Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (of order \(6\), degree \(2\), not 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.4 | ||
Root | \(1.35234 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.n.1849.4 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.486319 | − | 0.280776i | 0.183811 | − | 0.106124i | −0.405271 | − | 0.914197i | \(-0.632823\pi\) |
0.589082 | + | 0.808073i | \(0.299489\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.06155 | + | 3.57071i | −0.621582 | + | 1.07661i | 0.367610 | + | 0.929980i | \(0.380176\pi\) |
−0.989191 | + | 0.146631i | \(0.953157\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −2.21837 | + | 2.84233i | −0.615265 | + | 0.788320i | ||||
\(14\) | 0.561553 | 0.150081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.70469 | − | 1.56155i | 0.655983 | − | 0.378732i | −0.134761 | − | 0.990878i | \(-0.543027\pi\) |
0.790745 | + | 0.612146i | \(0.209693\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.280776 | + | 0.486319i | 0.0644145 | + | 0.111569i | 0.896434 | − | 0.443177i | \(-0.146149\pi\) |
−0.832020 | + | 0.554746i | \(0.812815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.561553 | −0.122541 | ||||||||
\(22\) | −3.57071 | + | 2.06155i | −0.761279 | + | 0.439525i | ||||
\(23\) | −4.05703 | − | 2.34233i | −0.845950 | − | 0.488409i | 0.0133324 | − | 0.999911i | \(-0.495756\pi\) |
−0.859282 | + | 0.511502i | \(0.829089\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.34233 | + | 1.35234i | −0.655485 | + | 0.265217i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.486319 | + | 0.280776i | 0.0919057 | + | 0.0530618i | ||||
\(29\) | 1.21922 | − | 2.11176i | 0.226404 | − | 0.392143i | −0.730336 | − | 0.683088i | \(-0.760636\pi\) |
0.956740 | + | 0.290945i | \(0.0939697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.68466 | −1.20060 | −0.600300 | − | 0.799775i | \(-0.704952\pi\) | ||||
−0.600300 | + | 0.799775i | \(0.704952\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 3.57071 | − | 2.06155i | 0.621582 | − | 0.358870i | ||||
\(34\) | 3.12311 | 0.535608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −3.57071 | − | 2.06155i | −0.587022 | − | 0.338917i | 0.176897 | − | 0.984229i | \(-0.443394\pi\) |
−0.763919 | + | 0.645312i | \(0.776727\pi\) | |||||||
\(38\) | 0.561553i | 0.0910959i | ||||||||
\(39\) | 3.34233 | − | 1.35234i | 0.535201 | − | 0.216548i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.12311 | + | 10.6055i | −0.956268 | + | 1.65631i | −0.224830 | + | 0.974398i | \(0.572183\pi\) |
−0.731438 | + | 0.681908i | \(0.761151\pi\) | |||||||
\(42\) | −0.486319 | − | 0.280776i | −0.0750407 | − | 0.0433247i | ||||
\(43\) | 0.379706 | − | 0.219224i | 0.0579047 | − | 0.0334313i | −0.470768 | − | 0.882257i | \(-0.656023\pi\) |
0.528673 | + | 0.848826i | \(0.322690\pi\) | |||||||
\(44\) | −4.12311 | −0.621582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34233 | − | 4.05703i | −0.345358 | − | 0.598177i | ||||
\(47\) | − | 7.00000i | − | 1.02105i | −0.859861 | − | 0.510527i | \(-0.829450\pi\) | ||
0.859861 | − | 0.510527i | \(-0.170550\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | −3.34233 | + | 5.78908i | −0.477476 | + | 0.827012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12311 | −0.437322 | ||||||||
\(52\) | −3.57071 | − | 0.500000i | −0.495169 | − | 0.0693375i | ||||
\(53\) | 8.56155i | 1.17602i | 0.808854 | + | 0.588010i | \(0.200088\pi\) | ||||
−0.808854 | + | 0.588010i | \(0.799912\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.280776 | + | 0.486319i | 0.0375203 | + | 0.0649871i | ||||
\(57\) | − | 0.561553i | − | 0.0743795i | ||||||
\(58\) | 2.11176 | − | 1.21922i | 0.277287 | − | 0.160092i | ||||
\(59\) | 3.21922 | + | 5.57586i | 0.419107 | + | 0.725915i | 0.995850 | − | 0.0910109i | \(-0.0290098\pi\) |
−0.576743 | + | 0.816926i | \(0.695676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | −5.78908 | − | 3.34233i | −0.735214 | − | 0.424476i | ||||
\(63\) | 0.486319 | + | 0.280776i | 0.0612704 | + | 0.0353745i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.12311 | 0.507519 | ||||||||
\(67\) | −1.94528 | − | 1.12311i | −0.237653 | − | 0.137209i | 0.376444 | − | 0.926439i | \(-0.377147\pi\) |
−0.614098 | + | 0.789230i | \(0.710480\pi\) | |||||||
\(68\) | 2.70469 | + | 1.56155i | 0.327992 | + | 0.189366i | ||||
\(69\) | 2.34233 | + | 4.05703i | 0.281983 | + | 0.488409i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.56155 | + | 11.3649i | 0.778713 | + | 1.34877i | 0.932684 | + | 0.360695i | \(0.117461\pi\) |
−0.153971 | + | 0.988075i | \(0.549206\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 9.36932i | 1.09660i | 0.836283 | + | 0.548298i | \(0.184724\pi\) | ||||
−0.836283 | + | 0.548298i | \(0.815276\pi\) | |||||||
\(74\) | −2.06155 | − | 3.57071i | −0.239651 | − | 0.415087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.280776 | + | 0.486319i | −0.0322073 | + | 0.0557846i | ||||
\(77\) | 2.31534i | 0.263858i | ||||||||
\(78\) | 3.57071 | + | 0.500000i | 0.404304 | + | 0.0566139i | ||||
\(79\) | −11.5616 | −1.30078 | −0.650388 | − | 0.759602i | \(-0.725394\pi\) | ||||
−0.650388 | + | 0.759602i | \(0.725394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −10.6055 | + | 6.12311i | −1.17118 | + | 0.676184i | ||||
\(83\) | − | 7.12311i | − | 0.781862i | −0.920420 | − | 0.390931i | \(-0.872153\pi\) | ||
0.920420 | − | 0.390931i | \(-0.127847\pi\) | |||||||
\(84\) | −0.280776 | − | 0.486319i | −0.0306352 | − | 0.0530618i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.438447 | 0.0472790 | ||||||||
\(87\) | −2.11176 | + | 1.21922i | −0.226404 | + | 0.130714i | ||||
\(88\) | −3.57071 | − | 2.06155i | −0.380639 | − | 0.219762i | ||||
\(89\) | −9.40388 | + | 16.2880i | −0.996810 | + | 1.72652i | −0.429281 | + | 0.903171i | \(0.641233\pi\) |
−0.567529 | + | 0.823354i | \(0.692100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.280776 | + | 2.00514i | −0.0294334 | + | 0.210196i | ||||
\(92\) | − | 4.68466i | − | 0.488409i | ||||||
\(93\) | 5.78908 | + | 3.34233i | 0.600300 | + | 0.346583i | ||||
\(94\) | 3.50000 | − | 6.06218i | 0.360997 | − | 0.625266i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.16879 | − | 3.56155i | 0.626346 | − | 0.361621i | −0.152990 | − | 0.988228i | \(-0.548890\pi\) |
0.779335 | + | 0.626607i | \(0.215557\pi\) | |||||||
\(98\) | −5.78908 | + | 3.34233i | −0.584786 | + | 0.337626i | ||||
\(99\) | −4.12311 | −0.414388 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.43845 | − | 7.68762i | 0.441642 | − | 0.764946i | −0.556170 | − | 0.831069i | \(-0.687729\pi\) |
0.997812 | + | 0.0661225i | \(0.0210628\pi\) | |||||||
\(102\) | −2.70469 | − | 1.56155i | −0.267804 | − | 0.154617i | ||||
\(103\) | 4.56155i | 0.449463i | 0.974421 | + | 0.224732i | \(0.0721505\pi\) | ||||
−0.974421 | + | 0.224732i | \(0.927849\pi\) | |||||||
\(104\) | −2.84233 | − | 2.21837i | −0.278713 | − | 0.217529i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.28078 | + | 7.41452i | −0.415786 | + | 0.720162i | ||||
\(107\) | 1.73205 | + | 1.00000i | 0.167444 | + | 0.0966736i | 0.581380 | − | 0.813632i | \(-0.302513\pi\) |
−0.413936 | + | 0.910306i | \(0.635846\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 3.75379 | 0.359548 | 0.179774 | − | 0.983708i | \(-0.442463\pi\) | ||||
0.179774 | + | 0.983708i | \(0.442463\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.06155 | + | 3.57071i | 0.195674 | + | 0.338917i | ||||
\(112\) | 0.561553i | 0.0530618i | ||||||||
\(113\) | 7.52113 | − | 4.34233i | 0.707529 | − | 0.408492i | −0.102617 | − | 0.994721i | \(-0.532721\pi\) |
0.810145 | + | 0.586229i | \(0.199388\pi\) | |||||||
\(114\) | 0.280776 | − | 0.486319i | 0.0262971 | − | 0.0455479i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.43845 | 0.226404 | ||||||||
\(117\) | −3.57071 | − | 0.500000i | −0.330113 | − | 0.0462250i | ||||
\(118\) | 6.43845i | 0.592707i | ||||||||
\(119\) | 0.876894 | − | 1.51883i | 0.0803848 | − | 0.139231i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | ||||
\(122\) | − | 6.00000i | − | 0.543214i | ||||||
\(123\) | 10.6055 | − | 6.12311i | 0.956268 | − | 0.552102i | ||||
\(124\) | −3.34233 | − | 5.78908i | −0.300150 | − | 0.519875i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.280776 | + | 0.486319i | 0.0250136 | + | 0.0433247i | ||||
\(127\) | −7.41452 | − | 4.28078i | −0.657932 | − | 0.379857i | 0.133556 | − | 0.991041i | \(-0.457360\pi\) |
−0.791489 | + | 0.611184i | \(0.790694\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −0.438447 | −0.0386031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12311 | −0.185497 | −0.0927483 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927483 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(132\) | 3.57071 | + | 2.06155i | 0.310791 | + | 0.179435i | ||||
\(133\) | 0.273094 | + | 0.157671i | 0.0236802 | + | 0.0136718i | ||||
\(134\) | −1.12311 | − | 1.94528i | −0.0970215 | − | 0.168046i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.56155 | + | 2.70469i | 0.133902 | + | 0.231925i | ||||
\(137\) | −10.2258 | + | 5.90388i | −0.873651 | + | 0.504403i | −0.868560 | − | 0.495584i | \(-0.834954\pi\) |
−0.00509126 | + | 0.999987i | \(0.501621\pi\) | |||||||
\(138\) | 4.68466i | 0.398785i | ||||||||
\(139\) | 6.28078 | + | 10.8786i | 0.532729 | + | 0.922713i | 0.999270 | + | 0.0382133i | \(0.0121666\pi\) |
−0.466541 | + | 0.884500i | \(0.654500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.50000 | + | 6.06218i | −0.294753 | + | 0.510527i | ||||
\(142\) | 13.1231i | 1.10127i | ||||||||
\(143\) | −5.57586 | − | 13.7808i | −0.466277 | − | 1.15241i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.68466 | + | 8.11407i | −0.387705 | + | 0.671525i | ||||
\(147\) | 5.78908 | − | 3.34233i | 0.477476 | − | 0.275671i | ||||
\(148\) | − | 4.12311i | − | 0.338917i | ||||||
\(149\) | −1.09612 | − | 1.89853i | −0.0897975 | − | 0.155534i | 0.817628 | − | 0.575747i | \(-0.195289\pi\) |
−0.907425 | + | 0.420213i | \(0.861955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3693 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715051\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715051\pi\) | |||||||
\(152\) | −0.486319 | + | 0.280776i | −0.0394457 | + | 0.0227740i | ||||
\(153\) | 2.70469 | + | 1.56155i | 0.218661 | + | 0.126244i | ||||
\(154\) | −1.15767 | + | 2.00514i | −0.0932878 | + | 0.161579i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.84233 | + | 2.21837i | 0.227568 | + | 0.177612i | ||||
\(157\) | − | 13.8769i | − | 1.10750i | −0.832684 | − | 0.553748i | \(-0.813197\pi\) | ||
0.832684 | − | 0.553748i | \(-0.186803\pi\) | |||||||
\(158\) | −10.0126 | − | 5.78078i | −0.796560 | − | 0.459894i | ||||
\(159\) | 4.28078 | − | 7.41452i | 0.339488 | − | 0.588010i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.63068 | −0.207327 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −12.5041 | + | 7.21922i | −0.979394 | + | 0.565453i | −0.902087 | − | 0.431554i | \(-0.857965\pi\) |
−0.0773067 | + | 0.997007i | \(0.524632\pi\) | |||||||
\(164\) | −12.2462 | −0.956268 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.56155 | − | 6.16879i | 0.276430 | − | 0.478791i | ||||
\(167\) | 3.78394 | + | 2.18466i | 0.292810 | + | 0.169054i | 0.639208 | − | 0.769034i | \(-0.279262\pi\) |
−0.346398 | + | 0.938087i | \(0.612595\pi\) | |||||||
\(168\) | − | 0.561553i | − | 0.0433247i | ||||||
\(169\) | −3.15767 | − | 12.6107i | −0.242898 | − | 0.970052i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.280776 | + | 0.486319i | −0.0214715 | + | 0.0371897i | ||||
\(172\) | 0.379706 | + | 0.219224i | 0.0289523 | + | 0.0167156i | ||||
\(173\) | 17.4739 | − | 10.0885i | 1.32851 | − | 0.767018i | 0.343444 | − | 0.939173i | \(-0.388407\pi\) |
0.985070 | + | 0.172156i | \(0.0550732\pi\) | |||||||
\(174\) | −2.43845 | −0.184858 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.06155 | − | 3.57071i | −0.155395 | − | 0.269153i | ||||
\(177\) | − | 6.43845i | − | 0.483943i | ||||||
\(178\) | −16.2880 | + | 9.40388i | −1.22084 | + | 0.704851i | ||||
\(179\) | −6.34233 | + | 10.9852i | −0.474048 | + | 0.821075i | −0.999559 | − | 0.0297120i | \(-0.990541\pi\) |
0.525511 | + | 0.850787i | \(0.323874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.87689 | 0.213838 | 0.106919 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106919 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(182\) | −1.24573 | + | 1.59612i | −0.0923398 | + | 0.118312i | ||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | 2.34233 | − | 4.05703i | 0.172679 | − | 0.299088i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.34233 | + | 5.78908i | 0.245071 | + | 0.424476i | ||||
\(187\) | 12.8769i | 0.941652i | ||||||||
\(188\) | 6.06218 | − | 3.50000i | 0.442130 | − | 0.255264i | ||||
\(189\) | −0.280776 | − | 0.486319i | −0.0204235 | − | 0.0353745i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.43845 | − | 9.41967i | −0.393512 | − | 0.681583i | 0.599398 | − | 0.800451i | \(-0.295407\pi\) |
−0.992910 | + | 0.118868i | \(0.962073\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 7.12311 | 0.511409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 11.0918 | + | 6.40388i | 0.790262 | + | 0.456258i | 0.840055 | − | 0.542502i | \(-0.182523\pi\) |
−0.0497931 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(198\) | −3.57071 | − | 2.06155i | −0.253760 | − | 0.146508i | ||||
\(199\) | 1.43845 | + | 2.49146i | 0.101969 | + | 0.176615i | 0.912496 | − | 0.409086i | \(-0.134152\pi\) |
−0.810527 | + | 0.585701i | \(0.800819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.12311 | + | 1.94528i | 0.0792178 | + | 0.137209i | ||||
\(202\) | 7.68762 | − | 4.43845i | 0.540899 | − | 0.312288i | ||||
\(203\) | − | 1.36932i | − | 0.0961072i | ||||||
\(204\) | −1.56155 | − | 2.70469i | −0.109331 | − | 0.189366i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.28078 | + | 3.95042i | −0.158909 | + | 0.275239i | ||||
\(207\) | − | 4.68466i | − | 0.325606i | ||||||
\(208\) | −1.35234 | − | 3.34233i | −0.0937682 | − | 0.231749i | ||||
\(209\) | −2.31534 | −0.160156 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9654 | − | 18.9927i | 0.754892 | − | 1.30751i | −0.190536 | − | 0.981680i | \(-0.561023\pi\) |
0.945428 | − | 0.325831i | \(-0.105644\pi\) | |||||||
\(212\) | −7.41452 | + | 4.28078i | −0.509231 | + | 0.294005i | ||||
\(213\) | − | 13.1231i | − | 0.899180i | ||||||
\(214\) | 1.00000 | + | 1.73205i | 0.0683586 | + | 0.118401i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.25088 | + | 1.87689i | −0.220684 | + | 0.127412i | ||||
\(218\) | 3.25088 | + | 1.87689i | 0.220177 | + | 0.127119i | ||||
\(219\) | 4.68466 | − | 8.11407i | 0.316560 | − | 0.548298i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56155 | + | 11.1517i | −0.105041 | + | 0.750146i | ||||
\(222\) | 4.12311i | 0.276725i | ||||||||
\(223\) | −23.6427 | − | 13.6501i | −1.58323 | − | 0.914078i | −0.994384 | − | 0.105832i | \(-0.966249\pi\) |
−0.588845 | − | 0.808246i | \(-0.700417\pi\) | |||||||
\(224\) | −0.280776 | + | 0.486319i | −0.0187602 | + | 0.0324936i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.68466 | 0.577695 | ||||||||
\(227\) | 17.3205 | − | 10.0000i | 1.14960 | − | 0.663723i | 0.200812 | − | 0.979630i | \(-0.435642\pi\) |
0.948790 | + | 0.315906i | \(0.102309\pi\) | |||||||
\(228\) | 0.486319 | − | 0.280776i | 0.0322073 | − | 0.0185949i | ||||
\(229\) | 24.2462 | 1.60223 | 0.801117 | − | 0.598507i | \(-0.204239\pi\) | ||||
0.801117 | + | 0.598507i | \(0.204239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.15767 | − | 2.00514i | 0.0761691 | − | 0.131929i | ||||
\(232\) | 2.11176 | + | 1.21922i | 0.138644 | + | 0.0800460i | ||||
\(233\) | − | 5.31534i | − | 0.348220i | −0.984726 | − | 0.174110i | \(-0.944295\pi\) | ||
0.984726 | − | 0.174110i | \(-0.0557048\pi\) | |||||||
\(234\) | −2.84233 | − | 2.21837i | −0.185809 | − | 0.145019i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.21922 | + | 5.57586i | −0.209554 | + | 0.362957i | ||||
\(237\) | 10.0126 | + | 5.78078i | 0.650388 | + | 0.375502i | ||||
\(238\) | 1.51883 | − | 0.876894i | 0.0984508 | − | 0.0568406i | ||||
\(239\) | 11.3693 | 0.735420 | 0.367710 | − | 0.929941i | \(-0.380142\pi\) | ||||
0.367710 | + | 0.929941i | \(0.380142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0616 | + | 24.3553i | 0.905784 | + | 1.56886i | 0.819861 | + | 0.572563i | \(0.194051\pi\) |
0.0859232 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(242\) | − | 6.00000i | − | 0.385695i | ||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.00000 | − | 5.19615i | 0.192055 | − | 0.332650i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.2462 | 0.780790 | ||||||||
\(247\) | −2.00514 | − | 0.280776i | −0.127584 | − | 0.0178654i | ||||
\(248\) | − | 6.68466i | − | 0.424476i | ||||||
\(249\) | −3.56155 | + | 6.16879i | −0.225704 | + | 0.390931i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.06155 | + | 7.03482i | 0.256363 | + | 0.444034i | 0.965265 | − | 0.261273i | \(-0.0841424\pi\) |
−0.708902 | + | 0.705307i | \(0.750809\pi\) | |||||||
\(252\) | 0.561553i | 0.0353745i | ||||||||
\(253\) | 16.7276 | − | 9.65767i | 1.05165 | − | 0.607173i | ||||
\(254\) | −4.28078 | − | 7.41452i | −0.268600 | − | 0.465229i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.81645 | − | 2.78078i | −0.300442 | − | 0.173460i | 0.342200 | − | 0.939627i | \(-0.388828\pi\) |
−0.642641 | + | 0.766167i | \(0.722161\pi\) | |||||||
\(258\) | −0.379706 | − | 0.219224i | −0.0236395 | − | 0.0136483i | ||||
\(259\) | −2.31534 | −0.143868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.43845 | 0.150936 | ||||||||
\(262\) | −1.83866 | − | 1.06155i | −0.113593 | − | 0.0655830i | ||||
\(263\) | 11.2583 | + | 6.50000i | 0.694218 | + | 0.400807i | 0.805190 | − | 0.593016i | \(-0.202063\pi\) |
−0.110972 | + | 0.993824i | \(0.535396\pi\) | |||||||
\(264\) | 2.06155 | + | 3.57071i | 0.126880 | + | 0.219762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.157671 | + | 0.273094i | 0.00966742 | + | 0.0167445i | ||||
\(267\) | 16.2880 | − | 9.40388i | 0.996810 | − | 0.575508i | ||||
\(268\) | − | 2.24621i | − | 0.137209i | ||||||
\(269\) | 10.6847 | + | 18.5064i | 0.651455 | + | 1.12835i | 0.982770 | + | 0.184833i | \(0.0591745\pi\) |
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.58854 | − | 11.4117i | 0.400225 | − | 0.693211i | −0.593528 | − | 0.804814i | \(-0.702265\pi\) |
0.993753 | + | 0.111603i | \(0.0355985\pi\) | |||||||
\(272\) | 3.12311i | 0.189366i | ||||||||
\(273\) | 1.24573 | − | 1.59612i | 0.0753951 | − | 0.0966015i | ||||
\(274\) | −11.8078 | −0.713333 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.34233 | + | 4.05703i | −0.140992 | + | 0.244205i | ||||
\(277\) | 0.866025 | − | 0.500000i | 0.0520344 | − | 0.0300421i | −0.473757 | − | 0.880656i | \(-0.657103\pi\) |
0.525792 | + | 0.850613i | \(0.323769\pi\) | |||||||
\(278\) | 12.5616i | 0.753392i | ||||||||
\(279\) | −3.34233 | − | 5.78908i | −0.200100 | − | 0.346583i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2462 | 0.969168 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(282\) | −6.06218 | + | 3.50000i | −0.360997 | + | 0.208422i | ||||
\(283\) | −13.4767 | − | 7.78078i | −0.801107 | − | 0.462519i | 0.0427513 | − | 0.999086i | \(-0.486388\pi\) |
−0.843858 | + | 0.536567i | \(0.819721\pi\) | |||||||
\(284\) | −6.56155 | + | 11.3649i | −0.389357 | + | 0.674385i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.06155 | − | 14.7224i | 0.121902 | − | 0.870556i | ||||
\(287\) | 6.87689i | 0.405930i | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −3.62311 | + | 6.27540i | −0.213124 | + | 0.369141i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.12311 | −0.417564 | ||||||||
\(292\) | −8.11407 | + | 4.68466i | −0.474840 | + | 0.274149i | ||||
\(293\) | 3.40423 | − | 1.96543i | 0.198877 | − | 0.114822i | −0.397254 | − | 0.917709i | \(-0.630037\pi\) |
0.596132 | + | 0.802887i | \(0.296704\pi\) | |||||||
\(294\) | 6.68466 | 0.389857 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.06155 | − | 3.57071i | 0.119825 | − | 0.207544i | ||||
\(297\) | 3.57071 | + | 2.06155i | 0.207194 | + | 0.119623i | ||||
\(298\) | − | 2.19224i | − | 0.126993i | ||||||
\(299\) | 15.6577 | − | 6.33527i | 0.905506 | − | 0.366378i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.123106 | − | 0.213225i | 0.00709569 | − | 0.0122901i | ||||
\(302\) | −13.3102 | − | 7.68466i | −0.765917 | − | 0.442202i | ||||
\(303\) | −7.68762 | + | 4.43845i | −0.441642 | + | 0.254982i | ||||
\(304\) | −0.561553 | −0.0322073 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56155 | + | 2.70469i | 0.0892680 | + | 0.154617i | ||||
\(307\) | − | 25.6155i | − | 1.46196i | −0.682401 | − | 0.730978i | \(-0.739064\pi\) | ||
0.682401 | − | 0.730978i | \(-0.260936\pi\) | |||||||
\(308\) | −2.00514 | + | 1.15767i | −0.114254 | + | 0.0659644i | ||||
\(309\) | 2.28078 | − | 3.95042i | 0.129749 | − | 0.224732i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7386 | 1.74303 | 0.871514 | − | 0.490371i | \(-0.163139\pi\) | ||||
0.871514 | + | 0.490371i | \(0.163139\pi\) | |||||||
\(312\) | 1.35234 | + | 3.34233i | 0.0765614 | + | 0.189222i | ||||
\(313\) | 31.3693i | 1.77310i | 0.462634 | + | 0.886549i | \(0.346904\pi\) | ||||
−0.462634 | + | 0.886549i | \(0.653096\pi\) | |||||||
\(314\) | 6.93845 | − | 12.0177i | 0.391559 | − | 0.678200i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.78078 | − | 10.0126i | −0.325194 | − | 0.563253i | ||||
\(317\) | 24.8078i | 1.39334i | 0.717390 | + | 0.696671i | \(0.245336\pi\) | ||||
−0.717390 | + | 0.696671i | \(0.754664\pi\) | |||||||
\(318\) | 7.41452 | − | 4.28078i | 0.415786 | − | 0.240054i | ||||
\(319\) | 5.02699 | + | 8.70700i | 0.281457 | + | 0.487498i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | − | 1.73205i | −0.0558146 | − | 0.0966736i | ||||
\(322\) | −2.27824 | − | 1.31534i | −0.126961 | − | 0.0733011i | ||||
\(323\) | 1.51883 | + | 0.876894i | 0.0845097 | + | 0.0487917i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.4384 | −0.799672 | ||||||||
\(327\) | −3.25088 | − | 1.87689i | −0.179774 | − | 0.103792i | ||||
\(328\) | −10.6055 | − | 6.12311i | −0.585592 | − | 0.338092i | ||||
\(329\) | −1.96543 | − | 3.40423i | −0.108358 | − | 0.187681i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3693 | − | 26.6204i | −0.844774 | − | 1.46319i | −0.885817 | − | 0.464034i | \(-0.846401\pi\) |
0.0410432 | − | 0.999157i | \(-0.486932\pi\) | |||||||
\(332\) | 6.16879 | − | 3.56155i | 0.338556 | − | 0.195466i | ||||
\(333\) | − | 4.12311i | − | 0.225945i | ||||||
\(334\) | 2.18466 | + | 3.78394i | 0.119539 | + | 0.207048i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.280776 | − | 0.486319i | 0.0153176 | − | 0.0265309i | ||||
\(337\) | 6.00000i | 0.326841i | 0.986557 | + | 0.163420i | \(0.0522527\pi\) | ||||
−0.986557 | + | 0.163420i | \(0.947747\pi\) | |||||||
\(338\) | 3.57071 | − | 12.5000i | 0.194221 | − | 0.679910i | ||||
\(339\) | −8.68466 | −0.471686 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.7808 | − | 23.8690i | 0.746271 | − | 1.29258i | ||||
\(342\) | −0.486319 | + | 0.280776i | −0.0262971 | + | 0.0151826i | ||||
\(343\) | 7.68466i | 0.414933i | ||||||||
\(344\) | 0.219224 | + | 0.379706i | 0.0118197 | + | 0.0204724i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1771 | 1.08473 | ||||||||
\(347\) | −0.759413 | + | 0.438447i | −0.0407674 | + | 0.0235371i | −0.520245 | − | 0.854017i | \(-0.674159\pi\) |
0.479478 | + | 0.877554i | \(0.340826\pi\) | |||||||
\(348\) | −2.11176 | − | 1.21922i | −0.113202 | − | 0.0653572i | ||||
\(349\) | 4.24621 | − | 7.35465i | 0.227294 | − | 0.393686i | −0.729711 | − | 0.683756i | \(-0.760345\pi\) |
0.957005 | + | 0.290070i | \(0.0936787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.84233 | + | 2.21837i | 0.151712 | + | 0.118408i | ||||
\(352\) | − | 4.12311i | − | 0.219762i | ||||||
\(353\) | 22.3969 | + | 12.9309i | 1.19207 | + | 0.688241i | 0.958775 | − | 0.284166i | \(-0.0917166\pi\) |
0.233293 | + | 0.972407i | \(0.425050\pi\) | |||||||
\(354\) | 3.21922 | − | 5.57586i | 0.171100 | − | 0.296354i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.8078 | −0.996810 | ||||||||
\(357\) | −1.51883 | + | 0.876894i | −0.0803848 | + | 0.0464102i | ||||
\(358\) | −10.9852 | + | 6.34233i | −0.580588 | + | 0.335203i | ||||
\(359\) | −13.1231 | −0.692611 | −0.346306 | − | 0.938122i | \(-0.612564\pi\) | ||||
−0.346306 | + | 0.938122i | \(0.612564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.34233 | − | 16.1814i | 0.491702 | − | 0.851652i | ||||
\(362\) | 2.49146 | + | 1.43845i | 0.130948 | + | 0.0756031i | ||||
\(363\) | 6.00000i | 0.314918i | ||||||||
\(364\) | −1.87689 | + | 0.759413i | −0.0983760 | + | 0.0398040i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | 10.8188 | + | 6.24621i | 0.564734 | + | 0.326050i | 0.755044 | − | 0.655675i | \(-0.227616\pi\) |
−0.190309 | + | 0.981724i | \(0.560949\pi\) | |||||||
\(368\) | 4.05703 | − | 2.34233i | 0.211487 | − | 0.122102i | ||||
\(369\) | −12.2462 | −0.637512 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.40388 | + | 4.16365i | 0.124803 | + | 0.216166i | ||||
\(372\) | 6.68466i | 0.346583i | ||||||||
\(373\) | −22.3502 | + | 12.9039i | −1.15725 | + | 0.668138i | −0.950643 | − | 0.310287i | \(-0.899575\pi\) |
−0.206605 | + | 0.978424i | \(0.566242\pi\) | |||||||
\(374\) | −6.43845 | + | 11.1517i | −0.332924 | + | 0.576642i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 3.29762 | + | 8.15009i | 0.169836 | + | 0.419751i | ||||
\(378\) | − | 0.561553i | − | 0.0288832i | ||||||
\(379\) | −8.84233 | + | 15.3154i | −0.454200 | + | 0.786697i | −0.998642 | − | 0.0521012i | \(-0.983408\pi\) |
0.544442 | + | 0.838799i | \(0.316741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.28078 | + | 7.41452i | 0.219311 | + | 0.379857i | ||||
\(382\) | − | 10.8769i | − | 0.556510i | ||||||
\(383\) | 0.166481 | − | 0.0961180i | 0.00850679 | − | 0.00491140i | −0.495741 | − | 0.868471i | \(-0.665103\pi\) |
0.504247 | + | 0.863559i | \(0.331770\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.379706 | + | 0.219224i | 0.0193016 | + | 0.0111438i | ||||
\(388\) | 6.16879 | + | 3.56155i | 0.313173 | + | 0.180810i | ||||
\(389\) | 18.0540 | 0.915373 | 0.457686 | − | 0.889114i | \(-0.348678\pi\) | ||||
0.457686 | + | 0.889114i | \(0.348678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6307 | −0.739905 | ||||||||
\(392\) | −5.78908 | − | 3.34233i | −0.292393 | − | 0.168813i | ||||
\(393\) | 1.83866 | + | 1.06155i | 0.0927483 | + | 0.0535483i | ||||
\(394\) | 6.40388 | + | 11.0918i | 0.322623 | + | 0.558799i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.06155 | − | 3.57071i | −0.103597 | − | 0.179435i | ||||
\(397\) | 17.4271 | − | 10.0616i | 0.874642 | − | 0.504975i | 0.00575403 | − | 0.999983i | \(-0.498168\pi\) |
0.868888 | + | 0.495009i | \(0.164835\pi\) | |||||||
\(398\) | 2.87689i | 0.144206i | ||||||||
\(399\) | −0.157671 | − | 0.273094i | −0.00789341 | − | 0.0136718i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.157671 | + | 0.273094i | −0.00787370 | + | 0.0136377i | −0.869935 | − | 0.493166i | \(-0.835840\pi\) |
0.862062 | + | 0.506803i | \(0.169173\pi\) | |||||||
\(402\) | 2.24621i | 0.112031i | ||||||||
\(403\) | 14.8290 | − | 19.0000i | 0.738687 | − | 0.946457i | ||||
\(404\) | 8.87689 | 0.441642 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.684658 | − | 1.18586i | 0.0339790 | − | 0.0588534i | ||||
\(407\) | 14.7224 | − | 8.50000i | 0.729764 | − | 0.421329i | ||||
\(408\) | − | 3.12311i | − | 0.154617i | ||||||
\(409\) | −9.40388 | − | 16.2880i | −0.464992 | − | 0.805390i | 0.534209 | − | 0.845352i | \(-0.320609\pi\) |
−0.999201 | + | 0.0399625i | \(0.987276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8078 | 0.582434 | ||||||||
\(412\) | −3.95042 | + | 2.28078i | −0.194623 | + | 0.112366i | ||||
\(413\) | 3.13114 | + | 1.80776i | 0.154073 | + | 0.0889543i | ||||
\(414\) | 2.34233 | − | 4.05703i | 0.115119 | − | 0.199392i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 3.57071i | 0.0245145 | − | 0.175069i | ||||
\(417\) | − | 12.5616i | − | 0.615142i | ||||||
\(418\) | −2.00514 | − | 1.15767i | −0.0980748 | − | 0.0566235i | ||||
\(419\) | 16.2462 | − | 28.1393i | 0.793679 | − | 1.37469i | −0.129995 | − | 0.991515i | \(-0.541496\pi\) |
0.923674 | − | 0.383178i | \(-0.125171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.4924 | −1.58358 | −0.791792 | − | 0.610791i | \(-0.790852\pi\) | ||||
−0.791792 | + | 0.610791i | \(0.790852\pi\) | |||||||
\(422\) | 18.9927 | − | 10.9654i | 0.924550 | − | 0.533789i | ||||
\(423\) | 6.06218 | − | 3.50000i | 0.294753 | − | 0.170176i | ||||
\(424\) | −8.56155 | −0.415786 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.56155 | − | 11.3649i | 0.317908 | − | 0.550633i | ||||
\(427\) | −2.91791 | − | 1.68466i | −0.141208 | − | 0.0815263i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | −2.06155 | + | 14.7224i | −0.0995327 | + | 0.710806i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3693 | − | 19.6922i | 0.547641 | − | 0.948542i | −0.450795 | − | 0.892628i | \(-0.648859\pi\) |
0.998436 | − | 0.0559140i | \(-0.0178073\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −16.2281 | + | 9.36932i | −0.779874 | + | 0.450261i | −0.836386 | − | 0.548141i | \(-0.815336\pi\) |
0.0565114 | + | 0.998402i | \(0.482002\pi\) | |||||||
\(434\) | −3.75379 | −0.180188 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.87689 | + | 3.25088i | 0.0898869 | + | 0.155689i | ||||
\(437\) | − | 2.63068i | − | 0.125843i | ||||||
\(438\) | 8.11407 | − | 4.68466i | 0.387705 | − | 0.223842i | ||||
\(439\) | 12.5616 | − | 21.7572i | 0.599530 | − | 1.03842i | −0.393360 | − | 0.919384i | \(-0.628687\pi\) |
0.992890 | − | 0.119032i | \(-0.0379792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | −6.92820 | + | 8.87689i | −0.329541 | + | 0.422231i | ||||
\(443\) | − | 13.1231i | − | 0.623498i | −0.950165 | − | 0.311749i | \(-0.899085\pi\) | ||
0.950165 | − | 0.311749i | \(-0.100915\pi\) | |||||||
\(444\) | −2.06155 | + | 3.57071i | −0.0978370 | + | 0.169459i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.6501 | − | 23.6427i | −0.646351 | − | 1.11951i | ||||
\(447\) | 2.19224i | 0.103689i | ||||||||
\(448\) | −0.486319 | + | 0.280776i | −0.0229764 | + | 0.0132654i | ||||
\(449\) | −10.0885 | − | 17.4739i | −0.476108 | − | 0.824643i | 0.523518 | − | 0.852015i | \(-0.324619\pi\) |
−0.999625 | + | 0.0273722i | \(0.991286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.2462 | − | 43.7277i | −1.18880 | − | 2.05906i | ||||
\(452\) | 7.52113 | + | 4.34233i | 0.353764 | + | 0.204246i | ||||
\(453\) | 13.3102 | + | 7.68466i | 0.625369 | + | 0.361057i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.561553 | 0.0262971 | ||||||||
\(457\) | 17.5337 | + | 10.1231i | 0.820193 | + | 0.473539i | 0.850483 | − | 0.526002i | \(-0.176310\pi\) |
−0.0302897 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(458\) | 20.9978 | + | 12.1231i | 0.981164 | + | 0.566476i | ||||
\(459\) | −1.56155 | − | 2.70469i | −0.0728870 | − | 0.126244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0270 | + | 26.0275i | 0.699877 | + | 1.21222i | 0.968509 | + | 0.248979i | \(0.0800950\pi\) |
−0.268632 | + | 0.963243i | \(0.586572\pi\) | |||||||
\(462\) | 2.00514 | − | 1.15767i | 0.0932878 | − | 0.0538597i | ||||
\(463\) | − | 7.61553i | − | 0.353924i | −0.984218 | − | 0.176962i | \(-0.943373\pi\) | ||
0.984218 | − | 0.176962i | \(-0.0566269\pi\) | |||||||
\(464\) | 1.21922 | + | 2.11176i | 0.0566010 | + | 0.0980359i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.65767 | − | 4.60322i | 0.123114 | − | 0.213240i | ||||
\(467\) | 17.8617i | 0.826543i | 0.910608 | + | 0.413271i | \(0.135614\pi\) | ||||
−0.910608 | + | 0.413271i | \(0.864386\pi\) | |||||||
\(468\) | −1.35234 | − | 3.34233i | −0.0625121 | − | 0.154499i | ||||
\(469\) | −1.26137 | −0.0582445 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.93845 | + | 12.0177i | −0.319707 | + | 0.553748i | ||||
\(472\) | −5.57586 | + | 3.21922i | −0.256650 | + | 0.148177i | ||||
\(473\) | 1.80776i | 0.0831211i | ||||||||
\(474\) | 5.78078 | + | 10.0126i | 0.265520 | + | 0.459894i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.75379 | 0.0803848 | ||||||||
\(477\) | −7.41452 | + | 4.28078i | −0.339488 | + | 0.196003i | ||||
\(478\) | 9.84612 | + | 5.68466i | 0.450351 | + | 0.260010i | ||||
\(479\) | −19.1231 | + | 33.1222i | −0.873757 | + | 1.51339i | −0.0156760 | + | 0.999877i | \(0.504990\pi\) |
−0.858081 | + | 0.513514i | \(0.828343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7808 | − | 5.57586i | 0.628349 | − | 0.254237i | ||||
\(482\) | 28.1231i | 1.28097i | ||||||||
\(483\) | 2.27824 | + | 1.31534i | 0.103663 | + | 0.0598501i | ||||
\(484\) | 3.00000 | − | 5.19615i | 0.136364 | − | 0.236189i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −11.3051 | + | 6.52699i | −0.512282 | + | 0.295766i | −0.733771 | − | 0.679397i | \(-0.762242\pi\) |
0.221489 | + | 0.975163i | \(0.428908\pi\) | |||||||
\(488\) | 5.19615 | − | 3.00000i | 0.235219 | − | 0.135804i | ||||
\(489\) | 14.4384 | 0.652929 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.71922 | − | 15.1021i | 0.393493 | − | 0.681550i | −0.599415 | − | 0.800439i | \(-0.704600\pi\) |
0.992908 | + | 0.118889i | \(0.0379332\pi\) | |||||||
\(492\) | 10.6055 | + | 6.12311i | 0.478134 | + | 0.276051i | ||||
\(493\) | − | 7.61553i | − | 0.342986i | ||||||
\(494\) | −1.59612 | − | 1.24573i | −0.0718127 | − | 0.0560481i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.34233 | − | 5.78908i | 0.150075 | − | 0.259938i | ||||
\(497\) | 6.38202 | + | 3.68466i | 0.286273 | + | 0.165280i | ||||
\(498\) | −6.16879 | + | 3.56155i | −0.276430 | + | 0.159597i | ||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.18466 | − | 3.78394i | −0.0976033 | − | 0.169054i | ||||
\(502\) | 8.12311i | 0.362552i | ||||||||
\(503\) | −37.2858 | + | 21.5270i | −1.66249 | + | 0.959841i | −0.690974 | + | 0.722879i | \(0.742818\pi\) |
−0.971519 | + | 0.236962i | \(0.923848\pi\) | |||||||
\(504\) | −0.280776 | + | 0.486319i | −0.0125068 | + | 0.0216624i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19.3153 | 0.858672 | ||||||||
\(507\) | −3.57071 | + | 12.5000i | −0.158581 | + | 0.555144i | ||||
\(508\) | − | 8.56155i | − | 0.379857i | ||||||
\(509\) | 20.2732 | − | 35.1142i | 0.898594 | − | 1.55641i | 0.0693009 | − | 0.997596i | \(-0.477923\pi\) |
0.829293 | − | 0.558814i | \(-0.188744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.63068 | + | 4.55648i | 0.116375 | + | 0.201567i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0.486319 | − | 0.280776i | 0.0214715 | − | 0.0123966i | ||||
\(514\) | −2.78078 | − | 4.81645i | −0.122655 | − | 0.212444i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.219224 | − | 0.379706i | −0.00965078 | − | 0.0167156i | ||||
\(517\) | 24.9950 | + | 14.4309i | 1.09928 | + | 0.634669i | ||||
\(518\) | −2.00514 | − | 1.15767i | −0.0881010 | − | 0.0508651i | ||||
\(519\) | −20.1771 | −0.885676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.31534 | −0.276680 | −0.138340 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138340 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(522\) | 2.11176 | + | 1.21922i | 0.0924291 | + | 0.0533640i | ||||
\(523\) | 25.8143 | + | 14.9039i | 1.12878 | + | 0.651701i | 0.943628 | − | 0.331009i | \(-0.107389\pi\) |
0.185152 | + | 0.982710i | \(0.440722\pi\) | |||||||
\(524\) | −1.06155 | − | 1.83866i | −0.0463741 | − | 0.0803224i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.50000 | + | 11.2583i | 0.283413 | + | 0.490887i | ||||
\(527\) | −18.0799 | + | 10.4384i | −0.787574 | + | 0.454706i | ||||
\(528\) | 4.12311i | 0.179435i | ||||||||
\(529\) | −0.526988 | − | 0.912769i | −0.0229125 | − | 0.0396856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.21922 | + | 5.57586i | −0.139702 | + | 0.241972i | ||||
\(532\) | 0.315342i | 0.0136718i | ||||||||
\(533\) | −16.5611 | − | 40.9309i | −0.717341 | − | 1.77291i | ||||
\(534\) | 18.8078 | 0.813892 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.12311 | − | 1.94528i | 0.0485108 | − | 0.0840231i | ||||
\(537\) | 10.9852 | − | 6.34233i | 0.474048 | − | 0.273692i | ||||
\(538\) | 21.3693i | 0.921297i | ||||||||
\(539\) | −13.7808 | − | 23.8690i | −0.593580 | − | 1.02811i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3693 | −1.17670 | −0.588349 | − | 0.808607i | \(-0.700222\pi\) | ||||
−0.588349 | + | 0.808607i | \(0.700222\pi\) | |||||||
\(542\) | 11.4117 | − | 6.58854i | 0.490174 | − | 0.283002i | ||||
\(543\) | −2.49146 | − | 1.43845i | −0.106919 | − | 0.0617297i | ||||
\(544\) | −1.56155 | + | 2.70469i | −0.0669510 | + | 0.115963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.87689 | − | 0.759413i | 0.0803237 | − | 0.0324999i | ||||
\(547\) | 5.61553i | 0.240103i | 0.992768 | + | 0.120051i | \(0.0383059\pi\) | ||||
−0.992768 | + | 0.120051i | \(0.961694\pi\) | |||||||
\(548\) | −10.2258 | − | 5.90388i | −0.436826 | − | 0.252201i | ||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.36932 | 0.0583349 | ||||||||
\(552\) | −4.05703 | + | 2.34233i | −0.172679 | + | 0.0996962i | ||||
\(553\) | −5.62260 | + | 3.24621i | −0.239097 | + | 0.138043i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.28078 | + | 10.8786i | −0.266364 | + | 0.461356i | ||||
\(557\) | −7.41452 | − | 4.28078i | −0.314163 | − | 0.181382i | 0.334625 | − | 0.942352i | \(-0.391390\pi\) |
−0.648788 | + | 0.760969i | \(0.724724\pi\) | |||||||
\(558\) | − | 6.68466i | − | 0.282984i | ||||||
\(559\) | −0.219224 | + | 1.56557i | −0.00927217 | + | 0.0662165i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.43845 | − | 11.1517i | 0.271831 | − | 0.470826i | ||||
\(562\) | 14.0696 | + | 8.12311i | 0.593492 | + | 0.342653i | ||||
\(563\) | −28.5657 | + | 16.4924i | −1.20390 | + | 0.695073i | −0.961420 | − | 0.275083i | \(-0.911295\pi\) |
−0.242481 | + | 0.970156i | \(0.577961\pi\) | |||||||
\(564\) | −7.00000 | −0.294753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.78078 | − | 13.4767i | −0.327050 | − | 0.566468i | ||||
\(567\) | 0.561553i | 0.0235830i | ||||||||
\(568\) | −11.3649 | + | 6.56155i | −0.476862 | + | 0.275317i | ||||
\(569\) | 13.0885 | − | 22.6700i | 0.548700 | − | 0.950377i | −0.449664 | − | 0.893198i | \(-0.648456\pi\) |
0.998364 | − | 0.0571787i | \(-0.0182105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.6847 | 0.991172 | 0.495586 | − | 0.868559i | \(-0.334953\pi\) | ||||
0.495586 | + | 0.868559i | \(0.334953\pi\) | |||||||
\(572\) | 9.14657 | − | 11.7192i | 0.382437 | − | 0.490005i | ||||
\(573\) | 10.8769i | 0.454389i | ||||||||
\(574\) | −3.43845 | + | 5.95557i | −0.143518 | + | 0.248580i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 40.7386i | 1.69597i | 0.530019 | + | 0.847986i | \(0.322185\pi\) | ||||
−0.530019 | + | 0.847986i | \(0.677815\pi\) | |||||||
\(578\) | −6.27540 | + | 3.62311i | −0.261022 | + | 0.150701i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.00000 | − | 3.46410i | −0.0829740 | − | 0.143715i | ||||
\(582\) | −6.16879 | − | 3.56155i | −0.255705 | − | 0.147631i | ||||
\(583\) | −30.5709 | − | 17.6501i | −1.26612 | − | 0.730992i | ||||
\(584\) | −9.36932 | −0.387705 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.93087 | 0.162383 | ||||||||
\(587\) | −34.8542 | − | 20.1231i | −1.43859 | − | 0.830569i | −0.440837 | − | 0.897587i | \(-0.645318\pi\) |
−0.997752 | + | 0.0670179i | \(0.978652\pi\) | |||||||
\(588\) | 5.78908 | + | 3.34233i | 0.238738 | + | 0.137835i | ||||
\(589\) | −1.87689 | − | 3.25088i | −0.0773361 | − | 0.133950i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.40388 | − | 11.0918i | −0.263421 | − | 0.456258i | ||||
\(592\) | 3.57071 | − | 2.06155i | 0.146755 | − | 0.0847293i | ||||
\(593\) | 33.1771i | 1.36242i | 0.732088 | + | 0.681210i | \(0.238546\pi\) | ||||
−0.732088 | + | 0.681210i | \(0.761454\pi\) | |||||||
\(594\) | 2.06155 | + | 3.57071i | 0.0845865 | + | 0.146508i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.09612 | − | 1.89853i | 0.0448987 | − | 0.0777669i | ||||
\(597\) | − | 2.87689i | − | 0.117743i | ||||||
\(598\) | 16.7276 | + | 2.34233i | 0.684041 | + | 0.0957850i | ||||
\(599\) | 14.0000 | 0.572024 | 0.286012 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286012 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9924 | + | 25.9676i | −0.611554 | + | 1.05924i | 0.379425 | + | 0.925222i | \(0.376122\pi\) |
−0.990979 | + | 0.134020i | \(0.957212\pi\) | |||||||
\(602\) | 0.213225 | − | 0.123106i | 0.00869041 | − | 0.00501741i | ||||
\(603\) | − | 2.24621i | − | 0.0914728i | ||||||
\(604\) | −7.68466 | − | 13.3102i | −0.312684 | − | 0.541585i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.87689 | −0.360599 | ||||||||
\(607\) | −28.0794 | + | 16.2116i | −1.13971 | + | 0.658010i | −0.946358 | − | 0.323120i | \(-0.895268\pi\) |
−0.193349 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(608\) | −0.486319 | − | 0.280776i | −0.0197228 | − | 0.0113870i | ||||
\(609\) | −0.684658 | + | 1.18586i | −0.0277438 | + | 0.0480536i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.8963 | + | 15.5286i | 0.804918 | + | 0.628219i | ||||
\(612\) | 3.12311i | 0.126244i | ||||||||
\(613\) | −17.2139 | − | 9.93845i | −0.695263 | − | 0.401410i | 0.110318 | − | 0.993896i | \(-0.464813\pi\) |
−0.805581 | + | 0.592486i | \(0.798146\pi\) | |||||||
\(614\) | 12.8078 | − | 22.1837i | 0.516879 | − | 0.895261i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.31534 | −0.0932878 | ||||||||
\(617\) | 25.3878 | − | 14.6577i | 1.02208 | − | 0.590096i | 0.107371 | − | 0.994219i | \(-0.465757\pi\) |
0.914704 | + | 0.404123i | \(0.132423\pi\) | |||||||
\(618\) | 3.95042 | − | 2.28078i | 0.158909 | − | 0.0917463i | ||||
\(619\) | 20.5616 | 0.826439 | 0.413219 | − | 0.910632i | \(-0.364404\pi\) | ||||
0.413219 | + | 0.910632i | \(0.364404\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.34233 | + | 4.05703i | −0.0939944 | + | 0.162803i | ||||
\(622\) | 26.6204 | + | 15.3693i | 1.06738 | + | 0.616253i | ||||
\(623\) | 10.5616i | 0.423140i | ||||||||
\(624\) | −0.500000 | + | 3.57071i | −0.0200160 | + | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.6847 | + | 27.1666i | −0.626885 | + | 1.08580i | ||||
\(627\) | 2.00514 | + | 1.15767i | 0.0800778 | + | 0.0462329i | ||||
\(628\) | 12.0177 | − | 6.93845i | 0.479560 | − | 0.276874i | ||||
\(629\) | −12.8769 | −0.513435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.87689 | + | 11.9111i | 0.273765 | + | 0.474175i | 0.969823 | − | 0.243811i | \(-0.0783977\pi\) |
−0.696058 | + | 0.717986i | \(0.745064\pi\) | |||||||
\(632\) | − | 11.5616i | − | 0.459894i | ||||||
\(633\) | −18.9927 | + | 10.9654i | −0.754892 | + | 0.435837i | ||||
\(634\) | −12.4039 | + | 21.4842i | −0.492621 | + | 0.853245i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.56155 | 0.339488 | ||||||||
\(637\) | −9.03996 | − | 22.3423i | −0.358176 | − | 0.885235i | ||||
\(638\) | 10.0540i | 0.398041i | ||||||||
\(639\) | −6.56155 | + | 11.3649i | −0.259571 | + | 0.449590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.71922 | + | 9.90599i | 0.225896 | + | 0.391263i | 0.956588 | − | 0.291444i | \(-0.0941358\pi\) |
−0.730692 | + | 0.682707i | \(0.760802\pi\) | |||||||
\(642\) | − | 2.00000i | − | 0.0789337i | ||||||
\(643\) | 18.8393 | − | 10.8769i | 0.742951 | − | 0.428943i | −0.0801904 | − | 0.996780i | \(-0.525553\pi\) |
0.823141 | + | 0.567837i | \(0.192220\pi\) | |||||||
\(644\) | −1.31534 | − | 2.27824i | −0.0518317 | − | 0.0897752i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.876894 | + | 1.51883i | 0.0345009 | + | 0.0597574i | ||||
\(647\) | 30.3576 | + | 17.5270i | 1.19348 | + | 0.689057i | 0.959094 | − | 0.283086i | \(-0.0913583\pi\) |
0.234387 | + | 0.972143i | \(0.424692\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −26.5464 | −1.04204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.75379 | 0.147123 | ||||||||
\(652\) | −12.5041 | − | 7.21922i | −0.489697 | − | 0.282727i | ||||
\(653\) | 38.5914 | + | 22.2808i | 1.51020 | + | 0.871914i | 0.999929 | + | 0.0119002i | \(0.00378803\pi\) |
0.510270 | + | 0.860014i | \(0.329545\pi\) | |||||||
\(654\) | −1.87689 | − | 3.25088i | −0.0733924 | − | 0.127119i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.12311 | − | 10.6055i | −0.239067 | − | 0.414076i | ||||
\(657\) | −8.11407 | + | 4.68466i | −0.316560 | + | 0.182766i | ||||
\(658\) | − | 3.93087i | − | 0.153241i | ||||||
\(659\) | −3.02699 | − | 5.24290i | −0.117915 | − | 0.204234i | 0.801026 | − | 0.598629i | \(-0.204288\pi\) |
−0.918941 | + | 0.394395i | \(0.870954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8078 | + | 25.6478i | −0.575955 | + | 0.997584i | 0.419982 | + | 0.907532i | \(0.362036\pi\) |
−0.995937 | + | 0.0900513i | \(0.971297\pi\) | |||||||
\(662\) | − | 30.7386i | − | 1.19469i | ||||||
\(663\) | 6.92820 | − | 8.87689i | 0.269069 | − | 0.344750i | ||||
\(664\) | 7.12311 | 0.276430 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.06155 | − | 3.57071i | 0.0798835 | − | 0.138362i | ||||
\(667\) | −9.89286 | + | 5.71165i | −0.383053 | + | 0.221156i | ||||
\(668\) | 4.36932i | 0.169054i | ||||||||
\(669\) | 13.6501 | + | 23.6427i | 0.527743 | + | 0.914078i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.7386 | 0.955024 | ||||||||
\(672\) | 0.486319 | − | 0.280776i | 0.0187602 | − | 0.0108312i | ||||
\(673\) | −22.3034 | − | 12.8769i | −0.859734 | − | 0.496368i | 0.00418904 | − | 0.999991i | \(-0.498667\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(674\) | −3.00000 | + | 5.19615i | −0.115556 | + | 0.200148i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.34233 | − | 9.03996i | 0.359320 | − | 0.347691i | ||||
\(677\) | 37.1231i | 1.42676i | 0.700779 | + | 0.713378i | \(0.252836\pi\) | ||||
−0.700779 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(678\) | −7.52113 | − | 4.34233i | −0.288847 | − | 0.166766i | ||||
\(679\) | 2.00000 | − | 3.46410i | 0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 23.8690 | − | 13.7808i | 0.913991 | − | 0.527693i | ||||
\(683\) | 14.8290 | − | 8.56155i | 0.567418 | − | 0.327599i | −0.188700 | − | 0.982035i | \(-0.560427\pi\) |
0.756117 | + | 0.654436i | \(0.227094\pi\) | |||||||
\(684\) | −0.561553 | −0.0214715 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.84233 | + | 6.65511i | −0.146701 | + | 0.254093i | ||||
\(687\) | −20.9978 | − | 12.1231i | −0.801117 | − | 0.462525i | ||||
\(688\) | 0.438447i | 0.0167156i | ||||||||
\(689\) | −24.3348 | − | 18.9927i | −0.927080 | − | 0.723564i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2808 | − | 17.8068i | 0.391099 | − | 0.677404i | −0.601496 | − | 0.798876i | \(-0.705428\pi\) |
0.992595 | + | 0.121472i | \(0.0387616\pi\) | |||||||
\(692\) | 17.4739 | + | 10.0885i | 0.664257 | + | 0.383509i | ||||
\(693\) | −2.00514 | + | 1.15767i | −0.0761691 | + | 0.0439763i | ||||
\(694\) | −0.876894 | −0.0332865 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.21922 | − | 2.11176i | −0.0462146 | − | 0.0800460i | ||||
\(697\) | 38.2462i | 1.44868i | ||||||||
\(698\) | 7.35465 | − | 4.24621i | 0.278378 | − | 0.160721i | ||||
\(699\) | −2.65767 | + | 4.60322i | −0.100522 | + | 0.174110i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.3002 | −1.37104 | −0.685520 | − | 0.728054i | \(-0.740425\pi\) | ||||
−0.685520 | + | 0.728054i | \(0.740425\pi\) | |||||||
\(702\) | 1.35234 | + | 3.34233i | 0.0510410 | + | 0.126148i | ||||
\(703\) | − | 2.31534i | − | 0.0873248i | ||||||
\(704\) | 2.06155 | − | 3.57071i | 0.0776977 | − | 0.134576i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.9309 | + | 22.3969i | 0.486660 | + | 0.842919i | ||||
\(707\) | − | 4.98485i | − | 0.187474i | ||||||
\(708\) | 5.57586 | − | 3.21922i | 0.209554 | − | 0.120986i | ||||
\(709\) | 17.1231 | + | 29.6581i | 0.643072 | + | 1.11383i | 0.984743 | + | 0.174013i | \(0.0556736\pi\) |
−0.341672 | + | 0.939819i | \(0.610993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.78078 | − | 10.0126i | −0.216796 | − | 0.375502i | ||||
\(712\) | −16.2880 | − | 9.40388i | −0.610419 | − | 0.352425i | ||||
\(713\) | 27.1199 | + | 15.6577i | 1.01565 | + | 0.586384i | ||||
\(714\) | −1.75379 | −0.0656339 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.6847 | −0.474048 | ||||||||
\(717\) | −9.84612 | − | 5.68466i | −0.367710 | − | 0.212297i | ||||
\(718\) | −11.3649 | − | 6.56155i | −0.424136 | − | 0.244875i | ||||
\(719\) | 22.4924 | + | 38.9580i | 0.838826 | + | 1.45289i | 0.890877 | + | 0.454245i | \(0.150091\pi\) |
−0.0520512 | + | 0.998644i | \(0.516576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28078 | + | 2.21837i | 0.0476986 | + | 0.0826164i | ||||
\(722\) | 16.1814 | − | 9.34233i | 0.602209 | − | 0.347685i | ||||
\(723\) | − | 28.1231i | − | 1.04591i | ||||||
\(724\) | 1.43845 | + | 2.49146i | 0.0534595 | + | 0.0925945i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.00000 | + | 5.19615i | −0.111340 | + | 0.192847i | ||||
\(727\) | − | 38.4233i | − | 1.42504i | −0.701651 | − | 0.712521i | \(-0.747554\pi\) | ||
0.701651 | − | 0.712521i | \(-0.252446\pi\) | |||||||
\(728\) | −2.00514 | − | 0.280776i | −0.0743156 | − | 0.0104063i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.684658 | − | 1.18586i | 0.0253230 | − | 0.0438607i | ||||
\(732\) | −5.19615 | + | 3.00000i | −0.192055 | + | 0.110883i | ||||
\(733\) | 20.0691i | 0.741270i | 0.928779 | + | 0.370635i | \(0.120860\pi\) | ||||
−0.928779 | + | 0.370635i | \(0.879140\pi\) | |||||||
\(734\) | 6.24621 | + | 10.8188i | 0.230552 | + | 0.399328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | 8.02058 | − | 4.63068i | 0.295442 | − | 0.170573i | ||||
\(738\) | −10.6055 | − | 6.12311i | −0.390395 | − | 0.225395i | ||||
\(739\) | −13.7732 | + | 23.8559i | −0.506655 | + | 0.877553i | 0.493315 | + | 0.869851i | \(0.335785\pi\) |
−0.999970 | + | 0.00770202i | \(0.997548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.59612 | + | 1.24573i | 0.0586349 | + | 0.0457631i | ||||
\(742\) | 4.80776i | 0.176499i | ||||||||
\(743\) | −11.4117 | − | 6.58854i | −0.418654 | − | 0.241710i | 0.275847 | − | 0.961202i | \(-0.411042\pi\) |
−0.694501 | + | 0.719491i | \(0.744375\pi\) | |||||||
\(744\) | −3.34233 | + | 5.78908i | −0.122536 | + | 0.212238i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.8078 | −0.944889 | ||||||||
\(747\) | 6.16879 | − | 3.56155i | 0.225704 | − | 0.130310i | ||||
\(748\) | −11.1517 | + | 6.43845i | −0.407747 | + | 0.235413i | ||||
\(749\) | 1.12311 | 0.0410374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9039 | − | 20.6181i | 0.434379 | − | 0.752366i | −0.562866 | − | 0.826548i | \(-0.690301\pi\) |
0.997245 | + | 0.0741820i | \(0.0236346\pi\) | |||||||
\(752\) | 6.06218 | + | 3.50000i | 0.221065 | + | 0.127632i | ||||
\(753\) | − | 8.12311i | − | 0.296022i | ||||||
\(754\) | −1.21922 | + | 8.70700i | −0.0444015 | + | 0.317090i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.280776 | − | 0.486319i | 0.0102117 | − | 0.0176873i | ||||
\(757\) | −24.6153 | − | 14.2116i | −0.894658 | − | 0.516531i | −0.0191948 | − | 0.999816i | \(-0.506110\pi\) |
−0.875463 | + | 0.483285i | \(0.839444\pi\) | |||||||
\(758\) | −15.3154 | + | 8.84233i | −0.556279 | + | 0.321168i | ||||
\(759\) | −19.3153 | −0.701102 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.96543 | + | 15.5286i | 0.324997 | + | 0.562911i | 0.981512 | − | 0.191402i | \(-0.0613035\pi\) |
−0.656515 | + | 0.754313i | \(0.727970\pi\) | |||||||
\(762\) | 8.56155i | 0.310152i | ||||||||
\(763\) | 1.82554 | − | 1.05398i | 0.0660889 | − | 0.0381565i | ||||
\(764\) | 5.43845 | − | 9.41967i | 0.196756 | − | 0.340792i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.192236 | 0.00694577 | ||||||||
\(767\) | −22.9899 | − | 3.21922i | −0.830116 | − | 0.116239i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −16.6577 | + | 28.8519i | −0.600691 | + | 1.04043i | 0.392026 | + | 0.919954i | \(0.371774\pi\) |
−0.992717 | + | 0.120473i | \(0.961559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78078 | + | 4.81645i | 0.100147 | + | 0.173460i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.9380 | − | 12.0885i | 0.753086 | − | 0.434795i | −0.0737217 | − | 0.997279i | \(-0.523488\pi\) |
0.826808 | + | 0.562484i | \(0.190154\pi\) | |||||||
\(774\) | 0.219224 | + | 0.379706i | 0.00787983 | + | 0.0136483i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.56155 | + | 6.16879i | 0.127852 | + | 0.221447i | ||||
\(777\) | 2.00514 | + | 1.15767i | 0.0719342 | + | 0.0415312i | ||||
\(778\) | 15.6352 | + | 9.02699i | 0.560549 | + | 0.323633i | ||||
\(779\) | −6.87689 | −0.246390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1080 | −1.93613 | ||||||||
\(782\) | −12.6705 | − | 7.31534i | −0.453098 | − | 0.261596i | ||||
\(783\) | −2.11176 | − | 1.21922i | −0.0754680 | − | 0.0435715i | ||||
\(784\) | −3.34233 | − | 5.78908i | −0.119369 | − | 0.206753i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.06155 | + | 1.83866i | 0.0378643 | + | 0.0655830i | ||||
\(787\) | −27.1199 | + | 15.6577i | −0.966719 | + | 0.558136i | −0.898235 | − | 0.439516i | \(-0.855150\pi\) |
−0.0684848 | + | 0.997652i | \(0.521816\pi\) | |||||||
\(788\) | 12.8078i | 0.456258i | ||||||||
\(789\) | −6.50000 | − | 11.2583i | −0.231406 | − | 0.400807i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.43845 | − | 4.22351i | 0.0867012 | − | 0.150171i | ||||
\(792\) | − | 4.12311i | − | 0.146508i | ||||||
\(793\) | 21.4243 | + | 3.00000i | 0.760799 | + | 0.106533i | ||||
\(794\) | 20.1231 | 0.714142 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.43845 | + | 2.49146i | −0.0509844 | + | 0.0883076i | ||||
\(797\) | −11.3649 | + | 6.56155i | −0.402567 | + | 0.232422i | −0.687591 | − | 0.726098i | \(-0.741332\pi\) |
0.285024 | + | 0.958520i | \(0.407998\pi\) | |||||||
\(798\) | − | 0.315342i | − | 0.0111630i | ||||||
\(799\) | −10.9309 | − | 18.9328i | −0.386706 | − | 0.669795i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.8078 | −0.664540 | ||||||||
\(802\) | −0.273094 | + | 0.157671i | −0.00964328 | + | 0.00556755i | ||||
\(803\) | −33.4552 | − | 19.3153i | −1.18061 | − | 0.681624i | ||||
\(804\) | −1.12311 | + | 1.94528i | −0.0396089 | + | 0.0686046i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.3423 | − | 9.03996i | 0.786975 | − | 0.318419i | ||||
\(807\) | − | 21.3693i | − | 0.752236i | ||||||
\(808\) | 7.68762 | + | 4.43845i | 0.270449 | + | 0.156144i | ||||
\(809\) | −7.24621 | + | 12.5508i | −0.254763 | + | 0.441263i | −0.964831 | − | 0.262870i | \(-0.915331\pi\) |
0.710068 | + | 0.704133i | \(0.248664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5464 | 1.66958 | 0.834790 | − | 0.550569i | \(-0.185589\pi\) | ||||
0.834790 | + | 0.550569i | \(0.185589\pi\) | |||||||
\(812\) | 1.18586 | − | 0.684658i | 0.0416156 | − | 0.0240268i | ||||
\(813\) | −11.4117 | + | 6.58854i | −0.400225 | + | 0.231070i | ||||
\(814\) | 17.0000 | 0.595850 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.56155 | − | 2.70469i | 0.0546653 | − | 0.0946830i | ||||
\(817\) | 0.213225 | + | 0.123106i | 0.00745981 | + | 0.00430692i | ||||
\(818\) | − | 18.8078i | − | 0.657598i | ||||||
\(819\) | −1.87689 | + | 0.759413i | −0.0655840 | + | 0.0265360i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.21922 | − | 7.30791i | 0.147252 | − | 0.255048i | −0.782959 | − | 0.622073i | \(-0.786291\pi\) |
0.930211 | + | 0.367026i | \(0.119624\pi\) | |||||||
\(822\) | 10.2258 | + | 5.90388i | 0.356667 | + | 0.205922i | ||||
\(823\) | 4.37687 | − | 2.52699i | 0.152568 | − | 0.0880853i | −0.421772 | − | 0.906702i | \(-0.638592\pi\) |
0.574341 | + | 0.818616i | \(0.305259\pi\) | |||||||
\(824\) | −4.56155 | −0.158909 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.80776 | + | 3.13114i | 0.0629002 | + | 0.108946i | ||||
\(827\) | 28.2462i | 0.982217i | 0.871098 | + | 0.491109i | \(0.163408\pi\) | ||||
−0.871098 | + | 0.491109i | \(0.836592\pi\) | |||||||
\(828\) | 4.05703 | − | 2.34233i | 0.140992 | − | 0.0814016i | ||||
\(829\) | 6.19224 | − | 10.7253i | 0.215065 | − | 0.372504i | −0.738228 | − | 0.674552i | \(-0.764337\pi\) |
0.953293 | + | 0.302048i | \(0.0976702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | 2.21837 | − | 2.84233i | 0.0769081 | − | 0.0985400i | ||||
\(833\) | 20.8769i | 0.723342i | ||||||||
\(834\) | 6.28078 | − | 10.8786i | 0.217486 | − | 0.376696i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.15767 | − | 2.00514i | −0.0400389 | − | 0.0693494i | ||||
\(837\) | 6.68466i | 0.231056i | ||||||||
\(838\) | 28.1393 | − | 16.2462i | 0.972055 | − | 0.561216i | ||||
\(839\) | 18.3693 | + | 31.8166i | 0.634179 | + | 1.09843i | 0.986688 | + | 0.162622i | \(0.0519952\pi\) |
−0.352509 | + | 0.935808i | \(0.614671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5270 | + | 19.9653i | 0.397482 | + | 0.688460i | ||||
\(842\) | −28.1393 | − | 16.2462i | −0.969743 | − | 0.559881i | ||||
\(843\) | −14.0696 | − | 8.12311i | −0.484584 | − | 0.279775i | ||||
\(844\) | 21.9309 | 0.754892 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | −2.91791 | − | 1.68466i | −0.100261 | − | 0.0578855i | ||||
\(848\) | −7.41452 | − | 4.28078i | −0.254616 | − | 0.147002i | ||||
\(849\) | 7.78078 | + | 13.4767i | 0.267036 | + | 0.462519i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.65767 | + | 16.7276i | 0.331061 | + | 0.573414i | ||||
\(852\) | 11.3649 | − | 6.56155i | 0.389357 | − | 0.224795i | ||||
\(853\) | 2.30019i | 0.0787569i | 0.999224 | + | 0.0393784i | \(0.0125378\pi\) | ||||
−0.999224 | + | 0.0393784i | \(0.987462\pi\) | |||||||
\(854\) | −1.68466 | − | 2.91791i | −0.0576478 | − | 0.0998490i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.00000 | + | 1.73205i | −0.0341793 | + | 0.0592003i | ||||
\(857\) | 6.19224i | 0.211523i | 0.994392 | + | 0.105761i | \(0.0337280\pi\) | ||||
−0.994392 | + | 0.105761i | \(0.966272\pi\) | |||||||
\(858\) | −9.14657 | + | 11.7192i | −0.312259 | + | 0.400088i | ||||
\(859\) | −39.7926 | −1.35771 | −0.678853 | − | 0.734274i | \(-0.737523\pi\) | ||||
−0.678853 | + | 0.734274i | \(0.737523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.43845 | − | 5.95557i | 0.117182 | − | 0.202965i | ||||
\(862\) | 19.6922 | − | 11.3693i | 0.670720 | − | 0.387240i | ||||
\(863\) | 2.43845i | 0.0830057i | 0.999138 | + | 0.0415029i | \(0.0132146\pi\) | ||||
−0.999138 | + | 0.0415029i | \(0.986785\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.7386 | −0.636765 | ||||||||
\(867\) | 6.27540 | − | 3.62311i | 0.213124 | − | 0.123047i | ||||
\(868\) | −3.25088 | − | 1.87689i | −0.110342 | − | 0.0637059i | ||||
\(869\) | 23.8348 | − | 41.2830i | 0.808539 | − | 1.40043i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.50758 | − | 3.03765i | 0.254385 | − | 0.102927i | ||||
\(872\) | 3.75379i | 0.127119i | ||||||||
\(873\) | 6.16879 | + | 3.56155i | 0.208782 | + | 0.120540i | ||||
\(874\) | 1.31534 | − | 2.27824i | 0.0444921 | − | 0.0770626i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.36932 | 0.316560 | ||||||||
\(877\) | −7.30791 | + | 4.21922i | −0.246771 | + | 0.142473i | −0.618285 | − | 0.785954i | \(-0.712172\pi\) |
0.371514 | + | 0.928427i | \(0.378839\pi\) | |||||||
\(878\) | 21.7572 | − | 12.5616i | 0.734272 | − | 0.423932i | ||||
\(879\) | −3.93087 | −0.132585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2808 | − | 21.2709i | 0.413750 | − | 0.716636i | −0.581546 | − | 0.813513i | \(-0.697552\pi\) |
0.995296 | + | 0.0968774i | \(0.0308855\pi\) | |||||||
\(882\) | −5.78908 | − | 3.34233i | −0.194929 | − | 0.112542i | ||||
\(883\) | − | 19.1771i | − | 0.645360i | −0.946508 | − | 0.322680i | \(-0.895416\pi\) | ||
0.946508 | − | 0.322680i | \(-0.104584\pi\) | |||||||
\(884\) | −10.4384 | + | 4.22351i | −0.351083 | + | 0.142052i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.56155 | − | 11.3649i | 0.220440 | − | 0.381813i | ||||
\(887\) | −28.6723 | − | 16.5540i | −0.962722 | − | 0.555828i | −0.0657126 | − | 0.997839i | \(-0.520932\pi\) |
−0.897010 | + | 0.442010i | \(0.854265\pi\) | |||||||
\(888\) | −3.57071 | + | 2.06155i | −0.119825 | + | 0.0691812i | ||||
\(889\) | −4.80776 | −0.161247 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.06155 | − | 3.57071i | −0.0690646 | − | 0.119623i | ||||
\(892\) | − | 27.3002i | − | 0.914078i | ||||||
\(893\) | 3.40423 | − | 1.96543i | 0.113918 | − | 0.0657708i | ||||
\(894\) | −1.09612 | + | 1.89853i | −0.0366597 | + | 0.0634964i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.561553 | −0.0187602 | ||||||||
\(897\) | −16.7276 | − | 2.34233i | −0.558518 | − | 0.0782081i | ||||
\(898\) | − | 20.1771i | − | 0.673318i | ||||||
\(899\) | −8.15009 | + | 14.1164i | −0.271821 | + | 0.470807i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.3693 | + | 23.1563i | 0.445397 | + | 0.771449i | ||||
\(902\) | − | 50.4924i | − | 1.68121i | ||||||
\(903\) | −0.213225 | + | 0.123106i | −0.00709569 | + | 0.00409670i | ||||
\(904\) | 4.34233 | + | 7.52113i | 0.144424 | + | 0.250149i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.68466 | + | 13.3102i | 0.255306 | + | 0.442202i | ||||
\(907\) | −46.6924 | − | 26.9579i | −1.55039 | − | 0.895121i | −0.998109 | − | 0.0614661i | \(-0.980422\pi\) |
−0.552286 | − | 0.833655i | \(-0.686244\pi\) | |||||||
\(908\) | 17.3205 | + | 10.0000i | 0.574801 | + | 0.331862i | ||||
\(909\) | 8.87689 | 0.294428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6307 | −0.617262 | −0.308631 | − | 0.951182i | \(-0.599871\pi\) | ||||
−0.308631 | + | 0.951182i | \(0.599871\pi\) | |||||||
\(912\) | 0.486319 | + | 0.280776i | 0.0161036 | + | 0.00929744i | ||||
\(913\) | 25.4346 | + | 14.6847i | 0.841762 | + | 0.485991i | ||||
\(914\) | 10.1231 | + | 17.5337i | 0.334843 | + | 0.579964i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.1231 | + | 20.9978i | 0.400559 | + | 0.693788i | ||||
\(917\) | −1.03251 | + | 0.596118i | −0.0340964 | + | 0.0196855i | ||||
\(918\) | − | 3.12311i | − | 0.103078i | ||||||
\(919\) | 8.31534 | + | 14.4026i | 0.274298 | + | 0.475098i | 0.969958 | − | 0.243274i | \(-0.0782213\pi\) |
−0.695660 | + | 0.718371i | \(0.744888\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.8078 | + | 22.1837i | −0.422030 | + | 0.730978i | ||||
\(922\) | 30.0540i | 0.989775i | ||||||||
\(923\) | −46.8589 | − | 6.56155i | −1.54238 | − | 0.215976i | ||||
\(924\) | 2.31534 | 0.0761691 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.80776 | − | 6.59524i | 0.125131 | − | 0.216733i | ||||
\(927\) | −3.95042 | + | 2.28078i | −0.129749 | + | 0.0749105i | ||||
\(928\) | 2.43845i | 0.0800460i | ||||||||
\(929\) | −12.5616 | − | 21.7572i | −0.412131 | − | 0.713832i | 0.582991 | − | 0.812478i | \(-0.301882\pi\) |
−0.995123 | + | 0.0986462i | \(0.968549\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.75379 | −0.123025 | ||||||||
\(932\) | 4.60322 | − | 2.65767i | 0.150784 | − | 0.0870549i | ||||
\(933\) | −26.6204 | − | 15.3693i | −0.871514 | − | 0.503169i | ||||
\(934\) | −8.93087 | + | 15.4687i | −0.292227 | + | 0.506152i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 3.57071i | 0.0163430 | − | 0.116712i | ||||
\(937\) | − | 53.2311i | − | 1.73898i | −0.493948 | − | 0.869491i | \(-0.664447\pi\) | ||
0.493948 | − | 0.869491i | \(-0.335553\pi\) | |||||||
\(938\) | −1.09238 | − | 0.630683i | −0.0356673 | − | 0.0205925i | ||||
\(939\) | 15.6847 | − | 27.1666i | 0.511849 | − | 0.886549i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.3693 | −0.827016 | −0.413508 | − | 0.910500i | \(-0.635697\pi\) | ||||
−0.413508 | + | 0.910500i | \(0.635697\pi\) | |||||||
\(942\) | −12.0177 | + | 6.93845i | −0.391559 | + | 0.226067i | ||||
\(943\) | 49.6833 | − | 28.6847i | 1.61791 | − | 0.934101i | ||||
\(944\) | −6.43845 | −0.209554 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.903882 | + | 1.56557i | −0.0293877 | + | 0.0509011i | ||||
\(947\) | −37.9854 | − | 21.9309i | −1.23436 | − | 0.712658i | −0.266423 | − | 0.963856i | \(-0.585842\pi\) |
−0.967936 | + | 0.251199i | \(0.919175\pi\) | |||||||
\(948\) | 11.5616i | 0.375502i | ||||||||
\(949\) | −26.6307 | − | 20.7846i | −0.864469 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.4039 | − | 21.4842i | 0.402223 | − | 0.696671i | ||||
\(952\) | 1.51883 | + | 0.876894i | 0.0492254 | + | 0.0284203i | ||||
\(953\) | 44.3207 | − | 25.5885i | 1.43569 | − | 0.828894i | 0.438141 | − | 0.898906i | \(-0.355637\pi\) |
0.997546 | + | 0.0700123i | \(0.0223039\pi\) | |||||||
\(954\) | −8.56155 | −0.277191 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.68466 | + | 9.84612i | 0.183855 | + | 0.318446i | ||||
\(957\) | − | 10.0540i | − | 0.324999i | ||||||
\(958\) | −33.1222 | + | 19.1231i | −1.07013 | + | 0.617839i | ||||
\(959\) | −3.31534 | + | 5.74234i | −0.107058 | + | 0.185430i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6847 | 0.441441 | ||||||||
\(962\) | 14.7224 | + | 2.06155i | 0.474670 | + | 0.0664671i | ||||
\(963\) | 2.00000i | 0.0644491i | ||||||||
\(964\) | −14.0616 | + | 24.3553i | −0.452892 | + | 0.784432i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.31534 | + | 2.27824i | 0.0423204 | + | 0.0733011i | ||||
\(967\) | − | 15.6847i | − | 0.504385i | −0.967677 | − | 0.252192i | \(-0.918848\pi\) | ||
0.967677 | − | 0.252192i | \(-0.0811516\pi\) | |||||||
\(968\) | 5.19615 | − | 3.00000i | 0.167011 | − | 0.0964237i | ||||
\(969\) | −0.876894 | − | 1.51883i | −0.0281699 | − | 0.0487917i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.15767 | + | 3.73720i | 0.0692430 | + | 0.119932i | 0.898568 | − | 0.438834i | \(-0.144608\pi\) |
−0.829325 | + | 0.558766i | \(0.811275\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | 6.10892 | + | 3.52699i | 0.195843 | + | 0.113070i | ||||
\(974\) | −13.0540 | −0.418276 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −41.8292 | − | 24.1501i | −1.33823 | − | 0.772630i | −0.351689 | − | 0.936117i | \(-0.614392\pi\) |
−0.986545 | + | 0.163487i | \(0.947726\pi\) | |||||||
\(978\) | 12.5041 | + | 7.21922i | 0.399836 | + | 0.230845i | ||||
\(979\) | −38.7732 | − | 67.1572i | −1.23920 | − | 2.14635i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.87689 | + | 3.25088i | 0.0599246 | + | 0.103792i | ||||
\(982\) | 15.1021 | − | 8.71922i | 0.481929 | − | 0.278242i | ||||
\(983\) | 32.1231i | 1.02457i | 0.858816 | + | 0.512284i | \(0.171200\pi\) | ||||
−0.858816 | + | 0.512284i | \(0.828800\pi\) | |||||||
\(984\) | 6.12311 | + | 10.6055i | 0.195197 | + | 0.338092i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.80776 | − | 6.59524i | 0.121264 | − | 0.210035i | ||||
\(987\) | 3.93087i | 0.125121i | ||||||||
\(988\) | −0.759413 | − | 1.87689i | −0.0241601 | − | 0.0597120i | ||||
\(989\) | −2.05398 | −0.0653126 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.7116 | + | 42.8018i | −0.784991 | + | 1.35964i | 0.144013 | + | 0.989576i | \(0.453999\pi\) |
−0.929004 | + | 0.370069i | \(0.879334\pi\) | |||||||
\(992\) | 5.78908 | − | 3.34233i | 0.183804 | − | 0.106119i | ||||
\(993\) | 30.7386i | 0.975461i | ||||||||
\(994\) | 3.68466 | + | 6.38202i | 0.116870 | + | 0.202425i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.12311 | −0.225704 | ||||||||
\(997\) | 32.5161 | − | 18.7732i | 1.02980 | − | 0.594553i | 0.112870 | − | 0.993610i | \(-0.463996\pi\) |
0.916926 | + | 0.399057i | \(0.130662\pi\) | |||||||
\(998\) | −3.46410 | − | 2.00000i | −0.109654 | − | 0.0633089i | ||||
\(999\) | −2.06155 | + | 3.57071i | −0.0652246 | + | 0.112972i |
(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 | 1950.2.z.n.1699.4 | 8 | ||
5.2 | odd | 4 | 390.2.i.g.61.2 | ✓ | 4 | ||
5.3 | odd | 4 | 1950.2.i.bi.451.1 | 4 | |||
5.4 | even | 2 | inner | 1950.2.z.n.1699.1 | 8 | ||
13.3 | even | 3 | inner | 1950.2.z.n.1849.1 | 8 | ||
15.2 | even | 4 | 1170.2.i.o.451.2 | 4 | |||
65.3 | odd | 12 | 1950.2.i.bi.601.1 | 4 | |||
65.7 | even | 12 | 5070.2.b.r.1351.4 | 4 | |||
65.17 | odd | 12 | 5070.2.a.bb.1.2 | 2 | |||
65.22 | odd | 12 | 5070.2.a.bi.1.1 | 2 | |||
65.29 | even | 6 | inner | 1950.2.z.n.1849.4 | 8 | ||
65.32 | even | 12 | 5070.2.b.r.1351.1 | 4 | |||
65.42 | odd | 12 | 390.2.i.g.211.2 | yes | 4 | ||
195.107 | even | 12 | 1170.2.i.o.991.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.2 | ✓ | 4 | 5.2 | odd | 4 | ||
390.2.i.g.211.2 | yes | 4 | 65.42 | odd | 12 | ||
1170.2.i.o.451.2 | 4 | 15.2 | even | 4 | |||
1170.2.i.o.991.2 | 4 | 195.107 | even | 12 | |||
1950.2.i.bi.451.1 | 4 | 5.3 | odd | 4 | |||
1950.2.i.bi.601.1 | 4 | 65.3 | odd | 12 | |||
1950.2.z.n.1699.1 | 8 | 5.4 | even | 2 | inner | ||
1950.2.z.n.1699.4 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.n.1849.1 | 8 | 13.3 | even | 3 | inner | ||
1950.2.z.n.1849.4 | 8 | 65.29 | even | 6 | inner | ||
5070.2.a.bb.1.2 | 2 | 65.17 | odd | 12 | |||
5070.2.a.bi.1.1 | 2 | 65.22 | odd | 12 | |||
5070.2.b.r.1351.1 | 4 | 65.32 | even | 12 | |||
5070.2.b.r.1351.4 | 4 | 65.7 | even | 12 |