Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(251,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.h (of order \(2\), degree \(1\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.6 | ||
Root | \(-0.470943 - 1.33350i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.251 |
Dual form | 280.2.h.b.251.5 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.470943 | + | 1.33350i | −0.333007 | + | 0.942924i | ||||
\(3\) | 0.528177i | 0.304943i | 0.988308 | + | 0.152472i | \(0.0487232\pi\) | ||||
−0.988308 | + | 0.152472i | \(0.951277\pi\) | |||||||
\(4\) | −1.55642 | − | 1.25600i | −0.778212 | − | 0.628001i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.704322 | − | 0.248741i | −0.287538 | − | 0.101548i | ||||
\(7\) | 2.17448 | − | 1.50719i | 0.821878 | − | 0.569664i | ||||
\(8\) | 2.40786 | − | 1.48398i | 0.851308 | − | 0.524666i | ||||
\(9\) | 2.72103 | 0.907010 | ||||||||
\(10\) | −0.470943 | + | 1.33350i | −0.148925 | + | 0.421689i | ||||
\(11\) | 3.04781 | 0.918950 | 0.459475 | − | 0.888191i | \(-0.348038\pi\) | ||||
0.459475 | + | 0.888191i | \(0.348038\pi\) | |||||||
\(12\) | 0.663391 | − | 0.822067i | 0.191505 | − | 0.237310i | ||||
\(13\) | −4.75069 | −1.31760 | −0.658802 | − | 0.752317i | \(-0.728936\pi\) | ||||
−0.658802 | + | 0.752317i | \(0.728936\pi\) | |||||||
\(14\) | 0.985772 | + | 3.60947i | 0.263459 | + | 0.964671i | ||||
\(15\) | 0.528177i | 0.136375i | ||||||||
\(16\) | 0.844916 | + | 3.90975i | 0.211229 | + | 0.977437i | ||||
\(17\) | 6.78894i | 1.64656i | 0.567635 | + | 0.823280i | \(0.307858\pi\) | ||||
−0.567635 | + | 0.823280i | \(0.692142\pi\) | |||||||
\(18\) | −1.28145 | + | 3.62848i | −0.302041 | + | 0.855242i | ||||
\(19\) | − | 0.584285i | − | 0.134044i | −0.997751 | − | 0.0670221i | \(-0.978650\pi\) | ||
0.997751 | − | 0.0670221i | \(-0.0213498\pi\) | |||||||
\(20\) | −1.55642 | − | 1.25600i | −0.348027 | − | 0.280851i | ||||
\(21\) | 0.796062 | + | 1.14851i | 0.173715 | + | 0.250626i | ||||
\(22\) | −1.43535 | + | 4.06425i | −0.306017 | + | 0.866500i | ||||
\(23\) | − | 5.80481i | − | 1.21039i | −0.796079 | − | 0.605193i | \(-0.793096\pi\) | ||
0.796079 | − | 0.605193i | \(-0.206904\pi\) | |||||||
\(24\) | 0.783804 | + | 1.27178i | 0.159993 | + | 0.259600i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.23730 | − | 6.33502i | 0.438772 | − | 1.24240i | ||||
\(27\) | 3.02172i | 0.581529i | ||||||||
\(28\) | −5.27745 | − | 0.385331i | −0.997345 | − | 0.0728206i | ||||
\(29\) | − | 0.185682i | − | 0.0344802i | −0.999851 | − | 0.0172401i | \(-0.994512\pi\) | ||
0.999851 | − | 0.0172401i | \(-0.00548797\pi\) | |||||||
\(30\) | −0.704322 | − | 0.248741i | −0.128591 | − | 0.0454138i | ||||
\(31\) | 3.12589 | 0.561427 | 0.280714 | − | 0.959792i | \(-0.409429\pi\) | ||||
0.280714 | + | 0.959792i | \(0.409429\pi\) | |||||||
\(32\) | −5.61154 | − | 0.714577i | −0.991989 | − | 0.126321i | ||||
\(33\) | 1.60978i | 0.280227i | ||||||||
\(34\) | −9.05303 | − | 3.19721i | −1.55258 | − | 0.548317i | ||||
\(35\) | 2.17448 | − | 1.50719i | 0.367555 | − | 0.254761i | ||||
\(36\) | −4.23508 | − | 3.41762i | −0.705846 | − | 0.569603i | ||||
\(37\) | 7.04672i | 1.15847i | 0.815159 | + | 0.579237i | \(0.196649\pi\) | ||||
−0.815159 | + | 0.579237i | \(0.803351\pi\) | |||||||
\(38\) | 0.779143 | + | 0.275165i | 0.126394 | + | 0.0446377i | ||||
\(39\) | − | 2.50920i | − | 0.401794i | ||||||
\(40\) | 2.40786 | − | 1.48398i | 0.380716 | − | 0.234638i | ||||
\(41\) | − | 3.83583i | − | 0.599056i | −0.954087 | − | 0.299528i | \(-0.903171\pi\) | ||
0.954087 | − | 0.299528i | \(-0.0968292\pi\) | |||||||
\(42\) | −1.90644 | + | 0.520662i | −0.294170 | + | 0.0803399i | ||||
\(43\) | −1.43554 | −0.218917 | −0.109459 | − | 0.993991i | \(-0.534912\pi\) | ||||
−0.109459 | + | 0.993991i | \(0.534912\pi\) | |||||||
\(44\) | −4.74369 | − | 3.82806i | −0.715138 | − | 0.577102i | ||||
\(45\) | 2.72103 | 0.405627 | ||||||||
\(46\) | 7.74069 | + | 2.73374i | 1.14130 | + | 0.403067i | ||||
\(47\) | 2.95871 | 0.431572 | 0.215786 | − | 0.976441i | \(-0.430769\pi\) | ||||
0.215786 | + | 0.976441i | \(0.430769\pi\) | |||||||
\(48\) | −2.06504 | + | 0.446265i | −0.298062 | + | 0.0644128i | ||||
\(49\) | 2.45676 | − | 6.55472i | 0.350966 | − | 0.936388i | ||||
\(50\) | −0.470943 | + | 1.33350i | −0.0666014 | + | 0.188585i | ||||
\(51\) | −3.58576 | −0.502107 | ||||||||
\(52\) | 7.39409 | + | 5.96688i | 1.02538 | + | 0.827457i | ||||
\(53\) | − | 0.535513i | − | 0.0735584i | −0.999323 | − | 0.0367792i | \(-0.988290\pi\) | ||
0.999323 | − | 0.0367792i | \(-0.0117098\pi\) | |||||||
\(54\) | −4.02945 | − | 1.42306i | −0.548338 | − | 0.193653i | ||||
\(55\) | 3.04781 | 0.410967 | ||||||||
\(56\) | 2.99922 | − | 6.85600i | 0.400787 | − | 0.916171i | ||||
\(57\) | 0.308606 | 0.0408759 | ||||||||
\(58\) | 0.247606 | + | 0.0874456i | 0.0325123 | + | 0.0114822i | ||||
\(59\) | − | 1.52116i | − | 0.198038i | −0.995086 | − | 0.0990188i | \(-0.968430\pi\) | ||
0.995086 | − | 0.0990188i | \(-0.0315704\pi\) | |||||||
\(60\) | 0.663391 | − | 0.822067i | 0.0856435 | − | 0.106128i | ||||
\(61\) | −13.2354 | −1.69461 | −0.847307 | − | 0.531103i | \(-0.821778\pi\) | ||||
−0.847307 | + | 0.531103i | \(0.821778\pi\) | |||||||
\(62\) | −1.47212 | + | 4.16837i | −0.186959 | + | 0.529383i | ||||
\(63\) | 5.91683 | − | 4.10111i | 0.745451 | − | 0.516691i | ||||
\(64\) | 3.59560 | − | 7.14644i | 0.449450 | − | 0.893305i | ||||
\(65\) | −4.75069 | −0.589250 | ||||||||
\(66\) | −2.14664 | − | 0.758117i | −0.264233 | − | 0.0933177i | ||||
\(67\) | −9.13242 | −1.11570 | −0.557851 | − | 0.829941i | \(-0.688374\pi\) | ||||
−0.557851 | + | 0.829941i | \(0.688374\pi\) | |||||||
\(68\) | 8.52693 | − | 10.5665i | 1.03404 | − | 1.28137i | ||||
\(69\) | 3.06597 | 0.369099 | ||||||||
\(70\) | 0.985772 | + | 3.60947i | 0.117822 | + | 0.431414i | ||||
\(71\) | − | 9.68233i | − | 1.14908i | −0.818476 | − | 0.574540i | \(-0.805181\pi\) | ||
0.818476 | − | 0.574540i | \(-0.194819\pi\) | |||||||
\(72\) | 6.55186 | − | 4.03795i | 0.772145 | − | 0.475878i | ||||
\(73\) | 12.4295i | 1.45476i | 0.686235 | + | 0.727380i | \(0.259262\pi\) | ||||
−0.686235 | + | 0.727380i | \(0.740738\pi\) | |||||||
\(74\) | −9.39678 | − | 3.31861i | −1.09235 | − | 0.385780i | ||||
\(75\) | 0.528177i | 0.0609886i | ||||||||
\(76\) | −0.733864 | + | 0.909396i | −0.0841800 | + | 0.104315i | ||||
\(77\) | 6.62742 | − | 4.59363i | 0.755264 | − | 0.523493i | ||||
\(78\) | 3.34601 | + | 1.18169i | 0.378861 | + | 0.133800i | ||||
\(79\) | − | 2.81383i | − | 0.316580i | −0.987393 | − | 0.158290i | \(-0.949402\pi\) | ||
0.987393 | − | 0.158290i | \(-0.0505982\pi\) | |||||||
\(80\) | 0.844916 | + | 3.90975i | 0.0944645 | + | 0.437123i | ||||
\(81\) | 6.56709 | 0.729676 | ||||||||
\(82\) | 5.11507 | + | 1.80646i | 0.564865 | + | 0.199490i | ||||
\(83\) | − | 13.4535i | − | 1.47671i | −0.674412 | − | 0.738355i | \(-0.735603\pi\) | ||
0.674412 | − | 0.738355i | \(-0.264397\pi\) | |||||||
\(84\) | 0.203523 | − | 2.78743i | 0.0222061 | − | 0.304133i | ||||
\(85\) | 6.78894i | 0.736364i | ||||||||
\(86\) | 0.676056 | − | 1.91428i | 0.0729010 | − | 0.206422i | ||||
\(87\) | 0.0980728 | 0.0105145 | ||||||||
\(88\) | 7.33871 | − | 4.52289i | 0.782309 | − | 0.482142i | ||||
\(89\) | − | 3.10041i | − | 0.328642i | −0.986407 | − | 0.164321i | \(-0.947457\pi\) | ||
0.986407 | − | 0.164321i | \(-0.0525434\pi\) | |||||||
\(90\) | −1.28145 | + | 3.62848i | −0.135077 | + | 0.382476i | ||||
\(91\) | −10.3303 | + | 7.16019i | −1.08291 | + | 0.750591i | ||||
\(92\) | −7.29085 | + | 9.03475i | −0.760124 | + | 0.941938i | ||||
\(93\) | 1.65102i | 0.171203i | ||||||||
\(94\) | −1.39338 | + | 3.94543i | −0.143717 | + | 0.406940i | ||||
\(95\) | − | 0.584285i | − | 0.0599464i | ||||||
\(96\) | 0.377423 | − | 2.96389i | 0.0385206 | − | 0.302500i | ||||
\(97\) | − | 13.5027i | − | 1.37099i | −0.728077 | − | 0.685495i | \(-0.759586\pi\) | ||
0.728077 | − | 0.685495i | \(-0.240414\pi\) | |||||||
\(98\) | 7.58370 | + | 6.36298i | 0.766069 | + | 0.642758i | ||||
\(99\) | 8.29319 | 0.833497 | ||||||||
\(100\) | −1.55642 | − | 1.25600i | −0.155642 | − | 0.125600i | ||||
\(101\) | −1.29842 | −0.129198 | −0.0645988 | − | 0.997911i | \(-0.520577\pi\) | ||||
−0.0645988 | + | 0.997911i | \(0.520577\pi\) | |||||||
\(102\) | 1.68869 | − | 4.78160i | 0.167205 | − | 0.473449i | ||||
\(103\) | −19.0846 | −1.88046 | −0.940232 | − | 0.340535i | \(-0.889392\pi\) | ||||
−0.940232 | + | 0.340535i | \(0.889392\pi\) | |||||||
\(104\) | −11.4390 | + | 7.04993i | −1.12169 | + | 0.691302i | ||||
\(105\) | 0.796062 | + | 1.14851i | 0.0776877 | + | 0.112083i | ||||
\(106\) | 0.714105 | + | 0.252196i | 0.0693600 | + | 0.0244955i | ||||
\(107\) | −3.81102 | −0.368425 | −0.184213 | − | 0.982886i | \(-0.558973\pi\) | ||||
−0.184213 | + | 0.982886i | \(0.558973\pi\) | |||||||
\(108\) | 3.79528 | − | 4.70307i | 0.365201 | − | 0.452553i | ||||
\(109\) | 15.1487i | 1.45098i | 0.688233 | + | 0.725490i | \(0.258387\pi\) | ||||
−0.688233 | + | 0.725490i | \(0.741613\pi\) | |||||||
\(110\) | −1.43535 | + | 4.06425i | −0.136855 | + | 0.387511i | ||||
\(111\) | −3.72192 | −0.353269 | ||||||||
\(112\) | 7.72998 | + | 7.22823i | 0.730415 | + | 0.683004i | ||||
\(113\) | −16.6411 | −1.56546 | −0.782732 | − | 0.622359i | \(-0.786175\pi\) | ||||
−0.782732 | + | 0.622359i | \(0.786175\pi\) | |||||||
\(114\) | −0.145336 | + | 0.411525i | −0.0136120 | + | 0.0385429i | ||||
\(115\) | − | 5.80481i | − | 0.541301i | ||||||
\(116\) | −0.233217 | + | 0.289000i | −0.0216536 | + | 0.0268330i | ||||
\(117\) | −12.9268 | −1.19508 | ||||||||
\(118\) | 2.02846 | + | 0.716378i | 0.186734 | + | 0.0659479i | ||||
\(119\) | 10.2322 | + | 14.7624i | 0.937986 | + | 1.35327i | ||||
\(120\) | 0.783804 | + | 1.27178i | 0.0715512 | + | 0.116097i | ||||
\(121\) | −1.71084 | −0.155531 | ||||||||
\(122\) | 6.23311 | − | 17.6493i | 0.564319 | − | 1.59789i | ||||
\(123\) | 2.02600 | 0.182678 | ||||||||
\(124\) | −4.86522 | − | 3.92613i | −0.436909 | − | 0.352577i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.68232 | + | 9.82147i | 0.238960 | + | 0.874966i | ||||
\(127\) | 15.9073i | 1.41154i | 0.708440 | + | 0.705771i | \(0.249399\pi\) | ||||
−0.708440 | + | 0.705771i | \(0.750601\pi\) | |||||||
\(128\) | 7.83643 | + | 8.16029i | 0.692649 | + | 0.721275i | ||||
\(129\) | − | 0.758217i | − | 0.0667573i | ||||||
\(130\) | 2.23730 | − | 6.33502i | 0.196225 | − | 0.555618i | ||||
\(131\) | 20.2439i | 1.76872i | 0.466806 | + | 0.884360i | \(0.345405\pi\) | ||||
−0.466806 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(132\) | 2.02189 | − | 2.50551i | 0.175983 | − | 0.218076i | ||||
\(133\) | −0.880629 | − | 1.27052i | −0.0763602 | − | 0.110168i | ||||
\(134\) | 4.30085 | − | 12.1780i | 0.371537 | − | 1.05202i | ||||
\(135\) | 3.02172i | 0.260068i | ||||||||
\(136\) | 10.0747 | + | 16.3468i | 0.863895 | + | 1.40173i | ||||
\(137\) | 6.38933 | 0.545877 | 0.272939 | − | 0.962031i | \(-0.412004\pi\) | ||||
0.272939 | + | 0.962031i | \(0.412004\pi\) | |||||||
\(138\) | −1.44390 | + | 4.08845i | −0.122913 | + | 0.348032i | ||||
\(139\) | − | 21.8128i | − | 1.85014i | −0.379801 | − | 0.925068i | \(-0.624008\pi\) | ||
0.379801 | − | 0.925068i | \(-0.375992\pi\) | |||||||
\(140\) | −5.27745 | − | 0.385331i | −0.446026 | − | 0.0325664i | ||||
\(141\) | 1.56272i | 0.131605i | ||||||||
\(142\) | 12.9113 | + | 4.55983i | 1.08350 | + | 0.382652i | ||||
\(143\) | −14.4792 | −1.21081 | ||||||||
\(144\) | 2.29904 | + | 10.6385i | 0.191587 | + | 0.886545i | ||||
\(145\) | − | 0.185682i | − | 0.0154200i | ||||||
\(146\) | −16.5747 | − | 5.85358i | −1.37173 | − | 0.484446i | ||||
\(147\) | 3.46205 | + | 1.29760i | 0.285545 | + | 0.107025i | ||||
\(148\) | 8.85070 | − | 10.9677i | 0.727523 | − | 0.901539i | ||||
\(149\) | − | 11.5156i | − | 0.943396i | −0.881760 | − | 0.471698i | \(-0.843641\pi\) | ||
0.881760 | − | 0.471698i | \(-0.156359\pi\) | |||||||
\(150\) | −0.704322 | − | 0.248741i | −0.0575076 | − | 0.0203096i | ||||
\(151\) | 7.70970i | 0.627407i | 0.949521 | + | 0.313703i | \(0.101570\pi\) | ||||
−0.949521 | + | 0.313703i | \(0.898430\pi\) | |||||||
\(152\) | −0.867068 | − | 1.40688i | −0.0703285 | − | 0.114113i | ||||
\(153\) | 18.4729i | 1.49345i | ||||||||
\(154\) | 3.00445 | + | 11.0010i | 0.242105 | + | 0.886484i | ||||
\(155\) | 3.12589 | 0.251078 | ||||||||
\(156\) | −3.15157 | + | 3.90539i | −0.252327 | + | 0.312681i | ||||
\(157\) | 4.42111 | 0.352843 | 0.176422 | − | 0.984315i | \(-0.443548\pi\) | ||||
0.176422 | + | 0.984315i | \(0.443548\pi\) | |||||||
\(158\) | 3.75223 | + | 1.32515i | 0.298511 | + | 0.105424i | ||||
\(159\) | 0.282846 | 0.0224311 | ||||||||
\(160\) | −5.61154 | − | 0.714577i | −0.443631 | − | 0.0564923i | ||||
\(161\) | −8.74895 | − | 12.6225i | −0.689514 | − | 0.994790i | ||||
\(162\) | −3.09273 | + | 8.75719i | −0.242988 | + | 0.688030i | ||||
\(163\) | 17.5475 | 1.37443 | 0.687213 | − | 0.726456i | \(-0.258834\pi\) | ||||
0.687213 | + | 0.726456i | \(0.258834\pi\) | |||||||
\(164\) | −4.81781 | + | 5.97018i | −0.376208 | + | 0.466193i | ||||
\(165\) | 1.60978i | 0.125321i | ||||||||
\(166\) | 17.9402 | + | 6.33582i | 1.39243 | + | 0.491755i | ||||
\(167\) | −1.57597 | −0.121952 | −0.0609760 | − | 0.998139i | \(-0.519421\pi\) | ||||
−0.0609760 | + | 0.998139i | \(0.519421\pi\) | |||||||
\(168\) | 3.62118 | + | 1.58412i | 0.279380 | + | 0.122217i | ||||
\(169\) | 9.56903 | 0.736079 | ||||||||
\(170\) | −9.05303 | − | 3.19721i | −0.694336 | − | 0.245215i | ||||
\(171\) | − | 1.58986i | − | 0.121579i | ||||||
\(172\) | 2.23430 | + | 1.80304i | 0.170364 | + | 0.137480i | ||||
\(173\) | 0.208914 | 0.0158835 | 0.00794173 | − | 0.999968i | \(-0.497472\pi\) | ||||
0.00794173 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(174\) | −0.0461867 | + | 0.130780i | −0.00350141 | + | 0.00991439i | ||||
\(175\) | 2.17448 | − | 1.50719i | 0.164376 | − | 0.113933i | ||||
\(176\) | 2.57514 | + | 11.9162i | 0.194109 | + | 0.898215i | ||||
\(177\) | 0.803439 | 0.0603902 | ||||||||
\(178\) | 4.13438 | + | 1.46012i | 0.309885 | + | 0.109440i | ||||
\(179\) | −5.84685 | −0.437014 | −0.218507 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218507 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(180\) | −4.23508 | − | 3.41762i | −0.315664 | − | 0.254734i | ||||
\(181\) | 8.66680 | 0.644198 | 0.322099 | − | 0.946706i | \(-0.395612\pi\) | ||||
0.322099 | + | 0.946706i | \(0.395612\pi\) | |||||||
\(182\) | −4.68310 | − | 17.1475i | −0.347134 | − | 1.27105i | ||||
\(183\) | − | 6.99061i | − | 0.516761i | ||||||
\(184\) | −8.61422 | − | 13.9772i | −0.635049 | − | 1.03041i | ||||
\(185\) | 7.04672i | 0.518085i | ||||||||
\(186\) | −2.20163 | − | 0.777539i | −0.161432 | − | 0.0570119i | ||||
\(187\) | 20.6914i | 1.51311i | ||||||||
\(188\) | −4.60501 | − | 3.71615i | −0.335855 | − | 0.271028i | ||||
\(189\) | 4.55430 | + | 6.57067i | 0.331276 | + | 0.477946i | ||||
\(190\) | 0.779143 | + | 0.275165i | 0.0565249 | + | 0.0199626i | ||||
\(191\) | 12.9741i | 0.938770i | 0.882993 | + | 0.469385i | \(0.155524\pi\) | ||||
−0.882993 | + | 0.469385i | \(0.844476\pi\) | |||||||
\(192\) | 3.77459 | + | 1.89911i | 0.272407 | + | 0.137057i | ||||
\(193\) | −24.5869 | −1.76980 | −0.884901 | − | 0.465780i | \(-0.845774\pi\) | ||||
−0.884901 | + | 0.465780i | \(0.845774\pi\) | |||||||
\(194\) | 18.0058 | + | 6.35900i | 1.29274 | + | 0.456550i | ||||
\(195\) | − | 2.50920i | − | 0.179688i | ||||||
\(196\) | −12.0565 | + | 7.11623i | −0.861179 | + | 0.508302i | ||||
\(197\) | − | 7.21194i | − | 0.513829i | −0.966434 | − | 0.256915i | \(-0.917294\pi\) | ||
0.966434 | − | 0.256915i | \(-0.0827059\pi\) | |||||||
\(198\) | −3.90562 | + | 11.0589i | −0.277560 | + | 0.785924i | ||||
\(199\) | 6.32808 | 0.448585 | 0.224293 | − | 0.974522i | \(-0.427993\pi\) | ||||
0.224293 | + | 0.974522i | \(0.427993\pi\) | |||||||
\(200\) | 2.40786 | − | 1.48398i | 0.170262 | − | 0.104933i | ||||
\(201\) | − | 4.82353i | − | 0.340226i | ||||||
\(202\) | 0.611482 | − | 1.73144i | 0.0430237 | − | 0.121823i | ||||
\(203\) | −0.279858 | − | 0.403762i | −0.0196422 | − | 0.0283385i | ||||
\(204\) | 5.58097 | + | 4.50373i | 0.390746 | + | 0.315324i | ||||
\(205\) | − | 3.83583i | − | 0.267906i | ||||||
\(206\) | 8.98777 | − | 25.4493i | 0.626208 | − | 1.77313i | ||||
\(207\) | − | 15.7951i | − | 1.09783i | ||||||
\(208\) | −4.01393 | − | 18.5740i | −0.278316 | − | 1.28787i | ||||
\(209\) | − | 1.78079i | − | 0.123180i | ||||||
\(210\) | −1.90644 | + | 0.520662i | −0.131557 | + | 0.0359291i | ||||
\(211\) | −10.2211 | −0.703650 | −0.351825 | − | 0.936066i | \(-0.614439\pi\) | ||||
−0.351825 | + | 0.936066i | \(0.614439\pi\) | |||||||
\(212\) | −0.672606 | + | 0.833486i | −0.0461948 | + | 0.0572441i | ||||
\(213\) | 5.11398 | 0.350404 | ||||||||
\(214\) | 1.79477 | − | 5.08198i | 0.122688 | − | 0.347397i | ||||
\(215\) | −1.43554 | −0.0979028 | ||||||||
\(216\) | 4.48417 | + | 7.27587i | 0.305109 | + | 0.495061i | ||||
\(217\) | 6.79721 | − | 4.71131i | 0.461424 | − | 0.319825i | ||||
\(218\) | −20.2007 | − | 7.13417i | −1.36816 | − | 0.483187i | ||||
\(219\) | −6.56496 | −0.443619 | ||||||||
\(220\) | −4.74369 | − | 3.82806i | −0.319820 | − | 0.258088i | ||||
\(221\) | − | 32.2521i | − | 2.16951i | ||||||
\(222\) | 1.75281 | − | 4.96316i | 0.117641 | − | 0.333106i | ||||
\(223\) | −2.64553 | −0.177158 | −0.0885790 | − | 0.996069i | \(-0.528233\pi\) | ||||
−0.0885790 | + | 0.996069i | \(0.528233\pi\) | |||||||
\(224\) | −13.2792 | + | 6.90382i | −0.887254 | + | 0.461281i | ||||
\(225\) | 2.72103 | 0.181402 | ||||||||
\(226\) | 7.83702 | − | 22.1909i | 0.521311 | − | 1.47611i | ||||
\(227\) | − | 16.2979i | − | 1.08173i | −0.841109 | − | 0.540866i | \(-0.818097\pi\) | ||
0.841109 | − | 0.540866i | \(-0.181903\pi\) | |||||||
\(228\) | −0.480322 | − | 0.387610i | −0.0318101 | − | 0.0256701i | ||||
\(229\) | −5.51840 | −0.364666 | −0.182333 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182333 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(230\) | 7.74069 | + | 2.73374i | 0.510406 | + | 0.180257i | ||||
\(231\) | 2.42625 | + | 3.50045i | 0.159635 | + | 0.230313i | ||||
\(232\) | −0.275548 | − | 0.447096i | −0.0180906 | − | 0.0293533i | ||||
\(233\) | 18.6314 | 1.22058 | 0.610291 | − | 0.792177i | \(-0.291053\pi\) | ||||
0.610291 | + | 0.792177i | \(0.291053\pi\) | |||||||
\(234\) | 6.08777 | − | 17.2378i | 0.397970 | − | 1.12687i | ||||
\(235\) | 2.95871 | 0.193005 | ||||||||
\(236\) | −1.91057 | + | 2.36756i | −0.124368 | + | 0.154115i | ||||
\(237\) | 1.48620 | 0.0965390 | ||||||||
\(238\) | −24.5045 | + | 6.69235i | −1.58839 | + | 0.433801i | ||||
\(239\) | 5.77674i | 0.373666i | 0.982392 | + | 0.186833i | \(0.0598223\pi\) | ||||
−0.982392 | + | 0.186833i | \(0.940178\pi\) | |||||||
\(240\) | −2.06504 | + | 0.446265i | −0.133298 | + | 0.0288063i | ||||
\(241\) | − | 1.42853i | − | 0.0920200i | −0.998941 | − | 0.0460100i | \(-0.985349\pi\) | ||
0.998941 | − | 0.0460100i | \(-0.0146506\pi\) | |||||||
\(242\) | 0.805710 | − | 2.28140i | 0.0517930 | − | 0.146654i | ||||
\(243\) | 12.5337i | 0.804039i | ||||||||
\(244\) | 20.5999 | + | 16.6237i | 1.31877 | + | 1.06422i | ||||
\(245\) | 2.45676 | − | 6.55472i | 0.156957 | − | 0.418766i | ||||
\(246\) | −0.954130 | + | 2.70166i | −0.0608331 | + | 0.172252i | ||||
\(247\) | 2.77576i | 0.176617i | ||||||||
\(248\) | 7.52672 | − | 4.63877i | 0.477947 | − | 0.294562i | ||||
\(249\) | 7.10581 | 0.450312 | ||||||||
\(250\) | −0.470943 | + | 1.33350i | −0.0297851 | + | 0.0843377i | ||||
\(251\) | 11.6354i | 0.734419i | 0.930138 | + | 0.367210i | \(0.119687\pi\) | ||||
−0.930138 | + | 0.367210i | \(0.880313\pi\) | |||||||
\(252\) | −14.3601 | − | 1.04850i | −0.904602 | − | 0.0660490i | ||||
\(253\) | − | 17.6920i | − | 1.11228i | ||||||
\(254\) | −21.2123 | − | 7.49142i | −1.33098 | − | 0.470054i | ||||
\(255\) | −3.58576 | −0.224549 | ||||||||
\(256\) | −14.5722 | + | 6.60681i | −0.910765 | + | 0.412926i | ||||
\(257\) | − | 12.0011i | − | 0.748611i | −0.927305 | − | 0.374306i | \(-0.877881\pi\) | ||
0.927305 | − | 0.374306i | \(-0.122119\pi\) | |||||||
\(258\) | 1.01108 | + | 0.357077i | 0.0629471 | + | 0.0222307i | ||||
\(259\) | 10.6207 | + | 15.3230i | 0.659941 | + | 0.952124i | ||||
\(260\) | 7.39409 | + | 5.96688i | 0.458562 | + | 0.370050i | ||||
\(261\) | − | 0.505246i | − | 0.0312739i | ||||||
\(262\) | −26.9952 | − | 9.53374i | −1.66777 | − | 0.588996i | ||||
\(263\) | 26.7775i | 1.65117i | 0.564277 | + | 0.825585i | \(0.309155\pi\) | ||||
−0.564277 | + | 0.825585i | \(0.690845\pi\) | |||||||
\(264\) | 2.38889 | + | 3.87614i | 0.147026 | + | 0.238560i | ||||
\(265\) | − | 0.535513i | − | 0.0328963i | ||||||
\(266\) | 2.10896 | − | 0.575973i | 0.129309 | − | 0.0353151i | ||||
\(267\) | 1.63756 | 0.100217 | ||||||||
\(268\) | 14.2139 | + | 11.4703i | 0.868253 | + | 0.700662i | ||||
\(269\) | 19.0365 | 1.16067 | 0.580337 | − | 0.814376i | \(-0.302921\pi\) | ||||
0.580337 | + | 0.814376i | \(0.302921\pi\) | |||||||
\(270\) | −4.02945 | − | 1.42306i | −0.245224 | − | 0.0866045i | ||||
\(271\) | 2.47835 | 0.150549 | 0.0752745 | − | 0.997163i | \(-0.476017\pi\) | ||||
0.0752745 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(272\) | −26.5430 | + | 5.73608i | −1.60941 | + | 0.347801i | ||||
\(273\) | −3.78184 | − | 5.45622i | −0.228888 | − | 0.330226i | ||||
\(274\) | −3.00901 | + | 8.52015i | −0.181781 | + | 0.514721i | ||||
\(275\) | 3.04781 | 0.183790 | ||||||||
\(276\) | −4.77194 | − | 3.85086i | −0.287237 | − | 0.231795i | ||||
\(277\) | − | 16.0967i | − | 0.967159i | −0.875301 | − | 0.483579i | \(-0.839336\pi\) | ||
0.875301 | − | 0.483579i | \(-0.160664\pi\) | |||||||
\(278\) | 29.0873 | + | 10.2726i | 1.74454 | + | 0.616109i | ||||
\(279\) | 8.50565 | 0.509220 | ||||||||
\(280\) | 2.99922 | − | 6.85600i | 0.179238 | − | 0.409724i | ||||
\(281\) | 17.4111 | 1.03866 | 0.519328 | − | 0.854575i | \(-0.326182\pi\) | ||||
0.519328 | + | 0.854575i | \(0.326182\pi\) | |||||||
\(282\) | −2.08388 | − | 0.735954i | −0.124093 | − | 0.0438254i | ||||
\(283\) | − | 29.4211i | − | 1.74890i | −0.485114 | − | 0.874451i | \(-0.661222\pi\) | ||
0.485114 | − | 0.874451i | \(-0.338778\pi\) | |||||||
\(284\) | −12.1610 | + | 15.0698i | −0.721624 | + | 0.894229i | ||||
\(285\) | 0.308606 | 0.0182802 | ||||||||
\(286\) | 6.81888 | − | 19.3080i | 0.403209 | − | 1.14170i | ||||
\(287\) | −5.78132 | − | 8.34095i | −0.341261 | − | 0.492351i | ||||
\(288\) | −15.2692 | − | 1.94439i | −0.899744 | − | 0.114574i | ||||
\(289\) | −29.0897 | −1.71116 | ||||||||
\(290\) | 0.247606 | + | 0.0874456i | 0.0145399 | + | 0.00513498i | ||||
\(291\) | 7.13181 | 0.418074 | ||||||||
\(292\) | 15.6115 | − | 19.3456i | 0.913591 | − | 1.13211i | ||||
\(293\) | 23.7367 | 1.38671 | 0.693357 | − | 0.720594i | \(-0.256131\pi\) | ||||
0.693357 | + | 0.720594i | \(0.256131\pi\) | |||||||
\(294\) | −3.36078 | + | 4.00553i | −0.196005 | + | 0.233607i | ||||
\(295\) | − | 1.52116i | − | 0.0885651i | ||||||
\(296\) | 10.4572 | + | 16.9675i | 0.607812 | + | 0.986218i | ||||
\(297\) | 9.20962i | 0.534396i | ||||||||
\(298\) | 15.3560 | + | 5.42320i | 0.889551 | + | 0.314158i | ||||
\(299\) | 27.5768i | 1.59481i | ||||||||
\(300\) | 0.663391 | − | 0.822067i | 0.0383009 | − | 0.0474621i | ||||
\(301\) | −3.12155 | + | 2.16362i | −0.179923 | + | 0.124709i | ||||
\(302\) | −10.2809 | − | 3.63083i | −0.591597 | − | 0.208931i | ||||
\(303\) | − | 0.685795i | − | 0.0393979i | ||||||
\(304\) | 2.28441 | − | 0.493672i | 0.131020 | − | 0.0283140i | ||||
\(305\) | −13.2354 | −0.757855 | ||||||||
\(306\) | −24.6336 | − | 8.69969i | −1.40821 | − | 0.497328i | ||||
\(307\) | − | 3.27590i | − | 0.186965i | −0.995621 | − | 0.0934827i | \(-0.970200\pi\) | ||
0.995621 | − | 0.0934827i | \(-0.0298000\pi\) | |||||||
\(308\) | −16.0847 | − | 1.17442i | −0.916510 | − | 0.0669185i | ||||
\(309\) | − | 10.0801i | − | 0.573434i | ||||||
\(310\) | −1.47212 | + | 4.16837i | −0.0836107 | + | 0.236747i | ||||
\(311\) | −20.9116 | −1.18579 | −0.592893 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592893 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(312\) | −3.72361 | − | 6.04182i | −0.210808 | − | 0.342050i | ||||
\(313\) | 13.8819i | 0.784650i | 0.919827 | + | 0.392325i | \(0.128329\pi\) | ||||
−0.919827 | + | 0.392325i | \(0.871671\pi\) | |||||||
\(314\) | −2.08209 | + | 5.89554i | −0.117499 | + | 0.332704i | ||||
\(315\) | 5.91683 | − | 4.10111i | 0.333376 | − | 0.231071i | ||||
\(316\) | −3.53418 | + | 4.37951i | −0.198813 | + | 0.246367i | ||||
\(317\) | − | 5.93227i | − | 0.333190i | −0.986025 | − | 0.166595i | \(-0.946723\pi\) | ||
0.986025 | − | 0.166595i | \(-0.0532772\pi\) | |||||||
\(318\) | −0.133204 | + | 0.377174i | −0.00746973 | + | 0.0211509i | ||||
\(319\) | − | 0.565923i | − | 0.0316856i | ||||||
\(320\) | 3.59560 | − | 7.14644i | 0.201000 | − | 0.399498i | ||||
\(321\) | − | 2.01289i | − | 0.112349i | ||||||
\(322\) | 20.9523 | − | 5.72222i | 1.16762 | − | 0.318887i | ||||
\(323\) | 3.96668 | 0.220712 | ||||||||
\(324\) | −10.2212 | − | 8.24828i | −0.567843 | − | 0.458238i | ||||
\(325\) | −4.75069 | −0.263521 | ||||||||
\(326\) | −8.26388 | + | 23.3995i | −0.457694 | + | 1.29598i | ||||
\(327\) | −8.00118 | −0.442466 | ||||||||
\(328\) | −5.69230 | − | 9.23615i | −0.314305 | − | 0.509981i | ||||
\(329\) | 6.43367 | − | 4.45934i | 0.354700 | − | 0.245851i | ||||
\(330\) | −2.14664 | − | 0.758117i | −0.118169 | − | 0.0417330i | ||||
\(331\) | −7.33151 | −0.402976 | −0.201488 | − | 0.979491i | \(-0.564578\pi\) | ||||
−0.201488 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(332\) | −16.8976 | + | 20.9393i | −0.927376 | + | 1.14919i | ||||
\(333\) | 19.1743i | 1.05075i | ||||||||
\(334\) | 0.742192 | − | 2.10155i | 0.0406109 | − | 0.114992i | ||||
\(335\) | −9.13242 | −0.498957 | ||||||||
\(336\) | −3.81779 | + | 4.08280i | −0.208277 | + | 0.222735i | ||||
\(337\) | −16.5861 | −0.903505 | −0.451752 | − | 0.892143i | \(-0.649201\pi\) | ||||
−0.451752 | + | 0.892143i | \(0.649201\pi\) | |||||||
\(338\) | −4.50647 | + | 12.7603i | −0.245120 | + | 0.694067i | ||||
\(339\) | − | 8.78945i | − | 0.477378i | ||||||
\(340\) | 8.52693 | − | 10.5665i | 0.462438 | − | 0.573048i | ||||
\(341\) | 9.52714 | 0.515923 | ||||||||
\(342\) | 2.12007 | + | 0.748733i | 0.114640 | + | 0.0404868i | ||||
\(343\) | −4.53701 | − | 17.9559i | −0.244976 | − | 0.969529i | ||||
\(344\) | −3.45657 | + | 2.13031i | −0.186366 | + | 0.114859i | ||||
\(345\) | 3.06597 | 0.165066 | ||||||||
\(346\) | −0.0983868 | + | 0.278586i | −0.00528931 | + | 0.0149769i | ||||
\(347\) | 28.9802 | 1.55574 | 0.777870 | − | 0.628425i | \(-0.216300\pi\) | ||||
0.777870 | + | 0.628425i | \(0.216300\pi\) | |||||||
\(348\) | −0.152643 | − | 0.123180i | −0.00818252 | − | 0.00660313i | ||||
\(349\) | 10.2706 | 0.549772 | 0.274886 | − | 0.961477i | \(-0.411360\pi\) | ||||
0.274886 | + | 0.961477i | \(0.411360\pi\) | |||||||
\(350\) | 0.985772 | + | 3.60947i | 0.0526918 | + | 0.192934i | ||||
\(351\) | − | 14.3552i | − | 0.766225i | ||||||
\(352\) | −17.1029 | − | 2.17790i | −0.911589 | − | 0.116082i | ||||
\(353\) | 24.6097i | 1.30984i | 0.755697 | + | 0.654921i | \(0.227298\pi\) | ||||
−0.755697 | + | 0.654921i | \(0.772702\pi\) | |||||||
\(354\) | −0.378374 | + | 1.07138i | −0.0201104 | + | 0.0569434i | ||||
\(355\) | − | 9.68233i | − | 0.513885i | ||||||
\(356\) | −3.89412 | + | 4.82555i | −0.206388 | + | 0.255754i | ||||
\(357\) | −7.79718 | + | 5.40442i | −0.412671 | + | 0.286032i | ||||
\(358\) | 2.75354 | − | 7.79676i | 0.145529 | − | 0.412072i | ||||
\(359\) | 5.06081i | 0.267099i | 0.991042 | + | 0.133550i | \(0.0426375\pi\) | ||||
−0.991042 | + | 0.133550i | \(0.957362\pi\) | |||||||
\(360\) | 6.55186 | − | 4.03795i | 0.345314 | − | 0.212819i | ||||
\(361\) | 18.6586 | 0.982032 | ||||||||
\(362\) | −4.08157 | + | 11.5571i | −0.214523 | + | 0.607430i | ||||
\(363\) | − | 0.903627i | − | 0.0474281i | ||||||
\(364\) | 25.0715 | + | 1.83059i | 1.31411 | + | 0.0959487i | ||||
\(365\) | 12.4295i | 0.650589i | ||||||||
\(366\) | 9.32196 | + | 3.29218i | 0.487266 | + | 0.172085i | ||||
\(367\) | −12.8106 | −0.668708 | −0.334354 | − | 0.942447i | \(-0.608518\pi\) | ||||
−0.334354 | + | 0.942447i | \(0.608518\pi\) | |||||||
\(368\) | 22.6953 | − | 4.90458i | 1.18308 | − | 0.255669i | ||||
\(369\) | − | 10.4374i | − | 0.543350i | ||||||
\(370\) | −9.39678 | − | 3.31861i | −0.488515 | − | 0.172526i | ||||
\(371\) | −0.807120 | − | 1.16447i | −0.0419036 | − | 0.0604560i | ||||
\(372\) | 2.07369 | − | 2.56970i | 0.107516 | − | 0.133232i | ||||
\(373\) | 12.4155i | 0.642849i | 0.946935 | + | 0.321425i | \(0.104162\pi\) | ||||
−0.946935 | + | 0.321425i | \(0.895838\pi\) | |||||||
\(374\) | −27.5919 | − | 9.74449i | −1.42674 | − | 0.503875i | ||||
\(375\) | 0.528177i | 0.0272749i | ||||||||
\(376\) | 7.12417 | − | 4.39067i | 0.367401 | − | 0.226431i | ||||
\(377\) | 0.882116i | 0.0454313i | ||||||||
\(378\) | −10.9068 | + | 2.97872i | −0.560984 | + | 0.153209i | ||||
\(379\) | 9.41586 | 0.483660 | 0.241830 | − | 0.970319i | \(-0.422252\pi\) | ||||
0.241830 | + | 0.970319i | \(0.422252\pi\) | |||||||
\(380\) | −0.733864 | + | 0.909396i | −0.0376464 | + | 0.0466511i | ||||
\(381\) | −8.40185 | −0.430440 | ||||||||
\(382\) | −17.3009 | − | 6.11005i | −0.885189 | − | 0.312617i | ||||
\(383\) | 28.8384 | 1.47358 | 0.736788 | − | 0.676124i | \(-0.236342\pi\) | ||||
0.736788 | + | 0.676124i | \(0.236342\pi\) | |||||||
\(384\) | −4.31008 | + | 4.13902i | −0.219948 | + | 0.211218i | ||||
\(385\) | 6.62742 | − | 4.59363i | 0.337765 | − | 0.234113i | ||||
\(386\) | 11.5790 | − | 32.7865i | 0.589357 | − | 1.66879i | ||||
\(387\) | −3.90614 | −0.198560 | ||||||||
\(388\) | −16.9594 | + | 21.0159i | −0.860984 | + | 1.06692i | ||||
\(389\) | − | 4.35382i | − | 0.220747i | −0.993890 | − | 0.110374i | \(-0.964795\pi\) | ||
0.993890 | − | 0.110374i | \(-0.0352048\pi\) | |||||||
\(390\) | 3.34601 | + | 1.18169i | 0.169432 | + | 0.0598373i | ||||
\(391\) | 39.4085 | 1.99297 | ||||||||
\(392\) | −3.81153 | − | 19.4286i | −0.192511 | − | 0.981295i | ||||
\(393\) | −10.6924 | −0.539359 | ||||||||
\(394\) | 9.61709 | + | 3.39641i | 0.484502 | + | 0.171109i | ||||
\(395\) | − | 2.81383i | − | 0.141579i | ||||||
\(396\) | −12.9077 | − | 10.4163i | −0.648637 | − | 0.523437i | ||||
\(397\) | −16.9988 | −0.853148 | −0.426574 | − | 0.904453i | \(-0.640280\pi\) | ||||
−0.426574 | + | 0.904453i | \(0.640280\pi\) | |||||||
\(398\) | −2.98017 | + | 8.43847i | −0.149382 | + | 0.422982i | ||||
\(399\) | 0.671059 | − | 0.465128i | 0.0335950 | − | 0.0232855i | ||||
\(400\) | 0.844916 | + | 3.90975i | 0.0422458 | + | 0.195487i | ||||
\(401\) | 10.4337 | 0.521035 | 0.260518 | − | 0.965469i | \(-0.416107\pi\) | ||||
0.260518 | + | 0.965469i | \(0.416107\pi\) | |||||||
\(402\) | 6.43216 | + | 2.27161i | 0.320807 | + | 0.113298i | ||||
\(403\) | −14.8501 | −0.739738 | ||||||||
\(404\) | 2.02089 | + | 1.63082i | 0.100543 | + | 0.0811362i | ||||
\(405\) | 6.56709 | 0.326321 | ||||||||
\(406\) | 0.670212 | − | 0.183040i | 0.0332621 | − | 0.00908412i | ||||
\(407\) | 21.4771i | 1.06458i | ||||||||
\(408\) | −8.63402 | + | 5.32120i | −0.427448 | + | 0.263439i | ||||
\(409\) | 27.7527i | 1.37228i | 0.727469 | + | 0.686141i | \(0.240697\pi\) | ||||
−0.727469 | + | 0.686141i | \(0.759303\pi\) | |||||||
\(410\) | 5.11507 | + | 1.80646i | 0.252615 | + | 0.0892147i | ||||
\(411\) | 3.37470i | 0.166461i | ||||||||
\(412\) | 29.7038 | + | 23.9703i | 1.46340 | + | 1.18093i | ||||
\(413\) | −2.29267 | − | 3.30773i | −0.112815 | − | 0.162763i | ||||
\(414\) | 21.0626 | + | 7.43858i | 1.03517 | + | 0.365586i | ||||
\(415\) | − | 13.4535i | − | 0.660405i | ||||||
\(416\) | 26.6587 | + | 3.39473i | 1.30705 | + | 0.166440i | ||||
\(417\) | 11.5210 | 0.564186 | ||||||||
\(418\) | 2.37468 | + | 0.838652i | 0.116149 | + | 0.0410198i | ||||
\(419\) | 30.1125i | 1.47109i | 0.677476 | + | 0.735545i | \(0.263074\pi\) | ||||
−0.677476 | + | 0.735545i | \(0.736926\pi\) | |||||||
\(420\) | 0.203523 | − | 2.78743i | 0.00993089 | − | 0.136013i | ||||
\(421\) | 27.1321i | 1.32234i | 0.750236 | + | 0.661170i | \(0.229940\pi\) | ||||
−0.750236 | + | 0.661170i | \(0.770060\pi\) | |||||||
\(422\) | 4.81356 | − | 13.6298i | 0.234321 | − | 0.663489i | ||||
\(423\) | 8.05074 | 0.391440 | ||||||||
\(424\) | −0.794691 | − | 1.28944i | −0.0385936 | − | 0.0626209i | ||||
\(425\) | 6.78894i | 0.329312i | ||||||||
\(426\) | −2.40840 | + | 6.81948i | −0.116687 | + | 0.330405i | ||||
\(427\) | −28.7801 | + | 19.9482i | −1.39277 | + | 0.965361i | ||||
\(428\) | 5.93156 | + | 4.78665i | 0.286713 | + | 0.231371i | ||||
\(429\) | − | 7.64758i | − | 0.369229i | ||||||
\(430\) | 0.676056 | − | 1.91428i | 0.0326023 | − | 0.0923149i | ||||
\(431\) | 3.80266i | 0.183167i | 0.995797 | + | 0.0915837i | \(0.0291929\pi\) | ||||
−0.995797 | + | 0.0915837i | \(0.970807\pi\) | |||||||
\(432\) | −11.8141 | + | 2.55309i | −0.568408 | + | 0.122836i | ||||
\(433\) | − | 6.04283i | − | 0.290400i | −0.989402 | − | 0.145200i | \(-0.953617\pi\) | ||
0.989402 | − | 0.145200i | \(-0.0463825\pi\) | |||||||
\(434\) | 3.08142 | + | 11.2828i | 0.147913 | + | 0.541592i | ||||
\(435\) | 0.0980728 | 0.00470223 | ||||||||
\(436\) | 19.0268 | − | 23.5778i | 0.911217 | − | 1.12917i | ||||
\(437\) | −3.39167 | −0.162245 | ||||||||
\(438\) | 3.09173 | − | 8.75435i | 0.147728 | − | 0.418299i | ||||
\(439\) | −20.7511 | −0.990398 | −0.495199 | − | 0.868780i | \(-0.664905\pi\) | ||||
−0.495199 | + | 0.868780i | \(0.664905\pi\) | |||||||
\(440\) | 7.33871 | − | 4.52289i | 0.349859 | − | 0.215621i | ||||
\(441\) | 6.68492 | − | 17.8356i | 0.318329 | − | 0.849313i | ||||
\(442\) | 43.0081 | + | 15.1889i | 2.04569 | + | 0.722464i | ||||
\(443\) | 40.9174 | 1.94404 | 0.972022 | − | 0.234891i | \(-0.0754733\pi\) | ||||
0.972022 | + | 0.234891i | \(0.0754733\pi\) | |||||||
\(444\) | 5.79288 | + | 4.67474i | 0.274918 | + | 0.221853i | ||||
\(445\) | − | 3.10041i | − | 0.146973i | ||||||
\(446\) | 1.24590 | − | 3.52781i | 0.0589949 | − | 0.167047i | ||||
\(447\) | 6.08228 | 0.287682 | ||||||||
\(448\) | −2.95246 | − | 20.9591i | −0.139491 | − | 0.990223i | ||||
\(449\) | 9.64737 | 0.455288 | 0.227644 | − | 0.973744i | \(-0.426898\pi\) | ||||
0.227644 | + | 0.973744i | \(0.426898\pi\) | |||||||
\(450\) | −1.28145 | + | 3.62848i | −0.0604082 | + | 0.171048i | ||||
\(451\) | − | 11.6909i | − | 0.550503i | ||||||
\(452\) | 25.9006 | + | 20.9013i | 1.21826 | + | 0.983114i | ||||
\(453\) | −4.07209 | −0.191323 | ||||||||
\(454\) | 21.7332 | + | 7.67540i | 1.01999 | + | 0.360224i | ||||
\(455\) | −10.3303 | + | 7.16019i | −0.484292 | + | 0.335675i | ||||
\(456\) | 0.743081 | − | 0.457965i | 0.0347980 | − | 0.0214462i | ||||
\(457\) | 8.31667 | 0.389037 | 0.194519 | − | 0.980899i | \(-0.437686\pi\) | ||||
0.194519 | + | 0.980899i | \(0.437686\pi\) | |||||||
\(458\) | 2.59886 | − | 7.35877i | 0.121437 | − | 0.343853i | ||||
\(459\) | −20.5142 | −0.957523 | ||||||||
\(460\) | −7.29085 | + | 9.03475i | −0.339938 | + | 0.421247i | ||||
\(461\) | −14.8017 | −0.689385 | −0.344693 | − | 0.938716i | \(-0.612017\pi\) | ||||
−0.344693 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(462\) | −5.81046 | + | 1.58688i | −0.270327 | + | 0.0738284i | ||||
\(463\) | − | 10.2328i | − | 0.475556i | −0.971319 | − | 0.237778i | \(-0.923581\pi\) | ||
0.971319 | − | 0.237778i | \(-0.0764191\pi\) | |||||||
\(464\) | 0.725969 | − | 0.156885i | 0.0337023 | − | 0.00728323i | ||||
\(465\) | 1.65102i | 0.0765644i | ||||||||
\(466\) | −8.77432 | + | 24.8449i | −0.406463 | + | 1.15092i | ||||
\(467\) | − | 1.49149i | − | 0.0690179i | −0.999404 | − | 0.0345090i | \(-0.989013\pi\) | ||
0.999404 | − | 0.0345090i | \(-0.0109867\pi\) | |||||||
\(468\) | 20.1195 | + | 16.2360i | 0.930026 | + | 0.750511i | ||||
\(469\) | −19.8583 | + | 13.7643i | −0.916971 | + | 0.635575i | ||||
\(470\) | −1.39338 | + | 3.94543i | −0.0642721 | + | 0.181989i | ||||
\(471\) | 2.33513i | 0.107597i | ||||||||
\(472\) | −2.25737 | − | 3.66273i | −0.103904 | − | 0.168591i | ||||
\(473\) | −4.37524 | −0.201174 | ||||||||
\(474\) | −0.699916 | + | 1.98184i | −0.0321482 | + | 0.0910290i | ||||
\(475\) | − | 0.584285i | − | 0.0268089i | ||||||
\(476\) | 2.61599 | − | 35.8283i | 0.119904 | − | 1.64219i | ||||
\(477\) | − | 1.45715i | − | 0.0667182i | ||||||
\(478\) | −7.70326 | − | 2.72052i | −0.352339 | − | 0.124434i | ||||
\(479\) | −33.0698 | −1.51100 | −0.755499 | − | 0.655150i | \(-0.772605\pi\) | ||||
−0.755499 | + | 0.655150i | \(0.772605\pi\) | |||||||
\(480\) | 0.377423 | − | 2.96389i | 0.0172269 | − | 0.135282i | ||||
\(481\) | − | 33.4768i | − | 1.52641i | ||||||
\(482\) | 1.90494 | + | 0.672759i | 0.0867679 | + | 0.0306433i | ||||
\(483\) | 6.66689 | − | 4.62099i | 0.303354 | − | 0.210262i | ||||
\(484\) | 2.66280 | + | 2.14882i | 0.121036 | + | 0.0976737i | ||||
\(485\) | − | 13.5027i | − | 0.613126i | ||||||
\(486\) | −16.7137 | − | 5.90268i | −0.758148 | − | 0.267751i | ||||
\(487\) | − | 30.3143i | − | 1.37367i | −0.726811 | − | 0.686837i | \(-0.758999\pi\) | ||
0.726811 | − | 0.686837i | \(-0.241001\pi\) | |||||||
\(488\) | −31.8689 | + | 19.6410i | −1.44264 | + | 0.889107i | ||||
\(489\) | 9.26819i | 0.419122i | ||||||||
\(490\) | 7.58370 | + | 6.36298i | 0.342596 | + | 0.287450i | ||||
\(491\) | −24.0080 | −1.08347 | −0.541733 | − | 0.840551i | \(-0.682232\pi\) | ||||
−0.541733 | + | 0.840551i | \(0.682232\pi\) | |||||||
\(492\) | −3.15331 | − | 2.54466i | −0.142162 | − | 0.114722i | ||||
\(493\) | 1.26058 | 0.0567738 | ||||||||
\(494\) | −3.70146 | − | 1.30722i | −0.166537 | − | 0.0588148i | ||||
\(495\) | 8.29319 | 0.372751 | ||||||||
\(496\) | 2.64112 | + | 12.2215i | 0.118590 | + | 0.548759i | ||||
\(497\) | −14.5931 | − | 21.0541i | −0.654590 | − | 0.944404i | ||||
\(498\) | −3.34643 | + | 9.47557i | −0.149957 | + | 0.424611i | ||||
\(499\) | −36.6238 | −1.63951 | −0.819754 | − | 0.572716i | \(-0.805890\pi\) | ||||
−0.819754 | + | 0.572716i | \(0.805890\pi\) | |||||||
\(500\) | −1.55642 | − | 1.25600i | −0.0696054 | − | 0.0561701i | ||||
\(501\) | − | 0.832390i | − | 0.0371884i | ||||||
\(502\) | −15.5157 | − | 5.47961i | −0.692502 | − | 0.244567i | ||||
\(503\) | −0.225539 | −0.0100563 | −0.00502815 | − | 0.999987i | \(-0.501601\pi\) | ||||
−0.00502815 | + | 0.999987i | \(0.501601\pi\) | |||||||
\(504\) | 8.16096 | − | 18.6554i | 0.363518 | − | 0.830976i | ||||
\(505\) | −1.29842 | −0.0577789 | ||||||||
\(506\) | 23.5922 | + | 8.33191i | 1.04880 | + | 0.370399i | ||||
\(507\) | 5.05414i | 0.224462i | ||||||||
\(508\) | 19.9796 | − | 24.7585i | 0.886450 | − | 1.09848i | ||||
\(509\) | 11.4130 | 0.505871 | 0.252935 | − | 0.967483i | \(-0.418604\pi\) | ||||
0.252935 | + | 0.967483i | \(0.418604\pi\) | |||||||
\(510\) | 1.68869 | − | 4.78160i | 0.0747765 | − | 0.211733i | ||||
\(511\) | 18.7336 | + | 27.0277i | 0.828725 | + | 1.19564i | ||||
\(512\) | −1.94746 | − | 22.5435i | −0.0860665 | − | 0.996289i | ||||
\(513\) | 1.76554 | 0.0779507 | ||||||||
\(514\) | 16.0035 | + | 5.65186i | 0.705884 | + | 0.249293i | ||||
\(515\) | −19.0846 | −0.840969 | ||||||||
\(516\) | −0.952322 | + | 1.18011i | −0.0419237 | + | 0.0519513i | ||||
\(517\) | 9.01759 | 0.396593 | ||||||||
\(518\) | −25.4349 | + | 6.94647i | −1.11755 | + | 0.305210i | ||||
\(519\) | 0.110344i | 0.00484355i | ||||||||
\(520\) | −11.4390 | + | 7.04993i | −0.501633 | + | 0.309160i | ||||
\(521\) | 18.6069i | 0.815183i | 0.913164 | + | 0.407591i | \(0.133631\pi\) | ||||
−0.913164 | + | 0.407591i | \(0.866369\pi\) | |||||||
\(522\) | 0.673743 | + | 0.237942i | 0.0294889 | + | 0.0104144i | ||||
\(523\) | − | 35.5417i | − | 1.55413i | −0.629420 | − | 0.777065i | \(-0.716708\pi\) | ||
0.629420 | − | 0.777065i | \(-0.283292\pi\) | |||||||
\(524\) | 25.4264 | − | 31.5081i | 1.11076 | − | 1.37644i | ||||
\(525\) | 0.796062 | + | 1.14851i | 0.0347430 | + | 0.0501252i | ||||
\(526\) | −35.7077 | − | 12.6107i | −1.55693 | − | 0.549852i | ||||
\(527\) | 21.2215i | 0.924424i | ||||||||
\(528\) | −6.29385 | + | 1.36013i | −0.273904 | + | 0.0591921i | ||||
\(529\) | −10.6958 | −0.465035 | ||||||||
\(530\) | 0.714105 | + | 0.252196i | 0.0310187 | + | 0.0109547i | ||||
\(531\) | − | 4.13911i | − | 0.179622i | ||||||
\(532\) | −0.225143 | + | 3.08354i | −0.00976119 | + | 0.133688i | ||||
\(533\) | 18.2228i | 0.789319i | ||||||||
\(534\) | −0.771199 | + | 2.18368i | −0.0333731 | + | 0.0944972i | ||||
\(535\) | −3.81102 | −0.164765 | ||||||||
\(536\) | −21.9896 | + | 13.5523i | −0.949806 | + | 0.585371i | ||||
\(537\) | − | 3.08817i | − | 0.133265i | ||||||
\(538\) | −8.96510 | + | 25.3851i | −0.386513 | + | 1.09443i | ||||
\(539\) | 7.48775 | − | 19.9775i | 0.322520 | − | 0.860494i | ||||
\(540\) | 3.79528 | − | 4.70307i | 0.163323 | − | 0.202388i | ||||
\(541\) | 40.2046i | 1.72853i | 0.503035 | + | 0.864266i | \(0.332216\pi\) | ||||
−0.503035 | + | 0.864266i | \(0.667784\pi\) | |||||||
\(542\) | −1.16716 | + | 3.30487i | −0.0501339 | + | 0.141956i | ||||
\(543\) | 4.57760i | 0.196444i | ||||||||
\(544\) | 4.85122 | − | 38.0964i | 0.207994 | − | 1.63337i | ||||
\(545\) | 15.1487i | 0.648898i | ||||||||
\(546\) | 9.05689 | − | 2.47350i | 0.387599 | − | 0.105856i | ||||
\(547\) | −6.38283 | −0.272910 | −0.136455 | − | 0.990646i | \(-0.543571\pi\) | ||||
−0.136455 | + | 0.990646i | \(0.543571\pi\) | |||||||
\(548\) | −9.94451 | − | 8.02501i | −0.424808 | − | 0.342812i | ||||
\(549\) | −36.0138 | −1.53703 | ||||||||
\(550\) | −1.43535 | + | 4.06425i | −0.0612034 | + | 0.173300i | ||||
\(551\) | −0.108491 | −0.00462188 | ||||||||
\(552\) | 7.38242 | − | 4.54983i | 0.314217 | − | 0.193654i | ||||
\(553\) | −4.24097 | − | 6.11863i | −0.180344 | − | 0.260190i | ||||
\(554\) | 21.4649 | + | 7.58065i | 0.911957 | + | 0.322071i | ||||
\(555\) | −3.72192 | −0.157987 | ||||||||
\(556\) | −27.3969 | + | 33.9500i | −1.16189 | + | 1.43980i | ||||
\(557\) | 33.9096i | 1.43680i | 0.695631 | + | 0.718399i | \(0.255125\pi\) | ||||
−0.695631 | + | 0.718399i | \(0.744875\pi\) | |||||||
\(558\) | −4.00568 | + | 11.3422i | −0.169574 | + | 0.480156i | ||||
\(559\) | 6.81978 | 0.288446 | ||||||||
\(560\) | 7.72998 | + | 7.22823i | 0.326651 | + | 0.305449i | ||||
\(561\) | −10.9287 | −0.461411 | ||||||||
\(562\) | −8.19962 | + | 23.2176i | −0.345880 | + | 0.979375i | ||||
\(563\) | − | 13.9112i | − | 0.586288i | −0.956068 | − | 0.293144i | \(-0.905298\pi\) | ||
0.956068 | − | 0.293144i | \(-0.0947016\pi\) | |||||||
\(564\) | 1.96278 | − | 2.43226i | 0.0826481 | − | 0.102417i | ||||
\(565\) | −16.6411 | −0.700097 | ||||||||
\(566\) | 39.2329 | + | 13.8557i | 1.64908 | + | 0.582397i | ||||
\(567\) | 14.2800 | − | 9.89784i | 0.599705 | − | 0.415670i | ||||
\(568\) | −14.3684 | − | 23.3137i | −0.602884 | − | 0.978222i | ||||
\(569\) | −23.6948 | −0.993336 | −0.496668 | − | 0.867940i | \(-0.665443\pi\) | ||||
−0.496668 | + | 0.867940i | \(0.665443\pi\) | |||||||
\(570\) | −0.145336 | + | 0.411525i | −0.00608745 | + | 0.0172369i | ||||
\(571\) | 20.9646 | 0.877340 | 0.438670 | − | 0.898648i | \(-0.355450\pi\) | ||||
0.438670 | + | 0.898648i | \(0.355450\pi\) | |||||||
\(572\) | 22.5358 | + | 18.1859i | 0.942269 | + | 0.760391i | ||||
\(573\) | −6.85260 | −0.286271 | ||||||||
\(574\) | 13.8453 | − | 3.78126i | 0.577892 | − | 0.157827i | ||||
\(575\) | − | 5.80481i | − | 0.242077i | ||||||
\(576\) | 9.78374 | − | 19.4457i | 0.407656 | − | 0.810237i | ||||
\(577\) | − | 11.5447i | − | 0.480614i | −0.970697 | − | 0.240307i | \(-0.922752\pi\) | ||
0.970697 | − | 0.240307i | \(-0.0772481\pi\) | |||||||
\(578\) | 13.6996 | − | 38.7911i | 0.569829 | − | 1.61350i | ||||
\(579\) | − | 12.9862i | − | 0.539689i | ||||||
\(580\) | −0.233217 | + | 0.289000i | −0.00968380 | + | 0.0120001i | ||||
\(581\) | −20.2769 | − | 29.2544i | −0.841229 | − | 1.21368i | ||||
\(582\) | −3.35868 | + | 9.51024i | −0.139222 | + | 0.394212i | ||||
\(583\) | − | 1.63214i | − | 0.0675965i | ||||||
\(584\) | 18.4451 | + | 29.9285i | 0.763264 | + | 1.23845i | ||||
\(585\) | −12.9268 | −0.534456 | ||||||||
\(586\) | −11.1786 | + | 31.6528i | −0.461786 | + | 1.30757i | ||||
\(587\) | − | 8.38593i | − | 0.346124i | −0.984911 | − | 0.173062i | \(-0.944634\pi\) | ||
0.984911 | − | 0.173062i | \(-0.0553661\pi\) | |||||||
\(588\) | −3.75863 | − | 6.36797i | −0.155003 | − | 0.262611i | ||||
\(589\) | − | 1.82641i | − | 0.0752561i | ||||||
\(590\) | 2.02846 | + | 0.716378i | 0.0835102 | + | 0.0294928i | ||||
\(591\) | 3.80918 | 0.156689 | ||||||||
\(592\) | −27.5509 | + | 5.95389i | −1.13234 | + | 0.244703i | ||||
\(593\) | − | 26.8713i | − | 1.10347i | −0.834018 | − | 0.551737i | \(-0.813965\pi\) | ||
0.834018 | − | 0.551737i | \(-0.186035\pi\) | |||||||
\(594\) | −12.2810 | − | 4.33721i | −0.503895 | − | 0.177958i | ||||
\(595\) | 10.2322 | + | 14.7624i | 0.419480 | + | 0.605201i | ||||
\(596\) | −14.4636 | + | 17.9232i | −0.592454 | + | 0.734162i | ||||
\(597\) | 3.34234i | 0.136793i | ||||||||
\(598\) | −36.7736 | − | 12.9871i | −1.50378 | − | 0.531083i | ||||
\(599\) | − | 34.0473i | − | 1.39113i | −0.718462 | − | 0.695566i | \(-0.755153\pi\) | ||
0.718462 | − | 0.695566i | \(-0.244847\pi\) | |||||||
\(600\) | 0.783804 | + | 1.27178i | 0.0319987 | + | 0.0519201i | ||||
\(601\) | 24.5067i | 0.999649i | 0.866127 | + | 0.499825i | \(0.166602\pi\) | ||||
−0.866127 | + | 0.499825i | \(0.833398\pi\) | |||||||
\(602\) | −1.41511 | − | 5.18152i | −0.0576757 | − | 0.211183i | ||||
\(603\) | −24.8496 | −1.01195 | ||||||||
\(604\) | 9.68340 | − | 11.9996i | 0.394012 | − | 0.488256i | ||||
\(605\) | −1.71084 | −0.0695556 | ||||||||
\(606\) | 0.914505 | + | 0.322970i | 0.0371492 | + | 0.0131198i | ||||
\(607\) | 36.7082 | 1.48994 | 0.744971 | − | 0.667097i | \(-0.232463\pi\) | ||||
0.744971 | + | 0.667097i | \(0.232463\pi\) | |||||||
\(608\) | −0.417517 | + | 3.27874i | −0.0169326 | + | 0.132971i | ||||
\(609\) | 0.213258 | − | 0.147814i | 0.00864164 | − | 0.00598974i | ||||
\(610\) | 6.23311 | − | 17.6493i | 0.252371 | − | 0.714600i | ||||
\(611\) | −14.0559 | −0.568641 | ||||||||
\(612\) | 23.2020 | − | 28.7517i | 0.937886 | − | 1.16222i | ||||
\(613\) | 41.6702i | 1.68304i | 0.540224 | + | 0.841521i | \(0.318339\pi\) | ||||
−0.540224 | + | 0.841521i | \(0.681661\pi\) | |||||||
\(614\) | 4.36840 | + | 1.54276i | 0.176294 | + | 0.0622608i | ||||
\(615\) | 2.02600 | 0.0816961 | ||||||||
\(616\) | 9.14106 | − | 20.8958i | 0.368304 | − | 0.841915i | ||||
\(617\) | 18.6715 | 0.751688 | 0.375844 | − | 0.926683i | \(-0.377353\pi\) | ||||
0.375844 | + | 0.926683i | \(0.377353\pi\) | |||||||
\(618\) | 13.4417 | + | 4.74713i | 0.540705 | + | 0.190958i | ||||
\(619\) | − | 19.0302i | − | 0.764888i | −0.923979 | − | 0.382444i | \(-0.875083\pi\) | ||
0.923979 | − | 0.382444i | \(-0.124917\pi\) | |||||||
\(620\) | −4.86522 | − | 3.92613i | −0.195392 | − | 0.157677i | ||||
\(621\) | 17.5405 | 0.703875 | ||||||||
\(622\) | 9.84816 | − | 27.8855i | 0.394875 | − | 1.11811i | ||||
\(623\) | −4.67290 | − | 6.74178i | −0.187216 | − | 0.270104i | ||||
\(624\) | 9.81035 | − | 2.12007i | 0.392728 | − | 0.0848705i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.5114 | − | 6.53758i | −0.739866 | − | 0.261294i | ||||
\(627\) | 0.940573 | 0.0375629 | ||||||||
\(628\) | −6.88113 | − | 5.55293i | −0.274587 | − | 0.221586i | ||||
\(629\) | −47.8398 | −1.90750 | ||||||||
\(630\) | 2.68232 | + | 9.82147i | 0.106866 | + | 0.391297i | ||||
\(631\) | − | 28.1199i | − | 1.11944i | −0.828683 | − | 0.559718i | \(-0.810910\pi\) | ||
0.828683 | − | 0.559718i | \(-0.189090\pi\) | |||||||
\(632\) | −4.17567 | − | 6.77531i | −0.166099 | − | 0.269507i | ||||
\(633\) | − | 5.39855i | − | 0.214573i | ||||||
\(634\) | 7.91067 | + | 2.79377i | 0.314173 | + | 0.110955i | ||||
\(635\) | 15.9073i | 0.631261i | ||||||||
\(636\) | −0.440228 | − | 0.355255i | −0.0174562 | − | 0.0140868i | ||||
\(637\) | −11.6713 | + | 31.1394i | −0.462434 | + | 1.23379i | ||||
\(638\) | 0.754657 | + | 0.266518i | 0.0298771 | + | 0.0105515i | ||||
\(639\) | − | 26.3459i | − | 1.04223i | ||||||
\(640\) | 7.83643 | + | 8.16029i | 0.309762 | + | 0.322564i | ||||
\(641\) | −7.40297 | −0.292400 | −0.146200 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146200 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(642\) | 2.68418 | + | 0.947958i | 0.105936 | + | 0.0374129i | ||||
\(643\) | − | 10.9752i | − | 0.432819i | −0.976303 | − | 0.216409i | \(-0.930565\pi\) | ||
0.976303 | − | 0.216409i | \(-0.0694346\pi\) | |||||||
\(644\) | −2.23677 | + | 30.6346i | −0.0881411 | + | 1.20717i | ||||
\(645\) | − | 0.758217i | − | 0.0298548i | ||||||
\(646\) | −1.86808 | + | 5.28955i | −0.0734987 | + | 0.208115i | ||||
\(647\) | 37.3313 | 1.46765 | 0.733823 | − | 0.679340i | \(-0.237734\pi\) | ||||
0.733823 | + | 0.679340i | \(0.237734\pi\) | |||||||
\(648\) | 15.8126 | − | 9.74543i | 0.621179 | − | 0.382837i | ||||
\(649\) | − | 4.63620i | − | 0.181987i | ||||||
\(650\) | 2.23730 | − | 6.33502i | 0.0877543 | − | 0.248480i | ||||
\(651\) | 2.48841 | + | 3.59013i | 0.0975283 | + | 0.140708i | ||||
\(652\) | −27.3114 | − | 22.0397i | −1.06960 | − | 0.863142i | ||||
\(653\) | − | 27.0398i | − | 1.05815i | −0.848575 | − | 0.529074i | \(-0.822539\pi\) | ||
0.848575 | − | 0.529074i | \(-0.177461\pi\) | |||||||
\(654\) | 3.76810 | − | 10.6695i | 0.147344 | − | 0.417212i | ||||
\(655\) | 20.2439i | 0.790995i | ||||||||
\(656\) | 14.9971 | − | 3.24095i | 0.585539 | − | 0.126538i | ||||
\(657\) | 33.8210i | 1.31948i | ||||||||
\(658\) | 2.91662 | + | 10.6794i | 0.113701 | + | 0.416325i | ||||
\(659\) | 16.0036 | 0.623410 | 0.311705 | − | 0.950179i | \(-0.399100\pi\) | ||||
0.311705 | + | 0.950179i | \(0.399100\pi\) | |||||||
\(660\) | 2.02189 | − | 2.50551i | 0.0787020 | − | 0.0975267i | ||||
\(661\) | 28.7776 | 1.11932 | 0.559659 | − | 0.828723i | \(-0.310932\pi\) | ||||
0.559659 | + | 0.828723i | \(0.310932\pi\) | |||||||
\(662\) | 3.45273 | − | 9.77654i | 0.134194 | − | 0.379976i | ||||
\(663\) | 17.0348 | 0.661578 | ||||||||
\(664\) | −19.9647 | − | 32.3941i | −0.774780 | − | 1.25714i | ||||
\(665\) | −0.880629 | − | 1.27052i | −0.0341493 | − | 0.0492686i | ||||
\(666\) | −25.5689 | − | 9.03003i | −0.990775 | − | 0.349907i | ||||
\(667\) | −1.07785 | −0.0417344 | ||||||||
\(668\) | 2.45288 | + | 1.97942i | 0.0949046 | + | 0.0765861i | ||||
\(669\) | − | 1.39731i | − | 0.0540231i | ||||||
\(670\) | 4.30085 | − | 12.1780i | 0.166156 | − | 0.470479i | ||||
\(671\) | −40.3389 | −1.55727 | ||||||||
\(672\) | −3.64644 | − | 7.01377i | −0.140664 | − | 0.270562i | ||||
\(673\) | 19.6820 | 0.758685 | 0.379342 | − | 0.925256i | \(-0.376150\pi\) | ||||
0.379342 | + | 0.925256i | \(0.376150\pi\) | |||||||
\(674\) | 7.81113 | − | 22.1176i | 0.300874 | − | 0.851937i | ||||
\(675\) | 3.02172i | 0.116306i | ||||||||
\(676\) | −14.8935 | − | 12.0187i | −0.572826 | − | 0.462259i | ||||
\(677\) | 41.7128 | 1.60315 | 0.801576 | − | 0.597893i | \(-0.203995\pi\) | ||||
0.801576 | + | 0.597893i | \(0.203995\pi\) | |||||||
\(678\) | 11.7207 | + | 4.13933i | 0.450131 | + | 0.158970i | ||||
\(679\) | −20.3511 | − | 29.3614i | −0.781004 | − | 1.12679i | ||||
\(680\) | 10.0747 | + | 16.3468i | 0.386346 | + | 0.626873i | ||||
\(681\) | 8.60819 | 0.329866 | ||||||||
\(682\) | −4.48674 | + | 12.7044i | −0.171806 | + | 0.486477i | ||||
\(683\) | −22.1942 | −0.849237 | −0.424618 | − | 0.905372i | \(-0.639592\pi\) | ||||
−0.424618 | + | 0.905372i | \(0.639592\pi\) | |||||||
\(684\) | −1.99687 | + | 2.47449i | −0.0763521 | + | 0.0946146i | ||||
\(685\) | 6.38933 | 0.244124 | ||||||||
\(686\) | 26.0808 | + | 2.40614i | 0.995771 | + | 0.0918668i | ||||
\(687\) | − | 2.91469i | − | 0.111202i | ||||||
\(688\) | −1.21291 | − | 5.61258i | −0.0462417 | − | 0.213978i | ||||
\(689\) | 2.54406i | 0.0969208i | ||||||||
\(690\) | −1.44390 | + | 4.08845i | −0.0549682 | + | 0.155645i | ||||
\(691\) | 7.35566i | 0.279822i | 0.990164 | + | 0.139911i | \(0.0446817\pi\) | ||||
−0.990164 | + | 0.139911i | \(0.955318\pi\) | |||||||
\(692\) | −0.325159 | − | 0.262397i | −0.0123607 | − | 0.00997483i | ||||
\(693\) | 18.0334 | − | 12.4994i | 0.685032 | − | 0.474813i | ||||
\(694\) | −13.6481 | + | 38.6450i | −0.518073 | + | 1.46695i | ||||
\(695\) | − | 21.8128i | − | 0.827406i | ||||||
\(696\) | 0.236146 | − | 0.145538i | 0.00895109 | − | 0.00551661i | ||||
\(697\) | 26.0412 | 0.986382 | ||||||||
\(698\) | −4.83687 | + | 13.6958i | −0.183078 | + | 0.518393i | ||||
\(699\) | 9.84066i | 0.372208i | ||||||||
\(700\) | −5.27745 | − | 0.385331i | −0.199469 | − | 0.0145641i | ||||
\(701\) | − | 10.2820i | − | 0.388346i | −0.980967 | − | 0.194173i | \(-0.937798\pi\) | ||
0.980967 | − | 0.194173i | \(-0.0622024\pi\) | |||||||
\(702\) | 19.1426 | + | 6.76050i | 0.722492 | + | 0.255159i | ||||
\(703\) | 4.11730 | 0.155287 | ||||||||
\(704\) | 10.9587 | − | 21.7810i | 0.413022 | − | 0.820903i | ||||
\(705\) | 1.56272i | 0.0588555i | ||||||||
\(706\) | −32.8169 | − | 11.5898i | −1.23508 | − | 0.436187i | ||||
\(707\) | −2.82339 | + | 1.95696i | −0.106185 | + | 0.0735992i | ||||
\(708\) | −1.25049 | − | 1.00912i | −0.0469964 | − | 0.0379251i | ||||
\(709\) | − | 10.8180i | − | 0.406277i | −0.979150 | − | 0.203139i | \(-0.934886\pi\) | ||
0.979150 | − | 0.203139i | \(-0.0651142\pi\) | |||||||
\(710\) | 12.9113 | + | 4.55983i | 0.484554 | + | 0.171127i | ||||
\(711\) | − | 7.65651i | − | 0.287142i | ||||||
\(712\) | −4.60094 | − | 7.46535i | −0.172428 | − | 0.279776i | ||||
\(713\) | − | 18.1452i | − | 0.679544i | ||||||
\(714\) | −3.53475 | − | 12.9427i | −0.132285 | − | 0.484368i | ||||
\(715\) | −14.4792 | −0.541491 | ||||||||
\(716\) | 9.10019 | + | 7.34366i | 0.340090 | + | 0.274446i | ||||
\(717\) | −3.05114 | −0.113947 | ||||||||
\(718\) | −6.74857 | − | 2.38335i | −0.251854 | − | 0.0889459i | ||||
\(719\) | 29.4274 | 1.09746 | 0.548729 | − | 0.836000i | \(-0.315112\pi\) | ||||
0.548729 | + | 0.836000i | \(0.315112\pi\) | |||||||
\(720\) | 2.29904 | + | 10.6385i | 0.0856802 | + | 0.396475i | ||||
\(721\) | −41.4992 | + | 28.7641i | −1.54551 | + | 1.07123i | ||||
\(722\) | −8.78715 | + | 24.8812i | −0.327024 | + | 0.925982i | ||||
\(723\) | 0.754518 | 0.0280608 | ||||||||
\(724\) | −13.4892 | − | 10.8855i | −0.501323 | − | 0.404557i | ||||
\(725\) | − | 0.185682i | − | 0.00689605i | ||||||
\(726\) | 1.20498 | + | 0.425557i | 0.0447211 | + | 0.0157939i | ||||
\(727\) | −31.0932 | −1.15318 | −0.576591 | − | 0.817033i | \(-0.695617\pi\) | ||||
−0.576591 | + | 0.817033i | \(0.695617\pi\) | |||||||
\(728\) | −14.2484 | + | 32.5707i | −0.528079 | + | 1.20715i | ||||
\(729\) | 13.0812 | 0.484490 | ||||||||
\(730\) | −16.5747 | − | 5.85358i | −0.613456 | − | 0.216651i | ||||
\(731\) | − | 9.74577i | − | 0.360460i | ||||||
\(732\) | −8.78023 | + | 10.8804i | −0.324527 | + | 0.402150i | ||||
\(733\) | −10.0076 | −0.369639 | −0.184820 | − | 0.982772i | \(-0.559170\pi\) | ||||
−0.184820 | + | 0.982772i | \(0.559170\pi\) | |||||||
\(734\) | 6.03307 | − | 17.0829i | 0.222685 | − | 0.630541i | ||||
\(735\) | 3.46205 | + | 1.29760i | 0.127700 | + | 0.0478629i | ||||
\(736\) | −4.14798 | + | 32.5739i | −0.152897 | + | 1.20069i | ||||
\(737\) | −27.8339 | −1.02527 | ||||||||
\(738\) | 13.9182 | + | 4.91543i | 0.512338 | + | 0.180939i | ||||
\(739\) | 40.1592 | 1.47728 | 0.738641 | − | 0.674099i | \(-0.235468\pi\) | ||||
0.738641 | + | 0.674099i | \(0.235468\pi\) | |||||||
\(740\) | 8.85070 | − | 10.9677i | 0.325358 | − | 0.403180i | ||||
\(741\) | −1.46609 | −0.0538582 | ||||||||
\(742\) | 1.93292 | − | 0.527894i | 0.0709596 | − | 0.0193796i | ||||
\(743\) | 41.3554i | 1.51718i | 0.651567 | + | 0.758591i | \(0.274112\pi\) | ||||
−0.651567 | + | 0.758591i | \(0.725888\pi\) | |||||||
\(744\) | 2.45009 | + | 3.97544i | 0.0898246 | + | 0.145747i | ||||
\(745\) | − | 11.5156i | − | 0.421899i | ||||||
\(746\) | −16.5560 | − | 5.84699i | −0.606158 | − | 0.214073i | ||||
\(747\) | − | 36.6073i | − | 1.33939i | ||||||
\(748\) | 25.9885 | − | 32.2046i | 0.950233 | − | 1.17752i | ||||
\(749\) | −8.28700 | + | 5.74393i | −0.302800 | + | 0.209878i | ||||
\(750\) | −0.704322 | − | 0.248741i | −0.0257182 | − | 0.00908275i | ||||
\(751\) | − | 10.4171i | − | 0.380126i | −0.981772 | − | 0.190063i | \(-0.939131\pi\) | ||
0.981772 | − | 0.190063i | \(-0.0608693\pi\) | |||||||
\(752\) | 2.49986 | + | 11.5678i | 0.0911605 | + | 0.421835i | ||||
\(753\) | −6.14554 | −0.223956 | ||||||||
\(754\) | −1.17630 | − | 0.415427i | −0.0428383 | − | 0.0151290i | ||||
\(755\) | 7.70970i | 0.280585i | ||||||||
\(756\) | 1.16436 | − | 15.9470i | 0.0423473 | − | 0.579985i | ||||
\(757\) | − | 31.7145i | − | 1.15268i | −0.817209 | − | 0.576341i | \(-0.804480\pi\) | ||
0.817209 | − | 0.576341i | \(-0.195520\pi\) | |||||||
\(758\) | −4.43434 | + | 12.5560i | −0.161062 | + | 0.456055i | ||||
\(759\) | 9.34449 | 0.339183 | ||||||||
\(760\) | −0.867068 | − | 1.40688i | −0.0314519 | − | 0.0510329i | ||||
\(761\) | 11.9199i | 0.432095i | 0.976383 | + | 0.216047i | \(0.0693166\pi\) | ||||
−0.976383 | + | 0.216047i | \(0.930683\pi\) | |||||||
\(762\) | 3.95680 | − | 11.2038i | 0.143340 | − | 0.405872i | ||||
\(763\) | 22.8319 | + | 32.9406i | 0.826571 | + | 1.19253i | ||||
\(764\) | 16.2955 | − | 20.1932i | 0.589549 | − | 0.730563i | ||||
\(765\) | 18.4729i | 0.667890i | ||||||||
\(766\) | −13.5813 | + | 38.4560i | −0.490711 | + | 1.38947i | ||||
\(767\) | 7.22653i | 0.260935i | ||||||||
\(768\) | −3.48957 | − | 7.69672i | −0.125919 | − | 0.277731i | ||||
\(769\) | 9.56458i | 0.344908i | 0.985018 | + | 0.172454i | \(0.0551695\pi\) | ||||
−0.985018 | + | 0.172454i | \(0.944830\pi\) | |||||||
\(770\) | 3.00445 | + | 11.0010i | 0.108273 | + | 0.396448i | ||||
\(771\) | 6.33873 | 0.228284 | ||||||||
\(772\) | 38.2676 | + | 30.8812i | 1.37728 | + | 1.11144i | ||||
\(773\) | 30.6270 | 1.10158 | 0.550788 | − | 0.834645i | \(-0.314327\pi\) | ||||
0.550788 | + | 0.834645i | \(0.314327\pi\) | |||||||
\(774\) | 1.83957 | − | 5.20882i | 0.0661219 | − | 0.187227i | ||||
\(775\) | 3.12589 | 0.112285 | ||||||||
\(776\) | −20.0377 | − | 32.5126i | −0.719313 | − | 1.16714i | ||||
\(777\) | −8.09325 | + | 5.60963i | −0.290344 | + | 0.201244i | ||||
\(778\) | 5.80580 | + | 2.05040i | 0.208148 | + | 0.0735105i | ||||
\(779\) | −2.24122 | −0.0803001 | ||||||||
\(780\) | −3.15157 | + | 3.90539i | −0.112844 | + | 0.139835i | ||||
\(781\) | − | 29.5099i | − | 1.05595i | ||||||
\(782\) | −18.5592 | + | 52.5511i | −0.663675 | + | 1.87922i | ||||
\(783\) | 0.561078 | 0.0200513 | ||||||||
\(784\) | 27.7030 | + | 4.06713i | 0.989394 | + | 0.145255i | ||||
\(785\) | 4.42111 | 0.157796 | ||||||||
\(786\) | 5.03550 | − | 14.2582i | 0.179610 | − | 0.508574i | ||||
\(787\) | 26.7295i | 0.952804i | 0.879228 | + | 0.476402i | \(0.158059\pi\) | ||||
−0.879228 | + | 0.476402i | \(0.841941\pi\) | |||||||
\(788\) | −9.05821 | + | 11.2248i | −0.322685 | + | 0.399868i | ||||
\(789\) | −14.1432 | −0.503513 | ||||||||
\(790\) | 3.75223 | + | 1.32515i | 0.133498 | + | 0.0471469i | ||||
\(791\) | −36.1858 | + | 25.0813i | −1.28662 | + | 0.891789i | ||||
\(792\) | 19.9689 | − | 12.3069i | 0.709562 | − | 0.437308i | ||||
\(793\) | 62.8771 | 2.23283 | ||||||||
\(794\) | 8.00549 | − | 22.6679i | 0.284104 | − | 0.804454i | ||||
\(795\) | 0.282846 | 0.0100315 | ||||||||
\(796\) | −9.84918 | − | 7.94808i | −0.349095 | − | 0.281712i | ||||
\(797\) | 1.38276 | 0.0489799 | 0.0244899 | − | 0.999700i | \(-0.492204\pi\) | ||||
0.0244899 | + | 0.999700i | \(0.492204\pi\) | |||||||
\(798\) | 0.304215 | + | 1.11390i | 0.0107691 | + | 0.0394318i | ||||
\(799\) | 20.0865i | 0.710610i | ||||||||
\(800\) | −5.61154 | − | 0.714577i | −0.198398 | − | 0.0252641i | ||||
\(801\) | − | 8.43630i | − | 0.298082i | ||||||
\(802\) | −4.91369 | + | 13.9133i | −0.173508 | + | 0.491297i | ||||
\(803\) | 37.8827i | 1.33685i | ||||||||
\(804\) | −6.05837 | + | 7.50746i | −0.213662 | + | 0.264768i | ||||
\(805\) | −8.74895 | − | 12.6225i | −0.308360 | − | 0.444883i | ||||
\(806\) | 6.99358 | − | 19.8026i | 0.246338 | − | 0.697517i | ||||
\(807\) | 10.0546i | 0.353939i | ||||||||
\(808\) | −3.12641 | + | 1.92683i | −0.109987 | + | 0.0677856i | ||||
\(809\) | 3.98813 | 0.140215 | 0.0701075 | − | 0.997539i | \(-0.477666\pi\) | ||||
0.0701075 | + | 0.997539i | \(0.477666\pi\) | |||||||
\(810\) | −3.09273 | + | 8.75719i | −0.108667 | + | 0.307696i | ||||
\(811\) | − | 19.2038i | − | 0.674338i | −0.941444 | − | 0.337169i | \(-0.890531\pi\) | ||
0.941444 | − | 0.337169i | \(-0.109469\pi\) | |||||||
\(812\) | −0.0715489 | + | 0.979927i | −0.00251087 | + | 0.0343887i | ||||
\(813\) | 1.30901i | 0.0459089i | ||||||||
\(814\) | −28.6396 | − | 10.1145i | −1.00382 | − | 0.354513i | ||||
\(815\) | 17.5475 | 0.614662 | ||||||||
\(816\) | −3.02967 | − | 14.0194i | −0.106060 | − | 0.490778i | ||||
\(817\) | 0.838763i | 0.0293446i | ||||||||
\(818\) | −37.0081 | − | 13.0699i | −1.29396 | − | 0.456980i | ||||
\(819\) | −28.1090 | + | 19.4831i | −0.982209 | + | 0.680794i | ||||
\(820\) | −4.81781 | + | 5.97018i | −0.168245 | + | 0.208488i | ||||
\(821\) | 39.4413i | 1.37651i | 0.725468 | + | 0.688256i | \(0.241623\pi\) | ||||
−0.725468 | + | 0.688256i | \(0.758377\pi\) | |||||||
\(822\) | −4.50014 | − | 1.58929i | −0.156961 | − | 0.0554329i | ||||
\(823\) | 0.408196i | 0.0142288i | 0.999975 | + | 0.00711440i | \(0.00226460\pi\) | ||||
−0.999975 | + | 0.00711440i | \(0.997735\pi\) | |||||||
\(824\) | −45.9531 | + | 28.3212i | −1.60085 | + | 0.986616i | ||||
\(825\) | 1.60978i | 0.0560455i | ||||||||
\(826\) | 5.49056 | − | 1.49951i | 0.191041 | − | 0.0521747i | ||||
\(827\) | 33.9219 | 1.17958 | 0.589790 | − | 0.807557i | \(-0.299211\pi\) | ||||
0.589790 | + | 0.807557i | \(0.299211\pi\) | |||||||
\(828\) | −19.8386 | + | 24.5838i | −0.689440 | + | 0.854347i | ||||
\(829\) | 16.5466 | 0.574686 | 0.287343 | − | 0.957828i | \(-0.407228\pi\) | ||||
0.287343 | + | 0.957828i | \(0.407228\pi\) | |||||||
\(830\) | 17.9402 | + | 6.33582i | 0.622712 | + | 0.219920i | ||||
\(831\) | 8.50192 | 0.294928 | ||||||||
\(832\) | −17.0816 | + | 33.9505i | −0.592197 | + | 1.17702i | ||||
\(833\) | 44.4996 | + | 16.6788i | 1.54182 | + | 0.577887i | ||||
\(834\) | −5.42574 | + | 15.3632i | −0.187878 | + | 0.531985i | ||||
\(835\) | −1.57597 | −0.0545386 | ||||||||
\(836\) | −2.23668 | + | 2.77167i | −0.0773572 | + | 0.0958602i | ||||
\(837\) | 9.44556i | 0.326486i | ||||||||
\(838\) | −40.1549 | − | 14.1813i | −1.38713 | − | 0.489884i | ||||
\(839\) | −33.4148 | −1.15361 | −0.576804 | − | 0.816883i | \(-0.695700\pi\) | ||||
−0.576804 | + | 0.816883i | \(0.695700\pi\) | |||||||
\(840\) | 3.62118 | + | 1.58412i | 0.124943 | + | 0.0546573i | ||||
\(841\) | 28.9655 | 0.998811 | ||||||||
\(842\) | −36.1806 | − | 12.7777i | −1.24687 | − | 0.440349i | ||||
\(843\) | 9.19612i | 0.316731i | ||||||||
\(844\) | 15.9084 | + | 12.8377i | 0.547589 | + | 0.441893i | ||||
\(845\) | 9.56903 | 0.329185 | ||||||||
\(846\) | −3.79144 | + | 10.7356i | −0.130352 | + | 0.369098i | ||||
\(847\) | −3.72020 | + | 2.57856i | −0.127828 | + | 0.0886005i | ||||
\(848\) | 2.09372 | − | 0.452464i | 0.0718987 | − | 0.0155377i | ||||
\(849\) | 15.5395 | 0.533315 | ||||||||
\(850\) | −9.05303 | − | 3.19721i | −0.310516 | − | 0.109663i | ||||
\(851\) | 40.9049 | 1.40220 | ||||||||
\(852\) | −7.95953 | − | 6.42317i | −0.272689 | − | 0.220054i | ||||
\(853\) | −12.1851 | −0.417211 | −0.208606 | − | 0.978000i | \(-0.566893\pi\) | ||||
−0.208606 | + | 0.978000i | \(0.566893\pi\) | |||||||
\(854\) | −13.0471 | − | 47.7726i | −0.446461 | − | 1.63475i | ||||
\(855\) | − | 1.58986i | − | 0.0543720i | ||||||
\(856\) | −9.17641 | + | 5.65548i | −0.313643 | + | 0.193300i | ||||
\(857\) | 16.0726i | 0.549031i | 0.961583 | + | 0.274515i | \(0.0885174\pi\) | ||||
−0.961583 | + | 0.274515i | \(0.911483\pi\) | |||||||
\(858\) | 10.1980 | + | 3.60158i | 0.348155 | + | 0.122956i | ||||
\(859\) | 21.5250i | 0.734425i | 0.930137 | + | 0.367212i | \(0.119688\pi\) | ||||
−0.930137 | + | 0.367212i | \(0.880312\pi\) | |||||||
\(860\) | 2.23430 | + | 1.80304i | 0.0761891 | + | 0.0614831i | ||||
\(861\) | 4.40550 | − | 3.05356i | 0.150139 | − | 0.104065i | ||||
\(862\) | −5.07083 | − | 1.79084i | −0.172713 | − | 0.0609961i | ||||
\(863\) | − | 3.22755i | − | 0.109867i | −0.998490 | − | 0.0549336i | \(-0.982505\pi\) | ||
0.998490 | − | 0.0549336i | \(-0.0174947\pi\) | |||||||
\(864\) | 2.15925 | − | 16.9565i | 0.0734591 | − | 0.576871i | ||||
\(865\) | 0.208914 | 0.00710330 | ||||||||
\(866\) | 8.05809 | + | 2.84583i | 0.273825 | + | 0.0967052i | ||||
\(867\) | − | 15.3645i | − | 0.521807i | ||||||
\(868\) | −16.4968 | − | 1.20450i | −0.559936 | − | 0.0408835i | ||||
\(869\) | − | 8.57602i | − | 0.290922i | ||||||
\(870\) | −0.0461867 | + | 0.130780i | −0.00156588 | + | 0.00443385i | ||||
\(871\) | 43.3853 | 1.47005 | ||||||||
\(872\) | 22.4803 | + | 36.4759i | 0.761281 | + | 1.23523i | ||||
\(873\) | − | 36.7412i | − | 1.24350i | ||||||
\(874\) | 1.59728 | − | 4.52277i | 0.0540289 | − | 0.152985i | ||||
\(875\) | 2.17448 | − | 1.50719i | 0.0735110 | − | 0.0509523i | ||||
\(876\) | 10.2179 | + | 8.24561i | 0.345230 | + | 0.278593i | ||||
\(877\) | − | 27.5777i | − | 0.931233i | −0.884987 | − | 0.465616i | \(-0.845833\pi\) | ||
0.884987 | − | 0.465616i | \(-0.154167\pi\) | |||||||
\(878\) | 9.77261 | − | 27.6716i | 0.329810 | − | 0.933870i | ||||
\(879\) | 12.5372i | 0.422869i | ||||||||
\(880\) | 2.57514 | + | 11.9162i | 0.0868081 | + | 0.401694i | ||||
\(881\) | − | 20.1792i | − | 0.679856i | −0.940452 | − | 0.339928i | \(-0.889597\pi\) | ||
0.940452 | − | 0.339928i | \(-0.110403\pi\) | |||||||
\(882\) | 20.6355 | + | 17.3139i | 0.694832 | + | 0.582988i | ||||
\(883\) | 4.97245 | 0.167336 | 0.0836681 | − | 0.996494i | \(-0.473336\pi\) | ||||
0.0836681 | + | 0.996494i | \(0.473336\pi\) | |||||||
\(884\) | −40.5088 | + | 50.1980i | −1.36246 | + | 1.68834i | ||||
\(885\) | 0.803439 | 0.0270073 | ||||||||
\(886\) | −19.2698 | + | 54.5632i | −0.647381 | + | 1.83309i | ||||
\(887\) | 5.11354 | 0.171696 | 0.0858480 | − | 0.996308i | \(-0.472640\pi\) | ||||
0.0858480 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(888\) | −8.96186 | + | 5.52325i | −0.300740 | + | 0.185348i | ||||
\(889\) | 23.9753 | + | 34.5901i | 0.804105 | + | 1.16012i | ||||
\(890\) | 4.13438 | + | 1.46012i | 0.138585 | + | 0.0489432i | ||||
\(891\) | 20.0152 | 0.670536 | ||||||||
\(892\) | 4.11757 | + | 3.32280i | 0.137867 | + | 0.111255i | ||||
\(893\) | − | 1.72873i | − | 0.0578498i | ||||||
\(894\) | −2.86441 | + | 8.11070i | −0.0958002 | + | 0.271262i | ||||
\(895\) | −5.84685 | −0.195439 | ||||||||
\(896\) | 29.3393 | + | 5.93345i | 0.980157 | + | 0.198223i | ||||
\(897\) | −14.5654 | −0.486326 | ||||||||
\(898\) | −4.54337 | + | 12.8647i | −0.151614 | + | 0.429302i | ||||
\(899\) | − | 0.580422i | − | 0.0193581i | ||||||
\(900\) | −4.23508 | − | 3.41762i | −0.141169 | − | 0.113921i | ||||
\(901\) | 3.63557 | 0.121118 | ||||||||
\(902\) | 15.5898 | + | 5.50575i | 0.519082 | + | 0.183321i | ||||
\(903\) | −1.14278 | − | 1.64873i | −0.0380292 | − | 0.0548663i | ||||
\(904\) | −40.0695 | + | 24.6951i | −1.33269 | + | 0.821347i | ||||
\(905\) | 8.66680 | 0.288094 | ||||||||
\(906\) | 1.91772 | − | 5.43011i | 0.0637120 | − | 0.180403i | ||||
\(907\) | −26.8798 | −0.892530 | −0.446265 | − | 0.894901i | \(-0.647246\pi\) | ||||
−0.446265 | + | 0.894901i | \(0.647246\pi\) | |||||||
\(908\) | −20.4702 | + | 25.3665i | −0.679329 | + | 0.841817i | ||||
\(909\) | −3.53304 | −0.117183 | ||||||||
\(910\) | −4.68310 | − | 17.1475i | −0.155243 | − | 0.568432i | ||||
\(911\) | − | 43.0775i | − | 1.42722i | −0.700543 | − | 0.713610i | \(-0.747059\pi\) | ||
0.700543 | − | 0.713610i | \(-0.252941\pi\) | |||||||
\(912\) | 0.260746 | + | 1.20657i | 0.00863417 | + | 0.0399536i | ||||
\(913\) | − | 41.0036i | − | 1.35702i | ||||||
\(914\) | −3.91668 | + | 11.0902i | −0.129552 | + | 0.366833i | ||||
\(915\) | − | 6.99061i | − | 0.231103i | ||||||
\(916\) | 8.58898 | + | 6.93113i | 0.283788 | + | 0.229011i | ||||
\(917\) | 30.5114 | + | 44.0201i | 1.00758 | + | 1.45367i | ||||
\(918\) | 9.66105 | − | 27.3557i | 0.318862 | − | 0.902872i | ||||
\(919\) | − | 6.42394i | − | 0.211906i | −0.994371 | − | 0.105953i | \(-0.966211\pi\) | ||
0.994371 | − | 0.105953i | \(-0.0337893\pi\) | |||||||
\(920\) | −8.61422 | − | 13.9772i | −0.284003 | − | 0.460814i | ||||
\(921\) | 1.73025 | 0.0570138 | ||||||||
\(922\) | 6.97078 | − | 19.7381i | 0.229570 | − | 0.650038i | ||||
\(923\) | 45.9977i | 1.51403i | ||||||||
\(924\) | 0.620299 | − | 8.49556i | 0.0204063 | − | 0.279483i | ||||
\(925\) | 7.04672i | 0.231695i | ||||||||
\(926\) | 13.6453 | + | 4.81905i | 0.448414 | + | 0.158364i | ||||
\(927\) | −51.9298 | −1.70560 | ||||||||
\(928\) | −0.132684 | + | 1.04196i | −0.00435556 | + | 0.0342040i | ||||
\(929\) | − | 8.92552i | − | 0.292837i | −0.989223 | − | 0.146418i | \(-0.953225\pi\) | ||
0.989223 | − | 0.146418i | \(-0.0467746\pi\) | |||||||
\(930\) | −2.20163 | − | 0.777539i | −0.0721945 | − | 0.0254965i | ||||
\(931\) | −3.82983 | − | 1.43545i | −0.125517 | − | 0.0470450i | ||||
\(932\) | −28.9983 | − | 23.4011i | −0.949872 | − | 0.766527i | ||||
\(933\) | − | 11.0450i | − | 0.361597i | ||||||
\(934\) | 1.98890 | + | 0.702407i | 0.0650787 | + | 0.0229835i | ||||
\(935\) | 20.6914i | 0.676682i | ||||||||
\(936\) | −31.1259 | + | 19.1831i | −1.01738 | + | 0.627018i | ||||
\(937\) | 23.5181i | 0.768304i | 0.923270 | + | 0.384152i | \(0.125506\pi\) | ||||
−0.923270 | + | 0.384152i | \(0.874494\pi\) | |||||||
\(938\) | −9.00248 | − | 32.9632i | −0.293942 | − | 1.07629i | ||||
\(939\) | −7.33209 | −0.239274 | ||||||||
\(940\) | −4.60501 | − | 3.71615i | −0.150199 | − | 0.121207i | ||||
\(941\) | −0.932766 | −0.0304073 | −0.0152037 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152037 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(942\) | −3.11389 | − | 1.09971i | −0.101456 | − | 0.0358306i | ||||
\(943\) | −22.2663 | −0.725089 | ||||||||
\(944\) | 5.94733 | − | 1.28525i | 0.193569 | − | 0.0418313i | ||||
\(945\) | 4.55430 | + | 6.57067i | 0.148151 | + | 0.213744i | ||||
\(946\) | 2.06049 | − | 5.83437i | 0.0669924 | − | 0.189692i | ||||
\(947\) | 18.3452 | 0.596140 | 0.298070 | − | 0.954544i | \(-0.403657\pi\) | ||||
0.298070 | + | 0.954544i | \(0.403657\pi\) | |||||||
\(948\) | −2.31316 | − | 1.86667i | −0.0751278 | − | 0.0606266i | ||||
\(949\) | − | 59.0486i | − | 1.91680i | ||||||
\(950\) | 0.779143 | + | 0.275165i | 0.0252787 | + | 0.00892754i | ||||
\(951\) | 3.13329 | 0.101604 | ||||||||
\(952\) | 46.5450 | + | 20.3615i | 1.50853 | + | 0.659921i | ||||
\(953\) | −47.3388 | −1.53345 | −0.766727 | − | 0.641973i | \(-0.778116\pi\) | ||||
−0.766727 | + | 0.641973i | \(0.778116\pi\) | |||||||
\(954\) | 1.94310 | + | 0.686234i | 0.0629102 | + | 0.0222176i | ||||
\(955\) | 12.9741i | 0.419831i | ||||||||
\(956\) | 7.25560 | − | 8.99106i | 0.234663 | − | 0.290792i | ||||
\(957\) | 0.298908 | 0.00966231 | ||||||||
\(958\) | 15.5740 | − | 44.0984i | 0.503173 | − | 1.42476i | ||||
\(959\) | 13.8935 | − | 9.62993i | 0.448644 | − | 0.310967i | ||||
\(960\) | 3.77459 | + | 1.89911i | 0.121824 | + | 0.0612937i | ||||
\(961\) | −21.2288 | −0.684800 | ||||||||
\(962\) | 44.6412 | + | 15.7657i | 1.43929 | + | 0.508306i | ||||
\(963\) | −10.3699 | −0.334165 | ||||||||
\(964\) | −1.79424 | + | 2.22341i | −0.0577886 | + | 0.0716111i | ||||
\(965\) | −24.5869 | −0.791479 | ||||||||
\(966\) | 3.02234 | + | 11.0665i | 0.0972423 | + | 0.356059i | ||||
\(967\) | 6.55903i | 0.210924i | 0.994423 | + | 0.105462i | \(0.0336322\pi\) | ||||
−0.994423 | + | 0.105462i | \(0.966368\pi\) | |||||||
\(968\) | −4.11947 | + | 2.53886i | −0.132405 | + | 0.0816019i | ||||
\(969\) | 2.09511i | 0.0673046i | ||||||||
\(970\) | 18.0058 | + | 6.35900i | 0.578131 | + | 0.204175i | ||||
\(971\) | − | 40.6590i | − | 1.30481i | −0.757871 | − | 0.652404i | \(-0.773760\pi\) | ||
0.757871 | − | 0.652404i | \(-0.226240\pi\) | |||||||
\(972\) | 15.7424 | − | 19.5078i | 0.504938 | − | 0.625713i | ||||
\(973\) | −32.8760 | − | 47.4316i | −1.05396 | − | 1.52059i | ||||
\(974\) | 40.4241 | + | 14.2763i | 1.29527 | + | 0.457443i | ||||
\(975\) | − | 2.50920i | − | 0.0803588i | ||||||
\(976\) | −11.1828 | − | 51.7469i | −0.357952 | − | 1.65638i | ||||
\(977\) | 5.28576 | 0.169106 | 0.0845532 | − | 0.996419i | \(-0.473054\pi\) | ||||
0.0845532 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(978\) | −12.3591 | − | 4.36479i | −0.395200 | − | 0.139571i | ||||
\(979\) | − | 9.44946i | − | 0.302006i | ||||||
\(980\) | −12.0565 | + | 7.11623i | −0.385131 | + | 0.227320i | ||||
\(981\) | 41.2200i | 1.31605i | ||||||||
\(982\) | 11.3064 | − | 32.0146i | 0.360802 | − | 1.02163i | ||||
\(983\) | 11.2577 | 0.359066 | 0.179533 | − | 0.983752i | \(-0.442541\pi\) | ||||
0.179533 | + | 0.983752i | \(0.442541\pi\) | |||||||
\(984\) | 4.87832 | − | 3.00654i | 0.155515 | − | 0.0958450i | ||||
\(985\) | − | 7.21194i | − | 0.229791i | ||||||
\(986\) | −0.593663 | + | 1.68098i | −0.0189061 | + | 0.0535334i | ||||
\(987\) | 2.35532 | + | 3.39811i | 0.0749706 | + | 0.108163i | ||||
\(988\) | 3.48636 | − | 4.32026i | 0.110916 | − | 0.137446i | ||||
\(989\) | 8.33301i | 0.264974i | ||||||||
\(990\) | −3.90562 | + | 11.0589i | −0.124129 | + | 0.351476i | ||||
\(991\) | 14.3170i | 0.454796i | 0.973802 | + | 0.227398i | \(0.0730218\pi\) | ||||
−0.973802 | + | 0.227398i | \(0.926978\pi\) | |||||||
\(992\) | −17.5411 | − | 2.23369i | −0.556930 | − | 0.0709198i | ||||
\(993\) | − | 3.87233i | − | 0.122885i | ||||||
\(994\) | 34.9480 | − | 9.54457i | 1.10848 | − | 0.302735i | ||||
\(995\) | 6.32808 | 0.200614 | ||||||||
\(996\) | −11.0597 | − | 8.92492i | −0.350439 | − | 0.282797i | ||||
\(997\) | 18.4076 | 0.582974 | 0.291487 | − | 0.956575i | \(-0.405850\pi\) | ||||
0.291487 | + | 0.956575i | \(0.405850\pi\) | |||||||
\(998\) | 17.2478 | − | 48.8378i | 0.545968 | − | 1.54593i | ||||
\(999\) | −21.2932 | −0.673687 |
(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 | 280.2.h.b.251.6 | yes | 16 | |
4.3 | odd | 2 | 1120.2.h.b.111.8 | 16 | |||
7.6 | odd | 2 | 280.2.h.a.251.6 | yes | 16 | ||
8.3 | odd | 2 | 280.2.h.a.251.5 | ✓ | 16 | ||
8.5 | even | 2 | 1120.2.h.a.111.8 | 16 | |||
28.27 | even | 2 | 1120.2.h.a.111.9 | 16 | |||
56.13 | odd | 2 | 1120.2.h.b.111.9 | 16 | |||
56.27 | even | 2 | inner | 280.2.h.b.251.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.5 | ✓ | 16 | 8.3 | odd | 2 | ||
280.2.h.a.251.6 | yes | 16 | 7.6 | odd | 2 | ||
280.2.h.b.251.5 | yes | 16 | 56.27 | even | 2 | inner | |
280.2.h.b.251.6 | yes | 16 | 1.1 | even | 1 | trivial | |
1120.2.h.a.111.8 | 16 | 8.5 | even | 2 | |||
1120.2.h.a.111.9 | 16 | 28.27 | even | 2 | |||
1120.2.h.b.111.8 | 16 | 4.3 | odd | 2 | |||
1120.2.h.b.111.9 | 16 | 56.13 | odd | 2 |