Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + 6290 x^{10} - 9228 x^{9} - 12411 x^{8} + 14224 x^{7} + 14618 x^{6} - 10744 x^{5} + \cdots - 176 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(1.11352\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11352 | 0.787374 | 0.393687 | − | 0.919244i | \(-0.371199\pi\) | ||||
0.393687 | + | 0.919244i | \(0.371199\pi\) | |||||||
\(3\) | 2.27506 | 1.31351 | 0.656754 | − | 0.754105i | \(-0.271929\pi\) | ||||
0.656754 | + | 0.754105i | \(0.271929\pi\) | |||||||
\(4\) | −0.760083 | −0.380042 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.53332 | 1.03422 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.07340 | −1.08661 | ||||||||
\(9\) | 2.17591 | 0.725304 | ||||||||
\(10\) | 1.11352 | 0.352125 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.72924 | −0.499188 | ||||||||
\(13\) | 4.17534 | 1.15803 | 0.579015 | − | 0.815317i | \(-0.303437\pi\) | ||||
0.579015 | + | 0.815317i | \(0.303437\pi\) | |||||||
\(14\) | 1.11352 | 0.297600 | ||||||||
\(15\) | 2.27506 | 0.587419 | ||||||||
\(16\) | −1.90211 | −0.475527 | ||||||||
\(17\) | 5.01458 | 1.21621 | 0.608107 | − | 0.793855i | \(-0.291929\pi\) | ||||
0.608107 | + | 0.793855i | \(0.291929\pi\) | |||||||
\(18\) | 2.42291 | 0.571086 | ||||||||
\(19\) | 0.312580 | 0.0717107 | 0.0358553 | − | 0.999357i | \(-0.488584\pi\) | ||||
0.0358553 | + | 0.999357i | \(0.488584\pi\) | |||||||
\(20\) | −0.760083 | −0.169960 | ||||||||
\(21\) | 2.27506 | 0.496459 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.02983 | −0.214735 | −0.107368 | − | 0.994219i | \(-0.534242\pi\) | ||||
−0.107368 | + | 0.994219i | \(0.534242\pi\) | |||||||
\(24\) | −6.99217 | −1.42727 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.64930 | 0.911803 | ||||||||
\(27\) | −1.87485 | −0.360815 | ||||||||
\(28\) | −0.760083 | −0.143642 | ||||||||
\(29\) | 2.15091 | 0.399414 | 0.199707 | − | 0.979856i | \(-0.436001\pi\) | ||||
0.199707 | + | 0.979856i | \(0.436001\pi\) | |||||||
\(30\) | 2.53332 | 0.462519 | ||||||||
\(31\) | 10.5165 | 1.88883 | 0.944414 | − | 0.328760i | \(-0.106631\pi\) | ||||
0.944414 | + | 0.328760i | \(0.106631\pi\) | |||||||
\(32\) | 4.02876 | 0.712192 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.58381 | 0.957616 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.65387 | −0.275646 | ||||||||
\(37\) | −2.11848 | −0.348276 | −0.174138 | − | 0.984721i | \(-0.555714\pi\) | ||||
−0.174138 | + | 0.984721i | \(0.555714\pi\) | |||||||
\(38\) | 0.348062 | 0.0564631 | ||||||||
\(39\) | 9.49915 | 1.52108 | ||||||||
\(40\) | −3.07340 | −0.485946 | ||||||||
\(41\) | −11.3552 | −1.77338 | −0.886689 | − | 0.462367i | \(-0.847000\pi\) | ||||
−0.886689 | + | 0.462367i | \(0.847000\pi\) | |||||||
\(42\) | 2.53332 | 0.390900 | ||||||||
\(43\) | −7.14249 | −1.08922 | −0.544610 | − | 0.838689i | \(-0.683322\pi\) | ||||
−0.544610 | + | 0.838689i | \(0.683322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.17591 | 0.324366 | ||||||||
\(46\) | −1.14673 | −0.169077 | ||||||||
\(47\) | 3.94104 | 0.574860 | 0.287430 | − | 0.957802i | \(-0.407199\pi\) | ||||
0.287430 | + | 0.957802i | \(0.407199\pi\) | |||||||
\(48\) | −4.32742 | −0.624609 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.11352 | 0.157475 | ||||||||
\(51\) | 11.4085 | 1.59751 | ||||||||
\(52\) | −3.17360 | −0.440099 | ||||||||
\(53\) | −1.36714 | −0.187791 | −0.0938954 | − | 0.995582i | \(-0.529932\pi\) | ||||
−0.0938954 | + | 0.995582i | \(0.529932\pi\) | |||||||
\(54\) | −2.08768 | −0.284097 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.07340 | −0.410700 | ||||||||
\(57\) | 0.711138 | 0.0941926 | ||||||||
\(58\) | 2.39507 | 0.314489 | ||||||||
\(59\) | 11.8053 | 1.53692 | 0.768461 | − | 0.639897i | \(-0.221023\pi\) | ||||
0.768461 | + | 0.639897i | \(0.221023\pi\) | |||||||
\(60\) | −1.72924 | −0.223244 | ||||||||
\(61\) | −11.9389 | −1.52861 | −0.764307 | − | 0.644853i | \(-0.776919\pi\) | ||||
−0.764307 | + | 0.644853i | \(0.776919\pi\) | |||||||
\(62\) | 11.7103 | 1.48721 | ||||||||
\(63\) | 2.17591 | 0.274139 | ||||||||
\(64\) | 8.29031 | 1.03629 | ||||||||
\(65\) | 4.17534 | 0.517887 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7596 | 1.43666 | 0.718331 | − | 0.695701i | \(-0.244906\pi\) | ||||
0.718331 | + | 0.695701i | \(0.244906\pi\) | |||||||
\(68\) | −3.81150 | −0.462212 | ||||||||
\(69\) | −2.34293 | −0.282056 | ||||||||
\(70\) | 1.11352 | 0.133091 | ||||||||
\(71\) | 8.76864 | 1.04065 | 0.520323 | − | 0.853969i | \(-0.325812\pi\) | ||||
0.520323 | + | 0.853969i | \(0.325812\pi\) | |||||||
\(72\) | −6.68744 | −0.788122 | ||||||||
\(73\) | 8.87242 | 1.03844 | 0.519219 | − | 0.854641i | \(-0.326223\pi\) | ||||
0.519219 | + | 0.854641i | \(0.326223\pi\) | |||||||
\(74\) | −2.35896 | −0.274224 | ||||||||
\(75\) | 2.27506 | 0.262702 | ||||||||
\(76\) | −0.237586 | −0.0272530 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.5775 | 1.19766 | ||||||||
\(79\) | −1.61328 | −0.181508 | −0.0907538 | − | 0.995873i | \(-0.528928\pi\) | ||||
−0.0907538 | + | 0.995873i | \(0.528928\pi\) | |||||||
\(80\) | −1.90211 | −0.212662 | ||||||||
\(81\) | −10.7931 | −1.19924 | ||||||||
\(82\) | −12.6441 | −1.39631 | ||||||||
\(83\) | −14.3618 | −1.57642 | −0.788208 | − | 0.615410i | \(-0.788991\pi\) | ||||
−0.788208 | + | 0.615410i | \(0.788991\pi\) | |||||||
\(84\) | −1.72924 | −0.188675 | ||||||||
\(85\) | 5.01458 | 0.543907 | ||||||||
\(86\) | −7.95328 | −0.857624 | ||||||||
\(87\) | 4.89346 | 0.524634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0930 | 1.28185 | 0.640926 | − | 0.767603i | \(-0.278551\pi\) | ||||
0.640926 | + | 0.767603i | \(0.278551\pi\) | |||||||
\(90\) | 2.42291 | 0.255397 | ||||||||
\(91\) | 4.17534 | 0.437694 | ||||||||
\(92\) | 0.782759 | 0.0816082 | ||||||||
\(93\) | 23.9258 | 2.48099 | ||||||||
\(94\) | 4.38841 | 0.452630 | ||||||||
\(95\) | 0.312580 | 0.0320700 | ||||||||
\(96\) | 9.16569 | 0.935470 | ||||||||
\(97\) | −6.89342 | −0.699921 | −0.349961 | − | 0.936764i | \(-0.613805\pi\) | ||||
−0.349961 | + | 0.936764i | \(0.613805\pi\) | |||||||
\(98\) | 1.11352 | 0.112482 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.760083 | −0.0760083 | ||||||||
\(101\) | −8.55470 | −0.851224 | −0.425612 | − | 0.904906i | \(-0.639941\pi\) | ||||
−0.425612 | + | 0.904906i | \(0.639941\pi\) | |||||||
\(102\) | 12.7035 | 1.25784 | ||||||||
\(103\) | 6.76626 | 0.666700 | 0.333350 | − | 0.942803i | \(-0.391821\pi\) | ||||
0.333350 | + | 0.942803i | \(0.391821\pi\) | |||||||
\(104\) | −12.8325 | −1.25833 | ||||||||
\(105\) | 2.27506 | 0.222023 | ||||||||
\(106\) | −1.52233 | −0.147862 | ||||||||
\(107\) | 8.94463 | 0.864710 | 0.432355 | − | 0.901703i | \(-0.357683\pi\) | ||||
0.432355 | + | 0.901703i | \(0.357683\pi\) | |||||||
\(108\) | 1.42504 | 0.137125 | ||||||||
\(109\) | 13.0660 | 1.25150 | 0.625749 | − | 0.780025i | \(-0.284793\pi\) | ||||
0.625749 | + | 0.780025i | \(0.284793\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.81968 | −0.457463 | ||||||||
\(112\) | −1.90211 | −0.179732 | ||||||||
\(113\) | 7.00687 | 0.659151 | 0.329576 | − | 0.944129i | \(-0.393094\pi\) | ||||
0.329576 | + | 0.944129i | \(0.393094\pi\) | |||||||
\(114\) | 0.791863 | 0.0741648 | ||||||||
\(115\) | −1.02983 | −0.0960324 | ||||||||
\(116\) | −1.63487 | −0.151794 | ||||||||
\(117\) | 9.08517 | 0.839924 | ||||||||
\(118\) | 13.1454 | 1.21013 | ||||||||
\(119\) | 5.01458 | 0.459686 | ||||||||
\(120\) | −6.99217 | −0.638295 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −13.2941 | −1.20359 | ||||||||
\(123\) | −25.8337 | −2.32935 | ||||||||
\(124\) | −7.99345 | −0.717833 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.42291 | 0.215850 | ||||||||
\(127\) | 4.24376 | 0.376573 | 0.188286 | − | 0.982114i | \(-0.439707\pi\) | ||||
0.188286 | + | 0.982114i | \(0.439707\pi\) | |||||||
\(128\) | 1.17386 | 0.103755 | ||||||||
\(129\) | −16.2496 | −1.43070 | ||||||||
\(130\) | 4.64930 | 0.407771 | ||||||||
\(131\) | 11.3525 | 0.991870 | 0.495935 | − | 0.868360i | \(-0.334825\pi\) | ||||
0.495935 | + | 0.868360i | \(0.334825\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.312580 | 0.0271041 | ||||||||
\(134\) | 13.0945 | 1.13119 | ||||||||
\(135\) | −1.87485 | −0.161361 | ||||||||
\(136\) | −15.4118 | −1.32155 | ||||||||
\(137\) | −0.885628 | −0.0756643 | −0.0378322 | − | 0.999284i | \(-0.512045\pi\) | ||||
−0.0378322 | + | 0.999284i | \(0.512045\pi\) | |||||||
\(138\) | −2.60889 | −0.222084 | ||||||||
\(139\) | 14.2443 | 1.20818 | 0.604092 | − | 0.796915i | \(-0.293536\pi\) | ||||
0.604092 | + | 0.796915i | \(0.293536\pi\) | |||||||
\(140\) | −0.760083 | −0.0642387 | ||||||||
\(141\) | 8.96611 | 0.755083 | ||||||||
\(142\) | 9.76402 | 0.819378 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.13882 | −0.344902 | ||||||||
\(145\) | 2.15091 | 0.178623 | ||||||||
\(146\) | 9.87957 | 0.817639 | ||||||||
\(147\) | 2.27506 | 0.187644 | ||||||||
\(148\) | 1.61022 | 0.132359 | ||||||||
\(149\) | −7.94306 | −0.650720 | −0.325360 | − | 0.945590i | \(-0.605486\pi\) | ||||
−0.325360 | + | 0.945590i | \(0.605486\pi\) | |||||||
\(150\) | 2.53332 | 0.206845 | ||||||||
\(151\) | −14.3899 | −1.17103 | −0.585515 | − | 0.810662i | \(-0.699108\pi\) | ||||
−0.585515 | + | 0.810662i | \(0.699108\pi\) | |||||||
\(152\) | −0.960681 | −0.0779215 | ||||||||
\(153\) | 10.9113 | 0.882125 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5165 | 0.844709 | ||||||||
\(156\) | −7.22015 | −0.578074 | ||||||||
\(157\) | −12.1593 | −0.970416 | −0.485208 | − | 0.874399i | \(-0.661256\pi\) | ||||
−0.485208 | + | 0.874399i | \(0.661256\pi\) | |||||||
\(158\) | −1.79641 | −0.142914 | ||||||||
\(159\) | −3.11032 | −0.246665 | ||||||||
\(160\) | 4.02876 | 0.318502 | ||||||||
\(161\) | −1.02983 | −0.0811622 | ||||||||
\(162\) | −12.0183 | −0.944249 | ||||||||
\(163\) | 16.3139 | 1.27780 | 0.638902 | − | 0.769288i | \(-0.279389\pi\) | ||||
0.638902 | + | 0.769288i | \(0.279389\pi\) | |||||||
\(164\) | 8.63086 | 0.673957 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.9921 | −1.24123 | ||||||||
\(167\) | −10.5623 | −0.817337 | −0.408669 | − | 0.912683i | \(-0.634007\pi\) | ||||
−0.408669 | + | 0.912683i | \(0.634007\pi\) | |||||||
\(168\) | −6.99217 | −0.539458 | ||||||||
\(169\) | 4.43343 | 0.341033 | ||||||||
\(170\) | 5.58381 | 0.428259 | ||||||||
\(171\) | 0.680146 | 0.0520120 | ||||||||
\(172\) | 5.42889 | 0.413949 | ||||||||
\(173\) | −8.13127 | −0.618209 | −0.309104 | − | 0.951028i | \(-0.600029\pi\) | ||||
−0.309104 | + | 0.951028i | \(0.600029\pi\) | |||||||
\(174\) | 5.44894 | 0.413083 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.8579 | 2.01876 | ||||||||
\(178\) | 13.4657 | 1.00930 | ||||||||
\(179\) | −21.2805 | −1.59058 | −0.795291 | − | 0.606228i | \(-0.792682\pi\) | ||||
−0.795291 | + | 0.606228i | \(0.792682\pi\) | |||||||
\(180\) | −1.65387 | −0.123273 | ||||||||
\(181\) | −2.81598 | −0.209310 | −0.104655 | − | 0.994509i | \(-0.533374\pi\) | ||||
−0.104655 | + | 0.994509i | \(0.533374\pi\) | |||||||
\(182\) | 4.64930 | 0.344629 | ||||||||
\(183\) | −27.1616 | −2.00785 | ||||||||
\(184\) | 3.16508 | 0.233333 | ||||||||
\(185\) | −2.11848 | −0.155754 | ||||||||
\(186\) | 26.6418 | 1.95347 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.99552 | −0.218470 | ||||||||
\(189\) | −1.87485 | −0.136375 | ||||||||
\(190\) | 0.348062 | 0.0252511 | ||||||||
\(191\) | −1.48362 | −0.107351 | −0.0536755 | − | 0.998558i | \(-0.517094\pi\) | ||||
−0.0536755 | + | 0.998558i | \(0.517094\pi\) | |||||||
\(192\) | 18.8610 | 1.36117 | ||||||||
\(193\) | 7.36948 | 0.530467 | 0.265233 | − | 0.964184i | \(-0.414551\pi\) | ||||
0.265233 | + | 0.964184i | \(0.414551\pi\) | |||||||
\(194\) | −7.67593 | −0.551100 | ||||||||
\(195\) | 9.49915 | 0.680248 | ||||||||
\(196\) | −0.760083 | −0.0542916 | ||||||||
\(197\) | 4.74986 | 0.338413 | 0.169207 | − | 0.985581i | \(-0.445879\pi\) | ||||
0.169207 | + | 0.985581i | \(0.445879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5306 | 1.31360 | 0.656801 | − | 0.754064i | \(-0.271909\pi\) | ||||
0.656801 | + | 0.754064i | \(0.271909\pi\) | |||||||
\(200\) | −3.07340 | −0.217322 | ||||||||
\(201\) | 26.7538 | 1.88707 | ||||||||
\(202\) | −9.52579 | −0.670232 | ||||||||
\(203\) | 2.15091 | 0.150964 | ||||||||
\(204\) | −8.67139 | −0.607119 | ||||||||
\(205\) | −11.3552 | −0.793078 | ||||||||
\(206\) | 7.53434 | 0.524942 | ||||||||
\(207\) | −2.24083 | −0.155748 | ||||||||
\(208\) | −7.94194 | −0.550674 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.53332 | 0.174816 | ||||||||
\(211\) | −1.09345 | −0.0752763 | −0.0376382 | − | 0.999291i | \(-0.511983\pi\) | ||||
−0.0376382 | + | 0.999291i | \(0.511983\pi\) | |||||||
\(212\) | 1.03914 | 0.0713683 | ||||||||
\(213\) | 19.9492 | 1.36690 | ||||||||
\(214\) | 9.95998 | 0.680851 | ||||||||
\(215\) | −7.14249 | −0.487114 | ||||||||
\(216\) | 5.76216 | 0.392065 | ||||||||
\(217\) | 10.5165 | 0.713910 | ||||||||
\(218\) | 14.5492 | 0.985397 | ||||||||
\(219\) | 20.1853 | 1.36400 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.9375 | 1.40841 | ||||||||
\(222\) | −5.36678 | −0.360195 | ||||||||
\(223\) | −19.5847 | −1.31149 | −0.655743 | − | 0.754984i | \(-0.727644\pi\) | ||||
−0.655743 | + | 0.754984i | \(0.727644\pi\) | |||||||
\(224\) | 4.02876 | 0.269183 | ||||||||
\(225\) | 2.17591 | 0.145061 | ||||||||
\(226\) | 7.80226 | 0.518999 | ||||||||
\(227\) | −9.66593 | −0.641551 | −0.320775 | − | 0.947155i | \(-0.603943\pi\) | ||||
−0.320775 | + | 0.947155i | \(0.603943\pi\) | |||||||
\(228\) | −0.540524 | −0.0357971 | ||||||||
\(229\) | −15.4487 | −1.02088 | −0.510440 | − | 0.859914i | \(-0.670517\pi\) | ||||
−0.510440 | + | 0.859914i | \(0.670517\pi\) | |||||||
\(230\) | −1.14673 | −0.0756135 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.61060 | −0.434007 | ||||||||
\(233\) | 9.47282 | 0.620585 | 0.310293 | − | 0.950641i | \(-0.399573\pi\) | ||||
0.310293 | + | 0.950641i | \(0.399573\pi\) | |||||||
\(234\) | 10.1165 | 0.661335 | ||||||||
\(235\) | 3.94104 | 0.257085 | ||||||||
\(236\) | −8.97302 | −0.584094 | ||||||||
\(237\) | −3.67030 | −0.238412 | ||||||||
\(238\) | 5.58381 | 0.361945 | ||||||||
\(239\) | −26.7655 | −1.73132 | −0.865659 | − | 0.500634i | \(-0.833100\pi\) | ||||
−0.865659 | + | 0.500634i | \(0.833100\pi\) | |||||||
\(240\) | −4.32742 | −0.279333 | ||||||||
\(241\) | 0.595851 | 0.0383821 | 0.0191911 | − | 0.999816i | \(-0.493891\pi\) | ||||
0.0191911 | + | 0.999816i | \(0.493891\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.9305 | −1.21439 | ||||||||
\(244\) | 9.07452 | 0.580937 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −28.7662 | −1.83407 | ||||||||
\(247\) | 1.30512 | 0.0830431 | ||||||||
\(248\) | −32.3215 | −2.05242 | ||||||||
\(249\) | −32.6741 | −2.07063 | ||||||||
\(250\) | 1.11352 | 0.0704249 | ||||||||
\(251\) | −12.8329 | −0.810005 | −0.405002 | − | 0.914316i | \(-0.632729\pi\) | ||||
−0.405002 | + | 0.914316i | \(0.632729\pi\) | |||||||
\(252\) | −1.65387 | −0.104184 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.72549 | 0.296504 | ||||||||
\(255\) | 11.4085 | 0.714427 | ||||||||
\(256\) | −15.2735 | −0.954594 | ||||||||
\(257\) | −16.9113 | −1.05490 | −0.527449 | − | 0.849587i | \(-0.676852\pi\) | ||||
−0.527449 | + | 0.849587i | \(0.676852\pi\) | |||||||
\(258\) | −18.0942 | −1.12650 | ||||||||
\(259\) | −2.11848 | −0.131636 | ||||||||
\(260\) | −3.17360 | −0.196818 | ||||||||
\(261\) | 4.68020 | 0.289697 | ||||||||
\(262\) | 12.6412 | 0.780973 | ||||||||
\(263\) | −25.4109 | −1.56690 | −0.783450 | − | 0.621455i | \(-0.786542\pi\) | ||||
−0.783450 | + | 0.621455i | \(0.786542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.36714 | −0.0839826 | ||||||||
\(266\) | 0.348062 | 0.0213411 | ||||||||
\(267\) | 27.5123 | 1.68372 | ||||||||
\(268\) | −8.93826 | −0.545991 | ||||||||
\(269\) | −3.23176 | −0.197044 | −0.0985221 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985221 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(270\) | −2.08768 | −0.127052 | ||||||||
\(271\) | −23.6985 | −1.43958 | −0.719791 | − | 0.694190i | \(-0.755763\pi\) | ||||
−0.719791 | + | 0.694190i | \(0.755763\pi\) | |||||||
\(272\) | −9.53827 | −0.578342 | ||||||||
\(273\) | 9.49915 | 0.574915 | ||||||||
\(274\) | −0.986161 | −0.0595762 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.78083 | 0.107193 | ||||||||
\(277\) | 0.376998 | 0.0226516 | 0.0113258 | − | 0.999936i | \(-0.496395\pi\) | ||||
0.0113258 | + | 0.999936i | \(0.496395\pi\) | |||||||
\(278\) | 15.8612 | 0.951293 | ||||||||
\(279\) | 22.8831 | 1.36997 | ||||||||
\(280\) | −3.07340 | −0.183671 | ||||||||
\(281\) | 9.76106 | 0.582296 | 0.291148 | − | 0.956678i | \(-0.405963\pi\) | ||||
0.291148 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(282\) | 9.98390 | 0.594533 | ||||||||
\(283\) | −15.9320 | −0.947056 | −0.473528 | − | 0.880779i | \(-0.657020\pi\) | ||||
−0.473528 | + | 0.880779i | \(0.657020\pi\) | |||||||
\(284\) | −6.66490 | −0.395489 | ||||||||
\(285\) | 0.711138 | 0.0421242 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3552 | −0.670274 | ||||||||
\(288\) | 8.76624 | 0.516556 | ||||||||
\(289\) | 8.14599 | 0.479176 | ||||||||
\(290\) | 2.39507 | 0.140644 | ||||||||
\(291\) | −15.6830 | −0.919352 | ||||||||
\(292\) | −6.74377 | −0.394649 | ||||||||
\(293\) | 4.04334 | 0.236214 | 0.118107 | − | 0.993001i | \(-0.462317\pi\) | ||||
0.118107 | + | 0.993001i | \(0.462317\pi\) | |||||||
\(294\) | 2.53332 | 0.147746 | ||||||||
\(295\) | 11.8053 | 0.687332 | ||||||||
\(296\) | 6.51093 | 0.378440 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.84472 | −0.512361 | ||||||||
\(299\) | −4.29990 | −0.248670 | ||||||||
\(300\) | −1.72924 | −0.0998375 | ||||||||
\(301\) | −7.14249 | −0.411686 | ||||||||
\(302\) | −16.0233 | −0.922039 | ||||||||
\(303\) | −19.4625 | −1.11809 | ||||||||
\(304\) | −0.594560 | −0.0341004 | ||||||||
\(305\) | −11.9389 | −0.683617 | ||||||||
\(306\) | 12.1499 | 0.694563 | ||||||||
\(307\) | −27.9625 | −1.59590 | −0.797951 | − | 0.602722i | \(-0.794083\pi\) | ||||
−0.797951 | + | 0.602722i | \(0.794083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.3937 | 0.875716 | ||||||||
\(310\) | 11.7103 | 0.665102 | ||||||||
\(311\) | −25.7900 | −1.46242 | −0.731209 | − | 0.682154i | \(-0.761043\pi\) | ||||
−0.731209 | + | 0.682154i | \(0.761043\pi\) | |||||||
\(312\) | −29.1947 | −1.65282 | ||||||||
\(313\) | −5.19429 | −0.293599 | −0.146799 | − | 0.989166i | \(-0.546897\pi\) | ||||
−0.146799 | + | 0.989166i | \(0.546897\pi\) | |||||||
\(314\) | −13.5396 | −0.764081 | ||||||||
\(315\) | 2.17591 | 0.122599 | ||||||||
\(316\) | 1.22622 | 0.0689805 | ||||||||
\(317\) | 18.8735 | 1.06004 | 0.530021 | − | 0.847984i | \(-0.322184\pi\) | ||||
0.530021 | + | 0.847984i | \(0.322184\pi\) | |||||||
\(318\) | −3.46340 | −0.194218 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.29031 | 0.463442 | ||||||||
\(321\) | 20.3496 | 1.13580 | ||||||||
\(322\) | −1.14673 | −0.0639050 | ||||||||
\(323\) | 1.56745 | 0.0872155 | ||||||||
\(324\) | 8.20368 | 0.455760 | ||||||||
\(325\) | 4.17534 | 0.231606 | ||||||||
\(326\) | 18.1658 | 1.00611 | ||||||||
\(327\) | 29.7260 | 1.64385 | ||||||||
\(328\) | 34.8989 | 1.92697 | ||||||||
\(329\) | 3.94104 | 0.217276 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2955 | −0.730785 | −0.365393 | − | 0.930854i | \(-0.619065\pi\) | ||||
−0.365393 | + | 0.930854i | \(0.619065\pi\) | |||||||
\(332\) | 10.9162 | 0.599103 | ||||||||
\(333\) | −4.60963 | −0.252606 | ||||||||
\(334\) | −11.7613 | −0.643550 | ||||||||
\(335\) | 11.7596 | 0.642495 | ||||||||
\(336\) | −4.32742 | −0.236080 | ||||||||
\(337\) | −6.70480 | −0.365234 | −0.182617 | − | 0.983184i | \(-0.558457\pi\) | ||||
−0.182617 | + | 0.983184i | \(0.558457\pi\) | |||||||
\(338\) | 4.93669 | 0.268521 | ||||||||
\(339\) | 15.9411 | 0.865801 | ||||||||
\(340\) | −3.81150 | −0.206707 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.757353 | 0.0409530 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 21.9517 | 1.18356 | ||||||||
\(345\) | −2.34293 | −0.126139 | ||||||||
\(346\) | −9.05429 | −0.486762 | ||||||||
\(347\) | 20.0331 | 1.07543 | 0.537717 | − | 0.843126i | \(-0.319287\pi\) | ||||
0.537717 | + | 0.843126i | \(0.319287\pi\) | |||||||
\(348\) | −3.71944 | −0.199383 | ||||||||
\(349\) | −2.33534 | −0.125008 | −0.0625039 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625039 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(350\) | 1.11352 | 0.0595199 | ||||||||
\(351\) | −7.82813 | −0.417835 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.08902 | −0.217636 | −0.108818 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108818 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(354\) | 29.9066 | 1.58952 | ||||||||
\(355\) | 8.76864 | 0.465391 | ||||||||
\(356\) | −9.19166 | −0.487157 | ||||||||
\(357\) | 11.4085 | 0.603801 | ||||||||
\(358\) | −23.6962 | −1.25238 | ||||||||
\(359\) | 22.3068 | 1.17731 | 0.588654 | − | 0.808385i | \(-0.299658\pi\) | ||||
0.588654 | + | 0.808385i | \(0.299658\pi\) | |||||||
\(360\) | −6.68744 | −0.352459 | ||||||||
\(361\) | −18.9023 | −0.994858 | ||||||||
\(362\) | −3.13563 | −0.164805 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.17360 | −0.166342 | ||||||||
\(365\) | 8.87242 | 0.464403 | ||||||||
\(366\) | −30.2449 | −1.58093 | ||||||||
\(367\) | −7.37748 | −0.385101 | −0.192551 | − | 0.981287i | \(-0.561676\pi\) | ||||
−0.192551 | + | 0.981287i | \(0.561676\pi\) | |||||||
\(368\) | 1.95885 | 0.102112 | ||||||||
\(369\) | −24.7078 | −1.28624 | ||||||||
\(370\) | −2.35896 | −0.122637 | ||||||||
\(371\) | −1.36714 | −0.0709783 | ||||||||
\(372\) | −18.1856 | −0.942879 | ||||||||
\(373\) | 6.98127 | 0.361476 | 0.180738 | − | 0.983531i | \(-0.442151\pi\) | ||||
0.180738 | + | 0.983531i | \(0.442151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.27506 | 0.117484 | ||||||||
\(376\) | −12.1124 | −0.624648 | ||||||||
\(377\) | 8.98078 | 0.462534 | ||||||||
\(378\) | −2.08768 | −0.107378 | ||||||||
\(379\) | 10.5931 | 0.544129 | 0.272065 | − | 0.962279i | \(-0.412294\pi\) | ||||
0.272065 | + | 0.962279i | \(0.412294\pi\) | |||||||
\(380\) | −0.237586 | −0.0121879 | ||||||||
\(381\) | 9.65482 | 0.494632 | ||||||||
\(382\) | −1.65204 | −0.0845255 | ||||||||
\(383\) | −18.8440 | −0.962883 | −0.481442 | − | 0.876478i | \(-0.659887\pi\) | ||||
−0.481442 | + | 0.876478i | \(0.659887\pi\) | |||||||
\(384\) | 2.67060 | 0.136283 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.20603 | 0.417676 | ||||||||
\(387\) | −15.5414 | −0.790016 | ||||||||
\(388\) | 5.23957 | 0.265999 | ||||||||
\(389\) | −17.5458 | −0.889606 | −0.444803 | − | 0.895629i | \(-0.646726\pi\) | ||||
−0.444803 | + | 0.895629i | \(0.646726\pi\) | |||||||
\(390\) | 10.5775 | 0.535610 | ||||||||
\(391\) | −5.16418 | −0.261164 | ||||||||
\(392\) | −3.07340 | −0.155230 | ||||||||
\(393\) | 25.8276 | 1.30283 | ||||||||
\(394\) | 5.28904 | 0.266458 | ||||||||
\(395\) | −1.61328 | −0.0811727 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0385 | 0.654384 | 0.327192 | − | 0.944958i | \(-0.393898\pi\) | ||||
0.327192 | + | 0.944958i | \(0.393898\pi\) | |||||||
\(398\) | 20.6341 | 1.03430 | ||||||||
\(399\) | 0.711138 | 0.0356014 | ||||||||
\(400\) | −1.90211 | −0.0951054 | ||||||||
\(401\) | −31.2032 | −1.55821 | −0.779107 | − | 0.626891i | \(-0.784327\pi\) | ||||
−0.779107 | + | 0.626891i | \(0.784327\pi\) | |||||||
\(402\) | 29.7908 | 1.48583 | ||||||||
\(403\) | 43.9101 | 2.18732 | ||||||||
\(404\) | 6.50228 | 0.323501 | ||||||||
\(405\) | −10.7931 | −0.536316 | ||||||||
\(406\) | 2.39507 | 0.118865 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −35.0628 | −1.73587 | ||||||||
\(409\) | 4.00622 | 0.198095 | 0.0990473 | − | 0.995083i | \(-0.468420\pi\) | ||||
0.0990473 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(410\) | −12.6441 | −0.624450 | ||||||||
\(411\) | −2.01486 | −0.0993857 | ||||||||
\(412\) | −5.14292 | −0.253374 | ||||||||
\(413\) | 11.8053 | 0.580902 | ||||||||
\(414\) | −2.49520 | −0.122632 | ||||||||
\(415\) | −14.3618 | −0.704994 | ||||||||
\(416\) | 16.8214 | 0.824739 | ||||||||
\(417\) | 32.4066 | 1.58696 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.4722 | 1.43981 | 0.719904 | − | 0.694073i | \(-0.244186\pi\) | ||||
0.719904 | + | 0.694073i | \(0.244186\pi\) | |||||||
\(420\) | −1.72924 | −0.0843781 | ||||||||
\(421\) | 20.4435 | 0.996357 | 0.498178 | − | 0.867075i | \(-0.334003\pi\) | ||||
0.498178 | + | 0.867075i | \(0.334003\pi\) | |||||||
\(422\) | −1.21758 | −0.0592707 | ||||||||
\(423\) | 8.57536 | 0.416948 | ||||||||
\(424\) | 4.20175 | 0.204055 | ||||||||
\(425\) | 5.01458 | 0.243243 | ||||||||
\(426\) | 22.2138 | 1.07626 | ||||||||
\(427\) | −11.9389 | −0.577762 | ||||||||
\(428\) | −6.79866 | −0.328626 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.95328 | −0.383541 | ||||||||
\(431\) | −14.6351 | −0.704948 | −0.352474 | − | 0.935822i | \(-0.614659\pi\) | ||||
−0.352474 | + | 0.935822i | \(0.614659\pi\) | |||||||
\(432\) | 3.56617 | 0.171577 | ||||||||
\(433\) | 35.0436 | 1.68409 | 0.842044 | − | 0.539409i | \(-0.181352\pi\) | ||||
0.842044 | + | 0.539409i | \(0.181352\pi\) | |||||||
\(434\) | 11.7103 | 0.562114 | ||||||||
\(435\) | 4.89346 | 0.234623 | ||||||||
\(436\) | −9.93126 | −0.475621 | ||||||||
\(437\) | −0.321905 | −0.0153988 | ||||||||
\(438\) | 22.4767 | 1.07398 | ||||||||
\(439\) | −30.3987 | −1.45085 | −0.725425 | − | 0.688301i | \(-0.758357\pi\) | ||||
−0.725425 | + | 0.688301i | \(0.758357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.17591 | 0.103615 | ||||||||
\(442\) | 23.3143 | 1.10895 | ||||||||
\(443\) | −21.3935 | −1.01644 | −0.508219 | − | 0.861228i | \(-0.669696\pi\) | ||||
−0.508219 | + | 0.861228i | \(0.669696\pi\) | |||||||
\(444\) | 3.66335 | 0.173855 | ||||||||
\(445\) | 12.0930 | 0.573262 | ||||||||
\(446\) | −21.8078 | −1.03263 | ||||||||
\(447\) | −18.0710 | −0.854727 | ||||||||
\(448\) | 8.29031 | 0.391680 | ||||||||
\(449\) | 16.2274 | 0.765816 | 0.382908 | − | 0.923786i | \(-0.374923\pi\) | ||||
0.382908 | + | 0.923786i | \(0.374923\pi\) | |||||||
\(450\) | 2.42291 | 0.114217 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.32581 | −0.250505 | ||||||||
\(453\) | −32.7378 | −1.53816 | ||||||||
\(454\) | −10.7632 | −0.505140 | ||||||||
\(455\) | 4.17534 | 0.195743 | ||||||||
\(456\) | −2.18561 | −0.102351 | ||||||||
\(457\) | 23.0581 | 1.07861 | 0.539306 | − | 0.842110i | \(-0.318687\pi\) | ||||
0.539306 | + | 0.842110i | \(0.318687\pi\) | |||||||
\(458\) | −17.2024 | −0.803814 | ||||||||
\(459\) | −9.40159 | −0.438828 | ||||||||
\(460\) | 0.782759 | 0.0364963 | ||||||||
\(461\) | −8.06731 | −0.375732 | −0.187866 | − | 0.982195i | \(-0.560157\pi\) | ||||
−0.187866 | + | 0.982195i | \(0.560157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.7289 | −1.24220 | −0.621100 | − | 0.783732i | \(-0.713314\pi\) | ||||
−0.621100 | + | 0.783732i | \(0.713314\pi\) | |||||||
\(464\) | −4.09126 | −0.189932 | ||||||||
\(465\) | 23.9258 | 1.10953 | ||||||||
\(466\) | 10.5481 | 0.488633 | ||||||||
\(467\) | −24.7786 | −1.14662 | −0.573308 | − | 0.819340i | \(-0.694340\pi\) | ||||
−0.573308 | + | 0.819340i | \(0.694340\pi\) | |||||||
\(468\) | −6.90548 | −0.319206 | ||||||||
\(469\) | 11.7596 | 0.543007 | ||||||||
\(470\) | 4.38841 | 0.202422 | ||||||||
\(471\) | −27.6631 | −1.27465 | ||||||||
\(472\) | −36.2824 | −1.67003 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.08694 | −0.187719 | ||||||||
\(475\) | 0.312580 | 0.0143421 | ||||||||
\(476\) | −3.81150 | −0.174700 | ||||||||
\(477\) | −2.97477 | −0.136205 | ||||||||
\(478\) | −29.8038 | −1.36320 | ||||||||
\(479\) | 3.03628 | 0.138731 | 0.0693655 | − | 0.997591i | \(-0.477903\pi\) | ||||
0.0693655 | + | 0.997591i | \(0.477903\pi\) | |||||||
\(480\) | 9.16569 | 0.418355 | ||||||||
\(481\) | −8.84537 | −0.403314 | ||||||||
\(482\) | 0.663489 | 0.0302211 | ||||||||
\(483\) | −2.34293 | −0.106607 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.89342 | −0.313014 | ||||||||
\(486\) | −21.0794 | −0.956183 | ||||||||
\(487\) | 39.8582 | 1.80615 | 0.903073 | − | 0.429487i | \(-0.141306\pi\) | ||||
0.903073 | + | 0.429487i | \(0.141306\pi\) | |||||||
\(488\) | 36.6928 | 1.66101 | ||||||||
\(489\) | 37.1152 | 1.67841 | ||||||||
\(490\) | 1.11352 | 0.0503035 | ||||||||
\(491\) | −25.2397 | −1.13905 | −0.569525 | − | 0.821974i | \(-0.692873\pi\) | ||||
−0.569525 | + | 0.821974i | \(0.692873\pi\) | |||||||
\(492\) | 19.6358 | 0.885248 | ||||||||
\(493\) | 10.7859 | 0.485773 | ||||||||
\(494\) | 1.45328 | 0.0653860 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0036 | −0.898188 | ||||||||
\(497\) | 8.76864 | 0.393327 | ||||||||
\(498\) | −36.3831 | −1.63036 | ||||||||
\(499\) | 25.3540 | 1.13500 | 0.567501 | − | 0.823373i | \(-0.307910\pi\) | ||||
0.567501 | + | 0.823373i | \(0.307910\pi\) | |||||||
\(500\) | −0.760083 | −0.0339919 | ||||||||
\(501\) | −24.0300 | −1.07358 | ||||||||
\(502\) | −14.2896 | −0.637777 | ||||||||
\(503\) | 19.9335 | 0.888789 | 0.444394 | − | 0.895831i | \(-0.353419\pi\) | ||||
0.444394 | + | 0.895831i | \(0.353419\pi\) | |||||||
\(504\) | −6.68744 | −0.297882 | ||||||||
\(505\) | −8.55470 | −0.380679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0863 | 0.447950 | ||||||||
\(508\) | −3.22561 | −0.143113 | ||||||||
\(509\) | 7.03658 | 0.311891 | 0.155945 | − | 0.987766i | \(-0.450158\pi\) | ||||
0.155945 | + | 0.987766i | \(0.450158\pi\) | |||||||
\(510\) | 12.7035 | 0.562521 | ||||||||
\(511\) | 8.87242 | 0.392493 | ||||||||
\(512\) | −19.3550 | −0.855378 | ||||||||
\(513\) | −0.586040 | −0.0258743 | ||||||||
\(514\) | −18.8310 | −0.830600 | ||||||||
\(515\) | 6.76626 | 0.298157 | ||||||||
\(516\) | 12.3511 | 0.543725 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.35896 | −0.103647 | ||||||||
\(519\) | −18.4991 | −0.812023 | ||||||||
\(520\) | −12.8325 | −0.562741 | ||||||||
\(521\) | −24.3393 | −1.06632 | −0.533161 | − | 0.846014i | \(-0.678996\pi\) | ||||
−0.533161 | + | 0.846014i | \(0.678996\pi\) | |||||||
\(522\) | 5.21147 | 0.228100 | ||||||||
\(523\) | −21.2450 | −0.928980 | −0.464490 | − | 0.885578i | \(-0.653762\pi\) | ||||
−0.464490 | + | 0.885578i | \(0.653762\pi\) | |||||||
\(524\) | −8.62882 | −0.376952 | ||||||||
\(525\) | 2.27506 | 0.0992919 | ||||||||
\(526\) | −28.2954 | −1.23374 | ||||||||
\(527\) | 52.7360 | 2.29722 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9394 | −0.953889 | ||||||||
\(530\) | −1.52233 | −0.0661258 | ||||||||
\(531\) | 25.6873 | 1.11474 | ||||||||
\(532\) | −0.237586 | −0.0103007 | ||||||||
\(533\) | −47.4116 | −2.05362 | ||||||||
\(534\) | 30.6353 | 1.32572 | ||||||||
\(535\) | 8.94463 | 0.386710 | ||||||||
\(536\) | −36.1419 | −1.56109 | ||||||||
\(537\) | −48.4146 | −2.08924 | ||||||||
\(538\) | −3.59862 | −0.155148 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.42504 | 0.0613241 | ||||||||
\(541\) | −38.9615 | −1.67509 | −0.837543 | − | 0.546371i | \(-0.816009\pi\) | ||||
−0.837543 | + | 0.546371i | \(0.816009\pi\) | |||||||
\(542\) | −26.3887 | −1.13349 | ||||||||
\(543\) | −6.40652 | −0.274930 | ||||||||
\(544\) | 20.2026 | 0.866177 | ||||||||
\(545\) | 13.0660 | 0.559687 | ||||||||
\(546\) | 10.5775 | 0.452673 | ||||||||
\(547\) | 1.11963 | 0.0478718 | 0.0239359 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239359 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(548\) | 0.673151 | 0.0287556 | ||||||||
\(549\) | −25.9779 | −1.10871 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.672331 | 0.0286423 | ||||||||
\(552\) | 7.20077 | 0.306485 | ||||||||
\(553\) | −1.61328 | −0.0686034 | ||||||||
\(554\) | 0.419793 | 0.0178353 | ||||||||
\(555\) | −4.81968 | −0.204584 | ||||||||
\(556\) | −10.8268 | −0.459160 | ||||||||
\(557\) | −13.1234 | −0.556058 | −0.278029 | − | 0.960573i | \(-0.589681\pi\) | ||||
−0.278029 | + | 0.960573i | \(0.589681\pi\) | |||||||
\(558\) | 25.4807 | 1.07868 | ||||||||
\(559\) | −29.8223 | −1.26135 | ||||||||
\(560\) | −1.90211 | −0.0803787 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.8691 | 0.458485 | ||||||||
\(563\) | 19.6066 | 0.826322 | 0.413161 | − | 0.910658i | \(-0.364425\pi\) | ||||
0.413161 | + | 0.910658i | \(0.364425\pi\) | |||||||
\(564\) | −6.81499 | −0.286963 | ||||||||
\(565\) | 7.00687 | 0.294781 | ||||||||
\(566\) | −17.7405 | −0.745688 | ||||||||
\(567\) | −10.7931 | −0.453269 | ||||||||
\(568\) | −26.9495 | −1.13078 | ||||||||
\(569\) | −34.5612 | −1.44888 | −0.724441 | − | 0.689337i | \(-0.757902\pi\) | ||||
−0.724441 | + | 0.689337i | \(0.757902\pi\) | |||||||
\(570\) | 0.791863 | 0.0331675 | ||||||||
\(571\) | 0.701299 | 0.0293484 | 0.0146742 | − | 0.999892i | \(-0.495329\pi\) | ||||
0.0146742 | + | 0.999892i | \(0.495329\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.37533 | −0.141007 | ||||||||
\(574\) | −12.6441 | −0.527756 | ||||||||
\(575\) | −1.02983 | −0.0429470 | ||||||||
\(576\) | 18.0390 | 0.751624 | ||||||||
\(577\) | −0.0841312 | −0.00350243 | −0.00175121 | − | 0.999998i | \(-0.500557\pi\) | ||||
−0.00175121 | + | 0.999998i | \(0.500557\pi\) | |||||||
\(578\) | 9.07069 | 0.377291 | ||||||||
\(579\) | 16.7660 | 0.696772 | ||||||||
\(580\) | −1.63487 | −0.0678843 | ||||||||
\(581\) | −14.3618 | −0.595829 | ||||||||
\(582\) | −17.4632 | −0.723874 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.2684 | −1.12838 | ||||||||
\(585\) | 9.08517 | 0.375625 | ||||||||
\(586\) | 4.50232 | 0.185989 | ||||||||
\(587\) | 38.9212 | 1.60645 | 0.803226 | − | 0.595675i | \(-0.203115\pi\) | ||||
0.803226 | + | 0.595675i | \(0.203115\pi\) | |||||||
\(588\) | −1.72924 | −0.0713125 | ||||||||
\(589\) | 3.28726 | 0.135449 | ||||||||
\(590\) | 13.1454 | 0.541188 | ||||||||
\(591\) | 10.8062 | 0.444509 | ||||||||
\(592\) | 4.02958 | 0.165615 | ||||||||
\(593\) | −26.3594 | −1.08245 | −0.541225 | − | 0.840878i | \(-0.682039\pi\) | ||||
−0.541225 | + | 0.840878i | \(0.682039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.01458 | 0.205578 | ||||||||
\(596\) | 6.03738 | 0.247301 | ||||||||
\(597\) | 42.1584 | 1.72543 | ||||||||
\(598\) | −4.78800 | −0.195796 | ||||||||
\(599\) | −22.1910 | −0.906700 | −0.453350 | − | 0.891333i | \(-0.649771\pi\) | ||||
−0.453350 | + | 0.891333i | \(0.649771\pi\) | |||||||
\(600\) | −6.99217 | −0.285454 | ||||||||
\(601\) | −14.5234 | −0.592421 | −0.296210 | − | 0.955123i | \(-0.595723\pi\) | ||||
−0.296210 | + | 0.955123i | \(0.595723\pi\) | |||||||
\(602\) | −7.95328 | −0.324151 | ||||||||
\(603\) | 25.5878 | 1.04202 | ||||||||
\(604\) | 10.9375 | 0.445040 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.6718 | −0.880356 | ||||||||
\(607\) | 42.3001 | 1.71691 | 0.858454 | − | 0.512890i | \(-0.171425\pi\) | ||||
0.858454 | + | 0.512890i | \(0.171425\pi\) | |||||||
\(608\) | 1.25931 | 0.0510717 | ||||||||
\(609\) | 4.89346 | 0.198293 | ||||||||
\(610\) | −13.2941 | −0.538262 | ||||||||
\(611\) | 16.4552 | 0.665704 | ||||||||
\(612\) | −8.29348 | −0.335244 | ||||||||
\(613\) | 25.2536 | 1.01998 | 0.509992 | − | 0.860179i | \(-0.329648\pi\) | ||||
0.509992 | + | 0.860179i | \(0.329648\pi\) | |||||||
\(614\) | −31.1366 | −1.25657 | ||||||||
\(615\) | −25.8337 | −1.04172 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9481 | 1.36670 | 0.683350 | − | 0.730091i | \(-0.260522\pi\) | ||||
0.683350 | + | 0.730091i | \(0.260522\pi\) | |||||||
\(618\) | 17.1411 | 0.689516 | ||||||||
\(619\) | −31.4892 | −1.26566 | −0.632830 | − | 0.774291i | \(-0.718107\pi\) | ||||
−0.632830 | + | 0.774291i | \(0.718107\pi\) | |||||||
\(620\) | −7.99345 | −0.321025 | ||||||||
\(621\) | 1.93078 | 0.0774797 | ||||||||
\(622\) | −28.7176 | −1.15147 | ||||||||
\(623\) | 12.0930 | 0.484495 | ||||||||
\(624\) | −18.0684 | −0.723315 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.78393 | −0.231172 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.24207 | 0.368799 | ||||||||
\(629\) | −10.6233 | −0.423578 | ||||||||
\(630\) | 2.42291 | 0.0965311 | ||||||||
\(631\) | 28.5949 | 1.13834 | 0.569172 | − | 0.822219i | \(-0.307264\pi\) | ||||
0.569172 | + | 0.822219i | \(0.307264\pi\) | |||||||
\(632\) | 4.95823 | 0.197228 | ||||||||
\(633\) | −2.48767 | −0.0988761 | ||||||||
\(634\) | 21.0160 | 0.834651 | ||||||||
\(635\) | 4.24376 | 0.168408 | ||||||||
\(636\) | 2.36411 | 0.0937429 | ||||||||
\(637\) | 4.17534 | 0.165433 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.0798 | 0.754785 | ||||||||
\(640\) | 1.17386 | 0.0464008 | ||||||||
\(641\) | −28.2997 | −1.11777 | −0.558885 | − | 0.829245i | \(-0.688771\pi\) | ||||
−0.558885 | + | 0.829245i | \(0.688771\pi\) | |||||||
\(642\) | 22.6596 | 0.894303 | ||||||||
\(643\) | 15.8817 | 0.626314 | 0.313157 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313157 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(644\) | 0.782759 | 0.0308450 | ||||||||
\(645\) | −16.2496 | −0.639828 | ||||||||
\(646\) | 1.74538 | 0.0686713 | ||||||||
\(647\) | −16.0475 | −0.630894 | −0.315447 | − | 0.948943i | \(-0.602154\pi\) | ||||
−0.315447 | + | 0.948943i | \(0.602154\pi\) | |||||||
\(648\) | 33.1716 | 1.30310 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.64930 | 0.182361 | ||||||||
\(651\) | 23.9258 | 0.937726 | ||||||||
\(652\) | −12.3999 | −0.485618 | ||||||||
\(653\) | −21.5898 | −0.844874 | −0.422437 | − | 0.906392i | \(-0.638825\pi\) | ||||
−0.422437 | + | 0.906392i | \(0.638825\pi\) | |||||||
\(654\) | 33.1004 | 1.29433 | ||||||||
\(655\) | 11.3525 | 0.443578 | ||||||||
\(656\) | 21.5987 | 0.843289 | ||||||||
\(657\) | 19.3056 | 0.753183 | ||||||||
\(658\) | 4.38841 | 0.171078 | ||||||||
\(659\) | −34.0482 | −1.32633 | −0.663164 | − | 0.748474i | \(-0.730787\pi\) | ||||
−0.663164 | + | 0.748474i | \(0.730787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.5458 | 1.49926 | 0.749629 | − | 0.661858i | \(-0.230232\pi\) | ||||
0.749629 | + | 0.661858i | \(0.230232\pi\) | |||||||
\(662\) | −14.8047 | −0.575401 | ||||||||
\(663\) | 47.6342 | 1.84996 | ||||||||
\(664\) | 44.1396 | 1.71295 | ||||||||
\(665\) | 0.312580 | 0.0121213 | ||||||||
\(666\) | −5.13289 | −0.198896 | ||||||||
\(667\) | −2.21508 | −0.0857682 | ||||||||
\(668\) | 8.02824 | 0.310622 | ||||||||
\(669\) | −44.5563 | −1.72265 | ||||||||
\(670\) | 13.0945 | 0.505884 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 9.16569 | 0.353574 | ||||||||
\(673\) | −34.2289 | −1.31943 | −0.659715 | − | 0.751516i | \(-0.729323\pi\) | ||||
−0.659715 | + | 0.751516i | \(0.729323\pi\) | |||||||
\(674\) | −7.46590 | −0.287576 | ||||||||
\(675\) | −1.87485 | −0.0721630 | ||||||||
\(676\) | −3.36977 | −0.129607 | ||||||||
\(677\) | 38.9730 | 1.49785 | 0.748926 | − | 0.662653i | \(-0.230570\pi\) | ||||
0.748926 | + | 0.662653i | \(0.230570\pi\) | |||||||
\(678\) | 17.7506 | 0.681709 | ||||||||
\(679\) | −6.89342 | −0.264545 | ||||||||
\(680\) | −15.4118 | −0.591015 | ||||||||
\(681\) | −21.9906 | −0.842682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.8225 | 1.48550 | 0.742750 | − | 0.669569i | \(-0.233521\pi\) | ||||
0.742750 | + | 0.669569i | \(0.233521\pi\) | |||||||
\(684\) | −0.516967 | −0.0197667 | ||||||||
\(685\) | −0.885628 | −0.0338381 | ||||||||
\(686\) | 1.11352 | 0.0425142 | ||||||||
\(687\) | −35.1468 | −1.34093 | ||||||||
\(688\) | 13.5858 | 0.517953 | ||||||||
\(689\) | −5.70826 | −0.217467 | ||||||||
\(690\) | −2.60889 | −0.0993189 | ||||||||
\(691\) | −4.42354 | −0.168279 | −0.0841397 | − | 0.996454i | \(-0.526814\pi\) | ||||
−0.0841397 | + | 0.996454i | \(0.526814\pi\) | |||||||
\(692\) | 6.18044 | 0.234945 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3072 | 0.846769 | ||||||||
\(695\) | 14.2443 | 0.540316 | ||||||||
\(696\) | −15.0395 | −0.570072 | ||||||||
\(697\) | −56.9413 | −2.15681 | ||||||||
\(698\) | −2.60044 | −0.0984280 | ||||||||
\(699\) | 21.5513 | 0.815144 | ||||||||
\(700\) | −0.760083 | −0.0287284 | ||||||||
\(701\) | −15.9428 | −0.602150 | −0.301075 | − | 0.953601i | \(-0.597345\pi\) | ||||
−0.301075 | + | 0.953601i | \(0.597345\pi\) | |||||||
\(702\) | −8.71675 | −0.328992 | ||||||||
\(703\) | −0.662194 | −0.0249751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.96611 | 0.337683 | ||||||||
\(706\) | −4.55318 | −0.171361 | ||||||||
\(707\) | −8.55470 | −0.321733 | ||||||||
\(708\) | −20.4142 | −0.767213 | ||||||||
\(709\) | 37.8285 | 1.42068 | 0.710340 | − | 0.703859i | \(-0.248541\pi\) | ||||
0.710340 | + | 0.703859i | \(0.248541\pi\) | |||||||
\(710\) | 9.76402 | 0.366437 | ||||||||
\(711\) | −3.51035 | −0.131648 | ||||||||
\(712\) | −37.1665 | −1.39287 | ||||||||
\(713\) | −10.8303 | −0.405597 | ||||||||
\(714\) | 12.7035 | 0.475417 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.1750 | 0.604487 | ||||||||
\(717\) | −60.8933 | −2.27410 | ||||||||
\(718\) | 24.8390 | 0.926982 | ||||||||
\(719\) | 32.2686 | 1.20342 | 0.601708 | − | 0.798716i | \(-0.294487\pi\) | ||||
0.601708 | + | 0.798716i | \(0.294487\pi\) | |||||||
\(720\) | −4.13882 | −0.154245 | ||||||||
\(721\) | 6.76626 | 0.251989 | ||||||||
\(722\) | −21.0480 | −0.783325 | ||||||||
\(723\) | 1.35560 | 0.0504152 | ||||||||
\(724\) | 2.14038 | 0.0795464 | ||||||||
\(725\) | 2.15091 | 0.0798828 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5177 | −1.13184 | −0.565919 | − | 0.824461i | \(-0.691479\pi\) | ||||
−0.565919 | + | 0.824461i | \(0.691479\pi\) | |||||||
\(728\) | −12.8325 | −0.475603 | ||||||||
\(729\) | −10.6887 | −0.395879 | ||||||||
\(730\) | 9.87957 | 0.365659 | ||||||||
\(731\) | −35.8166 | −1.32472 | ||||||||
\(732\) | 20.6451 | 0.763065 | ||||||||
\(733\) | 29.9784 | 1.10728 | 0.553638 | − | 0.832757i | \(-0.313239\pi\) | ||||
0.553638 | + | 0.832757i | \(0.313239\pi\) | |||||||
\(734\) | −8.21494 | −0.303219 | ||||||||
\(735\) | 2.27506 | 0.0839170 | ||||||||
\(736\) | −4.14895 | −0.152932 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −27.5125 | −1.01275 | ||||||||
\(739\) | −27.2743 | −1.00330 | −0.501651 | − | 0.865070i | \(-0.667274\pi\) | ||||
−0.501651 | + | 0.865070i | \(0.667274\pi\) | |||||||
\(740\) | 1.61022 | 0.0591929 | ||||||||
\(741\) | 2.96924 | 0.109078 | ||||||||
\(742\) | −1.52233 | −0.0558865 | ||||||||
\(743\) | 8.95224 | 0.328426 | 0.164213 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164213 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(744\) | −73.5335 | −2.69587 | ||||||||
\(745\) | −7.94306 | −0.291011 | ||||||||
\(746\) | 7.77375 | 0.284617 | ||||||||
\(747\) | −31.2501 | −1.14338 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94463 | 0.326830 | ||||||||
\(750\) | 2.53332 | 0.0925037 | ||||||||
\(751\) | 7.39028 | 0.269675 | 0.134838 | − | 0.990868i | \(-0.456949\pi\) | ||||
0.134838 | + | 0.990868i | \(0.456949\pi\) | |||||||
\(752\) | −7.49628 | −0.273361 | ||||||||
\(753\) | −29.1956 | −1.06395 | ||||||||
\(754\) | 10.0002 | 0.364187 | ||||||||
\(755\) | −14.3899 | −0.523700 | ||||||||
\(756\) | 1.42504 | 0.0518283 | ||||||||
\(757\) | 46.1150 | 1.67608 | 0.838039 | − | 0.545610i | \(-0.183702\pi\) | ||||
0.838039 | + | 0.545610i | \(0.183702\pi\) | |||||||
\(758\) | 11.7955 | 0.428433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.960681 | −0.0348475 | ||||||||
\(761\) | −11.4980 | −0.416803 | −0.208402 | − | 0.978043i | \(-0.566826\pi\) | ||||
−0.208402 | + | 0.978043i | \(0.566826\pi\) | |||||||
\(762\) | 10.7508 | 0.389460 | ||||||||
\(763\) | 13.0660 | 0.473022 | ||||||||
\(764\) | 1.12768 | 0.0407979 | ||||||||
\(765\) | 10.9113 | 0.394498 | ||||||||
\(766\) | −20.9831 | −0.758150 | ||||||||
\(767\) | 49.2912 | 1.77980 | ||||||||
\(768\) | −34.7482 | −1.25387 | ||||||||
\(769\) | −12.6422 | −0.455888 | −0.227944 | − | 0.973674i | \(-0.573200\pi\) | ||||
−0.227944 | + | 0.973674i | \(0.573200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.4743 | −1.38562 | ||||||||
\(772\) | −5.60142 | −0.201599 | ||||||||
\(773\) | 38.8039 | 1.39568 | 0.697839 | − | 0.716254i | \(-0.254145\pi\) | ||||
0.697839 | + | 0.716254i | \(0.254145\pi\) | |||||||
\(774\) | −17.3056 | −0.622038 | ||||||||
\(775\) | 10.5165 | 0.377765 | ||||||||
\(776\) | 21.1862 | 0.760541 | ||||||||
\(777\) | −4.81968 | −0.172905 | ||||||||
\(778\) | −19.5375 | −0.700453 | ||||||||
\(779\) | −3.54939 | −0.127170 | ||||||||
\(780\) | −7.22015 | −0.258523 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.75039 | −0.205634 | ||||||||
\(783\) | −4.03264 | −0.144115 | ||||||||
\(784\) | −1.90211 | −0.0679324 | ||||||||
\(785\) | −12.1593 | −0.433983 | ||||||||
\(786\) | 28.7594 | 1.02581 | ||||||||
\(787\) | −30.2463 | −1.07816 | −0.539082 | − | 0.842253i | \(-0.681229\pi\) | ||||
−0.539082 | + | 0.842253i | \(0.681229\pi\) | |||||||
\(788\) | −3.61029 | −0.128611 | ||||||||
\(789\) | −57.8113 | −2.05814 | ||||||||
\(790\) | −1.79641 | −0.0639133 | ||||||||
\(791\) | 7.00687 | 0.249136 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.8487 | −1.77018 | ||||||||
\(794\) | 14.5186 | 0.515245 | ||||||||
\(795\) | −3.11032 | −0.110312 | ||||||||
\(796\) | −14.0848 | −0.499223 | ||||||||
\(797\) | 24.9560 | 0.883987 | 0.441993 | − | 0.897018i | \(-0.354271\pi\) | ||||
0.441993 | + | 0.897018i | \(0.354271\pi\) | |||||||
\(798\) | 0.791863 | 0.0280317 | ||||||||
\(799\) | 19.7626 | 0.699152 | ||||||||
\(800\) | 4.02876 | 0.142438 | ||||||||
\(801\) | 26.3132 | 0.929733 | ||||||||
\(802\) | −34.7453 | −1.22690 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −20.3351 | −0.717164 | ||||||||
\(805\) | −1.02983 | −0.0362968 | ||||||||
\(806\) | 48.8946 | 1.72224 | ||||||||
\(807\) | −7.35247 | −0.258819 | ||||||||
\(808\) | 26.2920 | 0.924948 | ||||||||
\(809\) | 52.4442 | 1.84384 | 0.921919 | − | 0.387382i | \(-0.126621\pi\) | ||||
0.921919 | + | 0.387382i | \(0.126621\pi\) | |||||||
\(810\) | −12.0183 | −0.422281 | ||||||||
\(811\) | 50.8600 | 1.78594 | 0.892968 | − | 0.450119i | \(-0.148619\pi\) | ||||
0.892968 | + | 0.450119i | \(0.148619\pi\) | |||||||
\(812\) | −1.63487 | −0.0573727 | ||||||||
\(813\) | −53.9156 | −1.89090 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.3139 | 0.571451 | ||||||||
\(816\) | −21.7002 | −0.759658 | ||||||||
\(817\) | −2.23260 | −0.0781087 | ||||||||
\(818\) | 4.46098 | 0.155975 | ||||||||
\(819\) | 9.08517 | 0.317461 | ||||||||
\(820\) | 8.63086 | 0.301403 | ||||||||
\(821\) | 36.9164 | 1.28839 | 0.644196 | − | 0.764861i | \(-0.277192\pi\) | ||||
0.644196 | + | 0.764861i | \(0.277192\pi\) | |||||||
\(822\) | −2.24358 | −0.0782538 | ||||||||
\(823\) | 9.01322 | 0.314181 | 0.157090 | − | 0.987584i | \(-0.449789\pi\) | ||||
0.157090 | + | 0.987584i | \(0.449789\pi\) | |||||||
\(824\) | −20.7954 | −0.724442 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.1454 | 0.457387 | ||||||||
\(827\) | −2.33667 | −0.0812540 | −0.0406270 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406270 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(828\) | 1.70321 | 0.0591908 | ||||||||
\(829\) | 13.5307 | 0.469941 | 0.234970 | − | 0.972003i | \(-0.424501\pi\) | ||||
0.234970 | + | 0.972003i | \(0.424501\pi\) | |||||||
\(830\) | −15.9921 | −0.555094 | ||||||||
\(831\) | 0.857693 | 0.0297530 | ||||||||
\(832\) | 34.6148 | 1.20005 | ||||||||
\(833\) | 5.01458 | 0.173745 | ||||||||
\(834\) | 36.0853 | 1.24953 | ||||||||
\(835\) | −10.5623 | −0.365524 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.7170 | −0.681518 | ||||||||
\(838\) | 32.8177 | 1.13367 | ||||||||
\(839\) | −8.47250 | −0.292503 | −0.146252 | − | 0.989247i | \(-0.546721\pi\) | ||||
−0.146252 | + | 0.989247i | \(0.546721\pi\) | |||||||
\(840\) | −6.99217 | −0.241253 | ||||||||
\(841\) | −24.3736 | −0.840468 | ||||||||
\(842\) | 22.7642 | 0.784506 | ||||||||
\(843\) | 22.2070 | 0.764851 | ||||||||
\(844\) | 0.831114 | 0.0286081 | ||||||||
\(845\) | 4.43343 | 0.152515 | ||||||||
\(846\) | 9.54879 | 0.328294 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.60044 | 0.0892996 | ||||||||
\(849\) | −36.2462 | −1.24397 | ||||||||
\(850\) | 5.58381 | 0.191523 | ||||||||
\(851\) | 2.18168 | 0.0747870 | ||||||||
\(852\) | −15.1631 | −0.519478 | ||||||||
\(853\) | −20.0059 | −0.684988 | −0.342494 | − | 0.939520i | \(-0.611272\pi\) | ||||
−0.342494 | + | 0.939520i | \(0.611272\pi\) | |||||||
\(854\) | −13.2941 | −0.454915 | ||||||||
\(855\) | 0.680146 | 0.0232605 | ||||||||
\(856\) | −27.4904 | −0.939602 | ||||||||
\(857\) | 27.4144 | 0.936458 | 0.468229 | − | 0.883607i | \(-0.344892\pi\) | ||||
0.468229 | + | 0.883607i | \(0.344892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.23732 | 0.110456 | 0.0552279 | − | 0.998474i | \(-0.482411\pi\) | ||||
0.0552279 | + | 0.998474i | \(0.482411\pi\) | |||||||
\(860\) | 5.42889 | 0.185124 | ||||||||
\(861\) | −25.8337 | −0.880410 | ||||||||
\(862\) | −16.2964 | −0.555058 | ||||||||
\(863\) | −19.9925 | −0.680553 | −0.340276 | − | 0.940325i | \(-0.610521\pi\) | ||||
−0.340276 | + | 0.940325i | \(0.610521\pi\) | |||||||
\(864\) | −7.55333 | −0.256970 | ||||||||
\(865\) | −8.13127 | −0.276471 | ||||||||
\(866\) | 39.0216 | 1.32601 | ||||||||
\(867\) | 18.5326 | 0.629401 | ||||||||
\(868\) | −7.99345 | −0.271315 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.44894 | 0.184736 | ||||||||
\(871\) | 49.1002 | 1.66370 | ||||||||
\(872\) | −40.1570 | −1.35989 | ||||||||
\(873\) | −14.9995 | −0.507656 | ||||||||
\(874\) | −0.358446 | −0.0121246 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −15.3425 | −0.518375 | ||||||||
\(877\) | 3.34642 | 0.113001 | 0.0565003 | − | 0.998403i | \(-0.482006\pi\) | ||||
0.0565003 | + | 0.998403i | \(0.482006\pi\) | |||||||
\(878\) | −33.8494 | −1.14236 | ||||||||
\(879\) | 9.19885 | 0.310269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.4904 | 1.59999 | 0.799996 | − | 0.600005i | \(-0.204835\pi\) | ||||
0.799996 | + | 0.600005i | \(0.204835\pi\) | |||||||
\(882\) | 2.42291 | 0.0815837 | ||||||||
\(883\) | −32.5105 | −1.09407 | −0.547034 | − | 0.837111i | \(-0.684243\pi\) | ||||
−0.547034 | + | 0.837111i | \(0.684243\pi\) | |||||||
\(884\) | −15.9143 | −0.535255 | ||||||||
\(885\) | 26.8579 | 0.902817 | ||||||||
\(886\) | −23.8220 | −0.800317 | ||||||||
\(887\) | 56.2965 | 1.89025 | 0.945126 | − | 0.326705i | \(-0.105938\pi\) | ||||
0.945126 | + | 0.326705i | \(0.105938\pi\) | |||||||
\(888\) | 14.8128 | 0.497084 | ||||||||
\(889\) | 4.24376 | 0.142331 | ||||||||
\(890\) | 13.4657 | 0.451372 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.8860 | 0.498419 | ||||||||
\(893\) | 1.23189 | 0.0412236 | ||||||||
\(894\) | −20.1223 | −0.672990 | ||||||||
\(895\) | −21.2805 | −0.711330 | ||||||||
\(896\) | 1.17386 | 0.0392158 | ||||||||
\(897\) | −9.78254 | −0.326630 | ||||||||
\(898\) | 18.0694 | 0.602984 | ||||||||
\(899\) | 22.6202 | 0.754424 | ||||||||
\(900\) | −1.65387 | −0.0551291 | ||||||||
\(901\) | −6.85562 | −0.228394 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.2496 | −0.540754 | ||||||||
\(904\) | −21.5349 | −0.716240 | ||||||||
\(905\) | −2.81598 | −0.0936062 | ||||||||
\(906\) | −36.4541 | −1.21111 | ||||||||
\(907\) | 23.4679 | 0.779238 | 0.389619 | − | 0.920976i | \(-0.372607\pi\) | ||||
0.389619 | + | 0.920976i | \(0.372607\pi\) | |||||||
\(908\) | 7.34691 | 0.243816 | ||||||||
\(909\) | −18.6143 | −0.617397 | ||||||||
\(910\) | 4.64930 | 0.154123 | ||||||||
\(911\) | 7.44129 | 0.246541 | 0.123270 | − | 0.992373i | \(-0.460662\pi\) | ||||
0.123270 | + | 0.992373i | \(0.460662\pi\) | |||||||
\(912\) | −1.35266 | −0.0447911 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 25.6755 | 0.849271 | ||||||||
\(915\) | −27.1616 | −0.897936 | ||||||||
\(916\) | 11.7423 | 0.387976 | ||||||||
\(917\) | 11.3525 | 0.374892 | ||||||||
\(918\) | −10.4688 | −0.345522 | ||||||||
\(919\) | −17.1308 | −0.565093 | −0.282546 | − | 0.959254i | \(-0.591179\pi\) | ||||
−0.282546 | + | 0.959254i | \(0.591179\pi\) | |||||||
\(920\) | 3.16508 | 0.104350 | ||||||||
\(921\) | −63.6164 | −2.09623 | ||||||||
\(922\) | −8.98307 | −0.295842 | ||||||||
\(923\) | 36.6120 | 1.20510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.11848 | −0.0696552 | ||||||||
\(926\) | −29.7631 | −0.978076 | ||||||||
\(927\) | 14.7228 | 0.483560 | ||||||||
\(928\) | 8.66552 | 0.284459 | ||||||||
\(929\) | −28.3985 | −0.931725 | −0.465862 | − | 0.884857i | \(-0.654256\pi\) | ||||
−0.465862 | + | 0.884857i | \(0.654256\pi\) | |||||||
\(930\) | 26.6418 | 0.873618 | ||||||||
\(931\) | 0.312580 | 0.0102444 | ||||||||
\(932\) | −7.20013 | −0.235848 | ||||||||
\(933\) | −58.6739 | −1.92090 | ||||||||
\(934\) | −27.5913 | −0.902816 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −27.9223 | −0.912669 | ||||||||
\(937\) | −29.1310 | −0.951669 | −0.475834 | − | 0.879535i | \(-0.657854\pi\) | ||||
−0.475834 | + | 0.879535i | \(0.657854\pi\) | |||||||
\(938\) | 13.0945 | 0.427550 | ||||||||
\(939\) | −11.8173 | −0.385645 | ||||||||
\(940\) | −2.99552 | −0.0977030 | ||||||||
\(941\) | 2.40040 | 0.0782508 | 0.0391254 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391254 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(942\) | −30.8033 | −1.00363 | ||||||||
\(943\) | 11.6939 | 0.380806 | ||||||||
\(944\) | −22.4550 | −0.730848 | ||||||||
\(945\) | −1.87485 | −0.0609889 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.37029 | −0.304493 | −0.152247 | − | 0.988343i | \(-0.548651\pi\) | ||||
−0.152247 | + | 0.988343i | \(0.548651\pi\) | |||||||
\(948\) | 2.78974 | 0.0906064 | ||||||||
\(949\) | 37.0453 | 1.20254 | ||||||||
\(950\) | 0.348062 | 0.0112926 | ||||||||
\(951\) | 42.9385 | 1.39238 | ||||||||
\(952\) | −15.4118 | −0.499499 | ||||||||
\(953\) | 18.0336 | 0.584165 | 0.292082 | − | 0.956393i | \(-0.405652\pi\) | ||||
0.292082 | + | 0.956393i | \(0.405652\pi\) | |||||||
\(954\) | −3.31246 | −0.107245 | ||||||||
\(955\) | −1.48362 | −0.0480089 | ||||||||
\(956\) | 20.3440 | 0.657973 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.38094 | 0.109233 | ||||||||
\(959\) | −0.885628 | −0.0285984 | ||||||||
\(960\) | 18.8610 | 0.608735 | ||||||||
\(961\) | 79.5977 | 2.56767 | ||||||||
\(962\) | −9.84945 | −0.317559 | ||||||||
\(963\) | 19.4627 | 0.627178 | ||||||||
\(964\) | −0.452896 | −0.0145868 | ||||||||
\(965\) | 7.36948 | 0.237232 | ||||||||
\(966\) | −2.60889 | −0.0839398 | ||||||||
\(967\) | −48.0532 | −1.54529 | −0.772643 | − | 0.634840i | \(-0.781066\pi\) | ||||
−0.772643 | + | 0.634840i | \(0.781066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.56606 | 0.114558 | ||||||||
\(970\) | −7.67593 | −0.246459 | ||||||||
\(971\) | −43.3729 | −1.39190 | −0.695951 | − | 0.718089i | \(-0.745017\pi\) | ||||
−0.695951 | + | 0.718089i | \(0.745017\pi\) | |||||||
\(972\) | 14.3888 | 0.461520 | ||||||||
\(973\) | 14.2443 | 0.456650 | ||||||||
\(974\) | 44.3827 | 1.42211 | ||||||||
\(975\) | 9.49915 | 0.304216 | ||||||||
\(976\) | 22.7090 | 0.726897 | ||||||||
\(977\) | −54.0777 | −1.73010 | −0.865049 | − | 0.501688i | \(-0.832713\pi\) | ||||
−0.865049 | + | 0.501688i | \(0.832713\pi\) | |||||||
\(978\) | 41.3283 | 1.32153 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.760083 | −0.0242800 | ||||||||
\(981\) | 28.4305 | 0.907717 | ||||||||
\(982\) | −28.1047 | −0.896858 | ||||||||
\(983\) | −42.6369 | −1.35991 | −0.679954 | − | 0.733255i | \(-0.738000\pi\) | ||||
−0.679954 | + | 0.733255i | \(0.738000\pi\) | |||||||
\(984\) | 79.3972 | 2.53109 | ||||||||
\(985\) | 4.74986 | 0.151343 | ||||||||
\(986\) | 12.0103 | 0.382485 | ||||||||
\(987\) | 8.96611 | 0.285394 | ||||||||
\(988\) | −0.992003 | −0.0315598 | ||||||||
\(989\) | 7.35557 | 0.233894 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.3376 | −1.66256 | −0.831280 | − | 0.555855i | \(-0.812391\pi\) | ||||
−0.831280 | + | 0.555855i | \(0.812391\pi\) | |||||||
\(992\) | 42.3687 | 1.34521 | ||||||||
\(993\) | −30.2480 | −0.959892 | ||||||||
\(994\) | 9.76402 | 0.309696 | ||||||||
\(995\) | 18.5306 | 0.587460 | ||||||||
\(996\) | 24.8350 | 0.786927 | ||||||||
\(997\) | −10.1811 | −0.322438 | −0.161219 | − | 0.986919i | \(-0.551543\pi\) | ||||
−0.161219 | + | 0.986919i | \(0.551543\pi\) | |||||||
\(998\) | 28.2321 | 0.893672 | ||||||||
\(999\) | 3.97183 | 0.125663 |
(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 | 4235.2.a.bp.1.12 | 18 | ||
11.7 | odd | 10 | 385.2.n.f.71.4 | ✓ | 36 | ||
11.8 | odd | 10 | 385.2.n.f.141.4 | yes | 36 | ||
11.10 | odd | 2 | 4235.2.a.bo.1.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.f.71.4 | ✓ | 36 | 11.7 | odd | 10 | ||
385.2.n.f.141.4 | yes | 36 | 11.8 | odd | 10 | ||
4235.2.a.bo.1.7 | 18 | 11.10 | odd | 2 | |||
4235.2.a.bp.1.12 | 18 | 1.1 | even | 1 | trivial |