Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.32624\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32624 | 0.937791 | 0.468896 | − | 0.883254i | \(-0.344652\pi\) | ||||
0.468896 | + | 0.883254i | \(0.344652\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.241096 | −0.120548 | ||||||||
\(5\) | 0.903630 | 0.404116 | 0.202058 | − | 0.979374i | \(-0.435237\pi\) | ||||
0.202058 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(6\) | −1.32624 | −0.541434 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.97222 | −1.05084 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.19843 | 0.378976 | ||||||||
\(11\) | −0.215437 | −0.0649566 | −0.0324783 | − | 0.999472i | \(-0.510340\pi\) | ||||
−0.0324783 | + | 0.999472i | \(0.510340\pi\) | |||||||
\(12\) | 0.241096 | 0.0695983 | ||||||||
\(13\) | −4.39375 | −1.21861 | −0.609303 | − | 0.792937i | \(-0.708551\pi\) | ||||
−0.609303 | + | 0.792937i | \(0.708551\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.903630 | −0.233316 | ||||||||
\(16\) | −3.45968 | −0.864920 | ||||||||
\(17\) | −7.88448 | −1.91227 | −0.956133 | − | 0.292932i | \(-0.905369\pi\) | ||||
−0.956133 | + | 0.292932i | \(0.905369\pi\) | |||||||
\(18\) | 1.32624 | 0.312597 | ||||||||
\(19\) | 6.94919 | 1.59425 | 0.797126 | − | 0.603812i | \(-0.206352\pi\) | ||||
0.797126 | + | 0.603812i | \(0.206352\pi\) | |||||||
\(20\) | −0.217861 | −0.0487153 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.285720 | −0.0609157 | ||||||||
\(23\) | 2.86954 | 0.598341 | 0.299171 | − | 0.954200i | \(-0.403290\pi\) | ||||
0.299171 | + | 0.954200i | \(0.403290\pi\) | |||||||
\(24\) | 2.97222 | 0.606703 | ||||||||
\(25\) | −4.18345 | −0.836690 | ||||||||
\(26\) | −5.82715 | −1.14280 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.84470 | −0.899639 | −0.449819 | − | 0.893119i | \(-0.648512\pi\) | ||||
−0.449819 | + | 0.893119i | \(0.648512\pi\) | |||||||
\(30\) | −1.19843 | −0.218802 | ||||||||
\(31\) | 4.36016 | 0.783108 | 0.391554 | − | 0.920155i | \(-0.371938\pi\) | ||||
0.391554 | + | 0.920155i | \(0.371938\pi\) | |||||||
\(32\) | 1.35609 | 0.239725 | ||||||||
\(33\) | 0.215437 | 0.0375027 | ||||||||
\(34\) | −10.4567 | −1.79331 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.241096 | −0.0401826 | ||||||||
\(37\) | 5.19593 | 0.854206 | 0.427103 | − | 0.904203i | \(-0.359534\pi\) | ||||
0.427103 | + | 0.904203i | \(0.359534\pi\) | |||||||
\(38\) | 9.21627 | 1.49508 | ||||||||
\(39\) | 4.39375 | 0.703563 | ||||||||
\(40\) | −2.68579 | −0.424661 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4746 | 1.74985 | 0.874927 | − | 0.484256i | \(-0.160910\pi\) | ||||
0.874927 | + | 0.484256i | \(0.160910\pi\) | |||||||
\(44\) | 0.0519408 | 0.00783037 | ||||||||
\(45\) | 0.903630 | 0.134705 | ||||||||
\(46\) | 3.80570 | 0.561119 | ||||||||
\(47\) | 0.643892 | 0.0939213 | 0.0469607 | − | 0.998897i | \(-0.485046\pi\) | ||||
0.0469607 | + | 0.998897i | \(0.485046\pi\) | |||||||
\(48\) | 3.45968 | 0.499362 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.54825 | −0.784641 | ||||||||
\(51\) | 7.88448 | 1.10405 | ||||||||
\(52\) | 1.05931 | 0.146900 | ||||||||
\(53\) | −1.87995 | −0.258232 | −0.129116 | − | 0.991630i | \(-0.541214\pi\) | ||||
−0.129116 | + | 0.991630i | \(0.541214\pi\) | |||||||
\(54\) | −1.32624 | −0.180478 | ||||||||
\(55\) | −0.194675 | −0.0262500 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.94919 | −0.920442 | ||||||||
\(58\) | −6.42523 | −0.843673 | ||||||||
\(59\) | −9.92968 | −1.29273 | −0.646367 | − | 0.763026i | \(-0.723713\pi\) | ||||
−0.646367 | + | 0.763026i | \(0.723713\pi\) | |||||||
\(60\) | 0.217861 | 0.0281258 | ||||||||
\(61\) | −2.61168 | −0.334391 | −0.167195 | − | 0.985924i | \(-0.553471\pi\) | ||||
−0.167195 | + | 0.985924i | \(0.553471\pi\) | |||||||
\(62\) | 5.78261 | 0.734392 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.71786 | 1.08973 | ||||||||
\(65\) | −3.97032 | −0.492458 | ||||||||
\(66\) | 0.285720 | 0.0351697 | ||||||||
\(67\) | 13.5451 | 1.65480 | 0.827401 | − | 0.561611i | \(-0.189818\pi\) | ||||
0.827401 | + | 0.561611i | \(0.189818\pi\) | |||||||
\(68\) | 1.90091 | 0.230520 | ||||||||
\(69\) | −2.86954 | −0.345453 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.978400 | 0.116115 | 0.0580573 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580573 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(72\) | −2.97222 | −0.350280 | ||||||||
\(73\) | −9.48157 | −1.10973 | −0.554867 | − | 0.831939i | \(-0.687231\pi\) | ||||
−0.554867 | + | 0.831939i | \(0.687231\pi\) | |||||||
\(74\) | 6.89104 | 0.801067 | ||||||||
\(75\) | 4.18345 | 0.483063 | ||||||||
\(76\) | −1.67542 | −0.192184 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.82715 | 0.659795 | ||||||||
\(79\) | 10.6043 | 1.19307 | 0.596536 | − | 0.802586i | \(-0.296543\pi\) | ||||
0.596536 | + | 0.802586i | \(0.296543\pi\) | |||||||
\(80\) | −3.12627 | −0.349528 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.32624 | −0.146458 | ||||||||
\(83\) | 9.10249 | 0.999129 | 0.499564 | − | 0.866277i | \(-0.333493\pi\) | ||||
0.499564 | + | 0.866277i | \(0.333493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12465 | −0.772777 | ||||||||
\(86\) | 15.2180 | 1.64100 | ||||||||
\(87\) | 4.84470 | 0.519407 | ||||||||
\(88\) | 0.640326 | 0.0682590 | ||||||||
\(89\) | 6.38298 | 0.676595 | 0.338297 | − | 0.941039i | \(-0.390149\pi\) | ||||
0.338297 | + | 0.941039i | \(0.390149\pi\) | |||||||
\(90\) | 1.19843 | 0.126325 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.691834 | −0.0721287 | ||||||||
\(93\) | −4.36016 | −0.452128 | ||||||||
\(94\) | 0.853954 | 0.0880786 | ||||||||
\(95\) | 6.27950 | 0.644263 | ||||||||
\(96\) | −1.35609 | −0.138405 | ||||||||
\(97\) | 9.92473 | 1.00770 | 0.503852 | − | 0.863790i | \(-0.331916\pi\) | ||||
0.503852 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.215437 | −0.0216522 | ||||||||
\(100\) | 1.00861 | 0.100861 | ||||||||
\(101\) | 1.26362 | 0.125735 | 0.0628673 | − | 0.998022i | \(-0.479976\pi\) | ||||
0.0628673 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(102\) | 10.4567 | 1.03537 | ||||||||
\(103\) | −2.98031 | −0.293659 | −0.146829 | − | 0.989162i | \(-0.546907\pi\) | ||||
−0.146829 | + | 0.989162i | \(0.546907\pi\) | |||||||
\(104\) | 13.0592 | 1.28056 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.49327 | −0.242167 | ||||||||
\(107\) | 7.10706 | 0.687066 | 0.343533 | − | 0.939141i | \(-0.388376\pi\) | ||||
0.343533 | + | 0.939141i | \(0.388376\pi\) | |||||||
\(108\) | 0.241096 | 0.0231994 | ||||||||
\(109\) | 16.1938 | 1.55108 | 0.775540 | − | 0.631298i | \(-0.217478\pi\) | ||||
0.775540 | + | 0.631298i | \(0.217478\pi\) | |||||||
\(110\) | −0.258185 | −0.0246170 | ||||||||
\(111\) | −5.19593 | −0.493176 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.43547 | 0.511326 | 0.255663 | − | 0.966766i | \(-0.417706\pi\) | ||||
0.255663 | + | 0.966766i | \(0.417706\pi\) | |||||||
\(114\) | −9.21627 | −0.863183 | ||||||||
\(115\) | 2.59301 | 0.241799 | ||||||||
\(116\) | 1.16804 | 0.108449 | ||||||||
\(117\) | −4.39375 | −0.406202 | ||||||||
\(118\) | −13.1691 | −1.21232 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.68579 | 0.245178 | ||||||||
\(121\) | −10.9536 | −0.995781 | ||||||||
\(122\) | −3.46370 | −0.313589 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −1.05122 | −0.0944020 | ||||||||
\(125\) | −8.29845 | −0.742236 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.08737 | −0.717638 | −0.358819 | − | 0.933407i | \(-0.616821\pi\) | ||||
−0.358819 | + | 0.933407i | \(0.616821\pi\) | |||||||
\(128\) | 8.84977 | 0.782216 | ||||||||
\(129\) | −11.4746 | −1.01028 | ||||||||
\(130\) | −5.26559 | −0.461823 | ||||||||
\(131\) | 2.14995 | 0.187842 | 0.0939208 | − | 0.995580i | \(-0.470060\pi\) | ||||
0.0939208 | + | 0.995580i | \(0.470060\pi\) | |||||||
\(132\) | −0.0519408 | −0.00452087 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.9641 | 1.55186 | ||||||||
\(135\) | −0.903630 | −0.0777721 | ||||||||
\(136\) | 23.4344 | 2.00949 | ||||||||
\(137\) | 4.74993 | 0.405814 | 0.202907 | − | 0.979198i | \(-0.434961\pi\) | ||||
0.202907 | + | 0.979198i | \(0.434961\pi\) | |||||||
\(138\) | −3.80570 | −0.323962 | ||||||||
\(139\) | −4.62192 | −0.392026 | −0.196013 | − | 0.980601i | \(-0.562800\pi\) | ||||
−0.196013 | + | 0.980601i | \(0.562800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.643892 | −0.0542255 | ||||||||
\(142\) | 1.29759 | 0.108891 | ||||||||
\(143\) | 0.946574 | 0.0791565 | ||||||||
\(144\) | −3.45968 | −0.288307 | ||||||||
\(145\) | −4.37782 | −0.363558 | ||||||||
\(146\) | −12.5748 | −1.04070 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.25272 | −0.102973 | ||||||||
\(149\) | −16.9602 | −1.38944 | −0.694718 | − | 0.719282i | \(-0.744471\pi\) | ||||
−0.694718 | + | 0.719282i | \(0.744471\pi\) | |||||||
\(150\) | 5.54825 | 0.453013 | ||||||||
\(151\) | 17.0675 | 1.38894 | 0.694468 | − | 0.719523i | \(-0.255640\pi\) | ||||
0.694468 | + | 0.719523i | \(0.255640\pi\) | |||||||
\(152\) | −20.6545 | −1.67530 | ||||||||
\(153\) | −7.88448 | −0.637422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.93997 | 0.316466 | ||||||||
\(156\) | −1.05931 | −0.0848129 | ||||||||
\(157\) | 17.6287 | 1.40693 | 0.703463 | − | 0.710732i | \(-0.251636\pi\) | ||||
0.703463 | + | 0.710732i | \(0.251636\pi\) | |||||||
\(158\) | 14.0638 | 1.11885 | ||||||||
\(159\) | 1.87995 | 0.149090 | ||||||||
\(160\) | 1.22540 | 0.0968767 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.32624 | 0.104199 | ||||||||
\(163\) | 1.57864 | 0.123649 | 0.0618243 | − | 0.998087i | \(-0.480308\pi\) | ||||
0.0618243 | + | 0.998087i | \(0.480308\pi\) | |||||||
\(164\) | 0.241096 | 0.0188264 | ||||||||
\(165\) | 0.194675 | 0.0151554 | ||||||||
\(166\) | 12.0721 | 0.936974 | ||||||||
\(167\) | 2.38357 | 0.184446 | 0.0922230 | − | 0.995738i | \(-0.470603\pi\) | ||||
0.0922230 | + | 0.995738i | \(0.470603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.30501 | 0.485001 | ||||||||
\(170\) | −9.44898 | −0.724704 | ||||||||
\(171\) | 6.94919 | 0.531418 | ||||||||
\(172\) | −2.76646 | −0.210941 | ||||||||
\(173\) | −25.3677 | −1.92867 | −0.964335 | − | 0.264686i | \(-0.914732\pi\) | ||||
−0.964335 | + | 0.264686i | \(0.914732\pi\) | |||||||
\(174\) | 6.42523 | 0.487095 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.745342 | 0.0561823 | ||||||||
\(177\) | 9.92968 | 0.746361 | ||||||||
\(178\) | 8.46534 | 0.634504 | ||||||||
\(179\) | −7.55216 | −0.564475 | −0.282237 | − | 0.959345i | \(-0.591077\pi\) | ||||
−0.282237 | + | 0.959345i | \(0.591077\pi\) | |||||||
\(180\) | −0.217861 | −0.0162384 | ||||||||
\(181\) | −6.02737 | −0.448011 | −0.224005 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224005 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.61168 | 0.193061 | ||||||||
\(184\) | −8.52893 | −0.628761 | ||||||||
\(185\) | 4.69520 | 0.345198 | ||||||||
\(186\) | −5.78261 | −0.424001 | ||||||||
\(187\) | 1.69861 | 0.124214 | ||||||||
\(188\) | −0.155240 | −0.0113220 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.32810 | 0.604184 | ||||||||
\(191\) | 9.74507 | 0.705128 | 0.352564 | − | 0.935788i | \(-0.385310\pi\) | ||||
0.352564 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(192\) | −8.71786 | −0.629157 | ||||||||
\(193\) | 25.0321 | 1.80185 | 0.900923 | − | 0.433978i | \(-0.142891\pi\) | ||||
0.900923 | + | 0.433978i | \(0.142891\pi\) | |||||||
\(194\) | 13.1625 | 0.945016 | ||||||||
\(195\) | 3.97032 | 0.284321 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1663 | 1.36554 | 0.682772 | − | 0.730631i | \(-0.260774\pi\) | ||||
0.682772 | + | 0.730631i | \(0.260774\pi\) | |||||||
\(198\) | −0.285720 | −0.0203052 | ||||||||
\(199\) | 10.3001 | 0.730152 | 0.365076 | − | 0.930978i | \(-0.381043\pi\) | ||||
0.365076 | + | 0.930978i | \(0.381043\pi\) | |||||||
\(200\) | 12.4342 | 0.879228 | ||||||||
\(201\) | −13.5451 | −0.955400 | ||||||||
\(202\) | 1.67586 | 0.117913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.90091 | −0.133091 | ||||||||
\(205\) | −0.903630 | −0.0631123 | ||||||||
\(206\) | −3.95260 | −0.275390 | ||||||||
\(207\) | 2.86954 | 0.199447 | ||||||||
\(208\) | 15.2010 | 1.05400 | ||||||||
\(209\) | −1.49711 | −0.103557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1371 | −1.59282 | −0.796411 | − | 0.604756i | \(-0.793271\pi\) | ||||
−0.796411 | + | 0.604756i | \(0.793271\pi\) | |||||||
\(212\) | 0.453249 | 0.0311293 | ||||||||
\(213\) | −0.978400 | −0.0670388 | ||||||||
\(214\) | 9.42565 | 0.644324 | ||||||||
\(215\) | 10.3688 | 0.707143 | ||||||||
\(216\) | 2.97222 | 0.202234 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 21.4768 | 1.45459 | ||||||||
\(219\) | 9.48157 | 0.640705 | ||||||||
\(220\) | 0.0469353 | 0.00316438 | ||||||||
\(221\) | 34.6424 | 2.33030 | ||||||||
\(222\) | −6.89104 | −0.462496 | ||||||||
\(223\) | −18.4257 | −1.23388 | −0.616938 | − | 0.787012i | \(-0.711627\pi\) | ||||
−0.616938 | + | 0.787012i | \(0.711627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.18345 | −0.278897 | ||||||||
\(226\) | 7.20872 | 0.479517 | ||||||||
\(227\) | −4.13746 | −0.274613 | −0.137307 | − | 0.990529i | \(-0.543845\pi\) | ||||
−0.137307 | + | 0.990529i | \(0.543845\pi\) | |||||||
\(228\) | 1.67542 | 0.110957 | ||||||||
\(229\) | 8.10981 | 0.535912 | 0.267956 | − | 0.963431i | \(-0.413652\pi\) | ||||
0.267956 | + | 0.963431i | \(0.413652\pi\) | |||||||
\(230\) | 3.43894 | 0.226757 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.3995 | 0.945376 | ||||||||
\(233\) | 5.35817 | 0.351025 | 0.175513 | − | 0.984477i | \(-0.443842\pi\) | ||||
0.175513 | + | 0.984477i | \(0.443842\pi\) | |||||||
\(234\) | −5.82715 | −0.380933 | ||||||||
\(235\) | 0.581840 | 0.0379551 | ||||||||
\(236\) | 2.39400 | 0.155836 | ||||||||
\(237\) | −10.6043 | −0.688821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.6504 | 1.85324 | 0.926621 | − | 0.375996i | \(-0.122699\pi\) | ||||
0.926621 | + | 0.375996i | \(0.122699\pi\) | |||||||
\(240\) | 3.12627 | 0.201800 | ||||||||
\(241\) | −18.5866 | −1.19727 | −0.598636 | − | 0.801021i | \(-0.704290\pi\) | ||||
−0.598636 | + | 0.801021i | \(0.704290\pi\) | |||||||
\(242\) | −14.5271 | −0.933834 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.629664 | 0.0403101 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.32624 | 0.0845578 | ||||||||
\(247\) | −30.5330 | −1.94277 | ||||||||
\(248\) | −12.9594 | −0.822921 | ||||||||
\(249\) | −9.10249 | −0.576847 | ||||||||
\(250\) | −11.0057 | −0.696062 | ||||||||
\(251\) | 5.97228 | 0.376967 | 0.188484 | − | 0.982076i | \(-0.439643\pi\) | ||||
0.188484 | + | 0.982076i | \(0.439643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.618205 | −0.0388662 | ||||||||
\(254\) | −10.7258 | −0.672995 | ||||||||
\(255\) | 7.12465 | 0.446163 | ||||||||
\(256\) | −5.69883 | −0.356177 | ||||||||
\(257\) | 10.2788 | 0.641175 | 0.320587 | − | 0.947219i | \(-0.396120\pi\) | ||||
0.320587 | + | 0.947219i | \(0.396120\pi\) | |||||||
\(258\) | −15.2180 | −0.947430 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.957227 | 0.0593647 | ||||||||
\(261\) | −4.84470 | −0.299880 | ||||||||
\(262\) | 2.85134 | 0.176156 | ||||||||
\(263\) | 26.7187 | 1.64755 | 0.823773 | − | 0.566920i | \(-0.191865\pi\) | ||||
0.823773 | + | 0.566920i | \(0.191865\pi\) | |||||||
\(264\) | −0.640326 | −0.0394093 | ||||||||
\(265\) | −1.69878 | −0.104355 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.38298 | −0.390632 | ||||||||
\(268\) | −3.26567 | −0.199483 | ||||||||
\(269\) | −30.4667 | −1.85759 | −0.928794 | − | 0.370597i | \(-0.879153\pi\) | ||||
−0.928794 | + | 0.370597i | \(0.879153\pi\) | |||||||
\(270\) | −1.19843 | −0.0729340 | ||||||||
\(271\) | 10.8647 | 0.659985 | 0.329992 | − | 0.943984i | \(-0.392954\pi\) | ||||
0.329992 | + | 0.943984i | \(0.392954\pi\) | |||||||
\(272\) | 27.2778 | 1.65396 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.29953 | 0.380568 | ||||||||
\(275\) | 0.901269 | 0.0543485 | ||||||||
\(276\) | 0.691834 | 0.0416435 | ||||||||
\(277\) | 3.89451 | 0.233999 | 0.116999 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.116999 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(278\) | −6.12976 | −0.367639 | ||||||||
\(279\) | 4.36016 | 0.261036 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.57428 | 0.571154 | 0.285577 | − | 0.958356i | \(-0.407815\pi\) | ||||
0.285577 | + | 0.958356i | \(0.407815\pi\) | |||||||
\(282\) | −0.853954 | −0.0508522 | ||||||||
\(283\) | −11.9864 | −0.712520 | −0.356260 | − | 0.934387i | \(-0.615948\pi\) | ||||
−0.356260 | + | 0.934387i | \(0.615948\pi\) | |||||||
\(284\) | −0.235888 | −0.0139974 | ||||||||
\(285\) | −6.27950 | −0.371965 | ||||||||
\(286\) | 1.25538 | 0.0742322 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.35609 | 0.0799084 | ||||||||
\(289\) | 45.1650 | 2.65676 | ||||||||
\(290\) | −5.80603 | −0.340942 | ||||||||
\(291\) | −9.92473 | −0.581798 | ||||||||
\(292\) | 2.28596 | 0.133776 | ||||||||
\(293\) | 6.71477 | 0.392281 | 0.196140 | − | 0.980576i | \(-0.437159\pi\) | ||||
0.196140 | + | 0.980576i | \(0.437159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.97276 | −0.522414 | ||||||||
\(296\) | −15.4435 | −0.897634 | ||||||||
\(297\) | 0.215437 | 0.0125009 | ||||||||
\(298\) | −22.4933 | −1.30300 | ||||||||
\(299\) | −12.6081 | −0.729142 | ||||||||
\(300\) | −1.00861 | −0.0582322 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 22.6356 | 1.30253 | ||||||||
\(303\) | −1.26362 | −0.0725929 | ||||||||
\(304\) | −24.0420 | −1.37890 | ||||||||
\(305\) | −2.35999 | −0.135133 | ||||||||
\(306\) | −10.4567 | −0.597769 | ||||||||
\(307\) | 29.8411 | 1.70312 | 0.851562 | − | 0.524255i | \(-0.175656\pi\) | ||||
0.851562 | + | 0.524255i | \(0.175656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.98031 | 0.169544 | ||||||||
\(310\) | 5.22534 | 0.296779 | ||||||||
\(311\) | 13.2611 | 0.751970 | 0.375985 | − | 0.926626i | \(-0.377304\pi\) | ||||
0.375985 | + | 0.926626i | \(0.377304\pi\) | |||||||
\(312\) | −13.0592 | −0.739332 | ||||||||
\(313\) | 26.2366 | 1.48298 | 0.741489 | − | 0.670965i | \(-0.234120\pi\) | ||||
0.741489 | + | 0.670965i | \(0.234120\pi\) | |||||||
\(314\) | 23.3799 | 1.31940 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.55664 | −0.143822 | ||||||||
\(317\) | −6.00428 | −0.337234 | −0.168617 | − | 0.985682i | \(-0.553930\pi\) | ||||
−0.168617 | + | 0.985682i | \(0.553930\pi\) | |||||||
\(318\) | 2.49327 | 0.139815 | ||||||||
\(319\) | 1.04373 | 0.0584375 | ||||||||
\(320\) | 7.87772 | 0.440378 | ||||||||
\(321\) | −7.10706 | −0.396678 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −54.7907 | −3.04864 | ||||||||
\(324\) | −0.241096 | −0.0133942 | ||||||||
\(325\) | 18.3810 | 1.01960 | ||||||||
\(326\) | 2.09365 | 0.115957 | ||||||||
\(327\) | −16.1938 | −0.895517 | ||||||||
\(328\) | 2.97222 | 0.164114 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.258185 | 0.0142126 | ||||||||
\(331\) | −20.4201 | −1.12239 | −0.561194 | − | 0.827684i | \(-0.689658\pi\) | ||||
−0.561194 | + | 0.827684i | \(0.689658\pi\) | |||||||
\(332\) | −2.19457 | −0.120443 | ||||||||
\(333\) | 5.19593 | 0.284735 | ||||||||
\(334\) | 3.16117 | 0.172972 | ||||||||
\(335\) | 12.2398 | 0.668732 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0542 | −1.09242 | −0.546211 | − | 0.837647i | \(-0.683930\pi\) | ||||
−0.546211 | + | 0.837647i | \(0.683930\pi\) | |||||||
\(338\) | 8.36194 | 0.454829 | ||||||||
\(339\) | −5.43547 | −0.295214 | ||||||||
\(340\) | 1.71772 | 0.0931566 | ||||||||
\(341\) | −0.939338 | −0.0508680 | ||||||||
\(342\) | 9.21627 | 0.498359 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −34.1049 | −1.83882 | ||||||||
\(345\) | −2.59301 | −0.139603 | ||||||||
\(346\) | −33.6436 | −1.80869 | ||||||||
\(347\) | 32.7373 | 1.75743 | 0.878715 | − | 0.477347i | \(-0.158402\pi\) | ||||
0.878715 | + | 0.477347i | \(0.158402\pi\) | |||||||
\(348\) | −1.16804 | −0.0626133 | ||||||||
\(349\) | 0.0574302 | 0.00307417 | 0.00153708 | − | 0.999999i | \(-0.499511\pi\) | ||||
0.00153708 | + | 0.999999i | \(0.499511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.39375 | 0.234521 | ||||||||
\(352\) | −0.292151 | −0.0155717 | ||||||||
\(353\) | 0.486551 | 0.0258965 | 0.0129483 | − | 0.999916i | \(-0.495878\pi\) | ||||
0.0129483 | + | 0.999916i | \(0.495878\pi\) | |||||||
\(354\) | 13.1691 | 0.699931 | ||||||||
\(355\) | 0.884111 | 0.0469238 | ||||||||
\(356\) | −1.53891 | −0.0815620 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0160 | −0.529360 | ||||||||
\(359\) | −11.9174 | −0.628978 | −0.314489 | − | 0.949261i | \(-0.601833\pi\) | ||||
−0.314489 | + | 0.949261i | \(0.601833\pi\) | |||||||
\(360\) | −2.68579 | −0.141554 | ||||||||
\(361\) | 29.2912 | 1.54164 | ||||||||
\(362\) | −7.99372 | −0.420141 | ||||||||
\(363\) | 10.9536 | 0.574914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.56783 | −0.448461 | ||||||||
\(366\) | 3.46370 | 0.181051 | ||||||||
\(367\) | 28.8901 | 1.50805 | 0.754026 | − | 0.656845i | \(-0.228109\pi\) | ||||
0.754026 | + | 0.656845i | \(0.228109\pi\) | |||||||
\(368\) | −9.92771 | −0.517518 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 6.22695 | 0.323724 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.05122 | 0.0545030 | ||||||||
\(373\) | 5.71033 | 0.295670 | 0.147835 | − | 0.989012i | \(-0.452770\pi\) | ||||
0.147835 | + | 0.989012i | \(0.452770\pi\) | |||||||
\(374\) | 2.25275 | 0.116487 | ||||||||
\(375\) | 8.29845 | 0.428530 | ||||||||
\(376\) | −1.91379 | −0.0986963 | ||||||||
\(377\) | 21.2864 | 1.09631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1130 | 0.776302 | 0.388151 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388151 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(380\) | −1.51396 | −0.0776644 | ||||||||
\(381\) | 8.08737 | 0.414329 | ||||||||
\(382\) | 12.9243 | 0.661263 | ||||||||
\(383\) | 35.7518 | 1.82683 | 0.913416 | − | 0.407027i | \(-0.133435\pi\) | ||||
0.913416 | + | 0.407027i | \(0.133435\pi\) | |||||||
\(384\) | −8.84977 | −0.451613 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.1984 | 1.68976 | ||||||||
\(387\) | 11.4746 | 0.583284 | ||||||||
\(388\) | −2.39281 | −0.121476 | ||||||||
\(389\) | −32.5460 | −1.65015 | −0.825074 | − | 0.565025i | \(-0.808867\pi\) | ||||
−0.825074 | + | 0.565025i | \(0.808867\pi\) | |||||||
\(390\) | 5.26559 | 0.266633 | ||||||||
\(391\) | −22.6249 | −1.14419 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.14995 | −0.108450 | ||||||||
\(394\) | 25.4191 | 1.28060 | ||||||||
\(395\) | 9.58233 | 0.482140 | ||||||||
\(396\) | 0.0519408 | 0.00261012 | ||||||||
\(397\) | −26.1714 | −1.31351 | −0.656753 | − | 0.754106i | \(-0.728071\pi\) | ||||
−0.656753 | + | 0.754106i | \(0.728071\pi\) | |||||||
\(398\) | 13.6603 | 0.684730 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.4734 | 0.723671 | ||||||||
\(401\) | 24.2772 | 1.21234 | 0.606172 | − | 0.795333i | \(-0.292704\pi\) | ||||
0.606172 | + | 0.795333i | \(0.292704\pi\) | |||||||
\(402\) | −17.9641 | −0.895966 | ||||||||
\(403\) | −19.1574 | −0.954300 | ||||||||
\(404\) | −0.304653 | −0.0151570 | ||||||||
\(405\) | 0.903630 | 0.0449017 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.11939 | −0.0554863 | ||||||||
\(408\) | −23.4344 | −1.16018 | ||||||||
\(409\) | 2.40378 | 0.118859 | 0.0594296 | − | 0.998232i | \(-0.481072\pi\) | ||||
0.0594296 | + | 0.998232i | \(0.481072\pi\) | |||||||
\(410\) | −1.19843 | −0.0591861 | ||||||||
\(411\) | −4.74993 | −0.234297 | ||||||||
\(412\) | 0.718540 | 0.0353999 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.80570 | 0.187040 | ||||||||
\(415\) | 8.22529 | 0.403764 | ||||||||
\(416\) | −5.95831 | −0.292130 | ||||||||
\(417\) | 4.62192 | 0.226336 | ||||||||
\(418\) | −1.98552 | −0.0971150 | ||||||||
\(419\) | 13.1533 | 0.642579 | 0.321289 | − | 0.946981i | \(-0.395884\pi\) | ||||
0.321289 | + | 0.946981i | \(0.395884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7974 | 1.50097 | 0.750486 | − | 0.660886i | \(-0.229819\pi\) | ||||
0.750486 | + | 0.660886i | \(0.229819\pi\) | |||||||
\(422\) | −30.6852 | −1.49373 | ||||||||
\(423\) | 0.643892 | 0.0313071 | ||||||||
\(424\) | 5.58765 | 0.271360 | ||||||||
\(425\) | 32.9843 | 1.59998 | ||||||||
\(426\) | −1.29759 | −0.0628684 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.71348 | −0.0828242 | ||||||||
\(429\) | −0.946574 | −0.0457010 | ||||||||
\(430\) | 13.7514 | 0.663153 | ||||||||
\(431\) | 9.41915 | 0.453705 | 0.226852 | − | 0.973929i | \(-0.427157\pi\) | ||||
0.226852 | + | 0.973929i | \(0.427157\pi\) | |||||||
\(432\) | 3.45968 | 0.166454 | ||||||||
\(433\) | −0.269336 | −0.0129434 | −0.00647172 | − | 0.999979i | \(-0.502060\pi\) | ||||
−0.00647172 | + | 0.999979i | \(0.502060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.37782 | 0.209900 | ||||||||
\(436\) | −3.90424 | −0.186979 | ||||||||
\(437\) | 19.9410 | 0.953907 | ||||||||
\(438\) | 12.5748 | 0.600848 | ||||||||
\(439\) | 29.4106 | 1.40369 | 0.701845 | − | 0.712330i | \(-0.252360\pi\) | ||||
0.701845 | + | 0.712330i | \(0.252360\pi\) | |||||||
\(440\) | 0.578618 | 0.0275845 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.9440 | 2.18533 | ||||||||
\(443\) | −16.2242 | −0.770833 | −0.385417 | − | 0.922743i | \(-0.625942\pi\) | ||||
−0.385417 | + | 0.922743i | \(0.625942\pi\) | |||||||
\(444\) | 1.25272 | 0.0594513 | ||||||||
\(445\) | 5.76785 | 0.273422 | ||||||||
\(446\) | −24.4368 | −1.15712 | ||||||||
\(447\) | 16.9602 | 0.802191 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2100 | 0.529031 | 0.264516 | − | 0.964381i | \(-0.414788\pi\) | ||||
0.264516 | + | 0.964381i | \(0.414788\pi\) | |||||||
\(450\) | −5.54825 | −0.261547 | ||||||||
\(451\) | 0.215437 | 0.0101445 | ||||||||
\(452\) | −1.31047 | −0.0616392 | ||||||||
\(453\) | −17.0675 | −0.801903 | ||||||||
\(454\) | −5.48726 | −0.257530 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.6545 | 0.967237 | ||||||||
\(457\) | −33.0572 | −1.54635 | −0.773174 | − | 0.634193i | \(-0.781332\pi\) | ||||
−0.773174 | + | 0.634193i | \(0.781332\pi\) | |||||||
\(458\) | 10.7555 | 0.502573 | ||||||||
\(459\) | 7.88448 | 0.368016 | ||||||||
\(460\) | −0.625162 | −0.0291484 | ||||||||
\(461\) | 3.50480 | 0.163235 | 0.0816174 | − | 0.996664i | \(-0.473991\pi\) | ||||
0.0816174 | + | 0.996664i | \(0.473991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2762 | −0.849368 | −0.424684 | − | 0.905342i | \(-0.639615\pi\) | ||||
−0.424684 | + | 0.905342i | \(0.639615\pi\) | |||||||
\(464\) | 16.7611 | 0.778116 | ||||||||
\(465\) | −3.93997 | −0.182712 | ||||||||
\(466\) | 7.10620 | 0.329189 | ||||||||
\(467\) | 41.1735 | 1.90528 | 0.952642 | − | 0.304093i | \(-0.0983534\pi\) | ||||
0.952642 | + | 0.304093i | \(0.0983534\pi\) | |||||||
\(468\) | 1.05931 | 0.0489668 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.771658 | 0.0355939 | ||||||||
\(471\) | −17.6287 | −0.812289 | ||||||||
\(472\) | 29.5132 | 1.35846 | ||||||||
\(473\) | −2.47204 | −0.113664 | ||||||||
\(474\) | −14.0638 | −0.645970 | ||||||||
\(475\) | −29.0716 | −1.33390 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.87995 | −0.0860772 | ||||||||
\(478\) | 37.9973 | 1.73795 | ||||||||
\(479\) | −39.0025 | −1.78207 | −0.891036 | − | 0.453933i | \(-0.850021\pi\) | ||||
−0.891036 | + | 0.453933i | \(0.850021\pi\) | |||||||
\(480\) | −1.22540 | −0.0559318 | ||||||||
\(481\) | −22.8296 | −1.04094 | ||||||||
\(482\) | −24.6503 | −1.12279 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.64086 | 0.120039 | ||||||||
\(485\) | 8.96829 | 0.407229 | ||||||||
\(486\) | −1.32624 | −0.0601593 | ||||||||
\(487\) | −13.4915 | −0.611356 | −0.305678 | − | 0.952135i | \(-0.598883\pi\) | ||||
−0.305678 | + | 0.952135i | \(0.598883\pi\) | |||||||
\(488\) | 7.76249 | 0.351391 | ||||||||
\(489\) | −1.57864 | −0.0713886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.1720 | −1.18113 | −0.590563 | − | 0.806992i | \(-0.701094\pi\) | ||||
−0.590563 | + | 0.806992i | \(0.701094\pi\) | |||||||
\(492\) | −0.241096 | −0.0108694 | ||||||||
\(493\) | 38.1980 | 1.72035 | ||||||||
\(494\) | −40.4939 | −1.82191 | ||||||||
\(495\) | −0.194675 | −0.00874999 | ||||||||
\(496\) | −15.0848 | −0.677326 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.0721 | −0.540962 | ||||||||
\(499\) | −28.9355 | −1.29533 | −0.647666 | − | 0.761924i | \(-0.724255\pi\) | ||||
−0.647666 | + | 0.761924i | \(0.724255\pi\) | |||||||
\(500\) | 2.00072 | 0.0894749 | ||||||||
\(501\) | −2.38357 | −0.106490 | ||||||||
\(502\) | 7.92066 | 0.353516 | ||||||||
\(503\) | −4.58143 | −0.204276 | −0.102138 | − | 0.994770i | \(-0.532568\pi\) | ||||
−0.102138 | + | 0.994770i | \(0.532568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14184 | 0.0508114 | ||||||||
\(506\) | −0.819886 | −0.0364484 | ||||||||
\(507\) | −6.30501 | −0.280015 | ||||||||
\(508\) | 1.94983 | 0.0865097 | ||||||||
\(509\) | 27.1220 | 1.20216 | 0.601080 | − | 0.799189i | \(-0.294737\pi\) | ||||
0.601080 | + | 0.799189i | \(0.294737\pi\) | |||||||
\(510\) | 9.44898 | 0.418408 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.2575 | −1.11624 | ||||||||
\(513\) | −6.94919 | −0.306814 | ||||||||
\(514\) | 13.6321 | 0.601288 | ||||||||
\(515\) | −2.69310 | −0.118672 | ||||||||
\(516\) | 2.76646 | 0.121787 | ||||||||
\(517\) | −0.138718 | −0.00610081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.3677 | 1.11352 | ||||||||
\(520\) | 11.8007 | 0.517494 | ||||||||
\(521\) | −23.2148 | −1.01706 | −0.508529 | − | 0.861045i | \(-0.669810\pi\) | ||||
−0.508529 | + | 0.861045i | \(0.669810\pi\) | |||||||
\(522\) | −6.42523 | −0.281224 | ||||||||
\(523\) | 24.2559 | 1.06063 | 0.530317 | − | 0.847799i | \(-0.322073\pi\) | ||||
0.530317 | + | 0.847799i | \(0.322073\pi\) | |||||||
\(524\) | −0.518342 | −0.0226439 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.4353 | 1.54505 | ||||||||
\(527\) | −34.3776 | −1.49751 | ||||||||
\(528\) | −0.745342 | −0.0324368 | ||||||||
\(529\) | −14.7657 | −0.641988 | ||||||||
\(530\) | −2.25299 | −0.0978636 | ||||||||
\(531\) | −9.92968 | −0.430912 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.39375 | 0.190314 | ||||||||
\(534\) | −8.46534 | −0.366331 | ||||||||
\(535\) | 6.42216 | 0.277654 | ||||||||
\(536\) | −40.2592 | −1.73893 | ||||||||
\(537\) | 7.55216 | 0.325900 | ||||||||
\(538\) | −40.4061 | −1.74203 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.217861 | 0.00937526 | ||||||||
\(541\) | −14.4341 | −0.620571 | −0.310286 | − | 0.950643i | \(-0.600425\pi\) | ||||
−0.310286 | + | 0.950643i | \(0.600425\pi\) | |||||||
\(542\) | 14.4092 | 0.618928 | ||||||||
\(543\) | 6.02737 | 0.258659 | ||||||||
\(544\) | −10.6921 | −0.458418 | ||||||||
\(545\) | 14.6332 | 0.626816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.1515 | −1.37470 | −0.687350 | − | 0.726326i | \(-0.741226\pi\) | ||||
−0.687350 | + | 0.726326i | \(0.741226\pi\) | |||||||
\(548\) | −1.14519 | −0.0489199 | ||||||||
\(549\) | −2.61168 | −0.111464 | ||||||||
\(550\) | 1.19530 | 0.0509676 | ||||||||
\(551\) | −33.6668 | −1.43425 | ||||||||
\(552\) | 8.52893 | 0.363015 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.16504 | 0.219442 | ||||||||
\(555\) | −4.69520 | −0.199300 | ||||||||
\(556\) | 1.11432 | 0.0472579 | ||||||||
\(557\) | −19.0479 | −0.807084 | −0.403542 | − | 0.914961i | \(-0.632221\pi\) | ||||
−0.403542 | + | 0.914961i | \(0.632221\pi\) | |||||||
\(558\) | 5.78261 | 0.244797 | ||||||||
\(559\) | −50.4163 | −2.13238 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.69861 | −0.0717152 | ||||||||
\(562\) | 12.6978 | 0.535623 | ||||||||
\(563\) | −36.8047 | −1.55113 | −0.775566 | − | 0.631267i | \(-0.782535\pi\) | ||||
−0.775566 | + | 0.631267i | \(0.782535\pi\) | |||||||
\(564\) | 0.155240 | 0.00653677 | ||||||||
\(565\) | 4.91165 | 0.206635 | ||||||||
\(566\) | −15.8969 | −0.668195 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.90802 | −0.122018 | ||||||||
\(569\) | 2.62085 | 0.109872 | 0.0549359 | − | 0.998490i | \(-0.482505\pi\) | ||||
0.0549359 | + | 0.998490i | \(0.482505\pi\) | |||||||
\(570\) | −8.32810 | −0.348826 | ||||||||
\(571\) | −21.1316 | −0.884330 | −0.442165 | − | 0.896934i | \(-0.645789\pi\) | ||||
−0.442165 | + | 0.896934i | \(0.645789\pi\) | |||||||
\(572\) | −0.228215 | −0.00954214 | ||||||||
\(573\) | −9.74507 | −0.407106 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0046 | −0.500626 | ||||||||
\(576\) | 8.71786 | 0.363244 | ||||||||
\(577\) | −4.01140 | −0.166997 | −0.0834983 | − | 0.996508i | \(-0.526609\pi\) | ||||
−0.0834983 | + | 0.996508i | \(0.526609\pi\) | |||||||
\(578\) | 59.8995 | 2.49149 | ||||||||
\(579\) | −25.0321 | −1.04030 | ||||||||
\(580\) | 1.05547 | 0.0438261 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.1625 | −0.545605 | ||||||||
\(583\) | 0.405011 | 0.0167738 | ||||||||
\(584\) | 28.1814 | 1.16615 | ||||||||
\(585\) | −3.97032 | −0.164153 | ||||||||
\(586\) | 8.90537 | 0.367877 | ||||||||
\(587\) | 5.11753 | 0.211223 | 0.105612 | − | 0.994407i | \(-0.466320\pi\) | ||||
0.105612 | + | 0.994407i | \(0.466320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.2996 | 1.24847 | ||||||||
\(590\) | −11.9000 | −0.489916 | ||||||||
\(591\) | −19.1663 | −0.788397 | ||||||||
\(592\) | −17.9763 | −0.738820 | ||||||||
\(593\) | −13.1478 | −0.539915 | −0.269957 | − | 0.962872i | \(-0.587010\pi\) | ||||
−0.269957 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(594\) | 0.285720 | 0.0117232 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.08904 | 0.167493 | ||||||||
\(597\) | −10.3001 | −0.421553 | ||||||||
\(598\) | −16.7213 | −0.683783 | ||||||||
\(599\) | −30.0137 | −1.22633 | −0.613164 | − | 0.789956i | \(-0.710103\pi\) | ||||
−0.613164 | + | 0.789956i | \(0.710103\pi\) | |||||||
\(600\) | −12.4342 | −0.507622 | ||||||||
\(601\) | 6.10032 | 0.248837 | 0.124419 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124419 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5451 | 0.551601 | ||||||||
\(604\) | −4.11491 | −0.167433 | ||||||||
\(605\) | −9.89799 | −0.402411 | ||||||||
\(606\) | −1.67586 | −0.0680770 | ||||||||
\(607\) | 13.5283 | 0.549097 | 0.274548 | − | 0.961573i | \(-0.411472\pi\) | ||||
0.274548 | + | 0.961573i | \(0.411472\pi\) | |||||||
\(608\) | 9.42372 | 0.382182 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.12991 | −0.126726 | ||||||||
\(611\) | −2.82910 | −0.114453 | ||||||||
\(612\) | 1.90091 | 0.0768398 | ||||||||
\(613\) | 9.77539 | 0.394824 | 0.197412 | − | 0.980321i | \(-0.436746\pi\) | ||||
0.197412 | + | 0.980321i | \(0.436746\pi\) | |||||||
\(614\) | 39.5764 | 1.59717 | ||||||||
\(615\) | 0.903630 | 0.0364379 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.6651 | 0.791686 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(618\) | 3.95260 | 0.158997 | ||||||||
\(619\) | 19.1835 | 0.771050 | 0.385525 | − | 0.922697i | \(-0.374020\pi\) | ||||
0.385525 | + | 0.922697i | \(0.374020\pi\) | |||||||
\(620\) | −0.949910 | −0.0381493 | ||||||||
\(621\) | −2.86954 | −0.115151 | ||||||||
\(622\) | 17.5874 | 0.705190 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.2010 | −0.608526 | ||||||||
\(625\) | 13.4185 | 0.536741 | ||||||||
\(626\) | 34.7959 | 1.39072 | ||||||||
\(627\) | 1.49711 | 0.0597888 | ||||||||
\(628\) | −4.25021 | −0.169602 | ||||||||
\(629\) | −40.9672 | −1.63347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.84041 | 0.232503 | 0.116252 | − | 0.993220i | \(-0.462912\pi\) | ||||
0.116252 | + | 0.993220i | \(0.462912\pi\) | |||||||
\(632\) | −31.5182 | −1.25373 | ||||||||
\(633\) | 23.1371 | 0.919616 | ||||||||
\(634\) | −7.96309 | −0.316255 | ||||||||
\(635\) | −7.30799 | −0.290009 | ||||||||
\(636\) | −0.453249 | −0.0179725 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.38423 | 0.0548021 | ||||||||
\(639\) | 0.978400 | 0.0387049 | ||||||||
\(640\) | 7.99692 | 0.316106 | ||||||||
\(641\) | −25.9972 | −1.02683 | −0.513414 | − | 0.858141i | \(-0.671620\pi\) | ||||
−0.513414 | + | 0.858141i | \(0.671620\pi\) | |||||||
\(642\) | −9.42565 | −0.372001 | ||||||||
\(643\) | 48.8910 | 1.92807 | 0.964036 | − | 0.265770i | \(-0.0856262\pi\) | ||||
0.964036 | + | 0.265770i | \(0.0856262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.3688 | −0.408269 | ||||||||
\(646\) | −72.6655 | −2.85898 | ||||||||
\(647\) | −24.2591 | −0.953724 | −0.476862 | − | 0.878978i | \(-0.658226\pi\) | ||||
−0.476862 | + | 0.878978i | \(0.658226\pi\) | |||||||
\(648\) | −2.97222 | −0.116760 | ||||||||
\(649\) | 2.13922 | 0.0839716 | ||||||||
\(650\) | 24.3776 | 0.956168 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.380603 | −0.0149056 | ||||||||
\(653\) | 32.6271 | 1.27680 | 0.638398 | − | 0.769707i | \(-0.279597\pi\) | ||||
0.638398 | + | 0.769707i | \(0.279597\pi\) | |||||||
\(654\) | −21.4768 | −0.839808 | ||||||||
\(655\) | 1.94276 | 0.0759098 | ||||||||
\(656\) | 3.45968 | 0.135078 | ||||||||
\(657\) | −9.48157 | −0.369911 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.8123 | 1.78459 | 0.892296 | − | 0.451450i | \(-0.149093\pi\) | ||||
0.892296 | + | 0.451450i | \(0.149093\pi\) | |||||||
\(660\) | −0.0469353 | −0.00182695 | ||||||||
\(661\) | −47.1834 | −1.83522 | −0.917610 | − | 0.397482i | \(-0.869884\pi\) | ||||
−0.917610 | + | 0.397482i | \(0.869884\pi\) | |||||||
\(662\) | −27.0819 | −1.05257 | ||||||||
\(663\) | −34.6424 | −1.34540 | ||||||||
\(664\) | −27.0546 | −1.04992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.89104 | 0.267022 | ||||||||
\(667\) | −13.9021 | −0.538291 | ||||||||
\(668\) | −0.574668 | −0.0222346 | ||||||||
\(669\) | 18.4257 | 0.712378 | ||||||||
\(670\) | 16.2329 | 0.627131 | ||||||||
\(671\) | 0.562651 | 0.0217209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.5537 | −0.830833 | −0.415417 | − | 0.909631i | \(-0.636364\pi\) | ||||
−0.415417 | + | 0.909631i | \(0.636364\pi\) | |||||||
\(674\) | −26.5966 | −1.02446 | ||||||||
\(675\) | 4.18345 | 0.161021 | ||||||||
\(676\) | −1.52011 | −0.0584658 | ||||||||
\(677\) | −11.7677 | −0.452271 | −0.226136 | − | 0.974096i | \(-0.572609\pi\) | ||||
−0.226136 | + | 0.974096i | \(0.572609\pi\) | |||||||
\(678\) | −7.20872 | −0.276849 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 21.1761 | 0.812065 | ||||||||
\(681\) | 4.13746 | 0.158548 | ||||||||
\(682\) | −1.24579 | −0.0477036 | ||||||||
\(683\) | 46.5738 | 1.78210 | 0.891048 | − | 0.453909i | \(-0.149971\pi\) | ||||
0.891048 | + | 0.453909i | \(0.149971\pi\) | |||||||
\(684\) | −1.67542 | −0.0640612 | ||||||||
\(685\) | 4.29218 | 0.163996 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.10981 | −0.309409 | ||||||||
\(688\) | −39.6983 | −1.51348 | ||||||||
\(689\) | 8.26005 | 0.314683 | ||||||||
\(690\) | −3.43894 | −0.130918 | ||||||||
\(691\) | −11.6480 | −0.443110 | −0.221555 | − | 0.975148i | \(-0.571113\pi\) | ||||
−0.221555 | + | 0.975148i | \(0.571113\pi\) | |||||||
\(692\) | 6.11604 | 0.232497 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.4174 | 1.64810 | ||||||||
\(695\) | −4.17651 | −0.158424 | ||||||||
\(696\) | −14.3995 | −0.545813 | ||||||||
\(697\) | 7.88448 | 0.298646 | ||||||||
\(698\) | 0.0761661 | 0.00288293 | ||||||||
\(699\) | −5.35817 | −0.202665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.2051 | −1.06529 | −0.532646 | − | 0.846338i | \(-0.678802\pi\) | ||||
−0.532646 | + | 0.846338i | \(0.678802\pi\) | |||||||
\(702\) | 5.82715 | 0.219932 | ||||||||
\(703\) | 36.1075 | 1.36182 | ||||||||
\(704\) | −1.87815 | −0.0707853 | ||||||||
\(705\) | −0.581840 | −0.0219134 | ||||||||
\(706\) | 0.645282 | 0.0242855 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.39400 | −0.0899721 | ||||||||
\(709\) | −11.5566 | −0.434017 | −0.217008 | − | 0.976170i | \(-0.569630\pi\) | ||||
−0.217008 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(710\) | 1.17254 | 0.0440047 | ||||||||
\(711\) | 10.6043 | 0.397691 | ||||||||
\(712\) | −18.9716 | −0.710992 | ||||||||
\(713\) | 12.5117 | 0.468566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.855353 | 0.0319884 | ||||||||
\(716\) | 1.82079 | 0.0680462 | ||||||||
\(717\) | −28.6504 | −1.06997 | ||||||||
\(718\) | −15.8053 | −0.589850 | ||||||||
\(719\) | 13.5921 | 0.506898 | 0.253449 | − | 0.967349i | \(-0.418435\pi\) | ||||
0.253449 | + | 0.967349i | \(0.418435\pi\) | |||||||
\(720\) | −3.12627 | −0.116509 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 38.8471 | 1.44574 | ||||||||
\(723\) | 18.5866 | 0.691245 | ||||||||
\(724\) | 1.45317 | 0.0540067 | ||||||||
\(725\) | 20.2676 | 0.752719 | ||||||||
\(726\) | 14.5271 | 0.539149 | ||||||||
\(727\) | 8.32332 | 0.308695 | 0.154348 | − | 0.988017i | \(-0.450672\pi\) | ||||
0.154348 | + | 0.988017i | \(0.450672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.3630 | −0.420563 | ||||||||
\(731\) | −90.4709 | −3.34619 | ||||||||
\(732\) | −0.629664 | −0.0232730 | ||||||||
\(733\) | 30.0076 | 1.10835 | 0.554177 | − | 0.832399i | \(-0.313033\pi\) | ||||
0.554177 | + | 0.832399i | \(0.313033\pi\) | |||||||
\(734\) | 38.3151 | 1.41424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.89136 | 0.143437 | ||||||||
\(737\) | −2.91812 | −0.107490 | ||||||||
\(738\) | −1.32624 | −0.0488195 | ||||||||
\(739\) | −28.2466 | −1.03907 | −0.519533 | − | 0.854450i | \(-0.673894\pi\) | ||||
−0.519533 | + | 0.854450i | \(0.673894\pi\) | |||||||
\(740\) | −1.13199 | −0.0416129 | ||||||||
\(741\) | 30.5330 | 1.12166 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.2535 | −1.66019 | −0.830095 | − | 0.557623i | \(-0.811714\pi\) | ||||
−0.830095 | + | 0.557623i | \(0.811714\pi\) | |||||||
\(744\) | 12.9594 | 0.475114 | ||||||||
\(745\) | −15.3258 | −0.561493 | ||||||||
\(746\) | 7.57325 | 0.277277 | ||||||||
\(747\) | 9.10249 | 0.333043 | ||||||||
\(748\) | −0.409526 | −0.0149738 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.0057 | 0.401872 | ||||||||
\(751\) | −17.3412 | −0.632791 | −0.316395 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316395 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(752\) | −2.22766 | −0.0812345 | ||||||||
\(753\) | −5.97228 | −0.217642 | ||||||||
\(754\) | 28.2308 | 1.02811 | ||||||||
\(755\) | 15.4227 | 0.561291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.9879 | −0.544744 | −0.272372 | − | 0.962192i | \(-0.587808\pi\) | ||||
−0.272372 | + | 0.962192i | \(0.587808\pi\) | |||||||
\(758\) | 20.0434 | 0.728010 | ||||||||
\(759\) | 0.618205 | 0.0224394 | ||||||||
\(760\) | −18.6641 | −0.677017 | ||||||||
\(761\) | −23.7391 | −0.860543 | −0.430272 | − | 0.902699i | \(-0.641582\pi\) | ||||
−0.430272 | + | 0.902699i | \(0.641582\pi\) | |||||||
\(762\) | 10.7258 | 0.388554 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.34949 | −0.0850016 | ||||||||
\(765\) | −7.12465 | −0.257592 | ||||||||
\(766\) | 47.4154 | 1.71319 | ||||||||
\(767\) | 43.6285 | 1.57533 | ||||||||
\(768\) | 5.69883 | 0.205639 | ||||||||
\(769\) | −16.3470 | −0.589488 | −0.294744 | − | 0.955576i | \(-0.595234\pi\) | ||||
−0.294744 | + | 0.955576i | \(0.595234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.2788 | −0.370183 | ||||||||
\(772\) | −6.03512 | −0.217209 | ||||||||
\(773\) | 29.9422 | 1.07695 | 0.538473 | − | 0.842643i | \(-0.319001\pi\) | ||||
0.538473 | + | 0.842643i | \(0.319001\pi\) | |||||||
\(774\) | 15.2180 | 0.546999 | ||||||||
\(775\) | −18.2405 | −0.655219 | ||||||||
\(776\) | −29.4985 | −1.05894 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −43.1637 | −1.54749 | ||||||||
\(779\) | −6.94919 | −0.248980 | ||||||||
\(780\) | −0.957227 | −0.0342742 | ||||||||
\(781\) | −0.210783 | −0.00754241 | ||||||||
\(782\) | −30.0059 | −1.07301 | ||||||||
\(783\) | 4.84470 | 0.173136 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.9298 | 0.568561 | ||||||||
\(786\) | −2.85134 | −0.101704 | ||||||||
\(787\) | −7.83527 | −0.279297 | −0.139649 | − | 0.990201i | \(-0.544597\pi\) | ||||
−0.139649 | + | 0.990201i | \(0.544597\pi\) | |||||||
\(788\) | −4.62092 | −0.164613 | ||||||||
\(789\) | −26.7187 | −0.951211 | ||||||||
\(790\) | 12.7084 | 0.452146 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.640326 | 0.0227530 | ||||||||
\(793\) | 11.4750 | 0.407491 | ||||||||
\(794\) | −34.7095 | −1.23179 | ||||||||
\(795\) | 1.69878 | 0.0602497 | ||||||||
\(796\) | −2.48330 | −0.0880182 | ||||||||
\(797\) | −1.40098 | −0.0496254 | −0.0248127 | − | 0.999692i | \(-0.507899\pi\) | ||||
−0.0248127 | + | 0.999692i | \(0.507899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.07675 | −0.179603 | ||||||||
\(800\) | −5.67314 | −0.200576 | ||||||||
\(801\) | 6.38298 | 0.225532 | ||||||||
\(802\) | 32.1973 | 1.13693 | ||||||||
\(803\) | 2.04268 | 0.0720845 | ||||||||
\(804\) | 3.26567 | 0.115171 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.4073 | −0.894934 | ||||||||
\(807\) | 30.4667 | 1.07248 | ||||||||
\(808\) | −3.75575 | −0.132127 | ||||||||
\(809\) | 18.1826 | 0.639265 | 0.319633 | − | 0.947542i | \(-0.396440\pi\) | ||||
0.319633 | + | 0.947542i | \(0.396440\pi\) | |||||||
\(810\) | 1.19843 | 0.0421085 | ||||||||
\(811\) | 49.1139 | 1.72462 | 0.862310 | − | 0.506380i | \(-0.169017\pi\) | ||||
0.862310 | + | 0.506380i | \(0.169017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.8647 | −0.381042 | ||||||||
\(814\) | −1.48458 | −0.0520346 | ||||||||
\(815\) | 1.42651 | 0.0499684 | ||||||||
\(816\) | −27.2778 | −0.954913 | ||||||||
\(817\) | 79.7388 | 2.78971 | ||||||||
\(818\) | 3.18798 | 0.111465 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.217861 | 0.00760805 | ||||||||
\(821\) | 11.8200 | 0.412521 | 0.206260 | − | 0.978497i | \(-0.433871\pi\) | ||||
0.206260 | + | 0.978497i | \(0.433871\pi\) | |||||||
\(822\) | −6.29953 | −0.219721 | ||||||||
\(823\) | −18.2077 | −0.634680 | −0.317340 | − | 0.948312i | \(-0.602790\pi\) | ||||
−0.317340 | + | 0.948312i | \(0.602790\pi\) | |||||||
\(824\) | 8.85815 | 0.308588 | ||||||||
\(825\) | −0.901269 | −0.0313781 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.3741 | −1.02144 | −0.510718 | − | 0.859748i | \(-0.670620\pi\) | ||||
−0.510718 | + | 0.859748i | \(0.670620\pi\) | |||||||
\(828\) | −0.691834 | −0.0240429 | ||||||||
\(829\) | 39.7415 | 1.38028 | 0.690140 | − | 0.723676i | \(-0.257549\pi\) | ||||
0.690140 | + | 0.723676i | \(0.257549\pi\) | |||||||
\(830\) | 10.9087 | 0.378646 | ||||||||
\(831\) | −3.89451 | −0.135099 | ||||||||
\(832\) | −38.3041 | −1.32795 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.12976 | 0.212256 | ||||||||
\(835\) | 2.15386 | 0.0745375 | ||||||||
\(836\) | 0.360946 | 0.0124836 | ||||||||
\(837\) | −4.36016 | −0.150709 | ||||||||
\(838\) | 17.4443 | 0.602605 | ||||||||
\(839\) | −8.72265 | −0.301139 | −0.150570 | − | 0.988599i | \(-0.548111\pi\) | ||||
−0.150570 | + | 0.988599i | \(0.548111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.52884 | −0.190650 | ||||||||
\(842\) | 40.8446 | 1.40760 | ||||||||
\(843\) | −9.57428 | −0.329756 | ||||||||
\(844\) | 5.57824 | 0.192011 | ||||||||
\(845\) | 5.69740 | 0.195996 | ||||||||
\(846\) | 0.853954 | 0.0293595 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.50405 | 0.223350 | ||||||||
\(849\) | 11.9864 | 0.411374 | ||||||||
\(850\) | 43.7450 | 1.50044 | ||||||||
\(851\) | 14.9100 | 0.511107 | ||||||||
\(852\) | 0.235888 | 0.00808138 | ||||||||
\(853\) | 3.60943 | 0.123585 | 0.0617923 | − | 0.998089i | \(-0.480318\pi\) | ||||
0.0617923 | + | 0.998089i | \(0.480318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.27950 | 0.214754 | ||||||||
\(856\) | −21.1238 | −0.721996 | ||||||||
\(857\) | 35.4588 | 1.21125 | 0.605625 | − | 0.795750i | \(-0.292923\pi\) | ||||
0.605625 | + | 0.795750i | \(0.292923\pi\) | |||||||
\(858\) | −1.25538 | −0.0428580 | ||||||||
\(859\) | −10.0643 | −0.343391 | −0.171695 | − | 0.985150i | \(-0.554924\pi\) | ||||
−0.171695 | + | 0.985150i | \(0.554924\pi\) | |||||||
\(860\) | −2.49986 | −0.0852445 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.4920 | 0.425480 | ||||||||
\(863\) | 11.1068 | 0.378080 | 0.189040 | − | 0.981969i | \(-0.439462\pi\) | ||||
0.189040 | + | 0.981969i | \(0.439462\pi\) | |||||||
\(864\) | −1.35609 | −0.0461351 | ||||||||
\(865\) | −22.9230 | −0.779406 | ||||||||
\(866\) | −0.357203 | −0.0121382 | ||||||||
\(867\) | −45.1650 | −1.53388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.28455 | −0.0774979 | ||||||||
\(870\) | 5.80603 | 0.196843 | ||||||||
\(871\) | −59.5139 | −2.01655 | ||||||||
\(872\) | −48.1315 | −1.62994 | ||||||||
\(873\) | 9.92473 | 0.335901 | ||||||||
\(874\) | 26.4465 | 0.894566 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.28596 | −0.0772356 | ||||||||
\(877\) | 13.9721 | 0.471806 | 0.235903 | − | 0.971777i | \(-0.424195\pi\) | ||||
0.235903 | + | 0.971777i | \(0.424195\pi\) | |||||||
\(878\) | 39.0054 | 1.31637 | ||||||||
\(879\) | −6.71477 | −0.226483 | ||||||||
\(880\) | 0.673514 | 0.0227041 | ||||||||
\(881\) | −51.0123 | −1.71865 | −0.859323 | − | 0.511433i | \(-0.829115\pi\) | ||||
−0.859323 | + | 0.511433i | \(0.829115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7434 | 1.03460 | 0.517299 | − | 0.855805i | \(-0.326938\pi\) | ||||
0.517299 | + | 0.855805i | \(0.326938\pi\) | |||||||
\(884\) | −8.35213 | −0.280913 | ||||||||
\(885\) | 8.97276 | 0.301616 | ||||||||
\(886\) | −21.5171 | −0.722881 | ||||||||
\(887\) | −20.6989 | −0.695002 | −0.347501 | − | 0.937680i | \(-0.612970\pi\) | ||||
−0.347501 | + | 0.937680i | \(0.612970\pi\) | |||||||
\(888\) | 15.4435 | 0.518249 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.64954 | 0.256413 | ||||||||
\(891\) | −0.215437 | −0.00721740 | ||||||||
\(892\) | 4.44235 | 0.148741 | ||||||||
\(893\) | 4.47453 | 0.149734 | ||||||||
\(894\) | 22.4933 | 0.752288 | ||||||||
\(895\) | −6.82436 | −0.228113 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.6081 | 0.420971 | ||||||||
\(898\) | 14.8671 | 0.496121 | ||||||||
\(899\) | −21.1237 | −0.704515 | ||||||||
\(900\) | 1.00861 | 0.0336204 | ||||||||
\(901\) | 14.8225 | 0.493808 | ||||||||
\(902\) | 0.285720 | 0.00951343 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1554 | −0.537322 | ||||||||
\(905\) | −5.44651 | −0.181048 | ||||||||
\(906\) | −22.6356 | −0.752018 | ||||||||
\(907\) | −8.10539 | −0.269135 | −0.134568 | − | 0.990904i | \(-0.542965\pi\) | ||||
−0.134568 | + | 0.990904i | \(0.542965\pi\) | |||||||
\(908\) | 0.997524 | 0.0331040 | ||||||||
\(909\) | 1.26362 | 0.0419116 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.1116 | −1.52775 | −0.763873 | − | 0.645366i | \(-0.776705\pi\) | ||||
−0.763873 | + | 0.645366i | \(0.776705\pi\) | |||||||
\(912\) | 24.0420 | 0.796109 | ||||||||
\(913\) | −1.96101 | −0.0649000 | ||||||||
\(914\) | −43.8416 | −1.45015 | ||||||||
\(915\) | 2.35999 | 0.0780189 | ||||||||
\(916\) | −1.95524 | −0.0646030 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.4567 | 0.345122 | ||||||||
\(919\) | 1.04637 | 0.0345167 | 0.0172583 | − | 0.999851i | \(-0.494506\pi\) | ||||
0.0172583 | + | 0.999851i | \(0.494506\pi\) | |||||||
\(920\) | −7.70700 | −0.254092 | ||||||||
\(921\) | −29.8411 | −0.983299 | ||||||||
\(922\) | 4.64819 | 0.153080 | ||||||||
\(923\) | −4.29884 | −0.141498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7369 | −0.714706 | ||||||||
\(926\) | −24.2386 | −0.796529 | ||||||||
\(927\) | −2.98031 | −0.0978862 | ||||||||
\(928\) | −6.56985 | −0.215666 | ||||||||
\(929\) | 14.8011 | 0.485607 | 0.242804 | − | 0.970075i | \(-0.421933\pi\) | ||||
0.242804 | + | 0.970075i | \(0.421933\pi\) | |||||||
\(930\) | −5.22534 | −0.171346 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.29183 | −0.0423153 | ||||||||
\(933\) | −13.2611 | −0.434150 | ||||||||
\(934\) | 54.6059 | 1.78676 | ||||||||
\(935\) | 1.53491 | 0.0501970 | ||||||||
\(936\) | 13.0592 | 0.426853 | ||||||||
\(937\) | −32.9556 | −1.07661 | −0.538306 | − | 0.842749i | \(-0.680936\pi\) | ||||
−0.538306 | + | 0.842749i | \(0.680936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.2366 | −0.856198 | ||||||||
\(940\) | −0.140279 | −0.00457540 | ||||||||
\(941\) | 3.10169 | 0.101112 | 0.0505562 | − | 0.998721i | \(-0.483901\pi\) | ||||
0.0505562 | + | 0.998721i | \(0.483901\pi\) | |||||||
\(942\) | −23.3799 | −0.761757 | ||||||||
\(943\) | −2.86954 | −0.0934452 | ||||||||
\(944\) | 34.3535 | 1.11811 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.27851 | −0.106594 | ||||||||
\(947\) | −8.87354 | −0.288351 | −0.144176 | − | 0.989552i | \(-0.546053\pi\) | ||||
−0.144176 | + | 0.989552i | \(0.546053\pi\) | |||||||
\(948\) | 2.55664 | 0.0830358 | ||||||||
\(949\) | 41.6596 | 1.35233 | ||||||||
\(950\) | −38.5558 | −1.25092 | ||||||||
\(951\) | 6.00428 | 0.194702 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.6737 | 0.864046 | 0.432023 | − | 0.901863i | \(-0.357800\pi\) | ||||
0.432023 | + | 0.901863i | \(0.357800\pi\) | |||||||
\(954\) | −2.49327 | −0.0807225 | ||||||||
\(955\) | 8.80594 | 0.284953 | ||||||||
\(956\) | −6.90749 | −0.223404 | ||||||||
\(957\) | −1.04373 | −0.0337389 | ||||||||
\(958\) | −51.7266 | −1.67121 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7.87772 | −0.254252 | ||||||||
\(961\) | −11.9890 | −0.386742 | ||||||||
\(962\) | −30.2775 | −0.976185 | ||||||||
\(963\) | 7.10706 | 0.229022 | ||||||||
\(964\) | 4.48116 | 0.144328 | ||||||||
\(965\) | 22.6197 | 0.728155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.537499 | 0.0172848 | 0.00864241 | − | 0.999963i | \(-0.497249\pi\) | ||||
0.00864241 | + | 0.999963i | \(0.497249\pi\) | |||||||
\(968\) | 32.5565 | 1.04641 | ||||||||
\(969\) | 54.7907 | 1.76013 | ||||||||
\(970\) | 11.8941 | 0.381896 | ||||||||
\(971\) | −29.9320 | −0.960565 | −0.480282 | − | 0.877114i | \(-0.659466\pi\) | ||||
−0.480282 | + | 0.877114i | \(0.659466\pi\) | |||||||
\(972\) | 0.241096 | 0.00773314 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.8929 | −0.573325 | ||||||||
\(975\) | −18.3810 | −0.588664 | ||||||||
\(976\) | 9.03557 | 0.289222 | ||||||||
\(977\) | −33.4972 | −1.07167 | −0.535836 | − | 0.844322i | \(-0.680003\pi\) | ||||
−0.535836 | + | 0.844322i | \(0.680003\pi\) | |||||||
\(978\) | −2.09365 | −0.0669476 | ||||||||
\(979\) | −1.37513 | −0.0439493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1938 | 0.517027 | ||||||||
\(982\) | −34.7103 | −1.10765 | ||||||||
\(983\) | 41.0970 | 1.31079 | 0.655396 | − | 0.755285i | \(-0.272502\pi\) | ||||
0.655396 | + | 0.755285i | \(0.272502\pi\) | |||||||
\(984\) | −2.97222 | −0.0947510 | ||||||||
\(985\) | 17.3193 | 0.551838 | ||||||||
\(986\) | 50.6595 | 1.61333 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.36136 | 0.234196 | ||||||||
\(989\) | 32.9267 | 1.04701 | ||||||||
\(990\) | −0.258185 | −0.00820566 | ||||||||
\(991\) | 12.1934 | 0.387335 | 0.193668 | − | 0.981067i | \(-0.437962\pi\) | ||||
0.193668 | + | 0.981067i | \(0.437962\pi\) | |||||||
\(992\) | 5.91277 | 0.187731 | ||||||||
\(993\) | 20.4201 | 0.648011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.30744 | 0.295066 | ||||||||
\(996\) | 2.19457 | 0.0695376 | ||||||||
\(997\) | 52.1158 | 1.65052 | 0.825262 | − | 0.564750i | \(-0.191027\pi\) | ||||
0.825262 | + | 0.564750i | \(0.191027\pi\) | |||||||
\(998\) | −38.3754 | −1.21475 | ||||||||
\(999\) | −5.19593 | −0.164392 |
(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 | 6027.2.a.bd.1.6 | ✓ | 10 | |
7.6 | odd | 2 | 6027.2.a.be.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bd.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6027.2.a.be.1.6 | yes | 10 | 7.6 | odd | 2 |