Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88369 | −1.33197 | −0.665985 | − | 0.745965i | \(-0.731988\pi\) | ||||
−0.665985 | + | 0.745965i | \(0.731988\pi\) | |||||||
\(3\) | 2.22834 | 1.28653 | 0.643267 | − | 0.765642i | \(-0.277578\pi\) | ||||
0.643267 | + | 0.765642i | \(0.277578\pi\) | |||||||
\(4\) | 1.54829 | 0.774143 | ||||||||
\(5\) | 0.640943 | 0.286639 | 0.143319 | − | 0.989677i | \(-0.454222\pi\) | ||||
0.143319 | + | 0.989677i | \(0.454222\pi\) | |||||||
\(6\) | −4.19751 | −1.71362 | ||||||||
\(7\) | −4.86422 | −1.83850 | −0.919252 | − | 0.393670i | \(-0.871205\pi\) | ||||
−0.919252 | + | 0.393670i | \(0.871205\pi\) | |||||||
\(8\) | 0.850890 | 0.300835 | ||||||||
\(9\) | 1.96551 | 0.655170 | ||||||||
\(10\) | −1.20734 | −0.381794 | ||||||||
\(11\) | 4.50890 | 1.35948 | 0.679742 | − | 0.733452i | \(-0.262092\pi\) | ||||
0.679742 | + | 0.733452i | \(0.262092\pi\) | |||||||
\(12\) | 3.45011 | 0.995961 | ||||||||
\(13\) | −0.00706194 | −0.00195863 | −0.000979315 | − | 1.00000i | \(-0.500312\pi\) | ||||
−0.000979315 | 1.00000i | \(0.500312\pi\) | ||||||||
\(14\) | 9.16269 | 2.44883 | ||||||||
\(15\) | 1.42824 | 0.368770 | ||||||||
\(16\) | −4.69938 | −1.17485 | ||||||||
\(17\) | −6.43690 | −1.56118 | −0.780588 | − | 0.625046i | \(-0.785080\pi\) | ||||
−0.780588 | + | 0.625046i | \(0.785080\pi\) | |||||||
\(18\) | −3.70241 | −0.872667 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.992363 | 0.221899 | ||||||||
\(21\) | −10.8392 | −2.36530 | ||||||||
\(22\) | −8.49336 | −1.81079 | ||||||||
\(23\) | −0.234352 | −0.0488658 | −0.0244329 | − | 0.999701i | \(-0.507778\pi\) | ||||
−0.0244329 | + | 0.999701i | \(0.507778\pi\) | |||||||
\(24\) | 1.89607 | 0.387034 | ||||||||
\(25\) | −4.58919 | −0.917838 | ||||||||
\(26\) | 0.0133025 | 0.00260884 | ||||||||
\(27\) | −2.30520 | −0.443635 | ||||||||
\(28\) | −7.53121 | −1.42326 | ||||||||
\(29\) | 8.13953 | 1.51147 | 0.755736 | − | 0.654876i | \(-0.227279\pi\) | ||||
0.755736 | + | 0.654876i | \(0.227279\pi\) | |||||||
\(30\) | −2.69036 | −0.491191 | ||||||||
\(31\) | 10.5789 | 1.90002 | 0.950011 | − | 0.312217i | \(-0.101072\pi\) | ||||
0.950011 | + | 0.312217i | \(0.101072\pi\) | |||||||
\(32\) | 7.15040 | 1.26402 | ||||||||
\(33\) | 10.0474 | 1.74902 | ||||||||
\(34\) | 12.1251 | 2.07944 | ||||||||
\(35\) | −3.11769 | −0.526986 | ||||||||
\(36\) | 3.04317 | 0.507196 | ||||||||
\(37\) | 1.87236 | 0.307814 | 0.153907 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153907 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(38\) | 1.88369 | 0.305575 | ||||||||
\(39\) | −0.0157364 | −0.00251984 | ||||||||
\(40\) | 0.545372 | 0.0862309 | ||||||||
\(41\) | 0.709329 | 0.110779 | 0.0553893 | − | 0.998465i | \(-0.482360\pi\) | ||||
0.0553893 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(42\) | 20.4176 | 3.15051 | ||||||||
\(43\) | 2.98280 | 0.454873 | 0.227436 | − | 0.973793i | \(-0.426966\pi\) | ||||
0.227436 | + | 0.973793i | \(0.426966\pi\) | |||||||
\(44\) | 6.98106 | 1.05243 | ||||||||
\(45\) | 1.25978 | 0.187797 | ||||||||
\(46\) | 0.441446 | 0.0650877 | ||||||||
\(47\) | −8.81646 | −1.28601 | −0.643006 | − | 0.765861i | \(-0.722313\pi\) | ||||
−0.643006 | + | 0.765861i | \(0.722313\pi\) | |||||||
\(48\) | −10.4718 | −1.51148 | ||||||||
\(49\) | 16.6607 | 2.38010 | ||||||||
\(50\) | 8.64461 | 1.22253 | ||||||||
\(51\) | −14.3436 | −2.00851 | ||||||||
\(52\) | −0.0109339 | −0.00151626 | ||||||||
\(53\) | 6.85127 | 0.941094 | 0.470547 | − | 0.882375i | \(-0.344057\pi\) | ||||
0.470547 | + | 0.882375i | \(0.344057\pi\) | |||||||
\(54\) | 4.34227 | 0.590908 | ||||||||
\(55\) | 2.88995 | 0.389680 | ||||||||
\(56\) | −4.13892 | −0.553086 | ||||||||
\(57\) | −2.22834 | −0.295151 | ||||||||
\(58\) | −15.3323 | −2.01323 | ||||||||
\(59\) | −9.51976 | −1.23937 | −0.619684 | − | 0.784852i | \(-0.712739\pi\) | ||||
−0.619684 | + | 0.784852i | \(0.712739\pi\) | |||||||
\(60\) | 2.21133 | 0.285481 | ||||||||
\(61\) | 2.64579 | 0.338758 | 0.169379 | − | 0.985551i | \(-0.445824\pi\) | ||||
0.169379 | + | 0.985551i | \(0.445824\pi\) | |||||||
\(62\) | −19.9273 | −2.53077 | ||||||||
\(63\) | −9.56069 | −1.20453 | ||||||||
\(64\) | −4.07036 | −0.508795 | ||||||||
\(65\) | −0.00452630 | −0.000561419 0 | ||||||||
\(66\) | −18.9261 | −2.32964 | ||||||||
\(67\) | 5.68863 | 0.694977 | 0.347489 | − | 0.937684i | \(-0.387035\pi\) | ||||
0.347489 | + | 0.937684i | \(0.387035\pi\) | |||||||
\(68\) | −9.96615 | −1.20857 | ||||||||
\(69\) | −0.522217 | −0.0628675 | ||||||||
\(70\) | 5.87276 | 0.701929 | ||||||||
\(71\) | −12.5229 | −1.48620 | −0.743098 | − | 0.669183i | \(-0.766644\pi\) | ||||
−0.743098 | + | 0.669183i | \(0.766644\pi\) | |||||||
\(72\) | 1.67243 | 0.197098 | ||||||||
\(73\) | 3.68045 | 0.430764 | 0.215382 | − | 0.976530i | \(-0.430900\pi\) | ||||
0.215382 | + | 0.976530i | \(0.430900\pi\) | |||||||
\(74\) | −3.52695 | −0.409999 | ||||||||
\(75\) | −10.2263 | −1.18083 | ||||||||
\(76\) | −1.54829 | −0.177601 | ||||||||
\(77\) | −21.9323 | −2.49941 | ||||||||
\(78\) | 0.0296425 | 0.00335636 | ||||||||
\(79\) | −9.08704 | −1.02237 | −0.511186 | − | 0.859470i | \(-0.670794\pi\) | ||||
−0.511186 | + | 0.859470i | \(0.670794\pi\) | |||||||
\(80\) | −3.01204 | −0.336756 | ||||||||
\(81\) | −11.0333 | −1.22592 | ||||||||
\(82\) | −1.33616 | −0.147554 | ||||||||
\(83\) | 10.1242 | 1.11127 | 0.555637 | − | 0.831425i | \(-0.312475\pi\) | ||||
0.555637 | + | 0.831425i | \(0.312475\pi\) | |||||||
\(84\) | −16.7821 | −1.83108 | ||||||||
\(85\) | −4.12568 | −0.447493 | ||||||||
\(86\) | −5.61867 | −0.605876 | ||||||||
\(87\) | 18.1377 | 1.94456 | ||||||||
\(88\) | 3.83657 | 0.408980 | ||||||||
\(89\) | −9.09239 | −0.963791 | −0.481896 | − | 0.876229i | \(-0.660052\pi\) | ||||
−0.481896 | + | 0.876229i | \(0.660052\pi\) | |||||||
\(90\) | −2.37304 | −0.250140 | ||||||||
\(91\) | 0.0343509 | 0.00360095 | ||||||||
\(92\) | −0.362844 | −0.0378291 | ||||||||
\(93\) | 23.5734 | 2.44444 | ||||||||
\(94\) | 16.6075 | 1.71293 | ||||||||
\(95\) | −0.640943 | −0.0657594 | ||||||||
\(96\) | 15.9335 | 1.62621 | ||||||||
\(97\) | −7.06949 | −0.717798 | −0.358899 | − | 0.933376i | \(-0.616848\pi\) | ||||
−0.358899 | + | 0.933376i | \(0.616848\pi\) | |||||||
\(98\) | −31.3835 | −3.17022 | ||||||||
\(99\) | 8.86229 | 0.890693 | ||||||||
\(100\) | −7.10538 | −0.710538 | ||||||||
\(101\) | −11.2418 | −1.11860 | −0.559300 | − | 0.828965i | \(-0.688930\pi\) | ||||
−0.559300 | + | 0.828965i | \(0.688930\pi\) | |||||||
\(102\) | 27.0189 | 2.67527 | ||||||||
\(103\) | −15.7547 | −1.55236 | −0.776179 | − | 0.630513i | \(-0.782845\pi\) | ||||
−0.776179 | + | 0.630513i | \(0.782845\pi\) | |||||||
\(104\) | −0.00600893 | −0.000589224 0 | ||||||||
\(105\) | −6.94729 | −0.677986 | ||||||||
\(106\) | −12.9057 | −1.25351 | ||||||||
\(107\) | 7.79754 | 0.753817 | 0.376908 | − | 0.926251i | \(-0.376987\pi\) | ||||
0.376908 | + | 0.926251i | \(0.376987\pi\) | |||||||
\(108\) | −3.56910 | −0.343437 | ||||||||
\(109\) | −13.6411 | −1.30658 | −0.653289 | − | 0.757108i | \(-0.726611\pi\) | ||||
−0.653289 | + | 0.757108i | \(0.726611\pi\) | |||||||
\(110\) | −5.44376 | −0.519042 | ||||||||
\(111\) | 4.17226 | 0.396014 | ||||||||
\(112\) | 22.8589 | 2.15996 | ||||||||
\(113\) | 0.00537413 | 0.000505555 0 | 0.000252778 | − | 1.00000i | \(-0.499920\pi\) | ||||
0.000252778 | 1.00000i | \(0.499920\pi\) | ||||||||
\(114\) | 4.19751 | 0.393132 | ||||||||
\(115\) | −0.150206 | −0.0140068 | ||||||||
\(116\) | 12.6023 | 1.17010 | ||||||||
\(117\) | −0.0138803 | −0.00128324 | ||||||||
\(118\) | 17.9323 | 1.65080 | ||||||||
\(119\) | 31.3105 | 2.87023 | ||||||||
\(120\) | 1.21528 | 0.110939 | ||||||||
\(121\) | 9.33014 | 0.848194 | ||||||||
\(122\) | −4.98384 | −0.451216 | ||||||||
\(123\) | 1.58063 | 0.142521 | ||||||||
\(124\) | 16.3791 | 1.47089 | ||||||||
\(125\) | −6.14613 | −0.549726 | ||||||||
\(126\) | 18.0094 | 1.60440 | ||||||||
\(127\) | −17.3073 | −1.53577 | −0.767886 | − | 0.640587i | \(-0.778691\pi\) | ||||
−0.767886 | + | 0.640587i | \(0.778691\pi\) | |||||||
\(128\) | −6.63350 | −0.586324 | ||||||||
\(129\) | 6.64670 | 0.585209 | ||||||||
\(130\) | 0.00852615 | 0.000747793 0 | ||||||||
\(131\) | 12.8052 | 1.11880 | 0.559399 | − | 0.828898i | \(-0.311032\pi\) | ||||
0.559399 | + | 0.828898i | \(0.311032\pi\) | |||||||
\(132\) | 15.5562 | 1.35399 | ||||||||
\(133\) | 4.86422 | 0.421782 | ||||||||
\(134\) | −10.7156 | −0.925688 | ||||||||
\(135\) | −1.47750 | −0.127163 | ||||||||
\(136\) | −5.47709 | −0.469656 | ||||||||
\(137\) | −12.9295 | −1.10464 | −0.552321 | − | 0.833632i | \(-0.686258\pi\) | ||||
−0.552321 | + | 0.833632i | \(0.686258\pi\) | |||||||
\(138\) | 0.983694 | 0.0837376 | ||||||||
\(139\) | 16.2582 | 1.37900 | 0.689499 | − | 0.724286i | \(-0.257831\pi\) | ||||
0.689499 | + | 0.724286i | \(0.257831\pi\) | |||||||
\(140\) | −4.82708 | −0.407963 | ||||||||
\(141\) | −19.6461 | −1.65450 | ||||||||
\(142\) | 23.5893 | 1.97957 | ||||||||
\(143\) | −0.0318415 | −0.00266272 | ||||||||
\(144\) | −9.23669 | −0.769724 | ||||||||
\(145\) | 5.21698 | 0.433246 | ||||||||
\(146\) | −6.93282 | −0.573764 | ||||||||
\(147\) | 37.1257 | 3.06208 | ||||||||
\(148\) | 2.89895 | 0.238292 | ||||||||
\(149\) | −9.79216 | −0.802205 | −0.401103 | − | 0.916033i | \(-0.631373\pi\) | ||||
−0.401103 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(150\) | 19.2632 | 1.57283 | ||||||||
\(151\) | 20.4959 | 1.66793 | 0.833966 | − | 0.551816i | \(-0.186065\pi\) | ||||
0.833966 | + | 0.551816i | \(0.186065\pi\) | |||||||
\(152\) | −0.850890 | −0.0690163 | ||||||||
\(153\) | −12.6518 | −1.02284 | ||||||||
\(154\) | 41.3136 | 3.32914 | ||||||||
\(155\) | 6.78046 | 0.544620 | ||||||||
\(156\) | −0.0243645 | −0.00195072 | ||||||||
\(157\) | 6.60026 | 0.526758 | 0.263379 | − | 0.964692i | \(-0.415163\pi\) | ||||
0.263379 | + | 0.964692i | \(0.415163\pi\) | |||||||
\(158\) | 17.1172 | 1.36177 | ||||||||
\(159\) | 15.2670 | 1.21075 | ||||||||
\(160\) | 4.58300 | 0.362318 | ||||||||
\(161\) | 1.13994 | 0.0898399 | ||||||||
\(162\) | 20.7833 | 1.63289 | ||||||||
\(163\) | −19.7074 | −1.54360 | −0.771802 | − | 0.635863i | \(-0.780644\pi\) | ||||
−0.771802 | + | 0.635863i | \(0.780644\pi\) | |||||||
\(164\) | 1.09824 | 0.0857585 | ||||||||
\(165\) | 6.43979 | 0.501337 | ||||||||
\(166\) | −19.0708 | −1.48018 | ||||||||
\(167\) | −17.9528 | −1.38923 | −0.694616 | − | 0.719381i | \(-0.744426\pi\) | ||||
−0.694616 | + | 0.719381i | \(0.744426\pi\) | |||||||
\(168\) | −9.22293 | −0.711564 | ||||||||
\(169\) | −13.0000 | −0.999996 | ||||||||
\(170\) | 7.77151 | 0.596048 | ||||||||
\(171\) | −1.96551 | −0.150306 | ||||||||
\(172\) | 4.61823 | 0.352136 | ||||||||
\(173\) | −17.6545 | −1.34225 | −0.671125 | − | 0.741345i | \(-0.734188\pi\) | ||||
−0.671125 | + | 0.741345i | \(0.734188\pi\) | |||||||
\(174\) | −34.1657 | −2.59010 | ||||||||
\(175\) | 22.3229 | 1.68745 | ||||||||
\(176\) | −21.1890 | −1.59718 | ||||||||
\(177\) | −21.2133 | −1.59449 | ||||||||
\(178\) | 17.1272 | 1.28374 | ||||||||
\(179\) | 9.02938 | 0.674888 | 0.337444 | − | 0.941346i | \(-0.390438\pi\) | ||||
0.337444 | + | 0.941346i | \(0.390438\pi\) | |||||||
\(180\) | 1.95050 | 0.145382 | ||||||||
\(181\) | 1.96760 | 0.146251 | 0.0731255 | − | 0.997323i | \(-0.476703\pi\) | ||||
0.0731255 | + | 0.997323i | \(0.476703\pi\) | |||||||
\(182\) | −0.0647063 | −0.00479635 | ||||||||
\(183\) | 5.89572 | 0.435824 | ||||||||
\(184\) | −0.199408 | −0.0147005 | ||||||||
\(185\) | 1.20008 | 0.0882314 | ||||||||
\(186\) | −44.4049 | −3.25592 | ||||||||
\(187\) | −29.0233 | −2.12239 | ||||||||
\(188\) | −13.6504 | −0.995558 | ||||||||
\(189\) | 11.2130 | 0.815625 | ||||||||
\(190\) | 1.20734 | 0.0875895 | ||||||||
\(191\) | −21.6261 | −1.56481 | −0.782403 | − | 0.622772i | \(-0.786006\pi\) | ||||
−0.782403 | + | 0.622772i | \(0.786006\pi\) | |||||||
\(192\) | −9.07017 | −0.654583 | ||||||||
\(193\) | −7.77340 | −0.559541 | −0.279771 | − | 0.960067i | \(-0.590258\pi\) | ||||
−0.279771 | + | 0.960067i | \(0.590258\pi\) | |||||||
\(194\) | 13.3167 | 0.956086 | ||||||||
\(195\) | −0.0100862 | −0.000722285 0 | ||||||||
\(196\) | 25.7955 | 1.84253 | ||||||||
\(197\) | 16.2108 | 1.15497 | 0.577485 | − | 0.816401i | \(-0.304034\pi\) | ||||
0.577485 | + | 0.816401i | \(0.304034\pi\) | |||||||
\(198\) | −16.6938 | −1.18638 | ||||||||
\(199\) | 9.46490 | 0.670949 | 0.335474 | − | 0.942049i | \(-0.391103\pi\) | ||||
0.335474 | + | 0.942049i | \(0.391103\pi\) | |||||||
\(200\) | −3.90490 | −0.276118 | ||||||||
\(201\) | 12.6762 | 0.894112 | ||||||||
\(202\) | 21.1761 | 1.48994 | ||||||||
\(203\) | −39.5925 | −2.77885 | ||||||||
\(204\) | −22.2080 | −1.55487 | ||||||||
\(205\) | 0.454640 | 0.0317534 | ||||||||
\(206\) | 29.6770 | 2.06769 | ||||||||
\(207\) | −0.460622 | −0.0320154 | ||||||||
\(208\) | 0.0331868 | 0.00230109 | ||||||||
\(209\) | −4.50890 | −0.311887 | ||||||||
\(210\) | 13.0865 | 0.903056 | ||||||||
\(211\) | 9.01433 | 0.620572 | 0.310286 | − | 0.950643i | \(-0.399575\pi\) | ||||
0.310286 | + | 0.950643i | \(0.399575\pi\) | |||||||
\(212\) | 10.6077 | 0.728541 | ||||||||
\(213\) | −27.9053 | −1.91204 | ||||||||
\(214\) | −14.6881 | −1.00406 | ||||||||
\(215\) | 1.91181 | 0.130384 | ||||||||
\(216\) | −1.96147 | −0.133461 | ||||||||
\(217\) | −51.4580 | −3.49320 | ||||||||
\(218\) | 25.6956 | 1.74032 | ||||||||
\(219\) | 8.20130 | 0.554193 | ||||||||
\(220\) | 4.47446 | 0.301668 | ||||||||
\(221\) | 0.0454570 | 0.00305777 | ||||||||
\(222\) | −7.85924 | −0.527478 | ||||||||
\(223\) | −20.3344 | −1.36169 | −0.680847 | − | 0.732426i | \(-0.738388\pi\) | ||||
−0.680847 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(224\) | −34.7811 | −2.32391 | ||||||||
\(225\) | −9.02011 | −0.601341 | ||||||||
\(226\) | −0.0101232 | −0.000673384 0 | ||||||||
\(227\) | −26.4399 | −1.75488 | −0.877438 | − | 0.479689i | \(-0.840749\pi\) | ||||
−0.877438 | + | 0.479689i | \(0.840749\pi\) | |||||||
\(228\) | −3.45011 | −0.228489 | ||||||||
\(229\) | −4.30401 | −0.284417 | −0.142208 | − | 0.989837i | \(-0.545420\pi\) | ||||
−0.142208 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(230\) | 0.282942 | 0.0186567 | ||||||||
\(231\) | −48.8726 | −3.21558 | ||||||||
\(232\) | 6.92584 | 0.454704 | ||||||||
\(233\) | −15.6891 | −1.02783 | −0.513914 | − | 0.857842i | \(-0.671805\pi\) | ||||
−0.513914 | + | 0.857842i | \(0.671805\pi\) | |||||||
\(234\) | 0.0261462 | 0.00170923 | ||||||||
\(235\) | −5.65085 | −0.368621 | ||||||||
\(236\) | −14.7393 | −0.959447 | ||||||||
\(237\) | −20.2490 | −1.31532 | ||||||||
\(238\) | −58.9793 | −3.82306 | ||||||||
\(239\) | 15.5769 | 1.00759 | 0.503793 | − | 0.863824i | \(-0.331937\pi\) | ||||
0.503793 | + | 0.863824i | \(0.331937\pi\) | |||||||
\(240\) | −6.71185 | −0.433248 | ||||||||
\(241\) | 7.98140 | 0.514127 | 0.257064 | − | 0.966395i | \(-0.417245\pi\) | ||||
0.257064 | + | 0.966395i | \(0.417245\pi\) | |||||||
\(242\) | −17.5751 | −1.12977 | ||||||||
\(243\) | −17.6704 | −1.13356 | ||||||||
\(244\) | 4.09643 | 0.262247 | ||||||||
\(245\) | 10.6785 | 0.682227 | ||||||||
\(246\) | −2.97741 | −0.189833 | ||||||||
\(247\) | 0.00706194 | 0.000449340 0 | ||||||||
\(248\) | 9.00145 | 0.571593 | ||||||||
\(249\) | 22.5601 | 1.42969 | ||||||||
\(250\) | 11.5774 | 0.732219 | ||||||||
\(251\) | −20.9390 | −1.32166 | −0.660828 | − | 0.750537i | \(-0.729795\pi\) | ||||
−0.660828 | + | 0.750537i | \(0.729795\pi\) | |||||||
\(252\) | −14.8027 | −0.932481 | ||||||||
\(253\) | −1.05667 | −0.0664322 | ||||||||
\(254\) | 32.6015 | 2.04560 | ||||||||
\(255\) | −9.19344 | −0.575716 | ||||||||
\(256\) | 20.6362 | 1.28976 | ||||||||
\(257\) | 21.3983 | 1.33479 | 0.667394 | − | 0.744705i | \(-0.267410\pi\) | ||||
0.667394 | + | 0.744705i | \(0.267410\pi\) | |||||||
\(258\) | −12.5203 | −0.779481 | ||||||||
\(259\) | −9.10758 | −0.565918 | ||||||||
\(260\) | −0.00700801 | −0.000434618 0 | ||||||||
\(261\) | 15.9983 | 0.990272 | ||||||||
\(262\) | −24.1211 | −1.49021 | ||||||||
\(263\) | 11.4105 | 0.703600 | 0.351800 | − | 0.936075i | \(-0.385570\pi\) | ||||
0.351800 | + | 0.936075i | \(0.385570\pi\) | |||||||
\(264\) | 8.54920 | 0.526167 | ||||||||
\(265\) | 4.39127 | 0.269754 | ||||||||
\(266\) | −9.16269 | −0.561800 | ||||||||
\(267\) | −20.2610 | −1.23995 | ||||||||
\(268\) | 8.80763 | 0.538012 | ||||||||
\(269\) | −10.6531 | −0.649528 | −0.324764 | − | 0.945795i | \(-0.605285\pi\) | ||||
−0.324764 | + | 0.945795i | \(0.605285\pi\) | |||||||
\(270\) | 2.78315 | 0.169377 | ||||||||
\(271\) | 2.39657 | 0.145581 | 0.0727905 | − | 0.997347i | \(-0.476810\pi\) | ||||
0.0727905 | + | 0.997347i | \(0.476810\pi\) | |||||||
\(272\) | 30.2494 | 1.83414 | ||||||||
\(273\) | 0.0765455 | 0.00463274 | ||||||||
\(274\) | 24.3552 | 1.47135 | ||||||||
\(275\) | −20.6922 | −1.24779 | ||||||||
\(276\) | −0.808541 | −0.0486684 | ||||||||
\(277\) | 5.35349 | 0.321660 | 0.160830 | − | 0.986982i | \(-0.448583\pi\) | ||||
0.160830 | + | 0.986982i | \(0.448583\pi\) | |||||||
\(278\) | −30.6253 | −1.83678 | ||||||||
\(279\) | 20.7929 | 1.24484 | ||||||||
\(280\) | −2.65281 | −0.158536 | ||||||||
\(281\) | −12.3671 | −0.737761 | −0.368880 | − | 0.929477i | \(-0.620259\pi\) | ||||
−0.368880 | + | 0.929477i | \(0.620259\pi\) | |||||||
\(282\) | 37.0071 | 2.20374 | ||||||||
\(283\) | −16.7113 | −0.993385 | −0.496692 | − | 0.867927i | \(-0.665452\pi\) | ||||
−0.496692 | + | 0.867927i | \(0.665452\pi\) | |||||||
\(284\) | −19.3890 | −1.15053 | ||||||||
\(285\) | −1.42824 | −0.0846017 | ||||||||
\(286\) | 0.0599796 | 0.00354667 | ||||||||
\(287\) | −3.45034 | −0.203667 | ||||||||
\(288\) | 14.0542 | 0.828151 | ||||||||
\(289\) | 24.4336 | 1.43727 | ||||||||
\(290\) | −9.82716 | −0.577071 | ||||||||
\(291\) | −15.7533 | −0.923472 | ||||||||
\(292\) | 5.69839 | 0.333473 | ||||||||
\(293\) | 31.7293 | 1.85365 | 0.926823 | − | 0.375498i | \(-0.122528\pi\) | ||||
0.926823 | + | 0.375498i | \(0.122528\pi\) | |||||||
\(294\) | −69.9333 | −4.07859 | ||||||||
\(295\) | −6.10163 | −0.355250 | ||||||||
\(296\) | 1.59317 | 0.0926012 | ||||||||
\(297\) | −10.3939 | −0.603114 | ||||||||
\(298\) | 18.4454 | 1.06851 | ||||||||
\(299\) | 0.00165498 | 9.57100e−5 0 | ||||||||
\(300\) | −15.8332 | −0.914131 | ||||||||
\(301\) | −14.5090 | −0.836285 | ||||||||
\(302\) | −38.6079 | −2.22163 | ||||||||
\(303\) | −25.0506 | −1.43912 | ||||||||
\(304\) | 4.69938 | 0.269528 | ||||||||
\(305\) | 1.69580 | 0.0971012 | ||||||||
\(306\) | 23.8320 | 1.36239 | ||||||||
\(307\) | 5.83357 | 0.332940 | 0.166470 | − | 0.986047i | \(-0.446763\pi\) | ||||
0.166470 | + | 0.986047i | \(0.446763\pi\) | |||||||
\(308\) | −33.9574 | −1.93490 | ||||||||
\(309\) | −35.1069 | −1.99716 | ||||||||
\(310\) | −12.7723 | −0.725417 | ||||||||
\(311\) | 1.90870 | 0.108232 | 0.0541162 | − | 0.998535i | \(-0.482766\pi\) | ||||
0.0541162 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(312\) | −0.0133900 | −0.000758057 0 | ||||||||
\(313\) | −27.4581 | −1.55202 | −0.776011 | − | 0.630719i | \(-0.782760\pi\) | ||||
−0.776011 | + | 0.630719i | \(0.782760\pi\) | |||||||
\(314\) | −12.4328 | −0.701626 | ||||||||
\(315\) | −6.12786 | −0.345266 | ||||||||
\(316\) | −14.0693 | −0.791461 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | −28.7582 | −1.61268 | ||||||||
\(319\) | 36.7003 | 2.05482 | ||||||||
\(320\) | −2.60887 | −0.145840 | ||||||||
\(321\) | 17.3756 | 0.969811 | ||||||||
\(322\) | −2.14729 | −0.119664 | ||||||||
\(323\) | 6.43690 | 0.358158 | ||||||||
\(324\) | −17.0827 | −0.949039 | ||||||||
\(325\) | 0.0324086 | 0.00179771 | ||||||||
\(326\) | 37.1226 | 2.05603 | ||||||||
\(327\) | −30.3970 | −1.68096 | ||||||||
\(328\) | 0.603561 | 0.0333261 | ||||||||
\(329\) | 42.8852 | 2.36434 | ||||||||
\(330\) | −12.1306 | −0.667766 | ||||||||
\(331\) | −20.7970 | −1.14311 | −0.571553 | − | 0.820565i | \(-0.693659\pi\) | ||||
−0.571553 | + | 0.820565i | \(0.693659\pi\) | |||||||
\(332\) | 15.6751 | 0.860284 | ||||||||
\(333\) | 3.68015 | 0.201671 | ||||||||
\(334\) | 33.8175 | 1.85041 | ||||||||
\(335\) | 3.64609 | 0.199207 | ||||||||
\(336\) | 50.9374 | 2.77886 | ||||||||
\(337\) | −0.0755458 | −0.00411524 | −0.00205762 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205762 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(338\) | 24.4879 | 1.33196 | ||||||||
\(339\) | 0.0119754 | 0.000650414 0 | ||||||||
\(340\) | −6.38774 | −0.346424 | ||||||||
\(341\) | 47.6990 | 2.58305 | ||||||||
\(342\) | 3.70241 | 0.200204 | ||||||||
\(343\) | −46.9917 | −2.53731 | ||||||||
\(344\) | 2.53803 | 0.136842 | ||||||||
\(345\) | −0.334711 | −0.0180203 | ||||||||
\(346\) | 33.2557 | 1.78784 | ||||||||
\(347\) | 2.55204 | 0.137001 | 0.0685004 | − | 0.997651i | \(-0.478179\pi\) | ||||
0.0685004 | + | 0.997651i | \(0.478179\pi\) | |||||||
\(348\) | 28.0823 | 1.50537 | ||||||||
\(349\) | 30.9630 | 1.65741 | 0.828704 | − | 0.559686i | \(-0.189078\pi\) | ||||
0.828704 | + | 0.559686i | \(0.189078\pi\) | |||||||
\(350\) | −42.0493 | −2.24763 | ||||||||
\(351\) | 0.0162791 | 0.000868917 0 | ||||||||
\(352\) | 32.2404 | 1.71842 | ||||||||
\(353\) | −28.2608 | −1.50417 | −0.752085 | − | 0.659067i | \(-0.770952\pi\) | ||||
−0.752085 | + | 0.659067i | \(0.770952\pi\) | |||||||
\(354\) | 39.9592 | 2.12381 | ||||||||
\(355\) | −8.02647 | −0.426001 | ||||||||
\(356\) | −14.0776 | −0.746112 | ||||||||
\(357\) | 69.7705 | 3.69265 | ||||||||
\(358\) | −17.0085 | −0.898930 | ||||||||
\(359\) | −7.32781 | −0.386747 | −0.193373 | − | 0.981125i | \(-0.561943\pi\) | ||||
−0.193373 | + | 0.981125i | \(0.561943\pi\) | |||||||
\(360\) | 1.07193 | 0.0564959 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −3.70636 | −0.194802 | ||||||||
\(363\) | 20.7907 | 1.09123 | ||||||||
\(364\) | 0.0531849 | 0.00278765 | ||||||||
\(365\) | 2.35896 | 0.123474 | ||||||||
\(366\) | −11.1057 | −0.580504 | ||||||||
\(367\) | 12.6177 | 0.658637 | 0.329319 | − | 0.944219i | \(-0.393181\pi\) | ||||
0.329319 | + | 0.944219i | \(0.393181\pi\) | |||||||
\(368\) | 1.10131 | 0.0574098 | ||||||||
\(369\) | 1.39420 | 0.0725789 | ||||||||
\(370\) | −2.26057 | −0.117522 | ||||||||
\(371\) | −33.3261 | −1.73020 | ||||||||
\(372\) | 36.4983 | 1.89235 | ||||||||
\(373\) | 15.0084 | 0.777108 | 0.388554 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388554 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(374\) | 54.6709 | 2.82696 | ||||||||
\(375\) | −13.6957 | −0.707242 | ||||||||
\(376\) | −7.50183 | −0.386877 | ||||||||
\(377\) | −0.0574808 | −0.00296041 | ||||||||
\(378\) | −21.1218 | −1.08639 | ||||||||
\(379\) | −6.21863 | −0.319430 | −0.159715 | − | 0.987163i | \(-0.551057\pi\) | ||||
−0.159715 | + | 0.987163i | \(0.551057\pi\) | |||||||
\(380\) | −0.992363 | −0.0509072 | ||||||||
\(381\) | −38.5665 | −1.97582 | ||||||||
\(382\) | 40.7368 | 2.08428 | ||||||||
\(383\) | 31.8025 | 1.62503 | 0.812517 | − | 0.582938i | \(-0.198097\pi\) | ||||
0.812517 | + | 0.582938i | \(0.198097\pi\) | |||||||
\(384\) | −14.7817 | −0.754326 | ||||||||
\(385\) | −14.0573 | −0.716429 | ||||||||
\(386\) | 14.6427 | 0.745292 | ||||||||
\(387\) | 5.86273 | 0.298019 | ||||||||
\(388\) | −10.9456 | −0.555678 | ||||||||
\(389\) | −6.94914 | −0.352335 | −0.176168 | − | 0.984360i | \(-0.556370\pi\) | ||||
−0.176168 | + | 0.984360i | \(0.556370\pi\) | |||||||
\(390\) | 0.0189992 | 0.000962061 0 | ||||||||
\(391\) | 1.50850 | 0.0762881 | ||||||||
\(392\) | 14.1764 | 0.716016 | ||||||||
\(393\) | 28.5345 | 1.43937 | ||||||||
\(394\) | −30.5361 | −1.53839 | ||||||||
\(395\) | −5.82427 | −0.293051 | ||||||||
\(396\) | 13.7213 | 0.689524 | ||||||||
\(397\) | −6.61385 | −0.331940 | −0.165970 | − | 0.986131i | \(-0.553075\pi\) | ||||
−0.165970 | + | 0.986131i | \(0.553075\pi\) | |||||||
\(398\) | −17.8289 | −0.893683 | ||||||||
\(399\) | 10.8392 | 0.542637 | ||||||||
\(400\) | 21.5664 | 1.07832 | ||||||||
\(401\) | −30.7993 | −1.53805 | −0.769023 | − | 0.639222i | \(-0.779257\pi\) | ||||
−0.769023 | + | 0.639222i | \(0.779257\pi\) | |||||||
\(402\) | −23.8781 | −1.19093 | ||||||||
\(403\) | −0.0747074 | −0.00372144 | ||||||||
\(404\) | −17.4055 | −0.865957 | ||||||||
\(405\) | −7.07172 | −0.351397 | ||||||||
\(406\) | 74.5799 | 3.70134 | ||||||||
\(407\) | 8.44228 | 0.418468 | ||||||||
\(408\) | −12.2048 | −0.604229 | ||||||||
\(409\) | −24.6120 | −1.21699 | −0.608493 | − | 0.793560i | \(-0.708226\pi\) | ||||
−0.608493 | + | 0.793560i | \(0.708226\pi\) | |||||||
\(410\) | −0.856400 | −0.0422946 | ||||||||
\(411\) | −28.8113 | −1.42116 | ||||||||
\(412\) | −24.3928 | −1.20175 | ||||||||
\(413\) | 46.3062 | 2.27858 | ||||||||
\(414\) | 0.867668 | 0.0426436 | ||||||||
\(415\) | 6.48903 | 0.318534 | ||||||||
\(416\) | −0.0504957 | −0.00247575 | ||||||||
\(417\) | 36.2287 | 1.77413 | ||||||||
\(418\) | 8.49336 | 0.415424 | ||||||||
\(419\) | 21.7303 | 1.06160 | 0.530798 | − | 0.847498i | \(-0.321892\pi\) | ||||
0.530798 | + | 0.847498i | \(0.321892\pi\) | |||||||
\(420\) | −10.7564 | −0.524858 | ||||||||
\(421\) | 8.37727 | 0.408283 | 0.204142 | − | 0.978941i | \(-0.434560\pi\) | ||||
0.204142 | + | 0.978941i | \(0.434560\pi\) | |||||||
\(422\) | −16.9802 | −0.826583 | ||||||||
\(423\) | −17.3289 | −0.842558 | ||||||||
\(424\) | 5.82967 | 0.283114 | ||||||||
\(425\) | 29.5401 | 1.43291 | ||||||||
\(426\) | 52.5650 | 2.54678 | ||||||||
\(427\) | −12.8697 | −0.622808 | ||||||||
\(428\) | 12.0728 | 0.583562 | ||||||||
\(429\) | −0.0709539 | −0.00342569 | ||||||||
\(430\) | −3.60125 | −0.173668 | ||||||||
\(431\) | −30.4200 | −1.46528 | −0.732640 | − | 0.680616i | \(-0.761712\pi\) | ||||
−0.732640 | + | 0.680616i | \(0.761712\pi\) | |||||||
\(432\) | 10.8330 | 0.521203 | ||||||||
\(433\) | −34.3801 | −1.65220 | −0.826102 | − | 0.563521i | \(-0.809446\pi\) | ||||
−0.826102 | + | 0.563521i | \(0.809446\pi\) | |||||||
\(434\) | 96.9309 | 4.65283 | ||||||||
\(435\) | 11.6252 | 0.557386 | ||||||||
\(436\) | −21.1203 | −1.01148 | ||||||||
\(437\) | 0.234352 | 0.0112106 | ||||||||
\(438\) | −15.4487 | −0.738168 | ||||||||
\(439\) | −1.91118 | −0.0912154 | −0.0456077 | − | 0.998959i | \(-0.514522\pi\) | ||||
−0.0456077 | + | 0.998959i | \(0.514522\pi\) | |||||||
\(440\) | 2.45903 | 0.117229 | ||||||||
\(441\) | 32.7467 | 1.55937 | ||||||||
\(442\) | −0.0856268 | −0.00407285 | ||||||||
\(443\) | −19.4956 | −0.926266 | −0.463133 | − | 0.886289i | \(-0.653275\pi\) | ||||
−0.463133 | + | 0.886289i | \(0.653275\pi\) | |||||||
\(444\) | 6.45985 | 0.306571 | ||||||||
\(445\) | −5.82771 | −0.276260 | ||||||||
\(446\) | 38.3037 | 1.81373 | ||||||||
\(447\) | −21.8203 | −1.03206 | ||||||||
\(448\) | 19.7992 | 0.935422 | ||||||||
\(449\) | 29.3232 | 1.38385 | 0.691925 | − | 0.721970i | \(-0.256763\pi\) | ||||
0.691925 | + | 0.721970i | \(0.256763\pi\) | |||||||
\(450\) | 16.9911 | 0.800967 | ||||||||
\(451\) | 3.19829 | 0.150602 | ||||||||
\(452\) | 0.00832069 | 0.000391372 0 | ||||||||
\(453\) | 45.6719 | 2.14585 | ||||||||
\(454\) | 49.8045 | 2.33744 | ||||||||
\(455\) | 0.0220170 | 0.00103217 | ||||||||
\(456\) | −1.89607 | −0.0887918 | ||||||||
\(457\) | −0.0902563 | −0.00422201 | −0.00211101 | − | 0.999998i | \(-0.500672\pi\) | ||||
−0.00211101 | + | 0.999998i | \(0.500672\pi\) | |||||||
\(458\) | 8.10741 | 0.378834 | ||||||||
\(459\) | 14.8383 | 0.692592 | ||||||||
\(460\) | −0.232562 | −0.0108433 | ||||||||
\(461\) | 29.3079 | 1.36500 | 0.682502 | − | 0.730883i | \(-0.260892\pi\) | ||||
0.682502 | + | 0.730883i | \(0.260892\pi\) | |||||||
\(462\) | 92.0609 | 4.28306 | ||||||||
\(463\) | −33.5933 | −1.56121 | −0.780606 | − | 0.625023i | \(-0.785090\pi\) | ||||
−0.780606 | + | 0.625023i | \(0.785090\pi\) | |||||||
\(464\) | −38.2508 | −1.77575 | ||||||||
\(465\) | 15.1092 | 0.700672 | ||||||||
\(466\) | 29.5534 | 1.36904 | ||||||||
\(467\) | 5.37396 | 0.248677 | 0.124339 | − | 0.992240i | \(-0.460319\pi\) | ||||
0.124339 | + | 0.992240i | \(0.460319\pi\) | |||||||
\(468\) | −0.0214907 | −0.000993408 0 | ||||||||
\(469\) | −27.6708 | −1.27772 | ||||||||
\(470\) | 10.6444 | 0.490992 | ||||||||
\(471\) | 14.7076 | 0.677692 | ||||||||
\(472\) | −8.10027 | −0.372845 | ||||||||
\(473\) | 13.4491 | 0.618392 | ||||||||
\(474\) | 38.1429 | 1.75196 | ||||||||
\(475\) | 4.58919 | 0.210567 | ||||||||
\(476\) | 48.4776 | 2.22197 | ||||||||
\(477\) | 13.4662 | 0.616577 | ||||||||
\(478\) | −29.3421 | −1.34207 | ||||||||
\(479\) | 36.8426 | 1.68338 | 0.841690 | − | 0.539961i | \(-0.181561\pi\) | ||||
0.841690 | + | 0.539961i | \(0.181561\pi\) | |||||||
\(480\) | 10.2125 | 0.466134 | ||||||||
\(481\) | −0.0132225 | −0.000602894 0 | ||||||||
\(482\) | −15.0345 | −0.684802 | ||||||||
\(483\) | 2.54018 | 0.115582 | ||||||||
\(484\) | 14.4457 | 0.656624 | ||||||||
\(485\) | −4.53115 | −0.205749 | ||||||||
\(486\) | 33.2855 | 1.50986 | ||||||||
\(487\) | −32.1548 | −1.45708 | −0.728538 | − | 0.685006i | \(-0.759800\pi\) | ||||
−0.728538 | + | 0.685006i | \(0.759800\pi\) | |||||||
\(488\) | 2.25127 | 0.101910 | ||||||||
\(489\) | −43.9149 | −1.98590 | ||||||||
\(490\) | −20.1151 | −0.908706 | ||||||||
\(491\) | −14.1248 | −0.637443 | −0.318722 | − | 0.947848i | \(-0.603254\pi\) | ||||
−0.318722 | + | 0.947848i | \(0.603254\pi\) | |||||||
\(492\) | 2.44727 | 0.110331 | ||||||||
\(493\) | −52.3933 | −2.35967 | ||||||||
\(494\) | −0.0133025 | −0.000598508 0 | ||||||||
\(495\) | 5.68022 | 0.255307 | ||||||||
\(496\) | −49.7142 | −2.23223 | ||||||||
\(497\) | 60.9142 | 2.73238 | ||||||||
\(498\) | −42.4963 | −1.90431 | ||||||||
\(499\) | 7.34031 | 0.328597 | 0.164299 | − | 0.986411i | \(-0.447464\pi\) | ||||
0.164299 | + | 0.986411i | \(0.447464\pi\) | |||||||
\(500\) | −9.51596 | −0.425567 | ||||||||
\(501\) | −40.0050 | −1.78729 | ||||||||
\(502\) | 39.4425 | 1.76041 | ||||||||
\(503\) | 14.4031 | 0.642202 | 0.321101 | − | 0.947045i | \(-0.395947\pi\) | ||||
0.321101 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(504\) | −8.13509 | −0.362366 | ||||||||
\(505\) | −7.20535 | −0.320634 | ||||||||
\(506\) | 1.99044 | 0.0884857 | ||||||||
\(507\) | −28.9683 | −1.28653 | ||||||||
\(508\) | −26.7966 | −1.18891 | ||||||||
\(509\) | 35.6530 | 1.58029 | 0.790146 | − | 0.612919i | \(-0.210005\pi\) | ||||
0.790146 | + | 0.612919i | \(0.210005\pi\) | |||||||
\(510\) | 17.3176 | 0.766836 | ||||||||
\(511\) | −17.9025 | −0.791961 | ||||||||
\(512\) | −25.6051 | −1.13160 | ||||||||
\(513\) | 2.30520 | 0.101777 | ||||||||
\(514\) | −40.3077 | −1.77790 | ||||||||
\(515\) | −10.0979 | −0.444966 | ||||||||
\(516\) | 10.2910 | 0.453036 | ||||||||
\(517\) | −39.7525 | −1.74831 | ||||||||
\(518\) | 17.1559 | 0.753785 | ||||||||
\(519\) | −39.3404 | −1.72685 | ||||||||
\(520\) | −0.00385138 | −0.000168894 0 | ||||||||
\(521\) | −6.85409 | −0.300283 | −0.150142 | − | 0.988665i | \(-0.547973\pi\) | ||||
−0.150142 | + | 0.988665i | \(0.547973\pi\) | |||||||
\(522\) | −30.1359 | −1.31901 | ||||||||
\(523\) | 23.2697 | 1.01751 | 0.508757 | − | 0.860910i | \(-0.330105\pi\) | ||||
0.508757 | + | 0.860910i | \(0.330105\pi\) | |||||||
\(524\) | 19.8262 | 0.866110 | ||||||||
\(525\) | 49.7430 | 2.17096 | ||||||||
\(526\) | −21.4938 | −0.937174 | ||||||||
\(527\) | −68.0951 | −2.96627 | ||||||||
\(528\) | −47.2164 | −2.05483 | ||||||||
\(529\) | −22.9451 | −0.997612 | ||||||||
\(530\) | −8.27179 | −0.359304 | ||||||||
\(531\) | −18.7112 | −0.811997 | ||||||||
\(532\) | 7.53121 | 0.326519 | ||||||||
\(533\) | −0.00500924 | −0.000216974 0 | ||||||||
\(534\) | 38.1653 | 1.65158 | ||||||||
\(535\) | 4.99778 | 0.216073 | ||||||||
\(536\) | 4.84040 | 0.209073 | ||||||||
\(537\) | 20.1206 | 0.868266 | ||||||||
\(538\) | 20.0670 | 0.865152 | ||||||||
\(539\) | 75.1212 | 3.23570 | ||||||||
\(540\) | −2.28759 | −0.0984422 | ||||||||
\(541\) | −20.1655 | −0.866982 | −0.433491 | − | 0.901158i | \(-0.642718\pi\) | ||||
−0.433491 | + | 0.901158i | \(0.642718\pi\) | |||||||
\(542\) | −4.51438 | −0.193909 | ||||||||
\(543\) | 4.38450 | 0.188157 | ||||||||
\(544\) | −46.0264 | −1.97336 | ||||||||
\(545\) | −8.74316 | −0.374516 | ||||||||
\(546\) | −0.144188 | −0.00617067 | ||||||||
\(547\) | 12.6986 | 0.542952 | 0.271476 | − | 0.962445i | \(-0.412488\pi\) | ||||
0.271476 | + | 0.962445i | \(0.412488\pi\) | |||||||
\(548\) | −20.0186 | −0.855150 | ||||||||
\(549\) | 5.20032 | 0.221944 | ||||||||
\(550\) | 38.9776 | 1.66201 | ||||||||
\(551\) | −8.13953 | −0.346755 | ||||||||
\(552\) | −0.444349 | −0.0189127 | ||||||||
\(553\) | 44.2014 | 1.87963 | ||||||||
\(554\) | −10.0843 | −0.428441 | ||||||||
\(555\) | 2.67418 | 0.113513 | ||||||||
\(556\) | 25.1723 | 1.06754 | ||||||||
\(557\) | 3.42970 | 0.145321 | 0.0726605 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726605 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(558\) | −39.1674 | −1.65809 | ||||||||
\(559\) | −0.0210643 | −0.000890927 0 | ||||||||
\(560\) | 14.6512 | 0.619127 | ||||||||
\(561\) | −64.6738 | −2.73053 | ||||||||
\(562\) | 23.2958 | 0.982675 | ||||||||
\(563\) | −9.88580 | −0.416637 | −0.208318 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208318 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(564\) | −30.4178 | −1.28082 | ||||||||
\(565\) | 0.00344451 | 0.000144912 0 | ||||||||
\(566\) | 31.4789 | 1.32316 | ||||||||
\(567\) | 53.6684 | 2.25386 | ||||||||
\(568\) | −10.6556 | −0.447099 | ||||||||
\(569\) | −15.5797 | −0.653135 | −0.326567 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326567 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(570\) | 2.69036 | 0.112687 | ||||||||
\(571\) | 2.27303 | 0.0951233 | 0.0475616 | − | 0.998868i | \(-0.484855\pi\) | ||||
0.0475616 | + | 0.998868i | \(0.484855\pi\) | |||||||
\(572\) | −0.0492998 | −0.00206133 | ||||||||
\(573\) | −48.1903 | −2.01318 | ||||||||
\(574\) | 6.49936 | 0.271278 | ||||||||
\(575\) | 1.07549 | 0.0448509 | ||||||||
\(576\) | −8.00035 | −0.333348 | ||||||||
\(577\) | −37.1794 | −1.54780 | −0.773899 | − | 0.633309i | \(-0.781696\pi\) | ||||
−0.773899 | + | 0.633309i | \(0.781696\pi\) | |||||||
\(578\) | −46.0253 | −1.91440 | ||||||||
\(579\) | −17.3218 | −0.719869 | ||||||||
\(580\) | 8.07737 | 0.335394 | ||||||||
\(581\) | −49.2463 | −2.04308 | ||||||||
\(582\) | 29.6742 | 1.23004 | ||||||||
\(583\) | 30.8916 | 1.27940 | ||||||||
\(584\) | 3.13166 | 0.129589 | ||||||||
\(585\) | −0.00889650 | −0.000367825 0 | ||||||||
\(586\) | −59.7682 | −2.46900 | ||||||||
\(587\) | −22.7649 | −0.939607 | −0.469803 | − | 0.882771i | \(-0.655675\pi\) | ||||
−0.469803 | + | 0.882771i | \(0.655675\pi\) | |||||||
\(588\) | 57.4812 | 2.37048 | ||||||||
\(589\) | −10.5789 | −0.435895 | ||||||||
\(590\) | 11.4936 | 0.473183 | ||||||||
\(591\) | 36.1232 | 1.48591 | ||||||||
\(592\) | −8.79894 | −0.361634 | ||||||||
\(593\) | 37.9661 | 1.55908 | 0.779541 | − | 0.626352i | \(-0.215453\pi\) | ||||
0.779541 | + | 0.626352i | \(0.215453\pi\) | |||||||
\(594\) | 19.5788 | 0.803330 | ||||||||
\(595\) | 20.0683 | 0.822718 | ||||||||
\(596\) | −15.1611 | −0.621021 | ||||||||
\(597\) | 21.0910 | 0.863199 | ||||||||
\(598\) | −0.00311747 | −0.000127483 0 | ||||||||
\(599\) | −13.7378 | −0.561313 | −0.280656 | − | 0.959808i | \(-0.590552\pi\) | ||||
−0.280656 | + | 0.959808i | \(0.590552\pi\) | |||||||
\(600\) | −8.70145 | −0.355235 | ||||||||
\(601\) | −7.88485 | −0.321630 | −0.160815 | − | 0.986985i | \(-0.551412\pi\) | ||||
−0.160815 | + | 0.986985i | \(0.551412\pi\) | |||||||
\(602\) | 27.3305 | 1.11391 | ||||||||
\(603\) | 11.1811 | 0.455329 | ||||||||
\(604\) | 31.7335 | 1.29122 | ||||||||
\(605\) | 5.98009 | 0.243125 | ||||||||
\(606\) | 47.1875 | 1.91686 | ||||||||
\(607\) | −36.1725 | −1.46820 | −0.734098 | − | 0.679044i | \(-0.762395\pi\) | ||||
−0.734098 | + | 0.679044i | \(0.762395\pi\) | |||||||
\(608\) | −7.15040 | −0.289987 | ||||||||
\(609\) | −88.2256 | −3.57508 | ||||||||
\(610\) | −3.19436 | −0.129336 | ||||||||
\(611\) | 0.0622613 | 0.00251882 | ||||||||
\(612\) | −19.5886 | −0.791822 | ||||||||
\(613\) | 17.5935 | 0.710595 | 0.355298 | − | 0.934753i | \(-0.384380\pi\) | ||||
0.355298 | + | 0.934753i | \(0.384380\pi\) | |||||||
\(614\) | −10.9886 | −0.443465 | ||||||||
\(615\) | 1.01309 | 0.0408519 | ||||||||
\(616\) | −18.6619 | −0.751911 | ||||||||
\(617\) | 14.4769 | 0.582817 | 0.291408 | − | 0.956599i | \(-0.405876\pi\) | ||||
0.291408 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(618\) | 66.1305 | 2.66016 | ||||||||
\(619\) | −4.56796 | −0.183602 | −0.0918009 | − | 0.995777i | \(-0.529262\pi\) | ||||
−0.0918009 | + | 0.995777i | \(0.529262\pi\) | |||||||
\(620\) | 10.4981 | 0.421613 | ||||||||
\(621\) | 0.540227 | 0.0216786 | ||||||||
\(622\) | −3.59540 | −0.144162 | ||||||||
\(623\) | 44.2274 | 1.77193 | ||||||||
\(624\) | 0.0739515 | 0.00296043 | ||||||||
\(625\) | 19.0066 | 0.760266 | ||||||||
\(626\) | 51.7225 | 2.06725 | ||||||||
\(627\) | −10.0474 | −0.401253 | ||||||||
\(628\) | 10.2191 | 0.407786 | ||||||||
\(629\) | −12.0522 | −0.480552 | ||||||||
\(630\) | 11.5430 | 0.459883 | ||||||||
\(631\) | 10.7287 | 0.427103 | 0.213552 | − | 0.976932i | \(-0.431497\pi\) | ||||
0.213552 | + | 0.976932i | \(0.431497\pi\) | |||||||
\(632\) | −7.73206 | −0.307565 | ||||||||
\(633\) | 20.0870 | 0.798388 | ||||||||
\(634\) | 1.88369 | 0.0748109 | ||||||||
\(635\) | −11.0930 | −0.440211 | ||||||||
\(636\) | 23.6376 | 0.937293 | ||||||||
\(637\) | −0.117657 | −0.00466173 | ||||||||
\(638\) | −69.1319 | −2.73696 | ||||||||
\(639\) | −24.6139 | −0.973711 | ||||||||
\(640\) | −4.25169 | −0.168063 | ||||||||
\(641\) | 4.14690 | 0.163793 | 0.0818964 | − | 0.996641i | \(-0.473902\pi\) | ||||
0.0818964 | + | 0.996641i | \(0.473902\pi\) | |||||||
\(642\) | −32.7302 | −1.29176 | ||||||||
\(643\) | 4.59085 | 0.181046 | 0.0905228 | − | 0.995894i | \(-0.471146\pi\) | ||||
0.0905228 | + | 0.995894i | \(0.471146\pi\) | |||||||
\(644\) | 1.76495 | 0.0695489 | ||||||||
\(645\) | 4.26016 | 0.167744 | ||||||||
\(646\) | −12.1251 | −0.477056 | ||||||||
\(647\) | −31.0569 | −1.22097 | −0.610486 | − | 0.792027i | \(-0.709026\pi\) | ||||
−0.610486 | + | 0.792027i | \(0.709026\pi\) | |||||||
\(648\) | −9.38812 | −0.368800 | ||||||||
\(649\) | −42.9236 | −1.68490 | ||||||||
\(650\) | −0.0610477 | −0.00239449 | ||||||||
\(651\) | −114.666 | −4.49412 | ||||||||
\(652\) | −30.5127 | −1.19497 | ||||||||
\(653\) | −19.9388 | −0.780265 | −0.390133 | − | 0.920759i | \(-0.627571\pi\) | ||||
−0.390133 | + | 0.920759i | \(0.627571\pi\) | |||||||
\(654\) | 57.2585 | 2.23899 | ||||||||
\(655\) | 8.20743 | 0.320691 | ||||||||
\(656\) | −3.33341 | −0.130148 | ||||||||
\(657\) | 7.23396 | 0.282224 | ||||||||
\(658\) | −80.7825 | −3.14923 | ||||||||
\(659\) | −2.94573 | −0.114749 | −0.0573746 | − | 0.998353i | \(-0.518273\pi\) | ||||
−0.0573746 | + | 0.998353i | \(0.518273\pi\) | |||||||
\(660\) | 9.97064 | 0.388106 | ||||||||
\(661\) | −16.4977 | −0.641688 | −0.320844 | − | 0.947132i | \(-0.603966\pi\) | ||||
−0.320844 | + | 0.947132i | \(0.603966\pi\) | |||||||
\(662\) | 39.1751 | 1.52258 | ||||||||
\(663\) | 0.101294 | 0.00393392 | ||||||||
\(664\) | 8.61456 | 0.334310 | ||||||||
\(665\) | 3.11769 | 0.120899 | ||||||||
\(666\) | −6.93225 | −0.268619 | ||||||||
\(667\) | −1.90751 | −0.0738593 | ||||||||
\(668\) | −27.7961 | −1.07546 | ||||||||
\(669\) | −45.3121 | −1.75187 | ||||||||
\(670\) | −6.86810 | −0.265338 | ||||||||
\(671\) | 11.9296 | 0.460536 | ||||||||
\(672\) | −77.5043 | −2.98979 | ||||||||
\(673\) | −48.0738 | −1.85311 | −0.926555 | − | 0.376159i | \(-0.877244\pi\) | ||||
−0.926555 | + | 0.376159i | \(0.877244\pi\) | |||||||
\(674\) | 0.142305 | 0.00548138 | ||||||||
\(675\) | 10.5790 | 0.407185 | ||||||||
\(676\) | −20.1276 | −0.774140 | ||||||||
\(677\) | 20.6462 | 0.793497 | 0.396749 | − | 0.917927i | \(-0.370139\pi\) | ||||
0.396749 | + | 0.917927i | \(0.370139\pi\) | |||||||
\(678\) | −0.0225579 | −0.000866332 0 | ||||||||
\(679\) | 34.3876 | 1.31968 | ||||||||
\(680\) | −3.51050 | −0.134622 | ||||||||
\(681\) | −58.9171 | −2.25771 | ||||||||
\(682\) | −89.8502 | −3.44054 | ||||||||
\(683\) | 31.3990 | 1.20145 | 0.600724 | − | 0.799457i | \(-0.294879\pi\) | ||||
0.600724 | + | 0.799457i | \(0.294879\pi\) | |||||||
\(684\) | −3.04317 | −0.116359 | ||||||||
\(685\) | −8.28707 | −0.316633 | ||||||||
\(686\) | 88.5177 | 3.37962 | ||||||||
\(687\) | −9.59080 | −0.365912 | ||||||||
\(688\) | −14.0173 | −0.534405 | ||||||||
\(689\) | −0.0483832 | −0.00184325 | ||||||||
\(690\) | 0.630492 | 0.0240024 | ||||||||
\(691\) | −13.2618 | −0.504502 | −0.252251 | − | 0.967662i | \(-0.581171\pi\) | ||||
−0.252251 | + | 0.967662i | \(0.581171\pi\) | |||||||
\(692\) | −27.3343 | −1.03909 | ||||||||
\(693\) | −43.1081 | −1.63754 | ||||||||
\(694\) | −4.80725 | −0.182481 | ||||||||
\(695\) | 10.4206 | 0.395274 | ||||||||
\(696\) | 15.4331 | 0.584992 | ||||||||
\(697\) | −4.56588 | −0.172945 | ||||||||
\(698\) | −58.3246 | −2.20762 | ||||||||
\(699\) | −34.9607 | −1.32234 | ||||||||
\(700\) | 34.5622 | 1.30633 | ||||||||
\(701\) | −13.2660 | −0.501050 | −0.250525 | − | 0.968110i | \(-0.580603\pi\) | ||||
−0.250525 | + | 0.968110i | \(0.580603\pi\) | |||||||
\(702\) | −0.0306649 | −0.00115737 | ||||||||
\(703\) | −1.87236 | −0.0706174 | ||||||||
\(704\) | −18.3528 | −0.691699 | ||||||||
\(705\) | −12.5920 | −0.474243 | ||||||||
\(706\) | 53.2345 | 2.00351 | ||||||||
\(707\) | 54.6826 | 2.05655 | ||||||||
\(708\) | −32.8442 | −1.23436 | ||||||||
\(709\) | 22.0145 | 0.826773 | 0.413386 | − | 0.910556i | \(-0.364346\pi\) | ||||
0.413386 | + | 0.910556i | \(0.364346\pi\) | |||||||
\(710\) | 15.1194 | 0.567420 | ||||||||
\(711\) | −17.8607 | −0.669828 | ||||||||
\(712\) | −7.73662 | −0.289942 | ||||||||
\(713\) | −2.47918 | −0.0928460 | ||||||||
\(714\) | −131.426 | −4.91849 | ||||||||
\(715\) | −0.0204086 | −0.000763239 0 | ||||||||
\(716\) | 13.9801 | 0.522459 | ||||||||
\(717\) | 34.7107 | 1.29629 | ||||||||
\(718\) | 13.8033 | 0.515135 | ||||||||
\(719\) | 4.32667 | 0.161357 | 0.0806787 | − | 0.996740i | \(-0.474291\pi\) | ||||
0.0806787 | + | 0.996740i | \(0.474291\pi\) | |||||||
\(720\) | −5.92020 | −0.220633 | ||||||||
\(721\) | 76.6344 | 2.85402 | ||||||||
\(722\) | −1.88369 | −0.0701037 | ||||||||
\(723\) | 17.7853 | 0.661442 | ||||||||
\(724\) | 3.04641 | 0.113219 | ||||||||
\(725\) | −37.3538 | −1.38729 | ||||||||
\(726\) | −39.1633 | −1.45349 | ||||||||
\(727\) | −14.3121 | −0.530808 | −0.265404 | − | 0.964137i | \(-0.585505\pi\) | ||||
−0.265404 | + | 0.964137i | \(0.585505\pi\) | |||||||
\(728\) | 0.0292288 | 0.00108329 | ||||||||
\(729\) | −6.27578 | −0.232436 | ||||||||
\(730\) | −4.44355 | −0.164463 | ||||||||
\(731\) | −19.2000 | −0.710136 | ||||||||
\(732\) | 9.12826 | 0.337390 | ||||||||
\(733\) | −19.6707 | −0.726553 | −0.363277 | − | 0.931681i | \(-0.618342\pi\) | ||||
−0.363277 | + | 0.931681i | \(0.618342\pi\) | |||||||
\(734\) | −23.7678 | −0.877285 | ||||||||
\(735\) | 23.7955 | 0.877709 | ||||||||
\(736\) | −1.67571 | −0.0617675 | ||||||||
\(737\) | 25.6495 | 0.944810 | ||||||||
\(738\) | −2.62623 | −0.0966729 | ||||||||
\(739\) | −33.1384 | −1.21902 | −0.609508 | − | 0.792780i | \(-0.708633\pi\) | ||||
−0.609508 | + | 0.792780i | \(0.708633\pi\) | |||||||
\(740\) | 1.85806 | 0.0683037 | ||||||||
\(741\) | 0.0157364 | 0.000578092 0 | ||||||||
\(742\) | 62.7760 | 2.30458 | ||||||||
\(743\) | −1.88309 | −0.0690839 | −0.0345419 | − | 0.999403i | \(-0.510997\pi\) | ||||
−0.0345419 | + | 0.999403i | \(0.510997\pi\) | |||||||
\(744\) | 20.0583 | 0.735374 | ||||||||
\(745\) | −6.27622 | −0.229943 | ||||||||
\(746\) | −28.2712 | −1.03508 | ||||||||
\(747\) | 19.8992 | 0.728074 | ||||||||
\(748\) | −44.9363 | −1.64304 | ||||||||
\(749\) | −37.9290 | −1.38590 | ||||||||
\(750\) | 25.7984 | 0.942025 | ||||||||
\(751\) | 45.7503 | 1.66945 | 0.834726 | − | 0.550666i | \(-0.185626\pi\) | ||||
0.834726 | + | 0.550666i | \(0.185626\pi\) | |||||||
\(752\) | 41.4319 | 1.51087 | ||||||||
\(753\) | −46.6592 | −1.70036 | ||||||||
\(754\) | 0.108276 | 0.00394318 | ||||||||
\(755\) | 13.1367 | 0.478094 | ||||||||
\(756\) | 17.3609 | 0.631410 | ||||||||
\(757\) | 44.7764 | 1.62743 | 0.813713 | − | 0.581267i | \(-0.197443\pi\) | ||||
0.813713 | + | 0.581267i | \(0.197443\pi\) | |||||||
\(758\) | 11.7140 | 0.425471 | ||||||||
\(759\) | −2.35462 | −0.0854673 | ||||||||
\(760\) | −0.545372 | −0.0197827 | ||||||||
\(761\) | −41.8409 | −1.51673 | −0.758366 | − | 0.651829i | \(-0.774002\pi\) | ||||
−0.758366 | + | 0.651829i | \(0.774002\pi\) | |||||||
\(762\) | 72.6473 | 2.63174 | ||||||||
\(763\) | 66.3533 | 2.40215 | ||||||||
\(764\) | −33.4833 | −1.21138 | ||||||||
\(765\) | −8.10908 | −0.293184 | ||||||||
\(766\) | −59.9061 | −2.16450 | ||||||||
\(767\) | 0.0672280 | 0.00242746 | ||||||||
\(768\) | 45.9845 | 1.65932 | ||||||||
\(769\) | 30.6861 | 1.10657 | 0.553285 | − | 0.832992i | \(-0.313374\pi\) | ||||
0.553285 | + | 0.832992i | \(0.313374\pi\) | |||||||
\(770\) | 26.4797 | 0.954261 | ||||||||
\(771\) | 47.6827 | 1.71725 | ||||||||
\(772\) | −12.0354 | −0.433165 | ||||||||
\(773\) | 20.0074 | 0.719617 | 0.359809 | − | 0.933026i | \(-0.382842\pi\) | ||||
0.359809 | + | 0.933026i | \(0.382842\pi\) | |||||||
\(774\) | −11.0436 | −0.396952 | ||||||||
\(775\) | −48.5485 | −1.74391 | ||||||||
\(776\) | −6.01536 | −0.215939 | ||||||||
\(777\) | −20.2948 | −0.728072 | ||||||||
\(778\) | 13.0900 | 0.469300 | ||||||||
\(779\) | −0.709329 | −0.0254144 | ||||||||
\(780\) | −0.0156162 | −0.000559151 0 | ||||||||
\(781\) | −56.4645 | −2.02046 | ||||||||
\(782\) | −2.84154 | −0.101613 | ||||||||
\(783\) | −18.7632 | −0.670542 | ||||||||
\(784\) | −78.2949 | −2.79625 | ||||||||
\(785\) | 4.23039 | 0.150989 | ||||||||
\(786\) | −53.7501 | −1.91720 | ||||||||
\(787\) | −51.1664 | −1.82388 | −0.911942 | − | 0.410320i | \(-0.865417\pi\) | ||||
−0.911942 | + | 0.410320i | \(0.865417\pi\) | |||||||
\(788\) | 25.0989 | 0.894112 | ||||||||
\(789\) | 25.4264 | 0.905205 | ||||||||
\(790\) | 10.9711 | 0.390335 | ||||||||
\(791\) | −0.0261410 | −0.000929466 0 | ||||||||
\(792\) | 7.54083 | 0.267952 | ||||||||
\(793\) | −0.0186844 | −0.000663502 0 | ||||||||
\(794\) | 12.4584 | 0.442133 | ||||||||
\(795\) | 9.78526 | 0.347047 | ||||||||
\(796\) | 14.6544 | 0.519410 | ||||||||
\(797\) | 39.8304 | 1.41087 | 0.705433 | − | 0.708776i | \(-0.250752\pi\) | ||||
0.705433 | + | 0.708776i | \(0.250752\pi\) | |||||||
\(798\) | −20.4176 | −0.722775 | ||||||||
\(799\) | 56.7506 | 2.00769 | ||||||||
\(800\) | −32.8145 | −1.16017 | ||||||||
\(801\) | −17.8712 | −0.631448 | ||||||||
\(802\) | 58.0164 | 2.04863 | ||||||||
\(803\) | 16.5948 | 0.585616 | ||||||||
\(804\) | 19.6264 | 0.692170 | ||||||||
\(805\) | 0.730637 | 0.0257516 | ||||||||
\(806\) | 0.140725 | 0.00495684 | ||||||||
\(807\) | −23.7387 | −0.835640 | ||||||||
\(808\) | −9.56553 | −0.336514 | ||||||||
\(809\) | 16.0888 | 0.565653 | 0.282826 | − | 0.959171i | \(-0.408728\pi\) | ||||
0.282826 | + | 0.959171i | \(0.408728\pi\) | |||||||
\(810\) | 13.3209 | 0.468050 | ||||||||
\(811\) | 48.4330 | 1.70071 | 0.850357 | − | 0.526206i | \(-0.176386\pi\) | ||||
0.850357 | + | 0.526206i | \(0.176386\pi\) | |||||||
\(812\) | −61.3005 | −2.15122 | ||||||||
\(813\) | 5.34037 | 0.187295 | ||||||||
\(814\) | −15.9026 | −0.557387 | ||||||||
\(815\) | −12.6313 | −0.442456 | ||||||||
\(816\) | 67.4061 | 2.35969 | ||||||||
\(817\) | −2.98280 | −0.104355 | ||||||||
\(818\) | 46.3614 | 1.62099 | ||||||||
\(819\) | 0.0675170 | 0.00235923 | ||||||||
\(820\) | 0.703912 | 0.0245817 | ||||||||
\(821\) | 28.1834 | 0.983609 | 0.491805 | − | 0.870706i | \(-0.336337\pi\) | ||||
0.491805 | + | 0.870706i | \(0.336337\pi\) | |||||||
\(822\) | 54.2716 | 1.89294 | ||||||||
\(823\) | 20.5763 | 0.717245 | 0.358622 | − | 0.933483i | \(-0.383247\pi\) | ||||
0.358622 | + | 0.933483i | \(0.383247\pi\) | |||||||
\(824\) | −13.4055 | −0.467003 | ||||||||
\(825\) | −46.1093 | −1.60532 | ||||||||
\(826\) | −87.2266 | −3.03500 | ||||||||
\(827\) | 46.4822 | 1.61634 | 0.808172 | − | 0.588946i | \(-0.200457\pi\) | ||||
0.808172 | + | 0.588946i | \(0.200457\pi\) | |||||||
\(828\) | −0.713174 | −0.0247845 | ||||||||
\(829\) | 29.6562 | 1.03000 | 0.515002 | − | 0.857189i | \(-0.327791\pi\) | ||||
0.515002 | + | 0.857189i | \(0.327791\pi\) | |||||||
\(830\) | −12.2233 | −0.424277 | ||||||||
\(831\) | 11.9294 | 0.413827 | ||||||||
\(832\) | 0.0287447 | 0.000996542 0 | ||||||||
\(833\) | −107.243 | −3.71575 | ||||||||
\(834\) | −68.2437 | −2.36309 | ||||||||
\(835\) | −11.5067 | −0.398207 | ||||||||
\(836\) | −6.98106 | −0.241445 | ||||||||
\(837\) | −24.3864 | −0.842916 | ||||||||
\(838\) | −40.9332 | −1.41401 | ||||||||
\(839\) | −5.64087 | −0.194745 | −0.0973723 | − | 0.995248i | \(-0.531044\pi\) | ||||
−0.0973723 | + | 0.995248i | \(0.531044\pi\) | |||||||
\(840\) | −5.91137 | −0.203962 | ||||||||
\(841\) | 37.2519 | 1.28455 | ||||||||
\(842\) | −15.7802 | −0.543821 | ||||||||
\(843\) | −27.5582 | −0.949155 | ||||||||
\(844\) | 13.9568 | 0.480412 | ||||||||
\(845\) | −8.33223 | −0.286637 | ||||||||
\(846\) | 32.6422 | 1.12226 | ||||||||
\(847\) | −45.3839 | −1.55941 | ||||||||
\(848\) | −32.1967 | −1.10564 | ||||||||
\(849\) | −37.2385 | −1.27802 | ||||||||
\(850\) | −55.6445 | −1.90859 | ||||||||
\(851\) | −0.438792 | −0.0150416 | ||||||||
\(852\) | −43.2054 | −1.48019 | ||||||||
\(853\) | 9.83203 | 0.336642 | 0.168321 | − | 0.985732i | \(-0.446165\pi\) | ||||
0.168321 | + | 0.985732i | \(0.446165\pi\) | |||||||
\(854\) | 24.2425 | 0.829562 | ||||||||
\(855\) | −1.25978 | −0.0430836 | ||||||||
\(856\) | 6.63485 | 0.226774 | ||||||||
\(857\) | 12.8043 | 0.437388 | 0.218694 | − | 0.975793i | \(-0.429820\pi\) | ||||
0.218694 | + | 0.975793i | \(0.429820\pi\) | |||||||
\(858\) | 0.133655 | 0.00456291 | ||||||||
\(859\) | −19.8645 | −0.677768 | −0.338884 | − | 0.940828i | \(-0.610049\pi\) | ||||
−0.338884 | + | 0.940828i | \(0.610049\pi\) | |||||||
\(860\) | 2.96002 | 0.100936 | ||||||||
\(861\) | −7.68853 | −0.262025 | ||||||||
\(862\) | 57.3018 | 1.95171 | ||||||||
\(863\) | −23.5287 | −0.800927 | −0.400463 | − | 0.916313i | \(-0.631151\pi\) | ||||
−0.400463 | + | 0.916313i | \(0.631151\pi\) | |||||||
\(864\) | −16.4831 | −0.560765 | ||||||||
\(865\) | −11.3156 | −0.384740 | ||||||||
\(866\) | 64.7615 | 2.20068 | ||||||||
\(867\) | 54.4465 | 1.84910 | ||||||||
\(868\) | −79.6717 | −2.70423 | ||||||||
\(869\) | −40.9725 | −1.38990 | ||||||||
\(870\) | −21.8983 | −0.742421 | ||||||||
\(871\) | −0.0401728 | −0.00136120 | ||||||||
\(872\) | −11.6071 | −0.393064 | ||||||||
\(873\) | −13.8952 | −0.470280 | ||||||||
\(874\) | −0.441446 | −0.0149321 | ||||||||
\(875\) | 29.8961 | 1.01067 | ||||||||
\(876\) | 12.6980 | 0.429024 | ||||||||
\(877\) | −27.4027 | −0.925324 | −0.462662 | − | 0.886535i | \(-0.653106\pi\) | ||||
−0.462662 | + | 0.886535i | \(0.653106\pi\) | |||||||
\(878\) | 3.60006 | 0.121496 | ||||||||
\(879\) | 70.7038 | 2.38478 | ||||||||
\(880\) | −13.5810 | −0.457814 | ||||||||
\(881\) | −29.6207 | −0.997945 | −0.498973 | − | 0.866618i | \(-0.666289\pi\) | ||||
−0.498973 | + | 0.866618i | \(0.666289\pi\) | |||||||
\(882\) | −61.6847 | −2.07703 | ||||||||
\(883\) | −10.1945 | −0.343073 | −0.171537 | − | 0.985178i | \(-0.554873\pi\) | ||||
−0.171537 | + | 0.985178i | \(0.554873\pi\) | |||||||
\(884\) | 0.0703804 | 0.00236715 | ||||||||
\(885\) | −13.5965 | −0.457042 | ||||||||
\(886\) | 36.7237 | 1.23376 | ||||||||
\(887\) | −46.9669 | −1.57699 | −0.788496 | − | 0.615039i | \(-0.789140\pi\) | ||||
−0.788496 | + | 0.615039i | \(0.789140\pi\) | |||||||
\(888\) | 3.55013 | 0.119135 | ||||||||
\(889\) | 84.1864 | 2.82352 | ||||||||
\(890\) | 10.9776 | 0.367970 | ||||||||
\(891\) | −49.7480 | −1.66662 | ||||||||
\(892\) | −31.4835 | −1.05415 | ||||||||
\(893\) | 8.81646 | 0.295032 | ||||||||
\(894\) | 41.1027 | 1.37468 | ||||||||
\(895\) | 5.78732 | 0.193449 | ||||||||
\(896\) | 32.2668 | 1.07796 | ||||||||
\(897\) | 0.00368786 | 0.000123134 0 | ||||||||
\(898\) | −55.2359 | −1.84325 | ||||||||
\(899\) | 86.1070 | 2.87183 | ||||||||
\(900\) | −13.9657 | −0.465523 | ||||||||
\(901\) | −44.1009 | −1.46921 | ||||||||
\(902\) | −6.02459 | −0.200597 | ||||||||
\(903\) | −32.3310 | −1.07591 | ||||||||
\(904\) | 0.00457279 | 0.000152089 0 | ||||||||
\(905\) | 1.26112 | 0.0419212 | ||||||||
\(906\) | −86.0316 | −2.85821 | ||||||||
\(907\) | 55.7990 | 1.85277 | 0.926387 | − | 0.376573i | \(-0.122897\pi\) | ||||
0.926387 | + | 0.376573i | \(0.122897\pi\) | |||||||
\(908\) | −40.9365 | −1.35853 | ||||||||
\(909\) | −22.0959 | −0.732874 | ||||||||
\(910\) | −0.0414731 | −0.00137482 | ||||||||
\(911\) | −59.0583 | −1.95669 | −0.978344 | − | 0.206987i | \(-0.933634\pi\) | ||||
−0.978344 | + | 0.206987i | \(0.933634\pi\) | |||||||
\(912\) | 10.4718 | 0.346757 | ||||||||
\(913\) | 45.6489 | 1.51076 | ||||||||
\(914\) | 0.170015 | 0.00562359 | ||||||||
\(915\) | 3.77882 | 0.124924 | ||||||||
\(916\) | −6.66383 | −0.220179 | ||||||||
\(917\) | −62.2875 | −2.05692 | ||||||||
\(918\) | −27.9507 | −0.922512 | ||||||||
\(919\) | −46.7807 | −1.54315 | −0.771577 | − | 0.636136i | \(-0.780532\pi\) | ||||
−0.771577 | + | 0.636136i | \(0.780532\pi\) | |||||||
\(920\) | −0.127809 | −0.00421374 | ||||||||
\(921\) | 12.9992 | 0.428338 | ||||||||
\(922\) | −55.2070 | −1.81814 | ||||||||
\(923\) | 0.0884360 | 0.00291091 | ||||||||
\(924\) | −75.6688 | −2.48932 | ||||||||
\(925\) | −8.59262 | −0.282524 | ||||||||
\(926\) | 63.2793 | 2.07949 | ||||||||
\(927\) | −30.9661 | −1.01706 | ||||||||
\(928\) | 58.2009 | 1.91054 | ||||||||
\(929\) | 47.8418 | 1.56964 | 0.784820 | − | 0.619724i | \(-0.212755\pi\) | ||||
0.784820 | + | 0.619724i | \(0.212755\pi\) | |||||||
\(930\) | −28.4610 | −0.933273 | ||||||||
\(931\) | −16.6607 | −0.546032 | ||||||||
\(932\) | −24.2912 | −0.795686 | ||||||||
\(933\) | 4.25324 | 0.139245 | ||||||||
\(934\) | −10.1229 | −0.331230 | ||||||||
\(935\) | −18.6023 | −0.608360 | ||||||||
\(936\) | −0.0118106 | −0.000386042 0 | ||||||||
\(937\) | −52.4058 | −1.71202 | −0.856012 | − | 0.516957i | \(-0.827065\pi\) | ||||
−0.856012 | + | 0.516957i | \(0.827065\pi\) | |||||||
\(938\) | 52.1232 | 1.70188 | ||||||||
\(939\) | −61.1860 | −1.99673 | ||||||||
\(940\) | −8.74913 | −0.285365 | ||||||||
\(941\) | −35.1544 | −1.14600 | −0.573000 | − | 0.819556i | \(-0.694220\pi\) | ||||
−0.573000 | + | 0.819556i | \(0.694220\pi\) | |||||||
\(942\) | −27.7046 | −0.902666 | ||||||||
\(943\) | −0.166233 | −0.00541328 | ||||||||
\(944\) | 44.7370 | 1.45607 | ||||||||
\(945\) | 7.18689 | 0.233789 | ||||||||
\(946\) | −25.3340 | −0.823679 | ||||||||
\(947\) | 9.53111 | 0.309719 | 0.154860 | − | 0.987936i | \(-0.450507\pi\) | ||||
0.154860 | + | 0.987936i | \(0.450507\pi\) | |||||||
\(948\) | −31.3513 | −1.01824 | ||||||||
\(949\) | −0.0259911 | −0.000843707 0 | ||||||||
\(950\) | −8.64461 | −0.280468 | ||||||||
\(951\) | −2.22834 | −0.0722590 | ||||||||
\(952\) | 26.6418 | 0.863465 | ||||||||
\(953\) | −39.0557 | −1.26514 | −0.632569 | − | 0.774504i | \(-0.718000\pi\) | ||||
−0.632569 | + | 0.774504i | \(0.718000\pi\) | |||||||
\(954\) | −25.3662 | −0.821261 | ||||||||
\(955\) | −13.8611 | −0.448534 | ||||||||
\(956\) | 24.1175 | 0.780016 | ||||||||
\(957\) | 81.7808 | 2.64360 | ||||||||
\(958\) | −69.4000 | −2.24221 | ||||||||
\(959\) | 62.8920 | 2.03089 | ||||||||
\(960\) | −5.81346 | −0.187629 | ||||||||
\(961\) | 80.9126 | 2.61008 | ||||||||
\(962\) | 0.0249071 | 0.000803036 0 | ||||||||
\(963\) | 15.3262 | 0.493878 | ||||||||
\(964\) | 12.3575 | 0.398008 | ||||||||
\(965\) | −4.98231 | −0.160386 | ||||||||
\(966\) | −4.78491 | −0.153952 | ||||||||
\(967\) | 11.6769 | 0.375502 | 0.187751 | − | 0.982217i | \(-0.439880\pi\) | ||||
0.187751 | + | 0.982217i | \(0.439880\pi\) | |||||||
\(968\) | 7.93892 | 0.255166 | ||||||||
\(969\) | 14.3436 | 0.460783 | ||||||||
\(970\) | 8.53527 | 0.274051 | ||||||||
\(971\) | 10.5351 | 0.338088 | 0.169044 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169044 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(972\) | −27.3588 | −0.877534 | ||||||||
\(973\) | −79.0833 | −2.53529 | ||||||||
\(974\) | 60.5697 | 1.94078 | ||||||||
\(975\) | 0.0722175 | 0.00231281 | ||||||||
\(976\) | −12.4336 | −0.397989 | ||||||||
\(977\) | 25.5942 | 0.818830 | 0.409415 | − | 0.912348i | \(-0.365733\pi\) | ||||
0.409415 | + | 0.912348i | \(0.365733\pi\) | |||||||
\(978\) | 82.7220 | 2.64516 | ||||||||
\(979\) | −40.9966 | −1.31026 | ||||||||
\(980\) | 16.5334 | 0.528141 | ||||||||
\(981\) | −26.8117 | −0.856032 | ||||||||
\(982\) | 26.6067 | 0.849055 | ||||||||
\(983\) | 22.0953 | 0.704732 | 0.352366 | − | 0.935862i | \(-0.385377\pi\) | ||||
0.352366 | + | 0.935862i | \(0.385377\pi\) | |||||||
\(984\) | 1.34494 | 0.0428751 | ||||||||
\(985\) | 10.3902 | 0.331059 | ||||||||
\(986\) | 98.6927 | 3.14301 | ||||||||
\(987\) | 95.5630 | 3.04180 | ||||||||
\(988\) | 0.0109339 | 0.000347854 0 | ||||||||
\(989\) | −0.699025 | −0.0222277 | ||||||||
\(990\) | −10.6998 | −0.340061 | ||||||||
\(991\) | 6.69407 | 0.212644 | 0.106322 | − | 0.994332i | \(-0.466093\pi\) | ||||
0.106322 | + | 0.994332i | \(0.466093\pi\) | |||||||
\(992\) | 75.6432 | 2.40167 | ||||||||
\(993\) | −46.3428 | −1.47064 | ||||||||
\(994\) | −114.743 | −3.63944 | ||||||||
\(995\) | 6.06646 | 0.192320 | ||||||||
\(996\) | 34.9296 | 1.10679 | ||||||||
\(997\) | 36.5166 | 1.15649 | 0.578247 | − | 0.815862i | \(-0.303737\pi\) | ||||
0.578247 | + | 0.815862i | \(0.303737\pi\) | |||||||
\(998\) | −13.8269 | −0.437682 | ||||||||
\(999\) | −4.31616 | −0.136557 |
(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 | 6023.2.a.b.1.20 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.20 | ✓ | 99 | 1.1 | even | 1 | trivial |