Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
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: | \( x^{10} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.19478\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.19478 | 1.26715 | 0.633577 | − | 0.773679i | \(-0.281586\pi\) | ||||
0.633577 | + | 0.773679i | \(0.281586\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.75416 | 1.23170 | 0.615849 | − | 0.787864i | \(-0.288813\pi\) | ||||
0.615849 | + | 0.787864i | \(0.288813\pi\) | |||||||
\(6\) | 2.19478 | 0.896014 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.81704 | 0.605681 | ||||||||
\(10\) | 2.75416 | 0.870943 | ||||||||
\(11\) | 0.941986 | 0.284019 | 0.142010 | − | 0.989865i | \(-0.454644\pi\) | ||||
0.142010 | + | 0.989865i | \(0.454644\pi\) | |||||||
\(12\) | 2.19478 | 0.633577 | ||||||||
\(13\) | 4.37963 | 1.21469 | 0.607346 | − | 0.794437i | \(-0.292234\pi\) | ||||
0.607346 | + | 0.794437i | \(0.292234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.04477 | 1.56075 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.93712 | 0.469821 | 0.234910 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234910 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(18\) | 1.81704 | 0.428281 | ||||||||
\(19\) | −2.67674 | −0.614085 | −0.307043 | − | 0.951696i | \(-0.599339\pi\) | ||||
−0.307043 | + | 0.951696i | \(0.599339\pi\) | |||||||
\(20\) | 2.75416 | 0.615849 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.941986 | 0.200832 | ||||||||
\(23\) | −4.18718 | −0.873088 | −0.436544 | − | 0.899683i | \(-0.643798\pi\) | ||||
−0.436544 | + | 0.899683i | \(0.643798\pi\) | |||||||
\(24\) | 2.19478 | 0.448007 | ||||||||
\(25\) | 2.58541 | 0.517082 | ||||||||
\(26\) | 4.37963 | 0.858917 | ||||||||
\(27\) | −2.59633 | −0.499664 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.145436 | −0.0270067 | −0.0135034 | − | 0.999909i | \(-0.504298\pi\) | ||||
−0.0135034 | + | 0.999909i | \(0.504298\pi\) | |||||||
\(30\) | 6.04477 | 1.10362 | ||||||||
\(31\) | 7.42842 | 1.33418 | 0.667092 | − | 0.744976i | \(-0.267539\pi\) | ||||
0.667092 | + | 0.744976i | \(0.267539\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.06745 | 0.359897 | ||||||||
\(34\) | 1.93712 | 0.332213 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.81704 | 0.302840 | ||||||||
\(37\) | −10.7123 | −1.76108 | −0.880542 | − | 0.473969i | \(-0.842821\pi\) | ||||
−0.880542 | + | 0.473969i | \(0.842821\pi\) | |||||||
\(38\) | −2.67674 | −0.434224 | ||||||||
\(39\) | 9.61232 | 1.53920 | ||||||||
\(40\) | 2.75416 | 0.435471 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.62329 | 1.31504 | 0.657520 | − | 0.753437i | \(-0.271606\pi\) | ||||
0.657520 | + | 0.753437i | \(0.271606\pi\) | |||||||
\(44\) | 0.941986 | 0.142010 | ||||||||
\(45\) | 5.00443 | 0.746016 | ||||||||
\(46\) | −4.18718 | −0.617366 | ||||||||
\(47\) | −4.43943 | −0.647558 | −0.323779 | − | 0.946133i | \(-0.604953\pi\) | ||||
−0.323779 | + | 0.946133i | \(0.604953\pi\) | |||||||
\(48\) | 2.19478 | 0.316789 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.58541 | 0.365632 | ||||||||
\(51\) | 4.25155 | 0.595335 | ||||||||
\(52\) | 4.37963 | 0.607346 | ||||||||
\(53\) | −5.12705 | −0.704254 | −0.352127 | − | 0.935952i | \(-0.614541\pi\) | ||||
−0.352127 | + | 0.935952i | \(0.614541\pi\) | |||||||
\(54\) | −2.59633 | −0.353315 | ||||||||
\(55\) | 2.59438 | 0.349826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.87484 | −0.778141 | ||||||||
\(58\) | −0.145436 | −0.0190966 | ||||||||
\(59\) | 5.20297 | 0.677368 | 0.338684 | − | 0.940900i | \(-0.390018\pi\) | ||||
0.338684 | + | 0.940900i | \(0.390018\pi\) | |||||||
\(60\) | 6.04477 | 0.780376 | ||||||||
\(61\) | −1.15333 | −0.147669 | −0.0738344 | − | 0.997271i | \(-0.523524\pi\) | ||||
−0.0738344 | + | 0.997271i | \(0.523524\pi\) | |||||||
\(62\) | 7.42842 | 0.943410 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.0622 | 1.49613 | ||||||||
\(66\) | 2.06745 | 0.254485 | ||||||||
\(67\) | 0.684330 | 0.0836042 | 0.0418021 | − | 0.999126i | \(-0.486690\pi\) | ||||
0.0418021 | + | 0.999126i | \(0.486690\pi\) | |||||||
\(68\) | 1.93712 | 0.234910 | ||||||||
\(69\) | −9.18993 | −1.10634 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.10892 | 0.487640 | 0.243820 | − | 0.969821i | \(-0.421599\pi\) | ||||
0.243820 | + | 0.969821i | \(0.421599\pi\) | |||||||
\(72\) | 1.81704 | 0.214140 | ||||||||
\(73\) | −15.0653 | −1.76326 | −0.881630 | − | 0.471941i | \(-0.843553\pi\) | ||||
−0.881630 | + | 0.471941i | \(0.843553\pi\) | |||||||
\(74\) | −10.7123 | −1.24527 | ||||||||
\(75\) | 5.67440 | 0.655223 | ||||||||
\(76\) | −2.67674 | −0.307043 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.61232 | 1.08838 | ||||||||
\(79\) | −12.4752 | −1.40357 | −0.701787 | − | 0.712387i | \(-0.747614\pi\) | ||||
−0.701787 | + | 0.712387i | \(0.747614\pi\) | |||||||
\(80\) | 2.75416 | 0.307925 | ||||||||
\(81\) | −11.1495 | −1.23883 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | −11.3239 | −1.24296 | −0.621482 | − | 0.783428i | \(-0.713469\pi\) | ||||
−0.621482 | + | 0.783428i | \(0.713469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.33514 | 0.578678 | ||||||||
\(86\) | 8.62329 | 0.929873 | ||||||||
\(87\) | −0.319198 | −0.0342217 | ||||||||
\(88\) | 0.941986 | 0.100416 | ||||||||
\(89\) | 11.7305 | 1.24343 | 0.621715 | − | 0.783244i | \(-0.286436\pi\) | ||||
0.621715 | + | 0.783244i | \(0.286436\pi\) | |||||||
\(90\) | 5.00443 | 0.527513 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.18718 | −0.436544 | ||||||||
\(93\) | 16.3037 | 1.69062 | ||||||||
\(94\) | −4.43943 | −0.457892 | ||||||||
\(95\) | −7.37216 | −0.756368 | ||||||||
\(96\) | 2.19478 | 0.224003 | ||||||||
\(97\) | 3.41721 | 0.346965 | 0.173482 | − | 0.984837i | \(-0.444498\pi\) | ||||
0.173482 | + | 0.984837i | \(0.444498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.71163 | 0.172025 | ||||||||
\(100\) | 2.58541 | 0.258541 | ||||||||
\(101\) | −1.15934 | −0.115359 | −0.0576795 | − | 0.998335i | \(-0.518370\pi\) | ||||
−0.0576795 | + | 0.998335i | \(0.518370\pi\) | |||||||
\(102\) | 4.25155 | 0.420966 | ||||||||
\(103\) | −6.82644 | −0.672629 | −0.336315 | − | 0.941750i | \(-0.609181\pi\) | ||||
−0.336315 | + | 0.941750i | \(0.609181\pi\) | |||||||
\(104\) | 4.37963 | 0.429458 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.12705 | −0.497983 | ||||||||
\(107\) | 4.00282 | 0.386968 | 0.193484 | − | 0.981103i | \(-0.438021\pi\) | ||||
0.193484 | + | 0.981103i | \(0.438021\pi\) | |||||||
\(108\) | −2.59633 | −0.249832 | ||||||||
\(109\) | 12.6076 | 1.20759 | 0.603796 | − | 0.797139i | \(-0.293654\pi\) | ||||
0.603796 | + | 0.797139i | \(0.293654\pi\) | |||||||
\(110\) | 2.59438 | 0.247365 | ||||||||
\(111\) | −23.5110 | −2.23156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1114 | 1.51563 | 0.757817 | − | 0.652467i | \(-0.226266\pi\) | ||||
0.757817 | + | 0.652467i | \(0.226266\pi\) | |||||||
\(114\) | −5.87484 | −0.550229 | ||||||||
\(115\) | −11.5322 | −1.07538 | ||||||||
\(116\) | −0.145436 | −0.0135034 | ||||||||
\(117\) | 7.95798 | 0.735715 | ||||||||
\(118\) | 5.20297 | 0.478972 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.04477 | 0.551809 | ||||||||
\(121\) | −10.1127 | −0.919333 | ||||||||
\(122\) | −1.15333 | −0.104418 | ||||||||
\(123\) | −2.19478 | −0.197896 | ||||||||
\(124\) | 7.42842 | 0.667092 | ||||||||
\(125\) | −6.65017 | −0.594810 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0764 | 1.16034 | 0.580172 | − | 0.814494i | \(-0.302985\pi\) | ||||
0.580172 | + | 0.814494i | \(0.302985\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 18.9262 | 1.66636 | ||||||||
\(130\) | 12.0622 | 1.05793 | ||||||||
\(131\) | −7.67673 | −0.670719 | −0.335360 | − | 0.942090i | \(-0.608858\pi\) | ||||
−0.335360 | + | 0.942090i | \(0.608858\pi\) | |||||||
\(132\) | 2.06745 | 0.179948 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.684330 | 0.0591171 | ||||||||
\(135\) | −7.15071 | −0.615435 | ||||||||
\(136\) | 1.93712 | 0.166107 | ||||||||
\(137\) | 8.04741 | 0.687536 | 0.343768 | − | 0.939055i | \(-0.388297\pi\) | ||||
0.343768 | + | 0.939055i | \(0.388297\pi\) | |||||||
\(138\) | −9.18993 | −0.782298 | ||||||||
\(139\) | −16.8676 | −1.43069 | −0.715346 | − | 0.698771i | \(-0.753731\pi\) | ||||
−0.715346 | + | 0.698771i | \(0.753731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.74356 | −0.820556 | ||||||||
\(142\) | 4.10892 | 0.344813 | ||||||||
\(143\) | 4.12555 | 0.344996 | ||||||||
\(144\) | 1.81704 | 0.151420 | ||||||||
\(145\) | −0.400553 | −0.0332641 | ||||||||
\(146\) | −15.0653 | −1.24681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.7123 | −0.880542 | ||||||||
\(149\) | 13.3134 | 1.09067 | 0.545337 | − | 0.838217i | \(-0.316402\pi\) | ||||
0.545337 | + | 0.838217i | \(0.316402\pi\) | |||||||
\(150\) | 5.67440 | 0.463312 | ||||||||
\(151\) | −5.12798 | −0.417309 | −0.208655 | − | 0.977989i | \(-0.566908\pi\) | ||||
−0.208655 | + | 0.977989i | \(0.566908\pi\) | |||||||
\(152\) | −2.67674 | −0.217112 | ||||||||
\(153\) | 3.51983 | 0.284561 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.4591 | 1.64331 | ||||||||
\(156\) | 9.61232 | 0.769601 | ||||||||
\(157\) | 18.3332 | 1.46315 | 0.731573 | − | 0.681764i | \(-0.238787\pi\) | ||||
0.731573 | + | 0.681764i | \(0.238787\pi\) | |||||||
\(158\) | −12.4752 | −0.992476 | ||||||||
\(159\) | −11.2527 | −0.892399 | ||||||||
\(160\) | 2.75416 | 0.217736 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.1495 | −0.875986 | ||||||||
\(163\) | 10.6522 | 0.834345 | 0.417173 | − | 0.908827i | \(-0.363021\pi\) | ||||
0.417173 | + | 0.908827i | \(0.363021\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 5.69409 | 0.443284 | ||||||||
\(166\) | −11.3239 | −0.878908 | ||||||||
\(167\) | −10.7679 | −0.833247 | −0.416623 | − | 0.909079i | \(-0.636787\pi\) | ||||
−0.416623 | + | 0.909079i | \(0.636787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.18119 | 0.475476 | ||||||||
\(170\) | 5.33514 | 0.409187 | ||||||||
\(171\) | −4.86374 | −0.371940 | ||||||||
\(172\) | 8.62329 | 0.657520 | ||||||||
\(173\) | 4.69347 | 0.356838 | 0.178419 | − | 0.983955i | \(-0.442902\pi\) | ||||
0.178419 | + | 0.983955i | \(0.442902\pi\) | |||||||
\(174\) | −0.319198 | −0.0241984 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.941986 | 0.0710049 | ||||||||
\(177\) | 11.4193 | 0.858330 | ||||||||
\(178\) | 11.7305 | 0.879237 | ||||||||
\(179\) | −1.85740 | −0.138829 | −0.0694145 | − | 0.997588i | \(-0.522113\pi\) | ||||
−0.0694145 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(180\) | 5.00443 | 0.373008 | ||||||||
\(181\) | −22.2499 | −1.65382 | −0.826912 | − | 0.562331i | \(-0.809905\pi\) | ||||
−0.826912 | + | 0.562331i | \(0.809905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.53130 | −0.187119 | ||||||||
\(184\) | −4.18718 | −0.308683 | ||||||||
\(185\) | −29.5033 | −2.16912 | ||||||||
\(186\) | 16.3037 | 1.19545 | ||||||||
\(187\) | 1.82474 | 0.133438 | ||||||||
\(188\) | −4.43943 | −0.323779 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.37216 | −0.534833 | ||||||||
\(191\) | −20.0369 | −1.44982 | −0.724910 | − | 0.688843i | \(-0.758119\pi\) | ||||
−0.724910 | + | 0.688843i | \(0.758119\pi\) | |||||||
\(192\) | 2.19478 | 0.158394 | ||||||||
\(193\) | 16.1054 | 1.15929 | 0.579646 | − | 0.814868i | \(-0.303191\pi\) | ||||
0.579646 | + | 0.814868i | \(0.303191\pi\) | |||||||
\(194\) | 3.41721 | 0.245341 | ||||||||
\(195\) | 26.4739 | 1.89583 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7466 | 1.05065 | 0.525327 | − | 0.850901i | \(-0.323943\pi\) | ||||
0.525327 | + | 0.850901i | \(0.323943\pi\) | |||||||
\(198\) | 1.71163 | 0.121640 | ||||||||
\(199\) | 19.0221 | 1.34844 | 0.674221 | − | 0.738530i | \(-0.264480\pi\) | ||||
0.674221 | + | 0.738530i | \(0.264480\pi\) | |||||||
\(200\) | 2.58541 | 0.182816 | ||||||||
\(201\) | 1.50195 | 0.105939 | ||||||||
\(202\) | −1.15934 | −0.0815712 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.25155 | 0.297668 | ||||||||
\(205\) | −2.75416 | −0.192359 | ||||||||
\(206\) | −6.82644 | −0.475621 | ||||||||
\(207\) | −7.60829 | −0.528812 | ||||||||
\(208\) | 4.37963 | 0.303673 | ||||||||
\(209\) | −2.52145 | −0.174412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.92033 | −0.269887 | −0.134943 | − | 0.990853i | \(-0.543085\pi\) | ||||
−0.134943 | + | 0.990853i | \(0.543085\pi\) | |||||||
\(212\) | −5.12705 | −0.352127 | ||||||||
\(213\) | 9.01817 | 0.617915 | ||||||||
\(214\) | 4.00282 | 0.273627 | ||||||||
\(215\) | 23.7499 | 1.61973 | ||||||||
\(216\) | −2.59633 | −0.176658 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.6076 | 0.853896 | ||||||||
\(219\) | −33.0650 | −2.23432 | ||||||||
\(220\) | 2.59438 | 0.174913 | ||||||||
\(221\) | 8.48388 | 0.570687 | ||||||||
\(222\) | −23.5110 | −1.57795 | ||||||||
\(223\) | 19.3451 | 1.29544 | 0.647722 | − | 0.761877i | \(-0.275722\pi\) | ||||
0.647722 | + | 0.761877i | \(0.275722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.69780 | 0.313187 | ||||||||
\(226\) | 16.1114 | 1.07172 | ||||||||
\(227\) | −26.5527 | −1.76236 | −0.881182 | − | 0.472777i | \(-0.843252\pi\) | ||||
−0.881182 | + | 0.472777i | \(0.843252\pi\) | |||||||
\(228\) | −5.87484 | −0.389070 | ||||||||
\(229\) | 8.09922 | 0.535211 | 0.267606 | − | 0.963529i | \(-0.413768\pi\) | ||||
0.267606 | + | 0.963529i | \(0.413768\pi\) | |||||||
\(230\) | −11.5322 | −0.760409 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.145436 | −0.00954831 | ||||||||
\(233\) | 7.49252 | 0.490851 | 0.245426 | − | 0.969415i | \(-0.421072\pi\) | ||||
0.245426 | + | 0.969415i | \(0.421072\pi\) | |||||||
\(234\) | 7.95798 | 0.520229 | ||||||||
\(235\) | −12.2269 | −0.797596 | ||||||||
\(236\) | 5.20297 | 0.338684 | ||||||||
\(237\) | −27.3803 | −1.77854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.63573 | −0.429230 | −0.214615 | − | 0.976699i | \(-0.568850\pi\) | ||||
−0.214615 | + | 0.976699i | \(0.568850\pi\) | |||||||
\(240\) | 6.04477 | 0.390188 | ||||||||
\(241\) | −7.64140 | −0.492226 | −0.246113 | − | 0.969241i | \(-0.579153\pi\) | ||||
−0.246113 | + | 0.969241i | \(0.579153\pi\) | |||||||
\(242\) | −10.1127 | −0.650067 | ||||||||
\(243\) | −16.6816 | −1.07013 | ||||||||
\(244\) | −1.15333 | −0.0738344 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.19478 | −0.139934 | ||||||||
\(247\) | −11.7231 | −0.745924 | ||||||||
\(248\) | 7.42842 | 0.471705 | ||||||||
\(249\) | −24.8535 | −1.57503 | ||||||||
\(250\) | −6.65017 | −0.420594 | ||||||||
\(251\) | 1.08536 | 0.0685073 | 0.0342536 | − | 0.999413i | \(-0.489095\pi\) | ||||
0.0342536 | + | 0.999413i | \(0.489095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.94427 | −0.247974 | ||||||||
\(254\) | 13.0764 | 0.820488 | ||||||||
\(255\) | 11.7094 | 0.733274 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.4160 | −1.83492 | −0.917460 | − | 0.397827i | \(-0.869764\pi\) | ||||
−0.917460 | + | 0.397827i | \(0.869764\pi\) | |||||||
\(258\) | 18.9262 | 1.17829 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0622 | 0.748067 | ||||||||
\(261\) | −0.264263 | −0.0163574 | ||||||||
\(262\) | −7.67673 | −0.474270 | ||||||||
\(263\) | −8.69298 | −0.536032 | −0.268016 | − | 0.963414i | \(-0.586368\pi\) | ||||
−0.268016 | + | 0.963414i | \(0.586368\pi\) | |||||||
\(264\) | 2.06745 | 0.127243 | ||||||||
\(265\) | −14.1207 | −0.867429 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.7458 | 1.57562 | ||||||||
\(268\) | 0.684330 | 0.0418021 | ||||||||
\(269\) | 2.35065 | 0.143322 | 0.0716608 | − | 0.997429i | \(-0.477170\pi\) | ||||
0.0716608 | + | 0.997429i | \(0.477170\pi\) | |||||||
\(270\) | −7.15071 | −0.435178 | ||||||||
\(271\) | −7.65699 | −0.465129 | −0.232564 | − | 0.972581i | \(-0.574712\pi\) | ||||
−0.232564 | + | 0.972581i | \(0.574712\pi\) | |||||||
\(272\) | 1.93712 | 0.117455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.04741 | 0.486162 | ||||||||
\(275\) | 2.43542 | 0.146861 | ||||||||
\(276\) | −9.18993 | −0.553169 | ||||||||
\(277\) | 6.81703 | 0.409596 | 0.204798 | − | 0.978804i | \(-0.434346\pi\) | ||||
0.204798 | + | 0.978804i | \(0.434346\pi\) | |||||||
\(278\) | −16.8676 | −1.01165 | ||||||||
\(279\) | 13.4977 | 0.808089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0572 | −1.55444 | −0.777222 | − | 0.629227i | \(-0.783372\pi\) | ||||
−0.777222 | + | 0.629227i | \(0.783372\pi\) | |||||||
\(282\) | −9.74356 | −0.580221 | ||||||||
\(283\) | −15.6449 | −0.929991 | −0.464996 | − | 0.885313i | \(-0.653944\pi\) | ||||
−0.464996 | + | 0.885313i | \(0.653944\pi\) | |||||||
\(284\) | 4.10892 | 0.243820 | ||||||||
\(285\) | −16.1803 | −0.958435 | ||||||||
\(286\) | 4.12555 | 0.243949 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.81704 | 0.107070 | ||||||||
\(289\) | −13.2476 | −0.779269 | ||||||||
\(290\) | −0.400553 | −0.0235213 | ||||||||
\(291\) | 7.50001 | 0.439658 | ||||||||
\(292\) | −15.0653 | −0.881630 | ||||||||
\(293\) | 5.27034 | 0.307897 | 0.153948 | − | 0.988079i | \(-0.450801\pi\) | ||||
0.153948 | + | 0.988079i | \(0.450801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3298 | 0.834314 | ||||||||
\(296\) | −10.7123 | −0.622637 | ||||||||
\(297\) | −2.44570 | −0.141914 | ||||||||
\(298\) | 13.3134 | 0.771223 | ||||||||
\(299\) | −18.3383 | −1.06053 | ||||||||
\(300\) | 5.67440 | 0.327611 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.12798 | −0.295082 | ||||||||
\(303\) | −2.54450 | −0.146178 | ||||||||
\(304\) | −2.67674 | −0.153521 | ||||||||
\(305\) | −3.17646 | −0.181884 | ||||||||
\(306\) | 3.51983 | 0.201215 | ||||||||
\(307\) | 9.11497 | 0.520219 | 0.260109 | − | 0.965579i | \(-0.416241\pi\) | ||||
0.260109 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9825 | −0.852325 | ||||||||
\(310\) | 20.4591 | 1.16200 | ||||||||
\(311\) | −9.85866 | −0.559033 | −0.279517 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279517 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(312\) | 9.61232 | 0.544190 | ||||||||
\(313\) | −25.9767 | −1.46829 | −0.734146 | − | 0.678992i | \(-0.762417\pi\) | ||||
−0.734146 | + | 0.678992i | \(0.762417\pi\) | |||||||
\(314\) | 18.3332 | 1.03460 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.4752 | −0.701787 | ||||||||
\(317\) | 14.1066 | 0.792304 | 0.396152 | − | 0.918185i | \(-0.370345\pi\) | ||||
0.396152 | + | 0.918185i | \(0.370345\pi\) | |||||||
\(318\) | −11.2527 | −0.631021 | ||||||||
\(319\) | −0.136998 | −0.00767043 | ||||||||
\(320\) | 2.75416 | 0.153962 | ||||||||
\(321\) | 8.78530 | 0.490348 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.18516 | −0.288510 | ||||||||
\(324\) | −11.1495 | −0.619416 | ||||||||
\(325\) | 11.3231 | 0.628095 | ||||||||
\(326\) | 10.6522 | 0.589971 | ||||||||
\(327\) | 27.6709 | 1.53021 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.69409 | 0.313449 | ||||||||
\(331\) | 19.8655 | 1.09191 | 0.545953 | − | 0.837816i | \(-0.316168\pi\) | ||||
0.545953 | + | 0.837816i | \(0.316168\pi\) | |||||||
\(332\) | −11.3239 | −0.621482 | ||||||||
\(333\) | −19.4646 | −1.06665 | ||||||||
\(334\) | −10.7679 | −0.589195 | ||||||||
\(335\) | 1.88476 | 0.102975 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.42571 | 0.186610 | 0.0933051 | − | 0.995638i | \(-0.470257\pi\) | ||||
0.0933051 | + | 0.995638i | \(0.470257\pi\) | |||||||
\(338\) | 6.18119 | 0.336213 | ||||||||
\(339\) | 35.3610 | 1.92054 | ||||||||
\(340\) | 5.33514 | 0.289339 | ||||||||
\(341\) | 6.99747 | 0.378934 | ||||||||
\(342\) | −4.86374 | −0.263001 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.62329 | 0.464937 | ||||||||
\(345\) | −25.3105 | −1.36267 | ||||||||
\(346\) | 4.69347 | 0.252323 | ||||||||
\(347\) | 30.8446 | 1.65582 | 0.827911 | − | 0.560859i | \(-0.189529\pi\) | ||||
0.827911 | + | 0.560859i | \(0.189529\pi\) | |||||||
\(348\) | −0.319198 | −0.0171108 | ||||||||
\(349\) | 13.8068 | 0.739063 | 0.369532 | − | 0.929218i | \(-0.379518\pi\) | ||||
0.369532 | + | 0.929218i | \(0.379518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3710 | −0.606937 | ||||||||
\(352\) | 0.941986 | 0.0502080 | ||||||||
\(353\) | 22.9751 | 1.22284 | 0.611422 | − | 0.791305i | \(-0.290598\pi\) | ||||
0.611422 | + | 0.791305i | \(0.290598\pi\) | |||||||
\(354\) | 11.4193 | 0.606931 | ||||||||
\(355\) | 11.3166 | 0.600625 | ||||||||
\(356\) | 11.7305 | 0.621715 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.85740 | −0.0981669 | ||||||||
\(359\) | −13.5421 | −0.714725 | −0.357362 | − | 0.933966i | \(-0.616324\pi\) | ||||
−0.357362 | + | 0.933966i | \(0.616324\pi\) | |||||||
\(360\) | 5.00443 | 0.263757 | ||||||||
\(361\) | −11.8351 | −0.622899 | ||||||||
\(362\) | −22.2499 | −1.16943 | ||||||||
\(363\) | −22.1950 | −1.16494 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.4923 | −2.17181 | ||||||||
\(366\) | −2.53130 | −0.132313 | ||||||||
\(367\) | 2.29213 | 0.119648 | 0.0598241 | − | 0.998209i | \(-0.480946\pi\) | ||||
0.0598241 | + | 0.998209i | \(0.480946\pi\) | |||||||
\(368\) | −4.18718 | −0.218272 | ||||||||
\(369\) | −1.81704 | −0.0945914 | ||||||||
\(370\) | −29.5033 | −1.53380 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16.3037 | 0.845308 | ||||||||
\(373\) | −4.33765 | −0.224595 | −0.112297 | − | 0.993675i | \(-0.535821\pi\) | ||||
−0.112297 | + | 0.993675i | \(0.535821\pi\) | |||||||
\(374\) | 1.82474 | 0.0943551 | ||||||||
\(375\) | −14.5956 | −0.753716 | ||||||||
\(376\) | −4.43943 | −0.228946 | ||||||||
\(377\) | −0.636954 | −0.0328048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.5685 | −1.46747 | −0.733733 | − | 0.679437i | \(-0.762224\pi\) | ||||
−0.733733 | + | 0.679437i | \(0.762224\pi\) | |||||||
\(380\) | −7.37216 | −0.378184 | ||||||||
\(381\) | 28.6998 | 1.47034 | ||||||||
\(382\) | −20.0369 | −1.02518 | ||||||||
\(383\) | −29.3175 | −1.49805 | −0.749026 | − | 0.662540i | \(-0.769478\pi\) | ||||
−0.749026 | + | 0.662540i | \(0.769478\pi\) | |||||||
\(384\) | 2.19478 | 0.112002 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.1054 | 0.819744 | ||||||||
\(387\) | 15.6689 | 0.796494 | ||||||||
\(388\) | 3.41721 | 0.173482 | ||||||||
\(389\) | 24.5307 | 1.24376 | 0.621878 | − | 0.783114i | \(-0.286370\pi\) | ||||
0.621878 | + | 0.783114i | \(0.286370\pi\) | |||||||
\(390\) | 26.4739 | 1.34056 | ||||||||
\(391\) | −8.11107 | −0.410195 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.8487 | −0.849905 | ||||||||
\(394\) | 14.7466 | 0.742924 | ||||||||
\(395\) | −34.3588 | −1.72878 | ||||||||
\(396\) | 1.71163 | 0.0860126 | ||||||||
\(397\) | −12.4038 | −0.622527 | −0.311263 | − | 0.950324i | \(-0.600752\pi\) | ||||
−0.311263 | + | 0.950324i | \(0.600752\pi\) | |||||||
\(398\) | 19.0221 | 0.953492 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.58541 | 0.129270 | ||||||||
\(401\) | 34.7546 | 1.73556 | 0.867781 | − | 0.496948i | \(-0.165546\pi\) | ||||
0.867781 | + | 0.496948i | \(0.165546\pi\) | |||||||
\(402\) | 1.50195 | 0.0749105 | ||||||||
\(403\) | 32.5337 | 1.62062 | ||||||||
\(404\) | −1.15934 | −0.0576795 | ||||||||
\(405\) | −30.7075 | −1.52587 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0908 | −0.500182 | ||||||||
\(408\) | 4.25155 | 0.210483 | ||||||||
\(409\) | 8.79422 | 0.434846 | 0.217423 | − | 0.976077i | \(-0.430235\pi\) | ||||
0.217423 | + | 0.976077i | \(0.430235\pi\) | |||||||
\(410\) | −2.75416 | −0.136018 | ||||||||
\(411\) | 17.6623 | 0.871215 | ||||||||
\(412\) | −6.82644 | −0.336315 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.60829 | −0.373927 | ||||||||
\(415\) | −31.1880 | −1.53096 | ||||||||
\(416\) | 4.37963 | 0.214729 | ||||||||
\(417\) | −37.0206 | −1.81291 | ||||||||
\(418\) | −2.52145 | −0.123328 | ||||||||
\(419\) | 12.0175 | 0.587095 | 0.293548 | − | 0.955944i | \(-0.405164\pi\) | ||||
0.293548 | + | 0.955944i | \(0.405164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7569 | 1.49900 | 0.749500 | − | 0.662004i | \(-0.230294\pi\) | ||||
0.749500 | + | 0.662004i | \(0.230294\pi\) | |||||||
\(422\) | −3.92033 | −0.190839 | ||||||||
\(423\) | −8.06664 | −0.392213 | ||||||||
\(424\) | −5.12705 | −0.248991 | ||||||||
\(425\) | 5.00825 | 0.242936 | ||||||||
\(426\) | 9.01817 | 0.436932 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00282 | 0.193484 | ||||||||
\(429\) | 9.05467 | 0.437163 | ||||||||
\(430\) | 23.7499 | 1.14532 | ||||||||
\(431\) | 6.72479 | 0.323922 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(432\) | −2.59633 | −0.124916 | ||||||||
\(433\) | 22.9072 | 1.10085 | 0.550425 | − | 0.834884i | \(-0.314466\pi\) | ||||
0.550425 | + | 0.834884i | \(0.314466\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.879124 | −0.0421508 | ||||||||
\(436\) | 12.6076 | 0.603796 | ||||||||
\(437\) | 11.2080 | 0.536150 | ||||||||
\(438\) | −33.0650 | −1.57990 | ||||||||
\(439\) | 35.0713 | 1.67386 | 0.836932 | − | 0.547307i | \(-0.184347\pi\) | ||||
0.836932 | + | 0.547307i | \(0.184347\pi\) | |||||||
\(440\) | 2.59438 | 0.123682 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.48388 | 0.403537 | ||||||||
\(443\) | −17.9822 | −0.854362 | −0.427181 | − | 0.904166i | \(-0.640493\pi\) | ||||
−0.427181 | + | 0.904166i | \(0.640493\pi\) | |||||||
\(444\) | −23.5110 | −1.11578 | ||||||||
\(445\) | 32.3077 | 1.53153 | ||||||||
\(446\) | 19.3451 | 0.916017 | ||||||||
\(447\) | 29.2199 | 1.38205 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.69654 | −0.363222 | −0.181611 | − | 0.983370i | \(-0.558131\pi\) | ||||
−0.181611 | + | 0.983370i | \(0.558131\pi\) | |||||||
\(450\) | 4.69780 | 0.221456 | ||||||||
\(451\) | −0.941986 | −0.0443564 | ||||||||
\(452\) | 16.1114 | 0.757817 | ||||||||
\(453\) | −11.2548 | −0.528796 | ||||||||
\(454\) | −26.5527 | −1.24618 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.87484 | −0.275114 | ||||||||
\(457\) | 29.8172 | 1.39479 | 0.697394 | − | 0.716688i | \(-0.254343\pi\) | ||||
0.697394 | + | 0.716688i | \(0.254343\pi\) | |||||||
\(458\) | 8.09922 | 0.378452 | ||||||||
\(459\) | −5.02940 | −0.234752 | ||||||||
\(460\) | −11.5322 | −0.537691 | ||||||||
\(461\) | 23.7507 | 1.10618 | 0.553089 | − | 0.833122i | \(-0.313449\pi\) | ||||
0.553089 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.90522 | −0.227965 | −0.113982 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113982 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(464\) | −0.145436 | −0.00675168 | ||||||||
\(465\) | 44.9031 | 2.08233 | ||||||||
\(466\) | 7.49252 | 0.347084 | ||||||||
\(467\) | 40.6774 | 1.88233 | 0.941163 | − | 0.337952i | \(-0.109734\pi\) | ||||
0.941163 | + | 0.337952i | \(0.109734\pi\) | |||||||
\(468\) | 7.95798 | 0.367858 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.2269 | −0.563986 | ||||||||
\(471\) | 40.2372 | 1.85403 | ||||||||
\(472\) | 5.20297 | 0.239486 | ||||||||
\(473\) | 8.12302 | 0.373497 | ||||||||
\(474\) | −27.3803 | −1.25762 | ||||||||
\(475\) | −6.92046 | −0.317532 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.31606 | −0.426553 | ||||||||
\(478\) | −6.63573 | −0.303511 | ||||||||
\(479\) | 14.6318 | 0.668543 | 0.334272 | − | 0.942477i | \(-0.391510\pi\) | ||||
0.334272 | + | 0.942477i | \(0.391510\pi\) | |||||||
\(480\) | 6.04477 | 0.275905 | ||||||||
\(481\) | −46.9157 | −2.13917 | ||||||||
\(482\) | −7.64140 | −0.348056 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.1127 | −0.459666 | ||||||||
\(485\) | 9.41155 | 0.427356 | ||||||||
\(486\) | −16.6816 | −0.756694 | ||||||||
\(487\) | −38.1002 | −1.72649 | −0.863243 | − | 0.504788i | \(-0.831571\pi\) | ||||
−0.863243 | + | 0.504788i | \(0.831571\pi\) | |||||||
\(488\) | −1.15333 | −0.0522088 | ||||||||
\(489\) | 23.3792 | 1.05724 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.0295 | −1.26495 | −0.632476 | − | 0.774580i | \(-0.717961\pi\) | ||||
−0.632476 | + | 0.774580i | \(0.717961\pi\) | |||||||
\(492\) | −2.19478 | −0.0989481 | ||||||||
\(493\) | −0.281726 | −0.0126883 | ||||||||
\(494\) | −11.7231 | −0.527448 | ||||||||
\(495\) | 4.71410 | 0.211883 | ||||||||
\(496\) | 7.42842 | 0.333546 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.8535 | −1.11371 | ||||||||
\(499\) | −9.47858 | −0.424319 | −0.212160 | − | 0.977235i | \(-0.568050\pi\) | ||||
−0.212160 | + | 0.977235i | \(0.568050\pi\) | |||||||
\(500\) | −6.65017 | −0.297405 | ||||||||
\(501\) | −23.6332 | −1.05585 | ||||||||
\(502\) | 1.08536 | 0.0484419 | ||||||||
\(503\) | 18.5815 | 0.828510 | 0.414255 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414255 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.19302 | −0.142088 | ||||||||
\(506\) | −3.94427 | −0.175344 | ||||||||
\(507\) | 13.5663 | 0.602502 | ||||||||
\(508\) | 13.0764 | 0.580172 | ||||||||
\(509\) | −37.4987 | −1.66210 | −0.831050 | − | 0.556198i | \(-0.812260\pi\) | ||||
−0.831050 | + | 0.556198i | \(0.812260\pi\) | |||||||
\(510\) | 11.7094 | 0.518503 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.94968 | 0.306836 | ||||||||
\(514\) | −29.4160 | −1.29748 | ||||||||
\(515\) | −18.8011 | −0.828477 | ||||||||
\(516\) | 18.9262 | 0.833179 | ||||||||
\(517\) | −4.18188 | −0.183919 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3011 | 0.452169 | ||||||||
\(520\) | 12.0622 | 0.528963 | ||||||||
\(521\) | −7.03604 | −0.308254 | −0.154127 | − | 0.988051i | \(-0.549257\pi\) | ||||
−0.154127 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(522\) | −0.264263 | −0.0115665 | ||||||||
\(523\) | 19.5035 | 0.852829 | 0.426415 | − | 0.904528i | \(-0.359776\pi\) | ||||
0.426415 | + | 0.904528i | \(0.359776\pi\) | |||||||
\(524\) | −7.67673 | −0.335360 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.69298 | −0.379032 | ||||||||
\(527\) | 14.3897 | 0.626827 | ||||||||
\(528\) | 2.06745 | 0.0899741 | ||||||||
\(529\) | −5.46751 | −0.237718 | ||||||||
\(530\) | −14.1207 | −0.613365 | ||||||||
\(531\) | 9.45401 | 0.410269 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.37963 | −0.189703 | ||||||||
\(534\) | 25.7458 | 1.11413 | ||||||||
\(535\) | 11.0244 | 0.476627 | ||||||||
\(536\) | 0.684330 | 0.0295586 | ||||||||
\(537\) | −4.07659 | −0.175918 | ||||||||
\(538\) | 2.35065 | 0.101344 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.15071 | −0.307717 | ||||||||
\(541\) | −43.8442 | −1.88501 | −0.942504 | − | 0.334194i | \(-0.891536\pi\) | ||||
−0.942504 | + | 0.334194i | \(0.891536\pi\) | |||||||
\(542\) | −7.65699 | −0.328896 | ||||||||
\(543\) | −48.8336 | −2.09565 | ||||||||
\(544\) | 1.93712 | 0.0830533 | ||||||||
\(545\) | 34.7234 | 1.48739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9132 | −1.57830 | −0.789148 | − | 0.614203i | \(-0.789477\pi\) | ||||
−0.789148 | + | 0.614203i | \(0.789477\pi\) | |||||||
\(548\) | 8.04741 | 0.343768 | ||||||||
\(549\) | −2.09565 | −0.0894402 | ||||||||
\(550\) | 2.43542 | 0.103847 | ||||||||
\(551\) | 0.389293 | 0.0165844 | ||||||||
\(552\) | −9.18993 | −0.391149 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.81703 | 0.289628 | ||||||||
\(555\) | −64.7531 | −2.74862 | ||||||||
\(556\) | −16.8676 | −0.715346 | ||||||||
\(557\) | −34.5045 | −1.46200 | −0.731002 | − | 0.682375i | \(-0.760947\pi\) | ||||
−0.731002 | + | 0.682375i | \(0.760947\pi\) | |||||||
\(558\) | 13.4977 | 0.571405 | ||||||||
\(559\) | 37.7669 | 1.59737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00490 | 0.169087 | ||||||||
\(562\) | −26.0572 | −1.09916 | ||||||||
\(563\) | −27.1529 | −1.14436 | −0.572179 | − | 0.820129i | \(-0.693902\pi\) | ||||
−0.572179 | + | 0.820129i | \(0.693902\pi\) | |||||||
\(564\) | −9.74356 | −0.410278 | ||||||||
\(565\) | 44.3735 | 1.86681 | ||||||||
\(566\) | −15.6449 | −0.657603 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.10892 | 0.172407 | ||||||||
\(569\) | 44.2444 | 1.85482 | 0.927411 | − | 0.374043i | \(-0.122029\pi\) | ||||
0.927411 | + | 0.374043i | \(0.122029\pi\) | |||||||
\(570\) | −16.1803 | −0.677716 | ||||||||
\(571\) | 12.3011 | 0.514787 | 0.257393 | − | 0.966307i | \(-0.417136\pi\) | ||||
0.257393 | + | 0.966307i | \(0.417136\pi\) | |||||||
\(572\) | 4.12555 | 0.172498 | ||||||||
\(573\) | −43.9766 | −1.83715 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8256 | −0.451458 | ||||||||
\(576\) | 1.81704 | 0.0757101 | ||||||||
\(577\) | 0.820956 | 0.0341768 | 0.0170884 | − | 0.999854i | \(-0.494560\pi\) | ||||
0.0170884 | + | 0.999854i | \(0.494560\pi\) | |||||||
\(578\) | −13.2476 | −0.551026 | ||||||||
\(579\) | 35.3478 | 1.46900 | ||||||||
\(580\) | −0.400553 | −0.0166321 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.50001 | 0.310885 | ||||||||
\(583\) | −4.82961 | −0.200022 | ||||||||
\(584\) | −15.0653 | −0.623407 | ||||||||
\(585\) | 21.9176 | 0.906180 | ||||||||
\(586\) | 5.27034 | 0.217716 | ||||||||
\(587\) | −16.5226 | −0.681963 | −0.340981 | − | 0.940070i | \(-0.610759\pi\) | ||||
−0.340981 | + | 0.940070i | \(0.610759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.8839 | −0.819302 | ||||||||
\(590\) | 14.3298 | 0.589949 | ||||||||
\(591\) | 32.3655 | 1.33134 | ||||||||
\(592\) | −10.7123 | −0.440271 | ||||||||
\(593\) | 25.4044 | 1.04323 | 0.521616 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521616 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(594\) | −2.44570 | −0.100348 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.3134 | 0.545337 | ||||||||
\(597\) | 41.7493 | 1.70868 | ||||||||
\(598\) | −18.3383 | −0.749910 | ||||||||
\(599\) | 8.31627 | 0.339794 | 0.169897 | − | 0.985462i | \(-0.445657\pi\) | ||||
0.169897 | + | 0.985462i | \(0.445657\pi\) | |||||||
\(600\) | 5.67440 | 0.231656 | ||||||||
\(601\) | 15.2562 | 0.622314 | 0.311157 | − | 0.950359i | \(-0.399284\pi\) | ||||
0.311157 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.24346 | 0.0506375 | ||||||||
\(604\) | −5.12798 | −0.208655 | ||||||||
\(605\) | −27.8519 | −1.13234 | ||||||||
\(606\) | −2.54450 | −0.103363 | ||||||||
\(607\) | −12.3665 | −0.501943 | −0.250971 | − | 0.967995i | \(-0.580750\pi\) | ||||
−0.250971 | + | 0.967995i | \(0.580750\pi\) | |||||||
\(608\) | −2.67674 | −0.108556 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.17646 | −0.128611 | ||||||||
\(611\) | −19.4431 | −0.786583 | ||||||||
\(612\) | 3.51983 | 0.142281 | ||||||||
\(613\) | −22.5143 | −0.909345 | −0.454673 | − | 0.890659i | \(-0.650244\pi\) | ||||
−0.454673 | + | 0.890659i | \(0.650244\pi\) | |||||||
\(614\) | 9.11497 | 0.367850 | ||||||||
\(615\) | −6.04477 | −0.243749 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.17499 | −0.0473035 | −0.0236517 | − | 0.999720i | \(-0.507529\pi\) | ||||
−0.0236517 | + | 0.999720i | \(0.507529\pi\) | |||||||
\(618\) | −14.9825 | −0.602685 | ||||||||
\(619\) | 23.1341 | 0.929838 | 0.464919 | − | 0.885353i | \(-0.346083\pi\) | ||||
0.464919 | + | 0.885353i | \(0.346083\pi\) | |||||||
\(620\) | 20.4591 | 0.821656 | ||||||||
\(621\) | 10.8713 | 0.436250 | ||||||||
\(622\) | −9.85866 | −0.395296 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.61232 | 0.384801 | ||||||||
\(625\) | −31.2427 | −1.24971 | ||||||||
\(626\) | −25.9767 | −1.03824 | ||||||||
\(627\) | −5.53401 | −0.221007 | ||||||||
\(628\) | 18.3332 | 0.731573 | ||||||||
\(629\) | −20.7509 | −0.827393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5041 | 0.975493 | 0.487747 | − | 0.872985i | \(-0.337819\pi\) | ||||
0.487747 | + | 0.872985i | \(0.337819\pi\) | |||||||
\(632\) | −12.4752 | −0.496238 | ||||||||
\(633\) | −8.60426 | −0.341988 | ||||||||
\(634\) | 14.1066 | 0.560243 | ||||||||
\(635\) | 36.0146 | 1.42920 | ||||||||
\(636\) | −11.2527 | −0.446199 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.136998 | −0.00542381 | ||||||||
\(639\) | 7.46609 | 0.295354 | ||||||||
\(640\) | 2.75416 | 0.108868 | ||||||||
\(641\) | −12.1070 | −0.478199 | −0.239100 | − | 0.970995i | \(-0.576852\pi\) | ||||
−0.239100 | + | 0.970995i | \(0.576852\pi\) | |||||||
\(642\) | 8.78530 | 0.346728 | ||||||||
\(643\) | −47.6407 | −1.87876 | −0.939382 | − | 0.342871i | \(-0.888601\pi\) | ||||
−0.939382 | + | 0.342871i | \(0.888601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 52.1258 | 2.05245 | ||||||||
\(646\) | −5.18516 | −0.204007 | ||||||||
\(647\) | −35.7979 | −1.40736 | −0.703680 | − | 0.710517i | \(-0.748461\pi\) | ||||
−0.703680 | + | 0.710517i | \(0.748461\pi\) | |||||||
\(648\) | −11.1495 | −0.437993 | ||||||||
\(649\) | 4.90112 | 0.192386 | ||||||||
\(650\) | 11.3231 | 0.444130 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.6522 | 0.417173 | ||||||||
\(653\) | 9.66097 | 0.378063 | 0.189032 | − | 0.981971i | \(-0.439465\pi\) | ||||
0.189032 | + | 0.981971i | \(0.439465\pi\) | |||||||
\(654\) | 27.6709 | 1.08202 | ||||||||
\(655\) | −21.1430 | −0.826124 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −27.3743 | −1.06797 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.42183 | 0.367022 | 0.183511 | − | 0.983018i | \(-0.441254\pi\) | ||||
0.183511 | + | 0.983018i | \(0.441254\pi\) | |||||||
\(660\) | 5.69409 | 0.221642 | ||||||||
\(661\) | −27.2806 | −1.06109 | −0.530546 | − | 0.847656i | \(-0.678013\pi\) | ||||
−0.530546 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(662\) | 19.8655 | 0.772093 | ||||||||
\(663\) | 18.6202 | 0.723149 | ||||||||
\(664\) | −11.3239 | −0.439454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.4646 | −0.754238 | ||||||||
\(667\) | 0.608965 | 0.0235792 | ||||||||
\(668\) | −10.7679 | −0.416623 | ||||||||
\(669\) | 42.4582 | 1.64153 | ||||||||
\(670\) | 1.88476 | 0.0728145 | ||||||||
\(671\) | −1.08642 | −0.0419408 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.9602 | 1.84873 | 0.924364 | − | 0.381511i | \(-0.124596\pi\) | ||||
0.924364 | + | 0.381511i | \(0.124596\pi\) | |||||||
\(674\) | 3.42571 | 0.131953 | ||||||||
\(675\) | −6.71257 | −0.258367 | ||||||||
\(676\) | 6.18119 | 0.237738 | ||||||||
\(677\) | −6.18995 | −0.237899 | −0.118950 | − | 0.992900i | \(-0.537953\pi\) | ||||
−0.118950 | + | 0.992900i | \(0.537953\pi\) | |||||||
\(678\) | 35.3610 | 1.35803 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.33514 | 0.204593 | ||||||||
\(681\) | −58.2772 | −2.23319 | ||||||||
\(682\) | 6.99747 | 0.267947 | ||||||||
\(683\) | 34.2974 | 1.31236 | 0.656178 | − | 0.754607i | \(-0.272172\pi\) | ||||
0.656178 | + | 0.754607i | \(0.272172\pi\) | |||||||
\(684\) | −4.86374 | −0.185970 | ||||||||
\(685\) | 22.1639 | 0.846838 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7760 | 0.678196 | ||||||||
\(688\) | 8.62329 | 0.328760 | ||||||||
\(689\) | −22.4546 | −0.855452 | ||||||||
\(690\) | −25.3105 | −0.963556 | ||||||||
\(691\) | −21.8304 | −0.830467 | −0.415234 | − | 0.909715i | \(-0.636300\pi\) | ||||
−0.415234 | + | 0.909715i | \(0.636300\pi\) | |||||||
\(692\) | 4.69347 | 0.178419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.8446 | 1.17084 | ||||||||
\(695\) | −46.4561 | −1.76218 | ||||||||
\(696\) | −0.319198 | −0.0120992 | ||||||||
\(697\) | −1.93712 | −0.0733737 | ||||||||
\(698\) | 13.8068 | 0.522597 | ||||||||
\(699\) | 16.4444 | 0.621985 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.0101 | 1.24677 | 0.623387 | − | 0.781914i | \(-0.285756\pi\) | ||||
0.623387 | + | 0.781914i | \(0.285756\pi\) | |||||||
\(702\) | −11.3710 | −0.429169 | ||||||||
\(703\) | 28.6739 | 1.08146 | ||||||||
\(704\) | 0.941986 | 0.0355024 | ||||||||
\(705\) | −26.8353 | −1.01068 | ||||||||
\(706\) | 22.9751 | 0.864681 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11.4193 | 0.429165 | ||||||||
\(709\) | 26.9684 | 1.01282 | 0.506410 | − | 0.862293i | \(-0.330972\pi\) | ||||
0.506410 | + | 0.862293i | \(0.330972\pi\) | |||||||
\(710\) | 11.3166 | 0.424706 | ||||||||
\(711\) | −22.6680 | −0.850117 | ||||||||
\(712\) | 11.7305 | 0.439619 | ||||||||
\(713\) | −31.1041 | −1.16486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3624 | 0.424931 | ||||||||
\(716\) | −1.85740 | −0.0694145 | ||||||||
\(717\) | −14.5639 | −0.543901 | ||||||||
\(718\) | −13.5421 | −0.505387 | ||||||||
\(719\) | 23.5529 | 0.878376 | 0.439188 | − | 0.898395i | \(-0.355266\pi\) | ||||
0.439188 | + | 0.898395i | \(0.355266\pi\) | |||||||
\(720\) | 5.00443 | 0.186504 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.8351 | −0.440456 | ||||||||
\(723\) | −16.7712 | −0.623726 | ||||||||
\(724\) | −22.2499 | −0.826912 | ||||||||
\(725\) | −0.376010 | −0.0139647 | ||||||||
\(726\) | −22.1950 | −0.823735 | ||||||||
\(727\) | −20.7516 | −0.769635 | −0.384818 | − | 0.922993i | \(-0.625736\pi\) | ||||
−0.384818 | + | 0.922993i | \(0.625736\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.16401 | −0.117185 | ||||||||
\(730\) | −41.4923 | −1.53570 | ||||||||
\(731\) | 16.7044 | 0.617833 | ||||||||
\(732\) | −2.53130 | −0.0935596 | ||||||||
\(733\) | 23.4007 | 0.864323 | 0.432161 | − | 0.901796i | \(-0.357751\pi\) | ||||
0.432161 | + | 0.901796i | \(0.357751\pi\) | |||||||
\(734\) | 2.29213 | 0.0846041 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.18718 | −0.154342 | ||||||||
\(737\) | 0.644629 | 0.0237452 | ||||||||
\(738\) | −1.81704 | −0.0668862 | ||||||||
\(739\) | −25.0297 | −0.920734 | −0.460367 | − | 0.887729i | \(-0.652282\pi\) | ||||
−0.460367 | + | 0.887729i | \(0.652282\pi\) | |||||||
\(740\) | −29.5033 | −1.08456 | ||||||||
\(741\) | −25.7296 | −0.945201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7028 | −0.576079 | −0.288040 | − | 0.957619i | \(-0.593003\pi\) | ||||
−0.288040 | + | 0.957619i | \(0.593003\pi\) | |||||||
\(744\) | 16.3037 | 0.597723 | ||||||||
\(745\) | 36.6672 | 1.34338 | ||||||||
\(746\) | −4.33765 | −0.158813 | ||||||||
\(747\) | −20.5761 | −0.752839 | ||||||||
\(748\) | 1.82474 | 0.0667191 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.5956 | −0.532957 | ||||||||
\(751\) | 17.3168 | 0.631900 | 0.315950 | − | 0.948776i | \(-0.397677\pi\) | ||||
0.315950 | + | 0.948776i | \(0.397677\pi\) | |||||||
\(752\) | −4.43943 | −0.161889 | ||||||||
\(753\) | 2.38212 | 0.0868093 | ||||||||
\(754\) | −0.636954 | −0.0231965 | ||||||||
\(755\) | −14.1233 | −0.514000 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.571470 | −0.0207704 | −0.0103852 | − | 0.999946i | \(-0.503306\pi\) | ||||
−0.0103852 | + | 0.999946i | \(0.503306\pi\) | |||||||
\(758\) | −28.5685 | −1.03766 | ||||||||
\(759\) | −8.65678 | −0.314221 | ||||||||
\(760\) | −7.37216 | −0.267417 | ||||||||
\(761\) | −52.3195 | −1.89658 | −0.948290 | − | 0.317406i | \(-0.897188\pi\) | ||||
−0.948290 | + | 0.317406i | \(0.897188\pi\) | |||||||
\(762\) | 28.6998 | 1.03968 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.0369 | −0.724910 | ||||||||
\(765\) | 9.69418 | 0.350494 | ||||||||
\(766\) | −29.3175 | −1.05928 | ||||||||
\(767\) | 22.7871 | 0.822794 | ||||||||
\(768\) | 2.19478 | 0.0791972 | ||||||||
\(769\) | 22.1042 | 0.797098 | 0.398549 | − | 0.917147i | \(-0.369514\pi\) | ||||
0.398549 | + | 0.917147i | \(0.369514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.5616 | −2.32513 | ||||||||
\(772\) | 16.1054 | 0.579646 | ||||||||
\(773\) | −34.0794 | −1.22575 | −0.612876 | − | 0.790179i | \(-0.709987\pi\) | ||||
−0.612876 | + | 0.790179i | \(0.709987\pi\) | |||||||
\(774\) | 15.6689 | 0.563206 | ||||||||
\(775\) | 19.2055 | 0.689882 | ||||||||
\(776\) | 3.41721 | 0.122671 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.5307 | 0.879469 | ||||||||
\(779\) | 2.67674 | 0.0959040 | ||||||||
\(780\) | 26.4739 | 0.947917 | ||||||||
\(781\) | 3.87055 | 0.138499 | ||||||||
\(782\) | −8.11107 | −0.290051 | ||||||||
\(783\) | 0.377598 | 0.0134943 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 50.4925 | 1.80215 | ||||||||
\(786\) | −16.8487 | −0.600974 | ||||||||
\(787\) | −3.37218 | −0.120205 | −0.0601027 | − | 0.998192i | \(-0.519143\pi\) | ||||
−0.0601027 | + | 0.998192i | \(0.519143\pi\) | |||||||
\(788\) | 14.7466 | 0.525327 | ||||||||
\(789\) | −19.0791 | −0.679235 | ||||||||
\(790\) | −34.3588 | −1.22243 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.71163 | 0.0608201 | ||||||||
\(793\) | −5.05116 | −0.179372 | ||||||||
\(794\) | −12.4038 | −0.440193 | ||||||||
\(795\) | −30.9918 | −1.09917 | ||||||||
\(796\) | 19.0221 | 0.674221 | ||||||||
\(797\) | −32.2341 | −1.14179 | −0.570895 | − | 0.821023i | \(-0.693404\pi\) | ||||
−0.570895 | + | 0.821023i | \(0.693404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.59971 | −0.304236 | ||||||||
\(800\) | 2.58541 | 0.0914080 | ||||||||
\(801\) | 21.3148 | 0.753121 | ||||||||
\(802\) | 34.7546 | 1.22723 | ||||||||
\(803\) | −14.1913 | −0.500800 | ||||||||
\(804\) | 1.50195 | 0.0529697 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.5337 | 1.14595 | ||||||||
\(807\) | 5.15915 | 0.181611 | ||||||||
\(808\) | −1.15934 | −0.0407856 | ||||||||
\(809\) | 36.8897 | 1.29697 | 0.648486 | − | 0.761226i | \(-0.275402\pi\) | ||||
0.648486 | + | 0.761226i | \(0.275402\pi\) | |||||||
\(810\) | −30.7075 | −1.07895 | ||||||||
\(811\) | 39.3323 | 1.38115 | 0.690573 | − | 0.723263i | \(-0.257359\pi\) | ||||
0.690573 | + | 0.723263i | \(0.257359\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.8054 | −0.589390 | ||||||||
\(814\) | −10.0908 | −0.353682 | ||||||||
\(815\) | 29.3379 | 1.02766 | ||||||||
\(816\) | 4.25155 | 0.148834 | ||||||||
\(817\) | −23.0823 | −0.807546 | ||||||||
\(818\) | 8.79422 | 0.307483 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.75416 | −0.0961795 | ||||||||
\(821\) | 3.30152 | 0.115224 | 0.0576118 | − | 0.998339i | \(-0.481651\pi\) | ||||
0.0576118 | + | 0.998339i | \(0.481651\pi\) | |||||||
\(822\) | 17.6623 | 0.616042 | ||||||||
\(823\) | −1.01850 | −0.0355026 | −0.0177513 | − | 0.999842i | \(-0.505651\pi\) | ||||
−0.0177513 | + | 0.999842i | \(0.505651\pi\) | |||||||
\(824\) | −6.82644 | −0.237810 | ||||||||
\(825\) | 5.34520 | 0.186096 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2299 | −0.877331 | −0.438665 | − | 0.898651i | \(-0.644549\pi\) | ||||
−0.438665 | + | 0.898651i | \(0.644549\pi\) | |||||||
\(828\) | −7.60829 | −0.264406 | ||||||||
\(829\) | −3.07175 | −0.106686 | −0.0533431 | − | 0.998576i | \(-0.516988\pi\) | ||||
−0.0533431 | + | 0.998576i | \(0.516988\pi\) | |||||||
\(830\) | −31.1880 | −1.08255 | ||||||||
\(831\) | 14.9619 | 0.519021 | ||||||||
\(832\) | 4.37963 | 0.151836 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.0206 | −1.28192 | ||||||||
\(835\) | −29.6566 | −1.02631 | ||||||||
\(836\) | −2.52145 | −0.0872061 | ||||||||
\(837\) | −19.2866 | −0.666643 | ||||||||
\(838\) | 12.0175 | 0.415139 | ||||||||
\(839\) | −51.1235 | −1.76498 | −0.882490 | − | 0.470331i | \(-0.844134\pi\) | ||||
−0.882490 | + | 0.470331i | \(0.844134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9788 | −0.999271 | ||||||||
\(842\) | 30.7569 | 1.05995 | ||||||||
\(843\) | −57.1898 | −1.96972 | ||||||||
\(844\) | −3.92033 | −0.134943 | ||||||||
\(845\) | 17.0240 | 0.585644 | ||||||||
\(846\) | −8.06664 | −0.277337 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.12705 | −0.176063 | ||||||||
\(849\) | −34.3370 | −1.17844 | ||||||||
\(850\) | 5.00825 | 0.171782 | ||||||||
\(851\) | 44.8541 | 1.53758 | ||||||||
\(852\) | 9.01817 | 0.308957 | ||||||||
\(853\) | −12.6692 | −0.433786 | −0.216893 | − | 0.976195i | \(-0.569592\pi\) | ||||
−0.216893 | + | 0.976195i | \(0.569592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.3955 | −0.458118 | ||||||||
\(856\) | 4.00282 | 0.136814 | ||||||||
\(857\) | 23.7478 | 0.811209 | 0.405604 | − | 0.914049i | \(-0.367061\pi\) | ||||
0.405604 | + | 0.914049i | \(0.367061\pi\) | |||||||
\(858\) | 9.05467 | 0.309121 | ||||||||
\(859\) | 49.8074 | 1.69941 | 0.849703 | − | 0.527262i | \(-0.176781\pi\) | ||||
0.849703 | + | 0.527262i | \(0.176781\pi\) | |||||||
\(860\) | 23.7499 | 0.809866 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.72479 | 0.229047 | ||||||||
\(863\) | −27.8130 | −0.946767 | −0.473383 | − | 0.880857i | \(-0.656967\pi\) | ||||
−0.473383 | + | 0.880857i | \(0.656967\pi\) | |||||||
\(864\) | −2.59633 | −0.0883289 | ||||||||
\(865\) | 12.9266 | 0.439517 | ||||||||
\(866\) | 22.9072 | 0.778419 | ||||||||
\(867\) | −29.0754 | −0.987454 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7515 | −0.398642 | ||||||||
\(870\) | −0.879124 | −0.0298051 | ||||||||
\(871\) | 2.99712 | 0.101553 | ||||||||
\(872\) | 12.6076 | 0.426948 | ||||||||
\(873\) | 6.20921 | 0.210150 | ||||||||
\(874\) | 11.2080 | 0.379116 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.0650 | −1.11716 | ||||||||
\(877\) | 19.5541 | 0.660296 | 0.330148 | − | 0.943929i | \(-0.392901\pi\) | ||||
0.330148 | + | 0.943929i | \(0.392901\pi\) | |||||||
\(878\) | 35.0713 | 1.18360 | ||||||||
\(879\) | 11.5672 | 0.390152 | ||||||||
\(880\) | 2.59438 | 0.0874566 | ||||||||
\(881\) | 18.2391 | 0.614491 | 0.307245 | − | 0.951630i | \(-0.400593\pi\) | ||||
0.307245 | + | 0.951630i | \(0.400593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.7823 | 0.766685 | 0.383343 | − | 0.923606i | \(-0.374773\pi\) | ||||
0.383343 | + | 0.923606i | \(0.374773\pi\) | |||||||
\(884\) | 8.48388 | 0.285344 | ||||||||
\(885\) | 31.4507 | 1.05720 | ||||||||
\(886\) | −17.9822 | −0.604125 | ||||||||
\(887\) | 13.2431 | 0.444661 | 0.222331 | − | 0.974971i | \(-0.428634\pi\) | ||||
0.222331 | + | 0.974971i | \(0.428634\pi\) | |||||||
\(888\) | −23.5110 | −0.788977 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.3077 | 1.08296 | ||||||||
\(891\) | −10.5027 | −0.351852 | ||||||||
\(892\) | 19.3451 | 0.647722 | ||||||||
\(893\) | 11.8832 | 0.397656 | ||||||||
\(894\) | 29.2199 | 0.977259 | ||||||||
\(895\) | −5.11559 | −0.170995 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.2485 | −1.34386 | ||||||||
\(898\) | −7.69654 | −0.256837 | ||||||||
\(899\) | −1.08036 | −0.0360319 | ||||||||
\(900\) | 4.69780 | 0.156593 | ||||||||
\(901\) | −9.93170 | −0.330873 | ||||||||
\(902\) | −0.941986 | −0.0313647 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1114 | 0.535858 | ||||||||
\(905\) | −61.2799 | −2.03701 | ||||||||
\(906\) | −11.2548 | −0.373915 | ||||||||
\(907\) | −53.2128 | −1.76690 | −0.883451 | − | 0.468523i | \(-0.844786\pi\) | ||||
−0.883451 | + | 0.468523i | \(0.844786\pi\) | |||||||
\(908\) | −26.5527 | −0.881182 | ||||||||
\(909\) | −2.10658 | −0.0698708 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1992 | 0.669230 | 0.334615 | − | 0.942355i | \(-0.391394\pi\) | ||||
0.334615 | + | 0.942355i | \(0.391394\pi\) | |||||||
\(912\) | −5.87484 | −0.194535 | ||||||||
\(913\) | −10.6670 | −0.353026 | ||||||||
\(914\) | 29.8172 | 0.986264 | ||||||||
\(915\) | −6.97162 | −0.230475 | ||||||||
\(916\) | 8.09922 | 0.267606 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.02940 | −0.165995 | ||||||||
\(919\) | −43.2365 | −1.42624 | −0.713120 | − | 0.701042i | \(-0.752719\pi\) | ||||
−0.713120 | + | 0.701042i | \(0.752719\pi\) | |||||||
\(920\) | −11.5322 | −0.380205 | ||||||||
\(921\) | 20.0053 | 0.659198 | ||||||||
\(922\) | 23.7507 | 0.782187 | ||||||||
\(923\) | 17.9956 | 0.592332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.6956 | −0.910624 | ||||||||
\(926\) | −4.90522 | −0.161196 | ||||||||
\(927\) | −12.4039 | −0.407398 | ||||||||
\(928\) | −0.145436 | −0.00477416 | ||||||||
\(929\) | 25.8421 | 0.847853 | 0.423927 | − | 0.905697i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905697i | \(0.360651\pi\) | |||||||
\(930\) | 44.9031 | 1.47243 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.49252 | 0.245426 | ||||||||
\(933\) | −21.6376 | −0.708382 | ||||||||
\(934\) | 40.6774 | 1.33101 | ||||||||
\(935\) | 5.02563 | 0.164356 | ||||||||
\(936\) | 7.95798 | 0.260115 | ||||||||
\(937\) | 7.35449 | 0.240261 | 0.120130 | − | 0.992758i | \(-0.461669\pi\) | ||||
0.120130 | + | 0.992758i | \(0.461669\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.0131 | −1.86055 | ||||||||
\(940\) | −12.2269 | −0.398798 | ||||||||
\(941\) | −22.6999 | −0.739996 | −0.369998 | − | 0.929033i | \(-0.620642\pi\) | ||||
−0.369998 | + | 0.929033i | \(0.620642\pi\) | |||||||
\(942\) | 40.2372 | 1.31100 | ||||||||
\(943\) | 4.18718 | 0.136353 | ||||||||
\(944\) | 5.20297 | 0.169342 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.12302 | 0.264102 | ||||||||
\(947\) | 27.3941 | 0.890190 | 0.445095 | − | 0.895483i | \(-0.353170\pi\) | ||||
0.445095 | + | 0.895483i | \(0.353170\pi\) | |||||||
\(948\) | −27.3803 | −0.889272 | ||||||||
\(949\) | −65.9805 | −2.14182 | ||||||||
\(950\) | −6.92046 | −0.224529 | ||||||||
\(951\) | 30.9608 | 1.00397 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.15195 | −0.296461 | −0.148230 | − | 0.988953i | \(-0.547358\pi\) | ||||
−0.148230 | + | 0.988953i | \(0.547358\pi\) | |||||||
\(954\) | −9.31606 | −0.301619 | ||||||||
\(955\) | −55.1849 | −1.78574 | ||||||||
\(956\) | −6.63573 | −0.214615 | ||||||||
\(957\) | −0.300681 | −0.00971962 | ||||||||
\(958\) | 14.6318 | 0.472731 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.04477 | 0.195094 | ||||||||
\(961\) | 24.1814 | 0.780045 | ||||||||
\(962\) | −46.9157 | −1.51262 | ||||||||
\(963\) | 7.27330 | 0.234379 | ||||||||
\(964\) | −7.64140 | −0.246113 | ||||||||
\(965\) | 44.3569 | 1.42790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.02296 | −0.258001 | −0.129000 | − | 0.991645i | \(-0.541177\pi\) | ||||
−0.129000 | + | 0.991645i | \(0.541177\pi\) | |||||||
\(968\) | −10.1127 | −0.325033 | ||||||||
\(969\) | −11.3803 | −0.365587 | ||||||||
\(970\) | 9.41155 | 0.302187 | ||||||||
\(971\) | −48.0783 | −1.54291 | −0.771454 | − | 0.636285i | \(-0.780470\pi\) | ||||
−0.771454 | + | 0.636285i | \(0.780470\pi\) | |||||||
\(972\) | −16.6816 | −0.535064 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −38.1002 | −1.22081 | ||||||||
\(975\) | 24.8518 | 0.795894 | ||||||||
\(976\) | −1.15333 | −0.0369172 | ||||||||
\(977\) | 30.7114 | 0.982544 | 0.491272 | − | 0.871006i | \(-0.336532\pi\) | ||||
0.491272 | + | 0.871006i | \(0.336532\pi\) | |||||||
\(978\) | 23.3792 | 0.747585 | ||||||||
\(979\) | 11.0500 | 0.353158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.9086 | 0.731415 | ||||||||
\(982\) | −28.0295 | −0.894456 | ||||||||
\(983\) | −16.6343 | −0.530552 | −0.265276 | − | 0.964172i | \(-0.585463\pi\) | ||||
−0.265276 | + | 0.964172i | \(0.585463\pi\) | |||||||
\(984\) | −2.19478 | −0.0699669 | ||||||||
\(985\) | 40.6146 | 1.29409 | ||||||||
\(986\) | −0.281726 | −0.00897199 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.7231 | −0.372962 | ||||||||
\(989\) | −36.1073 | −1.14814 | ||||||||
\(990\) | 4.71410 | 0.149824 | ||||||||
\(991\) | −12.2790 | −0.390055 | −0.195028 | − | 0.980798i | \(-0.562480\pi\) | ||||
−0.195028 | + | 0.980798i | \(0.562480\pi\) | |||||||
\(992\) | 7.42842 | 0.235852 | ||||||||
\(993\) | 43.6003 | 1.38361 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 52.3900 | 1.66087 | ||||||||
\(996\) | −24.8535 | −0.787514 | ||||||||
\(997\) | 28.3184 | 0.896852 | 0.448426 | − | 0.893820i | \(-0.351985\pi\) | ||||
0.448426 | + | 0.893820i | \(0.351985\pi\) | |||||||
\(998\) | −9.47858 | −0.300039 | ||||||||
\(999\) | 27.8125 | 0.879949 |
(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 | 4018.2.a.bt.1.9 | 10 | ||
7.2 | even | 3 | 574.2.e.h.165.2 | ✓ | 20 | ||
7.4 | even | 3 | 574.2.e.h.247.2 | yes | 20 | ||
7.6 | odd | 2 | 4018.2.a.bu.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.h.165.2 | ✓ | 20 | 7.2 | even | 3 | ||
574.2.e.h.247.2 | yes | 20 | 7.4 | even | 3 | ||
4018.2.a.bt.1.9 | 10 | 1.1 | even | 1 | trivial | ||
4018.2.a.bu.1.2 | 10 | 7.6 | odd | 2 |