Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(197,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.m (of order \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.16 | ||
Character | \(\chi\) | \(=\) | 784.197 |
Dual form | 784.2.m.l.589.16 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.395893 | + | 1.35767i | 0.279939 | + | 0.960018i | ||||
\(3\) | 2.06976 | − | 2.06976i | 1.19498 | − | 1.19498i | 0.219326 | − | 0.975652i | \(-0.429614\pi\) |
0.975652 | − | 0.219326i | \(-0.0703858\pi\) | |||||||
\(4\) | −1.68654 | + | 1.07498i | −0.843269 | + | 0.537492i | ||||
\(5\) | 2.64219 | + | 2.64219i | 1.18162 | + | 1.18162i | 0.979324 | + | 0.202300i | \(0.0648417\pi\) |
0.202300 | + | 0.979324i | \(0.435158\pi\) | |||||||
\(6\) | 3.62946 | + | 1.99065i | 1.48172 | + | 0.812679i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.12716 | − | 1.86418i | −0.752065 | − | 0.659088i | ||||
\(9\) | − | 5.56783i | − | 1.85594i | ||||||
\(10\) | −2.54120 | + | 4.63325i | −0.803598 | + | 1.46516i | ||||
\(11\) | 0.682946 | + | 0.682946i | 0.205916 | + | 0.205916i | 0.802529 | − | 0.596613i | \(-0.203487\pi\) |
−0.596613 | + | 0.802529i | \(0.703487\pi\) | |||||||
\(12\) | −1.26577 | + | 5.71569i | −0.365396 | + | 1.64998i | ||||
\(13\) | 4.19543 | − | 4.19543i | 1.16360 | − | 1.16360i | 0.179924 | − | 0.983681i | \(-0.442415\pi\) |
0.983681 | − | 0.179924i | \(-0.0575851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.9374 | 2.82403 | ||||||||
\(16\) | 1.68882 | − | 3.62600i | 0.422205 | − | 0.906501i | ||||
\(17\) | −1.45879 | −0.353808 | −0.176904 | − | 0.984228i | \(-0.556608\pi\) | ||||
−0.176904 | + | 0.984228i | \(0.556608\pi\) | |||||||
\(18\) | 7.55927 | − | 2.20426i | 1.78174 | − | 0.519550i | ||||
\(19\) | −2.68222 | + | 2.68222i | −0.615343 | + | 0.615343i | −0.944333 | − | 0.328990i | \(-0.893292\pi\) |
0.328990 | + | 0.944333i | \(0.393292\pi\) | |||||||
\(20\) | −7.29647 | − | 1.61584i | −1.63154 | − | 0.361313i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.656842 | + | 1.19759i | −0.140039 | + | 0.255327i | ||||
\(23\) | 1.79832i | 0.374977i | 0.982267 | + | 0.187488i | \(0.0600347\pi\) | ||||
−0.982267 | + | 0.187488i | \(0.939965\pi\) | |||||||
\(24\) | −8.26113 | + | 0.544304i | −1.68630 | + | 0.111106i | ||||
\(25\) | 8.96235i | 1.79247i | ||||||||
\(26\) | 7.35696 | + | 4.03507i | 1.44282 | + | 0.791343i | ||||
\(27\) | −5.31479 | − | 5.31479i | −1.02283 | − | 1.02283i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.295765 | + | 0.295765i | −0.0549222 | + | 0.0549222i | −0.734034 | − | 0.679112i | \(-0.762365\pi\) |
0.679112 | + | 0.734034i | \(0.262365\pi\) | |||||||
\(30\) | 4.33004 | + | 14.8494i | 0.790554 | + | 2.71112i | ||||
\(31\) | −1.16351 | −0.208973 | −0.104487 | − | 0.994526i | \(-0.533320\pi\) | ||||
−0.104487 | + | 0.994526i | \(0.533320\pi\) | |||||||
\(32\) | 5.59151 | + | 0.857349i | 0.988448 | + | 0.151559i | ||||
\(33\) | 2.82707 | 0.492130 | ||||||||
\(34\) | −0.577524 | − | 1.98056i | −0.0990446 | − | 0.339662i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.98533 | + | 9.39035i | 0.997554 | + | 1.56506i | ||||
\(37\) | 0.0493910 | + | 0.0493910i | 0.00811983 | + | 0.00811983i | 0.711155 | − | 0.703035i | \(-0.248172\pi\) |
−0.703035 | + | 0.711155i | \(0.748172\pi\) | |||||||
\(38\) | −4.70344 | − | 2.57970i | −0.762999 | − | 0.418482i | ||||
\(39\) | − | 17.3671i | − | 2.78096i | ||||||
\(40\) | −0.694841 | − | 10.5459i | −0.109864 | − | 1.66745i | ||||
\(41\) | 10.1128i | 1.57935i | 0.613522 | + | 0.789677i | \(0.289752\pi\) | ||||
−0.613522 | + | 0.789677i | \(0.710248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.55032 | − | 4.55032i | −0.693918 | − | 0.693918i | 0.269174 | − | 0.963092i | \(-0.413249\pi\) |
−0.963092 | + | 0.269174i | \(0.913249\pi\) | |||||||
\(44\) | −1.88597 | − | 0.417658i | −0.284321 | − | 0.0629643i | ||||
\(45\) | 14.7113 | − | 14.7113i | 2.19303 | − | 2.19303i | ||||
\(46\) | −2.44153 | + | 0.711944i | −0.359984 | + | 0.104970i | ||||
\(47\) | −11.0875 | −1.61728 | −0.808641 | − | 0.588302i | \(-0.799797\pi\) | ||||
−0.808641 | + | 0.588302i | \(0.799797\pi\) | |||||||
\(48\) | −4.00951 | − | 11.0004i | −0.578723 | − | 1.58777i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.1679 | + | 3.54813i | −1.72080 | + | 0.501781i | ||||
\(51\) | −3.01935 | + | 3.01935i | −0.422793 | + | 0.422793i | ||||
\(52\) | −2.56573 | + | 11.5858i | −0.355803 | + | 1.60666i | ||||
\(53\) | −0.417874 | − | 0.417874i | −0.0573994 | − | 0.0573994i | 0.677824 | − | 0.735224i | \(-0.262923\pi\) |
−0.735224 | + | 0.677824i | \(0.762923\pi\) | |||||||
\(54\) | 5.11164 | − | 9.31982i | 0.695607 | − | 1.26827i | ||||
\(55\) | 3.60895i | 0.486630i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1031i | 1.47064i | ||||||||
\(58\) | −0.518643 | − | 0.284460i | −0.0681012 | − | 0.0373515i | ||||
\(59\) | −3.74749 | − | 3.74749i | −0.487881 | − | 0.487881i | 0.419756 | − | 0.907637i | \(-0.362116\pi\) |
−0.907637 | + | 0.419756i | \(0.862116\pi\) | |||||||
\(60\) | −18.4464 | + | 11.7575i | −2.38141 | + | 1.51789i | ||||
\(61\) | 7.02257 | − | 7.02257i | 0.899148 | − | 0.899148i | −0.0962132 | − | 0.995361i | \(-0.530673\pi\) |
0.995361 | + | 0.0962132i | \(0.0306731\pi\) | |||||||
\(62\) | −0.460627 | − | 1.57967i | −0.0584997 | − | 0.200618i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.04964 | + | 7.93084i | 0.131205 | + | 0.991355i | ||||
\(65\) | 22.1703 | 2.74988 | ||||||||
\(66\) | 1.11922 | + | 3.83823i | 0.137766 | + | 0.472453i | ||||
\(67\) | 8.42467 | − | 8.42467i | 1.02924 | − | 1.02924i | 0.0296779 | − | 0.999560i | \(-0.490552\pi\) |
0.999560 | − | 0.0296779i | \(-0.00944816\pi\) | |||||||
\(68\) | 2.46030 | − | 1.56818i | 0.298356 | − | 0.190169i | ||||
\(69\) | 3.72210 | + | 3.72210i | 0.448089 | + | 0.448089i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.89148i | − | 0.343156i | −0.985171 | − | 0.171578i | \(-0.945113\pi\) | ||
0.985171 | − | 0.171578i | \(-0.0548865\pi\) | |||||||
\(72\) | −10.3795 | + | 11.8437i | −1.22323 | + | 1.39579i | ||||
\(73\) | − | 0.640221i | − | 0.0749322i | −0.999298 | − | 0.0374661i | \(-0.988071\pi\) | ||
0.999298 | − | 0.0374661i | \(-0.0119286\pi\) | |||||||
\(74\) | −0.0475032 | + | 0.0866103i | −0.00552213 | + | 0.0100682i | ||||
\(75\) | 18.5499 | + | 18.5499i | 2.14196 | + | 2.14196i | ||||
\(76\) | 1.64032 | − | 7.40701i | 0.188158 | − | 0.849642i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 23.5788 | − | 6.87551i | 2.66977 | − | 0.778498i | ||||
\(79\) | −0.749820 | −0.0843613 | −0.0421807 | − | 0.999110i | \(-0.513431\pi\) | ||||
−0.0421807 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(80\) | 14.0428 | − | 5.11841i | 1.57003 | − | 0.572256i | ||||
\(81\) | −5.29721 | −0.588579 | ||||||||
\(82\) | −13.7299 | + | 4.00359i | −1.51621 | + | 0.442122i | ||||
\(83\) | −4.51473 | + | 4.51473i | −0.495556 | + | 0.495556i | −0.910051 | − | 0.414495i | \(-0.863958\pi\) |
0.414495 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.85440 | − | 3.85440i | −0.418068 | − | 0.418068i | ||||
\(86\) | 4.37640 | − | 7.97928i | 0.471919 | − | 0.860428i | ||||
\(87\) | 1.22433i | 0.131262i | ||||||||
\(88\) | −0.179600 | − | 2.72587i | −0.0191455 | − | 0.290579i | ||||
\(89\) | 15.4712i | 1.63995i | 0.572401 | + | 0.819974i | \(0.306012\pi\) | ||||
−0.572401 | + | 0.819974i | \(0.693988\pi\) | |||||||
\(90\) | 25.7971 | + | 14.1490i | 2.71926 | + | 1.49143i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.93317 | − | 3.03294i | −0.201547 | − | 0.316206i | ||||
\(93\) | −2.40820 | + | 2.40820i | −0.249718 | + | 0.249718i | ||||
\(94\) | −4.38947 | − | 15.0532i | −0.452740 | − | 1.55262i | ||||
\(95\) | −14.1739 | −1.45421 | ||||||||
\(96\) | 13.3476 | − | 9.79858i | 1.36228 | − | 1.00006i | ||||
\(97\) | −13.7459 | −1.39569 | −0.697843 | − | 0.716250i | \(-0.745857\pi\) | ||||
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.80252 | − | 3.80252i | 0.382168 | − | 0.382168i | ||||
\(100\) | −9.63438 | − | 15.1153i | −0.963438 | − | 1.51153i | ||||
\(101\) | −3.27564 | − | 3.27564i | −0.325938 | − | 0.325938i | 0.525101 | − | 0.851040i | \(-0.324027\pi\) |
−0.851040 | + | 0.525101i | \(0.824027\pi\) | |||||||
\(102\) | −5.29462 | − | 2.90394i | −0.524245 | − | 0.287533i | ||||
\(103\) | − | 8.74763i | − | 0.861930i | −0.902369 | − | 0.430965i | \(-0.858173\pi\) | ||
0.902369 | − | 0.430965i | \(-0.141827\pi\) | |||||||
\(104\) | −16.7454 | + | 1.10331i | −1.64202 | + | 0.108189i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.401901 | − | 0.732768i | 0.0390361 | − | 0.0711727i | ||||
\(107\) | −3.17643 | − | 3.17643i | −0.307078 | − | 0.307078i | 0.536697 | − | 0.843775i | \(-0.319672\pi\) |
−0.843775 | + | 0.536697i | \(0.819672\pi\) | |||||||
\(108\) | 14.6769 | + | 3.25028i | 1.41229 | + | 0.312758i | ||||
\(109\) | 4.35303 | − | 4.35303i | 0.416945 | − | 0.416945i | −0.467204 | − | 0.884149i | \(-0.654739\pi\) |
0.884149 | + | 0.467204i | \(0.154739\pi\) | |||||||
\(110\) | −4.89976 | + | 1.42876i | −0.467174 | + | 0.136227i | ||||
\(111\) | 0.204455 | 0.0194060 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0896489 | 0.00843346 | 0.00421673 | − | 0.999991i | \(-0.498658\pi\) | ||||
0.00421673 | + | 0.999991i | \(0.498658\pi\) | |||||||
\(114\) | −15.0744 | + | 4.39564i | −1.41184 | + | 0.411690i | ||||
\(115\) | −4.75152 | + | 4.75152i | −0.443081 | + | 0.443081i | ||||
\(116\) | 0.180876 | − | 0.816762i | 0.0167939 | − | 0.0758345i | ||||
\(117\) | −23.3595 | − | 23.3595i | −2.15958 | − | 2.15958i | ||||
\(118\) | 3.60425 | − | 6.57145i | 0.331798 | − | 0.604951i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −23.2657 | − | 20.3893i | −2.12385 | − | 1.86128i | ||||
\(121\) | − | 10.0672i | − | 0.915197i | ||||||
\(122\) | 12.3145 | + | 6.75415i | 1.11490 | + | 0.611492i | ||||
\(123\) | 20.9311 | + | 20.9311i | 1.88729 | + | 1.88729i | ||||
\(124\) | 1.96231 | − | 1.25076i | 0.176221 | − | 0.112321i | ||||
\(125\) | −10.4693 | + | 10.4693i | −0.936401 | + | 0.936401i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0084 | −1.50925 | −0.754624 | − | 0.656157i | \(-0.772181\pi\) | ||||
−0.754624 | + | 0.656157i | \(0.772181\pi\) | |||||||
\(128\) | −10.3519 | + | 4.56483i | −0.914989 | + | 0.403478i | ||||
\(129\) | −18.8362 | −1.65843 | ||||||||
\(130\) | 8.77706 | + | 30.0999i | 0.769799 | + | 2.63994i | ||||
\(131\) | −14.0070 | + | 14.0070i | −1.22379 | + | 1.22379i | −0.257521 | + | 0.966273i | \(0.582906\pi\) |
−0.966273 | + | 0.257521i | \(0.917094\pi\) | |||||||
\(132\) | −4.76796 | + | 3.03905i | −0.414997 | + | 0.264516i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.7732 | + | 8.10266i | 1.27621 | + | 0.699963i | ||||
\(135\) | − | 28.0854i | − | 2.41720i | ||||||
\(136\) | 3.10308 | + | 2.71945i | 0.266087 | + | 0.233191i | ||||
\(137\) | − | 0.915437i | − | 0.0782111i | −0.999235 | − | 0.0391055i | \(-0.987549\pi\) | ||
0.999235 | − | 0.0391055i | \(-0.0124509\pi\) | |||||||
\(138\) | −3.57983 | + | 6.52694i | −0.304736 | + | 0.555610i | ||||
\(139\) | −2.74533 | − | 2.74533i | −0.232856 | − | 0.232856i | 0.581028 | − | 0.813884i | \(-0.302651\pi\) |
−0.813884 | + | 0.581028i | \(0.802651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.9485 | + | 22.9485i | −1.93262 | + | 1.93262i | ||||
\(142\) | 3.92568 | − | 1.14472i | 0.329436 | − | 0.0960625i | ||||
\(143\) | 5.73051 | 0.479209 | ||||||||
\(144\) | −20.1890 | − | 9.40305i | −1.68241 | − | 0.783587i | ||||
\(145\) | −1.56294 | −0.129795 | ||||||||
\(146\) | 0.869209 | − | 0.253459i | 0.0719362 | − | 0.0209764i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.136394 | − | 0.0302052i | −0.0112115 | − | 0.00248286i | ||||
\(149\) | −5.96683 | − | 5.96683i | −0.488822 | − | 0.488822i | 0.419112 | − | 0.907934i | \(-0.362341\pi\) |
−0.907934 | + | 0.419112i | \(0.862341\pi\) | |||||||
\(150\) | −17.8409 | + | 32.5285i | −1.45670 | + | 2.65594i | ||||
\(151\) | − | 5.07755i | − | 0.413206i | −0.978425 | − | 0.206603i | \(-0.933759\pi\) | ||
0.978425 | − | 0.206603i | \(-0.0662408\pi\) | |||||||
\(152\) | 10.7057 | − | 0.705367i | 0.868344 | − | 0.0572129i | ||||
\(153\) | 8.12229i | 0.656648i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.07423 | − | 3.07423i | −0.246928 | − | 0.246928i | ||||
\(156\) | 18.6694 | + | 29.2903i | 1.49474 | + | 2.34510i | ||||
\(157\) | 3.69391 | − | 3.69391i | 0.294806 | − | 0.294806i | −0.544169 | − | 0.838976i | \(-0.683155\pi\) |
0.838976 | + | 0.544169i | \(0.183155\pi\) | |||||||
\(158\) | −0.296848 | − | 1.01801i | −0.0236160 | − | 0.0809884i | ||||
\(159\) | −1.72980 | −0.137182 | ||||||||
\(160\) | 12.5085 | + | 17.0391i | 0.988888 | + | 1.34706i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.09713 | − | 7.19187i | −0.164766 | − | 0.565047i | ||||
\(163\) | 8.19576 | − | 8.19576i | 0.641941 | − | 0.641941i | −0.309091 | − | 0.951032i | \(-0.600025\pi\) |
0.951032 | + | 0.309091i | \(0.100025\pi\) | |||||||
\(164\) | −10.8711 | − | 17.0556i | −0.848891 | − | 1.33182i | ||||
\(165\) | 7.46966 | + | 7.46966i | 0.581512 | + | 0.581512i | ||||
\(166\) | −7.91686 | − | 4.34216i | −0.614468 | − | 0.337017i | ||||
\(167\) | − | 13.7471i | − | 1.06378i | −0.846813 | − | 0.531891i | \(-0.821482\pi\) | ||
0.846813 | − | 0.531891i | \(-0.178518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.2033i | − | 1.70795i | ||||||
\(170\) | 3.70708 | − | 6.75894i | 0.284320 | − | 0.518387i | ||||
\(171\) | 14.9341 | + | 14.9341i | 1.14204 | + | 1.14204i | ||||
\(172\) | 12.5658 | + | 2.78277i | 0.958135 | + | 0.212184i | ||||
\(173\) | −5.58305 | + | 5.58305i | −0.424472 | + | 0.424472i | −0.886740 | − | 0.462268i | \(-0.847036\pi\) |
0.462268 | + | 0.886740i | \(0.347036\pi\) | |||||||
\(174\) | −1.66223 | + | 0.484703i | −0.126014 | + | 0.0367452i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.62973 | − | 1.32299i | 0.273601 | − | 0.0997242i | ||||
\(177\) | −15.5128 | −1.16601 | ||||||||
\(178\) | −21.0048 | + | 6.12495i | −1.57438 | + | 0.459085i | ||||
\(179\) | 6.82530 | − | 6.82530i | 0.510147 | − | 0.510147i | −0.404424 | − | 0.914571i | \(-0.632528\pi\) |
0.914571 | + | 0.404424i | \(0.132528\pi\) | |||||||
\(180\) | −8.99672 | + | 40.6255i | −0.670576 | + | 3.02804i | ||||
\(181\) | 15.1263 | + | 15.1263i | 1.12433 | + | 1.12433i | 0.991083 | + | 0.133250i | \(0.0425412\pi\) |
0.133250 | + | 0.991083i | \(0.457459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 29.0701i | − | 2.14892i | ||||||
\(184\) | 3.35241 | − | 3.82533i | 0.247143 | − | 0.282007i | ||||
\(185\) | 0.261001i | 0.0191892i | ||||||||
\(186\) | −4.22292 | − | 2.31615i | −0.309640 | − | 0.169828i | ||||
\(187\) | −0.996274 | − | 0.996274i | −0.0728548 | − | 0.0728548i | ||||
\(188\) | 18.6995 | − | 11.9189i | 1.36380 | − | 0.869277i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.61134 | − | 19.2434i | −0.407089 | − | 1.39607i | ||||
\(191\) | 19.8728 | 1.43794 | 0.718971 | − | 0.695040i | \(-0.244613\pi\) | ||||
0.718971 | + | 0.695040i | \(0.244613\pi\) | |||||||
\(192\) | 18.5875 | + | 14.2424i | 1.34143 | + | 1.02786i | ||||
\(193\) | −11.8829 | −0.855352 | −0.427676 | − | 0.903932i | \(-0.640668\pi\) | ||||
−0.427676 | + | 0.903932i | \(0.640668\pi\) | |||||||
\(194\) | −5.44191 | − | 18.6624i | −0.390707 | − | 1.33988i | ||||
\(195\) | 45.8872 | − | 45.8872i | 3.28605 | − | 3.28605i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.61994 | + | 6.61994i | 0.471651 | + | 0.471651i | 0.902449 | − | 0.430797i | \(-0.141768\pi\) |
−0.430797 | + | 0.902449i | \(0.641768\pi\) | |||||||
\(198\) | 6.66796 | + | 3.65718i | 0.473872 | + | 0.259904i | ||||
\(199\) | 24.0632i | 1.70579i | 0.522079 | + | 0.852897i | \(0.325157\pi\) | ||||
−0.522079 | + | 0.852897i | \(0.674843\pi\) | |||||||
\(200\) | 16.7075 | − | 19.0644i | 1.18140 | − | 1.34805i | ||||
\(201\) | − | 34.8741i | − | 2.45983i | ||||||
\(202\) | 3.15044 | − | 5.74404i | 0.221664 | − | 0.404149i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.84649 | − | 8.33799i | 0.129280 | − | 0.583776i | ||||
\(205\) | −26.7200 | + | 26.7200i | −1.86620 | + | 1.86620i | ||||
\(206\) | 11.8764 | − | 3.46313i | 0.827468 | − | 0.241287i | ||||
\(207\) | 10.0128 | 0.695935 | ||||||||
\(208\) | −8.12733 | − | 22.2980i | −0.563529 | − | 1.54609i | ||||
\(209\) | −3.66362 | −0.253418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2158 | + | 18.2158i | −1.25403 | + | 1.25403i | −0.300133 | + | 0.953897i | \(0.597031\pi\) |
−0.953897 | + | 0.300133i | \(0.902969\pi\) | |||||||
\(212\) | 1.15397 | + | 0.255552i | 0.0792548 | + | 0.0175514i | ||||
\(213\) | −5.98468 | − | 5.98468i | −0.410063 | − | 0.410063i | ||||
\(214\) | 3.05502 | − | 5.57008i | 0.208837 | − | 0.380763i | ||||
\(215\) | − | 24.0457i | − | 1.63990i | ||||||
\(216\) | 1.39768 | + | 21.2132i | 0.0950999 | + | 1.44337i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.63332 | + | 4.18665i | 0.516994 | + | 0.283556i | ||||
\(219\) | −1.32510 | − | 1.32510i | −0.0895423 | − | 0.0895423i | ||||
\(220\) | −3.87956 | − | 6.08662i | −0.261560 | − | 0.410360i | ||||
\(221\) | −6.12026 | + | 6.12026i | −0.411693 | + | 0.411693i | ||||
\(222\) | 0.0809424 | + | 0.277583i | 0.00543250 | + | 0.0186301i | ||||
\(223\) | −8.33457 | −0.558124 | −0.279062 | − | 0.960273i | \(-0.590024\pi\) | ||||
−0.279062 | + | 0.960273i | \(0.590024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 49.9008 | 3.32672 | ||||||||
\(226\) | 0.0354914 | + | 0.121714i | 0.00236085 | + | 0.00809627i | ||||
\(227\) | 7.87294 | − | 7.87294i | 0.522545 | − | 0.522545i | −0.395794 | − | 0.918339i | \(-0.629531\pi\) |
0.918339 | + | 0.395794i | \(0.129531\pi\) | |||||||
\(228\) | −11.9357 | − | 18.7258i | −0.790459 | − | 1.24015i | ||||
\(229\) | 8.97014 | + | 8.97014i | 0.592763 | + | 0.592763i | 0.938377 | − | 0.345614i | \(-0.112329\pi\) |
−0.345614 | + | 0.938377i | \(0.612329\pi\) | |||||||
\(230\) | −8.33209 | − | 4.56990i | −0.549401 | − | 0.301330i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.18050 | − | 0.0777801i | 0.0775037 | − | 0.00510651i | ||||
\(233\) | 22.5390i | 1.47658i | 0.674483 | + | 0.738291i | \(0.264367\pi\) | ||||
−0.674483 | + | 0.738291i | \(0.735633\pi\) | |||||||
\(234\) | 22.4666 | − | 40.9623i | 1.46869 | − | 2.67779i | ||||
\(235\) | −29.2954 | − | 29.2954i | −1.91102 | − | 1.91102i | ||||
\(236\) | 10.3488 | + | 2.29179i | 0.673647 | + | 0.149183i | ||||
\(237\) | −1.55195 | + | 1.55195i | −0.100810 | + | 0.100810i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3677 | 0.864687 | 0.432344 | − | 0.901709i | \(-0.357687\pi\) | ||||
0.432344 | + | 0.901709i | \(0.357687\pi\) | |||||||
\(240\) | 18.4713 | − | 39.6591i | 1.19232 | − | 2.55998i | ||||
\(241\) | 19.3942 | 1.24929 | 0.624645 | − | 0.780909i | \(-0.285244\pi\) | ||||
0.624645 | + | 0.780909i | \(0.285244\pi\) | |||||||
\(242\) | 13.6679 | − | 3.98552i | 0.878606 | − | 0.256199i | ||||
\(243\) | 4.98040 | − | 4.98040i | 0.319493 | − | 0.319493i | ||||
\(244\) | −4.29467 | + | 19.3930i | −0.274938 | + | 1.24151i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.1311 | + | 36.7040i | −1.28351 | + | 2.34016i | ||||
\(247\) | 22.5062i | 1.43203i | ||||||||
\(248\) | 2.47498 | + | 2.16900i | 0.157162 | + | 0.137732i | ||||
\(249\) | 18.6888i | 1.18436i | ||||||||
\(250\) | −18.3585 | − | 10.0691i | −1.16110 | − | 0.636827i | ||||
\(251\) | 8.09990 | + | 8.09990i | 0.511261 | + | 0.511261i | 0.914913 | − | 0.403652i | \(-0.132259\pi\) |
−0.403652 | + | 0.914913i | \(0.632259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.22816 | + | 1.22816i | −0.0772136 | + | 0.0772136i | ||||
\(254\) | −6.73349 | − | 23.0918i | −0.422497 | − | 1.44891i | ||||
\(255\) | −15.9554 | −0.999165 | ||||||||
\(256\) | −10.2958 | − | 12.2473i | −0.643487 | − | 0.765457i | ||||
\(257\) | 16.9823 | 1.05932 | 0.529662 | − | 0.848209i | \(-0.322319\pi\) | ||||
0.529662 | + | 0.848209i | \(0.322319\pi\) | |||||||
\(258\) | −7.45711 | − | 25.5733i | −0.464259 | − | 1.59212i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −37.3910 | + | 23.8327i | −2.31889 | + | 1.47804i | ||||
\(261\) | 1.64677 | + | 1.64677i | 0.101933 | + | 0.101933i | ||||
\(262\) | −24.5621 | − | 13.4716i | −1.51745 | − | 0.832277i | ||||
\(263\) | − | 4.39734i | − | 0.271152i | −0.990767 | − | 0.135576i | \(-0.956712\pi\) | ||
0.990767 | − | 0.135576i | \(-0.0432884\pi\) | |||||||
\(264\) | −6.01363 | − | 5.27018i | −0.370114 | − | 0.324357i | ||||
\(265\) | − | 2.20820i | − | 0.135649i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.0218 | + | 32.0218i | 1.95970 | + | 1.95970i | ||||
\(268\) | −5.15214 | + | 23.2649i | −0.314717 | + | 1.42113i | ||||
\(269\) | −7.71509 | + | 7.71509i | −0.470397 | + | 0.470397i | −0.902043 | − | 0.431646i | \(-0.857933\pi\) |
0.431646 | + | 0.902043i | \(0.357933\pi\) | |||||||
\(270\) | 38.1307 | − | 11.1188i | 2.32056 | − | 0.676669i | ||||
\(271\) | 16.7376 | 1.01674 | 0.508369 | − | 0.861139i | \(-0.330248\pi\) | ||||
0.508369 | + | 0.861139i | \(0.330248\pi\) | |||||||
\(272\) | −2.46363 | + | 5.28957i | −0.149380 | + | 0.320728i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.24286 | − | 0.362415i | 0.0750840 | − | 0.0218943i | ||||
\(275\) | −6.12080 | + | 6.12080i | −0.369098 | + | 0.369098i | ||||
\(276\) | −10.2787 | − | 2.27626i | −0.618703 | − | 0.137015i | ||||
\(277\) | −13.6141 | − | 13.6141i | −0.817989 | − | 0.817989i | 0.167827 | − | 0.985816i | \(-0.446325\pi\) |
−0.985816 | + | 0.167827i | \(0.946325\pi\) | |||||||
\(278\) | 2.64040 | − | 4.81411i | 0.158360 | − | 0.288731i | ||||
\(279\) | 6.47824i | 0.387842i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.9711i | − | 0.893100i | −0.894759 | − | 0.446550i | \(-0.852652\pi\) | ||
0.894759 | − | 0.446550i | \(-0.147348\pi\) | |||||||
\(282\) | −40.2417 | − | 22.0714i | −2.39636 | − | 1.31433i | ||||
\(283\) | −6.66191 | − | 6.66191i | −0.396010 | − | 0.396010i | 0.480813 | − | 0.876823i | \(-0.340341\pi\) |
−0.876823 | + | 0.480813i | \(0.840341\pi\) | |||||||
\(284\) | 3.10830 | + | 4.87659i | 0.184444 | + | 0.289373i | ||||
\(285\) | −29.3365 | + | 29.3365i | −1.73775 | + | 1.73775i | ||||
\(286\) | 2.26867 | + | 7.78014i | 0.134149 | + | 0.460049i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.77357 | − | 31.1325i | 0.281285 | − | 1.83450i | ||||
\(289\) | −14.8719 | −0.874820 | ||||||||
\(290\) | −0.618756 | − | 2.12195i | −0.0363346 | − | 0.124605i | ||||
\(291\) | −28.4508 | + | 28.4508i | −1.66781 | + | 1.66781i | ||||
\(292\) | 0.688227 | + | 1.07976i | 0.0402754 | + | 0.0631880i | ||||
\(293\) | −1.24795 | − | 1.24795i | −0.0729060 | − | 0.0729060i | 0.669714 | − | 0.742620i | \(-0.266417\pi\) |
−0.742620 | + | 0.669714i | \(0.766417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 19.8031i | − | 1.15298i | ||||||
\(296\) | −0.0129888 | − | 0.197137i | −0.000754959 | − | 0.0114583i | ||||
\(297\) | − | 7.25942i | − | 0.421234i | ||||||
\(298\) | 5.73876 | − | 10.4632i | 0.332438 | − | 0.606118i | ||||
\(299\) | 7.54475 | + | 7.54475i | 0.436324 | + | 0.436324i | ||||
\(300\) | −51.2260 | − | 11.3443i | −2.95754 | − | 0.654962i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.89365 | − | 2.01017i | 0.396685 | − | 0.115672i | ||||
\(303\) | −13.5596 | −0.778978 | ||||||||
\(304\) | 5.19595 | + | 14.2555i | 0.298008 | + | 0.817610i | ||||
\(305\) | 37.1099 | 2.12491 | ||||||||
\(306\) | −11.0274 | + | 3.21556i | −0.630394 | + | 0.183821i | ||||
\(307\) | −17.4736 | + | 17.4736i | −0.997273 | + | 0.997273i | −0.999996 | − | 0.00272350i | \(-0.999133\pi\) |
0.00272350 | + | 0.999996i | \(0.499133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.1055 | − | 18.1055i | −1.02999 | − | 1.02999i | ||||
\(310\) | 2.95672 | − | 5.39085i | 0.167930 | − | 0.306180i | ||||
\(311\) | − | 28.4805i | − | 1.61498i | −0.589880 | − | 0.807491i | \(-0.700825\pi\) | ||
0.589880 | − | 0.807491i | \(-0.299175\pi\) | |||||||
\(312\) | −32.3755 | + | 36.9426i | −1.83290 | + | 2.09147i | ||||
\(313\) | 15.6876i | 0.886714i | 0.896345 | + | 0.443357i | \(0.146213\pi\) | ||||
−0.896345 | + | 0.443357i | \(0.853787\pi\) | |||||||
\(314\) | 6.47751 | + | 3.55272i | 0.365547 | + | 0.200492i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.26460 | − | 0.806044i | 0.0711393 | − | 0.0453435i | ||||
\(317\) | 11.9478 | − | 11.9478i | 0.671054 | − | 0.671054i | −0.286905 | − | 0.957959i | \(-0.592626\pi\) |
0.957959 | + | 0.286905i | \(0.0926263\pi\) | |||||||
\(318\) | −0.684815 | − | 2.34849i | −0.0384025 | − | 0.131697i | ||||
\(319\) | −0.403983 | −0.0226187 | ||||||||
\(320\) | −18.1815 | + | 23.7282i | −1.01637 | + | 1.32644i | ||||
\(321\) | −13.1489 | −0.733901 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.91279 | − | 3.91279i | 0.217714 | − | 0.217714i | ||||
\(324\) | 8.93395 | − | 5.69442i | 0.496331 | − | 0.316357i | ||||
\(325\) | 37.6009 | + | 37.6009i | 2.08573 | + | 2.08573i | ||||
\(326\) | 14.3718 | + | 7.88250i | 0.795979 | + | 0.436571i | ||||
\(327\) | − | 18.0195i | − | 0.996480i | ||||||
\(328\) | 18.8521 | − | 21.5116i | 1.04093 | − | 1.18778i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.18415 | + | 13.0985i | −0.395474 | + | 0.721050i | ||||
\(331\) | 21.0571 | + | 21.0571i | 1.15741 | + | 1.15741i | 0.985032 | + | 0.172374i | \(0.0551437\pi\) |
0.172374 | + | 0.985032i | \(0.444856\pi\) | |||||||
\(332\) | 2.76100 | − | 12.4675i | 0.151529 | − | 0.684244i | ||||
\(333\) | 0.275001 | − | 0.275001i | 0.0150699 | − | 0.0150699i | ||||
\(334\) | 18.6640 | − | 5.44237i | 1.02125 | − | 0.297793i | ||||
\(335\) | 44.5192 | 2.43234 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.90123 | −0.103567 | −0.0517833 | − | 0.998658i | \(-0.516491\pi\) | ||||
−0.0517833 | + | 0.998658i | \(0.516491\pi\) | |||||||
\(338\) | 30.1448 | − | 8.79015i | 1.63966 | − | 0.478121i | ||||
\(339\) | 0.185552 | − | 0.185552i | 0.0100778 | − | 0.0100778i | ||||
\(340\) | 10.6440 | + | 2.35717i | 0.577253 | + | 0.127836i | ||||
\(341\) | −0.794617 | − | 0.794617i | −0.0430309 | − | 0.0430309i | ||||
\(342\) | −14.3633 | + | 26.1879i | −0.776679 | + | 1.41608i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.19664 | + | 18.1619i | 0.0645185 | + | 0.979225i | ||||
\(345\) | 19.6690i | 1.05894i | ||||||||
\(346\) | −9.79024 | − | 5.36965i | −0.526326 | − | 0.288674i | ||||
\(347\) | −20.2774 | − | 20.2774i | −1.08855 | − | 1.08855i | −0.995678 | − | 0.0928678i | \(-0.970397\pi\) |
−0.0928678 | − | 0.995678i | \(-0.529603\pi\) | |||||||
\(348\) | −1.31613 | − | 2.06487i | −0.0705521 | − | 0.110689i | ||||
\(349\) | 5.48808 | − | 5.48808i | 0.293770 | − | 0.293770i | −0.544797 | − | 0.838568i | \(-0.683393\pi\) |
0.838568 | + | 0.544797i | \(0.183393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −44.5957 | −2.38034 | ||||||||
\(352\) | 3.23317 | + | 4.40422i | 0.172329 | + | 0.234746i | ||||
\(353\) | −2.10289 | −0.111925 | −0.0559627 | − | 0.998433i | \(-0.517823\pi\) | ||||
−0.0559627 | + | 0.998433i | \(0.517823\pi\) | |||||||
\(354\) | −6.14141 | − | 21.0613i | −0.326412 | − | 1.11939i | ||||
\(355\) | 7.63985 | − | 7.63985i | 0.405481 | − | 0.405481i | ||||
\(356\) | −16.6313 | − | 26.0928i | −0.881459 | − | 1.38292i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.9686 | + | 6.56442i | 0.632560 | + | 0.346941i | ||||
\(359\) | − | 10.7107i | − | 0.565288i | −0.959225 | − | 0.282644i | \(-0.908789\pi\) | ||
0.959225 | − | 0.282644i | \(-0.0912115\pi\) | |||||||
\(360\) | −58.7177 | + | 3.86875i | −3.09470 | + | 0.203901i | ||||
\(361\) | 4.61140i | 0.242705i | ||||||||
\(362\) | −14.5482 | + | 26.5250i | −0.764635 | + | 1.39412i | ||||
\(363\) | −20.8366 | − | 20.8366i | −1.09364 | − | 1.09364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.69159 | − | 1.69159i | 0.0885416 | − | 0.0885416i | ||||
\(366\) | 39.4676 | − | 11.5086i | 2.06300 | − | 0.601566i | ||||
\(367\) | −18.1890 | −0.949460 | −0.474730 | − | 0.880131i | \(-0.657454\pi\) | ||||
−0.474730 | + | 0.880131i | \(0.657454\pi\) | |||||||
\(368\) | 6.52073 | + | 3.03704i | 0.339916 | + | 0.158317i | ||||
\(369\) | 56.3063 | 2.93119 | ||||||||
\(370\) | −0.354353 | + | 0.103328i | −0.0184220 | + | 0.00537179i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.47274 | − | 6.65029i | 0.0763580 | − | 0.344801i | ||||
\(373\) | −0.690889 | − | 0.690889i | −0.0357729 | − | 0.0357729i | 0.688994 | − | 0.724767i | \(-0.258053\pi\) |
−0.724767 | + | 0.688994i | \(0.758053\pi\) | |||||||
\(374\) | 0.958194 | − | 1.74703i | 0.0495470 | − | 0.0903367i | ||||
\(375\) | 43.3378i | 2.23796i | ||||||||
\(376\) | 23.5850 | + | 20.6692i | 1.21630 | + | 1.06593i | ||||
\(377\) | 2.48173i | 0.127816i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6845 | + | 17.6845i | 0.908391 | + | 0.908391i | 0.996142 | − | 0.0877516i | \(-0.0279682\pi\) |
−0.0877516 | + | 0.996142i | \(0.527968\pi\) | |||||||
\(380\) | 23.9048 | − | 15.2367i | 1.22629 | − | 0.781626i | ||||
\(381\) | −35.2033 | + | 35.2033i | −1.80352 | + | 1.80352i | ||||
\(382\) | 7.86749 | + | 26.9807i | 0.402536 | + | 1.38045i | ||||
\(383\) | −11.2504 | −0.574869 | −0.287435 | − | 0.957800i | \(-0.592802\pi\) | ||||
−0.287435 | + | 0.957800i | \(0.592802\pi\) | |||||||
\(384\) | −11.9779 | + | 30.8741i | −0.611245 | + | 1.57554i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.70437 | − | 16.1331i | −0.239446 | − | 0.821153i | ||||
\(387\) | −25.3354 | + | 25.3354i | −1.28787 | + | 1.28787i | ||||
\(388\) | 23.1830 | − | 14.7766i | 1.17694 | − | 0.750171i | ||||
\(389\) | 25.1321 | + | 25.1321i | 1.27425 | + | 1.27425i | 0.943838 | + | 0.330408i | \(0.107186\pi\) |
0.330408 | + | 0.943838i | \(0.392814\pi\) | |||||||
\(390\) | 80.4661 | + | 44.1333i | 4.07456 | + | 2.23478i | ||||
\(391\) | − | 2.62338i | − | 0.132670i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 57.9821i | 2.92481i | ||||||||
\(394\) | −6.36691 | + | 11.6085i | −0.320760 | + | 0.584827i | ||||
\(395\) | −1.98117 | − | 1.98117i | −0.0996834 | − | 0.0996834i | ||||
\(396\) | −2.32545 | + | 10.5007i | −0.116858 | + | 0.527682i | ||||
\(397\) | 2.16775 | − | 2.16775i | 0.108796 | − | 0.108796i | −0.650613 | − | 0.759409i | \(-0.725488\pi\) |
0.759409 | + | 0.650613i | \(0.225488\pi\) | |||||||
\(398\) | −32.6699 | + | 9.52645i | −1.63759 | + | 0.477518i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 32.4975 | + | 15.1358i | 1.62487 | + | 0.756789i | ||||
\(401\) | 21.3633 | 1.06683 | 0.533416 | − | 0.845853i | \(-0.320908\pi\) | ||||
0.533416 | + | 0.845853i | \(0.320908\pi\) | |||||||
\(402\) | 47.3476 | − | 13.8064i | 2.36148 | − | 0.688602i | ||||
\(403\) | −4.88145 | + | 4.88145i | −0.243162 | + | 0.243162i | ||||
\(404\) | 9.04575 | + | 2.00323i | 0.450043 | + | 0.0996643i | ||||
\(405\) | −13.9963 | − | 13.9963i | −0.695479 | − | 0.695479i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0674628i | 0.00334400i | ||||||||
\(408\) | 12.0513 | − | 0.794025i | 0.596626 | − | 0.0393101i | ||||
\(409\) | − | 10.1161i | − | 0.500210i | −0.968219 | − | 0.250105i | \(-0.919535\pi\) | ||
0.968219 | − | 0.250105i | \(-0.0804652\pi\) | |||||||
\(410\) | −46.8551 | − | 25.6987i | −2.31401 | − | 1.26917i | ||||
\(411\) | −1.89474 | − | 1.89474i | −0.0934605 | − | 0.0934605i | ||||
\(412\) | 9.40357 | + | 14.7532i | 0.463280 | + | 0.726839i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.96398 | + | 13.5940i | 0.194819 | + | 0.668110i | ||||
\(415\) | −23.8576 | −1.17112 | ||||||||
\(416\) | 27.0558 | − | 19.8618i | 1.32652 | − | 0.973807i | ||||
\(417\) | −11.3644 | −0.556515 | ||||||||
\(418\) | −1.45040 | − | 4.97399i | −0.0709414 | − | 0.243286i | ||||
\(419\) | −17.7452 | + | 17.7452i | −0.866909 | + | 0.866909i | −0.992129 | − | 0.125220i | \(-0.960036\pi\) |
0.125220 | + | 0.992129i | \(0.460036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.2787 | − | 18.2787i | −0.890851 | − | 0.890851i | 0.103752 | − | 0.994603i | \(-0.466915\pi\) |
−0.994603 | + | 0.103752i | \(0.966915\pi\) | |||||||
\(422\) | −31.9426 | − | 17.5196i | −1.55494 | − | 0.852840i | ||||
\(423\) | 61.7334i | 3.00158i | ||||||||
\(424\) | 0.109892 | + | 1.66788i | 0.00533683 | + | 0.0809993i | ||||
\(425\) | − | 13.0742i | − | 0.634191i | ||||||
\(426\) | 5.75593 | − | 10.4945i | 0.278876 | − | 0.508461i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.77179 | + | 1.94256i | 0.424001 | + | 0.0938972i | ||||
\(429\) | 11.8608 | − | 11.8608i | 0.572644 | − | 0.572644i | ||||
\(430\) | 32.6461 | − | 9.51950i | 1.57433 | − | 0.459071i | ||||
\(431\) | 22.3440 | 1.07627 | 0.538136 | − | 0.842858i | \(-0.319128\pi\) | ||||
0.538136 | + | 0.842858i | \(0.319128\pi\) | |||||||
\(432\) | −28.2472 | + | 10.2957i | −1.35904 | + | 0.495353i | ||||
\(433\) | 9.86560 | 0.474111 | 0.237055 | − | 0.971496i | \(-0.423818\pi\) | ||||
0.237055 | + | 0.971496i | \(0.423818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.23491 | + | 3.23491i | −0.155102 | + | 0.155102i | ||||
\(436\) | −2.66211 | + | 12.0210i | −0.127492 | + | 0.575702i | ||||
\(437\) | −4.82350 | − | 4.82350i | −0.230739 | − | 0.230739i | ||||
\(438\) | 1.27446 | − | 2.32365i | 0.0608958 | − | 0.111028i | ||||
\(439\) | 19.4362i | 0.927640i | 0.885929 | + | 0.463820i | \(0.153522\pi\) | ||||
−0.885929 | + | 0.463820i | \(0.846478\pi\) | |||||||
\(440\) | 6.72774 | − | 7.67681i | 0.320732 | − | 0.365978i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.7323 | − | 5.88632i | −0.510481 | − | 0.279984i | ||||
\(443\) | 17.8660 | + | 17.8660i | 0.848841 | + | 0.848841i | 0.989989 | − | 0.141148i | \(-0.0450792\pi\) |
−0.141148 | + | 0.989989i | \(0.545079\pi\) | |||||||
\(444\) | −0.344822 | + | 0.219786i | −0.0163645 | + | 0.0104306i | ||||
\(445\) | −40.8780 | + | 40.8780i | −1.93780 | + | 1.93780i | ||||
\(446\) | −3.29960 | − | 11.3156i | −0.156240 | − | 0.535809i | ||||
\(447\) | −24.6998 | −1.16826 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.8980 | −0.891850 | −0.445925 | − | 0.895070i | \(-0.647125\pi\) | ||||
−0.445925 | + | 0.895070i | \(0.647125\pi\) | |||||||
\(450\) | 19.7554 | + | 67.7488i | 0.931277 | + | 3.19371i | ||||
\(451\) | −6.90650 | + | 6.90650i | −0.325214 | + | 0.325214i | ||||
\(452\) | −0.151196 | + | 0.0963712i | −0.00711167 | + | 0.00453292i | ||||
\(453\) | −10.5093 | − | 10.5093i | −0.493771 | − | 0.493771i | ||||
\(454\) | 13.8057 | + | 7.57202i | 0.647934 | + | 0.355372i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.6982 | − | 23.6181i | 0.969284 | − | 1.10602i | ||||
\(457\) | 9.22546i | 0.431549i | 0.976443 | + | 0.215774i | \(0.0692275\pi\) | ||||
−0.976443 | + | 0.215774i | \(0.930772\pi\) | |||||||
\(458\) | −8.62727 | + | 15.7297i | −0.403126 | + | 0.735001i | ||||
\(459\) | 7.75316 | + | 7.75316i | 0.361886 | + | 0.361886i | ||||
\(460\) | 2.90581 | − | 13.1214i | 0.135484 | − | 0.611789i | ||||
\(461\) | 10.6272 | − | 10.6272i | 0.494960 | − | 0.494960i | −0.414905 | − | 0.909865i | \(-0.636185\pi\) |
0.909865 | + | 0.414905i | \(0.136185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.4877 | 1.50983 | 0.754916 | − | 0.655821i | \(-0.227678\pi\) | ||||
0.754916 | + | 0.655821i | \(0.227678\pi\) | |||||||
\(464\) | 0.572952 | + | 1.57194i | 0.0265986 | + | 0.0729755i | ||||
\(465\) | −12.7258 | −0.590146 | ||||||||
\(466\) | −30.6006 | + | 8.92304i | −1.41754 | + | 0.413352i | ||||
\(467\) | −12.4328 | + | 12.4328i | −0.575323 | + | 0.575323i | −0.933611 | − | 0.358288i | \(-0.883360\pi\) |
0.358288 | + | 0.933611i | \(0.383360\pi\) | |||||||
\(468\) | 64.5076 | + | 14.2856i | 2.98187 | + | 0.660350i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28.1756 | − | 51.3713i | 1.29964 | − | 2.36958i | ||||
\(471\) | − | 15.2910i | − | 0.704574i | ||||||
\(472\) | 0.985510 | + | 14.9575i | 0.0453618 | + | 0.688475i | ||||
\(473\) | − | 6.21525i | − | 0.285777i | ||||||
\(474\) | −2.72144 | − | 1.49263i | −0.125000 | − | 0.0685587i | ||||
\(475\) | −24.0390 | − | 24.0390i | −1.10298 | − | 1.10298i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.32665 | + | 2.32665i | −0.106530 | + | 0.106530i | ||||
\(478\) | 5.29220 | + | 18.1490i | 0.242059 | + | 0.830115i | ||||
\(479\) | 36.2808 | 1.65771 | 0.828857 | − | 0.559461i | \(-0.188992\pi\) | ||||
0.828857 | + | 0.559461i | \(0.188992\pi\) | |||||||
\(480\) | 61.1566 | + | 9.37718i | 2.79140 | + | 0.428008i | ||||
\(481\) | 0.414434 | 0.0188965 | ||||||||
\(482\) | 7.67802 | + | 26.3309i | 0.349724 | + | 1.19934i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8220 | + | 16.9787i | 0.491911 | + | 0.771757i | ||||
\(485\) | −36.3193 | − | 36.3193i | −1.64918 | − | 1.64918i | ||||
\(486\) | 8.73344 | + | 4.79003i | 0.396157 | + | 0.217280i | ||||
\(487\) | − | 7.29888i | − | 0.330744i | −0.986231 | − | 0.165372i | \(-0.947118\pi\) | ||
0.986231 | − | 0.165372i | \(-0.0528824\pi\) | |||||||
\(488\) | −28.0295 | + | 1.84679i | −1.26884 | + | 0.0836002i | ||||
\(489\) | − | 33.9265i | − | 1.53421i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.4241 | + | 11.4241i | 0.515561 | + | 0.515561i | 0.916225 | − | 0.400664i | \(-0.131221\pi\) |
−0.400664 | + | 0.916225i | \(0.631221\pi\) | |||||||
\(492\) | −57.8017 | − | 12.8005i | −2.60590 | − | 0.577090i | ||||
\(493\) | 0.431459 | − | 0.431459i | 0.0194320 | − | 0.0194320i | ||||
\(494\) | −30.5559 | + | 8.91003i | −1.37478 | + | 0.400881i | ||||
\(495\) | 20.0940 | 0.903157 | ||||||||
\(496\) | −1.96496 | + | 4.21890i | −0.0882294 | + | 0.189434i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −25.3733 | + | 7.39877i | −1.13700 | + | 0.331547i | ||||
\(499\) | 16.3221 | − | 16.3221i | 0.730679 | − | 0.730679i | −0.240076 | − | 0.970754i | \(-0.577172\pi\) |
0.970754 | + | 0.240076i | \(0.0771722\pi\) | |||||||
\(500\) | 6.40253 | − | 28.9112i | 0.286330 | − | 1.29295i | ||||
\(501\) | −28.4532 | − | 28.4532i | −1.27119 | − | 1.27119i | ||||
\(502\) | −7.79030 | + | 14.2037i | −0.347698 | + | 0.633941i | ||||
\(503\) | 11.6303i | 0.518568i | 0.965801 | + | 0.259284i | \(0.0834866\pi\) | ||||
−0.965801 | + | 0.259284i | \(0.916513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 17.3097i | − | 0.770273i | ||||||
\(506\) | −2.15365 | − | 1.18121i | −0.0957415 | − | 0.0525114i | ||||
\(507\) | −45.9556 | − | 45.9556i | −2.04096 | − | 2.04096i | ||||
\(508\) | 28.6853 | − | 18.2837i | 1.27270 | − | 0.811209i | ||||
\(509\) | −19.8640 | + | 19.8640i | −0.880457 | + | 0.880457i | −0.993581 | − | 0.113124i | \(-0.963914\pi\) |
0.113124 | + | 0.993581i | \(0.463914\pi\) | |||||||
\(510\) | −6.31662 | − | 21.6621i | −0.279705 | − | 0.959216i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12.5518 | − | 18.8269i | 0.554716 | − | 0.832040i | ||||
\(513\) | 28.5109 | 1.25879 | ||||||||
\(514\) | 6.72315 | + | 23.0563i | 0.296546 | + | 1.01697i | ||||
\(515\) | 23.1129 | − | 23.1129i | 1.01848 | − | 1.01848i | ||||
\(516\) | 31.7679 | − | 20.2486i | 1.39850 | − | 0.891394i | ||||
\(517\) | −7.57218 | − | 7.57218i | −0.333024 | − | 0.333024i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.1112i | 1.01447i | ||||||||
\(520\) | −47.1598 | − | 41.3295i | −2.06809 | − | 1.81242i | ||||
\(521\) | − | 6.68809i | − | 0.293010i | −0.989210 | − | 0.146505i | \(-0.953197\pi\) | ||
0.989210 | − | 0.146505i | \(-0.0468025\pi\) | |||||||
\(522\) | −1.58383 | + | 2.88772i | −0.0693222 | + | 0.126392i | ||||
\(523\) | −9.25913 | − | 9.25913i | −0.404874 | − | 0.404874i | 0.475073 | − | 0.879946i | \(-0.342422\pi\) |
−0.879946 | + | 0.475073i | \(0.842422\pi\) | |||||||
\(524\) | 8.56600 | − | 38.6805i | 0.374208 | − | 1.68977i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.97014 | − | 1.74088i | 0.260310 | − | 0.0759058i | ||||
\(527\) | 1.69732 | 0.0739365 | ||||||||
\(528\) | 4.77440 | − | 10.2510i | 0.207779 | − | 0.446116i | ||||
\(529\) | 19.7660 | 0.859393 | ||||||||
\(530\) | 2.99801 | − | 0.874212i | 0.130225 | − | 0.0379734i | ||||
\(531\) | −20.8654 | + | 20.8654i | −0.905479 | + | 0.905479i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.4276 | + | 42.4276i | 1.83774 | + | 1.83774i | ||||
\(534\) | −30.7978 | + | 56.1522i | −1.33275 | + | 2.42994i | ||||
\(535\) | − | 16.7855i | − | 0.725700i | ||||||
\(536\) | −33.6258 | + | 2.21551i | −1.45241 | + | 0.0956955i | ||||
\(537\) | − | 28.2535i | − | 1.21923i | ||||||
\(538\) | −13.5289 | − | 7.42020i | −0.583272 | − | 0.319908i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30.1913 | + | 47.3670i | 1.29923 | + | 2.03835i | ||||
\(541\) | 13.4444 | − | 13.4444i | 0.578019 | − | 0.578019i | −0.356338 | − | 0.934357i | \(-0.615975\pi\) |
0.934357 | + | 0.356338i | \(0.115975\pi\) | |||||||
\(542\) | 6.62631 | + | 22.7242i | 0.284624 | + | 0.976088i | ||||
\(543\) | 62.6158 | 2.68710 | ||||||||
\(544\) | −8.15683 | − | 1.25069i | −0.349721 | − | 0.0536230i | ||||
\(545\) | 23.0031 | 0.985345 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0842 | + | 12.0842i | −0.516683 | + | 0.516683i | −0.916566 | − | 0.399883i | \(-0.869051\pi\) |
0.399883 | + | 0.916566i | \(0.369051\pi\) | |||||||
\(548\) | 0.984080 | + | 1.54392i | 0.0420378 | + | 0.0659530i | ||||
\(549\) | −39.1004 | − | 39.1004i | −1.66877 | − | 1.66877i | ||||
\(550\) | −10.7332 | − | 5.88684i | −0.457665 | − | 0.251016i | ||||
\(551\) | − | 1.58662i | − | 0.0675921i | ||||||
\(552\) | −0.978835 | − | 14.8562i | −0.0416620 | − | 0.632322i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0937 | − | 23.8731i | 0.556298 | − | 1.01427i | ||||
\(555\) | 0.540210 | + | 0.540210i | 0.0229306 | + | 0.0229306i | ||||
\(556\) | 7.58129 | + | 1.67892i | 0.321518 | + | 0.0712019i | ||||
\(557\) | 23.8656 | − | 23.8656i | 1.01122 | − | 1.01122i | 0.0112795 | − | 0.999936i | \(-0.496410\pi\) |
0.999936 | − | 0.0112795i | \(-0.00359046\pi\) | |||||||
\(558\) | −8.79532 | + | 2.56469i | −0.372336 | + | 0.108572i | ||||
\(559\) | −38.1812 | −1.61489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.12410 | −0.174120 | ||||||||
\(562\) | 20.3258 | − | 5.92695i | 0.857392 | − | 0.250013i | ||||
\(563\) | −20.6614 | + | 20.6614i | −0.870774 | + | 0.870774i | −0.992557 | − | 0.121783i | \(-0.961139\pi\) |
0.121783 | + | 0.992557i | \(0.461139\pi\) | |||||||
\(564\) | 14.0343 | − | 63.3729i | 0.590949 | − | 2.66848i | ||||
\(565\) | 0.236870 | + | 0.236870i | 0.00996518 | + | 0.00996518i | ||||
\(566\) | 6.40728 | − | 11.6821i | 0.269318 | − | 0.491035i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.39025 | + | 6.15065i | −0.226170 | + | 0.258076i | ||||
\(569\) | − | 26.4857i | − | 1.11034i | −0.831738 | − | 0.555169i | \(-0.812654\pi\) | ||
0.831738 | − | 0.555169i | \(-0.187346\pi\) | |||||||
\(570\) | −51.4435 | − | 28.2152i | −2.15473 | − | 1.18181i | ||||
\(571\) | 23.7561 | + | 23.7561i | 0.994161 | + | 0.994161i | 0.999983 | − | 0.00582227i | \(-0.00185330\pi\) |
−0.00582227 | + | 0.999983i | \(0.501853\pi\) | |||||||
\(572\) | −9.66471 | + | 6.16020i | −0.404102 | + | 0.257571i | ||||
\(573\) | 41.1319 | − | 41.1319i | 1.71831 | − | 1.71831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.1172 | −0.672134 | ||||||||
\(576\) | 44.1576 | − | 5.84421i | 1.83990 | − | 0.243509i | ||||
\(577\) | −27.5648 | −1.14754 | −0.573770 | − | 0.819017i | \(-0.694520\pi\) | ||||
−0.573770 | + | 0.819017i | \(0.694520\pi\) | |||||||
\(578\) | −5.88769 | − | 20.1912i | −0.244896 | − | 0.839842i | ||||
\(579\) | −24.5948 | + | 24.5948i | −1.02213 | + | 1.02213i | ||||
\(580\) | 2.63595 | − | 1.68013i | 0.109452 | − | 0.0697637i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −49.8902 | − | 27.3633i | −2.06802 | − | 1.13425i | ||||
\(583\) | − | 0.570770i | − | 0.0236389i | ||||||
\(584\) | −1.19349 | + | 1.36185i | −0.0493869 | + | 0.0563539i | ||||
\(585\) | − | 123.440i | − | 5.10363i | ||||||
\(586\) | 1.20025 | − | 2.18836i | 0.0495818 | − | 0.0904002i | ||||
\(587\) | 23.6471 | + | 23.6471i | 0.976018 | + | 0.976018i | 0.999719 | − | 0.0237007i | \(-0.00754488\pi\) |
−0.0237007 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.12080 | − | 3.12080i | 0.128590 | − | 0.128590i | ||||
\(590\) | 26.8861 | − | 7.83993i | 1.10689 | − | 0.322765i | ||||
\(591\) | 27.4034 | 1.12723 | ||||||||
\(592\) | 0.262504 | − | 0.0956795i | 0.0107889 | − | 0.00393240i | ||||
\(593\) | 41.8302 | 1.71776 | 0.858881 | − | 0.512175i | \(-0.171160\pi\) | ||||
0.858881 | + | 0.512175i | \(0.171160\pi\) | |||||||
\(594\) | 9.85590 | − | 2.87395i | 0.404393 | − | 0.117920i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.4775 | + | 3.64904i | 0.674946 | + | 0.149470i | ||||
\(597\) | 49.8051 | + | 49.8051i | 2.03839 | + | 2.03839i | ||||
\(598\) | −7.25637 | + | 13.2302i | −0.296735 | + | 0.541023i | ||||
\(599\) | 27.7720i | 1.13473i | 0.823465 | + | 0.567367i | \(0.192038\pi\) | ||||
−0.823465 | + | 0.567367i | \(0.807962\pi\) | |||||||
\(600\) | −4.87824 | − | 74.0392i | −0.199153 | − | 3.02264i | ||||
\(601\) | − | 26.3860i | − | 1.07631i | −0.842846 | − | 0.538154i | \(-0.819122\pi\) | ||
0.842846 | − | 0.538154i | \(-0.180878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.9071 | − | 46.9071i | −1.91021 | − | 1.91021i | ||||
\(604\) | 5.45829 | + | 8.56349i | 0.222095 | + | 0.348443i | ||||
\(605\) | 26.5994 | − | 26.5994i | 1.08142 | − | 1.08142i | ||||
\(606\) | −5.36814 | − | 18.4094i | −0.218066 | − | 0.747832i | ||||
\(607\) | 18.9982 | 0.771113 | 0.385557 | − | 0.922684i | \(-0.374009\pi\) | ||||
0.385557 | + | 0.922684i | \(0.374009\pi\) | |||||||
\(608\) | −17.2972 | + | 12.6981i | −0.701496 | + | 0.514974i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.6916 | + | 50.3830i | 0.594844 | + | 2.03995i | ||||
\(611\) | −46.5170 | + | 46.5170i | −1.88188 | + | 1.88188i | ||||
\(612\) | −8.73133 | − | 13.6985i | −0.352943 | − | 0.553731i | ||||
\(613\) | −3.03271 | − | 3.03271i | −0.122490 | − | 0.122490i | 0.643204 | − | 0.765694i | \(-0.277605\pi\) |
−0.765694 | + | 0.643204i | \(0.777605\pi\) | |||||||
\(614\) | −30.6411 | − | 16.8057i | −1.23657 | − | 0.678225i | ||||
\(615\) | 110.608i | 4.46014i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.11707i | − | 0.0449717i | −0.999747 | − | 0.0224859i | \(-0.992842\pi\) | ||
0.999747 | − | 0.0224859i | \(-0.00715808\pi\) | |||||||
\(618\) | 17.4135 | − | 31.7492i | 0.700473 | − | 1.27714i | ||||
\(619\) | 5.95717 | + | 5.95717i | 0.239439 | + | 0.239439i | 0.816618 | − | 0.577179i | \(-0.195846\pi\) |
−0.577179 | + | 0.816618i | \(0.695846\pi\) | |||||||
\(620\) | 8.48954 | + | 1.88005i | 0.340948 | + | 0.0755048i | ||||
\(621\) | 9.55772 | − | 9.55772i | 0.383538 | − | 0.383538i | ||||
\(622\) | 38.6672 | − | 11.2752i | 1.55041 | − | 0.452096i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −62.9731 | − | 29.3299i | −2.52094 | − | 1.17413i | ||||
\(625\) | −10.5119 | −0.420478 | ||||||||
\(626\) | −21.2986 | + | 6.21060i | −0.851261 | + | 0.248225i | ||||
\(627\) | −7.58282 | + | 7.58282i | −0.302829 | + | 0.302829i | ||||
\(628\) | −2.25903 | + | 10.2008i | −0.0901449 | + | 0.407057i | ||||
\(629\) | −0.0720511 | − | 0.0720511i | −0.00287287 | − | 0.00287287i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.4799i | − | 0.496819i | −0.968655 | − | 0.248409i | \(-0.920092\pi\) | ||
0.968655 | − | 0.248409i | \(-0.0799078\pi\) | |||||||
\(632\) | 1.59499 | + | 1.39780i | 0.0634452 | + | 0.0556016i | ||||
\(633\) | 75.4049i | 2.99708i | ||||||||
\(634\) | 20.9512 | + | 11.4911i | 0.832078 | + | 0.456370i | ||||
\(635\) | −44.9394 | − | 44.9394i | −1.78336 | − | 1.78336i | ||||
\(636\) | 2.91737 | − | 1.85951i | 0.115681 | − | 0.0737342i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.159934 | − | 0.548476i | −0.00633185 | − | 0.0217144i | ||||
\(639\) | −16.0993 | −0.636877 | ||||||||
\(640\) | −39.4129 | − | 15.2906i | −1.55793 | − | 0.604414i | ||||
\(641\) | −10.1980 | −0.402797 | −0.201398 | − | 0.979509i | \(-0.564549\pi\) | ||||
−0.201398 | + | 0.979509i | \(0.564549\pi\) | |||||||
\(642\) | −5.20557 | − | 17.8519i | −0.205447 | − | 0.704559i | ||||
\(643\) | 10.9741 | − | 10.9741i | 0.432777 | − | 0.432777i | −0.456795 | − | 0.889572i | \(-0.651003\pi\) |
0.889572 | + | 0.456795i | \(0.151003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −49.7688 | − | 49.7688i | −1.95964 | − | 1.95964i | ||||
\(646\) | 6.86133 | + | 3.76324i | 0.269955 | + | 0.148063i | ||||
\(647\) | − | 6.58567i | − | 0.258909i | −0.991585 | − | 0.129455i | \(-0.958677\pi\) | ||
0.991585 | − | 0.129455i | \(-0.0413227\pi\) | |||||||
\(648\) | 11.2680 | + | 9.87498i | 0.442650 | + | 0.387926i | ||||
\(649\) | − | 5.11866i | − | 0.200925i | ||||||
\(650\) | −36.1637 | + | 65.9356i | −1.41846 | + | 2.58621i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.01214 | + | 22.6328i | −0.196291 | + | 0.886367i | ||||
\(653\) | 3.62950 | − | 3.62950i | 0.142033 | − | 0.142033i | −0.632515 | − | 0.774548i | \(-0.717977\pi\) |
0.774548 | + | 0.632515i | \(0.217977\pi\) | |||||||
\(654\) | 24.4645 | − | 7.13379i | 0.956639 | − | 0.278953i | ||||
\(655\) | −74.0181 | −2.89213 | ||||||||
\(656\) | 36.6691 | + | 17.0787i | 1.43169 | + | 0.666811i | ||||
\(657\) | −3.56464 | −0.139070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.78706 | + | 5.78706i | −0.225432 | + | 0.225432i | −0.810781 | − | 0.585349i | \(-0.800957\pi\) |
0.585349 | + | 0.810781i | \(0.300957\pi\) | |||||||
\(660\) | −20.6276 | − | 4.56809i | −0.802929 | − | 0.177813i | ||||
\(661\) | 19.4549 | + | 19.4549i | 0.756709 | + | 0.756709i | 0.975722 | − | 0.219013i | \(-0.0702838\pi\) |
−0.219013 | + | 0.975722i | \(0.570284\pi\) | |||||||
\(662\) | −20.2523 | + | 36.9250i | −0.787127 | + | 1.43513i | ||||
\(663\) | 25.3349i | 0.983928i | ||||||||
\(664\) | 18.0198 | − | 1.18728i | 0.699306 | − | 0.0460754i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.482231 | + | 0.264489i | 0.0186861 | + | 0.0102488i | ||||
\(667\) | −0.531882 | − | 0.531882i | −0.0205946 | − | 0.0205946i | ||||
\(668\) | 14.7779 | + | 23.1850i | 0.571774 | + | 0.897053i | ||||
\(669\) | −17.2506 | + | 17.2506i | −0.666946 | + | 0.666946i | ||||
\(670\) | 17.6248 | + | 60.4424i | 0.680907 | + | 2.33509i | ||||
\(671\) | 9.59206 | 0.370297 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3667 | −1.44038 | −0.720190 | − | 0.693776i | \(-0.755946\pi\) | ||||
−0.720190 | + | 0.693776i | \(0.755946\pi\) | |||||||
\(674\) | −0.752683 | − | 2.58124i | −0.0289923 | − | 0.0994258i | ||||
\(675\) | 47.6330 | − | 47.6330i | 1.83339 | − | 1.83339i | ||||
\(676\) | 23.8682 | + | 37.4468i | 0.918009 | + | 1.44026i | ||||
\(677\) | 16.1658 | + | 16.1658i | 0.621303 | + | 0.621303i | 0.945865 | − | 0.324561i | \(-0.105217\pi\) |
−0.324561 | + | 0.945865i | \(0.605217\pi\) | |||||||
\(678\) | 0.325377 | + | 0.178460i | 0.0124960 | + | 0.00685370i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.01363 | + | 15.3842i | 0.0388708 | + | 0.589959i | ||||
\(681\) | − | 32.5902i | − | 1.24886i | ||||||
\(682\) | 0.764244 | − | 1.39341i | 0.0292644 | − | 0.0533564i | ||||
\(683\) | 13.2551 | + | 13.2551i | 0.507192 | + | 0.507192i | 0.913663 | − | 0.406472i | \(-0.133241\pi\) |
−0.406472 | + | 0.913663i | \(0.633241\pi\) | |||||||
\(684\) | −41.2409 | − | 9.13302i | −1.57689 | − | 0.349210i | ||||
\(685\) | 2.41876 | − | 2.41876i | 0.0924161 | − | 0.0924161i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.1321 | 1.41668 | ||||||||
\(688\) | −24.1842 | + | 8.81482i | −0.922012 | + | 0.336062i | ||||
\(689\) | −3.50632 | −0.133580 | ||||||||
\(690\) | −26.7040 | + | 7.78682i | −1.01661 | + | 0.296439i | ||||
\(691\) | 6.24472 | − | 6.24472i | 0.237560 | − | 0.237560i | −0.578279 | − | 0.815839i | \(-0.696275\pi\) |
0.815839 | + | 0.578279i | \(0.196275\pi\) | |||||||
\(692\) | 3.41433 | − | 15.4177i | 0.129794 | − | 0.586094i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.5023 | − | 35.5577i | 0.740298 | − | 1.34975i | ||||
\(695\) | − | 14.5074i | − | 0.550296i | ||||||
\(696\) | 2.28237 | − | 2.60434i | 0.0865130 | − | 0.0987174i | ||||
\(697\) | − | 14.7525i | − | 0.558789i | ||||||
\(698\) | 9.62370 | + | 5.27831i | 0.364262 | + | 0.199787i | ||||
\(699\) | 46.6504 | + | 46.6504i | 1.76448 | + | 1.76448i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1681 | − | 28.1681i | 1.06389 | − | 1.06389i | 0.0660783 | − | 0.997814i | \(-0.478951\pi\) |
0.997814 | − | 0.0660783i | \(-0.0210487\pi\) | |||||||
\(702\) | −17.6551 | − | 60.5463i | −0.666350 | − | 2.28517i | ||||
\(703\) | −0.264955 | −0.00999297 | ||||||||
\(704\) | −4.69949 | + | 6.13318i | −0.177119 | + | 0.231153i | ||||
\(705\) | −121.269 | −4.56725 | ||||||||
\(706\) | −0.832519 | − | 2.85503i | −0.0313322 | − | 0.107450i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 26.1629 | − | 16.6760i | 0.983263 | − | 0.626723i | ||||
\(709\) | 10.8738 | + | 10.8738i | 0.408376 | + | 0.408376i | 0.881172 | − | 0.472796i | \(-0.156755\pi\) |
−0.472796 | + | 0.881172i | \(0.656755\pi\) | |||||||
\(710\) | 13.3970 | + | 7.34783i | 0.502779 | + | 0.275759i | ||||
\(711\) | 4.17487i | 0.156570i | ||||||||
\(712\) | 28.8412 | − | 32.9098i | 1.08087 | − | 1.23335i | ||||
\(713\) | − | 2.09238i | − | 0.0783601i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.1411 | + | 15.1411i | 0.566245 | + | 0.566245i | ||||
\(716\) | −4.17404 | + | 18.8482i | −0.155991 | + | 0.704391i | ||||
\(717\) | 27.6680 | − | 27.6680i | 1.03328 | − | 1.03328i | ||||
\(718\) | 14.5416 | − | 4.24028i | 0.542686 | − | 0.158246i | ||||
\(719\) | 21.4416 | 0.799638 | 0.399819 | − | 0.916594i | \(-0.369073\pi\) | ||||
0.399819 | + | 0.916594i | \(0.369073\pi\) | |||||||
\(720\) | −28.4984 | − | 78.1877i | −1.06207 | − | 2.91388i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.26076 | + | 1.82562i | −0.233001 | + | 0.0679425i | ||||
\(723\) | 40.1413 | − | 40.1413i | 1.49287 | − | 1.49287i | ||||
\(724\) | −41.7717 | − | 9.25056i | −1.55243 | − | 0.343795i | ||||
\(725\) | −2.65075 | − | 2.65075i | −0.0984465 | − | 0.0984465i | ||||
\(726\) | 20.0402 | − | 36.5384i | 0.743762 | − | 1.35607i | ||||
\(727\) | − | 30.4747i | − | 1.13024i | −0.825007 | − | 0.565122i | \(-0.808829\pi\) | ||
0.825007 | − | 0.565122i | \(-0.191171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 36.5081i | − | 1.35215i | ||||||
\(730\) | 2.96630 | + | 1.62693i | 0.109788 | + | 0.0602153i | ||||
\(731\) | 6.63796 | + | 6.63796i | 0.245514 | + | 0.245514i | ||||
\(732\) | 31.2499 | + | 49.0278i | 1.15503 | + | 1.81212i | ||||
\(733\) | −32.8283 | + | 32.8283i | −1.21254 | + | 1.21254i | −0.242351 | + | 0.970189i | \(0.577919\pi\) |
−0.970189 | + | 0.242351i | \(0.922081\pi\) | |||||||
\(734\) | −7.20091 | − | 24.6947i | −0.265791 | − | 0.911499i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.54179 | + | 10.0553i | −0.0568312 | + | 0.370645i | ||||
\(737\) | 11.5072 | 0.423873 | ||||||||
\(738\) | 22.2913 | + | 76.4455i | 0.820554 | + | 2.81400i | ||||
\(739\) | −15.4736 | + | 15.4736i | −0.569207 | + | 0.569207i | −0.931906 | − | 0.362699i | \(-0.881855\pi\) |
0.362699 | + | 0.931906i | \(0.381855\pi\) | |||||||
\(740\) | −0.280572 | − | 0.440188i | −0.0103140 | − | 0.0161816i | ||||
\(741\) | 46.5824 | + | 46.5824i | 1.71125 | + | 1.71125i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 19.2071i | − | 0.704639i | −0.935880 | − | 0.352320i | \(-0.885393\pi\) | ||
0.935880 | − | 0.352320i | \(-0.114607\pi\) | |||||||
\(744\) | 9.61194 | − | 0.633305i | 0.352391 | − | 0.0232181i | ||||
\(745\) | − | 31.5310i | − | 1.15521i | ||||||
\(746\) | 0.664482 | − | 1.21152i | 0.0243284 | − | 0.0443568i | ||||
\(747\) | 25.1372 | + | 25.1372i | 0.919723 | + | 0.919723i | ||||
\(748\) | 2.75123 | + | 0.609275i | 0.100595 | + | 0.0222773i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −58.8385 | + | 17.1571i | −2.14848 | + | 0.626490i | ||||
\(751\) | −35.8573 | −1.30845 | −0.654225 | − | 0.756300i | \(-0.727005\pi\) | ||||
−0.654225 | + | 0.756300i | \(0.727005\pi\) | |||||||
\(752\) | −18.7248 | + | 40.2034i | −0.682824 | + | 1.46607i | ||||
\(753\) | 33.5297 | 1.22189 | ||||||||
\(754\) | −3.36937 | + | 0.982499i | −0.122705 | + | 0.0357805i | ||||
\(755\) | 13.4159 | − | 13.4159i | 0.488253 | − | 0.488253i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1772 | + | 22.1772i | 0.806045 | + | 0.806045i | 0.984033 | − | 0.177988i | \(-0.0569587\pi\) |
−0.177988 | + | 0.984033i | \(0.556959\pi\) | |||||||
\(758\) | −17.0085 | + | 31.0109i | −0.617778 | + | 1.12636i | ||||
\(759\) | 5.08399i | 0.184537i | ||||||||
\(760\) | 30.1501 | + | 26.4227i | 1.09366 | + | 0.958452i | ||||
\(761\) | 29.5689i | 1.07187i | 0.844258 | + | 0.535936i | \(0.180041\pi\) | ||||
−0.844258 | + | 0.535936i | \(0.819959\pi\) | |||||||
\(762\) | −61.7312 | − | 33.8577i | −2.23628 | − | 1.22654i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −33.5162 | + | 21.3629i | −1.21257 | + | 0.772883i | ||||
\(765\) | −21.4606 | + | 21.4606i | −0.775911 | + | 0.775911i | ||||
\(766\) | −4.45396 | − | 15.2744i | −0.160928 | − | 0.551885i | ||||
\(767\) | −31.4447 | −1.13540 | ||||||||
\(768\) | −46.6589 | − | 4.03920i | −1.68366 | − | 0.145752i | ||||
\(769\) | −30.8038 | −1.11081 | −0.555406 | − | 0.831579i | \(-0.687437\pi\) | ||||
−0.555406 | + | 0.831579i | \(0.687437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.1492 | − | 35.1492i | 1.26587 | − | 1.26587i | ||||
\(772\) | 20.0410 | − | 12.7740i | 0.721292 | − | 0.459745i | ||||
\(773\) | 36.3527 | + | 36.3527i | 1.30752 | + | 1.30752i | 0.923203 | + | 0.384313i | \(0.125562\pi\) |
0.384313 | + | 0.923203i | \(0.374438\pi\) | |||||||
\(774\) | −44.4273 | − | 24.3670i | −1.59690 | − | 0.875855i | ||||
\(775\) | − | 10.4278i | − | 0.374578i | ||||||
\(776\) | 29.2398 | + | 25.6249i | 1.04965 | + | 0.919881i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.1715 | + | 44.0707i | −0.866589 | + | 1.58001i | ||||
\(779\) | −27.1248 | − | 27.1248i | −0.971845 | − | 0.971845i | ||||
\(780\) | −28.0625 | + | 126.718i | −1.00480 | + | 4.53725i | ||||
\(781\) | 1.97472 | − | 1.97472i | 0.0706612 | − | 0.0706612i | ||||
\(782\) | 3.56168 | − | 1.03858i | 0.127365 | − | 0.0371394i | ||||
\(783\) | 3.14386 | 0.112352 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.5201 | 0.696701 | ||||||||
\(786\) | −78.7206 | + | 22.9547i | −2.80787 | + | 0.818768i | ||||
\(787\) | 7.35668 | − | 7.35668i | 0.262237 | − | 0.262237i | −0.563725 | − | 0.825962i | \(-0.690632\pi\) |
0.825962 | + | 0.563725i | \(0.190632\pi\) | |||||||
\(788\) | −18.2811 | − | 4.04845i | −0.651238 | − | 0.144220i | ||||
\(789\) | −9.10145 | − | 9.10145i | −0.324020 | − | 0.324020i | ||||
\(790\) | 1.90544 | − | 3.47410i | 0.0677926 | − | 0.123603i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −15.1772 | + | 0.999984i | −0.539298 | + | 0.0355329i | ||||
\(793\) | − | 58.9254i | − | 2.09250i | ||||||
\(794\) | 3.80129 | + | 2.08490i | 0.134903 | + | 0.0739902i | ||||
\(795\) | −4.57046 | − | 4.57046i | −0.162097 | − | 0.162097i | ||||
\(796\) | −25.8675 | − | 40.5835i | −0.916851 | − | 1.43844i | ||||
\(797\) | −18.5924 | + | 18.5924i | −0.658577 | + | 0.658577i | −0.955043 | − | 0.296466i | \(-0.904192\pi\) |
0.296466 | + | 0.955043i | \(0.404192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.1744 | 0.572208 | ||||||||
\(800\) | −7.68386 | + | 50.1130i | −0.271666 | + | 1.77176i | ||||
\(801\) | 86.1412 | 3.04365 | ||||||||
\(802\) | 8.45758 | + | 29.0043i | 0.298648 | + | 1.02418i | ||||
\(803\) | 0.437236 | − | 0.437236i | 0.0154297 | − | 0.0154297i | ||||
\(804\) | 37.4891 | + | 58.8165i | 1.32214 | + | 2.07430i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.55992 | − | 4.69486i | −0.301510 | − | 0.165370i | ||||
\(807\) | 31.9368i | 1.12423i | ||||||||
\(808\) | 0.861424 | + | 13.0742i | 0.0303048 | + | 0.459949i | ||||
\(809\) | 44.5183i | 1.56518i | 0.622538 | + | 0.782589i | \(0.286102\pi\) | ||||
−0.622538 | + | 0.782589i | \(0.713898\pi\) | |||||||
\(810\) | 13.4613 | − | 24.5433i | 0.472981 | − | 0.862364i | ||||
\(811\) | −20.8814 | − | 20.8814i | −0.733246 | − | 0.733246i | 0.238015 | − | 0.971261i | \(-0.423503\pi\) |
−0.971261 | + | 0.238015i | \(0.923503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.6429 | − | 34.6429i | 1.21498 | − | 1.21498i | ||||
\(814\) | −0.0915922 | + | 0.0267080i | −0.00321030 | + | 0.000936116i | ||||
\(815\) | 43.3095 | 1.51707 | ||||||||
\(816\) | 5.84903 | + | 16.0473i | 0.204757 | + | 0.561767i | ||||
\(817\) | 24.4099 | 0.853996 | ||||||||
\(818\) | 13.7344 | − | 4.00490i | 0.480211 | − | 0.140028i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.3407 | − | 73.7878i | 0.570641 | − | 2.57678i | ||||
\(821\) | −17.2139 | − | 17.2139i | −0.600770 | − | 0.600770i | 0.339747 | − | 0.940517i | \(-0.389659\pi\) |
−0.940517 | + | 0.339747i | \(0.889659\pi\) | |||||||
\(822\) | 1.82231 | − | 3.32254i | 0.0635605 | − | 0.115887i | ||||
\(823\) | − | 31.7106i | − | 1.10536i | −0.833392 | − | 0.552682i | \(-0.813604\pi\) | ||
0.833392 | − | 0.552682i | \(-0.186396\pi\) | |||||||
\(824\) | −16.3072 | + | 18.6076i | −0.568088 | + | 0.648228i | ||||
\(825\) | 25.3372i | 0.882127i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.2764 | − | 29.2764i | −1.01804 | − | 1.01804i | −0.999834 | − | 0.0182049i | \(-0.994205\pi\) |
−0.0182049 | − | 0.999834i | \(-0.505795\pi\) | |||||||
\(828\) | −16.8869 | + | 10.7636i | −0.586860 | + | 0.374059i | ||||
\(829\) | 0.222175 | − | 0.222175i | 0.00771644 | − | 0.00771644i | −0.703238 | − | 0.710954i | \(-0.748263\pi\) |
0.710954 | + | 0.703238i | \(0.248263\pi\) | |||||||
\(830\) | −9.44504 | − | 32.3907i | −0.327842 | − | 1.12430i | ||||
\(831\) | −56.3557 | −1.95496 | ||||||||
\(832\) | 37.6770 | + | 28.8696i | 1.30622 | + | 1.00087i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.49907 | − | 15.4290i | −0.155790 | − | 0.534264i | ||||
\(835\) | 36.3224 | − | 36.3224i | 1.25699 | − | 1.25699i | ||||
\(836\) | 6.17883 | − | 3.93833i | 0.213699 | − | 0.136210i | ||||
\(837\) | 6.18383 | + | 6.18383i | 0.213744 | + | 0.213744i | ||||
\(838\) | −31.1173 | − | 17.0669i | −1.07493 | − | 0.589567i | ||||
\(839\) | − | 1.52778i | − | 0.0527447i | −0.999652 | − | 0.0263723i | \(-0.991604\pi\) | ||
0.999652 | − | 0.0263723i | \(-0.00839555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8250i | 0.993967i | ||||||||
\(842\) | 17.5801 | − | 32.0529i | 0.605849 | − | 1.10462i | ||||
\(843\) | −30.9866 | − | 30.9866i | −1.06723 | − | 1.06723i | ||||
\(844\) | 11.1400 | − | 50.3034i | 0.383453 | − | 1.73152i | ||||
\(845\) | 58.6655 | − | 58.6655i | 2.01815 | − | 2.01815i | ||||
\(846\) | −83.8137 | + | 24.4398i | −2.88157 | + | 0.840259i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.22092 | + | 0.809498i | −0.0762668 | + | 0.0277983i | ||||
\(849\) | −27.5771 | −0.946445 | ||||||||
\(850\) | 17.7504 | − | 5.17598i | 0.608835 | − | 0.177534i | ||||
\(851\) | −0.0888211 | + | 0.0888211i | −0.00304475 | + | 0.00304475i | ||||
\(852\) | 16.5268 | + | 3.65995i | 0.566200 | + | 0.125388i | ||||
\(853\) | −35.7996 | − | 35.7996i | −1.22576 | − | 1.22576i | −0.965554 | − | 0.260202i | \(-0.916211\pi\) |
−0.260202 | − | 0.965554i | \(-0.583789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 78.9177i | 2.69893i | ||||||||
\(856\) | 0.835336 | + | 12.6782i | 0.0285512 | + | 0.433334i | ||||
\(857\) | 7.59086i | 0.259299i | 0.991560 | + | 0.129650i | \(0.0413852\pi\) | ||||
−0.991560 | + | 0.129650i | \(0.958615\pi\) | |||||||
\(858\) | 20.7986 | + | 11.4074i | 0.710054 | + | 0.389443i | ||||
\(859\) | 20.4192 | + | 20.4192i | 0.696695 | + | 0.696695i | 0.963696 | − | 0.267001i | \(-0.0860328\pi\) |
−0.267001 | + | 0.963696i | \(0.586033\pi\) | |||||||
\(860\) | 25.8487 | + | 40.5539i | 0.881433 | + | 1.38288i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.84583 | + | 30.3358i | 0.301290 | + | 1.03324i | ||||
\(863\) | −8.73810 | −0.297449 | −0.148724 | − | 0.988879i | \(-0.547517\pi\) | ||||
−0.148724 | + | 0.988879i | \(0.547517\pi\) | |||||||
\(864\) | −25.1611 | − | 34.2743i | −0.855996 | − | 1.16604i | ||||
\(865\) | −29.5030 | −1.00313 | ||||||||
\(866\) | 3.90572 | + | 13.3942i | 0.132722 | + | 0.455155i | ||||
\(867\) | −30.7814 | + | 30.7814i | −1.04539 | + | 1.04539i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.512086 | − | 0.512086i | −0.0173713 | − | 0.0173713i | ||||
\(870\) | −5.67261 | − | 3.11126i | −0.192320 | − | 0.105482i | ||||
\(871\) | − | 70.6903i | − | 2.39525i | ||||||
\(872\) | −17.3745 | + | 1.14476i | −0.588374 | + | 0.0387664i | ||||
\(873\) | 76.5349i | 2.59031i | ||||||||
\(874\) | 4.63913 | − | 8.45831i | 0.156921 | − | 0.286107i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.65930 | + | 0.810372i | 0.123636 | + | 0.0273799i | ||||
\(877\) | 15.9966 | − | 15.9966i | 0.540168 | − | 0.540168i | −0.383410 | − | 0.923578i | \(-0.625250\pi\) |
0.923578 | + | 0.383410i | \(0.125250\pi\) | |||||||
\(878\) | −26.3880 | + | 7.69466i | −0.890551 | + | 0.259682i | ||||
\(879\) | −5.16591 | −0.174242 | ||||||||
\(880\) | 13.0860 | + | 6.09485i | 0.441130 | + | 0.205457i | ||||
\(881\) | −19.9839 | −0.673273 | −0.336637 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336637 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.776332 | + | 0.776332i | −0.0261257 | + | 0.0261257i | −0.720049 | − | 0.693923i | \(-0.755881\pi\) |
0.693923 | + | 0.720049i | \(0.255881\pi\) | |||||||
\(884\) | 3.74286 | − | 16.9012i | 0.125886 | − | 0.568450i | ||||
\(885\) | −40.9878 | − | 40.9878i | −1.37779 | − | 1.37779i | ||||
\(886\) | −17.1832 | + | 31.3292i | −0.577279 | + | 1.05253i | ||||
\(887\) | − | 28.4143i | − | 0.954058i | −0.878887 | − | 0.477029i | \(-0.841714\pi\) | ||
0.878887 | − | 0.477029i | \(-0.158286\pi\) | |||||||
\(888\) | −0.434910 | − | 0.381142i | −0.0145946 | − | 0.0127903i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −71.6821 | − | 39.3155i | −2.40279 | − | 1.31786i | ||||
\(891\) | −3.61771 | − | 3.61771i | −0.121198 | − | 0.121198i | ||||
\(892\) | 14.0566 | − | 8.95953i | 0.470649 | − | 0.299987i | ||||
\(893\) | 29.7392 | − | 29.7392i | 0.995184 | − | 0.995184i | ||||
\(894\) | −9.77849 | − | 33.5342i | −0.327042 | − | 1.12155i | ||||
\(895\) | 36.0675 | 1.20560 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2317 | 1.04280 | ||||||||
\(898\) | −7.48157 | − | 25.6572i | −0.249663 | − | 0.856192i | ||||
\(899\) | 0.344127 | − | 0.344127i | 0.0114773 | − | 0.0114773i | ||||
\(900\) | −84.1596 | + | 53.6426i | −2.80532 | + | 1.78809i | ||||
\(901\) | 0.609590 | + | 0.609590i | 0.0203084 | + | 0.0203084i | ||||
\(902\) | −12.1110 | − | 6.64251i | −0.403251 | − | 0.221171i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.190698 | − | 0.167122i | −0.00634251 | − | 0.00555840i | ||||
\(905\) | 79.9334i | 2.65708i | ||||||||
\(906\) | 10.1076 | − | 18.4288i | 0.335804 | − | 0.612255i | ||||
\(907\) | 9.66456 | + | 9.66456i | 0.320906 | + | 0.320906i | 0.849115 | − | 0.528208i | \(-0.177136\pi\) |
−0.528208 | + | 0.849115i | \(0.677136\pi\) | |||||||
\(908\) | −4.81472 | + | 21.7413i | −0.159782 | + | 0.721510i | ||||
\(909\) | −18.2382 | + | 18.2382i | −0.604923 | + | 0.604923i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.3939 | −1.76902 | −0.884509 | − | 0.466523i | \(-0.845506\pi\) | ||||
−0.884509 | + | 0.466523i | \(0.845506\pi\) | |||||||
\(912\) | 40.2599 | + | 18.7511i | 1.33314 | + | 0.620912i | ||||
\(913\) | −6.16663 | −0.204086 | ||||||||
\(914\) | −12.5251 | + | 3.65229i | −0.414294 | + | 0.120807i | ||||
\(915\) | 76.8087 | − | 76.8087i | 2.53922 | − | 2.53922i | ||||
\(916\) | −24.7712 | − | 5.48572i | −0.818464 | − | 0.181253i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.45681 | + | 13.5957i | −0.246111 | + | 0.448723i | ||||
\(919\) | 5.20441i | 0.171678i | 0.996309 | + | 0.0858388i | \(0.0273570\pi\) | ||||
−0.996309 | + | 0.0858388i | \(0.972643\pi\) | |||||||
\(920\) | 18.9649 | − | 1.24955i | 0.625256 | − | 0.0411964i | ||||
\(921\) | 72.3325i | 2.38344i | ||||||||
\(922\) | 18.6355 | + | 10.2210i | 0.613729 | + | 0.336612i | ||||
\(923\) | −12.1310 | − | 12.1310i | −0.399297 | − | 0.399297i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.442660 | + | 0.442660i | −0.0145546 | + | 0.0145546i | ||||
\(926\) | 12.8617 | + | 44.1076i | 0.422660 | + | 1.44947i | ||||
\(927\) | −48.7053 | −1.59969 | ||||||||
\(928\) | −1.90735 | + | 1.40020i | −0.0626118 | + | 0.0459638i | ||||
\(929\) | 9.12328 | 0.299325 | 0.149663 | − | 0.988737i | \(-0.452181\pi\) | ||||
0.149663 | + | 0.988737i | \(0.452181\pi\) | |||||||
\(930\) | −5.03807 | − | 17.2775i | −0.165205 | − | 0.566551i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.2291 | − | 38.0129i | −0.793651 | − | 1.24515i | ||||
\(933\) | −58.9479 | − | 58.9479i | −1.92987 | − | 1.92987i | ||||
\(934\) | −21.8017 | − | 11.9576i | −0.713375 | − | 0.391265i | ||||
\(935\) | − | 5.26469i | − | 0.172174i | ||||||
\(936\) | 6.14305 | + | 93.2357i | 0.200792 | + | 3.04750i | ||||
\(937\) | − | 7.41975i | − | 0.242393i | −0.992629 | − | 0.121196i | \(-0.961327\pi\) | ||
0.992629 | − | 0.121196i | \(-0.0386731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.4695 | + | 32.4695i | 1.05960 | + | 1.05960i | ||||
\(940\) | 80.8998 | + | 17.9157i | 2.63866 | + | 0.584345i | ||||
\(941\) | −1.85479 | + | 1.85479i | −0.0604646 | + | 0.0604646i | −0.736692 | − | 0.676228i | \(-0.763613\pi\) |
0.676228 | + | 0.736692i | \(0.263613\pi\) | |||||||
\(942\) | 20.7602 | − | 6.05362i | 0.676404 | − | 0.197237i | ||||
\(943\) | −18.1861 | −0.592221 | ||||||||
\(944\) | −19.9172 | + | 7.25957i | −0.648250 | + | 0.236279i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.43826 | − | 2.46057i | 0.274351 | − | 0.0800001i | ||||
\(947\) | 12.4018 | − | 12.4018i | 0.403006 | − | 0.403006i | −0.476285 | − | 0.879291i | \(-0.658017\pi\) |
0.879291 | + | 0.476285i | \(0.158017\pi\) | |||||||
\(948\) | 0.949099 | − | 4.28574i | 0.0308253 | − | 0.139194i | ||||
\(949\) | −2.68600 | − | 2.68600i | −0.0871914 | − | 0.0871914i | ||||
\(950\) | 23.1202 | − | 42.1539i | 0.750117 | − | 1.36765i | ||||
\(951\) | − | 49.4581i | − | 1.60379i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 27.3756i | − | 0.886782i | −0.896328 | − | 0.443391i | \(-0.853775\pi\) | ||
0.896328 | − | 0.443391i | \(-0.146225\pi\) | |||||||
\(954\) | −4.07992 | − | 2.23772i | −0.132092 | − | 0.0724488i | ||||
\(955\) | 52.5076 | + | 52.5076i | 1.69911 | + | 1.69911i | ||||
\(956\) | −22.5452 | + | 14.3701i | −0.729164 | + | 0.464763i | ||||
\(957\) | −0.836149 | + | 0.836149i | −0.0270289 | + | 0.0270289i | ||||
\(958\) | 14.3633 | + | 49.2574i | 0.464058 | + | 1.59143i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 11.4803 | + | 86.7429i | 0.370527 | + | 2.79961i | ||||
\(961\) | −29.6462 | −0.956330 | ||||||||
\(962\) | 0.164071 | + | 0.562664i | 0.00528987 | + | 0.0181410i | ||||
\(963\) | −17.6858 | + | 17.6858i | −0.569918 | + | 0.569918i | ||||
\(964\) | −32.7090 | + | 20.8484i | −1.05349 | + | 0.671483i | ||||
\(965\) | −31.3970 | − | 31.3970i | −1.01070 | − | 1.01070i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2156i | 1.03598i | 0.855385 | + | 0.517992i | \(0.173320\pi\) | ||||
−0.855385 | + | 0.517992i | \(0.826680\pi\) | |||||||
\(968\) | −18.7671 | + | 21.4145i | −0.603196 | + | 0.688288i | ||||
\(969\) | − | 16.1971i | − | 0.520326i | ||||||
\(970\) | 34.9311 | − | 63.6883i | 1.12157 | − | 2.04491i | ||||
\(971\) | −24.7566 | − | 24.7566i | −0.794477 | − | 0.794477i | 0.187742 | − | 0.982218i | \(-0.439883\pi\) |
−0.982218 | + | 0.187742i | \(0.939883\pi\) | |||||||
\(972\) | −3.04578 | + | 13.7535i | −0.0976934 | + | 0.441143i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.90947 | − | 2.88957i | 0.317520 | − | 0.0925879i | ||||
\(975\) | 155.650 | 4.98479 | ||||||||
\(976\) | −13.6040 | − | 37.3237i | −0.435454 | − | 1.19470i | ||||
\(977\) | −3.14788 | −0.100710 | −0.0503548 | − | 0.998731i | \(-0.516035\pi\) | ||||
−0.0503548 | + | 0.998731i | \(0.516035\pi\) | |||||||
\(978\) | 46.0610 | − | 13.4313i | 1.47287 | − | 0.429485i | ||||
\(979\) | −10.5660 | + | 10.5660i | −0.337691 | + | 0.337691i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.2369 | − | 24.2369i | −0.773826 | − | 0.773826i | ||||
\(982\) | −10.9874 | + | 20.0328i | −0.350622 | + | 0.639273i | ||||
\(983\) | − | 51.2039i | − | 1.63315i | −0.577238 | − | 0.816576i | \(-0.695870\pi\) | ||
0.577238 | − | 0.816576i | \(-0.304130\pi\) | |||||||
\(984\) | −5.50444 | − | 83.5432i | −0.175475 | − | 2.66326i | ||||
\(985\) | 34.9823i | 1.11463i | ||||||||
\(986\) | 0.756591 | + | 0.414968i | 0.0240948 | + | 0.0132153i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.1938 | − | 37.9575i | −0.769706 | − | 1.20759i | ||||
\(989\) | 8.18296 | − | 8.18296i | 0.260203 | − | 0.260203i | ||||
\(990\) | 7.95507 | + | 27.2810i | 0.252829 | + | 0.867047i | ||||
\(991\) | −20.1603 | −0.640414 | −0.320207 | − | 0.947348i | \(-0.603752\pi\) | ||||
−0.320207 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(992\) | −6.50580 | − | 0.997538i | −0.206559 | − | 0.0316719i | ||||
\(993\) | 87.1665 | 2.76615 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −63.5795 | + | 63.5795i | −2.01561 | + | 2.01561i | ||||
\(996\) | −20.0902 | − | 31.5194i | −0.636582 | − | 0.998731i | ||||
\(997\) | 26.8634 | + | 26.8634i | 0.850773 | + | 0.850773i | 0.990228 | − | 0.139456i | \(-0.0445353\pi\) |
−0.139456 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(998\) | 28.6219 | + | 15.6983i | 0.906010 | + | 0.496919i | ||||
\(999\) | − | 0.525006i | − | 0.0166104i |
(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 | 784.2.m.l.197.16 | yes | 48 | |
7.2 | even | 3 | 784.2.x.p.165.18 | 96 | |||
7.3 | odd | 6 | 784.2.x.p.373.4 | 96 | |||
7.4 | even | 3 | 784.2.x.p.373.3 | 96 | |||
7.5 | odd | 6 | 784.2.x.p.165.17 | 96 | |||
7.6 | odd | 2 | inner | 784.2.m.l.197.15 | ✓ | 48 | |
16.13 | even | 4 | inner | 784.2.m.l.589.16 | yes | 48 | |
112.13 | odd | 4 | inner | 784.2.m.l.589.15 | yes | 48 | |
112.45 | odd | 12 | 784.2.x.p.765.17 | 96 | |||
112.61 | odd | 12 | 784.2.x.p.557.4 | 96 | |||
112.93 | even | 12 | 784.2.x.p.557.3 | 96 | |||
112.109 | even | 12 | 784.2.x.p.765.18 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.l.197.15 | ✓ | 48 | 7.6 | odd | 2 | inner | |
784.2.m.l.197.16 | yes | 48 | 1.1 | even | 1 | trivial | |
784.2.m.l.589.15 | yes | 48 | 112.13 | odd | 4 | inner | |
784.2.m.l.589.16 | yes | 48 | 16.13 | even | 4 | inner | |
784.2.x.p.165.17 | 96 | 7.5 | odd | 6 | |||
784.2.x.p.165.18 | 96 | 7.2 | even | 3 | |||
784.2.x.p.373.3 | 96 | 7.4 | even | 3 | |||
784.2.x.p.373.4 | 96 | 7.3 | odd | 6 | |||
784.2.x.p.557.3 | 96 | 112.93 | even | 12 | |||
784.2.x.p.557.4 | 96 | 112.61 | odd | 12 | |||
784.2.x.p.765.17 | 96 | 112.45 | odd | 12 | |||
784.2.x.p.765.18 | 96 | 112.109 | even | 12 |