Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(26,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 312x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 206.5 | ||
Root | \(-1.99567i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.206 |
Dual form | 315.2.bj.a.26.5 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72830 | − | 0.997835i | 1.22209 | − | 0.705576i | 0.256730 | − | 0.966483i | \(-0.417355\pi\) |
0.965364 | + | 0.260907i | \(0.0840217\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.991350 | − | 1.71707i | 0.495675 | − | 0.858534i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78020 | − | 1.95727i | 0.672852 | − | 0.739777i | ||||
\(8\) | 0.0345244i | 0.0122062i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.72830 | − | 0.997835i | −0.546537 | − | 0.315543i | ||||
\(11\) | 1.56652 | + | 0.904429i | 0.472323 | + | 0.272696i | 0.717212 | − | 0.696855i | \(-0.245418\pi\) |
−0.244889 | + | 0.969551i | \(0.578751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.33881i | − | 1.48072i | −0.672212 | − | 0.740359i | \(-0.734655\pi\) | ||
0.672212 | − | 0.740359i | \(-0.265345\pi\) | |||||||
\(14\) | 1.12369 | − | 5.15909i | 0.300319 | − | 1.37883i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.01715 | + | 3.49381i | 0.504288 | + | 0.873452i | ||||
\(17\) | −0.932008 | + | 1.61429i | −0.226045 | + | 0.391522i | −0.956632 | − | 0.291298i | \(-0.905913\pi\) |
0.730587 | + | 0.682819i | \(0.239246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.79482 | + | 1.03624i | −0.411760 | + | 0.237730i | −0.691546 | − | 0.722333i | \(-0.743070\pi\) |
0.279786 | + | 0.960062i | \(0.409737\pi\) | |||||||
\(20\) | −1.98270 | −0.443345 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.60989 | 0.769630 | ||||||||
\(23\) | −7.16531 | + | 4.13690i | −1.49407 | + | 0.862603i | −0.999977 | − | 0.00680565i | \(-0.997834\pi\) |
−0.494095 | + | 0.869408i | \(0.664500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −5.32725 | − | 9.22706i | −1.04476 | − | 1.80958i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.59596 | − | 4.99706i | −0.301608 | − | 0.944356i | ||||
\(29\) | 2.79369i | 0.518775i | 0.965773 | + | 0.259388i | \(0.0835207\pi\) | ||||
−0.965773 | + | 0.259388i | \(0.916479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.71938 | + | 3.87944i | 1.20684 | + | 0.696767i | 0.962067 | − | 0.272814i | \(-0.0879543\pi\) |
0.244770 | + | 0.969581i | \(0.421288\pi\) | |||||||
\(32\) | 6.91269 | + | 3.99104i | 1.22200 | + | 0.705523i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.71996i | 0.637968i | ||||||||
\(35\) | −2.58514 | − | 0.563064i | −0.436969 | − | 0.0951752i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.73210 | + | 6.46419i | 0.613554 | + | 1.06271i | 0.990636 | + | 0.136527i | \(0.0435940\pi\) |
−0.377083 | + | 0.926180i | \(0.623073\pi\) | |||||||
\(38\) | −2.06799 | + | 3.58187i | −0.335473 | + | 0.581056i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0298990 | − | 0.0172622i | 0.00472745 | − | 0.00272939i | ||||
\(41\) | −3.78017 | −0.590363 | −0.295182 | − | 0.955441i | \(-0.595380\pi\) | ||||
−0.295182 | + | 0.955441i | \(0.595380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.14243 | −0.479217 | −0.239608 | − | 0.970870i | \(-0.577019\pi\) | ||||
−0.239608 | + | 0.970870i | \(0.577019\pi\) | |||||||
\(44\) | 3.10594 | − | 1.79321i | 0.468237 | − | 0.270337i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.25588 | + | 14.2996i | −1.21726 | + | 2.10836i | ||||
\(47\) | −2.69021 | − | 4.65958i | −0.392407 | − | 0.679669i | 0.600359 | − | 0.799730i | \(-0.295024\pi\) |
−0.992766 | + | 0.120061i | \(0.961691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.661784 | − | 6.96865i | −0.0945405 | − | 0.995521i | ||||
\(50\) | 1.99567i | 0.282230i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.16710 | − | 5.29263i | −1.27125 | − | 0.733955i | ||||
\(53\) | 4.42119 | + | 2.55257i | 0.607297 | + | 0.350623i | 0.771907 | − | 0.635736i | \(-0.219303\pi\) |
−0.164610 | + | 0.986359i | \(0.552636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.80886i | − | 0.243906i | ||||||
\(56\) | 0.0675734 | + | 0.0614603i | 0.00902988 | + | 0.00821298i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.78764 | + | 4.82834i | 0.366036 | + | 0.633992i | ||||
\(59\) | −4.12369 | + | 7.14244i | −0.536859 | + | 0.929867i | 0.462212 | + | 0.886769i | \(0.347056\pi\) |
−0.999071 | + | 0.0430973i | \(0.986277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.75422 | + | 3.89955i | −0.864789 | + | 0.499286i | −0.865613 | − | 0.500713i | \(-0.833071\pi\) |
0.000823881 | 1.00000i | \(0.499738\pi\) | ||||||||
\(62\) | 15.4842 | 1.96649 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.86101 | 0.982626 | ||||||||
\(65\) | −4.62354 | + | 2.66940i | −0.573480 | + | 0.331099i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.60962 | − | 9.71614i | 0.685324 | − | 1.18702i | −0.288011 | − | 0.957627i | \(-0.592994\pi\) |
0.973335 | − | 0.229388i | \(-0.0736726\pi\) | |||||||
\(68\) | 1.84789 | + | 3.20064i | 0.224090 | + | 0.388135i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.02975 | + | 1.60640i | −0.601170 | + | 0.192002i | ||||
\(71\) | − | 9.97319i | − | 1.18360i | −0.806085 | − | 0.591800i | \(-0.798417\pi\) | ||
0.806085 | − | 0.591800i | \(-0.201583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.2718 | − | 8.23984i | −1.67039 | − | 0.964401i | −0.967418 | − | 0.253184i | \(-0.918522\pi\) |
−0.702973 | − | 0.711217i | \(-0.748144\pi\) | |||||||
\(74\) | 12.9004 | + | 7.44805i | 1.49964 | + | 0.865818i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.10910i | 0.471347i | ||||||||
\(77\) | 4.55892 | − | 1.45603i | 0.519537 | − | 0.165930i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.11854 | + | 3.66941i | 0.238354 | + | 0.412841i | 0.960242 | − | 0.279169i | \(-0.0900589\pi\) |
−0.721888 | + | 0.692010i | \(0.756726\pi\) | |||||||
\(80\) | 2.01715 | − | 3.49381i | 0.225524 | − | 0.390619i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.53327 | + | 3.77199i | −0.721479 | + | 0.416546i | ||||
\(83\) | 9.01001 | 0.988977 | 0.494489 | − | 0.869184i | \(-0.335355\pi\) | ||||
0.494489 | + | 0.869184i | \(0.335355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86402 | 0.202181 | ||||||||
\(86\) | −5.43107 | + | 3.13563i | −0.585648 | + | 0.338124i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0312249 | + | 0.0540831i | −0.00332858 | + | 0.00576528i | ||||
\(89\) | 3.37674 | + | 5.84868i | 0.357933 | + | 0.619959i | 0.987615 | − | 0.156894i | \(-0.0501482\pi\) |
−0.629682 | + | 0.776853i | \(0.716815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4495 | − | 9.50414i | −1.09540 | − | 0.996304i | ||||
\(92\) | 16.4045i | 1.71028i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.29898 | − | 5.36877i | −0.959117 | − | 0.553746i | ||||
\(95\) | 1.79482 | + | 1.03624i | 0.184145 | + | 0.106316i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.19212i | − | 0.222576i | −0.993788 | − | 0.111288i | \(-0.964502\pi\) | ||
0.993788 | − | 0.111288i | \(-0.0354976\pi\) | |||||||
\(98\) | −8.09732 | − | 11.3836i | −0.817953 | − | 1.14991i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.991350 | + | 1.71707i | 0.0991350 | + | 0.171707i | ||||
\(101\) | −2.63704 | + | 4.56749i | −0.262395 | + | 0.454482i | −0.966878 | − | 0.255239i | \(-0.917846\pi\) |
0.704483 | + | 0.709721i | \(0.251179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.68990 | − | 3.28507i | 0.560643 | − | 0.323687i | −0.192761 | − | 0.981246i | \(-0.561744\pi\) |
0.753403 | + | 0.657559i | \(0.228411\pi\) | |||||||
\(104\) | 0.184319 | 0.0180740 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.1882 | 0.989565 | ||||||||
\(107\) | 8.50847 | − | 4.91237i | 0.822545 | − | 0.474897i | −0.0287483 | − | 0.999587i | \(-0.509152\pi\) |
0.851293 | + | 0.524690i | \(0.175819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.55799 | + | 2.69851i | −0.149228 | + | 0.258471i | −0.930942 | − | 0.365166i | \(-0.881012\pi\) |
0.781714 | + | 0.623637i | \(0.214346\pi\) | |||||||
\(110\) | −1.80494 | − | 3.12625i | −0.172095 | − | 0.298077i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.4292 | + | 2.27157i | 0.985470 | + | 0.214643i | ||||
\(113\) | − | 16.5865i | − | 1.56032i | −0.625578 | − | 0.780161i | \(-0.715137\pi\) | ||
0.625578 | − | 0.780161i | \(-0.284863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.16531 | + | 4.13690i | 0.668169 | + | 0.385768i | ||||
\(116\) | 4.79696 | + | 2.76953i | 0.445387 | + | 0.257144i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.4591i | 1.51518i | ||||||||
\(119\) | 1.50043 | + | 4.69794i | 0.137544 | + | 0.430659i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.86401 | − | 6.69267i | −0.351274 | − | 0.608425i | ||||
\(122\) | −7.78222 | + | 13.4792i | −0.704569 | + | 1.22035i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.3225 | − | 7.69176i | 1.19640 | − | 0.690740i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5361 | 1.28987 | 0.644933 | − | 0.764239i | \(-0.276885\pi\) | ||||
0.644933 | + | 0.764239i | \(0.276885\pi\) | |||||||
\(128\) | −0.239183 | + | 0.138092i | −0.0211410 | + | 0.0122058i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.32725 | + | 9.22706i | −0.467231 | + | 0.809267i | ||||
\(131\) | −6.99970 | − | 12.1238i | −0.611567 | − | 1.05926i | −0.990976 | − | 0.134036i | \(-0.957206\pi\) |
0.379410 | − | 0.925229i | \(-0.376127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.16694 | + | 5.35765i | −0.101186 | + | 0.464567i | ||||
\(134\) | − | 22.3899i | − | 1.93419i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0557322 | − | 0.0321770i | −0.00477900 | − | 0.00275916i | ||||
\(137\) | −19.5272 | − | 11.2740i | −1.66832 | − | 0.963206i | −0.968543 | − | 0.248845i | \(-0.919949\pi\) |
−0.699778 | − | 0.714361i | \(-0.746718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.47837i | 0.634307i | 0.948374 | + | 0.317154i | \(0.102727\pi\) | ||||
−0.948374 | + | 0.317154i | \(0.897273\pi\) | |||||||
\(140\) | −3.52960 | + | 3.88067i | −0.298306 | + | 0.327977i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.95160 | − | 17.2367i | −0.835120 | − | 1.44647i | ||||
\(143\) | 4.82857 | − | 8.36333i | 0.403786 | − | 0.699377i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.41941 | − | 1.39685i | 0.200921 | − | 0.116002i | ||||
\(146\) | −32.8880 | −2.72183 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.7993 | 1.21649 | ||||||||
\(149\) | −10.4752 | + | 6.04787i | −0.858164 | + | 0.495461i | −0.863397 | − | 0.504525i | \(-0.831668\pi\) |
0.00523309 | + | 0.999986i | \(0.498334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.22818 | + | 10.7875i | −0.506842 | + | 0.877876i | 0.493126 | + | 0.869958i | \(0.335854\pi\) |
−0.999969 | + | 0.00791876i | \(0.997479\pi\) | |||||||
\(152\) | −0.0357755 | − | 0.0619650i | −0.00290178 | − | 0.00502603i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.42632 | − | 7.06551i | 0.517847 | − | 0.569355i | ||||
\(155\) | − | 7.75887i | − | 0.623208i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4669 | − | 8.35248i | −1.15459 | − | 0.666600i | −0.204585 | − | 0.978849i | \(-0.565584\pi\) |
−0.950000 | + | 0.312249i | \(0.898918\pi\) | |||||||
\(158\) | 7.32294 | + | 4.22790i | 0.582582 | + | 0.336354i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 7.98208i | − | 0.631039i | ||||||
\(161\) | −4.65868 | + | 21.3889i | −0.367155 | + | 1.68568i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.69006 | + | 16.7837i | 0.758984 | + | 1.31460i | 0.943369 | + | 0.331745i | \(0.107637\pi\) |
−0.184385 | + | 0.982854i | \(0.559029\pi\) | |||||||
\(164\) | −3.74747 | + | 6.49081i | −0.292628 | + | 0.506847i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.5720 | − | 8.99051i | 1.20862 | − | 0.697799i | ||||
\(167\) | 21.3710 | 1.65373 | 0.826867 | − | 0.562397i | \(-0.190121\pi\) | ||||
0.826867 | + | 0.562397i | \(0.190121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.5028 | −1.19253 | ||||||||
\(170\) | 3.22158 | − | 1.85998i | 0.247084 | − | 0.142654i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.11525 | + | 5.39577i | −0.237536 | + | 0.411424i | ||||
\(173\) | 8.43701 | + | 14.6133i | 0.641454 | + | 1.11103i | 0.985108 | + | 0.171935i | \(0.0550019\pi\) |
−0.343654 | + | 0.939096i | \(0.611665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.804943 | + | 2.52033i | 0.0608480 | + | 0.190519i | ||||
\(176\) | 7.29748i | 0.550068i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.6720 | + | 6.73885i | 0.874856 | + | 0.505098i | ||||
\(179\) | −16.6564 | − | 9.61657i | −1.24496 | − | 0.718776i | −0.274858 | − | 0.961485i | \(-0.588631\pi\) |
−0.970099 | + | 0.242708i | \(0.921964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.3009i | − | 1.65762i | −0.559533 | − | 0.828808i | \(-0.689020\pi\) | ||
0.559533 | − | 0.828808i | \(-0.310980\pi\) | |||||||
\(182\) | −27.5434 | − | 5.99917i | −2.04165 | − | 0.444688i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.142824 | − | 0.247378i | −0.0105291 | − | 0.0182370i | ||||
\(185\) | 3.73210 | − | 6.46419i | 0.274390 | − | 0.475257i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.92001 | + | 1.68587i | −0.213533 | + | 0.123283i | ||||
\(188\) | −10.6678 | −0.778026 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.13598 | 0.300056 | ||||||||
\(191\) | 15.9342 | − | 9.19964i | 1.15296 | − | 0.665662i | 0.203354 | − | 0.979105i | \(-0.434816\pi\) |
0.949607 | + | 0.313443i | \(0.101482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.12854 | − | 3.68674i | 0.153216 | − | 0.265377i | −0.779192 | − | 0.626785i | \(-0.784370\pi\) |
0.932408 | + | 0.361408i | \(0.117704\pi\) | |||||||
\(194\) | −2.18737 | − | 3.78864i | −0.157044 | − | 0.272008i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.6217 | − | 5.77204i | −0.901550 | − | 0.412289i | ||||
\(197\) | − | 1.54805i | − | 0.110294i | −0.998478 | − | 0.0551471i | \(-0.982437\pi\) | ||
0.998478 | − | 0.0551471i | \(-0.0175628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.13199 | − | 0.653554i | −0.0802445 | − | 0.0463292i | 0.459341 | − | 0.888260i | \(-0.348086\pi\) |
−0.539585 | + | 0.841931i | \(0.681419\pi\) | |||||||
\(200\) | −0.0298990 | − | 0.0172622i | −0.00211418 | − | 0.00122062i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5253i | 0.740559i | ||||||||
\(203\) | 5.46800 | + | 4.97333i | 0.383778 | + | 0.349059i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.89008 | + | 3.27372i | 0.132009 | + | 0.228647i | ||||
\(206\) | 6.55591 | − | 11.3552i | 0.456772 | − | 0.791152i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.6528 | − | 10.7692i | 1.29334 | − | 0.746708i | ||||
\(209\) | −3.74882 | −0.259311 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.71043 | −0.530808 | −0.265404 | − | 0.964137i | \(-0.585505\pi\) | ||||
−0.265404 | + | 0.964137i | \(0.585505\pi\) | |||||||
\(212\) | 8.76589 | − | 5.06099i | 0.602044 | − | 0.347590i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.80347 | − | 16.9801i | 0.670151 | − | 1.16074i | ||||
\(215\) | 1.57122 | + | 2.72143i | 0.107156 | + | 0.185600i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5549 | − | 6.24545i | 1.32747 | − | 0.423969i | ||||
\(218\) | 6.21846i | 0.421167i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.10594 | − | 1.79321i | −0.209402 | − | 0.120898i | ||||
\(221\) | 8.61836 | + | 4.97581i | 0.579733 | + | 0.334709i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.20752i | 0.281756i | 0.990027 | + | 0.140878i | \(0.0449926\pi\) | ||||
−0.990027 | + | 0.140878i | \(0.955007\pi\) | |||||||
\(224\) | 20.1175 | − | 6.42512i | 1.34416 | − | 0.429297i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.5506 | − | 28.6664i | −1.10093 | − | 1.90686i | ||||
\(227\) | −1.77198 | + | 3.06915i | −0.117610 | + | 0.203707i | −0.918820 | − | 0.394677i | \(-0.870857\pi\) |
0.801210 | + | 0.598383i | \(0.204190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4045 | + | 11.2032i | −1.28229 | + | 0.740329i | −0.977266 | − | 0.212017i | \(-0.931997\pi\) |
−0.305021 | + | 0.952346i | \(0.598664\pi\) | |||||||
\(230\) | 16.5118 | 1.08875 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0964505 | −0.00633229 | ||||||||
\(233\) | 20.8118 | − | 12.0157i | 1.36343 | − | 0.787175i | 0.373349 | − | 0.927691i | \(-0.378209\pi\) |
0.990078 | + | 0.140516i | \(0.0448760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.69021 | + | 4.65958i | −0.175490 | + | 0.303957i | ||||
\(236\) | 8.17604 | + | 14.1613i | 0.532215 | + | 0.921824i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.28096 | + | 6.62227i | 0.471954 | + | 0.429258i | ||||
\(239\) | − | 12.0933i | − | 0.782249i | −0.920338 | − | 0.391125i | \(-0.872086\pi\) | ||
0.920338 | − | 0.391125i | \(-0.127914\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3791 | + | 12.9206i | 1.44156 | + | 0.832287i | 0.997954 | − | 0.0639341i | \(-0.0203647\pi\) |
0.443609 | + | 0.896221i | \(0.353698\pi\) | |||||||
\(242\) | −13.3564 | − | 7.71130i | −0.858580 | − | 0.495701i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.4633i | 0.989935i | ||||||||
\(245\) | −5.70413 | + | 4.05744i | −0.364424 | + | 0.259221i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.53228 | + | 9.58219i | 0.352011 | + | 0.609700i | ||||
\(248\) | −0.133935 | + | 0.231983i | −0.00850490 | + | 0.0147309i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.72830 | − | 0.997835i | 0.109307 | − | 0.0631086i | ||||
\(251\) | 8.73604 | 0.551414 | 0.275707 | − | 0.961242i | \(-0.411088\pi\) | ||||
0.275707 | + | 0.961242i | \(0.411088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.9661 | −0.940912 | ||||||||
\(254\) | 25.1227 | − | 14.5046i | 1.57634 | − | 0.910099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.13660 | + | 14.0930i | −0.508537 | + | 0.880812i | ||||
\(257\) | 1.59437 | + | 2.76152i | 0.0994538 | + | 0.172259i | 0.911459 | − | 0.411392i | \(-0.134957\pi\) |
−0.812005 | + | 0.583651i | \(0.801624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.2960 | + | 4.20283i | 1.19900 | + | 0.261151i | ||||
\(260\) | 10.5853i | 0.656469i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.1952 | − | 13.9691i | −1.49478 | − | 0.863014i | ||||
\(263\) | −3.69226 | − | 2.13173i | −0.227674 | − | 0.131448i | 0.381824 | − | 0.924235i | \(-0.375296\pi\) |
−0.609499 | + | 0.792787i | \(0.708629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.10515i | − | 0.313607i | ||||||
\(266\) | 3.32923 | + | 10.4240i | 0.204128 | + | 0.639139i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.1222 | − | 19.2642i | −0.679396 | − | 1.17675i | ||||
\(269\) | −7.60636 | + | 13.1746i | −0.463768 | + | 0.803270i | −0.999145 | − | 0.0413434i | \(-0.986836\pi\) |
0.535377 | + | 0.844613i | \(0.320170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7593 | − | 7.36660i | 0.775074 | − | 0.447489i | −0.0596080 | − | 0.998222i | \(-0.518985\pi\) |
0.834682 | + | 0.550733i | \(0.185652\pi\) | |||||||
\(272\) | −7.52000 | −0.455967 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −44.9985 | −2.71846 | ||||||||
\(275\) | −1.56652 | + | 0.904429i | −0.0944646 | + | 0.0545391i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.556865 | + | 0.964519i | −0.0334588 | + | 0.0579523i | −0.882270 | − | 0.470744i | \(-0.843986\pi\) |
0.848811 | + | 0.528696i | \(0.177319\pi\) | |||||||
\(278\) | 7.46218 | + | 12.9249i | 0.447552 | + | 0.775183i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0194395 | − | 0.0892505i | 0.00116173 | − | 0.00533374i | ||||
\(281\) | 2.52283i | 0.150499i | 0.997165 | + | 0.0752496i | \(0.0239753\pi\) | ||||
−0.997165 | + | 0.0752496i | \(0.976025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.73524 | − | 1.57919i | −0.162593 | − | 0.0938731i | 0.416496 | − | 0.909138i | \(-0.363258\pi\) |
−0.579089 | + | 0.815265i | \(0.696591\pi\) | |||||||
\(284\) | −17.1247 | − | 9.88693i | −1.01616 | − | 0.586681i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 19.2725i | − | 1.13961i | ||||||
\(287\) | −6.72945 | + | 7.39880i | −0.397227 | + | 0.436737i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.76272 | + | 11.7134i | 0.397807 | + | 0.689022i | ||||
\(290\) | 2.78764 | − | 4.82834i | 0.163696 | − | 0.283530i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.2968 | + | 16.3371i | −1.65594 | + | 0.956059i | ||||
\(293\) | −19.0936 | −1.11546 | −0.557731 | − | 0.830022i | \(-0.688328\pi\) | ||||
−0.557731 | + | 0.830022i | \(0.688328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.24738 | 0.480181 | ||||||||
\(296\) | −0.223172 | + | 0.128849i | −0.0129716 | + | 0.00748917i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.0696 | + | 20.9051i | −0.699171 | + | 1.21100i | ||||
\(299\) | 22.0861 | + | 38.2542i | 1.27727 | + | 2.21230i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.59416 | + | 6.15058i | −0.322442 | + | 0.354513i | ||||
\(302\) | 24.8588i | 1.43046i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.24084 | − | 4.18050i | −0.415291 | − | 0.239768i | ||||
\(305\) | 6.75422 | + | 3.89955i | 0.386746 | + | 0.223288i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.53113i | 0.429825i | 0.976633 | + | 0.214912i | \(0.0689466\pi\) | ||||
−0.976633 | + | 0.214912i | \(0.931053\pi\) | |||||||
\(308\) | 2.01939 | − | 9.27142i | 0.115065 | − | 0.528288i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.74208 | − | 13.4097i | −0.439720 | − | 0.761618i | ||||
\(311\) | 5.05582 | − | 8.75693i | 0.286689 | − | 0.496560i | −0.686328 | − | 0.727292i | \(-0.740779\pi\) |
0.973017 | + | 0.230732i | \(0.0741120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8782 | + | 6.85785i | −0.671393 | + | 0.387629i | −0.796604 | − | 0.604501i | \(-0.793372\pi\) |
0.125211 | + | 0.992130i | \(0.460039\pi\) | |||||||
\(314\) | −33.3376 | −1.88135 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.40084 | 0.472584 | ||||||||
\(317\) | 2.60874 | − | 1.50616i | 0.146521 | − | 0.0845942i | −0.424947 | − | 0.905218i | \(-0.639707\pi\) |
0.571468 | + | 0.820624i | \(0.306374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.52670 | + | 4.37637i | −0.141468 | + | 0.245029i | ||||
\(320\) | −3.93050 | − | 6.80783i | −0.219722 | − | 0.380569i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.2910 | + | 41.6151i | 0.740680 | + | 2.31912i | ||||
\(323\) | − | 3.86313i | − | 0.214950i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.62354 | + | 2.66940i | 0.256468 | + | 0.148072i | ||||
\(326\) | 33.4947 | + | 19.3382i | 1.85510 | + | 1.07104i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 0.130508i | − | 0.00720610i | ||||||
\(329\) | −13.9091 | − | 3.02952i | −0.766836 | − | 0.167023i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.57680 | + | 9.65930i | 0.306529 | + | 0.530923i | 0.977600 | − | 0.210469i | \(-0.0674992\pi\) |
−0.671072 | + | 0.741392i | \(0.734166\pi\) | |||||||
\(332\) | 8.93208 | − | 15.4708i | 0.490211 | − | 0.849071i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 36.9355 | − | 21.3247i | 2.02102 | − | 1.16684i | ||||
\(335\) | −11.2192 | −0.612972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3801 | −0.728858 | −0.364429 | − | 0.931231i | \(-0.618736\pi\) | ||||
−0.364429 | + | 0.931231i | \(0.618736\pi\) | |||||||
\(338\) | −26.7936 | + | 15.4693i | −1.45738 | + | 0.841418i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.84789 | − | 3.20064i | 0.100216 | − | 0.173579i | ||||
\(341\) | 7.01735 | + | 12.1544i | 0.380011 | + | 0.658198i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.8176 | − | 11.1103i | −0.800075 | − | 0.599899i | ||||
\(344\) | − | 0.108491i | − | 0.00584942i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.1634 | + | 16.8375i | 1.56783 | + | 0.905189i | ||||
\(347\) | −21.2782 | − | 12.2850i | −1.14227 | − | 0.659491i | −0.195279 | − | 0.980748i | \(-0.562561\pi\) |
−0.946992 | + | 0.321257i | \(0.895895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2270i | 1.02920i | 0.857431 | + | 0.514599i | \(0.172059\pi\) | ||||
−0.857431 | + | 0.514599i | \(0.827941\pi\) | |||||||
\(350\) | 3.90606 | + | 3.55269i | 0.208788 | + | 0.189899i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.21923 | + | 12.5041i | 0.384786 | + | 0.666469i | ||||
\(353\) | 0.255875 | − | 0.443188i | 0.0136188 | − | 0.0235885i | −0.859136 | − | 0.511748i | \(-0.828998\pi\) |
0.872755 | + | 0.488159i | \(0.162332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.63704 | + | 4.98660i | −0.458406 | + | 0.264661i | ||||
\(356\) | 13.3901 | 0.709674 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.3830 | −2.02861 | ||||||||
\(359\) | −17.1761 | + | 9.91665i | −0.906522 | + | 0.523381i | −0.879311 | − | 0.476249i | \(-0.841996\pi\) |
−0.0272117 | + | 0.999630i | \(0.508663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.35242 | + | 12.7348i | −0.386969 | + | 0.670250i | ||||
\(362\) | −22.2527 | − | 38.5427i | −1.16957 | − | 2.02576i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −26.6783 | + | 8.52052i | −1.39832 | + | 0.446597i | ||||
\(365\) | 16.4797i | 0.862586i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6842 | + | 10.2100i | 0.923110 | + | 0.532958i | 0.884626 | − | 0.466301i | \(-0.154414\pi\) |
0.0384841 | + | 0.999259i | \(0.487747\pi\) | |||||||
\(368\) | −28.9070 | − | 16.6895i | −1.50688 | − | 0.869999i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 14.8961i | − | 0.774411i | ||||||
\(371\) | 12.8667 | − | 4.10935i | 0.668004 | − | 0.213347i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.637766 | + | 1.10464i | 0.0330223 | + | 0.0571962i | 0.882064 | − | 0.471129i | \(-0.156153\pi\) |
−0.849042 | + | 0.528325i | \(0.822820\pi\) | |||||||
\(374\) | −3.36444 | + | 5.82739i | −0.173971 | + | 0.301327i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.160869 | − | 0.0928778i | 0.00829619 | − | 0.00478981i | ||||
\(377\) | 14.9150 | 0.768160 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.4590 | 1.82140 | 0.910702 | − | 0.413063i | \(-0.135541\pi\) | ||||
0.910702 | + | 0.413063i | \(0.135541\pi\) | |||||||
\(380\) | 3.55859 | − | 2.05455i | 0.182552 | − | 0.105396i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.3594 | − | 31.7995i | 0.939351 | − | 1.62700i | ||||
\(383\) | −7.98563 | − | 13.8315i | −0.408046 | − | 0.706757i | 0.586624 | − | 0.809859i | \(-0.300457\pi\) |
−0.994671 | + | 0.103102i | \(0.967123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54042 | − | 3.22013i | −0.180436 | − | 0.164113i | ||||
\(386\) | − | 8.49573i | − | 0.432421i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.76401 | − | 2.17315i | −0.191089 | − | 0.110325i | ||||
\(389\) | 9.81632 | + | 5.66745i | 0.497707 | + | 0.287351i | 0.727766 | − | 0.685825i | \(-0.240559\pi\) |
−0.230059 | + | 0.973177i | \(0.573892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.4225i | − | 0.779949i | ||||||
\(392\) | 0.240588 | − | 0.0228477i | 0.0121515 | − | 0.00115398i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.54470 | − | 2.67550i | −0.0778210 | − | 0.134790i | ||||
\(395\) | 2.11854 | − | 3.66941i | 0.106595 | − | 0.184628i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.1694 | + | 15.1089i | −1.31341 | + | 0.758295i | −0.982659 | − | 0.185424i | \(-0.940634\pi\) |
−0.330747 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(398\) | −2.60855 | −0.130755 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.03430 | −0.201715 | ||||||||
\(401\) | −1.14576 | + | 0.661503i | −0.0572163 | + | 0.0330339i | −0.528335 | − | 0.849036i | \(-0.677184\pi\) |
0.471119 | + | 0.882070i | \(0.343850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7116 | − | 35.8735i | 1.03172 | − | 1.78698i | ||||
\(404\) | 5.22846 | + | 9.05596i | 0.260126 | + | 0.450551i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.4129 | + | 3.13924i | 0.715301 | + | 0.155798i | ||||
\(407\) | 13.5017i | 0.669254i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.6927 | + | 17.1431i | 1.46821 | + | 0.847671i | 0.999366 | − | 0.0356099i | \(-0.0113374\pi\) |
0.468844 | + | 0.883281i | \(0.344671\pi\) | |||||||
\(410\) | 6.53327 | + | 3.77199i | 0.322655 | + | 0.186285i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 13.0266i | − | 0.641775i | ||||||
\(413\) | 6.63867 | + | 20.7861i | 0.326668 | + | 1.02282i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.50501 | − | 7.80290i | −0.221142 | − | 0.383029i | ||||
\(416\) | 21.3074 | − | 36.9055i | 1.04468 | − | 1.80944i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.47909 | + | 3.74071i | −0.316903 | + | 0.182964i | ||||
\(419\) | −0.342185 | −0.0167168 | −0.00835841 | − | 0.999965i | \(-0.502661\pi\) | ||||
−0.00835841 | + | 0.999965i | \(0.502661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.27017 | −0.354326 | −0.177163 | − | 0.984181i | \(-0.556692\pi\) | ||||
−0.177163 | + | 0.984181i | \(0.556692\pi\) | |||||||
\(422\) | −13.3260 | + | 7.69374i | −0.648697 | + | 0.374526i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0881261 | + | 0.152639i | −0.00427978 | + | 0.00741280i | ||||
\(425\) | −0.932008 | − | 1.61429i | −0.0452090 | − | 0.0783043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.39140 | + | 20.1618i | −0.212515 | + | 0.975697i | ||||
\(428\) | − | 19.4795i | − | 0.941578i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.43107 | + | 3.13563i | 0.261910 | + | 0.151214i | ||||
\(431\) | −3.38713 | − | 1.95556i | −0.163152 | − | 0.0941960i | 0.416201 | − | 0.909273i | \(-0.363361\pi\) |
−0.579353 | + | 0.815077i | \(0.696695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.8856i | − | 1.19592i | −0.801525 | − | 0.597962i | \(-0.795977\pi\) | ||
0.801525 | − | 0.597962i | \(-0.204023\pi\) | |||||||
\(434\) | 27.5649 | − | 30.3066i | 1.32316 | − | 1.45476i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.08902 | + | 5.35035i | 0.147937 | + | 0.256235i | ||||
\(437\) | 8.57363 | − | 14.8500i | 0.410132 | − | 0.710370i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2143 | + | 7.05192i | −0.582956 | + | 0.336570i | −0.762307 | − | 0.647215i | \(-0.775933\pi\) |
0.179351 | + | 0.983785i | \(0.442600\pi\) | |||||||
\(440\) | 0.0624498 | 0.00297718 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.8602 | 0.944651 | ||||||||
\(443\) | 10.0493 | − | 5.80194i | 0.477454 | − | 0.275658i | −0.241901 | − | 0.970301i | \(-0.577771\pi\) |
0.719355 | + | 0.694643i | \(0.244437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.37674 | − | 5.84868i | 0.160073 | − | 0.277254i | ||||
\(446\) | 4.19841 | + | 7.27186i | 0.198801 | + | 0.344333i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.9942 | − | 15.3861i | 0.661162 | − | 0.726924i | ||||
\(449\) | − | 7.84978i | − | 0.370454i | −0.982696 | − | 0.185227i | \(-0.940698\pi\) | ||
0.982696 | − | 0.185227i | \(-0.0593021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.92170 | − | 3.41890i | −0.278842 | − | 0.160990i | ||||
\(452\) | −28.4801 | − | 16.4430i | −1.33959 | − | 0.773413i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.07256i | 0.331932i | ||||||||
\(455\) | −3.00609 | + | 13.8016i | −0.140928 | + | 0.647028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.774175 | + | 1.34091i | 0.0362144 | + | 0.0627252i | 0.883565 | − | 0.468309i | \(-0.155137\pi\) |
−0.847350 | + | 0.531035i | \(0.821803\pi\) | |||||||
\(458\) | −22.3579 | + | 38.7250i | −1.04472 | + | 1.80950i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.2067 | − | 8.20223i | 0.662389 | − | 0.382431i | ||||
\(461\) | 10.5782 | 0.492678 | 0.246339 | − | 0.969184i | \(-0.420772\pi\) | ||||
0.246339 | + | 0.969184i | \(0.420772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.32833 | 0.340576 | 0.170288 | − | 0.985394i | \(-0.445530\pi\) | ||||
0.170288 | + | 0.985394i | \(0.445530\pi\) | |||||||
\(464\) | −9.76062 | + | 5.63529i | −0.453125 | + | 0.261612i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.9794 | − | 41.5335i | 1.11082 | − | 1.92400i | ||||
\(467\) | 1.92851 | + | 3.34028i | 0.0892409 | + | 0.154570i | 0.907190 | − | 0.420720i | \(-0.138223\pi\) |
−0.817950 | + | 0.575290i | \(0.804889\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.03084 | − | 28.2762i | −0.417006 | − | 1.30567i | ||||
\(470\) | 10.7375i | 0.495286i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.246589 | − | 0.142368i | −0.0113502 | − | 0.00655302i | ||||
\(473\) | −4.92268 | − | 2.84211i | −0.226345 | − | 0.130680i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.07248i | − | 0.0950918i | ||||||
\(476\) | 9.55413 | + | 2.08096i | 0.437913 | + | 0.0953809i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0671 | − | 20.9008i | −0.551936 | − | 0.955982i | ||||
\(479\) | 9.52418 | − | 16.4964i | 0.435171 | − | 0.753738i | −0.562139 | − | 0.827043i | \(-0.690021\pi\) |
0.997310 | + | 0.0733051i | \(0.0233547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.5111 | − | 19.9250i | 1.57357 | − | 0.908500i | ||||
\(482\) | 51.5704 | 2.34897 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.3224 | −0.696471 | ||||||||
\(485\) | −1.89843 | + | 1.09606i | −0.0862032 | + | 0.0497694i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.79075 | − | 6.56577i | 0.171775 | − | 0.297523i | −0.767265 | − | 0.641330i | \(-0.778383\pi\) |
0.939041 | + | 0.343806i | \(0.111716\pi\) | |||||||
\(488\) | −0.134630 | − | 0.233185i | −0.00609440 | − | 0.0105558i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.80980 | + | 12.7043i | −0.262460 | + | 0.573921i | ||||
\(491\) | − | 22.2505i | − | 1.00415i | −0.864824 | − | 0.502075i | \(-0.832570\pi\) | ||
0.864824 | − | 0.502075i | \(-0.167430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.50981 | − | 2.60374i | −0.203112 | − | 0.117267i | ||||
\(494\) | 19.1229 | + | 11.0406i | 0.860380 | + | 0.496740i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.3016i | 1.40548i | ||||||||
\(497\) | −19.5202 | − | 17.7543i | −0.875601 | − | 0.796388i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7031 | − | 23.7344i | −0.613434 | − | 1.06250i | −0.990657 | − | 0.136377i | \(-0.956454\pi\) |
0.377223 | − | 0.926123i | \(-0.376879\pi\) | |||||||
\(500\) | 0.991350 | − | 1.71707i | 0.0443345 | − | 0.0767897i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.0985 | − | 8.71713i | 0.673880 | − | 0.389065i | ||||
\(503\) | 17.6283 | 0.786008 | 0.393004 | − | 0.919537i | \(-0.371436\pi\) | ||||
0.393004 | + | 0.919537i | \(0.371436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.27408 | 0.234693 | ||||||||
\(506\) | −25.8660 | + | 14.9337i | −1.14988 | + | 0.663885i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.4103 | − | 24.9594i | 0.639354 | − | 1.10739i | ||||
\(509\) | −18.0257 | − | 31.2214i | −0.798974 | − | 1.38386i | −0.920285 | − | 0.391250i | \(-0.872043\pi\) |
0.121310 | − | 0.992615i | \(-0.461290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.5343 | + | 13.2652i | −1.83737 | + | 0.586818i | ||||
\(512\) | 31.9236i | 1.41084i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.51109 | + | 3.18183i | 0.243084 | + | 0.140344i | ||||
\(515\) | −5.68990 | − | 3.28507i | −0.250727 | − | 0.144757i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.73241i | − | 0.428031i | ||||||
\(518\) | 37.5431 | − | 11.9905i | 1.64955 | − | 0.526833i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0921595 | − | 0.159625i | −0.00404146 | − | 0.00700002i | ||||
\(521\) | 0.602560 | − | 1.04366i | 0.0263986 | − | 0.0457238i | −0.852524 | − | 0.522688i | \(-0.824929\pi\) |
0.878923 | + | 0.476964i | \(0.158263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.4149 | + | 8.32246i | −0.630321 | + | 0.363916i | −0.780876 | − | 0.624686i | \(-0.785227\pi\) |
0.150556 | + | 0.988602i | \(0.451894\pi\) | |||||||
\(524\) | −27.7566 | −1.21255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.50844 | −0.370986 | ||||||||
\(527\) | −12.5250 | + | 7.23133i | −0.545599 | + | 0.315002i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7278 | − | 39.3657i | 0.988166 | − | 1.71155i | ||||
\(530\) | −5.09410 | − | 8.82324i | −0.221273 | − | 0.383257i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.04261 | + | 7.31502i | 0.348691 | + | 0.317146i | ||||
\(533\) | 20.1816i | 0.874162i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.50847 | − | 4.91237i | −0.367853 | − | 0.212380i | ||||
\(536\) | 0.335444 | + | 0.193669i | 0.0144890 | + | 0.00836521i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.3596i | 1.30889i | ||||||||
\(539\) | 5.26595 | − | 11.5150i | 0.226821 | − | 0.495988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3861 | + | 28.3815i | 0.704492 | + | 1.22022i | 0.966875 | + | 0.255252i | \(0.0821583\pi\) |
−0.262383 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(542\) | 14.7013 | − | 25.4634i | 0.631475 | − | 1.09375i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.8854 | + | 7.43937i | −0.552455 | + | 0.318960i | ||||
\(545\) | 3.11598 | 0.133474 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.72308 | 0.287458 | 0.143729 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143729 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(548\) | −38.7166 | + | 22.3530i | −1.65389 | + | 0.954874i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.80494 | + | 3.12625i | −0.0769630 | + | 0.133304i | ||||
\(551\) | −2.89493 | − | 5.01417i | −0.123328 | − | 0.213611i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9534 | + | 2.38574i | 0.465787 | + | 0.101452i | ||||
\(554\) | 2.22264i | 0.0944309i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8409 | + | 7.41369i | 0.544575 | + | 0.314410i | ||||
\(557\) | 11.7751 | + | 6.79833i | 0.498925 | + | 0.288054i | 0.728269 | − | 0.685291i | \(-0.240325\pi\) |
−0.229345 | + | 0.973345i | \(0.573658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7768i | 0.709585i | ||||||||
\(560\) | −3.24738 | − | 10.1678i | −0.137227 | − | 0.429667i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.51736 | + | 4.36020i | 0.106189 | + | 0.183924i | ||||
\(563\) | −7.57270 | + | 13.1163i | −0.319151 | + | 0.552786i | −0.980311 | − | 0.197459i | \(-0.936731\pi\) |
0.661160 | + | 0.750245i | \(0.270064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3643 | + | 8.29323i | −0.604310 | + | 0.348899i | ||||
\(566\) | −6.30308 | −0.264938 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.344319 | 0.0144473 | ||||||||
\(569\) | −12.4624 | + | 7.19517i | −0.522451 | + | 0.301637i | −0.737937 | − | 0.674870i | \(-0.764200\pi\) |
0.215486 | + | 0.976507i | \(0.430866\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.14329 | − | 14.1046i | 0.340786 | − | 0.590259i | −0.643793 | − | 0.765200i | \(-0.722640\pi\) |
0.984579 | + | 0.174941i | \(0.0559735\pi\) | |||||||
\(572\) | −9.57361 | − | 16.5820i | −0.400293 | − | 0.693328i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.24774 | + | 19.5022i | −0.177297 | + | 0.814008i | ||||
\(575\) | − | 8.27379i | − | 0.345041i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.3542 | − | 18.6797i | −1.34692 | − | 0.777646i | −0.359110 | − | 0.933295i | \(-0.616920\pi\) |
−0.987812 | + | 0.155649i | \(0.950253\pi\) | |||||||
\(578\) | 23.3760 | + | 13.4962i | 0.972315 | + | 0.561366i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 5.53905i | − | 0.229997i | ||||||
\(581\) | 16.0396 | − | 17.6350i | 0.665435 | − | 0.731623i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.61725 | + | 7.99731i | 0.191227 | + | 0.331215i | ||||
\(584\) | 0.284476 | − | 0.492726i | 0.0117717 | − | 0.0203892i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.9996 | + | 19.0523i | −1.36320 | + | 0.787043i | ||||
\(587\) | −0.949011 | −0.0391699 | −0.0195849 | − | 0.999808i | \(-0.506234\pi\) | ||||
−0.0195849 | + | 0.999808i | \(0.506234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0801 | −0.662569 | ||||||||
\(590\) | 14.2540 | − | 8.22953i | 0.586826 | − | 0.338804i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.0564 | + | 26.0785i | −0.618815 | + | 1.07182i | ||||
\(593\) | −22.4865 | − | 38.9477i | −0.923409 | − | 1.59939i | −0.794100 | − | 0.607788i | \(-0.792057\pi\) |
−0.129310 | − | 0.991604i | \(-0.541276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.31832 | − | 3.64838i | 0.136038 | − | 0.149569i | ||||
\(596\) | 23.9822i | 0.982351i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 76.3428 | + | 44.0765i | 3.12189 | + | 1.80242i | ||||
\(599\) | −9.36411 | − | 5.40637i | −0.382607 | − | 0.220898i | 0.296345 | − | 0.955081i | \(-0.404232\pi\) |
−0.678952 | + | 0.734183i | \(0.737566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.8186i | − | 1.09395i | −0.837148 | − | 0.546976i | \(-0.815779\pi\) | ||
0.837148 | − | 0.546976i | \(-0.184221\pi\) | |||||||
\(602\) | −3.53112 | + | 16.2121i | −0.143918 | + | 0.660756i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3486 | + | 21.3884i | 0.502458 | + | 0.870283i | ||||
\(605\) | −3.86401 | + | 6.69267i | −0.157095 | + | 0.272096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.15663 | + | 2.97718i | −0.209301 | + | 0.120840i | −0.600987 | − | 0.799259i | \(-0.705225\pi\) |
0.391685 | + | 0.920099i | \(0.371892\pi\) | |||||||
\(608\) | −16.5427 | −0.670895 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.5644 | 0.630186 | ||||||||
\(611\) | −24.8766 | + | 14.3625i | −1.00640 | + | 0.581045i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.10422 | + | 1.91257i | −0.0445991 | + | 0.0772478i | −0.887463 | − | 0.460879i | \(-0.847534\pi\) |
0.842864 | + | 0.538126i | \(0.180868\pi\) | |||||||
\(614\) | 7.51483 | + | 13.0161i | 0.303274 | + | 0.525286i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0502685 | + | 0.157394i | 0.00202538 | + | 0.00634159i | ||||
\(617\) | 4.90850i | 0.197609i | 0.995107 | + | 0.0988043i | \(0.0315018\pi\) | ||||
−0.995107 | + | 0.0988043i | \(0.968498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.3950 | + | 10.6203i | 0.739357 | + | 0.426868i | 0.821835 | − | 0.569725i | \(-0.192950\pi\) |
−0.0824787 | + | 0.996593i | \(0.526284\pi\) | |||||||
\(620\) | −13.3225 | − | 7.69176i | −0.535045 | − | 0.308909i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 20.1795i | − | 0.809124i | ||||||
\(623\) | 17.4587 | + | 3.80264i | 0.699467 | + | 0.152350i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −13.6860 | + | 23.7049i | −0.547003 | + | 0.947437i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.6836 | + | 16.5605i | −1.14460 | + | 0.660834i | ||||
\(629\) | −13.9134 | −0.554764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6373 | 0.741941 | 0.370971 | − | 0.928645i | \(-0.379025\pi\) | ||||
0.370971 | + | 0.928645i | \(0.379025\pi\) | |||||||
\(632\) | −0.126684 | + | 0.0731412i | −0.00503923 | + | 0.00290940i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.00579 | − | 5.20619i | 0.119375 | − | 0.206764i | ||||
\(635\) | −7.26803 | − | 12.5886i | −0.288423 | − | 0.499563i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.2043 | + | 3.53313i | −1.47409 | + | 0.139988i | ||||
\(638\) | 10.0849i | 0.399265i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.239183 | + | 0.138092i | 0.00945454 | + | 0.00545858i | ||||
\(641\) | −22.2460 | − | 12.8438i | −0.878665 | − | 0.507298i | −0.00844724 | − | 0.999964i | \(-0.502689\pi\) |
−0.870218 | + | 0.492667i | \(0.836022\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6090i | 0.536688i | 0.963323 | + | 0.268344i | \(0.0864763\pi\) | ||||
−0.963323 | + | 0.268344i | \(0.913524\pi\) | |||||||
\(644\) | 32.1079 | + | 29.2032i | 1.26523 | + | 1.15077i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.85477 | − | 6.67666i | −0.151664 | − | 0.262690i | ||||
\(647\) | −24.1947 | + | 41.9064i | −0.951190 | + | 1.64751i | −0.208335 | + | 0.978057i | \(0.566805\pi\) |
−0.742855 | + | 0.669452i | \(0.766529\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9197 | + | 7.45917i | −0.507141 | + | 0.292798i | ||||
\(650\) | 10.6545 | 0.417904 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 38.4250 | 1.50484 | ||||||||
\(653\) | 30.6260 | − | 17.6819i | 1.19849 | − | 0.691948i | 0.238271 | − | 0.971199i | \(-0.423420\pi\) |
0.960218 | + | 0.279251i | \(0.0900862\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.99970 | + | 12.1238i | −0.273501 | + | 0.473718i | ||||
\(656\) | −7.62517 | − | 13.2072i | −0.297713 | − | 0.515654i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.0621 | + | 8.64311i | −1.05499 | + | 0.336943i | ||||
\(659\) | − | 13.1110i | − | 0.510733i | −0.966844 | − | 0.255366i | \(-0.917804\pi\) | ||
0.966844 | − | 0.255366i | \(-0.0821961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8985 | − | 9.75637i | −0.657277 | − | 0.379479i | 0.133962 | − | 0.990987i | \(-0.457230\pi\) |
−0.791239 | + | 0.611508i | \(0.790563\pi\) | |||||||
\(662\) | 19.2768 | + | 11.1295i | 0.749213 | + | 0.432558i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.311065i | 0.0120717i | ||||||||
\(665\) | 5.22333 | − | 1.66823i | 0.202552 | − | 0.0646911i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5572 | − | 20.0177i | −0.447497 | − | 0.775088i | ||||
\(668\) | 21.1861 | − | 36.6954i | 0.819715 | − | 1.41979i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.3902 | + | 11.1949i | −0.749109 | + | 0.432498i | ||||
\(671\) | −14.1075 | −0.544613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.89071 | 0.188523 | 0.0942615 | − | 0.995547i | \(-0.469951\pi\) | ||||
0.0942615 | + | 0.995547i | \(0.469951\pi\) | |||||||
\(674\) | −23.1248 | + | 13.3511i | −0.890733 | + | 0.514265i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.3687 | + | 26.6194i | −0.591106 | + | 1.02382i | ||||
\(677\) | 2.74948 | + | 4.76225i | 0.105671 | + | 0.183028i | 0.914012 | − | 0.405687i | \(-0.132968\pi\) |
−0.808341 | + | 0.588715i | \(0.799634\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.29056 | − | 3.90240i | −0.164656 | − | 0.149760i | ||||
\(680\) | 0.0643540i | 0.00246786i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.2562 | + | 14.0043i | 0.928818 | + | 0.536253i | ||||
\(683\) | 24.6812 | + | 14.2497i | 0.944398 | + | 0.545249i | 0.891336 | − | 0.453343i | \(-0.149769\pi\) |
0.0530621 | + | 0.998591i | \(0.483102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.5481i | 0.861517i | ||||||||
\(686\) | −36.6955 | − | 4.41640i | −1.40104 | − | 0.168619i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.33876 | − | 10.9791i | −0.241663 | − | 0.418572i | ||||
\(689\) | 13.6277 | − | 23.6039i | 0.519174 | − | 0.899236i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0876 | + | 14.4843i | −0.954377 | + | 0.551010i | −0.894438 | − | 0.447192i | \(-0.852424\pi\) |
−0.0599391 | + | 0.998202i | \(0.519091\pi\) | |||||||
\(692\) | 33.4561 | 1.27181 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −49.0334 | −1.86128 | ||||||||
\(695\) | 6.47646 | − | 3.73919i | 0.245666 | − | 0.141835i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.52315 | − | 6.10227i | 0.133449 | − | 0.231140i | ||||
\(698\) | 19.1854 | + | 33.2301i | 0.726178 | + | 1.25778i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.12556 | + | 1.11639i | 0.193728 | + | 0.0421955i | ||||
\(701\) | 48.8594i | 1.84539i | 0.385527 | + | 0.922697i | \(0.374020\pi\) | ||||
−0.385527 | + | 0.922697i | \(0.625980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3969 | − | 7.73470i | −0.505274 | − | 0.291720i | ||||
\(704\) | 12.3144 | + | 7.10973i | 0.464117 | + | 0.267958i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.02128i | − | 0.0384365i | ||||||
\(707\) | 4.24533 | + | 13.2924i | 0.159662 | + | 0.499913i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.120139 | + | 0.208086i | 0.00451191 | + | 0.00781485i | 0.868273 | − | 0.496087i | \(-0.165230\pi\) |
−0.863761 | + | 0.503902i | \(0.831897\pi\) | |||||||
\(710\) | −9.95160 | + | 17.2367i | −0.373477 | + | 0.646881i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.201922 | + | 0.116580i | −0.00756735 | + | 0.00436901i | ||||
\(713\) | −64.1953 | −2.40413 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.65715 | −0.361157 | ||||||||
\(716\) | −33.0246 | + | 19.0668i | −1.23419 | + | 0.712559i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.7904 | + | 34.2779i | −0.738570 | + | 1.27924i | ||||
\(719\) | 23.5088 | + | 40.7184i | 0.876729 | + | 1.51854i | 0.854910 | + | 0.518777i | \(0.173612\pi\) |
0.0218189 | + | 0.999762i | \(0.493054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.69941 | − | 16.9847i | 0.137773 | − | 0.632544i | ||||
\(722\) | 29.3460i | 1.09215i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.2923 | − | 22.1080i | −1.42312 | − | 0.821639i | ||||
\(725\) | −2.41941 | − | 1.39685i | −0.0898545 | − | 0.0518775i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 46.1941i | − | 1.71325i | −0.515943 | − | 0.856623i | \(-0.672559\pi\) | ||
0.515943 | − | 0.856623i | \(-0.327441\pi\) | |||||||
\(728\) | 0.328125 | − | 0.360761i | 0.0121611 | − | 0.0133707i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.4440 | + | 28.4819i | 0.608620 | + | 1.05416i | ||||
\(731\) | 2.92877 | − | 5.07278i | 0.108325 | − | 0.187624i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.6161 | − | 19.9856i | 1.27857 | − | 0.738185i | 0.301988 | − | 0.953312i | \(-0.402350\pi\) |
0.976586 | + | 0.215127i | \(0.0690164\pi\) | |||||||
\(734\) | 40.7516 | 1.50417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −66.0421 | −2.43434 | ||||||||
\(737\) | 17.5751 | − | 10.1470i | 0.647388 | − | 0.373770i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.71338 | − | 13.3600i | 0.283741 | − | 0.491455i | −0.688562 | − | 0.725178i | \(-0.741758\pi\) |
0.972303 | + | 0.233723i | \(0.0750909\pi\) | |||||||
\(740\) | −7.39964 | − | 12.8166i | −0.272016 | − | 0.471146i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.1370 | − | 19.9410i | 0.665831 | − | 0.732058i | ||||
\(743\) | − | 22.5672i | − | 0.827912i | −0.910297 | − | 0.413956i | \(-0.864147\pi\) | ||
0.910297 | − | 0.413956i | \(-0.135853\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.4752 | + | 6.04787i | 0.383783 | + | 0.221577i | ||||
\(746\) | 2.20450 | + | 1.27277i | 0.0807126 | + | 0.0465994i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.68515i | 0.244433i | ||||||||
\(749\) | 5.53196 | − | 25.3983i | 0.202133 | − | 0.928035i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.95375 | − | 10.3122i | −0.217255 | − | 0.376297i | 0.736713 | − | 0.676206i | \(-0.236377\pi\) |
−0.953968 | + | 0.299909i | \(0.903044\pi\) | |||||||
\(752\) | 10.8531 | − | 18.7981i | 0.395772 | − | 0.685497i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.7776 | − | 14.8827i | 0.938764 | − | 0.541995i | ||||
\(755\) | 12.4564 | 0.453333 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.0491 | −0.765042 | −0.382521 | − | 0.923947i | \(-0.624944\pi\) | ||||
−0.382521 | + | 0.923947i | \(0.624944\pi\) | |||||||
\(758\) | 61.2838 | − | 35.3822i | 2.22593 | − | 1.28514i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0357755 | + | 0.0619650i | −0.00129772 | + | 0.00224771i | ||||
\(761\) | 23.7347 | + | 41.1097i | 0.860382 | + | 1.49023i | 0.871560 | + | 0.490288i | \(0.163109\pi\) |
−0.0111779 | + | 0.999938i | \(0.503558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.50818 | + | 7.85329i | 0.0908023 | + | 0.284308i | ||||
\(764\) | − | 36.4802i | − | 1.31981i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.6031 | − | 15.9367i | −0.997342 | − | 0.575816i | ||||
\(767\) | 38.1321 | + | 22.0156i | 1.37687 | + | 0.794937i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.1340i | − | 0.581809i | −0.956752 | − | 0.290904i | \(-0.906044\pi\) | ||
0.956752 | − | 0.290904i | \(-0.0939561\pi\) | |||||||
\(770\) | −9.33207 | − | 2.03260i | −0.336304 | − | 0.0732497i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.22026 | − | 7.30970i | −0.151890 | − | 0.263082i | ||||
\(773\) | 13.4018 | − | 23.2126i | 0.482030 | − | 0.834901i | −0.517757 | − | 0.855528i | \(-0.673233\pi\) |
0.999787 | + | 0.0206271i | \(0.00656626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.71938 | + | 3.87944i | −0.241367 | + | 0.139353i | ||||
\(776\) | 0.0756815 | 0.00271681 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.6207 | 0.810993 | ||||||||
\(779\) | 6.78472 | − | 3.91716i | 0.243088 | − | 0.140347i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.02005 | − | 15.6232i | 0.322763 | − | 0.559042i | ||||
\(782\) | −15.3891 | − | 26.6547i | −0.550313 | − | 0.953170i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.0122 | − | 16.3690i | 0.821864 | − | 0.584605i | ||||
\(785\) | 16.7050i | 0.596225i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.99556 | + | 1.15213i | 0.0711339 | + | 0.0410692i | 0.535145 | − | 0.844760i | \(-0.320257\pi\) |
−0.464011 | + | 0.885829i | \(0.653590\pi\) | |||||||
\(788\) | −2.65811 | − | 1.53466i | −0.0946914 | − | 0.0546701i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 8.45580i | − | 0.300844i | ||||||
\(791\) | −32.4641 | − | 29.5272i | −1.15429 | − | 1.04987i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.8189 | + | 36.0595i | 0.739302 | + | 1.28051i | ||||
\(794\) | −30.1524 | + | 52.2255i | −1.07007 | + | 1.85341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.24439 | + | 1.29580i | −0.0795504 | + | 0.0459284i | ||||
\(797\) | −2.87866 | −0.101967 | −0.0509837 | − | 0.998699i | \(-0.516236\pi\) | ||||
−0.0509837 | + | 0.998699i | \(0.516236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.0292 | 0.354807 | ||||||||
\(800\) | −6.91269 | + | 3.99104i | −0.244400 | + | 0.141105i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.32014 | + | 2.28655i | −0.0466158 | + | 0.0807409i | ||||
\(803\) | −14.9047 | − | 25.8157i | −0.525976 | − | 0.911017i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.8527 | − | 6.65993i | 0.734961 | − | 0.234732i | ||||
\(806\) | − | 82.6669i | − | 2.91182i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.157690 | − | 0.0910422i | −0.00554751 | − | 0.00320285i | ||||
\(809\) | 13.1435 | + | 7.58843i | 0.462102 | + | 0.266795i | 0.712928 | − | 0.701237i | \(-0.247369\pi\) |
−0.250825 | + | 0.968032i | \(0.580702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0791i | 1.05622i | 0.849176 | + | 0.528110i | \(0.177099\pi\) | ||||
−0.849176 | + | 0.528110i | \(0.822901\pi\) | |||||||
\(812\) | 13.9602 | − | 4.45862i | 0.489909 | − | 0.156467i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.4725 | + | 23.3350i | 0.472210 | + | 0.817891i | ||||
\(815\) | 9.69006 | − | 16.7837i | 0.339428 | − | 0.587906i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.64010 | − | 3.25631i | 0.197322 | − | 0.113924i | ||||
\(818\) | 68.4239 | 2.39239 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.49494 | 0.261735 | ||||||||
\(821\) | 25.7001 | − | 14.8379i | 0.896939 | − | 0.517848i | 0.0207329 | − | 0.999785i | \(-0.493400\pi\) |
0.876206 | + | 0.481937i | \(0.160067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.946045 | − | 1.63860i | 0.0329771 | − | 0.0571179i | −0.849066 | − | 0.528287i | \(-0.822835\pi\) |
0.882043 | + | 0.471169i | \(0.156168\pi\) | |||||||
\(824\) | 0.113415 | + | 0.196440i | 0.00395100 | + | 0.00684333i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32.2148 | + | 29.3004i | 1.12089 | + | 1.01949i | ||||
\(827\) | 38.5939i | 1.34204i | 0.741439 | + | 0.671020i | \(0.234144\pi\) | ||||
−0.741439 | + | 0.671020i | \(0.765856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.3366 | + | 15.2054i | 0.914708 | + | 0.528107i | 0.881943 | − | 0.471356i | \(-0.156235\pi\) |
0.0327650 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(830\) | −15.5720 | − | 8.99051i | −0.540512 | − | 0.312065i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 41.9684i | − | 1.45499i | ||||||
\(833\) | 11.8662 | + | 5.42653i | 0.411139 | + | 0.188018i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.6855 | − | 18.5078i | −0.369786 | − | 0.640489i | ||||
\(836\) | −3.71639 | + | 6.43698i | −0.128534 | + | 0.222628i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.591398 | + | 0.341444i | −0.0204295 | + | 0.0117950i | ||||
\(839\) | −15.0305 | −0.518909 | −0.259455 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259455 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1953 | 0.730872 | ||||||||
\(842\) | −12.5650 | + | 7.25443i | −0.433020 | + | 0.250004i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.64374 | + | 13.2393i | −0.263108 | + | 0.455717i | ||||
\(845\) | 7.75142 | + | 13.4259i | 0.266657 | + | 0.461863i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.9781 | − | 4.35138i | −0.686454 | − | 0.149515i | ||||
\(848\) | 20.5957i | 0.707259i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.22158 | − | 1.85998i | −0.110499 | − | 0.0637968i | ||||
\(851\) | −53.4834 | − | 30.8786i | −1.83339 | − | 1.05851i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.4211i | 1.17856i | 0.807930 | + | 0.589278i | \(0.200588\pi\) | ||||
−0.807930 | + | 0.589278i | \(0.799412\pi\) | |||||||
\(854\) | 12.5285 | + | 39.2275i | 0.428716 | + | 1.34234i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.169597 | + | 0.293750i | 0.00579669 | + | 0.0100402i | ||||
\(857\) | 10.9059 | − | 18.8896i | 0.372539 | − | 0.645256i | −0.617417 | − | 0.786636i | \(-0.711821\pi\) |
0.989955 | + | 0.141380i | \(0.0451540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.8026 | − | 19.5160i | 1.15333 | − | 0.665876i | 0.203635 | − | 0.979047i | \(-0.434725\pi\) |
0.949697 | + | 0.313171i | \(0.101391\pi\) | |||||||
\(860\) | 6.23050 | 0.212458 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.80531 | −0.265850 | ||||||||
\(863\) | −0.941464 | + | 0.543555i | −0.0320478 | + | 0.0185028i | −0.515938 | − | 0.856626i | \(-0.672557\pi\) |
0.483890 | + | 0.875129i | \(0.339223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.43701 | − | 14.6133i | 0.286867 | − | 0.496868i | ||||
\(866\) | −24.8317 | − | 43.0097i | −0.843815 | − | 1.46153i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.66191 | − | 39.7686i | 0.294004 | − | 1.34983i | ||||
\(869\) | 7.66426i | 0.259992i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.8726 | − | 29.9486i | −1.75764 | − | 1.01477i | ||||
\(872\) | −0.0931646 | − | 0.0537886i | −0.00315495 | − | 0.00182151i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 34.2203i | − | 1.15752i | ||||||
\(875\) | 1.78020 | − | 1.95727i | 0.0601817 | − | 0.0661677i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.64382 | + | 9.77538i | 0.190578 | + | 0.330091i | 0.945442 | − | 0.325790i | \(-0.105630\pi\) |
−0.754864 | + | 0.655882i | \(0.772297\pi\) | |||||||
\(878\) | −14.0733 | + | 24.3757i | −0.474951 | + | 0.822639i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.31980 | − | 3.64874i | 0.213040 | − | 0.122999i | ||||
\(881\) | −38.1260 | −1.28450 | −0.642249 | − | 0.766496i | \(-0.721998\pi\) | ||||
−0.642249 | + | 0.766496i | \(0.721998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.78789 | −0.295736 | −0.147868 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147868 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(884\) | 17.0876 | − | 9.86554i | 0.574719 | − | 0.331814i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.5788 | − | 20.0550i | 0.388996 | − | 0.673761i | ||||
\(887\) | 17.2377 | + | 29.8566i | 0.578787 | + | 1.00249i | 0.995619 | + | 0.0935043i | \(0.0298069\pi\) |
−0.416832 | + | 0.908983i | \(0.636860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.8771 | − | 28.4509i | 0.867889 | − | 0.954213i | ||||
\(890\) | − | 13.4777i | − | 0.451774i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.22460 | + | 4.17112i | 0.241897 | + | 0.139660i | ||||
\(893\) | 9.65687 | + | 5.57540i | 0.323155 | + | 0.186574i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.2331i | 0.642893i | ||||||||
\(896\) | −0.155510 | + | 0.713977i | −0.00519522 | + | 0.0238523i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.83279 | − | 13.5668i | −0.261384 | − | 0.452730i | ||||
\(899\) | −10.8379 | + | 18.7719i | −0.361466 | + | 0.626077i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.24117 | + | 4.75804i | −0.274553 | + | 0.158513i | ||||
\(902\) | −13.6460 | −0.454361 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.572637 | 0.0190456 | ||||||||
\(905\) | −19.3132 | + | 11.1505i | −0.641992 | + | 0.370654i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.84886 | + | 10.1305i | −0.194208 | + | 0.336378i | −0.946641 | − | 0.322291i | \(-0.895547\pi\) |
0.752432 | + | 0.658669i | \(0.228880\pi\) | |||||||
\(908\) | 3.51330 | + | 6.08521i | 0.116593 | + | 0.201945i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.57626 | + | 26.8529i | 0.284300 | + | 0.890163i | ||||
\(911\) | 17.0203i | 0.563908i | 0.959428 | + | 0.281954i | \(0.0909826\pi\) | ||||
−0.959428 | + | 0.281954i | \(0.909017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1143 | + | 8.14892i | 0.467117 | + | 0.269690i | ||||
\(914\) | 2.67602 | + | 1.54500i | 0.0885148 | + | 0.0511040i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.4252i | 1.46785i | ||||||||
\(917\) | −36.1904 | − | 7.88256i | −1.19511 | − | 0.260305i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8185 | − | 25.6665i | −0.488819 | − | 0.846658i | 0.511099 | − | 0.859522i | \(-0.329239\pi\) |
−0.999917 | + | 0.0128635i | \(0.995905\pi\) | |||||||
\(920\) | −0.142824 | + | 0.247378i | −0.00470876 | + | 0.00815582i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.2824 | − | 10.5553i | 0.602099 | − | 0.347622i | ||||
\(923\) | −53.2449 | −1.75258 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.46420 | −0.245422 | ||||||||
\(926\) | 12.6656 | − | 7.31246i | 0.416216 | − | 0.240302i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.1497 | + | 19.3119i | −0.366008 | + | 0.633945i | ||||
\(929\) | −0.569167 | − | 0.985826i | −0.0186738 | − | 0.0323439i | 0.856538 | − | 0.516085i | \(-0.172611\pi\) |
−0.875211 | + | 0.483741i | \(0.839278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.40897 | + | 11.8217i | 0.275593 | + | 0.387440i | ||||
\(932\) | − | 47.6471i | − | 1.56073i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.66610 | + | 3.84867i | 0.218121 | + | 0.125932i | ||||
\(935\) | 2.92001 | + | 1.68587i | 0.0954947 | + | 0.0551339i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.1424i | − | 0.331338i | −0.986181 | − | 0.165669i | \(-0.947022\pi\) | ||
0.986181 | − | 0.165669i | \(-0.0529783\pi\) | |||||||
\(938\) | −43.8230 | − | 39.8585i | −1.43087 | − | 1.30142i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.33388 | + | 9.23855i | 0.173972 | + | 0.301328i | ||||
\(941\) | −18.3854 | + | 31.8444i | −0.599346 | + | 1.03810i | 0.393572 | + | 0.919294i | \(0.371239\pi\) |
−0.992918 | + | 0.118804i | \(0.962094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0861 | − | 15.6382i | 0.882045 | − | 0.509249i | ||||
\(944\) | −33.2724 | −1.08292 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.3438 | −0.368820 | ||||||||
\(947\) | 21.0056 | − | 12.1276i | 0.682590 | − | 0.394094i | −0.118240 | − | 0.992985i | \(-0.537725\pi\) |
0.800830 | + | 0.598891i | \(0.204392\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.9909 | + | 76.1945i | −1.42801 | + | 2.47338i | ||||
\(950\) | −2.06799 | − | 3.58187i | −0.0670945 | − | 0.116211i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.162193 | + | 0.0518013i | −0.00525672 | + | 0.00167889i | ||||
\(953\) | 4.33668i | 0.140479i | 0.997530 | + | 0.0702394i | \(0.0223763\pi\) | ||||
−0.997530 | + | 0.0702394i | \(0.977624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.9342 | − | 9.19964i | −0.515620 | − | 0.297693i | ||||
\(956\) | −20.7650 | − | 11.9887i | −0.671588 | − | 0.387741i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 38.0142i | − | 1.22818i | ||||||
\(959\) | −56.8286 | + | 18.1499i | −1.83509 | + | 0.586091i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.6001 | + | 25.2880i | 0.470970 | + | 0.815743i | ||||
\(962\) | 39.7637 | − | 68.8727i | 1.28203 | − | 2.22054i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44.3710 | − | 25.6176i | 1.42909 | − | 0.825087i | ||||
\(965\) | −4.25708 | −0.137040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4312 | 1.04292 | 0.521458 | − | 0.853277i | \(-0.325388\pi\) | ||||
0.521458 | + | 0.853277i | \(0.325388\pi\) | |||||||
\(968\) | 0.231060 | − | 0.133403i | 0.00742656 | − | 0.00428773i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.18737 | + | 3.78864i | −0.0702322 | + | 0.121646i | ||||
\(971\) | −0.500111 | − | 0.866217i | −0.0160493 | − | 0.0277982i | 0.857889 | − | 0.513835i | \(-0.171776\pi\) |
−0.873939 | + | 0.486036i | \(0.838442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.6372 | + | 13.3130i | 0.469246 | + | 0.426795i | ||||
\(974\) | − | 15.1302i | − | 0.484802i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.2486 | − | 15.7320i | −0.872205 | − | 0.503568i | ||||
\(977\) | −19.4306 | − | 11.2183i | −0.621641 | − | 0.358905i | 0.155867 | − | 0.987778i | \(-0.450183\pi\) |
−0.777508 | + | 0.628874i | \(0.783516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.2161i | 0.390428i | ||||||||
\(980\) | 1.31212 | + | 13.8167i | 0.0419141 | + | 0.441360i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.2023 | − | 38.4555i | −0.708504 | − | 1.22716i | ||||
\(983\) | −9.56124 | + | 16.5606i | −0.304956 | + | 0.528200i | −0.977252 | − | 0.212083i | \(-0.931975\pi\) |
0.672295 | + | 0.740283i | \(0.265308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.34065 | + | 0.774027i | −0.0427168 | + | 0.0246625i | ||||
\(986\) | −10.3924 | −0.330962 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.9377 | 0.697931 | ||||||||
\(989\) | 22.5165 | − | 12.9999i | 0.715984 | − | 0.413373i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.45280 | + | 5.98043i | −0.109682 | + | 0.189975i | −0.915641 | − | 0.401996i | \(-0.868317\pi\) |
0.805959 | + | 0.591971i | \(0.201650\pi\) | |||||||
\(992\) | 30.9660 | + | 53.6347i | 0.983171 | + | 1.70290i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −51.4526 | − | 11.2068i | −1.63198 | − | 0.355458i | ||||
\(995\) | 1.30711i | 0.0414381i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.3034 | + | 19.8051i | 1.08640 | + | 0.627233i | 0.932616 | − | 0.360871i | \(-0.117521\pi\) |
0.153784 | + | 0.988104i | \(0.450854\pi\) | |||||||
\(998\) | −47.3661 | − | 27.3468i | −1.49935 | − | 0.865649i | ||||
\(999\) | 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 | 315.2.bj.a.206.5 | yes | 12 | |
3.2 | odd | 2 | 315.2.bj.b.206.2 | yes | 12 | ||
5.2 | odd | 4 | 1575.2.bc.d.899.10 | 24 | |||
5.3 | odd | 4 | 1575.2.bc.d.899.3 | 24 | |||
5.4 | even | 2 | 1575.2.bk.f.1151.2 | 12 | |||
7.3 | odd | 6 | 2205.2.b.a.881.10 | 12 | |||
7.4 | even | 3 | 2205.2.b.b.881.10 | 12 | |||
7.5 | odd | 6 | 315.2.bj.b.26.2 | yes | 12 | ||
15.2 | even | 4 | 1575.2.bc.c.899.3 | 24 | |||
15.8 | even | 4 | 1575.2.bc.c.899.10 | 24 | |||
15.14 | odd | 2 | 1575.2.bk.e.1151.5 | 12 | |||
21.5 | even | 6 | inner | 315.2.bj.a.26.5 | ✓ | 12 | |
21.11 | odd | 6 | 2205.2.b.a.881.3 | 12 | |||
21.17 | even | 6 | 2205.2.b.b.881.3 | 12 | |||
35.12 | even | 12 | 1575.2.bc.c.1349.10 | 24 | |||
35.19 | odd | 6 | 1575.2.bk.e.26.5 | 12 | |||
35.33 | even | 12 | 1575.2.bc.c.1349.3 | 24 | |||
105.47 | odd | 12 | 1575.2.bc.d.1349.3 | 24 | |||
105.68 | odd | 12 | 1575.2.bc.d.1349.10 | 24 | |||
105.89 | even | 6 | 1575.2.bk.f.26.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bj.a.26.5 | ✓ | 12 | 21.5 | even | 6 | inner | |
315.2.bj.a.206.5 | yes | 12 | 1.1 | even | 1 | trivial | |
315.2.bj.b.26.2 | yes | 12 | 7.5 | odd | 6 | ||
315.2.bj.b.206.2 | yes | 12 | 3.2 | odd | 2 | ||
1575.2.bc.c.899.3 | 24 | 15.2 | even | 4 | |||
1575.2.bc.c.899.10 | 24 | 15.8 | even | 4 | |||
1575.2.bc.c.1349.3 | 24 | 35.33 | even | 12 | |||
1575.2.bc.c.1349.10 | 24 | 35.12 | even | 12 | |||
1575.2.bc.d.899.3 | 24 | 5.3 | odd | 4 | |||
1575.2.bc.d.899.10 | 24 | 5.2 | odd | 4 | |||
1575.2.bc.d.1349.3 | 24 | 105.47 | odd | 12 | |||
1575.2.bc.d.1349.10 | 24 | 105.68 | odd | 12 | |||
1575.2.bk.e.26.5 | 12 | 35.19 | odd | 6 | |||
1575.2.bk.e.1151.5 | 12 | 15.14 | odd | 2 | |||
1575.2.bk.f.26.2 | 12 | 105.89 | even | 6 | |||
1575.2.bk.f.1151.2 | 12 | 5.4 | even | 2 | |||
2205.2.b.a.881.3 | 12 | 21.11 | odd | 6 | |||
2205.2.b.a.881.10 | 12 | 7.3 | odd | 6 | |||
2205.2.b.b.881.3 | 12 | 21.17 | even | 6 | |||
2205.2.b.b.881.10 | 12 | 7.4 | even | 3 |