Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(67,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.g (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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(1.82904 + 1.05600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.67 |
Dual form | 441.2.g.g.79.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23025 | + | 2.13086i | −0.869920 | + | 1.50675i | −0.00784213 | + | 0.999969i | \(0.502496\pi\) |
−0.862078 | + | 0.506776i | \(0.830837\pi\) | |||||||
\(3\) | −0.410052 | + | 1.68281i | −0.236743 | + | 0.971572i | ||||
\(4\) | −2.02704 | − | 3.51094i | −1.01352 | − | 1.75547i | ||||
\(5\) | −3.65808 | −1.63594 | −0.817970 | − | 0.575260i | \(-0.804901\pi\) | ||||
−0.817970 | + | 0.575260i | \(0.804901\pi\) | |||||||
\(6\) | −3.08137 | − | 2.94405i | −1.25796 | − | 1.20190i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.05408 | 1.78689 | ||||||||
\(9\) | −2.66372 | − | 1.38008i | −0.887905 | − | 0.460027i | ||||
\(10\) | 4.50036 | − | 7.79485i | 1.42314 | − | 2.46495i | ||||
\(11\) | 0.406421 | 0.122540 | 0.0612702 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612702 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(12\) | 6.73945 | − | 1.97146i | 1.94551 | − | 0.569113i | ||||
\(13\) | 0.243398 | − | 0.421578i | 0.0675065 | − | 0.116925i | −0.830297 | − | 0.557322i | \(-0.811829\pi\) |
0.897803 | + | 0.440397i | \(0.145162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 6.15585i | 0.387298 | − | 1.58943i | ||||
\(16\) | −2.16372 | + | 3.74766i | −0.540929 | + | 0.936916i | ||||
\(17\) | −2.42792 | + | 4.20528i | −0.588857 | + | 1.01993i | 0.405525 | + | 0.914084i | \(0.367089\pi\) |
−0.994382 | + | 0.105847i | \(0.966245\pi\) | |||||||
\(18\) | 6.21780 | − | 3.97816i | 1.46555 | − | 0.937660i | ||||
\(19\) | 0.986757 | + | 1.70911i | 0.226378 | + | 0.392097i | 0.956732 | − | 0.290971i | \(-0.0939784\pi\) |
−0.730354 | + | 0.683069i | \(0.760645\pi\) | |||||||
\(20\) | 7.41507 | + | 12.8433i | 1.65806 | + | 2.87185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | 4.64766 | 0.969105 | 0.484552 | − | 0.874762i | \(-0.338982\pi\) | ||||
0.484552 | + | 0.874762i | \(0.338982\pi\) | |||||||
\(24\) | −2.07244 | + | 8.50508i | −0.423034 | + | 1.73609i | ||||
\(25\) | 8.38151 | 1.67630 | ||||||||
\(26\) | 0.598883 | + | 1.03729i | 0.117451 | + | 0.203430i | ||||
\(27\) | 3.41468 | − | 3.91663i | 0.657155 | − | 0.753756i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82383 | − | 6.62307i | −0.710068 | − | 1.22987i | −0.964831 | − | 0.262870i | \(-0.915331\pi\) |
0.254764 | − | 0.967003i | \(-0.418002\pi\) | |||||||
\(30\) | 11.2719 | + | 10.7695i | 2.05795 | + | 1.96624i | ||||
\(31\) | −3.51360 | − | 6.08573i | −0.631061 | − | 1.09303i | −0.987335 | − | 0.158648i | \(-0.949286\pi\) |
0.356274 | − | 0.934381i | \(-0.384047\pi\) | |||||||
\(32\) | −0.269748 | − | 0.467216i | −0.0476851 | − | 0.0825930i | ||||
\(33\) | −0.166653 | + | 0.683930i | −0.0290106 | + | 0.119057i | ||||
\(34\) | −5.97391 | − | 10.3471i | −1.02452 | − | 1.77452i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.554084 | + | 12.1496i | 0.0923474 | + | 2.02494i | ||||
\(37\) | −1.16372 | − | 2.01561i | −0.191314 | − | 0.331365i | 0.754372 | − | 0.656447i | \(-0.227941\pi\) |
−0.945686 | + | 0.325082i | \(0.894608\pi\) | |||||||
\(38\) | −4.85584 | −0.787721 | ||||||||
\(39\) | 0.609631 | + | 0.582462i | 0.0976191 | + | 0.0932686i | ||||
\(40\) | −18.4882 | −2.92324 | ||||||||
\(41\) | −3.75700 | + | 6.50731i | −0.586744 | + | 1.01627i | 0.407911 | + | 0.913022i | \(0.366257\pi\) |
−0.994655 | + | 0.103249i | \(0.967076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16372 | + | 2.01561i | 0.177465 | + | 0.307378i | 0.941012 | − | 0.338374i | \(-0.109877\pi\) |
−0.763547 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(44\) | −0.823832 | − | 1.42692i | −0.124197 | − | 0.215116i | ||||
\(45\) | 9.74407 | + | 5.04844i | 1.45256 | + | 0.752577i | ||||
\(46\) | −5.71780 | + | 9.90352i | −0.843044 | + | 1.46019i | ||||
\(47\) | 3.15811 | − | 5.47002i | 0.460658 | − | 0.797884i | −0.538335 | − | 0.842731i | \(-0.680947\pi\) |
0.998994 | + | 0.0448469i | \(0.0142800\pi\) | |||||||
\(48\) | −5.41938 | − | 5.17786i | −0.782220 | − | 0.747360i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.3114 | + | 17.8598i | −1.45825 | + | 2.52576i | ||||
\(51\) | −6.08113 | − | 5.81012i | −0.851528 | − | 0.813579i | ||||
\(52\) | −1.97351 | −0.273677 | ||||||||
\(53\) | 1.78434 | − | 3.09056i | 0.245097 | − | 0.424521i | −0.717062 | − | 0.697010i | \(-0.754513\pi\) |
0.962159 | + | 0.272489i | \(0.0878467\pi\) | |||||||
\(54\) | 4.14487 | + | 12.0946i | 0.564046 | + | 1.64587i | ||||
\(55\) | −1.48672 | −0.200469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.28074 | + | 0.959702i | −0.434544 | + | 0.127116i | ||||
\(58\) | 18.8171 | 2.47081 | ||||||||
\(59\) | −3.05919 | − | 5.29868i | −0.398273 | − | 0.689829i | 0.595240 | − | 0.803548i | \(-0.297057\pi\) |
−0.993513 | + | 0.113719i | \(0.963724\pi\) | |||||||
\(60\) | −24.6534 | + | 7.21177i | −3.18274 | + | 0.931035i | ||||
\(61\) | 4.01356 | − | 6.95169i | 0.513884 | − | 0.890073i | −0.485987 | − | 0.873966i | \(-0.661540\pi\) |
0.999870 | − | 0.0161063i | \(-0.00512703\pi\) | |||||||
\(62\) | 17.2905 | 2.19589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.32743 | −0.915929 | ||||||||
\(65\) | −0.890369 | + | 1.54216i | −0.110437 | + | 0.191282i | ||||
\(66\) | −1.25233 | − | 1.19652i | −0.154151 | − | 0.147282i | ||||
\(67\) | −1.80039 | − | 3.11836i | −0.219952 | − | 0.380969i | 0.734841 | − | 0.678240i | \(-0.237257\pi\) |
−0.954793 | + | 0.297271i | \(0.903924\pi\) | |||||||
\(68\) | 19.6860 | 2.38728 | ||||||||
\(69\) | −1.90578 | + | 7.82115i | −0.229429 | + | 0.941555i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46050 | 1.00408 | 0.502039 | − | 0.864845i | \(-0.332584\pi\) | ||||
0.502039 | + | 0.864845i | \(0.332584\pi\) | |||||||
\(72\) | −13.4626 | − | 6.97504i | −1.58659 | − | 0.822017i | ||||
\(73\) | −0.986757 | + | 1.70911i | −0.115491 | + | 0.200037i | −0.917976 | − | 0.396636i | \(-0.870178\pi\) |
0.802485 | + | 0.596673i | \(0.203511\pi\) | |||||||
\(74\) | 5.72665 | 0.665710 | ||||||||
\(75\) | −3.43685 | + | 14.1045i | −0.396854 | + | 1.62865i | ||||
\(76\) | 4.00040 | − | 6.92889i | 0.458877 | − | 0.794798i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.99115 | + | 0.582462i | −0.225453 | + | 0.0659509i | ||||
\(79\) | −4.08113 | + | 7.06872i | −0.459163 | + | 0.795293i | −0.998917 | − | 0.0465297i | \(-0.985184\pi\) |
0.539754 | + | 0.841823i | \(0.318517\pi\) | |||||||
\(80\) | 7.91503 | − | 13.7092i | 0.884928 | − | 1.53274i | ||||
\(81\) | 5.19076 | + | 7.35228i | 0.576751 | + | 0.816920i | ||||
\(82\) | −9.24411 | − | 16.0113i | −1.02084 | − | 1.76815i | ||||
\(83\) | −6.08600 | − | 10.5413i | −0.668025 | − | 1.15705i | −0.978456 | − | 0.206457i | \(-0.933807\pi\) |
0.310431 | − | 0.950596i | \(-0.399527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.88151 | − | 15.3832i | 0.963336 | − | 1.66855i | ||||
\(86\) | −5.72665 | −0.617521 | ||||||||
\(87\) | 12.7134 | − | 3.71899i | 1.36301 | − | 0.398718i | ||||
\(88\) | 2.05408 | 0.218966 | ||||||||
\(89\) | −7.41507 | − | 12.8433i | −0.785996 | − | 1.36139i | −0.928402 | − | 0.371577i | \(-0.878817\pi\) |
0.142406 | − | 0.989808i | \(-0.454516\pi\) | |||||||
\(90\) | −22.7452 | + | 14.5524i | −2.39755 | + | 1.53396i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.42101 | − | 16.3177i | −0.982208 | − | 1.70123i | ||||
\(93\) | 11.6819 | − | 3.41726i | 1.21136 | − | 0.354354i | ||||
\(94\) | 7.77056 | + | 13.4590i | 0.801472 | + | 1.38819i | ||||
\(95\) | −3.60963 | − | 6.25206i | −0.370340 | − | 0.641448i | ||||
\(96\) | 0.896848 | − | 0.262352i | 0.0915342 | − | 0.0267762i | ||||
\(97\) | 4.74375 | + | 8.21642i | 0.481655 | + | 0.834251i | 0.999778 | − | 0.0210547i | \(-0.00670241\pi\) |
−0.518123 | + | 0.855306i | \(0.673369\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08259 | − | 0.560893i | −0.108804 | − | 0.0563719i | ||||
\(100\) | −16.9897 | − | 29.4270i | −1.69897 | − | 2.94270i | ||||
\(101\) | 8.71176 | 0.866852 | 0.433426 | − | 0.901189i | \(-0.357304\pi\) | ||||
0.433426 | + | 0.901189i | \(0.357304\pi\) | |||||||
\(102\) | 19.8619 | − | 5.81012i | 1.96662 | − | 0.575287i | ||||
\(103\) | 8.02712 | 0.790936 | 0.395468 | − | 0.918480i | \(-0.370582\pi\) | ||||
0.395468 | + | 0.918480i | \(0.370582\pi\) | |||||||
\(104\) | 1.23016 | − | 2.13069i | 0.120627 | − | 0.208931i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.39037 | + | 7.60434i | 0.426430 | + | 0.738599i | ||||
\(107\) | −6.42101 | − | 11.1215i | −0.620742 | − | 1.07516i | −0.989348 | − | 0.145571i | \(-0.953498\pi\) |
0.368605 | − | 0.929586i | \(-0.379835\pi\) | |||||||
\(108\) | −20.6727 | − | 4.04955i | −1.98924 | − | 0.389669i | ||||
\(109\) | −1.30039 | + | 2.25234i | −0.124555 | + | 0.215735i | −0.921559 | − | 0.388239i | \(-0.873084\pi\) |
0.797004 | + | 0.603974i | \(0.206417\pi\) | |||||||
\(110\) | 1.82904 | − | 3.16799i | 0.174392 | − | 0.302056i | ||||
\(111\) | 3.86908 | − | 1.13181i | 0.367237 | − | 0.107427i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.97509 | − | 12.0812i | 0.656162 | − | 1.13651i | −0.325440 | − | 0.945563i | \(-0.605512\pi\) |
0.981601 | − | 0.190942i | \(-0.0611544\pi\) | |||||||
\(114\) | 1.99115 | − | 8.17147i | 0.186488 | − | 0.765328i | ||||
\(115\) | −17.0015 | −1.58540 | ||||||||
\(116\) | −15.5021 | + | 26.8505i | −1.43934 | + | 2.49301i | ||||
\(117\) | −1.23016 | + | 0.787055i | −0.113728 | + | 0.0727633i | ||||
\(118\) | 15.0543 | 1.38586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.58113 | − | 31.1122i | 0.692059 | − | 2.84014i | ||||
\(121\) | −10.8348 | −0.984984 | ||||||||
\(122\) | 9.87538 | + | 17.1047i | 0.894075 | + | 1.54858i | ||||
\(123\) | −9.41002 | − | 8.99066i | −0.848473 | − | 0.810660i | ||||
\(124\) | −14.2444 | + | 24.6721i | −1.27919 | + | 2.21562i | ||||
\(125\) | −12.3698 | −1.10639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5438 | −1.37929 | −0.689643 | − | 0.724149i | \(-0.742233\pi\) | ||||
−0.689643 | + | 0.724149i | \(0.742233\pi\) | |||||||
\(128\) | 9.55408 | − | 16.5482i | 0.844470 | − | 1.46266i | ||||
\(129\) | −3.86908 | + | 1.13181i | −0.340654 | + | 0.0996502i | ||||
\(130\) | −2.19076 | − | 3.79450i | −0.192142 | − | 0.332800i | ||||
\(131\) | −8.51392 | −0.743864 | −0.371932 | − | 0.928260i | \(-0.621305\pi\) | ||||
−0.371932 | + | 0.928260i | \(0.621305\pi\) | |||||||
\(132\) | 2.73905 | − | 0.801244i | 0.238404 | − | 0.0697393i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.85973 | 0.765364 | ||||||||
\(135\) | −12.4911 | + | 14.3273i | −1.07507 | + | 1.23310i | ||||
\(136\) | −12.2709 | + | 21.2538i | −1.05222 | + | 1.82250i | ||||
\(137\) | 0.377242 | 0.0322300 | 0.0161150 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161150 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(138\) | −14.3212 | − | 13.6829i | −1.21910 | − | 1.16477i | ||||
\(139\) | 9.50067 | − | 16.4556i | 0.805837 | − | 1.39575i | −0.109888 | − | 0.993944i | \(-0.535049\pi\) |
0.915725 | − | 0.401806i | \(-0.131617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.91002 | + | 7.55750i | 0.666144 | + | 0.636457i | ||||
\(142\) | −10.4086 | + | 18.0281i | −0.873467 | + | 1.51289i | ||||
\(143\) | 0.0989221 | − | 0.171338i | 0.00827228 | − | 0.0143280i | ||||
\(144\) | 10.9356 | − | 6.99661i | 0.911300 | − | 0.583051i | ||||
\(145\) | 13.9879 | + | 24.2277i | 1.16163 | + | 2.01200i | ||||
\(146\) | −2.42792 | − | 4.20528i | −0.200936 | − | 0.348032i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.71780 | + | 8.17147i | −0.387801 | + | 0.671691i | ||||
\(149\) | −9.70175 | −0.794798 | −0.397399 | − | 0.917646i | \(-0.630087\pi\) | ||||
−0.397399 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(150\) | −25.8265 | − | 24.6756i | −2.10873 | − | 2.01475i | ||||
\(151\) | −12.8348 | −1.04448 | −0.522242 | − | 0.852798i | \(-0.674904\pi\) | ||||
−0.522242 | + | 0.852798i | \(0.674904\pi\) | |||||||
\(152\) | 4.98715 | + | 8.63800i | 0.404511 | + | 0.700634i | ||||
\(153\) | 12.2709 | − | 7.85095i | 0.992045 | − | 0.634711i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8530 | + | 22.2621i | 1.03238 | + | 1.78813i | ||||
\(156\) | 0.809243 | − | 3.32105i | 0.0647913 | − | 0.265897i | ||||
\(157\) | −10.4743 | − | 18.1420i | −0.835937 | − | 1.44789i | −0.893265 | − | 0.449531i | \(-0.851591\pi\) |
0.0573276 | − | 0.998355i | \(-0.481742\pi\) | |||||||
\(158\) | −10.0416 | − | 17.3926i | −0.798869 | − | 1.38368i | ||||
\(159\) | 4.46917 | + | 4.26999i | 0.354428 | + | 0.338633i | ||||
\(160\) | 0.986757 | + | 1.70911i | 0.0780100 | + | 0.135117i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −22.0526 | + | 2.01561i | −1.73262 | + | 0.158362i | ||||
\(163\) | 5.58113 | + | 9.66679i | 0.437148 | + | 0.757162i | 0.997468 | − | 0.0711140i | \(-0.0226554\pi\) |
−0.560321 | + | 0.828276i | \(0.689322\pi\) | |||||||
\(164\) | 30.4624 | 2.37871 | ||||||||
\(165\) | 0.609631 | − | 2.50187i | 0.0474597 | − | 0.194770i | ||||
\(166\) | 29.9492 | 2.32451 | ||||||||
\(167\) | −1.73012 | + | 2.99665i | −0.133880 | + | 0.231888i | −0.925169 | − | 0.379555i | \(-0.876077\pi\) |
0.791289 | + | 0.611443i | \(0.209410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38151 | + | 11.0531i | 0.490886 | + | 0.850239i | ||||
\(170\) | 21.8530 | + | 37.8505i | 1.67605 | + | 2.90300i | ||||
\(171\) | −0.269726 | − | 5.91439i | −0.0206265 | − | 0.452285i | ||||
\(172\) | 4.71780 | − | 8.17147i | 0.359729 | − | 0.623069i | ||||
\(173\) | 3.02680 | − | 5.24258i | 0.230124 | − | 0.398586i | −0.727721 | − | 0.685874i | \(-0.759420\pi\) |
0.957844 | + | 0.287288i | \(0.0927536\pi\) | |||||||
\(174\) | −7.71599 | + | 31.6657i | −0.584948 | + | 2.40057i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.879379 | + | 1.52313i | −0.0662857 | + | 0.114810i | ||||
\(177\) | 10.1711 | − | 2.97532i | 0.764507 | − | 0.223638i | ||||
\(178\) | 36.4896 | 2.73501 | ||||||||
\(179\) | −4.56654 | + | 7.90947i | −0.341319 | + | 0.591182i | −0.984678 | − | 0.174383i | \(-0.944207\pi\) |
0.643359 | + | 0.765565i | \(0.277540\pi\) | |||||||
\(180\) | −2.02688 | − | 44.4442i | −0.151075 | − | 3.31268i | ||||
\(181\) | 11.9478 | 0.888074 | 0.444037 | − | 0.896008i | \(-0.353546\pi\) | ||||
0.444037 | + | 0.896008i | \(0.353546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.0526 | + | 9.60462i | 0.743111 | + | 0.709994i | ||||
\(184\) | 23.4897 | 1.73168 | ||||||||
\(185\) | 4.25696 | + | 7.37327i | 0.312978 | + | 0.542093i | ||||
\(186\) | −7.08998 | + | 29.0966i | −0.519863 | + | 2.13347i | ||||
\(187\) | −0.986757 | + | 1.70911i | −0.0721588 | + | 0.124983i | ||||
\(188\) | −25.6065 | −1.86755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7630 | 1.28867 | ||||||||
\(191\) | −4.57014 | + | 7.91571i | −0.330683 | + | 0.572760i | −0.982646 | − | 0.185491i | \(-0.940613\pi\) |
0.651963 | + | 0.758251i | \(0.273946\pi\) | |||||||
\(192\) | 3.00463 | − | 12.3307i | 0.216840 | − | 0.889891i | ||||
\(193\) | −8.47150 | − | 14.6731i | −0.609792 | − | 1.05619i | −0.991274 | − | 0.131814i | \(-0.957920\pi\) |
0.381483 | − | 0.924376i | \(-0.375414\pi\) | |||||||
\(194\) | −23.3441 | −1.67601 | ||||||||
\(195\) | −2.23008 | − | 2.13069i | −0.159699 | − | 0.152582i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3173 | −1.51880 | −0.759398 | − | 0.650627i | \(-0.774506\pi\) | ||||
−0.759398 | + | 0.650627i | \(0.774506\pi\) | |||||||
\(198\) | 2.52704 | − | 1.61680i | 0.179589 | − | 0.114901i | ||||
\(199\) | −4.98715 | + | 8.63800i | −0.353530 | + | 0.612332i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.633335 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(200\) | 42.3609 | 2.99537 | ||||||||
\(201\) | 5.98587 | − | 1.75103i | 0.422211 | − | 0.123508i | ||||
\(202\) | −10.7177 | + | 18.5635i | −0.754092 | + | 1.30613i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.07227 | + | 33.1278i | −0.565172 | + | 2.31941i | ||||
\(205\) | 13.7434 | − | 23.8042i | 0.959879 | − | 1.66256i | ||||
\(206\) | −9.87538 | + | 17.1047i | −0.688051 | + | 1.19174i | ||||
\(207\) | −12.3801 | − | 6.41415i | −0.860473 | − | 0.445814i | ||||
\(208\) | 1.05329 | + | 1.82435i | 0.0730324 | + | 0.126496i | ||||
\(209\) | 0.401038 | + | 0.694619i | 0.0277404 | + | 0.0480478i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44592 | + | 4.23645i | −0.168384 | + | 0.291649i | −0.937852 | − | 0.347036i | \(-0.887188\pi\) |
0.769468 | + | 0.638685i | \(0.220521\pi\) | |||||||
\(212\) | −14.4677 | −0.993646 | ||||||||
\(213\) | −3.46924 | + | 14.2374i | −0.237709 | + | 0.975533i | ||||
\(214\) | 31.5979 | 2.15998 | ||||||||
\(215\) | −4.25696 | − | 7.37327i | −0.290322 | − | 0.502853i | ||||
\(216\) | 17.2581 | − | 19.7950i | 1.17426 | − | 1.34688i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.19961 | − | 5.54189i | −0.216705 | − | 0.375344i | ||||
\(219\) | −2.47150 | − | 2.36135i | −0.167008 | − | 0.159565i | ||||
\(220\) | 3.01364 | + | 5.21978i | 0.203179 | + | 0.351917i | ||||
\(221\) | 1.18190 | + | 2.04712i | 0.0795034 | + | 0.137704i | ||||
\(222\) | −2.34822 | + | 9.63688i | −0.157602 | + | 0.646785i | ||||
\(223\) | 11.7044 | + | 20.2727i | 0.783786 | + | 1.35756i | 0.929722 | + | 0.368263i | \(0.120047\pi\) |
−0.145936 | + | 0.989294i | \(0.546619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.3260 | − | 11.5672i | −1.48840 | − | 0.771144i | ||||
\(226\) | 17.1623 | + | 29.7259i | 1.14162 | + | 1.97734i | ||||
\(227\) | −6.11839 | −0.406092 | −0.203046 | − | 0.979169i | \(-0.565084\pi\) | ||||
−0.203046 | + | 0.979169i | \(0.565084\pi\) | |||||||
\(228\) | 10.0197 | + | 9.57312i | 0.663568 | + | 0.633995i | ||||
\(229\) | 1.46039 | 0.0965052 | 0.0482526 | − | 0.998835i | \(-0.484635\pi\) | ||||
0.0482526 | + | 0.998835i | \(0.484635\pi\) | |||||||
\(230\) | 20.9161 | − | 36.2278i | 1.37917 | − | 2.38879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3260 | − | 33.4736i | −1.26881 | − | 2.19765i | ||||
\(233\) | 6.62422 | + | 11.4735i | 0.433967 | + | 0.751653i | 0.997211 | − | 0.0746378i | \(-0.0237801\pi\) |
−0.563244 | + | 0.826291i | \(0.690447\pi\) | |||||||
\(234\) | −0.163702 | − | 3.58956i | −0.0107016 | − | 0.234657i | ||||
\(235\) | −11.5526 | + | 20.0097i | −0.753610 | + | 1.30529i | ||||
\(236\) | −12.4022 | + | 21.4813i | −0.807316 | + | 1.39831i | ||||
\(237\) | −10.2219 | − | 9.76631i | −0.663981 | − | 0.634390i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.69436 | + | 16.7911i | −0.627076 | + | 1.08613i | 0.361060 | + | 0.932543i | \(0.382415\pi\) |
−0.988136 | + | 0.153584i | \(0.950918\pi\) | |||||||
\(240\) | 19.8245 | + | 18.9410i | 1.27967 | + | 1.22264i | ||||
\(241\) | −5.05368 | −0.325536 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(242\) | 13.3296 | − | 23.0875i | 0.856857 | − | 1.48412i | ||||
\(243\) | −14.5010 | + | 5.72026i | −0.930239 | + | 0.366955i | ||||
\(244\) | −32.5426 | −2.08333 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.7345 | − | 8.99066i | 1.95956 | − | 0.573223i | ||||
\(247\) | 0.960699 | 0.0611278 | ||||||||
\(248\) | −17.7580 | − | 30.7578i | −1.12764 | − | 1.95312i | ||||
\(249\) | 20.2345 | − | 5.91913i | 1.28231 | − | 0.375110i | ||||
\(250\) | 15.2180 | − | 26.3584i | 0.962472 | − | 1.66705i | ||||
\(251\) | −15.0928 | −0.952647 | −0.476324 | − | 0.879270i | \(-0.658031\pi\) | ||||
−0.476324 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88891 | 0.118755 | ||||||||
\(254\) | 19.1228 | − | 33.1216i | 1.19987 | − | 2.07823i | ||||
\(255\) | 22.2452 | + | 21.2538i | 1.39305 | + | 1.33097i | ||||
\(256\) | 16.1804 | + | 28.0253i | 1.01128 | + | 1.75158i | ||||
\(257\) | −7.71184 | −0.481051 | −0.240526 | − | 0.970643i | \(-0.577320\pi\) | ||||
−0.240526 | + | 0.970643i | \(0.577320\pi\) | |||||||
\(258\) | 2.34822 | − | 9.63688i | 0.146194 | − | 0.599966i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.21926 | 0.447720 | ||||||||
\(261\) | 1.04523 | + | 22.9192i | 0.0646981 | + | 1.41866i | ||||
\(262\) | 10.4743 | − | 18.1420i | 0.647102 | − | 1.12081i | ||||
\(263\) | 4.21206 | 0.259727 | 0.129864 | − | 0.991532i | \(-0.458546\pi\) | ||||
0.129864 | + | 0.991532i | \(0.458546\pi\) | |||||||
\(264\) | −0.842281 | + | 3.45664i | −0.0518388 | + | 0.212741i | ||||
\(265\) | −6.52724 | + | 11.3055i | −0.400965 | + | 0.694492i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.6534 | − | 7.21177i | 1.50876 | − | 0.441353i | ||||
\(268\) | −7.29893 | + | 12.6421i | −0.445853 | + | 0.772240i | ||||
\(269\) | 10.3753 | − | 17.9706i | 0.632596 | − | 1.09569i | −0.354423 | − | 0.935085i | \(-0.615323\pi\) |
0.987019 | − | 0.160603i | \(-0.0513439\pi\) | |||||||
\(270\) | −15.1623 | − | 44.2431i | −0.922745 | − | 2.69255i | ||||
\(271\) | −14.2444 | − | 24.6721i | −0.865287 | − | 1.49872i | −0.866762 | − | 0.498723i | \(-0.833803\pi\) |
0.00147433 | − | 0.999999i | \(-0.499531\pi\) | |||||||
\(272\) | −10.5067 | − | 18.1981i | −0.637060 | − | 1.10342i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.464103 | + | 0.803851i | −0.0280375 | + | 0.0485624i | ||||
\(275\) | 3.40642 | 0.205415 | ||||||||
\(276\) | 31.3227 | − | 9.16270i | 1.88540 | − | 0.551530i | ||||
\(277\) | 17.1623 | 1.03118 | 0.515590 | − | 0.856835i | \(-0.327573\pi\) | ||||
0.515590 | + | 0.856835i | \(0.327573\pi\) | |||||||
\(278\) | 23.3765 | + | 40.4892i | 1.40203 | + | 2.42838i | ||||
\(279\) | 0.960429 | + | 21.0597i | 0.0574994 | + | 1.26081i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.72140 | − | 8.17770i | −0.281655 | − | 0.487841i | 0.690138 | − | 0.723678i | \(-0.257550\pi\) |
−0.971793 | + | 0.235837i | \(0.924217\pi\) | |||||||
\(282\) | −25.8353 | + | 7.55750i | −1.53847 | + | 0.450043i | ||||
\(283\) | 8.43422 | + | 14.6085i | 0.501362 | + | 0.868385i | 0.999999 | + | 0.00157378i | \(0.000500949\pi\) |
−0.498636 | + | 0.866811i | \(0.666166\pi\) | |||||||
\(284\) | −17.1498 | − | 29.7043i | −1.01765 | − | 1.76263i | ||||
\(285\) | 12.0012 | − | 3.51066i | 0.710889 | − | 0.207954i | ||||
\(286\) | 0.243398 | + | 0.421578i | 0.0143924 | + | 0.0249284i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0737345 | + | 1.61680i | 0.00434485 | + | 0.0952711i | ||||
\(289\) | −3.28959 | − | 5.69774i | −0.193505 | − | 0.335161i | ||||
\(290\) | −68.8344 | −4.04210 | ||||||||
\(291\) | −15.7719 | + | 4.61369i | −0.924564 | + | 0.270459i | ||||
\(292\) | 8.00079 | 0.468211 | ||||||||
\(293\) | −1.86143 | + | 3.22409i | −0.108746 | + | 0.188353i | −0.915262 | − | 0.402858i | \(-0.868017\pi\) |
0.806517 | + | 0.591211i | \(0.201350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1908 | + | 19.3830i | 0.651551 | + | 1.12852i | ||||
\(296\) | −5.88151 | − | 10.1871i | −0.341856 | − | 0.592112i | ||||
\(297\) | 1.38780 | − | 1.59180i | 0.0805280 | − | 0.0923655i | ||||
\(298\) | 11.9356 | − | 20.6731i | 0.691411 | − | 1.19756i | ||||
\(299\) | 1.13123 | − | 1.95935i | 0.0654209 | − | 0.113312i | ||||
\(300\) | 56.4868 | − | 16.5239i | 3.26126 | − | 0.954006i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.7901 | − | 27.3492i | 0.908617 | − | 1.57377i | ||||
\(303\) | −3.57227 | + | 14.6603i | −0.205222 | + | 0.842210i | ||||
\(304\) | −8.54024 | −0.489817 | ||||||||
\(305\) | −14.6819 | + | 25.4298i | −0.840683 | + | 1.45611i | ||||
\(306\) | 1.63295 | + | 35.8062i | 0.0933493 | + | 2.04691i | ||||
\(307\) | −30.5691 | −1.74467 | −0.872335 | − | 0.488908i | \(-0.837395\pi\) | ||||
−0.872335 | + | 0.488908i | \(0.837395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.29153 | + | 13.5081i | −0.187249 | + | 0.768451i | ||||
\(310\) | −63.2498 | −3.59235 | ||||||||
\(311\) | −5.21739 | − | 9.03678i | −0.295851 | − | 0.512429i | 0.679332 | − | 0.733831i | \(-0.262270\pi\) |
−0.975182 | + | 0.221403i | \(0.928936\pi\) | |||||||
\(312\) | 3.08113 | + | 2.94381i | 0.174434 | + | 0.166661i | ||||
\(313\) | −0.309930 | + | 0.536815i | −0.0175183 | + | 0.0303426i | −0.874652 | − | 0.484752i | \(-0.838910\pi\) |
0.857133 | + | 0.515095i | \(0.172243\pi\) | |||||||
\(314\) | 51.5440 | 2.90879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0905 | 1.86148 | ||||||||
\(317\) | −5.12422 | + | 8.87541i | −0.287805 | + | 0.498493i | −0.973285 | − | 0.229598i | \(-0.926259\pi\) |
0.685481 | + | 0.728091i | \(0.259592\pi\) | |||||||
\(318\) | −14.5970 | + | 4.26999i | −0.818557 | + | 0.239449i | ||||
\(319\) | −1.55408 | − | 2.69175i | −0.0870120 | − | 0.150709i | ||||
\(320\) | 26.8043 | 1.49841 | ||||||||
\(321\) | 21.3484 | − | 6.24496i | 1.19155 | − | 0.348560i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58307 | −0.533216 | ||||||||
\(324\) | 15.2915 | − | 33.1278i | 0.849530 | − | 1.84043i | ||||
\(325\) | 2.04005 | − | 3.53346i | 0.113161 | − | 0.196001i | ||||
\(326\) | −27.4648 | −1.52113 | ||||||||
\(327\) | −3.25704 | − | 3.11188i | −0.180115 | − | 0.172088i | ||||
\(328\) | −18.9882 | + | 32.8885i | −1.04845 | + | 1.81596i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.58113 | + | 4.37697i | 0.252183 | + | 0.240944i | ||||
\(331\) | 10.1819 | − | 17.6356i | 0.559648 | − | 0.969339i | −0.437878 | − | 0.899035i | \(-0.644270\pi\) |
0.997526 | − | 0.0703042i | \(-0.0223970\pi\) | |||||||
\(332\) | −24.6731 | + | 42.7351i | −1.35411 | + | 2.34539i | ||||
\(333\) | 0.318097 | + | 6.97504i | 0.0174316 | + | 0.382230i | ||||
\(334\) | −4.25696 | − | 7.37327i | −0.232930 | − | 0.403447i | ||||
\(335\) | 6.58596 | + | 11.4072i | 0.359829 | + | 0.623242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.85594 | − | 4.94662i | 0.155573 | − | 0.269460i | −0.777695 | − | 0.628642i | \(-0.783611\pi\) |
0.933267 | + | 0.359182i | \(0.116944\pi\) | |||||||
\(338\) | −31.4035 | −1.70812 | ||||||||
\(339\) | 17.4703 | + | 16.6917i | 0.948855 | + | 0.906569i | ||||
\(340\) | −72.0128 | −3.90544 | ||||||||
\(341\) | −1.42800 | − | 2.47337i | −0.0773305 | − | 0.133940i | ||||
\(342\) | 12.9346 | + | 6.70145i | 0.699422 | + | 0.362373i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.88151 | + | 10.1871i | 0.317110 | + | 0.549251i | ||||
\(345\) | 6.97150 | − | 28.6103i | 0.375333 | − | 1.54033i | ||||
\(346\) | 7.44746 | + | 12.8994i | 0.400378 | + | 0.693475i | ||||
\(347\) | −4.44066 | − | 7.69145i | −0.238387 | − | 0.412899i | 0.721865 | − | 0.692034i | \(-0.243285\pi\) |
−0.960252 | + | 0.279136i | \(0.909952\pi\) | |||||||
\(348\) | −38.8277 | − | 37.0973i | −2.08138 | − | 1.98862i | ||||
\(349\) | −10.4874 | − | 18.1648i | −0.561379 | − | 0.972337i | −0.997376 | − | 0.0723893i | \(-0.976938\pi\) |
0.435997 | − | 0.899948i | \(-0.356396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.820039 | − | 2.39285i | −0.0437704 | − | 0.127721i | ||||
\(352\) | −0.109631 | − | 0.189886i | −0.00584335 | − | 0.0101210i | ||||
\(353\) | −14.7654 | −0.785881 | −0.392941 | − | 0.919564i | \(-0.628542\pi\) | ||||
−0.392941 | + | 0.919564i | \(0.628542\pi\) | |||||||
\(354\) | −6.17305 | + | 25.3336i | −0.328094 | + | 1.34647i | ||||
\(355\) | −30.9492 | −1.64261 | ||||||||
\(356\) | −30.0613 | + | 52.0677i | −1.59325 | + | 2.75959i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2360 | − | 19.4613i | −0.593840 | − | 1.02856i | ||||
\(359\) | −3.60603 | − | 6.24583i | −0.190319 | − | 0.329642i | 0.755037 | − | 0.655682i | \(-0.227619\pi\) |
−0.945356 | + | 0.326040i | \(0.894286\pi\) | |||||||
\(360\) | 49.2474 | + | 25.5152i | 2.59556 | + | 1.34477i | ||||
\(361\) | 7.55262 | − | 13.0815i | 0.397506 | − | 0.688501i | ||||
\(362\) | −14.6988 | + | 25.4591i | −0.772554 | + | 1.33810i | ||||
\(363\) | 4.44284 | − | 18.2330i | 0.233188 | − | 0.956983i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.60963 | − | 6.25206i | 0.188937 | − | 0.327248i | ||||
\(366\) | −32.8334 | + | 9.60462i | −1.71623 | + | 0.502042i | ||||
\(367\) | −10.9742 | −0.572850 | −0.286425 | − | 0.958103i | \(-0.592467\pi\) | ||||
−0.286425 | + | 0.958103i | \(0.592467\pi\) | |||||||
\(368\) | −10.0562 | + | 17.4179i | −0.524217 | + | 0.907970i | ||||
\(369\) | 18.9882 | − | 12.1487i | 0.988485 | − | 0.632434i | ||||
\(370\) | −20.9485 | −1.08906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −35.6775 | − | 34.0875i | −1.84979 | − | 1.76736i | ||||
\(373\) | −0.543767 | −0.0281552 | −0.0140776 | − | 0.999901i | \(-0.504481\pi\) | ||||
−0.0140776 | + | 0.999901i | \(0.504481\pi\) | |||||||
\(374\) | −2.42792 | − | 4.20528i | −0.125545 | − | 0.217450i | ||||
\(375\) | 5.07227 | − | 20.8161i | 0.261931 | − | 1.07494i | ||||
\(376\) | 15.9614 | − | 27.6459i | 0.823145 | − | 1.42573i | ||||
\(377\) | −3.72286 | −0.191737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6912 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(380\) | −14.6337 | + | 25.3464i | −0.750695 | + | 1.30024i | ||||
\(381\) | 6.37375 | − | 26.1572i | 0.326537 | − | 1.34008i | ||||
\(382\) | −11.2448 | − | 19.4766i | −0.575336 | − | 0.996511i | ||||
\(383\) | 35.7139 | 1.82489 | 0.912447 | − | 0.409194i | \(-0.134190\pi\) | ||||
0.912447 | + | 0.409194i | \(0.134190\pi\) | |||||||
\(384\) | 23.9298 | + | 22.8633i | 1.22116 | + | 1.16674i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.6883 | 2.12188 | ||||||||
\(387\) | −0.318097 | − | 6.97504i | −0.0161698 | − | 0.354561i | ||||
\(388\) | 19.2316 | − | 33.3101i | 0.976336 | − | 1.69106i | ||||
\(389\) | 38.6591 | 1.96010 | 0.980048 | − | 0.198761i | \(-0.0636919\pi\) | ||||
0.980048 | + | 0.198761i | \(0.0636919\pi\) | |||||||
\(390\) | 7.28376 | − | 2.13069i | 0.368828 | − | 0.107892i | ||||
\(391\) | −11.2842 | + | 19.5447i | −0.570664 | + | 0.988420i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.49115 | − | 14.3273i | 0.176105 | − | 0.722718i | ||||
\(394\) | 26.2257 | − | 45.4242i | 1.32123 | − | 2.28844i | ||||
\(395\) | 14.9291 | − | 25.8579i | 0.751163 | − | 1.30105i | ||||
\(396\) | 0.225191 | + | 4.93786i | 0.0113163 | + | 0.248137i | ||||
\(397\) | 5.97391 | + | 10.3471i | 0.299822 | + | 0.519307i | 0.976095 | − | 0.217344i | \(-0.0697394\pi\) |
−0.676273 | + | 0.736651i | \(0.736406\pi\) | |||||||
\(398\) | −12.2709 | − | 21.2538i | −0.615085 | − | 1.06536i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.1352 | + | 31.4111i | −0.906761 | + | 1.57056i | ||||
\(401\) | 32.3566 | 1.61581 | 0.807906 | − | 0.589311i | \(-0.200601\pi\) | ||||
0.807906 | + | 0.589311i | \(0.200601\pi\) | |||||||
\(402\) | −3.63295 | + | 14.9093i | −0.181195 | + | 0.743606i | ||||
\(403\) | −3.42082 | −0.170403 | ||||||||
\(404\) | −17.6591 | − | 30.5865i | −0.878573 | − | 1.52173i | ||||
\(405\) | −18.9882 | − | 26.8952i | −0.943530 | − | 1.33643i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.472958 | − | 0.819187i | −0.0234437 | − | 0.0406056i | ||||
\(408\) | −30.7345 | − | 29.3648i | −1.52159 | − | 1.45378i | ||||
\(409\) | −9.48751 | − | 16.4328i | −0.469127 | − | 0.812552i | 0.530250 | − | 0.847841i | \(-0.322098\pi\) |
−0.999377 | + | 0.0352893i | \(0.988765\pi\) | |||||||
\(410\) | 33.8157 | + | 58.5704i | 1.67004 | + | 2.89259i | ||||
\(411\) | −0.154689 | + | 0.634828i | −0.00763024 | + | 0.0313138i | ||||
\(412\) | −16.2713 | − | 28.1827i | −0.801630 | − | 1.38846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 28.8982 | − | 18.4891i | 1.42027 | − | 0.908691i | ||||
\(415\) | 22.2630 | + | 38.5607i | 1.09285 | + | 1.89287i | ||||
\(416\) | −0.262624 | −0.0128762 | ||||||||
\(417\) | 23.7960 | + | 22.7355i | 1.16530 | + | 1.11336i | ||||
\(418\) | −1.97351 | −0.0965277 | ||||||||
\(419\) | 8.64523 | − | 14.9740i | 0.422347 | − | 0.731526i | −0.573822 | − | 0.818980i | \(-0.694540\pi\) |
0.996169 | + | 0.0874539i | \(0.0278730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.30039 | − | 16.1087i | −0.453273 | − | 0.785092i | 0.545314 | − | 0.838232i | \(-0.316410\pi\) |
−0.998587 | + | 0.0531397i | \(0.983077\pi\) | |||||||
\(422\) | −6.01819 | − | 10.4238i | −0.292961 | − | 0.507423i | ||||
\(423\) | −15.9614 | + | 10.2121i | −0.776069 | + | 0.496530i | ||||
\(424\) | 9.01819 | − | 15.6200i | 0.437962 | − | 0.758572i | ||||
\(425\) | −20.3496 | + | 35.2466i | −0.987103 | + | 1.70971i | ||||
\(426\) | −26.0699 | − | 24.9081i | −1.26309 | − | 1.20680i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0313 | + | 45.0876i | −1.25827 | + | 2.17939i | ||||
\(429\) | 0.247767 | + | 0.236725i | 0.0119623 | + | 0.0114292i | ||||
\(430\) | 20.9485 | 1.01023 | ||||||||
\(431\) | 7.93920 | − | 13.7511i | 0.382418 | − | 0.662367i | −0.608990 | − | 0.793178i | \(-0.708425\pi\) |
0.991407 | + | 0.130811i | \(0.0417582\pi\) | |||||||
\(432\) | 7.28982 | + | 21.2715i | 0.350732 | + | 1.02343i | ||||
\(433\) | 40.4367 | 1.94326 | 0.971631 | − | 0.236501i | \(-0.0760007\pi\) | ||||
0.971631 | + | 0.236501i | \(0.0760007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −46.5064 | + | 13.6043i | −2.22981 | + | 0.652278i | ||||
\(436\) | 10.5438 | 0.504955 | ||||||||
\(437\) | 4.58611 | + | 7.94338i | 0.219384 | + | 0.379984i | ||||
\(438\) | 8.07227 | − | 2.36135i | 0.385708 | − | 0.112830i | ||||
\(439\) | −6.23047 | + | 10.7915i | −0.297364 | + | 0.515050i | −0.975532 | − | 0.219857i | \(-0.929441\pi\) |
0.678168 | + | 0.734907i | \(0.262774\pi\) | |||||||
\(440\) | −7.51399 | −0.358216 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.81616 | −0.276646 | ||||||||
\(443\) | 4.11537 | − | 7.12802i | 0.195527 | − | 0.338663i | −0.751546 | − | 0.659680i | \(-0.770692\pi\) |
0.947073 | + | 0.321018i | \(0.104025\pi\) | |||||||
\(444\) | −11.8165 | − | 11.2899i | −0.560787 | − | 0.535795i | ||||
\(445\) | 27.1249 | + | 46.9817i | 1.28584 | + | 2.22715i | ||||
\(446\) | −57.5976 | −2.72732 | ||||||||
\(447\) | 3.97822 | − | 16.3262i | 0.188163 | − | 0.772204i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.64474 | 0.266392 | 0.133196 | − | 0.991090i | \(-0.457476\pi\) | ||||
0.133196 | + | 0.991090i | \(0.457476\pi\) | |||||||
\(450\) | 52.1146 | − | 33.3430i | 2.45670 | − | 1.57180i | ||||
\(451\) | −1.52692 | + | 2.64471i | −0.0718999 | + | 0.124534i | ||||
\(452\) | −56.5552 | −2.66013 | ||||||||
\(453\) | 5.26294 | − | 21.5986i | 0.247275 | − | 1.01479i | ||||
\(454\) | 7.52716 | − | 13.0374i | 0.353267 | − | 0.611876i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.5811 | + | 4.85041i | −0.776482 | + | 0.227141i | ||||
\(457\) | −2.53443 | + | 4.38977i | −0.118556 | + | 0.205345i | −0.919196 | − | 0.393801i | \(-0.871160\pi\) |
0.800640 | + | 0.599146i | \(0.204493\pi\) | |||||||
\(458\) | −1.79665 | + | 3.11188i | −0.0839518 | + | 0.145409i | ||||
\(459\) | 8.17996 | + | 23.8689i | 0.381808 | + | 1.11411i | ||||
\(460\) | 34.4628 | + | 59.6913i | 1.60683 | + | 2.78312i | ||||
\(461\) | 3.88831 | + | 6.73475i | 0.181097 | + | 0.313669i | 0.942254 | − | 0.334898i | \(-0.108702\pi\) |
−0.761158 | + | 0.648567i | \(0.775369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58998 | − | 7.95008i | 0.213314 | − | 0.369472i | −0.739435 | − | 0.673228i | \(-0.764907\pi\) |
0.952750 | + | 0.303756i | \(0.0982408\pi\) | |||||||
\(464\) | 33.0947 | 1.53638 | ||||||||
\(465\) | −42.7333 | + | 12.5006i | −1.98171 | + | 0.579702i | ||||
\(466\) | −32.5979 | −1.51007 | ||||||||
\(467\) | 6.88272 | + | 11.9212i | 0.318494 | + | 0.551648i | 0.980174 | − | 0.198138i | \(-0.0634895\pi\) |
−0.661680 | + | 0.749787i | \(0.730156\pi\) | |||||||
\(468\) | 5.25688 | + | 2.72361i | 0.242999 | + | 0.125899i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −28.4253 | − | 49.2340i | −1.31116 | − | 2.27100i | ||||
\(471\) | 34.8245 | − | 10.1871i | 1.60463 | − | 0.469396i | ||||
\(472\) | −15.4614 | − | 26.7800i | −0.711669 | − | 1.23265i | ||||
\(473\) | 0.472958 | + | 0.819187i | 0.0217466 | + | 0.0376663i | ||||
\(474\) | 33.3861 | − | 9.76631i | 1.53347 | − | 0.448581i | ||||
\(475\) | 8.27052 | + | 14.3250i | 0.379477 | + | 0.657274i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.01819 | + | 5.76985i | −0.412914 | + | 0.264183i | ||||
\(478\) | −23.8530 | − | 41.3146i | −1.09101 | − | 1.88969i | ||||
\(479\) | 8.71176 | 0.398050 | 0.199025 | − | 0.979994i | \(-0.436222\pi\) | ||||
0.199025 | + | 0.979994i | \(0.436222\pi\) | |||||||
\(480\) | −3.28074 | + | 0.959702i | −0.149745 | + | 0.0438042i | ||||
\(481\) | −1.13298 | −0.0516597 | ||||||||
\(482\) | 6.21731 | − | 10.7687i | 0.283191 | − | 0.490501i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.9626 | + | 38.0404i | 0.998302 | + | 1.72911i | ||||
\(485\) | −17.3530 | − | 30.0563i | −0.787960 | − | 1.36479i | ||||
\(486\) | 5.65082 | − | 37.9369i | 0.256326 | − | 1.72085i | ||||
\(487\) | 9.01819 | − | 15.6200i | 0.408653 | − | 0.707808i | −0.586086 | − | 0.810249i | \(-0.699332\pi\) |
0.994739 | + | 0.102441i | \(0.0326653\pi\) | |||||||
\(488\) | 20.2849 | − | 35.1344i | 0.918253 | − | 1.59046i | ||||
\(489\) | −18.5560 | + | 5.42810i | −0.839129 | + | 0.245467i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.02344 | + | 1.77266i | −0.0461874 | + | 0.0799989i | −0.888195 | − | 0.459467i | \(-0.848040\pi\) |
0.842007 | + | 0.539466i | \(0.181374\pi\) | |||||||
\(492\) | −12.4911 | + | 51.2624i | −0.563144 | + | 2.31109i | ||||
\(493\) | 37.1358 | 1.67251 | ||||||||
\(494\) | −1.18190 | + | 2.04712i | −0.0531763 | + | 0.0921041i | ||||
\(495\) | 3.96019 | + | 2.05179i | 0.177997 | + | 0.0922211i | ||||
\(496\) | 30.4097 | 1.36544 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.2807 | + | 50.3990i | −0.550313 | + | 2.25843i | ||||
\(499\) | −39.0875 | −1.74980 | −0.874899 | − | 0.484305i | \(-0.839072\pi\) | ||||
−0.874899 | + | 0.484305i | \(0.839072\pi\) | |||||||
\(500\) | 25.0742 | + | 43.4297i | 1.12135 | + | 1.94224i | ||||
\(501\) | −4.33336 | − | 4.14024i | −0.193600 | − | 0.184972i | ||||
\(502\) | 18.5679 | − | 32.1606i | 0.828727 | − | 1.43540i | ||||
\(503\) | 5.11846 | 0.228221 | 0.114111 | − | 0.993468i | \(-0.463598\pi\) | ||||
0.114111 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8683 | −1.41812 | ||||||||
\(506\) | −2.32383 | + | 4.02499i | −0.103307 | + | 0.178933i | ||||
\(507\) | −21.2171 | + | 6.20655i | −0.942283 | + | 0.275642i | ||||
\(508\) | 31.5079 | + | 54.5732i | 1.39794 | + | 2.42130i | ||||
\(509\) | −29.5272 | −1.30877 | −0.654386 | − | 0.756161i | \(-0.727073\pi\) | ||||
−0.654386 | + | 0.756161i | \(0.727073\pi\) | |||||||
\(510\) | −72.6562 | + | 21.2538i | −3.21727 | + | 0.941136i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −41.4078 | −1.82998 | ||||||||
\(513\) | 10.0634 | + | 1.97131i | 0.444311 | + | 0.0870354i | ||||
\(514\) | 9.48751 | − | 16.4328i | 0.418476 | − | 0.724822i | ||||
\(515\) | −29.3638 | −1.29392 | ||||||||
\(516\) | 11.8165 | + | 11.2899i | 0.520193 | + | 0.497010i | ||||
\(517\) | 1.28352 | − | 2.22313i | 0.0564493 | − | 0.0977730i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.58113 | + | 7.24327i | 0.332775 | + | 0.317944i | ||||
\(520\) | −4.50000 | + | 7.79423i | −0.197338 | + | 0.341800i | ||||
\(521\) | −0.532351 | + | 0.922058i | −0.0233227 | + | 0.0403961i | −0.877451 | − | 0.479666i | \(-0.840758\pi\) |
0.854128 | + | 0.520062i | \(0.174091\pi\) | |||||||
\(522\) | −50.1234 | − | 25.9691i | −2.19384 | − | 1.13664i | ||||
\(523\) | −6.69094 | − | 11.5890i | −0.292574 | − | 0.506754i | 0.681843 | − | 0.731498i | \(-0.261179\pi\) |
−0.974418 | + | 0.224745i | \(0.927845\pi\) | |||||||
\(524\) | 17.2581 | + | 29.8918i | 0.753922 | + | 1.30583i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.18190 | + | 8.97532i | −0.225942 | + | 0.391343i | ||||
\(527\) | 34.1230 | 1.48642 | ||||||||
\(528\) | −2.20255 | − | 2.10439i | −0.0958536 | − | 0.0915818i | ||||
\(529\) | −1.39922 | −0.0608358 | ||||||||
\(530\) | −16.0603 | − | 27.8173i | −0.697615 | − | 1.20830i | ||||
\(531\) | 0.836219 | + | 18.3361i | 0.0362888 | + | 0.795719i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82889 | + | 3.16774i | 0.0792181 | + | 0.137210i | ||||
\(534\) | −14.9626 | + | 61.4052i | −0.647497 | + | 2.65726i | ||||
\(535\) | 23.4885 | + | 40.6833i | 1.01550 | + | 1.75889i | ||||
\(536\) | −9.09931 | − | 15.7605i | −0.393031 | − | 0.680749i | ||||
\(537\) | −11.4376 | − | 10.9279i | −0.493571 | − | 0.471575i | ||||
\(538\) | 25.5286 | + | 44.2168i | 1.10062 | + | 1.90632i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.6224 | + | 14.8136i | 3.25427 | + | 0.637475i | ||||
\(541\) | 17.0438 | + | 29.5207i | 0.732769 | + | 1.26919i | 0.955695 | + | 0.294358i | \(0.0951056\pi\) |
−0.222927 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(542\) | 70.0970 | 3.01092 | ||||||||
\(543\) | −4.89922 | + | 20.1059i | −0.210246 | + | 0.862828i | ||||
\(544\) | 2.61970 | 0.112319 | ||||||||
\(545\) | 4.75692 | − | 8.23922i | 0.203764 | − | 0.352930i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.97150 | + | 5.14678i | 0.127052 | + | 0.220060i | 0.922533 | − | 0.385918i | \(-0.126115\pi\) |
−0.795481 | + | 0.605978i | \(0.792782\pi\) | |||||||
\(548\) | −0.764686 | − | 1.32448i | −0.0326658 | − | 0.0565788i | ||||
\(549\) | −20.2849 | + | 12.9783i | −0.865737 | + | 0.553900i | ||||
\(550\) | −4.19076 | + | 7.25860i | −0.178694 | + | 0.309508i | ||||
\(551\) | 7.54638 | − | 13.0707i | 0.321487 | − | 0.556831i | ||||
\(552\) | −9.63198 | + | 39.5287i | −0.409964 | + | 1.68245i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −21.1139 | + | 36.5704i | −0.897044 | + | 1.55373i | ||||
\(555\) | −14.1534 | + | 4.14024i | −0.600778 | + | 0.175743i | ||||
\(556\) | −77.0331 | −3.26693 | ||||||||
\(557\) | 15.0402 | − | 26.0503i | 0.637272 | − | 1.10379i | −0.348756 | − | 0.937213i | \(-0.613396\pi\) |
0.986029 | − | 0.166575i | \(-0.0532707\pi\) | |||||||
\(558\) | −46.0568 | − | 23.8622i | −1.94974 | − | 1.01017i | ||||
\(559\) | 1.13298 | 0.0479202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.47150 | − | 2.36135i | −0.104347 | − | 0.0996963i | ||||
\(562\) | 23.2340 | 0.980069 | ||||||||
\(563\) | −9.81060 | − | 16.9925i | −0.413468 | − | 0.716147i | 0.581799 | − | 0.813333i | \(-0.302349\pi\) |
−0.995266 | + | 0.0971860i | \(0.969016\pi\) | |||||||
\(564\) | 10.5000 | − | 43.0910i | 0.442130 | − | 1.81446i | ||||
\(565\) | −25.5154 | + | 44.1940i | −1.07344 | + | 1.85926i | ||||
\(566\) | −41.5049 | −1.74458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7601 | 1.79417 | ||||||||
\(569\) | 0.687159 | − | 1.19019i | 0.0288072 | − | 0.0498955i | −0.851262 | − | 0.524740i | \(-0.824162\pi\) |
0.880070 | + | 0.474845i | \(0.157496\pi\) | |||||||
\(570\) | −7.28376 | + | 29.8918i | −0.305083 | + | 1.25203i | ||||
\(571\) | −8.69076 | − | 15.0528i | −0.363697 | − | 0.629941i | 0.624869 | − | 0.780729i | \(-0.285152\pi\) |
−0.988566 | + | 0.150788i | \(0.951819\pi\) | |||||||
\(572\) | −0.802077 | −0.0335365 | ||||||||
\(573\) | −11.4467 | − | 10.9365i | −0.478191 | − | 0.456880i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.9545 | 1.62451 | ||||||||
\(576\) | 19.5182 | + | 10.1124i | 0.813258 | + | 0.421352i | ||||
\(577\) | −13.5274 | + | 23.4301i | −0.563153 | + | 0.975409i | 0.434066 | + | 0.900881i | \(0.357078\pi\) |
−0.997219 | + | 0.0745283i | \(0.976255\pi\) | |||||||
\(578\) | 16.1881 | 0.673337 | ||||||||
\(579\) | 28.1658 | − | 8.23922i | 1.17053 | − | 0.342410i | ||||
\(580\) | 56.7080 | − | 98.2211i | 2.35467 | − | 4.07841i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.57227 | − | 39.2837i | 0.396783 | − | 1.62836i | ||||
\(583\) | 0.725191 | − | 1.25607i | 0.0300344 | − | 0.0520210i | ||||
\(584\) | −4.98715 | + | 8.63800i | −0.206370 | + | 0.357443i | ||||
\(585\) | 4.50000 | − | 2.87911i | 0.186052 | − | 0.119036i | ||||
\(586\) | −4.58005 | − | 7.93288i | −0.189200 | − | 0.327704i | ||||
\(587\) | 3.75700 | + | 6.50731i | 0.155068 | + | 0.268585i | 0.933084 | − | 0.359659i | \(-0.117107\pi\) |
−0.778016 | + | 0.628245i | \(0.783774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93414 | − | 12.0103i | 0.285716 | − | 0.494875i | ||||
\(590\) | −55.0698 | −2.26719 | ||||||||
\(591\) | 8.74120 | − | 35.8730i | 0.359565 | − | 1.47562i | ||||
\(592\) | 10.0718 | 0.413948 | ||||||||
\(593\) | 17.7904 | + | 30.8139i | 0.730565 | + | 1.26538i | 0.956642 | + | 0.291266i | \(0.0940765\pi\) |
−0.226077 | + | 0.974109i | \(0.572590\pi\) | |||||||
\(594\) | 1.68456 | + | 4.91551i | 0.0691184 | + | 0.201686i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.6659 | + | 34.0623i | 0.805545 | + | 1.39524i | ||||
\(597\) | −12.4911 | − | 11.9345i | −0.511229 | − | 0.488445i | ||||
\(598\) | 2.78340 | + | 4.82100i | 0.113822 | + | 0.197145i | ||||
\(599\) | 5.74105 | + | 9.94379i | 0.234573 | + | 0.406292i | 0.959148 | − | 0.282903i | \(-0.0912975\pi\) |
−0.724576 | + | 0.689195i | \(0.757964\pi\) | |||||||
\(600\) | −17.3702 | + | 71.2854i | −0.709133 | + | 2.91021i | ||||
\(601\) | −0.190030 | − | 0.329142i | −0.00775150 | − | 0.0134260i | 0.862124 | − | 0.506698i | \(-0.169134\pi\) |
−0.869875 | + | 0.493272i | \(0.835801\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.492129 | + | 10.7911i | 0.0200411 | + | 0.439448i | ||||
\(604\) | 26.0167 | + | 45.0623i | 1.05861 | + | 1.83356i | ||||
\(605\) | 39.6346 | 1.61138 | ||||||||
\(606\) | −26.8442 | − | 25.6478i | −1.09047 | − | 1.04187i | ||||
\(607\) | 18.5409 | 0.752551 | 0.376275 | − | 0.926508i | \(-0.377205\pi\) | ||||
0.376275 | + | 0.926508i | \(0.377205\pi\) | |||||||
\(608\) | 0.532351 | − | 0.922058i | 0.0215897 | − | 0.0373944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.1249 | − | 62.5702i | −1.46265 | − | 2.53339i | ||||
\(611\) | −1.53736 | − | 2.66278i | −0.0621949 | − | 0.107725i | ||||
\(612\) | −52.4379 | − | 27.1682i | −2.11967 | − | 1.09821i | ||||
\(613\) | −3.66225 | + | 6.34321i | −0.147917 | + | 0.256200i | −0.930457 | − | 0.366400i | \(-0.880590\pi\) |
0.782540 | + | 0.622600i | \(0.213924\pi\) | |||||||
\(614\) | 37.6077 | − | 65.1385i | 1.51772 | − | 2.62877i | ||||
\(615\) | 34.4226 | + | 32.8885i | 1.38805 | + | 1.32619i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7427 | − | 22.0710i | 0.513002 | − | 0.888546i | −0.486884 | − | 0.873466i | \(-0.661867\pi\) |
0.999886 | − | 0.0150791i | \(-0.00480000\pi\) | |||||||
\(618\) | −24.7345 | − | 23.6322i | −0.994968 | − | 0.950627i | ||||
\(619\) | −32.8963 | −1.32222 | −0.661108 | − | 0.750291i | \(-0.729913\pi\) | ||||
−0.661108 | + | 0.750291i | \(0.729913\pi\) | |||||||
\(620\) | 52.1072 | − | 90.2523i | 2.09267 | − | 3.62462i | ||||
\(621\) | 15.8703 | − | 18.2032i | 0.636852 | − | 0.730468i | ||||
\(622\) | 25.6748 | 1.02947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.50194 | + | 1.02441i | −0.140190 | + | 0.0410092i | ||||
\(625\) | 3.34221 | 0.133689 | ||||||||
\(626\) | −0.762585 | − | 1.32084i | −0.0304790 | − | 0.0527912i | ||||
\(627\) | −1.33336 | + | 0.390043i | −0.0532493 | + | 0.0155768i | ||||
\(628\) | −42.4636 | + | 73.5490i | −1.69448 | + | 2.93493i | ||||
\(629\) | 11.3016 | 0.450626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8683 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(632\) | −20.6264 | + | 35.7259i | −0.820472 | + | 1.42110i | ||||
\(633\) | −6.12620 | − | 5.85318i | −0.243495 | − | 0.232643i | ||||
\(634\) | −12.6082 | − | 21.8380i | −0.500734 | − | 0.867297i | ||||
\(635\) | 56.8603 | 2.25643 | ||||||||
\(636\) | 5.93251 | − | 24.3464i | 0.235239 | − | 0.965399i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.64766 | 0.302774 | ||||||||
\(639\) | −22.5364 | − | 11.6762i | −0.891525 | − | 0.461902i | ||||
\(640\) | −34.9496 | + | 60.5344i | −1.38150 | + | 2.39283i | ||||
\(641\) | 11.4605 | 0.452663 | 0.226331 | − | 0.974050i | \(-0.427327\pi\) | ||||
0.226331 | + | 0.974050i | \(0.427327\pi\) | |||||||
\(642\) | −12.9568 | + | 53.1733i | −0.511362 | + | 2.09858i | ||||
\(643\) | −8.69078 | + | 15.0529i | −0.342731 | + | 0.593627i | −0.984939 | − | 0.172903i | \(-0.944685\pi\) |
0.642208 | + | 0.766531i | \(0.278019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.1534 | − | 4.14024i | 0.557290 | − | 0.163022i | ||||
\(646\) | 11.7896 | − | 20.4202i | 0.463855 | − | 0.803421i | ||||
\(647\) | 12.6720 | − | 21.9485i | 0.498186 | − | 0.862883i | −0.501812 | − | 0.864977i | \(-0.667333\pi\) |
0.999998 | + | 0.00209358i | \(0.000666408\pi\) | |||||||
\(648\) | 26.2345 | + | 37.1590i | 1.03059 | + | 1.45975i | ||||
\(649\) | −1.24332 | − | 2.15349i | −0.0488045 | − | 0.0845320i | ||||
\(650\) | 5.01954 | + | 8.69410i | 0.196883 | + | 0.341011i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.6264 | − | 39.1900i | 0.886116 | − | 1.53480i | ||||
\(653\) | 14.0833 | 0.551121 | 0.275560 | − | 0.961284i | \(-0.411137\pi\) | ||||
0.275560 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(654\) | 10.6380 | − | 3.11188i | 0.415977 | − | 0.121684i | ||||
\(655\) | 31.1445 | 1.21692 | ||||||||
\(656\) | −16.2581 | − | 28.1599i | −0.634774 | − | 1.09946i | ||||
\(657\) | 4.98715 | − | 3.19079i | 0.194567 | − | 0.124484i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.0854 | − | 33.0569i | −0.743462 | − | 1.28771i | −0.950910 | − | 0.309467i | \(-0.899849\pi\) |
0.207449 | − | 0.978246i | \(-0.433484\pi\) | |||||||
\(660\) | −10.0197 | + | 2.93101i | −0.390014 | + | 0.114089i | ||||
\(661\) | −0.176866 | − | 0.306341i | −0.00687930 | − | 0.0119153i | 0.862565 | − | 0.505946i | \(-0.168856\pi\) |
−0.869445 | + | 0.494031i | \(0.835523\pi\) | |||||||
\(662\) | 25.0526 | + | 43.3924i | 0.973698 | + | 1.68649i | ||||
\(663\) | −3.92955 | + | 1.14950i | −0.152611 | + | 0.0446428i | ||||
\(664\) | −30.7591 | − | 53.2764i | −1.19369 | − | 2.06752i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.2542 | − | 7.90324i | −0.591087 | − | 0.306244i | ||||
\(667\) | −17.7719 | − | 30.7818i | −0.688130 | − | 1.19188i | ||||
\(668\) | 14.0281 | 0.542762 | ||||||||
\(669\) | −38.9145 | + | 11.3835i | −1.50452 | + | 0.440112i | ||||
\(670\) | −32.4096 | −1.25209 | ||||||||
\(671\) | 1.63119 | − | 2.82531i | 0.0629715 | − | 0.109070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5555 | + | 18.2827i | 0.406886 | + | 0.704748i | 0.994539 | − | 0.104365i | \(-0.0332811\pi\) |
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(674\) | 7.02704 | + | 12.1712i | 0.270672 | + | 0.468817i | ||||
\(675\) | 28.6202 | − | 32.8273i | 1.10159 | − | 1.26352i | ||||
\(676\) | 25.8712 | − | 44.8102i | 0.995046 | − | 1.72347i | ||||
\(677\) | 10.5732 | − | 18.3133i | 0.406361 | − | 0.703837i | −0.588118 | − | 0.808775i | \(-0.700131\pi\) |
0.994479 | + | 0.104938i | \(0.0334643\pi\) | |||||||
\(678\) | −57.0605 | + | 16.6917i | −2.19140 | + | 0.641041i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 44.8879 | − | 77.7482i | 1.72137 | − | 2.98151i | ||||
\(681\) | 2.50885 | − | 10.2961i | 0.0961395 | − | 0.394547i | ||||
\(682\) | 7.02720 | 0.269085 | ||||||||
\(683\) | −17.3858 | + | 30.1131i | −0.665249 | + | 1.15224i | 0.313969 | + | 0.949433i | \(0.398341\pi\) |
−0.979218 | + | 0.202811i | \(0.934992\pi\) | |||||||
\(684\) | −20.2183 | + | 12.9357i | −0.773067 | + | 0.494610i | ||||
\(685\) | −1.37998 | −0.0527264 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.598835 | + | 2.45756i | −0.0228470 | + | 0.0937618i | ||||
\(688\) | −10.0718 | −0.383984 | ||||||||
\(689\) | −0.868609 | − | 1.50447i | −0.0330914 | − | 0.0573159i | ||||
\(690\) | 52.3879 | + | 50.0532i | 1.99437 | + | 1.90549i | ||||
\(691\) | 17.3246 | − | 30.0071i | 0.659059 | − | 1.14152i | −0.321801 | − | 0.946807i | \(-0.604288\pi\) |
0.980860 | − | 0.194716i | \(-0.0623785\pi\) | |||||||
\(692\) | −24.5418 | −0.932940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8525 | 0.829511 | ||||||||
\(695\) | −34.7542 | + | 60.1960i | −1.31830 | + | 2.28336i | ||||
\(696\) | 64.2544 | − | 18.7961i | 2.43556 | − | 0.712464i | ||||
\(697\) | −18.2434 | − | 31.5985i | −0.691017 | − | 1.19688i | ||||
\(698\) | 51.6087 | 1.95342 | ||||||||
\(699\) | −22.0240 | + | 6.44260i | −0.833024 | + | 0.243681i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6050 | −1.83579 | −0.917894 | − | 0.396826i | \(-0.870111\pi\) | ||||
−0.917894 | + | 0.396826i | \(0.870111\pi\) | |||||||
\(702\) | 6.10769 | + | 1.19643i | 0.230520 | + | 0.0451562i | ||||
\(703\) | 2.29661 | − | 3.97784i | 0.0866182 | − | 0.150027i | ||||
\(704\) | −2.97802 | −0.112238 | ||||||||
\(705\) | −28.9354 | − | 27.6459i | −1.08977 | − | 1.04121i | ||||
\(706\) | 18.1651 | − | 31.4629i | 0.683654 | − | 1.18412i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31.0634 | − | 29.6791i | −1.16743 | − | 1.11541i | ||||
\(709\) | −2.05408 | + | 3.55778i | −0.0771428 | + | 0.133615i | −0.902016 | − | 0.431702i | \(-0.857913\pi\) |
0.824873 | + | 0.565318i | \(0.191246\pi\) | |||||||
\(710\) | 38.0753 | − | 65.9483i | 1.42894 | − | 2.47500i | ||||
\(711\) | 20.6264 | − | 13.1968i | 0.773549 | − | 0.494918i | ||||
\(712\) | −37.4764 | − | 64.9110i | −1.40449 | − | 2.43264i | ||||
\(713\) | −16.3300 | − | 28.2844i | −0.611564 | − | 1.05926i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.361864 | + | 0.626767i | −0.0135330 | + | 0.0234398i | ||||
\(716\) | 37.0263 | 1.38374 | ||||||||
\(717\) | −24.2811 | − | 23.1990i | −0.906795 | − | 0.866383i | ||||
\(718\) | 17.7453 | 0.662249 | ||||||||
\(719\) | 24.1408 | + | 41.8131i | 0.900299 | + | 1.55936i | 0.827106 | + | 0.562047i | \(0.189986\pi\) |
0.0731939 | + | 0.997318i | \(0.476681\pi\) | |||||||
\(720\) | −40.0032 | + | 25.5941i | −1.49083 | + | 0.953837i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.5833 | + | 32.1872i | 0.691597 | + | 1.19788i | ||||
\(723\) | 2.07227 | − | 8.50440i | 0.0770686 | − | 0.316282i | ||||
\(724\) | −24.2187 | − | 41.9481i | −0.900082 | − | 1.55899i | ||||
\(725\) | −32.0495 | − | 55.5114i | −1.19029 | − | 2.06164i | ||||
\(726\) | 33.3861 | + | 31.8982i | 1.23907 | + | 1.18385i | ||||
\(727\) | −20.5151 | − | 35.5332i | −0.760863 | − | 1.31785i | −0.942406 | − | 0.334470i | \(-0.891443\pi\) |
0.181543 | − | 0.983383i | \(-0.441891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.67996 | − | 26.7480i | −0.136295 | − | 0.990668i | ||||
\(730\) | 8.88151 | + | 15.3832i | 0.328720 | + | 0.569359i | ||||
\(731\) | −11.3016 | −0.418006 | ||||||||
\(732\) | 13.3442 | − | 54.7631i | 0.493214 | − | 2.02410i | ||||
\(733\) | −30.5428 | −1.12812 | −0.564062 | − | 0.825733i | \(-0.690762\pi\) | ||||
−0.564062 | + | 0.825733i | \(0.690762\pi\) | |||||||
\(734\) | 13.5011 | − | 23.3845i | 0.498334 | − | 0.863139i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.25370 | − | 2.17147i | −0.0462118 | − | 0.0800413i | ||||
\(737\) | −0.731715 | − | 1.26737i | −0.0269531 | − | 0.0466841i | ||||
\(738\) | 2.52684 | + | 55.4071i | 0.0930143 | + | 2.03956i | ||||
\(739\) | −11.9100 | + | 20.6288i | −0.438117 | + | 0.758841i | −0.997544 | − | 0.0700384i | \(-0.977688\pi\) |
0.559427 | + | 0.828880i | \(0.311021\pi\) | |||||||
\(740\) | 17.2581 | − | 29.8918i | 0.634419 | − | 1.09885i | ||||
\(741\) | −0.393936 | + | 1.61668i | −0.0144716 | + | 0.0593901i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.26089 | + | 9.11213i | −0.193003 | + | 0.334292i | −0.946244 | − | 0.323453i | \(-0.895156\pi\) |
0.753241 | + | 0.657745i | \(0.228490\pi\) | |||||||
\(744\) | 59.0413 | − | 17.2711i | 2.16456 | − | 0.633191i | ||||
\(745\) | 35.4897 | 1.30024 | ||||||||
\(746\) | 0.668971 | − | 1.15869i | 0.0244928 | − | 0.0424227i | ||||
\(747\) | 1.66358 | + | 36.4781i | 0.0608673 | + | 1.33466i | ||||
\(748\) | 8.00079 | 0.292538 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 38.1160 | + | 36.4174i | 1.39180 | + | 1.32977i | ||||
\(751\) | −10.2704 | −0.374773 | −0.187386 | − | 0.982286i | \(-0.560002\pi\) | ||||
−0.187386 | + | 0.982286i | \(0.560002\pi\) | |||||||
\(752\) | 13.6665 | + | 23.6711i | 0.498367 | + | 0.863197i | ||||
\(753\) | 6.18882 | − | 25.3983i | 0.225533 | − | 0.925565i | ||||
\(754\) | 4.58005 | − | 7.93288i | 0.166796 | − | 0.288899i | ||||
\(755\) | 46.9507 | 1.70871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03930 | 0.292193 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(758\) | 27.9159 | − | 48.3518i | 1.01395 | − | 1.75622i | ||||
\(759\) | −0.774549 | + | 3.17868i | −0.0281144 | + | 0.115379i | ||||
\(760\) | −18.2434 | − | 31.5985i | −0.661757 | − | 1.14620i | ||||
\(761\) | −27.6604 | −1.00269 | −0.501345 | − | 0.865247i | \(-0.667161\pi\) | ||||
−0.501345 | + | 0.865247i | \(0.667161\pi\) | |||||||
\(762\) | 47.8961 | + | 45.7616i | 1.73509 | + | 1.65777i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 37.0554 | 1.34062 | ||||||||
\(765\) | −44.8879 | + | 28.7194i | −1.62293 | + | 1.03835i | ||||
\(766\) | −43.9371 | + | 76.1013i | −1.58751 | + | 2.74965i | ||||
\(767\) | −2.97841 | −0.107544 | ||||||||
\(768\) | −53.7962 | + | 15.7368i | −1.94120 | + | 0.567853i | ||||
\(769\) | −16.9613 | + | 29.3778i | −0.611640 | + | 1.05939i | 0.379324 | + | 0.925264i | \(0.376157\pi\) |
−0.990964 | + | 0.134128i | \(0.957177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16225 | − | 12.9776i | 0.113886 | − | 0.467376i | ||||
\(772\) | −34.3442 | + | 59.4858i | −1.23607 | + | 2.14094i | ||||
\(773\) | −14.2978 | + | 24.7645i | −0.514256 | + | 0.890717i | 0.485607 | + | 0.874177i | \(0.338599\pi\) |
−0.999863 | + | 0.0165403i | \(0.994735\pi\) | |||||||
\(774\) | 15.2542 | + | 7.90324i | 0.548300 | + | 0.284076i | ||||
\(775\) | −29.4493 | − | 51.0077i | −1.05785 | − | 1.83225i | ||||
\(776\) | 23.9753 | + | 41.5265i | 0.860664 | + | 1.49071i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47.5605 | + | 82.3772i | −1.70513 | + | 2.95337i | ||||
\(779\) | −14.8290 | −0.531303 | ||||||||
\(780\) | −2.96027 | + | 12.1487i | −0.105995 | + | 0.434992i | ||||
\(781\) | 3.43852 | 0.123040 | ||||||||
\(782\) | −27.7647 | − | 48.0899i | −0.992864 | − | 1.71969i | ||||
\(783\) | −38.9973 | − | 7.63912i | −1.39365 | − | 0.273000i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.3157 | + | 66.3647i | 1.36754 | + | 2.36866i | ||||
\(786\) | 26.2345 | + | 25.0654i | 0.935755 | + | 0.894052i | ||||
\(787\) | 23.0017 | + | 39.8402i | 0.819923 | + | 1.42015i | 0.905738 | + | 0.423838i | \(0.139317\pi\) |
−0.0858145 | + | 0.996311i | \(0.527349\pi\) | |||||||
\(788\) | 43.2111 | + | 74.8438i | 1.53933 | + | 2.66620i | ||||
\(789\) | −1.72716 | + | 7.08811i | −0.0614887 | + | 0.252344i | ||||
\(790\) | 36.7330 | + | 63.6235i | 1.30690 | + | 2.26362i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.47150 | − | 2.83480i | −0.194421 | − | 0.100730i | ||||
\(793\) | −1.95379 | − | 3.38406i | −0.0693810 | − | 0.120171i | ||||
\(794\) | −29.3977 | −1.04328 | ||||||||
\(795\) | −16.3485 | − | 15.6200i | −0.579823 | − | 0.553983i | ||||
\(796\) | 40.4367 | 1.43324 | ||||||||
\(797\) | −18.4558 | + | 31.9664i | −0.653739 | + | 1.13231i | 0.328469 | + | 0.944515i | \(0.393467\pi\) |
−0.982208 | + | 0.187795i | \(0.939866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3353 | + | 26.5615i | 0.542524 | + | 0.939679i | ||||
\(800\) | −2.26089 | − | 3.91598i | −0.0799346 | − | 0.138451i | ||||
\(801\) | 2.02688 | + | 44.4442i | 0.0716163 | + | 1.57036i | ||||
\(802\) | −39.8068 | + | 68.9474i | −1.40563 | + | 2.43462i | ||||
\(803\) | −0.401038 | + | 0.694619i | −0.0141523 | + | 0.0245126i | ||||
\(804\) | −18.2814 | − | 17.4666i | −0.644734 | − | 0.616001i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.20847 | − | 7.28928i | 0.148237 | − | 0.256754i | ||||
\(807\) | 25.9868 | + | 24.8286i | 0.914777 | + | 0.874010i | ||||
\(808\) | 44.0300 | 1.54897 | ||||||||
\(809\) | −23.8444 | + | 41.2996i | −0.838323 | + | 1.45202i | 0.0529735 | + | 0.998596i | \(0.483130\pi\) |
−0.891296 | + | 0.453422i | \(0.850203\pi\) | |||||||
\(810\) | 80.6701 | − | 7.37327i | 2.83446 | − | 0.259070i | ||||
\(811\) | 6.02728 | 0.211646 | 0.105823 | − | 0.994385i | \(-0.466252\pi\) | ||||
0.105823 | + | 0.994385i | \(0.466252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.3594 | − | 13.8539i | 1.66097 | − | 0.485877i | ||||
\(814\) | 2.32743 | 0.0815764 | ||||||||
\(815\) | −20.4162 | − | 35.3619i | −0.715148 | − | 1.23867i | ||||
\(816\) | 34.9322 | − | 10.2186i | 1.22287 | − | 0.357722i | ||||
\(817\) | −2.29661 | + | 3.97784i | −0.0803481 | + | 0.139167i | ||||
\(818\) | 46.6881 | 1.63241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.434 | −3.89143 | ||||||||
\(821\) | 19.6321 | − | 34.0038i | 0.685165 | − | 1.18674i | −0.288220 | − | 0.957564i | \(-0.593064\pi\) |
0.973385 | − | 0.229176i | \(-0.0736031\pi\) | |||||||
\(822\) | −1.16242 | − | 1.11062i | −0.0405442 | − | 0.0387373i | ||||
\(823\) | −11.3815 | − | 19.7134i | −0.396735 | − | 0.687165i | 0.596586 | − | 0.802549i | \(-0.296523\pi\) |
−0.993321 | + | 0.115384i | \(0.963190\pi\) | |||||||
\(824\) | 40.5697 | 1.41331 | ||||||||
\(825\) | −1.39681 | + | 5.73237i | −0.0486306 | + | 0.199575i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9286 | −1.00595 | −0.502973 | − | 0.864302i | \(-0.667760\pi\) | ||||
−0.502973 | + | 0.864302i | \(0.667760\pi\) | |||||||
\(828\) | 2.57520 | + | 56.4674i | 0.0894943 | + | 1.96238i | ||||
\(829\) | 16.9883 | − | 29.4247i | 0.590029 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342172\pi\) | |||||||
\(830\) | −109.557 | −3.80276 | ||||||||
\(831\) | −7.03741 | + | 28.8809i | −0.244125 | + | 1.00187i | ||||
\(832\) | −1.78348 | + | 3.08908i | −0.0618312 | + | 0.107095i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −77.7213 | + | 22.7355i | −2.69127 | + | 0.787267i | ||||
\(835\) | 6.32889 | − | 10.9620i | 0.219020 | − | 0.379354i | ||||
\(836\) | 1.62584 | − | 2.81604i | 0.0562310 | − | 0.0973949i | ||||
\(837\) | −35.8334 | − | 7.01935i | −1.23858 | − | 0.242624i | ||||
\(838\) | 21.2716 | + | 36.8435i | 0.734816 | + | 1.27274i | ||||
\(839\) | −19.0206 | − | 32.9446i | −0.656663 | − | 1.13737i | −0.981474 | − | 0.191595i | \(-0.938634\pi\) |
0.324811 | − | 0.945779i | \(-0.394699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7434 | + | 25.5363i | −0.508392 | + | 0.880561i | ||||
\(842\) | 45.7673 | 1.57725 | ||||||||
\(843\) | 15.6976 | − | 4.59195i | 0.540652 | − | 0.158155i | ||||
\(844\) | 19.8319 | 0.682642 | ||||||||
\(845\) | −23.3441 | − | 40.4331i | −0.803060 | − | 1.39094i | ||||
\(846\) | −2.12405 | − | 46.5749i | −0.0730264 | − | 1.60128i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.72159 | + | 13.3742i | 0.265161 | + | 0.459272i | ||||
\(849\) | −28.0418 | + | 8.20297i | −0.962393 | + | 0.281525i | ||||
\(850\) | −50.0704 | − | 86.7245i | −1.71740 | − | 2.97463i | ||||
\(851\) | −5.40856 | − | 9.36790i | −0.185403 | − | 0.321127i | ||||
\(852\) | 57.0191 | − | 16.6796i | 1.95344 | − | 0.571433i | ||||
\(853\) | −4.90746 | − | 8.49996i | −0.168028 | − | 0.291033i | 0.769698 | − | 0.638408i | \(-0.220407\pi\) |
−0.937726 | + | 0.347374i | \(0.887073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.986679 | + | 21.6353i | 0.0337437 | + | 0.739912i | ||||
\(856\) | −32.4523 | − | 56.2091i | −1.10920 | − | 1.92119i | ||||
\(857\) | 26.7360 | 0.913285 | 0.456642 | − | 0.889650i | \(-0.349052\pi\) | ||||
0.456642 | + | 0.889650i | \(0.349052\pi\) | |||||||
\(858\) | −0.809243 | + | 0.236725i | −0.0276271 | + | 0.00808165i | ||||
\(859\) | −18.4882 | −0.630810 | −0.315405 | − | 0.948957i | \(-0.602140\pi\) | ||||
−0.315405 | + | 0.948957i | \(0.602140\pi\) | |||||||
\(860\) | −17.2581 | + | 29.8918i | −0.588495 | + | 1.01930i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5344 | + | 33.8346i | 0.665345 | + | 1.15241i | ||||
\(863\) | 4.57393 | + | 7.92228i | 0.155698 | + | 0.269677i | 0.933313 | − | 0.359064i | \(-0.116904\pi\) |
−0.777615 | + | 0.628741i | \(0.783571\pi\) | |||||||
\(864\) | −2.75101 | − | 0.538892i | −0.0935914 | − | 0.0183335i | ||||
\(865\) | −11.0723 | + | 19.1777i | −0.376469 | + | 0.652063i | ||||
\(866\) | −49.7473 | + | 86.1649i | −1.69048 | + | 2.92800i | ||||
\(867\) | 10.9371 | − | 3.19940i | 0.371444 | − | 0.108657i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.65865 | + | 2.87287i | −0.0562660 | + | 0.0974555i | ||||
\(870\) | 28.2257 | − | 115.835i | 0.956940 | − | 3.92719i | ||||
\(871\) | −1.75285 | −0.0593929 | ||||||||
\(872\) | −6.57227 | + | 11.3835i | −0.222565 | + | 0.385494i | ||||
\(873\) | −1.29669 | − | 28.4330i | −0.0438862 | − | 0.962310i | ||||
\(874\) | −22.5683 | −0.763385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.28074 | + | 13.4638i | −0.110846 | + | 0.454901i | ||||
\(877\) | 22.6883 | 0.766130 | 0.383065 | − | 0.923721i | \(-0.374869\pi\) | ||||
0.383065 | + | 0.923721i | \(0.374869\pi\) | |||||||
\(878\) | −15.3301 | − | 26.5525i | −0.517366 | − | 0.896104i | ||||
\(879\) | −4.66225 | − | 4.45448i | −0.157254 | − | 0.150246i | ||||
\(880\) | 3.21683 | − | 5.57172i | 0.108439 | − | 0.187823i | ||||
\(881\) | 15.3696 | 0.517815 | 0.258907 | − | 0.965902i | \(-0.416638\pi\) | ||||
0.258907 | + | 0.965902i | \(0.416638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6372 | 0.997370 | 0.498685 | − | 0.866783i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333817\pi\) | |||||||
\(884\) | 4.79153 | − | 8.29918i | 0.161157 | − | 0.279132i | ||||
\(885\) | −37.2067 | + | 10.8839i | −1.25069 | + | 0.365859i | ||||
\(886\) | 10.1259 | + | 17.5385i | 0.340185 | + | 0.589219i | ||||
\(887\) | −18.7650 | −0.630069 | −0.315034 | − | 0.949080i | \(-0.602016\pi\) | ||||
−0.315034 | + | 0.949080i | \(0.602016\pi\) | |||||||
\(888\) | 19.5547 | − | 5.72026i | 0.656212 | − | 0.191959i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −133.482 | −4.47432 | ||||||||
\(891\) | 2.10963 | + | 2.98812i | 0.0706753 | + | 0.100106i | ||||
\(892\) | 47.4507 | − | 82.1870i | 1.58877 | − | 2.75183i | ||||
\(893\) | 12.4652 | 0.417131 | ||||||||
\(894\) | 29.8947 | + | 28.5624i | 0.999828 | + | 0.955270i | ||||
\(895\) | 16.7047 | − | 28.9335i | 0.558378 | − | 0.967139i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.83336 | + | 2.70709i | 0.0946031 | + | 0.0903871i | ||||
\(898\) | −6.94445 | + | 12.0281i | −0.231739 | + | 0.401384i | ||||
\(899\) | −26.8708 | + | 46.5416i | −0.896192 | + | 1.55225i | ||||
\(900\) | 4.64406 | + | 101.832i | 0.154802 | + | 3.39441i | ||||
\(901\) | 8.66445 | + | 15.0073i | 0.288655 | + | 0.499965i | ||||
\(902\) | −3.75700 | − | 6.50731i | −0.125094 | − | 0.216670i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.2527 | − | 61.0595i | 1.17249 | − | 2.03081i | ||||
\(905\) | −43.7060 | −1.45284 | ||||||||
\(906\) | 39.5488 | + | 37.7863i | 1.31392 | + | 1.25537i | ||||
\(907\) | −31.1082 | −1.03293 | −0.516465 | − | 0.856308i | \(-0.672752\pi\) | ||||
−0.516465 | + | 0.856308i | \(0.672752\pi\) | |||||||
\(908\) | 12.4022 | + | 21.4813i | 0.411582 | + | 0.712881i | ||||
\(909\) | −23.2056 | − | 12.0229i | −0.769683 | − | 0.398775i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.73764 | − | 15.1340i | −0.289491 | − | 0.501413i | 0.684197 | − | 0.729297i | \(-0.260153\pi\) |
−0.973688 | + | 0.227884i | \(0.926819\pi\) | |||||||
\(912\) | 3.50194 | − | 14.3716i | 0.115961 | − | 0.475892i | ||||
\(913\) | −2.47347 | − | 4.28418i | −0.0818600 | − | 0.141786i | ||||
\(914\) | −6.23599 | − | 10.8010i | −0.206268 | − | 0.357267i | ||||
\(915\) | −36.7732 | − | 35.1344i | −1.21569 | − | 1.16151i | ||||
\(916\) | −2.96027 | − | 5.12734i | −0.0978101 | − | 0.169412i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −60.9248 | − | 11.9345i | −2.01082 | − | 0.393896i | ||||
\(919\) | −21.0993 | − | 36.5451i | −0.696002 | − | 1.20551i | −0.969842 | − | 0.243736i | \(-0.921627\pi\) |
0.273840 | − | 0.961775i | \(-0.411706\pi\) | |||||||
\(920\) | −85.9270 | −2.83293 | ||||||||
\(921\) | 12.5349 | − | 51.4421i | 0.413039 | − | 1.69507i | ||||
\(922\) | −19.1344 | −0.630158 | ||||||||
\(923\) | 2.05927 | − | 3.56676i | 0.0677818 | − | 0.117401i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.75370 | − | 16.8939i | −0.320700 | − | 0.555468i | ||||
\(926\) | 11.2937 | + | 19.5612i | 0.371133 | + | 0.642821i | ||||
\(927\) | −21.3820 | − | 11.0781i | −0.702276 | − | 0.363851i | ||||
\(928\) | −2.06294 | + | 3.57311i | −0.0677193 | + | 0.117293i | ||||
\(929\) | −24.2056 | + | 41.9253i | −0.794159 | + | 1.37552i | 0.129213 | + | 0.991617i | \(0.458755\pi\) |
−0.923372 | + | 0.383907i | \(0.874578\pi\) | |||||||
\(930\) | 25.9357 | − | 106.438i | 0.850465 | − | 3.49022i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.8551 | − | 46.5145i | 0.879670 | − | 1.52363i | ||||
\(933\) | 17.3466 | − | 5.07434i | 0.567902 | − | 0.166126i | ||||
\(934\) | −33.8699 | −1.10826 | ||||||||
\(935\) | 3.60963 | − | 6.25206i | 0.118048 | − | 0.204464i | ||||
\(936\) | −6.21731 | + | 3.97784i | −0.203219 | + | 0.130020i | ||||
\(937\) | −22.6750 | −0.740762 | −0.370381 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370381 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.776271 | − | 0.741676i | −0.0253327 | − | 0.0242037i | ||||
\(940\) | 93.6706 | 3.05520 | ||||||||
\(941\) | 24.9753 | + | 43.2584i | 0.814170 | + | 1.41018i | 0.909922 | + | 0.414779i | \(0.136141\pi\) |
−0.0957523 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(942\) | −21.1357 | + | 86.7388i | −0.688638 | + | 2.82610i | ||||
\(943\) | −17.4613 | + | 30.2438i | −0.568617 | + | 0.984873i | ||||
\(944\) | 26.4769 | 0.861749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.32743 | −0.0756713 | ||||||||
\(947\) | −8.85613 | + | 15.3393i | −0.287786 | + | 0.498459i | −0.973281 | − | 0.229618i | \(-0.926252\pi\) |
0.685495 | + | 0.728077i | \(0.259586\pi\) | |||||||
\(948\) | −13.5688 | + | 55.6850i | −0.440694 | + | 1.80857i | ||||
\(949\) | 0.480350 | + | 0.831990i | 0.0155928 | + | 0.0270075i | ||||
\(950\) | −40.6993 | −1.32046 | ||||||||
\(951\) | −12.8345 | − | 12.2625i | −0.416186 | − | 0.397638i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0229 | 1.23168 | 0.615842 | − | 0.787870i | \(-0.288816\pi\) | ||||
0.615842 | + | 0.787870i | \(0.288816\pi\) | |||||||
\(954\) | −1.20009 | − | 26.3149i | −0.0388544 | − | 0.851975i | ||||
\(955\) | 16.7179 | − | 28.9563i | 0.540979 | − | 0.937002i | ||||
\(956\) | 78.6035 | 2.54222 | ||||||||
\(957\) | 5.16697 | − | 1.51147i | 0.167024 | − | 0.0488590i | ||||
\(958\) | −10.7177 | + | 18.5635i | −0.346272 | + | 0.599761i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.9911 | + | 45.1066i | −0.354738 | + | 1.45581i | ||||
\(961\) | −9.19076 | + | 15.9189i | −0.296476 | + | 0.513512i | ||||
\(962\) | 1.39386 | − | 2.41423i | 0.0449398 | − | 0.0778380i | ||||
\(963\) | 1.75516 | + | 38.4861i | 0.0565592 | + | 1.24020i | ||||
\(964\) | 10.2440 | + | 17.7432i | 0.329938 | + | 0.571469i | ||||
\(965\) | 30.9894 | + | 53.6752i | 0.997583 | + | 1.72786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5064 | − | 26.8579i | 0.498652 | − | 0.863691i | −0.501346 | − | 0.865247i | \(-0.667162\pi\) |
0.999999 | + | 0.00155529i | \(0.000495066\pi\) | |||||||
\(968\) | −54.7601 | −1.76006 | ||||||||
\(969\) | 3.92955 | − | 16.1265i | 0.126235 | − | 0.518058i | ||||
\(970\) | 85.3943 | 2.74185 | ||||||||
\(971\) | 7.28376 | + | 12.6158i | 0.233747 | + | 0.404862i | 0.958908 | − | 0.283718i | \(-0.0915679\pi\) |
−0.725161 | + | 0.688580i | \(0.758235\pi\) | |||||||
\(972\) | 49.4776 | + | 39.3169i | 1.58699 | + | 1.26109i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.1893 | + | 38.4330i | 0.710991 | + | 1.23147i | ||||
\(975\) | 5.10963 | + | 4.88192i | 0.163639 | + | 0.156346i | ||||
\(976\) | 17.3684 | + | 30.0830i | 0.555949 | + | 0.962932i | ||||
\(977\) | 23.9399 | + | 41.4651i | 0.765904 | + | 1.32659i | 0.939767 | + | 0.341815i | \(0.111042\pi\) |
−0.173863 | + | 0.984770i | \(0.555625\pi\) | |||||||
\(978\) | 11.2620 | − | 46.2181i | 0.360118 | − | 1.47789i | ||||
\(979\) | −3.01364 | − | 5.21978i | −0.0963163 | − | 0.166825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.57227 | − | 4.20495i | 0.209836 | − | 0.134254i | ||||
\(982\) | −2.51819 | − | 4.36163i | −0.0803586 | − | 0.139185i | ||||
\(983\) | −44.4257 | −1.41696 | −0.708479 | − | 0.705732i | \(-0.750618\pi\) | ||||
−0.708479 | + | 0.705732i | \(0.750618\pi\) | |||||||
\(984\) | −47.5590 | − | 45.4395i | −1.51613 | − | 1.44856i | ||||
\(985\) | 77.9803 | 2.48466 | ||||||||
\(986\) | −45.6864 | + | 79.1313i | −1.45495 | + | 2.52005i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.94738 | − | 3.37296i | −0.0619544 | − | 0.107308i | ||||
\(989\) | 5.40856 | + | 9.36790i | 0.171982 | + | 0.297882i | ||||
\(990\) | −9.24411 | + | 5.91439i | −0.293797 | + | 0.187972i | ||||
\(991\) | 20.8078 | − | 36.0401i | 0.660981 | − | 1.14485i | −0.319377 | − | 0.947628i | \(-0.603474\pi\) |
0.980358 | − | 0.197225i | \(-0.0631929\pi\) | |||||||
\(992\) | −1.89557 | + | 3.28322i | −0.0601844 | + | 0.104242i | ||||
\(993\) | 25.5023 | + | 24.3657i | 0.809290 | + | 0.773223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.2434 | − | 31.5985i | 0.578354 | − | 1.00174i | ||||
\(996\) | −61.7979 | − | 59.0439i | −1.95814 | − | 1.87088i | ||||
\(997\) | 13.0281 | 0.412606 | 0.206303 | − | 0.978488i | \(-0.433857\pi\) | ||||
0.206303 | + | 0.978488i | \(0.433857\pi\) | |||||||
\(998\) | 48.0875 | − | 83.2901i | 1.52218 | − | 2.63650i | ||||
\(999\) | −11.8681 | − | 2.32483i | −0.375491 | − | 0.0735544i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.g.g.67.1 | 12 | ||
3.2 | odd | 2 | 1323.2.g.g.361.6 | 12 | |||
7.2 | even | 3 | 441.2.h.g.373.5 | 12 | |||
7.3 | odd | 6 | 441.2.f.g.148.1 | ✓ | 12 | ||
7.4 | even | 3 | 441.2.f.g.148.2 | yes | 12 | ||
7.5 | odd | 6 | 441.2.h.g.373.6 | 12 | |||
7.6 | odd | 2 | inner | 441.2.g.g.67.2 | 12 | ||
9.2 | odd | 6 | 1323.2.h.g.802.1 | 12 | |||
9.7 | even | 3 | 441.2.h.g.214.5 | 12 | |||
21.2 | odd | 6 | 1323.2.h.g.226.1 | 12 | |||
21.5 | even | 6 | 1323.2.h.g.226.2 | 12 | |||
21.11 | odd | 6 | 1323.2.f.g.442.5 | 12 | |||
21.17 | even | 6 | 1323.2.f.g.442.6 | 12 | |||
21.20 | even | 2 | 1323.2.g.g.361.5 | 12 | |||
63.2 | odd | 6 | 1323.2.g.g.667.6 | 12 | |||
63.4 | even | 3 | 3969.2.a.be.1.5 | 6 | |||
63.11 | odd | 6 | 1323.2.f.g.883.5 | 12 | |||
63.16 | even | 3 | inner | 441.2.g.g.79.1 | 12 | ||
63.20 | even | 6 | 1323.2.h.g.802.2 | 12 | |||
63.25 | even | 3 | 441.2.f.g.295.2 | yes | 12 | ||
63.31 | odd | 6 | 3969.2.a.be.1.6 | 6 | |||
63.32 | odd | 6 | 3969.2.a.bd.1.2 | 6 | |||
63.34 | odd | 6 | 441.2.h.g.214.6 | 12 | |||
63.38 | even | 6 | 1323.2.f.g.883.6 | 12 | |||
63.47 | even | 6 | 1323.2.g.g.667.5 | 12 | |||
63.52 | odd | 6 | 441.2.f.g.295.1 | yes | 12 | ||
63.59 | even | 6 | 3969.2.a.bd.1.1 | 6 | |||
63.61 | odd | 6 | inner | 441.2.g.g.79.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.1 | ✓ | 12 | 7.3 | odd | 6 | ||
441.2.f.g.148.2 | yes | 12 | 7.4 | even | 3 | ||
441.2.f.g.295.1 | yes | 12 | 63.52 | odd | 6 | ||
441.2.f.g.295.2 | yes | 12 | 63.25 | even | 3 | ||
441.2.g.g.67.1 | 12 | 1.1 | even | 1 | trivial | ||
441.2.g.g.67.2 | 12 | 7.6 | odd | 2 | inner | ||
441.2.g.g.79.1 | 12 | 63.16 | even | 3 | inner | ||
441.2.g.g.79.2 | 12 | 63.61 | odd | 6 | inner | ||
441.2.h.g.214.5 | 12 | 9.7 | even | 3 | |||
441.2.h.g.214.6 | 12 | 63.34 | odd | 6 | |||
441.2.h.g.373.5 | 12 | 7.2 | even | 3 | |||
441.2.h.g.373.6 | 12 | 7.5 | odd | 6 | |||
1323.2.f.g.442.5 | 12 | 21.11 | odd | 6 | |||
1323.2.f.g.442.6 | 12 | 21.17 | even | 6 | |||
1323.2.f.g.883.5 | 12 | 63.11 | odd | 6 | |||
1323.2.f.g.883.6 | 12 | 63.38 | even | 6 | |||
1323.2.g.g.361.5 | 12 | 21.20 | even | 2 | |||
1323.2.g.g.361.6 | 12 | 3.2 | odd | 2 | |||
1323.2.g.g.667.5 | 12 | 63.47 | even | 6 | |||
1323.2.g.g.667.6 | 12 | 63.2 | odd | 6 | |||
1323.2.h.g.226.1 | 12 | 21.2 | odd | 6 | |||
1323.2.h.g.226.2 | 12 | 21.5 | even | 6 | |||
1323.2.h.g.802.1 | 12 | 9.2 | odd | 6 | |||
1323.2.h.g.802.2 | 12 | 63.20 | even | 6 | |||
3969.2.a.bd.1.1 | 6 | 63.59 | even | 6 | |||
3969.2.a.bd.1.2 | 6 | 63.32 | odd | 6 | |||
3969.2.a.be.1.5 | 6 | 63.4 | even | 3 | |||
3969.2.a.be.1.6 | 6 | 63.31 | odd | 6 |