Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(57,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.k (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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 268.1 | ||
Root | \(-0.419746 + 0.419746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.268 |
Dual form | 325.2.k.d.57.1 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38239 | −1.68461 | −0.842303 | − | 0.539005i | \(-0.818800\pi\) | ||||
−0.842303 | + | 0.539005i | \(0.818800\pi\) | |||||||
\(3\) | −0.648130 | − | 0.648130i | −0.374198 | − | 0.374198i | 0.494805 | − | 0.869004i | \(-0.335239\pi\) |
−0.869004 | + | 0.494805i | \(0.835239\pi\) | |||||||
\(4\) | 3.67579 | 1.83790 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.54410 | + | 1.54410i | 0.630376 | + | 0.630376i | ||||
\(7\) | 2.38239i | 0.900459i | 0.892913 | + | 0.450230i | \(0.148658\pi\) | ||||
−0.892913 | + | 0.450230i | \(0.851342\pi\) | |||||||
\(8\) | −3.99239 | −1.41152 | ||||||||
\(9\) | − | 2.15985i | − | 0.719951i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.88966 | + | 3.88966i | −1.17278 | + | 1.17278i | −0.191231 | + | 0.981545i | \(0.561248\pi\) |
−0.981545 | + | 0.191231i | \(0.938752\pi\) | |||||||
\(12\) | −2.38239 | − | 2.38239i | −0.687737 | − | 0.687737i | ||||
\(13\) | 2.31088 | − | 2.76764i | 0.640922 | − | 0.767606i | ||||
\(14\) | − | 5.67579i | − | 1.51692i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.15985 | 0.539963 | ||||||||
\(17\) | 0.262878 | + | 0.262878i | 0.0637573 | + | 0.0637573i | 0.738266 | − | 0.674509i | \(-0.235645\pi\) |
−0.674509 | + | 0.738266i | \(0.735645\pi\) | |||||||
\(18\) | 5.14562i | 1.21283i | ||||||||
\(19\) | −0.587589 | + | 0.587589i | −0.134802 | + | 0.134802i | −0.771288 | − | 0.636486i | \(-0.780387\pi\) |
0.636486 | + | 0.771288i | \(0.280387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.54410 | − | 1.54410i | 0.336950 | − | 0.336950i | ||||
\(22\) | 9.26669 | − | 9.26669i | 1.97566 | − | 1.97566i | ||||
\(23\) | −1.98090 | + | 1.98090i | −0.413046 | + | 0.413046i | −0.882798 | − | 0.469752i | \(-0.844343\pi\) |
0.469752 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(24\) | 2.58759 | + | 2.58759i | 0.528189 | + | 0.528189i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.50541 | + | 6.59361i | −1.07970 | + | 1.29311i | ||||
\(27\) | −3.34426 | + | 3.34426i | −0.643603 | + | 0.643603i | ||||
\(28\) | 8.75717i | 1.65495i | ||||||||
\(29\) | 7.92385i | 1.47142i | 0.677296 | + | 0.735711i | \(0.263152\pi\) | ||||
−0.677296 | + | 0.735711i | \(0.736848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59361 | + | 6.59361i | 1.18425 | + | 1.18425i | 0.978633 | + | 0.205615i | \(0.0659194\pi\) |
0.205615 | + | 0.978633i | \(0.434081\pi\) | |||||||
\(32\) | 2.83916 | 0.501897 | ||||||||
\(33\) | 5.04201 | 0.877702 | ||||||||
\(34\) | −0.626279 | − | 0.626279i | −0.107406 | − | 0.107406i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 7.93917i | − | 1.32319i | ||||||
\(37\) | 10.3366i | 1.69932i | 0.527328 | + | 0.849662i | \(0.323194\pi\) | ||||
−0.527328 | + | 0.849662i | \(0.676806\pi\) | |||||||
\(38\) | 1.39987 | − | 1.39987i | 0.227088 | − | 0.227088i | ||||
\(39\) | −3.29154 | + | 0.296046i | −0.527069 | + | 0.0474052i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37974 | − | 6.37974i | −0.996349 | − | 0.996349i | 0.00364462 | − | 0.999993i | \(-0.498840\pi\) |
−0.999993 | + | 0.00364462i | \(0.998840\pi\) | |||||||
\(42\) | −3.67865 | + | 3.67865i | −0.567628 | + | 0.567628i | ||||
\(43\) | −3.09762 | + | 3.09762i | −0.472383 | + | 0.472383i | −0.902685 | − | 0.430302i | \(-0.858407\pi\) |
0.430302 | + | 0.902685i | \(0.358407\pi\) | |||||||
\(44\) | −14.2976 | + | 14.2976i | −2.15544 | + | 2.15544i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.71928 | − | 4.71928i | 0.695820 | − | 0.695820i | ||||
\(47\) | 5.67137i | 0.827255i | 0.910446 | + | 0.413627i | \(0.135738\pi\) | ||||
−0.910446 | + | 0.413627i | \(0.864262\pi\) | |||||||
\(48\) | −1.39987 | − | 1.39987i | −0.202053 | − | 0.202053i | ||||
\(49\) | 1.32421 | 0.189173 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 0.340759i | − | 0.0477158i | ||||||
\(52\) | 8.49429 | − | 10.1733i | 1.17795 | − | 1.41078i | ||||
\(53\) | 1.54732 | + | 1.54732i | 0.212540 | + | 0.212540i | 0.805346 | − | 0.592805i | \(-0.201980\pi\) |
−0.592805 | + | 0.805346i | \(0.701980\pi\) | |||||||
\(54\) | 7.96733 | − | 7.96733i | 1.08422 | − | 1.08422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 9.51143i | − | 1.27102i | ||||||
\(57\) | 0.761669 | 0.100885 | ||||||||
\(58\) | − | 18.8777i | − | 2.47876i | ||||||
\(59\) | 5.49009 | + | 5.49009i | 0.714748 | + | 0.714748i | 0.967525 | − | 0.252776i | \(-0.0813437\pi\) |
−0.252776 | + | 0.967525i | \(0.581344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.11885 | 0.527365 | 0.263682 | − | 0.964610i | \(-0.415063\pi\) | ||||
0.263682 | + | 0.964610i | \(0.415063\pi\) | |||||||
\(62\) | −15.7086 | − | 15.7086i | −1.99499 | − | 1.99499i | ||||
\(63\) | 5.14562 | 0.648287 | ||||||||
\(64\) | −11.0837 | −1.38546 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.0120 | −1.47858 | ||||||||
\(67\) | 3.74764 | 0.457847 | 0.228924 | − | 0.973444i | \(-0.426479\pi\) | ||||
0.228924 | + | 0.973444i | \(0.426479\pi\) | |||||||
\(68\) | 0.966285 | + | 0.966285i | 0.117179 | + | 0.117179i | ||||
\(69\) | 2.56776 | 0.309122 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.04349 | − | 2.04349i | −0.242517 | − | 0.242517i | 0.575373 | − | 0.817891i | \(-0.304857\pi\) |
−0.817891 | + | 0.575373i | \(0.804857\pi\) | |||||||
\(72\) | 8.62298i | 1.01623i | ||||||||
\(73\) | −7.56049 | −0.884888 | −0.442444 | − | 0.896796i | \(-0.645889\pi\) | ||||
−0.442444 | + | 0.896796i | \(0.645889\pi\) | |||||||
\(74\) | − | 24.6258i | − | 2.86269i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.15985 | + | 2.15985i | −0.247752 | + | 0.247752i | ||||
\(77\) | −9.26669 | − | 9.26669i | −1.05604 | − | 1.05604i | ||||
\(78\) | 7.84175 | − | 0.705296i | 0.887903 | − | 0.0798591i | ||||
\(79\) | − | 6.07165i | − | 0.683114i | −0.939861 | − | 0.341557i | \(-0.889046\pi\) | ||
0.939861 | − | 0.341557i | \(-0.110954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.14453 | −0.238281 | ||||||||
\(82\) | 15.1991 | + | 15.1991i | 1.67845 | + | 1.67845i | ||||
\(83\) | − | 13.0415i | − | 1.43150i | −0.698359 | − | 0.715748i | \(-0.746086\pi\) | ||
0.698359 | − | 0.715748i | \(-0.253914\pi\) | |||||||
\(84\) | 5.67579 | − | 5.67579i | 0.619279 | − | 0.619279i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.37974 | − | 7.37974i | 0.795778 | − | 0.795778i | ||||
\(87\) | 5.13569 | − | 5.13569i | 0.550603 | − | 0.550603i | ||||
\(88\) | 15.5290 | − | 15.5290i | 1.65540 | − | 1.65540i | ||||
\(89\) | −2.23522 | − | 2.23522i | −0.236932 | − | 0.236932i | 0.578646 | − | 0.815579i | \(-0.303581\pi\) |
−0.815579 | + | 0.578646i | \(0.803581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59361 | + | 5.50541i | 0.691198 | + | 0.577124i | ||||
\(92\) | −7.28137 | + | 7.28137i | −0.759135 | + | 0.759135i | ||||
\(93\) | − | 8.54704i | − | 0.886287i | ||||||
\(94\) | − | 13.5114i | − | 1.39360i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.84015 | − | 1.84015i | −0.187809 | − | 0.187809i | ||||
\(97\) | −1.88723 | −0.191619 | −0.0958094 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958094 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(98\) | −3.15479 | −0.318682 | ||||||||
\(99\) | 8.40109 | + | 8.40109i | 0.844342 | + | 0.844342i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.40791i | 0.637611i | 0.947820 | + | 0.318805i | \(0.103282\pi\) | ||||
−0.947820 | + | 0.318805i | \(0.896718\pi\) | |||||||
\(102\) | 0.811821i | 0.0803822i | ||||||||
\(103\) | −6.56425 | + | 6.56425i | −0.646795 | + | 0.646795i | −0.952217 | − | 0.305422i | \(-0.901202\pi\) |
0.305422 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(104\) | −9.22591 | + | 11.0495i | −0.904675 | + | 1.08349i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.68632 | − | 3.68632i | −0.358047 | − | 0.358047i | ||||
\(107\) | −1.34459 | + | 1.34459i | −0.129987 | + | 0.129987i | −0.769107 | − | 0.639120i | \(-0.779299\pi\) |
0.639120 | + | 0.769107i | \(0.279299\pi\) | |||||||
\(108\) | −12.2928 | + | 12.2928i | −1.18287 | + | 1.18287i | ||||
\(109\) | −11.7474 | + | 11.7474i | −1.12520 | + | 1.12520i | −0.134254 | + | 0.990947i | \(0.542864\pi\) |
−0.990947 | + | 0.134254i | \(0.957136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.69945 | − | 6.69945i | 0.635884 | − | 0.635884i | ||||
\(112\) | 5.14562i | 0.486215i | ||||||||
\(113\) | 0.581032 | + | 0.581032i | 0.0546589 | + | 0.0546589i | 0.733908 | − | 0.679249i | \(-0.237694\pi\) |
−0.679249 | + | 0.733908i | \(0.737694\pi\) | |||||||
\(114\) | −1.81459 | −0.169952 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 29.1264i | 2.70432i | ||||||||
\(117\) | −5.97771 | − | 4.99115i | −0.552639 | − | 0.461432i | ||||
\(118\) | −13.0795 | − | 13.0795i | −1.20407 | − | 1.20407i | ||||
\(119\) | −0.626279 | + | 0.626279i | −0.0574109 | + | 0.0574109i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.2589i | − | 1.75081i | ||||||
\(122\) | −9.81271 | −0.888401 | ||||||||
\(123\) | 8.26981i | 0.745664i | ||||||||
\(124\) | 24.2367 | + | 24.2367i | 2.17652 | + | 2.17652i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.2589 | −1.09211 | ||||||||
\(127\) | −4.56648 | − | 4.56648i | −0.405209 | − | 0.405209i | 0.474855 | − | 0.880064i | \(-0.342501\pi\) |
−0.880064 | + | 0.474855i | \(0.842501\pi\) | |||||||
\(128\) | 20.7274 | 1.83206 | ||||||||
\(129\) | 4.01532 | 0.353530 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9085 | 1.30256 | 0.651282 | − | 0.758836i | \(-0.274232\pi\) | ||||
0.651282 | + | 0.758836i | \(0.274232\pi\) | |||||||
\(132\) | 18.5334 | 1.61312 | ||||||||
\(133\) | −1.39987 | − | 1.39987i | −0.121384 | − | 0.121384i | ||||
\(134\) | −8.92835 | −0.771292 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.04951 | − | 1.04951i | −0.0899949 | − | 0.0899949i | ||||
\(137\) | 9.21583i | 0.787362i | 0.919247 | + | 0.393681i | \(0.128798\pi\) | ||||
−0.919247 | + | 0.393681i | \(0.871202\pi\) | |||||||
\(138\) | −6.11742 | −0.520749 | ||||||||
\(139\) | − | 5.87665i | − | 0.498451i | −0.968446 | − | 0.249225i | \(-0.919824\pi\) | ||
0.968446 | − | 0.249225i | \(-0.0801760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.67579 | − | 3.67579i | 0.309557 | − | 0.309557i | ||||
\(142\) | 4.86839 | + | 4.86839i | 0.408546 | + | 0.408546i | ||||
\(143\) | 1.77667 | + | 19.7537i | 0.148573 | + | 1.65189i | ||||
\(144\) | − | 4.66497i | − | 0.388747i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 18.0120 | 1.49069 | ||||||||
\(147\) | −0.858261 | − | 0.858261i | −0.0707881 | − | 0.0707881i | ||||
\(148\) | 37.9951i | 3.12318i | ||||||||
\(149\) | −5.89568 | + | 5.89568i | −0.482993 | + | 0.482993i | −0.906086 | − | 0.423093i | \(-0.860944\pi\) |
0.423093 | + | 0.906086i | \(0.360944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9452 | + | 12.9452i | −1.05346 | + | 1.05346i | −0.0549773 | + | 0.998488i | \(0.517509\pi\) |
−0.998488 | + | 0.0549773i | \(0.982491\pi\) | |||||||
\(152\) | 2.34588 | − | 2.34588i | 0.190276 | − | 0.190276i | ||||
\(153\) | 0.567778 | − | 0.567778i | 0.0459022 | − | 0.0459022i | ||||
\(154\) | 22.0769 | + | 22.0769i | 1.77901 | + | 1.77901i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.0990 | + | 1.08820i | −0.968697 | + | 0.0871258i | ||||
\(157\) | 13.8195 | − | 13.8195i | 1.10291 | − | 1.10291i | 0.108855 | − | 0.994058i | \(-0.465282\pi\) |
0.994058 | − | 0.108855i | \(-0.0347183\pi\) | |||||||
\(158\) | 14.4651i | 1.15078i | ||||||||
\(159\) | − | 2.00573i | − | 0.159064i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.71928 | − | 4.71928i | −0.371931 | − | 0.371931i | ||||
\(162\) | 5.10911 | 0.401410 | ||||||||
\(163\) | 3.80590 | 0.298101 | 0.149051 | − | 0.988830i | \(-0.452378\pi\) | ||||
0.149051 | + | 0.988830i | \(0.452378\pi\) | |||||||
\(164\) | −23.4506 | − | 23.4506i | −1.83118 | − | 1.83118i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 31.0701i | 2.41150i | ||||||||
\(167\) | − | 18.2483i | − | 1.41210i | −0.708162 | − | 0.706050i | \(-0.750476\pi\) | ||
0.708162 | − | 0.706050i | \(-0.249524\pi\) | |||||||
\(168\) | −6.16465 | + | 6.16465i | −0.475613 | + | 0.475613i | ||||
\(169\) | −2.31971 | − | 12.7914i | −0.178439 | − | 0.983951i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.26911 | + | 1.26911i | 0.0970510 | + | 0.0970510i | ||||
\(172\) | −11.3862 | + | 11.3862i | −0.868190 | + | 0.868190i | ||||
\(173\) | −0.00740374 | + | 0.00740374i | −0.000562896 | + | 0.000562896i | −0.707388 | − | 0.706825i | \(-0.750127\pi\) |
0.706825 | + | 0.707388i | \(0.250127\pi\) | |||||||
\(174\) | −12.2352 | + | 12.2352i | −0.927549 | + | 0.927549i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.40109 | + | 8.40109i | −0.633256 | + | 0.633256i | ||||
\(177\) | − | 7.11659i | − | 0.534915i | ||||||
\(178\) | 5.32516 | + | 5.32516i | 0.399137 | + | 0.399137i | ||||
\(179\) | 12.0717 | 0.902278 | 0.451139 | − | 0.892454i | \(-0.351018\pi\) | ||||
0.451139 | + | 0.892454i | \(0.351018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.2589i | − | 1.35717i | −0.734521 | − | 0.678586i | \(-0.762593\pi\) | ||
0.734521 | − | 0.678586i | \(-0.237407\pi\) | |||||||
\(182\) | −15.7086 | − | 13.1160i | −1.16440 | − | 0.972226i | ||||
\(183\) | −2.66955 | − | 2.66955i | −0.197339 | − | 0.197339i | ||||
\(184\) | 7.90852 | − | 7.90852i | 0.583024 | − | 0.583024i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 20.3624i | 1.49304i | ||||||||
\(187\) | −2.04501 | −0.149546 | ||||||||
\(188\) | 20.8468i | 1.52041i | ||||||||
\(189\) | −7.96733 | − | 7.96733i | −0.579538 | − | 0.579538i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.39878 | −0.462999 | −0.231500 | − | 0.972835i | \(-0.574363\pi\) | ||||
−0.231500 | + | 0.972835i | \(0.574363\pi\) | |||||||
\(192\) | 7.18368 | + | 7.18368i | 0.518438 | + | 0.518438i | ||||
\(193\) | −12.4812 | −0.898414 | −0.449207 | − | 0.893428i | \(-0.648293\pi\) | ||||
−0.449207 | + | 0.893428i | \(0.648293\pi\) | |||||||
\(194\) | 4.49611 | 0.322802 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.86752 | 0.347680 | ||||||||
\(197\) | 19.8948 | 1.41745 | 0.708725 | − | 0.705485i | \(-0.249271\pi\) | ||||
0.708725 | + | 0.705485i | \(0.249271\pi\) | |||||||
\(198\) | −20.0147 | − | 20.0147i | −1.42238 | − | 1.42238i | ||||
\(199\) | 13.5740 | 0.962232 | 0.481116 | − | 0.876657i | \(-0.340232\pi\) | ||||
0.481116 | + | 0.876657i | \(0.340232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.42896 | − | 2.42896i | −0.171326 | − | 0.171326i | ||||
\(202\) | − | 15.2661i | − | 1.07412i | ||||||
\(203\) | −18.8777 | −1.32496 | ||||||||
\(204\) | − | 1.25256i | − | 0.0876966i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6386 | − | 15.6386i | 1.08959 | − | 1.08959i | ||||
\(207\) | 4.27845 | + | 4.27845i | 0.297373 | + | 0.297373i | ||||
\(208\) | 4.99115 | − | 5.97771i | 0.346074 | − | 0.414479i | ||||
\(209\) | − | 4.57104i | − | 0.316185i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6348 | −0.732129 | −0.366064 | − | 0.930590i | \(-0.619295\pi\) | ||||
−0.366064 | + | 0.930590i | \(0.619295\pi\) | |||||||
\(212\) | 5.68761 | + | 5.68761i | 0.390627 | + | 0.390627i | ||||
\(213\) | 2.64889i | 0.181499i | ||||||||
\(214\) | 3.20334 | − | 3.20334i | 0.218976 | − | 0.218976i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.3516 | − | 13.3516i | 0.908460 | − | 0.908460i | ||||
\(217\) | −15.7086 | + | 15.7086i | −1.06637 | + | 1.06637i | ||||
\(218\) | 27.9870 | − | 27.9870i | 1.89552 | − | 1.89552i | ||||
\(219\) | 4.90018 | + | 4.90018i | 0.331124 | + | 0.331124i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.33503 | − | 0.120074i | 0.0898039 | − | 0.00807708i | ||||
\(222\) | −15.9607 | + | 15.9607i | −1.07121 | + | 1.07121i | ||||
\(223\) | − | 10.1659i | − | 0.680757i | −0.940288 | − | 0.340379i | \(-0.889445\pi\) | ||
0.940288 | − | 0.340379i | \(-0.110555\pi\) | |||||||
\(224\) | 6.76399i | 0.451938i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38425 | − | 1.38425i | −0.0920787 | − | 0.0920787i | ||||
\(227\) | −18.5876 | −1.23370 | −0.616852 | − | 0.787080i | \(-0.711592\pi\) | ||||
−0.616852 | + | 0.787080i | \(0.711592\pi\) | |||||||
\(228\) | 2.79973 | 0.185417 | ||||||||
\(229\) | −6.29605 | − | 6.29605i | −0.416054 | − | 0.416054i | 0.467787 | − | 0.883841i | \(-0.345051\pi\) |
−0.883841 | + | 0.467787i | \(0.845051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0120i | 0.790335i | ||||||||
\(232\) | − | 31.6351i | − | 2.07694i | ||||||
\(233\) | 19.7706 | − | 19.7706i | 1.29521 | − | 1.29521i | 0.363696 | − | 0.931518i | \(-0.381515\pi\) |
0.931518 | − | 0.363696i | \(-0.118485\pi\) | |||||||
\(234\) | 14.2412 | + | 11.8909i | 0.930979 | + | 0.777331i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 20.1804 | + | 20.1804i | 1.31363 | + | 1.31363i | ||||
\(237\) | −3.93522 | + | 3.93522i | −0.255620 | + | 0.255620i | ||||
\(238\) | 1.49204 | − | 1.49204i | 0.0967147 | − | 0.0967147i | ||||
\(239\) | 10.0206 | − | 10.0206i | 0.648176 | − | 0.648176i | −0.304376 | − | 0.952552i | \(-0.598448\pi\) |
0.952552 | + | 0.304376i | \(0.0984480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.79586 | − | 2.79586i | 0.180097 | − | 0.180097i | −0.611301 | − | 0.791398i | \(-0.709353\pi\) |
0.791398 | + | 0.611301i | \(0.209353\pi\) | |||||||
\(242\) | 45.8822i | 2.94942i | ||||||||
\(243\) | 11.4227 | + | 11.4227i | 0.732767 | + | 0.732767i | ||||
\(244\) | 15.1400 | 0.969241 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 19.7019i | − | 1.25615i | ||||||
\(247\) | 0.268392 | + | 2.98408i | 0.0170774 | + | 0.189873i | ||||
\(248\) | −26.3243 | − | 26.3243i | −1.67159 | − | 1.67159i | ||||
\(249\) | −8.45262 | + | 8.45262i | −0.535663 | + | 0.535663i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.3744i | 1.41226i | 0.708081 | + | 0.706131i | \(0.249561\pi\) | ||||
−0.708081 | + | 0.706131i | \(0.750439\pi\) | |||||||
\(252\) | 18.9142 | 1.19148 | ||||||||
\(253\) | − | 15.4100i | − | 0.968821i | ||||||
\(254\) | 10.8791 | + | 10.8791i | 0.682617 | + | 0.682617i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.2134 | −1.70084 | ||||||||
\(257\) | 1.41312 | + | 1.41312i | 0.0881481 | + | 0.0881481i | 0.749806 | − | 0.661658i | \(-0.230147\pi\) |
−0.661658 | + | 0.749806i | \(0.730147\pi\) | |||||||
\(258\) | −9.56607 | −0.595558 | ||||||||
\(259\) | −24.6258 | −1.53017 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1143 | 1.05935 | ||||||||
\(262\) | −35.5179 | −2.19431 | ||||||||
\(263\) | −3.71113 | − | 3.71113i | −0.228838 | − | 0.228838i | 0.583369 | − | 0.812207i | \(-0.301734\pi\) |
−0.812207 | + | 0.583369i | \(0.801734\pi\) | |||||||
\(264\) | −20.1297 | −1.23890 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.33503 | + | 3.33503i | 0.204484 | + | 0.204484i | ||||
\(267\) | 2.89742i | 0.177319i | ||||||||
\(268\) | 13.7755 | 0.841475 | ||||||||
\(269\) | − | 0.372632i | − | 0.0227198i | −0.999935 | − | 0.0113599i | \(-0.996384\pi\) | ||
0.999935 | − | 0.0113599i | \(-0.00361604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.10584 | + | 3.10584i | −0.188666 | + | 0.188666i | −0.795119 | − | 0.606453i | \(-0.792592\pi\) |
0.606453 | + | 0.795119i | \(0.292592\pi\) | |||||||
\(272\) | 0.567778 | + | 0.567778i | 0.0344266 | + | 0.0344266i | ||||
\(273\) | −0.705296 | − | 7.84175i | −0.0426865 | − | 0.474604i | ||||
\(274\) | − | 21.9557i | − | 1.32639i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.43856 | 0.568134 | ||||||||
\(277\) | 12.4546 | + | 12.4546i | 0.748324 | + | 0.748324i | 0.974164 | − | 0.225840i | \(-0.0725128\pi\) |
−0.225840 | + | 0.974164i | \(0.572513\pi\) | |||||||
\(278\) | 14.0005i | 0.839693i | ||||||||
\(279\) | 14.2412 | − | 14.2412i | 0.852601 | − | 0.852601i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.18924 | + | 7.18924i | −0.428874 | + | 0.428874i | −0.888245 | − | 0.459370i | \(-0.848075\pi\) |
0.459370 | + | 0.888245i | \(0.348075\pi\) | |||||||
\(282\) | −8.75717 | + | 8.75717i | −0.521482 | + | 0.521482i | ||||
\(283\) | −21.6211 | + | 21.6211i | −1.28524 | + | 1.28524i | −0.347594 | + | 0.937645i | \(0.613001\pi\) |
−0.937645 | + | 0.347594i | \(0.886999\pi\) | |||||||
\(284\) | −7.51143 | − | 7.51143i | −0.445722 | − | 0.445722i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.23273 | − | 47.0611i | −0.250287 | − | 2.78278i | ||||
\(287\) | 15.1991 | − | 15.1991i | 0.897172 | − | 0.897172i | ||||
\(288\) | − | 6.13217i | − | 0.361342i | ||||||
\(289\) | − | 16.8618i | − | 0.991870i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.22317 | + | 1.22317i | 0.0717034 | + | 0.0717034i | ||||
\(292\) | −27.7908 | −1.62633 | ||||||||
\(293\) | 25.7477 | 1.50419 | 0.752097 | − | 0.659053i | \(-0.229043\pi\) | ||||
0.752097 | + | 0.659053i | \(0.229043\pi\) | |||||||
\(294\) | 2.04471 | + | 2.04471i | 0.119250 | + | 0.119250i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 41.2676i | − | 2.39863i | ||||||
\(297\) | − | 26.0160i | − | 1.50960i | ||||||
\(298\) | 14.0458 | − | 14.0458i | 0.813653 | − | 0.813653i | ||||
\(299\) | 0.904812 | + | 10.0600i | 0.0523267 | + | 0.581787i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.37974 | − | 7.37974i | −0.425361 | − | 0.425361i | ||||
\(302\) | 30.8405 | − | 30.8405i | 1.77467 | − | 1.77467i | ||||
\(303\) | 4.15316 | − | 4.15316i | 0.238593 | − | 0.238593i | ||||
\(304\) | −1.26911 | + | 1.26911i | −0.0727882 | + | 0.0727882i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.35267 | + | 1.35267i | −0.0773270 | + | 0.0773270i | ||||
\(307\) | 1.82202i | 0.103988i | 0.998647 | + | 0.0519940i | \(0.0165577\pi\) | ||||
−0.998647 | + | 0.0519940i | \(0.983442\pi\) | |||||||
\(308\) | −34.0624 | − | 34.0624i | −1.94089 | − | 1.94089i | ||||
\(309\) | 8.50898 | 0.484059 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.73334i | 0.438518i | 0.975667 | + | 0.219259i | \(0.0703639\pi\) | ||||
−0.975667 | + | 0.219259i | \(0.929636\pi\) | |||||||
\(312\) | 13.1411 | − | 1.18193i | 0.743970 | − | 0.0669136i | ||||
\(313\) | 13.6675 | + | 13.6675i | 0.772534 | + | 0.772534i | 0.978549 | − | 0.206015i | \(-0.0660496\pi\) |
−0.206015 | + | 0.978549i | \(0.566050\pi\) | |||||||
\(314\) | −32.9233 | + | 32.9233i | −1.85797 | + | 1.85797i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 22.3181i | − | 1.25549i | ||||||
\(317\) | 14.3180 | 0.804179 | 0.402089 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402089 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(318\) | 4.77843i | 0.267961i | ||||||||
\(319\) | −30.8210 | − | 30.8210i | −1.72565 | − | 1.72565i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.74294 | 0.0972815 | ||||||||
\(322\) | 11.2432 | + | 11.2432i | 0.626557 | + | 0.626557i | ||||
\(323\) | −0.308929 | −0.0171892 | ||||||||
\(324\) | −7.88284 | −0.437936 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.06715 | −0.502183 | ||||||||
\(327\) | 15.2278 | 0.842097 | ||||||||
\(328\) | 25.4704 | + | 25.4704i | 1.40637 | + | 1.40637i | ||||
\(329\) | −13.5114 | −0.744909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8440 | − | 10.8440i | −0.596039 | − | 0.596039i | 0.343217 | − | 0.939256i | \(-0.388483\pi\) |
−0.939256 | + | 0.343217i | \(0.888483\pi\) | |||||||
\(332\) | − | 47.9380i | − | 2.63094i | ||||||
\(333\) | 22.3255 | 1.22343 | ||||||||
\(334\) | 43.4747i | 2.37883i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.33503 | − | 3.33503i | 0.181941 | − | 0.181941i | ||||
\(337\) | 5.26248 | + | 5.26248i | 0.286665 | + | 0.286665i | 0.835760 | − | 0.549095i | \(-0.185027\pi\) |
−0.549095 | + | 0.835760i | \(0.685027\pi\) | |||||||
\(338\) | 5.52645 | + | 30.4740i | 0.300599 | + | 1.65757i | ||||
\(339\) | − | 0.753170i | − | 0.0409066i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.2938 | −2.77771 | ||||||||
\(342\) | −3.02351 | − | 3.02351i | −0.163493 | − | 0.163493i | ||||
\(343\) | 19.8315i | 1.07080i | ||||||||
\(344\) | 12.3669 | − | 12.3669i | 0.666779 | − | 0.666779i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0176386 | − | 0.0176386i | 0.000948257 | − | 0.000948257i | ||||
\(347\) | −7.90775 | + | 7.90775i | −0.424510 | + | 0.424510i | −0.886753 | − | 0.462243i | \(-0.847045\pi\) |
0.462243 | + | 0.886753i | \(0.347045\pi\) | |||||||
\(348\) | 18.8777 | − | 18.8777i | 1.01195 | − | 1.01195i | ||||
\(349\) | −1.59130 | − | 1.59130i | −0.0851802 | − | 0.0851802i | 0.663233 | − | 0.748413i | \(-0.269184\pi\) |
−0.748413 | + | 0.663233i | \(0.769184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.52755 | + | 16.9839i | 0.0815347 | + | 0.906533i | ||||
\(352\) | −11.0434 | + | 11.0434i | −0.588613 | + | 0.588613i | ||||
\(353\) | − | 19.3600i | − | 1.03043i | −0.857061 | − | 0.515215i | \(-0.827712\pi\) | ||
0.857061 | − | 0.515215i | \(-0.172288\pi\) | |||||||
\(354\) | 16.9545i | 0.901121i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.21618 | − | 8.21618i | −0.435457 | − | 0.435457i | ||||
\(357\) | 0.811821 | 0.0429661 | ||||||||
\(358\) | −28.7594 | −1.51998 | ||||||||
\(359\) | 3.46070 | + | 3.46070i | 0.182649 | + | 0.182649i | 0.792509 | − | 0.609860i | \(-0.208774\pi\) |
−0.609860 | + | 0.792509i | \(0.708774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3095i | 0.963657i | ||||||||
\(362\) | 43.4998i | 2.28630i | ||||||||
\(363\) | −12.4823 | + | 12.4823i | −0.655149 | + | 0.655149i | ||||
\(364\) | 24.2367 | + | 20.2367i | 1.27035 | + | 1.06069i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.35992 | + | 6.35992i | 0.332438 | + | 0.332438i | ||||
\(367\) | −7.68286 | + | 7.68286i | −0.401042 | + | 0.401042i | −0.878600 | − | 0.477558i | \(-0.841522\pi\) |
0.477558 | + | 0.878600i | \(0.341522\pi\) | |||||||
\(368\) | −4.27845 | + | 4.27845i | −0.223030 | + | 0.223030i | ||||
\(369\) | −13.7793 | + | 13.7793i | −0.717323 | + | 0.717323i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.68632 | + | 3.68632i | −0.191384 | + | 0.191384i | ||||
\(372\) | − | 31.4171i | − | 1.62890i | ||||||
\(373\) | 6.30515 | + | 6.30515i | 0.326469 | + | 0.326469i | 0.851242 | − | 0.524773i | \(-0.175850\pi\) |
−0.524773 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(374\) | 4.87202 | 0.251926 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 22.6423i | − | 1.16769i | ||||||
\(377\) | 21.9304 | + | 18.3110i | 1.12947 | + | 0.943066i | ||||
\(378\) | 18.9813 | + | 18.9813i | 0.976293 | + | 0.976293i | ||||
\(379\) | 0.333942 | − | 0.333942i | 0.0171534 | − | 0.0171534i | −0.698478 | − | 0.715631i | \(-0.746139\pi\) |
0.715631 | + | 0.698478i | \(0.246139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.91934i | 0.303257i | ||||||||
\(382\) | 15.2444 | 0.779971 | ||||||||
\(383\) | − | 5.09138i | − | 0.260158i | −0.991504 | − | 0.130079i | \(-0.958477\pi\) | ||
0.991504 | − | 0.130079i | \(-0.0415230\pi\) | |||||||
\(384\) | −13.4341 | − | 13.4341i | −0.685554 | − | 0.685554i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.7350 | 1.51347 | ||||||||
\(387\) | 6.69041 | + | 6.69041i | 0.340092 | + | 0.340092i | ||||
\(388\) | −6.93704 | −0.352175 | ||||||||
\(389\) | 33.6544 | 1.70634 | 0.853172 | − | 0.521629i | \(-0.174676\pi\) | ||||
0.853172 | + | 0.521629i | \(0.174676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.04147 | −0.0526694 | ||||||||
\(392\) | −5.28676 | −0.267022 | ||||||||
\(393\) | −9.66267 | − | 9.66267i | −0.487417 | − | 0.487417i | ||||
\(394\) | −47.3973 | −2.38784 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.8807 | + | 30.8807i | 1.55181 | + | 1.55181i | ||||
\(397\) | 11.6763i | 0.586019i | 0.956110 | + | 0.293010i | \(0.0946568\pi\) | ||||
−0.956110 | + | 0.293010i | \(0.905343\pi\) | |||||||
\(398\) | −32.3385 | −1.62098 | ||||||||
\(399\) | 1.81459i | 0.0908433i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.30809 | − | 6.30809i | 0.315011 | − | 0.315011i | −0.531836 | − | 0.846847i | \(-0.678498\pi\) |
0.846847 | + | 0.531836i | \(0.178498\pi\) | |||||||
\(402\) | 5.78673 | + | 5.78673i | 0.288616 | + | 0.288616i | ||||
\(403\) | 33.4858 | − | 3.01175i | 1.66805 | − | 0.150026i | ||||
\(404\) | 23.5541i | 1.17186i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 44.9741 | 2.23203 | ||||||||
\(407\) | −40.2058 | − | 40.2058i | −1.99293 | − | 1.99293i | ||||
\(408\) | 1.36044i | 0.0673519i | ||||||||
\(409\) | −12.8746 | + | 12.8746i | −0.636609 | + | 0.636609i | −0.949718 | − | 0.313108i | \(-0.898630\pi\) |
0.313108 | + | 0.949718i | \(0.398630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.97306 | − | 5.97306i | 0.294629 | − | 0.294629i | ||||
\(412\) | −24.1288 | + | 24.1288i | −1.18874 | + | 1.18874i | ||||
\(413\) | −13.0795 | + | 13.0795i | −0.643602 | + | 0.643602i | ||||
\(414\) | −10.1930 | − | 10.1930i | −0.500956 | − | 0.500956i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.56095 | − | 7.85778i | 0.321677 | − | 0.385260i | ||||
\(417\) | −3.80883 | + | 3.80883i | −0.186519 | + | 0.186519i | ||||
\(418\) | 10.8900i | 0.532648i | ||||||||
\(419\) | 31.0270i | 1.51577i | 0.652389 | + | 0.757884i | \(0.273767\pi\) | ||||
−0.652389 | + | 0.757884i | \(0.726233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.82280 | − | 6.82280i | −0.332523 | − | 0.332523i | 0.521021 | − | 0.853544i | \(-0.325551\pi\) |
−0.853544 | + | 0.521021i | \(0.825551\pi\) | |||||||
\(422\) | 25.3362 | 1.23335 | ||||||||
\(423\) | 12.2493 | 0.595583 | ||||||||
\(424\) | −6.17749 | − | 6.17749i | −0.300006 | − | 0.300006i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 6.31070i | − | 0.305755i | ||||||
\(427\) | 9.81271i | 0.474870i | ||||||||
\(428\) | −4.94243 | + | 4.94243i | −0.238902 | + | 0.238902i | ||||
\(429\) | 11.6515 | − | 13.9545i | 0.562538 | − | 0.673729i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.95943 | − | 8.95943i | −0.431560 | − | 0.431560i | 0.457599 | − | 0.889159i | \(-0.348710\pi\) |
−0.889159 | + | 0.457599i | \(0.848710\pi\) | |||||||
\(432\) | −7.22311 | + | 7.22311i | −0.347522 | + | 0.347522i | ||||
\(433\) | −15.4575 | + | 15.4575i | −0.742841 | + | 0.742841i | −0.973124 | − | 0.230283i | \(-0.926035\pi\) |
0.230283 | + | 0.973124i | \(0.426035\pi\) | |||||||
\(434\) | 37.4240 | − | 37.4240i | 1.79641 | − | 1.79641i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.1811 | + | 43.1811i | −2.06800 | + | 2.06800i | ||||
\(437\) | − | 2.32791i | − | 0.111359i | ||||||
\(438\) | −11.6742 | − | 11.6742i | −0.557813 | − | 0.557813i | ||||
\(439\) | 24.6942 | 1.17859 | 0.589294 | − | 0.807919i | \(-0.299406\pi\) | ||||
0.589294 | + | 0.807919i | \(0.299406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.86010i | − | 0.136195i | ||||||
\(442\) | −3.18057 | + | 0.286064i | −0.151284 | + | 0.0136067i | ||||
\(443\) | −22.0612 | − | 22.0612i | −1.04816 | − | 1.04816i | −0.998780 | − | 0.0493786i | \(-0.984276\pi\) |
−0.0493786 | − | 0.998780i | \(-0.515724\pi\) | |||||||
\(444\) | 24.6258 | − | 24.6258i | 1.16869 | − | 1.16869i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.2191i | 1.14681i | ||||||||
\(447\) | 7.64234 | 0.361470 | ||||||||
\(448\) | − | 26.4057i | − | 1.24755i | ||||||
\(449\) | 0.902668 | + | 0.902668i | 0.0425995 | + | 0.0425995i | 0.728086 | − | 0.685486i | \(-0.240410\pi\) |
−0.685486 | + | 0.728086i | \(0.740410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49.6300 | 2.33699 | ||||||||
\(452\) | 2.13575 | + | 2.13575i | 0.100457 | + | 0.100457i | ||||
\(453\) | 16.7803 | 0.788410 | ||||||||
\(454\) | 44.2830 | 2.07830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.04088 | −0.142402 | ||||||||
\(457\) | −31.9104 | −1.49271 | −0.746353 | − | 0.665550i | \(-0.768197\pi\) | ||||
−0.746353 | + | 0.665550i | \(0.768197\pi\) | |||||||
\(458\) | 14.9996 | + | 14.9996i | 0.700887 | + | 0.700887i | ||||
\(459\) | −1.75826 | −0.0820688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.65292 | − | 1.65292i | −0.0769842 | − | 0.0769842i | 0.667566 | − | 0.744550i | \(-0.267336\pi\) |
−0.744550 | + | 0.667566i | \(0.767336\pi\) | |||||||
\(462\) | − | 28.6174i | − | 1.33140i | ||||||
\(463\) | 3.04132 | 0.141342 | 0.0706710 | − | 0.997500i | \(-0.477486\pi\) | ||||
0.0706710 | + | 0.997500i | \(0.477486\pi\) | |||||||
\(464\) | 17.1143i | 0.794514i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.1013 | + | 47.1013i | −2.18192 | + | 2.18192i | ||||
\(467\) | 14.5459 | + | 14.5459i | 0.673102 | + | 0.673102i | 0.958430 | − | 0.285328i | \(-0.0921024\pi\) |
−0.285328 | + | 0.958430i | \(0.592102\pi\) | |||||||
\(468\) | −21.9728 | − | 18.3464i | −1.01569 | − | 0.848064i | ||||
\(469\) | 8.92835i | 0.412273i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9136 | −0.825416 | ||||||||
\(472\) | −21.9186 | − | 21.9186i | −1.00888 | − | 1.00888i | ||||
\(473\) | − | 24.0974i | − | 1.10800i | ||||||
\(474\) | 9.37524 | − | 9.37524i | 0.430619 | − | 0.430619i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.30207 | + | 2.30207i | −0.105515 | + | 0.105515i | ||||
\(477\) | 3.34198 | − | 3.34198i | 0.153019 | − | 0.153019i | ||||
\(478\) | −23.8729 | + | 23.8729i | −1.09192 | + | 1.09192i | ||||
\(479\) | −25.2765 | − | 25.2765i | −1.15491 | − | 1.15491i | −0.985554 | − | 0.169359i | \(-0.945830\pi\) |
−0.169359 | − | 0.985554i | \(-0.554170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.6080 | + | 23.8866i | 1.30441 | + | 1.08913i | ||||
\(482\) | −6.66084 | + | 6.66084i | −0.303393 | + | 0.303393i | ||||
\(483\) | 6.11742i | 0.278352i | ||||||||
\(484\) | − | 70.7916i | − | 3.21780i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27.2134 | − | 27.2134i | −1.23442 | − | 1.23442i | ||||
\(487\) | 20.4552 | 0.926915 | 0.463457 | − | 0.886119i | \(-0.346609\pi\) | ||||
0.463457 | + | 0.886119i | \(0.346609\pi\) | |||||||
\(488\) | −16.4440 | −0.744387 | ||||||||
\(489\) | −2.46672 | − | 2.46672i | −0.111549 | − | 0.111549i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.81787i | − | 0.352816i | −0.984317 | − | 0.176408i | \(-0.943552\pi\) | ||
0.984317 | − | 0.176408i | \(-0.0564477\pi\) | |||||||
\(492\) | 30.3981i | 1.37045i | ||||||||
\(493\) | −2.08301 | + | 2.08301i | −0.0938139 | + | 0.0938139i | ||||
\(494\) | −0.639415 | − | 7.10925i | −0.0287686 | − | 0.319860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.2412 | + | 14.2412i | 0.639450 | + | 0.639450i | ||||
\(497\) | 4.86839 | − | 4.86839i | 0.218377 | − | 0.218377i | ||||
\(498\) | 20.1375 | − | 20.1375i | 0.902381 | − | 0.902381i | ||||
\(499\) | 19.1295 | − | 19.1295i | 0.856354 | − | 0.856354i | −0.134552 | − | 0.990906i | \(-0.542960\pi\) |
0.990906 | + | 0.134552i | \(0.0429596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8273 | + | 11.8273i | −0.528405 | + | 0.528405i | ||||
\(502\) | − | 53.3047i | − | 2.37911i | ||||||
\(503\) | −1.20851 | − | 1.20851i | −0.0538846 | − | 0.0538846i | 0.679651 | − | 0.733536i | \(-0.262131\pi\) |
−0.733536 | + | 0.679651i | \(0.762131\pi\) | |||||||
\(504\) | −20.5433 | −0.915072 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 36.7128i | 1.63208i | ||||||||
\(507\) | −6.78700 | + | 9.79395i | −0.301421 | + | 0.434964i | ||||
\(508\) | −16.7854 | − | 16.7854i | −0.744732 | − | 0.744732i | ||||
\(509\) | −10.5094 | + | 10.5094i | −0.465822 | + | 0.465822i | −0.900558 | − | 0.434736i | \(-0.856842\pi\) |
0.434736 | + | 0.900558i | \(0.356842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 18.0120i | − | 0.796806i | ||||||
\(512\) | 23.3781 | 1.03318 | ||||||||
\(513\) | − | 3.93010i | − | 0.173518i | ||||||
\(514\) | −3.36661 | − | 3.36661i | −0.148495 | − | 0.148495i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.7595 | 0.649750 | ||||||||
\(517\) | −22.0597 | − | 22.0597i | −0.970185 | − | 0.970185i | ||||
\(518\) | 58.6683 | 2.57774 | ||||||||
\(519\) | 0.00959718 | 0.000421269 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.86424 | −0.388349 | −0.194175 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194175 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(522\) | −40.7731 | −1.78459 | ||||||||
\(523\) | −2.10327 | − | 2.10327i | −0.0919697 | − | 0.0919697i | 0.659625 | − | 0.751595i | \(-0.270715\pi\) |
−0.751595 | + | 0.659625i | \(0.770715\pi\) | |||||||
\(524\) | 54.8006 | 2.39398 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.84137 | + | 8.84137i | 0.385502 | + | 0.385502i | ||||
\(527\) | 3.46663i | 0.151009i | ||||||||
\(528\) | 10.8900 | 0.473927 | ||||||||
\(529\) | 15.1521i | 0.658786i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.8578 | − | 11.8578i | 0.514584 | − | 0.514584i | ||||
\(532\) | −5.14562 | − | 5.14562i | −0.223091 | − | 0.223091i | ||||
\(533\) | −32.3997 | + | 2.91407i | −1.40339 | + | 0.126222i | ||||
\(534\) | − | 6.90279i | − | 0.298713i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.9620 | −0.646262 | ||||||||
\(537\) | −7.82401 | − | 7.82401i | −0.337631 | − | 0.337631i | ||||
\(538\) | 0.887755i | 0.0382738i | ||||||||
\(539\) | −5.15072 | + | 5.15072i | −0.221857 | + | 0.221857i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31137 | − | 4.31137i | 0.185360 | − | 0.185360i | −0.608327 | − | 0.793687i | \(-0.708159\pi\) |
0.793687 | + | 0.608327i | \(0.208159\pi\) | |||||||
\(542\) | 7.39933 | − | 7.39933i | 0.317828 | − | 0.317828i | ||||
\(543\) | −11.8341 | + | 11.8341i | −0.507851 | + | 0.507851i | ||||
\(544\) | 0.746353 | + | 0.746353i | 0.0319996 | + | 0.0319996i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.68029 | + | 18.6821i | 0.0719099 | + | 0.799521i | ||||
\(547\) | −12.6865 | + | 12.6865i | −0.542435 | + | 0.542435i | −0.924242 | − | 0.381807i | \(-0.875302\pi\) |
0.381807 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(548\) | 33.8755i | 1.44709i | ||||||||
\(549\) | − | 8.89611i | − | 0.379677i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.65596 | − | 4.65596i | −0.198351 | − | 0.198351i | ||||
\(552\) | −10.2515 | −0.436333 | ||||||||
\(553\) | 14.4651 | 0.615117 | ||||||||
\(554\) | −29.6717 | − | 29.6717i | −1.26063 | − | 1.26063i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 21.6013i | − | 0.916100i | ||||||
\(557\) | − | 1.92751i | − | 0.0816713i | −0.999166 | − | 0.0408357i | \(-0.986998\pi\) | ||
0.999166 | − | 0.0408357i | \(-0.0130020\pi\) | |||||||
\(558\) | −33.9282 | + | 33.9282i | −1.43630 | + | 1.43630i | ||||
\(559\) | 1.41490 | + | 15.7313i | 0.0598437 | + | 0.665364i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.32543 | + | 1.32543i | 0.0559599 | + | 0.0559599i | ||||
\(562\) | 17.1276 | − | 17.1276i | 0.722484 | − | 0.722484i | ||||
\(563\) | −10.3956 | + | 10.3956i | −0.438124 | + | 0.438124i | −0.891380 | − | 0.453256i | \(-0.850262\pi\) |
0.453256 | + | 0.891380i | \(0.350262\pi\) | |||||||
\(564\) | 13.5114 | − | 13.5114i | 0.568934 | − | 0.568934i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 51.5098 | − | 51.5098i | 2.16512 | − | 2.16512i | ||||
\(567\) | − | 5.10911i | − | 0.214562i | ||||||
\(568\) | 8.15840 | + | 8.15840i | 0.342319 | + | 0.342319i | ||||
\(569\) | 25.2005 | 1.05646 | 0.528230 | − | 0.849101i | \(-0.322856\pi\) | ||||
0.528230 | + | 0.849101i | \(0.322856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 21.7839i | − | 0.911630i | −0.890075 | − | 0.455815i | \(-0.849348\pi\) | ||
0.890075 | − | 0.455815i | \(-0.150652\pi\) | |||||||
\(572\) | 6.53068 | + | 72.6105i | 0.273061 | + | 3.03600i | ||||
\(573\) | 4.14724 | + | 4.14724i | 0.173254 | + | 0.173254i | ||||
\(574\) | −36.2101 | + | 36.2101i | −1.51138 | + | 1.51138i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.9392i | 0.997465i | ||||||||
\(577\) | 36.6110 | 1.52414 | 0.762068 | − | 0.647497i | \(-0.224184\pi\) | ||||
0.762068 | + | 0.647497i | \(0.224184\pi\) | |||||||
\(578\) | 40.1714i | 1.67091i | ||||||||
\(579\) | 8.08943 | + | 8.08943i | 0.336185 | + | 0.336185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.0701 | 1.28900 | ||||||||
\(582\) | −2.91407 | − | 2.91407i | −0.120792 | − | 0.120792i | ||||
\(583\) | −12.0371 | −0.498524 | ||||||||
\(584\) | 30.1844 | 1.24904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.3410 | −2.53397 | ||||||||
\(587\) | −5.27384 | −0.217675 | −0.108837 | − | 0.994060i | \(-0.534713\pi\) | ||||
−0.108837 | + | 0.994060i | \(0.534713\pi\) | |||||||
\(588\) | −3.15479 | − | 3.15479i | −0.130101 | − | 0.130101i | ||||
\(589\) | −7.74867 | −0.319278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8945 | − | 12.8945i | −0.530407 | − | 0.530407i | ||||
\(592\) | 22.3255i | 0.917572i | ||||||||
\(593\) | −22.9283 | −0.941552 | −0.470776 | − | 0.882253i | \(-0.656026\pi\) | ||||
−0.470776 | + | 0.882253i | \(0.656026\pi\) | |||||||
\(594\) | 61.9804i | 2.54309i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6713 | + | 21.6713i | −0.887691 | + | 0.887691i | ||||
\(597\) | −8.79769 | − | 8.79769i | −0.360066 | − | 0.360066i | ||||
\(598\) | −2.15562 | − | 23.9669i | −0.0881498 | − | 0.980081i | ||||
\(599\) | − | 2.73954i | − | 0.111934i | −0.998433 | − | 0.0559672i | \(-0.982176\pi\) | ||
0.998433 | − | 0.0559672i | \(-0.0178242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.4400 | 1.73116 | 0.865582 | − | 0.500767i | \(-0.166949\pi\) | ||||
0.865582 | + | 0.500767i | \(0.166949\pi\) | |||||||
\(602\) | 17.5814 | + | 17.5814i | 0.716566 | + | 0.716566i | ||||
\(603\) | − | 8.09436i | − | 0.329628i | ||||||
\(604\) | −47.5838 | + | 47.5838i | −1.93616 | + | 1.93616i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.89446 | + | 9.89446i | −0.401935 | + | 0.401935i | ||||
\(607\) | 17.7698 | − | 17.7698i | 0.721255 | − | 0.721255i | −0.247606 | − | 0.968861i | \(-0.579644\pi\) |
0.968861 | + | 0.247606i | \(0.0796439\pi\) | |||||||
\(608\) | −1.66826 | + | 1.66826i | −0.0676568 | + | 0.0676568i | ||||
\(609\) | 12.2352 | + | 12.2352i | 0.495796 | + | 0.495796i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6963 | + | 13.1058i | 0.635006 | + | 0.530206i | ||||
\(612\) | 2.08703 | − | 2.08703i | 0.0843633 | − | 0.0843633i | ||||
\(613\) | − | 25.4815i | − | 1.02919i | −0.857435 | − | 0.514593i | \(-0.827943\pi\) | ||
0.857435 | − | 0.514593i | \(-0.172057\pi\) | |||||||
\(614\) | − | 4.34076i | − | 0.175179i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.9962 | + | 36.9962i | 1.49062 | + | 1.49062i | ||||
\(617\) | −17.0369 | −0.685880 | −0.342940 | − | 0.939357i | \(-0.611423\pi\) | ||||
−0.342940 | + | 0.939357i | \(0.611423\pi\) | |||||||
\(618\) | −20.2717 | −0.815449 | ||||||||
\(619\) | 26.5396 | + | 26.5396i | 1.06672 | + | 1.06672i | 0.997609 | + | 0.0691073i | \(0.0220151\pi\) |
0.0691073 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 13.2493i | − | 0.531675i | ||||||
\(622\) | − | 18.4239i | − | 0.738729i | ||||||
\(623\) | 5.32516 | − | 5.32516i | 0.213348 | − | 0.213348i | ||||
\(624\) | −7.10925 | + | 0.639415i | −0.284598 | + | 0.0255971i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5614 | − | 32.5614i | −1.30141 | − | 1.30141i | ||||
\(627\) | −2.96263 | + | 2.96263i | −0.118316 | + | 0.118316i | ||||
\(628\) | 50.7974 | − | 50.7974i | 2.02704 | − | 2.02704i | ||||
\(629\) | −2.71726 | + | 2.71726i | −0.108344 | + | 0.108344i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.89770 | + | 8.89770i | −0.354212 | + | 0.354212i | −0.861674 | − | 0.507462i | \(-0.830584\pi\) |
0.507462 | + | 0.861674i | \(0.330584\pi\) | |||||||
\(632\) | 24.2404i | 0.964231i | ||||||||
\(633\) | 6.89273 | + | 6.89273i | 0.273961 | + | 0.273961i | ||||
\(634\) | −34.1111 | −1.35472 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 7.37263i | − | 0.292344i | ||||||
\(637\) | 3.06008 | − | 3.66494i | 0.121245 | − | 0.145210i | ||||
\(638\) | 73.4278 | + | 73.4278i | 2.90703 | + | 2.90703i | ||||
\(639\) | −4.41364 | + | 4.41364i | −0.174601 | + | 0.174601i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 39.6332i | − | 1.56542i | −0.622388 | − | 0.782709i | \(-0.713838\pi\) | ||
0.622388 | − | 0.782709i | \(-0.286162\pi\) | |||||||
\(642\) | −4.15237 | −0.163881 | ||||||||
\(643\) | 2.08560i | 0.0822481i | 0.999154 | + | 0.0411240i | \(0.0130939\pi\) | ||||
−0.999154 | + | 0.0411240i | \(0.986906\pi\) | |||||||
\(644\) | −17.3471 | − | 17.3471i | −0.683571 | − | 0.683571i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.735989 | 0.0289571 | ||||||||
\(647\) | −9.45363 | − | 9.45363i | −0.371661 | − | 0.371661i | 0.496421 | − | 0.868082i | \(-0.334647\pi\) |
−0.868082 | + | 0.496421i | \(0.834647\pi\) | |||||||
\(648\) | 8.56180 | 0.336339 | ||||||||
\(649\) | −42.7091 | −1.67648 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.3624 | 0.798065 | ||||||||
\(652\) | 13.9897 | 0.547879 | ||||||||
\(653\) | 7.46934 | + | 7.46934i | 0.292298 | + | 0.292298i | 0.837987 | − | 0.545689i | \(-0.183732\pi\) |
−0.545689 | + | 0.837987i | \(0.683732\pi\) | |||||||
\(654\) | −36.2785 | −1.41860 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −13.7793 | − | 13.7793i | −0.537992 | − | 0.537992i | ||||
\(657\) | 16.3296i | 0.637076i | ||||||||
\(658\) | 32.1895 | 1.25488 | ||||||||
\(659\) | 13.0165i | 0.507053i | 0.967328 | + | 0.253526i | \(0.0815905\pi\) | ||||
−0.967328 | + | 0.253526i | \(0.918410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1615 | + | 10.1615i | −0.395238 | + | 0.395238i | −0.876550 | − | 0.481311i | \(-0.840161\pi\) |
0.481311 | + | 0.876550i | \(0.340161\pi\) | |||||||
\(662\) | 25.8346 | + | 25.8346i | 1.00409 | + | 1.00409i | ||||
\(663\) | −0.943099 | − | 0.787451i | −0.0366269 | − | 0.0305821i | ||||
\(664\) | 52.0669i | 2.02059i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −53.1881 | −2.06100 | ||||||||
\(667\) | −15.6963 | − | 15.6963i | −0.607765 | − | 0.607765i | ||||
\(668\) | − | 67.0771i | − | 2.59529i | ||||||
\(669\) | −6.58881 | + | 6.58881i | −0.254738 | + | 0.254738i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0209 | + | 16.0209i | −0.618481 | + | 0.618481i | ||||
\(672\) | 4.38395 | − | 4.38395i | 0.169115 | − | 0.169115i | ||||
\(673\) | −21.0987 | + | 21.0987i | −0.813295 | + | 0.813295i | −0.985126 | − | 0.171832i | \(-0.945031\pi\) |
0.171832 | + | 0.985126i | \(0.445031\pi\) | |||||||
\(674\) | −12.5373 | − | 12.5373i | −0.482918 | − | 0.482918i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.52676 | − | 47.0184i | −0.327952 | − | 1.80840i | ||||
\(677\) | −2.76719 | + | 2.76719i | −0.106352 | + | 0.106352i | −0.758280 | − | 0.651929i | \(-0.773960\pi\) |
0.651929 | + | 0.758280i | \(0.273960\pi\) | |||||||
\(678\) | 1.79435i | 0.0689114i | ||||||||
\(679\) | − | 4.49611i | − | 0.172545i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0472 | + | 12.0472i | 0.461650 | + | 0.461650i | ||||
\(682\) | 122.202 | 4.67935 | ||||||||
\(683\) | 43.9664 | 1.68233 | 0.841164 | − | 0.540780i | \(-0.181871\pi\) | ||||
0.841164 | + | 0.540780i | \(0.181871\pi\) | |||||||
\(684\) | 4.66497 | + | 4.66497i | 0.178370 | + | 0.178370i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 47.2465i | − | 1.80388i | ||||||
\(687\) | 8.16132i | 0.311374i | ||||||||
\(688\) | −6.69041 | + | 6.69041i | −0.255069 | + | 0.255069i | ||||
\(689\) | 7.85808 | − | 0.706766i | 0.299369 | − | 0.0269256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.17085 | + | 3.17085i | 0.120625 | + | 0.120625i | 0.764842 | − | 0.644218i | \(-0.222817\pi\) |
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(692\) | −0.0272146 | + | 0.0272146i | −0.00103454 | + | 0.00103454i | ||||
\(693\) | −20.0147 | + | 20.0147i | −0.760295 | + | 0.760295i | ||||
\(694\) | 18.8394 | − | 18.8394i | 0.715132 | − | 0.715132i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20.5037 | + | 20.5037i | −0.777189 | + | 0.777189i | ||||
\(697\) | − | 3.35419i | − | 0.127049i | ||||||
\(698\) | 3.79109 | + | 3.79109i | 0.143495 | + | 0.143495i | ||||
\(699\) | −25.6278 | −0.969334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.6817i | − | 1.08329i | −0.840606 | − | 0.541647i | \(-0.817801\pi\) | ||
0.840606 | − | 0.541647i | \(-0.182199\pi\) | |||||||
\(702\) | −3.63923 | − | 40.4623i | −0.137354 | − | 1.52715i | ||||
\(703\) | −6.07366 | − | 6.07366i | −0.229072 | − | 0.229072i | ||||
\(704\) | 43.1118 | − | 43.1118i | 1.62484 | − | 1.62484i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.1231i | 1.73587i | ||||||||
\(707\) | −15.2661 | −0.574143 | ||||||||
\(708\) | − | 26.1591i | − | 0.983118i | ||||||
\(709\) | −10.9424 | − | 10.9424i | −0.410952 | − | 0.410952i | 0.471118 | − | 0.882070i | \(-0.343851\pi\) |
−0.882070 | + | 0.471118i | \(0.843851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1139 | −0.491809 | ||||||||
\(712\) | 8.92385 | + | 8.92385i | 0.334435 | + | 0.334435i | ||||
\(713\) | −26.1226 | −0.978298 | ||||||||
\(714\) | −1.93407 | −0.0723809 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 44.3729 | 1.65829 | ||||||||
\(717\) | −12.9893 | −0.485093 | ||||||||
\(718\) | −8.24474 | − | 8.24474i | −0.307691 | − | 0.307691i | ||||
\(719\) | 1.67615 | 0.0625099 | 0.0312550 | − | 0.999511i | \(-0.490050\pi\) | ||||
0.0312550 | + | 0.999511i | \(0.490050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6386 | − | 15.6386i | −0.582413 | − | 0.582413i | ||||
\(722\) | − | 43.6203i | − | 1.62338i | ||||||
\(723\) | −3.62417 | −0.134784 | ||||||||
\(724\) | − | 67.1158i | − | 2.49434i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 29.7376 | − | 29.7376i | 1.10367 | − | 1.10367i | ||||
\(727\) | −9.40127 | − | 9.40127i | −0.348674 | − | 0.348674i | 0.510942 | − | 0.859615i | \(-0.329297\pi\) |
−0.859615 | + | 0.510942i | \(0.829297\pi\) | |||||||
\(728\) | −26.3243 | − | 21.9797i | −0.975642 | − | 0.814623i | ||||
\(729\) | − | 8.37322i | − | 0.310119i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.62859 | −0.0602357 | ||||||||
\(732\) | −9.81271 | − | 9.81271i | −0.362688 | − | 0.362688i | ||||
\(733\) | − | 17.2489i | − | 0.637104i | −0.947905 | − | 0.318552i | \(-0.896804\pi\) | ||
0.947905 | − | 0.318552i | \(-0.103196\pi\) | |||||||
\(734\) | 18.3036 | − | 18.3036i | 0.675598 | − | 0.675598i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.62409 | + | 5.62409i | −0.207307 | + | 0.207307i | ||||
\(737\) | −14.5770 | + | 14.5770i | −0.536952 | + | 0.536952i | ||||
\(738\) | 32.8277 | − | 32.8277i | 1.20841 | − | 1.20841i | ||||
\(739\) | 17.3014 | + | 17.3014i | 0.636442 | + | 0.636442i | 0.949676 | − | 0.313234i | \(-0.101412\pi\) |
−0.313234 | + | 0.949676i | \(0.601412\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.76012 | − | 2.10803i | 0.0646597 | − | 0.0774403i | ||||
\(742\) | 8.78225 | − | 8.78225i | 0.322406 | − | 0.322406i | ||||
\(743\) | 19.0572i | 0.699142i | 0.936910 | + | 0.349571i | \(0.113673\pi\) | ||||
−0.936910 | + | 0.349571i | \(0.886327\pi\) | |||||||
\(744\) | 34.1231i | 1.25101i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.0213 | − | 15.0213i | −0.549971 | − | 0.549971i | ||||
\(747\) | −28.1678 | −1.03061 | ||||||||
\(748\) | −7.51703 | −0.274850 | ||||||||
\(749\) | −3.20334 | − | 3.20334i | −0.117048 | − | 0.117048i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.28578i | 0.229371i | 0.993402 | + | 0.114686i | \(0.0365861\pi\) | ||||
−0.993402 | + | 0.114686i | \(0.963414\pi\) | |||||||
\(752\) | 12.2493i | 0.446687i | ||||||||
\(753\) | 14.5016 | − | 14.5016i | 0.528466 | − | 0.528466i | ||||
\(754\) | −52.2468 | − | 43.6240i | −1.90271 | − | 1.58869i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −29.2862 | − | 29.2862i | −1.06513 | − | 1.06513i | ||||
\(757\) | −1.17728 | + | 1.17728i | −0.0427888 | + | 0.0427888i | −0.728177 | − | 0.685389i | \(-0.759632\pi\) |
0.685389 | + | 0.728177i | \(0.259632\pi\) | |||||||
\(758\) | −0.795581 | + | 0.795581i | −0.0288968 | + | 0.0288968i | ||||
\(759\) | −9.98772 | + | 9.98772i | −0.362531 | + | 0.362531i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.23399 | − | 8.23399i | 0.298482 | − | 0.298482i | −0.541937 | − | 0.840419i | \(-0.682309\pi\) |
0.840419 | + | 0.541937i | \(0.182309\pi\) | |||||||
\(762\) | − | 14.1022i | − | 0.510869i | ||||||
\(763\) | −27.9870 | − | 27.9870i | −1.01320 | − | 1.01320i | ||||
\(764\) | −23.5206 | −0.850944 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.1297i | 0.438263i | ||||||||
\(767\) | 27.8815 | − | 2.50770i | 1.00674 | − | 0.0905477i | ||||
\(768\) | 17.6378 | + | 17.6378i | 0.636450 | + | 0.636450i | ||||
\(769\) | 33.1546 | − | 33.1546i | 1.19558 | − | 1.19558i | 0.220109 | − | 0.975475i | \(-0.429359\pi\) |
0.975475 | − | 0.220109i | \(-0.0706412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.83177i | − | 0.0659697i | ||||||
\(772\) | −45.8782 | −1.65119 | ||||||||
\(773\) | 53.2581i | 1.91556i | 0.287502 | + | 0.957780i | \(0.407175\pi\) | ||||
−0.287502 | + | 0.957780i | \(0.592825\pi\) | |||||||
\(774\) | −15.9392 | − | 15.9392i | −0.572922 | − | 0.572922i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.53454 | 0.270474 | ||||||||
\(777\) | 15.9607 | + | 15.9607i | 0.572588 | + | 0.572588i | ||||
\(778\) | −80.1779 | −2.87452 | ||||||||
\(779\) | 7.49734 | 0.268620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8969 | 0.568837 | ||||||||
\(782\) | 2.48119 | 0.0887272 | ||||||||
\(783\) | −26.4994 | − | 26.4994i | −0.947011 | − | 0.947011i | ||||
\(784\) | 2.86010 | 0.102146 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.0203 | + | 23.0203i | 0.821105 | + | 0.821105i | ||||
\(787\) | 39.5579i | 1.41009i | 0.709165 | + | 0.705043i | \(0.249072\pi\) | ||||
−0.709165 | + | 0.705043i | \(0.750928\pi\) | |||||||
\(788\) | 73.1293 | 2.60512 | ||||||||
\(789\) | 4.81060i | 0.171262i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.38425 | + | 1.38425i | −0.0492182 | + | 0.0492182i | ||||
\(792\) | −33.5404 | − | 33.5404i | −1.19181 | − | 1.19181i | ||||
\(793\) | 9.51815 | − | 11.3995i | 0.337999 | − | 0.404808i | ||||
\(794\) | − | 27.8176i | − | 0.987211i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 49.8950 | 1.76848 | ||||||||
\(797\) | 17.6570 | + | 17.6570i | 0.625443 | + | 0.625443i | 0.946918 | − | 0.321475i | \(-0.104179\pi\) |
−0.321475 | + | 0.946918i | \(0.604179\pi\) | |||||||
\(798\) | − | 4.32307i | − | 0.153035i | ||||||
\(799\) | −1.49088 | + | 1.49088i | −0.0527435 | + | 0.0527435i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.82774 | + | 4.82774i | −0.170580 | + | 0.170580i | ||||
\(802\) | −15.0283 | + | 15.0283i | −0.530669 | + | 0.530669i | ||||
\(803\) | 29.4077 | − | 29.4077i | 1.03778 | − | 1.03778i | ||||
\(804\) | −8.92835 | − | 8.92835i | −0.314879 | − | 0.314879i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −79.7763 | + | 7.17518i | −2.81000 | + | 0.252735i | ||||
\(807\) | −0.241514 | + | 0.241514i | −0.00850169 | + | 0.00850169i | ||||
\(808\) | − | 25.5829i | − | 0.900002i | ||||||
\(809\) | 26.8465i | 0.943871i | 0.881633 | + | 0.471936i | \(0.156445\pi\) | ||||
−0.881633 | + | 0.471936i | \(0.843555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1320 | + | 22.1320i | 0.777159 | + | 0.777159i | 0.979347 | − | 0.202188i | \(-0.0648051\pi\) |
−0.202188 | + | 0.979347i | \(0.564805\pi\) | |||||||
\(812\) | −69.3905 | −2.43513 | ||||||||
\(813\) | 4.02598 | 0.141197 | ||||||||
\(814\) | 95.7859 | + | 95.7859i | 3.35729 | + | 3.35729i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 0.735989i | − | 0.0257648i | ||||||
\(817\) | − | 3.64025i | − | 0.127356i | ||||||
\(818\) | 30.6724 | − | 30.6724i | 1.07244 | − | 1.07244i | ||||
\(819\) | 11.8909 | − | 14.2412i | 0.415501 | − | 0.497629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5151 | + | 32.5151i | 1.13479 | + | 1.13479i | 0.989371 | + | 0.145416i | \(0.0464519\pi\) |
0.145416 | + | 0.989371i | \(0.453548\pi\) | |||||||
\(822\) | −14.2302 | + | 14.2302i | −0.496334 | + | 0.496334i | ||||
\(823\) | 14.6543 | − | 14.6543i | 0.510816 | − | 0.510816i | −0.403960 | − | 0.914776i | \(-0.632367\pi\) |
0.914776 | + | 0.403960i | \(0.132367\pi\) | |||||||
\(824\) | 26.2071 | − | 26.2071i | 0.912966 | − | 0.912966i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.1606 | − | 31.1606i | 1.08422 | − | 1.08422i | ||||
\(827\) | 2.99000i | 0.103972i | 0.998648 | + | 0.0519862i | \(0.0165552\pi\) | ||||
−0.998648 | + | 0.0519862i | \(0.983445\pi\) | |||||||
\(828\) | 15.7267 | + | 15.7267i | 0.546541 | + | 0.546541i | ||||
\(829\) | −1.29806 | −0.0450836 | −0.0225418 | − | 0.999746i | \(-0.507176\pi\) | ||||
−0.0225418 | + | 0.999746i | \(0.507176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 16.1444i | − | 0.560043i | ||||||
\(832\) | −25.6131 | + | 30.6757i | −0.887973 | + | 1.06349i | ||||
\(833\) | 0.348106 | + | 0.348106i | 0.0120611 | + | 0.0120611i | ||||
\(834\) | 9.07414 | − | 9.07414i | 0.314212 | − | 0.314212i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 16.8022i | − | 0.581116i | ||||||
\(837\) | −44.1015 | −1.52437 | ||||||||
\(838\) | − | 73.9185i | − | 2.55347i | ||||||
\(839\) | 3.30809 | + | 3.30809i | 0.114208 | + | 0.114208i | 0.761901 | − | 0.647693i | \(-0.224266\pi\) |
−0.647693 | + | 0.761901i | \(0.724266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.7873 | −1.16508 | ||||||||
\(842\) | 16.2546 | + | 16.2546i | 0.560170 | + | 0.560170i | ||||
\(843\) | 9.31913 | 0.320968 | ||||||||
\(844\) | −39.0912 | −1.34558 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.1827 | −1.00332 | ||||||||
\(847\) | 45.8822 | 1.57653 | ||||||||
\(848\) | 3.34198 | + | 3.34198i | 0.114764 | + | 0.114764i | ||||
\(849\) | 28.0265 | 0.961868 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4757 | − | 20.4757i | −0.701899 | − | 0.701899i | ||||
\(852\) | 9.73678i | 0.333577i | ||||||||
\(853\) | −23.1640 | −0.793119 | −0.396560 | − | 0.918009i | \(-0.629796\pi\) | ||||
−0.396560 | + | 0.918009i | \(0.629796\pi\) | |||||||
\(854\) | − | 23.3777i | − | 0.799969i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.36813 | − | 5.36813i | 0.183479 | − | 0.183479i | ||||
\(857\) | 0.287160 | + | 0.287160i | 0.00980921 | + | 0.00980921i | 0.711994 | − | 0.702185i | \(-0.247792\pi\) |
−0.702185 | + | 0.711994i | \(0.747792\pi\) | |||||||
\(858\) | −27.7583 | + | 33.2451i | −0.947654 | + | 1.13497i | ||||
\(859\) | 34.3061i | 1.17051i | 0.810850 | + | 0.585254i | \(0.199005\pi\) | ||||
−0.810850 | + | 0.585254i | \(0.800995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.7019 | −0.671440 | ||||||||
\(862\) | 21.3449 | + | 21.3449i | 0.727009 | + | 0.727009i | ||||
\(863\) | − | 13.0838i | − | 0.445377i | −0.974890 | − | 0.222688i | \(-0.928517\pi\) | ||
0.974890 | − | 0.222688i | \(-0.0714833\pi\) | |||||||
\(864\) | −9.49489 | + | 9.49489i | −0.323023 | + | 0.323023i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.8258 | − | 36.8258i | 1.25139 | − | 1.25139i | ||||
\(867\) | −10.9286 | + | 10.9286i | −0.371156 | + | 0.371156i | ||||
\(868\) | −57.7414 | + | 57.7414i | −1.95987 | + | 1.95987i | ||||
\(869\) | 23.6167 | + | 23.6167i | 0.801140 | + | 0.801140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.66033 | − | 10.3721i | 0.293444 | − | 0.351446i | ||||
\(872\) | 46.9004 | − | 46.9004i | 1.58825 | − | 1.58825i | ||||
\(873\) | 4.07613i | 0.137956i | ||||||||
\(874\) | 5.54599i | 0.187596i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.0120 | + | 18.0120i | 0.608571 | + | 0.608571i | ||||
\(877\) | −43.5876 | −1.47185 | −0.735924 | − | 0.677064i | \(-0.763252\pi\) | ||||
−0.735924 | + | 0.677064i | \(0.763252\pi\) | |||||||
\(878\) | −58.8312 | −1.98546 | ||||||||
\(879\) | −16.6878 | − | 16.6878i | −0.562867 | − | 0.562867i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.6106i | 1.80619i | 0.429445 | + | 0.903093i | \(0.358709\pi\) | ||||
−0.429445 | + | 0.903093i | \(0.641291\pi\) | |||||||
\(882\) | 6.81388i | 0.229435i | ||||||||
\(883\) | 13.4449 | − | 13.4449i | 0.452458 | − | 0.452458i | −0.443712 | − | 0.896170i | \(-0.646339\pi\) |
0.896170 | + | 0.443712i | \(0.146339\pi\) | |||||||
\(884\) | 4.90730 | − | 0.441368i | 0.165050 | − | 0.0148448i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.5584 | + | 52.5584i | 1.76573 | + | 1.76573i | ||||
\(887\) | 16.8456 | − | 16.8456i | 0.565618 | − | 0.565618i | −0.365279 | − | 0.930898i | \(-0.619027\pi\) |
0.930898 | + | 0.365279i | \(0.119027\pi\) | |||||||
\(888\) | −26.7468 | + | 26.7468i | −0.897564 | + | 0.897564i | ||||
\(889\) | 10.8791 | − | 10.8791i | 0.364874 | − | 0.364874i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.34149 | − | 8.34149i | 0.279450 | − | 0.279450i | ||||
\(892\) | − | 37.3676i | − | 1.25116i | ||||||
\(893\) | −3.33244 | − | 3.33244i | −0.111516 | − | 0.111516i | ||||
\(894\) | −18.2071 | −0.608935 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 49.3808i | 1.64970i | ||||||||
\(897\) | 5.93378 | − | 7.10665i | 0.198123 | − | 0.237284i | ||||
\(898\) | −2.15051 | − | 2.15051i | −0.0717634 | − | 0.0717634i | ||||
\(899\) | −52.2468 | + | 52.2468i | −1.74253 | + | 1.74253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.813512i | 0.0271020i | ||||||||
\(902\) | −118.238 | −3.93690 | ||||||||
\(903\) | 9.56607i | 0.318339i | ||||||||
\(904\) | −2.31971 | − | 2.31971i | −0.0771523 | − | 0.0771523i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −39.9774 | −1.32816 | ||||||||
\(907\) | 18.6035 | + | 18.6035i | 0.617718 | + | 0.617718i | 0.944946 | − | 0.327228i | \(-0.106114\pi\) |
−0.327228 | + | 0.944946i | \(0.606114\pi\) | |||||||
\(908\) | −68.3242 | −2.26742 | ||||||||
\(909\) | 13.8401 | 0.459049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7993 | 0.589716 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(912\) | 1.64509 | 0.0544745 | ||||||||
\(913\) | 50.7271 | + | 50.7271i | 1.67882 | + | 1.67882i | ||||
\(914\) | 76.0231 | 2.51462 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.1429 | − | 23.1429i | −0.764664 | − | 0.764664i | ||||
\(917\) | 35.5179i | 1.17291i | ||||||||
\(918\) | 4.18888 | 0.138253 | ||||||||
\(919\) | − | 55.5174i | − | 1.83135i | −0.401920 | − | 0.915675i | \(-0.631657\pi\) | ||
0.401920 | − | 0.915675i | \(-0.368343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.18090 | − | 1.18090i | 0.0389121 | − | 0.0389121i | ||||
\(922\) | 3.93791 | + | 3.93791i | 0.129688 | + | 0.129688i | ||||
\(923\) | −10.3779 | + | 0.933401i | −0.341593 | + | 0.0307233i | ||||
\(924\) | 44.1538i | 1.45255i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.24561 | −0.238105 | ||||||||
\(927\) | 14.1778 | + | 14.1778i | 0.465661 | + | 0.465661i | ||||
\(928\) | 22.4971i | 0.738502i | ||||||||
\(929\) | 26.7318 | − | 26.7318i | 0.877040 | − | 0.877040i | −0.116187 | − | 0.993227i | \(-0.537067\pi\) |
0.993227 | + | 0.116187i | \(0.0370671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.778091 | + | 0.778091i | −0.0255009 | + | 0.0255009i | ||||
\(932\) | 72.6725 | − | 72.6725i | 2.38047 | − | 2.38047i | ||||
\(933\) | 5.01222 | − | 5.01222i | 0.164093 | − | 0.164093i | ||||
\(934\) | −34.6539 | − | 34.6539i | −1.13391 | − | 1.13391i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.8653 | + | 19.9266i | 0.780063 | + | 0.651322i | ||||
\(937\) | 43.2141 | − | 43.2141i | 1.41174 | − | 1.41174i | 0.664101 | − | 0.747643i | \(-0.268815\pi\) |
0.747643 | − | 0.664101i | \(-0.231185\pi\) | |||||||
\(938\) | − | 21.2708i | − | 0.694517i | ||||||
\(939\) | − | 17.7167i | − | 0.578162i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7446 | − | 16.7446i | −0.545859 | − | 0.545859i | 0.379381 | − | 0.925240i | \(-0.376137\pi\) |
−0.925240 | + | 0.379381i | \(0.876137\pi\) | |||||||
\(942\) | 42.6773 | 1.39050 | ||||||||
\(943\) | 25.2753 | 0.823076 | ||||||||
\(944\) | 11.8578 | + | 11.8578i | 0.385938 | + | 0.385938i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.4094i | 1.86654i | ||||||||
\(947\) | 5.66954i | 0.184235i | 0.995748 | + | 0.0921176i | \(0.0293636\pi\) | ||||
−0.995748 | + | 0.0921176i | \(0.970636\pi\) | |||||||
\(948\) | −14.4651 | + | 14.4651i | −0.469803 | + | 0.469803i | ||||
\(949\) | −17.4714 | + | 20.9247i | −0.567144 | + | 0.679246i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.27993 | − | 9.27993i | −0.300922 | − | 0.300922i | ||||
\(952\) | 2.50035 | − | 2.50035i | 0.0810367 | − | 0.0810367i | ||||
\(953\) | −8.52197 | + | 8.52197i | −0.276054 | + | 0.276054i | −0.831531 | − | 0.555478i | \(-0.812535\pi\) |
0.555478 | + | 0.831531i | \(0.312535\pi\) | |||||||
\(954\) | −7.96190 | + | 7.96190i | −0.257776 | + | 0.257776i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.8335 | − | 36.8335i | 1.19128 | − | 1.19128i | ||||
\(957\) | 39.9521i | 1.29147i | ||||||||
\(958\) | 60.2186 | + | 60.2186i | 1.94557 | + | 1.94557i | ||||
\(959\) | −21.9557 | −0.708987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.9514i | 1.80489i | ||||||||
\(962\) | −68.1554 | − | 56.9071i | −2.19742 | − | 1.83476i | ||||
\(963\) | 2.90412 | + | 2.90412i | 0.0935839 | + | 0.0935839i | ||||
\(964\) | 10.2770 | − | 10.2770i | 0.331000 | − | 0.331000i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | − | 14.5741i | − | 0.468913i | ||||||
\(967\) | 14.0855 | 0.452959 | 0.226480 | − | 0.974016i | \(-0.427278\pi\) | ||||
0.226480 | + | 0.974016i | \(0.427278\pi\) | |||||||
\(968\) | 76.8889i | 2.47130i | ||||||||
\(969\) | 0.200226 | + | 0.200226i | 0.00643219 | + | 0.00643219i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4963 | −1.33168 | −0.665840 | − | 0.746094i | \(-0.731927\pi\) | ||||
−0.665840 | + | 0.746094i | \(0.731927\pi\) | |||||||
\(972\) | 41.9875 | + | 41.9875i | 1.34675 | + | 1.34675i | ||||
\(973\) | 14.0005 | 0.448835 | ||||||||
\(974\) | −48.7323 | −1.56149 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.89611 | 0.284758 | ||||||||
\(977\) | 7.91854 | 0.253337 | 0.126668 | − | 0.991945i | \(-0.459572\pi\) | ||||
0.126668 | + | 0.991945i | \(0.459572\pi\) | |||||||
\(978\) | 5.87670 | + | 5.87670i | 0.187916 | + | 0.187916i | ||||
\(979\) | 17.3884 | 0.555737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.3728 | + | 25.3728i | 0.810090 | + | 0.810090i | ||||
\(982\) | 18.6252i | 0.594355i | ||||||||
\(983\) | 55.0656 | 1.75632 | 0.878160 | − | 0.478367i | \(-0.158771\pi\) | ||||
0.878160 | + | 0.478367i | \(0.158771\pi\) | |||||||
\(984\) | − | 33.0163i | − | 1.05252i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.96254 | − | 4.96254i | 0.158039 | − | 0.158039i | ||||
\(987\) | 8.75717 | + | 8.75717i | 0.278744 | + | 0.278744i | ||||
\(988\) | 0.986553 | + | 10.9689i | 0.0313864 | + | 0.348966i | ||||
\(989\) | − | 12.2721i | − | 0.390232i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.92894 | 0.251871 | 0.125936 | − | 0.992038i | \(-0.459807\pi\) | ||||
0.125936 | + | 0.992038i | \(0.459807\pi\) | |||||||
\(992\) | 18.7203 | + | 18.7203i | 0.594371 | + | 0.594371i | ||||
\(993\) | 14.0566i | 0.446074i | ||||||||
\(994\) | −11.5984 | + | 11.5984i | −0.367879 | + | 0.367879i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −31.0701 | + | 31.0701i | −0.984493 | + | 0.984493i | ||||
\(997\) | 20.5699 | − | 20.5699i | 0.651457 | − | 0.651457i | −0.301887 | − | 0.953344i | \(-0.597617\pi\) |
0.953344 | + | 0.301887i | \(0.0976166\pi\) | |||||||
\(998\) | −45.5740 | + | 45.5740i | −1.44262 | + | 1.44262i | ||||
\(999\) | −34.5682 | − | 34.5682i | −1.09369 | − | 1.09369i |
(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 | 325.2.k.d.268.1 | yes | 16 | |
5.2 | odd | 4 | 325.2.f.d.307.1 | yes | 16 | ||
5.3 | odd | 4 | 325.2.f.d.307.8 | yes | 16 | ||
5.4 | even | 2 | inner | 325.2.k.d.268.8 | yes | 16 | |
13.5 | odd | 4 | 325.2.f.d.18.8 | yes | 16 | ||
65.18 | even | 4 | inner | 325.2.k.d.57.8 | yes | 16 | |
65.44 | odd | 4 | 325.2.f.d.18.1 | ✓ | 16 | ||
65.57 | even | 4 | inner | 325.2.k.d.57.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.f.d.18.1 | ✓ | 16 | 65.44 | odd | 4 | ||
325.2.f.d.18.8 | yes | 16 | 13.5 | odd | 4 | ||
325.2.f.d.307.1 | yes | 16 | 5.2 | odd | 4 | ||
325.2.f.d.307.8 | yes | 16 | 5.3 | odd | 4 | ||
325.2.k.d.57.1 | yes | 16 | 65.57 | even | 4 | inner | |
325.2.k.d.57.8 | yes | 16 | 65.18 | even | 4 | inner | |
325.2.k.d.268.1 | yes | 16 | 1.1 | even | 1 | trivial | |
325.2.k.d.268.8 | yes | 16 | 5.4 | even | 2 | inner |