Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,2,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, 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("1911.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.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: | \(15.2594118263\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2196544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 7x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.10811\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10811 | −0.783553 | −0.391777 | − | 0.920060i | \(-0.628139\pi\) | ||||
−0.391777 | + | 0.920060i | \(0.628139\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.772089 | −0.386045 | ||||||||
\(5\) | 2.82337 | 1.26265 | 0.631325 | − | 0.775518i | \(-0.282511\pi\) | ||||
0.631325 | + | 0.775518i | \(0.282511\pi\) | |||||||
\(6\) | −1.10811 | −0.452385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07178 | 1.08604 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.12861 | −0.989354 | ||||||||
\(11\) | 5.50785 | 1.66068 | 0.830340 | − | 0.557258i | \(-0.188146\pi\) | ||||
0.830340 | + | 0.557258i | \(0.188146\pi\) | |||||||
\(12\) | −0.772089 | −0.222883 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82337 | 0.728992 | ||||||||
\(16\) | −1.85970 | −0.464925 | ||||||||
\(17\) | 5.68775 | 1.37948 | 0.689740 | − | 0.724057i | \(-0.257725\pi\) | ||||
0.689740 | + | 0.724057i | \(0.257725\pi\) | |||||||
\(18\) | −1.10811 | −0.261184 | ||||||||
\(19\) | 2.85970 | 0.656060 | 0.328030 | − | 0.944667i | \(-0.393615\pi\) | ||||
0.328030 | + | 0.944667i | \(0.393615\pi\) | |||||||
\(20\) | −2.17990 | −0.487439 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.10331 | −1.30123 | ||||||||
\(23\) | −4.90070 | −1.02187 | −0.510933 | − | 0.859620i | \(-0.670700\pi\) | ||||
−0.510933 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(24\) | 3.07178 | 0.627025 | ||||||||
\(25\) | 2.97143 | 0.594287 | ||||||||
\(26\) | −1.10811 | −0.217319 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.57275 | 1.40622 | 0.703112 | − | 0.711079i | \(-0.251793\pi\) | ||||
0.703112 | + | 0.711079i | \(0.251793\pi\) | |||||||
\(30\) | −3.12861 | −0.571204 | ||||||||
\(31\) | −6.33122 | −1.13712 | −0.568561 | − | 0.822641i | \(-0.692500\pi\) | ||||
−0.568561 | + | 0.822641i | \(0.692500\pi\) | |||||||
\(32\) | −4.08281 | −0.721746 | ||||||||
\(33\) | 5.50785 | 0.958794 | ||||||||
\(34\) | −6.30266 | −1.08090 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.772089 | −0.128682 | ||||||||
\(37\) | −9.90397 | −1.62820 | −0.814101 | − | 0.580723i | \(-0.802770\pi\) | ||||
−0.814101 | + | 0.580723i | \(0.802770\pi\) | |||||||
\(38\) | −3.16887 | −0.514058 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 8.67279 | 1.37129 | ||||||||
\(41\) | 11.0520 | 1.72604 | 0.863018 | − | 0.505172i | \(-0.168571\pi\) | ||||
0.863018 | + | 0.505172i | \(0.168571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.78704 | −0.425020 | −0.212510 | − | 0.977159i | \(-0.568164\pi\) | ||||
−0.212510 | + | 0.977159i | \(0.568164\pi\) | |||||||
\(44\) | −4.25255 | −0.641096 | ||||||||
\(45\) | 2.82337 | 0.420884 | ||||||||
\(46\) | 5.43052 | 0.800687 | ||||||||
\(47\) | −7.69551 | −1.12250 | −0.561252 | − | 0.827645i | \(-0.689680\pi\) | ||||
−0.561252 | + | 0.827645i | \(0.689680\pi\) | |||||||
\(48\) | −1.85970 | −0.268425 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.29268 | −0.465655 | ||||||||
\(51\) | 5.68775 | 0.796444 | ||||||||
\(52\) | −0.772089 | −0.107069 | ||||||||
\(53\) | −5.21949 | −0.716952 | −0.358476 | − | 0.933539i | \(-0.616704\pi\) | ||||
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(54\) | −1.10811 | −0.150795 | ||||||||
\(55\) | 15.5507 | 2.09686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.85970 | 0.378777 | ||||||||
\(58\) | −8.39145 | −1.10185 | ||||||||
\(59\) | −3.39419 | −0.441886 | −0.220943 | − | 0.975287i | \(-0.570914\pi\) | ||||
−0.220943 | + | 0.975287i | \(0.570914\pi\) | |||||||
\(60\) | −2.17990 | −0.281423 | ||||||||
\(61\) | 2.43245 | 0.311443 | 0.155721 | − | 0.987801i | \(-0.450230\pi\) | ||||
0.155721 | + | 0.987801i | \(0.450230\pi\) | |||||||
\(62\) | 7.01570 | 0.890995 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.24361 | 1.03045 | ||||||||
\(65\) | 2.82337 | 0.350196 | ||||||||
\(66\) | −6.10331 | −0.751266 | ||||||||
\(67\) | −5.19092 | −0.634172 | −0.317086 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317086 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(68\) | −4.39145 | −0.532541 | ||||||||
\(69\) | −4.90070 | −0.589975 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5870 | 1.37513 | 0.687564 | − | 0.726123i | \(-0.258680\pi\) | ||||
0.687564 | + | 0.726123i | \(0.258680\pi\) | |||||||
\(72\) | 3.07178 | 0.362013 | ||||||||
\(73\) | 6.68448 | 0.782359 | 0.391179 | − | 0.920314i | \(-0.372067\pi\) | ||||
0.391179 | + | 0.920314i | \(0.372067\pi\) | |||||||
\(74\) | 10.9747 | 1.27578 | ||||||||
\(75\) | 2.97143 | 0.343112 | ||||||||
\(76\) | −2.20794 | −0.253268 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.10811 | −0.125469 | ||||||||
\(79\) | −6.43379 | −0.723858 | −0.361929 | − | 0.932206i | \(-0.617882\pi\) | ||||
−0.361929 | + | 0.932206i | \(0.617882\pi\) | |||||||
\(80\) | −5.25063 | −0.587038 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.2469 | −1.35244 | ||||||||
\(83\) | −16.0553 | −1.76230 | −0.881149 | − | 0.472839i | \(-0.843229\pi\) | ||||
−0.881149 | + | 0.472839i | \(0.843229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.0586 | 1.74180 | ||||||||
\(86\) | 3.08836 | 0.333026 | ||||||||
\(87\) | 7.57275 | 0.811884 | ||||||||
\(88\) | 16.9189 | 1.80356 | ||||||||
\(89\) | −15.2558 | −1.61711 | −0.808557 | − | 0.588418i | \(-0.799751\pi\) | ||||
−0.808557 | + | 0.588418i | \(0.799751\pi\) | |||||||
\(90\) | −3.12861 | −0.329785 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.78378 | 0.394486 | ||||||||
\(93\) | −6.33122 | −0.656517 | ||||||||
\(94\) | 8.52748 | 0.879542 | ||||||||
\(95\) | 8.07400 | 0.828375 | ||||||||
\(96\) | −4.08281 | −0.416700 | ||||||||
\(97\) | 6.13113 | 0.622522 | 0.311261 | − | 0.950324i | \(-0.399249\pi\) | ||||
0.311261 | + | 0.950324i | \(0.399249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.50785 | 0.553560 | ||||||||
\(100\) | −2.29421 | −0.229421 | ||||||||
\(101\) | −5.32796 | −0.530151 | −0.265076 | − | 0.964228i | \(-0.585397\pi\) | ||||
−0.265076 | + | 0.964228i | \(0.585397\pi\) | |||||||
\(102\) | −6.30266 | −0.624056 | ||||||||
\(103\) | −1.54418 | −0.152152 | −0.0760762 | − | 0.997102i | \(-0.524239\pi\) | ||||
−0.0760762 | + | 0.997102i | \(0.524239\pi\) | |||||||
\(104\) | 3.07178 | 0.301213 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.78378 | 0.561770 | ||||||||
\(107\) | 14.7761 | 1.42846 | 0.714230 | − | 0.699911i | \(-0.246777\pi\) | ||||
0.714230 | + | 0.699911i | \(0.246777\pi\) | |||||||
\(108\) | −0.772089 | −0.0742943 | ||||||||
\(109\) | 8.78570 | 0.841517 | 0.420759 | − | 0.907173i | \(-0.361764\pi\) | ||||
0.420759 | + | 0.907173i | \(0.361764\pi\) | |||||||
\(110\) | −17.2319 | −1.64300 | ||||||||
\(111\) | −9.90397 | −0.940043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.51561 | 0.330721 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(114\) | −3.16887 | −0.296792 | ||||||||
\(115\) | −13.8365 | −1.29026 | ||||||||
\(116\) | −5.84683 | −0.542865 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 3.76115 | 0.346242 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.67279 | 0.791714 | ||||||||
\(121\) | 19.3364 | 1.75786 | ||||||||
\(122\) | −2.69542 | −0.244032 | ||||||||
\(123\) | 11.0520 | 0.996528 | ||||||||
\(124\) | 4.88827 | 0.438979 | ||||||||
\(125\) | −5.72740 | −0.512274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7287 | −1.39570 | −0.697850 | − | 0.716244i | \(-0.745860\pi\) | ||||
−0.697850 | + | 0.716244i | \(0.745860\pi\) | |||||||
\(128\) | −0.969216 | −0.0856674 | ||||||||
\(129\) | −2.78704 | −0.245386 | ||||||||
\(130\) | −3.12861 | −0.274397 | ||||||||
\(131\) | 0.302656 | 0.0264431 | 0.0132216 | − | 0.999913i | \(-0.495791\pi\) | ||||
0.0132216 | + | 0.999913i | \(0.495791\pi\) | |||||||
\(132\) | −4.25255 | −0.370137 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.75212 | 0.496908 | ||||||||
\(135\) | 2.82337 | 0.242997 | ||||||||
\(136\) | 17.4715 | 1.49817 | ||||||||
\(137\) | −0.733238 | −0.0626448 | −0.0313224 | − | 0.999509i | \(-0.509972\pi\) | ||||
−0.0313224 | + | 0.999509i | \(0.509972\pi\) | |||||||
\(138\) | 5.43052 | 0.462277 | ||||||||
\(139\) | 6.91313 | 0.586364 | 0.293182 | − | 0.956057i | \(-0.405286\pi\) | ||||
0.293182 | + | 0.956057i | \(0.405286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.69551 | −0.648079 | ||||||||
\(142\) | −12.8397 | −1.07749 | ||||||||
\(143\) | 5.50785 | 0.460590 | ||||||||
\(144\) | −1.85970 | −0.154975 | ||||||||
\(145\) | 21.3807 | 1.77557 | ||||||||
\(146\) | −7.40715 | −0.613020 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.64675 | 0.628559 | ||||||||
\(149\) | −21.6008 | −1.76961 | −0.884804 | − | 0.465963i | \(-0.845708\pi\) | ||||
−0.884804 | + | 0.465963i | \(0.845708\pi\) | |||||||
\(150\) | −3.29268 | −0.268846 | ||||||||
\(151\) | 5.82478 | 0.474014 | 0.237007 | − | 0.971508i | \(-0.423834\pi\) | ||||
0.237007 | + | 0.971508i | \(0.423834\pi\) | |||||||
\(152\) | 8.78438 | 0.712507 | ||||||||
\(153\) | 5.68775 | 0.459827 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.8754 | −1.43579 | ||||||||
\(156\) | −0.772089 | −0.0618166 | ||||||||
\(157\) | 5.57409 | 0.444861 | 0.222430 | − | 0.974949i | \(-0.428601\pi\) | ||||
0.222430 | + | 0.974949i | \(0.428601\pi\) | |||||||
\(158\) | 7.12936 | 0.567181 | ||||||||
\(159\) | −5.21949 | −0.413933 | ||||||||
\(160\) | −11.5273 | −0.911313 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.10811 | −0.0870615 | ||||||||
\(163\) | 22.3663 | 1.75187 | 0.875933 | − | 0.482433i | \(-0.160247\pi\) | ||||
0.875933 | + | 0.482433i | \(0.160247\pi\) | |||||||
\(164\) | −8.53315 | −0.666327 | ||||||||
\(165\) | 15.5507 | 1.21062 | ||||||||
\(166\) | 17.7911 | 1.38085 | ||||||||
\(167\) | −3.16554 | −0.244957 | −0.122478 | − | 0.992471i | \(-0.539084\pi\) | ||||
−0.122478 | + | 0.992471i | \(0.539084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −17.7947 | −1.36479 | ||||||||
\(171\) | 2.85970 | 0.218687 | ||||||||
\(172\) | 2.15185 | 0.164077 | ||||||||
\(173\) | −12.0410 | −0.915460 | −0.457730 | − | 0.889091i | \(-0.651337\pi\) | ||||
−0.457730 | + | 0.889091i | \(0.651337\pi\) | |||||||
\(174\) | −8.39145 | −0.636154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2430 | −0.772092 | ||||||||
\(177\) | −3.39419 | −0.255123 | ||||||||
\(178\) | 16.9051 | 1.26709 | ||||||||
\(179\) | 6.26031 | 0.467918 | 0.233959 | − | 0.972247i | \(-0.424832\pi\) | ||||
0.233959 | + | 0.972247i | \(0.424832\pi\) | |||||||
\(180\) | −2.17990 | −0.162480 | ||||||||
\(181\) | −4.23000 | −0.314413 | −0.157207 | − | 0.987566i | \(-0.550249\pi\) | ||||
−0.157207 | + | 0.987566i | \(0.550249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.43245 | 0.179812 | ||||||||
\(184\) | −15.0539 | −1.10979 | ||||||||
\(185\) | −27.9626 | −2.05585 | ||||||||
\(186\) | 7.01570 | 0.514416 | ||||||||
\(187\) | 31.3272 | 2.29088 | ||||||||
\(188\) | 5.94162 | 0.433337 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.94689 | −0.649076 | ||||||||
\(191\) | 16.3980 | 1.18652 | 0.593258 | − | 0.805012i | \(-0.297841\pi\) | ||||
0.593258 | + | 0.805012i | \(0.297841\pi\) | |||||||
\(192\) | 8.24361 | 0.594931 | ||||||||
\(193\) | 9.90397 | 0.712903 | 0.356452 | − | 0.934314i | \(-0.383986\pi\) | ||||
0.356452 | + | 0.934314i | \(0.383986\pi\) | |||||||
\(194\) | −6.79398 | −0.487779 | ||||||||
\(195\) | 2.82337 | 0.202186 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.64207 | 0.259487 | 0.129743 | − | 0.991548i | \(-0.458585\pi\) | ||||
0.129743 | + | 0.991548i | \(0.458585\pi\) | |||||||
\(198\) | −6.10331 | −0.433743 | ||||||||
\(199\) | −2.85836 | −0.202624 | −0.101312 | − | 0.994855i | \(-0.532304\pi\) | ||||
−0.101312 | + | 0.994855i | \(0.532304\pi\) | |||||||
\(200\) | 9.12760 | 0.645419 | ||||||||
\(201\) | −5.19092 | −0.366139 | ||||||||
\(202\) | 5.90397 | 0.415402 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.39145 | −0.307463 | ||||||||
\(205\) | 31.2040 | 2.17938 | ||||||||
\(206\) | 1.71112 | 0.119219 | ||||||||
\(207\) | −4.90070 | −0.340622 | ||||||||
\(208\) | −1.85970 | −0.128947 | ||||||||
\(209\) | 15.7508 | 1.08951 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.29215 | 0.639698 | 0.319849 | − | 0.947469i | \(-0.396368\pi\) | ||||
0.319849 | + | 0.947469i | \(0.396368\pi\) | |||||||
\(212\) | 4.02991 | 0.276775 | ||||||||
\(213\) | 11.5870 | 0.793931 | ||||||||
\(214\) | −16.3736 | −1.11927 | ||||||||
\(215\) | −7.86887 | −0.536652 | ||||||||
\(216\) | 3.07178 | 0.209008 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.73554 | −0.659374 | ||||||||
\(219\) | 6.68448 | 0.451695 | ||||||||
\(220\) | −12.0065 | −0.809480 | ||||||||
\(221\) | 5.68775 | 0.382599 | ||||||||
\(222\) | 10.9747 | 0.736574 | ||||||||
\(223\) | −18.6676 | −1.25008 | −0.625039 | − | 0.780594i | \(-0.714917\pi\) | ||||
−0.625039 | + | 0.780594i | \(0.714917\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.97143 | 0.198096 | ||||||||
\(226\) | −3.89569 | −0.259137 | ||||||||
\(227\) | 24.3411 | 1.61557 | 0.807787 | − | 0.589474i | \(-0.200665\pi\) | ||||
0.807787 | + | 0.589474i | \(0.200665\pi\) | |||||||
\(228\) | −2.20794 | −0.146225 | ||||||||
\(229\) | −14.5664 | −0.962576 | −0.481288 | − | 0.876563i | \(-0.659831\pi\) | ||||
−0.481288 | + | 0.876563i | \(0.659831\pi\) | |||||||
\(230\) | 15.3324 | 1.01099 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.2618 | 1.52721 | ||||||||
\(233\) | 7.14030 | 0.467777 | 0.233888 | − | 0.972263i | \(-0.424855\pi\) | ||||
0.233888 | + | 0.972263i | \(0.424855\pi\) | |||||||
\(234\) | −1.10811 | −0.0724395 | ||||||||
\(235\) | −21.7273 | −1.41733 | ||||||||
\(236\) | 2.62062 | 0.170588 | ||||||||
\(237\) | −6.43379 | −0.417920 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.44155 | −0.546039 | −0.273019 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273019 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(240\) | −5.25063 | −0.338927 | ||||||||
\(241\) | 17.0663 | 1.09934 | 0.549669 | − | 0.835382i | \(-0.314754\pi\) | ||||
0.549669 | + | 0.835382i | \(0.314754\pi\) | |||||||
\(242\) | −21.4269 | −1.37737 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.87806 | −0.120231 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.2469 | −0.780832 | ||||||||
\(247\) | 2.85970 | 0.181958 | ||||||||
\(248\) | −19.4481 | −1.23496 | ||||||||
\(249\) | −16.0553 | −1.01746 | ||||||||
\(250\) | 6.34660 | 0.401394 | ||||||||
\(251\) | 7.07283 | 0.446433 | 0.223217 | − | 0.974769i | \(-0.428344\pi\) | ||||
0.223217 | + | 0.974769i | \(0.428344\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.9923 | −1.69699 | ||||||||
\(254\) | 17.4292 | 1.09361 | ||||||||
\(255\) | 16.0586 | 1.00563 | ||||||||
\(256\) | −15.4132 | −0.963326 | ||||||||
\(257\) | −22.8304 | −1.42412 | −0.712061 | − | 0.702117i | \(-0.752238\pi\) | ||||
−0.712061 | + | 0.702117i | \(0.752238\pi\) | |||||||
\(258\) | 3.08836 | 0.192273 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.17990 | −0.135191 | ||||||||
\(261\) | 7.57275 | 0.468741 | ||||||||
\(262\) | −0.335376 | −0.0207196 | ||||||||
\(263\) | 17.5383 | 1.08146 | 0.540728 | − | 0.841197i | \(-0.318149\pi\) | ||||
0.540728 | + | 0.841197i | \(0.318149\pi\) | |||||||
\(264\) | 16.9189 | 1.04129 | ||||||||
\(265\) | −14.7366 | −0.905260 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2558 | −0.933641 | ||||||||
\(268\) | 4.00785 | 0.244819 | ||||||||
\(269\) | 11.3096 | 0.689560 | 0.344780 | − | 0.938684i | \(-0.387954\pi\) | ||||
0.344780 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(270\) | −3.12861 | −0.190401 | ||||||||
\(271\) | 10.5027 | 0.637996 | 0.318998 | − | 0.947755i | \(-0.396654\pi\) | ||||
0.318998 | + | 0.947755i | \(0.396654\pi\) | |||||||
\(272\) | −10.5775 | −0.641355 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.812510 | 0.0490855 | ||||||||
\(275\) | 16.3662 | 0.986919 | ||||||||
\(276\) | 3.78378 | 0.227757 | ||||||||
\(277\) | −23.9574 | −1.43946 | −0.719730 | − | 0.694254i | \(-0.755735\pi\) | ||||
−0.719730 | + | 0.694254i | \(0.755735\pi\) | |||||||
\(278\) | −7.66052 | −0.459448 | ||||||||
\(279\) | −6.33122 | −0.379040 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.06163 | 0.182641 | 0.0913207 | − | 0.995822i | \(-0.470891\pi\) | ||||
0.0913207 | + | 0.995822i | \(0.470891\pi\) | |||||||
\(282\) | 8.52748 | 0.507804 | ||||||||
\(283\) | −22.8143 | −1.35617 | −0.678084 | − | 0.734984i | \(-0.737190\pi\) | ||||
−0.678084 | + | 0.734984i | \(0.737190\pi\) | |||||||
\(284\) | −8.94623 | −0.530861 | ||||||||
\(285\) | 8.07400 | 0.478262 | ||||||||
\(286\) | −6.10331 | −0.360896 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.08281 | −0.240582 | ||||||||
\(289\) | 15.3504 | 0.902967 | ||||||||
\(290\) | −23.6922 | −1.39125 | ||||||||
\(291\) | 6.13113 | 0.359413 | ||||||||
\(292\) | −5.16101 | −0.302025 | ||||||||
\(293\) | 11.9623 | 0.698847 | 0.349423 | − | 0.936965i | \(-0.386378\pi\) | ||||
0.349423 | + | 0.936965i | \(0.386378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.58308 | −0.557948 | ||||||||
\(296\) | −30.4228 | −1.76829 | ||||||||
\(297\) | 5.50785 | 0.319598 | ||||||||
\(298\) | 23.9361 | 1.38658 | ||||||||
\(299\) | −4.90070 | −0.283415 | ||||||||
\(300\) | −2.29421 | −0.132456 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.45450 | −0.371415 | ||||||||
\(303\) | −5.32796 | −0.306083 | ||||||||
\(304\) | −5.31819 | −0.305019 | ||||||||
\(305\) | 6.86770 | 0.393243 | ||||||||
\(306\) | −6.30266 | −0.360299 | ||||||||
\(307\) | −3.56994 | −0.203747 | −0.101874 | − | 0.994797i | \(-0.532484\pi\) | ||||
−0.101874 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.54418 | −0.0878452 | ||||||||
\(310\) | 19.8079 | 1.12502 | ||||||||
\(311\) | −31.1741 | −1.76772 | −0.883860 | − | 0.467752i | \(-0.845064\pi\) | ||||
−0.883860 | + | 0.467752i | \(0.845064\pi\) | |||||||
\(312\) | 3.07178 | 0.173905 | ||||||||
\(313\) | −28.6690 | −1.62047 | −0.810233 | − | 0.586107i | \(-0.800660\pi\) | ||||
−0.810233 | + | 0.586107i | \(0.800660\pi\) | |||||||
\(314\) | −6.17671 | −0.348572 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.96746 | 0.279441 | ||||||||
\(317\) | 0.203271 | 0.0114168 | 0.00570842 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570842 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(318\) | 5.78378 | 0.324338 | ||||||||
\(319\) | 41.7095 | 2.33529 | ||||||||
\(320\) | 23.2748 | 1.30110 | ||||||||
\(321\) | 14.7761 | 0.824722 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.2652 | 0.905023 | ||||||||
\(324\) | −0.772089 | −0.0428938 | ||||||||
\(325\) | 2.97143 | 0.164825 | ||||||||
\(326\) | −24.7844 | −1.37268 | ||||||||
\(327\) | 8.78570 | 0.485850 | ||||||||
\(328\) | 33.9494 | 1.87454 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −17.2319 | −0.948586 | ||||||||
\(331\) | −7.35062 | −0.404027 | −0.202013 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202013 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(332\) | 12.3961 | 0.680325 | ||||||||
\(333\) | −9.90397 | −0.542734 | ||||||||
\(334\) | 3.50777 | 0.191937 | ||||||||
\(335\) | −14.6559 | −0.800738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.54552 | 0.411031 | 0.205515 | − | 0.978654i | \(-0.434113\pi\) | ||||
0.205515 | + | 0.978654i | \(0.434113\pi\) | |||||||
\(338\) | −1.10811 | −0.0602733 | ||||||||
\(339\) | 3.51561 | 0.190942 | ||||||||
\(340\) | −12.3987 | −0.672413 | ||||||||
\(341\) | −34.8714 | −1.88839 | ||||||||
\(342\) | −3.16887 | −0.171353 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.56120 | −0.461589 | ||||||||
\(345\) | −13.8365 | −0.744932 | ||||||||
\(346\) | 13.3428 | 0.717312 | ||||||||
\(347\) | 4.95918 | 0.266223 | 0.133111 | − | 0.991101i | \(-0.457503\pi\) | ||||
0.133111 | + | 0.991101i | \(0.457503\pi\) | |||||||
\(348\) | −5.84683 | −0.313423 | ||||||||
\(349\) | 31.3235 | 1.67671 | 0.838356 | − | 0.545124i | \(-0.183517\pi\) | ||||
0.838356 | + | 0.545124i | \(0.183517\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −22.4875 | −1.19859 | ||||||||
\(353\) | 36.7092 | 1.95383 | 0.976916 | − | 0.213626i | \(-0.0685273\pi\) | ||||
0.976916 | + | 0.213626i | \(0.0685273\pi\) | |||||||
\(354\) | 3.76115 | 0.199903 | ||||||||
\(355\) | 32.7145 | 1.73631 | ||||||||
\(356\) | 11.7789 | 0.624278 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.93712 | −0.366638 | ||||||||
\(359\) | −15.8170 | −0.834791 | −0.417396 | − | 0.908725i | \(-0.637057\pi\) | ||||
−0.417396 | + | 0.908725i | \(0.637057\pi\) | |||||||
\(360\) | 8.67279 | 0.457096 | ||||||||
\(361\) | −10.8221 | −0.569585 | ||||||||
\(362\) | 4.68731 | 0.246360 | ||||||||
\(363\) | 19.3364 | 1.01490 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.8728 | 0.987846 | ||||||||
\(366\) | −2.69542 | −0.140892 | ||||||||
\(367\) | −25.4752 | −1.32980 | −0.664899 | − | 0.746934i | \(-0.731525\pi\) | ||||
−0.664899 | + | 0.746934i | \(0.731525\pi\) | |||||||
\(368\) | 9.11383 | 0.475091 | ||||||||
\(369\) | 11.0520 | 0.575346 | ||||||||
\(370\) | 30.9857 | 1.61087 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.88827 | 0.253445 | ||||||||
\(373\) | 24.3364 | 1.26009 | 0.630046 | − | 0.776558i | \(-0.283036\pi\) | ||||
0.630046 | + | 0.776558i | \(0.283036\pi\) | |||||||
\(374\) | −34.7141 | −1.79502 | ||||||||
\(375\) | −5.72740 | −0.295762 | ||||||||
\(376\) | −23.6389 | −1.21908 | ||||||||
\(377\) | 7.57275 | 0.390016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.97278 | 0.101335 | 0.0506674 | − | 0.998716i | \(-0.483865\pi\) | ||||
0.0506674 | + | 0.998716i | \(0.483865\pi\) | |||||||
\(380\) | −6.23385 | −0.319790 | ||||||||
\(381\) | −15.7287 | −0.805808 | ||||||||
\(382\) | −18.1708 | −0.929699 | ||||||||
\(383\) | −4.95625 | −0.253253 | −0.126626 | − | 0.991950i | \(-0.540415\pi\) | ||||
−0.126626 | + | 0.991950i | \(0.540415\pi\) | |||||||
\(384\) | −0.969216 | −0.0494601 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.9747 | −0.558598 | ||||||||
\(387\) | −2.78704 | −0.141673 | ||||||||
\(388\) | −4.73378 | −0.240321 | ||||||||
\(389\) | 8.42860 | 0.427347 | 0.213673 | − | 0.976905i | \(-0.431457\pi\) | ||||
0.213673 | + | 0.976905i | \(0.431457\pi\) | |||||||
\(390\) | −3.12861 | −0.158423 | ||||||||
\(391\) | −27.8739 | −1.40965 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.302656 | 0.0152670 | ||||||||
\(394\) | −4.03582 | −0.203322 | ||||||||
\(395\) | −18.1650 | −0.913980 | ||||||||
\(396\) | −4.25255 | −0.213699 | ||||||||
\(397\) | −1.24287 | −0.0623777 | −0.0311888 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311888 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(398\) | 3.16738 | 0.158766 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.52597 | −0.276299 | ||||||||
\(401\) | 23.8061 | 1.18882 | 0.594409 | − | 0.804163i | \(-0.297386\pi\) | ||||
0.594409 | + | 0.804163i | \(0.297386\pi\) | |||||||
\(402\) | 5.75212 | 0.286890 | ||||||||
\(403\) | −6.33122 | −0.315381 | ||||||||
\(404\) | 4.11366 | 0.204662 | ||||||||
\(405\) | 2.82337 | 0.140295 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54.5496 | −2.70392 | ||||||||
\(408\) | 17.4715 | 0.864969 | ||||||||
\(409\) | −38.6015 | −1.90872 | −0.954361 | − | 0.298655i | \(-0.903462\pi\) | ||||
−0.954361 | + | 0.298655i | \(0.903462\pi\) | |||||||
\(410\) | −34.5775 | −1.70766 | ||||||||
\(411\) | −0.733238 | −0.0361680 | ||||||||
\(412\) | 1.19224 | 0.0587376 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.43052 | 0.266896 | ||||||||
\(415\) | −45.3301 | −2.22517 | ||||||||
\(416\) | −4.08281 | −0.200176 | ||||||||
\(417\) | 6.91313 | 0.338538 | ||||||||
\(418\) | −17.4536 | −0.853686 | ||||||||
\(419\) | −27.2457 | −1.33104 | −0.665520 | − | 0.746380i | \(-0.731790\pi\) | ||||
−0.665520 | + | 0.746380i | \(0.731790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6897 | 0.618457 | 0.309228 | − | 0.950988i | \(-0.399929\pi\) | ||||
0.309228 | + | 0.950988i | \(0.399929\pi\) | |||||||
\(422\) | −10.2967 | −0.501237 | ||||||||
\(423\) | −7.69551 | −0.374168 | ||||||||
\(424\) | −16.0331 | −0.778638 | ||||||||
\(425\) | 16.9008 | 0.819807 | ||||||||
\(426\) | −12.8397 | −0.622087 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.4085 | −0.551449 | ||||||||
\(429\) | 5.50785 | 0.265922 | ||||||||
\(430\) | 8.71958 | 0.420495 | ||||||||
\(431\) | −31.0197 | −1.49416 | −0.747082 | − | 0.664731i | \(-0.768546\pi\) | ||||
−0.747082 | + | 0.664731i | \(0.768546\pi\) | |||||||
\(432\) | −1.85970 | −0.0894749 | ||||||||
\(433\) | −16.4141 | −0.788812 | −0.394406 | − | 0.918936i | \(-0.629050\pi\) | ||||
−0.394406 | + | 0.918936i | \(0.629050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.3807 | 1.02513 | ||||||||
\(436\) | −6.78334 | −0.324863 | ||||||||
\(437\) | −14.0145 | −0.670406 | ||||||||
\(438\) | −7.40715 | −0.353927 | ||||||||
\(439\) | −12.4156 | −0.592564 | −0.296282 | − | 0.955100i | \(-0.595747\pi\) | ||||
−0.296282 | + | 0.955100i | \(0.595747\pi\) | |||||||
\(440\) | 47.7684 | 2.27727 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.30266 | −0.299787 | ||||||||
\(443\) | 16.4242 | 0.780337 | 0.390168 | − | 0.920744i | \(-0.372417\pi\) | ||||
0.390168 | + | 0.920744i | \(0.372417\pi\) | |||||||
\(444\) | 7.64675 | 0.362898 | ||||||||
\(445\) | −43.0729 | −2.04185 | ||||||||
\(446\) | 20.6858 | 0.979502 | ||||||||
\(447\) | −21.6008 | −1.02168 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9671 | −0.706340 | −0.353170 | − | 0.935559i | \(-0.614896\pi\) | ||||
−0.353170 | + | 0.935559i | \(0.614896\pi\) | |||||||
\(450\) | −3.29268 | −0.155218 | ||||||||
\(451\) | 60.8729 | 2.86639 | ||||||||
\(452\) | −2.71436 | −0.127673 | ||||||||
\(453\) | 5.82478 | 0.273672 | ||||||||
\(454\) | −26.9726 | −1.26589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.78438 | 0.411366 | ||||||||
\(457\) | 19.5263 | 0.913402 | 0.456701 | − | 0.889620i | \(-0.349031\pi\) | ||||
0.456701 | + | 0.889620i | \(0.349031\pi\) | |||||||
\(458\) | 16.1412 | 0.754229 | ||||||||
\(459\) | 5.68775 | 0.265481 | ||||||||
\(460\) | 10.6830 | 0.498098 | ||||||||
\(461\) | 10.7649 | 0.501371 | 0.250686 | − | 0.968069i | \(-0.419344\pi\) | ||||
0.250686 | + | 0.968069i | \(0.419344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3077 | −0.664935 | −0.332468 | − | 0.943115i | \(-0.607881\pi\) | ||||
−0.332468 | + | 0.943115i | \(0.607881\pi\) | |||||||
\(464\) | −14.0830 | −0.653789 | ||||||||
\(465\) | −17.8754 | −0.828952 | ||||||||
\(466\) | −7.91225 | −0.366528 | ||||||||
\(467\) | −29.0471 | −1.34414 | −0.672070 | − | 0.740488i | \(-0.734595\pi\) | ||||
−0.672070 | + | 0.740488i | \(0.734595\pi\) | |||||||
\(468\) | −0.772089 | −0.0356898 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.0762 | 1.11055 | ||||||||
\(471\) | 5.57409 | 0.256840 | ||||||||
\(472\) | −10.4262 | −0.479906 | ||||||||
\(473\) | −15.3506 | −0.705822 | ||||||||
\(474\) | 7.12936 | 0.327462 | ||||||||
\(475\) | 8.49741 | 0.389888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.21949 | −0.238984 | ||||||||
\(478\) | 9.35418 | 0.427850 | ||||||||
\(479\) | −7.20079 | −0.329012 | −0.164506 | − | 0.986376i | \(-0.552603\pi\) | ||||
−0.164506 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(480\) | −11.5273 | −0.526147 | ||||||||
\(481\) | −9.90397 | −0.451582 | ||||||||
\(482\) | −18.9114 | −0.861390 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.9294 | −0.678611 | ||||||||
\(485\) | 17.3105 | 0.786028 | ||||||||
\(486\) | −1.10811 | −0.0502650 | ||||||||
\(487\) | 6.23236 | 0.282415 | 0.141208 | − | 0.989980i | \(-0.454902\pi\) | ||||
0.141208 | + | 0.989980i | \(0.454902\pi\) | |||||||
\(488\) | 7.47195 | 0.338239 | ||||||||
\(489\) | 22.3663 | 1.01144 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.4957 | 0.518793 | 0.259396 | − | 0.965771i | \(-0.416476\pi\) | ||||
0.259396 | + | 0.965771i | \(0.416476\pi\) | |||||||
\(492\) | −8.53315 | −0.384704 | ||||||||
\(493\) | 43.0718 | 1.93986 | ||||||||
\(494\) | −3.16887 | −0.142574 | ||||||||
\(495\) | 15.5507 | 0.698953 | ||||||||
\(496\) | 11.7742 | 0.528676 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.7911 | 0.797236 | ||||||||
\(499\) | −11.3506 | −0.508124 | −0.254062 | − | 0.967188i | \(-0.581767\pi\) | ||||
−0.254062 | + | 0.967188i | \(0.581767\pi\) | |||||||
\(500\) | 4.42206 | 0.197761 | ||||||||
\(501\) | −3.16554 | −0.141426 | ||||||||
\(502\) | −7.83749 | −0.349804 | ||||||||
\(503\) | −19.0728 | −0.850416 | −0.425208 | − | 0.905096i | \(-0.639799\pi\) | ||||
−0.425208 | + | 0.905096i | \(0.639799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.0428 | −0.669396 | ||||||||
\(506\) | 29.9105 | 1.32968 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 12.1440 | 0.538803 | ||||||||
\(509\) | −7.91454 | −0.350806 | −0.175403 | − | 0.984497i | \(-0.556123\pi\) | ||||
−0.175403 | + | 0.984497i | \(0.556123\pi\) | |||||||
\(510\) | −17.7947 | −0.787965 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.0180 | 0.840485 | ||||||||
\(513\) | 2.85970 | 0.126259 | ||||||||
\(514\) | 25.2987 | 1.11588 | ||||||||
\(515\) | −4.35979 | −0.192115 | ||||||||
\(516\) | 2.15185 | 0.0947298 | ||||||||
\(517\) | −42.3857 | −1.86412 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0410 | −0.528541 | ||||||||
\(520\) | 8.67279 | 0.380327 | ||||||||
\(521\) | −26.3408 | −1.15401 | −0.577007 | − | 0.816739i | \(-0.695779\pi\) | ||||
−0.577007 | + | 0.816739i | \(0.695779\pi\) | |||||||
\(522\) | −8.39145 | −0.367284 | ||||||||
\(523\) | 5.54687 | 0.242548 | 0.121274 | − | 0.992619i | \(-0.461302\pi\) | ||||
0.121274 | + | 0.992619i | \(0.461302\pi\) | |||||||
\(524\) | −0.233677 | −0.0102082 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.4344 | −0.847379 | ||||||||
\(527\) | −36.0104 | −1.56864 | ||||||||
\(528\) | −10.2430 | −0.445767 | ||||||||
\(529\) | 1.01687 | 0.0442115 | ||||||||
\(530\) | 16.3298 | 0.709319 | ||||||||
\(531\) | −3.39419 | −0.147295 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0520 | 0.478716 | ||||||||
\(534\) | 16.9051 | 0.731557 | ||||||||
\(535\) | 41.7184 | 1.80365 | ||||||||
\(536\) | −15.9454 | −0.688736 | ||||||||
\(537\) | 6.26031 | 0.270152 | ||||||||
\(538\) | −12.5323 | −0.540307 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.17990 | −0.0938077 | ||||||||
\(541\) | 22.7107 | 0.976409 | 0.488204 | − | 0.872729i | \(-0.337652\pi\) | ||||
0.488204 | + | 0.872729i | \(0.337652\pi\) | |||||||
\(542\) | −11.6382 | −0.499904 | ||||||||
\(543\) | −4.23000 | −0.181527 | ||||||||
\(544\) | −23.2220 | −0.995635 | ||||||||
\(545\) | 24.8053 | 1.06254 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.2299 | −1.33529 | −0.667646 | − | 0.744478i | \(-0.732698\pi\) | ||||
−0.667646 | + | 0.744478i | \(0.732698\pi\) | |||||||
\(548\) | 0.566125 | 0.0241837 | ||||||||
\(549\) | 2.43245 | 0.103814 | ||||||||
\(550\) | −18.1356 | −0.773304 | ||||||||
\(551\) | 21.6558 | 0.922567 | ||||||||
\(552\) | −15.0539 | −0.640736 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.5475 | 1.12789 | ||||||||
\(555\) | −27.9626 | −1.18695 | ||||||||
\(556\) | −5.33755 | −0.226363 | ||||||||
\(557\) | −33.0837 | −1.40180 | −0.700900 | − | 0.713259i | \(-0.747218\pi\) | ||||
−0.700900 | + | 0.713259i | \(0.747218\pi\) | |||||||
\(558\) | 7.01570 | 0.296998 | ||||||||
\(559\) | −2.78704 | −0.117879 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.3272 | 1.32264 | ||||||||
\(562\) | −3.39262 | −0.143109 | ||||||||
\(563\) | −30.0065 | −1.26462 | −0.632312 | − | 0.774714i | \(-0.717894\pi\) | ||||
−0.632312 | + | 0.774714i | \(0.717894\pi\) | |||||||
\(564\) | 5.94162 | 0.250187 | ||||||||
\(565\) | 9.92588 | 0.417585 | ||||||||
\(566\) | 25.2808 | 1.06263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 35.5929 | 1.49344 | ||||||||
\(569\) | 32.1781 | 1.34897 | 0.674487 | − | 0.738287i | \(-0.264365\pi\) | ||||
0.674487 | + | 0.738287i | \(0.264365\pi\) | |||||||
\(570\) | −8.94689 | −0.374744 | ||||||||
\(571\) | −43.3615 | −1.81462 | −0.907311 | − | 0.420461i | \(-0.861868\pi\) | ||||
−0.907311 | + | 0.420461i | \(0.861868\pi\) | |||||||
\(572\) | −4.25255 | −0.177808 | ||||||||
\(573\) | 16.3980 | 0.685035 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.5621 | −0.607282 | ||||||||
\(576\) | 8.24361 | 0.343484 | ||||||||
\(577\) | −39.9509 | −1.66318 | −0.831589 | − | 0.555392i | \(-0.812568\pi\) | ||||
−0.831589 | + | 0.555392i | \(0.812568\pi\) | |||||||
\(578\) | −17.0100 | −0.707523 | ||||||||
\(579\) | 9.90397 | 0.411595 | ||||||||
\(580\) | −16.5078 | −0.685449 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.79398 | −0.281620 | ||||||||
\(583\) | −28.7482 | −1.19063 | ||||||||
\(584\) | 20.5333 | 0.849673 | ||||||||
\(585\) | 2.82337 | 0.116732 | ||||||||
\(586\) | −13.2556 | −0.547583 | ||||||||
\(587\) | −14.3837 | −0.593678 | −0.296839 | − | 0.954928i | \(-0.595933\pi\) | ||||
−0.296839 | + | 0.954928i | \(0.595933\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.1054 | −0.746020 | ||||||||
\(590\) | 10.6191 | 0.437182 | ||||||||
\(591\) | 3.64207 | 0.149815 | ||||||||
\(592\) | 18.4184 | 0.756992 | ||||||||
\(593\) | 7.35603 | 0.302076 | 0.151038 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151038 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(594\) | −6.10331 | −0.250422 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6778 | 0.683147 | ||||||||
\(597\) | −2.85836 | −0.116985 | ||||||||
\(598\) | 5.43052 | 0.222071 | ||||||||
\(599\) | −8.78643 | −0.359004 | −0.179502 | − | 0.983758i | \(-0.557449\pi\) | ||||
−0.179502 | + | 0.983758i | \(0.557449\pi\) | |||||||
\(600\) | 9.12760 | 0.372633 | ||||||||
\(601\) | −25.6277 | −1.04537 | −0.522687 | − | 0.852525i | \(-0.675070\pi\) | ||||
−0.522687 | + | 0.852525i | \(0.675070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.19092 | −0.211391 | ||||||||
\(604\) | −4.49725 | −0.182990 | ||||||||
\(605\) | 54.5939 | 2.21956 | ||||||||
\(606\) | 5.90397 | 0.239832 | ||||||||
\(607\) | 27.7091 | 1.12468 | 0.562339 | − | 0.826907i | \(-0.309902\pi\) | ||||
0.562339 | + | 0.826907i | \(0.309902\pi\) | |||||||
\(608\) | −11.6756 | −0.473509 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.61018 | −0.308127 | ||||||||
\(611\) | −7.69551 | −0.311327 | ||||||||
\(612\) | −4.39145 | −0.177514 | ||||||||
\(613\) | 33.7067 | 1.36140 | 0.680701 | − | 0.732561i | \(-0.261675\pi\) | ||||
0.680701 | + | 0.732561i | \(0.261675\pi\) | |||||||
\(614\) | 3.95589 | 0.159647 | ||||||||
\(615\) | 31.2040 | 1.25827 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.02392 | −0.242514 | −0.121257 | − | 0.992621i | \(-0.538692\pi\) | ||||
−0.121257 | + | 0.992621i | \(0.538692\pi\) | |||||||
\(618\) | 1.71112 | 0.0688314 | ||||||||
\(619\) | 6.61701 | 0.265960 | 0.132980 | − | 0.991119i | \(-0.457545\pi\) | ||||
0.132980 | + | 0.991119i | \(0.457545\pi\) | |||||||
\(620\) | 13.8014 | 0.554278 | ||||||||
\(621\) | −4.90070 | −0.196658 | ||||||||
\(622\) | 34.5444 | 1.38510 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.85970 | −0.0744476 | ||||||||
\(625\) | −31.0278 | −1.24111 | ||||||||
\(626\) | 31.7684 | 1.26972 | ||||||||
\(627\) | 15.7508 | 0.629026 | ||||||||
\(628\) | −4.30369 | −0.171736 | ||||||||
\(629\) | −56.3312 | −2.24607 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.19982 | 0.0477639 | 0.0238820 | − | 0.999715i | \(-0.492397\pi\) | ||||
0.0238820 | + | 0.999715i | \(0.492397\pi\) | |||||||
\(632\) | −19.7632 | −0.786138 | ||||||||
\(633\) | 9.29215 | 0.369330 | ||||||||
\(634\) | −0.225247 | −0.00894571 | ||||||||
\(635\) | −44.4081 | −1.76228 | ||||||||
\(636\) | 4.02991 | 0.159796 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −46.2188 | −1.82982 | ||||||||
\(639\) | 11.5870 | 0.458376 | ||||||||
\(640\) | −2.73646 | −0.108168 | ||||||||
\(641\) | 32.2258 | 1.27284 | 0.636422 | − | 0.771341i | \(-0.280414\pi\) | ||||
0.636422 | + | 0.771341i | \(0.280414\pi\) | |||||||
\(642\) | −16.3736 | −0.646213 | ||||||||
\(643\) | 3.28042 | 0.129367 | 0.0646836 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646836 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.86887 | −0.309836 | ||||||||
\(646\) | −18.0237 | −0.709133 | ||||||||
\(647\) | 10.0947 | 0.396864 | 0.198432 | − | 0.980115i | \(-0.436415\pi\) | ||||
0.198432 | + | 0.980115i | \(0.436415\pi\) | |||||||
\(648\) | 3.07178 | 0.120671 | ||||||||
\(649\) | −18.6947 | −0.733832 | ||||||||
\(650\) | −3.29268 | −0.129149 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.2688 | −0.676298 | ||||||||
\(653\) | −8.39119 | −0.328373 | −0.164186 | − | 0.986429i | \(-0.552500\pi\) | ||||
−0.164186 | + | 0.986429i | \(0.552500\pi\) | |||||||
\(654\) | −9.73554 | −0.380690 | ||||||||
\(655\) | 0.854509 | 0.0333884 | ||||||||
\(656\) | −20.5535 | −0.802478 | ||||||||
\(657\) | 6.68448 | 0.260786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.8448 | −1.39631 | −0.698157 | − | 0.715944i | \(-0.745996\pi\) | ||||
−0.698157 | + | 0.715944i | \(0.745996\pi\) | |||||||
\(660\) | −12.0065 | −0.467354 | ||||||||
\(661\) | 24.0899 | 0.936988 | 0.468494 | − | 0.883467i | \(-0.344797\pi\) | ||||
0.468494 | + | 0.883467i | \(0.344797\pi\) | |||||||
\(662\) | 8.14531 | 0.316577 | ||||||||
\(663\) | 5.68775 | 0.220894 | ||||||||
\(664\) | −49.3184 | −1.91392 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9747 | 0.425261 | ||||||||
\(667\) | −37.1118 | −1.43697 | ||||||||
\(668\) | 2.44408 | 0.0945642 | ||||||||
\(669\) | −18.6676 | −0.721733 | ||||||||
\(670\) | 16.2404 | 0.627421 | ||||||||
\(671\) | 13.3975 | 0.517207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7052 | 0.605392 | 0.302696 | − | 0.953087i | \(-0.402113\pi\) | ||||
0.302696 | + | 0.953087i | \(0.402113\pi\) | |||||||
\(674\) | −8.36128 | −0.322064 | ||||||||
\(675\) | 2.97143 | 0.114371 | ||||||||
\(676\) | −0.772089 | −0.0296957 | ||||||||
\(677\) | 27.8527 | 1.07046 | 0.535232 | − | 0.844705i | \(-0.320224\pi\) | ||||
0.535232 | + | 0.844705i | \(0.320224\pi\) | |||||||
\(678\) | −3.89569 | −0.149613 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 49.3286 | 1.89167 | ||||||||
\(681\) | 24.3411 | 0.932752 | ||||||||
\(682\) | 38.6414 | 1.47966 | ||||||||
\(683\) | −11.8326 | −0.452760 | −0.226380 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226380 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(684\) | −2.20794 | −0.0844228 | ||||||||
\(685\) | −2.07020 | −0.0790985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.5664 | −0.555743 | ||||||||
\(688\) | 5.18307 | 0.197603 | ||||||||
\(689\) | −5.21949 | −0.198847 | ||||||||
\(690\) | 15.3324 | 0.583694 | ||||||||
\(691\) | 21.1741 | 0.805499 | 0.402750 | − | 0.915310i | \(-0.368055\pi\) | ||||
0.402750 | + | 0.915310i | \(0.368055\pi\) | |||||||
\(692\) | 9.29672 | 0.353408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.49532 | −0.208600 | ||||||||
\(695\) | 19.5184 | 0.740373 | ||||||||
\(696\) | 23.2618 | 0.881738 | ||||||||
\(697\) | 62.8611 | 2.38103 | ||||||||
\(698\) | −34.7100 | −1.31379 | ||||||||
\(699\) | 7.14030 | 0.270071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.24436 | −0.0469987 | −0.0234993 | − | 0.999724i | \(-0.507481\pi\) | ||||
−0.0234993 | + | 0.999724i | \(0.507481\pi\) | |||||||
\(702\) | −1.10811 | −0.0418230 | ||||||||
\(703\) | −28.3224 | −1.06820 | ||||||||
\(704\) | 45.4046 | 1.71125 | ||||||||
\(705\) | −21.7273 | −0.818297 | ||||||||
\(706\) | −40.6778 | −1.53093 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.62062 | 0.0984889 | ||||||||
\(709\) | 28.9337 | 1.08663 | 0.543314 | − | 0.839530i | \(-0.317169\pi\) | ||||
0.543314 | + | 0.839530i | \(0.317169\pi\) | |||||||
\(710\) | −36.2513 | −1.36049 | ||||||||
\(711\) | −6.43379 | −0.241286 | ||||||||
\(712\) | −46.8626 | −1.75625 | ||||||||
\(713\) | 31.0274 | 1.16199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.5507 | 0.581564 | ||||||||
\(716\) | −4.83352 | −0.180637 | ||||||||
\(717\) | −8.44155 | −0.315255 | ||||||||
\(718\) | 17.5270 | 0.654103 | ||||||||
\(719\) | 42.7416 | 1.59399 | 0.796997 | − | 0.603983i | \(-0.206421\pi\) | ||||
0.796997 | + | 0.603983i | \(0.206421\pi\) | |||||||
\(720\) | −5.25063 | −0.195679 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.9921 | 0.446300 | ||||||||
\(723\) | 17.0663 | 0.634703 | ||||||||
\(724\) | 3.26594 | 0.121378 | ||||||||
\(725\) | 22.5019 | 0.835700 | ||||||||
\(726\) | −21.4269 | −0.795227 | ||||||||
\(727\) | 41.3249 | 1.53266 | 0.766328 | − | 0.642450i | \(-0.222082\pi\) | ||||
0.766328 | + | 0.642450i | \(0.222082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −20.9131 | −0.774030 | ||||||||
\(731\) | −15.8520 | −0.586307 | ||||||||
\(732\) | −1.87806 | −0.0694153 | ||||||||
\(733\) | 49.9312 | 1.84425 | 0.922126 | − | 0.386890i | \(-0.126451\pi\) | ||||
0.922126 | + | 0.386890i | \(0.126451\pi\) | |||||||
\(734\) | 28.2294 | 1.04197 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.0086 | 0.737528 | ||||||||
\(737\) | −28.5908 | −1.05316 | ||||||||
\(738\) | −12.2469 | −0.450814 | ||||||||
\(739\) | 4.87892 | 0.179474 | 0.0897370 | − | 0.995965i | \(-0.471397\pi\) | ||||
0.0897370 | + | 0.995965i | \(0.471397\pi\) | |||||||
\(740\) | 21.5896 | 0.793650 | ||||||||
\(741\) | 2.85970 | 0.105054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.31579 | 0.0482715 | 0.0241358 | − | 0.999709i | \(-0.492317\pi\) | ||||
0.0241358 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(744\) | −19.4481 | −0.713004 | ||||||||
\(745\) | −60.9872 | −2.23440 | ||||||||
\(746\) | −26.9675 | −0.987349 | ||||||||
\(747\) | −16.0553 | −0.587433 | ||||||||
\(748\) | −24.1874 | −0.884380 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.34660 | 0.231745 | ||||||||
\(751\) | −23.3924 | −0.853599 | −0.426800 | − | 0.904346i | \(-0.640359\pi\) | ||||
−0.426800 | + | 0.904346i | \(0.640359\pi\) | |||||||
\(752\) | 14.3113 | 0.521881 | ||||||||
\(753\) | 7.07283 | 0.257748 | ||||||||
\(754\) | −8.39145 | −0.305598 | ||||||||
\(755\) | 16.4455 | 0.598514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.5069 | 0.745336 | 0.372668 | − | 0.927965i | \(-0.378443\pi\) | ||||
0.372668 | + | 0.927965i | \(0.378443\pi\) | |||||||
\(758\) | −2.18606 | −0.0794012 | ||||||||
\(759\) | −26.9923 | −0.979759 | ||||||||
\(760\) | 24.8016 | 0.899648 | ||||||||
\(761\) | −43.3571 | −1.57169 | −0.785846 | − | 0.618422i | \(-0.787772\pi\) | ||||
−0.785846 | + | 0.618422i | \(0.787772\pi\) | |||||||
\(762\) | 17.4292 | 0.631393 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.6607 | −0.458048 | ||||||||
\(765\) | 16.0586 | 0.580601 | ||||||||
\(766\) | 5.49208 | 0.198437 | ||||||||
\(767\) | −3.39419 | −0.122557 | ||||||||
\(768\) | −15.4132 | −0.556177 | ||||||||
\(769\) | −28.8949 | −1.04198 | −0.520989 | − | 0.853563i | \(-0.674437\pi\) | ||||
−0.520989 | + | 0.853563i | \(0.674437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.8304 | −0.822218 | ||||||||
\(772\) | −7.64675 | −0.275212 | ||||||||
\(773\) | 30.3584 | 1.09191 | 0.545957 | − | 0.837813i | \(-0.316166\pi\) | ||||
0.545957 | + | 0.837813i | \(0.316166\pi\) | |||||||
\(774\) | 3.08836 | 0.111009 | ||||||||
\(775\) | −18.8128 | −0.675776 | ||||||||
\(776\) | 18.8335 | 0.676084 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.33983 | −0.334849 | ||||||||
\(779\) | 31.6055 | 1.13238 | ||||||||
\(780\) | −2.17990 | −0.0780528 | ||||||||
\(781\) | 63.8197 | 2.28365 | ||||||||
\(782\) | 30.8874 | 1.10453 | ||||||||
\(783\) | 7.57275 | 0.270628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.7377 | 0.561704 | ||||||||
\(786\) | −0.335376 | −0.0119625 | ||||||||
\(787\) | −28.5173 | −1.01653 | −0.508266 | − | 0.861200i | \(-0.669713\pi\) | ||||
−0.508266 | + | 0.861200i | \(0.669713\pi\) | |||||||
\(788\) | −2.81200 | −0.100174 | ||||||||
\(789\) | 17.5383 | 0.624379 | ||||||||
\(790\) | 20.1288 | 0.716152 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.9189 | 0.601188 | ||||||||
\(793\) | 2.43245 | 0.0863787 | ||||||||
\(794\) | 1.37723 | 0.0488762 | ||||||||
\(795\) | −14.7366 | −0.522652 | ||||||||
\(796\) | 2.20691 | 0.0782217 | ||||||||
\(797\) | −17.9047 | −0.634216 | −0.317108 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317108 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.7701 | −1.54847 | ||||||||
\(800\) | −12.1318 | −0.428924 | ||||||||
\(801\) | −15.2558 | −0.539038 | ||||||||
\(802\) | −26.3798 | −0.931502 | ||||||||
\(803\) | 36.8171 | 1.29925 | ||||||||
\(804\) | 4.00785 | 0.141346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.01570 | 0.247118 | ||||||||
\(807\) | 11.3096 | 0.398118 | ||||||||
\(808\) | −16.3663 | −0.575765 | ||||||||
\(809\) | −20.1911 | −0.709882 | −0.354941 | − | 0.934889i | \(-0.615499\pi\) | ||||
−0.354941 | + | 0.934889i | \(0.615499\pi\) | |||||||
\(810\) | −3.12861 | −0.109928 | ||||||||
\(811\) | 36.6521 | 1.28703 | 0.643515 | − | 0.765433i | \(-0.277475\pi\) | ||||
0.643515 | + | 0.765433i | \(0.277475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.5027 | 0.368347 | ||||||||
\(814\) | 60.4470 | 2.11867 | ||||||||
\(815\) | 63.1485 | 2.21199 | ||||||||
\(816\) | −10.5775 | −0.370287 | ||||||||
\(817\) | −7.97011 | −0.278839 | ||||||||
\(818\) | 42.7748 | 1.49559 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0923 | −0.841338 | ||||||||
\(821\) | 53.4565 | 1.86565 | 0.932823 | − | 0.360335i | \(-0.117337\pi\) | ||||
0.932823 | + | 0.360335i | \(0.117337\pi\) | |||||||
\(822\) | 0.812510 | 0.0283395 | ||||||||
\(823\) | 13.3793 | 0.466374 | 0.233187 | − | 0.972432i | \(-0.425085\pi\) | ||||
0.233187 | + | 0.972432i | \(0.425085\pi\) | |||||||
\(824\) | −4.74338 | −0.165244 | ||||||||
\(825\) | 16.3662 | 0.569798 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2237 | 0.633700 | 0.316850 | − | 0.948476i | \(-0.397375\pi\) | ||||
0.316850 | + | 0.948476i | \(0.397375\pi\) | |||||||
\(828\) | 3.78378 | 0.131495 | ||||||||
\(829\) | −9.85200 | −0.342174 | −0.171087 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171087 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(830\) | 50.2308 | 1.74354 | ||||||||
\(831\) | −23.9574 | −0.831073 | ||||||||
\(832\) | 8.24361 | 0.285796 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.66052 | −0.265262 | ||||||||
\(835\) | −8.93750 | −0.309295 | ||||||||
\(836\) | −12.1610 | −0.420598 | ||||||||
\(837\) | −6.33122 | −0.218839 | ||||||||
\(838\) | 30.1913 | 1.04294 | ||||||||
\(839\) | 1.06581 | 0.0367957 | 0.0183978 | − | 0.999831i | \(-0.494143\pi\) | ||||
0.0183978 | + | 0.999831i | \(0.494143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3465 | 0.977465 | ||||||||
\(842\) | −14.0616 | −0.484594 | ||||||||
\(843\) | 3.06163 | 0.105448 | ||||||||
\(844\) | −7.17436 | −0.246952 | ||||||||
\(845\) | 2.82337 | 0.0971270 | ||||||||
\(846\) | 8.52748 | 0.293181 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.70669 | 0.333329 | ||||||||
\(849\) | −22.8143 | −0.782984 | ||||||||
\(850\) | −18.7279 | −0.642362 | ||||||||
\(851\) | 48.5364 | 1.66381 | ||||||||
\(852\) | −8.94623 | −0.306493 | ||||||||
\(853\) | −34.9286 | −1.19593 | −0.597966 | − | 0.801521i | \(-0.704024\pi\) | ||||
−0.597966 | + | 0.801521i | \(0.704024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.07400 | 0.276125 | ||||||||
\(856\) | 45.3890 | 1.55136 | ||||||||
\(857\) | 19.6334 | 0.670665 | 0.335332 | − | 0.942100i | \(-0.391151\pi\) | ||||
0.335332 | + | 0.942100i | \(0.391151\pi\) | |||||||
\(858\) | −6.10331 | −0.208364 | ||||||||
\(859\) | −2.00922 | −0.0685538 | −0.0342769 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342769 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(860\) | 6.07546 | 0.207172 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.3732 | 1.17076 | ||||||||
\(863\) | −39.3913 | −1.34089 | −0.670447 | − | 0.741958i | \(-0.733898\pi\) | ||||
−0.670447 | + | 0.741958i | \(0.733898\pi\) | |||||||
\(864\) | −4.08281 | −0.138900 | ||||||||
\(865\) | −33.9962 | −1.15591 | ||||||||
\(866\) | 18.1887 | 0.618076 | ||||||||
\(867\) | 15.3504 | 0.521328 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.4364 | −1.20210 | ||||||||
\(870\) | −23.6922 | −0.803240 | ||||||||
\(871\) | −5.19092 | −0.175888 | ||||||||
\(872\) | 26.9878 | 0.913921 | ||||||||
\(873\) | 6.13113 | 0.207507 | ||||||||
\(874\) | 15.5297 | 0.525299 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.16101 | −0.174374 | ||||||||
\(877\) | −7.57140 | −0.255668 | −0.127834 | − | 0.991796i | \(-0.540802\pi\) | ||||
−0.127834 | + | 0.991796i | \(0.540802\pi\) | |||||||
\(878\) | 13.7579 | 0.464306 | ||||||||
\(879\) | 11.9623 | 0.403479 | ||||||||
\(880\) | −28.9197 | −0.974882 | ||||||||
\(881\) | −30.7644 | −1.03648 | −0.518240 | − | 0.855235i | \(-0.673413\pi\) | ||||
−0.518240 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8365 | 1.67713 | 0.838566 | − | 0.544799i | \(-0.183394\pi\) | ||||
0.838566 | + | 0.544799i | \(0.183394\pi\) | |||||||
\(884\) | −4.39145 | −0.147700 | ||||||||
\(885\) | −9.58308 | −0.322132 | ||||||||
\(886\) | −18.1998 | −0.611435 | ||||||||
\(887\) | −25.6416 | −0.860961 | −0.430480 | − | 0.902600i | \(-0.641656\pi\) | ||||
−0.430480 | + | 0.902600i | \(0.641656\pi\) | |||||||
\(888\) | −30.4228 | −1.02092 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 47.7295 | 1.59990 | ||||||||
\(891\) | 5.50785 | 0.184520 | ||||||||
\(892\) | 14.4131 | 0.482586 | ||||||||
\(893\) | −22.0068 | −0.736431 | ||||||||
\(894\) | 23.9361 | 0.800543 | ||||||||
\(895\) | 17.6752 | 0.590816 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.90070 | −0.163630 | ||||||||
\(898\) | 16.5852 | 0.553455 | ||||||||
\(899\) | −47.9447 | −1.59905 | ||||||||
\(900\) | −2.29421 | −0.0764737 | ||||||||
\(901\) | −29.6871 | −0.989022 | ||||||||
\(902\) | −67.4540 | −2.24597 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.7992 | 0.359176 | ||||||||
\(905\) | −11.9429 | −0.396994 | ||||||||
\(906\) | −6.45450 | −0.214436 | ||||||||
\(907\) | −10.5158 | −0.349171 | −0.174586 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174586 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(908\) | −18.7935 | −0.623684 | ||||||||
\(909\) | −5.32796 | −0.176717 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.6462 | 1.37980 | 0.689900 | − | 0.723905i | \(-0.257655\pi\) | ||||
0.689900 | + | 0.723905i | \(0.257655\pi\) | |||||||
\(912\) | −5.31819 | −0.176103 | ||||||||
\(913\) | −88.4302 | −2.92661 | ||||||||
\(914\) | −21.6373 | −0.715699 | ||||||||
\(915\) | 6.86770 | 0.227039 | ||||||||
\(916\) | 11.2466 | 0.371597 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.30266 | −0.208019 | ||||||||
\(919\) | 30.1328 | 0.993988 | 0.496994 | − | 0.867754i | \(-0.334437\pi\) | ||||
0.496994 | + | 0.867754i | \(0.334437\pi\) | |||||||
\(920\) | −42.5027 | −1.40127 | ||||||||
\(921\) | −3.56994 | −0.117633 | ||||||||
\(922\) | −11.9287 | −0.392851 | ||||||||
\(923\) | 11.5870 | 0.381392 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.4290 | −0.967619 | ||||||||
\(926\) | 15.8545 | 0.521012 | ||||||||
\(927\) | −1.54418 | −0.0507175 | ||||||||
\(928\) | −30.9181 | −1.01494 | ||||||||
\(929\) | −14.5483 | −0.477313 | −0.238657 | − | 0.971104i | \(-0.576707\pi\) | ||||
−0.238657 | + | 0.971104i | \(0.576707\pi\) | |||||||
\(930\) | 19.8079 | 0.649528 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.51295 | −0.180583 | ||||||||
\(933\) | −31.1741 | −1.02059 | ||||||||
\(934\) | 32.1874 | 1.05320 | ||||||||
\(935\) | 88.4485 | 2.89258 | ||||||||
\(936\) | 3.07178 | 0.100404 | ||||||||
\(937\) | 22.3753 | 0.730970 | 0.365485 | − | 0.930817i | \(-0.380903\pi\) | ||||
0.365485 | + | 0.930817i | \(0.380903\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.6690 | −0.935577 | ||||||||
\(940\) | 16.7754 | 0.547153 | ||||||||
\(941\) | −7.76092 | −0.252999 | −0.126499 | − | 0.991967i | \(-0.540374\pi\) | ||||
−0.126499 | + | 0.991967i | \(0.540374\pi\) | |||||||
\(942\) | −6.17671 | −0.201248 | ||||||||
\(943\) | −54.1627 | −1.76378 | ||||||||
\(944\) | 6.31218 | 0.205444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.0102 | 0.553049 | ||||||||
\(947\) | −53.1392 | −1.72679 | −0.863397 | − | 0.504526i | \(-0.831667\pi\) | ||||
−0.863397 | + | 0.504526i | \(0.831667\pi\) | |||||||
\(948\) | 4.96746 | 0.161336 | ||||||||
\(949\) | 6.68448 | 0.216987 | ||||||||
\(950\) | −9.41607 | −0.305498 | ||||||||
\(951\) | 0.203271 | 0.00659152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.79639 | 0.284943 | 0.142471 | − | 0.989799i | \(-0.454495\pi\) | ||||
0.142471 | + | 0.989799i | \(0.454495\pi\) | |||||||
\(954\) | 5.78378 | 0.187257 | ||||||||
\(955\) | 46.2976 | 1.49816 | ||||||||
\(956\) | 6.51763 | 0.210795 | ||||||||
\(957\) | 41.7095 | 1.34828 | ||||||||
\(958\) | 7.97927 | 0.257799 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 23.2748 | 0.751190 | ||||||||
\(961\) | 9.08438 | 0.293045 | ||||||||
\(962\) | 10.9747 | 0.353839 | ||||||||
\(963\) | 14.7761 | 0.476153 | ||||||||
\(964\) | −13.1767 | −0.424394 | ||||||||
\(965\) | 27.9626 | 0.900148 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.01839 | 0.0970648 | 0.0485324 | − | 0.998822i | \(-0.484546\pi\) | ||||
0.0485324 | + | 0.998822i | \(0.484546\pi\) | |||||||
\(968\) | 59.3973 | 1.90910 | ||||||||
\(969\) | 16.2652 | 0.522515 | ||||||||
\(970\) | −19.1819 | −0.615895 | ||||||||
\(971\) | 50.7702 | 1.62929 | 0.814647 | − | 0.579957i | \(-0.196931\pi\) | ||||
0.814647 | + | 0.579957i | \(0.196931\pi\) | |||||||
\(972\) | −0.772089 | −0.0247648 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.90615 | −0.221287 | ||||||||
\(975\) | 2.97143 | 0.0951620 | ||||||||
\(976\) | −4.52362 | −0.144798 | ||||||||
\(977\) | 35.2449 | 1.12758 | 0.563792 | − | 0.825917i | \(-0.309342\pi\) | ||||
0.563792 | + | 0.825917i | \(0.309342\pi\) | |||||||
\(978\) | −24.7844 | −0.792517 | ||||||||
\(979\) | −84.0268 | −2.68551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.78570 | 0.280506 | ||||||||
\(982\) | −12.7385 | −0.406502 | ||||||||
\(983\) | 57.5204 | 1.83461 | 0.917307 | − | 0.398180i | \(-0.130358\pi\) | ||||
0.917307 | + | 0.398180i | \(0.130358\pi\) | |||||||
\(984\) | 33.9494 | 1.08227 | ||||||||
\(985\) | 10.2829 | 0.327641 | ||||||||
\(986\) | −47.7284 | −1.51998 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.20794 | −0.0702440 | ||||||||
\(989\) | 13.6585 | 0.434314 | ||||||||
\(990\) | −17.2319 | −0.547666 | ||||||||
\(991\) | 35.4196 | 1.12514 | 0.562570 | − | 0.826749i | \(-0.309813\pi\) | ||||
0.562570 | + | 0.826749i | \(0.309813\pi\) | |||||||
\(992\) | 25.8492 | 0.820713 | ||||||||
\(993\) | −7.35062 | −0.233265 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.07020 | −0.255843 | ||||||||
\(996\) | 12.3961 | 0.392786 | ||||||||
\(997\) | −30.2365 | −0.957601 | −0.478800 | − | 0.877924i | \(-0.658928\pi\) | ||||
−0.478800 | + | 0.877924i | \(0.658928\pi\) | |||||||
\(998\) | 12.5778 | 0.398142 | ||||||||
\(999\) | −9.90397 | −0.313348 |
(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 | 1911.2.a.w.1.2 | yes | 5 | |
3.2 | odd | 2 | 5733.2.a.bn.1.4 | 5 | |||
7.6 | odd | 2 | 1911.2.a.v.1.2 | ✓ | 5 | ||
21.20 | even | 2 | 5733.2.a.bo.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1911.2.a.v.1.2 | ✓ | 5 | 7.6 | odd | 2 | ||
1911.2.a.w.1.2 | yes | 5 | 1.1 | even | 1 | trivial | |
5733.2.a.bn.1.4 | 5 | 3.2 | odd | 2 | |||
5733.2.a.bo.1.4 | 5 | 21.20 | even | 2 |