Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.3 | ||
Root | \(0.141226 + 0.244611i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.165 |
Dual form | 637.2.h.m.471.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52077 | −1.07535 | −0.537675 | − | 0.843152i | \(-0.680697\pi\) | ||||
−0.537675 | + | 0.843152i | \(0.680697\pi\) | |||||||
\(3\) | −1.06311 | − | 1.84135i | −0.613784 | − | 1.06311i | −0.990596 | − | 0.136816i | \(-0.956313\pi\) |
0.376812 | − | 0.926290i | \(-0.377020\pi\) | |||||||
\(4\) | 0.312752 | 0.156376 | ||||||||
\(5\) | 0.294696 | + | 0.510428i | 0.131792 | + | 0.228270i | 0.924367 | − | 0.381504i | \(-0.124594\pi\) |
−0.792575 | + | 0.609774i | \(0.791260\pi\) | |||||||
\(6\) | 1.61674 | + | 2.80028i | 0.660032 | + | 1.14321i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.56592 | 0.907190 | ||||||||
\(9\) | −0.760387 | + | 1.31703i | −0.253462 | + | 0.439009i | ||||
\(10\) | −0.448165 | − | 0.776245i | −0.141722 | − | 0.245470i | ||||
\(11\) | −0.760387 | − | 1.31703i | −0.229265 | − | 0.397099i | 0.728325 | − | 0.685232i | \(-0.240299\pi\) |
−0.957591 | + | 0.288132i | \(0.906966\pi\) | |||||||
\(12\) | −0.332488 | − | 0.575886i | −0.0959811 | − | 0.166244i | ||||
\(13\) | −3.32565 | + | 1.39285i | −0.922370 | + | 0.386308i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.626585 | − | 1.08528i | 0.161784 | − | 0.280217i | ||||
\(16\) | −4.52769 | −1.13192 | ||||||||
\(17\) | −4.79479 | −1.16291 | −0.581454 | − | 0.813579i | \(-0.697516\pi\) | ||||
−0.581454 | + | 0.813579i | \(0.697516\pi\) | |||||||
\(18\) | 1.15638 | − | 2.00290i | 0.272560 | − | 0.472088i | ||||
\(19\) | 0.841957 | − | 1.45831i | 0.193158 | − | 0.334560i | −0.753137 | − | 0.657864i | \(-0.771460\pi\) |
0.946295 | + | 0.323304i | \(0.104794\pi\) | |||||||
\(20\) | 0.0921666 | + | 0.159637i | 0.0206091 | + | 0.0356960i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.15638 | + | 2.00290i | 0.246540 | + | 0.427020i | ||||
\(23\) | 1.77394 | 0.369893 | 0.184946 | − | 0.982749i | \(-0.440789\pi\) | ||||
0.184946 | + | 0.982749i | \(0.440789\pi\) | |||||||
\(24\) | −2.72785 | − | 4.72477i | −0.556819 | − | 0.964439i | ||||
\(25\) | 2.32631 | − | 4.02929i | 0.465262 | − | 0.805857i | ||||
\(26\) | 5.05756 | − | 2.11821i | 0.991870 | − | 0.415416i | ||||
\(27\) | −3.14515 | −0.605284 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.44625 | + | 5.96909i | −0.639953 | + | 1.10843i | 0.345489 | + | 0.938423i | \(0.387713\pi\) |
−0.985443 | + | 0.170009i | \(0.945620\pi\) | |||||||
\(30\) | −0.952894 | + | 1.65046i | −0.173974 | + | 0.301332i | ||||
\(31\) | −3.04320 | + | 5.27098i | −0.546575 | + | 0.946695i | 0.451931 | + | 0.892053i | \(0.350735\pi\) |
−0.998506 | + | 0.0546426i | \(0.982598\pi\) | |||||||
\(32\) | 1.75375 | 0.310021 | ||||||||
\(33\) | −1.61674 | + | 2.80028i | −0.281439 | + | 0.487466i | ||||
\(34\) | 7.29179 | 1.25053 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.237812 | + | 0.411903i | −0.0396354 | + | 0.0686505i | ||||
\(37\) | 1.40913 | 0.231659 | 0.115830 | − | 0.993269i | \(-0.463047\pi\) | ||||
0.115830 | + | 0.993269i | \(0.463047\pi\) | |||||||
\(38\) | −1.28043 | + | 2.21776i | −0.207712 | + | 0.359768i | ||||
\(39\) | 6.10025 | + | 4.64295i | 0.976822 | + | 0.743467i | ||||
\(40\) | 0.756166 | + | 1.30972i | 0.119560 | + | 0.207085i | ||||
\(41\) | 0.677729 | − | 1.17386i | 0.105843 | − | 0.183326i | −0.808239 | − | 0.588855i | \(-0.799579\pi\) |
0.914082 | + | 0.405528i | \(0.132912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.77978 | + | 10.0109i | 0.881408 | + | 1.52664i | 0.849776 | + | 0.527144i | \(0.176737\pi\) |
0.0316319 | + | 0.999500i | \(0.489930\pi\) | |||||||
\(44\) | −0.237812 | − | 0.411903i | −0.0358516 | − | 0.0620967i | ||||
\(45\) | −0.896331 | −0.133617 | ||||||||
\(46\) | −2.69777 | −0.397764 | ||||||||
\(47\) | −0.232416 | − | 0.402556i | −0.0339013 | − | 0.0587188i | 0.848577 | − | 0.529072i | \(-0.177460\pi\) |
−0.882478 | + | 0.470353i | \(0.844127\pi\) | |||||||
\(48\) | 4.81341 | + | 8.33707i | 0.694756 | + | 1.20335i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.53779 | + | 6.12763i | −0.500319 | + | 0.866578i | ||||
\(51\) | 5.09737 | + | 8.82890i | 0.713775 | + | 1.23629i | ||||
\(52\) | −1.04010 | + | 0.435617i | −0.144236 | + | 0.0604093i | ||||
\(53\) | −4.12340 | + | 7.14194i | −0.566393 | + | 0.981021i | 0.430526 | + | 0.902578i | \(0.358328\pi\) |
−0.996919 | + | 0.0784430i | \(0.975005\pi\) | |||||||
\(54\) | 4.78306 | 0.650892 | ||||||||
\(55\) | 0.448165 | − | 0.776245i | 0.0604306 | − | 0.104669i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.58035 | −0.474230 | ||||||||
\(58\) | 5.24097 | − | 9.07763i | 0.688173 | − | 1.19195i | ||||
\(59\) | 11.8756 | 1.54608 | 0.773038 | − | 0.634359i | \(-0.218736\pi\) | ||||
0.773038 | + | 0.634359i | \(0.218736\pi\) | |||||||
\(60\) | 0.195966 | − | 0.339422i | 0.0252991 | − | 0.0438193i | ||||
\(61\) | 1.24009 | − | 2.14789i | 0.158777 | − | 0.275009i | −0.775651 | − | 0.631162i | \(-0.782578\pi\) |
0.934428 | + | 0.356153i | \(0.115912\pi\) | |||||||
\(62\) | 4.62802 | − | 8.01596i | 0.587759 | − | 1.01803i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.38833 | 0.798541 | ||||||||
\(65\) | −1.69101 | − | 1.28704i | −0.209744 | − | 0.159637i | ||||
\(66\) | 2.45870 | − | 4.25859i | 0.302645 | − | 0.524196i | ||||
\(67\) | 3.78642 | + | 6.55827i | 0.462585 | + | 0.801220i | 0.999089 | − | 0.0426774i | \(-0.0135888\pi\) |
−0.536504 | + | 0.843898i | \(0.680255\pi\) | |||||||
\(68\) | −1.49958 | −0.181851 | ||||||||
\(69\) | −1.88589 | − | 3.26646i | −0.227034 | − | 0.393235i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.30235 | − | 5.71984i | −0.391917 | − | 0.678821i | 0.600785 | − | 0.799411i | \(-0.294855\pi\) |
−0.992702 | + | 0.120590i | \(0.961521\pi\) | |||||||
\(72\) | −1.95109 | + | 3.37939i | −0.229939 | + | 0.398265i | ||||
\(73\) | −8.18558 | + | 14.1778i | −0.958049 | + | 1.65939i | −0.230819 | + | 0.972997i | \(0.574140\pi\) |
−0.727231 | + | 0.686393i | \(0.759193\pi\) | |||||||
\(74\) | −2.14296 | −0.249114 | ||||||||
\(75\) | −9.89245 | −1.14228 | ||||||||
\(76\) | 0.263323 | − | 0.456090i | 0.0302053 | − | 0.0523171i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.27710 | − | 7.06087i | −1.05042 | − | 0.799486i | ||||
\(79\) | 7.48116 | + | 12.9577i | 0.841696 | + | 1.45786i | 0.888460 | + | 0.458955i | \(0.151776\pi\) |
−0.0467635 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(80\) | −1.33429 | − | 2.31106i | −0.149178 | − | 0.258384i | ||||
\(81\) | 5.62478 | + | 9.74241i | 0.624976 | + | 1.08249i | ||||
\(82\) | −1.03067 | + | 1.78518i | −0.113819 | + | 0.197140i | ||||
\(83\) | −10.1222 | −1.11105 | −0.555526 | − | 0.831499i | \(-0.687483\pi\) | ||||
−0.555526 | + | 0.831499i | \(0.687483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41300 | − | 2.44740i | −0.153262 | − | 0.265457i | ||||
\(86\) | −8.78973 | − | 15.2243i | −0.947821 | − | 1.64167i | ||||
\(87\) | 14.6549 | 1.57117 | ||||||||
\(88\) | −1.95109 | − | 3.37939i | −0.207987 | − | 0.360244i | ||||
\(89\) | −16.4850 | −1.74741 | −0.873703 | − | 0.486460i | \(-0.838288\pi\) | ||||
−0.873703 | + | 0.486460i | \(0.838288\pi\) | |||||||
\(90\) | 1.36312 | 0.143685 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.554804 | 0.0578423 | ||||||||
\(93\) | 12.9410 | 1.34192 | ||||||||
\(94\) | 0.353452 | + | 0.612196i | 0.0364558 | + | 0.0631432i | ||||
\(95\) | 0.992484 | 0.101827 | ||||||||
\(96\) | −1.86442 | − | 3.22927i | −0.190286 | − | 0.329586i | ||||
\(97\) | −0.486935 | − | 0.843396i | −0.0494407 | − | 0.0856338i | 0.840246 | − | 0.542205i | \(-0.182411\pi\) |
−0.889687 | + | 0.456572i | \(0.849077\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.31275 | 0.232440 | ||||||||
\(100\) | 0.727557 | − | 1.26017i | 0.0727557 | − | 0.126017i | ||||
\(101\) | −1.47012 | − | 2.54632i | −0.146282 | − | 0.253368i | 0.783568 | − | 0.621305i | \(-0.213397\pi\) |
−0.929851 | + | 0.367937i | \(0.880064\pi\) | |||||||
\(102\) | −7.75195 | − | 13.4268i | −0.767557 | − | 1.32945i | ||||
\(103\) | 0.264341 | + | 0.457852i | 0.0260463 | + | 0.0451135i | 0.878755 | − | 0.477274i | \(-0.158375\pi\) |
−0.852708 | + | 0.522387i | \(0.825042\pi\) | |||||||
\(104\) | −8.53336 | + | 3.57395i | −0.836765 | + | 0.350455i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.27076 | − | 10.8613i | 0.609070 | − | 1.05494i | ||||
\(107\) | −19.3224 | −1.86797 | −0.933983 | − | 0.357318i | \(-0.883691\pi\) | ||||
−0.933983 | + | 0.357318i | \(0.883691\pi\) | |||||||
\(108\) | −0.983651 | −0.0946518 | ||||||||
\(109\) | 2.86620 | − | 4.96440i | 0.274532 | − | 0.475503i | −0.695485 | − | 0.718541i | \(-0.744810\pi\) |
0.970017 | + | 0.243037i | \(0.0781437\pi\) | |||||||
\(110\) | −0.681558 | + | 1.18049i | −0.0649840 | + | 0.112556i | ||||
\(111\) | −1.49805 | − | 2.59470i | −0.142189 | − | 0.246278i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.57480 | − | 4.45968i | −0.242216 | − | 0.419531i | 0.719129 | − | 0.694877i | \(-0.244541\pi\) |
−0.961345 | + | 0.275346i | \(0.911208\pi\) | |||||||
\(114\) | 5.44491 | 0.509962 | ||||||||
\(115\) | 0.522774 | + | 0.905470i | 0.0487489 | + | 0.0844355i | ||||
\(116\) | −1.07782 | + | 1.86684i | −0.100073 | + | 0.173332i | ||||
\(117\) | 0.694354 | − | 5.43908i | 0.0641931 | − | 0.502844i | ||||
\(118\) | −18.0602 | −1.66257 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.60777 | − | 2.78474i | 0.146769 | − | 0.254211i | ||||
\(121\) | 4.34362 | − | 7.52338i | 0.394875 | − | 0.683943i | ||||
\(122\) | −1.88589 | + | 3.26646i | −0.170740 | + | 0.295731i | ||||
\(123\) | −2.88199 | −0.259860 | ||||||||
\(124\) | −0.951766 | + | 1.64851i | −0.0854711 | + | 0.148040i | ||||
\(125\) | 5.68917 | 0.508855 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.50166 | − | 7.79710i | 0.399457 | − | 0.691881i | −0.594202 | − | 0.804316i | \(-0.702532\pi\) |
0.993659 | + | 0.112436i | \(0.0358652\pi\) | |||||||
\(128\) | −13.2227 | −1.16873 | ||||||||
\(129\) | 12.2890 | − | 21.2852i | 1.08199 | − | 1.87406i | ||||
\(130\) | 2.57164 | + | 1.95729i | 0.225548 | + | 0.171666i | ||||
\(131\) | 3.39920 | + | 5.88758i | 0.296989 | + | 0.514401i | 0.975446 | − | 0.220240i | \(-0.0706841\pi\) |
−0.678456 | + | 0.734641i | \(0.737351\pi\) | |||||||
\(132\) | −0.505639 | + | 0.875793i | −0.0440102 | + | 0.0762280i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.75829 | − | 9.97364i | −0.497440 | − | 0.861592i | ||||
\(135\) | −0.926861 | − | 1.60537i | −0.0797715 | − | 0.138168i | ||||
\(136\) | −12.3031 | −1.05498 | ||||||||
\(137\) | −14.0756 | −1.20256 | −0.601279 | − | 0.799039i | \(-0.705342\pi\) | ||||
−0.601279 | + | 0.799039i | \(0.705342\pi\) | |||||||
\(138\) | 2.86801 | + | 4.96754i | 0.244141 | + | 0.422865i | ||||
\(139\) | 8.64313 | + | 14.9703i | 0.733101 | + | 1.26977i | 0.955552 | + | 0.294824i | \(0.0952611\pi\) |
−0.222451 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.494165 | + | 0.855919i | −0.0416162 | + | 0.0720814i | ||||
\(142\) | 5.02213 | + | 8.69859i | 0.421448 | + | 0.729969i | ||||
\(143\) | 4.36321 | + | 3.32087i | 0.364870 | + | 0.277705i | ||||
\(144\) | 3.44280 | − | 5.96310i | 0.286900 | − | 0.496925i | ||||
\(145\) | −4.06238 | −0.337363 | ||||||||
\(146\) | 12.4484 | − | 21.5613i | 1.03024 | − | 1.78442i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.440707 | 0.0362259 | ||||||||
\(149\) | 8.56260 | − | 14.8309i | 0.701475 | − | 1.21499i | −0.266473 | − | 0.963842i | \(-0.585858\pi\) |
0.967949 | − | 0.251148i | \(-0.0808082\pi\) | |||||||
\(150\) | 15.0442 | 1.22835 | ||||||||
\(151\) | −7.89873 | + | 13.6810i | −0.642789 | + | 1.11334i | 0.342018 | + | 0.939693i | \(0.388890\pi\) |
−0.984807 | + | 0.173650i | \(0.944444\pi\) | |||||||
\(152\) | 2.16040 | − | 3.74191i | 0.175231 | − | 0.303509i | ||||
\(153\) | 3.64590 | − | 6.31488i | 0.294753 | − | 0.510528i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.58727 | −0.288137 | ||||||||
\(156\) | 1.90787 | + | 1.45209i | 0.152751 | + | 0.116260i | ||||
\(157\) | −1.89176 | + | 3.27662i | −0.150979 | + | 0.261503i | −0.931587 | − | 0.363517i | \(-0.881576\pi\) |
0.780609 | + | 0.625020i | \(0.214909\pi\) | |||||||
\(158\) | −11.3771 | − | 19.7058i | −0.905117 | − | 1.56771i | ||||
\(159\) | 17.5344 | 1.39057 | ||||||||
\(160\) | 0.516821 | + | 0.895161i | 0.0408583 | + | 0.0707687i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.55402 | − | 14.8160i | −0.672067 | − | 1.16406i | ||||
\(163\) | −0.857757 | + | 1.48568i | −0.0671847 | + | 0.116367i | −0.897661 | − | 0.440687i | \(-0.854735\pi\) |
0.830476 | + | 0.557054i | \(0.188068\pi\) | |||||||
\(164\) | 0.211961 | − | 0.367127i | 0.0165514 | − | 0.0286678i | ||||
\(165\) | −1.90579 | −0.148365 | ||||||||
\(166\) | 15.3935 | 1.19477 | ||||||||
\(167\) | 6.32605 | − | 10.9570i | 0.489524 | − | 0.847881i | −0.510403 | − | 0.859935i | \(-0.670504\pi\) |
0.999927 | + | 0.0120542i | \(0.00383706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.11992 | − | 9.26429i | 0.701532 | − | 0.712638i | ||||
\(170\) | 2.14886 | + | 3.72193i | 0.164810 | + | 0.285459i | ||||
\(171\) | 1.28043 | + | 2.21776i | 0.0979166 | + | 0.169596i | ||||
\(172\) | 1.80764 | + | 3.13092i | 0.137831 | + | 0.238730i | ||||
\(173\) | −5.74371 | + | 9.94839i | −0.436686 | + | 0.756362i | −0.997432 | − | 0.0716259i | \(-0.977181\pi\) |
0.560746 | + | 0.827988i | \(0.310515\pi\) | |||||||
\(174\) | −22.2868 | −1.68956 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.44280 | + | 5.96310i | 0.259510 | + | 0.449485i | ||||
\(177\) | −12.6251 | − | 21.8672i | −0.948958 | − | 1.64364i | ||||
\(178\) | 25.0699 | 1.87907 | ||||||||
\(179\) | 1.09225 | + | 1.89184i | 0.0816389 | + | 0.141403i | 0.903954 | − | 0.427630i | \(-0.140651\pi\) |
−0.822315 | + | 0.569032i | \(0.807318\pi\) | |||||||
\(180\) | −0.280329 | −0.0208945 | ||||||||
\(181\) | 11.5981 | 0.862081 | 0.431041 | − | 0.902333i | \(-0.358147\pi\) | ||||
0.431041 | + | 0.902333i | \(0.358147\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.27337 | −0.389819 | ||||||||
\(184\) | 4.55180 | 0.335563 | ||||||||
\(185\) | 0.415264 | + | 0.719258i | 0.0305308 | + | 0.0528809i | ||||
\(186\) | −19.6803 | −1.44303 | ||||||||
\(187\) | 3.64590 | + | 6.31488i | 0.266614 | + | 0.461790i | ||||
\(188\) | −0.0726885 | − | 0.125900i | −0.00530135 | − | 0.00918221i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.50934 | −0.109499 | ||||||||
\(191\) | −8.87961 | + | 15.3799i | −0.642506 | + | 1.11285i | 0.342365 | + | 0.939567i | \(0.388772\pi\) |
−0.984871 | + | 0.173286i | \(0.944561\pi\) | |||||||
\(192\) | −6.79147 | − | 11.7632i | −0.490132 | − | 0.848934i | ||||
\(193\) | −11.3189 | − | 19.6050i | −0.814756 | − | 1.41120i | −0.909503 | − | 0.415697i | \(-0.863538\pi\) |
0.0947474 | − | 0.995501i | \(-0.469796\pi\) | |||||||
\(194\) | 0.740517 | + | 1.28261i | 0.0531660 | + | 0.0920863i | ||||
\(195\) | −0.572172 | + | 4.48200i | −0.0409741 | + | 0.320962i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0032 | + | 17.3260i | −0.712696 | + | 1.23442i | 0.251146 | + | 0.967949i | \(0.419193\pi\) |
−0.963842 | + | 0.266476i | \(0.914141\pi\) | |||||||
\(198\) | −3.51717 | −0.249954 | ||||||||
\(199\) | 1.84885 | 0.131062 | 0.0655309 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655309 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(200\) | 5.96913 | − | 10.3388i | 0.422081 | − | 0.731066i | ||||
\(201\) | 8.05073 | − | 13.9443i | 0.567854 | − | 0.983553i | ||||
\(202\) | 2.23572 | + | 3.87237i | 0.157304 | + | 0.272459i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.59421 | + | 2.76126i | 0.111617 | + | 0.193327i | ||||
\(205\) | 0.798895 | 0.0557972 | ||||||||
\(206\) | −0.402003 | − | 0.696289i | −0.0280088 | − | 0.0485127i | ||||
\(207\) | −1.34888 | + | 2.33633i | −0.0937539 | + | 0.162386i | ||||
\(208\) | 15.0575 | − | 6.30641i | 1.04405 | − | 0.437271i | ||||
\(209\) | −2.56085 | −0.177138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.08474 | − | 14.0032i | 0.556576 | − | 0.964019i | −0.441203 | − | 0.897407i | \(-0.645448\pi\) |
0.997779 | − | 0.0666110i | \(-0.0212187\pi\) | |||||||
\(212\) | −1.28960 | + | 2.23366i | −0.0885702 | + | 0.153408i | ||||
\(213\) | −7.02150 | + | 12.1616i | −0.481105 | + | 0.833299i | ||||
\(214\) | 29.3850 | 2.00871 | ||||||||
\(215\) | −3.40655 | + | 5.90032i | −0.232325 | + | 0.402399i | ||||
\(216\) | −8.07020 | −0.549108 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.35884 | + | 7.54973i | −0.295218 | + | 0.511332i | ||||
\(219\) | 34.8085 | 2.35214 | ||||||||
\(220\) | 0.140165 | − | 0.242772i | 0.00944989 | − | 0.0163677i | ||||
\(221\) | 15.9458 | − | 6.67844i | 1.07263 | − | 0.449241i | ||||
\(222\) | 2.27820 | + | 3.94595i | 0.152902 | + | 0.264835i | ||||
\(223\) | −6.21589 | + | 10.7662i | −0.416247 | + | 0.720961i | −0.995558 | − | 0.0941455i | \(-0.969988\pi\) |
0.579312 | + | 0.815106i | \(0.303321\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.53779 | + | 6.12763i | 0.235853 | + | 0.408509i | ||||
\(226\) | 3.91568 | + | 6.78216i | 0.260467 | + | 0.451142i | ||||
\(227\) | −1.23497 | −0.0819681 | −0.0409841 | − | 0.999160i | \(-0.513049\pi\) | ||||
−0.0409841 | + | 0.999160i | \(0.513049\pi\) | |||||||
\(228\) | −1.11976 | −0.0741581 | ||||||||
\(229\) | 3.27757 | + | 5.67692i | 0.216588 | + | 0.375141i | 0.953763 | − | 0.300561i | \(-0.0971739\pi\) |
−0.737175 | + | 0.675702i | \(0.763841\pi\) | |||||||
\(230\) | −0.795020 | − | 1.37702i | −0.0524221 | − | 0.0907977i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.84282 | + | 15.3162i | −0.580559 | + | 1.00556i | ||||
\(233\) | −3.14944 | − | 5.45498i | −0.206326 | − | 0.357368i | 0.744228 | − | 0.667925i | \(-0.232818\pi\) |
−0.950555 | + | 0.310558i | \(0.899484\pi\) | |||||||
\(234\) | −1.05596 | + | 8.27162i | −0.0690300 | + | 0.540732i | ||||
\(235\) | 0.136984 | − | 0.237263i | 0.00893584 | − | 0.0154773i | ||||
\(236\) | 3.71413 | 0.241769 | ||||||||
\(237\) | 15.9065 | − | 27.5509i | 1.03324 | − | 1.78962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9193 | −1.22379 | −0.611895 | − | 0.790939i | \(-0.709592\pi\) | ||||
−0.611895 | + | 0.790939i | \(0.709592\pi\) | |||||||
\(240\) | −2.83698 | + | 4.91380i | −0.183126 | + | 0.317184i | ||||
\(241\) | −22.2968 | −1.43626 | −0.718131 | − | 0.695908i | \(-0.755002\pi\) | ||||
−0.718131 | + | 0.695908i | \(0.755002\pi\) | |||||||
\(242\) | −6.60567 | + | 11.4414i | −0.424628 | + | 0.735478i | ||||
\(243\) | 7.24176 | − | 12.5431i | 0.464559 | − | 0.804640i | ||||
\(244\) | 0.387839 | − | 0.671757i | 0.0248289 | − | 0.0430048i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.38285 | 0.279440 | ||||||||
\(247\) | −0.768841 | + | 6.02256i | −0.0489202 | + | 0.383206i | ||||
\(248\) | −7.80861 | + | 13.5249i | −0.495847 | + | 0.858833i | ||||
\(249\) | 10.7609 | + | 18.6385i | 0.681947 | + | 1.18117i | ||||
\(250\) | −8.65194 | −0.547197 | ||||||||
\(251\) | −3.47657 | − | 6.02160i | −0.219439 | − | 0.380080i | 0.735197 | − | 0.677853i | \(-0.237090\pi\) |
−0.954637 | + | 0.297773i | \(0.903756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.34888 | − | 2.33633i | −0.0848036 | − | 0.146884i | ||||
\(254\) | −6.84600 | + | 11.8576i | −0.429556 | + | 0.744013i | ||||
\(255\) | −3.00435 | + | 5.20368i | −0.188139 | + | 0.325867i | ||||
\(256\) | 7.33206 | 0.458254 | ||||||||
\(257\) | −21.1551 | −1.31962 | −0.659811 | − | 0.751432i | \(-0.729364\pi\) | ||||
−0.659811 | + | 0.751432i | \(0.729364\pi\) | |||||||
\(258\) | −18.6888 | + | 32.3700i | −1.16352 | + | 2.01527i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.528865 | − | 0.402523i | −0.0327988 | − | 0.0249634i | ||||
\(261\) | −5.24097 | − | 9.07763i | −0.324408 | − | 0.561891i | ||||
\(262\) | −5.16941 | − | 8.95368i | −0.319367 | − | 0.553160i | ||||
\(263\) | 4.21496 | + | 7.30053i | 0.259906 | + | 0.450170i | 0.966216 | − | 0.257732i | \(-0.0829752\pi\) |
−0.706311 | + | 0.707902i | \(0.749642\pi\) | |||||||
\(264\) | −4.14844 | + | 7.18530i | −0.255319 | + | 0.442225i | ||||
\(265\) | −4.86060 | −0.298584 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.5253 | + | 30.3547i | 1.07253 | + | 1.85768i | ||||
\(268\) | 1.18421 | + | 2.05111i | 0.0723371 | + | 0.125292i | ||||
\(269\) | 5.83039 | 0.355485 | 0.177743 | − | 0.984077i | \(-0.443121\pi\) | ||||
0.177743 | + | 0.984077i | \(0.443121\pi\) | |||||||
\(270\) | 1.40955 | + | 2.44141i | 0.0857823 | + | 0.148579i | ||||
\(271\) | −18.4299 | −1.11954 | −0.559769 | − | 0.828648i | \(-0.689110\pi\) | ||||
−0.559769 | + | 0.828648i | \(0.689110\pi\) | |||||||
\(272\) | 21.7093 | 1.31632 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.4058 | 1.29317 | ||||||||
\(275\) | −7.07558 | −0.426673 | ||||||||
\(276\) | −0.589815 | − | 1.02159i | −0.0355027 | − | 0.0614925i | ||||
\(277\) | −6.18307 | −0.371505 | −0.185752 | − | 0.982597i | \(-0.559472\pi\) | ||||
−0.185752 | + | 0.982597i | \(0.559472\pi\) | |||||||
\(278\) | −13.1442 | − | 22.7665i | −0.788340 | − | 1.36544i | ||||
\(279\) | −4.62802 | − | 8.01596i | −0.277072 | − | 0.479903i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.64049 | −0.336483 | −0.168242 | − | 0.985746i | \(-0.553809\pi\) | ||||
−0.168242 | + | 0.985746i | \(0.553809\pi\) | |||||||
\(282\) | 0.751513 | − | 1.30166i | 0.0447520 | − | 0.0775127i | ||||
\(283\) | −8.22771 | − | 14.2508i | −0.489086 | − | 0.847123i | 0.510835 | − | 0.859679i | \(-0.329336\pi\) |
−0.999921 | + | 0.0125564i | \(0.996003\pi\) | |||||||
\(284\) | −1.03282 | − | 1.78889i | −0.0612864 | − | 0.106151i | ||||
\(285\) | −1.05512 | − | 1.82751i | −0.0624996 | − | 0.108253i | ||||
\(286\) | −6.63545 | − | 5.05029i | −0.392362 | − | 0.298630i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.33353 | + | 2.30973i | −0.0785787 | + | 0.136102i | ||||
\(289\) | 5.99003 | 0.352355 | ||||||||
\(290\) | 6.17797 | 0.362783 | ||||||||
\(291\) | −1.03533 | + | 1.79324i | −0.0606919 | + | 0.105121i | ||||
\(292\) | −2.56005 | + | 4.43414i | −0.149816 | + | 0.259489i | ||||
\(293\) | 15.3086 | + | 26.5152i | 0.894335 | + | 1.54903i | 0.834625 | + | 0.550819i | \(0.185684\pi\) |
0.0597104 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.49970 | + | 6.06166i | 0.203760 | + | 0.352923i | ||||
\(296\) | 3.61571 | 0.210159 | ||||||||
\(297\) | 2.39153 | + | 4.14225i | 0.138771 | + | 0.240358i | ||||
\(298\) | −13.0218 | + | 22.5544i | −0.754331 | + | 1.30654i | ||||
\(299\) | −5.89952 | + | 2.47084i | −0.341178 | + | 0.142893i | ||||
\(300\) | −3.09388 | −0.178625 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.0122 | − | 20.8057i | 0.691223 | − | 1.19723i | ||||
\(303\) | −3.12578 | + | 5.41401i | −0.179571 | + | 0.311027i | ||||
\(304\) | −3.81212 | + | 6.60278i | −0.218640 | + | 0.378696i | ||||
\(305\) | 1.46179 | 0.0837019 | ||||||||
\(306\) | −5.54458 | + | 9.60350i | −0.316963 | + | 0.548995i | ||||
\(307\) | 9.96020 | 0.568459 | 0.284229 | − | 0.958756i | \(-0.408262\pi\) | ||||
0.284229 | + | 0.958756i | \(0.408262\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.562044 | − | 0.973489i | 0.0319736 | − | 0.0553799i | ||||
\(310\) | 5.45543 | 0.309847 | ||||||||
\(311\) | 13.8734 | − | 24.0294i | 0.786687 | − | 1.36258i | −0.141299 | − | 0.989967i | \(-0.545128\pi\) |
0.927986 | − | 0.372615i | \(-0.121539\pi\) | |||||||
\(312\) | 15.6528 | + | 11.9134i | 0.886164 | + | 0.674466i | ||||
\(313\) | −8.26136 | − | 14.3091i | −0.466960 | − | 0.808798i | 0.532328 | − | 0.846538i | \(-0.321317\pi\) |
−0.999288 | + | 0.0377401i | \(0.987984\pi\) | |||||||
\(314\) | 2.87693 | − | 4.98300i | 0.162355 | − | 0.281207i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.33975 | + | 4.05256i | 0.131621 | + | 0.227974i | ||||
\(317\) | −11.8396 | − | 20.5069i | −0.664980 | − | 1.15178i | −0.979291 | − | 0.202459i | \(-0.935107\pi\) |
0.314310 | − | 0.949320i | \(-0.398227\pi\) | |||||||
\(318\) | −26.6659 | −1.49535 | ||||||||
\(319\) | 10.4819 | 0.586876 | ||||||||
\(320\) | 1.88261 | + | 3.26078i | 0.105241 | + | 0.182283i | ||||
\(321\) | 20.5417 | + | 35.5793i | 1.14653 | + | 1.98584i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.03701 | + | 6.99230i | −0.224625 | + | 0.389062i | ||||
\(324\) | 1.75916 | + | 3.04696i | 0.0977312 | + | 0.169275i | ||||
\(325\) | −2.12429 | + | 16.6402i | −0.117834 | + | 0.923033i | ||||
\(326\) | 1.30445 | − | 2.25938i | 0.0722470 | − | 0.125136i | ||||
\(327\) | −12.1883 | −0.674014 | ||||||||
\(328\) | 1.73900 | − | 3.01203i | 0.0960202 | − | 0.166312i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.89827 | 0.159545 | ||||||||
\(331\) | −3.97604 | + | 6.88671i | −0.218543 | + | 0.378528i | −0.954363 | − | 0.298650i | \(-0.903464\pi\) |
0.735820 | + | 0.677178i | \(0.236797\pi\) | |||||||
\(332\) | −3.16573 | −0.173742 | ||||||||
\(333\) | −1.07148 | + | 1.85586i | −0.0587168 | + | 0.101700i | ||||
\(334\) | −9.62049 | + | 16.6632i | −0.526410 | + | 0.911768i | ||||
\(335\) | −2.23168 | + | 3.86539i | −0.121930 | + | 0.211189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.91326 | −0.431063 | −0.215531 | − | 0.976497i | \(-0.569148\pi\) | ||||
−0.215531 | + | 0.976497i | \(0.569148\pi\) | |||||||
\(338\) | −13.8693 | + | 14.0889i | −0.754392 | + | 0.766334i | ||||
\(339\) | −5.47456 | + | 9.48221i | −0.297337 | + | 0.515003i | ||||
\(340\) | −0.441920 | − | 0.765427i | −0.0239665 | − | 0.0415111i | ||||
\(341\) | 9.25603 | 0.501242 | ||||||||
\(342\) | −1.94724 | − | 3.37271i | −0.105294 | − | 0.182375i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.8305 | + | 25.6871i | 0.799605 | + | 1.38496i | ||||
\(345\) | 1.11153 | − | 1.92522i | 0.0598426 | − | 0.103650i | ||||
\(346\) | 8.73488 | − | 15.1292i | 0.469590 | − | 0.813353i | ||||
\(347\) | 7.13571 | 0.383065 | 0.191533 | − | 0.981486i | \(-0.438654\pi\) | ||||
0.191533 | + | 0.981486i | \(0.438654\pi\) | |||||||
\(348\) | 4.58335 | 0.245694 | ||||||||
\(349\) | −0.688402 | + | 1.19235i | −0.0368493 | + | 0.0638249i | −0.883862 | − | 0.467748i | \(-0.845065\pi\) |
0.847013 | + | 0.531573i | \(0.178399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.4597 | − | 4.38073i | 0.558296 | − | 0.233826i | ||||
\(352\) | −1.33353 | − | 2.30973i | −0.0710771 | − | 0.123109i | ||||
\(353\) | −0.346608 | − | 0.600342i | −0.0184481 | − | 0.0319530i | 0.856654 | − | 0.515891i | \(-0.172539\pi\) |
−0.875102 | + | 0.483938i | \(0.839206\pi\) | |||||||
\(354\) | 19.1999 | + | 33.2551i | 1.02046 | + | 1.76749i | ||||
\(355\) | 1.94638 | − | 3.37123i | 0.103303 | − | 0.178926i | ||||
\(356\) | −5.15571 | −0.273252 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.66107 | − | 2.87706i | −0.0877904 | − | 0.152057i | ||||
\(359\) | 2.90182 | + | 5.02611i | 0.153152 | + | 0.265268i | 0.932385 | − | 0.361467i | \(-0.117724\pi\) |
−0.779232 | + | 0.626735i | \(0.784391\pi\) | |||||||
\(360\) | −2.29991 | −0.121216 | ||||||||
\(361\) | 8.08222 | + | 13.9988i | 0.425380 | + | 0.736780i | ||||
\(362\) | −17.6381 | −0.927038 | ||||||||
\(363\) | −18.4709 | −0.969472 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.64902 | −0.505053 | ||||||||
\(366\) | 8.01960 | 0.419191 | ||||||||
\(367\) | −3.67578 | − | 6.36664i | −0.191874 | − | 0.332336i | 0.753997 | − | 0.656878i | \(-0.228123\pi\) |
−0.945871 | + | 0.324542i | \(0.894790\pi\) | |||||||
\(368\) | −8.03187 | −0.418690 | ||||||||
\(369\) | 1.03067 | + | 1.78518i | 0.0536546 | + | 0.0929325i | ||||
\(370\) | −0.631522 | − | 1.09383i | −0.0328313 | − | 0.0568654i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.04731 | 0.209843 | ||||||||
\(373\) | −9.19942 | + | 15.9339i | −0.476328 | + | 0.825024i | −0.999632 | − | 0.0271216i | \(-0.991366\pi\) |
0.523304 | + | 0.852146i | \(0.324699\pi\) | |||||||
\(374\) | −5.54458 | − | 9.60350i | −0.286704 | − | 0.496585i | ||||
\(375\) | −6.04819 | − | 10.4758i | −0.312327 | − | 0.540966i | ||||
\(376\) | −0.596361 | − | 1.03293i | −0.0307550 | − | 0.0532692i | ||||
\(377\) | 3.14698 | − | 24.6512i | 0.162078 | − | 1.26960i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.42550 | − | 4.20110i | 0.124590 | − | 0.215796i | −0.796983 | − | 0.604002i | \(-0.793572\pi\) |
0.921573 | + | 0.388206i | \(0.126905\pi\) | |||||||
\(380\) | 0.310401 | 0.0159232 | ||||||||
\(381\) | −19.1429 | −0.980723 | ||||||||
\(382\) | 13.5039 | − | 23.3894i | 0.690918 | − | 1.19671i | ||||
\(383\) | 11.4103 | − | 19.7631i | 0.583037 | − | 1.00985i | −0.412080 | − | 0.911148i | \(-0.635198\pi\) |
0.995117 | − | 0.0987019i | \(-0.0314690\pi\) | |||||||
\(384\) | 14.0571 | + | 24.3476i | 0.717349 | + | 1.24249i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.2136 | + | 29.8148i | 0.876147 | + | 1.51753i | ||||
\(387\) | −17.5795 | −0.893615 | ||||||||
\(388\) | −0.152290 | − | 0.263773i | −0.00773134 | − | 0.0133911i | ||||
\(389\) | 10.1561 | − | 17.5908i | 0.514933 | − | 0.891891i | −0.484916 | − | 0.874561i | \(-0.661150\pi\) |
0.999850 | − | 0.0173304i | \(-0.00551672\pi\) | |||||||
\(390\) | 0.870144 | − | 6.81610i | 0.0440615 | − | 0.345147i | ||||
\(391\) | −8.50569 | −0.430151 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.22741 | − | 12.5182i | 0.364575 | − | 0.631462i | ||||
\(394\) | 15.2125 | − | 26.3489i | 0.766397 | − | 1.32744i | ||||
\(395\) | −4.40933 | + | 7.63719i | −0.221858 | + | 0.384268i | ||||
\(396\) | 0.723317 | 0.0363481 | ||||||||
\(397\) | 17.0689 | − | 29.5641i | 0.856662 | − | 1.48378i | −0.0184326 | − | 0.999830i | \(-0.505868\pi\) |
0.875095 | − | 0.483952i | \(-0.160799\pi\) | |||||||
\(398\) | −2.81169 | −0.140937 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.5328 | + | 18.2434i | −0.526640 | + | 0.912168i | ||||
\(401\) | −3.02596 | −0.151109 | −0.0755547 | − | 0.997142i | \(-0.524073\pi\) | ||||
−0.0755547 | + | 0.997142i | \(0.524073\pi\) | |||||||
\(402\) | −12.2433 | + | 21.2061i | −0.610642 | + | 1.05766i | ||||
\(403\) | 2.77893 | − | 21.7682i | 0.138428 | − | 1.08435i | ||||
\(404\) | −0.459782 | − | 0.796365i | −0.0228750 | − | 0.0396207i | ||||
\(405\) | −3.31520 | + | 5.74209i | −0.164734 | + | 0.285327i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07148 | − | 1.85586i | −0.0531114 | − | 0.0919916i | ||||
\(408\) | 13.0795 | + | 22.6543i | 0.647530 | + | 1.12155i | ||||
\(409\) | 5.38325 | 0.266184 | 0.133092 | − | 0.991104i | \(-0.457509\pi\) | ||||
0.133092 | + | 0.991104i | \(0.457509\pi\) | |||||||
\(410\) | −1.21494 | −0.0600015 | ||||||||
\(411\) | 14.9638 | + | 25.9181i | 0.738111 | + | 1.27845i | ||||
\(412\) | 0.0826731 | + | 0.143194i | 0.00407301 | + | 0.00705466i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.05135 | − | 3.55304i | 0.100818 | − | 0.174622i | ||||
\(415\) | −2.98296 | − | 5.16664i | −0.146428 | − | 0.253620i | ||||
\(416\) | −5.83235 | + | 2.44271i | −0.285954 | + | 0.119764i | ||||
\(417\) | 18.3771 | − | 31.8301i | 0.899932 | − | 1.55873i | ||||
\(418\) | 3.89447 | 0.190485 | ||||||||
\(419\) | −2.94117 | + | 5.09426i | −0.143686 | + | 0.248871i | −0.928882 | − | 0.370376i | \(-0.879229\pi\) |
0.785196 | + | 0.619247i | \(0.212562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.7614 | −1.40174 | −0.700872 | − | 0.713287i | \(-0.747206\pi\) | ||||
−0.700872 | + | 0.713287i | \(0.747206\pi\) | |||||||
\(422\) | −12.2951 | + | 21.2957i | −0.598514 | + | 1.03666i | ||||
\(423\) | 0.706904 | 0.0343708 | ||||||||
\(424\) | −10.5803 | + | 18.3257i | −0.513826 | + | 0.889973i | ||||
\(425\) | −11.1542 | + | 19.3196i | −0.541057 | + | 0.937138i | ||||
\(426\) | 10.6781 | − | 18.4950i | 0.517356 | − | 0.896087i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.04311 | −0.292105 | ||||||||
\(429\) | 1.47634 | − | 11.5646i | 0.0712786 | − | 0.558346i | ||||
\(430\) | 5.18059 | − | 8.97305i | 0.249830 | − | 0.432719i | ||||
\(431\) | −4.19294 | − | 7.26238i | −0.201967 | − | 0.349817i | 0.747195 | − | 0.664605i | \(-0.231400\pi\) |
−0.949162 | + | 0.314788i | \(0.898067\pi\) | |||||||
\(432\) | 14.2403 | 0.685135 | ||||||||
\(433\) | 13.7996 | + | 23.9017i | 0.663168 | + | 1.14864i | 0.979779 | + | 0.200085i | \(0.0641218\pi\) |
−0.316611 | + | 0.948556i | \(0.602545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.31874 | + | 7.48028i | 0.207068 | + | 0.358652i | ||||
\(436\) | 0.896409 | − | 1.55263i | 0.0429302 | − | 0.0743573i | ||||
\(437\) | 1.49358 | − | 2.58696i | 0.0714478 | − | 0.123751i | ||||
\(438\) | −52.9359 | −2.52937 | ||||||||
\(439\) | 31.1737 | 1.48784 | 0.743921 | − | 0.668268i | \(-0.232964\pi\) | ||||
0.743921 | + | 0.668268i | \(0.232964\pi\) | |||||||
\(440\) | 1.14996 | − | 1.99178i | 0.0548221 | − | 0.0949546i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.2500 | + | 10.1564i | −1.15345 | + | 0.483090i | ||||
\(443\) | 11.7941 | + | 20.4281i | 0.560357 | + | 0.970566i | 0.997465 | + | 0.0711573i | \(0.0226692\pi\) |
−0.437109 | + | 0.899409i | \(0.643997\pi\) | |||||||
\(444\) | −0.468518 | − | 0.811497i | −0.0222349 | − | 0.0385119i | ||||
\(445\) | −4.85806 | − | 8.41440i | −0.230294 | − | 0.398881i | ||||
\(446\) | 9.45296 | − | 16.3730i | 0.447611 | − | 0.775284i | ||||
\(447\) | −36.4118 | −1.72222 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41328 | − | 2.44787i | −0.0666968 | − | 0.115522i | 0.830749 | − | 0.556648i | \(-0.187913\pi\) |
−0.897445 | + | 0.441125i | \(0.854579\pi\) | |||||||
\(450\) | −5.38018 | − | 9.31874i | −0.253624 | − | 0.439289i | ||||
\(451\) | −2.06134 | −0.0970649 | ||||||||
\(452\) | −0.805272 | − | 1.39477i | −0.0378768 | − | 0.0656046i | ||||
\(453\) | 33.5887 | 1.57814 | ||||||||
\(454\) | 1.87812 | 0.0881444 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.18691 | −0.430217 | ||||||||
\(457\) | −37.7432 | −1.76555 | −0.882776 | − | 0.469795i | \(-0.844328\pi\) | ||||
−0.882776 | + | 0.469795i | \(0.844328\pi\) | |||||||
\(458\) | −4.98444 | − | 8.63330i | −0.232908 | − | 0.403408i | ||||
\(459\) | 15.0803 | 0.703890 | ||||||||
\(460\) | 0.163498 | + | 0.283188i | 0.00762315 | + | 0.0132037i | ||||
\(461\) | −17.3293 | − | 30.0152i | −0.807106 | − | 1.39795i | −0.914860 | − | 0.403771i | \(-0.867699\pi\) |
0.107754 | − | 0.994178i | \(-0.465634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5114 | 0.860296 | 0.430148 | − | 0.902758i | \(-0.358461\pi\) | ||||
0.430148 | + | 0.902758i | \(0.358461\pi\) | |||||||
\(464\) | 15.6036 | − | 27.0262i | 0.724377 | − | 1.25466i | ||||
\(465\) | 3.81365 | + | 6.60543i | 0.176854 | + | 0.306320i | ||||
\(466\) | 4.78958 | + | 8.29579i | 0.221873 | + | 0.384295i | ||||
\(467\) | −3.31392 | − | 5.73987i | −0.153350 | − | 0.265610i | 0.779107 | − | 0.626891i | \(-0.215673\pi\) |
−0.932457 | + | 0.361281i | \(0.882339\pi\) | |||||||
\(468\) | 0.217161 | − | 1.70108i | 0.0100383 | − | 0.0786326i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.208321 | + | 0.360823i | −0.00960915 | + | 0.0166435i | ||||
\(471\) | 8.04455 | 0.370673 | ||||||||
\(472\) | 30.4720 | 1.40259 | ||||||||
\(473\) | 8.78973 | − | 15.2243i | 0.404152 | − | 0.700012i | ||||
\(474\) | −24.1902 | + | 41.8987i | −1.11109 | + | 1.92447i | ||||
\(475\) | −3.91730 | − | 6.78497i | −0.179738 | − | 0.311316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.27076 | − | 10.8613i | −0.287118 | − | 0.497304i | ||||
\(478\) | 28.7720 | 1.31600 | ||||||||
\(479\) | 8.72630 | + | 15.1144i | 0.398715 | + | 0.690594i | 0.993568 | − | 0.113240i | \(-0.0361230\pi\) |
−0.594853 | + | 0.803835i | \(0.702790\pi\) | |||||||
\(480\) | 1.09887 | − | 1.90330i | 0.0501564 | − | 0.0868734i | ||||
\(481\) | −4.68626 | + | 1.96271i | −0.213675 | + | 0.0894917i | ||||
\(482\) | 33.9083 | 1.54448 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.35848 | − | 2.35295i | 0.0617489 | − | 0.106952i | ||||
\(485\) | 0.286995 | − | 0.497090i | 0.0130318 | − | 0.0225717i | ||||
\(486\) | −11.0131 | + | 19.0752i | −0.499563 | + | 0.865269i | ||||
\(487\) | −35.5138 | −1.60928 | −0.804641 | − | 0.593762i | \(-0.797642\pi\) | ||||
−0.804641 | + | 0.593762i | \(0.797642\pi\) | |||||||
\(488\) | 3.18196 | − | 5.51132i | 0.144041 | − | 0.249486i | ||||
\(489\) | 3.64754 | 0.164948 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9059 | − | 25.8178i | 0.672695 | − | 1.16514i | −0.304442 | − | 0.952531i | \(-0.598470\pi\) |
0.977137 | − | 0.212611i | \(-0.0681966\pi\) | |||||||
\(492\) | −0.901347 | −0.0406359 | ||||||||
\(493\) | 16.5241 | − | 28.6205i | 0.744207 | − | 1.28900i | ||||
\(494\) | 1.16923 | − | 9.15895i | 0.0526063 | − | 0.412081i | ||||
\(495\) | 0.681558 | + | 1.18049i | 0.0306338 | + | 0.0530592i | ||||
\(496\) | 13.7787 | − | 23.8653i | 0.618680 | − | 1.07159i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.3649 | − | 28.3449i | −0.733331 | − | 1.27017i | ||||
\(499\) | 3.75483 | + | 6.50355i | 0.168089 | + | 0.291139i | 0.937748 | − | 0.347316i | \(-0.112907\pi\) |
−0.769659 | + | 0.638455i | \(0.779574\pi\) | |||||||
\(500\) | 1.77930 | 0.0795726 | ||||||||
\(501\) | −26.9010 | −1.20185 | ||||||||
\(502\) | 5.28708 | + | 9.15750i | 0.235974 | + | 0.408719i | ||||
\(503\) | −0.492171 | − | 0.852466i | −0.0219448 | − | 0.0380096i | 0.854844 | − | 0.518884i | \(-0.173652\pi\) |
−0.876789 | + | 0.480875i | \(0.840319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.866474 | − | 1.50078i | 0.0385576 | − | 0.0667837i | ||||
\(506\) | 2.05135 | + | 3.55304i | 0.0911934 | + | 0.157952i | ||||
\(507\) | −26.7543 | − | 6.94407i | −1.18820 | − | 0.308397i | ||||
\(508\) | 1.40790 | − | 2.43856i | 0.0624655 | − | 0.108193i | ||||
\(509\) | 12.9792 | 0.575291 | 0.287646 | − | 0.957737i | \(-0.407127\pi\) | ||||
0.287646 | + | 0.957737i | \(0.407127\pi\) | |||||||
\(510\) | 4.56893 | − | 7.91362i | 0.202316 | − | 0.350421i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.2950 | 0.675949 | ||||||||
\(513\) | −2.64808 | + | 4.58661i | −0.116916 | + | 0.202504i | ||||
\(514\) | 32.1722 | 1.41905 | ||||||||
\(515\) | −0.155800 | + | 0.269854i | −0.00686538 | + | 0.0118912i | ||||
\(516\) | 3.84342 | − | 6.65699i | 0.169197 | − | 0.293058i | ||||
\(517\) | −0.353452 | + | 0.612196i | −0.0155448 | + | 0.0269244i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.4247 | 1.07212 | ||||||||
\(520\) | −4.33899 | − | 3.30244i | −0.190277 | − | 0.144822i | ||||
\(521\) | 9.70730 | − | 16.8135i | 0.425285 | − | 0.736614i | −0.571162 | − | 0.820837i | \(-0.693507\pi\) |
0.996447 | + | 0.0842226i | \(0.0268407\pi\) | |||||||
\(522\) | 7.97033 | + | 13.8050i | 0.348852 | + | 0.604229i | ||||
\(523\) | 27.2719 | 1.19252 | 0.596259 | − | 0.802792i | \(-0.296653\pi\) | ||||
0.596259 | + | 0.802792i | \(0.296653\pi\) | |||||||
\(524\) | 1.06311 | + | 1.84135i | 0.0464420 | + | 0.0804399i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.41000 | − | 11.1024i | −0.279489 | − | 0.484090i | ||||
\(527\) | 14.5915 | − | 25.2732i | 0.635616 | − | 1.10092i | ||||
\(528\) | 7.32011 | − | 12.6788i | 0.318567 | − | 0.551774i | ||||
\(529\) | −19.8531 | −0.863179 | ||||||||
\(530\) | 7.39187 | 0.321082 | ||||||||
\(531\) | −9.03008 | + | 15.6406i | −0.391872 | + | 0.678742i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.618874 | + | 4.84783i | −0.0268064 | + | 0.209983i | ||||
\(534\) | −26.6520 | − | 46.1626i | −1.15334 | − | 1.99765i | ||||
\(535\) | −5.69422 | − | 9.86268i | −0.246183 | − | 0.426401i | ||||
\(536\) | 9.71566 | + | 16.8280i | 0.419652 | + | 0.726859i | ||||
\(537\) | 2.32236 | − | 4.02245i | 0.100217 | − | 0.173582i | ||||
\(538\) | −8.86670 | −0.382271 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.289878 | − | 0.502083i | −0.0124743 | − | 0.0216062i | ||||
\(541\) | 15.0495 | + | 26.0665i | 0.647029 | + | 1.12069i | 0.983829 | + | 0.179111i | \(0.0573223\pi\) |
−0.336799 | + | 0.941576i | \(0.609344\pi\) | |||||||
\(542\) | 28.0278 | 1.20389 | ||||||||
\(543\) | −12.3300 | − | 21.3562i | −0.529132 | − | 0.916483i | ||||
\(544\) | −8.40885 | −0.360526 | ||||||||
\(545\) | 3.37863 | 0.144724 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1451 | −1.11788 | −0.558942 | − | 0.829207i | \(-0.688793\pi\) | ||||
−0.558942 | + | 0.829207i | \(0.688793\pi\) | |||||||
\(548\) | −4.40216 | −0.188051 | ||||||||
\(549\) | 1.88589 | + | 3.26646i | 0.0804878 | + | 0.139409i | ||||
\(550\) | 10.7604 | 0.458823 | ||||||||
\(551\) | 5.80319 | + | 10.0514i | 0.247224 | + | 0.428205i | ||||
\(552\) | −4.83905 | − | 8.38147i | −0.205963 | − | 0.356739i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.40305 | 0.399497 | ||||||||
\(555\) | 0.882938 | − | 1.52929i | 0.0374786 | − | 0.0649149i | ||||
\(556\) | 2.70316 | + | 4.68200i | 0.114639 | + | 0.198561i | ||||
\(557\) | −8.95317 | − | 15.5073i | −0.379358 | − | 0.657067i | 0.611611 | − | 0.791159i | \(-0.290522\pi\) |
−0.990969 | + | 0.134091i | \(0.957188\pi\) | |||||||
\(558\) | 7.03817 | + | 12.1905i | 0.297949 | + | 0.516063i | ||||
\(559\) | −33.1652 | − | 25.2423i | −1.40274 | − | 1.06764i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.75195 | − | 13.4268i | 0.327287 | − | 0.566878i | ||||
\(562\) | 8.57790 | 0.361837 | ||||||||
\(563\) | −31.6549 | −1.33410 | −0.667048 | − | 0.745015i | \(-0.732442\pi\) | ||||
−0.667048 | + | 0.745015i | \(0.732442\pi\) | |||||||
\(564\) | −0.154551 | + | 0.267690i | −0.00650777 | + | 0.0112718i | ||||
\(565\) | 1.51756 | − | 2.62850i | 0.0638443 | − | 0.110582i | ||||
\(566\) | 12.5125 | + | 21.6722i | 0.525939 | + | 0.910953i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.47358 | − | 14.6767i | −0.355544 | − | 0.615820i | ||||
\(569\) | −26.1111 | −1.09463 | −0.547317 | − | 0.836925i | \(-0.684351\pi\) | ||||
−0.547317 | + | 0.836925i | \(0.684351\pi\) | |||||||
\(570\) | 1.60459 | + | 2.77923i | 0.0672089 | + | 0.116409i | ||||
\(571\) | −6.65205 | + | 11.5217i | −0.278380 | + | 0.482168i | −0.970982 | − | 0.239152i | \(-0.923131\pi\) |
0.692602 | + | 0.721320i | \(0.256464\pi\) | |||||||
\(572\) | 1.36460 | + | 1.03861i | 0.0570569 | + | 0.0434264i | ||||
\(573\) | 37.7599 | 1.57744 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.12674 | − | 7.14773i | 0.172097 | − | 0.298081i | ||||
\(576\) | −4.85760 | + | 8.41361i | −0.202400 | + | 0.350567i | ||||
\(577\) | 8.38564 | − | 14.5244i | 0.349099 | − | 0.604657i | −0.636991 | − | 0.770871i | \(-0.719821\pi\) |
0.986090 | + | 0.166214i | \(0.0531544\pi\) | |||||||
\(578\) | −9.10948 | −0.378905 | ||||||||
\(579\) | −24.0665 | + | 41.6844i | −1.00017 | + | 1.73234i | ||||
\(580\) | −1.27052 | −0.0527554 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.57450 | − | 2.72711i | 0.0652650 | − | 0.113042i | ||||
\(583\) | 12.5415 | 0.519417 | ||||||||
\(584\) | −21.0036 | + | 36.3792i | −0.869133 | + | 1.50538i | ||||
\(585\) | 2.98088 | − | 1.24846i | 0.123244 | − | 0.0516173i | ||||
\(586\) | −23.2808 | − | 40.3236i | −0.961723 | − | 1.66575i | ||||
\(587\) | 5.03261 | − | 8.71673i | 0.207718 | − | 0.359778i | −0.743277 | − | 0.668983i | \(-0.766730\pi\) |
0.950995 | + | 0.309205i | \(0.100063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.12448 | + | 8.87587i | 0.211151 | + | 0.365724i | ||||
\(590\) | −5.32225 | − | 9.21841i | −0.219114 | − | 0.379516i | ||||
\(591\) | 42.5377 | 1.74977 | ||||||||
\(592\) | −6.38009 | −0.262220 | ||||||||
\(593\) | −19.7161 | − | 34.1493i | −0.809643 | − | 1.40234i | −0.913111 | − | 0.407710i | \(-0.866327\pi\) |
0.103468 | − | 0.994633i | \(-0.467006\pi\) | |||||||
\(594\) | −3.63697 | − | 6.29942i | −0.149227 | − | 0.258468i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.67797 | − | 4.63838i | 0.109694 | − | 0.189995i | ||||
\(597\) | −1.96553 | − | 3.40439i | −0.0804436 | − | 0.139332i | ||||
\(598\) | 8.97183 | − | 3.75759i | 0.366886 | − | 0.153659i | ||||
\(599\) | −6.88601 | + | 11.9269i | −0.281355 | + | 0.487321i | −0.971719 | − | 0.236142i | \(-0.924117\pi\) |
0.690364 | + | 0.723462i | \(0.257450\pi\) | |||||||
\(600\) | −25.3833 | −1.03627 | ||||||||
\(601\) | −16.6312 | + | 28.8060i | −0.678399 | + | 1.17502i | 0.297064 | + | 0.954858i | \(0.403993\pi\) |
−0.975463 | + | 0.220164i | \(0.929341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.5166 | −0.468991 | ||||||||
\(604\) | −2.47034 | + | 4.27876i | −0.100517 | + | 0.174100i | ||||
\(605\) | 5.12019 | 0.208165 | ||||||||
\(606\) | 4.75360 | − | 8.23348i | 0.193102 | − | 0.334462i | ||||
\(607\) | −21.9824 | + | 38.0747i | −0.892240 | + | 1.54540i | −0.0550554 | + | 0.998483i | \(0.517534\pi\) |
−0.837184 | + | 0.546921i | \(0.815800\pi\) | |||||||
\(608\) | 1.47658 | − | 2.55751i | 0.0598831 | − | 0.103721i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.22305 | −0.0900088 | ||||||||
\(611\) | 1.33364 | + | 1.01504i | 0.0539531 | + | 0.0410641i | ||||
\(612\) | 1.14026 | − | 1.97499i | 0.0460923 | − | 0.0798342i | ||||
\(613\) | −1.35045 | − | 2.33906i | −0.0545443 | − | 0.0944736i | 0.837464 | − | 0.546492i | \(-0.184037\pi\) |
−0.892008 | + | 0.452019i | \(0.850704\pi\) | |||||||
\(614\) | −15.1472 | −0.611292 | ||||||||
\(615\) | −0.849310 | − | 1.47105i | −0.0342475 | − | 0.0593184i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00208 | − | 5.19975i | −0.120859 | − | 0.209334i | 0.799248 | − | 0.601002i | \(-0.205232\pi\) |
−0.920107 | + | 0.391668i | \(0.871898\pi\) | |||||||
\(618\) | −0.854742 | + | 1.48046i | −0.0343828 | + | 0.0595527i | ||||
\(619\) | 6.68204 | − | 11.5736i | 0.268574 | − | 0.465184i | −0.699920 | − | 0.714221i | \(-0.746781\pi\) |
0.968494 | + | 0.249038i | \(0.0801143\pi\) | |||||||
\(620\) | −1.12193 | −0.0450576 | ||||||||
\(621\) | −5.57932 | −0.223890 | ||||||||
\(622\) | −21.0983 | + | 36.5433i | −0.845963 | + | 1.46525i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27.6201 | − | 21.0218i | −1.10569 | − | 0.841547i | ||||
\(625\) | −9.95497 | − | 17.2425i | −0.398199 | − | 0.689701i | ||||
\(626\) | 12.5637 | + | 21.7609i | 0.502145 | + | 0.869741i | ||||
\(627\) | 2.72245 | + | 4.71543i | 0.108724 | + | 0.188316i | ||||
\(628\) | −0.591650 | + | 1.02477i | −0.0236094 | + | 0.0408927i | ||||
\(629\) | −6.75647 | −0.269398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2228 | − | 35.0270i | −0.805059 | − | 1.39440i | −0.916251 | − | 0.400604i | \(-0.868800\pi\) |
0.111192 | − | 0.993799i | \(-0.464533\pi\) | |||||||
\(632\) | 19.1961 | + | 33.2486i | 0.763579 | + | 1.32256i | ||||
\(633\) | −34.3797 | −1.36647 | ||||||||
\(634\) | 18.0054 | + | 31.1863i | 0.715086 | + | 1.23857i | ||||
\(635\) | 5.30648 | 0.210581 | ||||||||
\(636\) | 5.48393 | 0.217452 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.9407 | −0.631097 | ||||||||
\(639\) | 10.0443 | 0.397345 | ||||||||
\(640\) | −3.89667 | − | 6.74923i | −0.154029 | − | 0.266787i | ||||
\(641\) | 10.2198 | 0.403658 | 0.201829 | − | 0.979421i | \(-0.435311\pi\) | ||||
0.201829 | + | 0.979421i | \(0.435311\pi\) | |||||||
\(642\) | −31.2393 | − | 54.1081i | −1.23292 | − | 2.13548i | ||||
\(643\) | −15.9014 | − | 27.5420i | −0.627088 | − | 1.08615i | −0.988133 | − | 0.153600i | \(-0.950913\pi\) |
0.361045 | − | 0.932548i | \(-0.382420\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4861 | 0.570389 | ||||||||
\(646\) | 6.13937 | − | 10.6337i | 0.241550 | − | 0.418378i | ||||
\(647\) | 17.2617 | + | 29.8981i | 0.678626 | + | 1.17541i | 0.975395 | + | 0.220465i | \(0.0707575\pi\) |
−0.296769 | + | 0.954949i | \(0.595909\pi\) | |||||||
\(648\) | 14.4328 | + | 24.9983i | 0.566972 | + | 0.982025i | ||||
\(649\) | −9.03008 | − | 15.6406i | −0.354462 | − | 0.613946i | ||||
\(650\) | 3.23057 | − | 25.3060i | 0.126713 | − | 0.992582i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.268265 | + | 0.464649i | −0.0105061 | + | 0.0181970i | ||||
\(653\) | 10.1180 | 0.395947 | 0.197974 | − | 0.980207i | \(-0.436564\pi\) | ||||
0.197974 | + | 0.980207i | \(0.436564\pi\) | |||||||
\(654\) | 18.5356 | 0.724800 | ||||||||
\(655\) | −2.00346 | + | 3.47009i | −0.0782816 | + | 0.135588i | ||||
\(656\) | −3.06855 | + | 5.31488i | −0.119807 | + | 0.207511i | ||||
\(657\) | −12.4484 | − | 21.5613i | −0.485659 | − | 0.841185i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.3841 | + | 30.1101i | 0.677187 | + | 1.17292i | 0.975824 | + | 0.218556i | \(0.0701345\pi\) |
−0.298637 | + | 0.954367i | \(0.596532\pi\) | |||||||
\(660\) | −0.596039 | −0.0232008 | ||||||||
\(661\) | 8.28076 | + | 14.3427i | 0.322084 | + | 0.557866i | 0.980918 | − | 0.194422i | \(-0.0622833\pi\) |
−0.658834 | + | 0.752289i | \(0.728950\pi\) | |||||||
\(662\) | 6.04666 | − | 10.4731i | 0.235010 | − | 0.407050i | ||||
\(663\) | −29.2494 | − | 22.2620i | −1.13595 | − | 0.864583i | ||||
\(664\) | −25.9727 | −1.00794 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.62948 | − | 2.82234i | 0.0631411 | − | 0.109364i | ||||
\(667\) | −6.11346 | + | 10.5888i | −0.236714 | + | 0.410001i | ||||
\(668\) | 1.97848 | − | 3.42683i | 0.0765498 | − | 0.132588i | ||||
\(669\) | 26.4326 | 1.02194 | ||||||||
\(670\) | 3.39388 | − | 5.87838i | 0.131117 | − | 0.227102i | ||||
\(671\) | −3.77178 | −0.145608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9437 | − | 36.2756i | 0.807321 | − | 1.39832i | −0.107393 | − | 0.994217i | \(-0.534250\pi\) |
0.914713 | − | 0.404104i | \(-0.132417\pi\) | |||||||
\(674\) | 12.0343 | 0.463543 | ||||||||
\(675\) | −7.31659 | + | 12.6727i | −0.281616 | + | 0.487772i | ||||
\(676\) | 2.85227 | − | 2.89742i | 0.109703 | − | 0.111439i | ||||
\(677\) | 15.7858 | + | 27.3417i | 0.606696 | + | 1.05083i | 0.991781 | + | 0.127947i | \(0.0408387\pi\) |
−0.385085 | + | 0.922881i | \(0.625828\pi\) | |||||||
\(678\) | 8.32556 | − | 14.4203i | 0.319741 | − | 0.553808i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.62566 | − | 6.27983i | −0.139038 | − | 0.240820i | ||||
\(681\) | 1.31291 | + | 2.27402i | 0.0503107 | + | 0.0871408i | ||||
\(682\) | −14.0763 | −0.539011 | ||||||||
\(683\) | −26.2676 | −1.00510 | −0.502551 | − | 0.864548i | \(-0.667605\pi\) | ||||
−0.502551 | + | 0.864548i | \(0.667605\pi\) | |||||||
\(684\) | 0.400455 | + | 0.693609i | 0.0153118 | + | 0.0265208i | ||||
\(685\) | −4.14801 | − | 7.18457i | −0.158487 | − | 0.274508i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.96880 | − | 12.0703i | 0.265876 | − | 0.460512i | ||||
\(688\) | −26.1690 | − | 45.3261i | −0.997686 | − | 1.72804i | ||||
\(689\) | 3.76532 | − | 29.4949i | 0.143447 | − | 1.12367i | ||||
\(690\) | −1.69038 | + | 2.92783i | −0.0643517 | + | 0.111460i | ||||
\(691\) | 6.10095 | 0.232091 | 0.116046 | − | 0.993244i | \(-0.462978\pi\) | ||||
0.116046 | + | 0.993244i | \(0.462978\pi\) | |||||||
\(692\) | −1.79635 | + | 3.11138i | −0.0682872 | + | 0.118277i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.8518 | −0.411929 | ||||||||
\(695\) | −5.09419 | + | 8.82339i | −0.193234 | + | 0.334690i | ||||
\(696\) | 37.6034 | 1.42535 | ||||||||
\(697\) | −3.24957 | + | 5.62842i | −0.123086 | + | 0.213192i | ||||
\(698\) | 1.04690 | − | 1.81329i | 0.0396259 | − | 0.0686341i | ||||
\(699\) | −6.69636 | + | 11.5984i | −0.253280 | + | 0.438693i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.5701 | −0.776921 | −0.388461 | − | 0.921465i | \(-0.626993\pi\) | ||||
−0.388461 | + | 0.921465i | \(0.626993\pi\) | |||||||
\(702\) | −15.9068 | + | 6.66210i | −0.600363 | + | 0.251445i | ||||
\(703\) | 1.18642 | − | 2.05495i | 0.0447468 | − | 0.0775038i | ||||
\(704\) | −4.85760 | − | 8.41361i | −0.183078 | − | 0.317100i | ||||
\(705\) | −0.582513 | −0.0219387 | ||||||||
\(706\) | 0.527111 | + | 0.912984i | 0.0198381 | + | 0.0343606i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.94851 | − | 6.83902i | −0.148394 | − | 0.257026i | ||||
\(709\) | 21.5764 | − | 37.3715i | 0.810320 | − | 1.40352i | −0.102320 | − | 0.994751i | \(-0.532627\pi\) |
0.912640 | − | 0.408764i | \(-0.134040\pi\) | |||||||
\(710\) | −2.96000 | + | 5.12687i | −0.111087 | + | 0.192408i | ||||
\(711\) | −22.7543 | −0.853353 | ||||||||
\(712\) | −42.2992 | −1.58523 | ||||||||
\(713\) | −5.39847 | + | 9.35042i | −0.202174 | + | 0.350176i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.409246 | + | 3.20575i | −0.0153050 | + | 0.119888i | ||||
\(716\) | 0.341605 | + | 0.591677i | 0.0127664 | + | 0.0221120i | ||||
\(717\) | 20.1132 | + | 34.8372i | 0.751143 | + | 1.30102i | ||||
\(718\) | −4.41302 | − | 7.64357i | −0.164692 | − | 0.285255i | ||||
\(719\) | −14.1042 | + | 24.4292i | −0.525999 | + | 0.911057i | 0.473542 | + | 0.880771i | \(0.342975\pi\) |
−0.999541 | + | 0.0302857i | \(0.990358\pi\) | |||||||
\(720\) | 4.05831 | 0.151244 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2912 | − | 21.2890i | −0.457432 | − | 0.792295i | ||||
\(723\) | 23.7038 | + | 41.0562i | 0.881555 | + | 1.52690i | ||||
\(724\) | 3.62733 | 0.134809 | ||||||||
\(725\) | 16.0341 | + | 27.7719i | 0.595492 | + | 1.03142i | ||||
\(726\) | 28.0901 | 1.04252 | ||||||||
\(727\) | 19.5116 | 0.723646 | 0.361823 | − | 0.932247i | \(-0.382155\pi\) | ||||
0.361823 | + | 0.932247i | \(0.382155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.95370 | 0.109396 | ||||||||
\(730\) | 14.6740 | 0.543108 | ||||||||
\(731\) | −27.7128 | − | 48.0000i | −1.02500 | − | 1.77535i | ||||
\(732\) | −1.64926 | −0.0609582 | ||||||||
\(733\) | 10.1833 | + | 17.6380i | 0.376129 | + | 0.651475i | 0.990495 | − | 0.137546i | \(-0.0439215\pi\) |
−0.614366 | + | 0.789021i | \(0.710588\pi\) | |||||||
\(734\) | 5.59003 | + | 9.68222i | 0.206332 | + | 0.357377i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.11105 | 0.114675 | ||||||||
\(737\) | 5.75829 | − | 9.97364i | 0.212109 | − | 0.367384i | ||||
\(738\) | −1.56742 | − | 2.71485i | −0.0576975 | − | 0.0999349i | ||||
\(739\) | 5.20995 | + | 9.02391i | 0.191651 | + | 0.331950i | 0.945798 | − | 0.324757i | \(-0.105282\pi\) |
−0.754146 | + | 0.656706i | \(0.771949\pi\) | |||||||
\(740\) | 0.129874 | + | 0.224949i | 0.00477428 | + | 0.00826929i | ||||
\(741\) | 11.9070 | − | 4.98691i | 0.437415 | − | 0.183199i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.70470 | − | 15.0770i | 0.319344 | − | 0.553121i | −0.661007 | − | 0.750380i | \(-0.729871\pi\) |
0.980351 | + | 0.197259i | \(0.0632040\pi\) | |||||||
\(744\) | 33.2055 | 1.21737 | ||||||||
\(745\) | 10.0934 | 0.369795 | ||||||||
\(746\) | 13.9902 | − | 24.2318i | 0.512219 | − | 0.887189i | ||||
\(747\) | 7.69677 | − | 13.3312i | 0.281610 | − | 0.487763i | ||||
\(748\) | 1.14026 | + | 1.97499i | 0.0416921 | + | 0.0722128i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.19792 | + | 15.9313i | 0.335861 | + | 0.581728i | ||||
\(751\) | −1.81525 | −0.0662395 | −0.0331197 | − | 0.999451i | \(-0.510544\pi\) | ||||
−0.0331197 | + | 0.999451i | \(0.510544\pi\) | |||||||
\(752\) | 1.05231 | + | 1.82265i | 0.0383737 | + | 0.0664652i | ||||
\(753\) | −7.39193 | + | 12.8032i | −0.269377 | + | 0.466575i | ||||
\(754\) | −4.78584 | + | 37.4889i | −0.174290 | + | 1.36527i | ||||
\(755\) | −9.31088 | −0.338858 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.7814 | + | 46.3867i | −0.973385 | + | 1.68595i | −0.288220 | + | 0.957564i | \(0.593063\pi\) |
−0.685165 | + | 0.728388i | \(0.740270\pi\) | |||||||
\(758\) | −3.68864 | + | 6.38892i | −0.133978 | + | 0.232056i | ||||
\(759\) | −2.86801 | + | 4.96754i | −0.104102 | + | 0.180310i | ||||
\(760\) | 2.54664 | 0.0923762 | ||||||||
\(761\) | 1.84083 | − | 3.18841i | 0.0667300 | − | 0.115580i | −0.830730 | − | 0.556675i | \(-0.812077\pi\) |
0.897460 | + | 0.441096i | \(0.145410\pi\) | |||||||
\(762\) | 29.1121 | 1.05462 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.77711 | + | 4.81010i | −0.100472 | + | 0.174023i | ||||
\(765\) | 4.29772 | 0.155384 | ||||||||
\(766\) | −17.3524 | + | 30.0553i | −0.626968 | + | 1.08594i | ||||
\(767\) | −39.4942 | + | 16.5410i | −1.42605 | + | 0.597262i | ||||
\(768\) | −7.79476 | − | 13.5009i | −0.281269 | − | 0.487172i | ||||
\(769\) | 2.61897 | − | 4.53619i | 0.0944424 | − | 0.163579i | −0.814933 | − | 0.579555i | \(-0.803227\pi\) |
0.909376 | + | 0.415976i | \(0.136560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4902 | + | 38.9541i | 0.809963 | + | 1.40290i | ||||
\(772\) | −3.54002 | − | 6.13150i | −0.127408 | − | 0.220677i | ||||
\(773\) | 40.6138 | 1.46078 | 0.730388 | − | 0.683032i | \(-0.239339\pi\) | ||||
0.730388 | + | 0.683032i | \(0.239339\pi\) | |||||||
\(774\) | 26.7344 | 0.960948 | ||||||||
\(775\) | 14.1588 | + | 24.5238i | 0.508601 | + | 0.880922i | ||||
\(776\) | −1.24944 | − | 2.16409i | −0.0448522 | − | 0.0776862i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.4451 | + | 26.7517i | −0.553733 | + | 0.959094i | ||||
\(779\) | −1.14124 | − | 1.97668i | −0.0408890 | − | 0.0708219i | ||||
\(780\) | −0.178948 | + | 1.40175i | −0.00640736 | + | 0.0501908i | ||||
\(781\) | −5.02213 | + | 8.69859i | −0.179706 | + | 0.311260i | ||||
\(782\) | 12.9352 | 0.462563 | ||||||||
\(783\) | 10.8390 | − | 18.7737i | 0.387353 | − | 0.670916i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.22997 | −0.0795911 | ||||||||
\(786\) | −10.9913 | + | 19.0374i | −0.392045 | + | 0.679042i | ||||
\(787\) | −34.2000 | −1.21910 | −0.609550 | − | 0.792748i | \(-0.708650\pi\) | ||||
−0.609550 | + | 0.792748i | \(0.708650\pi\) | |||||||
\(788\) | −3.12851 | + | 5.41873i | −0.111448 | + | 0.193034i | ||||
\(789\) | 8.96190 | − | 15.5225i | 0.319052 | − | 0.552614i | ||||
\(790\) | 6.70559 | − | 11.6144i | 0.238574 | − | 0.413223i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.93434 | 0.210868 | ||||||||
\(793\) | −1.13240 | + | 8.87040i | −0.0402126 | + | 0.314997i | ||||
\(794\) | −25.9579 | + | 44.9604i | −0.921211 | + | 1.59558i | ||||
\(795\) | 5.16733 | + | 8.95007i | 0.183266 | + | 0.317426i | ||||
\(796\) | 0.578232 | 0.0204949 | ||||||||
\(797\) | 15.6903 | + | 27.1763i | 0.555778 | + | 0.962635i | 0.997843 | + | 0.0656522i | \(0.0209128\pi\) |
−0.442065 | + | 0.896983i | \(0.645754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.11439 | + | 1.93017i | 0.0394241 | + | 0.0682846i | ||||
\(800\) | 4.07976 | − | 7.06634i | 0.144241 | − | 0.249833i | ||||
\(801\) | 12.5350 | − | 21.7112i | 0.442901 | − | 0.767128i | ||||
\(802\) | 4.60180 | 0.162495 | ||||||||
\(803\) | 24.8968 | 0.878590 | ||||||||
\(804\) | 2.51788 | − | 4.36109i | 0.0887988 | − | 0.153804i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.22612 | + | 33.1044i | −0.148859 | + | 1.16605i | ||||
\(807\) | −6.19832 | − | 10.7358i | −0.218191 | − | 0.377918i | ||||
\(808\) | −3.77221 | − | 6.53365i | −0.132706 | − | 0.229853i | ||||
\(809\) | 18.9709 | + | 32.8585i | 0.666981 | + | 1.15524i | 0.978744 | + | 0.205085i | \(0.0657470\pi\) |
−0.311764 | + | 0.950160i | \(0.600920\pi\) | |||||||
\(810\) | 5.04167 | − | 8.73242i | 0.177146 | − | 0.306826i | ||||
\(811\) | 32.1023 | 1.12726 | 0.563632 | − | 0.826026i | \(-0.309403\pi\) | ||||
0.563632 | + | 0.826026i | \(0.309403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5930 | + | 33.9360i | 0.687155 | + | 1.19019i | ||||
\(814\) | 1.62948 | + | 2.82234i | 0.0571133 | + | 0.0989231i | ||||
\(815\) | −1.01111 | −0.0354176 | ||||||||
\(816\) | −23.0793 | − | 39.9745i | −0.807938 | − | 1.39939i | ||||
\(817\) | 19.4653 | 0.681004 | ||||||||
\(818\) | −8.18670 | −0.286241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.249856 | 0.00872534 | ||||||||
\(821\) | −16.9223 | −0.590594 | −0.295297 | − | 0.955406i | \(-0.595419\pi\) | ||||
−0.295297 | + | 0.955406i | \(0.595419\pi\) | |||||||
\(822\) | −22.7566 | − | 39.4156i | −0.793727 | − | 1.37478i | ||||
\(823\) | −14.4733 | −0.504508 | −0.252254 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252254 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(824\) | 0.678278 | + | 1.17481i | 0.0236289 | + | 0.0409265i | ||||
\(825\) | 7.52209 | + | 13.0286i | 0.261885 | + | 0.453599i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5792 | 0.959021 | 0.479511 | − | 0.877536i | \(-0.340814\pi\) | ||||
0.479511 | + | 0.877536i | \(0.340814\pi\) | |||||||
\(828\) | −0.421866 | + | 0.730693i | −0.0146608 | + | 0.0253933i | ||||
\(829\) | 10.5465 | + | 18.2671i | 0.366296 | + | 0.634443i | 0.988983 | − | 0.148028i | \(-0.0472925\pi\) |
−0.622687 | + | 0.782471i | \(0.713959\pi\) | |||||||
\(830\) | 4.53641 | + | 7.85729i | 0.157461 | + | 0.272730i | ||||
\(831\) | 6.57326 | + | 11.3852i | 0.228024 | + | 0.394949i | ||||
\(832\) | −21.2454 | + | 8.89800i | −0.736550 | + | 0.308483i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −27.9474 | + | 48.4064i | −0.967741 | + | 1.67618i | ||||
\(835\) | 7.45704 | 0.258061 | ||||||||
\(836\) | −0.800911 | −0.0277001 | ||||||||
\(837\) | 9.57131 | − | 16.5780i | 0.330833 | − | 0.573020i | ||||
\(838\) | 4.47286 | − | 7.74722i | 0.154512 | − | 0.267623i | ||||
\(839\) | −6.35488 | − | 11.0070i | −0.219395 | − | 0.380003i | 0.735228 | − | 0.677819i | \(-0.237075\pi\) |
−0.954623 | + | 0.297817i | \(0.903742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.25333 | − | 16.0272i | −0.319080 | − | 0.552663i | ||||
\(842\) | 43.7396 | 1.50736 | ||||||||
\(843\) | 5.99643 | + | 10.3861i | 0.206528 | + | 0.357717i | ||||
\(844\) | 2.52852 | − | 4.37952i | 0.0870351 | − | 0.150749i | ||||
\(845\) | 7.41635 | + | 1.92492i | 0.255130 | + | 0.0662191i | ||||
\(846\) | −1.07504 | −0.0369606 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 18.6695 | − | 32.3365i | 0.641113 | − | 1.11044i | ||||
\(849\) | −17.4938 | + | 30.3002i | −0.600387 | + | 1.03990i | ||||
\(850\) | 16.9630 | − | 29.3807i | 0.581825 | − | 1.00775i | ||||
\(851\) | 2.49971 | 0.0856890 | ||||||||
\(852\) | −2.19599 | + | 3.80356i | −0.0752333 | + | 0.130308i | ||||
\(853\) | 35.0471 | 1.19999 | 0.599996 | − | 0.800003i | \(-0.295169\pi\) | ||||
0.599996 | + | 0.800003i | \(0.295169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.754672 | + | 1.30713i | −0.0258092 | + | 0.0447029i | ||||
\(856\) | −49.5797 | −1.69460 | ||||||||
\(857\) | −12.7970 | + | 22.1651i | −0.437138 | + | 0.757145i | −0.997467 | − | 0.0711250i | \(-0.977341\pi\) |
0.560330 | + | 0.828270i | \(0.310674\pi\) | |||||||
\(858\) | −2.24518 | + | 17.5872i | −0.0766493 | + | 0.600417i | ||||
\(859\) | 0.372743 | + | 0.645610i | 0.0127178 | + | 0.0220279i | 0.872314 | − | 0.488946i | \(-0.162618\pi\) |
−0.859596 | + | 0.510974i | \(0.829285\pi\) | |||||||
\(860\) | −1.06541 | + | 1.84534i | −0.0363300 | + | 0.0629254i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.37651 | + | 11.0444i | 0.217185 | + | 0.376175i | ||||
\(863\) | 10.9908 | + | 19.0367i | 0.374132 | + | 0.648015i | 0.990197 | − | 0.139680i | \(-0.0446075\pi\) |
−0.616065 | + | 0.787695i | \(0.711274\pi\) | |||||||
\(864\) | −5.51579 | −0.187651 | ||||||||
\(865\) | −6.77058 | −0.230207 | ||||||||
\(866\) | −20.9861 | − | 36.3490i | −0.713137 | − | 1.23519i | ||||
\(867\) | −6.36804 | − | 11.0298i | −0.216270 | − | 0.374590i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3771 | − | 19.7058i | 0.385943 | − | 0.668473i | ||||
\(870\) | −6.56783 | − | 11.3758i | −0.222670 | − | 0.385676i | ||||
\(871\) | −21.7270 | − | 16.5366i | −0.736192 | − | 0.560321i | ||||
\(872\) | 7.35444 | − | 12.7383i | 0.249053 | − | 0.431372i | ||||
\(873\) | 1.48103 | 0.0501254 | ||||||||
\(874\) | −2.27140 | + | 3.93418i | −0.0768313 | + | 0.133076i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.8864 | 0.367818 | ||||||||
\(877\) | −14.7095 | + | 25.4776i | −0.496705 | + | 0.860319i | −0.999993 | − | 0.00380023i | \(-0.998790\pi\) |
0.503287 | + | 0.864119i | \(0.332124\pi\) | |||||||
\(878\) | −47.4082 | −1.59995 | ||||||||
\(879\) | 32.5492 | − | 56.3769i | 1.09786 | − | 1.90155i | ||||
\(880\) | −2.02915 | + | 3.51460i | −0.0684028 | + | 0.118477i | ||||
\(881\) | −24.1414 | + | 41.8142i | −0.813345 | + | 1.40876i | 0.0971649 | + | 0.995268i | \(0.469023\pi\) |
−0.910510 | + | 0.413487i | \(0.864311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4465 | 0.553469 | 0.276735 | − | 0.960946i | \(-0.410748\pi\) | ||||
0.276735 | + | 0.960946i | \(0.410748\pi\) | |||||||
\(884\) | 4.98708 | − | 2.08869i | 0.167734 | − | 0.0702504i | ||||
\(885\) | 7.44110 | − | 12.8884i | 0.250130 | − | 0.433238i | ||||
\(886\) | −17.9362 | − | 31.0664i | −0.602579 | − | 1.04370i | ||||
\(887\) | 29.1653 | 0.979276 | 0.489638 | − | 0.871926i | \(-0.337129\pi\) | ||||
0.489638 | + | 0.871926i | \(0.337129\pi\) | |||||||
\(888\) | −3.84388 | − | 6.65780i | −0.128992 | − | 0.223421i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.38800 | + | 12.7964i | 0.247646 | + | 0.428936i | ||||
\(891\) | 8.55402 | − | 14.8160i | 0.286571 | − | 0.496355i | ||||
\(892\) | −1.94403 | + | 3.36716i | −0.0650910 | + | 0.112741i | ||||
\(893\) | −0.782736 | −0.0261933 | ||||||||
\(894\) | 55.3741 | 1.85199 | ||||||||
\(895\) | −0.643765 | + | 1.11503i | −0.0215187 | + | 0.0372715i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.8215 | + | 8.23633i | 0.361320 | + | 0.275003i | ||||
\(898\) | 2.14928 | + | 3.72266i | 0.0717224 | + | 0.124227i | ||||
\(899\) | −20.9753 | − | 36.3302i | −0.699565 | − | 1.21168i | ||||
\(900\) | 1.10645 | + | 1.91643i | 0.0368817 | + | 0.0638809i | ||||
\(901\) | 19.7709 | − | 34.2441i | 0.658663 | − | 1.14084i | ||||
\(902\) | 3.13484 | 0.104379 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.60673 | − | 11.4432i | −0.219736 | − | 0.380595i | ||||
\(905\) | 3.41791 | + | 5.92000i | 0.113615 | + | 0.196787i | ||||
\(906\) | −51.0808 | −1.69705 | ||||||||
\(907\) | 17.6607 | + | 30.5893i | 0.586416 | + | 1.01570i | 0.994697 | + | 0.102846i | \(0.0327947\pi\) |
−0.408282 | + | 0.912856i | \(0.633872\pi\) | |||||||
\(908\) | −0.386240 | −0.0128178 | ||||||||
\(909\) | 4.47143 | 0.148308 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6496 | −1.44617 | −0.723087 | − | 0.690757i | \(-0.757278\pi\) | ||||
−0.723087 | + | 0.690757i | \(0.757278\pi\) | |||||||
\(912\) | 16.2107 | 0.536791 | ||||||||
\(913\) | 7.69677 | + | 13.3312i | 0.254726 | + | 0.441198i | ||||
\(914\) | 57.3988 | 1.89858 | ||||||||
\(915\) | −1.55404 | − | 2.69167i | −0.0513749 | − | 0.0889840i | ||||
\(916\) | 1.02507 | + | 1.77547i | 0.0338691 | + | 0.0586630i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −22.9338 | −0.756927 | ||||||||
\(919\) | 8.89389 | − | 15.4047i | 0.293382 | − | 0.508153i | −0.681225 | − | 0.732074i | \(-0.738552\pi\) |
0.974607 | + | 0.223921i | \(0.0718858\pi\) | |||||||
\(920\) | 1.34140 | + | 2.32337i | 0.0442245 | + | 0.0765991i | ||||
\(921\) | −10.5887 | − | 18.3403i | −0.348911 | − | 0.604332i | ||||
\(922\) | 26.3539 | + | 45.6463i | 0.867921 | + | 1.50328i | ||||
\(923\) | 18.9494 | + | 14.4225i | 0.623726 | + | 0.474723i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.27806 | − | 5.67777i | 0.107782 | − | 0.186684i | ||||
\(926\) | −28.1516 | −0.925118 | ||||||||
\(927\) | −0.804005 | −0.0264070 | ||||||||
\(928\) | −6.04385 | + | 10.4683i | −0.198399 | + | 0.343638i | ||||
\(929\) | −1.95710 | + | 3.38980i | −0.0642103 | + | 0.111216i | −0.896343 | − | 0.443360i | \(-0.853786\pi\) |
0.832133 | + | 0.554576i | \(0.187120\pi\) | |||||||
\(930\) | −5.79969 | − | 10.0454i | −0.190179 | − | 0.329401i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.984992 | − | 1.70606i | −0.0322645 | − | 0.0558837i | ||||
\(933\) | −58.9955 | −1.93142 | ||||||||
\(934\) | 5.03972 | + | 8.72905i | 0.164905 | + | 0.285623i | ||||
\(935\) | −2.14886 | + | 3.72193i | −0.0702752 | + | 0.121720i | ||||
\(936\) | 1.78166 | − | 13.9563i | 0.0582354 | − | 0.456175i | ||||
\(937\) | −0.207362 | −0.00677421 | −0.00338710 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338710 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.5654 | + | 30.4242i | −0.573225 | + | 0.992855i | ||||
\(940\) | 0.0428420 | − | 0.0742044i | 0.00139735 | − | 0.00242028i | ||||
\(941\) | −13.7328 | + | 23.7859i | −0.447677 | + | 0.775400i | −0.998234 | − | 0.0593977i | \(-0.981082\pi\) |
0.550557 | + | 0.834797i | \(0.314415\pi\) | |||||||
\(942\) | −12.2339 | −0.398603 | ||||||||
\(943\) | 1.20225 | − | 2.08236i | 0.0391507 | − | 0.0678111i | ||||
\(944\) | −53.7692 | −1.75004 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.3672 | + | 23.1527i | −0.434605 | + | 0.752758i | ||||
\(947\) | −23.0363 | −0.748580 | −0.374290 | − | 0.927312i | \(-0.622114\pi\) | ||||
−0.374290 | + | 0.927312i | \(0.622114\pi\) | |||||||
\(948\) | 4.97479 | − | 8.61660i | 0.161574 | − | 0.279854i | ||||
\(949\) | 7.47474 | − | 58.5518i | 0.242640 | − | 1.90067i | ||||
\(950\) | 5.95733 | + | 10.3184i | 0.193281 | + | 0.334773i | ||||
\(951\) | −25.1736 | + | 43.6019i | −0.816309 | + | 1.41389i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.22808 | − | 12.5194i | −0.234140 | − | 0.405543i | 0.724882 | − | 0.688873i | \(-0.241894\pi\) |
−0.959022 | + | 0.283330i | \(0.908561\pi\) | |||||||
\(954\) | 9.53641 | + | 16.5175i | 0.308753 | + | 0.534775i | ||||
\(955\) | −10.4671 | −0.338708 | ||||||||
\(956\) | −5.91706 | −0.191371 | ||||||||
\(957\) | −11.1434 | − | 19.3010i | −0.360215 | − | 0.623911i | ||||
\(958\) | −13.2707 | − | 22.9856i | −0.428758 | − | 0.742630i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.00283 | − | 6.93311i | 0.129191 | − | 0.223765i | ||||
\(961\) | −3.02213 | − | 5.23448i | −0.0974881 | − | 0.168854i | ||||
\(962\) | 7.12675 | − | 2.98483i | 0.229776 | − | 0.0962348i | ||||
\(963\) | 14.6925 | − | 25.4481i | 0.473459 | − | 0.820054i | ||||
\(964\) | −6.97336 | −0.224597 | ||||||||
\(965\) | 6.67129 | − | 11.5550i | 0.214756 | − | 0.371969i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3357 | 1.03984 | 0.519922 | − | 0.854213i | \(-0.325961\pi\) | ||||
0.519922 | + | 0.854213i | \(0.325961\pi\) | |||||||
\(968\) | 11.1454 | − | 19.3044i | 0.358227 | − | 0.620467i | ||||
\(969\) | 17.1671 | 0.551485 | ||||||||
\(970\) | −0.436454 | + | 0.755961i | −0.0140137 | + | 0.0242725i | ||||
\(971\) | −12.3118 | + | 21.3246i | −0.395103 | + | 0.684338i | −0.993114 | − | 0.117149i | \(-0.962624\pi\) |
0.598011 | + | 0.801488i | \(0.295958\pi\) | |||||||
\(972\) | 2.26487 | − | 3.92287i | 0.0726458 | − | 0.125826i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 54.0084 | 1.73054 | ||||||||
\(975\) | 32.8988 | − | 13.7787i | 1.05361 | − | 0.441272i | ||||
\(976\) | −5.61472 | + | 9.72499i | −0.179723 | + | 0.311289i | ||||
\(977\) | −3.00496 | − | 5.20474i | −0.0961372 | − | 0.166514i | 0.813945 | − | 0.580941i | \(-0.197315\pi\) |
−0.910083 | + | 0.414427i | \(0.863982\pi\) | |||||||
\(978\) | −5.54709 | −0.177376 | ||||||||
\(979\) | 12.5350 | + | 21.7112i | 0.400619 | + | 0.693893i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.35884 | + | 7.54973i | 0.139167 | + | 0.241044i | ||||
\(982\) | −22.6685 | + | 39.2630i | −0.723382 | + | 1.25293i | ||||
\(983\) | 17.9546 | − | 31.0984i | 0.572664 | − | 0.991884i | −0.423627 | − | 0.905837i | \(-0.639243\pi\) |
0.996291 | − | 0.0860467i | \(-0.0274234\pi\) | |||||||
\(984\) | −7.39496 | −0.235743 | ||||||||
\(985\) | −11.7916 | −0.375710 | ||||||||
\(986\) | −25.1294 | + | 43.5253i | −0.800282 | + | 1.38613i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.240456 | + | 1.88357i | −0.00764994 | + | 0.0599242i | ||||
\(989\) | 10.2530 | + | 17.7587i | 0.326027 | + | 0.564694i | ||||
\(990\) | −1.03650 | − | 1.79526i | −0.0329420 | − | 0.0570572i | ||||
\(991\) | −14.0000 | − | 24.2487i | −0.444724 | − | 0.770285i | 0.553309 | − | 0.832976i | \(-0.313365\pi\) |
−0.998033 | + | 0.0626912i | \(0.980032\pi\) | |||||||
\(992\) | −5.33700 | + | 9.24396i | −0.169450 | + | 0.293496i | ||||
\(993\) | 16.9078 | 0.536553 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.544849 | + | 0.943706i | 0.0172729 | + | 0.0299175i | ||||
\(996\) | 3.36550 | + | 5.82922i | 0.106640 | + | 0.184706i | ||||
\(997\) | −33.0081 | −1.04538 | −0.522688 | − | 0.852524i | \(-0.675071\pi\) | ||||
−0.522688 | + | 0.852524i | \(0.675071\pi\) | |||||||
\(998\) | −5.71024 | − | 9.89043i | −0.180755 | − | 0.313076i | ||||
\(999\) | −4.43191 | −0.140219 |
(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 | 637.2.h.m.165.3 | 16 | ||
7.2 | even | 3 | 637.2.g.m.373.6 | 16 | |||
7.3 | odd | 6 | 637.2.f.l.295.6 | yes | 16 | ||
7.4 | even | 3 | 637.2.f.l.295.5 | ✓ | 16 | ||
7.5 | odd | 6 | 637.2.g.m.373.5 | 16 | |||
7.6 | odd | 2 | inner | 637.2.h.m.165.4 | 16 | ||
13.3 | even | 3 | 637.2.g.m.263.6 | 16 | |||
91.3 | odd | 6 | 637.2.f.l.393.6 | yes | 16 | ||
91.4 | even | 6 | 8281.2.a.cl.1.6 | 8 | |||
91.16 | even | 3 | inner | 637.2.h.m.471.3 | 16 | ||
91.17 | odd | 6 | 8281.2.a.cl.1.5 | 8 | |||
91.55 | odd | 6 | 637.2.g.m.263.5 | 16 | |||
91.68 | odd | 6 | inner | 637.2.h.m.471.4 | 16 | ||
91.74 | even | 3 | 8281.2.a.ci.1.4 | 8 | |||
91.81 | even | 3 | 637.2.f.l.393.5 | yes | 16 | ||
91.87 | odd | 6 | 8281.2.a.ci.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.l.295.5 | ✓ | 16 | 7.4 | even | 3 | ||
637.2.f.l.295.6 | yes | 16 | 7.3 | odd | 6 | ||
637.2.f.l.393.5 | yes | 16 | 91.81 | even | 3 | ||
637.2.f.l.393.6 | yes | 16 | 91.3 | odd | 6 | ||
637.2.g.m.263.5 | 16 | 91.55 | odd | 6 | |||
637.2.g.m.263.6 | 16 | 13.3 | even | 3 | |||
637.2.g.m.373.5 | 16 | 7.5 | odd | 6 | |||
637.2.g.m.373.6 | 16 | 7.2 | even | 3 | |||
637.2.h.m.165.3 | 16 | 1.1 | even | 1 | trivial | ||
637.2.h.m.165.4 | 16 | 7.6 | odd | 2 | inner | ||
637.2.h.m.471.3 | 16 | 91.16 | even | 3 | inner | ||
637.2.h.m.471.4 | 16 | 91.68 | odd | 6 | inner | ||
8281.2.a.ci.1.3 | 8 | 91.87 | odd | 6 | |||
8281.2.a.ci.1.4 | 8 | 91.74 | even | 3 | |||
8281.2.a.cl.1.5 | 8 | 91.17 | odd | 6 | |||
8281.2.a.cl.1.6 | 8 | 91.4 | even | 6 |