Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, 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("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258847 | 0.183032 | 0.0915161 | − | 0.995804i | \(-0.470829\pi\) | ||||
0.0915161 | + | 0.995804i | \(0.470829\pi\) | |||||||
\(3\) | 2.67579 | 1.54487 | 0.772434 | − | 0.635095i | \(-0.219039\pi\) | ||||
0.772434 | + | 0.635095i | \(0.219039\pi\) | |||||||
\(4\) | −1.93300 | −0.966499 | ||||||||
\(5\) | −2.46163 | −1.10088 | −0.550438 | − | 0.834876i | \(-0.685539\pi\) | ||||
−0.550438 | + | 0.834876i | \(0.685539\pi\) | |||||||
\(6\) | 0.692619 | 0.282761 | ||||||||
\(7\) | 1.88069 | 0.710834 | 0.355417 | − | 0.934708i | \(-0.384339\pi\) | ||||
0.355417 | + | 0.934708i | \(0.384339\pi\) | |||||||
\(8\) | −1.01804 | −0.359933 | ||||||||
\(9\) | 4.15985 | 1.38662 | ||||||||
\(10\) | −0.637185 | −0.201496 | ||||||||
\(11\) | 2.17477 | 0.655718 | 0.327859 | − | 0.944727i | \(-0.393673\pi\) | ||||
0.327859 | + | 0.944727i | \(0.393673\pi\) | |||||||
\(12\) | −5.17230 | −1.49311 | ||||||||
\(13\) | 5.79098 | 1.60613 | 0.803064 | − | 0.595893i | \(-0.203202\pi\) | ||||
0.803064 | + | 0.595893i | \(0.203202\pi\) | |||||||
\(14\) | 0.486810 | 0.130105 | ||||||||
\(15\) | −6.58682 | −1.70071 | ||||||||
\(16\) | 3.60248 | 0.900620 | ||||||||
\(17\) | 5.77460 | 1.40055 | 0.700273 | − | 0.713875i | \(-0.253061\pi\) | ||||
0.700273 | + | 0.713875i | \(0.253061\pi\) | |||||||
\(18\) | 1.07676 | 0.253796 | ||||||||
\(19\) | −2.25742 | −0.517887 | −0.258944 | − | 0.965892i | \(-0.583374\pi\) | ||||
−0.258944 | + | 0.965892i | \(0.583374\pi\) | |||||||
\(20\) | 4.75833 | 1.06400 | ||||||||
\(21\) | 5.03233 | 1.09814 | ||||||||
\(22\) | 0.562932 | 0.120017 | ||||||||
\(23\) | −2.33879 | −0.487672 | −0.243836 | − | 0.969816i | \(-0.578406\pi\) | ||||
−0.243836 | + | 0.969816i | \(0.578406\pi\) | |||||||
\(24\) | −2.72407 | −0.556048 | ||||||||
\(25\) | 1.05964 | 0.211928 | ||||||||
\(26\) | 1.49897 | 0.293973 | ||||||||
\(27\) | 3.10353 | 0.597274 | ||||||||
\(28\) | −3.63537 | −0.687020 | ||||||||
\(29\) | 10.0750 | 1.87089 | 0.935443 | − | 0.353478i | \(-0.115001\pi\) | ||||
0.935443 | + | 0.353478i | \(0.115001\pi\) | |||||||
\(30\) | −1.70497 | −0.311284 | ||||||||
\(31\) | −9.67907 | −1.73841 | −0.869207 | − | 0.494449i | \(-0.835370\pi\) | ||||
−0.869207 | + | 0.494449i | \(0.835370\pi\) | |||||||
\(32\) | 2.96858 | 0.524775 | ||||||||
\(33\) | 5.81923 | 1.01300 | ||||||||
\(34\) | 1.49474 | 0.256345 | ||||||||
\(35\) | −4.62957 | −0.782540 | ||||||||
\(36\) | −8.04099 | −1.34017 | ||||||||
\(37\) | 8.94849 | 1.47112 | 0.735561 | − | 0.677458i | \(-0.236918\pi\) | ||||
0.735561 | + | 0.677458i | \(0.236918\pi\) | |||||||
\(38\) | −0.584325 | −0.0947900 | ||||||||
\(39\) | 15.4954 | 2.48126 | ||||||||
\(40\) | 2.50605 | 0.396241 | ||||||||
\(41\) | −1.23360 | −0.192657 | −0.0963283 | − | 0.995350i | \(-0.530710\pi\) | ||||
−0.0963283 | + | 0.995350i | \(0.530710\pi\) | |||||||
\(42\) | 1.30260 | 0.200996 | ||||||||
\(43\) | −11.2529 | −1.71605 | −0.858026 | − | 0.513606i | \(-0.828309\pi\) | ||||
−0.858026 | + | 0.513606i | \(0.828309\pi\) | |||||||
\(44\) | −4.20383 | −0.633751 | ||||||||
\(45\) | −10.2400 | −1.52650 | ||||||||
\(46\) | −0.605388 | −0.0892596 | ||||||||
\(47\) | 6.19029 | 0.902946 | 0.451473 | − | 0.892285i | \(-0.350899\pi\) | ||||
0.451473 | + | 0.892285i | \(0.350899\pi\) | |||||||
\(48\) | 9.63948 | 1.39134 | ||||||||
\(49\) | −3.46301 | −0.494716 | ||||||||
\(50\) | 0.274285 | 0.0387897 | ||||||||
\(51\) | 15.4516 | 2.16366 | ||||||||
\(52\) | −11.1940 | −1.55232 | ||||||||
\(53\) | −0.0669552 | −0.00919700 | −0.00459850 | − | 0.999989i | \(-0.501464\pi\) | ||||
−0.00459850 | + | 0.999989i | \(0.501464\pi\) | |||||||
\(54\) | 0.803338 | 0.109320 | ||||||||
\(55\) | −5.35349 | −0.721864 | ||||||||
\(56\) | −1.91462 | −0.255852 | ||||||||
\(57\) | −6.04038 | −0.800068 | ||||||||
\(58\) | 2.60789 | 0.342432 | ||||||||
\(59\) | −8.20161 | −1.06776 | −0.533879 | − | 0.845561i | \(-0.679266\pi\) | ||||
−0.533879 | + | 0.845561i | \(0.679266\pi\) | |||||||
\(60\) | 12.7323 | 1.64373 | ||||||||
\(61\) | −10.3312 | −1.32278 | −0.661388 | − | 0.750044i | \(-0.730032\pi\) | ||||
−0.661388 | + | 0.750044i | \(0.730032\pi\) | |||||||
\(62\) | −2.50539 | −0.318185 | ||||||||
\(63\) | 7.82339 | 0.985655 | ||||||||
\(64\) | −6.43655 | −0.804569 | ||||||||
\(65\) | −14.2553 | −1.76815 | ||||||||
\(66\) | 1.50629 | 0.185411 | ||||||||
\(67\) | 0.238391 | 0.0291241 | 0.0145621 | − | 0.999894i | \(-0.495365\pi\) | ||||
0.0145621 | + | 0.999894i | \(0.495365\pi\) | |||||||
\(68\) | −11.1623 | −1.35363 | ||||||||
\(69\) | −6.25812 | −0.753389 | ||||||||
\(70\) | −1.19835 | −0.143230 | ||||||||
\(71\) | 2.25584 | 0.267718 | 0.133859 | − | 0.991000i | \(-0.457263\pi\) | ||||
0.133859 | + | 0.991000i | \(0.457263\pi\) | |||||||
\(72\) | −4.23491 | −0.499089 | ||||||||
\(73\) | −9.40009 | −1.10020 | −0.550099 | − | 0.835100i | \(-0.685410\pi\) | ||||
−0.550099 | + | 0.835100i | \(0.685410\pi\) | |||||||
\(74\) | 2.31629 | 0.269263 | ||||||||
\(75\) | 2.83538 | 0.327402 | ||||||||
\(76\) | 4.36359 | 0.500538 | ||||||||
\(77\) | 4.09007 | 0.466106 | ||||||||
\(78\) | 4.01094 | 0.454150 | ||||||||
\(79\) | 1.71495 | 0.192947 | 0.0964733 | − | 0.995336i | \(-0.469244\pi\) | ||||
0.0964733 | + | 0.995336i | \(0.469244\pi\) | |||||||
\(80\) | −8.86799 | −0.991471 | ||||||||
\(81\) | −4.17517 | −0.463908 | ||||||||
\(82\) | −0.319314 | −0.0352623 | ||||||||
\(83\) | −1.43433 | −0.157438 | −0.0787192 | − | 0.996897i | \(-0.525083\pi\) | ||||
−0.0787192 | + | 0.996897i | \(0.525083\pi\) | |||||||
\(84\) | −9.72748 | −1.06136 | ||||||||
\(85\) | −14.2150 | −1.54183 | ||||||||
\(86\) | −2.91278 | −0.314093 | ||||||||
\(87\) | 26.9587 | 2.89027 | ||||||||
\(88\) | −2.21401 | −0.236014 | ||||||||
\(89\) | 15.0519 | 1.59550 | 0.797749 | − | 0.602989i | \(-0.206024\pi\) | ||||
0.797749 | + | 0.602989i | \(0.206024\pi\) | |||||||
\(90\) | −2.65060 | −0.279398 | ||||||||
\(91\) | 10.8910 | 1.14169 | ||||||||
\(92\) | 4.52088 | 0.471335 | ||||||||
\(93\) | −25.8992 | −2.68562 | ||||||||
\(94\) | 1.60233 | 0.165268 | ||||||||
\(95\) | 5.55694 | 0.570130 | ||||||||
\(96\) | 7.94329 | 0.810708 | ||||||||
\(97\) | 9.35744 | 0.950104 | 0.475052 | − | 0.879958i | \(-0.342429\pi\) | ||||
0.475052 | + | 0.879958i | \(0.342429\pi\) | |||||||
\(98\) | −0.896388 | −0.0905489 | ||||||||
\(99\) | 9.04673 | 0.909231 | ||||||||
\(100\) | −2.04829 | −0.204829 | ||||||||
\(101\) | −0.733101 | −0.0729463 | −0.0364731 | − | 0.999335i | \(-0.511612\pi\) | ||||
−0.0364731 | + | 0.999335i | \(0.511612\pi\) | |||||||
\(102\) | 3.99960 | 0.396019 | ||||||||
\(103\) | −4.03656 | −0.397734 | −0.198867 | − | 0.980026i | \(-0.563726\pi\) | ||||
−0.198867 | + | 0.980026i | \(0.563726\pi\) | |||||||
\(104\) | −5.89546 | −0.578098 | ||||||||
\(105\) | −12.3878 | −1.20892 | ||||||||
\(106\) | −0.0173311 | −0.00168335 | ||||||||
\(107\) | −13.2306 | −1.27905 | −0.639527 | − | 0.768768i | \(-0.720870\pi\) | ||||
−0.639527 | + | 0.768768i | \(0.720870\pi\) | |||||||
\(108\) | −5.99912 | −0.577265 | ||||||||
\(109\) | 5.99549 | 0.574264 | 0.287132 | − | 0.957891i | \(-0.407298\pi\) | ||||
0.287132 | + | 0.957891i | \(0.407298\pi\) | |||||||
\(110\) | −1.38573 | −0.132124 | ||||||||
\(111\) | 23.9443 | 2.27269 | ||||||||
\(112\) | 6.77514 | 0.640191 | ||||||||
\(113\) | 9.71932 | 0.914317 | 0.457158 | − | 0.889385i | \(-0.348867\pi\) | ||||
0.457158 | + | 0.889385i | \(0.348867\pi\) | |||||||
\(114\) | −1.56353 | −0.146438 | ||||||||
\(115\) | 5.75725 | 0.536866 | ||||||||
\(116\) | −19.4750 | −1.80821 | ||||||||
\(117\) | 24.0896 | 2.22709 | ||||||||
\(118\) | −2.12296 | −0.195434 | ||||||||
\(119\) | 10.8602 | 0.995556 | ||||||||
\(120\) | 6.70566 | 0.612140 | ||||||||
\(121\) | −6.27037 | −0.570034 | ||||||||
\(122\) | −2.67420 | −0.242110 | ||||||||
\(123\) | −3.30087 | −0.297629 | ||||||||
\(124\) | 18.7096 | 1.68018 | ||||||||
\(125\) | 9.69972 | 0.867569 | ||||||||
\(126\) | 2.02506 | 0.180406 | ||||||||
\(127\) | 12.9505 | 1.14917 | 0.574585 | − | 0.818445i | \(-0.305163\pi\) | ||||
0.574585 | + | 0.818445i | \(0.305163\pi\) | |||||||
\(128\) | −7.60323 | −0.672037 | ||||||||
\(129\) | −30.1104 | −2.65108 | ||||||||
\(130\) | −3.68993 | −0.323628 | ||||||||
\(131\) | −21.0455 | −1.83875 | −0.919376 | − | 0.393380i | \(-0.871306\pi\) | ||||
−0.919376 | + | 0.393380i | \(0.871306\pi\) | |||||||
\(132\) | −11.2486 | −0.979062 | ||||||||
\(133\) | −4.24550 | −0.368132 | ||||||||
\(134\) | 0.0617067 | 0.00533065 | ||||||||
\(135\) | −7.63975 | −0.657525 | ||||||||
\(136\) | −5.87879 | −0.504102 | ||||||||
\(137\) | 17.4982 | 1.49497 | 0.747485 | − | 0.664279i | \(-0.231261\pi\) | ||||
0.747485 | + | 0.664279i | \(0.231261\pi\) | |||||||
\(138\) | −1.61989 | −0.137894 | ||||||||
\(139\) | 5.41721 | 0.459482 | 0.229741 | − | 0.973252i | \(-0.426212\pi\) | ||||
0.229741 | + | 0.973252i | \(0.426212\pi\) | |||||||
\(140\) | 8.94895 | 0.756324 | ||||||||
\(141\) | 16.5639 | 1.39493 | ||||||||
\(142\) | 0.583915 | 0.0490011 | ||||||||
\(143\) | 12.5940 | 1.05317 | ||||||||
\(144\) | 14.9858 | 1.24882 | ||||||||
\(145\) | −24.8010 | −2.05961 | ||||||||
\(146\) | −2.43318 | −0.201372 | ||||||||
\(147\) | −9.26629 | −0.764271 | ||||||||
\(148\) | −17.2974 | −1.42184 | ||||||||
\(149\) | −20.6900 | −1.69499 | −0.847495 | − | 0.530804i | \(-0.821890\pi\) | ||||
−0.847495 | + | 0.530804i | \(0.821890\pi\) | |||||||
\(150\) | 0.733928 | 0.0599250 | ||||||||
\(151\) | −8.11163 | −0.660115 | −0.330057 | − | 0.943961i | \(-0.607068\pi\) | ||||
−0.330057 | + | 0.943961i | \(0.607068\pi\) | |||||||
\(152\) | 2.29815 | 0.186405 | ||||||||
\(153\) | 24.0215 | 1.94202 | ||||||||
\(154\) | 1.05870 | 0.0853124 | ||||||||
\(155\) | 23.8263 | 1.91378 | ||||||||
\(156\) | −29.9527 | −2.39813 | ||||||||
\(157\) | −0.536449 | −0.0428133 | −0.0214067 | − | 0.999771i | \(-0.506814\pi\) | ||||
−0.0214067 | + | 0.999771i | \(0.506814\pi\) | |||||||
\(158\) | 0.443908 | 0.0353154 | ||||||||
\(159\) | −0.179158 | −0.0142082 | ||||||||
\(160\) | −7.30755 | −0.577712 | ||||||||
\(161\) | −4.39854 | −0.346654 | ||||||||
\(162\) | −1.08073 | −0.0849101 | ||||||||
\(163\) | 7.37372 | 0.577554 | 0.288777 | − | 0.957396i | \(-0.406751\pi\) | ||||
0.288777 | + | 0.957396i | \(0.406751\pi\) | |||||||
\(164\) | 2.38455 | 0.186202 | ||||||||
\(165\) | −14.3248 | −1.11519 | ||||||||
\(166\) | −0.371272 | −0.0288163 | ||||||||
\(167\) | −4.57561 | −0.354071 | −0.177036 | − | 0.984204i | \(-0.556651\pi\) | ||||
−0.177036 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(168\) | −5.12313 | −0.395258 | ||||||||
\(169\) | 20.5354 | 1.57965 | ||||||||
\(170\) | −3.67949 | −0.282204 | ||||||||
\(171\) | −9.39053 | −0.718112 | ||||||||
\(172\) | 21.7519 | 1.65856 | ||||||||
\(173\) | 10.2956 | 0.782759 | 0.391379 | − | 0.920229i | \(-0.371998\pi\) | ||||
0.391379 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(174\) | 6.97816 | 0.529013 | ||||||||
\(175\) | 1.99286 | 0.150646 | ||||||||
\(176\) | 7.83457 | 0.590553 | ||||||||
\(177\) | −21.9458 | −1.64955 | ||||||||
\(178\) | 3.89613 | 0.292028 | ||||||||
\(179\) | −12.4323 | −0.929233 | −0.464616 | − | 0.885512i | \(-0.653808\pi\) | ||||
−0.464616 | + | 0.885512i | \(0.653808\pi\) | |||||||
\(180\) | 19.7940 | 1.47536 | ||||||||
\(181\) | −4.14942 | −0.308424 | −0.154212 | − | 0.988038i | \(-0.549284\pi\) | ||||
−0.154212 | + | 0.988038i | \(0.549284\pi\) | |||||||
\(182\) | 2.81910 | 0.208966 | ||||||||
\(183\) | −27.6442 | −2.04351 | ||||||||
\(184\) | 2.38099 | 0.175529 | ||||||||
\(185\) | −22.0279 | −1.61952 | ||||||||
\(186\) | −6.70391 | −0.491555 | ||||||||
\(187\) | 12.5584 | 0.918364 | ||||||||
\(188\) | −11.9658 | −0.872697 | ||||||||
\(189\) | 5.83677 | 0.424563 | ||||||||
\(190\) | 1.43839 | 0.104352 | ||||||||
\(191\) | −4.07924 | −0.295163 | −0.147582 | − | 0.989050i | \(-0.547149\pi\) | ||||
−0.147582 | + | 0.989050i | \(0.547149\pi\) | |||||||
\(192\) | −17.2229 | −1.24295 | ||||||||
\(193\) | −26.6618 | −1.91916 | −0.959581 | − | 0.281433i | \(-0.909190\pi\) | ||||
−0.959581 | + | 0.281433i | \(0.909190\pi\) | |||||||
\(194\) | 2.42214 | 0.173900 | ||||||||
\(195\) | −38.1441 | −2.73156 | ||||||||
\(196\) | 6.69399 | 0.478142 | ||||||||
\(197\) | 1.35535 | 0.0965644 | 0.0482822 | − | 0.998834i | \(-0.484625\pi\) | ||||
0.0482822 | + | 0.998834i | \(0.484625\pi\) | |||||||
\(198\) | 2.34171 | 0.166418 | ||||||||
\(199\) | −15.3182 | −1.08588 | −0.542940 | − | 0.839771i | \(-0.682689\pi\) | ||||
−0.542940 | + | 0.839771i | \(0.682689\pi\) | |||||||
\(200\) | −1.07876 | −0.0762799 | ||||||||
\(201\) | 0.637885 | 0.0449929 | ||||||||
\(202\) | −0.189761 | −0.0133515 | ||||||||
\(203\) | 18.9480 | 1.32989 | ||||||||
\(204\) | −29.8680 | −2.09118 | ||||||||
\(205\) | 3.03668 | 0.212091 | ||||||||
\(206\) | −1.04485 | −0.0727981 | ||||||||
\(207\) | −9.72904 | −0.676215 | ||||||||
\(208\) | 20.8619 | 1.44651 | ||||||||
\(209\) | −4.90937 | −0.339588 | ||||||||
\(210\) | −3.20653 | −0.221271 | ||||||||
\(211\) | −16.1659 | −1.11291 | −0.556453 | − | 0.830879i | \(-0.687838\pi\) | ||||
−0.556453 | + | 0.830879i | \(0.687838\pi\) | |||||||
\(212\) | 0.129424 | 0.00888890 | ||||||||
\(213\) | 6.03614 | 0.413590 | ||||||||
\(214\) | −3.42471 | −0.234108 | ||||||||
\(215\) | 27.7005 | 1.88916 | ||||||||
\(216\) | −3.15953 | −0.214978 | ||||||||
\(217\) | −18.2033 | −1.23572 | ||||||||
\(218\) | 1.55191 | 0.105109 | ||||||||
\(219\) | −25.1527 | −1.69966 | ||||||||
\(220\) | 10.3483 | 0.697681 | ||||||||
\(221\) | 33.4406 | 2.24946 | ||||||||
\(222\) | 6.19789 | 0.415975 | ||||||||
\(223\) | 20.8221 | 1.39435 | 0.697177 | − | 0.716899i | \(-0.254439\pi\) | ||||
0.697177 | + | 0.716899i | \(0.254439\pi\) | |||||||
\(224\) | 5.58297 | 0.373028 | ||||||||
\(225\) | 4.40796 | 0.293864 | ||||||||
\(226\) | 2.51581 | 0.167349 | ||||||||
\(227\) | 6.06934 | 0.402836 | 0.201418 | − | 0.979505i | \(-0.435445\pi\) | ||||
0.201418 | + | 0.979505i | \(0.435445\pi\) | |||||||
\(228\) | 11.6760 | 0.773265 | ||||||||
\(229\) | −10.2583 | −0.677886 | −0.338943 | − | 0.940807i | \(-0.610069\pi\) | ||||
−0.338943 | + | 0.940807i | \(0.610069\pi\) | |||||||
\(230\) | 1.49024 | 0.0982638 | ||||||||
\(231\) | 10.9442 | 0.720073 | ||||||||
\(232\) | −10.2568 | −0.673393 | ||||||||
\(233\) | 19.2229 | 1.25933 | 0.629666 | − | 0.776866i | \(-0.283192\pi\) | ||||
0.629666 | + | 0.776866i | \(0.283192\pi\) | |||||||
\(234\) | 6.23552 | 0.407628 | ||||||||
\(235\) | −15.2382 | −0.994032 | ||||||||
\(236\) | 15.8537 | 1.03199 | ||||||||
\(237\) | 4.58884 | 0.298077 | ||||||||
\(238\) | 2.81113 | 0.182219 | ||||||||
\(239\) | 10.2594 | 0.663625 | 0.331812 | − | 0.943345i | \(-0.392340\pi\) | ||||
0.331812 | + | 0.943345i | \(0.392340\pi\) | |||||||
\(240\) | −23.7289 | −1.53169 | ||||||||
\(241\) | −26.1029 | −1.68143 | −0.840717 | − | 0.541475i | \(-0.817866\pi\) | ||||
−0.840717 | + | 0.541475i | \(0.817866\pi\) | |||||||
\(242\) | −1.62306 | −0.104335 | ||||||||
\(243\) | −20.4825 | −1.31395 | ||||||||
\(244\) | 19.9702 | 1.27846 | ||||||||
\(245\) | 8.52466 | 0.544621 | ||||||||
\(246\) | −0.854417 | −0.0544757 | ||||||||
\(247\) | −13.0727 | −0.831793 | ||||||||
\(248\) | 9.85371 | 0.625711 | ||||||||
\(249\) | −3.83797 | −0.243222 | ||||||||
\(250\) | 2.51074 | 0.158793 | ||||||||
\(251\) | −23.2207 | −1.46568 | −0.732838 | − | 0.680403i | \(-0.761805\pi\) | ||||
−0.732838 | + | 0.680403i | \(0.761805\pi\) | |||||||
\(252\) | −15.1226 | −0.952635 | ||||||||
\(253\) | −5.08634 | −0.319775 | ||||||||
\(254\) | 3.35219 | 0.210335 | ||||||||
\(255\) | −38.0363 | −2.38192 | ||||||||
\(256\) | 10.9050 | 0.681565 | ||||||||
\(257\) | −25.0242 | −1.56097 | −0.780483 | − | 0.625178i | \(-0.785027\pi\) | ||||
−0.780483 | + | 0.625178i | \(0.785027\pi\) | |||||||
\(258\) | −7.79398 | −0.485232 | ||||||||
\(259\) | 16.8293 | 1.04572 | ||||||||
\(260\) | 27.5554 | 1.70891 | ||||||||
\(261\) | 41.9107 | 2.59420 | ||||||||
\(262\) | −5.44755 | −0.336551 | ||||||||
\(263\) | 6.34438 | 0.391211 | 0.195606 | − | 0.980683i | \(-0.437333\pi\) | ||||
0.195606 | + | 0.980683i | \(0.437333\pi\) | |||||||
\(264\) | −5.92423 | −0.364611 | ||||||||
\(265\) | 0.164819 | 0.0101248 | ||||||||
\(266\) | −1.09893 | −0.0673799 | ||||||||
\(267\) | 40.2757 | 2.46484 | ||||||||
\(268\) | −0.460810 | −0.0281484 | ||||||||
\(269\) | −12.3186 | −0.751075 | −0.375538 | − | 0.926807i | \(-0.622542\pi\) | ||||
−0.375538 | + | 0.926807i | \(0.622542\pi\) | |||||||
\(270\) | −1.97752 | −0.120348 | ||||||||
\(271\) | 16.4188 | 0.997371 | 0.498685 | − | 0.866783i | \(-0.333816\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333816\pi\) | |||||||
\(272\) | 20.8029 | 1.26136 | ||||||||
\(273\) | 29.1421 | 1.76376 | ||||||||
\(274\) | 4.52934 | 0.273627 | ||||||||
\(275\) | 2.30448 | 0.138965 | ||||||||
\(276\) | 12.0969 | 0.728150 | ||||||||
\(277\) | 2.50362 | 0.150428 | 0.0752141 | − | 0.997167i | \(-0.476036\pi\) | ||||
0.0752141 | + | 0.997167i | \(0.476036\pi\) | |||||||
\(278\) | 1.40223 | 0.0841000 | ||||||||
\(279\) | −40.2635 | −2.41052 | ||||||||
\(280\) | 4.71310 | 0.281661 | ||||||||
\(281\) | −5.07121 | −0.302523 | −0.151262 | − | 0.988494i | \(-0.548334\pi\) | ||||
−0.151262 | + | 0.988494i | \(0.548334\pi\) | |||||||
\(282\) | 4.28751 | 0.255317 | ||||||||
\(283\) | −1.32526 | −0.0787788 | −0.0393894 | − | 0.999224i | \(-0.512541\pi\) | ||||
−0.0393894 | + | 0.999224i | \(0.512541\pi\) | |||||||
\(284\) | −4.36053 | −0.258750 | ||||||||
\(285\) | 14.8692 | 0.880776 | ||||||||
\(286\) | 3.25993 | 0.192763 | ||||||||
\(287\) | −2.32002 | −0.136947 | ||||||||
\(288\) | 12.3488 | 0.727663 | ||||||||
\(289\) | 16.3460 | 0.961532 | ||||||||
\(290\) | −6.41966 | −0.376975 | ||||||||
\(291\) | 25.0386 | 1.46779 | ||||||||
\(292\) | 18.1704 | 1.06334 | ||||||||
\(293\) | 25.1442 | 1.46894 | 0.734469 | − | 0.678642i | \(-0.237431\pi\) | ||||
0.734469 | + | 0.678642i | \(0.237431\pi\) | |||||||
\(294\) | −2.39855 | −0.139886 | ||||||||
\(295\) | 20.1894 | 1.17547 | ||||||||
\(296\) | −9.10995 | −0.529505 | ||||||||
\(297\) | 6.74946 | 0.391644 | ||||||||
\(298\) | −5.35553 | −0.310237 | ||||||||
\(299\) | −13.5439 | −0.783264 | ||||||||
\(300\) | −5.48079 | −0.316433 | ||||||||
\(301\) | −21.1632 | −1.21983 | ||||||||
\(302\) | −2.09967 | −0.120822 | ||||||||
\(303\) | −1.96163 | −0.112692 | ||||||||
\(304\) | −8.13231 | −0.466420 | ||||||||
\(305\) | 25.4317 | 1.45621 | ||||||||
\(306\) | 6.21788 | 0.355453 | ||||||||
\(307\) | 18.8588 | 1.07633 | 0.538166 | − | 0.842839i | \(-0.319117\pi\) | ||||
0.538166 | + | 0.842839i | \(0.319117\pi\) | |||||||
\(308\) | −7.90609 | −0.450491 | ||||||||
\(309\) | −10.8010 | −0.614447 | ||||||||
\(310\) | 6.16736 | 0.350283 | ||||||||
\(311\) | 17.9045 | 1.01527 | 0.507636 | − | 0.861572i | \(-0.330519\pi\) | ||||
0.507636 | + | 0.861572i | \(0.330519\pi\) | |||||||
\(312\) | −15.7750 | −0.893085 | ||||||||
\(313\) | 5.73725 | 0.324288 | 0.162144 | − | 0.986767i | \(-0.448159\pi\) | ||||
0.162144 | + | 0.986767i | \(0.448159\pi\) | |||||||
\(314\) | −0.138858 | −0.00783621 | ||||||||
\(315\) | −19.2583 | −1.08508 | ||||||||
\(316\) | −3.31499 | −0.186483 | ||||||||
\(317\) | 13.5902 | 0.763300 | 0.381650 | − | 0.924307i | \(-0.375356\pi\) | ||||
0.381650 | + | 0.924307i | \(0.375356\pi\) | |||||||
\(318\) | −0.0463744 | −0.00260055 | ||||||||
\(319\) | 21.9109 | 1.22677 | ||||||||
\(320\) | 15.8444 | 0.885731 | ||||||||
\(321\) | −35.4024 | −1.97597 | ||||||||
\(322\) | −1.13855 | −0.0634487 | ||||||||
\(323\) | −13.0357 | −0.725326 | ||||||||
\(324\) | 8.07060 | 0.448367 | ||||||||
\(325\) | 6.13636 | 0.340384 | ||||||||
\(326\) | 1.90866 | 0.105711 | ||||||||
\(327\) | 16.0427 | 0.887162 | ||||||||
\(328\) | 1.25586 | 0.0693434 | ||||||||
\(329\) | 11.6420 | 0.641844 | ||||||||
\(330\) | −3.70793 | −0.204115 | ||||||||
\(331\) | −1.90596 | −0.104761 | −0.0523805 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523805 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(332\) | 2.77256 | 0.152164 | ||||||||
\(333\) | 37.2244 | 2.03989 | ||||||||
\(334\) | −1.18438 | −0.0648064 | ||||||||
\(335\) | −0.586832 | −0.0320620 | ||||||||
\(336\) | 18.1289 | 0.989011 | ||||||||
\(337\) | −0.393425 | −0.0214312 | −0.0107156 | − | 0.999943i | \(-0.503411\pi\) | ||||
−0.0107156 | + | 0.999943i | \(0.503411\pi\) | |||||||
\(338\) | 5.31552 | 0.289126 | ||||||||
\(339\) | 26.0069 | 1.41250 | ||||||||
\(340\) | 27.4775 | 1.49018 | ||||||||
\(341\) | −21.0498 | −1.13991 | ||||||||
\(342\) | −2.43071 | −0.131438 | ||||||||
\(343\) | −19.6777 | −1.06249 | ||||||||
\(344\) | 11.4559 | 0.617663 | ||||||||
\(345\) | 15.4052 | 0.829388 | ||||||||
\(346\) | 2.66498 | 0.143270 | ||||||||
\(347\) | 23.1336 | 1.24187 | 0.620937 | − | 0.783860i | \(-0.286752\pi\) | ||||
0.620937 | + | 0.783860i | \(0.286752\pi\) | |||||||
\(348\) | −52.1111 | −2.79345 | ||||||||
\(349\) | 11.9490 | 0.639613 | 0.319806 | − | 0.947483i | \(-0.396382\pi\) | ||||
0.319806 | + | 0.947483i | \(0.396382\pi\) | |||||||
\(350\) | 0.515844 | 0.0275730 | ||||||||
\(351\) | 17.9725 | 0.959299 | ||||||||
\(352\) | 6.45597 | 0.344104 | ||||||||
\(353\) | −7.64497 | −0.406901 | −0.203450 | − | 0.979085i | \(-0.565216\pi\) | ||||
−0.203450 | + | 0.979085i | \(0.565216\pi\) | |||||||
\(354\) | −5.68059 | −0.301920 | ||||||||
\(355\) | −5.55304 | −0.294725 | ||||||||
\(356\) | −29.0953 | −1.54205 | ||||||||
\(357\) | 29.0597 | 1.53800 | ||||||||
\(358\) | −3.21805 | −0.170079 | ||||||||
\(359\) | −16.3685 | −0.863895 | −0.431948 | − | 0.901899i | \(-0.642173\pi\) | ||||
−0.431948 | + | 0.901899i | \(0.642173\pi\) | |||||||
\(360\) | 10.4248 | 0.549435 | ||||||||
\(361\) | −13.9041 | −0.731793 | ||||||||
\(362\) | −1.07406 | −0.0564515 | ||||||||
\(363\) | −16.7782 | −0.880627 | ||||||||
\(364\) | −21.0523 | −1.10344 | ||||||||
\(365\) | 23.1396 | 1.21118 | ||||||||
\(366\) | −7.15559 | −0.374029 | ||||||||
\(367\) | −17.2762 | −0.901811 | −0.450905 | − | 0.892572i | \(-0.648899\pi\) | ||||
−0.450905 | + | 0.892572i | \(0.648899\pi\) | |||||||
\(368\) | −8.42545 | −0.439207 | ||||||||
\(369\) | −5.13161 | −0.267141 | ||||||||
\(370\) | −5.70185 | −0.296425 | ||||||||
\(371\) | −0.125922 | −0.00653754 | ||||||||
\(372\) | 50.0631 | 2.59565 | ||||||||
\(373\) | 19.8177 | 1.02612 | 0.513062 | − | 0.858352i | \(-0.328511\pi\) | ||||
0.513062 | + | 0.858352i | \(0.328511\pi\) | |||||||
\(374\) | 3.25071 | 0.168090 | ||||||||
\(375\) | 25.9544 | 1.34028 | ||||||||
\(376\) | −6.30198 | −0.325000 | ||||||||
\(377\) | 58.3443 | 3.00488 | ||||||||
\(378\) | 1.51083 | 0.0777086 | ||||||||
\(379\) | −31.6560 | −1.62606 | −0.813030 | − | 0.582222i | \(-0.802184\pi\) | ||||
−0.813030 | + | 0.582222i | \(0.802184\pi\) | |||||||
\(380\) | −10.7416 | −0.551030 | ||||||||
\(381\) | 34.6528 | 1.77532 | ||||||||
\(382\) | −1.05590 | −0.0540243 | ||||||||
\(383\) | −7.55621 | −0.386104 | −0.193052 | − | 0.981188i | \(-0.561839\pi\) | ||||
−0.193052 | + | 0.981188i | \(0.561839\pi\) | |||||||
\(384\) | −20.3447 | −1.03821 | ||||||||
\(385\) | −10.0682 | −0.513125 | ||||||||
\(386\) | −6.90133 | −0.351268 | ||||||||
\(387\) | −46.8105 | −2.37951 | ||||||||
\(388\) | −18.0879 | −0.918275 | ||||||||
\(389\) | −21.8357 | −1.10711 | −0.553556 | − | 0.832812i | \(-0.686730\pi\) | ||||
−0.553556 | + | 0.832812i | \(0.686730\pi\) | |||||||
\(390\) | −9.87347 | −0.499963 | ||||||||
\(391\) | −13.5056 | −0.683007 | ||||||||
\(392\) | 3.52549 | 0.178064 | ||||||||
\(393\) | −56.3133 | −2.84063 | ||||||||
\(394\) | 0.350826 | 0.0176744 | ||||||||
\(395\) | −4.22157 | −0.212410 | ||||||||
\(396\) | −17.4873 | −0.878771 | ||||||||
\(397\) | 21.7604 | 1.09212 | 0.546062 | − | 0.837745i | \(-0.316126\pi\) | ||||
0.546062 | + | 0.837745i | \(0.316126\pi\) | |||||||
\(398\) | −3.96507 | −0.198751 | ||||||||
\(399\) | −11.3601 | −0.568715 | ||||||||
\(400\) | 3.81734 | 0.190867 | ||||||||
\(401\) | −11.9702 | −0.597762 | −0.298881 | − | 0.954290i | \(-0.596613\pi\) | ||||
−0.298881 | + | 0.954290i | \(0.596613\pi\) | |||||||
\(402\) | 0.165114 | 0.00823515 | ||||||||
\(403\) | −56.0513 | −2.79211 | ||||||||
\(404\) | 1.41708 | 0.0705025 | ||||||||
\(405\) | 10.2777 | 0.510705 | ||||||||
\(406\) | 4.90462 | 0.243412 | ||||||||
\(407\) | 19.4609 | 0.964642 | ||||||||
\(408\) | −15.7304 | −0.778772 | ||||||||
\(409\) | 37.2651 | 1.84264 | 0.921320 | − | 0.388804i | \(-0.127112\pi\) | ||||
0.921320 | + | 0.388804i | \(0.127112\pi\) | |||||||
\(410\) | 0.786034 | 0.0388195 | ||||||||
\(411\) | 46.8214 | 2.30953 | ||||||||
\(412\) | 7.80266 | 0.384410 | ||||||||
\(413\) | −15.4247 | −0.758999 | ||||||||
\(414\) | −2.51833 | −0.123769 | ||||||||
\(415\) | 3.53080 | 0.173320 | ||||||||
\(416\) | 17.1910 | 0.842856 | ||||||||
\(417\) | 14.4953 | 0.709839 | ||||||||
\(418\) | −1.27077 | −0.0621555 | ||||||||
\(419\) | −5.31688 | −0.259746 | −0.129873 | − | 0.991531i | \(-0.541457\pi\) | ||||
−0.129873 | + | 0.991531i | \(0.541457\pi\) | |||||||
\(420\) | 23.9455 | 1.16842 | ||||||||
\(421\) | −0.0885710 | −0.00431668 | −0.00215834 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215834 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(422\) | −4.18449 | −0.203698 | ||||||||
\(423\) | 25.7507 | 1.25204 | ||||||||
\(424\) | 0.0681633 | 0.00331030 | ||||||||
\(425\) | 6.11901 | 0.296816 | ||||||||
\(426\) | 1.56243 | 0.0757002 | ||||||||
\(427\) | −19.4298 | −0.940273 | ||||||||
\(428\) | 25.5748 | 1.23621 | ||||||||
\(429\) | 33.6990 | 1.62700 | ||||||||
\(430\) | 7.17019 | 0.345777 | ||||||||
\(431\) | −12.4923 | −0.601732 | −0.300866 | − | 0.953666i | \(-0.597276\pi\) | ||||
−0.300866 | + | 0.953666i | \(0.597276\pi\) | |||||||
\(432\) | 11.1804 | 0.537917 | ||||||||
\(433\) | −32.3933 | −1.55672 | −0.778361 | − | 0.627817i | \(-0.783949\pi\) | ||||
−0.778361 | + | 0.627817i | \(0.783949\pi\) | |||||||
\(434\) | −4.71187 | −0.226177 | ||||||||
\(435\) | −66.3624 | −3.18183 | ||||||||
\(436\) | −11.5893 | −0.555025 | ||||||||
\(437\) | 5.27963 | 0.252559 | ||||||||
\(438\) | −6.51068 | −0.311092 | ||||||||
\(439\) | −37.7205 | −1.80030 | −0.900150 | − | 0.435579i | \(-0.856544\pi\) | ||||
−0.900150 | + | 0.435579i | \(0.856544\pi\) | |||||||
\(440\) | 5.45008 | 0.259822 | ||||||||
\(441\) | −14.4056 | −0.685982 | ||||||||
\(442\) | 8.65598 | 0.411723 | ||||||||
\(443\) | 23.3690 | 1.11030 | 0.555148 | − | 0.831751i | \(-0.312662\pi\) | ||||
0.555148 | + | 0.831751i | \(0.312662\pi\) | |||||||
\(444\) | −46.2843 | −2.19655 | ||||||||
\(445\) | −37.0523 | −1.75645 | ||||||||
\(446\) | 5.38974 | 0.255211 | ||||||||
\(447\) | −55.3621 | −2.61854 | ||||||||
\(448\) | −12.1052 | −0.571915 | ||||||||
\(449\) | 21.2211 | 1.00148 | 0.500742 | − | 0.865597i | \(-0.333061\pi\) | ||||
0.500742 | + | 0.865597i | \(0.333061\pi\) | |||||||
\(450\) | 1.14098 | 0.0537865 | ||||||||
\(451\) | −2.68281 | −0.126328 | ||||||||
\(452\) | −18.7874 | −0.883687 | ||||||||
\(453\) | −21.7050 | −1.01979 | ||||||||
\(454\) | 1.57103 | 0.0737320 | ||||||||
\(455\) | −26.8097 | −1.25686 | ||||||||
\(456\) | 6.14937 | 0.287970 | ||||||||
\(457\) | −11.7688 | −0.550523 | −0.275262 | − | 0.961369i | \(-0.588764\pi\) | ||||
−0.275262 | + | 0.961369i | \(0.588764\pi\) | |||||||
\(458\) | −2.65532 | −0.124075 | ||||||||
\(459\) | 17.9216 | 0.836511 | ||||||||
\(460\) | −11.1288 | −0.518881 | ||||||||
\(461\) | 27.8579 | 1.29747 | 0.648736 | − | 0.761014i | \(-0.275298\pi\) | ||||
0.648736 | + | 0.761014i | \(0.275298\pi\) | |||||||
\(462\) | 2.83286 | 0.131796 | ||||||||
\(463\) | −20.3394 | −0.945252 | −0.472626 | − | 0.881263i | \(-0.656694\pi\) | ||||
−0.472626 | + | 0.881263i | \(0.656694\pi\) | |||||||
\(464\) | 36.2951 | 1.68496 | ||||||||
\(465\) | 63.7543 | 2.95653 | ||||||||
\(466\) | 4.97578 | 0.230498 | ||||||||
\(467\) | 32.2678 | 1.49318 | 0.746588 | − | 0.665287i | \(-0.231691\pi\) | ||||
0.746588 | + | 0.665287i | \(0.231691\pi\) | |||||||
\(468\) | −46.5652 | −2.15248 | ||||||||
\(469\) | 0.448339 | 0.0207024 | ||||||||
\(470\) | −3.94436 | −0.181940 | ||||||||
\(471\) | −1.43543 | −0.0661409 | ||||||||
\(472\) | 8.34959 | 0.384321 | ||||||||
\(473\) | −24.4725 | −1.12525 | ||||||||
\(474\) | 1.18781 | 0.0545577 | ||||||||
\(475\) | −2.39206 | −0.109755 | ||||||||
\(476\) | −20.9928 | −0.962204 | ||||||||
\(477\) | −0.278524 | −0.0127527 | ||||||||
\(478\) | 2.65561 | 0.121465 | ||||||||
\(479\) | −14.2539 | −0.651277 | −0.325639 | − | 0.945494i | \(-0.605579\pi\) | ||||
−0.325639 | + | 0.945494i | \(0.605579\pi\) | |||||||
\(480\) | −19.5535 | −0.892489 | ||||||||
\(481\) | 51.8205 | 2.36281 | ||||||||
\(482\) | −6.75664 | −0.307756 | ||||||||
\(483\) | −11.7696 | −0.535534 | ||||||||
\(484\) | 12.1206 | 0.550937 | ||||||||
\(485\) | −23.0346 | −1.04595 | ||||||||
\(486\) | −5.30182 | −0.240495 | ||||||||
\(487\) | 16.3122 | 0.739178 | 0.369589 | − | 0.929195i | \(-0.379499\pi\) | ||||
0.369589 | + | 0.929195i | \(0.379499\pi\) | |||||||
\(488\) | 10.5176 | 0.476110 | ||||||||
\(489\) | 19.7305 | 0.892245 | ||||||||
\(490\) | 2.20658 | 0.0996831 | ||||||||
\(491\) | 13.8481 | 0.624956 | 0.312478 | − | 0.949925i | \(-0.398841\pi\) | ||||
0.312478 | + | 0.949925i | \(0.398841\pi\) | |||||||
\(492\) | 6.38057 | 0.287658 | ||||||||
\(493\) | 58.1793 | 2.62026 | ||||||||
\(494\) | −3.38381 | −0.152245 | ||||||||
\(495\) | −22.2697 | −1.00095 | ||||||||
\(496\) | −34.8687 | −1.56565 | ||||||||
\(497\) | 4.24252 | 0.190303 | ||||||||
\(498\) | −0.993446 | −0.0445174 | ||||||||
\(499\) | 22.0707 | 0.988019 | 0.494010 | − | 0.869456i | \(-0.335531\pi\) | ||||
0.494010 | + | 0.869456i | \(0.335531\pi\) | |||||||
\(500\) | −18.7495 | −0.838505 | ||||||||
\(501\) | −12.2434 | −0.546994 | ||||||||
\(502\) | −6.01059 | −0.268266 | ||||||||
\(503\) | 9.78331 | 0.436216 | 0.218108 | − | 0.975925i | \(-0.430011\pi\) | ||||
0.218108 | + | 0.975925i | \(0.430011\pi\) | |||||||
\(504\) | −7.96455 | −0.354769 | ||||||||
\(505\) | 1.80463 | 0.0803048 | ||||||||
\(506\) | −1.31658 | −0.0585291 | ||||||||
\(507\) | 54.9485 | 2.44035 | ||||||||
\(508\) | −25.0333 | −1.11067 | ||||||||
\(509\) | 10.7054 | 0.474507 | 0.237254 | − | 0.971448i | \(-0.423753\pi\) | ||||
0.237254 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(510\) | −9.84555 | −0.435968 | ||||||||
\(511\) | −17.6786 | −0.782057 | ||||||||
\(512\) | 18.0292 | 0.796785 | ||||||||
\(513\) | −7.00596 | −0.309321 | ||||||||
\(514\) | −6.47742 | −0.285707 | ||||||||
\(515\) | 9.93653 | 0.437856 | ||||||||
\(516\) | 58.2034 | 2.56226 | ||||||||
\(517\) | 13.4625 | 0.592078 | ||||||||
\(518\) | 4.35621 | 0.191401 | ||||||||
\(519\) | 27.5488 | 1.20926 | ||||||||
\(520\) | 14.5125 | 0.636414 | ||||||||
\(521\) | −1.36329 | −0.0597267 | −0.0298634 | − | 0.999554i | \(-0.509507\pi\) | ||||
−0.0298634 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(522\) | 10.8484 | 0.474823 | ||||||||
\(523\) | 1.14893 | 0.0502394 | 0.0251197 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251197 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(524\) | 40.6809 | 1.77715 | ||||||||
\(525\) | 5.33247 | 0.232728 | ||||||||
\(526\) | 1.64222 | 0.0716042 | ||||||||
\(527\) | −55.8928 | −2.43473 | ||||||||
\(528\) | 20.9637 | 0.912326 | ||||||||
\(529\) | −17.5300 | −0.762176 | ||||||||
\(530\) | 0.0426629 | 0.00185316 | ||||||||
\(531\) | −34.1175 | −1.48057 | ||||||||
\(532\) | 8.20655 | 0.355799 | ||||||||
\(533\) | −7.14377 | −0.309431 | ||||||||
\(534\) | 10.4252 | 0.451144 | ||||||||
\(535\) | 32.5690 | 1.40808 | ||||||||
\(536\) | −0.242692 | −0.0104827 | ||||||||
\(537\) | −33.2662 | −1.43554 | ||||||||
\(538\) | −3.18861 | −0.137471 | ||||||||
\(539\) | −7.53125 | −0.324394 | ||||||||
\(540\) | 14.7676 | 0.635498 | ||||||||
\(541\) | −12.4480 | −0.535181 | −0.267591 | − | 0.963533i | \(-0.586227\pi\) | ||||
−0.267591 | + | 0.963533i | \(0.586227\pi\) | |||||||
\(542\) | 4.24995 | 0.182551 | ||||||||
\(543\) | −11.1030 | −0.476475 | ||||||||
\(544\) | 17.1423 | 0.734972 | ||||||||
\(545\) | −14.7587 | −0.632193 | ||||||||
\(546\) | 7.54333 | 0.322825 | ||||||||
\(547\) | 38.3171 | 1.63832 | 0.819159 | − | 0.573566i | \(-0.194440\pi\) | ||||
0.819159 | + | 0.573566i | \(0.194440\pi\) | |||||||
\(548\) | −33.8239 | −1.44489 | ||||||||
\(549\) | −42.9763 | −1.83419 | ||||||||
\(550\) | 0.596506 | 0.0254351 | ||||||||
\(551\) | −22.7436 | −0.968908 | ||||||||
\(552\) | 6.37103 | 0.271169 | ||||||||
\(553\) | 3.22528 | 0.137153 | ||||||||
\(554\) | 0.648054 | 0.0275332 | ||||||||
\(555\) | −58.9421 | −2.50195 | ||||||||
\(556\) | −10.4715 | −0.444089 | ||||||||
\(557\) | 4.02221 | 0.170426 | 0.0852132 | − | 0.996363i | \(-0.472843\pi\) | ||||
0.0852132 | + | 0.996363i | \(0.472843\pi\) | |||||||
\(558\) | −10.4221 | −0.441202 | ||||||||
\(559\) | −65.1653 | −2.75620 | ||||||||
\(560\) | −16.6779 | −0.704771 | ||||||||
\(561\) | 33.6037 | 1.41875 | ||||||||
\(562\) | −1.31267 | −0.0553714 | ||||||||
\(563\) | 25.4776 | 1.07375 | 0.536877 | − | 0.843661i | \(-0.319604\pi\) | ||||
0.536877 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(564\) | −32.0180 | −1.34820 | ||||||||
\(565\) | −23.9254 | −1.00655 | ||||||||
\(566\) | −0.343040 | −0.0144191 | ||||||||
\(567\) | −7.85220 | −0.329761 | ||||||||
\(568\) | −2.29654 | −0.0963605 | ||||||||
\(569\) | −21.0793 | −0.883691 | −0.441846 | − | 0.897091i | \(-0.645676\pi\) | ||||
−0.441846 | + | 0.897091i | \(0.645676\pi\) | |||||||
\(570\) | 3.84884 | 0.161210 | ||||||||
\(571\) | 23.7934 | 0.995722 | 0.497861 | − | 0.867257i | \(-0.334119\pi\) | ||||
0.497861 | + | 0.867257i | \(0.334119\pi\) | |||||||
\(572\) | −24.3443 | −1.01789 | ||||||||
\(573\) | −10.9152 | −0.455988 | ||||||||
\(574\) | −0.600530 | −0.0250657 | ||||||||
\(575\) | −2.47828 | −0.103352 | ||||||||
\(576\) | −26.7751 | −1.11563 | ||||||||
\(577\) | −10.8946 | −0.453549 | −0.226774 | − | 0.973947i | \(-0.572818\pi\) | ||||
−0.226774 | + | 0.973947i | \(0.572818\pi\) | |||||||
\(578\) | 4.23111 | 0.175991 | ||||||||
\(579\) | −71.3415 | −2.96485 | ||||||||
\(580\) | 47.9404 | 1.99061 | ||||||||
\(581\) | −2.69753 | −0.111912 | ||||||||
\(582\) | 6.48114 | 0.268652 | ||||||||
\(583\) | −0.145612 | −0.00603064 | ||||||||
\(584\) | 9.56970 | 0.395997 | ||||||||
\(585\) | −59.2998 | −2.45175 | ||||||||
\(586\) | 6.50848 | 0.268863 | ||||||||
\(587\) | 7.49991 | 0.309555 | 0.154777 | − | 0.987949i | \(-0.450534\pi\) | ||||
0.154777 | + | 0.987949i | \(0.450534\pi\) | |||||||
\(588\) | 17.9117 | 0.738667 | ||||||||
\(589\) | 21.8497 | 0.900302 | ||||||||
\(590\) | 5.22594 | 0.215149 | ||||||||
\(591\) | 3.62662 | 0.149179 | ||||||||
\(592\) | 32.2368 | 1.32492 | ||||||||
\(593\) | 25.7995 | 1.05946 | 0.529730 | − | 0.848166i | \(-0.322293\pi\) | ||||
0.529730 | + | 0.848166i | \(0.322293\pi\) | |||||||
\(594\) | 1.74708 | 0.0716834 | ||||||||
\(595\) | −26.7339 | −1.09598 | ||||||||
\(596\) | 39.9937 | 1.63821 | ||||||||
\(597\) | −40.9884 | −1.67754 | ||||||||
\(598\) | −3.50579 | −0.143362 | ||||||||
\(599\) | 5.48616 | 0.224159 | 0.112079 | − | 0.993699i | \(-0.464249\pi\) | ||||
0.112079 | + | 0.993699i | \(0.464249\pi\) | |||||||
\(600\) | −2.88654 | −0.117842 | ||||||||
\(601\) | −5.96910 | −0.243485 | −0.121742 | − | 0.992562i | \(-0.538848\pi\) | ||||
−0.121742 | + | 0.992562i | \(0.538848\pi\) | |||||||
\(602\) | −5.47803 | −0.223268 | ||||||||
\(603\) | 0.991672 | 0.0403840 | ||||||||
\(604\) | 15.6798 | 0.638001 | ||||||||
\(605\) | 15.4354 | 0.627537 | ||||||||
\(606\) | −0.507760 | −0.0206263 | ||||||||
\(607\) | −7.03534 | −0.285556 | −0.142778 | − | 0.989755i | \(-0.545603\pi\) | ||||
−0.142778 | + | 0.989755i | \(0.545603\pi\) | |||||||
\(608\) | −6.70132 | −0.271774 | ||||||||
\(609\) | 50.7009 | 2.05450 | ||||||||
\(610\) | 6.58290 | 0.266534 | ||||||||
\(611\) | 35.8478 | 1.45025 | ||||||||
\(612\) | −46.4335 | −1.87696 | ||||||||
\(613\) | −0.971359 | −0.0392328 | −0.0196164 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196164 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(614\) | 4.88155 | 0.197003 | ||||||||
\(615\) | 8.12552 | 0.327653 | ||||||||
\(616\) | −4.16386 | −0.167767 | ||||||||
\(617\) | 17.1413 | 0.690084 | 0.345042 | − | 0.938587i | \(-0.387865\pi\) | ||||
0.345042 | + | 0.938587i | \(0.387865\pi\) | |||||||
\(618\) | −2.79580 | −0.112463 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −46.0563 | −1.84966 | ||||||||
\(621\) | −7.25851 | −0.291274 | ||||||||
\(622\) | 4.63452 | 0.185827 | ||||||||
\(623\) | 28.3079 | 1.13413 | ||||||||
\(624\) | 55.8220 | 2.23467 | ||||||||
\(625\) | −29.1754 | −1.16701 | ||||||||
\(626\) | 1.48507 | 0.0593552 | ||||||||
\(627\) | −13.1364 | −0.524619 | ||||||||
\(628\) | 1.03696 | 0.0413790 | ||||||||
\(629\) | 51.6740 | 2.06038 | ||||||||
\(630\) | −4.98495 | −0.198605 | ||||||||
\(631\) | 6.18468 | 0.246208 | 0.123104 | − | 0.992394i | \(-0.460715\pi\) | ||||
0.123104 | + | 0.992394i | \(0.460715\pi\) | |||||||
\(632\) | −1.74589 | −0.0694478 | ||||||||
\(633\) | −43.2566 | −1.71929 | ||||||||
\(634\) | 3.51777 | 0.139708 | ||||||||
\(635\) | −31.8794 | −1.26509 | ||||||||
\(636\) | 0.346312 | 0.0137322 | ||||||||
\(637\) | −20.0542 | −0.794577 | ||||||||
\(638\) | 5.67155 | 0.224539 | ||||||||
\(639\) | 9.38395 | 0.371223 | ||||||||
\(640\) | 18.7164 | 0.739829 | ||||||||
\(641\) | −20.5842 | −0.813028 | −0.406514 | − | 0.913644i | \(-0.633256\pi\) | ||||
−0.406514 | + | 0.913644i | \(0.633256\pi\) | |||||||
\(642\) | −9.16380 | −0.361666 | ||||||||
\(643\) | 42.6168 | 1.68064 | 0.840322 | − | 0.542088i | \(-0.182366\pi\) | ||||
0.840322 | + | 0.542088i | \(0.182366\pi\) | |||||||
\(644\) | 8.50237 | 0.335040 | ||||||||
\(645\) | 74.1209 | 2.91851 | ||||||||
\(646\) | −3.37424 | −0.132758 | ||||||||
\(647\) | −10.3100 | −0.405328 | −0.202664 | − | 0.979248i | \(-0.564960\pi\) | ||||
−0.202664 | + | 0.979248i | \(0.564960\pi\) | |||||||
\(648\) | 4.25050 | 0.166976 | ||||||||
\(649\) | −17.8366 | −0.700148 | ||||||||
\(650\) | 1.58838 | 0.0623012 | ||||||||
\(651\) | −48.7083 | −1.90903 | ||||||||
\(652\) | −14.2534 | −0.558206 | ||||||||
\(653\) | −8.69444 | −0.340240 | −0.170120 | − | 0.985423i | \(-0.554415\pi\) | ||||
−0.170120 | + | 0.985423i | \(0.554415\pi\) | |||||||
\(654\) | 4.15259 | 0.162379 | ||||||||
\(655\) | 51.8063 | 2.02424 | ||||||||
\(656\) | −4.44403 | −0.173510 | ||||||||
\(657\) | −39.1030 | −1.52555 | ||||||||
\(658\) | 3.01349 | 0.117478 | ||||||||
\(659\) | −19.8991 | −0.775157 | −0.387579 | − | 0.921837i | \(-0.626688\pi\) | ||||
−0.387579 | + | 0.921837i | \(0.626688\pi\) | |||||||
\(660\) | 27.6898 | 1.07783 | ||||||||
\(661\) | 24.9324 | 0.969756 | 0.484878 | − | 0.874582i | \(-0.338864\pi\) | ||||
0.484878 | + | 0.874582i | \(0.338864\pi\) | |||||||
\(662\) | −0.493351 | −0.0191746 | ||||||||
\(663\) | 89.4800 | 3.47512 | ||||||||
\(664\) | 1.46021 | 0.0566672 | ||||||||
\(665\) | 10.4509 | 0.405267 | ||||||||
\(666\) | 9.63541 | 0.373365 | ||||||||
\(667\) | −23.5634 | −0.912378 | ||||||||
\(668\) | 8.84465 | 0.342210 | ||||||||
\(669\) | 55.7157 | 2.15409 | ||||||||
\(670\) | −0.151899 | −0.00586838 | ||||||||
\(671\) | −22.4680 | −0.867368 | ||||||||
\(672\) | 14.9388 | 0.576279 | ||||||||
\(673\) | −21.1947 | −0.816996 | −0.408498 | − | 0.912759i | \(-0.633947\pi\) | ||||
−0.408498 | + | 0.912759i | \(0.633947\pi\) | |||||||
\(674\) | −0.101837 | −0.00392260 | ||||||||
\(675\) | 3.28863 | 0.126579 | ||||||||
\(676\) | −39.6949 | −1.52673 | ||||||||
\(677\) | −21.4905 | −0.825949 | −0.412974 | − | 0.910743i | \(-0.635510\pi\) | ||||
−0.412974 | + | 0.910743i | \(0.635510\pi\) | |||||||
\(678\) | 6.73179 | 0.258533 | ||||||||
\(679\) | 17.5984 | 0.675366 | ||||||||
\(680\) | 14.4714 | 0.554954 | ||||||||
\(681\) | 16.2403 | 0.622329 | ||||||||
\(682\) | −5.44866 | −0.208640 | ||||||||
\(683\) | 24.6755 | 0.944181 | 0.472090 | − | 0.881550i | \(-0.343500\pi\) | ||||
0.472090 | + | 0.881550i | \(0.343500\pi\) | |||||||
\(684\) | 18.1519 | 0.694055 | ||||||||
\(685\) | −43.0741 | −1.64578 | ||||||||
\(686\) | −5.09349 | −0.194471 | ||||||||
\(687\) | −27.4490 | −1.04724 | ||||||||
\(688\) | −40.5384 | −1.54551 | ||||||||
\(689\) | −0.387736 | −0.0147716 | ||||||||
\(690\) | 3.98758 | 0.151805 | ||||||||
\(691\) | 22.4535 | 0.854170 | 0.427085 | − | 0.904211i | \(-0.359540\pi\) | ||||
0.427085 | + | 0.904211i | \(0.359540\pi\) | |||||||
\(692\) | −19.9013 | −0.756536 | ||||||||
\(693\) | 17.0141 | 0.646312 | ||||||||
\(694\) | 5.98804 | 0.227303 | ||||||||
\(695\) | −13.3352 | −0.505833 | ||||||||
\(696\) | −27.4451 | −1.04030 | ||||||||
\(697\) | −7.12357 | −0.269825 | ||||||||
\(698\) | 3.09295 | 0.117070 | ||||||||
\(699\) | 51.4364 | 1.94550 | ||||||||
\(700\) | −3.85219 | −0.145599 | ||||||||
\(701\) | 28.3393 | 1.07036 | 0.535181 | − | 0.844738i | \(-0.320244\pi\) | ||||
0.535181 | + | 0.844738i | \(0.320244\pi\) | |||||||
\(702\) | 4.65211 | 0.175583 | ||||||||
\(703\) | −20.2005 | −0.761876 | ||||||||
\(704\) | −13.9980 | −0.527571 | ||||||||
\(705\) | −40.7743 | −1.53565 | ||||||||
\(706\) | −1.97887 | −0.0744759 | ||||||||
\(707\) | −1.37874 | −0.0518527 | ||||||||
\(708\) | 42.4212 | 1.59429 | ||||||||
\(709\) | 25.3207 | 0.950938 | 0.475469 | − | 0.879732i | \(-0.342278\pi\) | ||||
0.475469 | + | 0.879732i | \(0.342278\pi\) | |||||||
\(710\) | −1.43739 | −0.0539441 | ||||||||
\(711\) | 7.13393 | 0.267543 | ||||||||
\(712\) | −15.3235 | −0.574272 | ||||||||
\(713\) | 22.6373 | 0.847775 | ||||||||
\(714\) | 7.52200 | 0.281504 | ||||||||
\(715\) | −31.0019 | −1.15941 | ||||||||
\(716\) | 24.0316 | 0.898103 | ||||||||
\(717\) | 27.4520 | 1.02521 | ||||||||
\(718\) | −4.23692 | −0.158121 | ||||||||
\(719\) | 9.71575 | 0.362336 | 0.181168 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181168 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(720\) | −36.8895 | −1.37479 | ||||||||
\(721\) | −7.59151 | −0.282723 | ||||||||
\(722\) | −3.59902 | −0.133942 | ||||||||
\(723\) | −69.8458 | −2.59759 | ||||||||
\(724\) | 8.02083 | 0.298092 | ||||||||
\(725\) | 10.6759 | 0.396494 | ||||||||
\(726\) | −4.34298 | −0.161183 | ||||||||
\(727\) | −11.6133 | −0.430714 | −0.215357 | − | 0.976535i | \(-0.569092\pi\) | ||||
−0.215357 | + | 0.976535i | \(0.569092\pi\) | |||||||
\(728\) | −11.0875 | −0.410931 | ||||||||
\(729\) | −42.2813 | −1.56597 | ||||||||
\(730\) | 5.98960 | 0.221685 | ||||||||
\(731\) | −64.9811 | −2.40341 | ||||||||
\(732\) | 53.4361 | 1.97506 | ||||||||
\(733\) | −35.2914 | −1.30352 | −0.651759 | − | 0.758426i | \(-0.725969\pi\) | ||||
−0.651759 | + | 0.758426i | \(0.725969\pi\) | |||||||
\(734\) | −4.47189 | −0.165060 | ||||||||
\(735\) | 22.8102 | 0.841367 | ||||||||
\(736\) | −6.94288 | −0.255918 | ||||||||
\(737\) | 0.518446 | 0.0190972 | ||||||||
\(738\) | −1.32830 | −0.0488954 | ||||||||
\(739\) | −45.6431 | −1.67901 | −0.839504 | − | 0.543353i | \(-0.817155\pi\) | ||||
−0.839504 | + | 0.543353i | \(0.817155\pi\) | |||||||
\(740\) | 42.5799 | 1.56527 | ||||||||
\(741\) | −34.9797 | −1.28501 | ||||||||
\(742\) | −0.0325944 | −0.00119658 | ||||||||
\(743\) | −21.4039 | −0.785232 | −0.392616 | − | 0.919702i | \(-0.628430\pi\) | ||||
−0.392616 | + | 0.919702i | \(0.628430\pi\) | |||||||
\(744\) | 26.3665 | 0.966642 | ||||||||
\(745\) | 50.9312 | 1.86597 | ||||||||
\(746\) | 5.12975 | 0.187814 | ||||||||
\(747\) | −5.96661 | −0.218307 | ||||||||
\(748\) | −24.2754 | −0.887598 | ||||||||
\(749\) | −24.8827 | −0.909195 | ||||||||
\(750\) | 6.71821 | 0.245314 | ||||||||
\(751\) | 11.8967 | 0.434119 | 0.217059 | − | 0.976158i | \(-0.430354\pi\) | ||||
0.217059 | + | 0.976158i | \(0.430354\pi\) | |||||||
\(752\) | 22.3004 | 0.813211 | ||||||||
\(753\) | −62.1337 | −2.26428 | ||||||||
\(754\) | 15.1022 | 0.549990 | ||||||||
\(755\) | 19.9679 | 0.726705 | ||||||||
\(756\) | −11.2825 | −0.410340 | ||||||||
\(757\) | −7.01284 | −0.254886 | −0.127443 | − | 0.991846i | \(-0.540677\pi\) | ||||
−0.127443 | + | 0.991846i | \(0.540677\pi\) | |||||||
\(758\) | −8.19405 | −0.297621 | ||||||||
\(759\) | −13.6100 | −0.494011 | ||||||||
\(760\) | −5.65720 | −0.205208 | ||||||||
\(761\) | −40.4600 | −1.46667 | −0.733337 | − | 0.679866i | \(-0.762038\pi\) | ||||
−0.733337 | + | 0.679866i | \(0.762038\pi\) | |||||||
\(762\) | 8.96976 | 0.324940 | ||||||||
\(763\) | 11.2756 | 0.408206 | ||||||||
\(764\) | 7.88516 | 0.285275 | ||||||||
\(765\) | −59.1322 | −2.13793 | ||||||||
\(766\) | −1.95590 | −0.0706695 | ||||||||
\(767\) | −47.4953 | −1.71496 | ||||||||
\(768\) | 29.1796 | 1.05293 | ||||||||
\(769\) | −23.1438 | −0.834586 | −0.417293 | − | 0.908772i | \(-0.637021\pi\) | ||||
−0.417293 | + | 0.908772i | \(0.637021\pi\) | |||||||
\(770\) | −2.60613 | −0.0939184 | ||||||||
\(771\) | −66.9594 | −2.41149 | ||||||||
\(772\) | 51.5373 | 1.85487 | ||||||||
\(773\) | −4.39037 | −0.157910 | −0.0789552 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789552 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(774\) | −12.1167 | −0.435527 | ||||||||
\(775\) | −10.2564 | −0.368419 | ||||||||
\(776\) | −9.52628 | −0.341973 | ||||||||
\(777\) | 45.0317 | 1.61550 | ||||||||
\(778\) | −5.65209 | −0.202637 | ||||||||
\(779\) | 2.78476 | 0.0997744 | ||||||||
\(780\) | 73.7325 | 2.64005 | ||||||||
\(781\) | 4.90592 | 0.175548 | ||||||||
\(782\) | −3.49588 | −0.125012 | ||||||||
\(783\) | 31.2681 | 1.11743 | ||||||||
\(784\) | −12.4754 | −0.445551 | ||||||||
\(785\) | 1.32054 | 0.0471321 | ||||||||
\(786\) | −14.5765 | −0.519926 | ||||||||
\(787\) | −24.8822 | −0.886955 | −0.443478 | − | 0.896285i | \(-0.646255\pi\) | ||||
−0.443478 | + | 0.896285i | \(0.646255\pi\) | |||||||
\(788\) | −2.61988 | −0.0933294 | ||||||||
\(789\) | 16.9762 | 0.604370 | ||||||||
\(790\) | −1.09274 | −0.0388779 | ||||||||
\(791\) | 18.2790 | 0.649927 | ||||||||
\(792\) | −9.20996 | −0.327262 | ||||||||
\(793\) | −59.8278 | −2.12455 | ||||||||
\(794\) | 5.63260 | 0.199894 | ||||||||
\(795\) | 0.441022 | 0.0156414 | ||||||||
\(796\) | 29.6101 | 1.04950 | ||||||||
\(797\) | −55.2621 | −1.95748 | −0.978742 | − | 0.205098i | \(-0.934249\pi\) | ||||
−0.978742 | + | 0.205098i | \(0.934249\pi\) | |||||||
\(798\) | −2.94052 | −0.104093 | ||||||||
\(799\) | 35.7464 | 1.26462 | ||||||||
\(800\) | 3.14563 | 0.111215 | ||||||||
\(801\) | 62.6137 | 2.21235 | ||||||||
\(802\) | −3.09844 | −0.109410 | ||||||||
\(803\) | −20.4430 | −0.721419 | ||||||||
\(804\) | −1.23303 | −0.0434856 | ||||||||
\(805\) | 10.8276 | 0.381623 | ||||||||
\(806\) | −14.5087 | −0.511047 | ||||||||
\(807\) | −32.9619 | −1.16031 | ||||||||
\(808\) | 0.746328 | 0.0262557 | ||||||||
\(809\) | 15.3727 | 0.540474 | 0.270237 | − | 0.962794i | \(-0.412898\pi\) | ||||
0.270237 | + | 0.962794i | \(0.412898\pi\) | |||||||
\(810\) | 2.66036 | 0.0934755 | ||||||||
\(811\) | 28.4653 | 0.999552 | 0.499776 | − | 0.866155i | \(-0.333416\pi\) | ||||
0.499776 | + | 0.866155i | \(0.333416\pi\) | |||||||
\(812\) | −36.6264 | −1.28534 | ||||||||
\(813\) | 43.9333 | 1.54081 | ||||||||
\(814\) | 5.03739 | 0.176560 | ||||||||
\(815\) | −18.1514 | −0.635815 | ||||||||
\(816\) | 55.6642 | 1.94864 | ||||||||
\(817\) | 25.4025 | 0.888722 | ||||||||
\(818\) | 9.64594 | 0.337262 | ||||||||
\(819\) | 45.3051 | 1.58309 | ||||||||
\(820\) | −5.86990 | −0.204986 | ||||||||
\(821\) | 39.8830 | 1.39193 | 0.695963 | − | 0.718078i | \(-0.254978\pi\) | ||||
0.695963 | + | 0.718078i | \(0.254978\pi\) | |||||||
\(822\) | 12.1196 | 0.422718 | ||||||||
\(823\) | 33.8559 | 1.18014 | 0.590071 | − | 0.807351i | \(-0.299100\pi\) | ||||
0.590071 | + | 0.807351i | \(0.299100\pi\) | |||||||
\(824\) | 4.10939 | 0.143157 | ||||||||
\(825\) | 6.16630 | 0.214683 | ||||||||
\(826\) | −3.99262 | −0.138921 | ||||||||
\(827\) | −31.1589 | −1.08350 | −0.541750 | − | 0.840540i | \(-0.682238\pi\) | ||||
−0.541750 | + | 0.840540i | \(0.682238\pi\) | |||||||
\(828\) | 18.8062 | 0.653561 | ||||||||
\(829\) | 21.9578 | 0.762625 | 0.381312 | − | 0.924446i | \(-0.375472\pi\) | ||||
0.381312 | + | 0.924446i | \(0.375472\pi\) | |||||||
\(830\) | 0.913935 | 0.0317232 | ||||||||
\(831\) | 6.69917 | 0.232392 | ||||||||
\(832\) | −37.2739 | −1.29224 | ||||||||
\(833\) | −19.9975 | −0.692873 | ||||||||
\(834\) | 3.75207 | 0.129923 | ||||||||
\(835\) | 11.2635 | 0.389789 | ||||||||
\(836\) | 9.48980 | 0.328212 | ||||||||
\(837\) | −30.0393 | −1.03831 | ||||||||
\(838\) | −1.37626 | −0.0475419 | ||||||||
\(839\) | −13.3272 | −0.460106 | −0.230053 | − | 0.973178i | \(-0.573890\pi\) | ||||
−0.230053 | + | 0.973178i | \(0.573890\pi\) | |||||||
\(840\) | 12.6113 | 0.435130 | ||||||||
\(841\) | 72.5062 | 2.50021 | ||||||||
\(842\) | −0.0229263 | −0.000790092 0 | ||||||||
\(843\) | −13.5695 | −0.467358 | ||||||||
\(844\) | 31.2487 | 1.07562 | ||||||||
\(845\) | −50.5507 | −1.73900 | ||||||||
\(846\) | 6.66548 | 0.229164 | ||||||||
\(847\) | −11.7926 | −0.405199 | ||||||||
\(848\) | −0.241205 | −0.00828301 | ||||||||
\(849\) | −3.54613 | −0.121703 | ||||||||
\(850\) | 1.58388 | 0.0543268 | ||||||||
\(851\) | −20.9287 | −0.717425 | ||||||||
\(852\) | −11.6679 | −0.399734 | ||||||||
\(853\) | −11.1545 | −0.381923 | −0.190962 | − | 0.981597i | \(-0.561161\pi\) | ||||
−0.190962 | + | 0.981597i | \(0.561161\pi\) | |||||||
\(854\) | −5.02933 | −0.172100 | ||||||||
\(855\) | 23.1161 | 0.790553 | ||||||||
\(856\) | 13.4694 | 0.460373 | ||||||||
\(857\) | 22.5934 | 0.771777 | 0.385889 | − | 0.922545i | \(-0.373895\pi\) | ||||
0.385889 | + | 0.922545i | \(0.373895\pi\) | |||||||
\(858\) | 8.72288 | 0.297794 | ||||||||
\(859\) | 14.0664 | 0.479941 | 0.239970 | − | 0.970780i | \(-0.422862\pi\) | ||||
0.239970 | + | 0.970780i | \(0.422862\pi\) | |||||||
\(860\) | −53.5451 | −1.82587 | ||||||||
\(861\) | −6.20790 | −0.211565 | ||||||||
\(862\) | −3.23358 | −0.110136 | ||||||||
\(863\) | −49.7257 | −1.69268 | −0.846342 | − | 0.532640i | \(-0.821200\pi\) | ||||
−0.846342 | + | 0.532640i | \(0.821200\pi\) | |||||||
\(864\) | 9.21306 | 0.313435 | ||||||||
\(865\) | −25.3440 | −0.861720 | ||||||||
\(866\) | −8.38489 | −0.284930 | ||||||||
\(867\) | 43.7386 | 1.48544 | ||||||||
\(868\) | 35.1870 | 1.19432 | ||||||||
\(869\) | 3.72962 | 0.126519 | ||||||||
\(870\) | −17.1777 | −0.582377 | ||||||||
\(871\) | 1.38052 | 0.0467770 | ||||||||
\(872\) | −6.10366 | −0.206696 | ||||||||
\(873\) | 38.9256 | 1.31743 | ||||||||
\(874\) | 1.36661 | 0.0462264 | ||||||||
\(875\) | 18.2422 | 0.616697 | ||||||||
\(876\) | 48.6201 | 1.64272 | ||||||||
\(877\) | −0.725108 | −0.0244852 | −0.0122426 | − | 0.999925i | \(-0.503897\pi\) | ||||
−0.0122426 | + | 0.999925i | \(0.503897\pi\) | |||||||
\(878\) | −9.76382 | −0.329513 | ||||||||
\(879\) | 67.2805 | 2.26932 | ||||||||
\(880\) | −19.2858 | −0.650125 | ||||||||
\(881\) | 37.1950 | 1.25313 | 0.626566 | − | 0.779368i | \(-0.284460\pi\) | ||||
0.626566 | + | 0.779368i | \(0.284460\pi\) | |||||||
\(882\) | −3.72884 | −0.125557 | ||||||||
\(883\) | −57.5237 | −1.93583 | −0.967913 | − | 0.251285i | \(-0.919147\pi\) | ||||
−0.967913 | + | 0.251285i | \(0.919147\pi\) | |||||||
\(884\) | −64.6406 | −2.17410 | ||||||||
\(885\) | 54.0225 | 1.81595 | ||||||||
\(886\) | 6.04899 | 0.203220 | ||||||||
\(887\) | −34.2813 | −1.15105 | −0.575527 | − | 0.817782i | \(-0.695203\pi\) | ||||
−0.575527 | + | 0.817782i | \(0.695203\pi\) | |||||||
\(888\) | −24.3763 | −0.818015 | ||||||||
\(889\) | 24.3558 | 0.816869 | ||||||||
\(890\) | −9.59085 | −0.321486 | ||||||||
\(891\) | −9.08004 | −0.304193 | ||||||||
\(892\) | −40.2492 | −1.34764 | ||||||||
\(893\) | −13.9741 | −0.467624 | ||||||||
\(894\) | −14.3303 | −0.479276 | ||||||||
\(895\) | 30.6037 | 1.02297 | ||||||||
\(896\) | −14.2993 | −0.477706 | ||||||||
\(897\) | −36.2406 | −1.21004 | ||||||||
\(898\) | 5.49300 | 0.183304 | ||||||||
\(899\) | −97.5169 | −3.25237 | ||||||||
\(900\) | −8.52058 | −0.284019 | ||||||||
\(901\) | −0.386640 | −0.0128808 | ||||||||
\(902\) | −0.694435 | −0.0231221 | ||||||||
\(903\) | −56.6283 | −1.88447 | ||||||||
\(904\) | −9.89469 | −0.329092 | ||||||||
\(905\) | 10.2144 | 0.339537 | ||||||||
\(906\) | −5.61827 | −0.186654 | ||||||||
\(907\) | 21.9477 | 0.728761 | 0.364380 | − | 0.931250i | \(-0.381281\pi\) | ||||
0.364380 | + | 0.931250i | \(0.381281\pi\) | |||||||
\(908\) | −11.7320 | −0.389341 | ||||||||
\(909\) | −3.04959 | −0.101149 | ||||||||
\(910\) | −6.93960 | −0.230046 | ||||||||
\(911\) | 10.9369 | 0.362357 | 0.181179 | − | 0.983450i | \(-0.442009\pi\) | ||||
0.181179 | + | 0.983450i | \(0.442009\pi\) | |||||||
\(912\) | −21.7603 | −0.720557 | ||||||||
\(913\) | −3.11934 | −0.103235 | ||||||||
\(914\) | −3.04632 | −0.100763 | ||||||||
\(915\) | 68.0498 | 2.24966 | ||||||||
\(916\) | 19.8292 | 0.655176 | ||||||||
\(917\) | −39.5800 | −1.30705 | ||||||||
\(918\) | 4.63896 | 0.153108 | ||||||||
\(919\) | −15.1849 | −0.500905 | −0.250452 | − | 0.968129i | \(-0.580579\pi\) | ||||
−0.250452 | + | 0.968129i | \(0.580579\pi\) | |||||||
\(920\) | −5.86113 | −0.193236 | ||||||||
\(921\) | 50.4623 | 1.66279 | ||||||||
\(922\) | 7.21092 | 0.237479 | ||||||||
\(923\) | 13.0635 | 0.429990 | ||||||||
\(924\) | −21.1550 | −0.695950 | ||||||||
\(925\) | 9.48220 | 0.311773 | ||||||||
\(926\) | −5.26478 | −0.173011 | ||||||||
\(927\) | −16.7915 | −0.551505 | ||||||||
\(928\) | 29.9085 | 0.981794 | ||||||||
\(929\) | 18.6029 | 0.610341 | 0.305171 | − | 0.952298i | \(-0.401286\pi\) | ||||
0.305171 | + | 0.952298i | \(0.401286\pi\) | |||||||
\(930\) | 16.5026 | 0.541141 | ||||||||
\(931\) | 7.81746 | 0.256207 | ||||||||
\(932\) | −37.1578 | −1.21714 | ||||||||
\(933\) | 47.9088 | 1.56846 | ||||||||
\(934\) | 8.35241 | 0.273299 | ||||||||
\(935\) | −30.9143 | −1.01100 | ||||||||
\(936\) | −24.5243 | −0.801601 | ||||||||
\(937\) | 39.8655 | 1.30235 | 0.651175 | − | 0.758928i | \(-0.274277\pi\) | ||||
0.651175 | + | 0.758928i | \(0.274277\pi\) | |||||||
\(938\) | 0.116051 | 0.00378920 | ||||||||
\(939\) | 15.3517 | 0.500983 | ||||||||
\(940\) | 29.4555 | 0.960731 | ||||||||
\(941\) | −5.14348 | −0.167673 | −0.0838364 | − | 0.996480i | \(-0.526717\pi\) | ||||
−0.0838364 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(942\) | −0.371555 | −0.0121059 | ||||||||
\(943\) | 2.88514 | 0.0939532 | ||||||||
\(944\) | −29.5461 | −0.961645 | ||||||||
\(945\) | −14.3680 | −0.467391 | ||||||||
\(946\) | −6.33462 | −0.205956 | ||||||||
\(947\) | 6.13580 | 0.199387 | 0.0996933 | − | 0.995018i | \(-0.468214\pi\) | ||||
0.0996933 | + | 0.995018i | \(0.468214\pi\) | |||||||
\(948\) | −8.87022 | −0.288091 | ||||||||
\(949\) | −54.4357 | −1.76706 | ||||||||
\(950\) | −0.619175 | −0.0200887 | ||||||||
\(951\) | 36.3645 | 1.17920 | ||||||||
\(952\) | −11.0562 | −0.358333 | ||||||||
\(953\) | 37.8521 | 1.22615 | 0.613075 | − | 0.790025i | \(-0.289932\pi\) | ||||
0.613075 | + | 0.790025i | \(0.289932\pi\) | |||||||
\(954\) | −0.0720949 | −0.00233416 | ||||||||
\(955\) | 10.0416 | 0.324938 | ||||||||
\(956\) | −19.8314 | −0.641393 | ||||||||
\(957\) | 58.6289 | 1.89520 | ||||||||
\(958\) | −3.68957 | −0.119205 | ||||||||
\(959\) | 32.9086 | 1.06267 | ||||||||
\(960\) | 42.3964 | 1.36834 | ||||||||
\(961\) | 62.6845 | 2.02208 | ||||||||
\(962\) | 13.4136 | 0.432470 | ||||||||
\(963\) | −55.0376 | −1.77356 | ||||||||
\(964\) | 50.4568 | 1.62510 | ||||||||
\(965\) | 65.6317 | 2.11276 | ||||||||
\(966\) | −3.04651 | −0.0980200 | ||||||||
\(967\) | 33.1631 | 1.06645 | 0.533226 | − | 0.845973i | \(-0.320980\pi\) | ||||
0.533226 | + | 0.845973i | \(0.320980\pi\) | |||||||
\(968\) | 6.38351 | 0.205174 | ||||||||
\(969\) | −34.8808 | −1.12053 | ||||||||
\(970\) | −5.96243 | −0.191442 | ||||||||
\(971\) | 17.8174 | 0.571788 | 0.285894 | − | 0.958261i | \(-0.407710\pi\) | ||||
0.285894 | + | 0.958261i | \(0.407710\pi\) | |||||||
\(972\) | 39.5926 | 1.26993 | ||||||||
\(973\) | 10.1881 | 0.326615 | ||||||||
\(974\) | 4.22236 | 0.135293 | ||||||||
\(975\) | 16.4196 | 0.525849 | ||||||||
\(976\) | −37.2180 | −1.19132 | ||||||||
\(977\) | 2.19389 | 0.0701887 | 0.0350943 | − | 0.999384i | \(-0.488827\pi\) | ||||
0.0350943 | + | 0.999384i | \(0.488827\pi\) | |||||||
\(978\) | 5.10718 | 0.163309 | ||||||||
\(979\) | 32.7344 | 1.04620 | ||||||||
\(980\) | −16.4782 | −0.526376 | ||||||||
\(981\) | 24.9404 | 0.796284 | ||||||||
\(982\) | 3.58453 | 0.114387 | ||||||||
\(983\) | 17.3296 | 0.552729 | 0.276364 | − | 0.961053i | \(-0.410870\pi\) | ||||
0.276364 | + | 0.961053i | \(0.410870\pi\) | |||||||
\(984\) | 3.36042 | 0.107126 | ||||||||
\(985\) | −3.33636 | −0.106305 | ||||||||
\(986\) | 15.0595 | 0.479592 | ||||||||
\(987\) | 31.1516 | 0.991565 | ||||||||
\(988\) | 25.2694 | 0.803928 | ||||||||
\(989\) | 26.3182 | 0.836871 | ||||||||
\(990\) | −5.76444 | −0.183206 | ||||||||
\(991\) | 45.9501 | 1.45965 | 0.729826 | − | 0.683633i | \(-0.239601\pi\) | ||||
0.729826 | + | 0.683633i | \(0.239601\pi\) | |||||||
\(992\) | −28.7331 | −0.912276 | ||||||||
\(993\) | −5.09995 | −0.161842 | ||||||||
\(994\) | 1.09816 | 0.0348316 | ||||||||
\(995\) | 37.7079 | 1.19542 | ||||||||
\(996\) | 7.41879 | 0.235073 | ||||||||
\(997\) | −24.6533 | −0.780779 | −0.390389 | − | 0.920650i | \(-0.627660\pi\) | ||||
−0.390389 | + | 0.920650i | \(0.627660\pi\) | |||||||
\(998\) | 5.71292 | 0.180839 | ||||||||
\(999\) | 27.7719 | 0.878664 |
(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 | 619.2.a.b.1.14 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.17 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.4 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.14 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.17 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.4 | 30 | 4.3 | odd | 2 |