Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.03319 | −1.75121 | −0.875606 | − | 0.483026i | \(-0.839538\pi\) | ||||
−0.875606 | + | 0.483026i | \(0.839538\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.55972 | −1.59196 | −0.795978 | − | 0.605325i | \(-0.793043\pi\) | ||||
−0.795978 | + | 0.605325i | \(0.793043\pi\) | |||||||
\(6\) | −3.03319 | −1.23829 | ||||||||
\(7\) | −4.22109 | −1.59542 | −0.797710 | − | 0.603041i | \(-0.793956\pi\) | ||||
−0.797710 | + | 0.603041i | \(0.793956\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.20023 | 2.06674 | ||||||||
\(10\) | −3.55972 | −1.12568 | ||||||||
\(11\) | 0.539753 | 0.162742 | 0.0813709 | − | 0.996684i | \(-0.474070\pi\) | ||||
0.0813709 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(12\) | −3.03319 | −0.875606 | ||||||||
\(13\) | −2.53431 | −0.702890 | −0.351445 | − | 0.936209i | \(-0.614310\pi\) | ||||
−0.351445 | + | 0.936209i | \(0.614310\pi\) | |||||||
\(14\) | −4.22109 | −1.12813 | ||||||||
\(15\) | 10.7973 | 2.78785 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.56621 | −1.83508 | −0.917538 | − | 0.397648i | \(-0.869827\pi\) | ||||
−0.917538 | + | 0.397648i | \(0.869827\pi\) | |||||||
\(18\) | 6.20023 | 1.46141 | ||||||||
\(19\) | 8.08491 | 1.85481 | 0.927403 | − | 0.374064i | \(-0.122036\pi\) | ||||
0.927403 | + | 0.374064i | \(0.122036\pi\) | |||||||
\(20\) | −3.55972 | −0.795978 | ||||||||
\(21\) | 12.8033 | 2.79392 | ||||||||
\(22\) | 0.539753 | 0.115076 | ||||||||
\(23\) | −8.07968 | −1.68473 | −0.842365 | − | 0.538908i | \(-0.818837\pi\) | ||||
−0.842365 | + | 0.538908i | \(0.818837\pi\) | |||||||
\(24\) | −3.03319 | −0.619147 | ||||||||
\(25\) | 7.67163 | 1.53433 | ||||||||
\(26\) | −2.53431 | −0.497018 | ||||||||
\(27\) | −9.70689 | −1.86809 | ||||||||
\(28\) | −4.22109 | −0.797710 | ||||||||
\(29\) | 5.32885 | 0.989542 | 0.494771 | − | 0.869023i | \(-0.335252\pi\) | ||||
0.494771 | + | 0.869023i | \(0.335252\pi\) | |||||||
\(30\) | 10.7973 | 1.97131 | ||||||||
\(31\) | −8.35573 | −1.50073 | −0.750367 | − | 0.661022i | \(-0.770123\pi\) | ||||
−0.750367 | + | 0.661022i | \(0.770123\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.63717 | −0.284995 | ||||||||
\(34\) | −7.56621 | −1.29759 | ||||||||
\(35\) | 15.0259 | 2.53984 | ||||||||
\(36\) | 6.20023 | 1.03337 | ||||||||
\(37\) | 2.83287 | 0.465721 | 0.232861 | − | 0.972510i | \(-0.425191\pi\) | ||||
0.232861 | + | 0.972510i | \(0.425191\pi\) | |||||||
\(38\) | 8.08491 | 1.31155 | ||||||||
\(39\) | 7.68703 | 1.23091 | ||||||||
\(40\) | −3.55972 | −0.562842 | ||||||||
\(41\) | 0.736282 | 0.114988 | 0.0574940 | − | 0.998346i | \(-0.481689\pi\) | ||||
0.0574940 | + | 0.998346i | \(0.481689\pi\) | |||||||
\(42\) | 12.8033 | 1.97560 | ||||||||
\(43\) | 5.40877 | 0.824829 | 0.412414 | − | 0.910996i | \(-0.364686\pi\) | ||||
0.412414 | + | 0.910996i | \(0.364686\pi\) | |||||||
\(44\) | 0.539753 | 0.0813709 | ||||||||
\(45\) | −22.0711 | −3.29016 | ||||||||
\(46\) | −8.07968 | −1.19128 | ||||||||
\(47\) | 10.8385 | 1.58096 | 0.790482 | − | 0.612486i | \(-0.209830\pi\) | ||||
0.790482 | + | 0.612486i | \(0.209830\pi\) | |||||||
\(48\) | −3.03319 | −0.437803 | ||||||||
\(49\) | 10.8176 | 1.54537 | ||||||||
\(50\) | 7.67163 | 1.08493 | ||||||||
\(51\) | 22.9497 | 3.21361 | ||||||||
\(52\) | −2.53431 | −0.351445 | ||||||||
\(53\) | 4.18131 | 0.574348 | 0.287174 | − | 0.957878i | \(-0.407284\pi\) | ||||
0.287174 | + | 0.957878i | \(0.407284\pi\) | |||||||
\(54\) | −9.70689 | −1.32094 | ||||||||
\(55\) | −1.92137 | −0.259078 | ||||||||
\(56\) | −4.22109 | −0.564066 | ||||||||
\(57\) | −24.5231 | −3.24816 | ||||||||
\(58\) | 5.32885 | 0.699712 | ||||||||
\(59\) | −2.94928 | −0.383964 | −0.191982 | − | 0.981398i | \(-0.561491\pi\) | ||||
−0.191982 | + | 0.981398i | \(0.561491\pi\) | |||||||
\(60\) | 10.7973 | 1.39393 | ||||||||
\(61\) | 11.7171 | 1.50023 | 0.750113 | − | 0.661310i | \(-0.229999\pi\) | ||||
0.750113 | + | 0.661310i | \(0.229999\pi\) | |||||||
\(62\) | −8.35573 | −1.06118 | ||||||||
\(63\) | −26.1717 | −3.29732 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.02143 | 1.11897 | ||||||||
\(66\) | −1.63717 | −0.201522 | ||||||||
\(67\) | −0.652017 | −0.0796566 | −0.0398283 | − | 0.999207i | \(-0.512681\pi\) | ||||
−0.0398283 | + | 0.999207i | \(0.512681\pi\) | |||||||
\(68\) | −7.56621 | −0.917538 | ||||||||
\(69\) | 24.5072 | 2.95032 | ||||||||
\(70\) | 15.0259 | 1.79594 | ||||||||
\(71\) | 6.46973 | 0.767816 | 0.383908 | − | 0.923371i | \(-0.374578\pi\) | ||||
0.383908 | + | 0.923371i | \(0.374578\pi\) | |||||||
\(72\) | 6.20023 | 0.730704 | ||||||||
\(73\) | −13.6526 | −1.59791 | −0.798957 | − | 0.601388i | \(-0.794614\pi\) | ||||
−0.798957 | + | 0.601388i | \(0.794614\pi\) | |||||||
\(74\) | 2.83287 | 0.329315 | ||||||||
\(75\) | −23.2695 | −2.68693 | ||||||||
\(76\) | 8.08491 | 0.927403 | ||||||||
\(77\) | −2.27835 | −0.259642 | ||||||||
\(78\) | 7.68703 | 0.870384 | ||||||||
\(79\) | 9.44342 | 1.06247 | 0.531234 | − | 0.847225i | \(-0.321728\pi\) | ||||
0.531234 | + | 0.847225i | \(0.321728\pi\) | |||||||
\(80\) | −3.55972 | −0.397989 | ||||||||
\(81\) | 10.8421 | 1.20468 | ||||||||
\(82\) | 0.736282 | 0.0813088 | ||||||||
\(83\) | −3.28706 | −0.360802 | −0.180401 | − | 0.983593i | \(-0.557740\pi\) | ||||
−0.180401 | + | 0.983593i | \(0.557740\pi\) | |||||||
\(84\) | 12.8033 | 1.39696 | ||||||||
\(85\) | 26.9336 | 2.92136 | ||||||||
\(86\) | 5.40877 | 0.583242 | ||||||||
\(87\) | −16.1634 | −1.73290 | ||||||||
\(88\) | 0.539753 | 0.0575379 | ||||||||
\(89\) | −9.91472 | −1.05096 | −0.525479 | − | 0.850806i | \(-0.676114\pi\) | ||||
−0.525479 | + | 0.850806i | \(0.676114\pi\) | |||||||
\(90\) | −22.0711 | −2.32650 | ||||||||
\(91\) | 10.6975 | 1.12141 | ||||||||
\(92\) | −8.07968 | −0.842365 | ||||||||
\(93\) | 25.3445 | 2.62810 | ||||||||
\(94\) | 10.8385 | 1.11791 | ||||||||
\(95\) | −28.7801 | −2.95277 | ||||||||
\(96\) | −3.03319 | −0.309573 | ||||||||
\(97\) | 12.6908 | 1.28856 | 0.644279 | − | 0.764791i | \(-0.277158\pi\) | ||||
0.644279 | + | 0.764791i | \(0.277158\pi\) | |||||||
\(98\) | 10.8176 | 1.09274 | ||||||||
\(99\) | 3.34659 | 0.336345 | ||||||||
\(100\) | 7.67163 | 0.767163 | ||||||||
\(101\) | −11.7334 | −1.16752 | −0.583759 | − | 0.811927i | \(-0.698419\pi\) | ||||
−0.583759 | + | 0.811927i | \(0.698419\pi\) | |||||||
\(102\) | 22.9497 | 2.27236 | ||||||||
\(103\) | 15.2050 | 1.49819 | 0.749095 | − | 0.662462i | \(-0.230488\pi\) | ||||
0.749095 | + | 0.662462i | \(0.230488\pi\) | |||||||
\(104\) | −2.53431 | −0.248509 | ||||||||
\(105\) | −45.5764 | −4.44780 | ||||||||
\(106\) | 4.18131 | 0.406125 | ||||||||
\(107\) | −3.30305 | −0.319318 | −0.159659 | − | 0.987172i | \(-0.551040\pi\) | ||||
−0.159659 | + | 0.987172i | \(0.551040\pi\) | |||||||
\(108\) | −9.70689 | −0.934046 | ||||||||
\(109\) | 1.08226 | 0.103662 | 0.0518308 | − | 0.998656i | \(-0.483494\pi\) | ||||
0.0518308 | + | 0.998656i | \(0.483494\pi\) | |||||||
\(110\) | −1.92137 | −0.183196 | ||||||||
\(111\) | −8.59263 | −0.815577 | ||||||||
\(112\) | −4.22109 | −0.398855 | ||||||||
\(113\) | 11.4581 | 1.07789 | 0.538946 | − | 0.842340i | \(-0.318823\pi\) | ||||
0.538946 | + | 0.842340i | \(0.318823\pi\) | |||||||
\(114\) | −24.5231 | −2.29679 | ||||||||
\(115\) | 28.7614 | 2.68202 | ||||||||
\(116\) | 5.32885 | 0.494771 | ||||||||
\(117\) | −15.7133 | −1.45269 | ||||||||
\(118\) | −2.94928 | −0.271503 | ||||||||
\(119\) | 31.9376 | 2.92772 | ||||||||
\(120\) | 10.7973 | 0.985655 | ||||||||
\(121\) | −10.7087 | −0.973515 | ||||||||
\(122\) | 11.7171 | 1.06082 | ||||||||
\(123\) | −2.23328 | −0.201368 | ||||||||
\(124\) | −8.35573 | −0.750367 | ||||||||
\(125\) | −9.51028 | −0.850625 | ||||||||
\(126\) | −26.1717 | −2.33156 | ||||||||
\(127\) | 12.3867 | 1.09914 | 0.549571 | − | 0.835447i | \(-0.314791\pi\) | ||||
0.549571 | + | 0.835447i | \(0.314791\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.4058 | −1.44445 | ||||||||
\(130\) | 9.02143 | 0.791232 | ||||||||
\(131\) | 11.8748 | 1.03751 | 0.518754 | − | 0.854924i | \(-0.326396\pi\) | ||||
0.518754 | + | 0.854924i | \(0.326396\pi\) | |||||||
\(132\) | −1.63717 | −0.142498 | ||||||||
\(133\) | −34.1271 | −2.95920 | ||||||||
\(134\) | −0.652017 | −0.0563257 | ||||||||
\(135\) | 34.5538 | 2.97392 | ||||||||
\(136\) | −7.56621 | −0.648797 | ||||||||
\(137\) | −20.4929 | −1.75082 | −0.875411 | − | 0.483379i | \(-0.839409\pi\) | ||||
−0.875411 | + | 0.483379i | \(0.839409\pi\) | |||||||
\(138\) | 24.5072 | 2.08619 | ||||||||
\(139\) | −11.0098 | −0.933835 | −0.466918 | − | 0.884301i | \(-0.654636\pi\) | ||||
−0.466918 | + | 0.884301i | \(0.654636\pi\) | |||||||
\(140\) | 15.0259 | 1.26992 | ||||||||
\(141\) | −32.8753 | −2.76860 | ||||||||
\(142\) | 6.46973 | 0.542928 | ||||||||
\(143\) | −1.36790 | −0.114390 | ||||||||
\(144\) | 6.20023 | 0.516686 | ||||||||
\(145\) | −18.9692 | −1.57531 | ||||||||
\(146\) | −13.6526 | −1.12990 | ||||||||
\(147\) | −32.8117 | −2.70627 | ||||||||
\(148\) | 2.83287 | 0.232861 | ||||||||
\(149\) | 11.0189 | 0.902703 | 0.451352 | − | 0.892346i | \(-0.350942\pi\) | ||||
0.451352 | + | 0.892346i | \(0.350942\pi\) | |||||||
\(150\) | −23.2695 | −1.89995 | ||||||||
\(151\) | 11.2698 | 0.917124 | 0.458562 | − | 0.888662i | \(-0.348365\pi\) | ||||
0.458562 | + | 0.888662i | \(0.348365\pi\) | |||||||
\(152\) | 8.08491 | 0.655773 | ||||||||
\(153\) | −46.9122 | −3.79263 | ||||||||
\(154\) | −2.27835 | −0.183594 | ||||||||
\(155\) | 29.7441 | 2.38910 | ||||||||
\(156\) | 7.68703 | 0.615455 | ||||||||
\(157\) | 8.35931 | 0.667145 | 0.333573 | − | 0.942724i | \(-0.391746\pi\) | ||||
0.333573 | + | 0.942724i | \(0.391746\pi\) | |||||||
\(158\) | 9.44342 | 0.751279 | ||||||||
\(159\) | −12.6827 | −1.00580 | ||||||||
\(160\) | −3.55972 | −0.281421 | ||||||||
\(161\) | 34.1050 | 2.68785 | ||||||||
\(162\) | 10.8421 | 0.851839 | ||||||||
\(163\) | 8.38009 | 0.656379 | 0.328190 | − | 0.944612i | \(-0.393561\pi\) | ||||
0.328190 | + | 0.944612i | \(0.393561\pi\) | |||||||
\(164\) | 0.736282 | 0.0574940 | ||||||||
\(165\) | 5.82788 | 0.453700 | ||||||||
\(166\) | −3.28706 | −0.255126 | ||||||||
\(167\) | −16.8416 | −1.30324 | −0.651621 | − | 0.758545i | \(-0.725911\pi\) | ||||
−0.651621 | + | 0.758545i | \(0.725911\pi\) | |||||||
\(168\) | 12.8033 | 0.987800 | ||||||||
\(169\) | −6.57729 | −0.505945 | ||||||||
\(170\) | 26.9336 | 2.06571 | ||||||||
\(171\) | 50.1283 | 3.83341 | ||||||||
\(172\) | 5.40877 | 0.412414 | ||||||||
\(173\) | 17.3463 | 1.31882 | 0.659408 | − | 0.751785i | \(-0.270807\pi\) | ||||
0.659408 | + | 0.751785i | \(0.270807\pi\) | |||||||
\(174\) | −16.1634 | −1.22534 | ||||||||
\(175\) | −32.3826 | −2.44790 | ||||||||
\(176\) | 0.539753 | 0.0406854 | ||||||||
\(177\) | 8.94572 | 0.672402 | ||||||||
\(178\) | −9.91472 | −0.743140 | ||||||||
\(179\) | −3.22549 | −0.241085 | −0.120542 | − | 0.992708i | \(-0.538463\pi\) | ||||
−0.120542 | + | 0.992708i | \(0.538463\pi\) | |||||||
\(180\) | −22.0711 | −1.64508 | ||||||||
\(181\) | −22.3274 | −1.65958 | −0.829791 | − | 0.558075i | \(-0.811540\pi\) | ||||
−0.829791 | + | 0.558075i | \(0.811540\pi\) | |||||||
\(182\) | 10.6975 | 0.792953 | ||||||||
\(183\) | −35.5403 | −2.62721 | ||||||||
\(184\) | −8.07968 | −0.595642 | ||||||||
\(185\) | −10.0842 | −0.741408 | ||||||||
\(186\) | 25.3445 | 1.85835 | ||||||||
\(187\) | −4.08389 | −0.298643 | ||||||||
\(188\) | 10.8385 | 0.790482 | ||||||||
\(189\) | 40.9736 | 2.98039 | ||||||||
\(190\) | −28.7801 | −2.08792 | ||||||||
\(191\) | 2.14688 | 0.155343 | 0.0776713 | − | 0.996979i | \(-0.475252\pi\) | ||||
0.0776713 | + | 0.996979i | \(0.475252\pi\) | |||||||
\(192\) | −3.03319 | −0.218901 | ||||||||
\(193\) | 3.12109 | 0.224661 | 0.112331 | − | 0.993671i | \(-0.464168\pi\) | ||||
0.112331 | + | 0.993671i | \(0.464168\pi\) | |||||||
\(194\) | 12.6908 | 0.911148 | ||||||||
\(195\) | −27.3637 | −1.95955 | ||||||||
\(196\) | 10.8176 | 0.772684 | ||||||||
\(197\) | −13.9592 | −0.994553 | −0.497276 | − | 0.867592i | \(-0.665666\pi\) | ||||
−0.497276 | + | 0.867592i | \(0.665666\pi\) | |||||||
\(198\) | 3.34659 | 0.237832 | ||||||||
\(199\) | 19.4235 | 1.37689 | 0.688447 | − | 0.725287i | \(-0.258293\pi\) | ||||
0.688447 | + | 0.725287i | \(0.258293\pi\) | |||||||
\(200\) | 7.67163 | 0.542466 | ||||||||
\(201\) | 1.97769 | 0.139495 | ||||||||
\(202\) | −11.7334 | −0.825560 | ||||||||
\(203\) | −22.4935 | −1.57874 | ||||||||
\(204\) | 22.9497 | 1.60680 | ||||||||
\(205\) | −2.62096 | −0.183056 | ||||||||
\(206\) | 15.2050 | 1.05938 | ||||||||
\(207\) | −50.0959 | −3.48190 | ||||||||
\(208\) | −2.53431 | −0.175723 | ||||||||
\(209\) | 4.36386 | 0.301854 | ||||||||
\(210\) | −45.5764 | −3.14507 | ||||||||
\(211\) | −5.94554 | −0.409308 | −0.204654 | − | 0.978834i | \(-0.565607\pi\) | ||||
−0.204654 | + | 0.978834i | \(0.565607\pi\) | |||||||
\(212\) | 4.18131 | 0.287174 | ||||||||
\(213\) | −19.6239 | −1.34461 | ||||||||
\(214\) | −3.30305 | −0.225792 | ||||||||
\(215\) | −19.2537 | −1.31309 | ||||||||
\(216\) | −9.70689 | −0.660470 | ||||||||
\(217\) | 35.2703 | 2.39430 | ||||||||
\(218\) | 1.08226 | 0.0732998 | ||||||||
\(219\) | 41.4108 | 2.79829 | ||||||||
\(220\) | −1.92137 | −0.129539 | ||||||||
\(221\) | 19.1751 | 1.28986 | ||||||||
\(222\) | −8.59263 | −0.576700 | ||||||||
\(223\) | 12.4346 | 0.832683 | 0.416342 | − | 0.909208i | \(-0.363312\pi\) | ||||
0.416342 | + | 0.909208i | \(0.363312\pi\) | |||||||
\(224\) | −4.22109 | −0.282033 | ||||||||
\(225\) | 47.5659 | 3.17106 | ||||||||
\(226\) | 11.4581 | 0.762185 | ||||||||
\(227\) | −20.3942 | −1.35361 | −0.676804 | − | 0.736164i | \(-0.736635\pi\) | ||||
−0.676804 | + | 0.736164i | \(0.736635\pi\) | |||||||
\(228\) | −24.5231 | −1.62408 | ||||||||
\(229\) | −9.66862 | −0.638921 | −0.319460 | − | 0.947600i | \(-0.603502\pi\) | ||||
−0.319460 | + | 0.947600i | \(0.603502\pi\) | |||||||
\(230\) | 28.7614 | 1.89647 | ||||||||
\(231\) | 6.91065 | 0.454687 | ||||||||
\(232\) | 5.32885 | 0.349856 | ||||||||
\(233\) | 17.6336 | 1.15521 | 0.577607 | − | 0.816315i | \(-0.303987\pi\) | ||||
0.577607 | + | 0.816315i | \(0.303987\pi\) | |||||||
\(234\) | −15.7133 | −1.02721 | ||||||||
\(235\) | −38.5822 | −2.51683 | ||||||||
\(236\) | −2.94928 | −0.191982 | ||||||||
\(237\) | −28.6437 | −1.86061 | ||||||||
\(238\) | 31.9376 | 2.07021 | ||||||||
\(239\) | 3.61447 | 0.233801 | 0.116900 | − | 0.993144i | \(-0.462704\pi\) | ||||
0.116900 | + | 0.993144i | \(0.462704\pi\) | |||||||
\(240\) | 10.7973 | 0.696963 | ||||||||
\(241\) | −5.38886 | −0.347127 | −0.173564 | − | 0.984823i | \(-0.555528\pi\) | ||||
−0.173564 | + | 0.984823i | \(0.555528\pi\) | |||||||
\(242\) | −10.7087 | −0.688379 | ||||||||
\(243\) | −3.76556 | −0.241561 | ||||||||
\(244\) | 11.7171 | 0.750113 | ||||||||
\(245\) | −38.5076 | −2.46016 | ||||||||
\(246\) | −2.23328 | −0.142389 | ||||||||
\(247\) | −20.4896 | −1.30372 | ||||||||
\(248\) | −8.35573 | −0.530589 | ||||||||
\(249\) | 9.97028 | 0.631841 | ||||||||
\(250\) | −9.51028 | −0.601483 | ||||||||
\(251\) | −25.1584 | −1.58798 | −0.793992 | − | 0.607929i | \(-0.792001\pi\) | ||||
−0.793992 | + | 0.607929i | \(0.792001\pi\) | |||||||
\(252\) | −26.1717 | −1.64866 | ||||||||
\(253\) | −4.36103 | −0.274176 | ||||||||
\(254\) | 12.3867 | 0.777211 | ||||||||
\(255\) | −81.6947 | −5.11592 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.5405 | 0.969389 | 0.484695 | − | 0.874683i | \(-0.338931\pi\) | ||||
0.484695 | + | 0.874683i | \(0.338931\pi\) | |||||||
\(258\) | −16.4058 | −1.02138 | ||||||||
\(259\) | −11.9578 | −0.743022 | ||||||||
\(260\) | 9.02143 | 0.559485 | ||||||||
\(261\) | 33.0401 | 2.04513 | ||||||||
\(262\) | 11.8748 | 0.733629 | ||||||||
\(263\) | −3.64861 | −0.224983 | −0.112492 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112492 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(264\) | −1.63717 | −0.100761 | ||||||||
\(265\) | −14.8843 | −0.914337 | ||||||||
\(266\) | −34.1271 | −2.09247 | ||||||||
\(267\) | 30.0732 | 1.84045 | ||||||||
\(268\) | −0.652017 | −0.0398283 | ||||||||
\(269\) | −26.9893 | −1.64556 | −0.822782 | − | 0.568357i | \(-0.807579\pi\) | ||||
−0.822782 | + | 0.568357i | \(0.807579\pi\) | |||||||
\(270\) | 34.5538 | 2.10288 | ||||||||
\(271\) | −14.8651 | −0.902991 | −0.451496 | − | 0.892273i | \(-0.649109\pi\) | ||||
−0.451496 | + | 0.892273i | \(0.649109\pi\) | |||||||
\(272\) | −7.56621 | −0.458769 | ||||||||
\(273\) | −32.4476 | −1.96382 | ||||||||
\(274\) | −20.4929 | −1.23802 | ||||||||
\(275\) | 4.14079 | 0.249699 | ||||||||
\(276\) | 24.5072 | 1.47516 | ||||||||
\(277\) | −15.7356 | −0.945458 | −0.472729 | − | 0.881208i | \(-0.656731\pi\) | ||||
−0.472729 | + | 0.881208i | \(0.656731\pi\) | |||||||
\(278\) | −11.0098 | −0.660321 | ||||||||
\(279\) | −51.8074 | −3.10163 | ||||||||
\(280\) | 15.0259 | 0.897969 | ||||||||
\(281\) | −28.3852 | −1.69332 | −0.846660 | − | 0.532134i | \(-0.821390\pi\) | ||||
−0.846660 | + | 0.532134i | \(0.821390\pi\) | |||||||
\(282\) | −32.8753 | −1.95770 | ||||||||
\(283\) | −31.9000 | −1.89626 | −0.948129 | − | 0.317886i | \(-0.897027\pi\) | ||||
−0.948129 | + | 0.317886i | \(0.897027\pi\) | |||||||
\(284\) | 6.46973 | 0.383908 | ||||||||
\(285\) | 87.2953 | 5.17093 | ||||||||
\(286\) | −1.36790 | −0.0808856 | ||||||||
\(287\) | −3.10791 | −0.183454 | ||||||||
\(288\) | 6.20023 | 0.365352 | ||||||||
\(289\) | 40.2476 | 2.36750 | ||||||||
\(290\) | −18.9692 | −1.11391 | ||||||||
\(291\) | −38.4936 | −2.25654 | ||||||||
\(292\) | −13.6526 | −0.798957 | ||||||||
\(293\) | 30.1448 | 1.76108 | 0.880538 | − | 0.473976i | \(-0.157182\pi\) | ||||
0.880538 | + | 0.473976i | \(0.157182\pi\) | |||||||
\(294\) | −32.8117 | −1.91362 | ||||||||
\(295\) | 10.4986 | 0.611254 | ||||||||
\(296\) | 2.83287 | 0.164657 | ||||||||
\(297\) | −5.23933 | −0.304016 | ||||||||
\(298\) | 11.0189 | 0.638307 | ||||||||
\(299\) | 20.4764 | 1.18418 | ||||||||
\(300\) | −23.2695 | −1.34347 | ||||||||
\(301\) | −22.8309 | −1.31595 | ||||||||
\(302\) | 11.2698 | 0.648505 | ||||||||
\(303\) | 35.5896 | 2.04457 | ||||||||
\(304\) | 8.08491 | 0.463701 | ||||||||
\(305\) | −41.7098 | −2.38829 | ||||||||
\(306\) | −46.9122 | −2.68179 | ||||||||
\(307\) | 5.46963 | 0.312168 | 0.156084 | − | 0.987744i | \(-0.450113\pi\) | ||||
0.156084 | + | 0.987744i | \(0.450113\pi\) | |||||||
\(308\) | −2.27835 | −0.129821 | ||||||||
\(309\) | −46.1195 | −2.62365 | ||||||||
\(310\) | 29.7441 | 1.68935 | ||||||||
\(311\) | 22.6979 | 1.28708 | 0.643541 | − | 0.765411i | \(-0.277464\pi\) | ||||
0.643541 | + | 0.765411i | \(0.277464\pi\) | |||||||
\(312\) | 7.68703 | 0.435192 | ||||||||
\(313\) | −14.9946 | −0.847542 | −0.423771 | − | 0.905769i | \(-0.639294\pi\) | ||||
−0.423771 | + | 0.905769i | \(0.639294\pi\) | |||||||
\(314\) | 8.35931 | 0.471743 | ||||||||
\(315\) | 93.1640 | 5.24920 | ||||||||
\(316\) | 9.44342 | 0.531234 | ||||||||
\(317\) | −15.1517 | −0.851004 | −0.425502 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425502 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(318\) | −12.6827 | −0.711211 | ||||||||
\(319\) | 2.87626 | 0.161040 | ||||||||
\(320\) | −3.55972 | −0.198995 | ||||||||
\(321\) | 10.0188 | 0.559194 | ||||||||
\(322\) | 34.1050 | 1.90060 | ||||||||
\(323\) | −61.1722 | −3.40371 | ||||||||
\(324\) | 10.8421 | 0.602341 | ||||||||
\(325\) | −19.4423 | −1.07846 | ||||||||
\(326\) | 8.38009 | 0.464130 | ||||||||
\(327\) | −3.28269 | −0.181533 | ||||||||
\(328\) | 0.736282 | 0.0406544 | ||||||||
\(329\) | −45.7504 | −2.52230 | ||||||||
\(330\) | 5.82788 | 0.320814 | ||||||||
\(331\) | −21.1767 | −1.16398 | −0.581988 | − | 0.813198i | \(-0.697725\pi\) | ||||
−0.581988 | + | 0.813198i | \(0.697725\pi\) | |||||||
\(332\) | −3.28706 | −0.180401 | ||||||||
\(333\) | 17.5645 | 0.962526 | ||||||||
\(334\) | −16.8416 | −0.921531 | ||||||||
\(335\) | 2.32100 | 0.126810 | ||||||||
\(336\) | 12.8033 | 0.698480 | ||||||||
\(337\) | −19.0650 | −1.03854 | −0.519270 | − | 0.854610i | \(-0.673796\pi\) | ||||
−0.519270 | + | 0.854610i | \(0.673796\pi\) | |||||||
\(338\) | −6.57729 | −0.357757 | ||||||||
\(339\) | −34.7547 | −1.88762 | ||||||||
\(340\) | 26.9336 | 1.46068 | ||||||||
\(341\) | −4.51003 | −0.244232 | ||||||||
\(342\) | 50.1283 | 2.71063 | ||||||||
\(343\) | −16.1143 | −0.870090 | ||||||||
\(344\) | 5.40877 | 0.291621 | ||||||||
\(345\) | −87.2388 | −4.69678 | ||||||||
\(346\) | 17.3463 | 0.932543 | ||||||||
\(347\) | 7.60292 | 0.408146 | 0.204073 | − | 0.978956i | \(-0.434582\pi\) | ||||
0.204073 | + | 0.978956i | \(0.434582\pi\) | |||||||
\(348\) | −16.1634 | −0.866449 | ||||||||
\(349\) | 20.6054 | 1.10298 | 0.551490 | − | 0.834181i | \(-0.314059\pi\) | ||||
0.551490 | + | 0.834181i | \(0.314059\pi\) | |||||||
\(350\) | −32.3826 | −1.73092 | ||||||||
\(351\) | 24.6002 | 1.31306 | ||||||||
\(352\) | 0.539753 | 0.0287689 | ||||||||
\(353\) | 2.77705 | 0.147807 | 0.0739037 | − | 0.997265i | \(-0.476454\pi\) | ||||
0.0739037 | + | 0.997265i | \(0.476454\pi\) | |||||||
\(354\) | 8.94572 | 0.475460 | ||||||||
\(355\) | −23.0305 | −1.22233 | ||||||||
\(356\) | −9.91472 | −0.525479 | ||||||||
\(357\) | −96.8728 | −5.12705 | ||||||||
\(358\) | −3.22549 | −0.170473 | ||||||||
\(359\) | −21.8966 | −1.15566 | −0.577828 | − | 0.816159i | \(-0.696100\pi\) | ||||
−0.577828 | + | 0.816159i | \(0.696100\pi\) | |||||||
\(360\) | −22.0711 | −1.16325 | ||||||||
\(361\) | 46.3658 | 2.44030 | ||||||||
\(362\) | −22.3274 | −1.17350 | ||||||||
\(363\) | 32.4814 | 1.70483 | ||||||||
\(364\) | 10.6975 | 0.560703 | ||||||||
\(365\) | 48.5994 | 2.54381 | ||||||||
\(366\) | −35.5403 | −1.85772 | ||||||||
\(367\) | 21.9008 | 1.14321 | 0.571606 | − | 0.820529i | \(-0.306321\pi\) | ||||
0.571606 | + | 0.820529i | \(0.306321\pi\) | |||||||
\(368\) | −8.07968 | −0.421182 | ||||||||
\(369\) | 4.56512 | 0.237650 | ||||||||
\(370\) | −10.0842 | −0.524255 | ||||||||
\(371\) | −17.6497 | −0.916326 | ||||||||
\(372\) | 25.3445 | 1.31405 | ||||||||
\(373\) | −12.2184 | −0.632645 | −0.316323 | − | 0.948652i | \(-0.602448\pi\) | ||||
−0.316323 | + | 0.948652i | \(0.602448\pi\) | |||||||
\(374\) | −4.08389 | −0.211173 | ||||||||
\(375\) | 28.8465 | 1.48963 | ||||||||
\(376\) | 10.8385 | 0.558955 | ||||||||
\(377\) | −13.5049 | −0.695540 | ||||||||
\(378\) | 40.9736 | 2.10746 | ||||||||
\(379\) | 0.908152 | 0.0466486 | 0.0233243 | − | 0.999728i | \(-0.492575\pi\) | ||||
0.0233243 | + | 0.999728i | \(0.492575\pi\) | |||||||
\(380\) | −28.7801 | −1.47639 | ||||||||
\(381\) | −37.5712 | −1.92483 | ||||||||
\(382\) | 2.14688 | 0.109844 | ||||||||
\(383\) | −24.3990 | −1.24673 | −0.623365 | − | 0.781931i | \(-0.714235\pi\) | ||||
−0.623365 | + | 0.781931i | \(0.714235\pi\) | |||||||
\(384\) | −3.03319 | −0.154787 | ||||||||
\(385\) | 8.11028 | 0.413338 | ||||||||
\(386\) | 3.12109 | 0.158859 | ||||||||
\(387\) | 33.5356 | 1.70471 | ||||||||
\(388\) | 12.6908 | 0.644279 | ||||||||
\(389\) | 23.5296 | 1.19300 | 0.596498 | − | 0.802614i | \(-0.296558\pi\) | ||||
0.596498 | + | 0.802614i | \(0.296558\pi\) | |||||||
\(390\) | −27.3637 | −1.38561 | ||||||||
\(391\) | 61.1326 | 3.09161 | ||||||||
\(392\) | 10.8176 | 0.546370 | ||||||||
\(393\) | −36.0186 | −1.81690 | ||||||||
\(394\) | −13.9592 | −0.703255 | ||||||||
\(395\) | −33.6160 | −1.69140 | ||||||||
\(396\) | 3.34659 | 0.168173 | ||||||||
\(397\) | 8.10906 | 0.406982 | 0.203491 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203491 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(398\) | 19.4235 | 0.973611 | ||||||||
\(399\) | 103.514 | 5.18218 | ||||||||
\(400\) | 7.67163 | 0.383582 | ||||||||
\(401\) | −21.3491 | −1.06612 | −0.533061 | − | 0.846077i | \(-0.678958\pi\) | ||||
−0.533061 | + | 0.846077i | \(0.678958\pi\) | |||||||
\(402\) | 1.97769 | 0.0986382 | ||||||||
\(403\) | 21.1760 | 1.05485 | ||||||||
\(404\) | −11.7334 | −0.583759 | ||||||||
\(405\) | −38.5950 | −1.91780 | ||||||||
\(406\) | −22.4935 | −1.11634 | ||||||||
\(407\) | 1.52905 | 0.0757923 | ||||||||
\(408\) | 22.9497 | 1.13618 | ||||||||
\(409\) | 14.4921 | 0.716586 | 0.358293 | − | 0.933609i | \(-0.383359\pi\) | ||||
0.358293 | + | 0.933609i | \(0.383359\pi\) | |||||||
\(410\) | −2.62096 | −0.129440 | ||||||||
\(411\) | 62.1587 | 3.06606 | ||||||||
\(412\) | 15.2050 | 0.749095 | ||||||||
\(413\) | 12.4492 | 0.612583 | ||||||||
\(414\) | −50.0959 | −2.46208 | ||||||||
\(415\) | 11.7010 | 0.574382 | ||||||||
\(416\) | −2.53431 | −0.124255 | ||||||||
\(417\) | 33.3946 | 1.63534 | ||||||||
\(418\) | 4.36386 | 0.213443 | ||||||||
\(419\) | 22.3852 | 1.09359 | 0.546795 | − | 0.837266i | \(-0.315848\pi\) | ||||
0.546795 | + | 0.837266i | \(0.315848\pi\) | |||||||
\(420\) | −45.5764 | −2.22390 | ||||||||
\(421\) | 20.5334 | 1.00073 | 0.500367 | − | 0.865813i | \(-0.333198\pi\) | ||||
0.500367 | + | 0.865813i | \(0.333198\pi\) | |||||||
\(422\) | −5.94554 | −0.289424 | ||||||||
\(423\) | 67.2014 | 3.26744 | ||||||||
\(424\) | 4.18131 | 0.203063 | ||||||||
\(425\) | −58.0452 | −2.81561 | ||||||||
\(426\) | −19.6239 | −0.950781 | ||||||||
\(427\) | −49.4590 | −2.39349 | ||||||||
\(428\) | −3.30305 | −0.159659 | ||||||||
\(429\) | 4.14910 | 0.200320 | ||||||||
\(430\) | −19.2537 | −0.928496 | ||||||||
\(431\) | −20.7962 | −1.00172 | −0.500860 | − | 0.865528i | \(-0.666983\pi\) | ||||
−0.500860 | + | 0.865528i | \(0.666983\pi\) | |||||||
\(432\) | −9.70689 | −0.467023 | ||||||||
\(433\) | −21.9824 | −1.05641 | −0.528203 | − | 0.849118i | \(-0.677134\pi\) | ||||
−0.528203 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(434\) | 35.2703 | 1.69303 | ||||||||
\(435\) | 57.5372 | 2.75870 | ||||||||
\(436\) | 1.08226 | 0.0518308 | ||||||||
\(437\) | −65.3235 | −3.12485 | ||||||||
\(438\) | 41.4108 | 1.97869 | ||||||||
\(439\) | 32.2123 | 1.53741 | 0.768706 | − | 0.639603i | \(-0.220901\pi\) | ||||
0.768706 | + | 0.639603i | \(0.220901\pi\) | |||||||
\(440\) | −1.92137 | −0.0915979 | ||||||||
\(441\) | 67.0714 | 3.19388 | ||||||||
\(442\) | 19.1751 | 0.912067 | ||||||||
\(443\) | 32.4274 | 1.54067 | 0.770336 | − | 0.637639i | \(-0.220089\pi\) | ||||
0.770336 | + | 0.637639i | \(0.220089\pi\) | |||||||
\(444\) | −8.59263 | −0.407788 | ||||||||
\(445\) | 35.2937 | 1.67308 | ||||||||
\(446\) | 12.4346 | 0.588796 | ||||||||
\(447\) | −33.4224 | −1.58082 | ||||||||
\(448\) | −4.22109 | −0.199428 | ||||||||
\(449\) | 32.9473 | 1.55488 | 0.777440 | − | 0.628957i | \(-0.216518\pi\) | ||||
0.777440 | + | 0.628957i | \(0.216518\pi\) | |||||||
\(450\) | 47.5659 | 2.24228 | ||||||||
\(451\) | 0.397411 | 0.0187133 | ||||||||
\(452\) | 11.4581 | 0.538946 | ||||||||
\(453\) | −34.1835 | −1.60608 | ||||||||
\(454\) | −20.3942 | −0.957145 | ||||||||
\(455\) | −38.0802 | −1.78523 | ||||||||
\(456\) | −24.5231 | −1.14840 | ||||||||
\(457\) | −32.8041 | −1.53451 | −0.767255 | − | 0.641343i | \(-0.778378\pi\) | ||||
−0.767255 | + | 0.641343i | \(0.778378\pi\) | |||||||
\(458\) | −9.66862 | −0.451785 | ||||||||
\(459\) | 73.4444 | 3.42809 | ||||||||
\(460\) | 28.7614 | 1.34101 | ||||||||
\(461\) | −14.4291 | −0.672029 | −0.336014 | − | 0.941857i | \(-0.609079\pi\) | ||||
−0.336014 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(462\) | 6.91065 | 0.321512 | ||||||||
\(463\) | 25.2189 | 1.17202 | 0.586011 | − | 0.810303i | \(-0.300697\pi\) | ||||
0.586011 | + | 0.810303i | \(0.300697\pi\) | |||||||
\(464\) | 5.32885 | 0.247386 | ||||||||
\(465\) | −90.2194 | −4.18382 | ||||||||
\(466\) | 17.6336 | 0.816860 | ||||||||
\(467\) | 4.84703 | 0.224294 | 0.112147 | − | 0.993692i | \(-0.464227\pi\) | ||||
0.112147 | + | 0.993692i | \(0.464227\pi\) | |||||||
\(468\) | −15.7133 | −0.726346 | ||||||||
\(469\) | 2.75222 | 0.127086 | ||||||||
\(470\) | −38.5822 | −1.77966 | ||||||||
\(471\) | −25.3554 | −1.16831 | ||||||||
\(472\) | −2.94928 | −0.135752 | ||||||||
\(473\) | 2.91940 | 0.134234 | ||||||||
\(474\) | −28.6437 | −1.31565 | ||||||||
\(475\) | 62.0245 | 2.84588 | ||||||||
\(476\) | 31.9376 | 1.46386 | ||||||||
\(477\) | 25.9251 | 1.18703 | ||||||||
\(478\) | 3.61447 | 0.165322 | ||||||||
\(479\) | −1.02461 | −0.0468158 | −0.0234079 | − | 0.999726i | \(-0.507452\pi\) | ||||
−0.0234079 | + | 0.999726i | \(0.507452\pi\) | |||||||
\(480\) | 10.7973 | 0.492828 | ||||||||
\(481\) | −7.17937 | −0.327351 | ||||||||
\(482\) | −5.38886 | −0.245456 | ||||||||
\(483\) | −103.447 | −4.70700 | ||||||||
\(484\) | −10.7087 | −0.486758 | ||||||||
\(485\) | −45.1758 | −2.05133 | ||||||||
\(486\) | −3.76556 | −0.170809 | ||||||||
\(487\) | −2.65034 | −0.120098 | −0.0600491 | − | 0.998195i | \(-0.519126\pi\) | ||||
−0.0600491 | + | 0.998195i | \(0.519126\pi\) | |||||||
\(488\) | 11.7171 | 0.530410 | ||||||||
\(489\) | −25.4184 | −1.14946 | ||||||||
\(490\) | −38.5076 | −1.73959 | ||||||||
\(491\) | −30.7111 | −1.38597 | −0.692987 | − | 0.720951i | \(-0.743705\pi\) | ||||
−0.692987 | + | 0.720951i | \(0.743705\pi\) | |||||||
\(492\) | −2.23328 | −0.100684 | ||||||||
\(493\) | −40.3192 | −1.81589 | ||||||||
\(494\) | −20.4896 | −0.921873 | ||||||||
\(495\) | −11.9129 | −0.535447 | ||||||||
\(496\) | −8.35573 | −0.375183 | ||||||||
\(497\) | −27.3093 | −1.22499 | ||||||||
\(498\) | 9.97028 | 0.446779 | ||||||||
\(499\) | 9.11311 | 0.407959 | 0.203979 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203979 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(500\) | −9.51028 | −0.425313 | ||||||||
\(501\) | 51.0837 | 2.28225 | ||||||||
\(502\) | −25.1584 | −1.12287 | ||||||||
\(503\) | −6.56059 | −0.292522 | −0.146261 | − | 0.989246i | \(-0.546724\pi\) | ||||
−0.146261 | + | 0.989246i | \(0.546724\pi\) | |||||||
\(504\) | −26.1717 | −1.16578 | ||||||||
\(505\) | 41.7677 | 1.85864 | ||||||||
\(506\) | −4.36103 | −0.193872 | ||||||||
\(507\) | 19.9502 | 0.886018 | ||||||||
\(508\) | 12.3867 | 0.549571 | ||||||||
\(509\) | 7.46040 | 0.330676 | 0.165338 | − | 0.986237i | \(-0.447128\pi\) | ||||
0.165338 | + | 0.986237i | \(0.447128\pi\) | |||||||
\(510\) | −81.6947 | −3.61750 | ||||||||
\(511\) | 57.6287 | 2.54934 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −78.4793 | −3.46495 | ||||||||
\(514\) | 15.5405 | 0.685462 | ||||||||
\(515\) | −54.1255 | −2.38506 | ||||||||
\(516\) | −16.4058 | −0.722225 | ||||||||
\(517\) | 5.85014 | 0.257289 | ||||||||
\(518\) | −11.9578 | −0.525396 | ||||||||
\(519\) | −52.6146 | −2.30953 | ||||||||
\(520\) | 9.02143 | 0.395616 | ||||||||
\(521\) | 3.74531 | 0.164085 | 0.0820425 | − | 0.996629i | \(-0.473856\pi\) | ||||
0.0820425 | + | 0.996629i | \(0.473856\pi\) | |||||||
\(522\) | 33.0401 | 1.44612 | ||||||||
\(523\) | −10.0070 | −0.437574 | −0.218787 | − | 0.975773i | \(-0.570210\pi\) | ||||
−0.218787 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(524\) | 11.8748 | 0.518754 | ||||||||
\(525\) | 98.2226 | 4.28679 | ||||||||
\(526\) | −3.64861 | −0.159087 | ||||||||
\(527\) | 63.2212 | 2.75396 | ||||||||
\(528\) | −1.63717 | −0.0712488 | ||||||||
\(529\) | 42.2812 | 1.83831 | ||||||||
\(530\) | −14.8843 | −0.646534 | ||||||||
\(531\) | −18.2862 | −0.793554 | ||||||||
\(532\) | −34.1271 | −1.47960 | ||||||||
\(533\) | −1.86596 | −0.0808239 | ||||||||
\(534\) | 30.0732 | 1.30139 | ||||||||
\(535\) | 11.7580 | 0.508341 | ||||||||
\(536\) | −0.652017 | −0.0281628 | ||||||||
\(537\) | 9.78353 | 0.422190 | ||||||||
\(538\) | −26.9893 | −1.16359 | ||||||||
\(539\) | 5.83882 | 0.251496 | ||||||||
\(540\) | 34.5538 | 1.48696 | ||||||||
\(541\) | −7.73688 | −0.332634 | −0.166317 | − | 0.986072i | \(-0.553188\pi\) | ||||
−0.166317 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(542\) | −14.8651 | −0.638511 | ||||||||
\(543\) | 67.7231 | 2.90628 | ||||||||
\(544\) | −7.56621 | −0.324399 | ||||||||
\(545\) | −3.85254 | −0.165025 | ||||||||
\(546\) | −32.4476 | −1.38863 | ||||||||
\(547\) | 9.64163 | 0.412246 | 0.206123 | − | 0.978526i | \(-0.433915\pi\) | ||||
0.206123 | + | 0.978526i | \(0.433915\pi\) | |||||||
\(548\) | −20.4929 | −0.875411 | ||||||||
\(549\) | 72.6489 | 3.10058 | ||||||||
\(550\) | 4.14079 | 0.176564 | ||||||||
\(551\) | 43.0833 | 1.83541 | ||||||||
\(552\) | 24.5072 | 1.04310 | ||||||||
\(553\) | −39.8615 | −1.69508 | ||||||||
\(554\) | −15.7356 | −0.668540 | ||||||||
\(555\) | 30.5874 | 1.29836 | ||||||||
\(556\) | −11.0098 | −0.466918 | ||||||||
\(557\) | −13.5265 | −0.573135 | −0.286568 | − | 0.958060i | \(-0.592514\pi\) | ||||
−0.286568 | + | 0.958060i | \(0.592514\pi\) | |||||||
\(558\) | −51.8074 | −2.19318 | ||||||||
\(559\) | −13.7075 | −0.579764 | ||||||||
\(560\) | 15.0259 | 0.634960 | ||||||||
\(561\) | 12.3872 | 0.522988 | ||||||||
\(562\) | −28.3852 | −1.19736 | ||||||||
\(563\) | 43.2512 | 1.82282 | 0.911410 | − | 0.411500i | \(-0.134995\pi\) | ||||
0.911410 | + | 0.411500i | \(0.134995\pi\) | |||||||
\(564\) | −32.8753 | −1.38430 | ||||||||
\(565\) | −40.7878 | −1.71596 | ||||||||
\(566\) | −31.9000 | −1.34086 | ||||||||
\(567\) | −45.7656 | −1.92197 | ||||||||
\(568\) | 6.46973 | 0.271464 | ||||||||
\(569\) | 13.0064 | 0.545256 | 0.272628 | − | 0.962120i | \(-0.412107\pi\) | ||||
0.272628 | + | 0.962120i | \(0.412107\pi\) | |||||||
\(570\) | 87.2953 | 3.65640 | ||||||||
\(571\) | −13.2514 | −0.554552 | −0.277276 | − | 0.960790i | \(-0.589432\pi\) | ||||
−0.277276 | + | 0.960790i | \(0.589432\pi\) | |||||||
\(572\) | −1.36790 | −0.0571948 | ||||||||
\(573\) | −6.51188 | −0.272038 | ||||||||
\(574\) | −3.10791 | −0.129722 | ||||||||
\(575\) | −61.9843 | −2.58493 | ||||||||
\(576\) | 6.20023 | 0.258343 | ||||||||
\(577\) | −32.4321 | −1.35016 | −0.675082 | − | 0.737742i | \(-0.735892\pi\) | ||||
−0.675082 | + | 0.737742i | \(0.735892\pi\) | |||||||
\(578\) | 40.2476 | 1.67408 | ||||||||
\(579\) | −9.46686 | −0.393429 | ||||||||
\(580\) | −18.9692 | −0.787654 | ||||||||
\(581\) | 13.8750 | 0.575631 | ||||||||
\(582\) | −38.4936 | −1.59561 | ||||||||
\(583\) | 2.25688 | 0.0934703 | ||||||||
\(584\) | −13.6526 | −0.564948 | ||||||||
\(585\) | 55.9349 | 2.31262 | ||||||||
\(586\) | 30.1448 | 1.24527 | ||||||||
\(587\) | 4.68966 | 0.193563 | 0.0967814 | − | 0.995306i | \(-0.469145\pi\) | ||||
0.0967814 | + | 0.995306i | \(0.469145\pi\) | |||||||
\(588\) | −32.8117 | −1.35313 | ||||||||
\(589\) | −67.5553 | −2.78357 | ||||||||
\(590\) | 10.4986 | 0.432221 | ||||||||
\(591\) | 42.3409 | 1.74167 | ||||||||
\(592\) | 2.83287 | 0.116430 | ||||||||
\(593\) | 5.61726 | 0.230673 | 0.115337 | − | 0.993326i | \(-0.463205\pi\) | ||||
0.115337 | + | 0.993326i | \(0.463205\pi\) | |||||||
\(594\) | −5.23933 | −0.214972 | ||||||||
\(595\) | −113.689 | −4.66080 | ||||||||
\(596\) | 11.0189 | 0.451352 | ||||||||
\(597\) | −58.9151 | −2.41123 | ||||||||
\(598\) | 20.4764 | 0.837342 | ||||||||
\(599\) | −7.25280 | −0.296341 | −0.148171 | − | 0.988962i | \(-0.547339\pi\) | ||||
−0.148171 | + | 0.988962i | \(0.547339\pi\) | |||||||
\(600\) | −23.2695 | −0.949974 | ||||||||
\(601\) | −2.00906 | −0.0819514 | −0.0409757 | − | 0.999160i | \(-0.513047\pi\) | ||||
−0.0409757 | + | 0.999160i | \(0.513047\pi\) | |||||||
\(602\) | −22.8309 | −0.930517 | ||||||||
\(603\) | −4.04265 | −0.164630 | ||||||||
\(604\) | 11.2698 | 0.458562 | ||||||||
\(605\) | 38.1199 | 1.54979 | ||||||||
\(606\) | 35.5896 | 1.44573 | ||||||||
\(607\) | 35.9967 | 1.46106 | 0.730531 | − | 0.682879i | \(-0.239272\pi\) | ||||
0.730531 | + | 0.682879i | \(0.239272\pi\) | |||||||
\(608\) | 8.08491 | 0.327886 | ||||||||
\(609\) | 68.2271 | 2.76470 | ||||||||
\(610\) | −41.7098 | −1.68878 | ||||||||
\(611\) | −27.4682 | −1.11124 | ||||||||
\(612\) | −46.9122 | −1.89631 | ||||||||
\(613\) | 7.19977 | 0.290796 | 0.145398 | − | 0.989373i | \(-0.453554\pi\) | ||||
0.145398 | + | 0.989373i | \(0.453554\pi\) | |||||||
\(614\) | 5.46963 | 0.220736 | ||||||||
\(615\) | 7.94987 | 0.320570 | ||||||||
\(616\) | −2.27835 | −0.0917971 | ||||||||
\(617\) | 5.55936 | 0.223811 | 0.111906 | − | 0.993719i | \(-0.464305\pi\) | ||||
0.111906 | + | 0.993719i | \(0.464305\pi\) | |||||||
\(618\) | −46.1195 | −1.85520 | ||||||||
\(619\) | 18.6869 | 0.751088 | 0.375544 | − | 0.926804i | \(-0.377456\pi\) | ||||
0.375544 | + | 0.926804i | \(0.377456\pi\) | |||||||
\(620\) | 29.7441 | 1.19455 | ||||||||
\(621\) | 78.4286 | 3.14723 | ||||||||
\(622\) | 22.6979 | 0.910105 | ||||||||
\(623\) | 41.8509 | 1.67672 | ||||||||
\(624\) | 7.68703 | 0.307727 | ||||||||
\(625\) | −4.50420 | −0.180168 | ||||||||
\(626\) | −14.9946 | −0.599303 | ||||||||
\(627\) | −13.2364 | −0.528611 | ||||||||
\(628\) | 8.35931 | 0.333573 | ||||||||
\(629\) | −21.4341 | −0.854634 | ||||||||
\(630\) | 93.1640 | 3.71174 | ||||||||
\(631\) | 42.8040 | 1.70400 | 0.852000 | − | 0.523541i | \(-0.175389\pi\) | ||||
0.852000 | + | 0.523541i | \(0.175389\pi\) | |||||||
\(632\) | 9.44342 | 0.375639 | ||||||||
\(633\) | 18.0339 | 0.716784 | ||||||||
\(634\) | −15.1517 | −0.601751 | ||||||||
\(635\) | −44.0932 | −1.74979 | ||||||||
\(636\) | −12.6827 | −0.502902 | ||||||||
\(637\) | −27.4150 | −1.08622 | ||||||||
\(638\) | 2.87626 | 0.113872 | ||||||||
\(639\) | 40.1138 | 1.58688 | ||||||||
\(640\) | −3.55972 | −0.140710 | ||||||||
\(641\) | 23.7728 | 0.938969 | 0.469484 | − | 0.882941i | \(-0.344440\pi\) | ||||
0.469484 | + | 0.882941i | \(0.344440\pi\) | |||||||
\(642\) | 10.0188 | 0.395410 | ||||||||
\(643\) | −1.50015 | −0.0591601 | −0.0295800 | − | 0.999562i | \(-0.509417\pi\) | ||||
−0.0295800 | + | 0.999562i | \(0.509417\pi\) | |||||||
\(644\) | 34.1050 | 1.34393 | ||||||||
\(645\) | 58.4001 | 2.29950 | ||||||||
\(646\) | −61.1722 | −2.40679 | ||||||||
\(647\) | −15.9643 | −0.627623 | −0.313811 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313811 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(648\) | 10.8421 | 0.425919 | ||||||||
\(649\) | −1.59188 | −0.0624869 | ||||||||
\(650\) | −19.4423 | −0.762589 | ||||||||
\(651\) | −106.981 | −4.19293 | ||||||||
\(652\) | 8.38009 | 0.328190 | ||||||||
\(653\) | −5.55533 | −0.217397 | −0.108698 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108698 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(654\) | −3.28269 | −0.128363 | ||||||||
\(655\) | −42.2711 | −1.65167 | ||||||||
\(656\) | 0.736282 | 0.0287470 | ||||||||
\(657\) | −84.6491 | −3.30248 | ||||||||
\(658\) | −45.7504 | −1.78354 | ||||||||
\(659\) | −34.2032 | −1.33237 | −0.666184 | − | 0.745787i | \(-0.732074\pi\) | ||||
−0.666184 | + | 0.745787i | \(0.732074\pi\) | |||||||
\(660\) | 5.82788 | 0.226850 | ||||||||
\(661\) | −40.7184 | −1.58376 | −0.791880 | − | 0.610676i | \(-0.790898\pi\) | ||||
−0.791880 | + | 0.610676i | \(0.790898\pi\) | |||||||
\(662\) | −21.1767 | −0.823055 | ||||||||
\(663\) | −58.1617 | −2.25881 | ||||||||
\(664\) | −3.28706 | −0.127563 | ||||||||
\(665\) | 121.483 | 4.71091 | ||||||||
\(666\) | 17.5645 | 0.680609 | ||||||||
\(667\) | −43.0554 | −1.66711 | ||||||||
\(668\) | −16.8416 | −0.651621 | ||||||||
\(669\) | −37.7165 | −1.45820 | ||||||||
\(670\) | 2.32100 | 0.0896681 | ||||||||
\(671\) | 6.32436 | 0.244149 | ||||||||
\(672\) | 12.8033 | 0.493900 | ||||||||
\(673\) | −16.4992 | −0.635996 | −0.317998 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317998 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(674\) | −19.0650 | −0.734358 | ||||||||
\(675\) | −74.4677 | −2.86626 | ||||||||
\(676\) | −6.57729 | −0.252973 | ||||||||
\(677\) | −26.5630 | −1.02090 | −0.510449 | − | 0.859908i | \(-0.670521\pi\) | ||||
−0.510449 | + | 0.859908i | \(0.670521\pi\) | |||||||
\(678\) | −34.7547 | −1.33475 | ||||||||
\(679\) | −53.5690 | −2.05579 | ||||||||
\(680\) | 26.9336 | 1.03286 | ||||||||
\(681\) | 61.8593 | 2.37045 | ||||||||
\(682\) | −4.51003 | −0.172698 | ||||||||
\(683\) | 22.5665 | 0.863484 | 0.431742 | − | 0.901997i | \(-0.357899\pi\) | ||||
0.431742 | + | 0.901997i | \(0.357899\pi\) | |||||||
\(684\) | 50.1283 | 1.91670 | ||||||||
\(685\) | 72.9489 | 2.78723 | ||||||||
\(686\) | −16.1143 | −0.615247 | ||||||||
\(687\) | 29.3267 | 1.11889 | ||||||||
\(688\) | 5.40877 | 0.206207 | ||||||||
\(689\) | −10.5967 | −0.403703 | ||||||||
\(690\) | −87.2388 | −3.32112 | ||||||||
\(691\) | 14.5618 | 0.553956 | 0.276978 | − | 0.960876i | \(-0.410667\pi\) | ||||
0.276978 | + | 0.960876i | \(0.410667\pi\) | |||||||
\(692\) | 17.3463 | 0.659408 | ||||||||
\(693\) | −14.1263 | −0.536612 | ||||||||
\(694\) | 7.60292 | 0.288603 | ||||||||
\(695\) | 39.1917 | 1.48663 | ||||||||
\(696\) | −16.1634 | −0.612672 | ||||||||
\(697\) | −5.57087 | −0.211012 | ||||||||
\(698\) | 20.6054 | 0.779925 | ||||||||
\(699\) | −53.4860 | −2.02302 | ||||||||
\(700\) | −32.3826 | −1.22395 | ||||||||
\(701\) | −41.4929 | −1.56717 | −0.783583 | − | 0.621287i | \(-0.786610\pi\) | ||||
−0.783583 | + | 0.621287i | \(0.786610\pi\) | |||||||
\(702\) | 24.6002 | 0.928476 | ||||||||
\(703\) | 22.9035 | 0.863823 | ||||||||
\(704\) | 0.539753 | 0.0203427 | ||||||||
\(705\) | 117.027 | 4.40749 | ||||||||
\(706\) | 2.77705 | 0.104516 | ||||||||
\(707\) | 49.5277 | 1.86268 | ||||||||
\(708\) | 8.94572 | 0.336201 | ||||||||
\(709\) | 42.3149 | 1.58917 | 0.794584 | − | 0.607154i | \(-0.207689\pi\) | ||||
0.794584 | + | 0.607154i | \(0.207689\pi\) | |||||||
\(710\) | −23.0305 | −0.864317 | ||||||||
\(711\) | 58.5514 | 2.19585 | ||||||||
\(712\) | −9.91472 | −0.371570 | ||||||||
\(713\) | 67.5116 | 2.52833 | ||||||||
\(714\) | −96.8728 | −3.62538 | ||||||||
\(715\) | 4.86935 | 0.182103 | ||||||||
\(716\) | −3.22549 | −0.120542 | ||||||||
\(717\) | −10.9634 | −0.409434 | ||||||||
\(718\) | −21.8966 | −0.817172 | ||||||||
\(719\) | 2.71602 | 0.101290 | 0.0506452 | − | 0.998717i | \(-0.483872\pi\) | ||||
0.0506452 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(720\) | −22.0711 | −0.822541 | ||||||||
\(721\) | −64.1815 | −2.39024 | ||||||||
\(722\) | 46.3658 | 1.72556 | ||||||||
\(723\) | 16.3454 | 0.607893 | ||||||||
\(724\) | −22.3274 | −0.829791 | ||||||||
\(725\) | 40.8810 | 1.51828 | ||||||||
\(726\) | 32.4814 | 1.20550 | ||||||||
\(727\) | 39.8319 | 1.47728 | 0.738642 | − | 0.674097i | \(-0.235467\pi\) | ||||
0.738642 | + | 0.674097i | \(0.235467\pi\) | |||||||
\(728\) | 10.6975 | 0.396477 | ||||||||
\(729\) | −21.1048 | −0.781657 | ||||||||
\(730\) | 48.5994 | 1.79875 | ||||||||
\(731\) | −40.9239 | −1.51362 | ||||||||
\(732\) | −35.5403 | −1.31361 | ||||||||
\(733\) | −21.4927 | −0.793850 | −0.396925 | − | 0.917851i | \(-0.629923\pi\) | ||||
−0.396925 | + | 0.917851i | \(0.629923\pi\) | |||||||
\(734\) | 21.9008 | 0.808372 | ||||||||
\(735\) | 116.801 | 4.30826 | ||||||||
\(736\) | −8.07968 | −0.297821 | ||||||||
\(737\) | −0.351928 | −0.0129634 | ||||||||
\(738\) | 4.56512 | 0.168044 | ||||||||
\(739\) | −2.02398 | −0.0744533 | −0.0372266 | − | 0.999307i | \(-0.511852\pi\) | ||||
−0.0372266 | + | 0.999307i | \(0.511852\pi\) | |||||||
\(740\) | −10.0842 | −0.370704 | ||||||||
\(741\) | 62.1489 | 2.28310 | ||||||||
\(742\) | −17.6497 | −0.647940 | ||||||||
\(743\) | −16.5245 | −0.606227 | −0.303113 | − | 0.952955i | \(-0.598026\pi\) | ||||
−0.303113 | + | 0.952955i | \(0.598026\pi\) | |||||||
\(744\) | 25.3445 | 0.929174 | ||||||||
\(745\) | −39.2242 | −1.43706 | ||||||||
\(746\) | −12.2184 | −0.447348 | ||||||||
\(747\) | −20.3805 | −0.745685 | ||||||||
\(748\) | −4.08389 | −0.149322 | ||||||||
\(749\) | 13.9425 | 0.509447 | ||||||||
\(750\) | 28.8465 | 1.05332 | ||||||||
\(751\) | −13.2289 | −0.482729 | −0.241365 | − | 0.970435i | \(-0.577595\pi\) | ||||
−0.241365 | + | 0.970435i | \(0.577595\pi\) | |||||||
\(752\) | 10.8385 | 0.395241 | ||||||||
\(753\) | 76.3101 | 2.78089 | ||||||||
\(754\) | −13.5049 | −0.491821 | ||||||||
\(755\) | −40.1174 | −1.46002 | ||||||||
\(756\) | 40.9736 | 1.49020 | ||||||||
\(757\) | −20.0853 | −0.730012 | −0.365006 | − | 0.931005i | \(-0.618933\pi\) | ||||
−0.365006 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(758\) | 0.908152 | 0.0329856 | ||||||||
\(759\) | 13.2278 | 0.480140 | ||||||||
\(760\) | −28.7801 | −1.04396 | ||||||||
\(761\) | −21.7953 | −0.790078 | −0.395039 | − | 0.918664i | \(-0.629269\pi\) | ||||
−0.395039 | + | 0.918664i | \(0.629269\pi\) | |||||||
\(762\) | −37.5712 | −1.36106 | ||||||||
\(763\) | −4.56830 | −0.165384 | ||||||||
\(764\) | 2.14688 | 0.0776713 | ||||||||
\(765\) | 166.995 | 6.03770 | ||||||||
\(766\) | −24.3990 | −0.881572 | ||||||||
\(767\) | 7.47438 | 0.269884 | ||||||||
\(768\) | −3.03319 | −0.109451 | ||||||||
\(769\) | 35.0444 | 1.26373 | 0.631867 | − | 0.775077i | \(-0.282289\pi\) | ||||
0.631867 | + | 0.775077i | \(0.282289\pi\) | |||||||
\(770\) | 8.11028 | 0.292274 | ||||||||
\(771\) | −47.1372 | −1.69761 | ||||||||
\(772\) | 3.12109 | 0.112331 | ||||||||
\(773\) | 21.7085 | 0.780800 | 0.390400 | − | 0.920645i | \(-0.372337\pi\) | ||||
0.390400 | + | 0.920645i | \(0.372337\pi\) | |||||||
\(774\) | 33.5356 | 1.20541 | ||||||||
\(775\) | −64.1021 | −2.30262 | ||||||||
\(776\) | 12.6908 | 0.455574 | ||||||||
\(777\) | 36.2703 | 1.30119 | ||||||||
\(778\) | 23.5296 | 0.843576 | ||||||||
\(779\) | 5.95278 | 0.213280 | ||||||||
\(780\) | −27.3637 | −0.979777 | ||||||||
\(781\) | 3.49206 | 0.124956 | ||||||||
\(782\) | 61.1326 | 2.18610 | ||||||||
\(783\) | −51.7265 | −1.84856 | ||||||||
\(784\) | 10.8176 | 0.386342 | ||||||||
\(785\) | −29.7568 | −1.06207 | ||||||||
\(786\) | −36.0186 | −1.28474 | ||||||||
\(787\) | 3.34765 | 0.119331 | 0.0596655 | − | 0.998218i | \(-0.480997\pi\) | ||||
0.0596655 | + | 0.998218i | \(0.480997\pi\) | |||||||
\(788\) | −13.9592 | −0.497276 | ||||||||
\(789\) | 11.0669 | 0.393993 | ||||||||
\(790\) | −33.6160 | −1.19600 | ||||||||
\(791\) | −48.3658 | −1.71969 | ||||||||
\(792\) | 3.34659 | 0.118916 | ||||||||
\(793\) | −29.6948 | −1.05449 | ||||||||
\(794\) | 8.10906 | 0.287780 | ||||||||
\(795\) | 45.1469 | 1.60120 | ||||||||
\(796\) | 19.4235 | 0.688447 | ||||||||
\(797\) | 37.3341 | 1.32244 | 0.661222 | − | 0.750191i | \(-0.270038\pi\) | ||||
0.661222 | + | 0.750191i | \(0.270038\pi\) | |||||||
\(798\) | 103.514 | 3.66435 | ||||||||
\(799\) | −82.0067 | −2.90119 | ||||||||
\(800\) | 7.67163 | 0.271233 | ||||||||
\(801\) | −61.4735 | −2.17206 | ||||||||
\(802\) | −21.3491 | −0.753862 | ||||||||
\(803\) | −7.36903 | −0.260047 | ||||||||
\(804\) | 1.97769 | 0.0697477 | ||||||||
\(805\) | −121.404 | −4.27895 | ||||||||
\(806\) | 21.1760 | 0.745892 | ||||||||
\(807\) | 81.8635 | 2.88173 | ||||||||
\(808\) | −11.7334 | −0.412780 | ||||||||
\(809\) | −25.1471 | −0.884127 | −0.442063 | − | 0.896984i | \(-0.645753\pi\) | ||||
−0.442063 | + | 0.896984i | \(0.645753\pi\) | |||||||
\(810\) | −38.5950 | −1.35609 | ||||||||
\(811\) | −33.3245 | −1.17018 | −0.585091 | − | 0.810967i | \(-0.698941\pi\) | ||||
−0.585091 | + | 0.810967i | \(0.698941\pi\) | |||||||
\(812\) | −22.4935 | −0.789368 | ||||||||
\(813\) | 45.0887 | 1.58133 | ||||||||
\(814\) | 1.52905 | 0.0535933 | ||||||||
\(815\) | −29.8308 | −1.04493 | ||||||||
\(816\) | 22.9497 | 0.803402 | ||||||||
\(817\) | 43.7294 | 1.52990 | ||||||||
\(818\) | 14.4921 | 0.506703 | ||||||||
\(819\) | 66.3271 | 2.31766 | ||||||||
\(820\) | −2.62096 | −0.0915279 | ||||||||
\(821\) | 40.8658 | 1.42623 | 0.713113 | − | 0.701050i | \(-0.247285\pi\) | ||||
0.713113 | + | 0.701050i | \(0.247285\pi\) | |||||||
\(822\) | 62.1587 | 2.16803 | ||||||||
\(823\) | 12.1096 | 0.422116 | 0.211058 | − | 0.977474i | \(-0.432309\pi\) | ||||
0.211058 | + | 0.977474i | \(0.432309\pi\) | |||||||
\(824\) | 15.2050 | 0.529690 | ||||||||
\(825\) | −12.5598 | −0.437276 | ||||||||
\(826\) | 12.4492 | 0.433162 | ||||||||
\(827\) | 16.7267 | 0.581644 | 0.290822 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290822 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(828\) | −50.0959 | −1.74095 | ||||||||
\(829\) | −28.6371 | −0.994607 | −0.497304 | − | 0.867577i | \(-0.665676\pi\) | ||||
−0.497304 | + | 0.867577i | \(0.665676\pi\) | |||||||
\(830\) | 11.7010 | 0.406149 | ||||||||
\(831\) | 47.7289 | 1.65570 | ||||||||
\(832\) | −2.53431 | −0.0878613 | ||||||||
\(833\) | −81.8480 | −2.83587 | ||||||||
\(834\) | 33.3946 | 1.15636 | ||||||||
\(835\) | 59.9514 | 2.07470 | ||||||||
\(836\) | 4.36386 | 0.150927 | ||||||||
\(837\) | 81.1081 | 2.80351 | ||||||||
\(838\) | 22.3852 | 0.773285 | ||||||||
\(839\) | 22.8471 | 0.788771 | 0.394386 | − | 0.918945i | \(-0.370957\pi\) | ||||
0.394386 | + | 0.918945i | \(0.370957\pi\) | |||||||
\(840\) | −45.5764 | −1.57253 | ||||||||
\(841\) | −0.603370 | −0.0208059 | ||||||||
\(842\) | 20.5334 | 0.707626 | ||||||||
\(843\) | 86.0977 | 2.96536 | ||||||||
\(844\) | −5.94554 | −0.204654 | ||||||||
\(845\) | 23.4133 | 0.805443 | ||||||||
\(846\) | 67.2014 | 2.31043 | ||||||||
\(847\) | 45.2022 | 1.55317 | ||||||||
\(848\) | 4.18131 | 0.143587 | ||||||||
\(849\) | 96.7587 | 3.32075 | ||||||||
\(850\) | −58.0452 | −1.99093 | ||||||||
\(851\) | −22.8887 | −0.784615 | ||||||||
\(852\) | −19.6239 | −0.672304 | ||||||||
\(853\) | 14.9950 | 0.513418 | 0.256709 | − | 0.966489i | \(-0.417362\pi\) | ||||
0.256709 | + | 0.966489i | \(0.417362\pi\) | |||||||
\(854\) | −49.4590 | −1.69245 | ||||||||
\(855\) | −178.443 | −6.10262 | ||||||||
\(856\) | −3.30305 | −0.112896 | ||||||||
\(857\) | −20.8521 | −0.712295 | −0.356147 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356147 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(858\) | 4.14910 | 0.141648 | ||||||||
\(859\) | 38.5565 | 1.31553 | 0.657766 | − | 0.753223i | \(-0.271502\pi\) | ||||
0.657766 | + | 0.753223i | \(0.271502\pi\) | |||||||
\(860\) | −19.2537 | −0.656546 | ||||||||
\(861\) | 9.42688 | 0.321267 | ||||||||
\(862\) | −20.7962 | −0.708323 | ||||||||
\(863\) | 34.8459 | 1.18617 | 0.593084 | − | 0.805141i | \(-0.297910\pi\) | ||||
0.593084 | + | 0.805141i | \(0.297910\pi\) | |||||||
\(864\) | −9.70689 | −0.330235 | ||||||||
\(865\) | −61.7481 | −2.09950 | ||||||||
\(866\) | −21.9824 | −0.746992 | ||||||||
\(867\) | −122.078 | −4.14600 | ||||||||
\(868\) | 35.2703 | 1.19715 | ||||||||
\(869\) | 5.09712 | 0.172908 | ||||||||
\(870\) | 57.5372 | 1.95069 | ||||||||
\(871\) | 1.65241 | 0.0559898 | ||||||||
\(872\) | 1.08226 | 0.0366499 | ||||||||
\(873\) | 78.6860 | 2.66312 | ||||||||
\(874\) | −65.3235 | −2.20960 | ||||||||
\(875\) | 40.1437 | 1.35711 | ||||||||
\(876\) | 41.4108 | 1.39914 | ||||||||
\(877\) | 6.48816 | 0.219090 | 0.109545 | − | 0.993982i | \(-0.465061\pi\) | ||||
0.109545 | + | 0.993982i | \(0.465061\pi\) | |||||||
\(878\) | 32.2123 | 1.08711 | ||||||||
\(879\) | −91.4347 | −3.08402 | ||||||||
\(880\) | −1.92137 | −0.0647695 | ||||||||
\(881\) | 27.8005 | 0.936624 | 0.468312 | − | 0.883563i | \(-0.344862\pi\) | ||||
0.468312 | + | 0.883563i | \(0.344862\pi\) | |||||||
\(882\) | 67.0714 | 2.25841 | ||||||||
\(883\) | 12.4166 | 0.417851 | 0.208925 | − | 0.977932i | \(-0.433003\pi\) | ||||
0.208925 | + | 0.977932i | \(0.433003\pi\) | |||||||
\(884\) | 19.1751 | 0.644928 | ||||||||
\(885\) | −31.8443 | −1.07043 | ||||||||
\(886\) | 32.4274 | 1.08942 | ||||||||
\(887\) | −24.4194 | −0.819923 | −0.409962 | − | 0.912103i | \(-0.634458\pi\) | ||||
−0.409962 | + | 0.912103i | \(0.634458\pi\) | |||||||
\(888\) | −8.59263 | −0.288350 | ||||||||
\(889\) | −52.2853 | −1.75359 | ||||||||
\(890\) | 35.2937 | 1.18305 | ||||||||
\(891\) | 5.85208 | 0.196052 | ||||||||
\(892\) | 12.4346 | 0.416342 | ||||||||
\(893\) | 87.6286 | 2.93238 | ||||||||
\(894\) | −33.4224 | −1.11781 | ||||||||
\(895\) | 11.4819 | 0.383797 | ||||||||
\(896\) | −4.22109 | −0.141017 | ||||||||
\(897\) | −62.1087 | −2.07375 | ||||||||
\(898\) | 32.9473 | 1.09947 | ||||||||
\(899\) | −44.5264 | −1.48504 | ||||||||
\(900\) | 47.5659 | 1.58553 | ||||||||
\(901\) | −31.6367 | −1.05397 | ||||||||
\(902\) | 0.397411 | 0.0132323 | ||||||||
\(903\) | 69.2503 | 2.30451 | ||||||||
\(904\) | 11.4581 | 0.381092 | ||||||||
\(905\) | 79.4793 | 2.64198 | ||||||||
\(906\) | −34.1835 | −1.13567 | ||||||||
\(907\) | 16.0534 | 0.533045 | 0.266522 | − | 0.963829i | \(-0.414125\pi\) | ||||
0.266522 | + | 0.963829i | \(0.414125\pi\) | |||||||
\(908\) | −20.3942 | −0.676804 | ||||||||
\(909\) | −72.7498 | −2.41296 | ||||||||
\(910\) | −38.0802 | −1.26235 | ||||||||
\(911\) | 47.8056 | 1.58387 | 0.791935 | − | 0.610606i | \(-0.209074\pi\) | ||||
0.791935 | + | 0.610606i | \(0.209074\pi\) | |||||||
\(912\) | −24.5231 | −0.812039 | ||||||||
\(913\) | −1.77420 | −0.0587176 | ||||||||
\(914\) | −32.8041 | −1.08506 | ||||||||
\(915\) | 126.514 | 4.18241 | ||||||||
\(916\) | −9.66862 | −0.319460 | ||||||||
\(917\) | −50.1246 | −1.65526 | ||||||||
\(918\) | 73.4444 | 2.42403 | ||||||||
\(919\) | 13.5636 | 0.447421 | 0.223710 | − | 0.974656i | \(-0.428183\pi\) | ||||
0.223710 | + | 0.974656i | \(0.428183\pi\) | |||||||
\(920\) | 28.7614 | 0.948236 | ||||||||
\(921\) | −16.5904 | −0.546672 | ||||||||
\(922\) | −14.4291 | −0.475196 | ||||||||
\(923\) | −16.3963 | −0.539690 | ||||||||
\(924\) | 6.91065 | 0.227344 | ||||||||
\(925\) | 21.7328 | 0.714569 | ||||||||
\(926\) | 25.2189 | 0.828745 | ||||||||
\(927\) | 94.2743 | 3.09637 | ||||||||
\(928\) | 5.32885 | 0.174928 | ||||||||
\(929\) | −2.98388 | −0.0978981 | −0.0489490 | − | 0.998801i | \(-0.515587\pi\) | ||||
−0.0489490 | + | 0.998801i | \(0.515587\pi\) | |||||||
\(930\) | −90.2194 | −2.95841 | ||||||||
\(931\) | 87.4591 | 2.86636 | ||||||||
\(932\) | 17.6336 | 0.577607 | ||||||||
\(933\) | −68.8471 | −2.25395 | ||||||||
\(934\) | 4.84703 | 0.158600 | ||||||||
\(935\) | 14.5375 | 0.475428 | ||||||||
\(936\) | −15.7133 | −0.513604 | ||||||||
\(937\) | 17.6311 | 0.575983 | 0.287992 | − | 0.957633i | \(-0.407012\pi\) | ||||
0.287992 | + | 0.957633i | \(0.407012\pi\) | |||||||
\(938\) | 2.75222 | 0.0898632 | ||||||||
\(939\) | 45.4813 | 1.48423 | ||||||||
\(940\) | −38.5822 | −1.25841 | ||||||||
\(941\) | 37.9482 | 1.23707 | 0.618537 | − | 0.785755i | \(-0.287726\pi\) | ||||
0.618537 | + | 0.785755i | \(0.287726\pi\) | |||||||
\(942\) | −25.3554 | −0.826122 | ||||||||
\(943\) | −5.94892 | −0.193724 | ||||||||
\(944\) | −2.94928 | −0.0959909 | ||||||||
\(945\) | −145.855 | −4.74466 | ||||||||
\(946\) | 2.91940 | 0.0949178 | ||||||||
\(947\) | −23.1013 | −0.750692 | −0.375346 | − | 0.926885i | \(-0.622476\pi\) | ||||
−0.375346 | + | 0.926885i | \(0.622476\pi\) | |||||||
\(948\) | −28.6437 | −0.930303 | ||||||||
\(949\) | 34.5998 | 1.12316 | ||||||||
\(950\) | 62.0245 | 2.01234 | ||||||||
\(951\) | 45.9580 | 1.49029 | ||||||||
\(952\) | 31.9376 | 1.03510 | ||||||||
\(953\) | 1.09712 | 0.0355392 | 0.0177696 | − | 0.999842i | \(-0.494343\pi\) | ||||
0.0177696 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(954\) | 25.9251 | 0.839356 | ||||||||
\(955\) | −7.64229 | −0.247299 | ||||||||
\(956\) | 3.61447 | 0.116900 | ||||||||
\(957\) | −8.72425 | −0.282015 | ||||||||
\(958\) | −1.02461 | −0.0331038 | ||||||||
\(959\) | 86.5021 | 2.79330 | ||||||||
\(960\) | 10.7973 | 0.348482 | ||||||||
\(961\) | 38.8182 | 1.25220 | ||||||||
\(962\) | −7.17937 | −0.231472 | ||||||||
\(963\) | −20.4797 | −0.659949 | ||||||||
\(964\) | −5.38886 | −0.173564 | ||||||||
\(965\) | −11.1102 | −0.357651 | ||||||||
\(966\) | −103.447 | −3.32835 | ||||||||
\(967\) | −48.7805 | −1.56868 | −0.784338 | − | 0.620334i | \(-0.786997\pi\) | ||||
−0.784338 | + | 0.620334i | \(0.786997\pi\) | |||||||
\(968\) | −10.7087 | −0.344190 | ||||||||
\(969\) | 185.547 | 5.96062 | ||||||||
\(970\) | −45.1758 | −1.45051 | ||||||||
\(971\) | 39.5940 | 1.27063 | 0.635316 | − | 0.772252i | \(-0.280870\pi\) | ||||
0.635316 | + | 0.772252i | \(0.280870\pi\) | |||||||
\(972\) | −3.76556 | −0.120780 | ||||||||
\(973\) | 46.4731 | 1.48986 | ||||||||
\(974\) | −2.65034 | −0.0849223 | ||||||||
\(975\) | 58.9721 | 1.88862 | ||||||||
\(976\) | 11.7171 | 0.375056 | ||||||||
\(977\) | −19.8300 | −0.634419 | −0.317209 | − | 0.948356i | \(-0.602746\pi\) | ||||
−0.317209 | + | 0.948356i | \(0.602746\pi\) | |||||||
\(978\) | −25.4184 | −0.812790 | ||||||||
\(979\) | −5.35150 | −0.171035 | ||||||||
\(980\) | −38.5076 | −1.23008 | ||||||||
\(981\) | 6.71024 | 0.214242 | ||||||||
\(982\) | −30.7111 | −0.980031 | ||||||||
\(983\) | −39.0525 | −1.24558 | −0.622791 | − | 0.782388i | \(-0.714001\pi\) | ||||
−0.622791 | + | 0.782388i | \(0.714001\pi\) | |||||||
\(984\) | −2.23328 | −0.0711944 | ||||||||
\(985\) | 49.6909 | 1.58328 | ||||||||
\(986\) | −40.3192 | −1.28402 | ||||||||
\(987\) | 138.770 | 4.41708 | ||||||||
\(988\) | −20.4896 | −0.651862 | ||||||||
\(989\) | −43.7011 | −1.38961 | ||||||||
\(990\) | −11.9129 | −0.378618 | ||||||||
\(991\) | 37.2256 | 1.18251 | 0.591255 | − | 0.806485i | \(-0.298633\pi\) | ||||
0.591255 | + | 0.806485i | \(0.298633\pi\) | |||||||
\(992\) | −8.35573 | −0.265295 | ||||||||
\(993\) | 64.2328 | 2.03837 | ||||||||
\(994\) | −27.3093 | −0.866198 | ||||||||
\(995\) | −69.1422 | −2.19196 | ||||||||
\(996\) | 9.97028 | 0.315921 | ||||||||
\(997\) | 1.98664 | 0.0629175 | 0.0314588 | − | 0.999505i | \(-0.489985\pi\) | ||||
0.0314588 | + | 0.999505i | \(0.489985\pi\) | |||||||
\(998\) | 9.11311 | 0.288470 | ||||||||
\(999\) | −27.4984 | −0.870010 |
(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 | 8002.2.a.d.1.6 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.6 | ✓ | 69 | 1.1 | even | 1 | trivial |