Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19064 | −0.841907 | −0.420954 | − | 0.907082i | \(-0.638304\pi\) | ||||
−0.420954 | + | 0.907082i | \(0.638304\pi\) | |||||||
\(3\) | −0.642478 | −0.370935 | −0.185468 | − | 0.982650i | \(-0.559380\pi\) | ||||
−0.185468 | + | 0.982650i | \(0.559380\pi\) | |||||||
\(4\) | −0.582384 | −0.291192 | ||||||||
\(5\) | −0.355693 | −0.159071 | −0.0795354 | − | 0.996832i | \(-0.525344\pi\) | ||||
−0.0795354 | + | 0.996832i | \(0.525344\pi\) | |||||||
\(6\) | 0.764958 | 0.312293 | ||||||||
\(7\) | 0.205071 | 0.0775096 | 0.0387548 | − | 0.999249i | \(-0.487661\pi\) | ||||
0.0387548 | + | 0.999249i | \(0.487661\pi\) | |||||||
\(8\) | 3.07468 | 1.08706 | ||||||||
\(9\) | −2.58722 | −0.862407 | ||||||||
\(10\) | 0.423501 | 0.133923 | ||||||||
\(11\) | −1.45264 | −0.437988 | −0.218994 | − | 0.975726i | \(-0.570278\pi\) | ||||
−0.218994 | + | 0.975726i | \(0.570278\pi\) | |||||||
\(12\) | 0.374169 | 0.108013 | ||||||||
\(13\) | 5.41909 | 1.50299 | 0.751493 | − | 0.659741i | \(-0.229334\pi\) | ||||
0.751493 | + | 0.659741i | \(0.229334\pi\) | |||||||
\(14\) | −0.244165 | −0.0652559 | ||||||||
\(15\) | 0.228525 | 0.0590049 | ||||||||
\(16\) | −2.49606 | −0.624015 | ||||||||
\(17\) | 4.41807 | 1.07154 | 0.535770 | − | 0.844364i | \(-0.320021\pi\) | ||||
0.535770 | + | 0.844364i | \(0.320021\pi\) | |||||||
\(18\) | 3.08044 | 0.726067 | ||||||||
\(19\) | −2.06625 | −0.474031 | −0.237016 | − | 0.971506i | \(-0.576169\pi\) | ||||
−0.237016 | + | 0.971506i | \(0.576169\pi\) | |||||||
\(20\) | 0.207150 | 0.0463202 | ||||||||
\(21\) | −0.131754 | −0.0287510 | ||||||||
\(22\) | 1.72957 | 0.368745 | ||||||||
\(23\) | −8.86978 | −1.84948 | −0.924738 | − | 0.380604i | \(-0.875716\pi\) | ||||
−0.924738 | + | 0.380604i | \(0.875716\pi\) | |||||||
\(24\) | −1.97542 | −0.403230 | ||||||||
\(25\) | −4.87348 | −0.974696 | ||||||||
\(26\) | −6.45217 | −1.26537 | ||||||||
\(27\) | 3.58967 | 0.690832 | ||||||||
\(28\) | −0.119430 | −0.0225702 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.272090 | −0.0496767 | ||||||||
\(31\) | 3.96844 | 0.712752 | 0.356376 | − | 0.934343i | \(-0.384012\pi\) | ||||
0.356376 | + | 0.934343i | \(0.384012\pi\) | |||||||
\(32\) | −3.17746 | −0.561701 | ||||||||
\(33\) | 0.933291 | 0.162465 | ||||||||
\(34\) | −5.26032 | −0.902137 | ||||||||
\(35\) | −0.0729423 | −0.0123295 | ||||||||
\(36\) | 1.50676 | 0.251126 | ||||||||
\(37\) | 4.45603 | 0.732566 | 0.366283 | − | 0.930503i | \(-0.380630\pi\) | ||||
0.366283 | + | 0.930503i | \(0.380630\pi\) | |||||||
\(38\) | 2.46016 | 0.399090 | ||||||||
\(39\) | −3.48165 | −0.557510 | ||||||||
\(40\) | −1.09364 | −0.172920 | ||||||||
\(41\) | 0.903757 | 0.141143 | 0.0705716 | − | 0.997507i | \(-0.477518\pi\) | ||||
0.0705716 | + | 0.997507i | \(0.477518\pi\) | |||||||
\(42\) | 0.156871 | 0.0242057 | ||||||||
\(43\) | −7.33633 | −1.11878 | −0.559390 | − | 0.828905i | \(-0.688965\pi\) | ||||
−0.559390 | + | 0.828905i | \(0.688965\pi\) | |||||||
\(44\) | 0.845996 | 0.127539 | ||||||||
\(45\) | 0.920257 | 0.137184 | ||||||||
\(46\) | 10.5607 | 1.55709 | ||||||||
\(47\) | 4.59729 | 0.670584 | 0.335292 | − | 0.942114i | \(-0.391165\pi\) | ||||
0.335292 | + | 0.942114i | \(0.391165\pi\) | |||||||
\(48\) | 1.60366 | 0.231469 | ||||||||
\(49\) | −6.95795 | −0.993992 | ||||||||
\(50\) | 5.80255 | 0.820604 | ||||||||
\(51\) | −2.83852 | −0.397472 | ||||||||
\(52\) | −3.15600 | −0.437658 | ||||||||
\(53\) | 5.01563 | 0.688949 | 0.344475 | − | 0.938796i | \(-0.388057\pi\) | ||||
0.344475 | + | 0.938796i | \(0.388057\pi\) | |||||||
\(54\) | −4.27399 | −0.581617 | ||||||||
\(55\) | 0.516695 | 0.0696711 | ||||||||
\(56\) | 0.630528 | 0.0842579 | ||||||||
\(57\) | 1.32752 | 0.175835 | ||||||||
\(58\) | 1.19064 | 0.156338 | ||||||||
\(59\) | 14.0025 | 1.82297 | 0.911486 | − | 0.411330i | \(-0.134936\pi\) | ||||
0.911486 | + | 0.411330i | \(0.134936\pi\) | |||||||
\(60\) | −0.133089 | −0.0171818 | ||||||||
\(61\) | −8.00492 | −1.02492 | −0.512462 | − | 0.858710i | \(-0.671267\pi\) | ||||
−0.512462 | + | 0.858710i | \(0.671267\pi\) | |||||||
\(62\) | −4.72497 | −0.600071 | ||||||||
\(63\) | −0.530564 | −0.0668448 | ||||||||
\(64\) | 8.77532 | 1.09692 | ||||||||
\(65\) | −1.92753 | −0.239081 | ||||||||
\(66\) | −1.11121 | −0.136781 | ||||||||
\(67\) | 2.21279 | 0.270335 | 0.135168 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135168 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(68\) | −2.57302 | −0.312024 | ||||||||
\(69\) | 5.69864 | 0.686036 | ||||||||
\(70\) | 0.0868478 | 0.0103803 | ||||||||
\(71\) | 14.1001 | 1.67338 | 0.836688 | − | 0.547680i | \(-0.184489\pi\) | ||||
0.836688 | + | 0.547680i | \(0.184489\pi\) | |||||||
\(72\) | −7.95488 | −0.937492 | ||||||||
\(73\) | 7.81827 | 0.915060 | 0.457530 | − | 0.889194i | \(-0.348734\pi\) | ||||
0.457530 | + | 0.889194i | \(0.348734\pi\) | |||||||
\(74\) | −5.30551 | −0.616753 | ||||||||
\(75\) | 3.13111 | 0.361549 | ||||||||
\(76\) | 1.20335 | 0.138034 | ||||||||
\(77\) | −0.297895 | −0.0339483 | ||||||||
\(78\) | 4.14538 | 0.469372 | ||||||||
\(79\) | 4.40777 | 0.495913 | 0.247957 | − | 0.968771i | \(-0.420241\pi\) | ||||
0.247957 | + | 0.968771i | \(0.420241\pi\) | |||||||
\(80\) | 0.887831 | 0.0992625 | ||||||||
\(81\) | 5.45538 | 0.606153 | ||||||||
\(82\) | −1.07605 | −0.118829 | ||||||||
\(83\) | −12.1163 | −1.32994 | −0.664970 | − | 0.746870i | \(-0.731556\pi\) | ||||
−0.664970 | + | 0.746870i | \(0.731556\pi\) | |||||||
\(84\) | 0.0767313 | 0.00837207 | ||||||||
\(85\) | −1.57148 | −0.170451 | ||||||||
\(86\) | 8.73490 | 0.941909 | ||||||||
\(87\) | 0.642478 | 0.0688809 | ||||||||
\(88\) | −4.46641 | −0.476121 | ||||||||
\(89\) | 0.417775 | 0.0442841 | 0.0221420 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221420 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(90\) | −1.09569 | −0.115496 | ||||||||
\(91\) | 1.11130 | 0.116496 | ||||||||
\(92\) | 5.16562 | 0.538553 | ||||||||
\(93\) | −2.54964 | −0.264385 | ||||||||
\(94\) | −5.47371 | −0.564570 | ||||||||
\(95\) | 0.734952 | 0.0754045 | ||||||||
\(96\) | 2.04145 | 0.208355 | ||||||||
\(97\) | −4.93875 | −0.501454 | −0.250727 | − | 0.968058i | \(-0.580670\pi\) | ||||
−0.250727 | + | 0.968058i | \(0.580670\pi\) | |||||||
\(98\) | 8.28439 | 0.836849 | ||||||||
\(99\) | 3.75831 | 0.377724 | ||||||||
\(100\) | 2.83824 | 0.283824 | ||||||||
\(101\) | −17.1886 | −1.71033 | −0.855167 | − | 0.518353i | \(-0.826545\pi\) | ||||
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(102\) | 3.37964 | 0.334634 | ||||||||
\(103\) | 12.3007 | 1.21203 | 0.606013 | − | 0.795455i | \(-0.292768\pi\) | ||||
0.606013 | + | 0.795455i | \(0.292768\pi\) | |||||||
\(104\) | 16.6620 | 1.63384 | ||||||||
\(105\) | 0.0468639 | 0.00457345 | ||||||||
\(106\) | −5.97179 | −0.580031 | ||||||||
\(107\) | 9.54320 | 0.922576 | 0.461288 | − | 0.887250i | \(-0.347387\pi\) | ||||
0.461288 | + | 0.887250i | \(0.347387\pi\) | |||||||
\(108\) | −2.09057 | −0.201165 | ||||||||
\(109\) | 0.0890247 | 0.00852702 | 0.00426351 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426351 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(110\) | −0.615195 | −0.0586566 | ||||||||
\(111\) | −2.86290 | −0.271735 | ||||||||
\(112\) | −0.511870 | −0.0483671 | ||||||||
\(113\) | −17.4313 | −1.63979 | −0.819897 | − | 0.572511i | \(-0.805970\pi\) | ||||
−0.819897 | + | 0.572511i | \(0.805970\pi\) | |||||||
\(114\) | −1.58060 | −0.148037 | ||||||||
\(115\) | 3.15492 | 0.294198 | ||||||||
\(116\) | 0.582384 | 0.0540730 | ||||||||
\(117\) | −14.0204 | −1.29619 | ||||||||
\(118\) | −16.6719 | −1.53477 | ||||||||
\(119\) | 0.906019 | 0.0830546 | ||||||||
\(120\) | 0.702642 | 0.0641421 | ||||||||
\(121\) | −8.88983 | −0.808167 | ||||||||
\(122\) | 9.53095 | 0.862891 | ||||||||
\(123\) | −0.580644 | −0.0523549 | ||||||||
\(124\) | −2.31116 | −0.207548 | ||||||||
\(125\) | 3.51193 | 0.314116 | ||||||||
\(126\) | 0.631709 | 0.0562771 | ||||||||
\(127\) | −15.6074 | −1.38494 | −0.692468 | − | 0.721449i | \(-0.743476\pi\) | ||||
−0.692468 | + | 0.721449i | \(0.743476\pi\) | |||||||
\(128\) | −4.09329 | −0.361800 | ||||||||
\(129\) | 4.71343 | 0.414995 | ||||||||
\(130\) | 2.29499 | 0.201284 | ||||||||
\(131\) | 14.2133 | 1.24182 | 0.620912 | − | 0.783880i | \(-0.286762\pi\) | ||||
0.620912 | + | 0.783880i | \(0.286762\pi\) | |||||||
\(132\) | −0.543534 | −0.0473086 | ||||||||
\(133\) | −0.423729 | −0.0367420 | ||||||||
\(134\) | −2.63463 | −0.227597 | ||||||||
\(135\) | −1.27682 | −0.109891 | ||||||||
\(136\) | 13.5842 | 1.16483 | ||||||||
\(137\) | 5.70508 | 0.487418 | 0.243709 | − | 0.969848i | \(-0.421636\pi\) | ||||
0.243709 | + | 0.969848i | \(0.421636\pi\) | |||||||
\(138\) | −6.78501 | −0.577578 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 0.0424805 | 0.00359026 | ||||||||
\(141\) | −2.95366 | −0.248743 | ||||||||
\(142\) | −16.7881 | −1.40883 | ||||||||
\(143\) | −7.87200 | −0.658290 | ||||||||
\(144\) | 6.45786 | 0.538155 | ||||||||
\(145\) | 0.355693 | 0.0295387 | ||||||||
\(146\) | −9.30872 | −0.770395 | ||||||||
\(147\) | 4.47033 | 0.368707 | ||||||||
\(148\) | −2.59512 | −0.213318 | ||||||||
\(149\) | −9.98175 | −0.817737 | −0.408869 | − | 0.912593i | \(-0.634077\pi\) | ||||
−0.408869 | + | 0.912593i | \(0.634077\pi\) | |||||||
\(150\) | −3.72801 | −0.304391 | ||||||||
\(151\) | 7.35339 | 0.598410 | 0.299205 | − | 0.954189i | \(-0.403278\pi\) | ||||
0.299205 | + | 0.954189i | \(0.403278\pi\) | |||||||
\(152\) | −6.35307 | −0.515302 | ||||||||
\(153\) | −11.4305 | −0.924104 | ||||||||
\(154\) | 0.354684 | 0.0285813 | ||||||||
\(155\) | −1.41155 | −0.113378 | ||||||||
\(156\) | 2.02766 | 0.162343 | ||||||||
\(157\) | −16.5721 | −1.32259 | −0.661297 | − | 0.750124i | \(-0.729994\pi\) | ||||
−0.661297 | + | 0.750124i | \(0.729994\pi\) | |||||||
\(158\) | −5.24806 | −0.417513 | ||||||||
\(159\) | −3.22243 | −0.255555 | ||||||||
\(160\) | 1.13020 | 0.0893503 | ||||||||
\(161\) | −1.81893 | −0.143352 | ||||||||
\(162\) | −6.49537 | −0.510325 | ||||||||
\(163\) | −15.6672 | −1.22715 | −0.613575 | − | 0.789636i | \(-0.710269\pi\) | ||||
−0.613575 | + | 0.789636i | \(0.710269\pi\) | |||||||
\(164\) | −0.526334 | −0.0410998 | ||||||||
\(165\) | −0.331965 | −0.0258434 | ||||||||
\(166\) | 14.4262 | 1.11969 | ||||||||
\(167\) | 5.65637 | 0.437703 | 0.218852 | − | 0.975758i | \(-0.429769\pi\) | ||||
0.218852 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(168\) | −0.405101 | −0.0312542 | ||||||||
\(169\) | 16.3666 | 1.25897 | ||||||||
\(170\) | 1.87106 | 0.143504 | ||||||||
\(171\) | 5.34586 | 0.408808 | ||||||||
\(172\) | 4.27256 | 0.325780 | ||||||||
\(173\) | −7.61704 | −0.579113 | −0.289556 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289556 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(174\) | −0.764958 | −0.0579913 | ||||||||
\(175\) | −0.999410 | −0.0755483 | ||||||||
\(176\) | 3.62588 | 0.273311 | ||||||||
\(177\) | −8.99632 | −0.676205 | ||||||||
\(178\) | −0.497418 | −0.0372831 | ||||||||
\(179\) | 13.4824 | 1.00772 | 0.503862 | − | 0.863784i | \(-0.331912\pi\) | ||||
0.503862 | + | 0.863784i | \(0.331912\pi\) | |||||||
\(180\) | −0.535943 | −0.0399468 | ||||||||
\(181\) | −0.207060 | −0.0153906 | −0.00769531 | − | 0.999970i | \(-0.502450\pi\) | ||||
−0.00769531 | + | 0.999970i | \(0.502450\pi\) | |||||||
\(182\) | −1.32315 | −0.0980786 | ||||||||
\(183\) | 5.14299 | 0.380180 | ||||||||
\(184\) | −27.2717 | −2.01050 | ||||||||
\(185\) | −1.58498 | −0.116530 | ||||||||
\(186\) | 3.03569 | 0.222588 | ||||||||
\(187\) | −6.41788 | −0.469322 | ||||||||
\(188\) | −2.67739 | −0.195269 | ||||||||
\(189\) | 0.736137 | 0.0535461 | ||||||||
\(190\) | −0.875061 | −0.0634836 | ||||||||
\(191\) | −12.5549 | −0.908440 | −0.454220 | − | 0.890890i | \(-0.650082\pi\) | ||||
−0.454220 | + | 0.890890i | \(0.650082\pi\) | |||||||
\(192\) | −5.63796 | −0.406884 | ||||||||
\(193\) | −11.6429 | −0.838071 | −0.419035 | − | 0.907970i | \(-0.637632\pi\) | ||||
−0.419035 | + | 0.907970i | \(0.637632\pi\) | |||||||
\(194\) | 5.88026 | 0.422178 | ||||||||
\(195\) | 1.23840 | 0.0886836 | ||||||||
\(196\) | 4.05220 | 0.289443 | ||||||||
\(197\) | −2.51796 | −0.179397 | −0.0896985 | − | 0.995969i | \(-0.528590\pi\) | ||||
−0.0896985 | + | 0.995969i | \(0.528590\pi\) | |||||||
\(198\) | −4.47478 | −0.318009 | ||||||||
\(199\) | 9.26997 | 0.657130 | 0.328565 | − | 0.944481i | \(-0.393435\pi\) | ||||
0.328565 | + | 0.944481i | \(0.393435\pi\) | |||||||
\(200\) | −14.9844 | −1.05956 | ||||||||
\(201\) | −1.42167 | −0.100277 | ||||||||
\(202\) | 20.4654 | 1.43994 | ||||||||
\(203\) | −0.205071 | −0.0143932 | ||||||||
\(204\) | 1.65311 | 0.115741 | ||||||||
\(205\) | −0.321460 | −0.0224517 | ||||||||
\(206\) | −14.6457 | −1.02041 | ||||||||
\(207\) | 22.9481 | 1.59500 | ||||||||
\(208\) | −13.5264 | −0.937886 | ||||||||
\(209\) | 3.00153 | 0.207620 | ||||||||
\(210\) | −0.0557979 | −0.00385042 | ||||||||
\(211\) | 22.0221 | 1.51606 | 0.758031 | − | 0.652219i | \(-0.226162\pi\) | ||||
0.758031 | + | 0.652219i | \(0.226162\pi\) | |||||||
\(212\) | −2.92102 | −0.200617 | ||||||||
\(213\) | −9.05902 | −0.620714 | ||||||||
\(214\) | −11.3625 | −0.776724 | ||||||||
\(215\) | 2.60948 | 0.177965 | ||||||||
\(216\) | 11.0371 | 0.750979 | ||||||||
\(217\) | 0.813812 | 0.0552451 | ||||||||
\(218\) | −0.105996 | −0.00717896 | ||||||||
\(219\) | −5.02307 | −0.339428 | ||||||||
\(220\) | −0.300915 | −0.0202877 | ||||||||
\(221\) | 23.9419 | 1.61051 | ||||||||
\(222\) | 3.40868 | 0.228775 | ||||||||
\(223\) | −10.0768 | −0.674792 | −0.337396 | − | 0.941363i | \(-0.609546\pi\) | ||||
−0.337396 | + | 0.941363i | \(0.609546\pi\) | |||||||
\(224\) | −0.651606 | −0.0435372 | ||||||||
\(225\) | 12.6088 | 0.840585 | ||||||||
\(226\) | 20.7543 | 1.38055 | ||||||||
\(227\) | −28.4152 | −1.88598 | −0.942992 | − | 0.332815i | \(-0.892001\pi\) | ||||
−0.942992 | + | 0.332815i | \(0.892001\pi\) | |||||||
\(228\) | −0.773129 | −0.0512017 | ||||||||
\(229\) | −1.53508 | −0.101441 | −0.0507205 | − | 0.998713i | \(-0.516152\pi\) | ||||
−0.0507205 | + | 0.998713i | \(0.516152\pi\) | |||||||
\(230\) | −3.75636 | −0.247687 | ||||||||
\(231\) | 0.191391 | 0.0125926 | ||||||||
\(232\) | −3.07468 | −0.201863 | ||||||||
\(233\) | −14.7123 | −0.963833 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(234\) | 16.6932 | 1.09127 | ||||||||
\(235\) | −1.63523 | −0.106670 | ||||||||
\(236\) | −8.15485 | −0.530836 | ||||||||
\(237\) | −2.83190 | −0.183952 | ||||||||
\(238\) | −1.07874 | −0.0699243 | ||||||||
\(239\) | −9.57934 | −0.619636 | −0.309818 | − | 0.950796i | \(-0.600268\pi\) | ||||
−0.309818 | + | 0.950796i | \(0.600268\pi\) | |||||||
\(240\) | −0.570412 | −0.0368200 | ||||||||
\(241\) | −24.9634 | −1.60803 | −0.804017 | − | 0.594607i | \(-0.797308\pi\) | ||||
−0.804017 | + | 0.594607i | \(0.797308\pi\) | |||||||
\(242\) | 10.5846 | 0.680401 | ||||||||
\(243\) | −14.2740 | −0.915676 | ||||||||
\(244\) | 4.66194 | 0.298450 | ||||||||
\(245\) | 2.47489 | 0.158115 | ||||||||
\(246\) | 0.691336 | 0.0440780 | ||||||||
\(247\) | −11.1972 | −0.712462 | ||||||||
\(248\) | 12.2017 | 0.774808 | ||||||||
\(249\) | 7.78448 | 0.493322 | ||||||||
\(250\) | −4.18143 | −0.264457 | ||||||||
\(251\) | 16.7502 | 1.05726 | 0.528630 | − | 0.848852i | \(-0.322706\pi\) | ||||
0.528630 | + | 0.848852i | \(0.322706\pi\) | |||||||
\(252\) | 0.308992 | 0.0194647 | ||||||||
\(253\) | 12.8846 | 0.810048 | ||||||||
\(254\) | 18.5828 | 1.16599 | ||||||||
\(255\) | 1.00964 | 0.0632262 | ||||||||
\(256\) | −12.6770 | −0.792314 | ||||||||
\(257\) | 29.4059 | 1.83429 | 0.917143 | − | 0.398557i | \(-0.130489\pi\) | ||||
0.917143 | + | 0.398557i | \(0.130489\pi\) | |||||||
\(258\) | −5.61199 | −0.349387 | ||||||||
\(259\) | 0.913802 | 0.0567809 | ||||||||
\(260\) | 1.12257 | 0.0696186 | ||||||||
\(261\) | 2.58722 | 0.160145 | ||||||||
\(262\) | −16.9229 | −1.04550 | ||||||||
\(263\) | 11.5930 | 0.714854 | 0.357427 | − | 0.933941i | \(-0.383654\pi\) | ||||
0.357427 | + | 0.933941i | \(0.383654\pi\) | |||||||
\(264\) | 2.86957 | 0.176610 | ||||||||
\(265\) | −1.78402 | −0.109592 | ||||||||
\(266\) | 0.504507 | 0.0309333 | ||||||||
\(267\) | −0.268412 | −0.0164265 | ||||||||
\(268\) | −1.28869 | −0.0787195 | ||||||||
\(269\) | −0.906001 | −0.0552398 | −0.0276199 | − | 0.999618i | \(-0.508793\pi\) | ||||
−0.0276199 | + | 0.999618i | \(0.508793\pi\) | |||||||
\(270\) | 1.52023 | 0.0925182 | ||||||||
\(271\) | −21.1256 | −1.28329 | −0.641644 | − | 0.767003i | \(-0.721747\pi\) | ||||
−0.641644 | + | 0.767003i | \(0.721747\pi\) | |||||||
\(272\) | −11.0278 | −0.668657 | ||||||||
\(273\) | −0.713986 | −0.0432124 | ||||||||
\(274\) | −6.79268 | −0.410361 | ||||||||
\(275\) | 7.07942 | 0.426905 | ||||||||
\(276\) | −3.31880 | −0.199768 | ||||||||
\(277\) | 3.59494 | 0.215999 | 0.108000 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108000 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(278\) | 1.19064 | 0.0714096 | ||||||||
\(279\) | −10.2672 | −0.614683 | ||||||||
\(280\) | −0.224274 | −0.0134030 | ||||||||
\(281\) | −22.2466 | −1.32712 | −0.663562 | − | 0.748122i | \(-0.730956\pi\) | ||||
−0.663562 | + | 0.748122i | \(0.730956\pi\) | |||||||
\(282\) | 3.51674 | 0.209419 | ||||||||
\(283\) | 7.67119 | 0.456005 | 0.228003 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228003 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(284\) | −8.21168 | −0.487274 | ||||||||
\(285\) | −0.472191 | −0.0279702 | ||||||||
\(286\) | 9.37269 | 0.554219 | ||||||||
\(287\) | 0.185334 | 0.0109399 | ||||||||
\(288\) | 8.22080 | 0.484415 | ||||||||
\(289\) | 2.51937 | 0.148198 | ||||||||
\(290\) | −0.423501 | −0.0248688 | ||||||||
\(291\) | 3.17304 | 0.186007 | ||||||||
\(292\) | −4.55324 | −0.266458 | ||||||||
\(293\) | −26.0696 | −1.52300 | −0.761500 | − | 0.648164i | \(-0.775537\pi\) | ||||
−0.761500 | + | 0.648164i | \(0.775537\pi\) | |||||||
\(294\) | −5.32254 | −0.310417 | ||||||||
\(295\) | −4.98060 | −0.289982 | ||||||||
\(296\) | 13.7009 | 0.796347 | ||||||||
\(297\) | −5.21450 | −0.302576 | ||||||||
\(298\) | 11.8846 | 0.688459 | ||||||||
\(299\) | −48.0661 | −2.77974 | ||||||||
\(300\) | −1.82351 | −0.105280 | ||||||||
\(301\) | −1.50447 | −0.0867161 | ||||||||
\(302\) | −8.75521 | −0.503806 | ||||||||
\(303\) | 11.0433 | 0.634423 | ||||||||
\(304\) | 5.15749 | 0.295803 | ||||||||
\(305\) | 2.84729 | 0.163036 | ||||||||
\(306\) | 13.6096 | 0.778010 | ||||||||
\(307\) | 12.6116 | 0.719785 | 0.359892 | − | 0.932994i | \(-0.382813\pi\) | ||||
0.359892 | + | 0.932994i | \(0.382813\pi\) | |||||||
\(308\) | 0.173489 | 0.00988547 | ||||||||
\(309\) | −7.90295 | −0.449583 | ||||||||
\(310\) | 1.68064 | 0.0954538 | ||||||||
\(311\) | −10.1650 | −0.576404 | −0.288202 | − | 0.957570i | \(-0.593057\pi\) | ||||
−0.288202 | + | 0.957570i | \(0.593057\pi\) | |||||||
\(312\) | −10.7050 | −0.606049 | ||||||||
\(313\) | −12.1093 | −0.684458 | −0.342229 | − | 0.939617i | \(-0.611182\pi\) | ||||
−0.342229 | + | 0.939617i | \(0.611182\pi\) | |||||||
\(314\) | 19.7313 | 1.11350 | ||||||||
\(315\) | 0.188718 | 0.0106331 | ||||||||
\(316\) | −2.56702 | −0.144406 | ||||||||
\(317\) | −8.74270 | −0.491039 | −0.245519 | − | 0.969392i | \(-0.578958\pi\) | ||||
−0.245519 | + | 0.969392i | \(0.578958\pi\) | |||||||
\(318\) | 3.83675 | 0.215154 | ||||||||
\(319\) | 1.45264 | 0.0813323 | ||||||||
\(320\) | −3.12132 | −0.174487 | ||||||||
\(321\) | −6.13130 | −0.342216 | ||||||||
\(322\) | 2.16569 | 0.120689 | ||||||||
\(323\) | −9.12886 | −0.507944 | ||||||||
\(324\) | −3.17713 | −0.176507 | ||||||||
\(325\) | −26.4099 | −1.46496 | ||||||||
\(326\) | 18.6540 | 1.03315 | ||||||||
\(327\) | −0.0571965 | −0.00316297 | ||||||||
\(328\) | 2.77876 | 0.153432 | ||||||||
\(329\) | 0.942772 | 0.0519767 | ||||||||
\(330\) | 0.395250 | 0.0217578 | ||||||||
\(331\) | −30.2894 | −1.66486 | −0.832428 | − | 0.554133i | \(-0.813050\pi\) | ||||
−0.832428 | + | 0.554133i | \(0.813050\pi\) | |||||||
\(332\) | 7.05637 | 0.387268 | ||||||||
\(333\) | −11.5287 | −0.631771 | ||||||||
\(334\) | −6.73469 | −0.368506 | ||||||||
\(335\) | −0.787074 | −0.0430024 | ||||||||
\(336\) | 0.328865 | 0.0179411 | ||||||||
\(337\) | 6.26840 | 0.341462 | 0.170731 | − | 0.985318i | \(-0.445387\pi\) | ||||
0.170731 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(338\) | −19.4866 | −1.05993 | ||||||||
\(339\) | 11.1992 | 0.608257 | ||||||||
\(340\) | 0.915204 | 0.0496339 | ||||||||
\(341\) | −5.76472 | −0.312177 | ||||||||
\(342\) | −6.36497 | −0.344178 | ||||||||
\(343\) | −2.86237 | −0.154553 | ||||||||
\(344\) | −22.5569 | −1.21619 | ||||||||
\(345\) | −2.02697 | −0.109128 | ||||||||
\(346\) | 9.06912 | 0.487559 | ||||||||
\(347\) | −17.0573 | −0.915683 | −0.457842 | − | 0.889034i | \(-0.651377\pi\) | ||||
−0.457842 | + | 0.889034i | \(0.651377\pi\) | |||||||
\(348\) | −0.374169 | −0.0200576 | ||||||||
\(349\) | −14.9784 | −0.801778 | −0.400889 | − | 0.916127i | \(-0.631299\pi\) | ||||
−0.400889 | + | 0.916127i | \(0.631299\pi\) | |||||||
\(350\) | 1.18993 | 0.0636047 | ||||||||
\(351\) | 19.4528 | 1.03831 | ||||||||
\(352\) | 4.61572 | 0.246018 | ||||||||
\(353\) | 25.5484 | 1.35980 | 0.679902 | − | 0.733303i | \(-0.262022\pi\) | ||||
0.679902 | + | 0.733303i | \(0.262022\pi\) | |||||||
\(354\) | 10.7113 | 0.569302 | ||||||||
\(355\) | −5.01531 | −0.266185 | ||||||||
\(356\) | −0.243306 | −0.0128952 | ||||||||
\(357\) | −0.582098 | −0.0308079 | ||||||||
\(358\) | −16.0527 | −0.848410 | ||||||||
\(359\) | −12.2029 | −0.644044 | −0.322022 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322022 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(360\) | 2.82950 | 0.149128 | ||||||||
\(361\) | −14.7306 | −0.775294 | ||||||||
\(362\) | 0.246533 | 0.0129575 | ||||||||
\(363\) | 5.71153 | 0.299777 | ||||||||
\(364\) | −0.647203 | −0.0339227 | ||||||||
\(365\) | −2.78091 | −0.145559 | ||||||||
\(366\) | −6.12343 | −0.320077 | ||||||||
\(367\) | 20.3731 | 1.06347 | 0.531733 | − | 0.846912i | \(-0.321541\pi\) | ||||
0.531733 | + | 0.846912i | \(0.321541\pi\) | |||||||
\(368\) | 22.1395 | 1.15410 | ||||||||
\(369\) | −2.33822 | −0.121723 | ||||||||
\(370\) | 1.88713 | 0.0981074 | ||||||||
\(371\) | 1.02856 | 0.0534002 | ||||||||
\(372\) | 1.48487 | 0.0769868 | ||||||||
\(373\) | −8.01136 | −0.414813 | −0.207406 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207406 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(374\) | 7.64136 | 0.395125 | ||||||||
\(375\) | −2.25634 | −0.116517 | ||||||||
\(376\) | 14.1352 | 0.728968 | ||||||||
\(377\) | −5.41909 | −0.279097 | ||||||||
\(378\) | −0.876472 | −0.0450809 | ||||||||
\(379\) | −18.3147 | −0.940765 | −0.470383 | − | 0.882463i | \(-0.655884\pi\) | ||||
−0.470383 | + | 0.882463i | \(0.655884\pi\) | |||||||
\(380\) | −0.428025 | −0.0219572 | ||||||||
\(381\) | 10.0274 | 0.513721 | ||||||||
\(382\) | 14.9483 | 0.764822 | ||||||||
\(383\) | −28.7048 | −1.46674 | −0.733372 | − | 0.679827i | \(-0.762055\pi\) | ||||
−0.733372 | + | 0.679827i | \(0.762055\pi\) | |||||||
\(384\) | 2.62985 | 0.134204 | ||||||||
\(385\) | 0.105959 | 0.00540018 | ||||||||
\(386\) | 13.8624 | 0.705578 | ||||||||
\(387\) | 18.9807 | 0.964844 | ||||||||
\(388\) | 2.87625 | 0.146020 | ||||||||
\(389\) | 8.10744 | 0.411063 | 0.205532 | − | 0.978650i | \(-0.434108\pi\) | ||||
0.205532 | + | 0.978650i | \(0.434108\pi\) | |||||||
\(390\) | −1.47448 | −0.0746633 | ||||||||
\(391\) | −39.1873 | −1.98179 | ||||||||
\(392\) | −21.3935 | −1.08053 | ||||||||
\(393\) | −9.13176 | −0.460636 | ||||||||
\(394\) | 2.99797 | 0.151036 | ||||||||
\(395\) | −1.56781 | −0.0788853 | ||||||||
\(396\) | −2.18878 | −0.109990 | ||||||||
\(397\) | −33.1119 | −1.66184 | −0.830918 | − | 0.556395i | \(-0.812184\pi\) | ||||
−0.830918 | + | 0.556395i | \(0.812184\pi\) | |||||||
\(398\) | −11.0372 | −0.553243 | ||||||||
\(399\) | 0.272237 | 0.0136289 | ||||||||
\(400\) | 12.1645 | 0.608225 | ||||||||
\(401\) | −12.0019 | −0.599345 | −0.299673 | − | 0.954042i | \(-0.596877\pi\) | ||||
−0.299673 | + | 0.954042i | \(0.596877\pi\) | |||||||
\(402\) | 1.69269 | 0.0844238 | ||||||||
\(403\) | 21.5053 | 1.07126 | ||||||||
\(404\) | 10.0104 | 0.498036 | ||||||||
\(405\) | −1.94044 | −0.0964213 | ||||||||
\(406\) | 0.244165 | 0.0121177 | ||||||||
\(407\) | −6.47301 | −0.320855 | ||||||||
\(408\) | −8.72754 | −0.432077 | ||||||||
\(409\) | 7.36671 | 0.364260 | 0.182130 | − | 0.983274i | \(-0.441701\pi\) | ||||
0.182130 | + | 0.983274i | \(0.441701\pi\) | |||||||
\(410\) | 0.382742 | 0.0189023 | ||||||||
\(411\) | −3.66539 | −0.180800 | ||||||||
\(412\) | −7.16375 | −0.352932 | ||||||||
\(413\) | 2.87151 | 0.141298 | ||||||||
\(414\) | −27.3228 | −1.34284 | ||||||||
\(415\) | 4.30970 | 0.211555 | ||||||||
\(416\) | −17.2190 | −0.844229 | ||||||||
\(417\) | 0.642478 | 0.0314623 | ||||||||
\(418\) | −3.57373 | −0.174797 | ||||||||
\(419\) | −26.2137 | −1.28062 | −0.640312 | − | 0.768115i | \(-0.721195\pi\) | ||||
−0.640312 | + | 0.768115i | \(0.721195\pi\) | |||||||
\(420\) | −0.0272928 | −0.00133175 | ||||||||
\(421\) | −2.44758 | −0.119288 | −0.0596439 | − | 0.998220i | \(-0.518997\pi\) | ||||
−0.0596439 | + | 0.998220i | \(0.518997\pi\) | |||||||
\(422\) | −26.2203 | −1.27638 | ||||||||
\(423\) | −11.8942 | −0.578317 | ||||||||
\(424\) | 15.4215 | 0.748932 | ||||||||
\(425\) | −21.5314 | −1.04443 | ||||||||
\(426\) | 10.7860 | 0.522583 | ||||||||
\(427\) | −1.64158 | −0.0794414 | ||||||||
\(428\) | −5.55781 | −0.268647 | ||||||||
\(429\) | 5.05759 | 0.244183 | ||||||||
\(430\) | −3.10694 | −0.149830 | ||||||||
\(431\) | −29.3222 | −1.41240 | −0.706200 | − | 0.708012i | \(-0.749592\pi\) | ||||
−0.706200 | + | 0.708012i | \(0.749592\pi\) | |||||||
\(432\) | −8.96003 | −0.431090 | ||||||||
\(433\) | −15.6425 | −0.751729 | −0.375865 | − | 0.926675i | \(-0.622654\pi\) | ||||
−0.375865 | + | 0.926675i | \(0.622654\pi\) | |||||||
\(434\) | −0.968954 | −0.0465113 | ||||||||
\(435\) | −0.228525 | −0.0109569 | ||||||||
\(436\) | −0.0518466 | −0.00248300 | ||||||||
\(437\) | 18.3272 | 0.876710 | ||||||||
\(438\) | 5.98065 | 0.285767 | ||||||||
\(439\) | 22.0197 | 1.05094 | 0.525472 | − | 0.850811i | \(-0.323889\pi\) | ||||
0.525472 | + | 0.850811i | \(0.323889\pi\) | |||||||
\(440\) | 1.58867 | 0.0757369 | ||||||||
\(441\) | 18.0017 | 0.857226 | ||||||||
\(442\) | −28.5062 | −1.35590 | ||||||||
\(443\) | −5.85508 | −0.278183 | −0.139092 | − | 0.990280i | \(-0.544418\pi\) | ||||
−0.139092 | + | 0.990280i | \(0.544418\pi\) | |||||||
\(444\) | 1.66731 | 0.0791270 | ||||||||
\(445\) | −0.148600 | −0.00704430 | ||||||||
\(446\) | 11.9978 | 0.568112 | ||||||||
\(447\) | 6.41306 | 0.303327 | ||||||||
\(448\) | 1.79956 | 0.0850214 | ||||||||
\(449\) | 27.0739 | 1.27770 | 0.638849 | − | 0.769332i | \(-0.279411\pi\) | ||||
0.638849 | + | 0.769332i | \(0.279411\pi\) | |||||||
\(450\) | −15.0125 | −0.707695 | ||||||||
\(451\) | −1.31283 | −0.0618190 | ||||||||
\(452\) | 10.1517 | 0.477495 | ||||||||
\(453\) | −4.72439 | −0.221971 | ||||||||
\(454\) | 33.8322 | 1.58782 | ||||||||
\(455\) | −0.395281 | −0.0185311 | ||||||||
\(456\) | 4.08171 | 0.191144 | ||||||||
\(457\) | −20.5286 | −0.960287 | −0.480143 | − | 0.877190i | \(-0.659415\pi\) | ||||
−0.480143 | + | 0.877190i | \(0.659415\pi\) | |||||||
\(458\) | 1.82772 | 0.0854039 | ||||||||
\(459\) | 15.8594 | 0.740254 | ||||||||
\(460\) | −1.83738 | −0.0856681 | ||||||||
\(461\) | −10.2320 | −0.476554 | −0.238277 | − | 0.971197i | \(-0.576583\pi\) | ||||
−0.238277 | + | 0.971197i | \(0.576583\pi\) | |||||||
\(462\) | −0.227877 | −0.0106018 | ||||||||
\(463\) | 12.9004 | 0.599534 | 0.299767 | − | 0.954012i | \(-0.403091\pi\) | ||||
0.299767 | + | 0.954012i | \(0.403091\pi\) | |||||||
\(464\) | 2.49606 | 0.115877 | ||||||||
\(465\) | 0.906888 | 0.0420559 | ||||||||
\(466\) | 17.5170 | 0.811458 | ||||||||
\(467\) | 34.2076 | 1.58294 | 0.791468 | − | 0.611210i | \(-0.209317\pi\) | ||||
0.791468 | + | 0.611210i | \(0.209317\pi\) | |||||||
\(468\) | 8.16526 | 0.377439 | ||||||||
\(469\) | 0.453779 | 0.0209536 | ||||||||
\(470\) | 1.94696 | 0.0898065 | ||||||||
\(471\) | 10.6472 | 0.490597 | ||||||||
\(472\) | 43.0533 | 1.98169 | ||||||||
\(473\) | 10.6571 | 0.490012 | ||||||||
\(474\) | 3.37176 | 0.154870 | ||||||||
\(475\) | 10.0699 | 0.462037 | ||||||||
\(476\) | −0.527651 | −0.0241849 | ||||||||
\(477\) | −12.9765 | −0.594155 | ||||||||
\(478\) | 11.4055 | 0.521676 | ||||||||
\(479\) | 23.8492 | 1.08970 | 0.544848 | − | 0.838535i | \(-0.316587\pi\) | ||||
0.544848 | + | 0.838535i | \(0.316587\pi\) | |||||||
\(480\) | −0.726130 | −0.0331432 | ||||||||
\(481\) | 24.1476 | 1.10104 | ||||||||
\(482\) | 29.7223 | 1.35382 | ||||||||
\(483\) | 1.16863 | 0.0531743 | ||||||||
\(484\) | 5.17730 | 0.235332 | ||||||||
\(485\) | 1.75668 | 0.0797667 | ||||||||
\(486\) | 16.9951 | 0.770914 | ||||||||
\(487\) | −9.80750 | −0.444420 | −0.222210 | − | 0.974999i | \(-0.571327\pi\) | ||||
−0.222210 | + | 0.974999i | \(0.571327\pi\) | |||||||
\(488\) | −24.6126 | −1.11416 | ||||||||
\(489\) | 10.0658 | 0.455193 | ||||||||
\(490\) | −2.94670 | −0.133118 | ||||||||
\(491\) | 24.9459 | 1.12579 | 0.562897 | − | 0.826527i | \(-0.309687\pi\) | ||||
0.562897 | + | 0.826527i | \(0.309687\pi\) | |||||||
\(492\) | 0.338158 | 0.0152453 | ||||||||
\(493\) | −4.41807 | −0.198980 | ||||||||
\(494\) | 13.3318 | 0.599827 | ||||||||
\(495\) | −1.33680 | −0.0600848 | ||||||||
\(496\) | −9.90546 | −0.444768 | ||||||||
\(497\) | 2.89152 | 0.129703 | ||||||||
\(498\) | −9.26849 | −0.415331 | ||||||||
\(499\) | 25.9373 | 1.16111 | 0.580557 | − | 0.814220i | \(-0.302835\pi\) | ||||
0.580557 | + | 0.814220i | \(0.302835\pi\) | |||||||
\(500\) | −2.04529 | −0.0914683 | ||||||||
\(501\) | −3.63410 | −0.162360 | ||||||||
\(502\) | −19.9434 | −0.890115 | ||||||||
\(503\) | −29.5903 | −1.31937 | −0.659683 | − | 0.751544i | \(-0.729309\pi\) | ||||
−0.659683 | + | 0.751544i | \(0.729309\pi\) | |||||||
\(504\) | −1.63132 | −0.0726646 | ||||||||
\(505\) | 6.11388 | 0.272064 | ||||||||
\(506\) | −15.3409 | −0.681986 | ||||||||
\(507\) | −10.5152 | −0.466995 | ||||||||
\(508\) | 9.08952 | 0.403282 | ||||||||
\(509\) | 1.26580 | 0.0561056 | 0.0280528 | − | 0.999606i | \(-0.491069\pi\) | ||||
0.0280528 | + | 0.999606i | \(0.491069\pi\) | |||||||
\(510\) | −1.20212 | −0.0532306 | ||||||||
\(511\) | 1.60330 | 0.0709259 | ||||||||
\(512\) | 23.2803 | 1.02885 | ||||||||
\(513\) | −7.41717 | −0.327476 | ||||||||
\(514\) | −35.0117 | −1.54430 | ||||||||
\(515\) | −4.37528 | −0.192798 | ||||||||
\(516\) | −2.74503 | −0.120843 | ||||||||
\(517\) | −6.67822 | −0.293708 | ||||||||
\(518\) | −1.08801 | −0.0478043 | ||||||||
\(519\) | 4.89378 | 0.214813 | ||||||||
\(520\) | −5.92655 | −0.259896 | ||||||||
\(521\) | 14.7646 | 0.646851 | 0.323425 | − | 0.946254i | \(-0.395166\pi\) | ||||
0.323425 | + | 0.946254i | \(0.395166\pi\) | |||||||
\(522\) | −3.08044 | −0.134827 | ||||||||
\(523\) | −8.03979 | −0.351556 | −0.175778 | − | 0.984430i | \(-0.556244\pi\) | ||||
−0.175778 | + | 0.984430i | \(0.556244\pi\) | |||||||
\(524\) | −8.27762 | −0.361610 | ||||||||
\(525\) | 0.642099 | 0.0280235 | ||||||||
\(526\) | −13.8030 | −0.601841 | ||||||||
\(527\) | 17.5328 | 0.763743 | ||||||||
\(528\) | −2.32955 | −0.101381 | ||||||||
\(529\) | 55.6730 | 2.42056 | ||||||||
\(530\) | 2.12412 | 0.0922660 | ||||||||
\(531\) | −36.2276 | −1.57214 | ||||||||
\(532\) | 0.246773 | 0.0106990 | ||||||||
\(533\) | 4.89754 | 0.212136 | ||||||||
\(534\) | 0.319581 | 0.0138296 | ||||||||
\(535\) | −3.39445 | −0.146755 | ||||||||
\(536\) | 6.80362 | 0.293872 | ||||||||
\(537\) | −8.66217 | −0.373800 | ||||||||
\(538\) | 1.07872 | 0.0465068 | ||||||||
\(539\) | 10.1074 | 0.435357 | ||||||||
\(540\) | 0.743600 | 0.0319995 | ||||||||
\(541\) | −26.5059 | −1.13958 | −0.569788 | − | 0.821792i | \(-0.692975\pi\) | ||||
−0.569788 | + | 0.821792i | \(0.692975\pi\) | |||||||
\(542\) | 25.1529 | 1.08041 | ||||||||
\(543\) | 0.133031 | 0.00570892 | ||||||||
\(544\) | −14.0383 | −0.601886 | ||||||||
\(545\) | −0.0316655 | −0.00135640 | ||||||||
\(546\) | 0.850097 | 0.0363808 | ||||||||
\(547\) | −11.2535 | −0.481164 | −0.240582 | − | 0.970629i | \(-0.577338\pi\) | ||||
−0.240582 | + | 0.970629i | \(0.577338\pi\) | |||||||
\(548\) | −3.32255 | −0.141932 | ||||||||
\(549\) | 20.7105 | 0.883902 | ||||||||
\(550\) | −8.42902 | −0.359415 | ||||||||
\(551\) | 2.06625 | 0.0880254 | ||||||||
\(552\) | 17.5215 | 0.745765 | ||||||||
\(553\) | 0.903906 | 0.0384380 | ||||||||
\(554\) | −4.28027 | −0.181851 | ||||||||
\(555\) | 1.01831 | 0.0432250 | ||||||||
\(556\) | 0.582384 | 0.0246986 | ||||||||
\(557\) | −2.55814 | −0.108392 | −0.0541959 | − | 0.998530i | \(-0.517260\pi\) | ||||
−0.0541959 | + | 0.998530i | \(0.517260\pi\) | |||||||
\(558\) | 12.2245 | 0.517506 | ||||||||
\(559\) | −39.7563 | −1.68151 | ||||||||
\(560\) | 0.182068 | 0.00769380 | ||||||||
\(561\) | 4.12335 | 0.174088 | ||||||||
\(562\) | 26.4877 | 1.11731 | ||||||||
\(563\) | 4.62470 | 0.194908 | 0.0974539 | − | 0.995240i | \(-0.468930\pi\) | ||||
0.0974539 | + | 0.995240i | \(0.468930\pi\) | |||||||
\(564\) | 1.72017 | 0.0724321 | ||||||||
\(565\) | 6.20018 | 0.260843 | ||||||||
\(566\) | −9.13361 | −0.383914 | ||||||||
\(567\) | 1.11874 | 0.0469827 | ||||||||
\(568\) | 43.3533 | 1.81907 | ||||||||
\(569\) | 14.2623 | 0.597908 | 0.298954 | − | 0.954268i | \(-0.403362\pi\) | ||||
0.298954 | + | 0.954268i | \(0.403362\pi\) | |||||||
\(570\) | 0.562208 | 0.0235483 | ||||||||
\(571\) | −17.1570 | −0.717998 | −0.358999 | − | 0.933338i | \(-0.616882\pi\) | ||||
−0.358999 | + | 0.933338i | \(0.616882\pi\) | |||||||
\(572\) | 4.58453 | 0.191689 | ||||||||
\(573\) | 8.06625 | 0.336972 | ||||||||
\(574\) | −0.220666 | −0.00921042 | ||||||||
\(575\) | 43.2267 | 1.80268 | ||||||||
\(576\) | −22.7037 | −0.945988 | ||||||||
\(577\) | −33.3203 | −1.38714 | −0.693570 | − | 0.720389i | \(-0.743963\pi\) | ||||
−0.693570 | + | 0.720389i | \(0.743963\pi\) | |||||||
\(578\) | −2.99966 | −0.124769 | ||||||||
\(579\) | 7.48028 | 0.310870 | ||||||||
\(580\) | −0.207150 | −0.00860144 | ||||||||
\(581\) | −2.48471 | −0.103083 | ||||||||
\(582\) | −3.77794 | −0.156601 | ||||||||
\(583\) | −7.28591 | −0.301752 | ||||||||
\(584\) | 24.0387 | 0.994729 | ||||||||
\(585\) | 4.98696 | 0.206185 | ||||||||
\(586\) | 31.0394 | 1.28223 | ||||||||
\(587\) | −2.03049 | −0.0838074 | −0.0419037 | − | 0.999122i | \(-0.513342\pi\) | ||||
−0.0419037 | + | 0.999122i | \(0.513342\pi\) | |||||||
\(588\) | −2.60345 | −0.107364 | ||||||||
\(589\) | −8.19980 | −0.337867 | ||||||||
\(590\) | 5.93008 | 0.244138 | ||||||||
\(591\) | 1.61773 | 0.0665447 | ||||||||
\(592\) | −11.1225 | −0.457132 | ||||||||
\(593\) | −17.4811 | −0.717865 | −0.358932 | − | 0.933364i | \(-0.616859\pi\) | ||||
−0.358932 | + | 0.933364i | \(0.616859\pi\) | |||||||
\(594\) | 6.20858 | 0.254741 | ||||||||
\(595\) | −0.322265 | −0.0132116 | ||||||||
\(596\) | 5.81322 | 0.238119 | ||||||||
\(597\) | −5.95575 | −0.243753 | ||||||||
\(598\) | 57.2293 | 2.34028 | ||||||||
\(599\) | 22.3362 | 0.912633 | 0.456317 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456317 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(600\) | 9.62716 | 0.393027 | ||||||||
\(601\) | −15.8799 | −0.647755 | −0.323878 | − | 0.946099i | \(-0.604987\pi\) | ||||
−0.323878 | + | 0.946099i | \(0.604987\pi\) | |||||||
\(602\) | 1.79128 | 0.0730070 | ||||||||
\(603\) | −5.72498 | −0.233139 | ||||||||
\(604\) | −4.28250 | −0.174252 | ||||||||
\(605\) | 3.16205 | 0.128556 | ||||||||
\(606\) | −13.1486 | −0.534125 | ||||||||
\(607\) | −47.5812 | −1.93126 | −0.965631 | − | 0.259917i | \(-0.916305\pi\) | ||||
−0.965631 | + | 0.259917i | \(0.916305\pi\) | |||||||
\(608\) | 6.56545 | 0.266264 | ||||||||
\(609\) | 0.131754 | 0.00533893 | ||||||||
\(610\) | −3.39009 | −0.137261 | ||||||||
\(611\) | 24.9132 | 1.00788 | ||||||||
\(612\) | 6.65697 | 0.269092 | ||||||||
\(613\) | −19.8166 | −0.800384 | −0.400192 | − | 0.916431i | \(-0.631057\pi\) | ||||
−0.400192 | + | 0.916431i | \(0.631057\pi\) | |||||||
\(614\) | −15.0159 | −0.605992 | ||||||||
\(615\) | 0.206531 | 0.00832814 | ||||||||
\(616\) | −0.915931 | −0.0369039 | ||||||||
\(617\) | 29.1135 | 1.17207 | 0.586033 | − | 0.810287i | \(-0.300689\pi\) | ||||
0.586033 | + | 0.810287i | \(0.300689\pi\) | |||||||
\(618\) | 9.40954 | 0.378507 | ||||||||
\(619\) | −3.48859 | −0.140218 | −0.0701092 | − | 0.997539i | \(-0.522335\pi\) | ||||
−0.0701092 | + | 0.997539i | \(0.522335\pi\) | |||||||
\(620\) | 0.822062 | 0.0330148 | ||||||||
\(621\) | −31.8396 | −1.27768 | ||||||||
\(622\) | 12.1028 | 0.485279 | ||||||||
\(623\) | 0.0856736 | 0.00343244 | ||||||||
\(624\) | 8.69041 | 0.347895 | ||||||||
\(625\) | 23.1182 | 0.924730 | ||||||||
\(626\) | 14.4178 | 0.576250 | ||||||||
\(627\) | −1.92842 | −0.0770135 | ||||||||
\(628\) | 9.65131 | 0.385129 | ||||||||
\(629\) | 19.6871 | 0.784974 | ||||||||
\(630\) | −0.224695 | −0.00895205 | ||||||||
\(631\) | 5.68558 | 0.226339 | 0.113170 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113170 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(632\) | 13.5525 | 0.539089 | ||||||||
\(633\) | −14.1487 | −0.562361 | ||||||||
\(634\) | 10.4094 | 0.413409 | ||||||||
\(635\) | 5.55145 | 0.220303 | ||||||||
\(636\) | 1.87669 | 0.0744158 | ||||||||
\(637\) | −37.7058 | −1.49396 | ||||||||
\(638\) | −1.72957 | −0.0684743 | ||||||||
\(639\) | −36.4801 | −1.44313 | ||||||||
\(640\) | 1.45596 | 0.0575517 | ||||||||
\(641\) | −10.6836 | −0.421976 | −0.210988 | − | 0.977489i | \(-0.567668\pi\) | ||||
−0.210988 | + | 0.977489i | \(0.567668\pi\) | |||||||
\(642\) | 7.30015 | 0.288114 | ||||||||
\(643\) | −42.6495 | −1.68193 | −0.840966 | − | 0.541089i | \(-0.818012\pi\) | ||||
−0.840966 | + | 0.541089i | \(0.818012\pi\) | |||||||
\(644\) | 1.05932 | 0.0417430 | ||||||||
\(645\) | −1.67654 | −0.0660135 | ||||||||
\(646\) | 10.8692 | 0.427641 | ||||||||
\(647\) | 12.1181 | 0.476413 | 0.238207 | − | 0.971214i | \(-0.423440\pi\) | ||||
0.238207 | + | 0.971214i | \(0.423440\pi\) | |||||||
\(648\) | 16.7736 | 0.658927 | ||||||||
\(649\) | −20.3406 | −0.798440 | ||||||||
\(650\) | 31.4445 | 1.23336 | ||||||||
\(651\) | −0.522856 | −0.0204924 | ||||||||
\(652\) | 9.12434 | 0.357337 | ||||||||
\(653\) | 8.05822 | 0.315342 | 0.157671 | − | 0.987492i | \(-0.449601\pi\) | ||||
0.157671 | + | 0.987492i | \(0.449601\pi\) | |||||||
\(654\) | 0.0681002 | 0.00266293 | ||||||||
\(655\) | −5.05558 | −0.197538 | ||||||||
\(656\) | −2.25583 | −0.0880754 | ||||||||
\(657\) | −20.2276 | −0.789154 | ||||||||
\(658\) | −1.12250 | −0.0437596 | ||||||||
\(659\) | −14.1844 | −0.552546 | −0.276273 | − | 0.961079i | \(-0.589099\pi\) | ||||
−0.276273 | + | 0.961079i | \(0.589099\pi\) | |||||||
\(660\) | 0.193331 | 0.00752541 | ||||||||
\(661\) | 4.22367 | 0.164282 | 0.0821409 | − | 0.996621i | \(-0.473824\pi\) | ||||
0.0821409 | + | 0.996621i | \(0.473824\pi\) | |||||||
\(662\) | 36.0637 | 1.40165 | ||||||||
\(663\) | −15.3822 | −0.597395 | ||||||||
\(664\) | −37.2539 | −1.44573 | ||||||||
\(665\) | 0.150717 | 0.00584457 | ||||||||
\(666\) | 13.7265 | 0.531892 | ||||||||
\(667\) | 8.86978 | 0.343439 | ||||||||
\(668\) | −3.29418 | −0.127456 | ||||||||
\(669\) | 6.47412 | 0.250304 | ||||||||
\(670\) | 0.937119 | 0.0362041 | ||||||||
\(671\) | 11.6283 | 0.448905 | ||||||||
\(672\) | 0.418643 | 0.0161495 | ||||||||
\(673\) | 20.8298 | 0.802931 | 0.401466 | − | 0.915874i | \(-0.368501\pi\) | ||||
0.401466 | + | 0.915874i | \(0.368501\pi\) | |||||||
\(674\) | −7.46339 | −0.287479 | ||||||||
\(675\) | −17.4942 | −0.673352 | ||||||||
\(676\) | −9.53163 | −0.366601 | ||||||||
\(677\) | −33.4563 | −1.28583 | −0.642914 | − | 0.765938i | \(-0.722275\pi\) | ||||
−0.642914 | + | 0.765938i | \(0.722275\pi\) | |||||||
\(678\) | −13.3342 | −0.512096 | ||||||||
\(679\) | −1.01280 | −0.0388675 | ||||||||
\(680\) | −4.83179 | −0.185291 | ||||||||
\(681\) | 18.2562 | 0.699578 | ||||||||
\(682\) | 6.86368 | 0.262824 | ||||||||
\(683\) | 26.1033 | 0.998814 | 0.499407 | − | 0.866368i | \(-0.333551\pi\) | ||||
0.499407 | + | 0.866368i | \(0.333551\pi\) | |||||||
\(684\) | −3.11334 | −0.119042 | ||||||||
\(685\) | −2.02926 | −0.0775339 | ||||||||
\(686\) | 3.40804 | 0.130120 | ||||||||
\(687\) | 0.986257 | 0.0376280 | ||||||||
\(688\) | 18.3119 | 0.698135 | ||||||||
\(689\) | 27.1801 | 1.03548 | ||||||||
\(690\) | 2.41338 | 0.0918758 | ||||||||
\(691\) | −51.1642 | −1.94638 | −0.973188 | − | 0.230010i | \(-0.926124\pi\) | ||||
−0.973188 | + | 0.230010i | \(0.926124\pi\) | |||||||
\(692\) | 4.43604 | 0.168633 | ||||||||
\(693\) | 0.770720 | 0.0292772 | ||||||||
\(694\) | 20.3090 | 0.770920 | ||||||||
\(695\) | 0.355693 | 0.0134922 | ||||||||
\(696\) | 1.97542 | 0.0748780 | ||||||||
\(697\) | 3.99286 | 0.151241 | ||||||||
\(698\) | 17.8339 | 0.675023 | ||||||||
\(699\) | 9.45232 | 0.357519 | ||||||||
\(700\) | 0.582041 | 0.0219991 | ||||||||
\(701\) | 4.35600 | 0.164524 | 0.0822618 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822618 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(702\) | −23.1612 | −0.874162 | ||||||||
\(703\) | −9.20729 | −0.347259 | ||||||||
\(704\) | −12.7474 | −0.480436 | ||||||||
\(705\) | 1.05060 | 0.0395678 | ||||||||
\(706\) | −30.4189 | −1.14483 | ||||||||
\(707\) | −3.52489 | −0.132567 | ||||||||
\(708\) | 5.23932 | 0.196906 | ||||||||
\(709\) | 21.2807 | 0.799212 | 0.399606 | − | 0.916687i | \(-0.369147\pi\) | ||||
0.399606 | + | 0.916687i | \(0.369147\pi\) | |||||||
\(710\) | 5.97141 | 0.224103 | ||||||||
\(711\) | −11.4039 | −0.427679 | ||||||||
\(712\) | 1.28453 | 0.0481396 | ||||||||
\(713\) | −35.1992 | −1.31822 | ||||||||
\(714\) | 0.693067 | 0.0259374 | ||||||||
\(715\) | 2.80002 | 0.104715 | ||||||||
\(716\) | −7.85196 | −0.293441 | ||||||||
\(717\) | 6.15452 | 0.229845 | ||||||||
\(718\) | 14.5292 | 0.542225 | ||||||||
\(719\) | 10.9571 | 0.408631 | 0.204315 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204315 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(720\) | −2.29702 | −0.0856047 | ||||||||
\(721\) | 2.52252 | 0.0939436 | ||||||||
\(722\) | 17.5388 | 0.652726 | ||||||||
\(723\) | 16.0384 | 0.596476 | ||||||||
\(724\) | 0.120588 | 0.00448163 | ||||||||
\(725\) | 4.87348 | 0.180997 | ||||||||
\(726\) | −6.80035 | −0.252385 | ||||||||
\(727\) | 13.3017 | 0.493333 | 0.246666 | − | 0.969100i | \(-0.420665\pi\) | ||||
0.246666 | + | 0.969100i | \(0.420665\pi\) | |||||||
\(728\) | 3.41689 | 0.126638 | ||||||||
\(729\) | −7.19542 | −0.266497 | ||||||||
\(730\) | 3.31105 | 0.122547 | ||||||||
\(731\) | −32.4124 | −1.19882 | ||||||||
\(732\) | −2.99519 | −0.110706 | ||||||||
\(733\) | −19.3193 | −0.713574 | −0.356787 | − | 0.934186i | \(-0.616128\pi\) | ||||
−0.356787 | + | 0.934186i | \(0.616128\pi\) | |||||||
\(734\) | −24.2569 | −0.895339 | ||||||||
\(735\) | −1.59007 | −0.0586504 | ||||||||
\(736\) | 28.1834 | 1.03885 | ||||||||
\(737\) | −3.21439 | −0.118404 | ||||||||
\(738\) | 2.78397 | 0.102479 | ||||||||
\(739\) | 34.2719 | 1.26071 | 0.630356 | − | 0.776306i | \(-0.282909\pi\) | ||||
0.630356 | + | 0.776306i | \(0.282909\pi\) | |||||||
\(740\) | 0.923067 | 0.0339326 | ||||||||
\(741\) | 7.19398 | 0.264277 | ||||||||
\(742\) | −1.22464 | −0.0449580 | ||||||||
\(743\) | 45.8795 | 1.68316 | 0.841578 | − | 0.540135i | \(-0.181627\pi\) | ||||
0.841578 | + | 0.540135i | \(0.181627\pi\) | |||||||
\(744\) | −7.83932 | −0.287403 | ||||||||
\(745\) | 3.55044 | 0.130078 | ||||||||
\(746\) | 9.53862 | 0.349234 | ||||||||
\(747\) | 31.3476 | 1.14695 | ||||||||
\(748\) | 3.73767 | 0.136663 | ||||||||
\(749\) | 1.95703 | 0.0715085 | ||||||||
\(750\) | 2.68648 | 0.0980964 | ||||||||
\(751\) | −29.2344 | −1.06678 | −0.533389 | − | 0.845870i | \(-0.679082\pi\) | ||||
−0.533389 | + | 0.845870i | \(0.679082\pi\) | |||||||
\(752\) | −11.4751 | −0.418455 | ||||||||
\(753\) | −10.7616 | −0.392175 | ||||||||
\(754\) | 6.45217 | 0.234974 | ||||||||
\(755\) | −2.61555 | −0.0951896 | ||||||||
\(756\) | −0.428715 | −0.0155922 | ||||||||
\(757\) | −2.24805 | −0.0817067 | −0.0408533 | − | 0.999165i | \(-0.513008\pi\) | ||||
−0.0408533 | + | 0.999165i | \(0.513008\pi\) | |||||||
\(758\) | 21.8062 | 0.792037 | ||||||||
\(759\) | −8.27808 | −0.300475 | ||||||||
\(760\) | 2.25974 | 0.0819695 | ||||||||
\(761\) | −30.9130 | −1.12059 | −0.560297 | − | 0.828292i | \(-0.689313\pi\) | ||||
−0.560297 | + | 0.828292i | \(0.689313\pi\) | |||||||
\(762\) | −11.9390 | −0.432505 | ||||||||
\(763\) | 0.0182564 | 0.000660926 0 | ||||||||
\(764\) | 7.31177 | 0.264531 | ||||||||
\(765\) | 4.06576 | 0.146998 | ||||||||
\(766\) | 34.1769 | 1.23486 | ||||||||
\(767\) | 75.8810 | 2.73990 | ||||||||
\(768\) | 8.14471 | 0.293897 | ||||||||
\(769\) | 23.7353 | 0.855918 | 0.427959 | − | 0.903798i | \(-0.359233\pi\) | ||||
0.427959 | + | 0.903798i | \(0.359233\pi\) | |||||||
\(770\) | −0.126159 | −0.00454645 | ||||||||
\(771\) | −18.8926 | −0.680401 | ||||||||
\(772\) | 6.78062 | 0.244040 | ||||||||
\(773\) | 16.1748 | 0.581767 | 0.290883 | − | 0.956759i | \(-0.406051\pi\) | ||||
0.290883 | + | 0.956759i | \(0.406051\pi\) | |||||||
\(774\) | −22.5991 | −0.812309 | ||||||||
\(775\) | −19.3401 | −0.694717 | ||||||||
\(776\) | −15.1851 | −0.545113 | ||||||||
\(777\) | −0.587098 | −0.0210620 | ||||||||
\(778\) | −9.65301 | −0.346077 | ||||||||
\(779\) | −1.86739 | −0.0669063 | ||||||||
\(780\) | −0.721224 | −0.0258240 | ||||||||
\(781\) | −20.4824 | −0.732918 | ||||||||
\(782\) | 46.6579 | 1.66848 | ||||||||
\(783\) | −3.58967 | −0.128284 | ||||||||
\(784\) | 17.3674 | 0.620266 | ||||||||
\(785\) | 5.89457 | 0.210386 | ||||||||
\(786\) | 10.8726 | 0.387813 | ||||||||
\(787\) | 10.7081 | 0.381704 | 0.190852 | − | 0.981619i | \(-0.438875\pi\) | ||||
0.190852 | + | 0.981619i | \(0.438875\pi\) | |||||||
\(788\) | 1.46642 | 0.0522390 | ||||||||
\(789\) | −7.44824 | −0.265164 | ||||||||
\(790\) | 1.86670 | 0.0664141 | ||||||||
\(791\) | −3.57465 | −0.127100 | ||||||||
\(792\) | 11.5556 | 0.410610 | ||||||||
\(793\) | −43.3794 | −1.54045 | ||||||||
\(794\) | 39.4242 | 1.39911 | ||||||||
\(795\) | 1.14620 | 0.0406514 | ||||||||
\(796\) | −5.39868 | −0.191351 | ||||||||
\(797\) | 35.3402 | 1.25181 | 0.625907 | − | 0.779898i | \(-0.284729\pi\) | ||||
0.625907 | + | 0.779898i | \(0.284729\pi\) | |||||||
\(798\) | −0.324135 | −0.0114743 | ||||||||
\(799\) | 20.3112 | 0.718558 | ||||||||
\(800\) | 15.4853 | 0.547488 | ||||||||
\(801\) | −1.08088 | −0.0381909 | ||||||||
\(802\) | 14.2899 | 0.504593 | ||||||||
\(803\) | −11.3572 | −0.400785 | ||||||||
\(804\) | 0.827958 | 0.0291998 | ||||||||
\(805\) | 0.646982 | 0.0228031 | ||||||||
\(806\) | −25.6050 | −0.901899 | ||||||||
\(807\) | 0.582086 | 0.0204904 | ||||||||
\(808\) | −52.8496 | −1.85924 | ||||||||
\(809\) | 17.6977 | 0.622219 | 0.311110 | − | 0.950374i | \(-0.399299\pi\) | ||||
0.311110 | + | 0.950374i | \(0.399299\pi\) | |||||||
\(810\) | 2.31036 | 0.0811778 | ||||||||
\(811\) | −13.9831 | −0.491014 | −0.245507 | − | 0.969395i | \(-0.578954\pi\) | ||||
−0.245507 | + | 0.969395i | \(0.578954\pi\) | |||||||
\(812\) | 0.119430 | 0.00419118 | ||||||||
\(813\) | 13.5727 | 0.476016 | ||||||||
\(814\) | 7.70700 | 0.270130 | ||||||||
\(815\) | 5.57272 | 0.195204 | ||||||||
\(816\) | 7.08511 | 0.248028 | ||||||||
\(817\) | 15.1587 | 0.530337 | ||||||||
\(818\) | −8.77108 | −0.306674 | ||||||||
\(819\) | −2.87518 | −0.100467 | ||||||||
\(820\) | 0.187213 | 0.00653777 | ||||||||
\(821\) | 23.4837 | 0.819587 | 0.409794 | − | 0.912178i | \(-0.365601\pi\) | ||||
0.409794 | + | 0.912178i | \(0.365601\pi\) | |||||||
\(822\) | 4.36415 | 0.152217 | ||||||||
\(823\) | −28.7877 | −1.00348 | −0.501738 | − | 0.865019i | \(-0.667306\pi\) | ||||
−0.501738 | + | 0.865019i | \(0.667306\pi\) | |||||||
\(824\) | 37.8208 | 1.31755 | ||||||||
\(825\) | −4.54838 | −0.158354 | ||||||||
\(826\) | −3.41893 | −0.118960 | ||||||||
\(827\) | −5.66883 | −0.197124 | −0.0985622 | − | 0.995131i | \(-0.531424\pi\) | ||||
−0.0985622 | + | 0.995131i | \(0.531424\pi\) | |||||||
\(828\) | −13.3646 | −0.464452 | ||||||||
\(829\) | −54.0910 | −1.87866 | −0.939328 | − | 0.343019i | \(-0.888550\pi\) | ||||
−0.939328 | + | 0.343019i | \(0.888550\pi\) | |||||||
\(830\) | −5.13128 | −0.178109 | ||||||||
\(831\) | −2.30967 | −0.0801216 | ||||||||
\(832\) | 47.5543 | 1.64865 | ||||||||
\(833\) | −30.7407 | −1.06510 | ||||||||
\(834\) | −0.764958 | −0.0264883 | ||||||||
\(835\) | −2.01193 | −0.0696258 | ||||||||
\(836\) | −1.74804 | −0.0604573 | ||||||||
\(837\) | 14.2454 | 0.492392 | ||||||||
\(838\) | 31.2110 | 1.07817 | ||||||||
\(839\) | 11.5242 | 0.397860 | 0.198930 | − | 0.980014i | \(-0.436253\pi\) | ||||
0.198930 | + | 0.980014i | \(0.436253\pi\) | |||||||
\(840\) | 0.144092 | 0.00497163 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 2.91418 | 0.100429 | ||||||||
\(843\) | 14.2930 | 0.492277 | ||||||||
\(844\) | −12.8253 | −0.441465 | ||||||||
\(845\) | −5.82147 | −0.200265 | ||||||||
\(846\) | 14.1617 | 0.486889 | ||||||||
\(847\) | −1.82305 | −0.0626406 | ||||||||
\(848\) | −12.5193 | −0.429915 | ||||||||
\(849\) | −4.92858 | −0.169148 | ||||||||
\(850\) | 25.6361 | 0.879310 | ||||||||
\(851\) | −39.5240 | −1.35486 | ||||||||
\(852\) | 5.27583 | 0.180747 | ||||||||
\(853\) | 12.5581 | 0.429983 | 0.214991 | − | 0.976616i | \(-0.431028\pi\) | ||||
0.214991 | + | 0.976616i | \(0.431028\pi\) | |||||||
\(854\) | 1.95452 | 0.0668823 | ||||||||
\(855\) | −1.90148 | −0.0650294 | ||||||||
\(856\) | 29.3423 | 1.00290 | ||||||||
\(857\) | 7.46078 | 0.254855 | 0.127428 | − | 0.991848i | \(-0.459328\pi\) | ||||
0.127428 | + | 0.991848i | \(0.459328\pi\) | |||||||
\(858\) | −6.02175 | −0.205579 | ||||||||
\(859\) | −46.2580 | −1.57830 | −0.789151 | − | 0.614199i | \(-0.789479\pi\) | ||||
−0.789151 | + | 0.614199i | \(0.789479\pi\) | |||||||
\(860\) | −1.51972 | −0.0518221 | ||||||||
\(861\) | −0.119073 | −0.00405801 | ||||||||
\(862\) | 34.9121 | 1.18911 | ||||||||
\(863\) | 19.8442 | 0.675506 | 0.337753 | − | 0.941235i | \(-0.390333\pi\) | ||||
0.337753 | + | 0.941235i | \(0.390333\pi\) | |||||||
\(864\) | −11.4060 | −0.388041 | ||||||||
\(865\) | 2.70933 | 0.0921199 | ||||||||
\(866\) | 18.6245 | 0.632886 | ||||||||
\(867\) | −1.61864 | −0.0549720 | ||||||||
\(868\) | −0.473951 | −0.0160870 | ||||||||
\(869\) | −6.40291 | −0.217204 | ||||||||
\(870\) | 0.272090 | 0.00922473 | ||||||||
\(871\) | 11.9913 | 0.406310 | ||||||||
\(872\) | 0.273723 | 0.00926942 | ||||||||
\(873\) | 12.7776 | 0.432458 | ||||||||
\(874\) | −21.8211 | −0.738108 | ||||||||
\(875\) | 0.720195 | 0.0243470 | ||||||||
\(876\) | 2.92536 | 0.0988387 | ||||||||
\(877\) | −16.0313 | −0.541338 | −0.270669 | − | 0.962673i | \(-0.587245\pi\) | ||||
−0.270669 | + | 0.962673i | \(0.587245\pi\) | |||||||
\(878\) | −26.2175 | −0.884798 | ||||||||
\(879\) | 16.7491 | 0.564934 | ||||||||
\(880\) | −1.28970 | −0.0434758 | ||||||||
\(881\) | 17.5709 | 0.591979 | 0.295989 | − | 0.955191i | \(-0.404351\pi\) | ||||
0.295989 | + | 0.955191i | \(0.404351\pi\) | |||||||
\(882\) | −21.4335 | −0.721705 | ||||||||
\(883\) | −1.81821 | −0.0611876 | −0.0305938 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305938 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(884\) | −13.9434 | −0.468968 | ||||||||
\(885\) | 3.19993 | 0.107564 | ||||||||
\(886\) | 6.97128 | 0.234205 | ||||||||
\(887\) | 17.5395 | 0.588918 | 0.294459 | − | 0.955664i | \(-0.404861\pi\) | ||||
0.294459 | + | 0.955664i | \(0.404861\pi\) | |||||||
\(888\) | −8.80251 | −0.295393 | ||||||||
\(889\) | −3.20063 | −0.107346 | ||||||||
\(890\) | 0.176928 | 0.00593065 | ||||||||
\(891\) | −7.92471 | −0.265488 | ||||||||
\(892\) | 5.86856 | 0.196494 | ||||||||
\(893\) | −9.49918 | −0.317878 | ||||||||
\(894\) | −7.63563 | −0.255374 | ||||||||
\(895\) | −4.79561 | −0.160299 | ||||||||
\(896\) | −0.839416 | −0.0280429 | ||||||||
\(897\) | 30.8815 | 1.03110 | ||||||||
\(898\) | −32.2352 | −1.07570 | ||||||||
\(899\) | −3.96844 | −0.132355 | ||||||||
\(900\) | −7.34316 | −0.244772 | ||||||||
\(901\) | 22.1594 | 0.738237 | ||||||||
\(902\) | 1.56311 | 0.0520458 | ||||||||
\(903\) | 0.966589 | 0.0321661 | ||||||||
\(904\) | −53.5956 | −1.78256 | ||||||||
\(905\) | 0.0736496 | 0.00244820 | ||||||||
\(906\) | 5.62504 | 0.186879 | ||||||||
\(907\) | −7.75346 | −0.257449 | −0.128725 | − | 0.991680i | \(-0.541088\pi\) | ||||
−0.128725 | + | 0.991680i | \(0.541088\pi\) | |||||||
\(908\) | 16.5486 | 0.549184 | ||||||||
\(909\) | 44.4708 | 1.47500 | ||||||||
\(910\) | 0.470636 | 0.0156014 | ||||||||
\(911\) | 57.4872 | 1.90464 | 0.952318 | − | 0.305107i | \(-0.0986923\pi\) | ||||
0.952318 | + | 0.305107i | \(0.0986923\pi\) | |||||||
\(912\) | −3.31358 | −0.109724 | ||||||||
\(913\) | 17.6007 | 0.582498 | ||||||||
\(914\) | 24.4421 | 0.808472 | ||||||||
\(915\) | −1.82932 | −0.0604756 | ||||||||
\(916\) | 0.894008 | 0.0295388 | ||||||||
\(917\) | 2.91474 | 0.0962533 | ||||||||
\(918\) | −18.8828 | −0.623226 | ||||||||
\(919\) | −3.08439 | −0.101745 | −0.0508723 | − | 0.998705i | \(-0.516200\pi\) | ||||
−0.0508723 | + | 0.998705i | \(0.516200\pi\) | |||||||
\(920\) | 9.70037 | 0.319812 | ||||||||
\(921\) | −8.10271 | −0.266993 | ||||||||
\(922\) | 12.1826 | 0.401214 | ||||||||
\(923\) | 76.4098 | 2.51506 | ||||||||
\(924\) | −0.111463 | −0.00366687 | ||||||||
\(925\) | −21.7164 | −0.714030 | ||||||||
\(926\) | −15.3597 | −0.504752 | ||||||||
\(927\) | −31.8247 | −1.04526 | ||||||||
\(928\) | 3.17746 | 0.104305 | ||||||||
\(929\) | −26.2372 | −0.860814 | −0.430407 | − | 0.902635i | \(-0.641630\pi\) | ||||
−0.430407 | + | 0.902635i | \(0.641630\pi\) | |||||||
\(930\) | −1.07977 | −0.0354072 | ||||||||
\(931\) | 14.3769 | 0.471183 | ||||||||
\(932\) | 8.56820 | 0.280661 | ||||||||
\(933\) | 6.53079 | 0.213808 | ||||||||
\(934\) | −40.7288 | −1.33269 | ||||||||
\(935\) | 2.28279 | 0.0746554 | ||||||||
\(936\) | −43.1082 | −1.40904 | ||||||||
\(937\) | 12.3864 | 0.404648 | 0.202324 | − | 0.979319i | \(-0.435151\pi\) | ||||
0.202324 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(938\) | −0.540286 | −0.0176410 | ||||||||
\(939\) | 7.77996 | 0.253889 | ||||||||
\(940\) | 0.952330 | 0.0310616 | ||||||||
\(941\) | −47.8943 | −1.56131 | −0.780655 | − | 0.624962i | \(-0.785115\pi\) | ||||
−0.780655 | + | 0.624962i | \(0.785115\pi\) | |||||||
\(942\) | −12.6769 | −0.413037 | ||||||||
\(943\) | −8.01612 | −0.261041 | ||||||||
\(944\) | −34.9511 | −1.13756 | ||||||||
\(945\) | −0.261839 | −0.00851762 | ||||||||
\(946\) | −12.6887 | −0.412545 | ||||||||
\(947\) | 36.5231 | 1.18684 | 0.593421 | − | 0.804892i | \(-0.297777\pi\) | ||||
0.593421 | + | 0.804892i | \(0.297777\pi\) | |||||||
\(948\) | 1.64925 | 0.0535653 | ||||||||
\(949\) | 42.3680 | 1.37532 | ||||||||
\(950\) | −11.9895 | −0.388992 | ||||||||
\(951\) | 5.61699 | 0.182144 | ||||||||
\(952\) | 2.78572 | 0.0902857 | ||||||||
\(953\) | 44.0856 | 1.42807 | 0.714037 | − | 0.700108i | \(-0.246865\pi\) | ||||
0.714037 | + | 0.700108i | \(0.246865\pi\) | |||||||
\(954\) | 15.4503 | 0.500223 | ||||||||
\(955\) | 4.46569 | 0.144506 | ||||||||
\(956\) | 5.57886 | 0.180433 | ||||||||
\(957\) | −0.933291 | −0.0301690 | ||||||||
\(958\) | −28.3957 | −0.917423 | ||||||||
\(959\) | 1.16995 | 0.0377795 | ||||||||
\(960\) | 2.00538 | 0.0647234 | ||||||||
\(961\) | −15.2515 | −0.491984 | ||||||||
\(962\) | −28.7510 | −0.926971 | ||||||||
\(963\) | −24.6904 | −0.795636 | ||||||||
\(964\) | 14.5383 | 0.468247 | ||||||||
\(965\) | 4.14128 | 0.133313 | ||||||||
\(966\) | −1.39141 | −0.0447679 | ||||||||
\(967\) | −30.2021 | −0.971235 | −0.485618 | − | 0.874171i | \(-0.661405\pi\) | ||||
−0.485618 | + | 0.874171i | \(0.661405\pi\) | |||||||
\(968\) | −27.3334 | −0.878529 | ||||||||
\(969\) | 5.86510 | 0.188414 | ||||||||
\(970\) | −2.09157 | −0.0671562 | ||||||||
\(971\) | −13.0542 | −0.418928 | −0.209464 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209464 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(972\) | 8.31294 | 0.266638 | ||||||||
\(973\) | −0.205071 | −0.00657428 | ||||||||
\(974\) | 11.6772 | 0.374161 | ||||||||
\(975\) | 16.9678 | 0.543403 | ||||||||
\(976\) | 19.9807 | 0.639568 | ||||||||
\(977\) | 8.03930 | 0.257200 | 0.128600 | − | 0.991697i | \(-0.458952\pi\) | ||||
0.128600 | + | 0.991697i | \(0.458952\pi\) | |||||||
\(978\) | −11.9848 | −0.383231 | ||||||||
\(979\) | −0.606878 | −0.0193959 | ||||||||
\(980\) | −1.44134 | −0.0460419 | ||||||||
\(981\) | −0.230327 | −0.00735377 | ||||||||
\(982\) | −29.7015 | −0.947815 | ||||||||
\(983\) | 23.5683 | 0.751713 | 0.375857 | − | 0.926678i | \(-0.377348\pi\) | ||||
0.375857 | + | 0.926678i | \(0.377348\pi\) | |||||||
\(984\) | −1.78530 | −0.0569132 | ||||||||
\(985\) | 0.895620 | 0.0285368 | ||||||||
\(986\) | 5.26032 | 0.167523 | ||||||||
\(987\) | −0.605711 | −0.0192800 | ||||||||
\(988\) | 6.52109 | 0.207463 | ||||||||
\(989\) | 65.0716 | 2.06916 | ||||||||
\(990\) | 1.59165 | 0.0505859 | ||||||||
\(991\) | −21.7888 | −0.692143 | −0.346071 | − | 0.938208i | \(-0.612484\pi\) | ||||
−0.346071 | + | 0.938208i | \(0.612484\pi\) | |||||||
\(992\) | −12.6096 | −0.400354 | ||||||||
\(993\) | 19.4603 | 0.617554 | ||||||||
\(994\) | −3.44275 | −0.109198 | ||||||||
\(995\) | −3.29726 | −0.104530 | ||||||||
\(996\) | −4.53356 | −0.143651 | ||||||||
\(997\) | 54.9267 | 1.73955 | 0.869773 | − | 0.493452i | \(-0.164265\pi\) | ||||
0.869773 | + | 0.493452i | \(0.164265\pi\) | |||||||
\(998\) | −30.8819 | −0.977549 | ||||||||
\(999\) | 15.9957 | 0.506080 |
(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 | 4031.2.a.c.1.19 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.19 | ✓ | 61 | 1.1 | even | 1 | trivial |