Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.81598 | −1.99120 | −0.995600 | − | 0.0937098i | \(-0.970127\pi\) | ||||
−0.995600 | + | 0.0937098i | \(0.970127\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.92975 | 2.96487 | ||||||||
\(5\) | −4.24598 | −1.89886 | −0.949431 | − | 0.313976i | \(-0.898339\pi\) | ||||
−0.949431 | + | 0.313976i | \(0.898339\pi\) | |||||||
\(6\) | 2.81598 | 1.14962 | ||||||||
\(7\) | 0.0516498 | 0.0195218 | 0.00976090 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976090 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(8\) | −11.0661 | −3.91246 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 11.9566 | 3.78101 | ||||||||
\(11\) | −4.06087 | −1.22440 | −0.612199 | − | 0.790704i | \(-0.709715\pi\) | ||||
−0.612199 | + | 0.790704i | \(0.709715\pi\) | |||||||
\(12\) | −5.92975 | −1.71177 | ||||||||
\(13\) | −4.35985 | −1.20920 | −0.604602 | − | 0.796528i | \(-0.706668\pi\) | ||||
−0.604602 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(14\) | −0.145445 | −0.0388718 | ||||||||
\(15\) | 4.24598 | 1.09631 | ||||||||
\(16\) | 19.3024 | 4.82560 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.81598 | −0.663733 | ||||||||
\(19\) | −5.28010 | −1.21134 | −0.605669 | − | 0.795717i | \(-0.707094\pi\) | ||||
−0.605669 | + | 0.795717i | \(0.707094\pi\) | |||||||
\(20\) | −25.1776 | −5.62989 | ||||||||
\(21\) | −0.0516498 | −0.0112709 | ||||||||
\(22\) | 11.4353 | 2.43802 | ||||||||
\(23\) | 6.73037 | 1.40338 | 0.701689 | − | 0.712483i | \(-0.252429\pi\) | ||||
0.701689 | + | 0.712483i | \(0.252429\pi\) | |||||||
\(24\) | 11.0661 | 2.25886 | ||||||||
\(25\) | 13.0284 | 2.60568 | ||||||||
\(26\) | 12.2772 | 2.40777 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.306270 | 0.0578797 | ||||||||
\(29\) | 6.81104 | 1.26478 | 0.632389 | − | 0.774651i | \(-0.282074\pi\) | ||||
0.632389 | + | 0.774651i | \(0.282074\pi\) | |||||||
\(30\) | −11.9566 | −2.18297 | ||||||||
\(31\) | 5.25753 | 0.944280 | 0.472140 | − | 0.881523i | \(-0.343482\pi\) | ||||
0.472140 | + | 0.881523i | \(0.343482\pi\) | |||||||
\(32\) | −32.2230 | −5.69628 | ||||||||
\(33\) | 4.06087 | 0.706906 | ||||||||
\(34\) | −2.81598 | −0.482937 | ||||||||
\(35\) | −0.219304 | −0.0370692 | ||||||||
\(36\) | 5.92975 | 0.988291 | ||||||||
\(37\) | 10.7233 | 1.76290 | 0.881451 | − | 0.472275i | \(-0.156567\pi\) | ||||
0.881451 | + | 0.472275i | \(0.156567\pi\) | |||||||
\(38\) | 14.8687 | 2.41201 | ||||||||
\(39\) | 4.35985 | 0.698134 | ||||||||
\(40\) | 46.9865 | 7.42921 | ||||||||
\(41\) | −5.37399 | −0.839276 | −0.419638 | − | 0.907691i | \(-0.637843\pi\) | ||||
−0.419638 | + | 0.907691i | \(0.637843\pi\) | |||||||
\(42\) | 0.145445 | 0.0224426 | ||||||||
\(43\) | 7.06168 | 1.07690 | 0.538448 | − | 0.842659i | \(-0.319011\pi\) | ||||
0.538448 | + | 0.842659i | \(0.319011\pi\) | |||||||
\(44\) | −24.0799 | −3.63019 | ||||||||
\(45\) | −4.24598 | −0.632954 | ||||||||
\(46\) | −18.9526 | −2.79441 | ||||||||
\(47\) | −6.72574 | −0.981051 | −0.490525 | − | 0.871427i | \(-0.663195\pi\) | ||||
−0.490525 | + | 0.871427i | \(0.663195\pi\) | |||||||
\(48\) | −19.3024 | −2.78606 | ||||||||
\(49\) | −6.99733 | −0.999619 | ||||||||
\(50\) | −36.6877 | −5.18842 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −25.8528 | −3.58514 | ||||||||
\(53\) | 6.76745 | 0.929580 | 0.464790 | − | 0.885421i | \(-0.346130\pi\) | ||||
0.464790 | + | 0.885421i | \(0.346130\pi\) | |||||||
\(54\) | 2.81598 | 0.383206 | ||||||||
\(55\) | 17.2424 | 2.32496 | ||||||||
\(56\) | −0.571562 | −0.0763781 | ||||||||
\(57\) | 5.28010 | 0.699366 | ||||||||
\(58\) | −19.1798 | −2.51843 | ||||||||
\(59\) | −4.71390 | −0.613698 | −0.306849 | − | 0.951758i | \(-0.599275\pi\) | ||||
−0.306849 | + | 0.951758i | \(0.599275\pi\) | |||||||
\(60\) | 25.1776 | 3.25042 | ||||||||
\(61\) | −12.2611 | −1.56987 | −0.784936 | − | 0.619577i | \(-0.787304\pi\) | ||||
−0.784936 | + | 0.619577i | \(0.787304\pi\) | |||||||
\(62\) | −14.8051 | −1.88025 | ||||||||
\(63\) | 0.0516498 | 0.00650726 | ||||||||
\(64\) | 52.1346 | 6.51683 | ||||||||
\(65\) | 18.5118 | 2.29611 | ||||||||
\(66\) | −11.4353 | −1.40759 | ||||||||
\(67\) | −6.89514 | −0.842375 | −0.421188 | − | 0.906974i | \(-0.638387\pi\) | ||||
−0.421188 | + | 0.906974i | \(0.638387\pi\) | |||||||
\(68\) | 5.92975 | 0.719088 | ||||||||
\(69\) | −6.73037 | −0.810241 | ||||||||
\(70\) | 0.617557 | 0.0738121 | ||||||||
\(71\) | −3.50032 | −0.415411 | −0.207706 | − | 0.978191i | \(-0.566600\pi\) | ||||
−0.207706 | + | 0.978191i | \(0.566600\pi\) | |||||||
\(72\) | −11.0661 | −1.30415 | ||||||||
\(73\) | 2.03623 | 0.238323 | 0.119162 | − | 0.992875i | \(-0.461979\pi\) | ||||
0.119162 | + | 0.992875i | \(0.461979\pi\) | |||||||
\(74\) | −30.1967 | −3.51029 | ||||||||
\(75\) | −13.0284 | −1.50439 | ||||||||
\(76\) | −31.3097 | −3.59146 | ||||||||
\(77\) | −0.209743 | −0.0239024 | ||||||||
\(78\) | −12.2772 | −1.39012 | ||||||||
\(79\) | −14.8058 | −1.66578 | −0.832892 | − | 0.553435i | \(-0.813317\pi\) | ||||
−0.832892 | + | 0.553435i | \(0.813317\pi\) | |||||||
\(80\) | −81.9577 | −9.16315 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.1331 | 1.67117 | ||||||||
\(83\) | −7.14336 | −0.784085 | −0.392043 | − | 0.919947i | \(-0.628231\pi\) | ||||
−0.392043 | + | 0.919947i | \(0.628231\pi\) | |||||||
\(84\) | −0.306270 | −0.0334168 | ||||||||
\(85\) | −4.24598 | −0.460542 | ||||||||
\(86\) | −19.8855 | −2.14431 | ||||||||
\(87\) | −6.81104 | −0.730220 | ||||||||
\(88\) | 44.9380 | 4.79040 | ||||||||
\(89\) | 2.78938 | 0.295674 | 0.147837 | − | 0.989012i | \(-0.452769\pi\) | ||||
0.147837 | + | 0.989012i | \(0.452769\pi\) | |||||||
\(90\) | 11.9566 | 1.26034 | ||||||||
\(91\) | −0.225185 | −0.0236058 | ||||||||
\(92\) | 39.9094 | 4.16084 | ||||||||
\(93\) | −5.25753 | −0.545180 | ||||||||
\(94\) | 18.9396 | 1.95347 | ||||||||
\(95\) | 22.4192 | 2.30016 | ||||||||
\(96\) | 32.2230 | 3.28875 | ||||||||
\(97\) | 8.30804 | 0.843554 | 0.421777 | − | 0.906700i | \(-0.361407\pi\) | ||||
0.421777 | + | 0.906700i | \(0.361407\pi\) | |||||||
\(98\) | 19.7044 | 1.99044 | ||||||||
\(99\) | −4.06087 | −0.408133 | ||||||||
\(100\) | 77.2550 | 7.72550 | ||||||||
\(101\) | −12.2751 | −1.22141 | −0.610707 | − | 0.791857i | \(-0.709115\pi\) | ||||
−0.610707 | + | 0.791857i | \(0.709115\pi\) | |||||||
\(102\) | 2.81598 | 0.278824 | ||||||||
\(103\) | −14.2913 | −1.40816 | −0.704079 | − | 0.710121i | \(-0.748640\pi\) | ||||
−0.704079 | + | 0.710121i | \(0.748640\pi\) | |||||||
\(104\) | 48.2465 | 4.73096 | ||||||||
\(105\) | 0.219304 | 0.0214019 | ||||||||
\(106\) | −19.0570 | −1.85098 | ||||||||
\(107\) | −3.76324 | −0.363806 | −0.181903 | − | 0.983316i | \(-0.558226\pi\) | ||||
−0.181903 | + | 0.983316i | \(0.558226\pi\) | |||||||
\(108\) | −5.92975 | −0.570590 | ||||||||
\(109\) | −12.3326 | −1.18125 | −0.590623 | − | 0.806948i | \(-0.701118\pi\) | ||||
−0.590623 | + | 0.806948i | \(0.701118\pi\) | |||||||
\(110\) | −48.5542 | −4.62946 | ||||||||
\(111\) | −10.7233 | −1.01781 | ||||||||
\(112\) | 0.996966 | 0.0942044 | ||||||||
\(113\) | −1.49671 | −0.140799 | −0.0703993 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703993 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(114\) | −14.8687 | −1.39258 | ||||||||
\(115\) | −28.5770 | −2.66482 | ||||||||
\(116\) | 40.3877 | 3.74991 | ||||||||
\(117\) | −4.35985 | −0.403068 | ||||||||
\(118\) | 13.2743 | 1.22199 | ||||||||
\(119\) | 0.0516498 | 0.00473473 | ||||||||
\(120\) | −46.9865 | −4.28926 | ||||||||
\(121\) | 5.49065 | 0.499150 | ||||||||
\(122\) | 34.5270 | 3.12593 | ||||||||
\(123\) | 5.37399 | 0.484557 | ||||||||
\(124\) | 31.1758 | 2.79967 | ||||||||
\(125\) | −34.0884 | −3.04896 | ||||||||
\(126\) | −0.145445 | −0.0129573 | ||||||||
\(127\) | 3.34745 | 0.297038 | 0.148519 | − | 0.988910i | \(-0.452549\pi\) | ||||
0.148519 | + | 0.988910i | \(0.452549\pi\) | |||||||
\(128\) | −82.3640 | −7.28002 | ||||||||
\(129\) | −7.06168 | −0.621746 | ||||||||
\(130\) | −52.1290 | −4.57202 | ||||||||
\(131\) | −11.9733 | −1.04611 | −0.523056 | − | 0.852298i | \(-0.675208\pi\) | ||||
−0.523056 | + | 0.852298i | \(0.675208\pi\) | |||||||
\(132\) | 24.0799 | 2.09589 | ||||||||
\(133\) | −0.272716 | −0.0236475 | ||||||||
\(134\) | 19.4166 | 1.67734 | ||||||||
\(135\) | 4.24598 | 0.365436 | ||||||||
\(136\) | −11.0661 | −0.948910 | ||||||||
\(137\) | 6.15761 | 0.526080 | 0.263040 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263040 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(138\) | 18.9526 | 1.61335 | ||||||||
\(139\) | −10.9488 | −0.928661 | −0.464331 | − | 0.885662i | \(-0.653705\pi\) | ||||
−0.464331 | + | 0.885662i | \(0.653705\pi\) | |||||||
\(140\) | −1.30042 | −0.109905 | ||||||||
\(141\) | 6.72574 | 0.566410 | ||||||||
\(142\) | 9.85683 | 0.827167 | ||||||||
\(143\) | 17.7048 | 1.48055 | ||||||||
\(144\) | 19.3024 | 1.60853 | ||||||||
\(145\) | −28.9196 | −2.40164 | ||||||||
\(146\) | −5.73399 | −0.474549 | ||||||||
\(147\) | 6.99733 | 0.577130 | ||||||||
\(148\) | 63.5866 | 5.22678 | ||||||||
\(149\) | 12.8346 | 1.05145 | 0.525727 | − | 0.850653i | \(-0.323793\pi\) | ||||
0.525727 | + | 0.850653i | \(0.323793\pi\) | |||||||
\(150\) | 36.6877 | 2.99554 | ||||||||
\(151\) | −2.07020 | −0.168470 | −0.0842352 | − | 0.996446i | \(-0.526845\pi\) | ||||
−0.0842352 | + | 0.996446i | \(0.526845\pi\) | |||||||
\(152\) | 58.4301 | 4.73931 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 0.590633 | 0.0475945 | ||||||||
\(155\) | −22.3234 | −1.79306 | ||||||||
\(156\) | 25.8528 | 2.06988 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 41.6929 | 3.31691 | ||||||||
\(159\) | −6.76745 | −0.536693 | ||||||||
\(160\) | 136.819 | 10.8165 | ||||||||
\(161\) | 0.347622 | 0.0273965 | ||||||||
\(162\) | −2.81598 | −0.221244 | ||||||||
\(163\) | −12.7043 | −0.995079 | −0.497539 | − | 0.867441i | \(-0.665763\pi\) | ||||
−0.497539 | + | 0.867441i | \(0.665763\pi\) | |||||||
\(164\) | −31.8664 | −2.48835 | ||||||||
\(165\) | −17.2424 | −1.34232 | ||||||||
\(166\) | 20.1156 | 1.56127 | ||||||||
\(167\) | 19.0944 | 1.47757 | 0.738783 | − | 0.673943i | \(-0.235401\pi\) | ||||
0.738783 | + | 0.673943i | \(0.235401\pi\) | |||||||
\(168\) | 0.571562 | 0.0440969 | ||||||||
\(169\) | 6.00828 | 0.462175 | ||||||||
\(170\) | 11.9566 | 0.917030 | ||||||||
\(171\) | −5.28010 | −0.403779 | ||||||||
\(172\) | 41.8740 | 3.19286 | ||||||||
\(173\) | −12.2680 | −0.932716 | −0.466358 | − | 0.884596i | \(-0.654434\pi\) | ||||
−0.466358 | + | 0.884596i | \(0.654434\pi\) | |||||||
\(174\) | 19.1798 | 1.45401 | ||||||||
\(175\) | 0.672914 | 0.0508675 | ||||||||
\(176\) | −78.3846 | −5.90846 | ||||||||
\(177\) | 4.71390 | 0.354319 | ||||||||
\(178\) | −7.85484 | −0.588745 | ||||||||
\(179\) | −11.5661 | −0.864489 | −0.432244 | − | 0.901757i | \(-0.642278\pi\) | ||||
−0.432244 | + | 0.901757i | \(0.642278\pi\) | |||||||
\(180\) | −25.1776 | −1.87663 | ||||||||
\(181\) | 4.00986 | 0.298051 | 0.149025 | − | 0.988833i | \(-0.452386\pi\) | ||||
0.149025 | + | 0.988833i | \(0.452386\pi\) | |||||||
\(182\) | 0.634118 | 0.0470039 | ||||||||
\(183\) | 12.2611 | 0.906366 | ||||||||
\(184\) | −74.4789 | −5.49066 | ||||||||
\(185\) | −45.5310 | −3.34751 | ||||||||
\(186\) | 14.8051 | 1.08556 | ||||||||
\(187\) | −4.06087 | −0.296960 | ||||||||
\(188\) | −39.8820 | −2.90869 | ||||||||
\(189\) | −0.0516498 | −0.00375697 | ||||||||
\(190\) | −63.1321 | −4.58008 | ||||||||
\(191\) | 4.51279 | 0.326534 | 0.163267 | − | 0.986582i | \(-0.447797\pi\) | ||||
0.163267 | + | 0.986582i | \(0.447797\pi\) | |||||||
\(192\) | −52.1346 | −3.76249 | ||||||||
\(193\) | 8.27853 | 0.595902 | 0.297951 | − | 0.954581i | \(-0.403697\pi\) | ||||
0.297951 | + | 0.954581i | \(0.403697\pi\) | |||||||
\(194\) | −23.3953 | −1.67968 | ||||||||
\(195\) | −18.5118 | −1.32566 | ||||||||
\(196\) | −41.4924 | −2.96374 | ||||||||
\(197\) | −8.36548 | −0.596015 | −0.298008 | − | 0.954563i | \(-0.596322\pi\) | ||||
−0.298008 | + | 0.954563i | \(0.596322\pi\) | |||||||
\(198\) | 11.4353 | 0.812673 | ||||||||
\(199\) | 11.6725 | 0.827444 | 0.413722 | − | 0.910403i | \(-0.364229\pi\) | ||||
0.413722 | + | 0.910403i | \(0.364229\pi\) | |||||||
\(200\) | −144.173 | −10.1946 | ||||||||
\(201\) | 6.89514 | 0.486346 | ||||||||
\(202\) | 34.5663 | 2.43208 | ||||||||
\(203\) | 0.351789 | 0.0246907 | ||||||||
\(204\) | −5.92975 | −0.415165 | ||||||||
\(205\) | 22.8179 | 1.59367 | ||||||||
\(206\) | 40.2439 | 2.80392 | ||||||||
\(207\) | 6.73037 | 0.467793 | ||||||||
\(208\) | −84.1556 | −5.83514 | ||||||||
\(209\) | 21.4418 | 1.48316 | ||||||||
\(210\) | −0.617557 | −0.0426155 | ||||||||
\(211\) | −12.9686 | −0.892792 | −0.446396 | − | 0.894835i | \(-0.647293\pi\) | ||||
−0.446396 | + | 0.894835i | \(0.647293\pi\) | |||||||
\(212\) | 40.1293 | 2.75609 | ||||||||
\(213\) | 3.50032 | 0.239838 | ||||||||
\(214\) | 10.5972 | 0.724411 | ||||||||
\(215\) | −29.9838 | −2.04488 | ||||||||
\(216\) | 11.0661 | 0.752952 | ||||||||
\(217\) | 0.271550 | 0.0184340 | ||||||||
\(218\) | 34.7283 | 2.35210 | ||||||||
\(219\) | −2.03623 | −0.137596 | ||||||||
\(220\) | 102.243 | 6.89322 | ||||||||
\(221\) | −4.35985 | −0.293275 | ||||||||
\(222\) | 30.1967 | 2.02667 | ||||||||
\(223\) | 11.7529 | 0.787030 | 0.393515 | − | 0.919318i | \(-0.371259\pi\) | ||||
0.393515 | + | 0.919318i | \(0.371259\pi\) | |||||||
\(224\) | −1.66431 | −0.111202 | ||||||||
\(225\) | 13.0284 | 0.868559 | ||||||||
\(226\) | 4.21471 | 0.280358 | ||||||||
\(227\) | −19.9116 | −1.32158 | −0.660788 | − | 0.750572i | \(-0.729778\pi\) | ||||
−0.660788 | + | 0.750572i | \(0.729778\pi\) | |||||||
\(228\) | 31.3097 | 2.07353 | ||||||||
\(229\) | −5.43413 | −0.359097 | −0.179549 | − | 0.983749i | \(-0.557464\pi\) | ||||
−0.179549 | + | 0.983749i | \(0.557464\pi\) | |||||||
\(230\) | 80.4724 | 5.30619 | ||||||||
\(231\) | 0.209743 | 0.0138001 | ||||||||
\(232\) | −75.3716 | −4.94839 | ||||||||
\(233\) | −27.2094 | −1.78254 | −0.891272 | − | 0.453468i | \(-0.850186\pi\) | ||||
−0.891272 | + | 0.453468i | \(0.850186\pi\) | |||||||
\(234\) | 12.2772 | 0.802589 | ||||||||
\(235\) | 28.5574 | 1.86288 | ||||||||
\(236\) | −27.9523 | −1.81954 | ||||||||
\(237\) | 14.8058 | 0.961741 | ||||||||
\(238\) | −0.145445 | −0.00942779 | ||||||||
\(239\) | −0.173199 | −0.0112033 | −0.00560165 | − | 0.999984i | \(-0.501783\pi\) | ||||
−0.00560165 | + | 0.999984i | \(0.501783\pi\) | |||||||
\(240\) | 81.9577 | 5.29035 | ||||||||
\(241\) | 17.4422 | 1.12355 | 0.561775 | − | 0.827290i | \(-0.310119\pi\) | ||||
0.561775 | + | 0.827290i | \(0.310119\pi\) | |||||||
\(242\) | −15.4616 | −0.993908 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −72.7052 | −4.65447 | ||||||||
\(245\) | 29.7106 | 1.89814 | ||||||||
\(246\) | −15.1331 | −0.964848 | ||||||||
\(247\) | 23.0204 | 1.46476 | ||||||||
\(248\) | −58.1803 | −3.69445 | ||||||||
\(249\) | 7.14336 | 0.452692 | ||||||||
\(250\) | 95.9923 | 6.07109 | ||||||||
\(251\) | 20.9588 | 1.32291 | 0.661454 | − | 0.749986i | \(-0.269940\pi\) | ||||
0.661454 | + | 0.749986i | \(0.269940\pi\) | |||||||
\(252\) | 0.306270 | 0.0192932 | ||||||||
\(253\) | −27.3311 | −1.71829 | ||||||||
\(254\) | −9.42636 | −0.591462 | ||||||||
\(255\) | 4.24598 | 0.265894 | ||||||||
\(256\) | 127.666 | 7.97914 | ||||||||
\(257\) | −5.27856 | −0.329268 | −0.164634 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164634 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(258\) | 19.8855 | 1.23802 | ||||||||
\(259\) | 0.553857 | 0.0344150 | ||||||||
\(260\) | 109.771 | 6.80768 | ||||||||
\(261\) | 6.81104 | 0.421593 | ||||||||
\(262\) | 33.7166 | 2.08302 | ||||||||
\(263\) | 17.8038 | 1.09783 | 0.548915 | − | 0.835878i | \(-0.315041\pi\) | ||||
0.548915 | + | 0.835878i | \(0.315041\pi\) | |||||||
\(264\) | −44.9380 | −2.76574 | ||||||||
\(265\) | −28.7345 | −1.76514 | ||||||||
\(266\) | 0.767963 | 0.0470869 | ||||||||
\(267\) | −2.78938 | −0.170707 | ||||||||
\(268\) | −40.8864 | −2.49754 | ||||||||
\(269\) | 6.92771 | 0.422390 | 0.211195 | − | 0.977444i | \(-0.432265\pi\) | ||||
0.211195 | + | 0.977444i | \(0.432265\pi\) | |||||||
\(270\) | −11.9566 | −0.727656 | ||||||||
\(271\) | −5.74026 | −0.348696 | −0.174348 | − | 0.984684i | \(-0.555782\pi\) | ||||
−0.174348 | + | 0.984684i | \(0.555782\pi\) | |||||||
\(272\) | 19.3024 | 1.17038 | ||||||||
\(273\) | 0.225185 | 0.0136288 | ||||||||
\(274\) | −17.3397 | −1.04753 | ||||||||
\(275\) | −52.9066 | −3.19039 | ||||||||
\(276\) | −39.9094 | −2.40226 | ||||||||
\(277\) | 6.71496 | 0.403463 | 0.201731 | − | 0.979441i | \(-0.435343\pi\) | ||||
0.201731 | + | 0.979441i | \(0.435343\pi\) | |||||||
\(278\) | 30.8315 | 1.84915 | ||||||||
\(279\) | 5.25753 | 0.314760 | ||||||||
\(280\) | 2.42684 | 0.145032 | ||||||||
\(281\) | 3.50732 | 0.209229 | 0.104615 | − | 0.994513i | \(-0.466639\pi\) | ||||
0.104615 | + | 0.994513i | \(0.466639\pi\) | |||||||
\(282\) | −18.9396 | −1.12783 | ||||||||
\(283\) | −0.290625 | −0.0172759 | −0.00863793 | − | 0.999963i | \(-0.502750\pi\) | ||||
−0.00863793 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(284\) | −20.7560 | −1.23164 | ||||||||
\(285\) | −22.4192 | −1.32800 | ||||||||
\(286\) | −49.8563 | −2.94806 | ||||||||
\(287\) | −0.277566 | −0.0163842 | ||||||||
\(288\) | −32.2230 | −1.89876 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 81.4369 | 4.78214 | ||||||||
\(291\) | −8.30804 | −0.487026 | ||||||||
\(292\) | 12.0743 | 0.706598 | ||||||||
\(293\) | 22.2072 | 1.29736 | 0.648679 | − | 0.761062i | \(-0.275322\pi\) | ||||
0.648679 | + | 0.761062i | \(0.275322\pi\) | |||||||
\(294\) | −19.7044 | −1.14918 | ||||||||
\(295\) | 20.0152 | 1.16533 | ||||||||
\(296\) | −118.665 | −6.89728 | ||||||||
\(297\) | 4.06087 | 0.235635 | ||||||||
\(298\) | −36.1421 | −2.09365 | ||||||||
\(299\) | −29.3434 | −1.69697 | ||||||||
\(300\) | −77.2550 | −4.46032 | ||||||||
\(301\) | 0.364734 | 0.0210229 | ||||||||
\(302\) | 5.82964 | 0.335458 | ||||||||
\(303\) | 12.2751 | 0.705184 | ||||||||
\(304\) | −101.919 | −5.84544 | ||||||||
\(305\) | 52.0604 | 2.98097 | ||||||||
\(306\) | −2.81598 | −0.160979 | ||||||||
\(307\) | 11.4221 | 0.651893 | 0.325947 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325947 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(308\) | −1.24372 | −0.0708677 | ||||||||
\(309\) | 14.2913 | 0.813001 | ||||||||
\(310\) | 62.8622 | 3.57034 | ||||||||
\(311\) | −11.0051 | −0.624041 | −0.312020 | − | 0.950075i | \(-0.601006\pi\) | ||||
−0.312020 | + | 0.950075i | \(0.601006\pi\) | |||||||
\(312\) | −48.2465 | −2.73142 | ||||||||
\(313\) | 4.22402 | 0.238756 | 0.119378 | − | 0.992849i | \(-0.461910\pi\) | ||||
0.119378 | + | 0.992849i | \(0.461910\pi\) | |||||||
\(314\) | 2.81598 | 0.158915 | ||||||||
\(315\) | −0.219304 | −0.0123564 | ||||||||
\(316\) | −87.7948 | −4.93884 | ||||||||
\(317\) | 20.5233 | 1.15270 | 0.576351 | − | 0.817202i | \(-0.304476\pi\) | ||||
0.576351 | + | 0.817202i | \(0.304476\pi\) | |||||||
\(318\) | 19.0570 | 1.06866 | ||||||||
\(319\) | −27.6587 | −1.54859 | ||||||||
\(320\) | −221.363 | −12.3746 | ||||||||
\(321\) | 3.76324 | 0.210044 | ||||||||
\(322\) | −0.978897 | −0.0545518 | ||||||||
\(323\) | −5.28010 | −0.293793 | ||||||||
\(324\) | 5.92975 | 0.329430 | ||||||||
\(325\) | −56.8018 | −3.15080 | ||||||||
\(326\) | 35.7751 | 1.98140 | ||||||||
\(327\) | 12.3326 | 0.681993 | ||||||||
\(328\) | 59.4691 | 3.28363 | ||||||||
\(329\) | −0.347383 | −0.0191519 | ||||||||
\(330\) | 48.5542 | 2.67282 | ||||||||
\(331\) | −7.92050 | −0.435350 | −0.217675 | − | 0.976021i | \(-0.569847\pi\) | ||||
−0.217675 | + | 0.976021i | \(0.569847\pi\) | |||||||
\(332\) | −42.3583 | −2.32471 | ||||||||
\(333\) | 10.7233 | 0.587634 | ||||||||
\(334\) | −53.7694 | −2.94213 | ||||||||
\(335\) | 29.2766 | 1.59955 | ||||||||
\(336\) | −0.996966 | −0.0543890 | ||||||||
\(337\) | −15.1205 | −0.823666 | −0.411833 | − | 0.911259i | \(-0.635111\pi\) | ||||
−0.411833 | + | 0.911259i | \(0.635111\pi\) | |||||||
\(338\) | −16.9192 | −0.920283 | ||||||||
\(339\) | 1.49671 | 0.0812901 | ||||||||
\(340\) | −25.1776 | −1.36545 | ||||||||
\(341\) | −21.3501 | −1.15617 | ||||||||
\(342\) | 14.8687 | 0.804005 | ||||||||
\(343\) | −0.722960 | −0.0390361 | ||||||||
\(344\) | −78.1452 | −4.21331 | ||||||||
\(345\) | 28.5770 | 1.53854 | ||||||||
\(346\) | 34.5463 | 1.85722 | ||||||||
\(347\) | 27.3094 | 1.46604 | 0.733022 | − | 0.680205i | \(-0.238109\pi\) | ||||
0.733022 | + | 0.680205i | \(0.238109\pi\) | |||||||
\(348\) | −40.3877 | −2.16501 | ||||||||
\(349\) | −15.7609 | −0.843660 | −0.421830 | − | 0.906675i | \(-0.638612\pi\) | ||||
−0.421830 | + | 0.906675i | \(0.638612\pi\) | |||||||
\(350\) | −1.89491 | −0.101287 | ||||||||
\(351\) | 4.35985 | 0.232711 | ||||||||
\(352\) | 130.854 | 6.97452 | ||||||||
\(353\) | 15.0661 | 0.801885 | 0.400943 | − | 0.916103i | \(-0.368683\pi\) | ||||
0.400943 | + | 0.916103i | \(0.368683\pi\) | |||||||
\(354\) | −13.2743 | −0.705519 | ||||||||
\(355\) | 14.8623 | 0.788809 | ||||||||
\(356\) | 16.5403 | 0.876635 | ||||||||
\(357\) | −0.0516498 | −0.00273360 | ||||||||
\(358\) | 32.5698 | 1.72137 | ||||||||
\(359\) | −16.5372 | −0.872801 | −0.436401 | − | 0.899753i | \(-0.643747\pi\) | ||||
−0.436401 | + | 0.899753i | \(0.643747\pi\) | |||||||
\(360\) | 46.9865 | 2.47640 | ||||||||
\(361\) | 8.87945 | 0.467340 | ||||||||
\(362\) | −11.2917 | −0.593478 | ||||||||
\(363\) | −5.49065 | −0.288185 | ||||||||
\(364\) | −1.33529 | −0.0699883 | ||||||||
\(365\) | −8.64581 | −0.452543 | ||||||||
\(366\) | −34.5270 | −1.80476 | ||||||||
\(367\) | −13.6569 | −0.712882 | −0.356441 | − | 0.934318i | \(-0.616010\pi\) | ||||
−0.356441 | + | 0.934318i | \(0.616010\pi\) | |||||||
\(368\) | 129.912 | 6.77215 | ||||||||
\(369\) | −5.37399 | −0.279759 | ||||||||
\(370\) | 128.215 | 6.66556 | ||||||||
\(371\) | 0.349537 | 0.0181471 | ||||||||
\(372\) | −31.1758 | −1.61639 | ||||||||
\(373\) | −12.6906 | −0.657095 | −0.328548 | − | 0.944487i | \(-0.606559\pi\) | ||||
−0.328548 | + | 0.944487i | \(0.606559\pi\) | |||||||
\(374\) | 11.4353 | 0.591307 | ||||||||
\(375\) | 34.0884 | 1.76032 | ||||||||
\(376\) | 74.4277 | 3.83832 | ||||||||
\(377\) | −29.6951 | −1.52938 | ||||||||
\(378\) | 0.145445 | 0.00748088 | ||||||||
\(379\) | −0.568417 | −0.0291976 | −0.0145988 | − | 0.999893i | \(-0.504647\pi\) | ||||
−0.0145988 | + | 0.999893i | \(0.504647\pi\) | |||||||
\(380\) | 132.940 | 6.81969 | ||||||||
\(381\) | −3.34745 | −0.171495 | ||||||||
\(382\) | −12.7079 | −0.650194 | ||||||||
\(383\) | 15.4097 | 0.787400 | 0.393700 | − | 0.919239i | \(-0.371195\pi\) | ||||
0.393700 | + | 0.919239i | \(0.371195\pi\) | |||||||
\(384\) | 82.3640 | 4.20312 | ||||||||
\(385\) | 0.890566 | 0.0453874 | ||||||||
\(386\) | −23.3122 | −1.18656 | ||||||||
\(387\) | 7.06168 | 0.358965 | ||||||||
\(388\) | 49.2646 | 2.50103 | ||||||||
\(389\) | 27.5426 | 1.39646 | 0.698232 | − | 0.715872i | \(-0.253970\pi\) | ||||
0.698232 | + | 0.715872i | \(0.253970\pi\) | |||||||
\(390\) | 52.1290 | 2.63965 | ||||||||
\(391\) | 6.73037 | 0.340369 | ||||||||
\(392\) | 77.4331 | 3.91096 | ||||||||
\(393\) | 11.9733 | 0.603973 | ||||||||
\(394\) | 23.5570 | 1.18679 | ||||||||
\(395\) | 62.8653 | 3.16309 | ||||||||
\(396\) | −24.0799 | −1.21006 | ||||||||
\(397\) | −3.02548 | −0.151845 | −0.0759223 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759223 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(398\) | −32.8696 | −1.64761 | ||||||||
\(399\) | 0.272716 | 0.0136529 | ||||||||
\(400\) | 251.479 | 12.5740 | ||||||||
\(401\) | −6.83885 | −0.341516 | −0.170758 | − | 0.985313i | \(-0.554622\pi\) | ||||
−0.170758 | + | 0.985313i | \(0.554622\pi\) | |||||||
\(402\) | −19.4166 | −0.968411 | ||||||||
\(403\) | −22.9220 | −1.14183 | ||||||||
\(404\) | −72.7880 | −3.62134 | ||||||||
\(405\) | −4.24598 | −0.210985 | ||||||||
\(406\) | −0.990631 | −0.0491642 | ||||||||
\(407\) | −43.5460 | −2.15849 | ||||||||
\(408\) | 11.0661 | 0.547853 | ||||||||
\(409\) | −13.4382 | −0.664476 | −0.332238 | − | 0.943196i | \(-0.607804\pi\) | ||||
−0.332238 | + | 0.943196i | \(0.607804\pi\) | |||||||
\(410\) | −64.2547 | −3.17331 | ||||||||
\(411\) | −6.15761 | −0.303733 | ||||||||
\(412\) | −84.7435 | −4.17501 | ||||||||
\(413\) | −0.243472 | −0.0119805 | ||||||||
\(414\) | −18.9526 | −0.931469 | ||||||||
\(415\) | 30.3306 | 1.48887 | ||||||||
\(416\) | 140.488 | 6.88797 | ||||||||
\(417\) | 10.9488 | 0.536163 | ||||||||
\(418\) | −60.3797 | −2.95327 | ||||||||
\(419\) | −19.0390 | −0.930115 | −0.465057 | − | 0.885281i | \(-0.653966\pi\) | ||||
−0.465057 | + | 0.885281i | \(0.653966\pi\) | |||||||
\(420\) | 1.30042 | 0.0634540 | ||||||||
\(421\) | −28.6901 | −1.39827 | −0.699135 | − | 0.714990i | \(-0.746431\pi\) | ||||
−0.699135 | + | 0.714990i | \(0.746431\pi\) | |||||||
\(422\) | 36.5192 | 1.77773 | ||||||||
\(423\) | −6.72574 | −0.327017 | ||||||||
\(424\) | −74.8892 | −3.63694 | ||||||||
\(425\) | 13.0284 | 0.631970 | ||||||||
\(426\) | −9.85683 | −0.477565 | ||||||||
\(427\) | −0.633283 | −0.0306467 | ||||||||
\(428\) | −22.3151 | −1.07864 | ||||||||
\(429\) | −17.7048 | −0.854794 | ||||||||
\(430\) | 84.4337 | 4.07176 | ||||||||
\(431\) | 4.24230 | 0.204344 | 0.102172 | − | 0.994767i | \(-0.467421\pi\) | ||||
0.102172 | + | 0.994767i | \(0.467421\pi\) | |||||||
\(432\) | −19.3024 | −0.928688 | ||||||||
\(433\) | −7.33968 | −0.352723 | −0.176361 | − | 0.984325i | \(-0.556433\pi\) | ||||
−0.176361 | + | 0.984325i | \(0.556433\pi\) | |||||||
\(434\) | −0.764681 | −0.0367059 | ||||||||
\(435\) | 28.9196 | 1.38659 | ||||||||
\(436\) | −73.1290 | −3.50225 | ||||||||
\(437\) | −35.5370 | −1.69997 | ||||||||
\(438\) | 5.73399 | 0.273981 | ||||||||
\(439\) | −9.64569 | −0.460363 | −0.230182 | − | 0.973148i | \(-0.573932\pi\) | ||||
−0.230182 | + | 0.973148i | \(0.573932\pi\) | |||||||
\(440\) | −190.806 | −9.09631 | ||||||||
\(441\) | −6.99733 | −0.333206 | ||||||||
\(442\) | 12.2772 | 0.583969 | ||||||||
\(443\) | 12.1552 | 0.577512 | 0.288756 | − | 0.957403i | \(-0.406758\pi\) | ||||
0.288756 | + | 0.957403i | \(0.406758\pi\) | |||||||
\(444\) | −63.5866 | −3.01768 | ||||||||
\(445\) | −11.8437 | −0.561443 | ||||||||
\(446\) | −33.0958 | −1.56713 | ||||||||
\(447\) | −12.8346 | −0.607057 | ||||||||
\(448\) | 2.69274 | 0.127220 | ||||||||
\(449\) | 25.4215 | 1.19971 | 0.599857 | − | 0.800107i | \(-0.295224\pi\) | ||||
0.599857 | + | 0.800107i | \(0.295224\pi\) | |||||||
\(450\) | −36.6877 | −1.72947 | ||||||||
\(451\) | 21.8231 | 1.02761 | ||||||||
\(452\) | −8.87511 | −0.417450 | ||||||||
\(453\) | 2.07020 | 0.0972664 | ||||||||
\(454\) | 56.0706 | 2.63152 | ||||||||
\(455\) | 0.956133 | 0.0448242 | ||||||||
\(456\) | −58.4301 | −2.73624 | ||||||||
\(457\) | 18.1994 | 0.851330 | 0.425665 | − | 0.904881i | \(-0.360040\pi\) | ||||
0.425665 | + | 0.904881i | \(0.360040\pi\) | |||||||
\(458\) | 15.3024 | 0.715034 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −169.455 | −7.90086 | ||||||||
\(461\) | −0.589374 | −0.0274499 | −0.0137249 | − | 0.999906i | \(-0.504369\pi\) | ||||
−0.0137249 | + | 0.999906i | \(0.504369\pi\) | |||||||
\(462\) | −0.590633 | −0.0274787 | ||||||||
\(463\) | −33.1737 | −1.54171 | −0.770856 | − | 0.637010i | \(-0.780171\pi\) | ||||
−0.770856 | + | 0.637010i | \(0.780171\pi\) | |||||||
\(464\) | 131.469 | 6.10332 | ||||||||
\(465\) | 22.3234 | 1.03522 | ||||||||
\(466\) | 76.6210 | 3.54940 | ||||||||
\(467\) | −22.1450 | −1.02475 | −0.512375 | − | 0.858762i | \(-0.671234\pi\) | ||||
−0.512375 | + | 0.858762i | \(0.671234\pi\) | |||||||
\(468\) | −25.8528 | −1.19505 | ||||||||
\(469\) | −0.356133 | −0.0164447 | ||||||||
\(470\) | −80.4171 | −3.70936 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 52.1645 | 2.40107 | ||||||||
\(473\) | −28.6765 | −1.31855 | ||||||||
\(474\) | −41.6929 | −1.91502 | ||||||||
\(475\) | −68.7912 | −3.15636 | ||||||||
\(476\) | 0.306270 | 0.0140379 | ||||||||
\(477\) | 6.76745 | 0.309860 | ||||||||
\(478\) | 0.487725 | 0.0223080 | ||||||||
\(479\) | −0.471722 | −0.0215535 | −0.0107768 | − | 0.999942i | \(-0.503430\pi\) | ||||
−0.0107768 | + | 0.999942i | \(0.503430\pi\) | |||||||
\(480\) | −136.819 | −6.24488 | ||||||||
\(481\) | −46.7520 | −2.13171 | ||||||||
\(482\) | −49.1168 | −2.23721 | ||||||||
\(483\) | −0.347622 | −0.0158174 | ||||||||
\(484\) | 32.5582 | 1.47992 | ||||||||
\(485\) | −35.2758 | −1.60179 | ||||||||
\(486\) | 2.81598 | 0.127735 | ||||||||
\(487\) | −12.5418 | −0.568325 | −0.284163 | − | 0.958776i | \(-0.591716\pi\) | ||||
−0.284163 | + | 0.958776i | \(0.591716\pi\) | |||||||
\(488\) | 135.682 | 6.14205 | ||||||||
\(489\) | 12.7043 | 0.574509 | ||||||||
\(490\) | −83.6644 | −3.77957 | ||||||||
\(491\) | 34.7159 | 1.56671 | 0.783353 | − | 0.621577i | \(-0.213508\pi\) | ||||
0.783353 | + | 0.621577i | \(0.213508\pi\) | |||||||
\(492\) | 31.8664 | 1.43665 | ||||||||
\(493\) | 6.81104 | 0.306754 | ||||||||
\(494\) | −64.8251 | −2.91662 | ||||||||
\(495\) | 17.2424 | 0.774988 | ||||||||
\(496\) | 101.483 | 4.55672 | ||||||||
\(497\) | −0.180791 | −0.00810957 | ||||||||
\(498\) | −20.1156 | −0.901400 | ||||||||
\(499\) | 3.18817 | 0.142722 | 0.0713610 | − | 0.997451i | \(-0.477266\pi\) | ||||
0.0713610 | + | 0.997451i | \(0.477266\pi\) | |||||||
\(500\) | −202.136 | −9.03978 | ||||||||
\(501\) | −19.0944 | −0.853073 | ||||||||
\(502\) | −59.0196 | −2.63417 | ||||||||
\(503\) | 14.9017 | 0.664433 | 0.332217 | − | 0.943203i | \(-0.392203\pi\) | ||||
0.332217 | + | 0.943203i | \(0.392203\pi\) | |||||||
\(504\) | −0.571562 | −0.0254594 | ||||||||
\(505\) | 52.1197 | 2.31930 | ||||||||
\(506\) | 76.9640 | 3.42147 | ||||||||
\(507\) | −6.00828 | −0.266837 | ||||||||
\(508\) | 19.8495 | 0.880681 | ||||||||
\(509\) | −37.5932 | −1.66629 | −0.833145 | − | 0.553055i | \(-0.813462\pi\) | ||||
−0.833145 | + | 0.553055i | \(0.813462\pi\) | |||||||
\(510\) | −11.9566 | −0.529448 | ||||||||
\(511\) | 0.105171 | 0.00465249 | ||||||||
\(512\) | −194.778 | −8.60804 | ||||||||
\(513\) | 5.28010 | 0.233122 | ||||||||
\(514\) | 14.8643 | 0.655637 | ||||||||
\(515\) | 60.6804 | 2.67390 | ||||||||
\(516\) | −41.8740 | −1.84340 | ||||||||
\(517\) | 27.3124 | 1.20120 | ||||||||
\(518\) | −1.55965 | −0.0685271 | ||||||||
\(519\) | 12.2680 | 0.538504 | ||||||||
\(520\) | −204.854 | −8.98344 | ||||||||
\(521\) | −30.5592 | −1.33882 | −0.669412 | − | 0.742891i | \(-0.733454\pi\) | ||||
−0.669412 | + | 0.742891i | \(0.733454\pi\) | |||||||
\(522\) | −19.1798 | −0.839475 | ||||||||
\(523\) | 5.01460 | 0.219273 | 0.109637 | − | 0.993972i | \(-0.465031\pi\) | ||||
0.109637 | + | 0.993972i | \(0.465031\pi\) | |||||||
\(524\) | −70.9987 | −3.10159 | ||||||||
\(525\) | −0.672914 | −0.0293684 | ||||||||
\(526\) | −50.1352 | −2.18600 | ||||||||
\(527\) | 5.25753 | 0.229022 | ||||||||
\(528\) | 78.3846 | 3.41125 | ||||||||
\(529\) | 22.2978 | 0.969472 | ||||||||
\(530\) | 80.9157 | 3.51475 | ||||||||
\(531\) | −4.71390 | −0.204566 | ||||||||
\(532\) | −1.61714 | −0.0701118 | ||||||||
\(533\) | 23.4298 | 1.01486 | ||||||||
\(534\) | 7.85484 | 0.339912 | ||||||||
\(535\) | 15.9787 | 0.690818 | ||||||||
\(536\) | 76.3022 | 3.29575 | ||||||||
\(537\) | 11.5661 | 0.499113 | ||||||||
\(538\) | −19.5083 | −0.841062 | ||||||||
\(539\) | 28.4152 | 1.22393 | ||||||||
\(540\) | 25.1776 | 1.08347 | ||||||||
\(541\) | −2.26237 | −0.0972668 | −0.0486334 | − | 0.998817i | \(-0.515487\pi\) | ||||
−0.0486334 | + | 0.998817i | \(0.515487\pi\) | |||||||
\(542\) | 16.1645 | 0.694324 | ||||||||
\(543\) | −4.00986 | −0.172080 | ||||||||
\(544\) | −32.2230 | −1.38155 | ||||||||
\(545\) | 52.3639 | 2.24302 | ||||||||
\(546\) | −0.634118 | −0.0271377 | ||||||||
\(547\) | −15.0800 | −0.644774 | −0.322387 | − | 0.946608i | \(-0.604485\pi\) | ||||
−0.322387 | + | 0.946608i | \(0.604485\pi\) | |||||||
\(548\) | 36.5131 | 1.55976 | ||||||||
\(549\) | −12.2611 | −0.523291 | ||||||||
\(550\) | 148.984 | 6.35269 | ||||||||
\(551\) | −35.9630 | −1.53207 | ||||||||
\(552\) | 74.4789 | 3.17003 | ||||||||
\(553\) | −0.764718 | −0.0325191 | ||||||||
\(554\) | −18.9092 | −0.803375 | ||||||||
\(555\) | 45.5310 | 1.93268 | ||||||||
\(556\) | −64.9233 | −2.75336 | ||||||||
\(557\) | 1.98612 | 0.0841546 | 0.0420773 | − | 0.999114i | \(-0.486602\pi\) | ||||
0.0420773 | + | 0.999114i | \(0.486602\pi\) | |||||||
\(558\) | −14.8051 | −0.626750 | ||||||||
\(559\) | −30.7878 | −1.30219 | ||||||||
\(560\) | −4.23310 | −0.178881 | ||||||||
\(561\) | 4.06087 | 0.171450 | ||||||||
\(562\) | −9.87654 | −0.416617 | ||||||||
\(563\) | −13.9777 | −0.589089 | −0.294544 | − | 0.955638i | \(-0.595168\pi\) | ||||
−0.294544 | + | 0.955638i | \(0.595168\pi\) | |||||||
\(564\) | 39.8820 | 1.67933 | ||||||||
\(565\) | 6.35501 | 0.267357 | ||||||||
\(566\) | 0.818394 | 0.0343997 | ||||||||
\(567\) | 0.0516498 | 0.00216909 | ||||||||
\(568\) | 38.7349 | 1.62528 | ||||||||
\(569\) | −8.09275 | −0.339266 | −0.169633 | − | 0.985507i | \(-0.554258\pi\) | ||||
−0.169633 | + | 0.985507i | \(0.554258\pi\) | |||||||
\(570\) | 63.1321 | 2.64431 | ||||||||
\(571\) | −31.7412 | −1.32833 | −0.664164 | − | 0.747587i | \(-0.731212\pi\) | ||||
−0.664164 | + | 0.747587i | \(0.731212\pi\) | |||||||
\(572\) | 104.985 | 4.38964 | ||||||||
\(573\) | −4.51279 | −0.188525 | ||||||||
\(574\) | 0.781620 | 0.0326242 | ||||||||
\(575\) | 87.6858 | 3.65675 | ||||||||
\(576\) | 52.1346 | 2.17228 | ||||||||
\(577\) | −9.72273 | −0.404763 | −0.202381 | − | 0.979307i | \(-0.564868\pi\) | ||||
−0.202381 | + | 0.979307i | \(0.564868\pi\) | |||||||
\(578\) | −2.81598 | −0.117129 | ||||||||
\(579\) | −8.27853 | −0.344044 | ||||||||
\(580\) | −171.486 | −7.12056 | ||||||||
\(581\) | −0.368953 | −0.0153068 | ||||||||
\(582\) | 23.3953 | 0.969765 | ||||||||
\(583\) | −27.4817 | −1.13818 | ||||||||
\(584\) | −22.5331 | −0.932428 | ||||||||
\(585\) | 18.5118 | 0.765371 | ||||||||
\(586\) | −62.5351 | −2.58330 | ||||||||
\(587\) | 13.2141 | 0.545402 | 0.272701 | − | 0.962099i | \(-0.412083\pi\) | ||||
0.272701 | + | 0.962099i | \(0.412083\pi\) | |||||||
\(588\) | 41.4924 | 1.71112 | ||||||||
\(589\) | −27.7603 | −1.14384 | ||||||||
\(590\) | −56.3623 | −2.32040 | ||||||||
\(591\) | 8.36548 | 0.344110 | ||||||||
\(592\) | 206.986 | 8.50707 | ||||||||
\(593\) | 24.9497 | 1.02456 | 0.512281 | − | 0.858818i | \(-0.328801\pi\) | ||||
0.512281 | + | 0.858818i | \(0.328801\pi\) | |||||||
\(594\) | −11.4353 | −0.469197 | ||||||||
\(595\) | −0.219304 | −0.00899060 | ||||||||
\(596\) | 76.1061 | 3.11743 | ||||||||
\(597\) | −11.6725 | −0.477725 | ||||||||
\(598\) | 82.6304 | 3.37901 | ||||||||
\(599\) | 26.9894 | 1.10276 | 0.551378 | − | 0.834255i | \(-0.314102\pi\) | ||||
0.551378 | + | 0.834255i | \(0.314102\pi\) | |||||||
\(600\) | 144.173 | 5.88585 | ||||||||
\(601\) | −48.0430 | −1.95972 | −0.979858 | − | 0.199697i | \(-0.936004\pi\) | ||||
−0.979858 | + | 0.199697i | \(0.936004\pi\) | |||||||
\(602\) | −1.02708 | −0.0418608 | ||||||||
\(603\) | −6.89514 | −0.280792 | ||||||||
\(604\) | −12.2758 | −0.499494 | ||||||||
\(605\) | −23.3132 | −0.947818 | ||||||||
\(606\) | −34.5663 | −1.40416 | ||||||||
\(607\) | −31.8990 | −1.29474 | −0.647371 | − | 0.762175i | \(-0.724132\pi\) | ||||
−0.647371 | + | 0.762175i | \(0.724132\pi\) | |||||||
\(608\) | 170.141 | 6.90012 | ||||||||
\(609\) | −0.351789 | −0.0142552 | ||||||||
\(610\) | −146.601 | −5.93571 | ||||||||
\(611\) | 29.3232 | 1.18629 | ||||||||
\(612\) | 5.92975 | 0.239696 | ||||||||
\(613\) | −32.4981 | −1.31258 | −0.656292 | − | 0.754507i | \(-0.727876\pi\) | ||||
−0.656292 | + | 0.754507i | \(0.727876\pi\) | |||||||
\(614\) | −32.1644 | −1.29805 | ||||||||
\(615\) | −22.8179 | −0.920106 | ||||||||
\(616\) | 2.32104 | 0.0935172 | ||||||||
\(617\) | −36.2237 | −1.45831 | −0.729156 | − | 0.684348i | \(-0.760087\pi\) | ||||
−0.729156 | + | 0.684348i | \(0.760087\pi\) | |||||||
\(618\) | −40.2439 | −1.61885 | ||||||||
\(619\) | −33.7377 | −1.35603 | −0.678015 | − | 0.735048i | \(-0.737160\pi\) | ||||
−0.678015 | + | 0.735048i | \(0.737160\pi\) | |||||||
\(620\) | −132.372 | −5.31619 | ||||||||
\(621\) | −6.73037 | −0.270080 | ||||||||
\(622\) | 30.9901 | 1.24259 | ||||||||
\(623\) | 0.144071 | 0.00577208 | ||||||||
\(624\) | 84.1556 | 3.36892 | ||||||||
\(625\) | 79.5969 | 3.18388 | ||||||||
\(626\) | −11.8948 | −0.475411 | ||||||||
\(627\) | −21.4418 | −0.856303 | ||||||||
\(628\) | −5.92975 | −0.236623 | ||||||||
\(629\) | 10.7233 | 0.427567 | ||||||||
\(630\) | 0.617557 | 0.0246040 | ||||||||
\(631\) | 14.6574 | 0.583503 | 0.291752 | − | 0.956494i | \(-0.405762\pi\) | ||||
0.291752 | + | 0.956494i | \(0.405762\pi\) | |||||||
\(632\) | 163.843 | 6.51731 | ||||||||
\(633\) | 12.9686 | 0.515454 | ||||||||
\(634\) | −57.7931 | −2.29526 | ||||||||
\(635\) | −14.2132 | −0.564035 | ||||||||
\(636\) | −40.1293 | −1.59123 | ||||||||
\(637\) | 30.5073 | 1.20874 | ||||||||
\(638\) | 77.8865 | 3.08355 | ||||||||
\(639\) | −3.50032 | −0.138470 | ||||||||
\(640\) | 349.716 | 13.8238 | ||||||||
\(641\) | 21.1802 | 0.836566 | 0.418283 | − | 0.908317i | \(-0.362632\pi\) | ||||
0.418283 | + | 0.908317i | \(0.362632\pi\) | |||||||
\(642\) | −10.5972 | −0.418239 | ||||||||
\(643\) | 15.4097 | 0.607699 | 0.303849 | − | 0.952720i | \(-0.401728\pi\) | ||||
0.303849 | + | 0.952720i | \(0.401728\pi\) | |||||||
\(644\) | 2.06131 | 0.0812271 | ||||||||
\(645\) | 29.9838 | 1.18061 | ||||||||
\(646\) | 14.8687 | 0.585000 | ||||||||
\(647\) | −26.9858 | −1.06092 | −0.530461 | − | 0.847709i | \(-0.677981\pi\) | ||||
−0.530461 | + | 0.847709i | \(0.677981\pi\) | |||||||
\(648\) | −11.0661 | −0.434717 | ||||||||
\(649\) | 19.1425 | 0.751411 | ||||||||
\(650\) | 159.953 | 6.27386 | ||||||||
\(651\) | −0.271550 | −0.0106429 | ||||||||
\(652\) | −75.3334 | −2.95028 | ||||||||
\(653\) | 47.0120 | 1.83972 | 0.919861 | − | 0.392245i | \(-0.128301\pi\) | ||||
0.919861 | + | 0.392245i | \(0.128301\pi\) | |||||||
\(654\) | −34.7283 | −1.35798 | ||||||||
\(655\) | 50.8385 | 1.98642 | ||||||||
\(656\) | −103.731 | −4.05002 | ||||||||
\(657\) | 2.03623 | 0.0794410 | ||||||||
\(658\) | 0.978225 | 0.0381352 | ||||||||
\(659\) | 3.75131 | 0.146130 | 0.0730652 | − | 0.997327i | \(-0.476722\pi\) | ||||
0.0730652 | + | 0.997327i | \(0.476722\pi\) | |||||||
\(660\) | −102.243 | −3.97980 | ||||||||
\(661\) | 40.6523 | 1.58119 | 0.790595 | − | 0.612340i | \(-0.209772\pi\) | ||||
0.790595 | + | 0.612340i | \(0.209772\pi\) | |||||||
\(662\) | 22.3040 | 0.866869 | ||||||||
\(663\) | 4.35985 | 0.169322 | ||||||||
\(664\) | 79.0491 | 3.06770 | ||||||||
\(665\) | 1.15795 | 0.0449033 | ||||||||
\(666\) | −30.1967 | −1.17010 | ||||||||
\(667\) | 45.8408 | 1.77496 | ||||||||
\(668\) | 113.225 | 4.38080 | ||||||||
\(669\) | −11.7529 | −0.454392 | ||||||||
\(670\) | −82.4425 | −3.18503 | ||||||||
\(671\) | 49.7907 | 1.92215 | ||||||||
\(672\) | 1.66431 | 0.0642023 | ||||||||
\(673\) | 34.9762 | 1.34823 | 0.674117 | − | 0.738625i | \(-0.264524\pi\) | ||||
0.674117 | + | 0.738625i | \(0.264524\pi\) | |||||||
\(674\) | 42.5790 | 1.64008 | ||||||||
\(675\) | −13.0284 | −0.501463 | ||||||||
\(676\) | 35.6276 | 1.37029 | ||||||||
\(677\) | 7.88983 | 0.303231 | 0.151615 | − | 0.988440i | \(-0.451552\pi\) | ||||
0.151615 | + | 0.988440i | \(0.451552\pi\) | |||||||
\(678\) | −4.21471 | −0.161865 | ||||||||
\(679\) | 0.429109 | 0.0164677 | ||||||||
\(680\) | 46.9865 | 1.80185 | ||||||||
\(681\) | 19.9116 | 0.763013 | ||||||||
\(682\) | 60.1216 | 2.30217 | ||||||||
\(683\) | −30.4180 | −1.16391 | −0.581955 | − | 0.813221i | \(-0.697712\pi\) | ||||
−0.581955 | + | 0.813221i | \(0.697712\pi\) | |||||||
\(684\) | −31.3097 | −1.19715 | ||||||||
\(685\) | −26.1451 | −0.998954 | ||||||||
\(686\) | 2.03584 | 0.0777287 | ||||||||
\(687\) | 5.43413 | 0.207325 | ||||||||
\(688\) | 136.307 | 5.19667 | ||||||||
\(689\) | −29.5050 | −1.12405 | ||||||||
\(690\) | −80.4724 | −3.06353 | ||||||||
\(691\) | 14.7414 | 0.560787 | 0.280394 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280394 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(692\) | −72.7459 | −2.76538 | ||||||||
\(693\) | −0.209743 | −0.00796748 | ||||||||
\(694\) | −76.9027 | −2.91919 | ||||||||
\(695\) | 46.4882 | 1.76340 | ||||||||
\(696\) | 75.3716 | 2.85695 | ||||||||
\(697\) | −5.37399 | −0.203554 | ||||||||
\(698\) | 44.3823 | 1.67990 | ||||||||
\(699\) | 27.2094 | 1.02915 | ||||||||
\(700\) | 3.99021 | 0.150816 | ||||||||
\(701\) | −47.7801 | −1.80463 | −0.902314 | − | 0.431079i | \(-0.858133\pi\) | ||||
−0.902314 | + | 0.431079i | \(0.858133\pi\) | |||||||
\(702\) | −12.2772 | −0.463375 | ||||||||
\(703\) | −56.6202 | −2.13547 | ||||||||
\(704\) | −211.712 | −7.97919 | ||||||||
\(705\) | −28.5574 | −1.07553 | ||||||||
\(706\) | −42.4257 | −1.59671 | ||||||||
\(707\) | −0.634005 | −0.0238442 | ||||||||
\(708\) | 27.9523 | 1.05051 | ||||||||
\(709\) | 20.2838 | 0.761773 | 0.380886 | − | 0.924622i | \(-0.375619\pi\) | ||||
0.380886 | + | 0.924622i | \(0.375619\pi\) | |||||||
\(710\) | −41.8519 | −1.57068 | ||||||||
\(711\) | −14.8058 | −0.555261 | ||||||||
\(712\) | −30.8675 | −1.15681 | ||||||||
\(713\) | 35.3851 | 1.32518 | ||||||||
\(714\) | 0.145445 | 0.00544314 | ||||||||
\(715\) | −75.1742 | −2.81136 | ||||||||
\(716\) | −68.5839 | −2.56310 | ||||||||
\(717\) | 0.173199 | 0.00646823 | ||||||||
\(718\) | 46.5685 | 1.73792 | ||||||||
\(719\) | −20.7115 | −0.772409 | −0.386204 | − | 0.922413i | \(-0.626214\pi\) | ||||
−0.386204 | + | 0.922413i | \(0.626214\pi\) | |||||||
\(720\) | −81.9577 | −3.05438 | ||||||||
\(721\) | −0.738140 | −0.0274898 | ||||||||
\(722\) | −25.0044 | −0.930566 | ||||||||
\(723\) | −17.4422 | −0.648682 | ||||||||
\(724\) | 23.7775 | 0.883682 | ||||||||
\(725\) | 88.7368 | 3.29560 | ||||||||
\(726\) | 15.4616 | 0.573833 | ||||||||
\(727\) | 3.59014 | 0.133151 | 0.0665755 | − | 0.997781i | \(-0.478793\pi\) | ||||
0.0665755 | + | 0.997781i | \(0.478793\pi\) | |||||||
\(728\) | 2.49192 | 0.0923568 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.3464 | 0.901102 | ||||||||
\(731\) | 7.06168 | 0.261186 | ||||||||
\(732\) | 72.7052 | 2.68726 | ||||||||
\(733\) | −35.9031 | −1.32611 | −0.663055 | − | 0.748571i | \(-0.730740\pi\) | ||||
−0.663055 | + | 0.748571i | \(0.730740\pi\) | |||||||
\(734\) | 38.4575 | 1.41949 | ||||||||
\(735\) | −29.7106 | −1.09589 | ||||||||
\(736\) | −216.873 | −7.99404 | ||||||||
\(737\) | 28.0002 | 1.03140 | ||||||||
\(738\) | 15.1331 | 0.557056 | ||||||||
\(739\) | 9.36547 | 0.344514 | 0.172257 | − | 0.985052i | \(-0.444894\pi\) | ||||
0.172257 | + | 0.985052i | \(0.444894\pi\) | |||||||
\(740\) | −269.988 | −9.92494 | ||||||||
\(741\) | −23.0204 | −0.845677 | ||||||||
\(742\) | −0.984291 | −0.0361344 | ||||||||
\(743\) | −11.8837 | −0.435969 | −0.217985 | − | 0.975952i | \(-0.569948\pi\) | ||||
−0.217985 | + | 0.975952i | \(0.569948\pi\) | |||||||
\(744\) | 58.1803 | 2.13299 | ||||||||
\(745\) | −54.4956 | −1.99657 | ||||||||
\(746\) | 35.7365 | 1.30841 | ||||||||
\(747\) | −7.14336 | −0.261362 | ||||||||
\(748\) | −24.0799 | −0.880449 | ||||||||
\(749\) | −0.194371 | −0.00710215 | ||||||||
\(750\) | −95.9923 | −3.50514 | ||||||||
\(751\) | −14.9055 | −0.543908 | −0.271954 | − | 0.962310i | \(-0.587670\pi\) | ||||
−0.271954 | + | 0.962310i | \(0.587670\pi\) | |||||||
\(752\) | −129.823 | −4.73416 | ||||||||
\(753\) | −20.9588 | −0.763781 | ||||||||
\(754\) | 83.6208 | 3.04529 | ||||||||
\(755\) | 8.79003 | 0.319902 | ||||||||
\(756\) | −0.306270 | −0.0111389 | ||||||||
\(757\) | 42.6578 | 1.55042 | 0.775212 | − | 0.631701i | \(-0.217643\pi\) | ||||
0.775212 | + | 0.631701i | \(0.217643\pi\) | |||||||
\(758\) | 1.60065 | 0.0581383 | ||||||||
\(759\) | 27.3311 | 0.992057 | ||||||||
\(760\) | −248.093 | −8.99929 | ||||||||
\(761\) | 10.5539 | 0.382579 | 0.191290 | − | 0.981534i | \(-0.438733\pi\) | ||||
0.191290 | + | 0.981534i | \(0.438733\pi\) | |||||||
\(762\) | 9.42636 | 0.341481 | ||||||||
\(763\) | −0.636975 | −0.0230600 | ||||||||
\(764\) | 26.7597 | 0.968132 | ||||||||
\(765\) | −4.24598 | −0.153514 | ||||||||
\(766\) | −43.3935 | −1.56787 | ||||||||
\(767\) | 20.5519 | 0.742086 | ||||||||
\(768\) | −127.666 | −4.60676 | ||||||||
\(769\) | 29.1358 | 1.05066 | 0.525331 | − | 0.850898i | \(-0.323941\pi\) | ||||
0.525331 | + | 0.850898i | \(0.323941\pi\) | |||||||
\(770\) | −2.50782 | −0.0903754 | ||||||||
\(771\) | 5.27856 | 0.190103 | ||||||||
\(772\) | 49.0896 | 1.76677 | ||||||||
\(773\) | 41.7734 | 1.50249 | 0.751243 | − | 0.660026i | \(-0.229455\pi\) | ||||
0.751243 | + | 0.660026i | \(0.229455\pi\) | |||||||
\(774\) | −19.8855 | −0.714771 | ||||||||
\(775\) | 68.4971 | 2.46049 | ||||||||
\(776\) | −91.9375 | −3.30037 | ||||||||
\(777\) | −0.553857 | −0.0198695 | ||||||||
\(778\) | −77.5594 | −2.78064 | ||||||||
\(779\) | 28.3752 | 1.01665 | ||||||||
\(780\) | −109.771 | −3.93042 | ||||||||
\(781\) | 14.2143 | 0.508629 | ||||||||
\(782\) | −18.9526 | −0.677743 | ||||||||
\(783\) | −6.81104 | −0.243407 | ||||||||
\(784\) | −135.065 | −4.82376 | ||||||||
\(785\) | 4.24598 | 0.151546 | ||||||||
\(786\) | −33.7166 | −1.20263 | ||||||||
\(787\) | 44.8476 | 1.59864 | 0.799322 | − | 0.600903i | \(-0.205192\pi\) | ||||
0.799322 | + | 0.600903i | \(0.205192\pi\) | |||||||
\(788\) | −49.6052 | −1.76711 | ||||||||
\(789\) | −17.8038 | −0.633832 | ||||||||
\(790\) | −177.027 | −6.29835 | ||||||||
\(791\) | −0.0773048 | −0.00274864 | ||||||||
\(792\) | 44.9380 | 1.59680 | ||||||||
\(793\) | 53.4565 | 1.89830 | ||||||||
\(794\) | 8.51969 | 0.302353 | ||||||||
\(795\) | 28.7345 | 1.01911 | ||||||||
\(796\) | 69.2152 | 2.45327 | ||||||||
\(797\) | −51.7523 | −1.83316 | −0.916581 | − | 0.399849i | \(-0.869062\pi\) | ||||
−0.916581 | + | 0.399849i | \(0.869062\pi\) | |||||||
\(798\) | −0.767963 | −0.0271856 | ||||||||
\(799\) | −6.72574 | −0.237940 | ||||||||
\(800\) | −419.814 | −14.8427 | ||||||||
\(801\) | 2.78938 | 0.0985579 | ||||||||
\(802\) | 19.2581 | 0.680026 | ||||||||
\(803\) | −8.26887 | −0.291802 | ||||||||
\(804\) | 40.8864 | 1.44195 | ||||||||
\(805\) | −1.47600 | −0.0520221 | ||||||||
\(806\) | 64.5480 | 2.27361 | ||||||||
\(807\) | −6.92771 | −0.243867 | ||||||||
\(808\) | 135.837 | 4.77873 | ||||||||
\(809\) | −2.21921 | −0.0780234 | −0.0390117 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390117 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(810\) | 11.9566 | 0.420112 | ||||||||
\(811\) | 36.0095 | 1.26447 | 0.632233 | − | 0.774779i | \(-0.282139\pi\) | ||||
0.632233 | + | 0.774779i | \(0.282139\pi\) | |||||||
\(812\) | 2.08602 | 0.0732049 | ||||||||
\(813\) | 5.74026 | 0.201320 | ||||||||
\(814\) | 122.625 | 4.29799 | ||||||||
\(815\) | 53.9423 | 1.88952 | ||||||||
\(816\) | −19.3024 | −0.675720 | ||||||||
\(817\) | −37.2864 | −1.30448 | ||||||||
\(818\) | 37.8417 | 1.32310 | ||||||||
\(819\) | −0.225185 | −0.00786861 | ||||||||
\(820\) | 135.304 | 4.72503 | ||||||||
\(821\) | 35.9993 | 1.25639 | 0.628193 | − | 0.778058i | \(-0.283795\pi\) | ||||
0.628193 | + | 0.778058i | \(0.283795\pi\) | |||||||
\(822\) | 17.3397 | 0.604792 | ||||||||
\(823\) | 25.4428 | 0.886880 | 0.443440 | − | 0.896304i | \(-0.353758\pi\) | ||||
0.443440 | + | 0.896304i | \(0.353758\pi\) | |||||||
\(824\) | 158.148 | 5.50936 | ||||||||
\(825\) | 52.9066 | 1.84197 | ||||||||
\(826\) | 0.685613 | 0.0238555 | ||||||||
\(827\) | −12.3700 | −0.430145 | −0.215073 | − | 0.976598i | \(-0.568999\pi\) | ||||
−0.215073 | + | 0.976598i | \(0.568999\pi\) | |||||||
\(828\) | 39.9094 | 1.38695 | ||||||||
\(829\) | 50.1470 | 1.74168 | 0.870839 | − | 0.491568i | \(-0.163576\pi\) | ||||
0.870839 | + | 0.491568i | \(0.163576\pi\) | |||||||
\(830\) | −85.4104 | −2.96464 | ||||||||
\(831\) | −6.71496 | −0.232939 | ||||||||
\(832\) | −227.299 | −7.88018 | ||||||||
\(833\) | −6.99733 | −0.242443 | ||||||||
\(834\) | −30.8315 | −1.06761 | ||||||||
\(835\) | −81.0744 | −2.80569 | ||||||||
\(836\) | 127.144 | 4.39738 | ||||||||
\(837\) | −5.25753 | −0.181727 | ||||||||
\(838\) | 53.6134 | 1.85204 | ||||||||
\(839\) | −32.6743 | −1.12804 | −0.564021 | − | 0.825761i | \(-0.690746\pi\) | ||||
−0.564021 | + | 0.825761i | \(0.690746\pi\) | |||||||
\(840\) | −2.42684 | −0.0837340 | ||||||||
\(841\) | 17.3903 | 0.599664 | ||||||||
\(842\) | 80.7908 | 2.78423 | ||||||||
\(843\) | −3.50732 | −0.120798 | ||||||||
\(844\) | −76.9003 | −2.64702 | ||||||||
\(845\) | −25.5110 | −0.877607 | ||||||||
\(846\) | 18.9396 | 0.651156 | ||||||||
\(847\) | 0.283591 | 0.00974431 | ||||||||
\(848\) | 130.628 | 4.48579 | ||||||||
\(849\) | 0.290625 | 0.00997422 | ||||||||
\(850\) | −36.6877 | −1.25838 | ||||||||
\(851\) | 72.1719 | 2.47402 | ||||||||
\(852\) | 20.7560 | 0.711089 | ||||||||
\(853\) | −8.75886 | −0.299898 | −0.149949 | − | 0.988694i | \(-0.547911\pi\) | ||||
−0.149949 | + | 0.988694i | \(0.547911\pi\) | |||||||
\(854\) | 1.78331 | 0.0610237 | ||||||||
\(855\) | 22.4192 | 0.766721 | ||||||||
\(856\) | 41.6444 | 1.42338 | ||||||||
\(857\) | −21.1405 | −0.722145 | −0.361072 | − | 0.932538i | \(-0.617589\pi\) | ||||
−0.361072 | + | 0.932538i | \(0.617589\pi\) | |||||||
\(858\) | 49.8563 | 1.70207 | ||||||||
\(859\) | 39.8728 | 1.36044 | 0.680220 | − | 0.733008i | \(-0.261884\pi\) | ||||
0.680220 | + | 0.733008i | \(0.261884\pi\) | |||||||
\(860\) | −177.796 | −6.06280 | ||||||||
\(861\) | 0.277566 | 0.00945941 | ||||||||
\(862\) | −11.9462 | −0.406890 | ||||||||
\(863\) | −27.4924 | −0.935851 | −0.467926 | − | 0.883768i | \(-0.654999\pi\) | ||||
−0.467926 | + | 0.883768i | \(0.654999\pi\) | |||||||
\(864\) | 32.2230 | 1.09625 | ||||||||
\(865\) | 52.0896 | 1.77110 | ||||||||
\(866\) | 20.6684 | 0.702341 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 1.61023 | 0.0546546 | ||||||||
\(869\) | 60.1245 | 2.03958 | ||||||||
\(870\) | −81.4369 | −2.76097 | ||||||||
\(871\) | 30.0618 | 1.01860 | ||||||||
\(872\) | 136.473 | 4.62157 | ||||||||
\(873\) | 8.30804 | 0.281185 | ||||||||
\(874\) | 100.072 | 3.38497 | ||||||||
\(875\) | −1.76066 | −0.0595212 | ||||||||
\(876\) | −12.0743 | −0.407954 | ||||||||
\(877\) | −57.4522 | −1.94002 | −0.970012 | − | 0.243058i | \(-0.921849\pi\) | ||||
−0.970012 | + | 0.243058i | \(0.921849\pi\) | |||||||
\(878\) | 27.1621 | 0.916675 | ||||||||
\(879\) | −22.2072 | −0.749031 | ||||||||
\(880\) | 332.820 | 11.2193 | ||||||||
\(881\) | −3.37088 | −0.113568 | −0.0567839 | − | 0.998386i | \(-0.518085\pi\) | ||||
−0.0567839 | + | 0.998386i | \(0.518085\pi\) | |||||||
\(882\) | 19.7044 | 0.663480 | ||||||||
\(883\) | 13.7375 | 0.462304 | 0.231152 | − | 0.972918i | \(-0.425751\pi\) | ||||
0.231152 | + | 0.972918i | \(0.425751\pi\) | |||||||
\(884\) | −25.8528 | −0.869524 | ||||||||
\(885\) | −20.0152 | −0.672802 | ||||||||
\(886\) | −34.2288 | −1.14994 | ||||||||
\(887\) | 43.4992 | 1.46056 | 0.730280 | − | 0.683148i | \(-0.239390\pi\) | ||||
0.730280 | + | 0.683148i | \(0.239390\pi\) | |||||||
\(888\) | 118.665 | 3.98214 | ||||||||
\(889\) | 0.172895 | 0.00579872 | ||||||||
\(890\) | 33.3515 | 1.11795 | ||||||||
\(891\) | −4.06087 | −0.136044 | ||||||||
\(892\) | 69.6915 | 2.33344 | ||||||||
\(893\) | 35.5126 | 1.18838 | ||||||||
\(894\) | 36.1421 | 1.20877 | ||||||||
\(895\) | 49.1093 | 1.64154 | ||||||||
\(896\) | −4.25409 | −0.142119 | ||||||||
\(897\) | 29.3434 | 0.979747 | ||||||||
\(898\) | −71.5864 | −2.38887 | ||||||||
\(899\) | 35.8092 | 1.19431 | ||||||||
\(900\) | 77.2550 | 2.57517 | ||||||||
\(901\) | 6.76745 | 0.225456 | ||||||||
\(902\) | −61.4534 | −2.04617 | ||||||||
\(903\) | −0.364734 | −0.0121376 | ||||||||
\(904\) | 16.5627 | 0.550868 | ||||||||
\(905\) | −17.0258 | −0.565957 | ||||||||
\(906\) | −5.82964 | −0.193677 | ||||||||
\(907\) | 22.3081 | 0.740729 | 0.370365 | − | 0.928886i | \(-0.379233\pi\) | ||||
0.370365 | + | 0.928886i | \(0.379233\pi\) | |||||||
\(908\) | −118.071 | −3.91831 | ||||||||
\(909\) | −12.2751 | −0.407138 | ||||||||
\(910\) | −2.69245 | −0.0892540 | ||||||||
\(911\) | 42.5098 | 1.40841 | 0.704206 | − | 0.709996i | \(-0.251303\pi\) | ||||
0.704206 | + | 0.709996i | \(0.251303\pi\) | |||||||
\(912\) | 101.919 | 3.37486 | ||||||||
\(913\) | 29.0082 | 0.960033 | ||||||||
\(914\) | −51.2490 | −1.69517 | ||||||||
\(915\) | −52.0604 | −1.72106 | ||||||||
\(916\) | −32.2230 | −1.06468 | ||||||||
\(917\) | −0.618419 | −0.0204220 | ||||||||
\(918\) | 2.81598 | 0.0929412 | ||||||||
\(919\) | 37.9202 | 1.25087 | 0.625436 | − | 0.780275i | \(-0.284921\pi\) | ||||
0.625436 | + | 0.780275i | \(0.284921\pi\) | |||||||
\(920\) | 316.236 | 10.4260 | ||||||||
\(921\) | −11.4221 | −0.376371 | ||||||||
\(922\) | 1.65967 | 0.0546582 | ||||||||
\(923\) | 15.2609 | 0.502317 | ||||||||
\(924\) | 1.24372 | 0.0409155 | ||||||||
\(925\) | 139.707 | 4.59355 | ||||||||
\(926\) | 93.4165 | 3.06986 | ||||||||
\(927\) | −14.2913 | −0.469386 | ||||||||
\(928\) | −219.472 | −7.20453 | ||||||||
\(929\) | −14.5891 | −0.478654 | −0.239327 | − | 0.970939i | \(-0.576927\pi\) | ||||
−0.239327 | + | 0.970939i | \(0.576927\pi\) | |||||||
\(930\) | −62.8622 | −2.06133 | ||||||||
\(931\) | 36.9466 | 1.21088 | ||||||||
\(932\) | −161.345 | −5.28502 | ||||||||
\(933\) | 11.0051 | 0.360290 | ||||||||
\(934\) | 62.3600 | 2.04048 | ||||||||
\(935\) | 17.2424 | 0.563886 | ||||||||
\(936\) | 48.2465 | 1.57699 | ||||||||
\(937\) | 8.61972 | 0.281594 | 0.140797 | − | 0.990038i | \(-0.455034\pi\) | ||||
0.140797 | + | 0.990038i | \(0.455034\pi\) | |||||||
\(938\) | 1.00286 | 0.0327446 | ||||||||
\(939\) | −4.22402 | −0.137846 | ||||||||
\(940\) | 169.338 | 5.52320 | ||||||||
\(941\) | −4.65283 | −0.151678 | −0.0758390 | − | 0.997120i | \(-0.524163\pi\) | ||||
−0.0758390 | + | 0.997120i | \(0.524163\pi\) | |||||||
\(942\) | −2.81598 | −0.0917496 | ||||||||
\(943\) | −36.1689 | −1.17782 | ||||||||
\(944\) | −90.9897 | −2.96146 | ||||||||
\(945\) | 0.219304 | 0.00713397 | ||||||||
\(946\) | 80.7526 | 2.62549 | ||||||||
\(947\) | −41.2712 | −1.34113 | −0.670567 | − | 0.741849i | \(-0.733949\pi\) | ||||
−0.670567 | + | 0.741849i | \(0.733949\pi\) | |||||||
\(948\) | 87.7948 | 2.85144 | ||||||||
\(949\) | −8.87767 | −0.288181 | ||||||||
\(950\) | 193.715 | 6.28493 | ||||||||
\(951\) | −20.5233 | −0.665513 | ||||||||
\(952\) | −0.571562 | −0.0185244 | ||||||||
\(953\) | 28.4766 | 0.922447 | 0.461224 | − | 0.887284i | \(-0.347411\pi\) | ||||
0.461224 | + | 0.887284i | \(0.347411\pi\) | |||||||
\(954\) | −19.0570 | −0.616993 | ||||||||
\(955\) | −19.1612 | −0.620043 | ||||||||
\(956\) | −1.02703 | −0.0332164 | ||||||||
\(957\) | 27.6587 | 0.894080 | ||||||||
\(958\) | 1.32836 | 0.0429173 | ||||||||
\(959\) | 0.318040 | 0.0102700 | ||||||||
\(960\) | 221.363 | 7.14445 | ||||||||
\(961\) | −3.35838 | −0.108335 | ||||||||
\(962\) | 131.653 | 4.24466 | ||||||||
\(963\) | −3.76324 | −0.121269 | ||||||||
\(964\) | 103.428 | 3.33118 | ||||||||
\(965\) | −35.1505 | −1.13153 | ||||||||
\(966\) | 0.978897 | 0.0314955 | ||||||||
\(967\) | −31.3993 | −1.00973 | −0.504867 | − | 0.863197i | \(-0.668459\pi\) | ||||
−0.504867 | + | 0.863197i | \(0.668459\pi\) | |||||||
\(968\) | −60.7601 | −1.95290 | ||||||||
\(969\) | 5.28010 | 0.169621 | ||||||||
\(970\) | 99.3360 | 3.18949 | ||||||||
\(971\) | −19.6048 | −0.629149 | −0.314574 | − | 0.949233i | \(-0.601862\pi\) | ||||
−0.314574 | + | 0.949233i | \(0.601862\pi\) | |||||||
\(972\) | −5.92975 | −0.190197 | ||||||||
\(973\) | −0.565501 | −0.0181291 | ||||||||
\(974\) | 35.3176 | 1.13165 | ||||||||
\(975\) | 56.8018 | 1.81911 | ||||||||
\(976\) | −236.669 | −7.57558 | ||||||||
\(977\) | −26.1525 | −0.836693 | −0.418347 | − | 0.908287i | \(-0.637390\pi\) | ||||
−0.418347 | + | 0.908287i | \(0.637390\pi\) | |||||||
\(978\) | −35.7751 | −1.14396 | ||||||||
\(979\) | −11.3273 | −0.362022 | ||||||||
\(980\) | 176.176 | 5.62774 | ||||||||
\(981\) | −12.3326 | −0.393749 | ||||||||
\(982\) | −97.7593 | −3.11962 | ||||||||
\(983\) | 32.2084 | 1.02729 | 0.513645 | − | 0.858003i | \(-0.328295\pi\) | ||||
0.513645 | + | 0.858003i | \(0.328295\pi\) | |||||||
\(984\) | −59.4691 | −1.89581 | ||||||||
\(985\) | 35.5197 | 1.13175 | ||||||||
\(986\) | −19.1798 | −0.610808 | ||||||||
\(987\) | 0.347383 | 0.0110573 | ||||||||
\(988\) | 136.505 | 4.34281 | ||||||||
\(989\) | 47.5277 | 1.51129 | ||||||||
\(990\) | −48.5542 | −1.54315 | ||||||||
\(991\) | 50.1843 | 1.59416 | 0.797079 | − | 0.603876i | \(-0.206378\pi\) | ||||
0.797079 | + | 0.603876i | \(0.206378\pi\) | |||||||
\(992\) | −169.414 | −5.37889 | ||||||||
\(993\) | 7.92050 | 0.251349 | ||||||||
\(994\) | 0.509103 | 0.0161478 | ||||||||
\(995\) | −49.5614 | −1.57120 | ||||||||
\(996\) | 42.3583 | 1.34217 | ||||||||
\(997\) | −17.9517 | −0.568537 | −0.284268 | − | 0.958745i | \(-0.591751\pi\) | ||||
−0.284268 | + | 0.958745i | \(0.591751\pi\) | |||||||
\(998\) | −8.97782 | −0.284188 | ||||||||
\(999\) | −10.7233 | −0.339271 |
(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 | 8007.2.a.j.1.1 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.1 | ✓ | 64 | 1.1 | even | 1 | trivial |