Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(148,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.f (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 148.12 | ||
Character | \(\chi\) | \(=\) | 441.148 |
Dual form | 441.2.f.h.295.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35757 | + | 2.35137i | 0.959944 | + | 1.66267i | 0.722624 | + | 0.691241i | \(0.242936\pi\) |
0.237320 | + | 0.971432i | \(0.423731\pi\) | |||||||
\(3\) | 0.521588 | + | 1.65165i | 0.301139 | + | 0.953580i | ||||
\(4\) | −2.68597 | + | 4.65224i | −1.34299 | + | 2.32612i | ||||
\(5\) | 0.793197 | − | 1.37386i | 0.354728 | − | 0.614407i | −0.632343 | − | 0.774688i | \(-0.717907\pi\) |
0.987071 | + | 0.160281i | \(0.0512400\pi\) | |||||||
\(6\) | −3.17555 | + | 3.46867i | −1.29641 | + | 1.41608i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.15528 | −3.23688 | ||||||||
\(9\) | −2.45589 | + | 1.72296i | −0.818630 | + | 0.574321i | ||||
\(10\) | 4.30727 | 1.36208 | ||||||||
\(11\) | 0.674376 | + | 1.16805i | 0.203332 | + | 0.352181i | 0.949600 | − | 0.313464i | \(-0.101490\pi\) |
−0.746268 | + | 0.665646i | \(0.768156\pi\) | |||||||
\(12\) | −9.08484 | − | 2.00973i | −2.62257 | − | 0.580159i | ||||
\(13\) | 1.58916 | − | 2.75251i | 0.440754 | − | 0.763409i | −0.556991 | − | 0.830518i | \(-0.688044\pi\) |
0.997746 | + | 0.0671096i | \(0.0213777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.68285 | + | 0.593495i | 0.692709 | + | 0.153240i | ||||
\(16\) | −7.05696 | − | 12.2230i | −1.76424 | − | 3.05575i | ||||
\(17\) | 2.80054 | 0.679230 | 0.339615 | − | 0.940565i | \(-0.389703\pi\) | ||||
0.339615 | + | 0.940565i | \(0.389703\pi\) | |||||||
\(18\) | −7.38536 | − | 3.43568i | −1.74075 | − | 0.809799i | ||||
\(19\) | 0.625693 | 0.143544 | 0.0717719 | − | 0.997421i | \(-0.477135\pi\) | ||||
0.0717719 | + | 0.997421i | \(0.477135\pi\) | |||||||
\(20\) | 4.26101 | + | 7.38028i | 0.952791 | + | 1.65028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.83102 | + | 3.17142i | −0.390375 | + | 0.676149i | ||||
\(23\) | 0.142434 | − | 0.246702i | 0.0296995 | − | 0.0514410i | −0.850794 | − | 0.525500i | \(-0.823878\pi\) |
0.880493 | + | 0.474059i | \(0.157212\pi\) | |||||||
\(24\) | −4.77529 | − | 15.1213i | −0.974751 | − | 3.08663i | ||||
\(25\) | 1.24168 | + | 2.15065i | 0.248336 | + | 0.430130i | ||||
\(26\) | 8.62957 | 1.69240 | ||||||||
\(27\) | −4.12669 | − | 3.15760i | −0.794182 | − | 0.607679i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27396 | + | 3.93861i | 0.422264 | + | 0.731382i | 0.996161 | − | 0.0875454i | \(-0.0279023\pi\) |
−0.573897 | + | 0.818928i | \(0.694569\pi\) | |||||||
\(30\) | 2.24662 | + | 7.11410i | 0.410175 | + | 1.29885i | ||||
\(31\) | −3.71502 | + | 6.43461i | −0.667238 | + | 1.15569i | 0.311435 | + | 0.950267i | \(0.399190\pi\) |
−0.978673 | + | 0.205423i | \(0.934143\pi\) | |||||||
\(32\) | 10.0053 | − | 17.3297i | 1.76870 | − | 3.06348i | ||||
\(33\) | −1.57747 | + | 1.72308i | −0.274602 | + | 0.299949i | ||||
\(34\) | 3.80191 | + | 6.58511i | 0.652023 | + | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.41918 | − | 16.0532i | −0.236529 | − | 2.67554i | ||||
\(37\) | 8.02252 | 1.31889 | 0.659447 | − | 0.751751i | \(-0.270791\pi\) | ||||
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(38\) | 0.849420 | + | 1.47124i | 0.137794 | + | 0.238666i | ||||
\(39\) | 5.37507 | + | 1.18906i | 0.860700 | + | 0.190402i | ||||
\(40\) | −7.26194 | + | 12.5780i | −1.14821 | + | 1.98876i | ||||
\(41\) | 5.01329 | − | 8.68327i | 0.782944 | − | 1.35610i | −0.147275 | − | 0.989096i | \(-0.547050\pi\) |
0.930219 | − | 0.367004i | \(-0.119616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | − | 5.42022i | −0.477224 | − | 0.826576i | 0.522435 | − | 0.852679i | \(-0.325024\pi\) |
−0.999659 | + | 0.0261027i | \(0.991690\pi\) | |||||||
\(44\) | −7.24542 | −1.09229 | ||||||||
\(45\) | 0.419098 | + | 4.74069i | 0.0624754 | + | 0.706700i | ||||
\(46\) | 0.773452 | 0.114039 | ||||||||
\(47\) | −5.57383 | − | 9.65415i | −0.813026 | − | 1.40820i | −0.910737 | − | 0.412988i | \(-0.864485\pi\) |
0.0977106 | − | 0.995215i | \(-0.468848\pi\) | |||||||
\(48\) | 16.5073 | − | 18.0310i | 2.38262 | − | 2.60255i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.37132 | + | 5.83930i | −0.476777 | + | 0.825802i | ||||
\(51\) | 1.46073 | + | 4.62550i | 0.204543 | + | 0.647700i | ||||
\(52\) | 8.53689 | + | 14.7863i | 1.18385 | + | 2.05049i | ||||
\(53\) | 2.78698 | 0.382821 | 0.191410 | − | 0.981510i | \(-0.438694\pi\) | ||||
0.191410 | + | 0.981510i | \(0.438694\pi\) | |||||||
\(54\) | 1.82243 | − | 13.9900i | 0.248001 | − | 1.90380i | ||||
\(55\) | 2.13965 | 0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.326354 | + | 1.03343i | 0.0432266 | + | 0.136881i | ||||
\(58\) | −6.17410 | + | 10.6939i | −0.810699 | + | 1.40417i | ||||
\(59\) | −2.28734 | + | 3.96180i | −0.297787 | + | 0.515782i | −0.975629 | − | 0.219425i | \(-0.929582\pi\) |
0.677842 | + | 0.735207i | \(0.262915\pi\) | |||||||
\(60\) | −9.96715 | + | 10.8872i | −1.28675 | + | 1.40553i | ||||
\(61\) | 0.192507 | + | 0.333432i | 0.0246480 | + | 0.0426916i | 0.878086 | − | 0.478502i | \(-0.158820\pi\) |
−0.853438 | + | 0.521194i | \(0.825487\pi\) | |||||||
\(62\) | −20.1736 | −2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | −2.52104 | − | 4.36656i | −0.312696 | − | 0.541605i | ||||
\(66\) | −6.19311 | − | 1.37003i | −0.762320 | − | 0.168639i | ||||
\(67\) | 1.26958 | − | 2.19898i | 0.155104 | − | 0.268648i | −0.777993 | − | 0.628273i | \(-0.783762\pi\) |
0.933097 | + | 0.359625i | \(0.117095\pi\) | |||||||
\(68\) | −7.52217 | + | 13.0288i | −0.912197 | + | 1.57997i | ||||
\(69\) | 0.481757 | + | 0.106573i | 0.0579968 | + | 0.0128299i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45208 | −0.172330 | −0.0861651 | − | 0.996281i | \(-0.527461\pi\) | ||||
−0.0861651 | + | 0.996281i | \(0.527461\pi\) | |||||||
\(72\) | 22.4844 | − | 15.7742i | 2.64981 | − | 1.85901i | ||||
\(73\) | −0.468134 | −0.0547909 | −0.0273955 | − | 0.999625i | \(-0.508721\pi\) | ||||
−0.0273955 | + | 0.999625i | \(0.508721\pi\) | |||||||
\(74\) | 10.8911 | + | 18.8639i | 1.26606 | + | 2.19289i | ||||
\(75\) | −2.90448 | + | 3.17257i | −0.335380 | + | 0.366337i | ||||
\(76\) | −1.68059 | + | 2.91087i | −0.192777 | + | 0.333900i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.50108 | + | 14.2530i | 0.509647 | + | 1.61384i | ||||
\(79\) | 7.85620 | + | 13.6073i | 0.883892 | + | 1.53095i | 0.846978 | + | 0.531627i | \(0.178419\pi\) |
0.0369135 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(80\) | −22.3902 | −2.50330 | ||||||||
\(81\) | 3.06281 | − | 8.46281i | 0.340312 | − | 0.940313i | ||||
\(82\) | 27.2235 | 3.00633 | ||||||||
\(83\) | −6.99338 | − | 12.1129i | −0.767623 | − | 1.32956i | −0.938848 | − | 0.344331i | \(-0.888106\pi\) |
0.171225 | − | 0.985232i | \(-0.445228\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22138 | − | 3.84754i | 0.240942 | − | 0.417324i | ||||
\(86\) | 8.49665 | − | 14.7166i | 0.916217 | − | 1.58693i | ||||
\(87\) | −5.31914 | + | 5.81012i | −0.570272 | + | 0.622910i | ||||
\(88\) | −6.17410 | − | 10.6939i | −0.658162 | − | 1.13997i | ||||
\(89\) | −2.58706 | −0.274228 | −0.137114 | − | 0.990555i | \(-0.543783\pi\) | ||||
−0.137114 | + | 0.990555i | \(0.543783\pi\) | |||||||
\(90\) | −10.5782 | + | 7.42126i | −1.11504 | + | 0.782269i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.765146 | + | 1.32527i | 0.0797719 | + | 0.138169i | ||||
\(93\) | −12.5654 | − | 2.77970i | −1.30297 | − | 0.288241i | ||||
\(94\) | 15.1337 | − | 26.2123i | 1.56092 | − | 2.70359i | ||||
\(95\) | 0.496297 | − | 0.859612i | 0.0509190 | − | 0.0881944i | ||||
\(96\) | 33.8412 | + | 7.48628i | 3.45390 | + | 0.764065i | ||||
\(97\) | 7.22962 | + | 12.5221i | 0.734057 | + | 1.27142i | 0.955136 | + | 0.296168i | \(0.0957089\pi\) |
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.66871 | − | 1.70669i | −0.368719 | − | 0.171529i | ||||
\(100\) | −13.3405 | −1.33405 | ||||||||
\(101\) | −4.91888 | − | 8.51975i | −0.489447 | − | 0.847747i | 0.510479 | − | 0.859890i | \(-0.329468\pi\) |
−0.999926 | + | 0.0121430i | \(0.996135\pi\) | |||||||
\(102\) | −8.89326 | + | 9.71414i | −0.880564 | + | 0.961844i | ||||
\(103\) | −5.52897 | + | 9.57646i | −0.544786 | + | 0.943597i | 0.453834 | + | 0.891086i | \(0.350056\pi\) |
−0.998620 | + | 0.0525110i | \(0.983278\pi\) | |||||||
\(104\) | −14.5492 | + | 25.2000i | −1.42667 | + | 2.47106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78350 | + | 6.55322i | 0.367486 | + | 0.636505i | ||||
\(107\) | −1.92431 | −0.186030 | −0.0930149 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930149 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(108\) | 25.7741 | − | 10.7172i | 2.48011 | − | 1.03126i | ||||
\(109\) | −18.6068 | −1.78221 | −0.891105 | − | 0.453797i | \(-0.850069\pi\) | ||||
−0.891105 | + | 0.453797i | \(0.850069\pi\) | |||||||
\(110\) | 2.90472 | + | 5.03112i | 0.276954 | + | 0.479698i | ||||
\(111\) | 4.18445 | + | 13.2504i | 0.397170 | + | 1.25767i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.59338 | − | 2.75982i | 0.149893 | − | 0.259622i | −0.781295 | − | 0.624162i | \(-0.785440\pi\) |
0.931188 | + | 0.364540i | \(0.118774\pi\) | |||||||
\(114\) | −1.98692 | + | 2.17032i | −0.186092 | + | 0.203269i | ||||
\(115\) | −0.225956 | − | 0.391367i | −0.0210705 | − | 0.0364951i | ||||
\(116\) | −24.4312 | −2.26838 | ||||||||
\(117\) | 0.839659 | + | 9.49793i | 0.0776265 | + | 0.878084i | ||||
\(118\) | −12.4209 | −1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −24.5623 | − | 5.43361i | −2.24222 | − | 0.496019i | ||||
\(121\) | 4.59043 | − | 7.95086i | 0.417312 | − | 0.722806i | ||||
\(122\) | −0.522682 | + | 0.905312i | −0.0473214 | + | 0.0819631i | ||||
\(123\) | 16.9566 | + | 3.75110i | 1.52892 | + | 0.338226i | ||||
\(124\) | −19.9569 | − | 34.5664i | −1.79218 | − | 3.10415i | ||||
\(125\) | 11.8715 | 1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | 15.4267 | + | 26.7199i | 1.36354 | + | 2.36173i | ||||
\(129\) | 7.32007 | − | 7.99574i | 0.644496 | − | 0.703986i | ||||
\(130\) | 6.84495 | − | 11.8558i | 0.600341 | − | 1.03982i | ||||
\(131\) | 5.98629 | − | 10.3686i | 0.523024 | − | 0.905905i | −0.476616 | − | 0.879111i | \(-0.658137\pi\) |
0.999641 | − | 0.0267937i | \(-0.00852971\pi\) | |||||||
\(132\) | −3.77913 | − | 11.9669i | −0.328931 | − | 1.04158i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.89415 | 0.595564 | ||||||||
\(135\) | −7.61136 | + | 3.16489i | −0.655082 | + | 0.272390i | ||||
\(136\) | −25.6397 | −2.19859 | ||||||||
\(137\) | −8.27525 | − | 14.3332i | −0.707003 | − | 1.22456i | −0.965964 | − | 0.258677i | \(-0.916714\pi\) |
0.258961 | − | 0.965888i | \(-0.416620\pi\) | |||||||
\(138\) | 0.403424 | + | 1.27747i | 0.0343417 | + | 0.108746i | ||||
\(139\) | 3.95119 | − | 6.84367i | 0.335136 | − | 0.580472i | −0.648375 | − | 0.761321i | \(-0.724551\pi\) |
0.983511 | + | 0.180849i | \(0.0578845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0380 | − | 14.2415i | 1.09800 | − | 1.19935i | ||||
\(142\) | −1.97130 | − | 3.41438i | −0.165427 | − | 0.286529i | ||||
\(143\) | 4.28677 | 0.358478 | ||||||||
\(144\) | 38.3909 | + | 17.8595i | 3.19924 | + | 1.48829i | ||||
\(145\) | 7.21479 | 0.599156 | ||||||||
\(146\) | −0.635523 | − | 1.10076i | −0.0525962 | − | 0.0910994i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.5483 | + | 37.3227i | −1.77126 | + | 3.06791i | ||||
\(149\) | 6.83427 | − | 11.8373i | 0.559885 | − | 0.969749i | −0.437620 | − | 0.899160i | \(-0.644179\pi\) |
0.997505 | − | 0.0705895i | \(-0.0224881\pi\) | |||||||
\(150\) | −11.4029 | − | 2.52253i | −0.931045 | − | 0.205964i | ||||
\(151\) | −1.94982 | − | 3.37718i | −0.158674 | − | 0.274831i | 0.775717 | − | 0.631081i | \(-0.217389\pi\) |
−0.934391 | + | 0.356250i | \(0.884055\pi\) | |||||||
\(152\) | −5.72839 | −0.464634 | ||||||||
\(153\) | −6.87781 | + | 4.82522i | −0.556038 | + | 0.390096i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.89349 | + | 10.2078i | 0.473376 | + | 0.819912i | ||||
\(156\) | −19.9691 | + | 21.8123i | −1.59881 | + | 1.74638i | ||||
\(157\) | 0.147176 | − | 0.254917i | 0.0117459 | − | 0.0203446i | −0.860093 | − | 0.510138i | \(-0.829594\pi\) |
0.871839 | + | 0.489793i | \(0.162928\pi\) | |||||||
\(158\) | −21.3306 | + | 36.9457i | −1.69697 | + | 2.93925i | ||||
\(159\) | 1.45365 | + | 4.60311i | 0.115282 | + | 0.365050i | ||||
\(160\) | −15.8723 | − | 27.4917i | −1.25482 | − | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.0572 | − | 4.28703i | 1.89011 | − | 0.336821i | ||||
\(163\) | 10.7091 | 0.838802 | 0.419401 | − | 0.907801i | \(-0.362240\pi\) | ||||
0.419401 | + | 0.907801i | \(0.362240\pi\) | |||||||
\(164\) | 26.9311 | + | 46.6461i | 2.10297 | + | 3.64245i | ||||
\(165\) | 1.11602 | + | 3.53395i | 0.0868818 | + | 0.275118i | ||||
\(166\) | 18.9880 | − | 32.8881i | 1.47375 | − | 2.55261i | ||||
\(167\) | 1.59872 | − | 2.76907i | 0.123713 | − | 0.214277i | −0.797516 | − | 0.603298i | \(-0.793853\pi\) |
0.921229 | + | 0.389020i | \(0.127186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | + | 2.50997i | 0.111472 | + | 0.193074i | ||||
\(170\) | 12.0627 | 0.925164 | ||||||||
\(171\) | −1.53663 | + | 1.07804i | −0.117509 | + | 0.0824401i | ||||
\(172\) | 33.6216 | 2.56362 | ||||||||
\(173\) | 5.71875 | + | 9.90517i | 0.434789 | + | 0.753076i | 0.997278 | − | 0.0737284i | \(-0.0234898\pi\) |
−0.562490 | + | 0.826804i | \(0.690156\pi\) | |||||||
\(174\) | −20.8828 | − | 4.61966i | −1.58312 | − | 0.350216i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.51809 | − | 16.4858i | 0.717453 | − | 1.24266i | ||||
\(177\) | −7.73655 | − | 1.71146i | −0.581515 | − | 0.128642i | ||||
\(178\) | −3.51210 | − | 6.08314i | −0.263243 | − | 0.455951i | ||||
\(179\) | 1.09855 | 0.0821095 | 0.0410547 | − | 0.999157i | \(-0.486928\pi\) | ||||
0.0410547 | + | 0.999157i | \(0.486928\pi\) | |||||||
\(180\) | −23.1805 | − | 10.7836i | −1.72777 | − | 0.803764i | ||||
\(181\) | 3.19013 | 0.237120 | 0.118560 | − | 0.992947i | \(-0.462172\pi\) | ||||
0.118560 | + | 0.992947i | \(0.462172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.450303 | + | 0.491868i | −0.0332874 | + | 0.0363599i | ||||
\(184\) | −1.30402 | + | 2.25863i | −0.0961336 | + | 0.166508i | ||||
\(185\) | 6.36343 | − | 11.0218i | 0.467849 | − | 0.810338i | ||||
\(186\) | −10.5223 | − | 33.3197i | −0.771532 | − | 2.44312i | ||||
\(187\) | 1.88861 | + | 3.27118i | 0.138109 | + | 0.239212i | ||||
\(188\) | 59.8846 | 4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | −1.93407 | − | 3.34992i | −0.139945 | − | 0.242391i | 0.787531 | − | 0.616275i | \(-0.211359\pi\) |
−0.927475 | + | 0.373884i | \(0.878026\pi\) | |||||||
\(192\) | 13.6153 | + | 43.1139i | 0.982601 | + | 3.11148i | ||||
\(193\) | 2.06793 | − | 3.58175i | 0.148853 | − | 0.257820i | −0.781951 | − | 0.623340i | \(-0.785775\pi\) |
0.930804 | + | 0.365520i | \(0.119109\pi\) | |||||||
\(194\) | −19.6294 | + | 33.9991i | −1.40931 | + | 2.44099i | ||||
\(195\) | 5.89709 | − | 6.44141i | 0.422299 | − | 0.461279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.889267 | −0.0633576 | −0.0316788 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316788 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(198\) | −0.967449 | − | 10.9434i | −0.0687536 | − | 0.777717i | ||||
\(199\) | 6.32386 | 0.448287 | 0.224143 | − | 0.974556i | \(-0.428042\pi\) | ||||
0.224143 | + | 0.974556i | \(0.428042\pi\) | |||||||
\(200\) | −11.3679 | − | 19.6898i | −0.803833 | − | 1.39228i | ||||
\(201\) | 4.29414 | + | 0.949940i | 0.302885 | + | 0.0670036i | ||||
\(202\) | 13.3554 | − | 23.1323i | 0.939684 | − | 1.62758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −25.4424 | − | 5.62833i | −1.78133 | − | 0.394062i | ||||
\(205\) | −7.95305 | − | 13.7751i | −0.555465 | − | 0.962093i | ||||
\(206\) | −30.0238 | −2.09186 | ||||||||
\(207\) | 0.0752570 | + | 0.851282i | 0.00523073 | + | 0.0591682i | ||||
\(208\) | −44.8586 | −3.11038 | ||||||||
\(209\) | 0.421952 | + | 0.730843i | 0.0291870 | + | 0.0505535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71291 | − | 9.89505i | 0.393293 | − | 0.681204i | −0.599589 | − | 0.800308i | \(-0.704669\pi\) |
0.992882 | + | 0.119105i | \(0.0380025\pi\) | |||||||
\(212\) | −7.48574 | + | 12.9657i | −0.514123 | + | 0.890487i | ||||
\(213\) | −0.757388 | − | 2.39833i | −0.0518954 | − | 0.164331i | ||||
\(214\) | −2.61237 | − | 4.52476i | −0.178578 | − | 0.309307i | ||||
\(215\) | −9.92881 | −0.677139 | ||||||||
\(216\) | 37.7810 | + | 28.9087i | 2.57067 | + | 1.96699i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.2600 | − | 43.7516i | −1.71082 | − | 2.96323i | ||||
\(219\) | −0.244173 | − | 0.773193i | −0.0164997 | − | 0.0522475i | ||||
\(220\) | −5.74705 | + | 9.95417i | −0.387466 | + | 0.671110i | ||||
\(221\) | 4.45051 | − | 7.70850i | 0.299373 | − | 0.518530i | ||||
\(222\) | −25.4759 | + | 27.8275i | −1.70983 | + | 1.86766i | ||||
\(223\) | 8.35953 | + | 14.4791i | 0.559796 | + | 0.969595i | 0.997513 | + | 0.0704822i | \(0.0224538\pi\) |
−0.437717 | + | 0.899113i | \(0.644213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.75492 | − | 3.14240i | −0.450328 | − | 0.209493i | ||||
\(226\) | 8.65250 | 0.575555 | ||||||||
\(227\) | −8.53501 | − | 14.7831i | −0.566489 | − | 0.981187i | −0.996909 | − | 0.0785588i | \(-0.974968\pi\) |
0.430421 | − | 0.902628i | \(-0.358365\pi\) | |||||||
\(228\) | −5.68432 | − | 1.25747i | −0.376453 | − | 0.0832783i | ||||
\(229\) | −9.89471 | + | 17.1381i | −0.653861 | + | 1.13252i | 0.328317 | + | 0.944567i | \(0.393518\pi\) |
−0.982178 | + | 0.187953i | \(0.939815\pi\) | |||||||
\(230\) | 0.613500 | − | 1.06261i | 0.0404530 | − | 0.0700666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8187 | − | 36.0591i | −1.36682 | − | 2.36740i | ||||
\(233\) | 5.93159 | 0.388591 | 0.194296 | − | 0.980943i | \(-0.437758\pi\) | ||||
0.194296 | + | 0.980943i | \(0.437758\pi\) | |||||||
\(234\) | −21.1933 | + | 14.8684i | −1.38545 | + | 0.971979i | ||||
\(235\) | −17.6846 | −1.15361 | ||||||||
\(236\) | −12.2875 | − | 21.2826i | −0.799847 | − | 1.38538i | ||||
\(237\) | −18.3769 | + | 20.0731i | −1.19371 | + | 1.30389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.0277 | + | 17.3685i | −0.648637 | + | 1.12347i | 0.334812 | + | 0.942285i | \(0.391327\pi\) |
−0.983449 | + | 0.181187i | \(0.942006\pi\) | |||||||
\(240\) | −11.6785 | − | 36.9808i | −0.753842 | − | 2.38710i | ||||
\(241\) | −14.6444 | − | 25.3648i | −0.943326 | − | 1.63389i | −0.759069 | − | 0.651010i | \(-0.774346\pi\) |
−0.184256 | − | 0.982878i | \(-0.558988\pi\) | |||||||
\(242\) | 24.9273 | 1.60239 | ||||||||
\(243\) | 15.5751 | + | 0.644577i | 0.999145 | + | 0.0413497i | ||||
\(244\) | −2.06827 | −0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.1995 | + | 44.9637i | 0.905324 | + | 2.86678i | ||||
\(247\) | 0.994327 | − | 1.72223i | 0.0632675 | − | 0.109583i | ||||
\(248\) | 34.0121 | − | 58.9107i | 2.15977 | − | 3.74083i | ||||
\(249\) | 16.3586 | − | 17.8686i | 1.03668 | − | 1.13237i | ||||
\(250\) | 16.1164 | + | 27.9144i | 1.01929 | + | 1.76546i | ||||
\(251\) | −22.7856 | −1.43821 | −0.719106 | − | 0.694901i | \(-0.755448\pi\) | ||||
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | −11.3681 | − | 19.6901i | −0.713297 | − | 1.23547i | ||||
\(255\) | 7.51342 | + | 1.66210i | 0.470509 | + | 0.104085i | ||||
\(256\) | −15.7821 | + | 27.3354i | −0.986381 | + | 1.70846i | ||||
\(257\) | 12.1444 | − | 21.0348i | 0.757550 | − | 1.31211i | −0.186547 | − | 0.982446i | \(-0.559730\pi\) |
0.944097 | − | 0.329668i | \(-0.106937\pi\) | |||||||
\(258\) | 28.7385 | + | 6.35747i | 1.78918 | + | 0.395798i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.0857 | 1.67979 | ||||||||
\(261\) | −12.3707 | − | 5.75486i | −0.765726 | − | 0.356217i | ||||
\(262\) | 32.5071 | 2.00830 | ||||||||
\(263\) | 4.30578 | + | 7.45782i | 0.265506 | + | 0.459869i | 0.967696 | − | 0.252120i | \(-0.0811278\pi\) |
−0.702190 | + | 0.711989i | \(0.747794\pi\) | |||||||
\(264\) | 14.4422 | − | 15.7752i | 0.888854 | − | 0.970899i | ||||
\(265\) | 2.21062 | − | 3.82890i | 0.135797 | − | 0.235208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.34938 | − | 4.27291i | −0.0825807 | − | 0.261498i | ||||
\(268\) | 6.82011 | + | 11.8128i | 0.416605 | + | 0.721581i | ||||
\(269\) | −15.2312 | −0.928664 | −0.464332 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(270\) | −17.7748 | − | 13.6006i | −1.08174 | − | 0.827707i | ||||
\(271\) | −4.67820 | −0.284181 | −0.142090 | − | 0.989854i | \(-0.545382\pi\) | ||||
−0.142090 | + | 0.989854i | \(0.545382\pi\) | |||||||
\(272\) | −19.7633 | − | 34.2310i | −1.19832 | − | 2.07556i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.4684 | − | 38.9164i | 1.35737 | − | 2.35103i | ||||
\(275\) | −1.67472 | + | 2.90069i | −0.100989 | + | 0.174918i | ||||
\(276\) | −1.78979 | + | 1.95500i | −0.107733 | + | 0.117677i | ||||
\(277\) | 8.19537 | + | 14.1948i | 0.492412 | + | 0.852883i | 0.999962 | − | 0.00873986i | \(-0.00278202\pi\) |
−0.507550 | + | 0.861622i | \(0.669449\pi\) | |||||||
\(278\) | 21.4560 | 1.28685 | ||||||||
\(279\) | −1.96289 | − | 22.2035i | −0.117515 | − | 1.32929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.75702 | + | 3.04325i | 0.104815 | + | 0.181545i | 0.913663 | − | 0.406473i | \(-0.133242\pi\) |
−0.808848 | + | 0.588018i | \(0.799908\pi\) | |||||||
\(282\) | 51.1871 | + | 11.3235i | 3.04815 | + | 0.674305i | ||||
\(283\) | −13.0354 | + | 22.5780i | −0.774874 | + | 1.34212i | 0.159992 | + | 0.987118i | \(0.448853\pi\) |
−0.934865 | + | 0.355002i | \(0.884480\pi\) | |||||||
\(284\) | 3.90025 | − | 6.75543i | 0.231437 | − | 0.400861i | ||||
\(285\) | 1.67864 | + | 0.371346i | 0.0994341 | + | 0.0219966i | ||||
\(286\) | 5.81958 | + | 10.0798i | 0.344119 | + | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.28645 | + | 59.7985i | 0.311507 | + | 3.52366i | ||||
\(289\) | −9.15699 | −0.538647 | ||||||||
\(290\) | 9.79455 | + | 16.9647i | 0.575156 | + | 0.996199i | ||||
\(291\) | −16.9112 | + | 18.4722i | −0.991352 | + | 1.08286i | ||||
\(292\) | 1.25740 | − | 2.17787i | 0.0735835 | − | 0.127450i | ||||
\(293\) | −9.44192 | + | 16.3539i | −0.551603 | + | 0.955404i | 0.446556 | + | 0.894756i | \(0.352650\pi\) |
−0.998159 | + | 0.0606487i | \(0.980683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | + | 6.28497i | 0.211267 | + | 0.365925i | ||||
\(296\) | −73.4484 | −4.26910 | ||||||||
\(297\) | 0.905298 | − | 6.94961i | 0.0525307 | − | 0.403257i | ||||
\(298\) | 37.1119 | 2.14983 | ||||||||
\(299\) | −0.452700 | − | 0.784099i | −0.0261803 | − | 0.0453456i | ||||
\(300\) | −6.95823 | − | 22.0338i | −0.401733 | − | 1.27212i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.29401 | − | 9.16950i | 0.304636 | − | 0.527645i | ||||
\(303\) | 11.5060 | − | 12.5681i | 0.661003 | − | 0.722017i | ||||
\(304\) | −4.41549 | − | 7.64785i | −0.253246 | − | 0.438634i | ||||
\(305\) | 0.610783 | 0.0349734 | ||||||||
\(306\) | −20.6830 | − | 9.62176i | −1.18237 | − | 0.550039i | ||||
\(307\) | −21.6407 | −1.23510 | −0.617551 | − | 0.786531i | \(-0.711875\pi\) | ||||
−0.617551 | + | 0.786531i | \(0.711875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7008 | − | 4.13696i | −1.06385 | − | 0.235343i | ||||
\(310\) | −16.0016 | + | 27.7156i | −0.908830 | + | 1.57414i | ||||
\(311\) | −2.24724 | + | 3.89234i | −0.127429 | + | 0.220714i | −0.922680 | − | 0.385567i | \(-0.874006\pi\) |
0.795251 | + | 0.606281i | \(0.207339\pi\) | |||||||
\(312\) | −49.2103 | − | 10.8862i | −2.78598 | − | 0.616309i | ||||
\(313\) | −4.30102 | − | 7.44958i | −0.243108 | − | 0.421075i | 0.718490 | − | 0.695537i | \(-0.244834\pi\) |
−0.961598 | + | 0.274462i | \(0.911500\pi\) | |||||||
\(314\) | 0.799206 | 0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | 4.03128 | + | 6.98237i | 0.226419 | + | 0.392169i | 0.956744 | − | 0.290930i | \(-0.0939648\pi\) |
−0.730325 | + | 0.683100i | \(0.760631\pi\) | |||||||
\(318\) | −8.85019 | + | 9.66711i | −0.496294 | + | 0.542104i | ||||
\(319\) | −3.06701 | + | 5.31221i | −0.171719 | + | 0.297427i | ||||
\(320\) | 20.7053 | − | 35.8626i | 1.15746 | − | 2.00478i | ||||
\(321\) | −1.00370 | − | 3.17828i | −0.0560208 | − | 0.177394i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75228 | 0.0974992 | ||||||||
\(324\) | 31.1444 | + | 36.9798i | 1.73025 | + | 2.05443i | ||||
\(325\) | 7.89291 | 0.437820 | ||||||||
\(326\) | 14.5383 | + | 25.1811i | 0.805203 | + | 1.39465i | ||||
\(327\) | −9.70510 | − | 30.7319i | −0.536693 | − | 1.69948i | ||||
\(328\) | −45.8981 | + | 79.4978i | −2.53430 | + | 4.38953i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.79458 | + | 7.42175i | −0.374029 | + | 0.408554i | ||||
\(331\) | 11.4513 | + | 19.8342i | 0.629419 | + | 1.09019i | 0.987668 | + | 0.156560i | \(0.0500405\pi\) |
−0.358249 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(332\) | 75.1361 | 4.12363 | ||||||||
\(333\) | −19.7024 | + | 13.8225i | −1.07969 | + | 0.757468i | ||||
\(334\) | 8.68150 | 0.475030 | ||||||||
\(335\) | −2.01405 | − | 3.48844i | −0.110039 | − | 0.190594i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81891 | + | 11.8107i | −0.371450 | + | 0.643369i | −0.989789 | − | 0.142542i | \(-0.954472\pi\) |
0.618339 | + | 0.785911i | \(0.287806\pi\) | |||||||
\(338\) | −3.93458 | + | 6.81489i | −0.214013 | + | 0.370681i | ||||
\(339\) | 5.38935 | + | 1.19222i | 0.292709 | + | 0.0647525i | ||||
\(340\) | 11.9331 | + | 20.6688i | 0.647164 | + | 1.12092i | ||||
\(341\) | −10.0213 | −0.542683 | ||||||||
\(342\) | −4.62097 | − | 2.14968i | −0.249873 | − | 0.116242i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 28.6502 | + | 49.6237i | 1.54472 | + | 2.67553i | ||||
\(345\) | 0.528545 | − | 0.577332i | 0.0284559 | − | 0.0310825i | ||||
\(346\) | −15.5272 | + | 26.8938i | −0.834746 | + | 1.44582i | ||||
\(347\) | 1.41282 | − | 2.44707i | 0.0758440 | − | 0.131366i | −0.825609 | − | 0.564243i | \(-0.809168\pi\) |
0.901453 | + | 0.432877i | \(0.142502\pi\) | |||||||
\(348\) | −12.7430 | − | 40.3517i | −0.683097 | − | 2.16308i | ||||
\(349\) | −1.81202 | − | 3.13851i | −0.0969951 | − | 0.168000i | 0.813444 | − | 0.581643i | \(-0.197590\pi\) |
−0.910440 | + | 0.413642i | \(0.864256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.2493 | + | 6.34083i | −0.813947 | + | 0.338448i | ||||
\(352\) | 26.9893 | 1.43854 | ||||||||
\(353\) | 1.37701 | + | 2.38504i | 0.0732907 | + | 0.126943i | 0.900342 | − | 0.435184i | \(-0.143317\pi\) |
−0.827051 | + | 0.562127i | \(0.809983\pi\) | |||||||
\(354\) | −6.47859 | − | 20.5149i | −0.344333 | − | 1.09036i | ||||
\(355\) | −1.15179 | + | 1.99495i | −0.0611304 | + | 0.105881i | ||||
\(356\) | 6.94877 | − | 12.0356i | 0.368284 | − | 0.637887i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.49135 | + | 2.58310i | 0.0788205 | + | 0.136521i | ||||
\(359\) | −16.8015 | −0.886750 | −0.443375 | − | 0.896336i | \(-0.646219\pi\) | ||||
−0.443375 | + | 0.896336i | \(0.646219\pi\) | |||||||
\(360\) | −3.83696 | − | 43.4024i | −0.202226 | − | 2.28750i | ||||
\(361\) | −18.6085 | −0.979395 | ||||||||
\(362\) | 4.33081 | + | 7.50119i | 0.227622 | + | 0.394254i | ||||
\(363\) | 15.5264 | + | 3.43471i | 0.814922 | + | 0.180276i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.371322 | + | 0.643149i | −0.0194359 | + | 0.0336640i | ||||
\(366\) | −1.76788 | − | 0.391087i | −0.0924087 | − | 0.0204425i | ||||
\(367\) | 11.9670 | + | 20.7274i | 0.624670 | + | 1.08196i | 0.988605 | + | 0.150536i | \(0.0480999\pi\) |
−0.363934 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(368\) | −4.02059 | −0.209588 | ||||||||
\(369\) | 2.64885 | + | 29.9629i | 0.137894 | + | 1.55981i | ||||
\(370\) | 34.5551 | 1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 46.6822 | − | 50.9912i | 2.42036 | − | 2.64377i | ||||
\(373\) | 9.58030 | − | 16.5936i | 0.496049 | − | 0.859182i | −0.503941 | − | 0.863738i | \(-0.668117\pi\) |
0.999990 | + | 0.00455622i | \(0.00145030\pi\) | |||||||
\(374\) | −5.12784 | + | 8.88168i | −0.265154 | + | 0.459261i | ||||
\(375\) | 6.19206 | + | 19.6076i | 0.319757 | + | 1.01253i | ||||
\(376\) | 51.0299 | + | 88.3865i | 2.63167 | + | 4.55818i | ||||
\(377\) | 14.4548 | 0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | 2.66608 | + | 4.61779i | 0.136767 | + | 0.236888i | ||||
\(381\) | −4.36771 | − | 13.8307i | −0.223765 | − | 0.708568i | ||||
\(382\) | 5.25127 | − | 9.09546i | 0.268678 | − | 0.465364i | ||||
\(383\) | 10.0718 | − | 17.4448i | 0.514643 | − | 0.891388i | −0.485213 | − | 0.874396i | \(-0.661258\pi\) |
0.999856 | − | 0.0169915i | \(-0.00540883\pi\) | |||||||
\(384\) | −36.0855 | + | 39.4164i | −1.84148 | + | 2.01146i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.2294 | 0.571561 | ||||||||
\(387\) | 17.0242 | + | 7.91970i | 0.865390 | + | 0.402581i | ||||
\(388\) | −77.6743 | −3.94332 | ||||||||
\(389\) | −6.69736 | − | 11.6002i | −0.339570 | − | 0.588152i | 0.644782 | − | 0.764366i | \(-0.276948\pi\) |
−0.984352 | + | 0.176215i | \(0.943615\pi\) | |||||||
\(390\) | 23.1519 | + | 5.12161i | 1.17234 | + | 0.259343i | ||||
\(391\) | 0.398891 | − | 0.690899i | 0.0201728 | − | 0.0349402i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2476 | + | 4.47913i | 1.02136 | + | 0.225942i | ||||
\(394\) | −1.20724 | − | 2.09100i | −0.0608198 | − | 0.105343i | ||||
\(395\) | 24.9261 | 1.25417 | ||||||||
\(396\) | 17.7940 | − | 12.4836i | 0.894181 | − | 0.627324i | ||||
\(397\) | −18.0133 | −0.904061 | −0.452031 | − | 0.892002i | \(-0.649300\pi\) | ||||
−0.452031 | + | 0.892002i | \(0.649300\pi\) | |||||||
\(398\) | 8.58506 | + | 14.8698i | 0.430330 | + | 0.745354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5249 | − | 30.3541i | 0.876247 | − | 1.51770i | ||||
\(401\) | −14.4337 | + | 25.0000i | −0.720787 | + | 1.24844i | 0.239898 | + | 0.970798i | \(0.422886\pi\) |
−0.960685 | + | 0.277642i | \(0.910447\pi\) | |||||||
\(402\) | 3.59591 | + | 11.3867i | 0.179348 | + | 0.567918i | ||||
\(403\) | 11.8075 | + | 20.4513i | 0.588176 | + | 1.01875i | ||||
\(404\) | 52.8479 | 2.62928 | ||||||||
\(405\) | −9.19729 | − | 10.9205i | −0.457017 | − | 0.542646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41019 | + | 9.37073i | 0.268173 | + | 0.464490i | ||||
\(408\) | −13.3734 | − | 42.3478i | −0.662080 | − | 2.09653i | ||||
\(409\) | 5.42937 | − | 9.40395i | 0.268465 | − | 0.464995i | −0.700000 | − | 0.714142i | \(-0.746817\pi\) |
0.968466 | + | 0.249147i | \(0.0801502\pi\) | |||||||
\(410\) | 21.5936 | − | 37.4012i | 1.06643 | − | 1.84711i | ||||
\(411\) | 19.3571 | − | 21.1438i | 0.954814 | − | 1.04295i | ||||
\(412\) | −29.7014 | − | 51.4443i | −1.46328 | − | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.89951 | + | 1.33263i | −0.0933561 | + | 0.0654951i | ||||
\(415\) | −22.1885 | −1.08919 | ||||||||
\(416\) | −31.8001 | − | 55.0793i | −1.55913 | − | 2.70049i | ||||
\(417\) | 13.3642 | + | 2.95641i | 0.654449 | + | 0.144776i | ||||
\(418\) | −1.14566 | + | 1.98434i | −0.0560359 | + | 0.0970570i | ||||
\(419\) | −0.247572 | + | 0.428807i | −0.0120947 | + | 0.0209486i | −0.872009 | − | 0.489489i | \(-0.837183\pi\) |
0.859915 | + | 0.510438i | \(0.170517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | + | 16.4600i | 0.463158 | + | 0.802212i | 0.999116 | − | 0.0420318i | \(-0.0133831\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(422\) | 31.0226 | 1.51016 | ||||||||
\(423\) | 30.3224 | + | 14.1061i | 1.47433 | + | 0.685860i | ||||
\(424\) | −25.5155 | −1.23914 | ||||||||
\(425\) | 3.47737 | + | 6.02298i | 0.168677 | + | 0.292157i | ||||
\(426\) | 4.61116 | − | 5.03679i | 0.223411 | − | 0.244033i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.16864 | − | 8.95234i | 0.249835 | − | 0.432728i | ||||
\(429\) | 2.23593 | + | 7.08024i | 0.107952 | + | 0.341837i | ||||
\(430\) | −13.4790 | − | 23.3464i | −0.650016 | − | 1.12586i | ||||
\(431\) | −16.9215 | −0.815078 | −0.407539 | − | 0.913188i | \(-0.633613\pi\) | ||||
−0.407539 | + | 0.913188i | \(0.633613\pi\) | |||||||
\(432\) | −9.47342 | + | 72.7236i | −0.455790 | + | 3.49892i | ||||
\(433\) | −33.4740 | −1.60866 | −0.804330 | − | 0.594183i | \(-0.797476\pi\) | ||||
−0.804330 | + | 0.594183i | \(0.797476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.76315 | + | 11.9163i | 0.180429 | + | 0.571343i | ||||
\(436\) | 49.9774 | − | 86.5634i | 2.39348 | − | 4.14564i | ||||
\(437\) | 0.0891197 | − | 0.154360i | 0.00426317 | − | 0.00738403i | ||||
\(438\) | 1.48658 | − | 1.62380i | 0.0710318 | − | 0.0775883i | ||||
\(439\) | −10.4657 | − | 18.1272i | −0.499502 | − | 0.865163i | 0.500498 | − | 0.865738i | \(-0.333150\pi\) |
−1.00000 | 0.000574559i | \(0.999817\pi\) | ||||||||
\(440\) | −19.5891 | −0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | 15.4290 | + | 26.7238i | 0.733054 | + | 1.26969i | 0.955572 | + | 0.294759i | \(0.0952393\pi\) |
−0.222517 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(444\) | −72.8833 | − | 16.1231i | −3.45889 | − | 0.765169i | ||||
\(445\) | −2.05205 | + | 3.55425i | −0.0972763 | + | 0.168487i | ||||
\(446\) | −22.6972 | + | 39.3128i | −1.07475 | + | 1.86151i | ||||
\(447\) | 23.1157 | + | 5.11362i | 1.09334 | + | 0.241866i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2789 | −1.57053 | −0.785263 | − | 0.619162i | \(-0.787472\pi\) | ||||
−0.785263 | + | 0.619162i | \(0.787472\pi\) | |||||||
\(450\) | −1.78129 | − | 20.1493i | −0.0839709 | − | 0.949849i | ||||
\(451\) | 13.5234 | 0.636791 | ||||||||
\(452\) | 8.55957 | + | 14.8256i | 0.402608 | + | 0.697338i | ||||
\(453\) | 4.56092 | − | 4.98191i | 0.214291 | − | 0.234071i | ||||
\(454\) | 23.1737 | − | 40.1380i | 1.08760 | − | 1.88377i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.98786 | − | 9.46130i | −0.139919 | − | 0.443066i | ||||
\(457\) | −11.8952 | − | 20.6031i | −0.556434 | − | 0.963772i | −0.997790 | − | 0.0664402i | \(-0.978836\pi\) |
0.441356 | − | 0.897332i | \(-0.354498\pi\) | |||||||
\(458\) | −53.7309 | −2.51068 | ||||||||
\(459\) | −11.5570 | − | 8.84296i | −0.539432 | − | 0.412754i | ||||
\(460\) | 2.42764 | 0.113189 | ||||||||
\(461\) | 8.53122 | + | 14.7765i | 0.397339 | + | 0.688211i | 0.993397 | − | 0.114731i | \(-0.0366005\pi\) |
−0.596058 | + | 0.802941i | \(0.703267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | − | 31.3922i | 0.842306 | − | 1.45892i | −0.0456338 | − | 0.998958i | \(-0.514531\pi\) |
0.887940 | − | 0.459959i | \(-0.152136\pi\) | |||||||
\(464\) | 32.0945 | − | 55.5893i | 1.48995 | − | 2.58067i | ||||
\(465\) | −13.7858 | + | 15.0583i | −0.639300 | + | 0.698310i | ||||
\(466\) | 8.05253 | + | 13.9474i | 0.373026 | + | 0.646100i | ||||
\(467\) | −8.19160 | −0.379062 | −0.189531 | − | 0.981875i | \(-0.560697\pi\) | ||||
−0.189531 | + | 0.981875i | \(0.560697\pi\) | |||||||
\(468\) | −46.4420 | − | 21.6049i | −2.14678 | − | 0.998686i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.0080 | − | 41.5830i | −1.10740 | − | 1.91808i | ||||
\(471\) | 0.497798 | + | 0.110122i | 0.0229373 | + | 0.00507415i | ||||
\(472\) | 20.9413 | − | 36.2714i | 0.963900 | − | 1.66952i | ||||
\(473\) | 4.22074 | − | 7.31054i | 0.194070 | − | 0.336139i | ||||
\(474\) | −72.1472 | − | 15.9603i | −3.31383 | − | 0.733079i | ||||
\(475\) | 0.776909 | + | 1.34565i | 0.0356470 | + | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.84451 | + | 4.80185i | −0.313389 | + | 0.219862i | ||||
\(478\) | −54.4530 | −2.49062 | ||||||||
\(479\) | 12.7775 | + | 22.1312i | 0.583817 | + | 1.01120i | 0.995022 | + | 0.0996574i | \(0.0317747\pi\) |
−0.411205 | + | 0.911543i | \(0.634892\pi\) | |||||||
\(480\) | 37.1278 | − | 40.5549i | 1.69464 | − | 1.85107i | ||||
\(481\) | 12.7491 | − | 22.0820i | 0.581308 | − | 1.00685i | ||||
\(482\) | 39.7614 | − | 68.8687i | 1.81108 | − | 3.13688i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.6596 | + | 42.7116i | 1.12089 | + | 1.94144i | ||||
\(485\) | 22.9381 | 1.04156 | ||||||||
\(486\) | 19.6286 | + | 37.4980i | 0.890372 | + | 1.70094i | ||||
\(487\) | −6.92281 | −0.313702 | −0.156851 | − | 0.987622i | \(-0.550134\pi\) | ||||
−0.156851 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(488\) | −1.76246 | − | 3.05266i | −0.0797826 | − | 0.138188i | ||||
\(489\) | 5.58574 | + | 17.6877i | 0.252596 | + | 0.799865i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7262 | − | 32.4348i | 0.845103 | − | 1.46376i | −0.0404294 | − | 0.999182i | \(-0.512873\pi\) |
0.885532 | − | 0.464578i | \(-0.153794\pi\) | |||||||
\(492\) | −62.9960 | + | 68.8108i | −2.84008 | + | 3.10223i | ||||
\(493\) | 6.36831 | + | 11.0302i | 0.286814 | + | 0.496777i | ||||
\(494\) | 5.39946 | 0.242933 | ||||||||
\(495\) | −5.25475 | + | 3.68654i | −0.236183 | + | 0.165698i | ||||
\(496\) | 104.867 | 4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 64.2235 | + | 14.2074i | 2.87793 | + | 0.636649i | ||||
\(499\) | −12.8125 | + | 22.1919i | −0.573566 | + | 0.993446i | 0.422630 | + | 0.906302i | \(0.361107\pi\) |
−0.996196 | + | 0.0871432i | \(0.972226\pi\) | |||||||
\(500\) | −31.8867 | + | 55.2293i | −1.42601 | + | 2.46993i | ||||
\(501\) | 5.40741 | + | 1.19622i | 0.241585 | + | 0.0534430i | ||||
\(502\) | −30.9329 | − | 53.5774i | −1.38060 | − | 2.39127i | ||||
\(503\) | −5.79692 | −0.258472 | −0.129236 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129236 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | 0.521598 | + | 0.903434i | 0.0231878 | + | 0.0401625i | ||||
\(507\) | −3.38974 | + | 3.70262i | −0.150543 | + | 0.164439i | ||||
\(508\) | 22.4920 | − | 38.9573i | 0.997921 | − | 1.72845i | ||||
\(509\) | −12.5697 | + | 21.7714i | −0.557144 | + | 0.965002i | 0.440589 | + | 0.897709i | \(0.354770\pi\) |
−0.997733 | + | 0.0672931i | \(0.978564\pi\) | |||||||
\(510\) | 6.29174 | + | 19.9233i | 0.278603 | + | 0.882218i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −23.9940 | −1.06039 | ||||||||
\(513\) | −2.58204 | − | 1.97568i | −0.114000 | − | 0.0872286i | ||||
\(514\) | 65.9475 | 2.90882 | ||||||||
\(515\) | 8.77113 | + | 15.1920i | 0.386502 | + | 0.669441i | ||||
\(516\) | 17.5366 | + | 55.5311i | 0.772007 | + | 2.44462i | ||||
\(517\) | 7.51771 | − | 13.0211i | 0.330629 | − | 0.572665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.3770 | + | 14.6118i | −0.587186 | + | 0.641386i | ||||
\(520\) | 23.0808 | + | 39.9771i | 1.01216 | + | 1.75311i | ||||
\(521\) | 7.29656 | 0.319668 | 0.159834 | − | 0.987144i | \(-0.448904\pi\) | ||||
0.159834 | + | 0.987144i | \(0.448904\pi\) | |||||||
\(522\) | −3.26218 | − | 36.9007i | −0.142782 | − | 1.61510i | ||||
\(523\) | 16.7727 | 0.733421 | 0.366710 | − | 0.930335i | \(-0.380484\pi\) | ||||
0.366710 | + | 0.930335i | \(0.380484\pi\) | |||||||
\(524\) | 32.1580 | + | 55.6993i | 1.40483 | + | 2.43324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6908 | + | 20.2490i | −0.509741 | + | 0.882898i | ||||
\(527\) | −10.4041 | + | 18.0204i | −0.453208 | + | 0.784979i | ||||
\(528\) | 32.1933 | + | 7.12174i | 1.40103 | + | 0.309934i | ||||
\(529\) | 11.4594 | + | 19.8483i | 0.498236 | + | 0.862970i | ||||
\(530\) | 12.0042 | 0.521431 | ||||||||
\(531\) | −1.20855 | − | 13.6707i | −0.0524468 | − | 0.593260i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9339 | − | 27.5982i | −0.690172 | − | 1.19541i | ||||
\(534\) | 8.21535 | − | 8.97366i | 0.355513 | − | 0.388328i | ||||
\(535\) | −1.52635 | + | 2.64372i | −0.0659900 | + | 0.114298i | ||||
\(536\) | −11.6234 | + | 20.1322i | −0.502053 | + | 0.869581i | ||||
\(537\) | 0.572991 | + | 1.81442i | 0.0247264 | + | 0.0782980i | ||||
\(538\) | −20.6774 | − | 35.8143i | −0.891466 | − | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.72007 | − | 43.9107i | 0.246153 | − | 1.88962i | ||||
\(541\) | −5.29816 | −0.227786 | −0.113893 | − | 0.993493i | \(-0.536332\pi\) | ||||
−0.113893 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(542\) | −6.35097 | − | 11.0002i | −0.272798 | − | 0.472499i | ||||
\(543\) | 1.66393 | + | 5.26898i | 0.0714062 | + | 0.226113i | ||||
\(544\) | 28.0202 | − | 48.5324i | 1.20136 | − | 2.08081i | ||||
\(545\) | −14.7589 | + | 25.5631i | −0.632200 | + | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | + | 28.4619i | 0.702603 | + | 1.21694i | 0.967550 | + | 0.252681i | \(0.0813123\pi\) |
−0.264947 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(548\) | 88.9084 | 3.79798 | ||||||||
\(549\) | −1.04727 | − | 0.487190i | −0.0446962 | − | 0.0207928i | ||||
\(550\) | −9.09416 | −0.387776 | ||||||||
\(551\) | 1.42280 | + | 2.46436i | 0.0606133 | + | 0.104985i | ||||
\(552\) | −4.41062 | − | 0.975709i | −0.187729 | − | 0.0415290i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.2515 | + | 38.5408i | −0.945376 | + | 1.63744i | ||||
\(555\) | 21.5232 | + | 4.76132i | 0.913610 | + | 0.202107i | ||||
\(556\) | 21.2256 | + | 36.7638i | 0.900166 | + | 1.55913i | ||||
\(557\) | −18.8160 | −0.797258 | −0.398629 | − | 0.917112i | \(-0.630514\pi\) | ||||
−0.398629 | + | 0.917112i | \(0.630514\pi\) | |||||||
\(558\) | 49.5441 | − | 34.7583i | 2.09737 | − | 1.47144i | ||||
\(559\) | −19.8923 | −0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41776 | + | 4.82554i | −0.186518 | + | 0.203734i | ||||
\(562\) | −4.77054 | + | 8.26282i | −0.201233 | + | 0.348546i | ||||
\(563\) | −13.8325 | + | 23.9586i | −0.582970 | + | 1.00973i | 0.412155 | + | 0.911114i | \(0.364776\pi\) |
−0.995125 | + | 0.0986197i | \(0.968557\pi\) | |||||||
\(564\) | 31.2351 | + | 98.9083i | 1.31523 | + | 4.16479i | ||||
\(565\) | −2.52773 | − | 4.37816i | −0.106343 | − | 0.184191i | ||||
\(566\) | −70.7856 | −2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | 20.0916 | + | 34.7996i | 0.842282 | + | 1.45888i | 0.887961 | + | 0.459920i | \(0.152122\pi\) |
−0.0456782 | + | 0.998956i | \(0.514545\pi\) | |||||||
\(570\) | 1.40569 | + | 4.45124i | 0.0588780 | + | 0.186442i | ||||
\(571\) | 3.40565 | − | 5.89875i | 0.142522 | − | 0.246855i | −0.785924 | − | 0.618323i | \(-0.787812\pi\) |
0.928446 | + | 0.371468i | \(0.121146\pi\) | |||||||
\(572\) | −11.5142 | + | 19.9431i | −0.481431 | + | 0.833863i | ||||
\(573\) | 4.52409 | − | 4.94169i | 0.188997 | − | 0.206442i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707427 | 0.0295017 | ||||||||
\(576\) | −64.1075 | + | 44.9755i | −2.67115 | + | 1.87398i | ||||
\(577\) | −36.4222 | −1.51628 | −0.758138 | − | 0.652094i | \(-0.773891\pi\) | ||||
−0.758138 | + | 0.652094i | \(0.773891\pi\) | |||||||
\(578\) | −12.4312 | − | 21.5315i | −0.517071 | − | 0.895593i | ||||
\(579\) | 6.99441 | + | 1.54729i | 0.290678 | + | 0.0643031i | ||||
\(580\) | −19.3787 | + | 33.5649i | −0.804658 | + | 1.39371i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −66.3930 | − | 14.6873i | −2.75208 | − | 0.608810i | ||||
\(583\) | 1.87947 | + | 3.25534i | 0.0778397 | + | 0.134822i | ||||
\(584\) | 4.28590 | 0.177352 | ||||||||
\(585\) | 13.7148 | + | 6.38015i | 0.567037 | + | 0.263787i | ||||
\(586\) | −51.2721 | −2.11803 | ||||||||
\(587\) | 5.57943 | + | 9.66385i | 0.230288 | + | 0.398870i | 0.957893 | − | 0.287126i | \(-0.0927000\pi\) |
−0.727605 | + | 0.685996i | \(0.759367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32446 | + | 4.02609i | −0.0957779 | + | 0.165892i | ||||
\(590\) | −9.85220 | + | 17.0645i | −0.405609 | + | 0.702535i | ||||
\(591\) | −0.463831 | − | 1.46876i | −0.0190795 | − | 0.0604166i | ||||
\(592\) | −56.6145 | − | 98.0593i | −2.32684 | − | 4.03021i | ||||
\(593\) | 19.8085 | 0.813439 | 0.406720 | − | 0.913553i | \(-0.366673\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366673\pi\) | |||||||
\(594\) | 17.5701 | − | 7.30586i | 0.720911 | − | 0.299763i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.7133 | + | 63.5893i | 1.50384 | + | 2.60472i | ||||
\(597\) | 3.29845 | + | 10.4448i | 0.134997 | + | 0.427477i | ||||
\(598\) | 1.22914 | − | 2.12893i | 0.0502633 | − | 0.0870586i | ||||
\(599\) | 9.06600 | − | 15.7028i | 0.370427 | − | 0.641598i | −0.619204 | − | 0.785230i | \(-0.712545\pi\) |
0.989631 | + | 0.143632i | \(0.0458781\pi\) | |||||||
\(600\) | 26.5913 | − | 29.0458i | 1.08558 | − | 1.18579i | ||||
\(601\) | −12.3285 | − | 21.3536i | −0.502889 | − | 0.871030i | −0.999994 | − | 0.00333942i | \(-0.998937\pi\) |
0.497105 | − | 0.867690i | \(-0.334396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.670802 | + | 7.58788i | 0.0273172 | + | 0.309003i | ||||
\(604\) | 20.9486 | 0.852387 | ||||||||
\(605\) | −7.28223 | − | 12.6132i | −0.296065 | − | 0.512799i | ||||
\(606\) | 45.1724 | + | 9.99295i | 1.83500 | + | 0.405936i | ||||
\(607\) | −8.63876 | + | 14.9628i | −0.350637 | + | 0.607320i | −0.986361 | − | 0.164596i | \(-0.947368\pi\) |
0.635725 | + | 0.771916i | \(0.280701\pi\) | |||||||
\(608\) | 6.26024 | − | 10.8431i | 0.253886 | − | 0.439744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.829179 | + | 1.43618i | 0.0335725 | + | 0.0581492i | ||||
\(611\) | −35.4308 | −1.43338 | ||||||||
\(612\) | −3.97445 | − | 44.9577i | −0.160658 | − | 1.81731i | ||||
\(613\) | 19.5566 | 0.789882 | 0.394941 | − | 0.918707i | \(-0.370765\pi\) | ||||
0.394941 | + | 0.918707i | \(0.370765\pi\) | |||||||
\(614\) | −29.3787 | − | 50.8855i | −1.18563 | − | 2.05357i | ||||
\(615\) | 18.6034 | − | 20.3206i | 0.750161 | − | 0.819404i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8723 | − | 18.8314i | 0.437702 | − | 0.758122i | −0.559810 | − | 0.828621i | \(-0.689126\pi\) |
0.997512 | + | 0.0704988i | \(0.0224591\pi\) | |||||||
\(618\) | −15.6601 | − | 49.5888i | −0.629940 | − | 1.99475i | ||||
\(619\) | −16.9024 | − | 29.2758i | −0.679366 | − | 1.17670i | −0.975172 | − | 0.221448i | \(-0.928922\pi\) |
0.295807 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(620\) | −63.3190 | −2.54295 | ||||||||
\(621\) | −1.36677 | + | 0.568317i | −0.0548464 | + | 0.0228058i | ||||
\(622\) | −12.2031 | −0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.3977 | − | 74.0906i | −0.936658 | − | 2.96600i | ||||
\(625\) | 3.20808 | − | 5.55655i | 0.128323 | − | 0.222262i | ||||
\(626\) | 11.6778 | − | 20.2266i | 0.466740 | − | 0.808418i | ||||
\(627\) | −0.987011 | + | 1.07812i | −0.0394174 | + | 0.0430558i | ||||
\(628\) | 0.790623 | + | 1.36940i | 0.0315493 | + | 0.0546450i | ||||
\(629\) | 22.4674 | 0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | −71.9258 | − | 124.579i | −2.86105 | − | 4.95549i | ||||
\(633\) | 19.3229 | + | 4.27458i | 0.768018 | + | 0.169899i | ||||
\(634\) | −10.9454 | + | 18.9581i | −0.434699 | + | 0.752921i | ||||
\(635\) | −6.64213 | + | 11.5045i | −0.263585 | + | 0.456542i | ||||
\(636\) | −25.3192 | − | 5.60107i | −1.00397 | − | 0.222097i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6547 | −0.659365 | ||||||||
\(639\) | 3.56615 | − | 2.50188i | 0.141075 | − | 0.0989728i | ||||
\(640\) | 48.9458 | 1.93475 | ||||||||
\(641\) | −7.95901 | − | 13.7854i | −0.314362 | − | 0.544491i | 0.664940 | − | 0.746897i | \(-0.268457\pi\) |
−0.979302 | + | 0.202406i | \(0.935124\pi\) | |||||||
\(642\) | 6.11074 | − | 6.67479i | 0.241172 | − | 0.263433i | ||||
\(643\) | −13.2527 | + | 22.9544i | −0.522636 | + | 0.905231i | 0.477017 | + | 0.878894i | \(0.341718\pi\) |
−0.999653 | + | 0.0263376i | \(0.991616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.17875 | − | 16.3989i | −0.203913 | − | 0.645707i | ||||
\(646\) | 2.37883 | + | 4.12026i | 0.0935938 | + | 0.162109i | ||||
\(647\) | 0.0160392 | 0.000630565 | 0.000315282 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000315282 | 1.00000i | \(0.499900\pi\) | ||||||||
\(648\) | −28.0408 | + | 77.4794i | −1.10155 | + | 3.04368i | ||||
\(649\) | −6.17012 | −0.242198 | ||||||||
\(650\) | 10.7152 | + | 18.5592i | 0.420283 | + | 0.727951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.7644 | + | 49.8214i | −1.12650 | + | 1.95115i | ||||
\(653\) | 16.6440 | − | 28.8282i | 0.651328 | − | 1.12813i | −0.331473 | − | 0.943465i | \(-0.607545\pi\) |
0.982801 | − | 0.184669i | \(-0.0591212\pi\) | |||||||
\(654\) | 59.0870 | − | 64.5410i | 2.31048 | − | 2.52375i | ||||
\(655\) | −9.49661 | − | 16.4486i | −0.371063 | − | 0.642700i | ||||
\(656\) | −141.514 | −5.52520 | ||||||||
\(657\) | 1.14969 | − | 0.806577i | 0.0448535 | − | 0.0314676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4156 | + | 33.6288i | 0.756324 | + | 1.30999i | 0.944713 | + | 0.327897i | \(0.106340\pi\) |
−0.188389 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(660\) | −19.4384 | − | 4.30012i | −0.756639 | − | 0.167382i | ||||
\(661\) | −2.65322 | + | 4.59551i | −0.103198 | + | 0.178745i | −0.913001 | − | 0.407958i | \(-0.866241\pi\) |
0.809802 | + | 0.586703i | \(0.199574\pi\) | |||||||
\(662\) | −31.0917 | + | 53.8525i | −1.20842 | + | 2.09304i | ||||
\(663\) | 15.0531 | + | 3.33001i | 0.584613 | + | 0.129327i | ||||
\(664\) | 64.0264 | + | 110.897i | 2.48471 | + | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −59.2492 | − | 27.5628i | −2.29586 | − | 1.06804i | ||||
\(667\) | 1.29555 | 0.0501640 | ||||||||
\(668\) | 8.58826 | + | 14.8753i | 0.332290 | + | 0.575543i | ||||
\(669\) | −19.5542 | + | 21.3592i | −0.756010 | + | 0.825793i | ||||
\(670\) | 5.46842 | − | 9.47158i | 0.211263 | − | 0.365919i | ||||
\(671\) | −0.259644 | + | 0.449717i | −0.0100235 | + | 0.0173611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03565 | − | 5.25789i | −0.117016 | − | 0.202677i | 0.801568 | − | 0.597903i | \(-0.203999\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(674\) | −37.0285 | −1.42628 | ||||||||
\(675\) | 1.66686 | − | 12.7958i | 0.0641574 | − | 0.492510i | ||||
\(676\) | −15.5693 | −0.598819 | ||||||||
\(677\) | 17.3925 | + | 30.1247i | 0.668449 | + | 1.15779i | 0.978338 | + | 0.207014i | \(0.0663747\pi\) |
−0.309889 | + | 0.950773i | \(0.600292\pi\) | |||||||
\(678\) | 4.51304 | + | 14.2909i | 0.173322 | + | 0.548838i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.3373 | + | 35.2253i | −0.779901 | + | 1.35083i | ||||
\(681\) | 19.9647 | − | 21.8075i | 0.765049 | − | 0.835666i | ||||
\(682\) | −13.6046 | − | 23.5638i | −0.520946 | − | 0.902305i | ||||
\(683\) | 19.4241 | 0.743243 | 0.371622 | − | 0.928384i | \(-0.378802\pi\) | ||||
0.371622 | + | 0.928384i | \(0.378802\pi\) | |||||||
\(684\) | −0.887968 | − | 10.0444i | −0.0339523 | − | 0.384057i | ||||
\(685\) | −26.2556 | −1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.4672 | − | 7.40354i | −1.27685 | − | 0.282463i | ||||
\(688\) | −44.1676 | + | 76.5006i | −1.68387 | + | 2.91656i | ||||
\(689\) | 4.42895 | − | 7.67117i | 0.168730 | − | 0.292248i | ||||
\(690\) | 2.07506 | + | 0.459040i | 0.0789961 | + | 0.0174754i | ||||
\(691\) | 3.31837 | + | 5.74759i | 0.126237 | + | 0.218649i | 0.922216 | − | 0.386676i | \(-0.126377\pi\) |
−0.795979 | + | 0.605324i | \(0.793043\pi\) | |||||||
\(692\) | −61.4416 | −2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | −6.26814 | − | 10.8567i | −0.237764 | − | 0.411820i | ||||
\(696\) | 48.6982 | − | 53.1933i | 1.84590 | − | 2.01629i | ||||
\(697\) | 14.0399 | − | 24.3178i | 0.531799 | − | 0.921103i | ||||
\(698\) | 4.91987 | − | 8.52147i | 0.186220 | − | 0.322542i | ||||
\(699\) | 3.09385 | + | 9.79690i | 0.117020 | + | 0.370553i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9153 | −0.525574 | −0.262787 | − | 0.964854i | \(-0.584642\pi\) | ||||
−0.262787 | + | 0.964854i | \(0.584642\pi\) | |||||||
\(702\) | −35.6116 | − | 27.2487i | −1.34407 | − | 1.02844i | ||||
\(703\) | 5.01963 | 0.189319 | ||||||||
\(704\) | 17.6036 | + | 30.4904i | 0.663462 | + | 1.14915i | ||||
\(705\) | −9.22406 | − | 29.2087i | −0.347398 | − | 1.10006i | ||||
\(706\) | −3.73876 | + | 6.47571i | −0.140710 | + | 0.243717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 28.7423 | − | 31.3954i | 1.08020 | − | 1.17991i | ||||
\(709\) | −17.0778 | − | 29.5796i | −0.641370 | − | 1.11089i | −0.985127 | − | 0.171827i | \(-0.945033\pi\) |
0.343757 | − | 0.939059i | \(-0.388300\pi\) | |||||||
\(710\) | −6.25450 | −0.234727 | ||||||||
\(711\) | −42.7389 | − | 19.8822i | −1.60283 | − | 0.745642i | ||||
\(712\) | 23.6852 | 0.887642 | ||||||||
\(713\) | 1.05829 | + | 1.83301i | 0.0396332 | + | 0.0686467i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.40025 | − | 5.88941i | 0.127162 | − | 0.220251i | ||||
\(716\) | −2.95068 | + | 5.11072i | −0.110272 | + | 0.190997i | ||||
\(717\) | −33.9169 | − | 7.50303i | −1.26665 | − | 0.280206i | ||||
\(718\) | −22.8092 | − | 39.5066i | −0.851231 | − | 1.47437i | ||||
\(719\) | −44.2900 | −1.65174 | −0.825870 | − | 0.563861i | \(-0.809316\pi\) | ||||
−0.825870 | + | 0.563861i | \(0.809316\pi\) | |||||||
\(720\) | 54.9879 | − | 38.5775i | 2.04928 | − | 1.43770i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.2623 | − | 43.7556i | −0.940165 | − | 1.62841i | ||||
\(723\) | 34.2554 | − | 37.4173i | 1.27397 | − | 1.39156i | ||||
\(724\) | −8.56860 | + | 14.8413i | −0.318450 | + | 0.551571i | ||||
\(725\) | −5.64705 | + | 9.78099i | −0.209726 | + | 0.363257i | ||||
\(726\) | 13.0018 | + | 41.1711i | 0.482541 | + | 1.52800i | ||||
\(727\) | 14.1247 | + | 24.4647i | 0.523857 | + | 0.907346i | 0.999614 | + | 0.0277700i | \(0.00884060\pi\) |
−0.475758 | + | 0.879576i | \(0.657826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.05919 | + | 26.0608i | 0.261451 | + | 0.965217i | ||||
\(730\) | −2.01638 | −0.0746295 | ||||||||
\(731\) | −8.76391 | − | 15.1795i | −0.324145 | − | 0.561435i | ||||
\(732\) | −1.07879 | − | 3.41606i | −0.0398731 | − | 0.126261i | ||||
\(733\) | 12.5084 | − | 21.6653i | 0.462010 | − | 0.800225i | −0.537051 | − | 0.843550i | \(-0.680462\pi\) |
0.999061 | + | 0.0433249i | \(0.0137951\pi\) | |||||||
\(734\) | −32.4919 | + | 56.2776i | −1.19930 | + | 2.07724i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.85018 | − | 4.93666i | −0.105059 | − | 0.181968i | ||||
\(737\) | 3.42470 | 0.126150 | ||||||||
\(738\) | −66.8579 | + | 46.9050i | −2.46107 | + | 1.72660i | ||||
\(739\) | 32.0230 | 1.17798 | 0.588992 | − | 0.808139i | \(-0.299525\pi\) | ||||
0.588992 | + | 0.808139i | \(0.299525\pi\) | |||||||
\(740\) | 34.1840 | + | 59.2084i | 1.25663 | + | 2.17655i | ||||
\(741\) | 3.36314 | + | 0.743987i | 0.123548 | + | 0.0273311i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4031 | − | 33.6072i | 0.711833 | − | 1.23293i | −0.252336 | − | 0.967640i | \(-0.581199\pi\) |
0.964169 | − | 0.265290i | \(-0.0854678\pi\) | |||||||
\(744\) | 115.040 | + | 25.4489i | 4.21757 | + | 0.933003i | ||||
\(745\) | −10.8418 | − | 18.7786i | −0.397214 | − | 0.687995i | ||||
\(746\) | 52.0236 | 1.90472 | ||||||||
\(747\) | 38.0450 | + | 17.6986i | 1.39200 | + | 0.647559i | ||||
\(748\) | −20.2911 | −0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −37.6987 | + | 41.1785i | −1.37656 | + | 1.50363i | ||||
\(751\) | −10.8495 | + | 18.7920i | −0.395905 | + | 0.685728i | −0.993216 | − | 0.116282i | \(-0.962903\pi\) |
0.597311 | + | 0.802010i | \(0.296236\pi\) | |||||||
\(752\) | −78.6685 | + | 136.258i | −2.86874 | + | 4.96881i | ||||
\(753\) | −11.8847 | − | 37.6337i | −0.433102 | − | 1.37145i | ||||
\(754\) | 19.6233 | + | 33.9885i | 0.714638 | + | 1.23779i | ||||
\(755\) | −6.18635 | −0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | 13.6802 | + | 23.6949i | 0.496889 | + | 0.860637i | ||||
\(759\) | 0.200402 | + | 0.634589i | 0.00727414 | + | 0.0230341i | ||||
\(760\) | −4.54374 | + | 7.86999i | −0.164819 | + | 0.285475i | ||||
\(761\) | 6.66048 | − | 11.5363i | 0.241442 | − | 0.418190i | −0.719683 | − | 0.694303i | \(-0.755713\pi\) |
0.961125 | + | 0.276113i | \(0.0890462\pi\) | |||||||
\(762\) | 26.5917 | − | 29.0462i | 0.963315 | − | 1.05223i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7795 | 0.751775 | ||||||||
\(765\) | 1.17370 | + | 13.2765i | 0.0424352 | + | 0.480012i | ||||
\(766\) | 54.6923 | 1.97611 | ||||||||
\(767\) | 7.26992 | + | 12.5919i | 0.262502 | + | 0.454666i | ||||
\(768\) | −53.3802 | − | 11.8087i | −1.92619 | − | 0.426109i | ||||
\(769\) | 27.3568 | − | 47.3833i | 0.986510 | − | 1.70869i | 0.351488 | − | 0.936192i | \(-0.385676\pi\) |
0.635022 | − | 0.772494i | \(-0.280991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.0765 | + | 9.08686i | 1.47933 | + | 0.327255i | ||||
\(772\) | 11.1088 | + | 19.2410i | 0.399814 | + | 0.692498i | ||||
\(773\) | 2.36042 | 0.0848983 | 0.0424491 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424491 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(774\) | 4.48934 | + | 50.7818i | 0.161366 | + | 1.82532i | ||||
\(775\) | −18.4515 | −0.662796 | ||||||||
\(776\) | −66.1892 | − | 114.643i | −2.37606 | − | 4.11545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1842 | − | 31.4960i | 0.651936 | − | 1.12919i | ||||
\(779\) | 3.13678 | − | 5.43306i | 0.112387 | − | 0.194660i | ||||
\(780\) | 14.1276 | + | 44.7361i | 0.505849 | + | 1.60181i | ||||
\(781\) | −0.979248 | − | 1.69611i | −0.0350403 | − | 0.0606915i | ||||
\(782\) | 2.16608 | 0.0774589 | ||||||||
\(783\) | 3.05261 | − | 23.4337i | 0.109092 | − | 0.837452i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.233479 | − | 0.404398i | −0.00833323 | − | 0.0144336i | ||||
\(786\) | 16.9553 | + | 53.6904i | 0.604777 | + | 1.91507i | ||||
\(787\) | 0.833971 | − | 1.44448i | 0.0297278 | − | 0.0514901i | −0.850779 | − | 0.525524i | \(-0.823869\pi\) |
0.880507 | + | 0.474034i | \(0.157203\pi\) | |||||||
\(788\) | 2.38855 | − | 4.13708i | 0.0850884 | − | 0.147377i | ||||
\(789\) | −10.0719 | + | 11.0015i | −0.358568 | + | 0.391665i | ||||
\(790\) | 33.8388 | + | 58.6105i | 1.20393 | + | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 33.5880 | + | 15.6252i | 1.19350 | + | 0.555218i | ||||
\(793\) | 1.22370 | 0.0434548 | ||||||||
\(794\) | −24.4542 | − | 42.3560i | −0.867848 | − | 1.50316i | ||||
\(795\) | 7.47704 | + | 1.65406i | 0.265183 | + | 0.0586633i | ||||
\(796\) | −16.9857 | + | 29.4201i | −0.602043 | + | 1.04277i | ||||
\(797\) | −14.3148 | + | 24.7939i | −0.507055 | + | 0.878244i | 0.492912 | + | 0.870079i | \(0.335932\pi\) |
−0.999967 | + | 0.00816511i | \(0.997401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | − | 27.0368i | −0.552232 | − | 0.956493i | ||||
\(800\) | 49.6934 | 1.75693 | ||||||||
\(801\) | 6.35353 | − | 4.45740i | 0.224491 | − | 0.157495i | ||||
\(802\) | −78.3791 | −2.76766 | ||||||||
\(803\) | −0.315698 | − | 0.546805i | −0.0111408 | − | 0.0192963i | ||||
\(804\) | −15.9533 | + | 17.4258i | −0.562629 | + | 0.614562i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.0591 | + | 55.5279i | −1.12923 | + | 1.95589i | ||||
\(807\) | −7.94443 | − | 25.1566i | −0.279657 | − | 0.885556i | ||||
\(808\) | 45.0337 | + | 78.0007i | 1.58428 | + | 2.74406i | ||||
\(809\) | −2.85691 | −0.100444 | −0.0502219 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502219 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(810\) | 13.1923 | − | 36.4516i | 0.463531 | − | 1.28078i | ||||
\(811\) | 26.2917 | 0.923225 | 0.461613 | − | 0.887082i | \(-0.347271\pi\) | ||||
0.461613 | + | 0.887082i | \(0.347271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.44010 | − | 7.72675i | −0.0855779 | − | 0.270989i | ||||
\(814\) | −14.6894 | + | 25.4428i | −0.514863 | + | 0.891769i | ||||
\(815\) | 8.49443 | − | 14.7128i | 0.297547 | − | 0.515366i | ||||
\(816\) | 46.2293 | − | 50.4965i | 1.61835 | − | 1.76773i | ||||
\(817\) | −1.95802 | − | 3.39139i | −0.0685025 | − | 0.118650i | ||||
\(818\) | 29.4829 | 1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | 1.32925 | + | 2.30232i | 0.0463910 | + | 0.0803517i | 0.888289 | − | 0.459286i | \(-0.151895\pi\) |
−0.841897 | + | 0.539638i | \(0.818561\pi\) | |||||||
\(822\) | 75.9956 | + | 16.8116i | 2.65065 | + | 0.586371i | ||||
\(823\) | 6.10769 | − | 10.5788i | 0.212901 | − | 0.368755i | −0.739721 | − | 0.672914i | \(-0.765042\pi\) |
0.952621 | + | 0.304160i | \(0.0983756\pi\) | |||||||
\(824\) | 50.6193 | − | 87.6752i | 1.76341 | − | 3.05431i | ||||
\(825\) | −5.66444 | − | 1.25308i | −0.197211 | − | 0.0436265i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.15812 | 0.318459 | 0.159230 | − | 0.987242i | \(-0.449099\pi\) | ||||
0.159230 | + | 0.987242i | \(0.449099\pi\) | |||||||
\(828\) | −4.16251 | − | 1.93641i | −0.144657 | − | 0.0672947i | ||||
\(829\) | 18.3431 | 0.637083 | 0.318541 | − | 0.947909i | \(-0.396807\pi\) | ||||
0.318541 | + | 0.947909i | \(0.396807\pi\) | |||||||
\(830\) | −30.1224 | − | 52.1735i | −1.04556 | − | 1.81097i | ||||
\(831\) | −19.1702 | + | 20.9397i | −0.665007 | + | 0.726391i | ||||
\(832\) | 41.4828 | − | 71.8503i | 1.43816 | − | 2.49096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.1912 | + | 35.4378i | 0.387520 | + | 1.22711i | ||||
\(835\) | −2.53620 | − | 4.39284i | −0.0877690 | − | 0.152020i | ||||
\(836\) | −4.53341 | −0.156791 | ||||||||
\(837\) | 35.6487 | − | 14.8231i | 1.23220 | − | 0.512362i | ||||
\(838\) | −1.34438 | −0.0464409 | ||||||||
\(839\) | −9.47055 | − | 16.4035i | −0.326960 | − | 0.566311i | 0.654947 | − | 0.755675i | \(-0.272691\pi\) |
−0.981907 | + | 0.189364i | \(0.939357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15821 | − | 7.20224i | 0.143387 | − | 0.248353i | ||||
\(842\) | −25.8024 | + | 44.6911i | −0.889211 | + | 1.54016i | ||||
\(843\) | −4.10994 | + | 4.48930i | −0.141554 | + | 0.154620i | ||||
\(844\) | 30.6895 | + | 53.1557i | 1.05637 | + | 1.82969i | ||||
\(845\) | 4.59778 | 0.158168 | ||||||||
\(846\) | 7.99612 | + | 90.4493i | 0.274912 | + | 3.10971i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.6676 | − | 34.0652i | −0.675387 | − | 1.16980i | ||||
\(849\) | −44.0900 | − | 9.75350i | −1.51316 | − | 0.334739i | ||||
\(850\) | −9.44151 | + | 16.3532i | −0.323841 | + | 0.560909i | ||||
\(851\) | 1.14268 | − | 1.97917i | 0.0391704 | − | 0.0678452i | ||||
\(852\) | 13.1919 | + | 2.91829i | 0.451948 | + | 0.0999790i | ||||
\(853\) | −9.97922 | − | 17.2845i | −0.341682 | − | 0.591811i | 0.643063 | − | 0.765813i | \(-0.277663\pi\) |
−0.984745 | + | 0.174002i | \(0.944330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.262227 | + | 2.96622i | 0.00896796 | + | 0.101442i | ||||
\(856\) | 17.6176 | 0.602156 | ||||||||
\(857\) | 8.20001 | + | 14.2028i | 0.280107 | + | 0.485159i | 0.971411 | − | 0.237405i | \(-0.0762967\pi\) |
−0.691304 | + | 0.722564i | \(0.742963\pi\) | |||||||
\(858\) | −13.6129 | + | 14.8694i | −0.464736 | + | 0.507633i | ||||
\(859\) | −16.8575 | + | 29.1981i | −0.575172 | + | 0.996226i | 0.420851 | + | 0.907130i | \(0.361731\pi\) |
−0.996023 | + | 0.0890968i | \(0.971602\pi\) | |||||||
\(860\) | 26.6685 | − | 46.1912i | 0.909389 | − | 1.57511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.9720 | − | 39.7887i | −0.782429 | − | 1.35521i | ||||
\(863\) | −28.6831 | −0.976383 | −0.488191 | − | 0.872737i | \(-0.662343\pi\) | ||||
−0.488191 | + | 0.872737i | \(0.662343\pi\) | |||||||
\(864\) | −96.0089 | + | 39.9216i | −3.26629 | + | 1.35816i | ||||
\(865\) | 18.1444 | 0.616927 | ||||||||
\(866\) | −45.4432 | − | 78.7100i | −1.54422 | − | 2.67467i | ||||
\(867\) | −4.77618 | − | 15.1241i | −0.162208 | − | 0.513643i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5961 | + | 18.3529i | −0.359447 | + | 0.622581i | ||||
\(870\) | −22.9110 | + | 25.0257i | −0.776754 | + | 0.848452i | ||||
\(871\) | −4.03513 | − | 6.98906i | −0.136725 | − | 0.236815i | ||||
\(872\) | 170.351 | 5.76880 | ||||||||
\(873\) | −39.3302 | − | 18.2965i | −1.33113 | − | 0.619243i | ||||
\(874\) | 0.483944 | 0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.25292 | + | 0.940823i | 0.143693 | + | 0.0317875i | ||||
\(877\) | 14.7621 | − | 25.5688i | 0.498482 | − | 0.863396i | −0.501517 | − | 0.865148i | \(-0.667224\pi\) |
0.999998 | + | 0.00175202i | \(0.000557684\pi\) | |||||||
\(878\) | 28.4159 | − | 49.2177i | 0.958989 | − | 1.66102i | ||||
\(879\) | −31.9357 | − | 7.06475i | −1.07716 | − | 0.238288i | ||||
\(880\) | −15.0994 | − | 26.1530i | −0.509001 | − | 0.881616i | ||||
\(881\) | 57.5032 | 1.93733 | 0.968666 | − | 0.248366i | \(-0.0798934\pi\) | ||||
0.968666 | + | 0.248366i | \(0.0798934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | 23.9079 | + | 41.4097i | 0.804109 | + | 1.39276i | ||||
\(885\) | −8.48791 | + | 9.27138i | −0.285318 | + | 0.311654i | ||||
\(886\) | −41.8918 | + | 72.5587i | −1.40738 | + | 2.43766i | ||||
\(887\) | −18.5475 | + | 32.1253i | −0.622766 | + | 1.07866i | 0.366203 | + | 0.930535i | \(0.380658\pi\) |
−0.988968 | + | 0.148127i | \(0.952676\pi\) | |||||||
\(888\) | −38.3098 | − | 121.311i | −1.28559 | − | 4.07093i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.1432 | −0.373519 | ||||||||
\(891\) | 11.9505 | − | 2.12960i | 0.400357 | − | 0.0713442i | ||||
\(892\) | −89.8139 | −3.00719 | ||||||||
\(893\) | −3.48750 | − | 6.04053i | −0.116705 | − | 0.202139i | ||||
\(894\) | 19.3571 | + | 61.2958i | 0.647399 | + | 2.05004i | ||||
\(895\) | 0.871366 | − | 1.50925i | 0.0291266 | − | 0.0504487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.05893 | − | 1.15668i | 0.0353568 | − | 0.0386204i | ||||
\(898\) | −45.1783 | − | 78.2511i | −1.50762 | − | 2.61127i | ||||
\(899\) | −33.7913 | −1.12700 | ||||||||
\(900\) | 32.7627 | − | 22.9851i | 1.09209 | − | 0.766170i | ||||
\(901\) | 7.80503 | 0.260023 | ||||||||
\(902\) | 18.3589 | + | 31.7985i | 0.611284 | + | 1.05877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5879 | + | 25.2669i | −0.485185 | + | 0.840366i | ||||
\(905\) | 2.53040 | − | 4.38278i | 0.0841133 | − | 0.145689i | ||||
\(906\) | 17.9061 | + | 3.96115i | 0.594890 | + | 0.131600i | ||||
\(907\) | −12.2044 | − | 21.1386i | −0.405240 | − | 0.701896i | 0.589110 | − | 0.808053i | \(-0.299479\pi\) |
−0.994349 | + | 0.106157i | \(0.966145\pi\) | |||||||
\(908\) | 91.6993 | 3.04315 | ||||||||
\(909\) | 26.7594 | + | 12.4485i | 0.887555 | + | 0.412892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5493 | − | 21.7360i | −0.415776 | − | 0.720146i | 0.579733 | − | 0.814806i | \(-0.303157\pi\) |
−0.995510 | + | 0.0946604i | \(0.969823\pi\) | |||||||
\(912\) | 10.3285 | − | 11.2819i | 0.342011 | − | 0.373580i | ||||
\(913\) | 9.43234 | − | 16.3373i | 0.312165 | − | 0.540685i | ||||
\(914\) | 32.2971 | − | 55.9401i | 1.06829 | − | 1.85034i | ||||
\(915\) | 0.318577 | + | 1.00880i | 0.0105318 | + | 0.0333499i | ||||
\(916\) | −53.1538 | − | 92.0652i | −1.75625 | − | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.10378 | − | 39.1796i | 0.168450 | − | 1.29312i | ||||
\(919\) | −28.5976 | −0.943348 | −0.471674 | − | 0.881773i | \(-0.656350\pi\) | ||||
−0.471674 | + | 0.881773i | \(0.656350\pi\) | |||||||
\(920\) | 2.06869 | + | 3.58307i | 0.0682026 | + | 0.118130i | ||||
\(921\) | −11.2876 | − | 35.7429i | −0.371938 | − | 1.17777i | ||||
\(922\) | −23.1634 | + | 40.1202i | −0.762846 | + | 1.32129i | ||||
\(923\) | −2.30759 | + | 3.99686i | −0.0759553 | + | 0.131558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96139 | + | 17.2536i | 0.327528 | + | 0.567296i | ||||
\(926\) | 98.4196 | 3.23427 | ||||||||
\(927\) | −2.92132 | − | 33.0450i | −0.0959488 | − | 1.08534i | ||||
\(928\) | 91.0065 | 2.98744 | ||||||||
\(929\) | 22.7285 | + | 39.3669i | 0.745698 | + | 1.29159i | 0.949868 | + | 0.312651i | \(0.101217\pi\) |
−0.204170 | + | 0.978935i | \(0.565450\pi\) | |||||||
\(930\) | −54.1227 | − | 11.9729i | −1.77475 | − | 0.392607i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.9321 | + | 27.5952i | −0.521873 | + | 0.903910i | ||||
\(933\) | −7.60091 | − | 1.68146i | −0.248843 | − | 0.0550485i | ||||
\(934\) | −11.1206 | − | 19.2615i | −0.363878 | − | 0.630256i | ||||
\(935\) | 5.99217 | 0.195965 | ||||||||
\(936\) | −7.68731 | − | 86.9562i | −0.251268 | − | 2.84225i | ||||
\(937\) | 27.0083 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0607 | − | 10.9894i | 0.328320 | − | 0.358625i | ||||
\(940\) | 47.5002 | − | 82.2728i | 1.54929 | − | 2.68344i | ||||
\(941\) | −6.35657 | + | 11.0099i | −0.207218 | + | 0.358912i | −0.950837 | − | 0.309691i | \(-0.899774\pi\) |
0.743619 | + | 0.668604i | \(0.233108\pi\) | |||||||
\(942\) | 0.416856 | + | 1.32001i | 0.0135819 | + | 0.0430082i | ||||
\(943\) | −1.42812 | − | 2.47358i | −0.0465060 | − | 0.0805508i | ||||
\(944\) | 64.5667 | 2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | −23.7724 | − | 41.1749i | −0.772498 | − | 1.33801i | −0.936190 | − | 0.351494i | \(-0.885674\pi\) |
0.163692 | − | 0.986511i | \(-0.447660\pi\) | |||||||
\(948\) | −44.0253 | − | 139.409i | −1.42987 | − | 4.52781i | ||||
\(949\) | −0.743940 | + | 1.28854i | −0.0241493 | + | 0.0418279i | ||||
\(950\) | −2.10941 | + | 3.65361i | −0.0684384 | + | 0.118539i | ||||
\(951\) | −9.42977 | + | 10.3002i | −0.305781 | + | 0.334006i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.2355 | 1.23857 | 0.619285 | − | 0.785166i | \(-0.287423\pi\) | ||||
0.619285 | + | 0.785166i | \(0.287423\pi\) | |||||||
\(954\) | −20.5828 | − | 9.57517i | −0.666394 | − | 0.310008i | ||||
\(955\) | −6.13640 | −0.198569 | ||||||||
\(956\) | −53.8682 | − | 93.3024i | −1.74222 | − | 3.01762i | ||||
\(957\) | −10.3736 | − | 2.29483i | −0.335332 | − | 0.0741815i | ||||
\(958\) | −34.6925 | + | 60.0891i | −1.12086 | + | 1.94139i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 70.0320 | + | 15.4923i | 2.26027 | + | 0.500013i | ||||
\(961\) | −12.1028 | − | 20.9627i | −0.390413 | − | 0.676215i | ||||
\(962\) | 69.2309 | 2.23209 | ||||||||
\(963\) | 4.72589 | − | 3.31551i | 0.152290 | − | 0.106841i | ||||
\(964\) | 157.337 | 5.06749 | ||||||||
\(965\) | −3.28054 | − | 5.68207i | −0.105604 | − | 0.182912i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4093 | + | 35.3499i | −0.656317 | + | 1.13678i | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(968\) | −42.0267 | + | 72.7924i | −1.35079 | + | 2.33964i | ||||
\(969\) | 0.913966 | + | 2.89415i | 0.0293608 | + | 0.0929733i | ||||
\(970\) | 31.1399 | + | 53.9359i | 0.999843 | + | 1.73178i | ||||
\(971\) | 44.9471 | 1.44242 | 0.721210 | − | 0.692717i | \(-0.243586\pi\) | ||||
0.721210 | + | 0.692717i | \(0.243586\pi\) | |||||||
\(972\) | −44.8331 | + | 70.7279i | −1.43802 | + | 2.26860i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.39817 | − | 16.2781i | −0.301137 | − | 0.521584i | ||||
\(975\) | 4.11685 | + | 13.0363i | 0.131845 | + | 0.417496i | ||||
\(976\) | 2.71703 | − | 4.70603i | 0.0869699 | − | 0.150636i | ||||
\(977\) | −26.7552 | + | 46.3414i | −0.855974 | + | 1.48259i | 0.0197635 | + | 0.999805i | \(0.493709\pi\) |
−0.875738 | + | 0.482787i | \(0.839625\pi\) | |||||||
\(978\) | −34.0074 | + | 37.1464i | −1.08744 | + | 1.18781i | ||||
\(979\) | −1.74465 | − | 3.02182i | −0.0557593 | − | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.6963 | − | 32.0588i | 1.45897 | − | 1.02356i | ||||
\(982\) | 101.688 | 3.24501 | ||||||||
\(983\) | −5.80278 | − | 10.0507i | −0.185080 | − | 0.320568i | 0.758524 | − | 0.651646i | \(-0.225921\pi\) |
−0.943603 | + | 0.331078i | \(0.892588\pi\) | |||||||
\(984\) | −155.242 | − | 34.3424i | −4.94895 | − | 1.09480i | ||||
\(985\) | −0.705363 | + | 1.22172i | −0.0224747 | + | 0.0389274i | ||||
\(986\) | −17.2908 | + | 29.9485i | −0.550651 | + | 0.953756i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.34147 | + | 9.25170i | 0.169935 | + | 0.294336i | ||||
\(989\) | −1.78291 | −0.0566932 | ||||||||
\(990\) | −15.8021 | − | 7.35117i | −0.502224 | − | 0.233635i | ||||
\(991\) | 26.0091 | 0.826208 | 0.413104 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413104 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(992\) | 74.3398 | + | 128.760i | 2.36029 | + | 4.08814i | ||||
\(993\) | −26.7863 | + | 29.2588i | −0.850037 | + | 0.928500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.01607 | − | 8.68808i | 0.159020 | − | 0.275431i | ||||
\(996\) | 39.1901 | + | 124.099i | 1.24179 | + | 3.93221i | ||||
\(997\) | 23.4499 | + | 40.6164i | 0.742666 | + | 1.28633i | 0.951277 | + | 0.308336i | \(0.0997721\pi\) |
−0.208612 | + | 0.977999i | \(0.566895\pi\) | |||||||
\(998\) | −69.5753 | −2.20237 | ||||||||
\(999\) | −33.1065 | − | 25.3319i | −1.04744 | − | 0.801465i |
(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 | 441.2.f.h.148.12 | yes | 24 | |
3.2 | odd | 2 | 1323.2.f.h.442.2 | 24 | |||
7.2 | even | 3 | 441.2.g.h.67.11 | 24 | |||
7.3 | odd | 6 | 441.2.h.h.373.1 | 24 | |||
7.4 | even | 3 | 441.2.h.h.373.2 | 24 | |||
7.5 | odd | 6 | 441.2.g.h.67.12 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.148.11 | ✓ | 24 | |
9.2 | odd | 6 | 1323.2.f.h.883.2 | 24 | |||
9.4 | even | 3 | 3969.2.a.bh.1.1 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bi.1.12 | 12 | |||
9.7 | even | 3 | inner | 441.2.f.h.295.12 | yes | 24 | |
21.2 | odd | 6 | 1323.2.g.h.361.1 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.361.2 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.226.12 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.226.11 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.442.1 | 24 | |||
63.2 | odd | 6 | 1323.2.h.h.802.12 | 24 | |||
63.11 | odd | 6 | 1323.2.g.h.667.1 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.16 | even | 3 | 441.2.h.h.214.2 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.883.1 | 24 | |||
63.25 | even | 3 | 441.2.g.h.79.11 | 24 | |||
63.34 | odd | 6 | inner | 441.2.f.h.295.11 | yes | 24 | |
63.38 | even | 6 | 1323.2.g.h.667.2 | 24 | |||
63.41 | even | 6 | 3969.2.a.bi.1.11 | 12 | |||
63.47 | even | 6 | 1323.2.h.h.802.11 | 24 | |||
63.52 | odd | 6 | 441.2.g.h.79.12 | 24 | |||
63.61 | odd | 6 | 441.2.h.h.214.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.148.12 | yes | 24 | 1.1 | even | 1 | trivial | |
441.2.f.h.295.11 | yes | 24 | 63.34 | odd | 6 | inner | |
441.2.f.h.295.12 | yes | 24 | 9.7 | even | 3 | inner | |
441.2.g.h.67.11 | 24 | 7.2 | even | 3 | |||
441.2.g.h.67.12 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.79.11 | 24 | 63.25 | even | 3 | |||
441.2.g.h.79.12 | 24 | 63.52 | odd | 6 | |||
441.2.h.h.214.1 | 24 | 63.61 | odd | 6 | |||
441.2.h.h.214.2 | 24 | 63.16 | even | 3 | |||
441.2.h.h.373.1 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.2 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.1 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.2 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.883.1 | 24 | 63.20 | even | 6 | |||
1323.2.f.h.883.2 | 24 | 9.2 | odd | 6 | |||
1323.2.g.h.361.1 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.361.2 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.667.1 | 24 | 63.11 | odd | 6 | |||
1323.2.g.h.667.2 | 24 | 63.38 | even | 6 | |||
1323.2.h.h.226.11 | 24 | 21.17 | even | 6 | |||
1323.2.h.h.226.12 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.802.11 | 24 | 63.47 | even | 6 | |||
1323.2.h.h.802.12 | 24 | 63.2 | odd | 6 | |||
3969.2.a.bh.1.1 | 12 | 9.4 | even | 3 | |||
3969.2.a.bh.1.2 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.41 | even | 6 | |||
3969.2.a.bi.1.12 | 12 | 9.5 | odd | 6 |