Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.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: | \(63.9841271397\) |
Analytic rank: | \(0\) |
Dimension: | \(129\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52474 | −1.78526 | −0.892629 | − | 0.450793i | \(-0.851141\pi\) | ||||
−0.892629 | + | 0.450793i | \(0.851141\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.37429 | 2.18714 | ||||||||
\(5\) | −3.85140 | −1.72240 | −0.861198 | − | 0.508269i | \(-0.830285\pi\) | ||||
−0.861198 | + | 0.508269i | \(0.830285\pi\) | |||||||
\(6\) | −2.52474 | −1.03072 | ||||||||
\(7\) | −2.38848 | −0.902761 | −0.451380 | − | 0.892332i | \(-0.649068\pi\) | ||||
−0.451380 | + | 0.892332i | \(0.649068\pi\) | |||||||
\(8\) | −5.99445 | −2.11936 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.72375 | 3.07492 | ||||||||
\(11\) | 2.74060 | 0.826322 | 0.413161 | − | 0.910658i | \(-0.364425\pi\) | ||||
0.413161 | + | 0.910658i | \(0.364425\pi\) | |||||||
\(12\) | 4.37429 | 1.26275 | ||||||||
\(13\) | −3.61293 | −1.00205 | −0.501023 | − | 0.865434i | \(-0.667043\pi\) | ||||
−0.501023 | + | 0.865434i | \(0.667043\pi\) | |||||||
\(14\) | 6.03028 | 1.61166 | ||||||||
\(15\) | −3.85140 | −0.994426 | ||||||||
\(16\) | 6.38582 | 1.59646 | ||||||||
\(17\) | 3.21123 | 0.778838 | 0.389419 | − | 0.921061i | \(-0.372676\pi\) | ||||
0.389419 | + | 0.921061i | \(0.372676\pi\) | |||||||
\(18\) | −2.52474 | −0.595086 | ||||||||
\(19\) | 2.80535 | 0.643592 | 0.321796 | − | 0.946809i | \(-0.395713\pi\) | ||||
0.321796 | + | 0.946809i | \(0.395713\pi\) | |||||||
\(20\) | −16.8471 | −3.76713 | ||||||||
\(21\) | −2.38848 | −0.521209 | ||||||||
\(22\) | −6.91929 | −1.47520 | ||||||||
\(23\) | 6.49753 | 1.35483 | 0.677414 | − | 0.735602i | \(-0.263101\pi\) | ||||
0.677414 | + | 0.735602i | \(0.263101\pi\) | |||||||
\(24\) | −5.99445 | −1.22361 | ||||||||
\(25\) | 9.83324 | 1.96665 | ||||||||
\(26\) | 9.12168 | 1.78891 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −10.4479 | −1.97447 | ||||||||
\(29\) | −8.36138 | −1.55267 | −0.776335 | − | 0.630320i | \(-0.782924\pi\) | ||||
−0.776335 | + | 0.630320i | \(0.782924\pi\) | |||||||
\(30\) | 9.72375 | 1.77531 | ||||||||
\(31\) | 8.59267 | 1.54329 | 0.771645 | − | 0.636054i | \(-0.219434\pi\) | ||||
0.771645 | + | 0.636054i | \(0.219434\pi\) | |||||||
\(32\) | −4.13361 | −0.730726 | ||||||||
\(33\) | 2.74060 | 0.477077 | ||||||||
\(34\) | −8.10750 | −1.39043 | ||||||||
\(35\) | 9.19898 | 1.55491 | ||||||||
\(36\) | 4.37429 | 0.729048 | ||||||||
\(37\) | 7.52532 | 1.23715 | 0.618577 | − | 0.785724i | \(-0.287709\pi\) | ||||
0.618577 | + | 0.785724i | \(0.287709\pi\) | |||||||
\(38\) | −7.08278 | −1.14898 | ||||||||
\(39\) | −3.61293 | −0.578531 | ||||||||
\(40\) | 23.0870 | 3.65037 | ||||||||
\(41\) | −8.06601 | −1.25970 | −0.629850 | − | 0.776717i | \(-0.716884\pi\) | ||||
−0.629850 | + | 0.776717i | \(0.716884\pi\) | |||||||
\(42\) | 6.03028 | 0.930493 | ||||||||
\(43\) | 7.98588 | 1.21783 | 0.608917 | − | 0.793234i | \(-0.291604\pi\) | ||||
0.608917 | + | 0.793234i | \(0.291604\pi\) | |||||||
\(44\) | 11.9882 | 1.80729 | ||||||||
\(45\) | −3.85140 | −0.574132 | ||||||||
\(46\) | −16.4045 | −2.41872 | ||||||||
\(47\) | 0.880568 | 0.128444 | 0.0642220 | − | 0.997936i | \(-0.479543\pi\) | ||||
0.0642220 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(48\) | 6.38582 | 0.921714 | ||||||||
\(49\) | −1.29516 | −0.185023 | ||||||||
\(50\) | −24.8263 | −3.51097 | ||||||||
\(51\) | 3.21123 | 0.449662 | ||||||||
\(52\) | −15.8040 | −2.19162 | ||||||||
\(53\) | −12.0805 | −1.65938 | −0.829691 | − | 0.558222i | \(-0.811484\pi\) | ||||
−0.829691 | + | 0.558222i | \(0.811484\pi\) | |||||||
\(54\) | −2.52474 | −0.343573 | ||||||||
\(55\) | −10.5551 | −1.42325 | ||||||||
\(56\) | 14.3176 | 1.91327 | ||||||||
\(57\) | 2.80535 | 0.371578 | ||||||||
\(58\) | 21.1103 | 2.77192 | ||||||||
\(59\) | 2.81822 | 0.366901 | 0.183451 | − | 0.983029i | \(-0.441273\pi\) | ||||
0.183451 | + | 0.983029i | \(0.441273\pi\) | |||||||
\(60\) | −16.8471 | −2.17495 | ||||||||
\(61\) | −0.790749 | −0.101245 | −0.0506225 | − | 0.998718i | \(-0.516121\pi\) | ||||
−0.0506225 | + | 0.998718i | \(0.516121\pi\) | |||||||
\(62\) | −21.6942 | −2.75517 | ||||||||
\(63\) | −2.38848 | −0.300920 | ||||||||
\(64\) | −2.33537 | −0.291922 | ||||||||
\(65\) | 13.9148 | 1.72592 | ||||||||
\(66\) | −6.91929 | −0.851706 | ||||||||
\(67\) | 1.16645 | 0.142504 | 0.0712521 | − | 0.997458i | \(-0.477301\pi\) | ||||
0.0712521 | + | 0.997458i | \(0.477301\pi\) | |||||||
\(68\) | 14.0468 | 1.70343 | ||||||||
\(69\) | 6.49753 | 0.782210 | ||||||||
\(70\) | −23.2250 | −2.77592 | ||||||||
\(71\) | −13.1614 | −1.56197 | −0.780987 | − | 0.624548i | \(-0.785283\pi\) | ||||
−0.780987 | + | 0.624548i | \(0.785283\pi\) | |||||||
\(72\) | −5.99445 | −0.706453 | ||||||||
\(73\) | 9.47889 | 1.10942 | 0.554710 | − | 0.832044i | \(-0.312829\pi\) | ||||
0.554710 | + | 0.832044i | \(0.312829\pi\) | |||||||
\(74\) | −18.9994 | −2.20864 | ||||||||
\(75\) | 9.83324 | 1.13545 | ||||||||
\(76\) | 12.2714 | 1.40763 | ||||||||
\(77\) | −6.54587 | −0.745971 | ||||||||
\(78\) | 9.12168 | 1.03283 | ||||||||
\(79\) | −3.34001 | −0.375781 | −0.187890 | − | 0.982190i | \(-0.560165\pi\) | ||||
−0.187890 | + | 0.982190i | \(0.560165\pi\) | |||||||
\(80\) | −24.5943 | −2.74973 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.3645 | 2.24889 | ||||||||
\(83\) | 6.64805 | 0.729718 | 0.364859 | − | 0.931063i | \(-0.381117\pi\) | ||||
0.364859 | + | 0.931063i | \(0.381117\pi\) | |||||||
\(84\) | −10.4479 | −1.13996 | ||||||||
\(85\) | −12.3677 | −1.34147 | ||||||||
\(86\) | −20.1622 | −2.17415 | ||||||||
\(87\) | −8.36138 | −0.896435 | ||||||||
\(88\) | −16.4284 | −1.75127 | ||||||||
\(89\) | −6.56077 | −0.695440 | −0.347720 | − | 0.937598i | \(-0.613044\pi\) | ||||
−0.347720 | + | 0.937598i | \(0.613044\pi\) | |||||||
\(90\) | 9.72375 | 1.02497 | ||||||||
\(91\) | 8.62940 | 0.904607 | ||||||||
\(92\) | 28.4220 | 2.96320 | ||||||||
\(93\) | 8.59267 | 0.891018 | ||||||||
\(94\) | −2.22320 | −0.229306 | ||||||||
\(95\) | −10.8045 | −1.10852 | ||||||||
\(96\) | −4.13361 | −0.421885 | ||||||||
\(97\) | 3.51600 | 0.356996 | 0.178498 | − | 0.983940i | \(-0.442876\pi\) | ||||
0.178498 | + | 0.983940i | \(0.442876\pi\) | |||||||
\(98\) | 3.26994 | 0.330314 | ||||||||
\(99\) | 2.74060 | 0.275441 | ||||||||
\(100\) | 43.0134 | 4.30134 | ||||||||
\(101\) | −6.21900 | −0.618814 | −0.309407 | − | 0.950930i | \(-0.600131\pi\) | ||||
−0.309407 | + | 0.950930i | \(0.600131\pi\) | |||||||
\(102\) | −8.10750 | −0.802763 | ||||||||
\(103\) | 0.411627 | 0.0405588 | 0.0202794 | − | 0.999794i | \(-0.493544\pi\) | ||||
0.0202794 | + | 0.999794i | \(0.493544\pi\) | |||||||
\(104\) | 21.6575 | 2.12369 | ||||||||
\(105\) | 9.19898 | 0.897729 | ||||||||
\(106\) | 30.5000 | 2.96243 | ||||||||
\(107\) | −9.11005 | −0.880701 | −0.440351 | − | 0.897826i | \(-0.645146\pi\) | ||||
−0.440351 | + | 0.897826i | \(0.645146\pi\) | |||||||
\(108\) | 4.37429 | 0.420916 | ||||||||
\(109\) | 17.9366 | 1.71802 | 0.859008 | − | 0.511962i | \(-0.171081\pi\) | ||||
0.859008 | + | 0.511962i | \(0.171081\pi\) | |||||||
\(110\) | 26.6489 | 2.54087 | ||||||||
\(111\) | 7.52532 | 0.714272 | ||||||||
\(112\) | −15.2524 | −1.44122 | ||||||||
\(113\) | −4.60725 | −0.433414 | −0.216707 | − | 0.976237i | \(-0.569532\pi\) | ||||
−0.216707 | + | 0.976237i | \(0.569532\pi\) | |||||||
\(114\) | −7.08278 | −0.663363 | ||||||||
\(115\) | −25.0245 | −2.33355 | ||||||||
\(116\) | −36.5751 | −3.39591 | ||||||||
\(117\) | −3.61293 | −0.334015 | ||||||||
\(118\) | −7.11526 | −0.655013 | ||||||||
\(119\) | −7.66996 | −0.703104 | ||||||||
\(120\) | 23.0870 | 2.10754 | ||||||||
\(121\) | −3.48911 | −0.317192 | ||||||||
\(122\) | 1.99643 | 0.180749 | ||||||||
\(123\) | −8.06601 | −0.727288 | ||||||||
\(124\) | 37.5868 | 3.37540 | ||||||||
\(125\) | −18.6147 | −1.66495 | ||||||||
\(126\) | 6.03028 | 0.537220 | ||||||||
\(127\) | −21.6363 | −1.91991 | −0.959956 | − | 0.280152i | \(-0.909615\pi\) | ||||
−0.959956 | + | 0.280152i | \(0.909615\pi\) | |||||||
\(128\) | 14.1634 | 1.25188 | ||||||||
\(129\) | 7.98588 | 0.703117 | ||||||||
\(130\) | −35.1312 | −3.08121 | ||||||||
\(131\) | 2.96309 | 0.258886 | 0.129443 | − | 0.991587i | \(-0.458681\pi\) | ||||
0.129443 | + | 0.991587i | \(0.458681\pi\) | |||||||
\(132\) | 11.9882 | 1.04344 | ||||||||
\(133\) | −6.70053 | −0.581010 | ||||||||
\(134\) | −2.94497 | −0.254407 | ||||||||
\(135\) | −3.85140 | −0.331475 | ||||||||
\(136\) | −19.2496 | −1.65064 | ||||||||
\(137\) | 8.00789 | 0.684160 | 0.342080 | − | 0.939671i | \(-0.388869\pi\) | ||||
0.342080 | + | 0.939671i | \(0.388869\pi\) | |||||||
\(138\) | −16.4045 | −1.39645 | ||||||||
\(139\) | −0.524472 | −0.0444851 | −0.0222425 | − | 0.999753i | \(-0.507081\pi\) | ||||
−0.0222425 | + | 0.999753i | \(0.507081\pi\) | |||||||
\(140\) | 40.2390 | 3.40082 | ||||||||
\(141\) | 0.880568 | 0.0741572 | ||||||||
\(142\) | 33.2291 | 2.78852 | ||||||||
\(143\) | −9.90159 | −0.828012 | ||||||||
\(144\) | 6.38582 | 0.532152 | ||||||||
\(145\) | 32.2030 | 2.67431 | ||||||||
\(146\) | −23.9317 | −1.98060 | ||||||||
\(147\) | −1.29516 | −0.106823 | ||||||||
\(148\) | 32.9179 | 2.70584 | ||||||||
\(149\) | 2.60479 | 0.213393 | 0.106696 | − | 0.994292i | \(-0.465973\pi\) | ||||
0.106696 | + | 0.994292i | \(0.465973\pi\) | |||||||
\(150\) | −24.8263 | −2.02706 | ||||||||
\(151\) | 7.29110 | 0.593342 | 0.296671 | − | 0.954980i | \(-0.404124\pi\) | ||||
0.296671 | + | 0.954980i | \(0.404124\pi\) | |||||||
\(152\) | −16.8165 | −1.36400 | ||||||||
\(153\) | 3.21123 | 0.259613 | ||||||||
\(154\) | 16.5266 | 1.33175 | ||||||||
\(155\) | −33.0938 | −2.65816 | ||||||||
\(156\) | −15.8040 | −1.26533 | ||||||||
\(157\) | −21.9592 | −1.75254 | −0.876269 | − | 0.481823i | \(-0.839975\pi\) | ||||
−0.876269 | + | 0.481823i | \(0.839975\pi\) | |||||||
\(158\) | 8.43265 | 0.670866 | ||||||||
\(159\) | −12.0805 | −0.958045 | ||||||||
\(160\) | 15.9202 | 1.25860 | ||||||||
\(161\) | −15.5192 | −1.22309 | ||||||||
\(162\) | −2.52474 | −0.198362 | ||||||||
\(163\) | −20.0097 | −1.56728 | −0.783639 | − | 0.621217i | \(-0.786639\pi\) | ||||
−0.783639 | + | 0.621217i | \(0.786639\pi\) | |||||||
\(164\) | −35.2831 | −2.75514 | ||||||||
\(165\) | −10.5551 | −0.821716 | ||||||||
\(166\) | −16.7846 | −1.30273 | ||||||||
\(167\) | −18.6278 | −1.44146 | −0.720732 | − | 0.693214i | \(-0.756194\pi\) | ||||
−0.720732 | + | 0.693214i | \(0.756194\pi\) | |||||||
\(168\) | 14.3176 | 1.10463 | ||||||||
\(169\) | 0.0532379 | 0.00409522 | ||||||||
\(170\) | 31.2252 | 2.39486 | ||||||||
\(171\) | 2.80535 | 0.214531 | ||||||||
\(172\) | 34.9325 | 2.66358 | ||||||||
\(173\) | 5.91824 | 0.449955 | 0.224978 | − | 0.974364i | \(-0.427769\pi\) | ||||
0.224978 | + | 0.974364i | \(0.427769\pi\) | |||||||
\(174\) | 21.1103 | 1.60037 | ||||||||
\(175\) | −23.4865 | −1.77541 | ||||||||
\(176\) | 17.5010 | 1.31919 | ||||||||
\(177\) | 2.81822 | 0.211830 | ||||||||
\(178\) | 16.5642 | 1.24154 | ||||||||
\(179\) | 5.05634 | 0.377928 | 0.188964 | − | 0.981984i | \(-0.439487\pi\) | ||||
0.188964 | + | 0.981984i | \(0.439487\pi\) | |||||||
\(180\) | −16.8471 | −1.25571 | ||||||||
\(181\) | −5.51490 | −0.409919 | −0.204960 | − | 0.978770i | \(-0.565706\pi\) | ||||
−0.204960 | + | 0.978770i | \(0.565706\pi\) | |||||||
\(182\) | −21.7870 | −1.61496 | ||||||||
\(183\) | −0.790749 | −0.0584539 | ||||||||
\(184\) | −38.9491 | −2.87136 | ||||||||
\(185\) | −28.9830 | −2.13087 | ||||||||
\(186\) | −21.6942 | −1.59070 | ||||||||
\(187\) | 8.80070 | 0.643571 | ||||||||
\(188\) | 3.85186 | 0.280926 | ||||||||
\(189\) | −2.38848 | −0.173736 | ||||||||
\(190\) | 27.2786 | 1.97900 | ||||||||
\(191\) | 13.0717 | 0.945832 | 0.472916 | − | 0.881107i | \(-0.343201\pi\) | ||||
0.472916 | + | 0.881107i | \(0.343201\pi\) | |||||||
\(192\) | −2.33537 | −0.168541 | ||||||||
\(193\) | 14.0284 | 1.00979 | 0.504893 | − | 0.863182i | \(-0.331532\pi\) | ||||
0.504893 | + | 0.863182i | \(0.331532\pi\) | |||||||
\(194\) | −8.87698 | −0.637330 | ||||||||
\(195\) | 13.9148 | 0.996460 | ||||||||
\(196\) | −5.66540 | −0.404672 | ||||||||
\(197\) | 7.84621 | 0.559020 | 0.279510 | − | 0.960143i | \(-0.409828\pi\) | ||||
0.279510 | + | 0.960143i | \(0.409828\pi\) | |||||||
\(198\) | −6.91929 | −0.491733 | ||||||||
\(199\) | −14.8347 | −1.05160 | −0.525800 | − | 0.850608i | \(-0.676234\pi\) | ||||
−0.525800 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(200\) | −58.9449 | −4.16803 | ||||||||
\(201\) | 1.16645 | 0.0822748 | ||||||||
\(202\) | 15.7013 | 1.10474 | ||||||||
\(203\) | 19.9710 | 1.40169 | ||||||||
\(204\) | 14.0468 | 0.983476 | ||||||||
\(205\) | 31.0654 | 2.16970 | ||||||||
\(206\) | −1.03925 | −0.0724078 | ||||||||
\(207\) | 6.49753 | 0.451609 | ||||||||
\(208\) | −23.0715 | −1.59972 | ||||||||
\(209\) | 7.68835 | 0.531815 | ||||||||
\(210\) | −23.2250 | −1.60268 | ||||||||
\(211\) | 25.2903 | 1.74105 | 0.870527 | − | 0.492121i | \(-0.163778\pi\) | ||||
0.870527 | + | 0.492121i | \(0.163778\pi\) | |||||||
\(212\) | −52.8435 | −3.62931 | ||||||||
\(213\) | −13.1614 | −0.901806 | ||||||||
\(214\) | 23.0005 | 1.57228 | ||||||||
\(215\) | −30.7568 | −2.09759 | ||||||||
\(216\) | −5.99445 | −0.407871 | ||||||||
\(217\) | −20.5234 | −1.39322 | ||||||||
\(218\) | −45.2852 | −3.06710 | ||||||||
\(219\) | 9.47889 | 0.640524 | ||||||||
\(220\) | −46.1712 | −3.11286 | ||||||||
\(221\) | −11.6019 | −0.780431 | ||||||||
\(222\) | −18.9994 | −1.27516 | ||||||||
\(223\) | 7.46384 | 0.499816 | 0.249908 | − | 0.968270i | \(-0.419600\pi\) | ||||
0.249908 | + | 0.968270i | \(0.419600\pi\) | |||||||
\(224\) | 9.87304 | 0.659670 | ||||||||
\(225\) | 9.83324 | 0.655550 | ||||||||
\(226\) | 11.6321 | 0.773755 | ||||||||
\(227\) | 18.5341 | 1.23015 | 0.615075 | − | 0.788468i | \(-0.289126\pi\) | ||||
0.615075 | + | 0.788468i | \(0.289126\pi\) | |||||||
\(228\) | 12.2714 | 0.812695 | ||||||||
\(229\) | 1.24767 | 0.0824483 | 0.0412241 | − | 0.999150i | \(-0.486874\pi\) | ||||
0.0412241 | + | 0.999150i | \(0.486874\pi\) | |||||||
\(230\) | 63.1803 | 4.16599 | ||||||||
\(231\) | −6.54587 | −0.430687 | ||||||||
\(232\) | 50.1219 | 3.29066 | ||||||||
\(233\) | 24.2907 | 1.59134 | 0.795668 | − | 0.605733i | \(-0.207120\pi\) | ||||
0.795668 | + | 0.605733i | \(0.207120\pi\) | |||||||
\(234\) | 9.12168 | 0.596303 | ||||||||
\(235\) | −3.39142 | −0.221232 | ||||||||
\(236\) | 12.3277 | 0.802466 | ||||||||
\(237\) | −3.34001 | −0.216957 | ||||||||
\(238\) | 19.3646 | 1.25522 | ||||||||
\(239\) | −1.69618 | −0.109716 | −0.0548582 | − | 0.998494i | \(-0.517471\pi\) | ||||
−0.0548582 | + | 0.998494i | \(0.517471\pi\) | |||||||
\(240\) | −24.5943 | −1.58756 | ||||||||
\(241\) | 27.2484 | 1.75522 | 0.877612 | − | 0.479371i | \(-0.159135\pi\) | ||||
0.877612 | + | 0.479371i | \(0.159135\pi\) | |||||||
\(242\) | 8.80908 | 0.566269 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.45897 | −0.221438 | ||||||||
\(245\) | 4.98817 | 0.318683 | ||||||||
\(246\) | 20.3645 | 1.29840 | ||||||||
\(247\) | −10.1355 | −0.644909 | ||||||||
\(248\) | −51.5083 | −3.27078 | ||||||||
\(249\) | 6.64805 | 0.421303 | ||||||||
\(250\) | 46.9973 | 2.97237 | ||||||||
\(251\) | −19.8275 | −1.25150 | −0.625749 | − | 0.780024i | \(-0.715207\pi\) | ||||
−0.625749 | + | 0.780024i | \(0.715207\pi\) | |||||||
\(252\) | −10.4479 | −0.658156 | ||||||||
\(253\) | 17.8071 | 1.11952 | ||||||||
\(254\) | 54.6259 | 3.42754 | ||||||||
\(255\) | −12.3677 | −0.774496 | ||||||||
\(256\) | −31.0881 | −1.94301 | ||||||||
\(257\) | 10.5451 | 0.657786 | 0.328893 | − | 0.944367i | \(-0.393324\pi\) | ||||
0.328893 | + | 0.944367i | \(0.393324\pi\) | |||||||
\(258\) | −20.1622 | −1.25525 | ||||||||
\(259\) | −17.9741 | −1.11685 | ||||||||
\(260\) | 60.8674 | 3.77483 | ||||||||
\(261\) | −8.36138 | −0.517557 | ||||||||
\(262\) | −7.48101 | −0.462178 | ||||||||
\(263\) | 0.231840 | 0.0142959 | 0.00714793 | − | 0.999974i | \(-0.497725\pi\) | ||||
0.00714793 | + | 0.999974i | \(0.497725\pi\) | |||||||
\(264\) | −16.4284 | −1.01110 | ||||||||
\(265\) | 46.5267 | 2.85811 | ||||||||
\(266\) | 16.9171 | 1.03725 | ||||||||
\(267\) | −6.56077 | −0.401513 | ||||||||
\(268\) | 5.10237 | 0.311677 | ||||||||
\(269\) | −7.83423 | −0.477662 | −0.238831 | − | 0.971061i | \(-0.576764\pi\) | ||||
−0.238831 | + | 0.971061i | \(0.576764\pi\) | |||||||
\(270\) | 9.72375 | 0.591769 | ||||||||
\(271\) | 5.91309 | 0.359195 | 0.179597 | − | 0.983740i | \(-0.442521\pi\) | ||||
0.179597 | + | 0.983740i | \(0.442521\pi\) | |||||||
\(272\) | 20.5063 | 1.24338 | ||||||||
\(273\) | 8.62940 | 0.522275 | ||||||||
\(274\) | −20.2178 | −1.22140 | ||||||||
\(275\) | 26.9490 | 1.62509 | ||||||||
\(276\) | 28.4220 | 1.71081 | ||||||||
\(277\) | 24.5162 | 1.47304 | 0.736518 | − | 0.676418i | \(-0.236469\pi\) | ||||
0.736518 | + | 0.676418i | \(0.236469\pi\) | |||||||
\(278\) | 1.32415 | 0.0794174 | ||||||||
\(279\) | 8.59267 | 0.514430 | ||||||||
\(280\) | −55.1428 | −3.29541 | ||||||||
\(281\) | 12.0700 | 0.720034 | 0.360017 | − | 0.932946i | \(-0.382771\pi\) | ||||
0.360017 | + | 0.932946i | \(0.382771\pi\) | |||||||
\(282\) | −2.22320 | −0.132390 | ||||||||
\(283\) | −24.9156 | −1.48108 | −0.740539 | − | 0.672013i | \(-0.765430\pi\) | ||||
−0.740539 | + | 0.672013i | \(0.765430\pi\) | |||||||
\(284\) | −57.5718 | −3.41626 | ||||||||
\(285\) | −10.8045 | −0.640005 | ||||||||
\(286\) | 24.9989 | 1.47822 | ||||||||
\(287\) | 19.2655 | 1.13721 | ||||||||
\(288\) | −4.13361 | −0.243575 | ||||||||
\(289\) | −6.68801 | −0.393412 | ||||||||
\(290\) | −81.3040 | −4.77434 | ||||||||
\(291\) | 3.51600 | 0.206112 | ||||||||
\(292\) | 41.4634 | 2.42646 | ||||||||
\(293\) | 3.10159 | 0.181197 | 0.0905986 | − | 0.995887i | \(-0.471122\pi\) | ||||
0.0905986 | + | 0.995887i | \(0.471122\pi\) | |||||||
\(294\) | 3.26994 | 0.190707 | ||||||||
\(295\) | −10.8541 | −0.631949 | ||||||||
\(296\) | −45.1101 | −2.62197 | ||||||||
\(297\) | 2.74060 | 0.159026 | ||||||||
\(298\) | −6.57641 | −0.380961 | ||||||||
\(299\) | −23.4751 | −1.35760 | ||||||||
\(300\) | 43.0134 | 2.48338 | ||||||||
\(301\) | −19.0741 | −1.09941 | ||||||||
\(302\) | −18.4081 | −1.05927 | ||||||||
\(303\) | −6.21900 | −0.357272 | ||||||||
\(304\) | 17.9145 | 1.02747 | ||||||||
\(305\) | 3.04549 | 0.174384 | ||||||||
\(306\) | −8.10750 | −0.463475 | ||||||||
\(307\) | −0.768827 | −0.0438793 | −0.0219396 | − | 0.999759i | \(-0.506984\pi\) | ||||
−0.0219396 | + | 0.999759i | \(0.506984\pi\) | |||||||
\(308\) | −28.6335 | −1.63155 | ||||||||
\(309\) | 0.411627 | 0.0234166 | ||||||||
\(310\) | 83.5530 | 4.74549 | ||||||||
\(311\) | −33.1149 | −1.87778 | −0.938888 | − | 0.344222i | \(-0.888143\pi\) | ||||
−0.938888 | + | 0.344222i | \(0.888143\pi\) | |||||||
\(312\) | 21.6575 | 1.22611 | ||||||||
\(313\) | 10.3270 | 0.583714 | 0.291857 | − | 0.956462i | \(-0.405727\pi\) | ||||
0.291857 | + | 0.956462i | \(0.405727\pi\) | |||||||
\(314\) | 55.4412 | 3.12873 | ||||||||
\(315\) | 9.19898 | 0.518304 | ||||||||
\(316\) | −14.6102 | −0.821887 | ||||||||
\(317\) | 22.8529 | 1.28355 | 0.641773 | − | 0.766894i | \(-0.278199\pi\) | ||||
0.641773 | + | 0.766894i | \(0.278199\pi\) | |||||||
\(318\) | 30.5000 | 1.71036 | ||||||||
\(319\) | −22.9152 | −1.28301 | ||||||||
\(320\) | 8.99445 | 0.502805 | ||||||||
\(321\) | −9.11005 | −0.508473 | ||||||||
\(322\) | 39.1819 | 2.18352 | ||||||||
\(323\) | 9.00863 | 0.501254 | ||||||||
\(324\) | 4.37429 | 0.243016 | ||||||||
\(325\) | −35.5268 | −1.97067 | ||||||||
\(326\) | 50.5191 | 2.79799 | ||||||||
\(327\) | 17.9366 | 0.991897 | ||||||||
\(328\) | 48.3513 | 2.66975 | ||||||||
\(329\) | −2.10322 | −0.115954 | ||||||||
\(330\) | 26.6489 | 1.46697 | ||||||||
\(331\) | 24.8871 | 1.36792 | 0.683961 | − | 0.729519i | \(-0.260256\pi\) | ||||
0.683961 | + | 0.729519i | \(0.260256\pi\) | |||||||
\(332\) | 29.0805 | 1.59600 | ||||||||
\(333\) | 7.52532 | 0.412385 | ||||||||
\(334\) | 47.0303 | 2.57338 | ||||||||
\(335\) | −4.49245 | −0.245449 | ||||||||
\(336\) | −15.2524 | −0.832087 | ||||||||
\(337\) | 15.1339 | 0.824397 | 0.412199 | − | 0.911094i | \(-0.364761\pi\) | ||||
0.412199 | + | 0.911094i | \(0.364761\pi\) | |||||||
\(338\) | −0.134412 | −0.00731103 | ||||||||
\(339\) | −4.60725 | −0.250232 | ||||||||
\(340\) | −54.0999 | −2.93398 | ||||||||
\(341\) | 23.5491 | 1.27525 | ||||||||
\(342\) | −7.08278 | −0.382993 | ||||||||
\(343\) | 19.8128 | 1.06979 | ||||||||
\(344\) | −47.8709 | −2.58103 | ||||||||
\(345\) | −25.0245 | −1.34728 | ||||||||
\(346\) | −14.9420 | −0.803286 | ||||||||
\(347\) | 34.4242 | 1.84799 | 0.923995 | − | 0.382405i | \(-0.124904\pi\) | ||||
0.923995 | + | 0.382405i | \(0.124904\pi\) | |||||||
\(348\) | −36.5751 | −1.96063 | ||||||||
\(349\) | 15.8342 | 0.847585 | 0.423792 | − | 0.905759i | \(-0.360699\pi\) | ||||
0.423792 | + | 0.905759i | \(0.360699\pi\) | |||||||
\(350\) | 59.2972 | 3.16957 | ||||||||
\(351\) | −3.61293 | −0.192844 | ||||||||
\(352\) | −11.3286 | −0.603815 | ||||||||
\(353\) | −32.5921 | −1.73470 | −0.867351 | − | 0.497697i | \(-0.834179\pi\) | ||||
−0.867351 | + | 0.497697i | \(0.834179\pi\) | |||||||
\(354\) | −7.11526 | −0.378172 | ||||||||
\(355\) | 50.6898 | 2.69034 | ||||||||
\(356\) | −28.6987 | −1.52103 | ||||||||
\(357\) | −7.66996 | −0.405937 | ||||||||
\(358\) | −12.7659 | −0.674699 | ||||||||
\(359\) | 16.6471 | 0.878601 | 0.439300 | − | 0.898340i | \(-0.355226\pi\) | ||||
0.439300 | + | 0.898340i | \(0.355226\pi\) | |||||||
\(360\) | 23.0870 | 1.21679 | ||||||||
\(361\) | −11.1300 | −0.585789 | ||||||||
\(362\) | 13.9237 | 0.731811 | ||||||||
\(363\) | −3.48911 | −0.183131 | ||||||||
\(364\) | 37.7475 | 1.97851 | ||||||||
\(365\) | −36.5069 | −1.91086 | ||||||||
\(366\) | 1.99643 | 0.104355 | ||||||||
\(367\) | 12.7814 | 0.667181 | 0.333591 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333591 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(368\) | 41.4920 | 2.16292 | ||||||||
\(369\) | −8.06601 | −0.419900 | ||||||||
\(370\) | 73.1743 | 3.80415 | ||||||||
\(371\) | 28.8540 | 1.49803 | ||||||||
\(372\) | 37.5868 | 1.94879 | ||||||||
\(373\) | −3.54559 | −0.183584 | −0.0917918 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917918 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(374\) | −22.2194 | −1.14894 | ||||||||
\(375\) | −18.6147 | −0.961261 | ||||||||
\(376\) | −5.27852 | −0.272219 | ||||||||
\(377\) | 30.2091 | 1.55585 | ||||||||
\(378\) | 6.03028 | 0.310164 | ||||||||
\(379\) | −13.3756 | −0.687059 | −0.343529 | − | 0.939142i | \(-0.611622\pi\) | ||||
−0.343529 | + | 0.939142i | \(0.611622\pi\) | |||||||
\(380\) | −47.2621 | −2.42449 | ||||||||
\(381\) | −21.6363 | −1.10846 | ||||||||
\(382\) | −33.0025 | −1.68855 | ||||||||
\(383\) | 3.25206 | 0.166172 | 0.0830862 | − | 0.996542i | \(-0.473522\pi\) | ||||
0.0830862 | + | 0.996542i | \(0.473522\pi\) | |||||||
\(384\) | 14.1634 | 0.722774 | ||||||||
\(385\) | 25.2107 | 1.28486 | ||||||||
\(386\) | −35.4180 | −1.80273 | ||||||||
\(387\) | 7.98588 | 0.405945 | ||||||||
\(388\) | 15.3800 | 0.780802 | ||||||||
\(389\) | 4.81363 | 0.244061 | 0.122030 | − | 0.992526i | \(-0.461059\pi\) | ||||
0.122030 | + | 0.992526i | \(0.461059\pi\) | |||||||
\(390\) | −35.1312 | −1.77894 | ||||||||
\(391\) | 20.8650 | 1.05519 | ||||||||
\(392\) | 7.76377 | 0.392130 | ||||||||
\(393\) | 2.96309 | 0.149468 | ||||||||
\(394\) | −19.8096 | −0.997994 | ||||||||
\(395\) | 12.8637 | 0.647244 | ||||||||
\(396\) | 11.9882 | 0.602428 | ||||||||
\(397\) | 39.3519 | 1.97501 | 0.987507 | − | 0.157578i | \(-0.0503684\pi\) | ||||
0.987507 | + | 0.157578i | \(0.0503684\pi\) | |||||||
\(398\) | 37.4536 | 1.87738 | ||||||||
\(399\) | −6.70053 | −0.335446 | ||||||||
\(400\) | 62.7933 | 3.13967 | ||||||||
\(401\) | −17.1791 | −0.857882 | −0.428941 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428941 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(402\) | −2.94497 | −0.146882 | ||||||||
\(403\) | −31.0447 | −1.54645 | ||||||||
\(404\) | −27.2037 | −1.35343 | ||||||||
\(405\) | −3.85140 | −0.191377 | ||||||||
\(406\) | −50.4215 | −2.50238 | ||||||||
\(407\) | 20.6239 | 1.02229 | ||||||||
\(408\) | −19.2496 | −0.952995 | ||||||||
\(409\) | 10.3295 | 0.510761 | 0.255380 | − | 0.966841i | \(-0.417799\pi\) | ||||
0.255380 | + | 0.966841i | \(0.417799\pi\) | |||||||
\(410\) | −78.4319 | −3.87348 | ||||||||
\(411\) | 8.00789 | 0.395000 | ||||||||
\(412\) | 1.80057 | 0.0887079 | ||||||||
\(413\) | −6.73127 | −0.331224 | ||||||||
\(414\) | −16.4045 | −0.806239 | ||||||||
\(415\) | −25.6042 | −1.25686 | ||||||||
\(416\) | 14.9344 | 0.732220 | ||||||||
\(417\) | −0.524472 | −0.0256835 | ||||||||
\(418\) | −19.4111 | −0.949426 | ||||||||
\(419\) | −19.8726 | −0.970842 | −0.485421 | − | 0.874280i | \(-0.661334\pi\) | ||||
−0.485421 | + | 0.874280i | \(0.661334\pi\) | |||||||
\(420\) | 40.2390 | 1.96346 | ||||||||
\(421\) | −3.97384 | −0.193673 | −0.0968365 | − | 0.995300i | \(-0.530872\pi\) | ||||
−0.0968365 | + | 0.995300i | \(0.530872\pi\) | |||||||
\(422\) | −63.8512 | −3.10823 | ||||||||
\(423\) | 0.880568 | 0.0428147 | ||||||||
\(424\) | 72.4159 | 3.51683 | ||||||||
\(425\) | 31.5768 | 1.53170 | ||||||||
\(426\) | 33.2291 | 1.60996 | ||||||||
\(427\) | 1.88869 | 0.0914001 | ||||||||
\(428\) | −39.8500 | −1.92622 | ||||||||
\(429\) | −9.90159 | −0.478053 | ||||||||
\(430\) | 77.6527 | 3.74475 | ||||||||
\(431\) | −25.5888 | −1.23257 | −0.616284 | − | 0.787524i | \(-0.711363\pi\) | ||||
−0.616284 | + | 0.787524i | \(0.711363\pi\) | |||||||
\(432\) | 6.38582 | 0.307238 | ||||||||
\(433\) | −9.55417 | −0.459144 | −0.229572 | − | 0.973292i | \(-0.573733\pi\) | ||||
−0.229572 | + | 0.973292i | \(0.573733\pi\) | |||||||
\(434\) | 51.8162 | 2.48726 | ||||||||
\(435\) | 32.2030 | 1.54402 | ||||||||
\(436\) | 78.4599 | 3.75755 | ||||||||
\(437\) | 18.2279 | 0.871957 | ||||||||
\(438\) | −23.9317 | −1.14350 | ||||||||
\(439\) | −0.00249176 | −0.000118925 0 | −5.94627e−5 | − | 1.00000i | \(-0.500019\pi\) | ||||
−5.94627e−5 | 1.00000i | \(0.500019\pi\) | ||||||||
\(440\) | 63.2722 | 3.01638 | ||||||||
\(441\) | −1.29516 | −0.0616743 | ||||||||
\(442\) | 29.2918 | 1.39327 | ||||||||
\(443\) | 29.2953 | 1.39186 | 0.695932 | − | 0.718108i | \(-0.254992\pi\) | ||||
0.695932 | + | 0.718108i | \(0.254992\pi\) | |||||||
\(444\) | 32.9179 | 1.56222 | ||||||||
\(445\) | 25.2681 | 1.19782 | ||||||||
\(446\) | −18.8442 | −0.892299 | ||||||||
\(447\) | 2.60479 | 0.123202 | ||||||||
\(448\) | 5.57800 | 0.263536 | ||||||||
\(449\) | −5.95252 | −0.280917 | −0.140458 | − | 0.990087i | \(-0.544858\pi\) | ||||
−0.140458 | + | 0.990087i | \(0.544858\pi\) | |||||||
\(450\) | −24.8263 | −1.17032 | ||||||||
\(451\) | −22.1057 | −1.04092 | ||||||||
\(452\) | −20.1535 | −0.947939 | ||||||||
\(453\) | 7.29110 | 0.342566 | ||||||||
\(454\) | −46.7937 | −2.19613 | ||||||||
\(455\) | −33.2352 | −1.55809 | ||||||||
\(456\) | −16.8165 | −0.787507 | ||||||||
\(457\) | −12.5805 | −0.588492 | −0.294246 | − | 0.955730i | \(-0.595068\pi\) | ||||
−0.294246 | + | 0.955730i | \(0.595068\pi\) | |||||||
\(458\) | −3.15003 | −0.147191 | ||||||||
\(459\) | 3.21123 | 0.149887 | ||||||||
\(460\) | −109.465 | −5.10381 | ||||||||
\(461\) | 28.7592 | 1.33945 | 0.669725 | − | 0.742610i | \(-0.266412\pi\) | ||||
0.669725 | + | 0.742610i | \(0.266412\pi\) | |||||||
\(462\) | 16.5266 | 0.768887 | ||||||||
\(463\) | −6.23576 | −0.289800 | −0.144900 | − | 0.989446i | \(-0.546286\pi\) | ||||
−0.144900 | + | 0.989446i | \(0.546286\pi\) | |||||||
\(464\) | −53.3943 | −2.47877 | ||||||||
\(465\) | −33.0938 | −1.53469 | ||||||||
\(466\) | −61.3276 | −2.84094 | ||||||||
\(467\) | −24.1476 | −1.11742 | −0.558709 | − | 0.829364i | \(-0.688703\pi\) | ||||
−0.558709 | + | 0.829364i | \(0.688703\pi\) | |||||||
\(468\) | −15.8040 | −0.730539 | ||||||||
\(469\) | −2.78603 | −0.128647 | ||||||||
\(470\) | 8.56243 | 0.394955 | ||||||||
\(471\) | −21.9592 | −1.01183 | ||||||||
\(472\) | −16.8937 | −0.777595 | ||||||||
\(473\) | 21.8861 | 1.00632 | ||||||||
\(474\) | 8.43265 | 0.387324 | ||||||||
\(475\) | 27.5857 | 1.26572 | ||||||||
\(476\) | −33.5506 | −1.53779 | ||||||||
\(477\) | −12.0805 | −0.553128 | ||||||||
\(478\) | 4.28239 | 0.195872 | ||||||||
\(479\) | −19.1698 | −0.875893 | −0.437946 | − | 0.899001i | \(-0.644294\pi\) | ||||
−0.437946 | + | 0.899001i | \(0.644294\pi\) | |||||||
\(480\) | 15.9202 | 0.726653 | ||||||||
\(481\) | −27.1884 | −1.23969 | ||||||||
\(482\) | −68.7950 | −3.13353 | ||||||||
\(483\) | −15.5192 | −0.706149 | ||||||||
\(484\) | −15.2624 | −0.693744 | ||||||||
\(485\) | −13.5415 | −0.614889 | ||||||||
\(486\) | −2.52474 | −0.114524 | ||||||||
\(487\) | −22.1688 | −1.00456 | −0.502281 | − | 0.864704i | \(-0.667506\pi\) | ||||
−0.502281 | + | 0.864704i | \(0.667506\pi\) | |||||||
\(488\) | 4.74011 | 0.214575 | ||||||||
\(489\) | −20.0097 | −0.904868 | ||||||||
\(490\) | −12.5938 | −0.568931 | ||||||||
\(491\) | 7.63490 | 0.344558 | 0.172279 | − | 0.985048i | \(-0.444887\pi\) | ||||
0.172279 | + | 0.985048i | \(0.444887\pi\) | |||||||
\(492\) | −35.2831 | −1.59068 | ||||||||
\(493\) | −26.8503 | −1.20928 | ||||||||
\(494\) | 25.5895 | 1.15133 | ||||||||
\(495\) | −10.5551 | −0.474418 | ||||||||
\(496\) | 54.8712 | 2.46379 | ||||||||
\(497\) | 31.4358 | 1.41009 | ||||||||
\(498\) | −16.7846 | −0.752134 | ||||||||
\(499\) | −14.9648 | −0.669918 | −0.334959 | − | 0.942233i | \(-0.608722\pi\) | ||||
−0.334959 | + | 0.942233i | \(0.608722\pi\) | |||||||
\(500\) | −81.4262 | −3.64149 | ||||||||
\(501\) | −18.6278 | −0.832229 | ||||||||
\(502\) | 50.0591 | 2.23425 | ||||||||
\(503\) | 33.3017 | 1.48485 | 0.742425 | − | 0.669929i | \(-0.233676\pi\) | ||||
0.742425 | + | 0.669929i | \(0.233676\pi\) | |||||||
\(504\) | 14.3176 | 0.637758 | ||||||||
\(505\) | 23.9518 | 1.06584 | ||||||||
\(506\) | −44.9583 | −1.99864 | ||||||||
\(507\) | 0.0532379 | 0.00236438 | ||||||||
\(508\) | −94.6434 | −4.19912 | ||||||||
\(509\) | −8.99566 | −0.398725 | −0.199363 | − | 0.979926i | \(-0.563887\pi\) | ||||
−0.199363 | + | 0.979926i | \(0.563887\pi\) | |||||||
\(510\) | 31.2252 | 1.38268 | ||||||||
\(511\) | −22.6401 | −1.00154 | ||||||||
\(512\) | 50.1625 | 2.21689 | ||||||||
\(513\) | 2.80535 | 0.123859 | ||||||||
\(514\) | −26.6236 | −1.17432 | ||||||||
\(515\) | −1.58534 | −0.0698583 | ||||||||
\(516\) | 34.9325 | 1.53782 | ||||||||
\(517\) | 2.41329 | 0.106136 | ||||||||
\(518\) | 45.3798 | 1.99387 | ||||||||
\(519\) | 5.91824 | 0.259782 | ||||||||
\(520\) | −83.4116 | −3.65784 | ||||||||
\(521\) | 13.4879 | 0.590914 | 0.295457 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295457 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(522\) | 21.1103 | 0.923972 | ||||||||
\(523\) | −4.89434 | −0.214015 | −0.107007 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107007 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(524\) | 12.9614 | 0.566221 | ||||||||
\(525\) | −23.4865 | −1.02504 | ||||||||
\(526\) | −0.585334 | −0.0255218 | ||||||||
\(527\) | 27.5930 | 1.20197 | ||||||||
\(528\) | 17.5010 | 0.761632 | ||||||||
\(529\) | 19.2178 | 0.835558 | ||||||||
\(530\) | −117.468 | −5.10247 | ||||||||
\(531\) | 2.81822 | 0.122300 | ||||||||
\(532\) | −29.3101 | −1.27075 | ||||||||
\(533\) | 29.1419 | 1.26228 | ||||||||
\(534\) | 16.5642 | 0.716803 | ||||||||
\(535\) | 35.0864 | 1.51692 | ||||||||
\(536\) | −6.99220 | −0.302017 | ||||||||
\(537\) | 5.05634 | 0.218197 | ||||||||
\(538\) | 19.7794 | 0.852749 | ||||||||
\(539\) | −3.54952 | −0.152889 | ||||||||
\(540\) | −16.8471 | −0.724984 | ||||||||
\(541\) | −21.5110 | −0.924830 | −0.462415 | − | 0.886663i | \(-0.653017\pi\) | ||||
−0.462415 | + | 0.886663i | \(0.653017\pi\) | |||||||
\(542\) | −14.9290 | −0.641255 | ||||||||
\(543\) | −5.51490 | −0.236667 | ||||||||
\(544\) | −13.2740 | −0.569117 | ||||||||
\(545\) | −69.0810 | −2.95910 | ||||||||
\(546\) | −21.7870 | −0.932396 | ||||||||
\(547\) | 31.1215 | 1.33066 | 0.665330 | − | 0.746549i | \(-0.268291\pi\) | ||||
0.665330 | + | 0.746549i | \(0.268291\pi\) | |||||||
\(548\) | 35.0288 | 1.49636 | ||||||||
\(549\) | −0.790749 | −0.0337484 | ||||||||
\(550\) | −68.0391 | −2.90120 | ||||||||
\(551\) | −23.4566 | −0.999287 | ||||||||
\(552\) | −38.9491 | −1.65778 | ||||||||
\(553\) | 7.97756 | 0.339240 | ||||||||
\(554\) | −61.8969 | −2.62975 | ||||||||
\(555\) | −28.9830 | −1.23026 | ||||||||
\(556\) | −2.29419 | −0.0972953 | ||||||||
\(557\) | 23.4618 | 0.994110 | 0.497055 | − | 0.867719i | \(-0.334415\pi\) | ||||
0.497055 | + | 0.867719i | \(0.334415\pi\) | |||||||
\(558\) | −21.6942 | −0.918389 | ||||||||
\(559\) | −28.8524 | −1.22033 | ||||||||
\(560\) | 58.7431 | 2.48235 | ||||||||
\(561\) | 8.80070 | 0.371566 | ||||||||
\(562\) | −30.4735 | −1.28545 | ||||||||
\(563\) | 14.2867 | 0.602112 | 0.301056 | − | 0.953607i | \(-0.402661\pi\) | ||||
0.301056 | + | 0.953607i | \(0.402661\pi\) | |||||||
\(564\) | 3.85186 | 0.162192 | ||||||||
\(565\) | 17.7444 | 0.746510 | ||||||||
\(566\) | 62.9053 | 2.64411 | ||||||||
\(567\) | −2.38848 | −0.100307 | ||||||||
\(568\) | 78.8955 | 3.31038 | ||||||||
\(569\) | −21.2898 | −0.892517 | −0.446258 | − | 0.894904i | \(-0.647244\pi\) | ||||
−0.446258 | + | 0.894904i | \(0.647244\pi\) | |||||||
\(570\) | 27.2786 | 1.14257 | ||||||||
\(571\) | 26.9396 | 1.12739 | 0.563694 | − | 0.825984i | \(-0.309380\pi\) | ||||
0.563694 | + | 0.825984i | \(0.309380\pi\) | |||||||
\(572\) | −43.3124 | −1.81098 | ||||||||
\(573\) | 13.0717 | 0.546077 | ||||||||
\(574\) | −48.6403 | −2.03021 | ||||||||
\(575\) | 63.8918 | 2.66447 | ||||||||
\(576\) | −2.33537 | −0.0973073 | ||||||||
\(577\) | 27.4739 | 1.14375 | 0.571877 | − | 0.820340i | \(-0.306216\pi\) | ||||
0.571877 | + | 0.820340i | \(0.306216\pi\) | |||||||
\(578\) | 16.8854 | 0.702342 | ||||||||
\(579\) | 14.0284 | 0.583000 | ||||||||
\(580\) | 140.865 | 5.84911 | ||||||||
\(581\) | −15.8787 | −0.658761 | ||||||||
\(582\) | −8.87698 | −0.367963 | ||||||||
\(583\) | −33.1078 | −1.37118 | ||||||||
\(584\) | −56.8207 | −2.35126 | ||||||||
\(585\) | 13.9148 | 0.575306 | ||||||||
\(586\) | −7.83071 | −0.323483 | ||||||||
\(587\) | −1.34629 | −0.0555672 | −0.0277836 | − | 0.999614i | \(-0.508845\pi\) | ||||
−0.0277836 | + | 0.999614i | \(0.508845\pi\) | |||||||
\(588\) | −5.66540 | −0.233637 | ||||||||
\(589\) | 24.1055 | 0.993249 | ||||||||
\(590\) | 27.4037 | 1.12819 | ||||||||
\(591\) | 7.84621 | 0.322750 | ||||||||
\(592\) | 48.0553 | 1.97506 | ||||||||
\(593\) | 31.7009 | 1.30180 | 0.650901 | − | 0.759163i | \(-0.274391\pi\) | ||||
0.650901 | + | 0.759163i | \(0.274391\pi\) | |||||||
\(594\) | −6.91929 | −0.283902 | ||||||||
\(595\) | 29.5400 | 1.21102 | ||||||||
\(596\) | 11.3941 | 0.466721 | ||||||||
\(597\) | −14.8347 | −0.607142 | ||||||||
\(598\) | 59.2684 | 2.42366 | ||||||||
\(599\) | 24.0642 | 0.983237 | 0.491618 | − | 0.870811i | \(-0.336405\pi\) | ||||
0.491618 | + | 0.870811i | \(0.336405\pi\) | |||||||
\(600\) | −58.9449 | −2.40641 | ||||||||
\(601\) | −44.7671 | −1.82609 | −0.913045 | − | 0.407859i | \(-0.866275\pi\) | ||||
−0.913045 | + | 0.407859i | \(0.866275\pi\) | |||||||
\(602\) | 48.1571 | 1.96274 | ||||||||
\(603\) | 1.16645 | 0.0475014 | ||||||||
\(604\) | 31.8934 | 1.29772 | ||||||||
\(605\) | 13.4379 | 0.546330 | ||||||||
\(606\) | 15.7013 | 0.637823 | ||||||||
\(607\) | −37.6117 | −1.52661 | −0.763305 | − | 0.646038i | \(-0.776425\pi\) | ||||
−0.763305 | + | 0.646038i | \(0.776425\pi\) | |||||||
\(608\) | −11.5962 | −0.470289 | ||||||||
\(609\) | 19.9710 | 0.809266 | ||||||||
\(610\) | −7.68905 | −0.311321 | ||||||||
\(611\) | −3.18143 | −0.128707 | ||||||||
\(612\) | 14.0468 | 0.567810 | ||||||||
\(613\) | −14.6798 | −0.592912 | −0.296456 | − | 0.955047i | \(-0.595805\pi\) | ||||
−0.296456 | + | 0.955047i | \(0.595805\pi\) | |||||||
\(614\) | 1.94108 | 0.0783358 | ||||||||
\(615\) | 31.0654 | 1.25268 | ||||||||
\(616\) | 39.2389 | 1.58098 | ||||||||
\(617\) | 9.57983 | 0.385670 | 0.192835 | − | 0.981231i | \(-0.438232\pi\) | ||||
0.192835 | + | 0.981231i | \(0.438232\pi\) | |||||||
\(618\) | −1.03925 | −0.0418047 | ||||||||
\(619\) | −40.1024 | −1.61185 | −0.805926 | − | 0.592016i | \(-0.798332\pi\) | ||||
−0.805926 | + | 0.592016i | \(0.798332\pi\) | |||||||
\(620\) | −144.762 | −5.81377 | ||||||||
\(621\) | 6.49753 | 0.260737 | ||||||||
\(622\) | 83.6065 | 3.35231 | ||||||||
\(623\) | 15.6703 | 0.627816 | ||||||||
\(624\) | −23.0715 | −0.923599 | ||||||||
\(625\) | 22.5265 | 0.901059 | ||||||||
\(626\) | −26.0728 | −1.04208 | ||||||||
\(627\) | 7.68835 | 0.307043 | ||||||||
\(628\) | −96.0560 | −3.83305 | ||||||||
\(629\) | 24.1655 | 0.963543 | ||||||||
\(630\) | −23.2250 | −0.925306 | ||||||||
\(631\) | 36.7149 | 1.46160 | 0.730799 | − | 0.682593i | \(-0.239148\pi\) | ||||
0.730799 | + | 0.682593i | \(0.239148\pi\) | |||||||
\(632\) | 20.0215 | 0.796414 | ||||||||
\(633\) | 25.2903 | 1.00520 | ||||||||
\(634\) | −57.6975 | −2.29146 | ||||||||
\(635\) | 83.3300 | 3.30685 | ||||||||
\(636\) | −52.8435 | −2.09538 | ||||||||
\(637\) | 4.67932 | 0.185401 | ||||||||
\(638\) | 57.8548 | 2.29050 | ||||||||
\(639\) | −13.1614 | −0.520658 | ||||||||
\(640\) | −54.5489 | −2.15624 | ||||||||
\(641\) | −41.6282 | −1.64422 | −0.822108 | − | 0.569331i | \(-0.807202\pi\) | ||||
−0.822108 | + | 0.569331i | \(0.807202\pi\) | |||||||
\(642\) | 23.0005 | 0.907755 | ||||||||
\(643\) | 7.73847 | 0.305176 | 0.152588 | − | 0.988290i | \(-0.451239\pi\) | ||||
0.152588 | + | 0.988290i | \(0.451239\pi\) | |||||||
\(644\) | −67.8855 | −2.67506 | ||||||||
\(645\) | −30.7568 | −1.21105 | ||||||||
\(646\) | −22.7444 | −0.894867 | ||||||||
\(647\) | 42.9923 | 1.69020 | 0.845101 | − | 0.534607i | \(-0.179540\pi\) | ||||
0.845101 | + | 0.534607i | \(0.179540\pi\) | |||||||
\(648\) | −5.99445 | −0.235484 | ||||||||
\(649\) | 7.72362 | 0.303179 | ||||||||
\(650\) | 89.6957 | 3.51816 | ||||||||
\(651\) | −20.5234 | −0.804376 | ||||||||
\(652\) | −87.5280 | −3.42786 | ||||||||
\(653\) | −43.7821 | −1.71333 | −0.856663 | − | 0.515876i | \(-0.827467\pi\) | ||||
−0.856663 | + | 0.515876i | \(0.827467\pi\) | |||||||
\(654\) | −45.2852 | −1.77079 | ||||||||
\(655\) | −11.4120 | −0.445904 | ||||||||
\(656\) | −51.5081 | −2.01105 | ||||||||
\(657\) | 9.47889 | 0.369807 | ||||||||
\(658\) | 5.31007 | 0.207008 | ||||||||
\(659\) | 35.6241 | 1.38772 | 0.693858 | − | 0.720111i | \(-0.255909\pi\) | ||||
0.693858 | + | 0.720111i | \(0.255909\pi\) | |||||||
\(660\) | −46.1712 | −1.79721 | ||||||||
\(661\) | −10.9606 | −0.426319 | −0.213160 | − | 0.977017i | \(-0.568375\pi\) | ||||
−0.213160 | + | 0.977017i | \(0.568375\pi\) | |||||||
\(662\) | −62.8334 | −2.44209 | ||||||||
\(663\) | −11.6019 | −0.450582 | ||||||||
\(664\) | −39.8514 | −1.54653 | ||||||||
\(665\) | 25.8064 | 1.00073 | ||||||||
\(666\) | −18.9994 | −0.736213 | ||||||||
\(667\) | −54.3283 | −2.10360 | ||||||||
\(668\) | −81.4834 | −3.15269 | ||||||||
\(669\) | 7.46384 | 0.288569 | ||||||||
\(670\) | 11.3422 | 0.438189 | ||||||||
\(671\) | −2.16713 | −0.0836610 | ||||||||
\(672\) | 9.87304 | 0.380861 | ||||||||
\(673\) | 11.8586 | 0.457114 | 0.228557 | − | 0.973531i | \(-0.426599\pi\) | ||||
0.228557 | + | 0.973531i | \(0.426599\pi\) | |||||||
\(674\) | −38.2091 | −1.47176 | ||||||||
\(675\) | 9.83324 | 0.378482 | ||||||||
\(676\) | 0.232878 | 0.00895685 | ||||||||
\(677\) | 32.5221 | 1.24993 | 0.624964 | − | 0.780654i | \(-0.285114\pi\) | ||||
0.624964 | + | 0.780654i | \(0.285114\pi\) | |||||||
\(678\) | 11.6321 | 0.446728 | ||||||||
\(679\) | −8.39791 | −0.322282 | ||||||||
\(680\) | 74.1376 | 2.84305 | ||||||||
\(681\) | 18.5341 | 0.710228 | ||||||||
\(682\) | −59.4552 | −2.27666 | ||||||||
\(683\) | 19.1058 | 0.731065 | 0.365532 | − | 0.930799i | \(-0.380887\pi\) | ||||
0.365532 | + | 0.930799i | \(0.380887\pi\) | |||||||
\(684\) | 12.2714 | 0.469210 | ||||||||
\(685\) | −30.8415 | −1.17839 | ||||||||
\(686\) | −50.0221 | −1.90985 | ||||||||
\(687\) | 1.24767 | 0.0476015 | ||||||||
\(688\) | 50.9964 | 1.94422 | ||||||||
\(689\) | 43.6459 | 1.66278 | ||||||||
\(690\) | 63.1803 | 2.40523 | ||||||||
\(691\) | −29.4203 | −1.11920 | −0.559601 | − | 0.828762i | \(-0.689045\pi\) | ||||
−0.559601 | + | 0.828762i | \(0.689045\pi\) | |||||||
\(692\) | 25.8881 | 0.984117 | ||||||||
\(693\) | −6.54587 | −0.248657 | ||||||||
\(694\) | −86.9121 | −3.29914 | ||||||||
\(695\) | 2.01995 | 0.0766210 | ||||||||
\(696\) | 50.1219 | 1.89987 | ||||||||
\(697\) | −25.9018 | −0.981101 | ||||||||
\(698\) | −39.9771 | −1.51316 | ||||||||
\(699\) | 24.2907 | 0.918758 | ||||||||
\(700\) | −102.737 | −3.88309 | ||||||||
\(701\) | −23.5389 | −0.889053 | −0.444526 | − | 0.895766i | \(-0.646628\pi\) | ||||
−0.444526 | + | 0.895766i | \(0.646628\pi\) | |||||||
\(702\) | 9.12168 | 0.344276 | ||||||||
\(703\) | 21.1112 | 0.796223 | ||||||||
\(704\) | −6.40033 | −0.241221 | ||||||||
\(705\) | −3.39142 | −0.127728 | ||||||||
\(706\) | 82.2864 | 3.09689 | ||||||||
\(707\) | 14.8540 | 0.558641 | ||||||||
\(708\) | 12.3277 | 0.463304 | ||||||||
\(709\) | −32.4617 | −1.21912 | −0.609562 | − | 0.792738i | \(-0.708655\pi\) | ||||
−0.609562 | + | 0.792738i | \(0.708655\pi\) | |||||||
\(710\) | −127.978 | −4.80294 | ||||||||
\(711\) | −3.34001 | −0.125260 | ||||||||
\(712\) | 39.3282 | 1.47389 | ||||||||
\(713\) | 55.8311 | 2.09089 | ||||||||
\(714\) | 19.3646 | 0.724703 | ||||||||
\(715\) | 38.1349 | 1.42617 | ||||||||
\(716\) | 22.1179 | 0.826584 | ||||||||
\(717\) | −1.69618 | −0.0633448 | ||||||||
\(718\) | −42.0295 | −1.56853 | ||||||||
\(719\) | 18.2122 | 0.679200 | 0.339600 | − | 0.940570i | \(-0.389708\pi\) | ||||
0.339600 | + | 0.940570i | \(0.389708\pi\) | |||||||
\(720\) | −24.5943 | −0.916576 | ||||||||
\(721\) | −0.983162 | −0.0366149 | ||||||||
\(722\) | 28.1003 | 1.04578 | ||||||||
\(723\) | 27.2484 | 1.01338 | ||||||||
\(724\) | −24.1238 | −0.896552 | ||||||||
\(725\) | −82.2195 | −3.05356 | ||||||||
\(726\) | 8.80908 | 0.326936 | ||||||||
\(727\) | −34.5138 | −1.28005 | −0.640024 | − | 0.768355i | \(-0.721075\pi\) | ||||
−0.640024 | + | 0.768355i | \(0.721075\pi\) | |||||||
\(728\) | −51.7285 | −1.91719 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 92.1703 | 3.41138 | ||||||||
\(731\) | 25.6445 | 0.948495 | ||||||||
\(732\) | −3.45897 | −0.127847 | ||||||||
\(733\) | 20.3054 | 0.749998 | 0.374999 | − | 0.927025i | \(-0.377643\pi\) | ||||
0.374999 | + | 0.927025i | \(0.377643\pi\) | |||||||
\(734\) | −32.2695 | −1.19109 | ||||||||
\(735\) | 4.98817 | 0.183992 | ||||||||
\(736\) | −26.8582 | −0.990007 | ||||||||
\(737\) | 3.19676 | 0.117754 | ||||||||
\(738\) | 20.3645 | 0.749629 | ||||||||
\(739\) | 44.9274 | 1.65268 | 0.826341 | − | 0.563171i | \(-0.190419\pi\) | ||||
0.826341 | + | 0.563171i | \(0.190419\pi\) | |||||||
\(740\) | −126.780 | −4.66052 | ||||||||
\(741\) | −10.1355 | −0.372338 | ||||||||
\(742\) | −72.8487 | −2.67436 | ||||||||
\(743\) | −43.1160 | −1.58177 | −0.790886 | − | 0.611964i | \(-0.790380\pi\) | ||||
−0.790886 | + | 0.611964i | \(0.790380\pi\) | |||||||
\(744\) | −51.5083 | −1.88839 | ||||||||
\(745\) | −10.0321 | −0.367547 | ||||||||
\(746\) | 8.95167 | 0.327744 | ||||||||
\(747\) | 6.64805 | 0.243239 | ||||||||
\(748\) | 38.4968 | 1.40758 | ||||||||
\(749\) | 21.7592 | 0.795063 | ||||||||
\(750\) | 46.9973 | 1.71610 | ||||||||
\(751\) | 22.4440 | 0.818994 | 0.409497 | − | 0.912311i | \(-0.365704\pi\) | ||||
0.409497 | + | 0.912311i | \(0.365704\pi\) | |||||||
\(752\) | 5.62315 | 0.205055 | ||||||||
\(753\) | −19.8275 | −0.722553 | ||||||||
\(754\) | −76.2699 | −2.77759 | ||||||||
\(755\) | −28.0809 | −1.02197 | ||||||||
\(756\) | −10.4479 | −0.379987 | ||||||||
\(757\) | 18.2227 | 0.662317 | 0.331158 | − | 0.943575i | \(-0.392561\pi\) | ||||
0.331158 | + | 0.943575i | \(0.392561\pi\) | |||||||
\(758\) | 33.7699 | 1.22658 | ||||||||
\(759\) | 17.8071 | 0.646358 | ||||||||
\(760\) | 64.7672 | 2.34935 | ||||||||
\(761\) | 14.4150 | 0.522545 | 0.261272 | − | 0.965265i | \(-0.415858\pi\) | ||||
0.261272 | + | 0.965265i | \(0.415858\pi\) | |||||||
\(762\) | 54.6259 | 1.97889 | ||||||||
\(763\) | −42.8412 | −1.55096 | ||||||||
\(764\) | 57.1792 | 2.06867 | ||||||||
\(765\) | −12.3677 | −0.447156 | ||||||||
\(766\) | −8.21059 | −0.296661 | ||||||||
\(767\) | −10.1820 | −0.367652 | ||||||||
\(768\) | −31.0881 | −1.12180 | ||||||||
\(769\) | −32.4294 | −1.16943 | −0.584717 | − | 0.811237i | \(-0.698794\pi\) | ||||
−0.584717 | + | 0.811237i | \(0.698794\pi\) | |||||||
\(770\) | −63.6504 | −2.29380 | ||||||||
\(771\) | 10.5451 | 0.379773 | ||||||||
\(772\) | 61.3642 | 2.20855 | ||||||||
\(773\) | −37.2204 | −1.33873 | −0.669363 | − | 0.742936i | \(-0.733433\pi\) | ||||
−0.669363 | + | 0.742936i | \(0.733433\pi\) | |||||||
\(774\) | −20.1622 | −0.724716 | ||||||||
\(775\) | 84.4938 | 3.03511 | ||||||||
\(776\) | −21.0765 | −0.756603 | ||||||||
\(777\) | −17.9741 | −0.644817 | ||||||||
\(778\) | −12.1531 | −0.435711 | ||||||||
\(779\) | −22.6280 | −0.810733 | ||||||||
\(780\) | 60.8674 | 2.17940 | ||||||||
\(781\) | −36.0702 | −1.29069 | ||||||||
\(782\) | −52.6787 | −1.88379 | ||||||||
\(783\) | −8.36138 | −0.298812 | ||||||||
\(784\) | −8.27066 | −0.295381 | ||||||||
\(785\) | 84.5737 | 3.01856 | ||||||||
\(786\) | −7.48101 | −0.266839 | ||||||||
\(787\) | 6.68368 | 0.238247 | 0.119124 | − | 0.992879i | \(-0.461992\pi\) | ||||
0.119124 | + | 0.992879i | \(0.461992\pi\) | |||||||
\(788\) | 34.3216 | 1.22266 | ||||||||
\(789\) | 0.231840 | 0.00825372 | ||||||||
\(790\) | −32.4775 | −1.15550 | ||||||||
\(791\) | 11.0043 | 0.391269 | ||||||||
\(792\) | −16.4284 | −0.583757 | ||||||||
\(793\) | 2.85692 | 0.101452 | ||||||||
\(794\) | −99.3530 | −3.52591 | ||||||||
\(795\) | 46.5267 | 1.65013 | ||||||||
\(796\) | −64.8910 | −2.30000 | ||||||||
\(797\) | 47.6171 | 1.68669 | 0.843343 | − | 0.537376i | \(-0.180584\pi\) | ||||
0.843343 | + | 0.537376i | \(0.180584\pi\) | |||||||
\(798\) | 16.9171 | 0.598858 | ||||||||
\(799\) | 2.82771 | 0.100037 | ||||||||
\(800\) | −40.6468 | −1.43708 | ||||||||
\(801\) | −6.56077 | −0.231813 | ||||||||
\(802\) | 43.3726 | 1.53154 | ||||||||
\(803\) | 25.9778 | 0.916738 | ||||||||
\(804\) | 5.10237 | 0.179947 | ||||||||
\(805\) | 59.7706 | 2.10664 | ||||||||
\(806\) | 78.3796 | 2.76080 | ||||||||
\(807\) | −7.83423 | −0.275778 | ||||||||
\(808\) | 37.2795 | 1.31149 | ||||||||
\(809\) | −0.798495 | −0.0280736 | −0.0140368 | − | 0.999901i | \(-0.504468\pi\) | ||||
−0.0140368 | + | 0.999901i | \(0.504468\pi\) | |||||||
\(810\) | 9.72375 | 0.341658 | ||||||||
\(811\) | −3.19469 | −0.112181 | −0.0560904 | − | 0.998426i | \(-0.517863\pi\) | ||||
−0.0560904 | + | 0.998426i | \(0.517863\pi\) | |||||||
\(812\) | 87.3589 | 3.06570 | ||||||||
\(813\) | 5.91309 | 0.207381 | ||||||||
\(814\) | −52.0699 | −1.82505 | ||||||||
\(815\) | 77.0651 | 2.69947 | ||||||||
\(816\) | 20.5063 | 0.717865 | ||||||||
\(817\) | 22.4032 | 0.783789 | ||||||||
\(818\) | −26.0792 | −0.911839 | ||||||||
\(819\) | 8.62940 | 0.301536 | ||||||||
\(820\) | 135.889 | 4.74545 | ||||||||
\(821\) | 30.3215 | 1.05823 | 0.529114 | − | 0.848550i | \(-0.322524\pi\) | ||||
0.529114 | + | 0.848550i | \(0.322524\pi\) | |||||||
\(822\) | −20.2178 | −0.705177 | ||||||||
\(823\) | 23.5609 | 0.821280 | 0.410640 | − | 0.911798i | \(-0.365305\pi\) | ||||
0.410640 | + | 0.911798i | \(0.365305\pi\) | |||||||
\(824\) | −2.46747 | −0.0859585 | ||||||||
\(825\) | 26.9490 | 0.938243 | ||||||||
\(826\) | 16.9947 | 0.591320 | ||||||||
\(827\) | −44.2385 | −1.53832 | −0.769162 | − | 0.639053i | \(-0.779326\pi\) | ||||
−0.769162 | + | 0.639053i | \(0.779326\pi\) | |||||||
\(828\) | 28.4220 | 0.987734 | ||||||||
\(829\) | 13.0384 | 0.452841 | 0.226421 | − | 0.974030i | \(-0.427298\pi\) | ||||
0.226421 | + | 0.974030i | \(0.427298\pi\) | |||||||
\(830\) | 64.6440 | 2.24382 | ||||||||
\(831\) | 24.5162 | 0.850457 | ||||||||
\(832\) | 8.43754 | 0.292519 | ||||||||
\(833\) | −4.15906 | −0.144103 | ||||||||
\(834\) | 1.32415 | 0.0458516 | ||||||||
\(835\) | 71.7431 | 2.48277 | ||||||||
\(836\) | 33.6311 | 1.16315 | ||||||||
\(837\) | 8.59267 | 0.297006 | ||||||||
\(838\) | 50.1732 | 1.73320 | ||||||||
\(839\) | 0.0618721 | 0.00213606 | 0.00106803 | − | 0.999999i | \(-0.499660\pi\) | ||||
0.00106803 | + | 0.999999i | \(0.499660\pi\) | |||||||
\(840\) | −55.1428 | −1.90261 | ||||||||
\(841\) | 40.9128 | 1.41078 | ||||||||
\(842\) | 10.0329 | 0.345756 | ||||||||
\(843\) | 12.0700 | 0.415712 | ||||||||
\(844\) | 110.627 | 3.80793 | ||||||||
\(845\) | −0.205040 | −0.00705360 | ||||||||
\(846\) | −2.22320 | −0.0764352 | ||||||||
\(847\) | 8.33367 | 0.286348 | ||||||||
\(848\) | −77.1438 | −2.64913 | ||||||||
\(849\) | −24.9156 | −0.855101 | ||||||||
\(850\) | −79.7231 | −2.73448 | ||||||||
\(851\) | 48.8960 | 1.67613 | ||||||||
\(852\) | −57.5718 | −1.97238 | ||||||||
\(853\) | 19.2790 | 0.660100 | 0.330050 | − | 0.943963i | \(-0.392934\pi\) | ||||
0.330050 | + | 0.943963i | \(0.392934\pi\) | |||||||
\(854\) | −4.76844 | −0.163173 | ||||||||
\(855\) | −10.8045 | −0.369507 | ||||||||
\(856\) | 54.6097 | 1.86652 | ||||||||
\(857\) | −10.9193 | −0.372998 | −0.186499 | − | 0.982455i | \(-0.559714\pi\) | ||||
−0.186499 | + | 0.982455i | \(0.559714\pi\) | |||||||
\(858\) | 24.9989 | 0.853448 | ||||||||
\(859\) | −45.3113 | −1.54600 | −0.773001 | − | 0.634404i | \(-0.781245\pi\) | ||||
−0.773001 | + | 0.634404i | \(0.781245\pi\) | |||||||
\(860\) | −134.539 | −4.58774 | ||||||||
\(861\) | 19.2655 | 0.656567 | ||||||||
\(862\) | 64.6049 | 2.20045 | ||||||||
\(863\) | 46.3825 | 1.57888 | 0.789439 | − | 0.613829i | \(-0.210372\pi\) | ||||
0.789439 | + | 0.613829i | \(0.210372\pi\) | |||||||
\(864\) | −4.13361 | −0.140628 | ||||||||
\(865\) | −22.7935 | −0.775001 | ||||||||
\(866\) | 24.1218 | 0.819690 | ||||||||
\(867\) | −6.68801 | −0.227137 | ||||||||
\(868\) | −89.7754 | −3.04717 | ||||||||
\(869\) | −9.15364 | −0.310516 | ||||||||
\(870\) | −81.3040 | −2.75647 | ||||||||
\(871\) | −4.21428 | −0.142796 | ||||||||
\(872\) | −107.520 | −3.64109 | ||||||||
\(873\) | 3.51600 | 0.118999 | ||||||||
\(874\) | −46.0205 | −1.55667 | ||||||||
\(875\) | 44.4609 | 1.50305 | ||||||||
\(876\) | 41.4634 | 1.40092 | ||||||||
\(877\) | 25.4440 | 0.859182 | 0.429591 | − | 0.903024i | \(-0.358658\pi\) | ||||
0.429591 | + | 0.903024i | \(0.358658\pi\) | |||||||
\(878\) | 0.00629104 | 0.000212312 0 | ||||||||
\(879\) | 3.10159 | 0.104614 | ||||||||
\(880\) | −67.4032 | −2.27216 | ||||||||
\(881\) | 24.5084 | 0.825708 | 0.412854 | − | 0.910797i | \(-0.364532\pi\) | ||||
0.412854 | + | 0.910797i | \(0.364532\pi\) | |||||||
\(882\) | 3.26994 | 0.110105 | ||||||||
\(883\) | −22.4176 | −0.754411 | −0.377206 | − | 0.926130i | \(-0.623115\pi\) | ||||
−0.377206 | + | 0.926130i | \(0.623115\pi\) | |||||||
\(884\) | −50.7502 | −1.70691 | ||||||||
\(885\) | −10.8541 | −0.364856 | ||||||||
\(886\) | −73.9630 | −2.48483 | ||||||||
\(887\) | −1.72541 | −0.0579337 | −0.0289669 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289669 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(888\) | −45.1101 | −1.51380 | ||||||||
\(889\) | 51.6779 | 1.73322 | ||||||||
\(890\) | −63.7953 | −2.13842 | ||||||||
\(891\) | 2.74060 | 0.0918136 | ||||||||
\(892\) | 32.6490 | 1.09317 | ||||||||
\(893\) | 2.47030 | 0.0826656 | ||||||||
\(894\) | −6.57641 | −0.219948 | ||||||||
\(895\) | −19.4739 | −0.650942 | ||||||||
\(896\) | −33.8291 | −1.13015 | ||||||||
\(897\) | −23.4751 | −0.783810 | ||||||||
\(898\) | 15.0285 | 0.501509 | ||||||||
\(899\) | −71.8466 | −2.39622 | ||||||||
\(900\) | 43.0134 | 1.43378 | ||||||||
\(901\) | −38.7932 | −1.29239 | ||||||||
\(902\) | 55.8111 | 1.85831 | ||||||||
\(903\) | −19.0741 | −0.634747 | ||||||||
\(904\) | 27.6179 | 0.918559 | ||||||||
\(905\) | 21.2401 | 0.706043 | ||||||||
\(906\) | −18.4081 | −0.611568 | ||||||||
\(907\) | −41.9545 | −1.39308 | −0.696538 | − | 0.717520i | \(-0.745277\pi\) | ||||
−0.696538 | + | 0.717520i | \(0.745277\pi\) | |||||||
\(908\) | 81.0734 | 2.69052 | ||||||||
\(909\) | −6.21900 | −0.206271 | ||||||||
\(910\) | 83.9102 | 2.78160 | ||||||||
\(911\) | −11.2720 | −0.373458 | −0.186729 | − | 0.982412i | \(-0.559789\pi\) | ||||
−0.186729 | + | 0.982412i | \(0.559789\pi\) | |||||||
\(912\) | 17.9145 | 0.593208 | ||||||||
\(913\) | 18.2196 | 0.602982 | ||||||||
\(914\) | 31.7625 | 1.05061 | ||||||||
\(915\) | 3.04549 | 0.100681 | ||||||||
\(916\) | 5.45766 | 0.180326 | ||||||||
\(917\) | −7.07727 | −0.233712 | ||||||||
\(918\) | −8.10750 | −0.267588 | ||||||||
\(919\) | 31.4022 | 1.03586 | 0.517931 | − | 0.855422i | \(-0.326702\pi\) | ||||
0.517931 | + | 0.855422i | \(0.326702\pi\) | |||||||
\(920\) | 150.008 | 4.94563 | ||||||||
\(921\) | −0.768827 | −0.0253337 | ||||||||
\(922\) | −72.6093 | −2.39126 | ||||||||
\(923\) | 47.5512 | 1.56517 | ||||||||
\(924\) | −28.6335 | −0.941974 | ||||||||
\(925\) | 73.9983 | 2.43305 | ||||||||
\(926\) | 15.7436 | 0.517368 | ||||||||
\(927\) | 0.411627 | 0.0135196 | ||||||||
\(928\) | 34.5627 | 1.13458 | ||||||||
\(929\) | −36.6322 | −1.20186 | −0.600931 | − | 0.799301i | \(-0.705203\pi\) | ||||
−0.600931 | + | 0.799301i | \(0.705203\pi\) | |||||||
\(930\) | 83.5530 | 2.73981 | ||||||||
\(931\) | −3.63338 | −0.119079 | ||||||||
\(932\) | 106.254 | 3.48048 | ||||||||
\(933\) | −33.1149 | −1.08413 | ||||||||
\(934\) | 60.9663 | 1.99488 | ||||||||
\(935\) | −33.8950 | −1.10848 | ||||||||
\(936\) | 21.6575 | 0.707898 | ||||||||
\(937\) | −22.0208 | −0.719387 | −0.359694 | − | 0.933070i | \(-0.617119\pi\) | ||||
−0.359694 | + | 0.933070i | \(0.617119\pi\) | |||||||
\(938\) | 7.03400 | 0.229668 | ||||||||
\(939\) | 10.3270 | 0.337008 | ||||||||
\(940\) | −14.8350 | −0.483865 | ||||||||
\(941\) | 42.9991 | 1.40173 | 0.700866 | − | 0.713293i | \(-0.252797\pi\) | ||||
0.700866 | + | 0.713293i | \(0.252797\pi\) | |||||||
\(942\) | 55.4412 | 1.80637 | ||||||||
\(943\) | −52.4091 | −1.70668 | ||||||||
\(944\) | 17.9967 | 0.585741 | ||||||||
\(945\) | 9.19898 | 0.299243 | ||||||||
\(946\) | −55.2566 | −1.79655 | ||||||||
\(947\) | 34.8175 | 1.13142 | 0.565708 | − | 0.824606i | \(-0.308603\pi\) | ||||
0.565708 | + | 0.824606i | \(0.308603\pi\) | |||||||
\(948\) | −14.6102 | −0.474517 | ||||||||
\(949\) | −34.2465 | −1.11169 | ||||||||
\(950\) | −69.6467 | −2.25964 | ||||||||
\(951\) | 22.8529 | 0.741056 | ||||||||
\(952\) | 45.9772 | 1.49013 | ||||||||
\(953\) | −26.7827 | −0.867575 | −0.433788 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433788 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(954\) | 30.5000 | 0.987475 | ||||||||
\(955\) | −50.3441 | −1.62910 | ||||||||
\(956\) | −7.41956 | −0.239966 | ||||||||
\(957\) | −22.9152 | −0.740744 | ||||||||
\(958\) | 48.3988 | 1.56369 | ||||||||
\(959\) | −19.1267 | −0.617633 | ||||||||
\(960\) | 8.99445 | 0.290295 | ||||||||
\(961\) | 42.8340 | 1.38174 | ||||||||
\(962\) | 68.6436 | 2.21316 | ||||||||
\(963\) | −9.11005 | −0.293567 | ||||||||
\(964\) | 119.192 | 3.83893 | ||||||||
\(965\) | −54.0289 | −1.73925 | ||||||||
\(966\) | 39.1819 | 1.26066 | ||||||||
\(967\) | −24.0113 | −0.772153 | −0.386076 | − | 0.922467i | \(-0.626170\pi\) | ||||
−0.386076 | + | 0.922467i | \(0.626170\pi\) | |||||||
\(968\) | 20.9153 | 0.672243 | ||||||||
\(969\) | 9.00863 | 0.289399 | ||||||||
\(970\) | 34.1888 | 1.09773 | ||||||||
\(971\) | 41.3098 | 1.32570 | 0.662848 | − | 0.748754i | \(-0.269348\pi\) | ||||
0.662848 | + | 0.748754i | \(0.269348\pi\) | |||||||
\(972\) | 4.37429 | 0.140305 | ||||||||
\(973\) | 1.25269 | 0.0401594 | ||||||||
\(974\) | 55.9702 | 1.79340 | ||||||||
\(975\) | −35.5268 | −1.13777 | ||||||||
\(976\) | −5.04958 | −0.161633 | ||||||||
\(977\) | 18.2498 | 0.583863 | 0.291932 | − | 0.956439i | \(-0.405702\pi\) | ||||
0.291932 | + | 0.956439i | \(0.405702\pi\) | |||||||
\(978\) | 50.5191 | 1.61542 | ||||||||
\(979\) | −17.9804 | −0.574658 | ||||||||
\(980\) | 21.8197 | 0.697005 | ||||||||
\(981\) | 17.9366 | 0.572672 | ||||||||
\(982\) | −19.2761 | −0.615125 | ||||||||
\(983\) | 38.8201 | 1.23817 | 0.619085 | − | 0.785324i | \(-0.287504\pi\) | ||||
0.619085 | + | 0.785324i | \(0.287504\pi\) | |||||||
\(984\) | 48.3513 | 1.54138 | ||||||||
\(985\) | −30.2189 | −0.962853 | ||||||||
\(986\) | 67.7900 | 2.15887 | ||||||||
\(987\) | −2.10322 | −0.0669462 | ||||||||
\(988\) | −44.3358 | −1.41051 | ||||||||
\(989\) | 51.8884 | 1.64996 | ||||||||
\(990\) | 26.6489 | 0.846958 | ||||||||
\(991\) | 0.0226372 | 0.000719095 0 | 0.000359548 | − | 1.00000i | \(-0.499886\pi\) | ||||
0.000359548 | 1.00000i | \(0.499886\pi\) | ||||||||
\(992\) | −35.5187 | −1.12772 | ||||||||
\(993\) | 24.8871 | 0.789770 | ||||||||
\(994\) | −79.3671 | −2.51737 | ||||||||
\(995\) | 57.1341 | 1.81127 | ||||||||
\(996\) | 29.0805 | 0.921450 | ||||||||
\(997\) | 46.0751 | 1.45921 | 0.729607 | − | 0.683867i | \(-0.239703\pi\) | ||||
0.729607 | + | 0.683867i | \(0.239703\pi\) | |||||||
\(998\) | 37.7822 | 1.19598 | ||||||||
\(999\) | 7.52532 | 0.238091 |
(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 | 8013.2.a.d.1.10 | ✓ | 129 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.d.1.10 | ✓ | 129 | 1.1 | even | 1 | trivial |