Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(391,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("588.391");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.b (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: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.7 | ||
Root | \(-1.33790 + 0.458297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.391 |
Dual form | 588.2.b.a.391.8 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33790 | − | 0.458297i | 0.946035 | − | 0.324065i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.57993 | − | 1.22631i | 0.789963 | − | 0.613154i | ||||
\(5\) | − | 2.45262i | − | 1.09684i | −0.836202 | − | 0.548422i | \(-0.815229\pi\) | ||
0.836202 | − | 0.548422i | \(-0.184771\pi\) | |||||||
\(6\) | −1.33790 | + | 0.458297i | −0.546193 | + | 0.187099i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.55176 | − | 2.36475i | 0.548631 | − | 0.836065i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.12403 | − | 3.28134i | −0.355449 | − | 1.03765i | ||||
\(11\) | 1.26539i | 0.381531i | 0.981636 | + | 0.190765i | \(0.0610970\pi\) | ||||
−0.981636 | + | 0.190765i | \(0.938903\pi\) | |||||||
\(12\) | −1.57993 | + | 1.22631i | −0.456086 | + | 0.354005i | ||||
\(13\) | − | 2.99744i | − | 0.831342i | −0.909515 | − | 0.415671i | \(-0.863547\pi\) | ||
0.909515 | − | 0.415671i | \(-0.136453\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.45262i | 0.633263i | ||||||||
\(16\) | 0.992338 | − | 3.87495i | 0.248084 | − | 0.968738i | ||||
\(17\) | 1.83319i | 0.444614i | 0.974977 | + | 0.222307i | \(0.0713587\pi\) | ||||
−0.974977 | + | 0.222307i | \(0.928641\pi\) | |||||||
\(18\) | 1.33790 | − | 0.458297i | 0.315345 | − | 0.108022i | ||||
\(19\) | −4.15985 | −0.954336 | −0.477168 | − | 0.878812i | \(-0.658337\pi\) | ||||
−0.477168 | + | 0.878812i | \(0.658337\pi\) | |||||||
\(20\) | −3.00766 | − | 3.87495i | −0.672534 | − | 0.866466i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.579927 | + | 1.69296i | 0.123641 | + | 0.360941i | ||||
\(23\) | − | 6.73842i | − | 1.40506i | −0.711655 | − | 0.702529i | \(-0.752054\pi\) | ||
0.711655 | − | 0.702529i | \(-0.247946\pi\) | |||||||
\(24\) | −1.55176 | + | 2.36475i | −0.316752 | + | 0.482702i | ||||
\(25\) | −1.01532 | −0.203065 | ||||||||
\(26\) | −1.37372 | − | 4.01027i | −0.269409 | − | 0.786478i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.42323 | −1.74985 | −0.874925 | − | 0.484258i | \(-0.839090\pi\) | ||||
−0.874925 | + | 0.484258i | \(0.839090\pi\) | |||||||
\(30\) | 1.12403 | + | 3.28134i | 0.205218 | + | 0.599088i | ||||
\(31\) | 9.43978 | 1.69543 | 0.847717 | − | 0.530448i | \(-0.177976\pi\) | ||||
0.847717 | + | 0.530448i | \(0.177976\pi\) | |||||||
\(32\) | −0.448237 | − | 5.63907i | −0.0792379 | − | 0.996856i | ||||
\(33\) | − | 1.26539i | − | 0.220277i | ||||||
\(34\) | 0.840146 | + | 2.45262i | 0.144084 | + | 0.420620i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.57993 | − | 1.22631i | 0.263321 | − | 0.204385i | ||||
\(37\) | 7.51143 | 1.23487 | 0.617436 | − | 0.786621i | \(-0.288171\pi\) | ||||
0.617436 | + | 0.786621i | \(0.288171\pi\) | |||||||
\(38\) | −5.56545 | + | 1.90645i | −0.902835 | + | 0.309267i | ||||
\(39\) | 2.99744i | 0.479975i | ||||||||
\(40\) | −5.79982 | − | 3.80588i | −0.917032 | − | 0.601762i | ||||
\(41\) | 1.08966i | 0.170176i | 0.996373 | + | 0.0850880i | \(0.0271171\pi\) | ||||
−0.996373 | + | 0.0850880i | \(0.972883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.27176i | 0.956435i | 0.878241 | + | 0.478218i | \(0.158717\pi\) | ||||
−0.878241 | + | 0.478218i | \(0.841283\pi\) | |||||||
\(44\) | 1.55176 | + | 1.99923i | 0.233937 | + | 0.301395i | ||||
\(45\) | − | 2.45262i | − | 0.365614i | ||||||
\(46\) | −3.08820 | − | 9.01530i | −0.455330 | − | 1.32923i | ||||
\(47\) | 7.35158 | 1.07234 | 0.536169 | − | 0.844111i | \(-0.319871\pi\) | ||||
0.536169 | + | 0.844111i | \(0.319871\pi\) | |||||||
\(48\) | −0.992338 | + | 3.87495i | −0.143232 | + | 0.559301i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.35840 | + | 0.465320i | −0.192106 | + | 0.0658063i | ||||
\(51\) | − | 1.83319i | − | 0.256698i | ||||||
\(52\) | −3.67579 | − | 4.73574i | −0.509740 | − | 0.656730i | ||||
\(53\) | −0.0716524 | −0.00984222 | −0.00492111 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00492111 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(54\) | −1.33790 | + | 0.458297i | −0.182064 | + | 0.0623664i | ||||
\(55\) | 3.10353 | 0.418479 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.15985 | 0.550986 | ||||||||
\(58\) | −12.6073 | + | 4.31864i | −1.65542 | + | 0.567066i | ||||
\(59\) | 3.36690 | 0.438334 | 0.219167 | − | 0.975687i | \(-0.429666\pi\) | ||||
0.219167 | + | 0.975687i | \(0.429666\pi\) | |||||||
\(60\) | 3.00766 | + | 3.87495i | 0.388288 | + | 0.500254i | ||||
\(61\) | 11.1024i | 1.42152i | 0.703436 | + | 0.710758i | \(0.251648\pi\) | ||||
−0.703436 | + | 0.710758i | \(0.748352\pi\) | |||||||
\(62\) | 12.6294 | − | 4.32623i | 1.60394 | − | 0.549432i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.18406 | − | 7.33906i | −0.398008 | − | 0.917382i | ||||
\(65\) | −7.35158 | −0.911851 | ||||||||
\(66\) | −0.579927 | − | 1.69296i | −0.0713841 | − | 0.208390i | ||||
\(67\) | 2.80766i | 0.343011i | 0.985183 | + | 0.171505i | \(0.0548631\pi\) | ||||
−0.985183 | + | 0.171505i | \(0.945137\pi\) | |||||||
\(68\) | 2.24806 | + | 2.89631i | 0.272617 | + | 0.351229i | ||||
\(69\) | 6.73842i | 0.811211i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.92285i | 0.346878i | 0.984845 | + | 0.173439i | \(0.0554880\pi\) | ||||
−0.984845 | + | 0.173439i | \(0.944512\pi\) | |||||||
\(72\) | 1.55176 | − | 2.36475i | 0.182877 | − | 0.278688i | ||||
\(73\) | 8.10495i | 0.948613i | 0.880360 | + | 0.474307i | \(0.157301\pi\) | ||||
−0.880360 | + | 0.474307i | \(0.842699\pi\) | |||||||
\(74\) | 10.0495 | − | 3.44247i | 1.16823 | − | 0.400179i | ||||
\(75\) | 1.01532 | 0.117240 | ||||||||
\(76\) | −6.57226 | + | 5.10126i | −0.753890 | + | 0.585155i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.37372 | + | 4.01027i | 0.155543 | + | 0.454073i | ||||
\(79\) | − | 1.78368i | − | 0.200680i | −0.994953 | − | 0.100340i | \(-0.968007\pi\) | ||
0.994953 | − | 0.100340i | \(-0.0319930\pi\) | |||||||
\(80\) | −9.50377 | − | 2.43382i | −1.06255 | − | 0.272110i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.499388 | + | 1.45785i | 0.0551481 | + | 0.160992i | ||||
\(83\) | 5.33626 | 0.585730 | 0.292865 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292865 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.49611 | 0.487672 | ||||||||
\(86\) | 2.87433 | + | 8.39096i | 0.309947 | + | 0.904821i | ||||
\(87\) | 9.42323 | 1.01028 | ||||||||
\(88\) | 2.99234 | + | 1.96359i | 0.318984 | + | 0.209320i | ||||
\(89\) | − | 8.57161i | − | 0.908589i | −0.890852 | − | 0.454294i | \(-0.849891\pi\) | ||
0.890852 | − | 0.454294i | \(-0.150109\pi\) | |||||||
\(90\) | −1.12403 | − | 3.28134i | −0.118483 | − | 0.345884i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.26338 | − | 10.6462i | −0.861517 | − | 1.10994i | ||||
\(93\) | −9.43978 | −0.978860 | ||||||||
\(94\) | 9.83564 | − | 3.36921i | 1.01447 | − | 0.347508i | ||||
\(95\) | 10.2025i | 1.04676i | ||||||||
\(96\) | 0.448237 | + | 5.63907i | 0.0457480 | + | 0.575535i | ||||
\(97\) | 7.10394i | 0.721296i | 0.932702 | + | 0.360648i | \(0.117444\pi\) | ||||
−0.932702 | + | 0.360648i | \(0.882556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.26539i | 0.127177i | ||||||||
\(100\) | −1.60414 | + | 1.24510i | −0.160414 | + | 0.124510i | ||||
\(101\) | 0.933313i | 0.0928682i | 0.998921 | + | 0.0464341i | \(0.0147857\pi\) | ||||
−0.998921 | + | 0.0464341i | \(0.985214\pi\) | |||||||
\(102\) | −0.840146 | − | 2.45262i | −0.0831869 | − | 0.242845i | ||||
\(103\) | 4.12921 | 0.406863 | 0.203431 | − | 0.979089i | \(-0.434791\pi\) | ||||
0.203431 | + | 0.979089i | \(0.434791\pi\) | |||||||
\(104\) | −7.08820 | − | 4.65132i | −0.695055 | − | 0.456100i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0958634 | + | 0.0328381i | −0.00931108 | + | 0.00318952i | ||||
\(107\) | 13.8424i | 1.33819i | 0.743176 | + | 0.669096i | \(0.233318\pi\) | ||||
−0.743176 | + | 0.669096i | \(0.766682\pi\) | |||||||
\(108\) | −1.57993 | + | 1.22631i | −0.152029 | + | 0.118002i | ||||
\(109\) | −0.984676 | −0.0943148 | −0.0471574 | − | 0.998887i | \(-0.515016\pi\) | ||||
−0.0471574 | + | 0.998887i | \(0.515016\pi\) | |||||||
\(110\) | 4.15219 | − | 1.42234i | 0.395896 | − | 0.135615i | ||||
\(111\) | −7.51143 | −0.712954 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.03187 | 0.473359 | 0.236679 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236679 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(114\) | 5.56545 | − | 1.90645i | 0.521252 | − | 0.178555i | ||||
\(115\) | −16.5268 | −1.54113 | ||||||||
\(116\) | −14.8880 | + | 11.5558i | −1.38232 | + | 1.07293i | ||||
\(117\) | − | 2.99744i | − | 0.277114i | ||||||
\(118\) | 4.50457 | − | 1.54304i | 0.414679 | − | 0.142049i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.79982 | + | 3.80588i | 0.529449 | + | 0.347428i | ||||
\(121\) | 9.39878 | 0.854434 | ||||||||
\(122\) | 5.08820 | + | 14.8538i | 0.460664 | + | 1.34480i | ||||
\(123\) | − | 1.08966i | − | 0.0982512i | ||||||
\(124\) | 14.9142 | − | 11.5761i | 1.33933 | − | 1.03956i | ||||
\(125\) | − | 9.77288i | − | 0.874113i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.38337i | 0.566433i | 0.959056 | + | 0.283216i | \(0.0914015\pi\) | ||||
−0.959056 | + | 0.283216i | \(0.908599\pi\) | |||||||
\(128\) | −7.62342 | − | 8.35964i | −0.673821 | − | 0.738895i | ||||
\(129\) | − | 6.27176i | − | 0.552198i | ||||||
\(130\) | −9.83564 | + | 3.36921i | −0.862643 | + | 0.295499i | ||||
\(131\) | −3.87202 | −0.338300 | −0.169150 | − | 0.985590i | \(-0.554102\pi\) | ||||
−0.169150 | + | 0.985590i | \(0.554102\pi\) | |||||||
\(132\) | −1.55176 | − | 1.99923i | −0.135064 | − | 0.174011i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.28674 | + | 3.75636i | 0.111158 | + | 0.324500i | ||||
\(135\) | 2.45262i | 0.211088i | ||||||||
\(136\) | 4.33503 | + | 2.84468i | 0.371726 | + | 0.243929i | ||||
\(137\) | −14.7032 | −1.25618 | −0.628088 | − | 0.778142i | \(-0.716162\pi\) | ||||
−0.628088 | + | 0.778142i | \(0.716162\pi\) | |||||||
\(138\) | 3.08820 | + | 9.01530i | 0.262885 | + | 0.767433i | ||||
\(139\) | −2.01655 | −0.171041 | −0.0855207 | − | 0.996336i | \(-0.527255\pi\) | ||||
−0.0855207 | + | 0.996336i | \(0.527255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.35158 | −0.619115 | ||||||||
\(142\) | 1.33953 | + | 3.91046i | 0.112411 | + | 0.328159i | ||||
\(143\) | 3.79295 | 0.317182 | ||||||||
\(144\) | 0.992338 | − | 3.87495i | 0.0826948 | − | 0.322913i | ||||
\(145\) | 23.1116i | 1.91931i | ||||||||
\(146\) | 3.71448 | + | 10.8436i | 0.307413 | + | 0.897421i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.8675 | − | 9.21133i | 0.975504 | − | 0.757167i | ||||
\(149\) | −0.496110 | −0.0406429 | −0.0203215 | − | 0.999793i | \(-0.506469\pi\) | ||||
−0.0203215 | + | 0.999793i | \(0.506469\pi\) | |||||||
\(150\) | 1.35840 | − | 0.465320i | 0.110913 | − | 0.0379933i | ||||
\(151\) | 13.2370i | 1.07721i | 0.842558 | + | 0.538605i | \(0.181049\pi\) | ||||
−0.842558 | + | 0.538605i | \(0.818951\pi\) | |||||||
\(152\) | −6.45511 | + | 9.83701i | −0.523578 | + | 0.797886i | ||||
\(153\) | 1.83319i | 0.148205i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.1522i | − | 1.85963i | ||||||
\(156\) | 3.67579 | + | 4.73574i | 0.294299 | + | 0.379163i | ||||
\(157\) | 5.06158i | 0.403958i | 0.979390 | + | 0.201979i | \(0.0647372\pi\) | ||||
−0.979390 | + | 0.201979i | \(0.935263\pi\) | |||||||
\(158\) | −0.817456 | − | 2.38638i | −0.0650333 | − | 0.189850i | ||||
\(159\) | 0.0716524 | 0.00568241 | ||||||||
\(160\) | −13.8305 | + | 1.09935i | −1.09339 | + | 0.0869115i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.33790 | − | 0.458297i | 0.105115 | − | 0.0360072i | ||||
\(163\) | 12.0357i | 0.942710i | 0.881944 | + | 0.471355i | \(0.156235\pi\) | ||||
−0.881944 | + | 0.471355i | \(0.843765\pi\) | |||||||
\(164\) | 1.33626 | + | 1.72158i | 0.104344 | + | 0.134433i | ||||
\(165\) | −3.10353 | −0.241609 | ||||||||
\(166\) | 7.13935 | − | 2.44559i | 0.554121 | − | 0.189815i | ||||
\(167\) | 7.46424 | 0.577600 | 0.288800 | − | 0.957389i | \(-0.406744\pi\) | ||||
0.288800 | + | 0.957389i | \(0.406744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01532 | 0.308871 | ||||||||
\(170\) | 6.01532 | − | 2.06056i | 0.461354 | − | 0.158037i | ||||
\(171\) | −4.15985 | −0.318112 | ||||||||
\(172\) | 7.69111 | + | 9.90893i | 0.586442 | + | 0.755549i | ||||
\(173\) | − | 4.36398i | − | 0.331787i | −0.986144 | − | 0.165894i | \(-0.946949\pi\) | ||
0.986144 | − | 0.165894i | \(-0.0530508\pi\) | |||||||
\(174\) | 12.6073 | − | 4.31864i | 0.955757 | − | 0.327396i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.90334 | + | 1.25570i | 0.369603 | + | 0.0946518i | ||||
\(177\) | −3.36690 | −0.253072 | ||||||||
\(178\) | −3.92835 | − | 11.4679i | −0.294442 | − | 0.859557i | ||||
\(179\) | − | 24.5667i | − | 1.83620i | −0.396343 | − | 0.918102i | \(-0.629721\pi\) | ||
0.396343 | − | 0.918102i | \(-0.370279\pi\) | |||||||
\(180\) | −3.00766 | − | 3.87495i | −0.224178 | − | 0.288822i | ||||
\(181\) | − | 11.7182i | − | 0.871011i | −0.900186 | − | 0.435505i | \(-0.856570\pi\) | ||
0.900186 | − | 0.435505i | \(-0.143430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.1024i | − | 0.820713i | ||||||
\(184\) | −15.9347 | − | 10.4564i | −1.17472 | − | 0.770858i | ||||
\(185\) | − | 18.4227i | − | 1.35446i | ||||||
\(186\) | −12.6294 | + | 4.32623i | −0.926035 | + | 0.317214i | ||||
\(187\) | −2.31971 | −0.169634 | ||||||||
\(188\) | 11.6150 | − | 9.01530i | 0.847108 | − | 0.657508i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.67579 | + | 13.6499i | 0.339217 | + | 0.990268i | ||||
\(191\) | − | 15.8919i | − | 1.14990i | −0.818190 | − | 0.574948i | \(-0.805022\pi\) | ||
0.818190 | − | 0.574948i | \(-0.194978\pi\) | |||||||
\(192\) | 3.18406 | + | 7.33906i | 0.229790 | + | 0.529651i | ||||
\(193\) | 19.7338 | 1.42047 | 0.710235 | − | 0.703964i | \(-0.248589\pi\) | ||||
0.710235 | + | 0.703964i | \(0.248589\pi\) | |||||||
\(194\) | 3.25572 | + | 9.50433i | 0.233747 | + | 0.682371i | ||||
\(195\) | 7.35158 | 0.526458 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.998775 | 0.0711598 | 0.0355799 | − | 0.999367i | \(-0.488672\pi\) | ||||
0.0355799 | + | 0.999367i | \(0.488672\pi\) | |||||||
\(198\) | 0.579927 | + | 1.69296i | 0.0412136 | + | 0.120314i | ||||
\(199\) | −2.70316 | −0.191622 | −0.0958110 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958110 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(200\) | −1.57554 | + | 2.40099i | −0.111408 | + | 0.169775i | ||||
\(201\) | − | 2.80766i | − | 0.198037i | ||||||
\(202\) | 0.427735 | + | 1.24868i | 0.0300953 | + | 0.0878565i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.24806 | − | 2.89631i | −0.157395 | − | 0.202782i | ||||
\(205\) | 2.67251 | 0.186656 | ||||||||
\(206\) | 5.52444 | − | 1.89240i | 0.384906 | − | 0.131850i | ||||
\(207\) | − | 6.73842i | − | 0.468353i | ||||||
\(208\) | −11.6150 | − | 2.97448i | −0.805353 | − | 0.206243i | ||||
\(209\) | − | 5.26385i | − | 0.364108i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.1798i | − | 1.25155i | −0.780004 | − | 0.625774i | \(-0.784783\pi\) | ||
0.780004 | − | 0.625774i | \(-0.215217\pi\) | |||||||
\(212\) | −0.113206 | + | 0.0878679i | −0.00777499 | + | 0.00603479i | ||||
\(213\) | − | 2.92285i | − | 0.200270i | ||||||
\(214\) | 6.34392 | + | 18.5196i | 0.433661 | + | 1.26598i | ||||
\(215\) | 15.3822 | 1.04906 | ||||||||
\(216\) | −1.55176 | + | 2.36475i | −0.105584 | + | 0.160901i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.31739 | + | 0.451274i | −0.0892251 | + | 0.0305642i | ||||
\(219\) | − | 8.10495i | − | 0.547682i | ||||||
\(220\) | 4.90334 | − | 3.80588i | 0.330583 | − | 0.256592i | ||||
\(221\) | 5.49489 | 0.369626 | ||||||||
\(222\) | −10.0495 | + | 3.44247i | −0.674479 | + | 0.231044i | ||||
\(223\) | −11.5996 | −0.776769 | −0.388385 | − | 0.921497i | \(-0.626967\pi\) | ||||
−0.388385 | + | 0.921497i | \(0.626967\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.01532 | −0.0676883 | ||||||||
\(226\) | 6.73212 | − | 2.30609i | 0.447814 | − | 0.153399i | ||||
\(227\) | −10.1611 | −0.674414 | −0.337207 | − | 0.941430i | \(-0.609482\pi\) | ||||
−0.337207 | + | 0.941430i | \(0.609482\pi\) | |||||||
\(228\) | 6.57226 | − | 5.10126i | 0.435259 | − | 0.337839i | ||||
\(229\) | − | 23.0970i | − | 1.52629i | −0.646228 | − | 0.763145i | \(-0.723654\pi\) | ||
0.646228 | − | 0.763145i | \(-0.276346\pi\) | |||||||
\(230\) | −22.1111 | + | 7.57417i | −1.45796 | + | 0.499426i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.6226 | + | 22.2836i | −0.960022 | + | 1.46299i | ||||
\(233\) | −6.85547 | −0.449117 | −0.224558 | − | 0.974461i | \(-0.572094\pi\) | ||||
−0.224558 | + | 0.974461i | \(0.572094\pi\) | |||||||
\(234\) | −1.37372 | − | 4.01027i | −0.0898030 | − | 0.262159i | ||||
\(235\) | − | 18.0306i | − | 1.17619i | ||||||
\(236\) | 5.31946 | − | 4.12886i | 0.346268 | − | 0.268766i | ||||
\(237\) | 1.78368i | 0.115863i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2257i | 1.43766i | 0.695184 | + | 0.718832i | \(0.255323\pi\) | ||||
−0.695184 | + | 0.718832i | \(0.744677\pi\) | |||||||
\(240\) | 9.50377 | + | 2.43382i | 0.613466 | + | 0.157103i | ||||
\(241\) | 15.4273i | 0.993762i | 0.867819 | + | 0.496881i | \(0.165522\pi\) | ||||
−0.867819 | + | 0.496881i | \(0.834478\pi\) | |||||||
\(242\) | 12.5746 | − | 4.30744i | 0.808325 | − | 0.276892i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.6150 | + | 17.5410i | 0.871608 | + | 1.12295i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.499388 | − | 1.45785i | −0.0318398 | − | 0.0929490i | ||||
\(247\) | 12.4689i | 0.793379i | ||||||||
\(248\) | 14.6483 | − | 22.3227i | 0.930168 | − | 1.41749i | ||||
\(249\) | −5.33626 | −0.338172 | ||||||||
\(250\) | −4.47889 | − | 13.0751i | −0.283270 | − | 0.826941i | ||||
\(251\) | −22.2954 | −1.40727 | −0.703636 | − | 0.710561i | \(-0.748441\pi\) | ||||
−0.703636 | + | 0.710561i | \(0.748441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.52676 | 0.536073 | ||||||||
\(254\) | 2.92548 | + | 8.54029i | 0.183561 | + | 0.535865i | ||||
\(255\) | −4.49611 | −0.281557 | ||||||||
\(256\) | −14.0305 | − | 7.69053i | −0.876908 | − | 0.480658i | ||||
\(257\) | − | 2.86976i | − | 0.179011i | −0.995986 | − | 0.0895055i | \(-0.971471\pi\) | ||
0.995986 | − | 0.0895055i | \(-0.0285287\pi\) | |||||||
\(258\) | −2.87433 | − | 8.39096i | −0.178948 | − | 0.522399i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.6150 | + | 9.01530i | −0.720329 | + | 0.559105i | ||||
\(261\) | −9.42323 | −0.583283 | ||||||||
\(262\) | −5.18036 | + | 1.77454i | −0.320043 | + | 0.109631i | ||||
\(263\) | − | 10.3714i | − | 0.639526i | −0.947498 | − | 0.319763i | \(-0.896397\pi\) | ||
0.947498 | − | 0.319763i | \(-0.103603\pi\) | |||||||
\(264\) | −2.99234 | − | 1.96359i | −0.184166 | − | 0.120851i | ||||
\(265\) | 0.175736i | 0.0107954i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.57161i | 0.524574i | ||||||||
\(268\) | 3.44306 | + | 4.43590i | 0.210318 | + | 0.270966i | ||||
\(269\) | 5.17319i | 0.315415i | 0.987486 | + | 0.157707i | \(0.0504103\pi\) | ||||
−0.987486 | + | 0.157707i | \(0.949590\pi\) | |||||||
\(270\) | 1.12403 | + | 3.28134i | 0.0684061 | + | 0.199696i | ||||
\(271\) | −24.2391 | −1.47242 | −0.736209 | − | 0.676755i | \(-0.763386\pi\) | ||||
−0.736209 | + | 0.676755i | \(0.763386\pi\) | |||||||
\(272\) | 7.10353 | + | 1.81914i | 0.430714 | + | 0.110302i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.6713 | + | 6.73842i | −1.18839 | + | 0.407083i | ||||
\(275\) | − | 1.28479i | − | 0.0774755i | ||||||
\(276\) | 8.26338 | + | 10.6462i | 0.497397 | + | 0.640827i | ||||
\(277\) | −3.01532 | −0.181173 | −0.0905866 | − | 0.995889i | \(-0.528874\pi\) | ||||
−0.0905866 | + | 0.995889i | \(0.528874\pi\) | |||||||
\(278\) | −2.69793 | + | 0.924179i | −0.161811 | + | 0.0554286i | ||||
\(279\) | 9.43978 | 0.565145 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.91922 | −0.412766 | −0.206383 | − | 0.978471i | \(-0.566169\pi\) | ||||
−0.206383 | + | 0.978471i | \(0.566169\pi\) | |||||||
\(282\) | −9.83564 | + | 3.36921i | −0.585704 | + | 0.200634i | ||||
\(283\) | −20.5740 | −1.22299 | −0.611497 | − | 0.791246i | \(-0.709433\pi\) | ||||
−0.611497 | + | 0.791246i | \(0.709433\pi\) | |||||||
\(284\) | 3.58431 | + | 4.61789i | 0.212690 | + | 0.274021i | ||||
\(285\) | − | 10.2025i | − | 0.604345i | ||||||
\(286\) | 5.07457 | − | 1.73830i | 0.300066 | − | 0.102788i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.448237 | − | 5.63907i | −0.0264126 | − | 0.332285i | ||||
\(289\) | 13.6394 | 0.802319 | ||||||||
\(290\) | 10.5920 | + | 30.9209i | 0.621982 | + | 1.81574i | ||||
\(291\) | − | 7.10394i | − | 0.416440i | ||||||
\(292\) | 9.93917 | + | 12.8052i | 0.581646 | + | 0.749370i | ||||
\(293\) | 28.3113i | 1.65396i | 0.562229 | + | 0.826982i | \(0.309944\pi\) | ||||
−0.562229 | + | 0.826982i | \(0.690056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.25772i | − | 0.480783i | ||||||
\(296\) | 11.6560 | − | 17.7626i | 0.677489 | − | 1.03243i | ||||
\(297\) | − | 1.26539i | − | 0.0734256i | ||||||
\(298\) | −0.663744 | + | 0.227366i | −0.0384496 | + | 0.0131710i | ||||
\(299\) | −20.1980 | −1.16808 | ||||||||
\(300\) | 1.60414 | − | 1.24510i | 0.0926149 | − | 0.0718859i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.06647 | + | 17.7097i | 0.349086 | + | 1.01908i | ||||
\(303\) | − | 0.933313i | − | 0.0536175i | ||||||
\(304\) | −4.12798 | + | 16.1192i | −0.236756 | + | 0.924502i | ||||
\(305\) | 27.2299 | 1.55918 | ||||||||
\(306\) | 0.840146 | + | 2.45262i | 0.0480280 | + | 0.140207i | ||||
\(307\) | 8.65596 | 0.494022 | 0.247011 | − | 0.969013i | \(-0.420552\pi\) | ||||
0.247011 | + | 0.969013i | \(0.420552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.12921 | −0.234902 | ||||||||
\(310\) | −10.6106 | − | 30.9752i | −0.602640 | − | 1.75927i | ||||
\(311\) | −9.34258 | −0.529769 | −0.264884 | − | 0.964280i | \(-0.585334\pi\) | ||||
−0.264884 | + | 0.964280i | \(0.585334\pi\) | |||||||
\(312\) | 7.08820 | + | 4.65132i | 0.401290 | + | 0.263329i | ||||
\(313\) | 7.37547i | 0.416886i | 0.978035 | + | 0.208443i | \(0.0668396\pi\) | ||||
−0.978035 | + | 0.208443i | \(0.933160\pi\) | |||||||
\(314\) | 2.31971 | + | 6.77186i | 0.130909 | + | 0.382158i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18734 | − | 2.81809i | −0.123048 | − | 0.158530i | ||||
\(317\) | −3.63028 | −0.203897 | −0.101949 | − | 0.994790i | \(-0.532508\pi\) | ||||
−0.101949 | + | 0.994790i | \(0.532508\pi\) | |||||||
\(318\) | 0.0958634 | − | 0.0328381i | 0.00537575 | − | 0.00184147i | ||||
\(319\) | − | 11.9241i | − | 0.667622i | ||||||
\(320\) | −17.9999 | + | 7.80929i | −1.00622 | + | 0.436552i | ||||
\(321\) | − | 13.8424i | − | 0.772605i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.62580i | − | 0.424311i | ||||||
\(324\) | 1.57993 | − | 1.22631i | 0.0877737 | − | 0.0681282i | ||||
\(325\) | 3.04338i | 0.168816i | ||||||||
\(326\) | 5.51594 | + | 16.1025i | 0.305499 | + | 0.891836i | ||||
\(327\) | 0.984676 | 0.0544527 | ||||||||
\(328\) | 2.57677 | + | 1.69089i | 0.142278 | + | 0.0933638i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.15219 | + | 1.42234i | −0.228571 | + | 0.0782971i | ||||
\(331\) | − | 0.628347i | − | 0.0345371i | −0.999851 | − | 0.0172685i | \(-0.994503\pi\) | ||
0.999851 | − | 0.0172685i | \(-0.00549702\pi\) | |||||||
\(332\) | 8.43090 | − | 6.54389i | 0.462705 | − | 0.359143i | ||||
\(333\) | 7.51143 | 0.411624 | ||||||||
\(334\) | 9.98637 | − | 3.42084i | 0.546430 | − | 0.187180i | ||||
\(335\) | 6.88612 | 0.376229 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3119 | −1.21541 | −0.607704 | − | 0.794164i | \(-0.707909\pi\) | ||||
−0.607704 | + | 0.794164i | \(0.707909\pi\) | |||||||
\(338\) | 5.37208 | − | 1.84021i | 0.292203 | − | 0.100094i | ||||
\(339\) | −5.03187 | −0.273294 | ||||||||
\(340\) | 7.10353 | − | 5.51362i | 0.385243 | − | 0.299018i | ||||
\(341\) | 11.9450i | 0.646860i | ||||||||
\(342\) | −5.56545 | + | 1.90645i | −0.300945 | + | 0.103089i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.8311 | + | 9.73229i | 0.799642 | + | 0.524730i | ||||
\(345\) | 16.5268 | 0.889771 | ||||||||
\(346\) | −2.00000 | − | 5.83854i | −0.107521 | − | 0.313882i | ||||
\(347\) | 6.89477i | 0.370130i | 0.982726 | + | 0.185065i | \(0.0592496\pi\) | ||||
−0.982726 | + | 0.185065i | \(0.940750\pi\) | |||||||
\(348\) | 14.8880 | − | 11.5558i | 0.798082 | − | 0.619455i | ||||
\(349\) | − | 13.4768i | − | 0.721399i | −0.932682 | − | 0.360699i | \(-0.882538\pi\) | ||
0.932682 | − | 0.360699i | \(-0.117462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.99744i | 0.159992i | ||||||||
\(352\) | 7.13564 | − | 0.567197i | 0.380331 | − | 0.0302317i | ||||
\(353\) | − | 28.5846i | − | 1.52140i | −0.649101 | − | 0.760702i | \(-0.724855\pi\) | ||
0.649101 | − | 0.760702i | \(-0.275145\pi\) | |||||||
\(354\) | −4.50457 | + | 1.54304i | −0.239415 | + | 0.0820119i | ||||
\(355\) | 7.16862 | 0.380471 | ||||||||
\(356\) | −10.5114 | − | 13.5425i | −0.557105 | − | 0.717752i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2589 | − | 32.8677i | −0.595050 | − | 1.73711i | ||||
\(359\) | 6.92820i | 0.365657i | 0.983145 | + | 0.182828i | \(0.0585252\pi\) | ||||
−0.983145 | + | 0.182828i | \(0.941475\pi\) | |||||||
\(360\) | −5.79982 | − | 3.80588i | −0.305677 | − | 0.200587i | ||||
\(361\) | −1.69562 | −0.0892430 | ||||||||
\(362\) | −5.37044 | − | 15.6778i | −0.282264 | − | 0.824006i | ||||
\(363\) | −9.39878 | −0.493308 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.8783 | 1.04048 | ||||||||
\(366\) | −5.08820 | − | 14.8538i | −0.265965 | − | 0.776423i | ||||
\(367\) | 12.9437 | 0.675654 | 0.337827 | − | 0.941208i | \(-0.390308\pi\) | ||||
0.337827 | + | 0.941208i | \(0.390308\pi\) | |||||||
\(368\) | −26.1111 | − | 6.68679i | −1.36113 | − | 0.348573i | ||||
\(369\) | 1.08966i | 0.0567253i | ||||||||
\(370\) | −8.44306 | − | 24.6476i | −0.438934 | − | 1.28137i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.9142 | + | 11.5761i | −0.773263 | + | 0.600192i | ||||
\(373\) | 3.07907 | 0.159428 | 0.0797141 | − | 0.996818i | \(-0.474599\pi\) | ||||
0.0797141 | + | 0.996818i | \(0.474599\pi\) | |||||||
\(374\) | −3.10353 | + | 1.06312i | −0.160479 | + | 0.0549724i | ||||
\(375\) | 9.77288i | 0.504669i | ||||||||
\(376\) | 11.4079 | − | 17.3846i | 0.588318 | − | 0.896544i | ||||
\(377\) | 28.2456i | 1.45472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.21020i | − | 0.267630i | −0.991006 | − | 0.133815i | \(-0.957277\pi\) | ||
0.991006 | − | 0.133815i | \(-0.0427228\pi\) | |||||||
\(380\) | 12.5114 | + | 16.1192i | 0.641823 | + | 0.826900i | ||||
\(381\) | − | 6.38337i | − | 0.327030i | ||||||
\(382\) | −7.28321 | − | 21.2617i | −0.372641 | − | 1.08784i | ||||
\(383\) | −38.8706 | −1.98619 | −0.993096 | − | 0.117301i | \(-0.962576\pi\) | ||||
−0.993096 | + | 0.117301i | \(0.962576\pi\) | |||||||
\(384\) | 7.62342 | + | 8.35964i | 0.389031 | + | 0.426601i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4018 | − | 9.04395i | 1.34381 | − | 0.460325i | ||||
\(387\) | 6.27176i | 0.318812i | ||||||||
\(388\) | 8.71162 | + | 11.2237i | 0.442265 | + | 0.569797i | ||||
\(389\) | −3.73503 | −0.189374 | −0.0946869 | − | 0.995507i | \(-0.530185\pi\) | ||||
−0.0946869 | + | 0.995507i | \(0.530185\pi\) | |||||||
\(390\) | 9.83564 | − | 3.36921i | 0.498047 | − | 0.170607i | ||||
\(391\) | 12.3528 | 0.624708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.87202 | 0.195318 | ||||||||
\(394\) | 1.33626 | − | 0.457736i | 0.0673196 | − | 0.0230604i | ||||
\(395\) | −4.37468 | −0.220114 | ||||||||
\(396\) | 1.55176 | + | 1.99923i | 0.0779790 | + | 0.100465i | ||||
\(397\) | 6.70976i | 0.336753i | 0.985723 | + | 0.168377i | \(0.0538525\pi\) | ||||
−0.985723 | + | 0.168377i | \(0.946148\pi\) | |||||||
\(398\) | −3.61655 | + | 1.23885i | −0.181281 | + | 0.0620980i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00754 | + | 3.93433i | −0.0503772 | + | 0.196717i | ||||
\(401\) | 5.84769 | 0.292020 | 0.146010 | − | 0.989283i | \(-0.453357\pi\) | ||||
0.146010 | + | 0.989283i | \(0.453357\pi\) | |||||||
\(402\) | −1.28674 | − | 3.75636i | −0.0641770 | − | 0.187350i | ||||
\(403\) | − | 28.2952i | − | 1.40949i | ||||||
\(404\) | 1.14453 | + | 1.47457i | 0.0569425 | + | 0.0733625i | ||||
\(405\) | − | 2.45262i | − | 0.121871i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.50492i | 0.471142i | ||||||||
\(408\) | −4.33503 | − | 2.84468i | −0.214616 | − | 0.140832i | ||||
\(409\) | − | 30.8651i | − | 1.52618i | −0.646293 | − | 0.763089i | \(-0.723682\pi\) | ||
0.646293 | − | 0.763089i | \(-0.276318\pi\) | |||||||
\(410\) | 3.57554 | − | 1.22481i | 0.176583 | − | 0.0604889i | ||||
\(411\) | 14.7032 | 0.725253 | ||||||||
\(412\) | 6.52384 | − | 5.06368i | 0.321407 | − | 0.249469i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.08820 | − | 9.01530i | −0.151777 | − | 0.443078i | ||||
\(415\) | − | 13.0878i | − | 0.642454i | ||||||
\(416\) | −16.9028 | + | 1.34357i | −0.828728 | + | 0.0658738i | ||||
\(417\) | 2.01655 | 0.0987508 | ||||||||
\(418\) | −2.41241 | − | 7.04249i | −0.117995 | − | 0.344459i | ||||
\(419\) | −29.0866 | −1.42097 | −0.710487 | − | 0.703710i | \(-0.751525\pi\) | ||||
−0.710487 | + | 0.703710i | \(0.751525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8642 | 0.675702 | 0.337851 | − | 0.941200i | \(-0.390300\pi\) | ||||
0.337851 | + | 0.941200i | \(0.390300\pi\) | |||||||
\(422\) | −8.33175 | − | 24.3227i | −0.405583 | − | 1.18401i | ||||
\(423\) | 7.35158 | 0.357446 | ||||||||
\(424\) | −0.111188 | + | 0.169440i | −0.00539974 | + | 0.00822873i | ||||
\(425\) | − | 1.86128i | − | 0.0902854i | ||||||
\(426\) | −1.33953 | − | 3.91046i | −0.0649006 | − | 0.189463i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.9750 | + | 21.8699i | 0.820517 | + | 1.05712i | ||||
\(429\) | −3.79295 | −0.183125 | ||||||||
\(430\) | 20.5798 | − | 7.04964i | 0.992447 | − | 0.339964i | ||||
\(431\) | 31.8995i | 1.53655i | 0.640123 | + | 0.768273i | \(0.278883\pi\) | ||||
−0.640123 | + | 0.768273i | \(0.721117\pi\) | |||||||
\(432\) | −0.992338 | + | 3.87495i | −0.0477439 | + | 0.186434i | ||||
\(433\) | − | 9.82239i | − | 0.472034i | −0.971749 | − | 0.236017i | \(-0.924158\pi\) | ||
0.971749 | − | 0.236017i | \(-0.0758421\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 23.1116i | − | 1.10811i | ||||||
\(436\) | −1.55572 | + | 1.20752i | −0.0745053 | + | 0.0578295i | ||||
\(437\) | 28.0308i | 1.34090i | ||||||||
\(438\) | −3.71448 | − | 10.8436i | −0.177485 | − | 0.518126i | ||||
\(439\) | 17.0398 | 0.813264 | 0.406632 | − | 0.913592i | \(-0.366703\pi\) | ||||
0.406632 | + | 0.913592i | \(0.366703\pi\) | |||||||
\(440\) | 4.81594 | − | 7.33906i | 0.229591 | − | 0.349876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.35158 | − | 2.51829i | 0.349679 | − | 0.119783i | ||||
\(443\) | 8.42931i | 0.400489i | 0.979746 | + | 0.200244i | \(0.0641736\pi\) | ||||
−0.979746 | + | 0.200244i | \(0.935826\pi\) | |||||||
\(444\) | −11.8675 | + | 9.21133i | −0.563207 | + | 0.437150i | ||||
\(445\) | −21.0229 | −0.996580 | ||||||||
\(446\) | −15.5191 | + | 5.31608i | −0.734851 | + | 0.251724i | ||||
\(447\) | 0.496110 | 0.0234652 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.64064 | 0.454970 | 0.227485 | − | 0.973782i | \(-0.426950\pi\) | ||||
0.227485 | + | 0.973782i | \(0.426950\pi\) | |||||||
\(450\) | −1.35840 | + | 0.465320i | −0.0640355 | + | 0.0219354i | ||||
\(451\) | −1.37885 | −0.0649274 | ||||||||
\(452\) | 7.94999 | − | 6.17063i | 0.373936 | − | 0.290242i | ||||
\(453\) | − | 13.2370i | − | 0.621928i | ||||||
\(454\) | −13.5945 | + | 4.65680i | −0.638020 | + | 0.218554i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.45511 | − | 9.83701i | 0.302288 | − | 0.460660i | ||||
\(457\) | −29.0457 | −1.35870 | −0.679351 | − | 0.733813i | \(-0.737739\pi\) | ||||
−0.679351 | + | 0.733813i | \(0.737739\pi\) | |||||||
\(458\) | −10.5853 | − | 30.9013i | −0.494617 | − | 1.44392i | ||||
\(459\) | − | 1.83319i | − | 0.0855660i | ||||||
\(460\) | −26.1111 | + | 20.2669i | −1.21743 | + | 0.944949i | ||||
\(461\) | − | 23.9796i | − | 1.11684i | −0.829559 | − | 0.558420i | \(-0.811408\pi\) | ||
0.829559 | − | 0.558420i | \(-0.188592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.4975i | 1.32439i | 0.749331 | + | 0.662196i | \(0.230375\pi\) | ||||
−0.749331 | + | 0.662196i | \(0.769625\pi\) | |||||||
\(464\) | −9.35103 | + | 36.5146i | −0.434111 | + | 1.69515i | ||||
\(465\) | 23.1522i | 1.07366i | ||||||||
\(466\) | −9.17190 | + | 3.14184i | −0.424880 | + | 0.145543i | ||||
\(467\) | 18.5815 | 0.859849 | 0.429925 | − | 0.902865i | \(-0.358540\pi\) | ||||
0.429925 | + | 0.902865i | \(0.358540\pi\) | |||||||
\(468\) | −3.67579 | − | 4.73574i | −0.169913 | − | 0.218910i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.26338 | − | 24.1231i | −0.381161 | − | 1.11271i | ||||
\(471\) | − | 5.06158i | − | 0.233225i | ||||||
\(472\) | 5.22464 | − | 7.96188i | 0.240483 | − | 0.366475i | ||||
\(473\) | −7.93625 | −0.364909 | ||||||||
\(474\) | 0.817456 | + | 2.38638i | 0.0375470 | + | 0.109610i | ||||
\(475\) | 4.22360 | 0.193792 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0716524 | −0.00328074 | ||||||||
\(478\) | 10.1860 | + | 29.7357i | 0.465897 | + | 1.36008i | ||||
\(479\) | 28.3414 | 1.29495 | 0.647475 | − | 0.762087i | \(-0.275825\pi\) | ||||
0.647475 | + | 0.762087i | \(0.275825\pi\) | |||||||
\(480\) | 13.8305 | − | 1.09935i | 0.631272 | − | 0.0501784i | ||||
\(481\) | − | 22.5151i | − | 1.02660i | ||||||
\(482\) | 7.07031 | + | 20.6402i | 0.322044 | + | 0.940134i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.8494 | − | 11.5258i | 0.674972 | − | 0.523900i | ||||
\(485\) | 17.4232 | 0.791148 | ||||||||
\(486\) | −1.33790 | + | 0.458297i | −0.0606882 | + | 0.0207888i | ||||
\(487\) | 41.5113i | 1.88106i | 0.339718 | + | 0.940528i | \(0.389669\pi\) | ||||
−0.339718 | + | 0.940528i | \(0.610331\pi\) | |||||||
\(488\) | 26.2544 | + | 17.2283i | 1.18848 | + | 0.779888i | ||||
\(489\) | − | 12.0357i | − | 0.544274i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.72728i | 0.0779509i | 0.999240 | + | 0.0389755i | \(0.0124094\pi\) | ||||
−0.999240 | + | 0.0389755i | \(0.987591\pi\) | |||||||
\(492\) | −1.33626 | − | 1.72158i | −0.0602431 | − | 0.0776148i | ||||
\(493\) | − | 17.2746i | − | 0.778008i | ||||||
\(494\) | 5.71448 | + | 16.6821i | 0.257107 | + | 0.750564i | ||||
\(495\) | 3.10353 | 0.139493 | ||||||||
\(496\) | 9.36745 | − | 36.5787i | 0.420611 | − | 1.64243i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.13935 | + | 2.44559i | −0.319922 | + | 0.109590i | ||||
\(499\) | − | 42.2870i | − | 1.89303i | −0.322663 | − | 0.946514i | \(-0.604578\pi\) | ||
0.322663 | − | 0.946514i | \(-0.395422\pi\) | |||||||
\(500\) | −11.9846 | − | 15.4404i | −0.535966 | − | 0.690517i | ||||
\(501\) | −7.46424 | −0.333478 | ||||||||
\(502\) | −29.8289 | + | 10.2179i | −1.33133 | + | 0.456048i | ||||
\(503\) | −4.23770 | −0.188950 | −0.0944748 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944748 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.28906 | 0.101862 | ||||||||
\(506\) | 11.4079 | − | 3.90779i | 0.507143 | − | 0.173723i | ||||
\(507\) | −4.01532 | −0.178327 | ||||||||
\(508\) | 7.82798 | + | 10.0853i | 0.347311 | + | 0.447461i | ||||
\(509\) | 41.7756i | 1.85167i | 0.377924 | + | 0.925836i | \(0.376638\pi\) | ||||
−0.377924 | + | 0.925836i | \(0.623362\pi\) | |||||||
\(510\) | −6.01532 | + | 2.06056i | −0.266363 | + | 0.0912429i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.2959 | − | 3.85896i | −0.985350 | − | 0.170544i | ||||
\(513\) | 4.15985 | 0.183662 | ||||||||
\(514\) | −1.31521 | − | 3.83944i | −0.0580112 | − | 0.169351i | ||||
\(515\) | − | 10.1274i | − | 0.446265i | ||||||
\(516\) | −7.69111 | − | 9.90893i | −0.338582 | − | 0.436216i | ||||
\(517\) | 9.30265i | 0.409130i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.36398i | 0.191557i | ||||||||
\(520\) | −11.4079 | + | 17.3846i | −0.500270 | + | 0.762367i | ||||
\(521\) | 34.9506i | 1.53121i | 0.643309 | + | 0.765607i | \(0.277561\pi\) | ||||
−0.643309 | + | 0.765607i | \(0.722439\pi\) | |||||||
\(522\) | −12.6073 | + | 4.31864i | −0.551806 | + | 0.189022i | ||||
\(523\) | 12.2701 | 0.536532 | 0.268266 | − | 0.963345i | \(-0.413549\pi\) | ||||
0.268266 | + | 0.963345i | \(0.413549\pi\) | |||||||
\(524\) | −6.11751 | + | 4.74829i | −0.267245 | + | 0.207430i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.75317 | − | 13.8758i | −0.207248 | − | 0.605014i | ||||
\(527\) | 17.3049i | 0.753814i | ||||||||
\(528\) | −4.90334 | − | 1.25570i | −0.213391 | − | 0.0546473i | ||||
\(529\) | −22.4063 | −0.974188 | ||||||||
\(530\) | 0.0805393 | + | 0.235116i | 0.00349840 | + | 0.0102128i | ||||
\(531\) | 3.36690 | 0.146111 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.26619 | 0.141474 | ||||||||
\(534\) | 3.92835 | + | 11.4679i | 0.169996 | + | 0.496265i | ||||
\(535\) | 33.9500 | 1.46779 | ||||||||
\(536\) | 6.63942 | + | 4.35683i | 0.286779 | + | 0.188186i | ||||
\(537\) | 24.5667i | 1.06013i | ||||||||
\(538\) | 2.37086 | + | 6.92118i | 0.102215 | + | 0.298393i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.00766 | + | 3.87495i | 0.129429 | + | 0.166751i | ||||
\(541\) | −0.935765 | −0.0402317 | −0.0201158 | − | 0.999798i | \(-0.506404\pi\) | ||||
−0.0201158 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(542\) | −32.4293 | + | 11.1087i | −1.39296 | + | 0.477159i | ||||
\(543\) | 11.7182i | 0.502878i | ||||||||
\(544\) | 10.3375 | − | 0.821704i | 0.443216 | − | 0.0352303i | ||||
\(545\) | 2.41503i | 0.103449i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.13048i | − | 0.304877i | −0.988313 | − | 0.152439i | \(-0.951287\pi\) | ||
0.988313 | − | 0.152439i | \(-0.0487127\pi\) | |||||||
\(548\) | −23.2299 | + | 18.0306i | −0.992333 | + | 0.770229i | ||||
\(549\) | 11.1024i | 0.473839i | ||||||||
\(550\) | −0.588814 | − | 1.71891i | −0.0251071 | − | 0.0732945i | ||||
\(551\) | 39.1993 | 1.66995 | ||||||||
\(552\) | 15.9347 | + | 10.4564i | 0.678224 | + | 0.445055i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.03419 | + | 1.38192i | −0.171396 | + | 0.0587120i | ||||
\(555\) | 18.4227i | 0.781998i | ||||||||
\(556\) | −3.18600 | + | 2.47291i | −0.135116 | + | 0.104875i | ||||
\(557\) | 9.95244 | 0.421698 | 0.210849 | − | 0.977519i | \(-0.432377\pi\) | ||||
0.210849 | + | 0.977519i | \(0.432377\pi\) | |||||||
\(558\) | 12.6294 | − | 4.32623i | 0.534647 | − | 0.183144i | ||||
\(559\) | 18.7993 | 0.795124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.31971 | 0.0979381 | ||||||||
\(562\) | −9.25719 | + | 3.17106i | −0.390491 | + | 0.133763i | ||||
\(563\) | 1.68906 | 0.0711855 | 0.0355927 | − | 0.999366i | \(-0.488668\pi\) | ||||
0.0355927 | + | 0.999366i | \(0.488668\pi\) | |||||||
\(564\) | −11.6150 | + | 9.01530i | −0.489078 | + | 0.379613i | ||||
\(565\) | − | 12.3413i | − | 0.519200i | ||||||
\(566\) | −27.5258 | + | 9.42899i | −1.15700 | + | 0.396330i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.91180 | + | 4.53557i | 0.290013 | + | 0.190308i | ||||
\(569\) | −13.9387 | −0.584341 | −0.292170 | − | 0.956366i | \(-0.594377\pi\) | ||||
−0.292170 | + | 0.956366i | \(0.594377\pi\) | |||||||
\(570\) | −4.67579 | − | 13.6499i | −0.195847 | − | 0.571732i | ||||
\(571\) | 18.6589i | 0.780853i | 0.920634 | + | 0.390426i | \(0.127672\pi\) | ||||
−0.920634 | + | 0.390426i | \(0.872328\pi\) | |||||||
\(572\) | 5.99258 | − | 4.65132i | 0.250562 | − | 0.194482i | ||||
\(573\) | 15.8919i | 0.663893i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.84168i | 0.285318i | ||||||||
\(576\) | −3.18406 | − | 7.33906i | −0.132669 | − | 0.305794i | ||||
\(577\) | 34.0165i | 1.41612i | 0.706150 | + | 0.708062i | \(0.250430\pi\) | ||||
−0.706150 | + | 0.708062i | \(0.749570\pi\) | |||||||
\(578\) | 18.2481 | − | 6.25091i | 0.759021 | − | 0.260004i | ||||
\(579\) | −19.7338 | −0.820109 | ||||||||
\(580\) | 28.3419 | + | 36.5146i | 1.17683 | + | 1.51619i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.25572 | − | 9.50433i | −0.134954 | − | 0.393967i | ||||
\(583\) | − | 0.0906685i | − | 0.00375511i | ||||||
\(584\) | 19.1662 | + | 12.5770i | 0.793102 | + | 0.520439i | ||||
\(585\) | −7.35158 | −0.303950 | ||||||||
\(586\) | 12.9750 | + | 37.8775i | 0.535992 | + | 1.56471i | ||||
\(587\) | 41.9153 | 1.73003 | 0.865015 | − | 0.501746i | \(-0.167309\pi\) | ||||
0.865015 | + | 0.501746i | \(0.167309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.2681 | −1.61801 | ||||||||
\(590\) | −3.78449 | − | 11.0480i | −0.155805 | − | 0.454838i | ||||
\(591\) | −0.998775 | −0.0410841 | ||||||||
\(592\) | 7.45388 | − | 29.1065i | 0.306353 | − | 1.19627i | ||||
\(593\) | − | 24.4051i | − | 1.00220i | −0.865391 | − | 0.501098i | \(-0.832930\pi\) | ||
0.865391 | − | 0.501098i | \(-0.167070\pi\) | |||||||
\(594\) | −0.579927 | − | 1.69296i | −0.0237947 | − | 0.0694632i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.783818 | + | 0.608384i | −0.0321064 | + | 0.0249204i | ||||
\(597\) | 2.70316 | 0.110633 | ||||||||
\(598\) | −27.0229 | + | 9.25671i | −1.10505 | + | 0.378535i | ||||
\(599\) | 20.7846i | 0.849236i | 0.905373 | + | 0.424618i | \(0.139592\pi\) | ||||
−0.905373 | + | 0.424618i | \(0.860408\pi\) | |||||||
\(600\) | 1.57554 | − | 2.40099i | 0.0643212 | − | 0.0980198i | ||||
\(601\) | 10.6623i | 0.434924i | 0.976069 | + | 0.217462i | \(0.0697778\pi\) | ||||
−0.976069 | + | 0.217462i | \(0.930222\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.80766i | 0.114337i | ||||||||
\(604\) | 16.2326 | + | 20.9135i | 0.660496 | + | 0.850957i | ||||
\(605\) | − | 23.0516i | − | 0.937180i | ||||||
\(606\) | −0.427735 | − | 1.24868i | −0.0173756 | − | 0.0507240i | ||||
\(607\) | 40.0429 | 1.62529 | 0.812646 | − | 0.582757i | \(-0.198026\pi\) | ||||
0.812646 | + | 0.582757i | \(0.198026\pi\) | |||||||
\(608\) | 1.86460 | + | 23.4577i | 0.0756196 | + | 0.951335i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.4308 | − | 12.4794i | 1.47504 | − | 0.505276i | ||||
\(611\) | − | 22.0360i | − | 0.891479i | ||||||
\(612\) | 2.24806 | + | 2.89631i | 0.0908722 | + | 0.117076i | ||||
\(613\) | 22.4961 | 0.908609 | 0.454305 | − | 0.890846i | \(-0.349888\pi\) | ||||
0.454305 | + | 0.890846i | \(0.349888\pi\) | |||||||
\(614\) | 11.5808 | − | 3.96701i | 0.467362 | − | 0.160095i | ||||
\(615\) | −2.67251 | −0.107766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0820 | −0.727954 | −0.363977 | − | 0.931408i | \(-0.618581\pi\) | ||||
−0.363977 | + | 0.931408i | \(0.618581\pi\) | |||||||
\(618\) | −5.52444 | + | 1.89240i | −0.222226 | + | 0.0761237i | ||||
\(619\) | 32.0929 | 1.28992 | 0.644962 | − | 0.764215i | \(-0.276873\pi\) | ||||
0.644962 | + | 0.764215i | \(0.276873\pi\) | |||||||
\(620\) | −28.3917 | − | 36.5787i | −1.14024 | − | 1.46904i | ||||
\(621\) | 6.73842i | 0.270404i | ||||||||
\(622\) | −12.4994 | + | 4.28168i | −0.501180 | + | 0.171680i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.6150 | + | 2.97448i | 0.464971 | + | 0.119074i | ||||
\(625\) | −29.0457 | −1.16183 | ||||||||
\(626\) | 3.38016 | + | 9.86760i | 0.135098 | + | 0.394389i | ||||
\(627\) | 5.26385i | 0.210218i | ||||||||
\(628\) | 6.20705 | + | 7.99692i | 0.247688 | + | 0.319112i | ||||
\(629\) | 13.7699i | 0.549041i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.95509i | 0.117640i | 0.998269 | + | 0.0588201i | \(0.0187338\pi\) | ||||
−0.998269 | + | 0.0588201i | \(0.981266\pi\) | |||||||
\(632\) | −4.21796 | − | 2.76785i | −0.167781 | − | 0.110099i | ||||
\(633\) | 18.1798i | 0.722582i | ||||||||
\(634\) | −4.85694 | + | 1.66375i | −0.192894 | + | 0.0660760i | ||||
\(635\) | 15.6560 | 0.621288 | ||||||||
\(636\) | 0.113206 | − | 0.0878679i | 0.00448889 | − | 0.00348419i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.46479 | − | 15.9532i | −0.216353 | − | 0.631593i | ||||
\(639\) | 2.92285i | 0.115626i | ||||||||
\(640\) | −20.5030 | + | 18.6973i | −0.810451 | + | 0.739076i | ||||
\(641\) | −41.4917 | −1.63882 | −0.819412 | − | 0.573205i | \(-0.805700\pi\) | ||||
−0.819412 | + | 0.573205i | \(0.805700\pi\) | |||||||
\(642\) | −6.34392 | − | 18.5196i | −0.250374 | − | 0.730911i | ||||
\(643\) | −16.7686 | −0.661290 | −0.330645 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330645 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3822 | −0.605675 | ||||||||
\(646\) | −3.49489 | − | 10.2025i | −0.137504 | − | 0.401413i | ||||
\(647\) | 18.6236 | 0.732169 | 0.366085 | − | 0.930582i | \(-0.380698\pi\) | ||||
0.366085 | + | 0.930582i | \(0.380698\pi\) | |||||||
\(648\) | 1.55176 | − | 2.36475i | 0.0609590 | − | 0.0928961i | ||||
\(649\) | 4.26046i | 0.167238i | ||||||||
\(650\) | 1.39477 | + | 4.07172i | 0.0547075 | + | 0.159706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.7595 | + | 19.0155i | 0.578026 | + | 0.744706i | ||||
\(653\) | 25.6609 | 1.00419 | 0.502095 | − | 0.864813i | \(-0.332563\pi\) | ||||
0.502095 | + | 0.864813i | \(0.332563\pi\) | |||||||
\(654\) | 1.31739 | − | 0.451274i | 0.0515141 | − | 0.0176462i | ||||
\(655\) | 9.49658i | 0.371062i | ||||||||
\(656\) | 4.22238 | + | 1.08131i | 0.164856 | + | 0.0422180i | ||||
\(657\) | 8.10495i | 0.316204i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.7044i | 1.07921i | 0.841919 | + | 0.539604i | \(0.181426\pi\) | ||||
−0.841919 | + | 0.539604i | \(0.818574\pi\) | |||||||
\(660\) | −4.90334 | + | 3.80588i | −0.190862 | + | 0.148144i | ||||
\(661\) | − | 34.1182i | − | 1.32704i | −0.748157 | − | 0.663522i | \(-0.769061\pi\) | ||
0.748157 | − | 0.663522i | \(-0.230939\pi\) | |||||||
\(662\) | −0.287970 | − | 0.840662i | −0.0111923 | − | 0.0326732i | ||||
\(663\) | −5.49489 | −0.213404 | ||||||||
\(664\) | 8.28060 | − | 12.6189i | 0.321350 | − | 0.489708i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0495 | − | 3.44247i | 0.389411 | − | 0.133393i | ||||
\(667\) | 63.4977i | 2.45864i | ||||||||
\(668\) | 11.7929 | − | 9.15345i | 0.456283 | − | 0.354158i | ||||
\(669\) | 11.5996 | 0.448468 | ||||||||
\(670\) | 9.21290 | − | 3.15589i | 0.355926 | − | 0.121923i | ||||
\(671\) | −14.0489 | −0.542352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7032 | −0.682407 | −0.341203 | − | 0.939990i | \(-0.610834\pi\) | ||||
−0.341203 | + | 0.939990i | \(0.610834\pi\) | |||||||
\(674\) | −29.8510 | + | 10.2255i | −1.14982 | + | 0.393872i | ||||
\(675\) | 1.01532 | 0.0390798 | ||||||||
\(676\) | 6.34392 | − | 4.92402i | 0.243997 | − | 0.189386i | ||||
\(677\) | 41.0852i | 1.57903i | 0.613730 | + | 0.789516i | \(0.289668\pi\) | ||||
−0.613730 | + | 0.789516i | \(0.710332\pi\) | |||||||
\(678\) | −6.73212 | + | 2.30609i | −0.258545 | + | 0.0885650i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.97690 | − | 10.6322i | 0.267552 | − | 0.407725i | ||||
\(681\) | 10.1611 | 0.389373 | ||||||||
\(682\) | 5.47438 | + | 15.9812i | 0.209625 | + | 0.611952i | ||||
\(683\) | 21.2282i | 0.812275i | 0.913812 | + | 0.406137i | \(0.133125\pi\) | ||||
−0.913812 | + | 0.406137i | \(0.866875\pi\) | |||||||
\(684\) | −6.57226 | + | 5.10126i | −0.251297 | + | 0.195052i | ||||
\(685\) | 36.0612i | 1.37783i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.0970i | 0.881204i | ||||||||
\(688\) | 24.3028 | + | 6.22371i | 0.926535 | + | 0.237277i | ||||
\(689\) | 0.214774i | 0.00818224i | ||||||||
\(690\) | 22.1111 | − | 7.57417i | 0.841754 | − | 0.288344i | ||||
\(691\) | −38.9757 | −1.48270 | −0.741352 | − | 0.671116i | \(-0.765815\pi\) | ||||
−0.741352 | + | 0.671116i | \(0.765815\pi\) | |||||||
\(692\) | −5.35158 | − | 6.89477i | −0.203437 | − | 0.262100i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.15985 | + | 9.22447i | 0.119946 | + | 0.350156i | ||||
\(695\) | 4.94582i | 0.187606i | ||||||||
\(696\) | 14.6226 | − | 22.2836i | 0.554269 | − | 0.844657i | ||||
\(697\) | −1.99755 | −0.0756626 | ||||||||
\(698\) | −6.17640 | − | 18.0306i | −0.233780 | − | 0.682468i | ||||
\(699\) | 6.85547 | 0.259298 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.28115 | 0.161697 | 0.0808485 | − | 0.996726i | \(-0.474237\pi\) | ||||
0.0808485 | + | 0.996726i | \(0.474237\pi\) | |||||||
\(702\) | 1.37372 | + | 4.01027i | 0.0518478 | + | 0.151358i | ||||
\(703\) | −31.2465 | −1.17848 | ||||||||
\(704\) | 9.28680 | − | 4.02910i | 0.350009 | − | 0.151852i | ||||
\(705\) | 18.0306i | 0.679072i | ||||||||
\(706\) | −13.1002 | − | 38.2432i | −0.493034 | − | 1.43930i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.31946 | + | 4.12886i | −0.199918 | + | 0.155172i | ||||
\(709\) | −43.7591 | −1.64341 | −0.821704 | − | 0.569914i | \(-0.806976\pi\) | ||||
−0.821704 | + | 0.569914i | \(0.806976\pi\) | |||||||
\(710\) | 9.59087 | − | 3.28536i | 0.359939 | − | 0.123297i | ||||
\(711\) | − | 1.78368i | − | 0.0668933i | ||||||
\(712\) | −20.2697 | − | 13.3011i | −0.759639 | − | 0.498480i | ||||
\(713\) | − | 63.6092i | − | 2.38218i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 9.30265i | − | 0.347899i | ||||||
\(716\) | −30.1264 | − | 38.8137i | −1.12588 | − | 1.45053i | ||||
\(717\) | − | 22.2257i | − | 0.830035i | ||||||
\(718\) | 3.17518 | + | 9.26921i | 0.118497 | + | 0.345924i | ||||
\(719\) | −41.5314 | −1.54886 | −0.774429 | − | 0.632660i | \(-0.781963\pi\) | ||||
−0.774429 | + | 0.632660i | \(0.781963\pi\) | |||||||
\(720\) | −9.50377 | − | 2.43382i | −0.354185 | − | 0.0907033i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.26856 | + | 0.777097i | −0.0844270 | + | 0.0289205i | ||||
\(723\) | − | 15.4273i | − | 0.573749i | ||||||
\(724\) | −14.3702 | − | 18.5140i | −0.534064 | − | 0.688067i | ||||
\(725\) | 9.56764 | 0.355333 | ||||||||
\(726\) | −12.5746 | + | 4.30744i | −0.466686 | + | 0.159864i | ||||
\(727\) | 7.19963 | 0.267020 | 0.133510 | − | 0.991047i | \(-0.457375\pi\) | ||||
0.133510 | + | 0.991047i | \(0.457375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 26.5951 | − | 9.11019i | 0.984330 | − | 0.337183i | ||||
\(731\) | −11.4973 | −0.425244 | ||||||||
\(732\) | −13.6150 | − | 17.5410i | −0.503223 | − | 0.648333i | ||||
\(733\) | − | 24.1585i | − | 0.892315i | −0.894954 | − | 0.446158i | \(-0.852792\pi\) | ||
0.894954 | − | 0.446158i | \(-0.147208\pi\) | |||||||
\(734\) | 17.3173 | − | 5.93205i | 0.639192 | − | 0.218956i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.9984 | + | 3.02041i | −1.40064 | + | 0.111334i | ||||
\(737\) | −3.55280 | −0.130869 | ||||||||
\(738\) | 0.499388 | + | 1.45785i | 0.0183827 | + | 0.0536641i | ||||
\(739\) | − | 9.43033i | − | 0.346900i | −0.984843 | − | 0.173450i | \(-0.944508\pi\) | ||
0.984843 | − | 0.173450i | \(-0.0554915\pi\) | |||||||
\(740\) | −22.5919 | − | 29.1065i | −0.830493 | − | 1.06997i | ||||
\(741\) | − | 12.4689i | − | 0.458058i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.32851i | − | 0.0854248i | −0.999087 | − | 0.0427124i | \(-0.986400\pi\) | ||
0.999087 | − | 0.0427124i | \(-0.0135999\pi\) | |||||||
\(744\) | −14.6483 | + | 22.3227i | −0.537033 | + | 0.818390i | ||||
\(745\) | 1.21677i | 0.0445789i | ||||||||
\(746\) | 4.11947 | − | 1.41113i | 0.150825 | − | 0.0516651i | ||||
\(747\) | 5.33626 | 0.195243 | ||||||||
\(748\) | −3.66497 | + | 2.84468i | −0.134005 | + | 0.104012i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.47889 | + | 13.0751i | 0.163546 | + | 0.477435i | ||||
\(751\) | − | 31.1577i | − | 1.13696i | −0.822696 | − | 0.568481i | \(-0.807531\pi\) | ||
0.822696 | − | 0.568481i | \(-0.192469\pi\) | |||||||
\(752\) | 7.29525 | − | 28.4870i | 0.266030 | − | 1.03882i | ||||
\(753\) | 22.2954 | 0.812489 | ||||||||
\(754\) | 12.9449 | + | 37.7897i | 0.471425 | + | 1.37622i | ||||
\(755\) | 32.4652 | 1.18153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.559856 | −0.0203483 | −0.0101742 | − | 0.999948i | \(-0.503239\pi\) | ||||
−0.0101742 | + | 0.999948i | \(0.503239\pi\) | |||||||
\(758\) | −2.38782 | − | 6.97070i | −0.0867296 | − | 0.253187i | ||||
\(759\) | −8.52676 | −0.309502 | ||||||||
\(760\) | 24.1264 | + | 15.8319i | 0.875156 | + | 0.574283i | ||||
\(761\) | − | 45.7488i | − | 1.65839i | −0.558958 | − | 0.829196i | \(-0.688799\pi\) | ||
0.558958 | − | 0.829196i | \(-0.311201\pi\) | |||||||
\(762\) | −2.92548 | − | 8.54029i | −0.105979 | − | 0.309382i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.4883 | − | 25.1080i | −0.705063 | − | 0.908376i | ||||
\(765\) | 4.49611 | 0.162557 | ||||||||
\(766\) | −52.0047 | + | 17.8143i | −1.87901 | + | 0.643656i | ||||
\(767\) | − | 10.0921i | − | 0.364405i | ||||||
\(768\) | 14.0305 | + | 7.69053i | 0.506283 | + | 0.277508i | ||||
\(769\) | 8.33377i | 0.300524i | 0.988646 | + | 0.150262i | \(0.0480117\pi\) | ||||
−0.988646 | + | 0.150262i | \(0.951988\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.86976i | 0.103352i | ||||||||
\(772\) | 31.1780 | − | 24.1997i | 1.12212 | − | 0.870967i | ||||
\(773\) | 30.6774i | 1.10339i | 0.834046 | + | 0.551695i | \(0.186019\pi\) | ||||
−0.834046 | + | 0.551695i | \(0.813981\pi\) | |||||||
\(774\) | 2.87433 | + | 8.39096i | 0.103316 | + | 0.301607i | ||||
\(775\) | −9.58444 | −0.344283 | ||||||||
\(776\) | 16.7990 | + | 11.0236i | 0.603050 | + | 0.395725i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.99708 | + | 1.71176i | −0.179154 | + | 0.0613695i | ||||
\(779\) | − | 4.53282i | − | 0.162405i | ||||||
\(780\) | 11.6150 | − | 9.01530i | 0.415882 | − | 0.322800i | ||||
\(781\) | −3.69855 | −0.132345 | ||||||||
\(782\) | 16.5268 | − | 5.66126i | 0.590996 | − | 0.202446i | ||||
\(783\) | 9.42323 | 0.336759 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4141 | 0.443078 | ||||||||
\(786\) | 5.18036 | − | 1.77454i | 0.184777 | − | 0.0632956i | ||||
\(787\) | 22.1584 | 0.789861 | 0.394931 | − | 0.918711i | \(-0.370769\pi\) | ||||
0.394931 | + | 0.918711i | \(0.370769\pi\) | |||||||
\(788\) | 1.57799 | − | 1.22481i | 0.0562136 | − | 0.0436319i | ||||
\(789\) | 10.3714i | 0.369230i | ||||||||
\(790\) | −5.85287 | + | 2.00491i | −0.208236 | + | 0.0713314i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.99234 | + | 1.96359i | 0.106328 | + | 0.0697732i | ||||
\(793\) | 33.2788 | 1.18177 | ||||||||
\(794\) | 3.07506 | + | 8.97695i | 0.109130 | + | 0.318580i | ||||
\(795\) | − | 0.175736i | − | 0.00623271i | ||||||
\(796\) | −4.27080 | + | 3.31491i | −0.151374 | + | 0.117494i | ||||
\(797\) | − | 24.1705i | − | 0.856164i | −0.903740 | − | 0.428082i | \(-0.859189\pi\) | ||
0.903740 | − | 0.428082i | \(-0.140811\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4768i | 0.476776i | ||||||||
\(800\) | 0.455106 | + | 5.72548i | 0.0160904 | + | 0.202426i | ||||
\(801\) | − | 8.57161i | − | 0.302863i | ||||||
\(802\) | 7.82360 | − | 2.67998i | 0.276261 | − | 0.0946334i | ||||
\(803\) | −10.2560 | −0.361925 | ||||||||
\(804\) | −3.44306 | − | 4.43590i | −0.121427 | − | 0.156442i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.9676 | − | 37.8560i | −0.456765 | − | 1.33342i | ||||
\(807\) | − | 5.17319i | − | 0.182105i | ||||||
\(808\) | 2.20705 | + | 1.44828i | 0.0776438 | + | 0.0509503i | ||||
\(809\) | 15.2209 | 0.535139 | 0.267569 | − | 0.963539i | \(-0.413780\pi\) | ||||
0.267569 | + | 0.963539i | \(0.413780\pi\) | |||||||
\(810\) | −1.12403 | − | 3.28134i | −0.0394943 | − | 0.115295i | ||||
\(811\) | −48.4574 | −1.70157 | −0.850785 | − | 0.525515i | \(-0.823873\pi\) | ||||
−0.850785 | + | 0.525515i | \(0.823873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.2391 | 0.850101 | ||||||||
\(814\) | 4.35608 | + | 12.7166i | 0.152681 | + | 0.445716i | ||||
\(815\) | 29.5190 | 1.03400 | ||||||||
\(816\) | −7.10353 | − | 1.81914i | −0.248673 | − | 0.0636828i | ||||
\(817\) | − | 26.0896i | − | 0.912760i | ||||||
\(818\) | −14.1454 | − | 41.2942i | −0.494581 | − | 1.44382i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.22238 | − | 3.27732i | 0.147452 | − | 0.114449i | ||||
\(821\) | 51.5293 | 1.79839 | 0.899193 | − | 0.437552i | \(-0.144154\pi\) | ||||
0.899193 | + | 0.437552i | \(0.144154\pi\) | |||||||
\(822\) | 19.6713 | − | 6.73842i | 0.686115 | − | 0.235029i | ||||
\(823\) | − | 2.19716i | − | 0.0765881i | −0.999267 | − | 0.0382941i | \(-0.987808\pi\) | ||
0.999267 | − | 0.0382941i | \(-0.0121924\pi\) | |||||||
\(824\) | 6.40755 | − | 9.76453i | 0.223217 | − | 0.340164i | ||||
\(825\) | 1.28479i | 0.0447305i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.2864i | − | 0.357693i | −0.983877 | − | 0.178846i | \(-0.942763\pi\) | ||
0.983877 | − | 0.178846i | \(-0.0572365\pi\) | |||||||
\(828\) | −8.26338 | − | 10.6462i | −0.287172 | − | 0.369981i | ||||
\(829\) | 0.765044i | 0.0265711i | 0.999912 | + | 0.0132855i | \(0.00422904\pi\) | ||||
−0.999912 | + | 0.0132855i | \(0.995771\pi\) | |||||||
\(830\) | −5.99810 | − | 17.5101i | −0.208197 | − | 0.607784i | ||||
\(831\) | 3.01532 | 0.104600 | ||||||||
\(832\) | −21.9984 | + | 9.54406i | −0.762658 | + | 0.330881i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.69793 | − | 0.924179i | 0.0934217 | − | 0.0320017i | ||||
\(835\) | − | 18.3069i | − | 0.633537i | ||||||
\(836\) | −6.45511 | − | 8.31651i | −0.223255 | − | 0.287632i | ||||
\(837\) | −9.43978 | −0.326287 | ||||||||
\(838\) | −38.9148 | + | 13.3303i | −1.34429 | + | 0.460488i | ||||
\(839\) | 3.50389 | 0.120968 | 0.0604839 | − | 0.998169i | \(-0.480736\pi\) | ||||
0.0604839 | + | 0.998169i | \(0.480736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.7973 | 2.06198 | ||||||||
\(842\) | 18.5489 | − | 6.35395i | 0.639237 | − | 0.218971i | ||||
\(843\) | 6.91922 | 0.238310 | ||||||||
\(844\) | −22.2940 | − | 28.7227i | −0.767392 | − | 0.988678i | ||||
\(845\) | − | 9.84805i | − | 0.338783i | ||||||
\(846\) | 9.83564 | − | 3.36921i | 0.338156 | − | 0.115836i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0711034 | + | 0.277650i | −0.00244170 | + | 0.00953453i | ||||
\(849\) | 20.5740 | 0.706096 | ||||||||
\(850\) | −0.853021 | − | 2.49020i | −0.0292584 | − | 0.0854132i | ||||
\(851\) | − | 50.6152i | − | 1.73507i | ||||||
\(852\) | −3.58431 | − | 4.61789i | −0.122796 | − | 0.158206i | ||||
\(853\) | 25.3974i | 0.869589i | 0.900530 | + | 0.434795i | \(0.143179\pi\) | ||||
−0.900530 | + | 0.434795i | \(0.856821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.2025i | 0.348919i | ||||||||
\(856\) | 32.7337 | + | 21.4801i | 1.11881 | + | 0.734173i | ||||
\(857\) | − | 28.9379i | − | 0.988499i | −0.869320 | − | 0.494249i | \(-0.835443\pi\) | ||
0.869320 | − | 0.494249i | \(-0.164557\pi\) | |||||||
\(858\) | −5.07457 | + | 1.73830i | −0.173243 | + | 0.0593445i | ||||
\(859\) | 4.68807 | 0.159955 | 0.0799775 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799775 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(860\) | 24.3028 | − | 18.8633i | 0.828718 | − | 0.643235i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6195 | + | 42.6782i | 0.497941 | + | 1.45363i | ||||
\(863\) | − | 43.4651i | − | 1.47957i | −0.672844 | − | 0.739784i | \(-0.734928\pi\) | ||
0.672844 | − | 0.739784i | \(-0.265072\pi\) | |||||||
\(864\) | 0.448237 | + | 5.63907i | 0.0152493 | + | 0.191845i | ||||
\(865\) | −10.7032 | −0.363918 | ||||||||
\(866\) | −4.50158 | − | 13.1413i | −0.152970 | − | 0.446560i | ||||
\(867\) | −13.6394 | −0.463219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.25706 | 0.0765655 | ||||||||
\(870\) | −10.5920 | − | 30.9209i | −0.359102 | − | 1.04832i | ||||
\(871\) | 8.41582 | 0.285159 | ||||||||
\(872\) | −1.52798 | + | 2.32851i | −0.0517440 | + | 0.0788533i | ||||
\(873\) | 7.10394i | 0.240432i | ||||||||
\(874\) | 12.8465 | + | 37.5023i | 0.434538 | + | 1.26854i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.93917 | − | 12.8052i | −0.335813 | − | 0.432649i | ||||
\(877\) | −46.0126 | −1.55374 | −0.776868 | − | 0.629663i | \(-0.783193\pi\) | ||||
−0.776868 | + | 0.629663i | \(0.783193\pi\) | |||||||
\(878\) | 22.7974 | − | 7.80929i | 0.769376 | − | 0.263551i | ||||
\(879\) | − | 28.3113i | − | 0.954916i | ||||||
\(880\) | 3.07975 | − | 12.0260i | 0.103818 | − | 0.405397i | ||||
\(881\) | 40.8047i | 1.37475i | 0.726304 | + | 0.687373i | \(0.241236\pi\) | ||||
−0.726304 | + | 0.687373i | \(0.758764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.06234i | 0.204014i | 0.994784 | + | 0.102007i | \(0.0325264\pi\) | ||||
−0.994784 | + | 0.102007i | \(0.967474\pi\) | |||||||
\(884\) | 8.68152 | − | 6.73842i | 0.291991 | − | 0.226638i | ||||
\(885\) | 8.25772i | 0.277580i | ||||||||
\(886\) | 3.86313 | + | 11.2775i | 0.129784 | + | 0.378876i | ||||
\(887\) | 44.2552 | 1.48595 | 0.742973 | − | 0.669322i | \(-0.233415\pi\) | ||||
0.742973 | + | 0.669322i | \(0.233415\pi\) | |||||||
\(888\) | −11.6560 | + | 17.7626i | −0.391149 | + | 0.596075i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −28.1264 | + | 9.63473i | −0.942799 | + | 0.322957i | ||||
\(891\) | 1.26539i | 0.0423923i | ||||||||
\(892\) | −18.3266 | + | 14.2247i | −0.613619 | + | 0.476279i | ||||
\(893\) | −30.5815 | −1.02337 | ||||||||
\(894\) | 0.663744 | − | 0.227366i | 0.0221989 | − | 0.00760426i | ||||
\(895\) | −60.2528 | −2.01403 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.1980 | 0.674393 | ||||||||
\(898\) | 12.8982 | − | 4.41828i | 0.430417 | − | 0.147440i | ||||
\(899\) | −88.9533 | −2.96676 | ||||||||
\(900\) | −1.60414 | + | 1.24510i | −0.0534713 | + | 0.0415033i | ||||
\(901\) | − | 0.131352i | − | 0.00437599i | ||||||
\(902\) | −1.84475 | + | 0.631922i | −0.0614236 | + | 0.0210407i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.80827 | − | 11.8991i | 0.259699 | − | 0.395759i | ||||
\(905\) | −28.7404 | −0.955362 | ||||||||
\(906\) | −6.06647 | − | 17.7097i | −0.201545 | − | 0.588365i | ||||
\(907\) | 6.40312i | 0.212612i | 0.994333 | + | 0.106306i | \(0.0339023\pi\) | ||||
−0.994333 | + | 0.106306i | \(0.966098\pi\) | |||||||
\(908\) | −16.0538 | + | 12.4606i | −0.532763 | + | 0.413520i | ||||
\(909\) | 0.933313i | 0.0309561i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.9687i | − | 1.62241i | −0.584765 | − | 0.811203i | \(-0.698813\pi\) | ||
0.584765 | − | 0.811203i | \(-0.301187\pi\) | |||||||
\(912\) | 4.12798 | − | 16.1192i | 0.136691 | − | 0.533761i | ||||
\(913\) | 6.75247i | 0.223474i | ||||||||
\(914\) | −38.8602 | + | 13.3116i | −1.28538 | + | 0.440308i | ||||
\(915\) | −27.2299 | −0.900193 | ||||||||
\(916\) | −28.3240 | − | 36.4915i | −0.935850 | − | 1.20571i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.840146 | − | 2.45262i | −0.0277290 | − | 0.0809484i | ||||
\(919\) | − | 24.5577i | − | 0.810085i | −0.914298 | − | 0.405042i | \(-0.867257\pi\) | ||
0.914298 | − | 0.405042i | \(-0.132743\pi\) | |||||||
\(920\) | −25.6456 | + | 39.0816i | −0.845511 | + | 1.28848i | ||||
\(921\) | −8.65596 | −0.285224 | ||||||||
\(922\) | −10.9898 | − | 32.0821i | −0.361929 | − | 1.05657i | ||||
\(923\) | 8.76108 | 0.288374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.62654 | −0.250759 | ||||||||
\(926\) | 13.0603 | + | 38.1267i | 0.429189 | + | 1.25292i | ||||
\(927\) | 4.12921 | 0.135621 | ||||||||
\(928\) | 4.22384 | + | 53.1382i | 0.138654 | + | 1.74435i | ||||
\(929\) | 9.83435i | 0.322655i | 0.986901 | + | 0.161327i | \(0.0515775\pi\) | ||||
−0.986901 | + | 0.161327i | \(0.948423\pi\) | |||||||
\(930\) | 10.6106 | + | 30.9752i | 0.347934 | + | 1.01572i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.8311 | + | 8.40692i | −0.354786 | + | 0.275378i | ||||
\(933\) | 9.34258 | 0.305862 | ||||||||
\(934\) | 24.8601 | − | 8.51585i | 0.813447 | − | 0.278647i | ||||
\(935\) | 5.68935i | 0.186062i | ||||||||
\(936\) | −7.08820 | − | 4.65132i | −0.231685 | − | 0.152033i | ||||
\(937\) | − | 38.1447i | − | 1.24613i | −0.782168 | − | 0.623067i | \(-0.785886\pi\) | ||
0.782168 | − | 0.623067i | \(-0.214114\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 7.37547i | − | 0.240689i | ||||||
\(940\) | −22.1111 | − | 28.4870i | −0.721184 | − | 0.929145i | ||||
\(941\) | 34.3856i | 1.12094i | 0.828176 | + | 0.560469i | \(0.189379\pi\) | ||||
−0.828176 | + | 0.560469i | \(0.810621\pi\) | |||||||
\(942\) | −2.31971 | − | 6.77186i | −0.0755802 | − | 0.220639i | ||||
\(943\) | 7.34258 | 0.239107 | ||||||||
\(944\) | 3.34111 | − | 13.0466i | 0.108744 | − | 0.424631i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.6179 | + | 3.63716i | −0.345217 | + | 0.118254i | ||||
\(947\) | 16.4695i | 0.535187i | 0.963532 | + | 0.267594i | \(0.0862285\pi\) | ||||
−0.963532 | + | 0.267594i | \(0.913772\pi\) | |||||||
\(948\) | 2.18734 | + | 2.81809i | 0.0710416 | + | 0.0915272i | ||||
\(949\) | 24.2942 | 0.788622 | ||||||||
\(950\) | 5.65073 | − | 1.93567i | 0.183334 | − | 0.0628013i | ||||
\(951\) | 3.63028 | 0.117720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4540 | −1.69915 | −0.849576 | − | 0.527466i | \(-0.823142\pi\) | ||||
−0.849576 | + | 0.527466i | \(0.823142\pi\) | |||||||
\(954\) | −0.0958634 | + | 0.0328381i | −0.00310369 | + | 0.00106317i | ||||
\(955\) | −38.9767 | −1.26126 | ||||||||
\(956\) | 27.2556 | + | 35.1150i | 0.881509 | + | 1.13570i | ||||
\(957\) | 11.9241i | 0.385452i | ||||||||
\(958\) | 37.9178 | − | 12.9888i | 1.22507 | − | 0.419648i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 17.9999 | − | 7.80929i | 0.580944 | − | 0.252044i | ||||
\(961\) | 58.1095 | 1.87450 | ||||||||
\(962\) | −10.3186 | − | 30.1229i | −0.332686 | − | 0.971200i | ||||
\(963\) | 13.8424i | 0.446064i | ||||||||
\(964\) | 18.9187 | + | 24.3741i | 0.609329 | + | 0.785036i | ||||
\(965\) | − | 48.3995i | − | 1.55803i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.3573i | − | 0.526016i | −0.964794 | − | 0.263008i | \(-0.915285\pi\) | ||
0.964794 | − | 0.263008i | \(-0.0847146\pi\) | |||||||
\(968\) | 14.5847 | − | 22.2257i | 0.468769 | − | 0.714362i | ||||
\(969\) | 7.62580i | 0.244976i | ||||||||
\(970\) | 23.3105 | − | 7.98502i | 0.748454 | − | 0.256384i | ||||
\(971\) | −23.3182 | −0.748318 | −0.374159 | − | 0.927365i | \(-0.622069\pi\) | ||||
−0.374159 | + | 0.927365i | \(0.622069\pi\) | |||||||
\(972\) | −1.57993 | + | 1.22631i | −0.0506762 | + | 0.0393338i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.0245 | + | 55.5377i | 0.609585 | + | 1.77954i | ||||
\(975\) | − | 3.04338i | − | 0.0974661i | ||||||
\(976\) | 43.0213 | + | 11.0173i | 1.37708 | + | 0.352656i | ||||
\(977\) | 39.9844 | 1.27922 | 0.639608 | − | 0.768701i | \(-0.279097\pi\) | ||||
0.639608 | + | 0.768701i | \(0.279097\pi\) | |||||||
\(978\) | −5.51594 | − | 16.1025i | −0.176380 | − | 0.514902i | ||||
\(979\) | 10.8465 | 0.346655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.984676 | −0.0314383 | ||||||||
\(982\) | 0.791607 | + | 2.31092i | 0.0252612 | + | 0.0737443i | ||||
\(983\) | 21.5255 | 0.686558 | 0.343279 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343279 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(984\) | −2.57677 | − | 1.69089i | −0.0821443 | − | 0.0539036i | ||||
\(985\) | − | 2.44961i | − | 0.0780511i | ||||||
\(986\) | −7.91689 | − | 23.1116i | −0.252125 | − | 0.736022i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.2908 | + | 19.7000i | 0.486464 | + | 0.626741i | ||||
\(989\) | 42.2618 | 1.34385 | ||||||||
\(990\) | 4.15219 | − | 1.42234i | 0.131965 | − | 0.0452049i | ||||
\(991\) | − | 11.1967i | − | 0.355676i | −0.984060 | − | 0.177838i | \(-0.943090\pi\) | ||
0.984060 | − | 0.177838i | \(-0.0569103\pi\) | |||||||
\(992\) | −4.23126 | − | 53.2316i | −0.134343 | − | 1.69010i | ||||
\(993\) | 0.628347i | 0.0199400i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.62982i | 0.210179i | ||||||||
\(996\) | −8.43090 | + | 6.54389i | −0.267143 | + | 0.207351i | ||||
\(997\) | − | 56.7766i | − | 1.79813i | −0.437813 | − | 0.899066i | \(-0.644247\pi\) | ||
0.437813 | − | 0.899066i | \(-0.355753\pi\) | |||||||
\(998\) | −19.3800 | − | 56.5756i | −0.613464 | − | 1.79087i | ||||
\(999\) | −7.51143 | −0.237651 |
(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 | 588.2.b.a.391.7 | 8 | ||
3.2 | odd | 2 | 1764.2.b.j.1567.2 | 8 | |||
4.3 | odd | 2 | 588.2.b.b.391.8 | 8 | |||
7.2 | even | 3 | 588.2.o.d.31.1 | 8 | |||
7.3 | odd | 6 | 588.2.o.b.19.2 | 8 | |||
7.4 | even | 3 | 84.2.o.b.19.2 | yes | 8 | ||
7.5 | odd | 6 | 84.2.o.a.31.1 | yes | 8 | ||
7.6 | odd | 2 | 588.2.b.b.391.7 | 8 | |||
12.11 | even | 2 | 1764.2.b.i.1567.1 | 8 | |||
21.5 | even | 6 | 252.2.bf.g.199.4 | 8 | |||
21.11 | odd | 6 | 252.2.bf.f.19.3 | 8 | |||
21.20 | even | 2 | 1764.2.b.i.1567.2 | 8 | |||
28.3 | even | 6 | 588.2.o.d.19.1 | 8 | |||
28.11 | odd | 6 | 84.2.o.a.19.1 | ✓ | 8 | ||
28.19 | even | 6 | 84.2.o.b.31.2 | yes | 8 | ||
28.23 | odd | 6 | 588.2.o.b.31.2 | 8 | |||
28.27 | even | 2 | inner | 588.2.b.a.391.8 | 8 | ||
56.5 | odd | 6 | 1344.2.bl.j.703.1 | 8 | |||
56.11 | odd | 6 | 1344.2.bl.j.1279.1 | 8 | |||
56.19 | even | 6 | 1344.2.bl.i.703.1 | 8 | |||
56.53 | even | 6 | 1344.2.bl.i.1279.1 | 8 | |||
84.11 | even | 6 | 252.2.bf.g.19.4 | 8 | |||
84.47 | odd | 6 | 252.2.bf.f.199.3 | 8 | |||
84.83 | odd | 2 | 1764.2.b.j.1567.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.1 | ✓ | 8 | 28.11 | odd | 6 | ||
84.2.o.a.31.1 | yes | 8 | 7.5 | odd | 6 | ||
84.2.o.b.19.2 | yes | 8 | 7.4 | even | 3 | ||
84.2.o.b.31.2 | yes | 8 | 28.19 | even | 6 | ||
252.2.bf.f.19.3 | 8 | 21.11 | odd | 6 | |||
252.2.bf.f.199.3 | 8 | 84.47 | odd | 6 | |||
252.2.bf.g.19.4 | 8 | 84.11 | even | 6 | |||
252.2.bf.g.199.4 | 8 | 21.5 | even | 6 | |||
588.2.b.a.391.7 | 8 | 1.1 | even | 1 | trivial | ||
588.2.b.a.391.8 | 8 | 28.27 | even | 2 | inner | ||
588.2.b.b.391.7 | 8 | 7.6 | odd | 2 | |||
588.2.b.b.391.8 | 8 | 4.3 | odd | 2 | |||
588.2.o.b.19.2 | 8 | 7.3 | odd | 6 | |||
588.2.o.b.31.2 | 8 | 28.23 | odd | 6 | |||
588.2.o.d.19.1 | 8 | 28.3 | even | 6 | |||
588.2.o.d.31.1 | 8 | 7.2 | even | 3 | |||
1344.2.bl.i.703.1 | 8 | 56.19 | even | 6 | |||
1344.2.bl.i.1279.1 | 8 | 56.53 | even | 6 | |||
1344.2.bl.j.703.1 | 8 | 56.5 | odd | 6 | |||
1344.2.bl.j.1279.1 | 8 | 56.11 | odd | 6 | |||
1764.2.b.i.1567.1 | 8 | 12.11 | even | 2 | |||
1764.2.b.i.1567.2 | 8 | 21.20 | even | 2 | |||
1764.2.b.j.1567.1 | 8 | 84.83 | odd | 2 | |||
1764.2.b.j.1567.2 | 8 | 3.2 | odd | 2 |