Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(307,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.y (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{8} + 295x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Root | \(-1.52891 - 1.52891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.307 |
Dual form | 819.2.y.h.811.3 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.403032 | + | 0.403032i | 0.284986 | + | 0.284986i | 0.835094 | − | 0.550107i | \(-0.185413\pi\) |
−0.550107 | + | 0.835094i | \(0.685413\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.67513i | − | 0.837565i | ||||||
\(5\) | −1.03221 | + | 1.03221i | −0.461620 | + | 0.461620i | −0.899186 | − | 0.437566i | \(-0.855841\pi\) |
0.437566 | + | 0.899186i | \(0.355841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60707 | + | 0.450747i | 0.985381 | + | 0.170366i | ||||
\(8\) | 1.48119 | − | 1.48119i | 0.523681 | − | 0.523681i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.832030 | −0.263111 | ||||||||
\(11\) | 0.596968 | − | 0.596968i | 0.179993 | − | 0.179993i | −0.611360 | − | 0.791353i | \(-0.709377\pi\) |
0.791353 | + | 0.611360i | \(0.209377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.59334 | + | 0.296512i | −0.996613 | + | 0.0822375i | ||||
\(14\) | 0.869067 | + | 1.23240i | 0.232268 | + | 0.329372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.15633 | −0.539081 | ||||||||
\(17\) | 7.34804 | 1.78216 | 0.891080 | − | 0.453845i | \(-0.149948\pi\) | ||||
0.891080 | + | 0.453845i | \(0.149948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.59334 | − | 3.59334i | 0.824368 | − | 0.824368i | −0.162363 | − | 0.986731i | \(-0.551911\pi\) |
0.986731 | + | 0.162363i | \(0.0519115\pi\) | |||||||
\(20\) | 1.72909 | + | 1.72909i | 0.386637 | + | 0.386637i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.481194 | 0.102591 | ||||||||
\(23\) | − | 4.44358i | − | 0.926551i | −0.886214 | − | 0.463276i | \(-0.846674\pi\) | ||
0.886214 | − | 0.463276i | \(-0.153326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.86907i | 0.573813i | ||||||||
\(26\) | −1.56773 | − | 1.32873i | −0.307458 | − | 0.260585i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.755061 | − | 4.36719i | 0.142693 | − | 0.825321i | ||||
\(29\) | 3.54420 | 0.658141 | 0.329071 | − | 0.944305i | \(-0.393265\pi\) | ||||
0.329071 | + | 0.944305i | \(0.393265\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27122 | + | 1.27122i | −0.228318 | + | 0.228318i | −0.811990 | − | 0.583672i | \(-0.801616\pi\) |
0.583672 | + | 0.811990i | \(0.301616\pi\) | |||||||
\(32\) | −3.83146 | − | 3.83146i | −0.677312 | − | 0.677312i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.96149 | + | 2.96149i | 0.507892 | + | 0.507892i | ||||
\(35\) | −3.15633 | + | 2.22579i | −0.533516 | + | 0.376227i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.88423 | − | 2.88423i | 0.474164 | − | 0.474164i | −0.429095 | − | 0.903259i | \(-0.641168\pi\) |
0.903259 | + | 0.429095i | \(0.141168\pi\) | |||||||
\(38\) | 2.89646 | 0.469868 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.05782i | 0.483484i | ||||||||
\(41\) | −1.23240 | + | 1.23240i | −0.192468 | + | 0.192468i | −0.796762 | − | 0.604294i | \(-0.793455\pi\) |
0.604294 | + | 0.796762i | \(0.293455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.66291i | − | 1.32108i | −0.750790 | − | 0.660541i | \(-0.770327\pi\) | ||
0.750790 | − | 0.660541i | \(-0.229673\pi\) | |||||||
\(44\) | −1.00000 | − | 1.00000i | −0.150756 | − | 0.150756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79090 | − | 1.79090i | 0.264055 | − | 0.264055i | ||||
\(47\) | −2.52230 | − | 2.52230i | −0.367915 | − | 0.367915i | 0.498801 | − | 0.866717i | \(-0.333774\pi\) |
−0.866717 | + | 0.498801i | \(0.833774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59365 | + | 2.35026i | 0.941951 | + | 0.335752i | ||||
\(50\) | −1.15633 | + | 1.15633i | −0.163529 | + | 0.163529i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.496696 | + | 6.01931i | 0.0688793 | + | 0.834728i | ||||
\(53\) | 9.79384 | 1.34529 | 0.672644 | − | 0.739966i | \(-0.265159\pi\) | ||||
0.672644 | + | 0.739966i | \(0.265159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23240i | 0.166177i | ||||||||
\(56\) | 4.52923 | − | 3.19394i | 0.605243 | − | 0.426808i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.42842 | + | 1.42842i | 0.187561 | + | 0.187561i | ||||
\(59\) | 1.08972 | + | 1.08972i | 0.141869 | + | 0.141869i | 0.774474 | − | 0.632605i | \(-0.218014\pi\) |
−0.632605 | + | 0.774474i | \(0.718014\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.10903i | − | 0.910218i | −0.890436 | − | 0.455109i | \(-0.849600\pi\) | ||
0.890436 | − | 0.455109i | \(-0.150400\pi\) | |||||||
\(62\) | −1.02469 | −0.130135 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.22425i | 0.153032i | ||||||||
\(65\) | 3.40303 | − | 4.01516i | 0.422094 | − | 0.498019i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76845 | + | 8.76845i | 1.07124 | + | 1.07124i | 0.997260 | + | 0.0739770i | \(0.0235691\pi\) |
0.0739770 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(68\) | − | 12.3089i | − | 1.49268i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.16916 | − | 0.375035i | −0.259265 | − | 0.0448253i | ||||
\(71\) | 1.46604 | + | 1.46604i | 0.173986 | + | 0.173986i | 0.788728 | − | 0.614742i | \(-0.210740\pi\) |
−0.614742 | + | 0.788728i | \(0.710740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.103857 | − | 0.103857i | −0.0121555 | − | 0.0121555i | 0.701003 | − | 0.713158i | \(-0.252736\pi\) |
−0.713158 | + | 0.701003i | \(0.752736\pi\) | |||||||
\(74\) | 2.32487 | 0.270261 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.01931 | − | 6.01931i | −0.690462 | − | 0.690462i | ||||
\(77\) | 1.82542 | − | 1.28726i | 0.208026 | − | 0.146697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.79877 | −0.539904 | −0.269952 | − | 0.962874i | \(-0.587008\pi\) | ||||
−0.269952 | + | 0.962874i | \(0.587008\pi\) | |||||||
\(80\) | 2.22579 | − | 2.22579i | 0.248851 | − | 0.248851i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.993391 | −0.109702 | ||||||||
\(83\) | −12.3165 | + | 12.3165i | −1.35191 | + | 1.35191i | −0.468379 | + | 0.883528i | \(0.655162\pi\) |
−0.883528 | + | 0.468379i | \(0.844838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.58475 | + | 7.58475i | −0.822682 | + | 0.822682i | ||||
\(86\) | 3.49143 | − | 3.49143i | 0.376490 | − | 0.376490i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.76845i | − | 0.188518i | ||||||
\(89\) | 6.89017 | + | 6.89017i | 0.730356 | + | 0.730356i | 0.970690 | − | 0.240334i | \(-0.0772570\pi\) |
−0.240334 | + | 0.970690i | \(0.577257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.50175 | − | 0.846661i | −0.996054 | − | 0.0887541i | ||||
\(92\) | −7.44358 | −0.776047 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.03313i | − | 0.209702i | ||||||
\(95\) | 7.41819i | 0.761090i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.05814 | + | 6.05814i | −0.615110 | + | 0.615110i | −0.944273 | − | 0.329163i | \(-0.893234\pi\) |
0.329163 | + | 0.944273i | \(0.393234\pi\) | |||||||
\(98\) | 1.71022 | + | 3.60468i | 0.172758 | + | 0.364128i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.80606 | 0.480606 | ||||||||
\(101\) | −12.8707 | −1.28068 | −0.640339 | − | 0.768092i | \(-0.721206\pi\) | ||||
−0.640339 | + | 0.768092i | \(0.721206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.11564 | −0.602592 | −0.301296 | − | 0.953531i | \(-0.597419\pi\) | ||||
−0.301296 | + | 0.953531i | \(0.597419\pi\) | |||||||
\(104\) | −4.88324 | + | 5.76162i | −0.478841 | + | 0.564974i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.94723 | + | 3.94723i | 0.383389 | + | 0.383389i | ||||
\(107\) | −8.86907 | −0.857405 | −0.428703 | − | 0.903446i | \(-0.641029\pi\) | ||||
−0.428703 | + | 0.903446i | \(0.641029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.59697 | − | 4.59697i | −0.440310 | − | 0.440310i | 0.451806 | − | 0.892116i | \(-0.350780\pi\) |
−0.892116 | + | 0.451806i | \(0.850780\pi\) | |||||||
\(110\) | −0.496696 | + | 0.496696i | −0.0473581 | + | 0.0473581i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.62170 | − | 0.971958i | −0.531200 | − | 0.0918414i | ||||
\(113\) | −1.60720 | −0.151193 | −0.0755964 | − | 0.997138i | \(-0.524086\pi\) | ||||
−0.0755964 | + | 0.997138i | \(0.524086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.58673 | + | 4.58673i | 0.427715 | + | 0.427715i | ||||
\(116\) | − | 5.93700i | − | 0.551236i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.878382i | 0.0808617i | ||||||||
\(119\) | 19.1569 | + | 3.31211i | 1.75611 | + | 0.303620i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2873i | 0.935205i | ||||||||
\(122\) | 2.86516 | − | 2.86516i | 0.259400 | − | 0.259400i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.12946 | + | 2.12946i | 0.191231 | + | 0.191231i | ||||
\(125\) | −8.12256 | − | 8.12256i | −0.726504 | − | 0.726504i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.54912i | − | 0.137462i | −0.997635 | − | 0.0687312i | \(-0.978105\pi\) | ||
0.997635 | − | 0.0687312i | \(-0.0218951\pi\) | |||||||
\(128\) | −8.15633 | + | 8.15633i | −0.720924 | + | 0.720924i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.98977 | − | 0.246707i | 0.262220 | − | 0.0216376i | ||||
\(131\) | 5.31490i | 0.464365i | 0.972672 | + | 0.232183i | \(0.0745867\pi\) | ||||
−0.972672 | + | 0.232183i | \(0.925413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9878 | − | 7.74841i | 0.952761 | − | 0.671872i | ||||
\(134\) | 7.06793i | 0.610576i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.8839 | − | 10.8839i | 0.933284 | − | 0.933284i | ||||
\(137\) | −12.7157 | + | 12.7157i | −1.08637 | + | 1.08637i | −0.0904753 | + | 0.995899i | \(0.528839\pi\) |
−0.995899 | + | 0.0904753i | \(0.971161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.94767i | 0.589294i | 0.955606 | + | 0.294647i | \(0.0952020\pi\) | ||||
−0.955606 | + | 0.294647i | \(0.904798\pi\) | |||||||
\(140\) | 3.72849 | + | 5.28726i | 0.315115 | + | 0.446855i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.18172i | 0.0991676i | ||||||||
\(143\) | −1.96810 | + | 2.32212i | −0.164581 | + | 0.194185i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.65837 | + | 3.65837i | −0.303811 | + | 0.303811i | ||||
\(146\) | − | 0.0837150i | − | 0.00692831i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.83146 | − | 4.83146i | −0.397143 | − | 0.397143i | ||||
\(149\) | 10.9653 | + | 10.9653i | 0.898315 | + | 0.898315i | 0.995287 | − | 0.0969724i | \(-0.0309158\pi\) |
−0.0969724 | + | 0.995287i | \(0.530916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.14117 | − | 6.14117i | 0.499761 | − | 0.499761i | −0.411602 | − | 0.911363i | \(-0.635031\pi\) |
0.911363 | + | 0.411602i | \(0.135031\pi\) | |||||||
\(152\) | − | 10.6449i | − | 0.863413i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.25451 | + | 0.216897i | 0.101091 | + | 0.0174781i | ||||
\(155\) | − | 2.62435i | − | 0.210793i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.69783i | − | 0.773971i | −0.922086 | − | 0.386985i | \(-0.873516\pi\) | ||
0.922086 | − | 0.386985i | \(-0.126484\pi\) | |||||||
\(158\) | −1.93406 | − | 1.93406i | −0.153865 | − | 0.153865i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.90977 | 0.625322 | ||||||||
\(161\) | 2.00293 | − | 11.5847i | 0.157853 | − | 0.913006i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.41327 | + | 5.41327i | −0.424000 | + | 0.424000i | −0.886578 | − | 0.462579i | \(-0.846924\pi\) |
0.462579 | + | 0.886578i | \(0.346924\pi\) | |||||||
\(164\) | 2.06443 | + | 2.06443i | 0.161205 | + | 0.161205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.92784 | −0.770550 | ||||||||
\(167\) | −8.90824 | − | 8.90824i | −0.689340 | − | 0.689340i | 0.272746 | − | 0.962086i | \(-0.412068\pi\) |
−0.962086 | + | 0.272746i | \(0.912068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8242 | − | 2.13093i | 0.986474 | − | 0.163918i | ||||
\(170\) | −6.11379 | −0.468906 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.5115 | −1.10649 | ||||||||
\(173\) | −7.15538 | −0.544014 | −0.272007 | − | 0.962295i | \(-0.587687\pi\) | ||||
−0.272007 | + | 0.962295i | \(0.587687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.29322 | + | 7.47987i | −0.0977586 | + | 0.565425i | ||||
\(176\) | −1.28726 | + | 1.28726i | −0.0970307 | + | 0.0970307i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.55391i | 0.416283i | ||||||||
\(179\) | − | 13.8119i | − | 1.03235i | −0.856482 | − | 0.516177i | \(-0.827355\pi\) | ||
0.856482 | − | 0.516177i | \(-0.172645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.56052 | −0.338981 | −0.169490 | − | 0.985532i | \(-0.554212\pi\) | ||||
−0.169490 | + | 0.985532i | \(0.554212\pi\) | |||||||
\(182\) | −3.48827 | − | 4.17074i | −0.258568 | − | 0.309156i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.58181 | − | 6.58181i | −0.485217 | − | 0.485217i | ||||
\(185\) | 5.95428i | 0.437767i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.38655 | − | 4.38655i | 0.320776 | − | 0.320776i | ||||
\(188\) | −4.22518 | + | 4.22518i | −0.308153 | + | 0.308153i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.98977 | + | 2.98977i | −0.216900 | + | 0.216900i | ||||
\(191\) | −3.70545 | −0.268117 | −0.134058 | − | 0.990973i | \(-0.542801\pi\) | ||||
−0.134058 | + | 0.990973i | \(0.542801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0508 | + | 17.0508i | −1.22734 | + | 1.22734i | −0.262377 | + | 0.964965i | \(0.584506\pi\) |
−0.964965 | + | 0.262377i | \(0.915494\pi\) | |||||||
\(194\) | −4.88324 | −0.350596 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.93700 | − | 11.0452i | 0.281214 | − | 0.788945i | ||||
\(197\) | 8.01810 | + | 8.01810i | 0.571266 | + | 0.571266i | 0.932482 | − | 0.361216i | \(-0.117638\pi\) |
−0.361216 | + | 0.932482i | \(0.617638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.57558 | −0.324354 | −0.162177 | − | 0.986762i | \(-0.551852\pi\) | ||||
−0.162177 | + | 0.986762i | \(0.551852\pi\) | |||||||
\(200\) | 4.24965 | + | 4.24965i | 0.300495 | + | 0.300495i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.18728 | − | 5.18728i | −0.364976 | − | 0.364976i | ||||
\(203\) | 9.23998 | + | 1.59754i | 0.648520 | + | 0.112125i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.54420i | − | 0.177695i | ||||||
\(206\) | −2.46480 | − | 2.46480i | −0.171731 | − | 0.171731i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.74841 | − | 0.639375i | 0.537255 | − | 0.0443327i | ||||
\(209\) | − | 4.29022i | − | 0.296761i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.594028 | −0.0408946 | −0.0204473 | − | 0.999791i | \(-0.506509\pi\) | ||||
−0.0204473 | + | 0.999791i | \(0.506509\pi\) | |||||||
\(212\) | − | 16.4060i | − | 1.12677i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.57452 | − | 3.57452i | −0.244349 | − | 0.244349i | ||||
\(215\) | 8.94198 | + | 8.94198i | 0.609838 | + | 0.609838i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.88717 | + | 2.74117i | −0.263878 | + | 0.186083i | ||||
\(218\) | − | 3.70545i | − | 0.250965i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.06443 | 0.139184 | ||||||||
\(221\) | −26.4040 | + | 2.17878i | −1.77612 | + | 0.146560i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.85764 | − | 2.85764i | 0.191361 | − | 0.191361i | −0.604923 | − | 0.796284i | \(-0.706796\pi\) |
0.796284 | + | 0.604923i | \(0.206796\pi\) | |||||||
\(224\) | −8.26187 | − | 11.7159i | −0.552019 | − | 0.782802i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.647754 | − | 0.647754i | −0.0430879 | − | 0.0430879i | ||||
\(227\) | 19.6570 | − | 19.6570i | 1.30468 | − | 1.30468i | 0.379477 | − | 0.925201i | \(-0.376104\pi\) |
0.925201 | − | 0.379477i | \(-0.123896\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2060 | − | 13.2060i | −0.872676 | − | 0.872676i | 0.120087 | − | 0.992763i | \(-0.461683\pi\) |
−0.992763 | + | 0.120087i | \(0.961683\pi\) | |||||||
\(230\) | 3.69720i | 0.243786i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.24965 | − | 5.24965i | 0.344656 | − | 0.344656i | ||||
\(233\) | 16.2243i | 1.06289i | 0.847094 | + | 0.531443i | \(0.178350\pi\) | ||||
−0.847094 | + | 0.531443i | \(0.821650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.20711 | 0.339674 | ||||||||
\(236\) | 1.82542 | − | 1.82542i | 0.118825 | − | 0.118825i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.38594 | + | 9.05571i | 0.413939 | + | 0.586994i | ||||
\(239\) | 0.843675 | + | 0.843675i | 0.0545728 | + | 0.0545728i | 0.733867 | − | 0.679294i | \(-0.237714\pi\) |
−0.679294 | + | 0.733867i | \(0.737714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2966 | + | 15.2966i | 0.985342 | + | 0.985342i | 0.999894 | − | 0.0145517i | \(-0.00463211\pi\) |
−0.0145517 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(242\) | −4.14609 | + | 4.14609i | −0.266521 | + | 0.266521i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.9086 | −0.762367 | ||||||||
\(245\) | −9.23204 | + | 4.38009i | −0.589813 | + | 0.279834i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.8466 | + | 13.9775i | −0.753782 | + | 0.889370i | ||||
\(248\) | 3.76585i | 0.239132i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 6.54730i | − | 0.414088i | ||||||
\(251\) | −27.4367 | −1.73179 | −0.865893 | − | 0.500229i | \(-0.833249\pi\) | ||||
−0.865893 | + | 0.500229i | \(0.833249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65268 | − | 2.65268i | −0.166772 | − | 0.166772i | ||||
\(254\) | 0.624346 | − | 0.624346i | 0.0391749 | − | 0.0391749i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.12601 | −0.257876 | ||||||||
\(257\) | −20.5727 | −1.28329 | −0.641645 | − | 0.767002i | \(-0.721748\pi\) | ||||
−0.641645 | + | 0.767002i | \(0.721748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.81944 | − | 6.21933i | 0.548014 | − | 0.386450i | ||||
\(260\) | −6.72592 | − | 5.70052i | −0.417124 | − | 0.353531i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.14207 | + | 2.14207i | −0.132338 | + | 0.132338i | ||||
\(263\) | 23.8568 | 1.47108 | 0.735538 | − | 0.677483i | \(-0.236929\pi\) | ||||
0.735538 | + | 0.677483i | \(0.236929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.1093 | + | 10.1093i | −0.621012 | + | 0.621012i | ||||
\(266\) | 7.55128 | + | 1.30557i | 0.462999 | + | 0.0800497i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.6883 | − | 14.6883i | 0.897231 | − | 0.897231i | ||||
\(269\) | 1.10840i | 0.0675803i | 0.999429 | + | 0.0337902i | \(0.0107578\pi\) | ||||
−0.999429 | + | 0.0337902i | \(0.989242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8894 | + | 20.8894i | 1.26894 | + | 1.26894i | 0.946637 | + | 0.322301i | \(0.104456\pi\) |
0.322301 | + | 0.946637i | \(0.395544\pi\) | |||||||
\(272\) | −15.8448 | −0.960730 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.2496 | −0.619204 | ||||||||
\(275\) | 1.71274 | + | 1.71274i | 0.103282 | + | 0.103282i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.8265i | − | 1.55177i | −0.630877 | − | 0.775883i | \(-0.717305\pi\) | ||
0.630877 | − | 0.775883i | \(-0.282695\pi\) | |||||||
\(278\) | −2.80013 | + | 2.80013i | −0.167941 | + | 0.167941i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.37830 | + | 7.97196i | −0.0823694 | + | 0.476416i | ||||
\(281\) | −12.0782 | + | 12.0782i | −0.720523 | + | 0.720523i | −0.968712 | − | 0.248189i | \(-0.920165\pi\) |
0.248189 | + | 0.968712i | \(0.420165\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3667 | −0.913458 | −0.456729 | − | 0.889606i | \(-0.650979\pi\) | ||||
−0.456729 | + | 0.889606i | \(0.650979\pi\) | |||||||
\(284\) | 2.45580 | − | 2.45580i | 0.145725 | − | 0.145725i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.72909 | + | 0.142680i | −0.102243 | + | 0.00843683i | ||||
\(287\) | −3.76845 | + | 2.65745i | −0.222445 | + | 0.156864i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.9937 | 2.17610 | ||||||||
\(290\) | −2.94888 | −0.173164 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.173973 | + | 0.173973i | −0.0101810 | + | 0.0101810i | ||||
\(293\) | 9.78662 | + | 9.78662i | 0.571741 | + | 0.571741i | 0.932615 | − | 0.360874i | \(-0.117522\pi\) |
−0.360874 | + | 0.932615i | \(0.617522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.24965 | −0.130979 | ||||||||
\(296\) | − | 8.54420i | − | 0.496621i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.83875i | 0.512015i | ||||||||
\(299\) | 1.31757 | + | 15.9673i | 0.0761972 | + | 0.923413i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.90478 | − | 22.5848i | 0.225068 | − | 1.30177i | ||||
\(302\) | 4.95017 | 0.284850 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.74841 | + | 7.74841i | −0.444402 | + | 0.444402i | ||||
\(305\) | 7.33804 | + | 7.33804i | 0.420175 | + | 0.420175i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.14125 | − | 8.14125i | −0.464645 | − | 0.464645i | 0.435529 | − | 0.900175i | \(-0.356561\pi\) |
−0.900175 | + | 0.435529i | \(0.856561\pi\) | |||||||
\(308\) | −2.15633 | − | 3.05782i | −0.122868 | − | 0.174235i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.05769 | − | 1.05769i | 0.0600730 | − | 0.0600730i | ||||
\(311\) | 32.4813 | 1.84184 | 0.920922 | − | 0.389747i | \(-0.127438\pi\) | ||||
0.920922 | + | 0.389747i | \(0.127438\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7346i | 1.11547i | 0.830020 | + | 0.557733i | \(0.188329\pi\) | ||||
−0.830020 | + | 0.557733i | \(0.811671\pi\) | |||||||
\(314\) | 3.90853 | − | 3.90853i | 0.220571 | − | 0.220571i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.03857i | 0.452205i | ||||||||
\(317\) | 8.11871 | + | 8.11871i | 0.455992 | + | 0.455992i | 0.897337 | − | 0.441345i | \(-0.145499\pi\) |
−0.441345 | + | 0.897337i | \(0.645499\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11577 | − | 2.11577i | 0.118461 | − | 0.118461i | ||||
\(320\) | −1.26369 | − | 1.26369i | −0.0706425 | − | 0.0706425i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.47626 | − | 3.86177i | 0.305180 | − | 0.215208i | ||||
\(323\) | 26.4040 | − | 26.4040i | 1.46916 | − | 1.46916i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.850712 | − | 10.3095i | −0.0471890 | − | 0.571870i | ||||
\(326\) | −4.36344 | −0.241668 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.65084i | 0.201584i | ||||||||
\(329\) | −5.43890 | − | 7.71274i | −0.299856 | − | 0.425217i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.806063 | − | 0.806063i | −0.0443053 | − | 0.0443053i | 0.684607 | − | 0.728912i | \(-0.259974\pi\) |
−0.728912 | + | 0.684607i | \(0.759974\pi\) | |||||||
\(332\) | 20.6317 | + | 20.6317i | 1.13231 | + | 1.13231i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 7.18061i | − | 0.392905i | ||||||
\(335\) | −18.1018 | −0.989009 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.6058i | 1.44931i | 0.689112 | + | 0.724655i | \(0.258001\pi\) | ||||
−0.689112 | + | 0.724655i | \(0.741999\pi\) | |||||||
\(338\) | 6.02738 | + | 4.30971i | 0.327846 | + | 0.234417i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.7054 | + | 12.7054i | 0.689050 | + | 0.689050i | ||||
\(341\) | 1.51776i | 0.0821912i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1308 | + | 9.09937i | 0.870979 | + | 0.491320i | ||||
\(344\) | −12.8315 | − | 12.8315i | −0.691826 | − | 0.691826i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.88385 | − | 2.88385i | −0.155037 | − | 0.155037i | ||||
\(347\) | 20.2071 | 1.08477 | 0.542387 | − | 0.840129i | \(-0.317521\pi\) | ||||
0.542387 | + | 0.840129i | \(0.317521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.31459 | − | 2.31459i | −0.123897 | − | 0.123897i | 0.642439 | − | 0.766336i | \(-0.277922\pi\) |
−0.766336 | + | 0.642439i | \(0.777922\pi\) | |||||||
\(350\) | −3.53583 | + | 2.49341i | −0.188998 | + | 0.133279i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.57452 | −0.243822 | ||||||||
\(353\) | 10.7412 | − | 10.7412i | 0.571696 | − | 0.571696i | −0.360906 | − | 0.932602i | \(-0.617533\pi\) |
0.932602 | + | 0.360906i | \(0.117533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.02653 | −0.160631 | ||||||||
\(356\) | 11.5419 | − | 11.5419i | 0.611721 | − | 0.611721i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.56665 | − | 5.56665i | 0.294207 | − | 0.294207i | ||||
\(359\) | 16.9726 | − | 16.9726i | 0.895781 | − | 0.895781i | −0.0992789 | − | 0.995060i | \(-0.531654\pi\) |
0.995060 | + | 0.0992789i | \(0.0316536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 6.82416i | − | 0.359166i | ||||||
\(362\) | −1.83803 | − | 1.83803i | −0.0966049 | − | 0.0966049i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.41827 | + | 15.9167i | −0.0743374 | + | 0.834260i | ||||
\(365\) | 0.214405 | 0.0112225 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.79778i | − | 0.511440i | −0.966751 | − | 0.255720i | \(-0.917688\pi\) | ||
0.966751 | − | 0.255720i | \(-0.0823125\pi\) | |||||||
\(368\) | 9.58181i | 0.499486i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.39976 | + | 2.39976i | −0.124758 | + | 0.124758i | ||||
\(371\) | 25.5333 | + | 4.41455i | 1.32562 | + | 0.229192i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.96731 | −0.308976 | −0.154488 | − | 0.987995i | \(-0.549373\pi\) | ||||
−0.154488 | + | 0.987995i | \(0.549373\pi\) | |||||||
\(374\) | 3.53583 | 0.182834 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.47204 | −0.385341 | ||||||||
\(377\) | −12.7355 | + | 1.05090i | −0.655912 | + | 0.0541239i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.14117 | + | 2.14117i | 0.109984 | + | 0.109984i | 0.759957 | − | 0.649973i | \(-0.225220\pi\) |
−0.649973 | + | 0.759957i | \(0.725220\pi\) | |||||||
\(380\) | 12.4264 | 0.637463 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.49341 | − | 1.49341i | −0.0764097 | − | 0.0764097i | ||||
\(383\) | −2.91152 | + | 2.91152i | −0.148772 | + | 0.148772i | −0.777569 | − | 0.628798i | \(-0.783547\pi\) |
0.628798 | + | 0.777569i | \(0.283547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.555500 | + | 3.21295i | −0.0283109 | + | 0.163747i | ||||
\(386\) | −13.7440 | −0.699552 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.1482 | + | 10.1482i | 0.515195 | + | 0.515195i | ||||
\(389\) | − | 17.4436i | − | 0.884425i | −0.896910 | − | 0.442212i | \(-0.854194\pi\) | ||
0.896910 | − | 0.442212i | \(-0.145806\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 32.6516i | − | 1.65126i | ||||||
\(392\) | 13.2477 | − | 6.28529i | 0.669109 | − | 0.317455i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.46310i | 0.325606i | ||||||||
\(395\) | 4.95336 | − | 4.95336i | 0.249230 | − | 0.249230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1870 | + | 10.1870i | 0.511270 | + | 0.511270i | 0.914916 | − | 0.403645i | \(-0.132257\pi\) |
−0.403645 | + | 0.914916i | \(0.632257\pi\) | |||||||
\(398\) | −1.84410 | − | 1.84410i | −0.0924365 | − | 0.0924365i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 6.18664i | − | 0.309332i | ||||||
\(401\) | −15.5950 | + | 15.5950i | −0.778776 | + | 0.778776i | −0.979623 | − | 0.200846i | \(-0.935631\pi\) |
0.200846 | + | 0.979623i | \(0.435631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.19100 | − | 4.94486i | 0.208768 | − | 0.246321i | ||||
\(404\) | 21.5600i | 1.07265i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.08015 | + | 4.36786i | 0.152865 | + | 0.216773i | ||||
\(407\) | − | 3.44358i | − | 0.170692i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.79921 | − | 1.79921i | 0.0889652 | − | 0.0889652i | −0.661224 | − | 0.750189i | \(-0.729963\pi\) |
0.750189 | + | 0.661224i | \(0.229963\pi\) | |||||||
\(410\) | 1.02539 | − | 1.02539i | 0.0506405 | − | 0.0506405i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.2445i | 0.504710i | ||||||||
\(413\) | 2.34979 | + | 3.33216i | 0.115626 | + | 0.163965i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 25.4264i | − | 1.24813i | ||||||
\(416\) | 14.9038 | + | 12.6316i | 0.730718 | + | 0.619317i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.72909 | − | 1.72909i | 0.0845728 | − | 0.0845728i | ||||
\(419\) | − | 16.5064i | − | 0.806392i | −0.915114 | − | 0.403196i | \(-0.867899\pi\) | ||
0.915114 | − | 0.403196i | \(-0.132101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.53492 | − | 8.53492i | −0.415967 | − | 0.415967i | 0.467844 | − | 0.883811i | \(-0.345031\pi\) |
−0.883811 | + | 0.467844i | \(0.845031\pi\) | |||||||
\(422\) | −0.239412 | − | 0.239412i | −0.0116544 | − | 0.0116544i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.5066 | − | 14.5066i | 0.704502 | − | 0.704502i | ||||
\(425\) | 21.0820i | 1.02263i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.20438 | − | 18.5338i | 0.155071 | − | 0.896911i | ||||
\(428\) | 14.8568i | 0.718133i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.20780i | 0.347591i | ||||||||
\(431\) | −24.2071 | − | 24.2071i | −1.16602 | − | 1.16602i | −0.983135 | − | 0.182880i | \(-0.941458\pi\) |
−0.182880 | − | 0.983135i | \(-0.558542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.8708 | −1.72384 | −0.861920 | − | 0.507044i | \(-0.830738\pi\) | ||||
−0.861920 | + | 0.507044i | \(0.830738\pi\) | |||||||
\(434\) | −2.67143 | − | 0.461874i | −0.128233 | − | 0.0221707i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.70052 | + | 7.70052i | −0.368788 | + | 0.368788i | ||||
\(437\) | −15.9673 | − | 15.9673i | −0.763819 | − | 0.763819i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5299 | 0.502563 | 0.251281 | − | 0.967914i | \(-0.419148\pi\) | ||||
0.251281 | + | 0.967914i | \(0.419148\pi\) | |||||||
\(440\) | 1.82542 | + | 1.82542i | 0.0870236 | + | 0.0870236i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.5198 | − | 9.76353i | −0.547939 | − | 0.464404i | ||||
\(443\) | −12.8618 | −0.611081 | −0.305541 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305541 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.2243 | −0.674294 | ||||||||
\(446\) | 2.30344 | 0.109071 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.551829 | + | 3.19172i | −0.0260715 | + | 0.150795i | ||||
\(449\) | −9.65069 | + | 9.65069i | −0.455444 | + | 0.455444i | −0.897157 | − | 0.441712i | \(-0.854371\pi\) |
0.441712 | + | 0.897157i | \(0.354371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.47141i | 0.0692858i | ||||||||
\(452\) | 2.69227i | 0.126634i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.8448 | 0.743631 | ||||||||
\(455\) | 10.6818 | − | 8.93390i | 0.500769 | − | 0.418828i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.1217 | − | 22.1217i | −1.03481 | − | 1.03481i | −0.999372 | − | 0.0354353i | \(-0.988718\pi\) |
−0.0354353 | − | 0.999372i | \(-0.511282\pi\) | |||||||
\(458\) | − | 10.6449i | − | 0.497402i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.68337 | − | 7.68337i | 0.358239 | − | 0.358239i | ||||
\(461\) | −0.593023 | + | 0.593023i | −0.0276198 | + | 0.0276198i | −0.720782 | − | 0.693162i | \(-0.756217\pi\) |
0.693162 | + | 0.720782i | \(0.256217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.47096 | − | 2.47096i | 0.114835 | − | 0.114835i | −0.647354 | − | 0.762189i | \(-0.724124\pi\) |
0.762189 | + | 0.647354i | \(0.224124\pi\) | |||||||
\(464\) | −7.64244 | −0.354792 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.53889 | + | 6.53889i | −0.302908 | + | 0.302908i | ||||
\(467\) | 13.3860 | 0.619432 | 0.309716 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309716 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.9076 | + | 26.8123i | 0.873073 | + | 1.23808i | ||||
\(470\) | 2.09863 | + | 2.09863i | 0.0968026 | + | 0.0968026i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.22817 | 0.148589 | ||||||||
\(473\) | −5.17148 | − | 5.17148i | −0.237785 | − | 0.237785i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3095 | + | 10.3095i | 0.473034 | + | 0.473034i | ||||
\(476\) | 5.54821 | − | 32.0903i | 0.254302 | − | 1.47085i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.680055i | 0.0311050i | ||||||||
\(479\) | 8.85827 | + | 8.85827i | 0.404745 | + | 0.404745i | 0.879901 | − | 0.475157i | \(-0.157609\pi\) |
−0.475157 | + | 0.879901i | \(0.657609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.50879 | + | 11.2192i | −0.433564 | + | 0.511552i | ||||
\(482\) | 12.3301i | 0.561619i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.2325 | 0.783296 | ||||||||
\(485\) | − | 12.5066i | − | 0.567895i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.9805 | + | 17.9805i | 0.814774 | + | 0.814774i | 0.985345 | − | 0.170572i | \(-0.0545614\pi\) |
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(488\) | −10.5299 | − | 10.5299i | −0.476664 | − | 0.476664i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.48612 | − | 1.95549i | −0.247838 | − | 0.0883400i | ||||
\(491\) | − | 19.4944i | − | 0.879769i | −0.898054 | − | 0.439884i | \(-0.855019\pi\) | ||
0.898054 | − | 0.439884i | \(-0.144981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.0429 | 1.17291 | ||||||||
\(494\) | −10.4080 | + | 0.858833i | −0.468276 | + | 0.0386407i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.74117 | − | 2.74117i | 0.123082 | − | 0.123082i | ||||
\(497\) | 3.16125 | + | 4.48287i | 0.141801 | + | 0.201084i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2150 | + | 10.2150i | 0.457285 | + | 0.457285i | 0.897763 | − | 0.440478i | \(-0.145191\pi\) |
−0.440478 | + | 0.897763i | \(0.645191\pi\) | |||||||
\(500\) | −13.6064 | + | 13.6064i | −0.608495 | + | 0.608495i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.0578 | − | 11.0578i | −0.493536 | − | 0.493536i | ||||
\(503\) | 31.8196i | 1.41877i | 0.704824 | + | 0.709383i | \(0.251026\pi\) | ||||
−0.704824 | + | 0.709383i | \(0.748974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2853 | − | 13.2853i | 0.591187 | − | 0.591187i | ||||
\(506\) | − | 2.13823i | − | 0.0950558i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.59498 | −0.115134 | ||||||||
\(509\) | 13.6139 | − | 13.6139i | 0.603425 | − | 0.603425i | −0.337795 | − | 0.941220i | \(-0.609681\pi\) |
0.941220 | + | 0.337795i | \(0.109681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.223949 | − | 0.317575i | −0.00990691 | − | 0.0140487i | ||||
\(512\) | 14.6497 | + | 14.6497i | 0.647433 | + | 0.647433i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.29145 | − | 8.29145i | −0.365720 | − | 0.365720i | ||||
\(515\) | 6.31265 | − | 6.31265i | 0.278169 | − | 0.278169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.01147 | −0.132444 | ||||||||
\(518\) | 6.06110 | + | 1.04793i | 0.266310 | + | 0.0460433i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.906679 | − | 10.9878i | −0.0397605 | − | 0.481846i | ||||
\(521\) | − | 21.6750i | − | 0.949601i | −0.880094 | − | 0.474800i | \(-0.842520\pi\) | ||
0.880094 | − | 0.474800i | \(-0.157480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.77309i | 0.383620i | 0.981432 | + | 0.191810i | \(0.0614358\pi\) | ||||
−0.981432 | + | 0.191810i | \(0.938564\pi\) | |||||||
\(524\) | 8.90316 | 0.388936 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.61507 | + | 9.61507i | 0.419237 | + | 0.419237i | ||||
\(527\) | −9.34098 | + | 9.34098i | −0.406900 | + | 0.406900i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.25457 | 0.141503 | ||||||||
\(530\) | −8.14877 | −0.353960 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.9796 | − | 18.4060i | −0.562737 | − | 0.798000i | ||||
\(533\) | 4.06300 | − | 4.79384i | 0.175988 | − | 0.207644i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.15478 | − | 9.15478i | 0.395796 | − | 0.395796i | ||||
\(536\) | 25.9756 | 1.12197 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.446720 | + | 0.446720i | −0.0192595 | + | 0.0192595i | ||||
\(539\) | 5.33923 | − | 2.53317i | 0.229977 | − | 0.109111i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2853 | + | 23.2853i | −1.00111 | + | 1.00111i | −0.00111270 | + | 0.999999i | \(0.500354\pi\) |
−0.999999 | + | 0.00111270i | \(0.999646\pi\) | |||||||
\(542\) | 16.8382i | 0.723260i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.1537 | − | 28.1537i | −1.20708 | − | 1.20708i | ||||
\(545\) | 9.49011 | 0.406512 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1744 | −0.648812 | −0.324406 | − | 0.945918i | \(-0.605164\pi\) | ||||
−0.324406 | + | 0.945918i | \(0.605164\pi\) | |||||||
\(548\) | 21.3004 | + | 21.3004i | 0.909909 | + | 0.909909i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.38058i | 0.0588681i | ||||||||
\(551\) | 12.7355 | − | 12.7355i | 0.542551 | − | 0.542551i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5107 | − | 2.16303i | −0.532011 | − | 0.0919815i | ||||
\(554\) | 10.4089 | − | 10.4089i | 0.442232 | − | 0.442232i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6383 | 0.493572 | ||||||||
\(557\) | −8.45676 | + | 8.45676i | −0.358324 | + | 0.358324i | −0.863195 | − | 0.504871i | \(-0.831540\pi\) |
0.504871 | + | 0.863195i | \(0.331540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.56865 | + | 31.1288i | 0.108642 | + | 1.31661i | ||||
\(560\) | 6.80606 | − | 4.79953i | 0.287609 | − | 0.202817i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.73577 | −0.410678 | ||||||||
\(563\) | −6.34858 | −0.267561 | −0.133780 | − | 0.991011i | \(-0.542712\pi\) | ||||
−0.133780 | + | 0.991011i | \(0.542712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.65898 | − | 1.65898i | 0.0697937 | − | 0.0697937i | ||||
\(566\) | −6.19329 | − | 6.19329i | −0.260323 | − | 0.260323i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.34297 | 0.182227 | ||||||||
\(569\) | − | 36.6140i | − | 1.53494i | −0.641085 | − | 0.767470i | \(-0.721515\pi\) | ||
0.641085 | − | 0.767470i | \(-0.278485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.8070i | − | 0.787049i | −0.919314 | − | 0.393525i | \(-0.871256\pi\) | ||
0.919314 | − | 0.393525i | \(-0.128744\pi\) | |||||||
\(572\) | 3.88985 | + | 3.29683i | 0.162643 | + | 0.137847i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.58984 | − | 0.447768i | −0.108098 | − | 0.0186895i | ||||
\(575\) | 12.7489 | 0.531668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3416 | − | 31.3416i | 1.30477 | − | 1.30477i | 0.379627 | − | 0.925140i | \(-0.376052\pi\) |
0.925140 | − | 0.379627i | \(-0.123948\pi\) | |||||||
\(578\) | 14.9096 | + | 14.9096i | 0.620158 | + | 0.620158i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.12825 | + | 6.12825i | 0.254462 | + | 0.254462i | ||||
\(581\) | −37.6615 | + | 26.5583i | −1.56246 | + | 1.10182i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.84661 | − | 5.84661i | 0.242142 | − | 0.242142i | ||||
\(584\) | −0.307664 | −0.0127312 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.88864i | 0.325877i | ||||||||
\(587\) | −3.36694 | + | 3.36694i | −0.138969 | + | 0.138969i | −0.773169 | − | 0.634200i | \(-0.781329\pi\) |
0.634200 | + | 0.773169i | \(0.281329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.13586i | 0.376436i | ||||||||
\(590\) | −0.906679 | − | 0.906679i | −0.0373274 | − | 0.0373274i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.21933 | + | 6.21933i | −0.255613 | + | 0.255613i | ||||
\(593\) | −10.6837 | − | 10.6837i | −0.438726 | − | 0.438726i | 0.452857 | − | 0.891583i | \(-0.350405\pi\) |
−0.891583 | + | 0.452857i | \(0.850405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.1928 | + | 16.3552i | −0.950812 | + | 0.670497i | ||||
\(596\) | 18.3684 | − | 18.3684i | 0.752397 | − | 0.752397i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.90430 | + | 6.96635i | −0.241445 | + | 0.284875i | ||||
\(599\) | 12.8437 | 0.524778 | 0.262389 | − | 0.964962i | \(-0.415490\pi\) | ||||
0.262389 | + | 0.964962i | \(0.415490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5732i | − | 0.798409i | −0.916862 | − | 0.399205i | \(-0.869286\pi\) | ||
0.916862 | − | 0.399205i | \(-0.130714\pi\) | |||||||
\(602\) | 10.6762 | − | 7.52865i | 0.435128 | − | 0.306845i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.2873 | − | 10.2873i | −0.418583 | − | 0.418583i | ||||
\(605\) | −10.6187 | − | 10.6187i | −0.431710 | − | 0.431710i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.9804i | 1.70393i | 0.523598 | + | 0.851965i | \(0.324589\pi\) | ||||
−0.523598 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(608\) | −27.5354 | −1.11671 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.91493i | 0.239488i | ||||||||
\(611\) | 9.81137 | + | 8.31559i | 0.396926 | + | 0.336413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.4993 | + | 20.4993i | 0.827959 | + | 0.827959i | 0.987234 | − | 0.159276i | \(-0.0509158\pi\) |
−0.159276 | + | 0.987234i | \(0.550916\pi\) | |||||||
\(614\) | − | 6.56236i | − | 0.264835i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.797125 | − | 4.61048i | 0.0321171 | − | 0.185762i | ||||
\(617\) | −8.21440 | − | 8.21440i | −0.330699 | − | 0.330699i | 0.522153 | − | 0.852852i | \(-0.325129\pi\) |
−0.852852 | + | 0.522153i | \(0.825129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.6973 | + | 26.6973i | 1.07306 | + | 1.07306i | 0.997112 | + | 0.0759445i | \(0.0241972\pi\) |
0.0759445 | + | 0.997112i | \(0.475803\pi\) | |||||||
\(620\) | −4.39612 | −0.176553 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.0910 | + | 13.0910i | 0.524900 | + | 0.524900i | ||||
\(623\) | 14.8574 | + | 21.0689i | 0.595251 | + | 0.844107i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.42311 | 0.0969246 | ||||||||
\(626\) | −7.95367 | + | 7.95367i | −0.317893 | + | 0.317893i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.2451 | −0.648251 | ||||||||
\(629\) | 21.1934 | − | 21.1934i | 0.845036 | − | 0.845036i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.13093 | − | 5.13093i | 0.204259 | − | 0.204259i | −0.597563 | − | 0.801822i | \(-0.703864\pi\) |
0.801822 | + | 0.597563i | \(0.203864\pi\) | |||||||
\(632\) | −7.10791 | + | 7.10791i | −0.282737 | + | 0.282737i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.54420i | 0.259903i | ||||||||
\(635\) | 1.59903 | + | 1.59903i | 0.0634554 | + | 0.0634554i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.3901 | − | 6.49019i | −0.966371 | − | 0.257151i | ||||
\(638\) | 1.70545 | 0.0675193 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 16.8382i | − | 0.665586i | ||||||
\(641\) | 16.3357i | 0.645220i | 0.946532 | + | 0.322610i | \(0.104560\pi\) | ||||
−0.946532 | + | 0.322610i | \(0.895440\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.1910 | − | 28.1910i | 1.11175 | − | 1.11175i | 0.118832 | − | 0.992914i | \(-0.462085\pi\) |
0.992914 | − | 0.118832i | \(-0.0379150\pi\) | |||||||
\(644\) | −19.4060 | − | 3.35517i | −0.764702 | − | 0.132212i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.2833 | 0.837380 | ||||||||
\(647\) | −11.1139 | −0.436932 | −0.218466 | − | 0.975845i | \(-0.570105\pi\) | ||||
−0.218466 | + | 0.975845i | \(0.570105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.30105 | 0.0510709 | ||||||||
\(650\) | 3.81220 | − | 4.49793i | 0.149527 | − | 0.176423i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.06793 | + | 9.06793i | 0.355127 | + | 0.355127i | ||||
\(653\) | −4.95651 | −0.193963 | −0.0969816 | − | 0.995286i | \(-0.530919\pi\) | ||||
−0.0969816 | + | 0.995286i | \(0.530919\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.48612 | − | 5.48612i | −0.214360 | − | 0.214360i | ||||
\(656\) | 2.65745 | − | 2.65745i | 0.103756 | − | 0.103756i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.916430 | − | 5.30053i | 0.0357262 | − | 0.206636i | ||||
\(659\) | −26.1514 | −1.01871 | −0.509357 | − | 0.860555i | \(-0.670117\pi\) | ||||
−0.509357 | + | 0.860555i | \(0.670117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.2906 | − | 22.2906i | −0.867006 | − | 0.867006i | 0.125134 | − | 0.992140i | \(-0.460064\pi\) |
−0.992140 | + | 0.125134i | \(0.960064\pi\) | |||||||
\(662\) | − | 0.649738i | − | 0.0252528i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 36.4861i | 1.41594i | ||||||||
\(665\) | −3.34373 | + | 19.3398i | −0.129664 | + | 0.749964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 15.7489i | − | 0.609801i | ||||||
\(668\) | −14.9225 | + | 14.9225i | −0.577368 | + | 0.577368i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.29562 | − | 7.29562i | −0.281854 | − | 0.281854i | ||||
\(671\) | −4.24387 | − | 4.24387i | −0.163833 | − | 0.163833i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.38550i | 0.0534072i | 0.999643 | + | 0.0267036i | \(0.00850104\pi\) | ||||
−0.999643 | + | 0.0267036i | \(0.991499\pi\) | |||||||
\(674\) | −10.7230 | + | 10.7230i | −0.413034 | + | 0.413034i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.56959 | − | 21.4821i | −0.137292 | − | 0.826237i | ||||
\(677\) | − | 14.1868i | − | 0.545242i | −0.962122 | − | 0.272621i | \(-0.912110\pi\) | ||
0.962122 | − | 0.272621i | \(-0.0878905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5247 | + | 13.0633i | −0.710912 | + | 0.501324i | ||||
\(680\) | 22.4690i | 0.861646i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.611704 | + | 0.611704i | −0.0234234 | + | 0.0234234i | ||||
\(683\) | −27.2882 | + | 27.2882i | −1.04415 | + | 1.04415i | −0.0451754 | + | 0.998979i | \(0.514385\pi\) |
−0.998979 | + | 0.0451754i | \(0.985615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.2506i | − | 1.00298i | ||||||
\(686\) | 2.83387 | + | 10.1685i | 0.108198 | + | 0.388237i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.6801i | 0.712170i | ||||||||
\(689\) | −35.1926 | + | 2.90399i | −1.34073 | + | 0.110633i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1937 | − | 16.1937i | 0.616037 | − | 0.616037i | −0.328475 | − | 0.944513i | \(-0.606535\pi\) |
0.944513 | + | 0.328475i | \(0.106535\pi\) | |||||||
\(692\) | 11.9862i | 0.455647i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.14411 | + | 8.14411i | 0.309146 | + | 0.309146i | ||||
\(695\) | −7.17148 | − | 7.17148i | −0.272030 | − | 0.272030i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.05571 | + | 9.05571i | −0.343009 | + | 0.343009i | ||||
\(698\) | − | 1.86570i | − | 0.0706180i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.5298 | + | 2.16632i | 0.473580 | + | 0.0818792i | ||||
\(701\) | 15.2981i | 0.577800i | 0.957359 | + | 0.288900i | \(0.0932895\pi\) | ||||
−0.957359 | + | 0.288900i | \(0.906711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 20.7280i | − | 0.781771i | ||||||
\(704\) | 0.730841 | + | 0.730841i | 0.0275446 | + | 0.0275446i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.65808 | 0.325851 | ||||||||
\(707\) | −33.5547 | − | 5.80141i | −1.26196 | − | 0.218185i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.74107 | + | 2.74107i | −0.102943 | + | 0.102943i | −0.756703 | − | 0.653759i | \(-0.773191\pi\) |
0.653759 | + | 0.756703i | \(0.273191\pi\) | |||||||
\(710\) | −1.21979 | − | 1.21979i | −0.0457778 | − | 0.0457778i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.4113 | 0.764948 | ||||||||
\(713\) | 5.64878 | + | 5.64878i | 0.211548 | + | 0.211548i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.365420 | − | 4.42842i | −0.0136659 | − | 0.165614i | ||||
\(716\) | −23.1368 | −0.864663 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.6810 | 0.510571 | ||||||||
\(719\) | 5.99456 | 0.223559 | 0.111780 | − | 0.993733i | \(-0.464345\pi\) | ||||
0.111780 | + | 0.993733i | \(0.464345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9439 | − | 2.75661i | −0.593782 | − | 0.102661i | ||||
\(722\) | 2.75035 | − | 2.75035i | 0.102358 | − | 0.102358i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.63947i | 0.283919i | ||||||||
\(725\) | 10.1685i | 0.377650i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6184 | 0.542168 | 0.271084 | − | 0.962556i | \(-0.412618\pi\) | ||||
0.271084 | + | 0.962556i | \(0.412618\pi\) | |||||||
\(728\) | −15.3280 | + | 12.8199i | −0.568093 | + | 0.475136i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0864119 | + | 0.0864119i | 0.00319825 | + | 0.00319825i | ||||
\(731\) | − | 63.6554i | − | 2.35438i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.0685 | + | 28.0685i | −1.03673 | + | 1.03673i | −0.0374350 | + | 0.999299i | \(0.511919\pi\) |
−0.999299 | + | 0.0374350i | \(0.988081\pi\) | |||||||
\(734\) | 3.94881 | − | 3.94881i | 0.145753 | − | 0.145753i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.0254 | + | 17.0254i | −0.627564 | + | 0.627564i | ||||
\(737\) | 10.4690 | 0.385630 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.6028 | + | 16.6028i | −0.610746 | + | 0.610746i | −0.943140 | − | 0.332395i | \(-0.892143\pi\) |
0.332395 | + | 0.943140i | \(0.392143\pi\) | |||||||
\(740\) | 9.97420 | 0.366659 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.51151 | + | 12.0699i | 0.312467 | + | 0.443101i | ||||
\(743\) | 2.87636 | + | 2.87636i | 0.105523 | + | 0.105523i | 0.757897 | − | 0.652374i | \(-0.226227\pi\) |
−0.652374 | + | 0.757897i | \(0.726227\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6371 | −0.829361 | ||||||||
\(746\) | −2.40502 | − | 2.40502i | −0.0880539 | − | 0.0880539i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.34804 | − | 7.34804i | −0.268671 | − | 0.268671i | ||||
\(749\) | −23.1223 | − | 3.99771i | −0.844871 | − | 0.146073i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.9438i | − | 1.67651i | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||
0.545275 | − | 0.838257i | \(-0.316425\pi\) | |||||||
\(752\) | 5.43890 | + | 5.43890i | 0.198336 | + | 0.198336i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.55636 | − | 4.70927i | −0.202351 | − | 0.171501i | ||||
\(755\) | 12.6780i | 0.461400i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.7889 | −0.900969 | −0.450484 | − | 0.892784i | \(-0.648749\pi\) | ||||
−0.450484 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(758\) | 1.72592i | 0.0626881i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.9878 | + | 10.9878i | 0.398569 | + | 0.398569i | ||||
\(761\) | −10.8450 | − | 10.8450i | −0.393133 | − | 0.393133i | 0.482670 | − | 0.875802i | \(-0.339667\pi\) |
−0.875802 | + | 0.482670i | \(0.839667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.91256 | − | 14.0567i | −0.358859 | − | 0.508887i | ||||
\(764\) | 6.20711i | 0.224565i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.34687 | −0.0847958 | ||||||||
\(767\) | −4.23884 | − | 3.59261i | −0.153056 | − | 0.129722i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.63670 | + | 4.63670i | −0.167204 | + | 0.167204i | −0.785749 | − | 0.618545i | \(-0.787722\pi\) |
0.618545 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(770\) | −1.51881 | + | 1.07104i | −0.0547340 | + | 0.0385975i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.5623 | + | 28.5623i | 1.02798 | + | 1.02798i | ||||
\(773\) | 5.68398 | − | 5.68398i | 0.204438 | − | 0.204438i | −0.597460 | − | 0.801899i | \(-0.703823\pi\) |
0.801899 | + | 0.597460i | \(0.203823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.64722 | − | 3.64722i | −0.131012 | − | 0.131012i | ||||
\(776\) | 17.9466i | 0.644244i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.03032 | − | 7.03032i | 0.252049 | − | 0.252049i | ||||
\(779\) | 8.85685i | 0.317330i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.75035 | 0.0626326 | ||||||||
\(782\) | 13.1596 | − | 13.1596i | 0.470588 | − | 0.470588i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.2181 | − | 5.06793i | −0.507788 | − | 0.180997i | ||||
\(785\) | 10.0102 | + | 10.0102i | 0.357281 | + | 0.357281i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.65662 | − | 8.65662i | −0.308575 | − | 0.308575i | 0.535781 | − | 0.844357i | \(-0.320017\pi\) |
−0.844357 | + | 0.535781i | \(0.820017\pi\) | |||||||
\(788\) | 13.4314 | − | 13.4314i | 0.478473 | − | 0.478473i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.99272 | 0.142055 | ||||||||
\(791\) | −4.19009 | − | 0.724442i | −0.148983 | − | 0.0257582i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.10791 | + | 25.5452i | 0.0748541 | + | 0.907135i | ||||
\(794\) | 8.21136i | 0.291410i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.66469i | 0.271668i | ||||||||
\(797\) | 28.1163 | 0.995931 | 0.497966 | − | 0.867197i | \(-0.334081\pi\) | ||||
0.497966 | + | 0.867197i | \(0.334081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.5340 | − | 18.5340i | −0.655685 | − | 0.655685i | ||||
\(800\) | 10.9927 | − | 10.9927i | 0.388651 | − | 0.388651i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.5705 | −0.443881 | ||||||||
\(803\) | −0.123998 | −0.00437580 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.89048 | + | 14.0254i | 0.348594 | + | 0.494330i | ||||
\(806\) | 3.68204 | − | 0.303831i | 0.129694 | − | 0.0107020i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.0639 | + | 19.0639i | −0.670667 | + | 0.670667i | ||||
\(809\) | −0.687350 | −0.0241659 | −0.0120830 | − | 0.999927i | \(-0.503846\pi\) | ||||
−0.0120830 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.354016 | + | 0.354016i | −0.0124312 | + | 0.0124312i | −0.713295 | − | 0.700864i | \(-0.752798\pi\) |
0.700864 | + | 0.713295i | \(0.252798\pi\) | |||||||
\(812\) | 2.67608 | − | 15.4782i | 0.0939122 | − | 0.543178i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.38787 | − | 1.38787i | 0.0486449 | − | 0.0486449i | ||||
\(815\) | − | 11.1753i | − | 0.391454i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.1288 | − | 31.1288i | −1.08906 | − | 1.08906i | ||||
\(818\) | 1.45028 | 0.0507078 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.26187 | −0.148831 | ||||||||
\(821\) | −20.8773 | − | 20.8773i | −0.728623 | − | 0.728623i | 0.241722 | − | 0.970346i | \(-0.422288\pi\) |
−0.970346 | + | 0.241722i | \(0.922288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3611i | 0.361164i | 0.983560 | + | 0.180582i | \(0.0577981\pi\) | ||||
−0.983560 | + | 0.180582i | \(0.942202\pi\) | |||||||
\(824\) | −9.05845 | + | 9.05845i | −0.315566 | + | 0.315566i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.395928 | + | 2.29001i | −0.0137761 | + | 0.0796795i | ||||
\(827\) | −33.3235 | + | 33.3235i | −1.15877 | + | 1.15877i | −0.174030 | + | 0.984740i | \(0.555679\pi\) |
−0.984740 | + | 0.174030i | \(0.944321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8647 | −0.689929 | −0.344964 | − | 0.938616i | \(-0.612109\pi\) | ||||
−0.344964 | + | 0.938616i | \(0.612109\pi\) | |||||||
\(830\) | 10.2477 | − | 10.2477i | 0.355702 | − | 0.355702i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.363005 | − | 4.39916i | −0.0125849 | − | 0.152513i | ||||
\(833\) | 48.4504 | + | 17.2698i | 1.67871 | + | 0.598364i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.3904 | 0.636427 | ||||||||
\(836\) | −7.18668 | −0.248556 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.65262 | − | 6.65262i | 0.229811 | − | 0.229811i | ||||
\(839\) | 16.2048 | + | 16.2048i | 0.559453 | + | 0.559453i | 0.929152 | − | 0.369698i | \(-0.120539\pi\) |
−0.369698 | + | 0.929152i | \(0.620539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4387 | −0.566850 | ||||||||
\(842\) | − | 6.87969i | − | 0.237090i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.995075i | 0.0342519i | ||||||||
\(845\) | −11.0377 | + | 15.4369i | −0.379709 | + | 0.531044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.63695 | + | 26.8196i | −0.159328 | + | 0.921533i | ||||
\(848\) | −21.1187 | −0.725220 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.49672 | + | 8.49672i | −0.291435 | + | 0.291435i | ||||
\(851\) | −12.8163 | − | 12.8163i | −0.439337 | − | 0.439337i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.4778 | − | 12.4778i | −0.427232 | − | 0.427232i | 0.460452 | − | 0.887684i | \(-0.347687\pi\) |
−0.887684 | + | 0.460452i | \(0.847687\pi\) | |||||||
\(854\) | 8.76116 | − | 6.17823i | 0.299801 | − | 0.211415i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.1368 | + | 13.1368i | −0.449007 | + | 0.449007i | ||||
\(857\) | −27.2501 | −0.930845 | −0.465422 | − | 0.885089i | \(-0.654098\pi\) | ||||
−0.465422 | + | 0.885089i | \(0.654098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.7834i | − | 0.777361i | −0.921373 | − | 0.388680i | \(-0.872931\pi\) | ||
0.921373 | − | 0.388680i | \(-0.127069\pi\) | |||||||
\(860\) | 14.9790 | − | 14.9790i | 0.510779 | − | 0.510779i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.5125i | − | 0.664597i | ||||||
\(863\) | 21.1187 | + | 21.1187i | 0.718889 | + | 0.718889i | 0.968378 | − | 0.249488i | \(-0.0802624\pi\) |
−0.249488 | + | 0.968378i | \(0.580262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.38589 | − | 7.38589i | 0.251128 | − | 0.251128i | ||||
\(866\) | −14.4571 | − | 14.4571i | −0.491271 | − | 0.491271i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.59181 | + | 6.51151i | 0.155856 | + | 0.221015i | ||||
\(869\) | −2.86471 | + | 2.86471i | −0.0971787 | + | 0.0971787i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.1080 | − | 28.9081i | −1.15570 | − | 0.979513i | ||||
\(872\) | −13.6180 | −0.461164 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 12.8707i | − | 0.435356i | ||||||
\(875\) | −17.5149 | − | 24.8373i | −0.592111 | − | 0.839655i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0455 | + | 14.0455i | 0.474282 | + | 0.474282i | 0.903297 | − | 0.429015i | \(-0.141139\pi\) |
−0.429015 | + | 0.903297i | \(0.641139\pi\) | |||||||
\(878\) | 4.24387 | + | 4.24387i | 0.143224 | + | 0.143224i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 2.65745i | − | 0.0895827i | ||||||
\(881\) | 13.3800 | 0.450782 | 0.225391 | − | 0.974268i | \(-0.427634\pi\) | ||||
0.225391 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.63893i | 0.0551545i | 0.999620 | + | 0.0275773i | \(0.00877923\pi\) | ||||
−0.999620 | + | 0.0275773i | \(0.991221\pi\) | |||||||
\(884\) | 3.64974 | + | 44.2301i | 0.122754 | + | 1.48762i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.18370 | − | 5.18370i | −0.174150 | − | 0.174150i | ||||
\(887\) | − | 21.4198i | − | 0.719206i | −0.933105 | − | 0.359603i | \(-0.882912\pi\) | ||
0.933105 | − | 0.359603i | \(-0.117088\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.698263 | − | 4.03868i | 0.0234190 | − | 0.135453i | ||||
\(890\) | −5.73283 | − | 5.73283i | −0.192165 | − | 0.192165i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.78691 | − | 4.78691i | −0.160278 | − | 0.160278i | ||||
\(893\) | −18.1270 | −0.606596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2569 | + | 14.2569i | 0.476555 | + | 0.476555i | ||||
\(896\) | −24.9406 | + | 17.5877i | −0.833206 | + | 0.587563i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.77907 | −0.259591 | ||||||||
\(899\) | −4.50546 | + | 4.50546i | −0.150266 | + | 0.150266i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.9655 | 2.39752 | ||||||||
\(902\) | −0.593023 | + | 0.593023i | −0.0197455 | + | 0.0197455i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.38058 | + | 2.38058i | −0.0791769 | + | 0.0791769i | ||||
\(905\) | 4.70743 | − | 4.70743i | 0.156480 | − | 0.156480i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.59991i | − | 0.0863285i | −0.999068 | − | 0.0431643i | \(-0.986256\pi\) | ||
0.999068 | − | 0.0431643i | \(-0.0137439\pi\) | |||||||
\(908\) | −32.9280 | − | 32.9280i | −1.09275 | − | 1.09275i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.90574 | + | 0.704447i | 0.262073 | + | 0.0233522i | ||||
\(911\) | −41.2579 | −1.36694 | −0.683468 | − | 0.729981i | \(-0.739529\pi\) | ||||
−0.683468 | + | 0.729981i | \(0.739529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.7051i | 0.486667i | ||||||||
\(914\) | − | 17.8315i | − | 0.589812i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.1218 | + | 22.1218i | −0.730924 | + | 0.730924i | ||||
\(917\) | −2.39568 | + | 13.8563i | −0.0791123 | + | 0.457577i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.3039 | −1.59340 | −0.796700 | − | 0.604375i | \(-0.793423\pi\) | ||||
−0.796700 | + | 0.604375i | \(0.793423\pi\) | |||||||
\(920\) | 13.5877 | 0.447972 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.478014 | −0.0157426 | ||||||||
\(923\) | −5.70266 | − | 4.83327i | −0.187705 | − | 0.159089i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.27504 | + | 8.27504i | 0.272082 | + | 0.272082i | ||||
\(926\) | 1.99175 | 0.0654530 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.5794 | − | 13.5794i | −0.445767 | − | 0.445767i | ||||
\(929\) | −19.1804 | + | 19.1804i | −0.629289 | + | 0.629289i | −0.947889 | − | 0.318600i | \(-0.896787\pi\) |
0.318600 | + | 0.947889i | \(0.396787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.1385 | − | 15.2479i | 1.05330 | − | 0.499731i | ||||
\(932\) | 27.1777 | 0.890237 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.39500 | + | 5.39500i | 0.176530 | + | 0.176530i | ||||
\(935\) | 9.05571i | 0.296153i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.66644i | 0.0871088i | 0.999051 | + | 0.0435544i | \(0.0138682\pi\) | ||||
−0.999051 | + | 0.0435544i | \(0.986132\pi\) | |||||||
\(938\) | −3.18585 | + | 18.4266i | −0.104022 | + | 0.601650i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 8.72259i | − | 0.284500i | ||||||
\(941\) | 31.9331 | − | 31.9331i | 1.04099 | − | 1.04099i | 0.0418672 | − | 0.999123i | \(-0.486669\pi\) |
0.999123 | − | 0.0418672i | \(-0.0133307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.47626 | + | 5.47626i | 0.178332 | + | 0.178332i | ||||
\(944\) | −2.34979 | − | 2.34979i | −0.0764791 | − | 0.0764791i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 4.16854i | − | 0.135531i | ||||||
\(947\) | 8.43041 | − | 8.43041i | 0.273951 | − | 0.273951i | −0.556737 | − | 0.830689i | \(-0.687947\pi\) |
0.830689 | + | 0.556737i | \(0.187947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.403987 | + | 0.342397i | 0.0131140 | + | 0.0111147i | ||||
\(950\) | 8.31014i | 0.269616i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33.2809 | − | 23.4692i | 1.07864 | − | 0.760640i | ||||
\(953\) | 20.8846i | 0.676519i | 0.941053 | + | 0.338259i | \(0.109838\pi\) | ||||
−0.941053 | + | 0.338259i | \(0.890162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.82482 | − | 3.82482i | 0.123768 | − | 0.123768i | ||||
\(956\) | 1.41327 | − | 1.41327i | 0.0457083 | − | 0.0457083i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.14032i | 0.230693i | ||||||||
\(959\) | −38.8823 | + | 27.4191i | −1.25557 | + | 0.885410i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7680i | 0.895742i | ||||||||
\(962\) | −8.35404 | + | 0.689351i | −0.269345 | + | 0.0222256i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.6239 | − | 25.6239i | 0.825289 | − | 0.825289i | ||||
\(965\) | − | 35.2001i | − | 1.13313i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9628 | + | 20.9628i | 0.674117 | + | 0.674117i | 0.958663 | − | 0.284545i | \(-0.0918426\pi\) |
−0.284545 | + | 0.958663i | \(0.591843\pi\) | |||||||
\(968\) | 15.2374 | + | 15.2374i | 0.489749 | + | 0.489749i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.04055 | − | 5.04055i | 0.161842 | − | 0.161842i | ||||
\(971\) | 12.7719i | 0.409869i | 0.978776 | + | 0.204935i | \(0.0656982\pi\) | ||||
−0.978776 | + | 0.204935i | \(0.934302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.13164 | + | 18.1131i | −0.100396 | + | 0.580679i | ||||
\(974\) | 14.4934i | 0.464399i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.3294i | 0.490682i | ||||||||
\(977\) | 27.8222 | + | 27.8222i | 0.890110 | + | 0.890110i | 0.994533 | − | 0.104423i | \(-0.0332995\pi\) |
−0.104423 | + | 0.994533i | \(0.533299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.22642 | 0.262918 | ||||||||
\(980\) | 7.33722 | + | 15.4649i | 0.234379 | + | 0.494007i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.85685 | − | 7.85685i | 0.250722 | − | 0.250722i | ||||
\(983\) | 35.8970 | + | 35.8970i | 1.14494 | + | 1.14494i | 0.987535 | + | 0.157402i | \(0.0503119\pi\) |
0.157402 | + | 0.987535i | \(0.449688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.5528 | −0.527416 | ||||||||
\(986\) | 10.4961 | + | 10.4961i | 0.334264 | + | 0.334264i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.4142 | + | 19.8446i | 0.744906 | + | 0.631342i | ||||
\(989\) | −38.4944 | −1.22405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.69418 | −0.276180 | −0.138090 | − | 0.990420i | \(-0.544096\pi\) | ||||
−0.138090 | + | 0.990420i | \(0.544096\pi\) | |||||||
\(992\) | 9.74126 | 0.309285 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.532656 | + | 3.08082i | −0.0168948 | + | 0.0977178i | ||||
\(995\) | 4.72298 | − | 4.72298i | 0.149728 | − | 0.149728i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5673i | 0.841394i | 0.907201 | + | 0.420697i | \(0.138214\pi\) | ||||
−0.907201 | + | 0.420697i | \(0.861786\pi\) | |||||||
\(998\) | 8.23392i | 0.260640i | ||||||||
\(999\) | 0 | 0 |
(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 | 819.2.y.h.307.3 | 12 | ||
3.2 | odd | 2 | 91.2.i.a.34.4 | yes | 12 | ||
7.6 | odd | 2 | inner | 819.2.y.h.307.4 | 12 | ||
13.5 | odd | 4 | inner | 819.2.y.h.811.4 | 12 | ||
21.2 | odd | 6 | 637.2.bc.a.619.3 | 24 | |||
21.5 | even | 6 | 637.2.bc.a.619.4 | 24 | |||
21.11 | odd | 6 | 637.2.bc.a.411.4 | 24 | |||
21.17 | even | 6 | 637.2.bc.a.411.3 | 24 | |||
21.20 | even | 2 | 91.2.i.a.34.3 | ✓ | 12 | ||
39.5 | even | 4 | 91.2.i.a.83.4 | yes | 12 | ||
91.83 | even | 4 | inner | 819.2.y.h.811.3 | 12 | ||
273.5 | odd | 12 | 637.2.bc.a.31.4 | 24 | |||
273.44 | even | 12 | 637.2.bc.a.31.3 | 24 | |||
273.83 | odd | 4 | 91.2.i.a.83.3 | yes | 12 | ||
273.122 | odd | 12 | 637.2.bc.a.460.3 | 24 | |||
273.200 | even | 12 | 637.2.bc.a.460.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.3 | ✓ | 12 | 21.20 | even | 2 | ||
91.2.i.a.34.4 | yes | 12 | 3.2 | odd | 2 | ||
91.2.i.a.83.3 | yes | 12 | 273.83 | odd | 4 | ||
91.2.i.a.83.4 | yes | 12 | 39.5 | even | 4 | ||
637.2.bc.a.31.3 | 24 | 273.44 | even | 12 | |||
637.2.bc.a.31.4 | 24 | 273.5 | odd | 12 | |||
637.2.bc.a.411.3 | 24 | 21.17 | even | 6 | |||
637.2.bc.a.411.4 | 24 | 21.11 | odd | 6 | |||
637.2.bc.a.460.3 | 24 | 273.122 | odd | 12 | |||
637.2.bc.a.460.4 | 24 | 273.200 | even | 12 | |||
637.2.bc.a.619.3 | 24 | 21.2 | odd | 6 | |||
637.2.bc.a.619.4 | 24 | 21.5 | even | 6 | |||
819.2.y.h.307.3 | 12 | 1.1 | even | 1 | trivial | ||
819.2.y.h.307.4 | 12 | 7.6 | odd | 2 | inner | ||
819.2.y.h.811.3 | 12 | 91.83 | even | 4 | inner | ||
819.2.y.h.811.4 | 12 | 13.5 | odd | 4 | inner |