Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.80778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80778 | −1.98540 | −0.992701 | − | 0.120604i | \(-0.961517\pi\) | ||||
−0.992701 | + | 0.120604i | \(0.961517\pi\) | |||||||
\(3\) | −0.314338 | −0.181483 | −0.0907415 | − | 0.995874i | \(-0.528924\pi\) | ||||
−0.0907415 | + | 0.995874i | \(0.528924\pi\) | |||||||
\(4\) | 5.88364 | 2.94182 | ||||||||
\(5\) | −0.925514 | −0.413902 | −0.206951 | − | 0.978351i | \(-0.566354\pi\) | ||||
−0.206951 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(6\) | 0.882592 | 0.360317 | ||||||||
\(7\) | 2.15050 | 0.812812 | 0.406406 | − | 0.913692i | \(-0.366782\pi\) | ||||
0.406406 | + | 0.913692i | \(0.366782\pi\) | |||||||
\(8\) | −10.9044 | −3.85529 | ||||||||
\(9\) | −2.90119 | −0.967064 | ||||||||
\(10\) | 2.59864 | 0.821762 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.84945 | −0.533890 | ||||||||
\(13\) | 1.28180 | 0.355508 | 0.177754 | − | 0.984075i | \(-0.443117\pi\) | ||||
0.177754 | + | 0.984075i | \(0.443117\pi\) | |||||||
\(14\) | −6.03813 | −1.61376 | ||||||||
\(15\) | 0.290924 | 0.0751162 | ||||||||
\(16\) | 18.8499 | 4.71248 | ||||||||
\(17\) | 3.37980 | 0.819723 | 0.409861 | − | 0.912148i | \(-0.365577\pi\) | ||||
0.409861 | + | 0.912148i | \(0.365577\pi\) | |||||||
\(18\) | 8.14591 | 1.92001 | ||||||||
\(19\) | 2.49477 | 0.572340 | 0.286170 | − | 0.958179i | \(-0.407618\pi\) | ||||
0.286170 | + | 0.958179i | \(0.407618\pi\) | |||||||
\(20\) | −5.44539 | −1.21763 | ||||||||
\(21\) | −0.675983 | −0.147512 | ||||||||
\(22\) | −2.80778 | −0.598621 | ||||||||
\(23\) | −4.09102 | −0.853036 | −0.426518 | − | 0.904479i | \(-0.640260\pi\) | ||||
−0.426518 | + | 0.904479i | \(0.640260\pi\) | |||||||
\(24\) | 3.42767 | 0.699669 | ||||||||
\(25\) | −4.14342 | −0.828685 | ||||||||
\(26\) | −3.59902 | −0.705825 | ||||||||
\(27\) | 1.85497 | 0.356989 | ||||||||
\(28\) | 12.6528 | 2.39115 | ||||||||
\(29\) | 3.04284 | 0.565041 | 0.282521 | − | 0.959261i | \(-0.408829\pi\) | ||||
0.282521 | + | 0.959261i | \(0.408829\pi\) | |||||||
\(30\) | −0.816851 | −0.149136 | ||||||||
\(31\) | 4.27147 | 0.767178 | 0.383589 | − | 0.923504i | \(-0.374688\pi\) | ||||
0.383589 | + | 0.923504i | \(0.374688\pi\) | |||||||
\(32\) | −31.1176 | −5.50087 | ||||||||
\(33\) | −0.314338 | −0.0547192 | ||||||||
\(34\) | −9.48975 | −1.62748 | ||||||||
\(35\) | −1.99032 | −0.336425 | ||||||||
\(36\) | −17.0696 | −2.84493 | ||||||||
\(37\) | −10.1339 | −1.66600 | −0.832999 | − | 0.553275i | \(-0.813378\pi\) | ||||
−0.832999 | + | 0.553275i | \(0.813378\pi\) | |||||||
\(38\) | −7.00478 | −1.13632 | ||||||||
\(39\) | −0.402918 | −0.0645186 | ||||||||
\(40\) | 10.0922 | 1.59571 | ||||||||
\(41\) | 8.77104 | 1.36981 | 0.684903 | − | 0.728634i | \(-0.259844\pi\) | ||||
0.684903 | + | 0.728634i | \(0.259844\pi\) | |||||||
\(42\) | 1.89801 | 0.292870 | ||||||||
\(43\) | 6.55254 | 0.999253 | 0.499626 | − | 0.866241i | \(-0.333471\pi\) | ||||
0.499626 | + | 0.866241i | \(0.333471\pi\) | |||||||
\(44\) | 5.88364 | 0.886992 | ||||||||
\(45\) | 2.68509 | 0.400270 | ||||||||
\(46\) | 11.4867 | 1.69362 | ||||||||
\(47\) | −1.94970 | −0.284393 | −0.142197 | − | 0.989838i | \(-0.545417\pi\) | ||||
−0.142197 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(48\) | −5.92524 | −0.855235 | ||||||||
\(49\) | −2.37535 | −0.339336 | ||||||||
\(50\) | 11.6338 | 1.64527 | ||||||||
\(51\) | −1.06240 | −0.148766 | ||||||||
\(52\) | 7.54165 | 1.04584 | ||||||||
\(53\) | 3.62325 | 0.497691 | 0.248846 | − | 0.968543i | \(-0.419949\pi\) | ||||
0.248846 | + | 0.968543i | \(0.419949\pi\) | |||||||
\(54\) | −5.20834 | −0.708766 | ||||||||
\(55\) | −0.925514 | −0.124796 | ||||||||
\(56\) | −23.4499 | −3.13363 | ||||||||
\(57\) | −0.784201 | −0.103870 | ||||||||
\(58\) | −8.54363 | −1.12183 | ||||||||
\(59\) | 14.7925 | 1.92582 | 0.962911 | − | 0.269819i | \(-0.0869639\pi\) | ||||
0.962911 | + | 0.269819i | \(0.0869639\pi\) | |||||||
\(60\) | 1.71169 | 0.220978 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −11.9934 | −1.52316 | ||||||||
\(63\) | −6.23901 | −0.786042 | ||||||||
\(64\) | 49.6717 | 6.20896 | ||||||||
\(65\) | −1.18632 | −0.147145 | ||||||||
\(66\) | 0.882592 | 0.108640 | ||||||||
\(67\) | 7.30698 | 0.892690 | 0.446345 | − | 0.894861i | \(-0.352725\pi\) | ||||
0.446345 | + | 0.894861i | \(0.352725\pi\) | |||||||
\(68\) | 19.8855 | 2.41148 | ||||||||
\(69\) | 1.28596 | 0.154812 | ||||||||
\(70\) | 5.58838 | 0.667939 | ||||||||
\(71\) | −1.70617 | −0.202486 | −0.101243 | − | 0.994862i | \(-0.532282\pi\) | ||||
−0.101243 | + | 0.994862i | \(0.532282\pi\) | |||||||
\(72\) | 31.6358 | 3.72831 | ||||||||
\(73\) | 9.85356 | 1.15327 | 0.576636 | − | 0.817001i | \(-0.304365\pi\) | ||||
0.576636 | + | 0.817001i | \(0.304365\pi\) | |||||||
\(74\) | 28.4537 | 3.30767 | ||||||||
\(75\) | 1.30243 | 0.150392 | ||||||||
\(76\) | 14.6783 | 1.68372 | ||||||||
\(77\) | 2.15050 | 0.245072 | ||||||||
\(78\) | 1.13131 | 0.128095 | ||||||||
\(79\) | 0.979456 | 0.110197 | 0.0550987 | − | 0.998481i | \(-0.482453\pi\) | ||||
0.0550987 | + | 0.998481i | \(0.482453\pi\) | |||||||
\(80\) | −17.4459 | −1.95051 | ||||||||
\(81\) | 8.12049 | 0.902277 | ||||||||
\(82\) | −24.6272 | −2.71962 | ||||||||
\(83\) | −1.70128 | −0.186740 | −0.0933700 | − | 0.995631i | \(-0.529764\pi\) | ||||
−0.0933700 | + | 0.995631i | \(0.529764\pi\) | |||||||
\(84\) | −3.97724 | −0.433952 | ||||||||
\(85\) | −3.12806 | −0.339285 | ||||||||
\(86\) | −18.3981 | −1.98392 | ||||||||
\(87\) | −0.956480 | −0.102545 | ||||||||
\(88\) | −10.9044 | −1.16241 | ||||||||
\(89\) | 17.1623 | 1.81920 | 0.909602 | − | 0.415481i | \(-0.136387\pi\) | ||||
0.909602 | + | 0.415481i | \(0.136387\pi\) | |||||||
\(90\) | −7.53916 | −0.794697 | ||||||||
\(91\) | 2.75651 | 0.288961 | ||||||||
\(92\) | −24.0701 | −2.50948 | ||||||||
\(93\) | −1.34268 | −0.139230 | ||||||||
\(94\) | 5.47433 | 0.564634 | ||||||||
\(95\) | −2.30895 | −0.236893 | ||||||||
\(96\) | 9.78145 | 0.998315 | ||||||||
\(97\) | −7.48635 | −0.760123 | −0.380062 | − | 0.924961i | \(-0.624097\pi\) | ||||
−0.380062 | + | 0.924961i | \(0.624097\pi\) | |||||||
\(98\) | 6.66947 | 0.673718 | ||||||||
\(99\) | −2.90119 | −0.291581 | ||||||||
\(100\) | −24.3784 | −2.43784 | ||||||||
\(101\) | 13.8305 | 1.37619 | 0.688093 | − | 0.725623i | \(-0.258448\pi\) | ||||
0.688093 | + | 0.725623i | \(0.258448\pi\) | |||||||
\(102\) | 2.98299 | 0.295360 | ||||||||
\(103\) | 18.9824 | 1.87039 | 0.935197 | − | 0.354127i | \(-0.115222\pi\) | ||||
0.935197 | + | 0.354127i | \(0.115222\pi\) | |||||||
\(104\) | −13.9773 | −1.37058 | ||||||||
\(105\) | 0.625632 | 0.0610554 | ||||||||
\(106\) | −10.1733 | −0.988116 | ||||||||
\(107\) | −4.24599 | −0.410475 | −0.205237 | − | 0.978712i | \(-0.565797\pi\) | ||||
−0.205237 | + | 0.978712i | \(0.565797\pi\) | |||||||
\(108\) | 10.9140 | 1.05020 | ||||||||
\(109\) | −3.61620 | −0.346369 | −0.173185 | − | 0.984889i | \(-0.555406\pi\) | ||||
−0.173185 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(110\) | 2.59864 | 0.247771 | ||||||||
\(111\) | 3.18546 | 0.302350 | ||||||||
\(112\) | 40.5367 | 3.83036 | ||||||||
\(113\) | −9.77038 | −0.919120 | −0.459560 | − | 0.888147i | \(-0.651993\pi\) | ||||
−0.459560 | + | 0.888147i | \(0.651993\pi\) | |||||||
\(114\) | 2.20187 | 0.206224 | ||||||||
\(115\) | 3.78629 | 0.353074 | ||||||||
\(116\) | 17.9030 | 1.66225 | ||||||||
\(117\) | −3.71875 | −0.343799 | ||||||||
\(118\) | −41.5342 | −3.82353 | ||||||||
\(119\) | 7.26827 | 0.666281 | ||||||||
\(120\) | −3.17235 | −0.289595 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.80778 | 0.254205 | ||||||||
\(123\) | −2.75707 | −0.248597 | ||||||||
\(124\) | 25.1318 | 2.25690 | ||||||||
\(125\) | 8.46237 | 0.756897 | ||||||||
\(126\) | 17.5178 | 1.56061 | ||||||||
\(127\) | 14.8970 | 1.32189 | 0.660947 | − | 0.750432i | \(-0.270155\pi\) | ||||
0.660947 | + | 0.750432i | \(0.270155\pi\) | |||||||
\(128\) | −77.2320 | −6.82641 | ||||||||
\(129\) | −2.05971 | −0.181347 | ||||||||
\(130\) | 3.33094 | 0.292143 | ||||||||
\(131\) | 5.18238 | 0.452787 | 0.226393 | − | 0.974036i | \(-0.427307\pi\) | ||||
0.226393 | + | 0.974036i | \(0.427307\pi\) | |||||||
\(132\) | −1.84945 | −0.160974 | ||||||||
\(133\) | 5.36501 | 0.465205 | ||||||||
\(134\) | −20.5164 | −1.77235 | ||||||||
\(135\) | −1.71680 | −0.147758 | ||||||||
\(136\) | −36.8548 | −3.16027 | ||||||||
\(137\) | 0.507156 | 0.0433292 | 0.0216646 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216646 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(138\) | −3.61070 | −0.307363 | ||||||||
\(139\) | −11.6343 | −0.986809 | −0.493405 | − | 0.869800i | \(-0.664248\pi\) | ||||
−0.493405 | + | 0.869800i | \(0.664248\pi\) | |||||||
\(140\) | −11.7103 | −0.989701 | ||||||||
\(141\) | 0.612865 | 0.0516125 | ||||||||
\(142\) | 4.79056 | 0.402015 | ||||||||
\(143\) | 1.28180 | 0.107190 | ||||||||
\(144\) | −54.6872 | −4.55727 | ||||||||
\(145\) | −2.81619 | −0.233872 | ||||||||
\(146\) | −27.6666 | −2.28971 | ||||||||
\(147\) | 0.746663 | 0.0615837 | ||||||||
\(148\) | −59.6240 | −4.90106 | ||||||||
\(149\) | 6.22561 | 0.510022 | 0.255011 | − | 0.966938i | \(-0.417921\pi\) | ||||
0.255011 | + | 0.966938i | \(0.417921\pi\) | |||||||
\(150\) | −3.65695 | −0.298589 | ||||||||
\(151\) | 15.4941 | 1.26089 | 0.630447 | − | 0.776232i | \(-0.282872\pi\) | ||||
0.630447 | + | 0.776232i | \(0.282872\pi\) | |||||||
\(152\) | −27.2040 | −2.20654 | ||||||||
\(153\) | −9.80546 | −0.792724 | ||||||||
\(154\) | −6.03813 | −0.486567 | ||||||||
\(155\) | −3.95330 | −0.317537 | ||||||||
\(156\) | −2.37063 | −0.189802 | ||||||||
\(157\) | 5.74821 | 0.458757 | 0.229379 | − | 0.973337i | \(-0.426331\pi\) | ||||
0.229379 | + | 0.973337i | \(0.426331\pi\) | |||||||
\(158\) | −2.75010 | −0.218786 | ||||||||
\(159\) | −1.13892 | −0.0903225 | ||||||||
\(160\) | 28.7998 | 2.27682 | ||||||||
\(161\) | −8.79773 | −0.693358 | ||||||||
\(162\) | −22.8006 | −1.79138 | ||||||||
\(163\) | −20.2692 | −1.58761 | −0.793805 | − | 0.608173i | \(-0.791903\pi\) | ||||
−0.793805 | + | 0.608173i | \(0.791903\pi\) | |||||||
\(164\) | 51.6056 | 4.02972 | ||||||||
\(165\) | 0.290924 | 0.0226484 | ||||||||
\(166\) | 4.77683 | 0.370754 | ||||||||
\(167\) | −16.4779 | −1.27510 | −0.637548 | − | 0.770411i | \(-0.720051\pi\) | ||||
−0.637548 | + | 0.770411i | \(0.720051\pi\) | |||||||
\(168\) | 7.37120 | 0.568700 | ||||||||
\(169\) | −11.3570 | −0.873614 | ||||||||
\(170\) | 8.78290 | 0.673617 | ||||||||
\(171\) | −7.23781 | −0.553489 | ||||||||
\(172\) | 38.5528 | 2.93962 | ||||||||
\(173\) | 9.01499 | 0.685397 | 0.342698 | − | 0.939445i | \(-0.388659\pi\) | ||||
0.342698 | + | 0.939445i | \(0.388659\pi\) | |||||||
\(174\) | 2.68559 | 0.203594 | ||||||||
\(175\) | −8.91043 | −0.673565 | ||||||||
\(176\) | 18.8499 | 1.42087 | ||||||||
\(177\) | −4.64985 | −0.349504 | ||||||||
\(178\) | −48.1881 | −3.61185 | ||||||||
\(179\) | −6.57826 | −0.491683 | −0.245841 | − | 0.969310i | \(-0.579064\pi\) | ||||
−0.245841 | + | 0.969310i | \(0.579064\pi\) | |||||||
\(180\) | 15.7981 | 1.17752 | ||||||||
\(181\) | 6.52787 | 0.485213 | 0.242606 | − | 0.970125i | \(-0.421998\pi\) | ||||
0.242606 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(182\) | −7.73968 | −0.573704 | ||||||||
\(183\) | 0.314338 | 0.0232365 | ||||||||
\(184\) | 44.6101 | 3.28870 | ||||||||
\(185\) | 9.37903 | 0.689560 | ||||||||
\(186\) | 3.76996 | 0.276427 | ||||||||
\(187\) | 3.37980 | 0.247156 | ||||||||
\(188\) | −11.4713 | −0.836633 | ||||||||
\(189\) | 3.98911 | 0.290165 | ||||||||
\(190\) | 6.48302 | 0.470328 | ||||||||
\(191\) | 0.270665 | 0.0195847 | 0.00979233 | − | 0.999952i | \(-0.496883\pi\) | ||||
0.00979233 | + | 0.999952i | \(0.496883\pi\) | |||||||
\(192\) | −15.6137 | −1.12682 | ||||||||
\(193\) | 14.1506 | 1.01858 | 0.509290 | − | 0.860595i | \(-0.329908\pi\) | ||||
0.509290 | + | 0.860595i | \(0.329908\pi\) | |||||||
\(194\) | 21.0200 | 1.50915 | ||||||||
\(195\) | 0.372907 | 0.0267044 | ||||||||
\(196\) | −13.9757 | −0.998265 | ||||||||
\(197\) | 4.32566 | 0.308190 | 0.154095 | − | 0.988056i | \(-0.450754\pi\) | ||||
0.154095 | + | 0.988056i | \(0.450754\pi\) | |||||||
\(198\) | 8.14591 | 0.578905 | ||||||||
\(199\) | −15.7244 | −1.11467 | −0.557336 | − | 0.830287i | \(-0.688176\pi\) | ||||
−0.557336 | + | 0.830287i | \(0.688176\pi\) | |||||||
\(200\) | 45.1816 | 3.19482 | ||||||||
\(201\) | −2.29686 | −0.162008 | ||||||||
\(202\) | −38.8330 | −2.73228 | ||||||||
\(203\) | 6.54363 | 0.459273 | ||||||||
\(204\) | −6.25078 | −0.437642 | ||||||||
\(205\) | −8.11772 | −0.566966 | ||||||||
\(206\) | −53.2985 | −3.71348 | ||||||||
\(207\) | 11.8688 | 0.824940 | ||||||||
\(208\) | 24.1618 | 1.67532 | ||||||||
\(209\) | 2.49477 | 0.172567 | ||||||||
\(210\) | −1.75664 | −0.121220 | ||||||||
\(211\) | −16.5499 | −1.13934 | −0.569672 | − | 0.821872i | \(-0.692930\pi\) | ||||
−0.569672 | + | 0.821872i | \(0.692930\pi\) | |||||||
\(212\) | 21.3179 | 1.46412 | ||||||||
\(213\) | 0.536315 | 0.0367477 | ||||||||
\(214\) | 11.9218 | 0.814957 | ||||||||
\(215\) | −6.06447 | −0.413593 | ||||||||
\(216\) | −20.2273 | −1.37629 | ||||||||
\(217\) | 9.18579 | 0.623572 | ||||||||
\(218\) | 10.1535 | 0.687682 | ||||||||
\(219\) | −3.09735 | −0.209299 | ||||||||
\(220\) | −5.44539 | −0.367128 | ||||||||
\(221\) | 4.33224 | 0.291418 | ||||||||
\(222\) | −8.94407 | −0.600286 | ||||||||
\(223\) | 7.41270 | 0.496391 | 0.248196 | − | 0.968710i | \(-0.420162\pi\) | ||||
0.248196 | + | 0.968710i | \(0.420162\pi\) | |||||||
\(224\) | −66.9185 | −4.47118 | ||||||||
\(225\) | 12.0209 | 0.801391 | ||||||||
\(226\) | 27.4331 | 1.82482 | ||||||||
\(227\) | −7.12725 | −0.473052 | −0.236526 | − | 0.971625i | \(-0.576009\pi\) | ||||
−0.236526 | + | 0.971625i | \(0.576009\pi\) | |||||||
\(228\) | −4.61396 | −0.305567 | ||||||||
\(229\) | −7.06659 | −0.466973 | −0.233487 | − | 0.972360i | \(-0.575014\pi\) | ||||
−0.233487 | + | 0.972360i | \(0.575014\pi\) | |||||||
\(230\) | −10.6311 | −0.700993 | ||||||||
\(231\) | −0.675983 | −0.0444764 | ||||||||
\(232\) | −33.1804 | −2.17840 | ||||||||
\(233\) | −8.29637 | −0.543514 | −0.271757 | − | 0.962366i | \(-0.587605\pi\) | ||||
−0.271757 | + | 0.962366i | \(0.587605\pi\) | |||||||
\(234\) | 10.4414 | 0.682578 | ||||||||
\(235\) | 1.80447 | 0.117711 | ||||||||
\(236\) | 87.0338 | 5.66542 | ||||||||
\(237\) | −0.307880 | −0.0199990 | ||||||||
\(238\) | −20.4077 | −1.32284 | ||||||||
\(239\) | 22.5856 | 1.46094 | 0.730470 | − | 0.682945i | \(-0.239301\pi\) | ||||
0.730470 | + | 0.682945i | \(0.239301\pi\) | |||||||
\(240\) | 5.48389 | 0.353984 | ||||||||
\(241\) | 25.6415 | 1.65171 | 0.825857 | − | 0.563880i | \(-0.190692\pi\) | ||||
0.825857 | + | 0.563880i | \(0.190692\pi\) | |||||||
\(242\) | −2.80778 | −0.180491 | ||||||||
\(243\) | −8.11748 | −0.520736 | ||||||||
\(244\) | −5.88364 | −0.376661 | ||||||||
\(245\) | 2.19842 | 0.140452 | ||||||||
\(246\) | 7.74125 | 0.493564 | ||||||||
\(247\) | 3.19780 | 0.203471 | ||||||||
\(248\) | −46.5778 | −2.95770 | ||||||||
\(249\) | 0.534778 | 0.0338901 | ||||||||
\(250\) | −23.7605 | −1.50274 | ||||||||
\(251\) | 8.82926 | 0.557298 | 0.278649 | − | 0.960393i | \(-0.410113\pi\) | ||||
0.278649 | + | 0.960393i | \(0.410113\pi\) | |||||||
\(252\) | −36.7081 | −2.31239 | ||||||||
\(253\) | −4.09102 | −0.257200 | ||||||||
\(254\) | −41.8275 | −2.62449 | ||||||||
\(255\) | 0.983266 | 0.0615745 | ||||||||
\(256\) | 117.507 | 7.34420 | ||||||||
\(257\) | −0.859825 | −0.0536344 | −0.0268172 | − | 0.999640i | \(-0.508537\pi\) | ||||
−0.0268172 | + | 0.999640i | \(0.508537\pi\) | |||||||
\(258\) | 5.78322 | 0.360047 | ||||||||
\(259\) | −21.7929 | −1.35414 | ||||||||
\(260\) | −6.97990 | −0.432875 | ||||||||
\(261\) | −8.82787 | −0.546431 | ||||||||
\(262\) | −14.5510 | −0.898963 | ||||||||
\(263\) | −25.3778 | −1.56486 | −0.782430 | − | 0.622739i | \(-0.786020\pi\) | ||||
−0.782430 | + | 0.622739i | \(0.786020\pi\) | |||||||
\(264\) | 3.42767 | 0.210958 | ||||||||
\(265\) | −3.35336 | −0.205996 | ||||||||
\(266\) | −15.0638 | −0.923619 | ||||||||
\(267\) | −5.39477 | −0.330155 | ||||||||
\(268\) | 42.9916 | 2.62613 | ||||||||
\(269\) | −20.8909 | −1.27374 | −0.636869 | − | 0.770972i | \(-0.719771\pi\) | ||||
−0.636869 | + | 0.770972i | \(0.719771\pi\) | |||||||
\(270\) | 4.82039 | 0.293360 | ||||||||
\(271\) | −9.70675 | −0.589643 | −0.294821 | − | 0.955552i | \(-0.595260\pi\) | ||||
−0.294821 | + | 0.955552i | \(0.595260\pi\) | |||||||
\(272\) | 63.7090 | 3.86293 | ||||||||
\(273\) | −0.866476 | −0.0524415 | ||||||||
\(274\) | −1.42398 | −0.0860259 | ||||||||
\(275\) | −4.14342 | −0.249858 | ||||||||
\(276\) | 7.56613 | 0.455428 | ||||||||
\(277\) | −13.9726 | −0.839533 | −0.419767 | − | 0.907632i | \(-0.637888\pi\) | ||||
−0.419767 | + | 0.907632i | \(0.637888\pi\) | |||||||
\(278\) | 32.6666 | 1.95921 | ||||||||
\(279\) | −12.3924 | −0.741911 | ||||||||
\(280\) | 21.7032 | 1.29702 | ||||||||
\(281\) | 24.9986 | 1.49129 | 0.745646 | − | 0.666343i | \(-0.232141\pi\) | ||||
0.745646 | + | 0.666343i | \(0.232141\pi\) | |||||||
\(282\) | −1.72079 | −0.102472 | ||||||||
\(283\) | −11.3548 | −0.674971 | −0.337486 | − | 0.941331i | \(-0.609576\pi\) | ||||
−0.337486 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(284\) | −10.0385 | −0.595676 | ||||||||
\(285\) | 0.725789 | 0.0429920 | ||||||||
\(286\) | −3.59902 | −0.212814 | ||||||||
\(287\) | 18.8621 | 1.11340 | ||||||||
\(288\) | 90.2782 | 5.31969 | ||||||||
\(289\) | −5.57692 | −0.328054 | ||||||||
\(290\) | 7.90725 | 0.464330 | ||||||||
\(291\) | 2.35324 | 0.137949 | ||||||||
\(292\) | 57.9748 | 3.39272 | ||||||||
\(293\) | −2.47923 | −0.144838 | −0.0724190 | − | 0.997374i | \(-0.523072\pi\) | ||||
−0.0724190 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(294\) | −2.09647 | −0.122268 | ||||||||
\(295\) | −13.6907 | −0.797102 | ||||||||
\(296\) | 110.504 | 6.42290 | ||||||||
\(297\) | 1.85497 | 0.107636 | ||||||||
\(298\) | −17.4802 | −1.01260 | ||||||||
\(299\) | −5.24387 | −0.303261 | ||||||||
\(300\) | 7.66305 | 0.442427 | ||||||||
\(301\) | 14.0912 | 0.812205 | ||||||||
\(302\) | −43.5041 | −2.50338 | ||||||||
\(303\) | −4.34745 | −0.249754 | ||||||||
\(304\) | 47.0263 | 2.69714 | ||||||||
\(305\) | 0.925514 | 0.0529948 | ||||||||
\(306\) | 27.5316 | 1.57388 | ||||||||
\(307\) | 9.35056 | 0.533665 | 0.266832 | − | 0.963743i | \(-0.414023\pi\) | ||||
0.266832 | + | 0.963743i | \(0.414023\pi\) | |||||||
\(308\) | 12.6528 | 0.720958 | ||||||||
\(309\) | −5.96690 | −0.339445 | ||||||||
\(310\) | 11.1000 | 0.630438 | ||||||||
\(311\) | −25.7183 | −1.45835 | −0.729175 | − | 0.684327i | \(-0.760096\pi\) | ||||
−0.729175 | + | 0.684327i | \(0.760096\pi\) | |||||||
\(312\) | 4.39359 | 0.248738 | ||||||||
\(313\) | 21.0513 | 1.18989 | 0.594944 | − | 0.803767i | \(-0.297174\pi\) | ||||
0.594944 | + | 0.803767i | \(0.297174\pi\) | |||||||
\(314\) | −16.1397 | −0.910818 | ||||||||
\(315\) | 5.77429 | 0.325345 | ||||||||
\(316\) | 5.76276 | 0.324181 | ||||||||
\(317\) | 11.2767 | 0.633362 | 0.316681 | − | 0.948532i | \(-0.397432\pi\) | ||||
0.316681 | + | 0.948532i | \(0.397432\pi\) | |||||||
\(318\) | 3.19785 | 0.179326 | ||||||||
\(319\) | 3.04284 | 0.170366 | ||||||||
\(320\) | −45.9718 | −2.56990 | ||||||||
\(321\) | 1.33467 | 0.0744942 | ||||||||
\(322\) | 24.7021 | 1.37659 | ||||||||
\(323\) | 8.43184 | 0.469160 | ||||||||
\(324\) | 47.7780 | 2.65433 | ||||||||
\(325\) | −5.31104 | −0.294604 | ||||||||
\(326\) | 56.9116 | 3.15204 | ||||||||
\(327\) | 1.13671 | 0.0628601 | ||||||||
\(328\) | −95.6430 | −5.28100 | ||||||||
\(329\) | −4.19283 | −0.231158 | ||||||||
\(330\) | −0.816851 | −0.0449662 | ||||||||
\(331\) | 8.75133 | 0.481016 | 0.240508 | − | 0.970647i | \(-0.422686\pi\) | ||||
0.240508 | + | 0.970647i | \(0.422686\pi\) | |||||||
\(332\) | −10.0097 | −0.549355 | ||||||||
\(333\) | 29.4003 | 1.61113 | ||||||||
\(334\) | 46.2662 | 2.53158 | ||||||||
\(335\) | −6.76272 | −0.369487 | ||||||||
\(336\) | −12.7422 | −0.695145 | ||||||||
\(337\) | −9.44596 | −0.514554 | −0.257277 | − | 0.966338i | \(-0.582825\pi\) | ||||
−0.257277 | + | 0.966338i | \(0.582825\pi\) | |||||||
\(338\) | 31.8879 | 1.73448 | ||||||||
\(339\) | 3.07120 | 0.166805 | ||||||||
\(340\) | −18.4043 | −0.998116 | ||||||||
\(341\) | 4.27147 | 0.231313 | ||||||||
\(342\) | 20.3222 | 1.09890 | ||||||||
\(343\) | −20.1617 | −1.08863 | ||||||||
\(344\) | −71.4515 | −3.85241 | ||||||||
\(345\) | −1.19018 | −0.0640769 | ||||||||
\(346\) | −25.3121 | −1.36079 | ||||||||
\(347\) | −33.9545 | −1.82277 | −0.911385 | − | 0.411554i | \(-0.864986\pi\) | ||||
−0.911385 | + | 0.411554i | \(0.864986\pi\) | |||||||
\(348\) | −5.62758 | −0.301670 | ||||||||
\(349\) | 14.7560 | 0.789869 | 0.394935 | − | 0.918709i | \(-0.370767\pi\) | ||||
0.394935 | + | 0.918709i | \(0.370767\pi\) | |||||||
\(350\) | 25.0185 | 1.33730 | ||||||||
\(351\) | 2.37770 | 0.126912 | ||||||||
\(352\) | −31.1176 | −1.65858 | ||||||||
\(353\) | 34.1765 | 1.81903 | 0.909516 | − | 0.415668i | \(-0.136452\pi\) | ||||
0.909516 | + | 0.415668i | \(0.136452\pi\) | |||||||
\(354\) | 13.0558 | 0.693906 | ||||||||
\(355\) | 1.57909 | 0.0838093 | ||||||||
\(356\) | 100.977 | 5.35177 | ||||||||
\(357\) | −2.28469 | −0.120919 | ||||||||
\(358\) | 18.4703 | 0.976187 | ||||||||
\(359\) | −21.4057 | −1.12975 | −0.564874 | − | 0.825177i | \(-0.691075\pi\) | ||||
−0.564874 | + | 0.825177i | \(0.691075\pi\) | |||||||
\(360\) | −29.2793 | −1.54316 | ||||||||
\(361\) | −12.7761 | −0.672427 | ||||||||
\(362\) | −18.3288 | −0.963342 | ||||||||
\(363\) | −0.314338 | −0.0164985 | ||||||||
\(364\) | 16.2183 | 0.850071 | ||||||||
\(365\) | −9.11961 | −0.477342 | ||||||||
\(366\) | −0.882592 | −0.0461338 | ||||||||
\(367\) | −17.5398 | −0.915569 | −0.457785 | − | 0.889063i | \(-0.651357\pi\) | ||||
−0.457785 | + | 0.889063i | \(0.651357\pi\) | |||||||
\(368\) | −77.1153 | −4.01991 | ||||||||
\(369\) | −25.4465 | −1.32469 | ||||||||
\(370\) | −26.3343 | −1.36905 | ||||||||
\(371\) | 7.79179 | 0.404529 | ||||||||
\(372\) | −7.89987 | −0.409589 | ||||||||
\(373\) | −25.2457 | −1.30717 | −0.653586 | − | 0.756852i | \(-0.726736\pi\) | ||||
−0.653586 | + | 0.756852i | \(0.726736\pi\) | |||||||
\(374\) | −9.48975 | −0.490703 | ||||||||
\(375\) | −2.66004 | −0.137364 | ||||||||
\(376\) | 21.2603 | 1.09642 | ||||||||
\(377\) | 3.90032 | 0.200876 | ||||||||
\(378\) | −11.2005 | −0.576094 | ||||||||
\(379\) | −37.0350 | −1.90236 | −0.951180 | − | 0.308636i | \(-0.900127\pi\) | ||||
−0.951180 | + | 0.308636i | \(0.900127\pi\) | |||||||
\(380\) | −13.5850 | −0.696896 | ||||||||
\(381\) | −4.68269 | −0.239901 | ||||||||
\(382\) | −0.759969 | −0.0388834 | ||||||||
\(383\) | −23.3312 | −1.19217 | −0.596085 | − | 0.802922i | \(-0.703278\pi\) | ||||
−0.596085 | + | 0.802922i | \(0.703278\pi\) | |||||||
\(384\) | 24.2769 | 1.23888 | ||||||||
\(385\) | −1.99032 | −0.101436 | ||||||||
\(386\) | −39.7317 | −2.02229 | ||||||||
\(387\) | −19.0102 | −0.966341 | ||||||||
\(388\) | −44.0469 | −2.23614 | ||||||||
\(389\) | −20.1435 | −1.02132 | −0.510658 | − | 0.859784i | \(-0.670598\pi\) | ||||
−0.510658 | + | 0.859784i | \(0.670598\pi\) | |||||||
\(390\) | −1.04704 | −0.0530189 | ||||||||
\(391\) | −13.8268 | −0.699253 | ||||||||
\(392\) | 25.9018 | 1.30824 | ||||||||
\(393\) | −1.62902 | −0.0821731 | ||||||||
\(394\) | −12.1455 | −0.611881 | ||||||||
\(395\) | −0.906500 | −0.0456110 | ||||||||
\(396\) | −17.0696 | −0.857778 | ||||||||
\(397\) | 31.2800 | 1.56990 | 0.784949 | − | 0.619561i | \(-0.212689\pi\) | ||||
0.784949 | + | 0.619561i | \(0.212689\pi\) | |||||||
\(398\) | 44.1506 | 2.21307 | ||||||||
\(399\) | −1.68642 | −0.0844268 | ||||||||
\(400\) | −78.1032 | −3.90516 | ||||||||
\(401\) | 7.49218 | 0.374142 | 0.187071 | − | 0.982346i | \(-0.440101\pi\) | ||||
0.187071 | + | 0.982346i | \(0.440101\pi\) | |||||||
\(402\) | 6.44908 | 0.321651 | ||||||||
\(403\) | 5.47517 | 0.272738 | ||||||||
\(404\) | 81.3736 | 4.04849 | ||||||||
\(405\) | −7.51563 | −0.373454 | ||||||||
\(406\) | −18.3731 | −0.911841 | ||||||||
\(407\) | −10.1339 | −0.502317 | ||||||||
\(408\) | 11.5848 | 0.573535 | ||||||||
\(409\) | −27.4150 | −1.35558 | −0.677792 | − | 0.735253i | \(-0.737063\pi\) | ||||
−0.677792 | + | 0.735253i | \(0.737063\pi\) | |||||||
\(410\) | 22.7928 | 1.12566 | ||||||||
\(411\) | −0.159418 | −0.00786352 | ||||||||
\(412\) | 111.686 | 5.50236 | ||||||||
\(413\) | 31.8113 | 1.56533 | ||||||||
\(414\) | −33.3251 | −1.63784 | ||||||||
\(415\) | 1.57456 | 0.0772922 | ||||||||
\(416\) | −39.8866 | −1.95560 | ||||||||
\(417\) | 3.65710 | 0.179089 | ||||||||
\(418\) | −7.00478 | −0.342615 | ||||||||
\(419\) | −7.28945 | −0.356113 | −0.178057 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178057 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(420\) | 3.68099 | 0.179614 | ||||||||
\(421\) | 11.5102 | 0.560972 | 0.280486 | − | 0.959858i | \(-0.409504\pi\) | ||||
0.280486 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(422\) | 46.4686 | 2.26206 | ||||||||
\(423\) | 5.65646 | 0.275026 | ||||||||
\(424\) | −39.5093 | −1.91874 | ||||||||
\(425\) | −14.0040 | −0.679292 | ||||||||
\(426\) | −1.50586 | −0.0729589 | ||||||||
\(427\) | −2.15050 | −0.104070 | ||||||||
\(428\) | −24.9818 | −1.20754 | ||||||||
\(429\) | −0.402918 | −0.0194531 | ||||||||
\(430\) | 17.0277 | 0.821148 | ||||||||
\(431\) | 32.4200 | 1.56161 | 0.780807 | − | 0.624772i | \(-0.214808\pi\) | ||||
0.780807 | + | 0.624772i | \(0.214808\pi\) | |||||||
\(432\) | 34.9660 | 1.68230 | ||||||||
\(433\) | 7.53054 | 0.361894 | 0.180947 | − | 0.983493i | \(-0.442084\pi\) | ||||
0.180947 | + | 0.983493i | \(0.442084\pi\) | |||||||
\(434\) | −25.7917 | −1.23804 | ||||||||
\(435\) | 0.885235 | 0.0424438 | ||||||||
\(436\) | −21.2764 | −1.01896 | ||||||||
\(437\) | −10.2062 | −0.488227 | ||||||||
\(438\) | 8.69667 | 0.415543 | ||||||||
\(439\) | −38.7914 | −1.85141 | −0.925705 | − | 0.378246i | \(-0.876527\pi\) | ||||
−0.925705 | + | 0.378246i | \(0.876527\pi\) | |||||||
\(440\) | 10.0922 | 0.481126 | ||||||||
\(441\) | 6.89135 | 0.328159 | ||||||||
\(442\) | −12.1640 | −0.578581 | ||||||||
\(443\) | −33.6344 | −1.59802 | −0.799008 | − | 0.601320i | \(-0.794642\pi\) | ||||
−0.799008 | + | 0.601320i | \(0.794642\pi\) | |||||||
\(444\) | 18.7421 | 0.889459 | ||||||||
\(445\) | −15.8840 | −0.752973 | ||||||||
\(446\) | −20.8132 | −0.985535 | ||||||||
\(447\) | −1.95695 | −0.0925604 | ||||||||
\(448\) | 106.819 | 5.04672 | ||||||||
\(449\) | 0.126699 | 0.00597931 | 0.00298966 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00298966 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(450\) | −33.7520 | −1.59108 | ||||||||
\(451\) | 8.77104 | 0.413012 | ||||||||
\(452\) | −57.4854 | −2.70389 | ||||||||
\(453\) | −4.87039 | −0.228831 | ||||||||
\(454\) | 20.0118 | 0.939198 | ||||||||
\(455\) | −2.55119 | −0.119602 | ||||||||
\(456\) | 8.55125 | 0.400449 | ||||||||
\(457\) | 32.4488 | 1.51789 | 0.758947 | − | 0.651153i | \(-0.225714\pi\) | ||||
0.758947 | + | 0.651153i | \(0.225714\pi\) | |||||||
\(458\) | 19.8414 | 0.927129 | ||||||||
\(459\) | 6.26943 | 0.292632 | ||||||||
\(460\) | 22.2772 | 1.03868 | ||||||||
\(461\) | −32.4994 | −1.51365 | −0.756825 | − | 0.653618i | \(-0.773250\pi\) | ||||
−0.756825 | + | 0.653618i | \(0.773250\pi\) | |||||||
\(462\) | 1.89801 | 0.0883036 | ||||||||
\(463\) | 14.2867 | 0.663958 | 0.331979 | − | 0.943287i | \(-0.392284\pi\) | ||||
0.331979 | + | 0.943287i | \(0.392284\pi\) | |||||||
\(464\) | 57.3573 | 2.66275 | ||||||||
\(465\) | 1.24267 | 0.0576276 | ||||||||
\(466\) | 23.2944 | 1.07909 | ||||||||
\(467\) | 35.9475 | 1.66345 | 0.831726 | − | 0.555187i | \(-0.187353\pi\) | ||||
0.831726 | + | 0.555187i | \(0.187353\pi\) | |||||||
\(468\) | −21.8798 | −1.01139 | ||||||||
\(469\) | 15.7137 | 0.725590 | ||||||||
\(470\) | −5.06657 | −0.233704 | ||||||||
\(471\) | −1.80688 | −0.0832567 | ||||||||
\(472\) | −161.304 | −7.42460 | ||||||||
\(473\) | 6.55254 | 0.301286 | ||||||||
\(474\) | 0.864460 | 0.0397059 | ||||||||
\(475\) | −10.3369 | −0.474290 | ||||||||
\(476\) | 42.7639 | 1.96008 | ||||||||
\(477\) | −10.5117 | −0.481299 | ||||||||
\(478\) | −63.4154 | −2.90055 | ||||||||
\(479\) | 17.5255 | 0.800762 | 0.400381 | − | 0.916349i | \(-0.368878\pi\) | ||||
0.400381 | + | 0.916349i | \(0.368878\pi\) | |||||||
\(480\) | −9.05286 | −0.413205 | ||||||||
\(481\) | −12.9896 | −0.592275 | ||||||||
\(482\) | −71.9957 | −3.27932 | ||||||||
\(483\) | 2.76546 | 0.125833 | ||||||||
\(484\) | 5.88364 | 0.267438 | ||||||||
\(485\) | 6.92872 | 0.314617 | ||||||||
\(486\) | 22.7921 | 1.03387 | ||||||||
\(487\) | 17.3183 | 0.784769 | 0.392384 | − | 0.919801i | \(-0.371650\pi\) | ||||
0.392384 | + | 0.919801i | \(0.371650\pi\) | |||||||
\(488\) | 10.9044 | 0.493619 | ||||||||
\(489\) | 6.37139 | 0.288124 | ||||||||
\(490\) | −6.17268 | −0.278853 | ||||||||
\(491\) | −18.0984 | −0.816768 | −0.408384 | − | 0.912810i | \(-0.633908\pi\) | ||||
−0.408384 | + | 0.912810i | \(0.633908\pi\) | |||||||
\(492\) | −16.2216 | −0.731326 | ||||||||
\(493\) | 10.2842 | 0.463177 | ||||||||
\(494\) | −8.97873 | −0.403972 | ||||||||
\(495\) | 2.68509 | 0.120686 | ||||||||
\(496\) | 80.5168 | 3.61531 | ||||||||
\(497\) | −3.66913 | −0.164583 | ||||||||
\(498\) | −1.50154 | −0.0672855 | ||||||||
\(499\) | 7.27284 | 0.325577 | 0.162788 | − | 0.986661i | \(-0.447951\pi\) | ||||
0.162788 | + | 0.986661i | \(0.447951\pi\) | |||||||
\(500\) | 49.7895 | 2.22665 | ||||||||
\(501\) | 5.17961 | 0.231408 | ||||||||
\(502\) | −24.7906 | −1.10646 | ||||||||
\(503\) | 21.3581 | 0.952312 | 0.476156 | − | 0.879361i | \(-0.342030\pi\) | ||||
0.476156 | + | 0.879361i | \(0.342030\pi\) | |||||||
\(504\) | 68.0327 | 3.03042 | ||||||||
\(505\) | −12.8003 | −0.569606 | ||||||||
\(506\) | 11.4867 | 0.510645 | ||||||||
\(507\) | 3.56993 | 0.158546 | ||||||||
\(508\) | 87.6485 | 3.88877 | ||||||||
\(509\) | −34.8721 | −1.54568 | −0.772840 | − | 0.634601i | \(-0.781165\pi\) | ||||
−0.772840 | + | 0.634601i | \(0.781165\pi\) | |||||||
\(510\) | −2.76080 | −0.122250 | ||||||||
\(511\) | 21.1901 | 0.937394 | ||||||||
\(512\) | −175.470 | −7.75477 | ||||||||
\(513\) | 4.62772 | 0.204319 | ||||||||
\(514\) | 2.41420 | 0.106486 | ||||||||
\(515\) | −17.5685 | −0.774161 | ||||||||
\(516\) | −12.1186 | −0.533491 | ||||||||
\(517\) | −1.94970 | −0.0857477 | ||||||||
\(518\) | 61.1896 | 2.68852 | ||||||||
\(519\) | −2.83375 | −0.124388 | ||||||||
\(520\) | 12.9362 | 0.567288 | ||||||||
\(521\) | 19.0611 | 0.835083 | 0.417541 | − | 0.908658i | \(-0.362892\pi\) | ||||
0.417541 | + | 0.908658i | \(0.362892\pi\) | |||||||
\(522\) | 24.7867 | 1.08489 | ||||||||
\(523\) | −3.89662 | −0.170387 | −0.0851936 | − | 0.996364i | \(-0.527151\pi\) | ||||
−0.0851936 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(524\) | 30.4912 | 1.33202 | ||||||||
\(525\) | 2.80089 | 0.122241 | ||||||||
\(526\) | 71.2552 | 3.10687 | ||||||||
\(527\) | 14.4367 | 0.628874 | ||||||||
\(528\) | −5.92524 | −0.257863 | ||||||||
\(529\) | −6.26357 | −0.272329 | ||||||||
\(530\) | 9.41551 | 0.408984 | ||||||||
\(531\) | −42.9159 | −1.86239 | ||||||||
\(532\) | 31.5658 | 1.36855 | ||||||||
\(533\) | 11.2427 | 0.486977 | ||||||||
\(534\) | 15.1473 | 0.655489 | ||||||||
\(535\) | 3.92972 | 0.169897 | ||||||||
\(536\) | −79.6783 | −3.44158 | ||||||||
\(537\) | 2.06780 | 0.0892320 | ||||||||
\(538\) | 58.6570 | 2.52888 | ||||||||
\(539\) | −2.37535 | −0.102314 | ||||||||
\(540\) | −10.1010 | −0.434679 | ||||||||
\(541\) | −12.8680 | −0.553240 | −0.276620 | − | 0.960979i | \(-0.589214\pi\) | ||||
−0.276620 | + | 0.960979i | \(0.589214\pi\) | |||||||
\(542\) | 27.2544 | 1.17068 | ||||||||
\(543\) | −2.05196 | −0.0880579 | ||||||||
\(544\) | −105.171 | −4.50919 | ||||||||
\(545\) | 3.34684 | 0.143363 | ||||||||
\(546\) | 2.43288 | 0.104117 | ||||||||
\(547\) | 34.3657 | 1.46937 | 0.734685 | − | 0.678408i | \(-0.237330\pi\) | ||||
0.734685 | + | 0.678408i | \(0.237330\pi\) | |||||||
\(548\) | 2.98392 | 0.127467 | ||||||||
\(549\) | 2.90119 | 0.123820 | ||||||||
\(550\) | 11.6338 | 0.496068 | ||||||||
\(551\) | 7.59120 | 0.323396 | ||||||||
\(552\) | −14.0226 | −0.596843 | ||||||||
\(553\) | 2.10632 | 0.0895698 | ||||||||
\(554\) | 39.2321 | 1.66681 | ||||||||
\(555\) | −2.94818 | −0.125143 | ||||||||
\(556\) | −68.4520 | −2.90301 | ||||||||
\(557\) | −12.3790 | −0.524514 | −0.262257 | − | 0.964998i | \(-0.584467\pi\) | ||||
−0.262257 | + | 0.964998i | \(0.584467\pi\) | |||||||
\(558\) | 34.7950 | 1.47299 | ||||||||
\(559\) | 8.39905 | 0.355242 | ||||||||
\(560\) | −37.5173 | −1.58540 | ||||||||
\(561\) | −1.06240 | −0.0448546 | ||||||||
\(562\) | −70.1906 | −2.96081 | ||||||||
\(563\) | 9.49421 | 0.400133 | 0.200067 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200067 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(564\) | 3.60587 | 0.151835 | ||||||||
\(565\) | 9.04263 | 0.380426 | ||||||||
\(566\) | 31.8817 | 1.34009 | ||||||||
\(567\) | 17.4631 | 0.733382 | ||||||||
\(568\) | 18.6048 | 0.780641 | ||||||||
\(569\) | 6.04259 | 0.253318 | 0.126659 | − | 0.991946i | \(-0.459575\pi\) | ||||
0.126659 | + | 0.991946i | \(0.459575\pi\) | |||||||
\(570\) | −2.03786 | −0.0853565 | ||||||||
\(571\) | −1.82447 | −0.0763518 | −0.0381759 | − | 0.999271i | \(-0.512155\pi\) | ||||
−0.0381759 | + | 0.999271i | \(0.512155\pi\) | |||||||
\(572\) | 7.54165 | 0.315332 | ||||||||
\(573\) | −0.0850803 | −0.00355428 | ||||||||
\(574\) | −52.9607 | −2.21054 | ||||||||
\(575\) | 16.9508 | 0.706898 | ||||||||
\(576\) | −144.107 | −6.00446 | ||||||||
\(577\) | 23.1142 | 0.962257 | 0.481128 | − | 0.876650i | \(-0.340227\pi\) | ||||
0.481128 | + | 0.876650i | \(0.340227\pi\) | |||||||
\(578\) | 15.6588 | 0.651320 | ||||||||
\(579\) | −4.44805 | −0.184855 | ||||||||
\(580\) | −16.5694 | −0.688009 | ||||||||
\(581\) | −3.65861 | −0.151785 | ||||||||
\(582\) | −6.60739 | −0.273885 | ||||||||
\(583\) | 3.62325 | 0.150059 | ||||||||
\(584\) | −107.447 | −4.44620 | ||||||||
\(585\) | 3.44175 | 0.142299 | ||||||||
\(586\) | 6.96113 | 0.287562 | ||||||||
\(587\) | 7.48479 | 0.308930 | 0.154465 | − | 0.987998i | \(-0.450635\pi\) | ||||
0.154465 | + | 0.987998i | \(0.450635\pi\) | |||||||
\(588\) | 4.39309 | 0.181168 | ||||||||
\(589\) | 10.6563 | 0.439087 | ||||||||
\(590\) | 38.4404 | 1.58257 | ||||||||
\(591\) | −1.35972 | −0.0559313 | ||||||||
\(592\) | −191.022 | −7.85098 | ||||||||
\(593\) | 32.3650 | 1.32907 | 0.664535 | − | 0.747257i | \(-0.268630\pi\) | ||||
0.664535 | + | 0.747257i | \(0.268630\pi\) | |||||||
\(594\) | −5.20834 | −0.213701 | ||||||||
\(595\) | −6.72688 | −0.275775 | ||||||||
\(596\) | 36.6293 | 1.50039 | ||||||||
\(597\) | 4.94276 | 0.202294 | ||||||||
\(598\) | 14.7236 | 0.602094 | ||||||||
\(599\) | −4.41532 | −0.180405 | −0.0902025 | − | 0.995923i | \(-0.528751\pi\) | ||||
−0.0902025 | + | 0.995923i | \(0.528751\pi\) | |||||||
\(600\) | −14.2023 | −0.579805 | ||||||||
\(601\) | 6.09179 | 0.248489 | 0.124245 | − | 0.992252i | \(-0.460349\pi\) | ||||
0.124245 | + | 0.992252i | \(0.460349\pi\) | |||||||
\(602\) | −39.5651 | −1.61255 | ||||||||
\(603\) | −21.1990 | −0.863288 | ||||||||
\(604\) | 91.1618 | 3.70932 | ||||||||
\(605\) | −0.925514 | −0.0376275 | ||||||||
\(606\) | 12.2067 | 0.495862 | ||||||||
\(607\) | −5.02420 | −0.203926 | −0.101963 | − | 0.994788i | \(-0.532512\pi\) | ||||
−0.101963 | + | 0.994788i | \(0.532512\pi\) | |||||||
\(608\) | −77.6314 | −3.14837 | ||||||||
\(609\) | −2.05691 | −0.0833502 | ||||||||
\(610\) | −2.59864 | −0.105216 | ||||||||
\(611\) | −2.49913 | −0.101104 | ||||||||
\(612\) | −57.6918 | −2.33205 | ||||||||
\(613\) | 24.6618 | 0.996081 | 0.498041 | − | 0.867154i | \(-0.334053\pi\) | ||||
0.498041 | + | 0.867154i | \(0.334053\pi\) | |||||||
\(614\) | −26.2543 | −1.05954 | ||||||||
\(615\) | 2.55171 | 0.102895 | ||||||||
\(616\) | −23.4499 | −0.944824 | ||||||||
\(617\) | −20.6110 | −0.829769 | −0.414884 | − | 0.909874i | \(-0.636178\pi\) | ||||
−0.414884 | + | 0.909874i | \(0.636178\pi\) | |||||||
\(618\) | 16.7537 | 0.673934 | ||||||||
\(619\) | −9.61501 | −0.386460 | −0.193230 | − | 0.981153i | \(-0.561896\pi\) | ||||
−0.193230 | + | 0.981153i | \(0.561896\pi\) | |||||||
\(620\) | −23.2598 | −0.934136 | ||||||||
\(621\) | −7.58870 | −0.304524 | ||||||||
\(622\) | 72.2113 | 2.89541 | ||||||||
\(623\) | 36.9076 | 1.47867 | ||||||||
\(624\) | −7.59498 | −0.304042 | ||||||||
\(625\) | 12.8851 | 0.515403 | ||||||||
\(626\) | −59.1073 | −2.36240 | ||||||||
\(627\) | −0.784201 | −0.0313180 | ||||||||
\(628\) | 33.8204 | 1.34958 | ||||||||
\(629\) | −34.2505 | −1.36566 | ||||||||
\(630\) | −16.2130 | −0.645939 | ||||||||
\(631\) | −5.13378 | −0.204372 | −0.102186 | − | 0.994765i | \(-0.532584\pi\) | ||||
−0.102186 | + | 0.994765i | \(0.532584\pi\) | |||||||
\(632\) | −10.6804 | −0.424843 | ||||||||
\(633\) | 5.20227 | 0.206772 | ||||||||
\(634\) | −31.6625 | −1.25748 | ||||||||
\(635\) | −13.7874 | −0.547135 | ||||||||
\(636\) | −6.70101 | −0.265712 | ||||||||
\(637\) | −3.04473 | −0.120636 | ||||||||
\(638\) | −8.54363 | −0.338246 | ||||||||
\(639\) | 4.94994 | 0.195817 | ||||||||
\(640\) | 71.4793 | 2.82547 | ||||||||
\(641\) | 29.1002 | 1.14939 | 0.574694 | − | 0.818368i | \(-0.305121\pi\) | ||||
0.574694 | + | 0.818368i | \(0.305121\pi\) | |||||||
\(642\) | −3.74747 | −0.147901 | ||||||||
\(643\) | 16.4391 | 0.648295 | 0.324148 | − | 0.946007i | \(-0.394923\pi\) | ||||
0.324148 | + | 0.946007i | \(0.394923\pi\) | |||||||
\(644\) | −51.7627 | −2.03973 | ||||||||
\(645\) | 1.90629 | 0.0750601 | ||||||||
\(646\) | −23.6748 | −0.931472 | ||||||||
\(647\) | −4.33767 | −0.170531 | −0.0852657 | − | 0.996358i | \(-0.527174\pi\) | ||||
−0.0852657 | + | 0.996358i | \(0.527174\pi\) | |||||||
\(648\) | −88.5491 | −3.47854 | ||||||||
\(649\) | 14.7925 | 0.580657 | ||||||||
\(650\) | 14.9123 | 0.584907 | ||||||||
\(651\) | −2.88744 | −0.113168 | ||||||||
\(652\) | −119.257 | −4.67046 | ||||||||
\(653\) | −10.1254 | −0.396237 | −0.198118 | − | 0.980178i | \(-0.563483\pi\) | ||||
−0.198118 | + | 0.980178i | \(0.563483\pi\) | |||||||
\(654\) | −3.19163 | −0.124803 | ||||||||
\(655\) | −4.79636 | −0.187409 | ||||||||
\(656\) | 165.333 | 6.45519 | ||||||||
\(657\) | −28.5871 | −1.11529 | ||||||||
\(658\) | 11.7726 | 0.458942 | ||||||||
\(659\) | 39.5009 | 1.53873 | 0.769367 | − | 0.638807i | \(-0.220572\pi\) | ||||
0.769367 | + | 0.638807i | \(0.220572\pi\) | |||||||
\(660\) | 1.71169 | 0.0666275 | ||||||||
\(661\) | −9.22386 | −0.358767 | −0.179383 | − | 0.983779i | \(-0.557410\pi\) | ||||
−0.179383 | + | 0.983779i | \(0.557410\pi\) | |||||||
\(662\) | −24.5718 | −0.955011 | ||||||||
\(663\) | −1.36179 | −0.0528874 | ||||||||
\(664\) | 18.5515 | 0.719937 | ||||||||
\(665\) | −4.96539 | −0.192550 | ||||||||
\(666\) | −82.5496 | −3.19873 | ||||||||
\(667\) | −12.4483 | −0.482001 | ||||||||
\(668\) | −96.9497 | −3.75110 | ||||||||
\(669\) | −2.33009 | −0.0900865 | ||||||||
\(670\) | 18.9882 | 0.733579 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 21.0350 | 0.811443 | ||||||||
\(673\) | 38.6270 | 1.48896 | 0.744481 | − | 0.667644i | \(-0.232697\pi\) | ||||
0.744481 | + | 0.667644i | \(0.232697\pi\) | |||||||
\(674\) | 26.5222 | 1.02160 | ||||||||
\(675\) | −7.68592 | −0.295831 | ||||||||
\(676\) | −66.8204 | −2.57002 | ||||||||
\(677\) | 40.8075 | 1.56836 | 0.784180 | − | 0.620534i | \(-0.213084\pi\) | ||||
0.784180 | + | 0.620534i | \(0.213084\pi\) | |||||||
\(678\) | −8.62326 | −0.331174 | ||||||||
\(679\) | −16.0994 | −0.617838 | ||||||||
\(680\) | 34.1096 | 1.30804 | ||||||||
\(681\) | 2.24036 | 0.0858509 | ||||||||
\(682\) | −11.9934 | −0.459249 | ||||||||
\(683\) | 35.7397 | 1.36754 | 0.683770 | − | 0.729698i | \(-0.260339\pi\) | ||||
0.683770 | + | 0.729698i | \(0.260339\pi\) | |||||||
\(684\) | −42.5847 | −1.62827 | ||||||||
\(685\) | −0.469380 | −0.0179341 | ||||||||
\(686\) | 56.6096 | 2.16137 | ||||||||
\(687\) | 2.22130 | 0.0847477 | ||||||||
\(688\) | 123.515 | 4.70896 | ||||||||
\(689\) | 4.64428 | 0.176933 | ||||||||
\(690\) | 3.34175 | 0.127218 | ||||||||
\(691\) | −45.6560 | −1.73684 | −0.868418 | − | 0.495833i | \(-0.834863\pi\) | ||||
−0.868418 | + | 0.495833i | \(0.834863\pi\) | |||||||
\(692\) | 53.0409 | 2.01631 | ||||||||
\(693\) | −6.23901 | −0.237000 | ||||||||
\(694\) | 95.3367 | 3.61893 | ||||||||
\(695\) | 10.7677 | 0.408443 | ||||||||
\(696\) | 10.4298 | 0.395342 | ||||||||
\(697\) | 29.6444 | 1.12286 | ||||||||
\(698\) | −41.4316 | −1.56821 | ||||||||
\(699\) | 2.60786 | 0.0986385 | ||||||||
\(700\) | −52.4258 | −1.98151 | ||||||||
\(701\) | −44.8562 | −1.69419 | −0.847097 | − | 0.531438i | \(-0.821652\pi\) | ||||
−0.847097 | + | 0.531438i | \(0.821652\pi\) | |||||||
\(702\) | −6.67606 | −0.251972 | ||||||||
\(703\) | −25.2817 | −0.953517 | ||||||||
\(704\) | 49.6717 | 1.87207 | ||||||||
\(705\) | −0.567215 | −0.0213625 | ||||||||
\(706\) | −95.9602 | −3.61151 | ||||||||
\(707\) | 29.7425 | 1.11858 | ||||||||
\(708\) | −27.3580 | −1.02818 | ||||||||
\(709\) | 36.1315 | 1.35695 | 0.678473 | − | 0.734626i | \(-0.262642\pi\) | ||||
0.678473 | + | 0.734626i | \(0.262642\pi\) | |||||||
\(710\) | −4.43373 | −0.166395 | ||||||||
\(711\) | −2.84159 | −0.106568 | ||||||||
\(712\) | −187.145 | −7.01356 | ||||||||
\(713\) | −17.4747 | −0.654431 | ||||||||
\(714\) | 6.41491 | 0.240072 | ||||||||
\(715\) | −1.18632 | −0.0443660 | ||||||||
\(716\) | −38.7041 | −1.44644 | ||||||||
\(717\) | −7.09950 | −0.265136 | ||||||||
\(718\) | 60.1024 | 2.24300 | ||||||||
\(719\) | 13.3034 | 0.496134 | 0.248067 | − | 0.968743i | \(-0.420205\pi\) | ||||
0.248067 | + | 0.968743i | \(0.420205\pi\) | |||||||
\(720\) | 50.6138 | 1.88626 | ||||||||
\(721\) | 40.8217 | 1.52028 | ||||||||
\(722\) | 35.8725 | 1.33504 | ||||||||
\(723\) | −8.06009 | −0.299758 | ||||||||
\(724\) | 38.4076 | 1.42741 | ||||||||
\(725\) | −12.6078 | −0.468241 | ||||||||
\(726\) | 0.882592 | 0.0327561 | ||||||||
\(727\) | 2.51921 | 0.0934324 | 0.0467162 | − | 0.998908i | \(-0.485124\pi\) | ||||
0.0467162 | + | 0.998908i | \(0.485124\pi\) | |||||||
\(728\) | −30.0581 | −1.11403 | ||||||||
\(729\) | −21.8098 | −0.807772 | ||||||||
\(730\) | 25.6059 | 0.947715 | ||||||||
\(731\) | 22.1463 | 0.819110 | ||||||||
\(732\) | 1.84945 | 0.0683576 | ||||||||
\(733\) | −43.4999 | −1.60671 | −0.803353 | − | 0.595503i | \(-0.796953\pi\) | ||||
−0.803353 | + | 0.595503i | \(0.796953\pi\) | |||||||
\(734\) | 49.2479 | 1.81777 | ||||||||
\(735\) | −0.691047 | −0.0254896 | ||||||||
\(736\) | 127.303 | 4.69244 | ||||||||
\(737\) | 7.30698 | 0.269156 | ||||||||
\(738\) | 71.4482 | 2.63004 | ||||||||
\(739\) | −3.09184 | −0.113735 | −0.0568675 | − | 0.998382i | \(-0.518111\pi\) | ||||
−0.0568675 | + | 0.998382i | \(0.518111\pi\) | |||||||
\(740\) | 55.1828 | 2.02856 | ||||||||
\(741\) | −1.00519 | −0.0369266 | ||||||||
\(742\) | −21.8776 | −0.803153 | ||||||||
\(743\) | −15.2046 | −0.557802 | −0.278901 | − | 0.960320i | \(-0.589970\pi\) | ||||
−0.278901 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(744\) | 14.6412 | 0.536771 | ||||||||
\(745\) | −5.76189 | −0.211099 | ||||||||
\(746\) | 70.8844 | 2.59526 | ||||||||
\(747\) | 4.93575 | 0.180590 | ||||||||
\(748\) | 19.8855 | 0.727087 | ||||||||
\(749\) | −9.13099 | −0.333639 | ||||||||
\(750\) | 7.46881 | 0.272723 | ||||||||
\(751\) | 36.4173 | 1.32889 | 0.664443 | − | 0.747339i | \(-0.268669\pi\) | ||||
0.664443 | + | 0.747339i | \(0.268669\pi\) | |||||||
\(752\) | −36.7517 | −1.34020 | ||||||||
\(753\) | −2.77537 | −0.101140 | ||||||||
\(754\) | −10.9512 | −0.398820 | ||||||||
\(755\) | −14.3400 | −0.521887 | ||||||||
\(756\) | 23.4705 | 0.853612 | ||||||||
\(757\) | −31.5613 | −1.14712 | −0.573558 | − | 0.819165i | \(-0.694437\pi\) | ||||
−0.573558 | + | 0.819165i | \(0.694437\pi\) | |||||||
\(758\) | 103.986 | 3.77695 | ||||||||
\(759\) | 1.28596 | 0.0466774 | ||||||||
\(760\) | 25.1777 | 0.913291 | ||||||||
\(761\) | −0.550823 | −0.0199673 | −0.00998365 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998365 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(762\) | 13.1480 | 0.476301 | ||||||||
\(763\) | −7.77664 | −0.281533 | ||||||||
\(764\) | 1.59250 | 0.0576145 | ||||||||
\(765\) | 9.07509 | 0.328111 | ||||||||
\(766\) | 65.5089 | 2.36693 | ||||||||
\(767\) | 18.9611 | 0.684644 | ||||||||
\(768\) | −36.9369 | −1.33285 | ||||||||
\(769\) | −11.4441 | −0.412684 | −0.206342 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206342 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(770\) | 5.58838 | 0.201391 | ||||||||
\(771\) | 0.270276 | 0.00973374 | ||||||||
\(772\) | 83.2567 | 2.99648 | ||||||||
\(773\) | 14.4160 | 0.518507 | 0.259254 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259254 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(774\) | 53.3764 | 1.91858 | ||||||||
\(775\) | −17.6985 | −0.635749 | ||||||||
\(776\) | 81.6342 | 2.93050 | ||||||||
\(777\) | 6.85032 | 0.245754 | ||||||||
\(778\) | 56.5585 | 2.02772 | ||||||||
\(779\) | 21.8818 | 0.783995 | ||||||||
\(780\) | 2.19405 | 0.0785595 | ||||||||
\(781\) | −1.70617 | −0.0610517 | ||||||||
\(782\) | 38.8227 | 1.38830 | ||||||||
\(783\) | 5.64437 | 0.201713 | ||||||||
\(784\) | −44.7752 | −1.59911 | ||||||||
\(785\) | −5.32005 | −0.189881 | ||||||||
\(786\) | 4.57393 | 0.163147 | ||||||||
\(787\) | −41.1337 | −1.46626 | −0.733128 | − | 0.680090i | \(-0.761941\pi\) | ||||
−0.733128 | + | 0.680090i | \(0.761941\pi\) | |||||||
\(788\) | 25.4506 | 0.906640 | ||||||||
\(789\) | 7.97719 | 0.283995 | ||||||||
\(790\) | 2.54525 | 0.0905561 | ||||||||
\(791\) | −21.0112 | −0.747072 | ||||||||
\(792\) | 31.6358 | 1.12413 | ||||||||
\(793\) | −1.28180 | −0.0455181 | ||||||||
\(794\) | −87.8274 | −3.11688 | ||||||||
\(795\) | 1.05409 | 0.0373847 | ||||||||
\(796\) | −92.5165 | −3.27916 | ||||||||
\(797\) | −9.03032 | −0.319870 | −0.159935 | − | 0.987128i | \(-0.551129\pi\) | ||||
−0.159935 | + | 0.987128i | \(0.551129\pi\) | |||||||
\(798\) | 4.73511 | 0.167621 | ||||||||
\(799\) | −6.58961 | −0.233124 | ||||||||
\(800\) | 128.934 | 4.55849 | ||||||||
\(801\) | −49.7912 | −1.75929 | ||||||||
\(802\) | −21.0364 | −0.742822 | ||||||||
\(803\) | 9.85356 | 0.347725 | ||||||||
\(804\) | −13.5139 | −0.476598 | ||||||||
\(805\) | 8.14242 | 0.286983 | ||||||||
\(806\) | −15.3731 | −0.541494 | ||||||||
\(807\) | 6.56679 | 0.231162 | ||||||||
\(808\) | −150.813 | −5.30559 | ||||||||
\(809\) | 31.6245 | 1.11186 | 0.555928 | − | 0.831230i | \(-0.312363\pi\) | ||||
0.555928 | + | 0.831230i | \(0.312363\pi\) | |||||||
\(810\) | 21.1022 | 0.741457 | ||||||||
\(811\) | 1.29817 | 0.0455850 | 0.0227925 | − | 0.999740i | \(-0.492744\pi\) | ||||
0.0227925 | + | 0.999740i | \(0.492744\pi\) | |||||||
\(812\) | 38.5003 | 1.35110 | ||||||||
\(813\) | 3.05120 | 0.107010 | ||||||||
\(814\) | 28.4537 | 0.997301 | ||||||||
\(815\) | 18.7595 | 0.657115 | ||||||||
\(816\) | −20.0261 | −0.701055 | ||||||||
\(817\) | 16.3471 | 0.571912 | ||||||||
\(818\) | 76.9754 | 2.69138 | ||||||||
\(819\) | −7.99717 | −0.279444 | ||||||||
\(820\) | −47.7617 | −1.66791 | ||||||||
\(821\) | 3.13968 | 0.109575 | 0.0547877 | − | 0.998498i | \(-0.482552\pi\) | ||||
0.0547877 | + | 0.998498i | \(0.482552\pi\) | |||||||
\(822\) | 0.447611 | 0.0156122 | ||||||||
\(823\) | −26.7530 | −0.932551 | −0.466276 | − | 0.884639i | \(-0.654404\pi\) | ||||
−0.466276 | + | 0.884639i | \(0.654404\pi\) | |||||||
\(824\) | −206.992 | −7.21091 | ||||||||
\(825\) | 1.30243 | 0.0453450 | ||||||||
\(826\) | −89.3192 | −3.10781 | ||||||||
\(827\) | −45.5079 | −1.58246 | −0.791232 | − | 0.611517i | \(-0.790560\pi\) | ||||
−0.791232 | + | 0.611517i | \(0.790560\pi\) | |||||||
\(828\) | 69.8319 | 2.42683 | ||||||||
\(829\) | −35.0823 | −1.21846 | −0.609230 | − | 0.792994i | \(-0.708521\pi\) | ||||
−0.609230 | + | 0.792994i | \(0.708521\pi\) | |||||||
\(830\) | −4.42102 | −0.153456 | ||||||||
\(831\) | 4.39212 | 0.152361 | ||||||||
\(832\) | 63.6692 | 2.20733 | ||||||||
\(833\) | −8.02822 | −0.278161 | ||||||||
\(834\) | −10.2683 | −0.355564 | ||||||||
\(835\) | 15.2505 | 0.527765 | ||||||||
\(836\) | 14.6783 | 0.507661 | ||||||||
\(837\) | 7.92344 | 0.273874 | ||||||||
\(838\) | 20.4672 | 0.707028 | ||||||||
\(839\) | −25.6791 | −0.886540 | −0.443270 | − | 0.896388i | \(-0.646182\pi\) | ||||
−0.443270 | + | 0.896388i | \(0.646182\pi\) | |||||||
\(840\) | −6.82214 | −0.235386 | ||||||||
\(841\) | −19.7411 | −0.680728 | ||||||||
\(842\) | −32.3181 | −1.11375 | ||||||||
\(843\) | −7.85800 | −0.270644 | ||||||||
\(844\) | −97.3738 | −3.35174 | ||||||||
\(845\) | 10.5110 | 0.361591 | ||||||||
\(846\) | −15.8821 | −0.546038 | ||||||||
\(847\) | 2.15050 | 0.0738920 | ||||||||
\(848\) | 68.2979 | 2.34536 | ||||||||
\(849\) | 3.56923 | 0.122496 | ||||||||
\(850\) | 39.3201 | 1.34867 | ||||||||
\(851\) | 41.4578 | 1.42116 | ||||||||
\(852\) | 3.15548 | 0.108105 | ||||||||
\(853\) | −46.7559 | −1.60089 | −0.800446 | − | 0.599405i | \(-0.795404\pi\) | ||||
−0.800446 | + | 0.599405i | \(0.795404\pi\) | |||||||
\(854\) | 6.03813 | 0.206621 | ||||||||
\(855\) | 6.69870 | 0.229091 | ||||||||
\(856\) | 46.2999 | 1.58250 | ||||||||
\(857\) | 34.3556 | 1.17357 | 0.586783 | − | 0.809744i | \(-0.300394\pi\) | ||||
0.586783 | + | 0.809744i | \(0.300394\pi\) | |||||||
\(858\) | 1.13131 | 0.0386222 | ||||||||
\(859\) | −10.8578 | −0.370463 | −0.185231 | − | 0.982695i | \(-0.559303\pi\) | ||||
−0.185231 | + | 0.982695i | \(0.559303\pi\) | |||||||
\(860\) | −35.6811 | −1.21672 | ||||||||
\(861\) | −5.92908 | −0.202062 | ||||||||
\(862\) | −91.0282 | −3.10043 | ||||||||
\(863\) | −15.5913 | −0.530733 | −0.265366 | − | 0.964148i | \(-0.585493\pi\) | ||||
−0.265366 | + | 0.964148i | \(0.585493\pi\) | |||||||
\(864\) | −57.7222 | −1.96375 | ||||||||
\(865\) | −8.34350 | −0.283687 | ||||||||
\(866\) | −21.1441 | −0.718506 | ||||||||
\(867\) | 1.75304 | 0.0595363 | ||||||||
\(868\) | 54.0459 | 1.83444 | ||||||||
\(869\) | 0.979456 | 0.0332258 | ||||||||
\(870\) | −2.48555 | −0.0842680 | ||||||||
\(871\) | 9.36610 | 0.317358 | ||||||||
\(872\) | 39.4325 | 1.33535 | ||||||||
\(873\) | 21.7193 | 0.735088 | ||||||||
\(874\) | 28.6567 | 0.969326 | ||||||||
\(875\) | 18.1983 | 0.615215 | ||||||||
\(876\) | −18.2237 | −0.615720 | ||||||||
\(877\) | −4.18657 | −0.141370 | −0.0706852 | − | 0.997499i | \(-0.522519\pi\) | ||||
−0.0706852 | + | 0.997499i | \(0.522519\pi\) | |||||||
\(878\) | 108.918 | 3.67579 | ||||||||
\(879\) | 0.779315 | 0.0262856 | ||||||||
\(880\) | −17.4459 | −0.588100 | ||||||||
\(881\) | 30.4025 | 1.02428 | 0.512142 | − | 0.858901i | \(-0.328852\pi\) | ||||
0.512142 | + | 0.858901i | \(0.328852\pi\) | |||||||
\(882\) | −19.3494 | −0.651528 | ||||||||
\(883\) | 19.6875 | 0.662538 | 0.331269 | − | 0.943536i | \(-0.392523\pi\) | ||||
0.331269 | + | 0.943536i | \(0.392523\pi\) | |||||||
\(884\) | 25.4893 | 0.857298 | ||||||||
\(885\) | 4.30350 | 0.144661 | ||||||||
\(886\) | 94.4379 | 3.17270 | ||||||||
\(887\) | 50.0134 | 1.67929 | 0.839643 | − | 0.543138i | \(-0.182764\pi\) | ||||
0.839643 | + | 0.543138i | \(0.182764\pi\) | |||||||
\(888\) | −34.7355 | −1.16565 | ||||||||
\(889\) | 32.0360 | 1.07445 | ||||||||
\(890\) | 44.5987 | 1.49495 | ||||||||
\(891\) | 8.12049 | 0.272047 | ||||||||
\(892\) | 43.6136 | 1.46029 | ||||||||
\(893\) | −4.86406 | −0.162770 | ||||||||
\(894\) | 5.49468 | 0.183769 | ||||||||
\(895\) | 6.08827 | 0.203509 | ||||||||
\(896\) | −166.087 | −5.54859 | ||||||||
\(897\) | 1.64835 | 0.0550367 | ||||||||
\(898\) | −0.355744 | −0.0118713 | ||||||||
\(899\) | 12.9974 | 0.433488 | ||||||||
\(900\) | 70.7264 | 2.35755 | ||||||||
\(901\) | 12.2459 | 0.407969 | ||||||||
\(902\) | −24.6272 | −0.819995 | ||||||||
\(903\) | −4.42941 | −0.147401 | ||||||||
\(904\) | 106.540 | 3.54348 | ||||||||
\(905\) | −6.04164 | −0.200831 | ||||||||
\(906\) | 13.6750 | 0.454321 | ||||||||
\(907\) | −31.0590 | −1.03130 | −0.515648 | − | 0.856801i | \(-0.672449\pi\) | ||||
−0.515648 | + | 0.856801i | \(0.672449\pi\) | |||||||
\(908\) | −41.9341 | −1.39163 | ||||||||
\(909\) | −40.1249 | −1.33086 | ||||||||
\(910\) | 7.16319 | 0.237457 | ||||||||
\(911\) | −30.0086 | −0.994231 | −0.497115 | − | 0.867684i | \(-0.665607\pi\) | ||||
−0.497115 | + | 0.867684i | \(0.665607\pi\) | |||||||
\(912\) | −14.7821 | −0.489485 | ||||||||
\(913\) | −1.70128 | −0.0563043 | ||||||||
\(914\) | −91.1093 | −3.01363 | ||||||||
\(915\) | −0.290924 | −0.00961765 | ||||||||
\(916\) | −41.5772 | −1.37375 | ||||||||
\(917\) | 11.1447 | 0.368031 | ||||||||
\(918\) | −17.6032 | −0.580992 | ||||||||
\(919\) | 50.0513 | 1.65104 | 0.825520 | − | 0.564373i | \(-0.190882\pi\) | ||||
0.825520 | + | 0.564373i | \(0.190882\pi\) | |||||||
\(920\) | −41.2873 | −1.36120 | ||||||||
\(921\) | −2.93924 | −0.0968511 | ||||||||
\(922\) | 91.2513 | 3.00520 | ||||||||
\(923\) | −2.18698 | −0.0719852 | ||||||||
\(924\) | −3.97724 | −0.130842 | ||||||||
\(925\) | 41.9889 | 1.38059 | ||||||||
\(926\) | −40.1139 | −1.31822 | ||||||||
\(927\) | −55.0717 | −1.80879 | ||||||||
\(928\) | −94.6860 | −3.10822 | ||||||||
\(929\) | −22.9587 | −0.753250 | −0.376625 | − | 0.926366i | \(-0.622915\pi\) | ||||
−0.376625 | + | 0.926366i | \(0.622915\pi\) | |||||||
\(930\) | −3.48915 | −0.114414 | ||||||||
\(931\) | −5.92596 | −0.194216 | ||||||||
\(932\) | −48.8129 | −1.59892 | ||||||||
\(933\) | 8.08423 | 0.264666 | ||||||||
\(934\) | −100.933 | −3.30262 | ||||||||
\(935\) | −3.12806 | −0.102298 | ||||||||
\(936\) | 40.5508 | 1.32544 | ||||||||
\(937\) | 11.9593 | 0.390693 | 0.195347 | − | 0.980734i | \(-0.437417\pi\) | ||||
0.195347 | + | 0.980734i | \(0.437417\pi\) | |||||||
\(938\) | −44.1205 | −1.44059 | ||||||||
\(939\) | −6.61721 | −0.215944 | ||||||||
\(940\) | 10.6169 | 0.346284 | ||||||||
\(941\) | −37.0349 | −1.20730 | −0.603651 | − | 0.797249i | \(-0.706288\pi\) | ||||
−0.603651 | + | 0.797249i | \(0.706288\pi\) | |||||||
\(942\) | 5.07333 | 0.165298 | ||||||||
\(943\) | −35.8825 | −1.16849 | ||||||||
\(944\) | 278.838 | 9.07540 | ||||||||
\(945\) | −3.69197 | −0.120100 | ||||||||
\(946\) | −18.3981 | −0.598174 | ||||||||
\(947\) | 19.8675 | 0.645607 | 0.322804 | − | 0.946466i | \(-0.395375\pi\) | ||||
0.322804 | + | 0.946466i | \(0.395375\pi\) | |||||||
\(948\) | −1.81145 | −0.0588333 | ||||||||
\(949\) | 12.6303 | 0.409997 | ||||||||
\(950\) | 29.0238 | 0.941655 | ||||||||
\(951\) | −3.54469 | −0.114944 | ||||||||
\(952\) | −79.2561 | −2.56871 | ||||||||
\(953\) | −53.6192 | −1.73690 | −0.868449 | − | 0.495779i | \(-0.834883\pi\) | ||||
−0.868449 | + | 0.495779i | \(0.834883\pi\) | |||||||
\(954\) | 29.5146 | 0.955572 | ||||||||
\(955\) | −0.250504 | −0.00810614 | ||||||||
\(956\) | 132.885 | 4.29782 | ||||||||
\(957\) | −0.956480 | −0.0309186 | ||||||||
\(958\) | −49.2079 | −1.58983 | ||||||||
\(959\) | 1.09064 | 0.0352185 | ||||||||
\(960\) | 14.4507 | 0.466394 | ||||||||
\(961\) | −12.7546 | −0.411437 | ||||||||
\(962\) | 36.4719 | 1.17590 | ||||||||
\(963\) | 12.3184 | 0.396955 | ||||||||
\(964\) | 150.865 | 4.85904 | ||||||||
\(965\) | −13.0965 | −0.421592 | ||||||||
\(966\) | −7.76481 | −0.249829 | ||||||||
\(967\) | 26.4148 | 0.849444 | 0.424722 | − | 0.905324i | \(-0.360372\pi\) | ||||
0.424722 | + | 0.905324i | \(0.360372\pi\) | |||||||
\(968\) | −10.9044 | −0.350481 | ||||||||
\(969\) | −2.65045 | −0.0851446 | ||||||||
\(970\) | −19.4543 | −0.624641 | ||||||||
\(971\) | −13.0181 | −0.417771 | −0.208886 | − | 0.977940i | \(-0.566984\pi\) | ||||
−0.208886 | + | 0.977940i | \(0.566984\pi\) | |||||||
\(972\) | −47.7603 | −1.53191 | ||||||||
\(973\) | −25.0196 | −0.802091 | ||||||||
\(974\) | −48.6261 | −1.55808 | ||||||||
\(975\) | 1.66946 | 0.0534656 | ||||||||
\(976\) | −18.8499 | −0.603371 | ||||||||
\(977\) | 31.6372 | 1.01216 | 0.506081 | − | 0.862486i | \(-0.331094\pi\) | ||||
0.506081 | + | 0.862486i | \(0.331094\pi\) | |||||||
\(978\) | −17.8895 | −0.572042 | ||||||||
\(979\) | 17.1623 | 0.548511 | ||||||||
\(980\) | 12.9347 | 0.413184 | ||||||||
\(981\) | 10.4913 | 0.334961 | ||||||||
\(982\) | 50.8163 | 1.62161 | ||||||||
\(983\) | 9.72173 | 0.310075 | 0.155037 | − | 0.987909i | \(-0.450450\pi\) | ||||
0.155037 | + | 0.987909i | \(0.450450\pi\) | |||||||
\(984\) | 30.0642 | 0.958412 | ||||||||
\(985\) | −4.00345 | −0.127561 | ||||||||
\(986\) | −28.8758 | −0.919593 | ||||||||
\(987\) | 1.31796 | 0.0419513 | ||||||||
\(988\) | 18.8147 | 0.598576 | ||||||||
\(989\) | −26.8065 | −0.852399 | ||||||||
\(990\) | −7.53916 | −0.239610 | ||||||||
\(991\) | −14.9500 | −0.474902 | −0.237451 | − | 0.971399i | \(-0.576312\pi\) | ||||
−0.237451 | + | 0.971399i | \(0.576312\pi\) | |||||||
\(992\) | −132.918 | −4.22015 | ||||||||
\(993\) | −2.75087 | −0.0872963 | ||||||||
\(994\) | 10.3021 | 0.326763 | ||||||||
\(995\) | 14.5531 | 0.461365 | ||||||||
\(996\) | 3.14644 | 0.0996987 | ||||||||
\(997\) | 24.9411 | 0.789893 | 0.394946 | − | 0.918704i | \(-0.370763\pi\) | ||||
0.394946 | + | 0.918704i | \(0.370763\pi\) | |||||||
\(998\) | −20.4205 | −0.646401 | ||||||||
\(999\) | −18.7980 | −0.594742 |
(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 | 671.2.a.c.1.1 | ✓ | 19 | |
3.2 | odd | 2 | 6039.2.a.k.1.19 | 19 | |||
11.10 | odd | 2 | 7381.2.a.i.1.19 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.c.1.1 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6039.2.a.k.1.19 | 19 | 3.2 | odd | 2 | |||
7381.2.a.i.1.19 | 19 | 11.10 | odd | 2 |