Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-1.90109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90109 | 1.34427 | 0.672137 | − | 0.740427i | \(-0.265377\pi\) | ||||
0.672137 | + | 0.740427i | \(0.265377\pi\) | |||||||
\(3\) | −2.82058 | −1.62846 | −0.814231 | − | 0.580542i | \(-0.802841\pi\) | ||||
−0.814231 | + | 0.580542i | \(0.802841\pi\) | |||||||
\(4\) | 1.61414 | 0.807072 | ||||||||
\(5\) | −3.37266 | −1.50830 | −0.754150 | − | 0.656703i | \(-0.771951\pi\) | ||||
−0.754150 | + | 0.656703i | \(0.771951\pi\) | |||||||
\(6\) | −5.36217 | −2.18910 | ||||||||
\(7\) | −1.68862 | −0.638237 | −0.319118 | − | 0.947715i | \(-0.603387\pi\) | ||||
−0.319118 | + | 0.947715i | \(0.603387\pi\) | |||||||
\(8\) | −0.733548 | −0.259348 | ||||||||
\(9\) | 4.95566 | 1.65189 | ||||||||
\(10\) | −6.41173 | −2.02757 | ||||||||
\(11\) | −2.68837 | −0.810573 | −0.405287 | − | 0.914190i | \(-0.632828\pi\) | ||||
−0.405287 | + | 0.914190i | \(0.632828\pi\) | |||||||
\(12\) | −4.55282 | −1.31428 | ||||||||
\(13\) | −1.63521 | −0.453525 | −0.226763 | − | 0.973950i | \(-0.572814\pi\) | ||||
−0.226763 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(14\) | −3.21021 | −0.857965 | ||||||||
\(15\) | 9.51285 | 2.45621 | ||||||||
\(16\) | −4.62283 | −1.15571 | ||||||||
\(17\) | 0.886205 | 0.214936 | 0.107468 | − | 0.994209i | \(-0.465726\pi\) | ||||
0.107468 | + | 0.994209i | \(0.465726\pi\) | |||||||
\(18\) | 9.42115 | 2.22059 | ||||||||
\(19\) | −0.0521266 | −0.0119587 | −0.00597933 | − | 0.999982i | \(-0.501903\pi\) | ||||
−0.00597933 | + | 0.999982i | \(0.501903\pi\) | |||||||
\(20\) | −5.44396 | −1.21731 | ||||||||
\(21\) | 4.76287 | 1.03934 | ||||||||
\(22\) | −5.11083 | −1.08963 | ||||||||
\(23\) | −6.14849 | −1.28205 | −0.641024 | − | 0.767521i | \(-0.721490\pi\) | ||||
−0.641024 | + | 0.767521i | \(0.721490\pi\) | |||||||
\(24\) | 2.06903 | 0.422339 | ||||||||
\(25\) | 6.37484 | 1.27497 | ||||||||
\(26\) | −3.10868 | −0.609662 | ||||||||
\(27\) | −5.51609 | −1.06157 | ||||||||
\(28\) | −2.72567 | −0.515103 | ||||||||
\(29\) | −2.73270 | −0.507450 | −0.253725 | − | 0.967276i | \(-0.581656\pi\) | ||||
−0.253725 | + | 0.967276i | \(0.581656\pi\) | |||||||
\(30\) | 18.0848 | 3.30181 | ||||||||
\(31\) | 8.21703 | 1.47582 | 0.737911 | − | 0.674898i | \(-0.235812\pi\) | ||||
0.737911 | + | 0.674898i | \(0.235812\pi\) | |||||||
\(32\) | −7.32132 | −1.29424 | ||||||||
\(33\) | 7.58275 | 1.31999 | ||||||||
\(34\) | 1.68476 | 0.288933 | ||||||||
\(35\) | 5.69513 | 0.962652 | ||||||||
\(36\) | 7.99914 | 1.33319 | ||||||||
\(37\) | −0.691432 | −0.113671 | −0.0568354 | − | 0.998384i | \(-0.518101\pi\) | ||||
−0.0568354 | + | 0.998384i | \(0.518101\pi\) | |||||||
\(38\) | −0.0990973 | −0.0160757 | ||||||||
\(39\) | 4.61223 | 0.738548 | ||||||||
\(40\) | 2.47401 | 0.391175 | ||||||||
\(41\) | 8.95440 | 1.39844 | 0.699221 | − | 0.714905i | \(-0.253530\pi\) | ||||
0.699221 | + | 0.714905i | \(0.253530\pi\) | |||||||
\(42\) | 9.05465 | 1.39716 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −4.33941 | −0.654191 | ||||||||
\(45\) | −16.7138 | −2.49154 | ||||||||
\(46\) | −11.6888 | −1.72342 | ||||||||
\(47\) | 9.18009 | 1.33905 | 0.669527 | − | 0.742788i | \(-0.266497\pi\) | ||||
0.669527 | + | 0.742788i | \(0.266497\pi\) | |||||||
\(48\) | 13.0390 | 1.88202 | ||||||||
\(49\) | −4.14857 | −0.592654 | ||||||||
\(50\) | 12.1191 | 1.71390 | ||||||||
\(51\) | −2.49961 | −0.350016 | ||||||||
\(52\) | −2.63946 | −0.366027 | ||||||||
\(53\) | −4.71607 | −0.647801 | −0.323901 | − | 0.946091i | \(-0.604994\pi\) | ||||
−0.323901 | + | 0.946091i | \(0.604994\pi\) | |||||||
\(54\) | −10.4866 | −1.42704 | ||||||||
\(55\) | 9.06695 | 1.22259 | ||||||||
\(56\) | 1.23868 | 0.165526 | ||||||||
\(57\) | 0.147027 | 0.0194742 | ||||||||
\(58\) | −5.19511 | −0.682152 | ||||||||
\(59\) | 11.3107 | 1.47252 | 0.736262 | − | 0.676697i | \(-0.236589\pi\) | ||||
0.736262 | + | 0.676697i | \(0.236589\pi\) | |||||||
\(60\) | 15.3551 | 1.98234 | ||||||||
\(61\) | −9.69602 | −1.24145 | −0.620724 | − | 0.784029i | \(-0.713161\pi\) | ||||
−0.620724 | + | 0.784029i | \(0.713161\pi\) | |||||||
\(62\) | 15.6213 | 1.98391 | ||||||||
\(63\) | −8.36821 | −1.05429 | ||||||||
\(64\) | −4.67282 | −0.584103 | ||||||||
\(65\) | 5.51500 | 0.684052 | ||||||||
\(66\) | 14.4155 | 1.77442 | ||||||||
\(67\) | −5.11532 | −0.624935 | −0.312468 | − | 0.949928i | \(-0.601156\pi\) | ||||
−0.312468 | + | 0.949928i | \(0.601156\pi\) | |||||||
\(68\) | 1.43046 | 0.173469 | ||||||||
\(69\) | 17.3423 | 2.08777 | ||||||||
\(70\) | 10.8270 | 1.29407 | ||||||||
\(71\) | 8.68000 | 1.03013 | 0.515063 | − | 0.857152i | \(-0.327769\pi\) | ||||
0.515063 | + | 0.857152i | \(0.327769\pi\) | |||||||
\(72\) | −3.63521 | −0.428414 | ||||||||
\(73\) | −7.27808 | −0.851834 | −0.425917 | − | 0.904762i | \(-0.640048\pi\) | ||||
−0.425917 | + | 0.904762i | \(0.640048\pi\) | |||||||
\(74\) | −1.31447 | −0.152805 | ||||||||
\(75\) | −17.9807 | −2.07623 | ||||||||
\(76\) | −0.0841398 | −0.00965150 | ||||||||
\(77\) | 4.53962 | 0.517338 | ||||||||
\(78\) | 8.76827 | 0.992811 | ||||||||
\(79\) | 4.37248 | 0.491942 | 0.245971 | − | 0.969277i | \(-0.420893\pi\) | ||||
0.245971 | + | 0.969277i | \(0.420893\pi\) | |||||||
\(80\) | 15.5912 | 1.74315 | ||||||||
\(81\) | 0.691576 | 0.0768418 | ||||||||
\(82\) | 17.0231 | 1.87989 | ||||||||
\(83\) | 14.6813 | 1.61148 | 0.805740 | − | 0.592269i | \(-0.201768\pi\) | ||||
0.805740 | + | 0.592269i | \(0.201768\pi\) | |||||||
\(84\) | 7.68796 | 0.838825 | ||||||||
\(85\) | −2.98887 | −0.324188 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.70780 | 0.826363 | ||||||||
\(88\) | 1.97205 | 0.210221 | ||||||||
\(89\) | 8.65498 | 0.917426 | 0.458713 | − | 0.888584i | \(-0.348311\pi\) | ||||
0.458713 | + | 0.888584i | \(0.348311\pi\) | |||||||
\(90\) | −31.7743 | −3.34931 | ||||||||
\(91\) | 2.76124 | 0.289457 | ||||||||
\(92\) | −9.92454 | −1.03470 | ||||||||
\(93\) | −23.1768 | −2.40332 | ||||||||
\(94\) | 17.4522 | 1.80006 | ||||||||
\(95\) | 0.175805 | 0.0180372 | ||||||||
\(96\) | 20.6503 | 2.10762 | ||||||||
\(97\) | −12.9655 | −1.31645 | −0.658224 | − | 0.752822i | \(-0.728692\pi\) | ||||
−0.658224 | + | 0.752822i | \(0.728692\pi\) | |||||||
\(98\) | −7.88681 | −0.796689 | ||||||||
\(99\) | −13.3226 | −1.33897 | ||||||||
\(100\) | 10.2899 | 1.02899 | ||||||||
\(101\) | −14.5701 | −1.44978 | −0.724892 | − | 0.688863i | \(-0.758110\pi\) | ||||
−0.724892 | + | 0.688863i | \(0.758110\pi\) | |||||||
\(102\) | −4.75199 | −0.470517 | ||||||||
\(103\) | 3.37055 | 0.332110 | 0.166055 | − | 0.986116i | \(-0.446897\pi\) | ||||
0.166055 | + | 0.986116i | \(0.446897\pi\) | |||||||
\(104\) | 1.19950 | 0.117621 | ||||||||
\(105\) | −16.0636 | −1.56764 | ||||||||
\(106\) | −8.96566 | −0.870822 | ||||||||
\(107\) | −7.76033 | −0.750219 | −0.375110 | − | 0.926980i | \(-0.622395\pi\) | ||||
−0.375110 | + | 0.926980i | \(0.622395\pi\) | |||||||
\(108\) | −8.90375 | −0.856764 | ||||||||
\(109\) | 8.28134 | 0.793209 | 0.396604 | − | 0.917990i | \(-0.370188\pi\) | ||||
0.396604 | + | 0.917990i | \(0.370188\pi\) | |||||||
\(110\) | 17.2371 | 1.64349 | ||||||||
\(111\) | 1.95024 | 0.185108 | ||||||||
\(112\) | 7.80618 | 0.737615 | ||||||||
\(113\) | 2.07646 | 0.195337 | 0.0976683 | − | 0.995219i | \(-0.468862\pi\) | ||||
0.0976683 | + | 0.995219i | \(0.468862\pi\) | |||||||
\(114\) | 0.279512 | 0.0261787 | ||||||||
\(115\) | 20.7368 | 1.93371 | ||||||||
\(116\) | −4.41097 | −0.409548 | ||||||||
\(117\) | −8.10353 | −0.749172 | ||||||||
\(118\) | 21.5026 | 1.97947 | ||||||||
\(119\) | −1.49646 | −0.137180 | ||||||||
\(120\) | −6.97813 | −0.637014 | ||||||||
\(121\) | −3.77268 | −0.342971 | ||||||||
\(122\) | −18.4330 | −1.66885 | ||||||||
\(123\) | −25.2566 | −2.27731 | ||||||||
\(124\) | 13.2635 | 1.19109 | ||||||||
\(125\) | −4.63685 | −0.414733 | ||||||||
\(126\) | −15.9087 | −1.41726 | ||||||||
\(127\) | −11.2912 | −1.00193 | −0.500964 | − | 0.865468i | \(-0.667021\pi\) | ||||
−0.500964 | + | 0.865468i | \(0.667021\pi\) | |||||||
\(128\) | 5.75917 | 0.509044 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.4845 | 0.919553 | ||||||||
\(131\) | −11.7393 | −1.02567 | −0.512834 | − | 0.858488i | \(-0.671404\pi\) | ||||
−0.512834 | + | 0.858488i | \(0.671404\pi\) | |||||||
\(132\) | 12.2396 | 1.06532 | ||||||||
\(133\) | 0.0880218 | 0.00763246 | ||||||||
\(134\) | −9.72468 | −0.840084 | ||||||||
\(135\) | 18.6039 | 1.60117 | ||||||||
\(136\) | −0.650074 | −0.0557434 | ||||||||
\(137\) | −2.98373 | −0.254917 | −0.127459 | − | 0.991844i | \(-0.540682\pi\) | ||||
−0.127459 | + | 0.991844i | \(0.540682\pi\) | |||||||
\(138\) | 32.9693 | 2.80653 | ||||||||
\(139\) | −9.87911 | −0.837935 | −0.418968 | − | 0.908001i | \(-0.637608\pi\) | ||||
−0.418968 | + | 0.908001i | \(0.637608\pi\) | |||||||
\(140\) | 9.19275 | 0.776930 | ||||||||
\(141\) | −25.8932 | −2.18060 | ||||||||
\(142\) | 16.5015 | 1.38477 | ||||||||
\(143\) | 4.39604 | 0.367615 | ||||||||
\(144\) | −22.9092 | −1.90910 | ||||||||
\(145\) | 9.21647 | 0.765386 | ||||||||
\(146\) | −13.8363 | −1.14510 | ||||||||
\(147\) | 11.7014 | 0.965113 | ||||||||
\(148\) | −1.11607 | −0.0917404 | ||||||||
\(149\) | 23.8152 | 1.95102 | 0.975510 | − | 0.219955i | \(-0.0705909\pi\) | ||||
0.975510 | + | 0.219955i | \(0.0705909\pi\) | |||||||
\(150\) | −34.1830 | −2.79103 | ||||||||
\(151\) | 11.9409 | 0.971734 | 0.485867 | − | 0.874033i | \(-0.338504\pi\) | ||||
0.485867 | + | 0.874033i | \(0.338504\pi\) | |||||||
\(152\) | 0.0382374 | 0.00310146 | ||||||||
\(153\) | 4.39173 | 0.355050 | ||||||||
\(154\) | 8.63023 | 0.695444 | ||||||||
\(155\) | −27.7132 | −2.22598 | ||||||||
\(156\) | 7.44480 | 0.596061 | ||||||||
\(157\) | 4.48669 | 0.358077 | 0.179039 | − | 0.983842i | \(-0.442701\pi\) | ||||
0.179039 | + | 0.983842i | \(0.442701\pi\) | |||||||
\(158\) | 8.31248 | 0.661305 | ||||||||
\(159\) | 13.3020 | 1.05492 | ||||||||
\(160\) | 24.6923 | 1.95210 | ||||||||
\(161\) | 10.3824 | 0.818251 | ||||||||
\(162\) | 1.31475 | 0.103296 | ||||||||
\(163\) | 2.85903 | 0.223937 | 0.111968 | − | 0.993712i | \(-0.464284\pi\) | ||||
0.111968 | + | 0.993712i | \(0.464284\pi\) | |||||||
\(164\) | 14.4537 | 1.12864 | ||||||||
\(165\) | −25.5740 | −1.99094 | ||||||||
\(166\) | 27.9104 | 2.16627 | ||||||||
\(167\) | −1.92534 | −0.148988 | −0.0744938 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744938 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(168\) | −3.49380 | −0.269552 | ||||||||
\(169\) | −10.3261 | −0.794315 | ||||||||
\(170\) | −5.68211 | −0.435798 | ||||||||
\(171\) | −0.258322 | −0.0197543 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.98860 | 0.227219 | 0.113610 | − | 0.993525i | \(-0.463759\pi\) | ||||
0.113610 | + | 0.993525i | \(0.463759\pi\) | |||||||
\(174\) | 14.6532 | 1.11086 | ||||||||
\(175\) | −10.7647 | −0.813731 | ||||||||
\(176\) | 12.4279 | 0.936785 | ||||||||
\(177\) | −31.9026 | −2.39795 | ||||||||
\(178\) | 16.4539 | 1.23327 | ||||||||
\(179\) | 4.40660 | 0.329364 | 0.164682 | − | 0.986347i | \(-0.447340\pi\) | ||||
0.164682 | + | 0.986347i | \(0.447340\pi\) | |||||||
\(180\) | −26.9784 | −2.01085 | ||||||||
\(181\) | −25.4863 | −1.89438 | −0.947191 | − | 0.320670i | \(-0.896092\pi\) | ||||
−0.947191 | + | 0.320670i | \(0.896092\pi\) | |||||||
\(182\) | 5.24936 | 0.389109 | ||||||||
\(183\) | 27.3484 | 2.02165 | ||||||||
\(184\) | 4.51021 | 0.332497 | ||||||||
\(185\) | 2.33197 | 0.171449 | ||||||||
\(186\) | −44.0611 | −3.23072 | ||||||||
\(187\) | −2.38245 | −0.174222 | ||||||||
\(188\) | 14.8180 | 1.08071 | ||||||||
\(189\) | 9.31455 | 0.677534 | ||||||||
\(190\) | 0.334222 | 0.0242470 | ||||||||
\(191\) | −1.62590 | −0.117646 | −0.0588231 | − | 0.998268i | \(-0.518735\pi\) | ||||
−0.0588231 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(192\) | 13.1801 | 0.951189 | ||||||||
\(193\) | −6.53242 | −0.470214 | −0.235107 | − | 0.971969i | \(-0.575544\pi\) | ||||
−0.235107 | + | 0.971969i | \(0.575544\pi\) | |||||||
\(194\) | −24.6486 | −1.76967 | ||||||||
\(195\) | −15.5555 | −1.11395 | ||||||||
\(196\) | −6.69639 | −0.478314 | ||||||||
\(197\) | 11.6943 | 0.833183 | 0.416592 | − | 0.909094i | \(-0.363225\pi\) | ||||
0.416592 | + | 0.909094i | \(0.363225\pi\) | |||||||
\(198\) | −25.3275 | −1.79995 | ||||||||
\(199\) | 7.38810 | 0.523729 | 0.261864 | − | 0.965105i | \(-0.415663\pi\) | ||||
0.261864 | + | 0.965105i | \(0.415663\pi\) | |||||||
\(200\) | −4.67625 | −0.330661 | ||||||||
\(201\) | 14.4281 | 1.01768 | ||||||||
\(202\) | −27.6992 | −1.94891 | ||||||||
\(203\) | 4.61448 | 0.323873 | ||||||||
\(204\) | −4.03473 | −0.282488 | ||||||||
\(205\) | −30.2002 | −2.10927 | ||||||||
\(206\) | 6.40772 | 0.446447 | ||||||||
\(207\) | −30.4698 | −2.11780 | ||||||||
\(208\) | 7.55929 | 0.524142 | ||||||||
\(209\) | 0.140135 | 0.00969337 | ||||||||
\(210\) | −30.5383 | −2.10734 | ||||||||
\(211\) | −14.1914 | −0.976975 | −0.488488 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488488 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(212\) | −7.61241 | −0.522822 | ||||||||
\(213\) | −24.4826 | −1.67752 | ||||||||
\(214\) | −14.7531 | −1.00850 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.04632 | 0.275317 | ||||||||
\(217\) | −13.8754 | −0.941924 | ||||||||
\(218\) | 15.7436 | 1.06629 | ||||||||
\(219\) | 20.5284 | 1.38718 | ||||||||
\(220\) | 14.6354 | 0.986715 | ||||||||
\(221\) | −1.44913 | −0.0974791 | ||||||||
\(222\) | 3.70758 | 0.248836 | ||||||||
\(223\) | 3.46847 | 0.232266 | 0.116133 | − | 0.993234i | \(-0.462950\pi\) | ||||
0.116133 | + | 0.993234i | \(0.462950\pi\) | |||||||
\(224\) | 12.3629 | 0.826031 | ||||||||
\(225\) | 31.5915 | 2.10610 | ||||||||
\(226\) | 3.94753 | 0.262586 | ||||||||
\(227\) | −17.4816 | −1.16029 | −0.580147 | − | 0.814512i | \(-0.697005\pi\) | ||||
−0.580147 | + | 0.814512i | \(0.697005\pi\) | |||||||
\(228\) | 0.237323 | 0.0157171 | ||||||||
\(229\) | 13.9382 | 0.921063 | 0.460531 | − | 0.887643i | \(-0.347659\pi\) | ||||
0.460531 | + | 0.887643i | \(0.347659\pi\) | |||||||
\(230\) | 39.4224 | 2.59944 | ||||||||
\(231\) | −12.8044 | −0.842465 | ||||||||
\(232\) | 2.00457 | 0.131606 | ||||||||
\(233\) | −23.2023 | −1.52004 | −0.760018 | − | 0.649902i | \(-0.774810\pi\) | ||||
−0.760018 | + | 0.649902i | \(0.774810\pi\) | |||||||
\(234\) | −15.4055 | −1.00709 | ||||||||
\(235\) | −30.9613 | −2.01969 | ||||||||
\(236\) | 18.2570 | 1.18843 | ||||||||
\(237\) | −12.3329 | −0.801109 | ||||||||
\(238\) | −2.84491 | −0.184408 | ||||||||
\(239\) | 11.5715 | 0.748497 | 0.374248 | − | 0.927328i | \(-0.377901\pi\) | ||||
0.374248 | + | 0.927328i | \(0.377901\pi\) | |||||||
\(240\) | −43.9763 | −2.83866 | ||||||||
\(241\) | 29.1016 | 1.87460 | 0.937298 | − | 0.348528i | \(-0.113318\pi\) | ||||
0.937298 | + | 0.348528i | \(0.113318\pi\) | |||||||
\(242\) | −7.17221 | −0.461047 | ||||||||
\(243\) | 14.5976 | 0.936438 | ||||||||
\(244\) | −15.6508 | −1.00194 | ||||||||
\(245\) | 13.9917 | 0.893899 | ||||||||
\(246\) | −48.0150 | −3.06133 | ||||||||
\(247\) | 0.0852378 | 0.00542355 | ||||||||
\(248\) | −6.02759 | −0.382752 | ||||||||
\(249\) | −41.4097 | −2.62423 | ||||||||
\(250\) | −8.81507 | −0.557514 | ||||||||
\(251\) | 13.1355 | 0.829104 | 0.414552 | − | 0.910026i | \(-0.363938\pi\) | ||||
0.414552 | + | 0.910026i | \(0.363938\pi\) | |||||||
\(252\) | −13.5075 | −0.850891 | ||||||||
\(253\) | 16.5294 | 1.03919 | ||||||||
\(254\) | −21.4655 | −1.34687 | ||||||||
\(255\) | 8.43034 | 0.527928 | ||||||||
\(256\) | 20.2944 | 1.26840 | ||||||||
\(257\) | 11.2265 | 0.700290 | 0.350145 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16756 | 0.0725489 | ||||||||
\(260\) | 8.90200 | 0.552079 | ||||||||
\(261\) | −13.5423 | −0.838250 | ||||||||
\(262\) | −22.3175 | −1.37878 | ||||||||
\(263\) | 11.3232 | 0.698217 | 0.349109 | − | 0.937082i | \(-0.386484\pi\) | ||||
0.349109 | + | 0.937082i | \(0.386484\pi\) | |||||||
\(264\) | −5.56231 | −0.342337 | ||||||||
\(265\) | 15.9057 | 0.977078 | ||||||||
\(266\) | 0.167337 | 0.0102601 | ||||||||
\(267\) | −24.4120 | −1.49399 | ||||||||
\(268\) | −8.25685 | −0.504368 | ||||||||
\(269\) | 16.6704 | 1.01641 | 0.508205 | − | 0.861236i | \(-0.330309\pi\) | ||||
0.508205 | + | 0.861236i | \(0.330309\pi\) | |||||||
\(270\) | 35.3677 | 2.15241 | ||||||||
\(271\) | −12.4955 | −0.759046 | −0.379523 | − | 0.925182i | \(-0.623912\pi\) | ||||
−0.379523 | + | 0.925182i | \(0.623912\pi\) | |||||||
\(272\) | −4.09677 | −0.248403 | ||||||||
\(273\) | −7.78829 | −0.471369 | ||||||||
\(274\) | −5.67234 | −0.342679 | ||||||||
\(275\) | −17.1379 | −1.03345 | ||||||||
\(276\) | 27.9929 | 1.68498 | ||||||||
\(277\) | 17.0842 | 1.02649 | 0.513246 | − | 0.858242i | \(-0.328443\pi\) | ||||
0.513246 | + | 0.858242i | \(0.328443\pi\) | |||||||
\(278\) | −18.7811 | −1.12641 | ||||||||
\(279\) | 40.7208 | 2.43789 | ||||||||
\(280\) | −4.17765 | −0.249662 | ||||||||
\(281\) | 10.8965 | 0.650029 | 0.325015 | − | 0.945709i | \(-0.394631\pi\) | ||||
0.325015 | + | 0.945709i | \(0.394631\pi\) | |||||||
\(282\) | −49.2252 | −2.93132 | ||||||||
\(283\) | −12.9997 | −0.772753 | −0.386377 | − | 0.922341i | \(-0.626274\pi\) | ||||
−0.386377 | + | 0.922341i | \(0.626274\pi\) | |||||||
\(284\) | 14.0108 | 0.831385 | ||||||||
\(285\) | −0.495872 | −0.0293729 | ||||||||
\(286\) | 8.35727 | 0.494176 | ||||||||
\(287\) | −15.1206 | −0.892538 | ||||||||
\(288\) | −36.2819 | −2.13793 | ||||||||
\(289\) | −16.2146 | −0.953802 | ||||||||
\(290\) | 17.5213 | 1.02889 | ||||||||
\(291\) | 36.5702 | 2.14379 | ||||||||
\(292\) | −11.7479 | −0.687491 | ||||||||
\(293\) | 14.9815 | 0.875231 | 0.437616 | − | 0.899162i | \(-0.355823\pi\) | ||||
0.437616 | + | 0.899162i | \(0.355823\pi\) | |||||||
\(294\) | 22.2454 | 1.29738 | ||||||||
\(295\) | −38.1470 | −2.22101 | ||||||||
\(296\) | 0.507199 | 0.0294803 | ||||||||
\(297\) | 14.8293 | 0.860481 | ||||||||
\(298\) | 45.2749 | 2.62271 | ||||||||
\(299\) | 10.0541 | 0.581441 | ||||||||
\(300\) | −29.0235 | −1.67567 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 22.7007 | 1.30628 | ||||||||
\(303\) | 41.0962 | 2.36092 | ||||||||
\(304\) | 0.240972 | 0.0138207 | ||||||||
\(305\) | 32.7014 | 1.87247 | ||||||||
\(306\) | 8.34908 | 0.477285 | ||||||||
\(307\) | −0.0407881 | −0.00232790 | −0.00116395 | − | 0.999999i | \(-0.500370\pi\) | ||||
−0.00116395 | + | 0.999999i | \(0.500370\pi\) | |||||||
\(308\) | 7.32760 | 0.417529 | ||||||||
\(309\) | −9.50690 | −0.540829 | ||||||||
\(310\) | −52.6854 | −2.99233 | ||||||||
\(311\) | 22.5862 | 1.28075 | 0.640374 | − | 0.768063i | \(-0.278779\pi\) | ||||
0.640374 | + | 0.768063i | \(0.278779\pi\) | |||||||
\(312\) | −3.38329 | −0.191541 | ||||||||
\(313\) | 23.6277 | 1.33552 | 0.667759 | − | 0.744377i | \(-0.267254\pi\) | ||||
0.667759 | + | 0.744377i | \(0.267254\pi\) | |||||||
\(314\) | 8.52961 | 0.481354 | ||||||||
\(315\) | 28.2231 | 1.59019 | ||||||||
\(316\) | 7.05781 | 0.397033 | ||||||||
\(317\) | −22.3450 | −1.25502 | −0.627510 | − | 0.778609i | \(-0.715926\pi\) | ||||
−0.627510 | + | 0.778609i | \(0.715926\pi\) | |||||||
\(318\) | 25.2884 | 1.41810 | ||||||||
\(319\) | 7.34651 | 0.411325 | ||||||||
\(320\) | 15.7598 | 0.881002 | ||||||||
\(321\) | 21.8886 | 1.22170 | ||||||||
\(322\) | 19.7379 | 1.09995 | ||||||||
\(323\) | −0.0461949 | −0.00257035 | ||||||||
\(324\) | 1.11630 | 0.0620168 | ||||||||
\(325\) | −10.4242 | −0.578230 | ||||||||
\(326\) | 5.43528 | 0.301032 | ||||||||
\(327\) | −23.3582 | −1.29171 | ||||||||
\(328\) | −6.56849 | −0.362684 | ||||||||
\(329\) | −15.5017 | −0.854634 | ||||||||
\(330\) | −48.6185 | −2.67636 | ||||||||
\(331\) | −10.1515 | −0.557978 | −0.278989 | − | 0.960294i | \(-0.589999\pi\) | ||||
−0.278989 | + | 0.960294i | \(0.589999\pi\) | |||||||
\(332\) | 23.6977 | 1.30058 | ||||||||
\(333\) | −3.42650 | −0.187771 | ||||||||
\(334\) | −3.66025 | −0.200280 | ||||||||
\(335\) | 17.2522 | 0.942590 | ||||||||
\(336\) | −22.0179 | −1.20118 | ||||||||
\(337\) | 1.25513 | 0.0683710 | 0.0341855 | − | 0.999416i | \(-0.489116\pi\) | ||||
0.0341855 | + | 0.999416i | \(0.489116\pi\) | |||||||
\(338\) | −19.6308 | −1.06778 | ||||||||
\(339\) | −5.85680 | −0.318098 | ||||||||
\(340\) | −4.82446 | −0.261643 | ||||||||
\(341\) | −22.0904 | −1.19626 | ||||||||
\(342\) | −0.491093 | −0.0265552 | ||||||||
\(343\) | 18.8257 | 1.01649 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −58.4896 | −3.14898 | ||||||||
\(346\) | 5.68160 | 0.305445 | ||||||||
\(347\) | 15.8168 | 0.849088 | 0.424544 | − | 0.905407i | \(-0.360434\pi\) | ||||
0.424544 | + | 0.905407i | \(0.360434\pi\) | |||||||
\(348\) | 12.4415 | 0.666934 | ||||||||
\(349\) | 16.1432 | 0.864125 | 0.432062 | − | 0.901844i | \(-0.357786\pi\) | ||||
0.432062 | + | 0.901844i | \(0.357786\pi\) | |||||||
\(350\) | −20.4646 | −1.09388 | ||||||||
\(351\) | 9.01995 | 0.481449 | ||||||||
\(352\) | 19.6824 | 1.04907 | ||||||||
\(353\) | 10.6460 | 0.566630 | 0.283315 | − | 0.959027i | \(-0.408566\pi\) | ||||
0.283315 | + | 0.959027i | \(0.408566\pi\) | |||||||
\(354\) | −60.6497 | −3.22350 | ||||||||
\(355\) | −29.2747 | −1.55374 | ||||||||
\(356\) | 13.9704 | 0.740429 | ||||||||
\(357\) | 4.22088 | 0.223393 | ||||||||
\(358\) | 8.37734 | 0.442756 | ||||||||
\(359\) | 9.38632 | 0.495391 | 0.247696 | − | 0.968838i | \(-0.420327\pi\) | ||||
0.247696 | + | 0.968838i | \(0.420327\pi\) | |||||||
\(360\) | 12.2603 | 0.646177 | ||||||||
\(361\) | −18.9973 | −0.999857 | ||||||||
\(362\) | −48.4518 | −2.54657 | ||||||||
\(363\) | 10.6411 | 0.558515 | ||||||||
\(364\) | 4.45704 | 0.233612 | ||||||||
\(365\) | 24.5465 | 1.28482 | ||||||||
\(366\) | 51.9917 | 2.71765 | ||||||||
\(367\) | 31.7133 | 1.65542 | 0.827710 | − | 0.561156i | \(-0.189643\pi\) | ||||
0.827710 | + | 0.561156i | \(0.189643\pi\) | |||||||
\(368\) | 28.4234 | 1.48167 | ||||||||
\(369\) | 44.3750 | 2.31007 | ||||||||
\(370\) | 4.43328 | 0.230475 | ||||||||
\(371\) | 7.96362 | 0.413451 | ||||||||
\(372\) | −37.4106 | −1.93965 | ||||||||
\(373\) | 2.36635 | 0.122525 | 0.0612626 | − | 0.998122i | \(-0.480487\pi\) | ||||
0.0612626 | + | 0.998122i | \(0.480487\pi\) | |||||||
\(374\) | −4.52924 | −0.234202 | ||||||||
\(375\) | 13.0786 | 0.675376 | ||||||||
\(376\) | −6.73404 | −0.347282 | ||||||||
\(377\) | 4.46854 | 0.230141 | ||||||||
\(378\) | 17.7078 | 0.910791 | ||||||||
\(379\) | −15.7225 | −0.807611 | −0.403805 | − | 0.914845i | \(-0.632313\pi\) | ||||
−0.403805 | + | 0.914845i | \(0.632313\pi\) | |||||||
\(380\) | 0.283775 | 0.0145573 | ||||||||
\(381\) | 31.8476 | 1.63160 | ||||||||
\(382\) | −3.09099 | −0.158149 | ||||||||
\(383\) | 7.97855 | 0.407685 | 0.203842 | − | 0.979004i | \(-0.434657\pi\) | ||||
0.203842 | + | 0.979004i | \(0.434657\pi\) | |||||||
\(384\) | −16.2442 | −0.828958 | ||||||||
\(385\) | −15.3106 | −0.780300 | ||||||||
\(386\) | −12.4187 | −0.632097 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.9282 | −1.06247 | ||||||||
\(389\) | −13.8198 | −0.700689 | −0.350345 | − | 0.936621i | \(-0.613936\pi\) | ||||
−0.350345 | + | 0.936621i | \(0.613936\pi\) | |||||||
\(390\) | −29.5724 | −1.49746 | ||||||||
\(391\) | −5.44882 | −0.275559 | ||||||||
\(392\) | 3.04318 | 0.153704 | ||||||||
\(393\) | 33.1116 | 1.67026 | ||||||||
\(394\) | 22.2319 | 1.12003 | ||||||||
\(395\) | −14.7469 | −0.741996 | ||||||||
\(396\) | −21.5046 | −1.08065 | ||||||||
\(397\) | −28.1747 | −1.41405 | −0.707023 | − | 0.707190i | \(-0.749962\pi\) | ||||
−0.707023 | + | 0.707190i | \(0.749962\pi\) | |||||||
\(398\) | 14.0454 | 0.704035 | ||||||||
\(399\) | −0.248272 | −0.0124292 | ||||||||
\(400\) | −29.4698 | −1.47349 | ||||||||
\(401\) | −9.23181 | −0.461015 | −0.230507 | − | 0.973071i | \(-0.574039\pi\) | ||||
−0.230507 | + | 0.973071i | \(0.574039\pi\) | |||||||
\(402\) | 27.4292 | 1.36804 | ||||||||
\(403\) | −13.4366 | −0.669323 | ||||||||
\(404\) | −23.5183 | −1.17008 | ||||||||
\(405\) | −2.33245 | −0.115900 | ||||||||
\(406\) | 8.77255 | 0.435374 | ||||||||
\(407\) | 1.85882 | 0.0921384 | ||||||||
\(408\) | 1.83359 | 0.0907760 | ||||||||
\(409\) | 15.3188 | 0.757467 | 0.378733 | − | 0.925506i | \(-0.376360\pi\) | ||||
0.378733 | + | 0.925506i | \(0.376360\pi\) | |||||||
\(410\) | −57.4132 | −2.83544 | ||||||||
\(411\) | 8.41584 | 0.415123 | ||||||||
\(412\) | 5.44055 | 0.268037 | ||||||||
\(413\) | −19.0994 | −0.939819 | ||||||||
\(414\) | −57.9258 | −2.84690 | ||||||||
\(415\) | −49.5150 | −2.43059 | ||||||||
\(416\) | 11.9719 | 0.586970 | ||||||||
\(417\) | 27.8648 | 1.36454 | ||||||||
\(418\) | 0.266410 | 0.0130305 | ||||||||
\(419\) | −0.596119 | −0.0291223 | −0.0145612 | − | 0.999894i | \(-0.504635\pi\) | ||||
−0.0145612 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(420\) | −25.9289 | −1.26520 | ||||||||
\(421\) | 30.8627 | 1.50415 | 0.752077 | − | 0.659075i | \(-0.229052\pi\) | ||||
0.752077 | + | 0.659075i | \(0.229052\pi\) | |||||||
\(422\) | −26.9791 | −1.31332 | ||||||||
\(423\) | 45.4934 | 2.21197 | ||||||||
\(424\) | 3.45946 | 0.168006 | ||||||||
\(425\) | 5.64941 | 0.274037 | ||||||||
\(426\) | −46.5436 | −2.25505 | ||||||||
\(427\) | 16.3729 | 0.792338 | ||||||||
\(428\) | −12.5263 | −0.605481 | ||||||||
\(429\) | −12.3994 | −0.598647 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.7925 | 1.33872 | 0.669359 | − | 0.742939i | \(-0.266569\pi\) | ||||
0.669359 | + | 0.742939i | \(0.266569\pi\) | |||||||
\(432\) | 25.4999 | 1.22687 | ||||||||
\(433\) | 23.4693 | 1.12786 | 0.563932 | − | 0.825821i | \(-0.309288\pi\) | ||||
0.563932 | + | 0.825821i | \(0.309288\pi\) | |||||||
\(434\) | −26.3784 | −1.26620 | ||||||||
\(435\) | −25.9958 | −1.24640 | ||||||||
\(436\) | 13.3673 | 0.640176 | ||||||||
\(437\) | 0.320500 | 0.0153316 | ||||||||
\(438\) | 39.0263 | 1.86475 | ||||||||
\(439\) | 27.1891 | 1.29767 | 0.648834 | − | 0.760930i | \(-0.275257\pi\) | ||||
0.648834 | + | 0.760930i | \(0.275257\pi\) | |||||||
\(440\) | −6.65104 | −0.317076 | ||||||||
\(441\) | −20.5589 | −0.978996 | ||||||||
\(442\) | −2.75493 | −0.131039 | ||||||||
\(443\) | −12.5086 | −0.594302 | −0.297151 | − | 0.954831i | \(-0.596036\pi\) | ||||
−0.297151 | + | 0.954831i | \(0.596036\pi\) | |||||||
\(444\) | 3.14796 | 0.149396 | ||||||||
\(445\) | −29.1903 | −1.38375 | ||||||||
\(446\) | 6.59386 | 0.312229 | ||||||||
\(447\) | −67.1727 | −3.17716 | ||||||||
\(448\) | 7.89061 | 0.372796 | ||||||||
\(449\) | −41.1059 | −1.93991 | −0.969954 | − | 0.243286i | \(-0.921774\pi\) | ||||
−0.969954 | + | 0.243286i | \(0.921774\pi\) | |||||||
\(450\) | 60.0583 | 2.83118 | ||||||||
\(451\) | −24.0727 | −1.13354 | ||||||||
\(452\) | 3.35170 | 0.157651 | ||||||||
\(453\) | −33.6802 | −1.58243 | ||||||||
\(454\) | −33.2341 | −1.55975 | ||||||||
\(455\) | −9.31272 | −0.436587 | ||||||||
\(456\) | −0.107851 | −0.00505061 | ||||||||
\(457\) | −37.2883 | −1.74427 | −0.872137 | − | 0.489262i | \(-0.837266\pi\) | ||||
−0.872137 | + | 0.489262i | \(0.837266\pi\) | |||||||
\(458\) | 26.4978 | 1.23816 | ||||||||
\(459\) | −4.88839 | −0.228170 | ||||||||
\(460\) | 33.4721 | 1.56064 | ||||||||
\(461\) | −6.56035 | −0.305546 | −0.152773 | − | 0.988261i | \(-0.548820\pi\) | ||||
−0.152773 | + | 0.988261i | \(0.548820\pi\) | |||||||
\(462\) | −24.3422 | −1.13250 | ||||||||
\(463\) | 17.3213 | 0.804988 | 0.402494 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402494 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(464\) | 12.6328 | 0.586463 | ||||||||
\(465\) | 78.1674 | 3.62493 | ||||||||
\(466\) | −44.1097 | −2.04334 | ||||||||
\(467\) | 17.2171 | 0.796712 | 0.398356 | − | 0.917231i | \(-0.369581\pi\) | ||||
0.398356 | + | 0.917231i | \(0.369581\pi\) | |||||||
\(468\) | −13.0803 | −0.604635 | ||||||||
\(469\) | 8.63781 | 0.398857 | ||||||||
\(470\) | −58.8603 | −2.71502 | ||||||||
\(471\) | −12.6551 | −0.583115 | ||||||||
\(472\) | −8.29692 | −0.381897 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −23.4460 | −1.07691 | ||||||||
\(475\) | −0.332298 | −0.0152469 | ||||||||
\(476\) | −2.41550 | −0.110714 | ||||||||
\(477\) | −23.3712 | −1.07009 | ||||||||
\(478\) | 21.9984 | 1.00618 | ||||||||
\(479\) | −37.9019 | −1.73178 | −0.865890 | − | 0.500234i | \(-0.833247\pi\) | ||||
−0.865890 | + | 0.500234i | \(0.833247\pi\) | |||||||
\(480\) | −69.6466 | −3.17892 | ||||||||
\(481\) | 1.13064 | 0.0515525 | ||||||||
\(482\) | 55.3247 | 2.51997 | ||||||||
\(483\) | −29.2845 | −1.33249 | ||||||||
\(484\) | −6.08965 | −0.276802 | ||||||||
\(485\) | 43.7283 | 1.98560 | ||||||||
\(486\) | 27.7514 | 1.25883 | ||||||||
\(487\) | −3.26385 | −0.147899 | −0.0739497 | − | 0.997262i | \(-0.523560\pi\) | ||||
−0.0739497 | + | 0.997262i | \(0.523560\pi\) | |||||||
\(488\) | 7.11250 | 0.321968 | ||||||||
\(489\) | −8.06413 | −0.364673 | ||||||||
\(490\) | 26.5995 | 1.20164 | ||||||||
\(491\) | 34.1726 | 1.54219 | 0.771095 | − | 0.636721i | \(-0.219710\pi\) | ||||
0.771095 | + | 0.636721i | \(0.219710\pi\) | |||||||
\(492\) | −40.7678 | −1.83795 | ||||||||
\(493\) | −2.42173 | −0.109069 | ||||||||
\(494\) | 0.162045 | 0.00729074 | ||||||||
\(495\) | 44.9327 | 2.01957 | ||||||||
\(496\) | −37.9859 | −1.70562 | ||||||||
\(497\) | −14.6572 | −0.657464 | ||||||||
\(498\) | −78.7236 | −3.52769 | ||||||||
\(499\) | 36.7104 | 1.64338 | 0.821692 | − | 0.569932i | \(-0.193030\pi\) | ||||
0.821692 | + | 0.569932i | \(0.193030\pi\) | |||||||
\(500\) | −7.48454 | −0.334719 | ||||||||
\(501\) | 5.43058 | 0.242621 | ||||||||
\(502\) | 24.9717 | 1.11454 | ||||||||
\(503\) | 6.83246 | 0.304644 | 0.152322 | − | 0.988331i | \(-0.451325\pi\) | ||||
0.152322 | + | 0.988331i | \(0.451325\pi\) | |||||||
\(504\) | 6.13848 | 0.273430 | ||||||||
\(505\) | 49.1402 | 2.18671 | ||||||||
\(506\) | 31.4239 | 1.39696 | ||||||||
\(507\) | 29.1256 | 1.29351 | ||||||||
\(508\) | −18.2256 | −0.808628 | ||||||||
\(509\) | −21.5010 | −0.953014 | −0.476507 | − | 0.879171i | \(-0.658097\pi\) | ||||
−0.476507 | + | 0.879171i | \(0.658097\pi\) | |||||||
\(510\) | 16.0268 | 0.709680 | ||||||||
\(511\) | 12.2899 | 0.543672 | ||||||||
\(512\) | 27.0630 | 1.19603 | ||||||||
\(513\) | 0.287535 | 0.0126950 | ||||||||
\(514\) | 21.3426 | 0.941382 | ||||||||
\(515\) | −11.3677 | −0.500922 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.6795 | −1.08540 | ||||||||
\(518\) | 2.21964 | 0.0975255 | ||||||||
\(519\) | −8.42959 | −0.370018 | ||||||||
\(520\) | −4.04552 | −0.177408 | ||||||||
\(521\) | −3.09271 | −0.135494 | −0.0677471 | − | 0.997703i | \(-0.521581\pi\) | ||||
−0.0677471 | + | 0.997703i | \(0.521581\pi\) | |||||||
\(522\) | −25.7452 | −1.12684 | ||||||||
\(523\) | −16.5023 | −0.721594 | −0.360797 | − | 0.932644i | \(-0.617495\pi\) | ||||
−0.360797 | + | 0.932644i | \(0.617495\pi\) | |||||||
\(524\) | −18.9489 | −0.827787 | ||||||||
\(525\) | 30.3625 | 1.32513 | ||||||||
\(526\) | 21.5264 | 0.938595 | ||||||||
\(527\) | 7.28198 | 0.317208 | ||||||||
\(528\) | −35.0537 | −1.52552 | ||||||||
\(529\) | 14.8039 | 0.643648 | ||||||||
\(530\) | 30.2381 | 1.31346 | ||||||||
\(531\) | 56.0518 | 2.43244 | ||||||||
\(532\) | 0.142080 | 0.00615994 | ||||||||
\(533\) | −14.6423 | −0.634229 | ||||||||
\(534\) | −46.4095 | −2.00834 | ||||||||
\(535\) | 26.1730 | 1.13156 | ||||||||
\(536\) | 3.75233 | 0.162076 | ||||||||
\(537\) | −12.4291 | −0.536357 | ||||||||
\(538\) | 31.6919 | 1.36633 | ||||||||
\(539\) | 11.1529 | 0.480389 | ||||||||
\(540\) | 30.0293 | 1.29226 | ||||||||
\(541\) | −9.90010 | −0.425639 | −0.212819 | − | 0.977092i | \(-0.568265\pi\) | ||||
−0.212819 | + | 0.977092i | \(0.568265\pi\) | |||||||
\(542\) | −23.7550 | −1.02037 | ||||||||
\(543\) | 71.8861 | 3.08493 | ||||||||
\(544\) | −6.48819 | −0.278179 | ||||||||
\(545\) | −27.9302 | −1.19640 | ||||||||
\(546\) | −14.8062 | −0.633649 | ||||||||
\(547\) | 0.825233 | 0.0352844 | 0.0176422 | − | 0.999844i | \(-0.494384\pi\) | ||||
0.0176422 | + | 0.999844i | \(0.494384\pi\) | |||||||
\(548\) | −4.81617 | −0.205736 | ||||||||
\(549\) | −48.0501 | −2.05073 | ||||||||
\(550\) | −32.5807 | −1.38925 | ||||||||
\(551\) | 0.142446 | 0.00606842 | ||||||||
\(552\) | −12.7214 | −0.541459 | ||||||||
\(553\) | −7.38344 | −0.313976 | ||||||||
\(554\) | 32.4786 | 1.37989 | ||||||||
\(555\) | −6.57749 | −0.279199 | ||||||||
\(556\) | −15.9463 | −0.676274 | ||||||||
\(557\) | 1.58630 | 0.0672137 | 0.0336069 | − | 0.999435i | \(-0.489301\pi\) | ||||
0.0336069 | + | 0.999435i | \(0.489301\pi\) | |||||||
\(558\) | 77.4139 | 3.27719 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −26.3276 | −1.11254 | ||||||||
\(561\) | 6.71987 | 0.283713 | ||||||||
\(562\) | 20.7152 | 0.873817 | ||||||||
\(563\) | −4.01671 | −0.169284 | −0.0846420 | − | 0.996411i | \(-0.526975\pi\) | ||||
−0.0846420 | + | 0.996411i | \(0.526975\pi\) | |||||||
\(564\) | −41.7953 | −1.75990 | ||||||||
\(565\) | −7.00318 | −0.294626 | ||||||||
\(566\) | −24.7136 | −1.03879 | ||||||||
\(567\) | −1.16781 | −0.0490433 | ||||||||
\(568\) | −6.36720 | −0.267162 | ||||||||
\(569\) | 14.8231 | 0.621415 | 0.310708 | − | 0.950506i | \(-0.399434\pi\) | ||||
0.310708 | + | 0.950506i | \(0.399434\pi\) | |||||||
\(570\) | −0.942698 | −0.0394853 | ||||||||
\(571\) | 6.04978 | 0.253176 | 0.126588 | − | 0.991955i | \(-0.459597\pi\) | ||||
0.126588 | + | 0.991955i | \(0.459597\pi\) | |||||||
\(572\) | 7.09584 | 0.296692 | ||||||||
\(573\) | 4.58598 | 0.191582 | ||||||||
\(574\) | −28.7455 | −1.19982 | ||||||||
\(575\) | −39.1956 | −1.63457 | ||||||||
\(576\) | −23.1569 | −0.964872 | ||||||||
\(577\) | 4.28375 | 0.178335 | 0.0891674 | − | 0.996017i | \(-0.471579\pi\) | ||||
0.0891674 | + | 0.996017i | \(0.471579\pi\) | |||||||
\(578\) | −30.8255 | −1.28217 | ||||||||
\(579\) | 18.4252 | 0.765726 | ||||||||
\(580\) | 14.8767 | 0.617722 | ||||||||
\(581\) | −24.7911 | −1.02851 | ||||||||
\(582\) | 69.5233 | 2.88183 | ||||||||
\(583\) | 12.6785 | 0.525090 | ||||||||
\(584\) | 5.33882 | 0.220922 | ||||||||
\(585\) | 27.3305 | 1.12998 | ||||||||
\(586\) | 28.4813 | 1.17655 | ||||||||
\(587\) | 47.3730 | 1.95529 | 0.977647 | − | 0.210251i | \(-0.0674283\pi\) | ||||
0.977647 | + | 0.210251i | \(0.0674283\pi\) | |||||||
\(588\) | 18.8877 | 0.778916 | ||||||||
\(589\) | −0.428326 | −0.0176489 | ||||||||
\(590\) | −72.5209 | −2.98564 | ||||||||
\(591\) | −32.9846 | −1.35681 | ||||||||
\(592\) | 3.19637 | 0.131370 | ||||||||
\(593\) | −15.1212 | −0.620955 | −0.310478 | − | 0.950581i | \(-0.600489\pi\) | ||||
−0.310478 | + | 0.950581i | \(0.600489\pi\) | |||||||
\(594\) | 28.1918 | 1.15672 | ||||||||
\(595\) | 5.04705 | 0.206909 | ||||||||
\(596\) | 38.4412 | 1.57461 | ||||||||
\(597\) | −20.8387 | −0.852872 | ||||||||
\(598\) | 19.1137 | 0.781616 | ||||||||
\(599\) | 35.9933 | 1.47065 | 0.735323 | − | 0.677717i | \(-0.237030\pi\) | ||||
0.735323 | + | 0.677717i | \(0.237030\pi\) | |||||||
\(600\) | 13.1897 | 0.538468 | ||||||||
\(601\) | −36.4362 | −1.48626 | −0.743132 | − | 0.669144i | \(-0.766661\pi\) | ||||
−0.743132 | + | 0.669144i | \(0.766661\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.3498 | −1.03232 | ||||||||
\(604\) | 19.2743 | 0.784259 | ||||||||
\(605\) | 12.7240 | 0.517303 | ||||||||
\(606\) | 78.1276 | 3.17372 | ||||||||
\(607\) | −13.6794 | −0.555228 | −0.277614 | − | 0.960693i | \(-0.589544\pi\) | ||||
−0.277614 | + | 0.960693i | \(0.589544\pi\) | |||||||
\(608\) | 0.381635 | 0.0154774 | ||||||||
\(609\) | −13.0155 | −0.527415 | ||||||||
\(610\) | 62.1682 | 2.51712 | ||||||||
\(611\) | −15.0114 | −0.607295 | ||||||||
\(612\) | 7.08888 | 0.286551 | ||||||||
\(613\) | 41.7078 | 1.68456 | 0.842282 | − | 0.539037i | \(-0.181212\pi\) | ||||
0.842282 | + | 0.539037i | \(0.181212\pi\) | |||||||
\(614\) | −0.0775419 | −0.00312933 | ||||||||
\(615\) | 85.1819 | 3.43487 | ||||||||
\(616\) | −3.33003 | −0.134171 | ||||||||
\(617\) | −11.6939 | −0.470777 | −0.235389 | − | 0.971901i | \(-0.575636\pi\) | ||||
−0.235389 | + | 0.971901i | \(0.575636\pi\) | |||||||
\(618\) | −18.0735 | −0.727022 | ||||||||
\(619\) | 43.8396 | 1.76206 | 0.881031 | − | 0.473059i | \(-0.156850\pi\) | ||||
0.881031 | + | 0.473059i | \(0.156850\pi\) | |||||||
\(620\) | −44.7332 | −1.79653 | ||||||||
\(621\) | 33.9156 | 1.36099 | ||||||||
\(622\) | 42.9385 | 1.72168 | ||||||||
\(623\) | −14.6149 | −0.585535 | ||||||||
\(624\) | −21.3216 | −0.853545 | ||||||||
\(625\) | −16.2357 | −0.649426 | ||||||||
\(626\) | 44.9184 | 1.79530 | ||||||||
\(627\) | −0.395263 | −0.0157853 | ||||||||
\(628\) | 7.24217 | 0.288994 | ||||||||
\(629\) | −0.612751 | −0.0244320 | ||||||||
\(630\) | 53.6547 | 2.13765 | ||||||||
\(631\) | 8.09337 | 0.322192 | 0.161096 | − | 0.986939i | \(-0.448497\pi\) | ||||
0.161096 | + | 0.986939i | \(0.448497\pi\) | |||||||
\(632\) | −3.20742 | −0.127585 | ||||||||
\(633\) | 40.0279 | 1.59097 | ||||||||
\(634\) | −42.4798 | −1.68709 | ||||||||
\(635\) | 38.0812 | 1.51121 | ||||||||
\(636\) | 21.4714 | 0.851396 | ||||||||
\(637\) | 6.78378 | 0.268783 | ||||||||
\(638\) | 13.9664 | 0.552934 | ||||||||
\(639\) | 43.0151 | 1.70165 | ||||||||
\(640\) | −19.4237 | −0.767790 | ||||||||
\(641\) | 25.9425 | 1.02467 | 0.512333 | − | 0.858787i | \(-0.328781\pi\) | ||||
0.512333 | + | 0.858787i | \(0.328781\pi\) | |||||||
\(642\) | 41.6122 | 1.64230 | ||||||||
\(643\) | 31.3696 | 1.23710 | 0.618549 | − | 0.785747i | \(-0.287721\pi\) | ||||
0.618549 | + | 0.785747i | \(0.287721\pi\) | |||||||
\(644\) | 16.7587 | 0.660387 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0878206 | −0.00345525 | ||||||||
\(647\) | −12.1068 | −0.475969 | −0.237985 | − | 0.971269i | \(-0.576487\pi\) | ||||
−0.237985 | + | 0.971269i | \(0.576487\pi\) | |||||||
\(648\) | −0.507304 | −0.0199288 | ||||||||
\(649\) | −30.4072 | −1.19359 | ||||||||
\(650\) | −19.8173 | −0.777299 | ||||||||
\(651\) | 39.1367 | 1.53389 | ||||||||
\(652\) | 4.61489 | 0.180733 | ||||||||
\(653\) | −26.0448 | −1.01921 | −0.509605 | − | 0.860408i | \(-0.670209\pi\) | ||||
−0.509605 | + | 0.860408i | \(0.670209\pi\) | |||||||
\(654\) | −44.4060 | −1.73641 | ||||||||
\(655\) | 39.5927 | 1.54701 | ||||||||
\(656\) | −41.3947 | −1.61619 | ||||||||
\(657\) | −36.0677 | −1.40713 | ||||||||
\(658\) | −29.4700 | −1.14886 | ||||||||
\(659\) | 23.7088 | 0.923563 | 0.461781 | − | 0.886994i | \(-0.347210\pi\) | ||||
0.461781 | + | 0.886994i | \(0.347210\pi\) | |||||||
\(660\) | −41.2802 | −1.60683 | ||||||||
\(661\) | 22.0660 | 0.858266 | 0.429133 | − | 0.903241i | \(-0.358819\pi\) | ||||
0.429133 | + | 0.903241i | \(0.358819\pi\) | |||||||
\(662\) | −19.2990 | −0.750076 | ||||||||
\(663\) | 4.08738 | 0.158741 | ||||||||
\(664\) | −10.7694 | −0.417935 | ||||||||
\(665\) | −0.296868 | −0.0115120 | ||||||||
\(666\) | −6.51409 | −0.252416 | ||||||||
\(667\) | 16.8020 | 0.650575 | ||||||||
\(668\) | −3.10778 | −0.120244 | ||||||||
\(669\) | −9.78308 | −0.378236 | ||||||||
\(670\) | 32.7980 | 1.26710 | ||||||||
\(671\) | 26.0665 | 1.00628 | ||||||||
\(672\) | −34.8705 | −1.34516 | ||||||||
\(673\) | −32.0895 | −1.23696 | −0.618479 | − | 0.785802i | \(-0.712251\pi\) | ||||
−0.618479 | + | 0.785802i | \(0.712251\pi\) | |||||||
\(674\) | 2.38611 | 0.0919094 | ||||||||
\(675\) | −35.1641 | −1.35347 | ||||||||
\(676\) | −16.6678 | −0.641069 | ||||||||
\(677\) | −4.14125 | −0.159161 | −0.0795806 | − | 0.996828i | \(-0.525358\pi\) | ||||
−0.0795806 | + | 0.996828i | \(0.525358\pi\) | |||||||
\(678\) | −11.1343 | −0.427611 | ||||||||
\(679\) | 21.8938 | 0.840206 | ||||||||
\(680\) | 2.19248 | 0.0840778 | ||||||||
\(681\) | 49.3082 | 1.88950 | ||||||||
\(682\) | −41.9958 | −1.60810 | ||||||||
\(683\) | 11.8890 | 0.454918 | 0.227459 | − | 0.973788i | \(-0.426958\pi\) | ||||
0.227459 | + | 0.973788i | \(0.426958\pi\) | |||||||
\(684\) | −0.416968 | −0.0159432 | ||||||||
\(685\) | 10.0631 | 0.384492 | ||||||||
\(686\) | 35.7893 | 1.36644 | ||||||||
\(687\) | −39.3138 | −1.49992 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.71175 | 0.293794 | ||||||||
\(690\) | −111.194 | −4.23309 | ||||||||
\(691\) | −26.2811 | −0.999781 | −0.499891 | − | 0.866089i | \(-0.666626\pi\) | ||||
−0.499891 | + | 0.866089i | \(0.666626\pi\) | |||||||
\(692\) | 4.82403 | 0.183382 | ||||||||
\(693\) | 22.4968 | 0.854583 | ||||||||
\(694\) | 30.0691 | 1.14141 | ||||||||
\(695\) | 33.3189 | 1.26386 | ||||||||
\(696\) | −5.65404 | −0.214316 | ||||||||
\(697\) | 7.93544 | 0.300576 | ||||||||
\(698\) | 30.6896 | 1.16162 | ||||||||
\(699\) | 65.4440 | 2.47532 | ||||||||
\(700\) | −17.3757 | −0.656739 | ||||||||
\(701\) | 2.70781 | 0.102273 | 0.0511364 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511364 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(702\) | 17.1477 | 0.647200 | ||||||||
\(703\) | 0.0360420 | 0.00135935 | ||||||||
\(704\) | 12.5623 | 0.473458 | ||||||||
\(705\) | 87.3289 | 3.28899 | ||||||||
\(706\) | 20.2390 | 0.761706 | ||||||||
\(707\) | 24.6034 | 0.925306 | ||||||||
\(708\) | −51.4954 | −1.93532 | ||||||||
\(709\) | 39.0604 | 1.46694 | 0.733472 | − | 0.679719i | \(-0.237898\pi\) | ||||
0.733472 | + | 0.679719i | \(0.237898\pi\) | |||||||
\(710\) | −55.6538 | −2.08865 | ||||||||
\(711\) | 21.6685 | 0.812633 | ||||||||
\(712\) | −6.34885 | −0.237933 | ||||||||
\(713\) | −50.5223 | −1.89208 | ||||||||
\(714\) | 8.02428 | 0.300301 | ||||||||
\(715\) | −14.8263 | −0.554474 | ||||||||
\(716\) | 7.11288 | 0.265821 | ||||||||
\(717\) | −32.6383 | −1.21890 | ||||||||
\(718\) | 17.8442 | 0.665941 | ||||||||
\(719\) | 20.6795 | 0.771217 | 0.385608 | − | 0.922663i | \(-0.373992\pi\) | ||||
0.385608 | + | 0.922663i | \(0.373992\pi\) | |||||||
\(720\) | 77.2648 | 2.87949 | ||||||||
\(721\) | −5.69157 | −0.211965 | ||||||||
\(722\) | −36.1155 | −1.34408 | ||||||||
\(723\) | −82.0832 | −3.05271 | ||||||||
\(724\) | −41.1385 | −1.52890 | ||||||||
\(725\) | −17.4205 | −0.646982 | ||||||||
\(726\) | 20.2298 | 0.750797 | ||||||||
\(727\) | −3.22067 | −0.119448 | −0.0597240 | − | 0.998215i | \(-0.519022\pi\) | ||||
−0.0597240 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(728\) | −2.02550 | −0.0750701 | ||||||||
\(729\) | −43.2484 | −1.60179 | ||||||||
\(730\) | 46.6651 | 1.72715 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 44.1442 | 1.63162 | ||||||||
\(733\) | −21.2006 | −0.783063 | −0.391531 | − | 0.920165i | \(-0.628055\pi\) | ||||
−0.391531 | + | 0.920165i | \(0.628055\pi\) | |||||||
\(734\) | 60.2898 | 2.22534 | ||||||||
\(735\) | −39.4648 | −1.45568 | ||||||||
\(736\) | 45.0150 | 1.65928 | ||||||||
\(737\) | 13.7519 | 0.506556 | ||||||||
\(738\) | 84.3608 | 3.10536 | ||||||||
\(739\) | −47.6889 | −1.75427 | −0.877133 | − | 0.480248i | \(-0.840547\pi\) | ||||
−0.877133 | + | 0.480248i | \(0.840547\pi\) | |||||||
\(740\) | 3.76413 | 0.138372 | ||||||||
\(741\) | −0.240420 | −0.00883205 | ||||||||
\(742\) | 15.1396 | 0.555791 | ||||||||
\(743\) | 20.2305 | 0.742184 | 0.371092 | − | 0.928596i | \(-0.378983\pi\) | ||||
0.371092 | + | 0.928596i | \(0.378983\pi\) | |||||||
\(744\) | 17.0013 | 0.623297 | ||||||||
\(745\) | −80.3207 | −2.94272 | ||||||||
\(746\) | 4.49865 | 0.164707 | ||||||||
\(747\) | 72.7554 | 2.66198 | ||||||||
\(748\) | −3.84561 | −0.140609 | ||||||||
\(749\) | 13.1042 | 0.478818 | ||||||||
\(750\) | 24.8636 | 0.907890 | ||||||||
\(751\) | 1.07558 | 0.0392483 | 0.0196242 | − | 0.999807i | \(-0.493753\pi\) | ||||
0.0196242 | + | 0.999807i | \(0.493753\pi\) | |||||||
\(752\) | −42.4380 | −1.54755 | ||||||||
\(753\) | −37.0496 | −1.35016 | ||||||||
\(754\) | 8.49509 | 0.309373 | ||||||||
\(755\) | −40.2725 | −1.46567 | ||||||||
\(756\) | 15.0350 | 0.546819 | ||||||||
\(757\) | 8.60082 | 0.312602 | 0.156301 | − | 0.987709i | \(-0.450043\pi\) | ||||
0.156301 | + | 0.987709i | \(0.450043\pi\) | |||||||
\(758\) | −29.8899 | −1.08565 | ||||||||
\(759\) | −46.6224 | −1.69229 | ||||||||
\(760\) | −0.128962 | −0.00467793 | ||||||||
\(761\) | −1.67778 | −0.0608195 | −0.0304097 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304097 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(762\) | 60.5451 | 2.19332 | ||||||||
\(763\) | −13.9840 | −0.506255 | ||||||||
\(764\) | −2.62444 | −0.0949489 | ||||||||
\(765\) | −14.8118 | −0.535522 | ||||||||
\(766\) | 15.1679 | 0.548040 | ||||||||
\(767\) | −18.4953 | −0.667826 | ||||||||
\(768\) | −57.2418 | −2.06554 | ||||||||
\(769\) | 12.8315 | 0.462717 | 0.231358 | − | 0.972869i | \(-0.425683\pi\) | ||||
0.231358 | + | 0.972869i | \(0.425683\pi\) | |||||||
\(770\) | −29.1068 | −1.04894 | ||||||||
\(771\) | −31.6652 | −1.14040 | ||||||||
\(772\) | −10.5443 | −0.379497 | ||||||||
\(773\) | −1.53985 | −0.0553844 | −0.0276922 | − | 0.999616i | \(-0.508816\pi\) | ||||
−0.0276922 | + | 0.999616i | \(0.508816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 52.3822 | 1.88162 | ||||||||
\(776\) | 9.51083 | 0.341419 | ||||||||
\(777\) | −3.29320 | −0.118143 | ||||||||
\(778\) | −26.2726 | −0.941918 | ||||||||
\(779\) | −0.466762 | −0.0167235 | ||||||||
\(780\) | −25.1088 | −0.899039 | ||||||||
\(781\) | −23.3350 | −0.834993 | ||||||||
\(782\) | −10.3587 | −0.370426 | ||||||||
\(783\) | 15.0738 | 0.538694 | ||||||||
\(784\) | 19.1781 | 0.684934 | ||||||||
\(785\) | −15.1321 | −0.540087 | ||||||||
\(786\) | 62.9482 | 2.24529 | ||||||||
\(787\) | −39.3350 | −1.40214 | −0.701070 | − | 0.713092i | \(-0.747294\pi\) | ||||
−0.701070 | + | 0.713092i | \(0.747294\pi\) | |||||||
\(788\) | 18.8762 | 0.672438 | ||||||||
\(789\) | −31.9379 | −1.13702 | ||||||||
\(790\) | −28.0352 | −0.997446 | ||||||||
\(791\) | −3.50634 | −0.124671 | ||||||||
\(792\) | 9.77279 | 0.347261 | ||||||||
\(793\) | 15.8550 | 0.563028 | ||||||||
\(794\) | −53.5626 | −1.90087 | ||||||||
\(795\) | −44.8632 | −1.59113 | ||||||||
\(796\) | 11.9255 | 0.422687 | ||||||||
\(797\) | −9.05554 | −0.320764 | −0.160382 | − | 0.987055i | \(-0.551273\pi\) | ||||
−0.160382 | + | 0.987055i | \(0.551273\pi\) | |||||||
\(798\) | −0.471988 | −0.0167082 | ||||||||
\(799\) | 8.13545 | 0.287811 | ||||||||
\(800\) | −46.6722 | −1.65011 | ||||||||
\(801\) | 42.8911 | 1.51548 | ||||||||
\(802\) | −17.5505 | −0.619730 | ||||||||
\(803\) | 19.5661 | 0.690474 | ||||||||
\(804\) | 23.2891 | 0.821343 | ||||||||
\(805\) | −35.0164 | −1.23417 | ||||||||
\(806\) | −25.5441 | −0.899753 | ||||||||
\(807\) | −47.0201 | −1.65519 | ||||||||
\(808\) | 10.6879 | 0.375999 | ||||||||
\(809\) | 37.3018 | 1.31146 | 0.655730 | − | 0.754995i | \(-0.272361\pi\) | ||||
0.655730 | + | 0.754995i | \(0.272361\pi\) | |||||||
\(810\) | −4.43420 | −0.155802 | ||||||||
\(811\) | 9.71236 | 0.341047 | 0.170524 | − | 0.985354i | \(-0.445454\pi\) | ||||
0.170524 | + | 0.985354i | \(0.445454\pi\) | |||||||
\(812\) | 7.44844 | 0.261389 | ||||||||
\(813\) | 35.2445 | 1.23608 | ||||||||
\(814\) | 3.53379 | 0.123859 | ||||||||
\(815\) | −9.64255 | −0.337764 | ||||||||
\(816\) | 11.5553 | 0.404515 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 29.1225 | 1.01824 | ||||||||
\(819\) | 13.6838 | 0.478149 | ||||||||
\(820\) | −48.7474 | −1.70233 | ||||||||
\(821\) | 3.15605 | 0.110147 | 0.0550734 | − | 0.998482i | \(-0.482461\pi\) | ||||
0.0550734 | + | 0.998482i | \(0.482461\pi\) | |||||||
\(822\) | 15.9993 | 0.558039 | ||||||||
\(823\) | 13.5953 | 0.473903 | 0.236952 | − | 0.971521i | \(-0.423852\pi\) | ||||
0.236952 | + | 0.971521i | \(0.423852\pi\) | |||||||
\(824\) | −2.47246 | −0.0861323 | ||||||||
\(825\) | 48.3388 | 1.68294 | ||||||||
\(826\) | −36.3096 | −1.26337 | ||||||||
\(827\) | −1.89128 | −0.0657661 | −0.0328831 | − | 0.999459i | \(-0.510469\pi\) | ||||
−0.0328831 | + | 0.999459i | \(0.510469\pi\) | |||||||
\(828\) | −49.1826 | −1.70921 | ||||||||
\(829\) | −10.0682 | −0.349682 | −0.174841 | − | 0.984597i | \(-0.555941\pi\) | ||||
−0.174841 | + | 0.984597i | \(0.555941\pi\) | |||||||
\(830\) | −94.1324 | −3.26738 | ||||||||
\(831\) | −48.1874 | −1.67160 | ||||||||
\(832\) | 7.64104 | 0.264905 | ||||||||
\(833\) | −3.67649 | −0.127383 | ||||||||
\(834\) | 52.9735 | 1.83432 | ||||||||
\(835\) | 6.49353 | 0.224718 | ||||||||
\(836\) | 0.226199 | 0.00782324 | ||||||||
\(837\) | −45.3259 | −1.56669 | ||||||||
\(838\) | −1.13328 | −0.0391483 | ||||||||
\(839\) | −36.5404 | −1.26151 | −0.630757 | − | 0.775980i | \(-0.717256\pi\) | ||||
−0.630757 | + | 0.775980i | \(0.717256\pi\) | |||||||
\(840\) | 11.7834 | 0.406566 | ||||||||
\(841\) | −21.5323 | −0.742495 | ||||||||
\(842\) | 58.6727 | 2.02199 | ||||||||
\(843\) | −30.7343 | −1.05855 | ||||||||
\(844\) | −22.9069 | −0.788489 | ||||||||
\(845\) | 34.8264 | 1.19806 | ||||||||
\(846\) | 86.4871 | 2.97349 | ||||||||
\(847\) | 6.37061 | 0.218897 | ||||||||
\(848\) | 21.8016 | 0.748669 | ||||||||
\(849\) | 36.6667 | 1.25840 | ||||||||
\(850\) | 10.7400 | 0.368380 | ||||||||
\(851\) | 4.25126 | 0.145731 | ||||||||
\(852\) | −39.5184 | −1.35388 | ||||||||
\(853\) | 1.47142 | 0.0503805 | 0.0251903 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251903 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(854\) | 31.1263 | 1.06512 | ||||||||
\(855\) | 0.871231 | 0.0297955 | ||||||||
\(856\) | 5.69258 | 0.194568 | ||||||||
\(857\) | 12.1732 | 0.415829 | 0.207915 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207915 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(858\) | −23.5723 | −0.804746 | ||||||||
\(859\) | 11.0240 | 0.376135 | 0.188068 | − | 0.982156i | \(-0.439778\pi\) | ||||
0.188068 | + | 0.982156i | \(0.439778\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.6487 | 1.45346 | ||||||||
\(862\) | 52.8360 | 1.79960 | ||||||||
\(863\) | −26.8685 | −0.914613 | −0.457307 | − | 0.889309i | \(-0.651186\pi\) | ||||
−0.457307 | + | 0.889309i | \(0.651186\pi\) | |||||||
\(864\) | 40.3850 | 1.37393 | ||||||||
\(865\) | −10.0795 | −0.342715 | ||||||||
\(866\) | 44.6173 | 1.51616 | ||||||||
\(867\) | 45.7347 | 1.55323 | ||||||||
\(868\) | −22.3969 | −0.760200 | ||||||||
\(869\) | −11.7548 | −0.398755 | ||||||||
\(870\) | −49.4203 | −1.67551 | ||||||||
\(871\) | 8.36461 | 0.283424 | ||||||||
\(872\) | −6.07476 | −0.205717 | ||||||||
\(873\) | −64.2527 | −2.17462 | ||||||||
\(874\) | 0.609299 | 0.0206098 | ||||||||
\(875\) | 7.82986 | 0.264698 | ||||||||
\(876\) | 33.1357 | 1.11955 | ||||||||
\(877\) | −1.81534 | −0.0612995 | −0.0306498 | − | 0.999530i | \(-0.509758\pi\) | ||||
−0.0306498 | + | 0.999530i | \(0.509758\pi\) | |||||||
\(878\) | 51.6890 | 1.74442 | ||||||||
\(879\) | −42.2566 | −1.42528 | ||||||||
\(880\) | −41.9149 | −1.41295 | ||||||||
\(881\) | 17.6708 | 0.595345 | 0.297673 | − | 0.954668i | \(-0.403790\pi\) | ||||
0.297673 | + | 0.954668i | \(0.403790\pi\) | |||||||
\(882\) | −39.0844 | −1.31604 | ||||||||
\(883\) | 3.60305 | 0.121252 | 0.0606262 | − | 0.998161i | \(-0.480690\pi\) | ||||
0.0606262 | + | 0.998161i | \(0.480690\pi\) | |||||||
\(884\) | −2.33910 | −0.0786726 | ||||||||
\(885\) | 107.597 | 3.61682 | ||||||||
\(886\) | −23.7800 | −0.798904 | ||||||||
\(887\) | 0.358075 | 0.0120230 | 0.00601149 | − | 0.999982i | \(-0.498086\pi\) | ||||
0.00601149 | + | 0.999982i | \(0.498086\pi\) | |||||||
\(888\) | −1.43059 | −0.0480076 | ||||||||
\(889\) | 19.0664 | 0.639468 | ||||||||
\(890\) | −55.4934 | −1.86014 | ||||||||
\(891\) | −1.85921 | −0.0622859 | ||||||||
\(892\) | 5.59860 | 0.187455 | ||||||||
\(893\) | −0.478527 | −0.0160133 | ||||||||
\(894\) | −127.701 | −4.27097 | ||||||||
\(895\) | −14.8619 | −0.496780 | ||||||||
\(896\) | −9.72503 | −0.324890 | ||||||||
\(897\) | −28.3583 | −0.946855 | ||||||||
\(898\) | −78.1461 | −2.60777 | ||||||||
\(899\) | −22.4547 | −0.748906 | ||||||||
\(900\) | 50.9932 | 1.69977 | ||||||||
\(901\) | −4.17940 | −0.139236 | ||||||||
\(902\) | −45.7644 | −1.52379 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.52318 | −0.0506602 | ||||||||
\(905\) | 85.9566 | 2.85730 | ||||||||
\(906\) | −64.0290 | −2.12722 | ||||||||
\(907\) | −13.3010 | −0.441654 | −0.220827 | − | 0.975313i | \(-0.570876\pi\) | ||||
−0.220827 | + | 0.975313i | \(0.570876\pi\) | |||||||
\(908\) | −28.2178 | −0.936441 | ||||||||
\(909\) | −72.2047 | −2.39488 | ||||||||
\(910\) | −17.7043 | −0.586893 | ||||||||
\(911\) | −28.4342 | −0.942066 | −0.471033 | − | 0.882116i | \(-0.656119\pi\) | ||||
−0.471033 | + | 0.882116i | \(0.656119\pi\) | |||||||
\(912\) | −0.679681 | −0.0225065 | ||||||||
\(913\) | −39.4687 | −1.30622 | ||||||||
\(914\) | −70.8884 | −2.34478 | ||||||||
\(915\) | −92.2367 | −3.04925 | ||||||||
\(916\) | 22.4983 | 0.743364 | ||||||||
\(917\) | 19.8232 | 0.654619 | ||||||||
\(918\) | −9.29326 | −0.306723 | ||||||||
\(919\) | 23.2436 | 0.766736 | 0.383368 | − | 0.923596i | \(-0.374764\pi\) | ||||
0.383368 | + | 0.923596i | \(0.374764\pi\) | |||||||
\(920\) | −15.2114 | −0.501505 | ||||||||
\(921\) | 0.115046 | 0.00379090 | ||||||||
\(922\) | −12.4718 | −0.410738 | ||||||||
\(923\) | −14.1936 | −0.467188 | ||||||||
\(924\) | −20.6681 | −0.679929 | ||||||||
\(925\) | −4.40777 | −0.144926 | ||||||||
\(926\) | 32.9293 | 1.08212 | ||||||||
\(927\) | 16.7033 | 0.548608 | ||||||||
\(928\) | 20.0070 | 0.656761 | ||||||||
\(929\) | −20.6404 | −0.677190 | −0.338595 | − | 0.940932i | \(-0.609952\pi\) | ||||
−0.338595 | + | 0.940932i | \(0.609952\pi\) | |||||||
\(930\) | 148.603 | 4.87289 | ||||||||
\(931\) | 0.216251 | 0.00708734 | ||||||||
\(932\) | −37.4519 | −1.22678 | ||||||||
\(933\) | −63.7063 | −2.08565 | ||||||||
\(934\) | 32.7312 | 1.07100 | ||||||||
\(935\) | 8.03518 | 0.262778 | ||||||||
\(936\) | 5.94433 | 0.194297 | ||||||||
\(937\) | 0.590111 | 0.0192781 | 0.00963904 | − | 0.999954i | \(-0.496932\pi\) | ||||
0.00963904 | + | 0.999954i | \(0.496932\pi\) | |||||||
\(938\) | 16.4213 | 0.536173 | ||||||||
\(939\) | −66.6439 | −2.17484 | ||||||||
\(940\) | −49.9760 | −1.63004 | ||||||||
\(941\) | −8.30853 | −0.270850 | −0.135425 | − | 0.990788i | \(-0.543240\pi\) | ||||
−0.135425 | + | 0.990788i | \(0.543240\pi\) | |||||||
\(942\) | −24.0584 | −0.783866 | ||||||||
\(943\) | −55.0560 | −1.79287 | ||||||||
\(944\) | −52.2873 | −1.70181 | ||||||||
\(945\) | −31.4148 | −1.02192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.7590 | −0.609586 | −0.304793 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304793 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(948\) | −19.9071 | −0.646552 | ||||||||
\(949\) | 11.9012 | 0.386328 | ||||||||
\(950\) | −0.631729 | −0.0204960 | ||||||||
\(951\) | 63.0258 | 2.04375 | ||||||||
\(952\) | 1.09773 | 0.0355775 | ||||||||
\(953\) | 15.8962 | 0.514929 | 0.257464 | − | 0.966288i | \(-0.417113\pi\) | ||||
0.257464 | + | 0.966288i | \(0.417113\pi\) | |||||||
\(954\) | −44.4308 | −1.43850 | ||||||||
\(955\) | 5.48362 | 0.177446 | ||||||||
\(956\) | 18.6780 | 0.604091 | ||||||||
\(957\) | −20.7214 | −0.669827 | ||||||||
\(958\) | −72.0548 | −2.32799 | ||||||||
\(959\) | 5.03838 | 0.162698 | ||||||||
\(960\) | −44.4519 | −1.43468 | ||||||||
\(961\) | 36.5196 | 1.17805 | ||||||||
\(962\) | 2.14944 | 0.0693007 | ||||||||
\(963\) | −38.4575 | −1.23928 | ||||||||
\(964\) | 46.9741 | 1.51293 | ||||||||
\(965\) | 22.0316 | 0.709224 | ||||||||
\(966\) | −55.6724 | −1.79123 | ||||||||
\(967\) | −55.5030 | −1.78486 | −0.892428 | − | 0.451191i | \(-0.850999\pi\) | ||||
−0.892428 | + | 0.451191i | \(0.850999\pi\) | |||||||
\(968\) | 2.76744 | 0.0889490 | ||||||||
\(969\) | 0.130296 | 0.00418572 | ||||||||
\(970\) | 83.1314 | 2.66919 | ||||||||
\(971\) | −38.9315 | −1.24937 | −0.624685 | − | 0.780877i | \(-0.714773\pi\) | ||||
−0.624685 | + | 0.780877i | \(0.714773\pi\) | |||||||
\(972\) | 23.5626 | 0.755772 | ||||||||
\(973\) | 16.6820 | 0.534801 | ||||||||
\(974\) | −6.20488 | −0.198817 | ||||||||
\(975\) | 29.4022 | 0.941625 | ||||||||
\(976\) | 44.8230 | 1.43475 | ||||||||
\(977\) | −44.8825 | −1.43592 | −0.717959 | − | 0.696085i | \(-0.754923\pi\) | ||||
−0.717959 | + | 0.696085i | \(0.754923\pi\) | |||||||
\(978\) | −15.3306 | −0.490220 | ||||||||
\(979\) | −23.2678 | −0.743641 | ||||||||
\(980\) | 22.5847 | 0.721441 | ||||||||
\(981\) | 41.0395 | 1.31029 | ||||||||
\(982\) | 64.9652 | 2.07312 | ||||||||
\(983\) | −7.80558 | −0.248959 | −0.124480 | − | 0.992222i | \(-0.539726\pi\) | ||||
−0.124480 | + | 0.992222i | \(0.539726\pi\) | |||||||
\(984\) | 18.5269 | 0.590617 | ||||||||
\(985\) | −39.4408 | −1.25669 | ||||||||
\(986\) | −4.60394 | −0.146619 | ||||||||
\(987\) | 43.7236 | 1.39174 | ||||||||
\(988\) | 0.137586 | 0.00437720 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 85.4211 | 2.71486 | ||||||||
\(991\) | −23.9015 | −0.759256 | −0.379628 | − | 0.925139i | \(-0.623948\pi\) | ||||
−0.379628 | + | 0.925139i | \(0.623948\pi\) | |||||||
\(992\) | −60.1595 | −1.91007 | ||||||||
\(993\) | 28.6332 | 0.908646 | ||||||||
\(994\) | −27.8646 | −0.883812 | ||||||||
\(995\) | −24.9176 | −0.789940 | ||||||||
\(996\) | −66.8412 | −2.11794 | ||||||||
\(997\) | 14.5624 | 0.461195 | 0.230597 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230597 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(998\) | 69.7898 | 2.20916 | ||||||||
\(999\) | 3.81400 | 0.120670 |
(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 | 1849.2.a.p.1.17 | ✓ | 20 | |
43.42 | odd | 2 | 1849.2.a.r.1.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.p.1.17 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1849.2.a.r.1.4 | yes | 20 | 43.42 | odd | 2 |