||||||||
\(567\) | −16.2096 | −0.680741 | ||||||||
\(568\) | −34.2568 | −1.43738 | ||||||||
\(569\) | −42.4671 | −1.78032 | −0.890158 | − | 0.455653i | \(-0.849406\pi\) | ||||
−0.890158 | + | 0.455653i | \(0.849406\pi\) | |||||||
\(570\) | 152.913 | 6.40480 | ||||||||
\(571\) | −10.2811 | −0.430253 | −0.215126 | − | 0.976586i | \(-0.569016\pi\) | ||||
−0.215126 | + | 0.976586i | \(0.569016\pi\) | |||||||
\(572\) | −10.4466 | −0.436792 | ||||||||
\(573\) | −60.6445 | −2.53346 | ||||||||
\(574\) | 19.7369 | 0.823804 | ||||||||
\(575\) | −29.8778 | −1.24599 | ||||||||
\(576\) | 113.059 | 4.71081 | ||||||||
\(577\) | −19.6631 | −0.818585 | −0.409293 | − | 0.912403i | \(-0.634224\pi\) | ||||
−0.409293 | + | 0.912403i | \(0.634224\pi\) | |||||||
\(578\) | 46.5396 | 1.93579 | ||||||||
\(579\) | 11.6768 | 0.485270 | ||||||||
\(580\) | −35.8670 | −1.48930 | ||||||||
\(581\) | 6.08548 | 0.252468 | ||||||||
\(582\) | 45.8937 | 1.90236 | ||||||||
\(583\) | 12.5376 | 0.519256 | ||||||||
\(584\) | 89.3840 | 3.69874 | ||||||||
\(585\) | 9.20018 | 0.380381 | ||||||||
\(586\) | 52.8939 | 2.18503 | ||||||||
\(587\) | −8.83037 | −0.364468 | −0.182234 | − | 0.983255i | \(-0.558333\pi\) | ||||
−0.182234 | + | 0.983255i | \(0.558333\pi\) | |||||||
\(588\) | 50.3915 | 2.07811 | ||||||||
\(589\) | 49.1647 | 2.02580 | ||||||||
\(590\) | −39.6690 | −1.63315 | ||||||||
\(591\) | −27.3337 | −1.12436 | ||||||||
\(592\) | −3.12973 | −0.128631 | ||||||||
\(593\) | 29.6565 | 1.21784 | 0.608922 | − | 0.793230i | \(-0.291602\pi\) | ||||
0.608922 | + | 0.793230i | \(0.291602\pi\) | |||||||
\(594\) | −0.634491 | −0.0260335 | ||||||||
\(595\) | 2.08526 | 0.0854871 | ||||||||
\(596\) | 76.8621 | 3.14840 | ||||||||
\(597\) | −29.1448 | −1.19282 | ||||||||
\(598\) | 23.0088 | 0.940899 | ||||||||
\(599\) | −38.4774 | −1.57214 | −0.786071 | − | 0.618136i | \(-0.787888\pi\) | ||||
−0.786071 | + | 0.618136i | \(0.787888\pi\) | |||||||
\(600\) | 90.5060 | 3.69489 | ||||||||
\(601\) | −9.23740 | −0.376801 | −0.188401 | − | 0.982092i | \(-0.560330\pi\) | ||||
−0.188401 | + | 0.982092i | \(0.560330\pi\) | |||||||
\(602\) | 10.7884 | 0.439702 | ||||||||
\(603\) | 3.76948 | 0.153505 | ||||||||
\(604\) | 67.0816 | 2.72951 | ||||||||
\(605\) | −22.7133 | −0.923425 | ||||||||
\(606\) | 120.822 | 4.90806 | ||||||||
\(607\) | 23.9098 | 0.970469 | 0.485234 | − | 0.874384i | \(-0.338734\pi\) | ||||
0.485234 | + | 0.874384i | \(0.338734\pi\) | |||||||
\(608\) | −193.391 | −7.84306 | ||||||||
\(609\) | 9.75902 | 0.395455 | ||||||||
\(610\) | −22.1364 | −0.896276 | ||||||||
\(611\) | −4.62573 | −0.187137 | ||||||||
\(612\) | 6.63413 | 0.268169 | ||||||||
\(613\) | 3.55509 | 0.143589 | 0.0717944 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717944 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(614\) | 12.9343 | 0.521986 | ||||||||
\(615\) | 28.2411 | 1.13879 | ||||||||
\(616\) | 33.2999 | 1.34169 | ||||||||
\(617\) | 16.5606 | 0.666705 | 0.333352 | − | 0.942802i | \(-0.391820\pi\) | ||||
0.333352 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(618\) | 91.3136 | 3.67317 | ||||||||
\(619\) | −9.77712 | −0.392976 | −0.196488 | − | 0.980506i | \(-0.562954\pi\) | ||||
−0.196488 | + | 0.980506i | \(0.562954\pi\) | |||||||
\(620\) | 106.612 | 4.28163 | ||||||||
\(621\) | 1.03107 | 0.0413754 | ||||||||
\(622\) | −48.2919 | −1.93633 | ||||||||
\(623\) | 17.7129 | 0.709650 | ||||||||
\(624\) | −41.3494 | −1.65530 | ||||||||
\(625\) | −29.8768 | −1.19507 | ||||||||
\(626\) | 58.3460 | 2.33198 | ||||||||
\(627\) | 34.0866 | 1.36129 | ||||||||
\(628\) | 75.1651 | 2.99941 | ||||||||
\(629\) | −0.0736403 | −0.00293623 | ||||||||
\(630\) | −45.4942 | −1.81253 | ||||||||
\(631\) | 36.1880 | 1.44062 | 0.720310 | − | 0.693652i | \(-0.243999\pi\) | ||||
0.720310 | + | 0.693652i | \(0.243999\pi\) | |||||||
\(632\) | −88.1180 | −3.50514 | ||||||||
\(633\) | −18.0719 | −0.718294 | ||||||||
\(634\) | −37.5307 | −1.49054 | ||||||||
\(635\) | 34.1258 | 1.35424 | ||||||||
\(636\) | 95.7407 | 3.79637 | ||||||||
\(637\) | −3.72652 | −0.147650 | ||||||||
\(638\) | −10.8366 | −0.429026 | ||||||||
\(639\) | 10.4328 | 0.412714 | ||||||||
\(640\) | −152.307 | −6.02046 | ||||||||
\(641\) | −3.00417 | −0.118658 | −0.0593288 | − | 0.998238i | \(-0.518896\pi\) | ||||
−0.0593288 | + | 0.998238i | \(0.518896\pi\) | |||||||
\(642\) | 87.6193 | 3.45806 | ||||||||
\(643\) | 42.9281 | 1.69292 | 0.846459 | − | 0.532453i | \(-0.178730\pi\) | ||||
0.846459 | + | 0.532453i | \(0.178730\pi\) | |||||||
\(644\) | −83.9451 | −3.30790 | ||||||||
\(645\) | 15.4368 | 0.607825 | ||||||||
\(646\) | −8.15411 | −0.320819 | ||||||||
\(647\) | −27.3258 | −1.07429 | −0.537144 | − | 0.843491i | \(-0.680497\pi\) | ||||
−0.537144 | + | 0.843491i | \(0.680497\pi\) | |||||||
\(648\) | 88.6037 | 3.48068 | ||||||||
\(649\) | −8.84285 | −0.347112 | ||||||||
\(650\) | −10.3828 | −0.407246 | ||||||||
\(651\) | −29.0079 | −1.13691 | ||||||||
\(652\) | −71.4023 | −2.79633 | ||||||||
\(653\) | 2.76399 | 0.108163 | 0.0540817 | − | 0.998537i | \(-0.482777\pi\) | ||||
0.0540817 | + | 0.998537i | \(0.482777\pi\) | |||||||
\(654\) | −126.831 | −4.95950 | ||||||||
\(655\) | −57.0946 | −2.23087 | ||||||||
\(656\) | −64.0038 | −2.49893 | ||||||||
\(657\) | −27.2216 | −1.06202 | ||||||||
\(658\) | 22.8739 | 0.891718 | ||||||||
\(659\) | 18.7322 | 0.729705 | 0.364852 | − | 0.931065i | \(-0.381119\pi\) | ||||
0.364852 | + | 0.931065i | \(0.381119\pi\) | |||||||
\(660\) | 73.9154 | 2.87715 | ||||||||
\(661\) | −17.7576 | −0.690689 | −0.345344 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345344 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(662\) | −23.6989 | −0.921083 | ||||||||
\(663\) | −0.972923 | −0.0377852 | ||||||||
\(664\) | −33.2639 | −1.29089 | ||||||||
\(665\) | 41.2563 | 1.59985 | ||||||||
\(666\) | 1.60662 | 0.0622552 | ||||||||
\(667\) | 17.6099 | 0.681857 | ||||||||
\(668\) | −34.4281 | −1.33206 | ||||||||
\(669\) | 4.32212 | 0.167103 | ||||||||
\(670\) | −10.0467 | −0.388139 | ||||||||
\(671\) | −4.93455 | −0.190496 | ||||||||
\(672\) | 114.104 | 4.40164 | ||||||||
\(673\) | −51.7364 | −1.99429 | −0.997145 | − | 0.0755122i | \(-0.975941\pi\) | ||||
−0.997145 | + | 0.0755122i | \(0.975941\pi\) | |||||||
\(674\) | 0.384411 | 0.0148070 | ||||||||
\(675\) | −0.465272 | −0.0179083 | ||||||||
\(676\) | −67.2637 | −2.58707 | ||||||||
\(677\) | 4.51667 | 0.173590 | 0.0867949 | − | 0.996226i | \(-0.472338\pi\) | ||||
0.0867949 | + | 0.996226i | \(0.472338\pi\) | |||||||
\(678\) | 100.380 | 3.85505 | ||||||||
\(679\) | 12.3823 | 0.475188 | ||||||||
\(680\) | −11.3982 | −0.437102 | ||||||||
\(681\) | 8.61822 | 0.330251 | ||||||||
\(682\) | 32.2110 | 1.23342 | ||||||||
\(683\) | −26.7038 | −1.02179 | −0.510896 | − | 0.859642i | \(-0.670686\pi\) | ||||
−0.510896 | + | 0.859642i | \(0.670686\pi\) | |||||||
\(684\) | 131.255 | 5.01865 | ||||||||
\(685\) | 25.1056 | 0.959236 | ||||||||
\(686\) | 53.8665 | 2.05663 | ||||||||
\(687\) | 13.3305 | 0.508591 | ||||||||
\(688\) | −34.9850 | −1.33379 | ||||||||
\(689\) | −7.08015 | −0.269732 | ||||||||
\(690\) | −162.800 | −6.19771 | ||||||||
\(691\) | 31.3020 | 1.19078 | 0.595392 | − | 0.803435i | \(-0.296997\pi\) | ||||
0.595392 | + | 0.803435i | \(0.296997\pi\) | |||||||
\(692\) | 75.3804 | 2.86553 | ||||||||
\(693\) | −10.1414 | −0.385239 | ||||||||
\(694\) | −45.3621 | −1.72192 | ||||||||
\(695\) | −46.4895 | −1.76345 | ||||||||
\(696\) | −53.3439 | −2.02199 | ||||||||
\(697\) | −1.50597 | −0.0570425 | ||||||||
\(698\) | 33.8993 | 1.28311 | ||||||||
\(699\) | 8.17506 | 0.309209 | ||||||||
\(700\) | 37.8804 | 1.43175 | ||||||||
\(701\) | 3.47270 | 0.131162 | 0.0655811 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655811 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(702\) | 0.358304 | 0.0135233 | ||||||||
\(703\) | −1.45696 | −0.0549503 | ||||||||
\(704\) | −67.1725 | −2.53166 | ||||||||
\(705\) | 32.7297 | 1.23267 | ||||||||
\(706\) | 70.7118 | 2.66127 | ||||||||
\(707\) | 32.5982 | 1.22598 | ||||||||
\(708\) | −67.5263 | −2.53779 | ||||||||
\(709\) | 43.1219 | 1.61948 | 0.809739 | − | 0.586790i | \(-0.199609\pi\) | ||||
0.809739 | + | 0.586790i | \(0.199609\pi\) | |||||||
\(710\) | −27.8064 | −1.04355 | ||||||||
\(711\) | 26.8360 | 1.00643 | ||||||||
\(712\) | −96.8204 | −3.62850 | ||||||||
\(713\) | −52.3439 | −1.96029 | ||||||||
\(714\) | 4.81103 | 0.180048 | ||||||||
\(715\) | −5.46614 | −0.204422 | ||||||||
\(716\) | −83.3755 | −3.11589 | ||||||||
\(717\) | −28.7872 | −1.07508 | ||||||||
\(718\) | −64.8699 | −2.42092 | ||||||||
\(719\) | −44.7395 | −1.66850 | −0.834251 | − | 0.551386i | \(-0.814099\pi\) | ||||
−0.834251 | + | 0.551386i | \(0.814099\pi\) | |||||||
\(720\) | 147.531 | 5.49814 | ||||||||
\(721\) | 24.6367 | 0.917520 | ||||||||
\(722\) | −108.852 | −4.05105 | ||||||||
\(723\) | −51.3763 | −1.91070 | ||||||||
\(724\) | 114.900 | 4.27021 | ||||||||
\(725\) | −7.94650 | −0.295126 | ||||||||
\(726\) | −52.4033 | −1.94487 | ||||||||
\(727\) | 37.4335 | 1.38833 | 0.694167 | − | 0.719814i | \(-0.255773\pi\) | ||||
0.694167 | + | 0.719814i | \(0.255773\pi\) | |||||||
\(728\) | −18.8048 | −0.696953 | ||||||||
\(729\) | −27.9191 | −1.03404 | ||||||||
\(730\) | 72.5534 | 2.68532 | ||||||||
\(731\) | −0.823174 | −0.0304462 | ||||||||
\(732\) | −37.6815 | −1.39275 | ||||||||
\(733\) | 15.3900 | 0.568443 | 0.284221 | − | 0.958759i | \(-0.408265\pi\) | ||||
0.284221 | + | 0.958759i | \(0.408265\pi\) | |||||||
\(734\) | 12.9849 | 0.479280 | ||||||||
\(735\) | 26.3673 | 0.972571 | ||||||||
\(736\) | 205.897 | 7.58946 | ||||||||
\(737\) | −2.23958 | −0.0824958 | ||||||||
\(738\) | 32.8558 | 1.20944 | ||||||||
\(739\) | 5.01382 | 0.184437 | 0.0922183 | − | 0.995739i | \(-0.470604\pi\) | ||||
0.0922183 | + | 0.995739i | \(0.470604\pi\) | |||||||
\(740\) | −3.15936 | −0.116140 | ||||||||
\(741\) | −19.2491 | −0.707133 | ||||||||
\(742\) | 35.0108 | 1.28529 | ||||||||
\(743\) | 45.9362 | 1.68524 | 0.842618 | − | 0.538512i | \(-0.181013\pi\) | ||||
0.842618 | + | 0.538512i | \(0.181013\pi\) | |||||||
\(744\) | 158.560 | 5.81310 | ||||||||
\(745\) | 40.2180 | 1.47347 | ||||||||
\(746\) | 13.5632 | 0.496586 | ||||||||
\(747\) | 10.1304 | 0.370652 | ||||||||
\(748\) | −3.94156 | −0.144118 | ||||||||
\(749\) | 23.6400 | 0.863787 | ||||||||
\(750\) | −26.5730 | −0.970307 | ||||||||
\(751\) | 1.73530 | 0.0633219 | 0.0316610 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316610 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(752\) | −74.1765 | −2.70494 | ||||||||
\(753\) | −23.3810 | −0.852051 | ||||||||
\(754\) | 6.11956 | 0.222861 | ||||||||
\(755\) | 35.1003 | 1.27743 | ||||||||
\(756\) | −1.30723 | −0.0475437 | ||||||||
\(757\) | 12.8895 | 0.468477 | 0.234238 | − | 0.972179i | \(-0.424740\pi\) | ||||
0.234238 | + | 0.972179i | \(0.424740\pi\) | |||||||
\(758\) | −37.0532 | −1.34583 | ||||||||
\(759\) | −36.2908 | −1.31727 | ||||||||
\(760\) | −225.512 | −8.18017 | ||||||||
\(761\) | 20.2540 | 0.734209 | 0.367104 | − | 0.930180i | \(-0.380349\pi\) | ||||
0.367104 | + | 0.930180i | \(0.380349\pi\) | |||||||
\(762\) | 78.7339 | 2.85223 | ||||||||
\(763\) | −34.2195 | −1.23883 | ||||||||
\(764\) | 138.742 | 5.01951 | ||||||||
\(765\) | 3.47129 | 0.125505 | ||||||||
\(766\) | 20.7597 | 0.750078 | ||||||||
\(767\) | 4.99365 | 0.180310 | ||||||||
\(768\) | −169.111 | −6.10228 | ||||||||
\(769\) | −6.01347 | −0.216851 | −0.108426 | − | 0.994105i | \(-0.534581\pi\) | ||||
−0.108426 | + | 0.994105i | \(0.534581\pi\) | |||||||
\(770\) | 27.0297 | 0.974082 | ||||||||
\(771\) | 18.6531 | 0.671776 | ||||||||
\(772\) | −26.7140 | −0.961458 | ||||||||
\(773\) | 19.5548 | 0.703337 | 0.351668 | − | 0.936125i | \(-0.385615\pi\) | ||||
0.351668 | + | 0.936125i | \(0.385615\pi\) | |||||||
\(774\) | 17.9593 | 0.645533 | ||||||||
\(775\) | 23.6203 | 0.848466 | ||||||||
\(776\) | −67.6829 | −2.42968 | ||||||||
\(777\) | 0.859626 | 0.0308389 | ||||||||
\(778\) | 64.9341 | 2.32800 | ||||||||
\(779\) | −29.7952 | −1.06752 | ||||||||
\(780\) | −41.7409 | −1.49456 | ||||||||
\(781\) | −6.19847 | −0.221799 | ||||||||
\(782\) | 8.68138 | 0.310446 | ||||||||
\(783\) | 0.274230 | 0.00980017 | ||||||||
\(784\) | −59.7570 | −2.13418 | ||||||||
\(785\) | 39.3300 | 1.40375 | ||||||||
\(786\) | −131.727 | −4.69854 | ||||||||
\(787\) | 54.7724 | 1.95243 | 0.976213 | − | 0.216814i | \(-0.0695664\pi\) | ||||
0.976213 | + | 0.216814i | \(0.0695664\pi\) | |||||||
\(788\) | 62.5337 | 2.22767 | ||||||||
\(789\) | −46.8850 | −1.66915 | ||||||||
\(790\) | −71.5257 | −2.54477 | ||||||||
\(791\) | 27.0828 | 0.962952 | ||||||||
\(792\) | 55.4339 | 1.96976 | ||||||||
\(793\) | 2.78659 | 0.0989548 | ||||||||
\(794\) | −62.4363 | −2.21578 | ||||||||
\(795\) | 50.0961 | 1.77673 | ||||||||
\(796\) | 66.6772 | 2.36331 | ||||||||
\(797\) | −5.68298 | −0.201302 | −0.100651 | − | 0.994922i | \(-0.532092\pi\) | ||||
−0.100651 | + | 0.994922i | \(0.532092\pi\) | |||||||
\(798\) | 95.1853 | 3.36952 | ||||||||
\(799\) | −1.74532 | −0.0617451 | ||||||||
\(800\) | −92.9114 | −3.28491 | ||||||||
\(801\) | 29.4863 | 1.04185 | ||||||||
\(802\) | −8.64522 | −0.305273 | ||||||||
\(803\) | 16.1733 | 0.570743 | ||||||||
\(804\) | −17.1020 | −0.603140 | ||||||||
\(805\) | −43.9241 | −1.54812 | ||||||||
\(806\) | −18.1899 | −0.640712 | ||||||||
\(807\) | 32.3567 | 1.13901 | ||||||||
\(808\) | −178.185 | −6.26854 | ||||||||
\(809\) | −44.0649 | −1.54924 | −0.774620 | − | 0.632427i | \(-0.782059\pi\) | ||||
−0.774620 | + | 0.632427i | \(0.782059\pi\) | |||||||
\(810\) | 71.9200 | 2.52701 | ||||||||
\(811\) | −48.6506 | −1.70835 | −0.854176 | − | 0.519984i | \(-0.825938\pi\) | ||||
−0.854176 | + | 0.519984i | \(0.825938\pi\) | |||||||
\(812\) | −22.3266 | −0.783510 | ||||||||
\(813\) | −20.7345 | −0.727192 | ||||||||
\(814\) | −0.954547 | −0.0334569 | ||||||||
\(815\) | −37.3611 | −1.30870 | ||||||||
\(816\) | −15.6014 | −0.546159 | ||||||||
\(817\) | −16.2863 | −0.569787 | ||||||||
\(818\) | 27.5299 | 0.962560 | ||||||||
\(819\) | 5.72695 | 0.200116 | ||||||||
\(820\) | −64.6097 | −2.25627 | ||||||||
\(821\) | 33.1946 | 1.15850 | 0.579250 | − | 0.815150i | \(-0.303345\pi\) | ||||
0.579250 | + | 0.815150i | \(0.303345\pi\) | |||||||
\(822\) | 57.9228 | 2.02029 | ||||||||
\(823\) | 36.3943 | 1.26863 | 0.634313 | − | 0.773077i | \(-0.281283\pi\) | ||||
0.634313 | + | 0.773077i | \(0.281283\pi\) | |||||||
\(824\) | −134.667 | −4.69135 | ||||||||
\(825\) | 16.3763 | 0.570149 | ||||||||
\(826\) | −24.6933 | −0.859189 | ||||||||
\(827\) | 49.2420 | 1.71231 | 0.856156 | − | 0.516717i | \(-0.172846\pi\) | ||||
0.856156 | + | 0.516717i | \(0.172846\pi\) | |||||||
\(828\) | −139.742 | −4.85638 | ||||||||
\(829\) | −31.6484 | −1.09919 | −0.549597 | − | 0.835430i | \(-0.685219\pi\) | ||||
−0.549597 | + | 0.835430i | \(0.685219\pi\) | |||||||
\(830\) | −27.0005 | −0.937200 | ||||||||
\(831\) | 75.2657 | 2.61094 | ||||||||
\(832\) | 37.9330 | 1.31509 | ||||||||
\(833\) | −1.40604 | −0.0487165 | ||||||||
\(834\) | −107.259 | −3.71408 | ||||||||
\(835\) | −18.0144 | −0.623415 | ||||||||
\(836\) | −77.9830 | −2.69710 | ||||||||
\(837\) | −0.815125 | −0.0281748 | ||||||||
\(838\) | 94.0628 | 3.24935 | ||||||||
\(839\) | −38.1706 | −1.31780 | −0.658898 | − | 0.752232i | \(-0.728977\pi\) | ||||
−0.658898 | + | 0.752232i | \(0.728977\pi\) | |||||||
\(840\) | 133.055 | 4.59083 | ||||||||
\(841\) | −24.3164 | −0.838495 | ||||||||
\(842\) | −73.3387 | −2.52742 | ||||||||
\(843\) | −0.264397 | −0.00910633 | ||||||||
\(844\) | 41.3448 | 1.42315 | ||||||||
\(845\) | −35.1956 | −1.21077 | ||||||||
\(846\) | 38.0779 | 1.30914 | ||||||||
\(847\) | −14.1386 | −0.485808 | ||||||||
\(848\) | −113.535 | −3.89879 | ||||||||
\(849\) | 6.63409 | 0.227681 | ||||||||
\(850\) | −3.91749 | −0.134369 | ||||||||
\(851\) | 1.55117 | 0.0531735 | ||||||||
\(852\) | −47.3331 | −1.62161 | ||||||||
\(853\) | 3.86153 | 0.132216 | 0.0661081 | − | 0.997812i | \(-0.478942\pi\) | ||||
0.0661081 | + | 0.997812i | \(0.478942\pi\) | |||||||
\(854\) | −13.7795 | −0.471525 | ||||||||
\(855\) | 68.6789 | 2.34877 | ||||||||
\(856\) | −129.219 | −4.41661 | ||||||||
\(857\) | −0.0133006 | −0.000454339 0 | −0.000227170 | − | 1.00000i | \(-0.500072\pi\) | ||||
−0.000227170 | 1.00000i | \(0.500072\pi\) | ||||||||
\(858\) | −12.6113 | −0.430543 | ||||||||
\(859\) | −4.54946 | −0.155226 | −0.0776128 | − | 0.996984i | \(-0.524730\pi\) | ||||
−0.0776128 | + | 0.996984i | \(0.524730\pi\) | |||||||
\(860\) | −35.3163 | −1.20427 | ||||||||
\(861\) | 17.5796 | 0.599111 | ||||||||
\(862\) | −112.292 | −3.82469 | ||||||||
\(863\) | −10.9433 | −0.372515 | −0.186257 | − | 0.982501i | \(-0.559636\pi\) | ||||
−0.186257 | + | 0.982501i | \(0.559636\pi\) | |||||||
\(864\) | 3.20633 | 0.109081 | ||||||||
\(865\) | 39.4427 | 1.34109 | ||||||||
\(866\) | 96.3381 | 3.27370 | ||||||||
\(867\) | 41.4526 | 1.40780 | ||||||||
\(868\) | 66.3639 | 2.25254 | ||||||||
\(869\) | −15.9442 | −0.540870 | ||||||||
\(870\) | −43.2995 | −1.46799 | ||||||||
\(871\) | 1.26471 | 0.0428532 | ||||||||
\(872\) | 187.048 | 6.33424 | ||||||||
\(873\) | 20.6126 | 0.697631 | ||||||||
\(874\) | 171.759 | 5.80985 | ||||||||
\(875\) | −7.16948 | −0.242373 | ||||||||
\(876\) | 123.503 | 4.17279 | ||||||||
\(877\) | 9.41049 | 0.317770 | 0.158885 | − | 0.987297i | \(-0.449210\pi\) | ||||
0.158885 | + | 0.987297i | \(0.449210\pi\) | |||||||
\(878\) | −47.5471 | −1.60464 | ||||||||
\(879\) | 47.1123 | 1.58906 | ||||||||
\(880\) | −87.6529 | −2.95478 | ||||||||
\(881\) | 7.89653 | 0.266041 | 0.133020 | − | 0.991113i | \(-0.457532\pi\) | ||||
0.133020 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(882\) | 30.6758 | 1.03291 | ||||||||
\(883\) | −49.4232 | −1.66322 | −0.831611 | − | 0.555359i | \(-0.812581\pi\) | ||||
−0.831611 | + | 0.555359i | \(0.812581\pi\) | |||||||
\(884\) | 2.22584 | 0.0748632 | ||||||||
\(885\) | −35.3330 | −1.18771 | ||||||||
\(886\) | −8.96428 | −0.301161 | ||||||||
\(887\) | 19.4916 | 0.654464 | 0.327232 | − | 0.944944i | \(-0.393884\pi\) | ||||
0.327232 | + | 0.944944i | \(0.393884\pi\) | |||||||
\(888\) | −4.69881 | −0.157682 | ||||||||
\(889\) | 21.2427 | 0.712457 | ||||||||
\(890\) | −78.5895 | −2.63433 | ||||||||
\(891\) | 16.0321 | 0.537095 | ||||||||
\(892\) | −9.88810 | −0.331078 | ||||||||
\(893\) | −34.5309 | −1.15553 | ||||||||
\(894\) | 92.7896 | 3.10335 | ||||||||
\(895\) | −43.6261 | −1.45826 | ||||||||
\(896\) | −94.8083 | −3.16732 | ||||||||
\(897\) | 20.4938 | 0.684268 | ||||||||
\(898\) | −46.4349 | −1.54955 | ||||||||
\(899\) | −13.9217 | −0.464315 | ||||||||
\(900\) | 63.0590 | 2.10197 | ||||||||
\(901\) | −2.67139 | −0.0889970 | ||||||||
\(902\) | −19.5208 | −0.649970 | ||||||||
\(903\) | 9.60916 | 0.319773 | ||||||||
\(904\) | −148.037 | −4.92365 | ||||||||
\(905\) | 60.1210 | 1.99849 | ||||||||
\(906\) | 80.9824 | 2.69046 | ||||||||
\(907\) | −23.5915 | −0.783343 | −0.391672 | − | 0.920105i | \(-0.628103\pi\) | ||||
−0.391672 | + | 0.920105i | \(0.628103\pi\) | |||||||
\(908\) | −19.7167 | −0.654321 | ||||||||
\(909\) | 54.2657 | 1.79988 | ||||||||
\(910\) | −15.2640 | −0.505995 | ||||||||
\(911\) | 31.6918 | 1.04999 | 0.524997 | − | 0.851104i | \(-0.324066\pi\) | ||||
0.524997 | + | 0.851104i | \(0.324066\pi\) | |||||||
\(912\) | −308.671 | −10.2211 | ||||||||
\(913\) | −6.01882 | −0.199194 | ||||||||
\(914\) | −35.0611 | −1.15972 | ||||||||
\(915\) | −19.7168 | −0.651816 | ||||||||
\(916\) | −30.4974 | −1.00766 | ||||||||
\(917\) | −35.5404 | −1.17365 | ||||||||
\(918\) | 0.135191 | 0.00446196 | ||||||||
\(919\) | 1.57127 | 0.0518316 | 0.0259158 | − | 0.999664i | \(-0.491750\pi\) | ||||
0.0259158 | + | 0.999664i | \(0.491750\pi\) | |||||||
\(920\) | 240.094 | 7.91567 | ||||||||
\(921\) | 11.5205 | 0.379614 | ||||||||
\(922\) | 60.9817 | 2.00832 | ||||||||
\(923\) | 3.50035 | 0.115215 | ||||||||
\(924\) | 46.0110 | 1.51365 | ||||||||
\(925\) | −0.699969 | −0.0230149 | ||||||||
\(926\) | 56.6568 | 1.86186 | ||||||||
\(927\) | 41.0124 | 1.34702 | ||||||||
\(928\) | 54.7616 | 1.79764 | ||||||||
\(929\) | −0.256912 | −0.00842900 | −0.00421450 | − | 0.999991i | \(-0.501342\pi\) | ||||
−0.00421450 | + | 0.999991i | \(0.501342\pi\) | |||||||
\(930\) | 128.704 | 4.22037 | ||||||||
\(931\) | −27.8183 | −0.911707 | ||||||||
\(932\) | −18.7028 | −0.612631 | ||||||||
\(933\) | −43.0133 | −1.40819 | ||||||||
\(934\) | −62.4482 | −2.04337 | ||||||||
\(935\) | −2.06241 | −0.0674482 | ||||||||
\(936\) | −31.3041 | −1.02321 | ||||||||
\(937\) | 38.3170 | 1.25176 | 0.625881 | − | 0.779919i | \(-0.284740\pi\) | ||||
0.625881 | + | 0.779919i | \(0.284740\pi\) | |||||||
\(938\) | −6.25391 | −0.204198 | ||||||||
\(939\) | 51.9685 | 1.69593 | ||||||||
\(940\) | −74.8788 | −2.44228 | ||||||||
\(941\) | 41.8092 | 1.36294 | 0.681471 | − | 0.731845i | \(-0.261340\pi\) | ||||
0.681471 | + | 0.731845i | \(0.261340\pi\) | |||||||
\(942\) | 90.7409 | 2.95650 | ||||||||
\(943\) | 31.7219 | 1.03301 | ||||||||
\(944\) | 80.0763 | 2.60626 | ||||||||
\(945\) | −0.684008 | −0.0222508 | ||||||||
\(946\) | −10.6702 | −0.346919 | ||||||||
\(947\) | −30.1945 | −0.981191 | −0.490595 | − | 0.871388i | \(-0.663221\pi\) | ||||
−0.490595 | + | 0.871388i | \(0.663221\pi\) | |||||||
\(948\) | −121.754 | −3.95439 | ||||||||
\(949\) | −9.13323 | −0.296477 | ||||||||
\(950\) | −77.5068 | −2.51465 | ||||||||
\(951\) | −33.4284 | −1.08399 | ||||||||
\(952\) | −7.09520 | −0.229957 | ||||||||
\(953\) | −0.688318 | −0.0222968 | −0.0111484 | − | 0.999938i | \(-0.503549\pi\) | ||||
−0.0111484 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(954\) | 58.2820 | 1.88695 | ||||||||
\(955\) | 72.5965 | 2.34917 | ||||||||
\(956\) | 65.8590 | 2.13003 | ||||||||
\(957\) | −9.65212 | −0.312009 | ||||||||
\(958\) | −72.6529 | −2.34731 | ||||||||
\(959\) | 15.6278 | 0.504648 | ||||||||
\(960\) | −268.398 | −8.66251 | ||||||||
\(961\) | 10.3811 | 0.334876 | ||||||||
\(962\) | 0.539043 | 0.0173795 | ||||||||
\(963\) | 39.3532 | 1.26814 | ||||||||
\(964\) | 117.538 | 3.78565 | ||||||||
\(965\) | −13.9781 | −0.449969 | ||||||||
\(966\) | −101.340 | −3.26057 | ||||||||
\(967\) | −36.3829 | −1.17000 | −0.584998 | − | 0.811035i | \(-0.698905\pi\) | ||||
−0.584998 | + | 0.811035i | \(0.698905\pi\) | |||||||
\(968\) | 77.2831 | 2.48397 | ||||||||
\(969\) | −7.26282 | −0.233315 | ||||||||
\(970\) | −54.9385 | −1.76397 | ||||||||
\(971\) | −19.8341 | −0.636506 | −0.318253 | − | 0.948006i | \(-0.603096\pi\) | ||||
−0.318253 | + | 0.948006i | \(0.603096\pi\) | |||||||
\(972\) | 124.565 | 3.99541 | ||||||||
\(973\) | −28.9389 | −0.927737 | ||||||||
\(974\) | −63.8726 | −2.04661 | ||||||||
\(975\) | −9.24787 | −0.296169 | ||||||||
\(976\) | 44.6847 | 1.43032 | ||||||||
\(977\) | 25.0471 | 0.801329 | 0.400665 | − | 0.916225i | \(-0.368779\pi\) | ||||
0.400665 | + | 0.916225i | \(0.368779\pi\) | |||||||
\(978\) | −86.1984 | −2.75632 | ||||||||
\(979\) | −17.5188 | −0.559904 | ||||||||
\(980\) | −60.3228 | −1.92694 | ||||||||
\(981\) | −56.9648 | −1.81875 | ||||||||
\(982\) | 58.9757 | 1.88199 | ||||||||
\(983\) | 7.17206 | 0.228753 | 0.114377 | − | 0.993437i | \(-0.463513\pi\) | ||||
0.114377 | + | 0.993437i | \(0.463513\pi\) | |||||||
\(984\) | −96.0920 | −3.06330 | ||||||||
\(985\) | 32.7207 | 1.04257 | ||||||||
\(986\) | 2.30896 | 0.0735321 | ||||||||
\(987\) | 20.3737 | 0.648501 | ||||||||
\(988\) | 44.0379 | 1.40103 | ||||||||
\(989\) | 17.3395 | 0.551363 | ||||||||
\(990\) | 44.9959 | 1.43006 | ||||||||
\(991\) | 14.5637 | 0.462630 | 0.231315 | − | 0.972879i | \(-0.425697\pi\) | ||||
0.231315 | + | 0.972879i | \(0.425697\pi\) | |||||||
\(992\) | −162.774 | −5.16809 | ||||||||
\(993\) | −21.1085 | −0.669857 | ||||||||
\(994\) | −17.3090 | −0.549007 | ||||||||
\(995\) | 34.8887 | 1.10605 | ||||||||
\(996\) | −45.9613 | −1.45634 | ||||||||
\(997\) | 6.17579 | 0.195589 | 0.0977946 | − | 0.995207i | \(-0.468821\pi\) | ||||
0.0977946 | + | 0.995207i | \(0.468821\pi\) | |||||||
\(998\) | −55.2386 | −1.74855 | ||||||||
\(999\) | 0.0241556 | 0.000764249 0 |
(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 | 6029.2.a.b.1.4 | ✓ | 268 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.b.1.4 | ✓ | 268 | 1.1 | even | 1 | trivial |