Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.2696112.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.3 | ||
Root | \(-0.906803 - 1.57063i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.508 |
Dual form | 637.2.e.j.79.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.906803 | + | 1.57063i | 0.641207 | + | 1.11060i | 0.985164 | + | 0.171617i | \(0.0548992\pi\) |
−0.343957 | + | 0.938985i | \(0.611767\pi\) | |||||||
\(3\) | 1.55139 | − | 2.68708i | 0.895694 | − | 1.55139i | 0.0627507 | − | 0.998029i | \(-0.480013\pi\) |
0.832943 | − | 0.553358i | \(-0.186654\pi\) | |||||||
\(4\) | −0.644584 | + | 1.11645i | −0.322292 | + | 0.558226i | ||||
\(5\) | −1.40680 | − | 2.43665i | −0.629142 | − | 1.08971i | −0.987724 | − | 0.156207i | \(-0.950073\pi\) |
0.358583 | − | 0.933498i | \(-0.383260\pi\) | |||||||
\(6\) | 5.62721 | 2.29730 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.28917 | 0.455790 | ||||||||
\(9\) | −3.31361 | − | 5.73933i | −1.10454 | − | 1.91311i | ||||
\(10\) | 2.55139 | − | 4.41913i | 0.806820 | − | 1.39745i | ||||
\(11\) | −1.55139 | + | 2.68708i | −0.467761 | + | 0.810186i | −0.999321 | − | 0.0368347i | \(-0.988273\pi\) |
0.531560 | + | 0.847020i | \(0.321606\pi\) | |||||||
\(12\) | 2.00000 | + | 3.46410i | 0.577350 | + | 1.00000i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.72999 | −2.25407 | ||||||||
\(16\) | 2.45819 | + | 4.25771i | 0.614548 | + | 1.06443i | ||||
\(17\) | 0.262219 | − | 0.454177i | 0.0635974 | − | 0.110154i | −0.832474 | − | 0.554065i | \(-0.813076\pi\) |
0.896071 | + | 0.443911i | \(0.146409\pi\) | |||||||
\(18\) | 6.00958 | − | 10.4089i | 1.41647 | − | 2.45340i | ||||
\(19\) | −0.406803 | − | 0.704604i | −0.0933271 | − | 0.161647i | 0.815582 | − | 0.578641i | \(-0.196417\pi\) |
−0.908909 | + | 0.416994i | \(0.863084\pi\) | |||||||
\(20\) | 3.62721 | 0.811069 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.62721 | −1.19973 | ||||||||
\(23\) | −3.66902 | − | 6.35493i | −0.765044 | − | 1.32510i | −0.940223 | − | 0.340559i | \(-0.889384\pi\) |
0.175179 | − | 0.984537i | \(-0.443949\pi\) | |||||||
\(24\) | 2.00000 | − | 3.46410i | 0.408248 | − | 0.707107i | ||||
\(25\) | −1.45819 | + | 2.52566i | −0.291638 | + | 0.505132i | ||||
\(26\) | 0.906803 | + | 1.57063i | 0.177839 | + | 0.308026i | ||||
\(27\) | −11.2544 | −2.16592 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.28917 | 1.53926 | 0.769630 | − | 0.638490i | \(-0.220441\pi\) | ||||
0.769630 | + | 0.638490i | \(0.220441\pi\) | |||||||
\(30\) | −7.91638 | − | 13.7116i | −1.44533 | − | 2.50338i | ||||
\(31\) | −0.695972 | + | 1.20546i | −0.125000 | + | 0.216507i | −0.921733 | − | 0.387825i | \(-0.873226\pi\) |
0.796733 | + | 0.604332i | \(0.206560\pi\) | |||||||
\(32\) | −3.16902 | + | 5.48891i | −0.560209 | + | 0.970311i | ||||
\(33\) | 4.81361 | + | 8.33741i | 0.837941 | + | 1.45136i | ||||
\(34\) | 0.951124 | 0.163116 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.54359 | 1.42393 | ||||||||
\(37\) | 3.07583 | + | 5.32749i | 0.505663 | + | 0.875833i | 0.999979 | + | 0.00655099i | \(0.00208526\pi\) |
−0.494316 | + | 0.869282i | \(0.664581\pi\) | |||||||
\(38\) | 0.737781 | − | 1.27787i | 0.119684 | − | 0.207299i | ||||
\(39\) | 1.55139 | − | 2.68708i | 0.248421 | − | 0.430277i | ||||
\(40\) | −1.81361 | − | 3.14126i | −0.286756 | − | 0.496677i | ||||
\(41\) | −4.20555 | −0.656797 | −0.328398 | − | 0.944539i | \(-0.606509\pi\) | ||||
−0.328398 | + | 0.944539i | \(0.606509\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.75971 | 1.03085 | 0.515423 | − | 0.856936i | \(-0.327635\pi\) | ||||
0.515423 | + | 0.856936i | \(0.327635\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | −9.32318 | + | 16.1482i | −1.38982 | + | 2.40724i | ||||
\(46\) | 6.65416 | − | 11.5253i | 0.981103 | − | 1.69932i | ||||
\(47\) | 2.98514 | + | 5.17041i | 0.435427 | + | 0.754183i | 0.997330 | − | 0.0730207i | \(-0.0232639\pi\) |
−0.561903 | + | 0.827203i | \(0.689931\pi\) | |||||||
\(48\) | 15.2544 | 2.20179 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.28917 | −0.748001 | ||||||||
\(51\) | −0.813607 | − | 1.40921i | −0.113928 | − | 0.197329i | ||||
\(52\) | −0.644584 | + | 1.11645i | −0.0893878 | + | 0.154824i | ||||
\(53\) | 1.24736 | − | 2.16049i | 0.171338 | − | 0.296766i | −0.767550 | − | 0.640989i | \(-0.778524\pi\) |
0.938888 | + | 0.344223i | \(0.111858\pi\) | |||||||
\(54\) | −10.2056 | − | 17.6765i | −1.38880 | − | 2.40547i | ||||
\(55\) | 8.72999 | 1.17715 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.52444 | −0.334370 | ||||||||
\(58\) | 7.51664 | + | 13.0192i | 0.986984 | + | 1.70951i | ||||
\(59\) | 2.23527 | − | 3.87160i | 0.291007 | − | 0.504039i | −0.683041 | − | 0.730380i | \(-0.739343\pi\) |
0.974048 | + | 0.226341i | \(0.0726763\pi\) | |||||||
\(60\) | 5.62721 | − | 9.74662i | 0.726470 | − | 1.25828i | ||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | −2.52444 | −0.320604 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.66196 | −0.207744 | ||||||||
\(65\) | −1.40680 | − | 2.43665i | −0.174492 | − | 0.302230i | ||||
\(66\) | −8.72999 | + | 15.1208i | −1.07459 | + | 1.86124i | ||||
\(67\) | −5.01916 | + | 8.69343i | −0.613188 | + | 1.06207i | 0.377512 | + | 0.926005i | \(0.376780\pi\) |
−0.990700 | + | 0.136067i | \(0.956554\pi\) | |||||||
\(68\) | 0.338044 | + | 0.585510i | 0.0409939 | + | 0.0710035i | ||||
\(69\) | −22.7683 | −2.74098 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.72999 | −1.03606 | −0.518029 | − | 0.855363i | \(-0.673334\pi\) | ||||
−0.518029 | + | 0.855363i | \(0.673334\pi\) | |||||||
\(72\) | −4.27180 | − | 7.39897i | −0.503436 | − | 0.871977i | ||||
\(73\) | 1.17153 | − | 2.02916i | 0.137118 | − | 0.237495i | −0.789287 | − | 0.614025i | \(-0.789549\pi\) |
0.926404 | + | 0.376530i | \(0.122883\pi\) | |||||||
\(74\) | −5.57834 | + | 9.66196i | −0.648469 | + | 1.12318i | ||||
\(75\) | 4.52444 | + | 7.83656i | 0.522437 | + | 0.904888i | ||||
\(76\) | 1.04888 | 0.120314 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.62721 | 0.637156 | ||||||||
\(79\) | 6.77180 | + | 11.7291i | 0.761887 | + | 1.31963i | 0.941877 | + | 0.335958i | \(0.109060\pi\) |
−0.179990 | + | 0.983668i | \(0.557607\pi\) | |||||||
\(80\) | 6.91638 | − | 11.9795i | 0.773275 | − | 1.33935i | ||||
\(81\) | −7.51916 | + | 13.0236i | −0.835462 | + | 1.44706i | ||||
\(82\) | −3.81361 | − | 6.60536i | −0.421142 | − | 0.729440i | ||||
\(83\) | 16.4791 | 1.80882 | 0.904410 | − | 0.426665i | \(-0.140312\pi\) | ||||
0.904410 | + | 0.426665i | \(0.140312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47556 | −0.160047 | ||||||||
\(86\) | 6.12972 | + | 10.6170i | 0.660985 | + | 1.14486i | ||||
\(87\) | 12.8597 | − | 22.2737i | 1.37871 | − | 2.38799i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | 5.32318 | + | 9.22003i | 0.564256 | + | 0.977321i | 0.997118 | + | 0.0758606i | \(0.0241704\pi\) |
−0.432862 | + | 0.901460i | \(0.642496\pi\) | |||||||
\(90\) | −33.8172 | −3.56464 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.45998 | 0.986271 | ||||||||
\(93\) | 2.15944 | + | 3.74027i | 0.223924 | + | 0.387848i | ||||
\(94\) | −5.41387 | + | 9.37710i | −0.558398 | + | 0.967174i | ||||
\(95\) | −1.14458 | + | 1.98248i | −0.117432 | + | 0.203398i | ||||
\(96\) | 9.83276 | + | 17.0308i | 1.00355 | + | 1.73820i | ||||
\(97\) | −1.18639 | −0.120460 | −0.0602300 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602300 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.5628 | 2.06663 | ||||||||
\(100\) | −1.87985 | − | 3.25600i | −0.187985 | − | 0.325600i | ||||
\(101\) | −6.55139 | + | 11.3473i | −0.651887 | + | 1.12910i | 0.330777 | + | 0.943709i | \(0.392689\pi\) |
−0.982664 | + | 0.185393i | \(0.940644\pi\) | |||||||
\(102\) | 1.47556 | − | 2.55575i | 0.146102 | − | 0.253057i | ||||
\(103\) | −2.20555 | − | 3.82012i | −0.217319 | − | 0.376408i | 0.736668 | − | 0.676254i | \(-0.236398\pi\) |
−0.953988 | + | 0.299846i | \(0.903065\pi\) | |||||||
\(104\) | 1.28917 | 0.126413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.52444 | 0.439452 | ||||||||
\(107\) | −0.289169 | − | 0.500855i | −0.0279550 | − | 0.0484194i | 0.851709 | − | 0.524014i | \(-0.175566\pi\) |
−0.879664 | + | 0.475595i | \(0.842233\pi\) | |||||||
\(108\) | 7.25443 | − | 12.5650i | 0.698057 | − | 1.20907i | ||||
\(109\) | −2.78666 | + | 4.82663i | −0.266913 | + | 0.462307i | −0.968063 | − | 0.250707i | \(-0.919337\pi\) |
0.701150 | + | 0.713014i | \(0.252670\pi\) | |||||||
\(110\) | 7.91638 | + | 13.7116i | 0.754797 | + | 1.30735i | ||||
\(111\) | 19.0872 | 1.81168 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.44584 | 0.512302 | 0.256151 | − | 0.966637i | \(-0.417546\pi\) | ||||
0.256151 | + | 0.966637i | \(0.417546\pi\) | |||||||
\(114\) | −2.28917 | − | 3.96496i | −0.214400 | − | 0.371352i | ||||
\(115\) | −10.3232 | + | 17.8803i | −0.962642 | + | 1.66734i | ||||
\(116\) | −5.34307 | + | 9.25446i | −0.496091 | + | 0.859255i | ||||
\(117\) | −3.31361 | − | 5.73933i | −0.306343 | − | 0.530602i | ||||
\(118\) | 8.10780 | 0.746383 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.2544 | −1.02738 | ||||||||
\(121\) | 0.686393 | + | 1.18887i | 0.0623994 | + | 0.108079i | ||||
\(122\) | −1.81361 | + | 3.14126i | −0.164196 | + | 0.284396i | ||||
\(123\) | −6.52444 | + | 11.3007i | −0.588289 | + | 1.01895i | ||||
\(124\) | −0.897225 | − | 1.55404i | −0.0805732 | − | 0.139557i | ||||
\(125\) | −5.86248 | −0.524356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8816 | −1.14306 | −0.571530 | − | 0.820581i | \(-0.693650\pi\) | ||||
−0.571530 | + | 0.820581i | \(0.693650\pi\) | |||||||
\(128\) | 4.83098 | + | 8.36750i | 0.427002 | + | 0.739589i | ||||
\(129\) | 10.4869 | − | 18.1639i | 0.923322 | − | 1.59924i | ||||
\(130\) | 2.55139 | − | 4.41913i | 0.223771 | − | 0.387584i | ||||
\(131\) | −4.52444 | − | 7.83656i | −0.395302 | − | 0.684683i | 0.597838 | − | 0.801617i | \(-0.296027\pi\) |
−0.993140 | + | 0.116934i | \(0.962693\pi\) | |||||||
\(132\) | −12.4111 | −1.08025 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.2056 | −1.57272 | ||||||||
\(135\) | 15.8328 | + | 27.4232i | 1.36267 | + | 2.36021i | ||||
\(136\) | 0.338044 | − | 0.585510i | 0.0289871 | − | 0.0502071i | ||||
\(137\) | 3.12972 | − | 5.42084i | 0.267390 | − | 0.463134i | −0.700797 | − | 0.713361i | \(-0.747172\pi\) |
0.968187 | + | 0.250227i | \(0.0805053\pi\) | |||||||
\(138\) | −20.6464 | − | 35.7606i | −1.75754 | − | 3.04414i | ||||
\(139\) | −11.5733 | −0.981636 | −0.490818 | − | 0.871262i | \(-0.663302\pi\) | ||||
−0.490818 | + | 0.871262i | \(0.663302\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.5244 | 1.56004 | ||||||||
\(142\) | −7.91638 | − | 13.7116i | −0.664328 | − | 1.15065i | ||||
\(143\) | −1.55139 | + | 2.68708i | −0.129734 | + | 0.224705i | ||||
\(144\) | 16.2910 | − | 28.2168i | 1.35758 | − | 2.35140i | ||||
\(145\) | −11.6612 | − | 20.1978i | −0.968412 | − | 1.67734i | ||||
\(146\) | 4.24940 | 0.351683 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.93051 | −0.651884 | ||||||||
\(149\) | −4.26222 | − | 7.38238i | −0.349175 | − | 0.604788i | 0.636928 | − | 0.770923i | \(-0.280205\pi\) |
−0.986103 | + | 0.166135i | \(0.946871\pi\) | |||||||
\(150\) | −8.20555 | + | 14.2124i | −0.669980 | + | 1.16044i | ||||
\(151\) | 5.99221 | − | 10.3788i | 0.487639 | − | 0.844615i | −0.512260 | − | 0.858830i | \(-0.671192\pi\) |
0.999899 | + | 0.0142150i | \(0.00452494\pi\) | |||||||
\(152\) | −0.524438 | − | 0.908353i | −0.0425375 | − | 0.0736772i | ||||
\(153\) | −3.47556 | −0.280983 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.91638 | 0.314571 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 6.41387 | − | 11.1091i | 0.511883 | − | 0.886607i | −0.488023 | − | 0.872831i | \(-0.662282\pi\) |
0.999905 | − | 0.0137756i | \(-0.00438504\pi\) | |||||||
\(158\) | −12.2814 | + | 21.2720i | −0.977054 | + | 1.69231i | ||||
\(159\) | −3.87028 | − | 6.70351i | −0.306933 | − | 0.531623i | ||||
\(160\) | 17.8328 | 1.40980 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −27.2736 | −2.14282 | ||||||||
\(163\) | 6.72999 | + | 11.6567i | 0.527133 | + | 0.913022i | 0.999500 | + | 0.0316196i | \(0.0100665\pi\) |
−0.472367 | + | 0.881402i | \(0.656600\pi\) | |||||||
\(164\) | 2.71083 | − | 4.69530i | 0.211680 | − | 0.366641i | ||||
\(165\) | 13.5436 | − | 23.4582i | 1.05437 | − | 1.82622i | ||||
\(166\) | 14.9433 | + | 25.8826i | 1.15983 | + | 2.00888i | ||||
\(167\) | −2.02972 | −0.157064 | −0.0785322 | − | 0.996912i | \(-0.525023\pi\) | ||||
−0.0785322 | + | 0.996912i | \(0.525023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.33804 | − | 2.31756i | −0.102623 | − | 0.177749i | ||||
\(171\) | −2.69597 | + | 4.66956i | −0.206166 | + | 0.357090i | ||||
\(172\) | −4.35720 | + | 7.54689i | −0.332233 | + | 0.575445i | ||||
\(173\) | −10.1489 | − | 17.5784i | −0.771605 | − | 1.33646i | −0.936683 | − | 0.350179i | \(-0.886121\pi\) |
0.165078 | − | 0.986281i | \(-0.447212\pi\) | |||||||
\(174\) | 46.6449 | 3.53614 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.2544 | −1.14985 | ||||||||
\(177\) | −6.93554 | − | 12.0127i | −0.521307 | − | 0.902930i | ||||
\(178\) | −9.65416 | + | 16.7215i | −0.723610 | + | 1.25333i | ||||
\(179\) | 5.50179 | − | 9.52937i | 0.411223 | − | 0.712259i | −0.583801 | − | 0.811897i | \(-0.698435\pi\) |
0.995024 | + | 0.0996381i | \(0.0317685\pi\) | |||||||
\(180\) | −12.0192 | − | 20.8178i | −0.895855 | − | 1.55167i | ||||
\(181\) | 0.691675 | 0.0514118 | 0.0257059 | − | 0.999670i | \(-0.491817\pi\) | ||||
0.0257059 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.20555 | 0.458727 | ||||||||
\(184\) | −4.72999 | − | 8.19258i | −0.348699 | − | 0.603965i | ||||
\(185\) | 8.65416 | − | 14.9894i | 0.636267 | − | 1.10205i | ||||
\(186\) | −3.91638 | + | 6.78337i | −0.287163 | + | 0.497381i | ||||
\(187\) | 0.813607 | + | 1.40921i | 0.0594968 | + | 0.103051i | ||||
\(188\) | −7.69670 | −0.561339 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.15165 | −0.301192 | ||||||||
\(191\) | −3.91638 | − | 6.78337i | −0.283379 | − | 0.490828i | 0.688835 | − | 0.724918i | \(-0.258122\pi\) |
−0.972215 | + | 0.234090i | \(0.924789\pi\) | |||||||
\(192\) | −2.57834 | + | 4.46581i | −0.186075 | + | 0.322292i | ||||
\(193\) | 6.10278 | − | 10.5703i | 0.439287 | − | 0.760868i | −0.558347 | − | 0.829607i | \(-0.688564\pi\) |
0.997635 | + | 0.0687393i | \(0.0218977\pi\) | |||||||
\(194\) | −1.07583 | − | 1.86338i | −0.0772398 | − | 0.133783i | ||||
\(195\) | −8.72999 | −0.625167 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.8222 | −1.34103 | −0.670513 | − | 0.741898i | \(-0.733926\pi\) | ||||
−0.670513 | + | 0.741898i | \(0.733926\pi\) | |||||||
\(198\) | 18.6464 | + | 32.2965i | 1.32514 | + | 2.29521i | ||||
\(199\) | −10.8058 | + | 18.7162i | −0.766004 | + | 1.32676i | 0.173710 | + | 0.984797i | \(0.444424\pi\) |
−0.939714 | + | 0.341961i | \(0.888909\pi\) | |||||||
\(200\) | −1.87985 | + | 3.25600i | −0.132926 | + | 0.230234i | ||||
\(201\) | 15.5733 | + | 26.9738i | 1.09846 | + | 1.90258i | ||||
\(202\) | −23.7633 | −1.67198 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.09775 | 0.146872 | ||||||||
\(205\) | 5.91638 | + | 10.2475i | 0.413218 | + | 0.715715i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | −24.3154 | + | 42.1155i | −1.69004 | + | 2.92723i | ||||
\(208\) | 2.45819 | + | 4.25771i | 0.170445 | + | 0.295219i | ||||
\(209\) | 2.52444 | 0.174619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3764 | −1.19624 | −0.598119 | − | 0.801407i | \(-0.704085\pi\) | ||||
−0.598119 | + | 0.801407i | \(0.704085\pi\) | |||||||
\(212\) | 1.60806 | + | 2.78524i | 0.110442 | + | 0.191291i | ||||
\(213\) | −13.5436 | + | 23.4582i | −0.927992 | + | 1.60733i | ||||
\(214\) | 0.524438 | − | 0.908353i | 0.0358498 | − | 0.0620937i | ||||
\(215\) | −9.50958 | − | 16.4711i | −0.648548 | − | 1.12332i | ||||
\(216\) | −14.5089 | −0.987202 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.1078 | −0.684586 | ||||||||
\(219\) | −3.63501 | − | 6.29602i | −0.245631 | − | 0.425445i | ||||
\(220\) | −5.62721 | + | 9.74662i | −0.379387 | + | 0.657117i | ||||
\(221\) | 0.262219 | − | 0.454177i | 0.0176388 | − | 0.0305512i | ||||
\(222\) | 17.3083 | + | 29.9789i | 1.16166 | + | 2.01205i | ||||
\(223\) | −10.5486 | −0.706388 | −0.353194 | − | 0.935550i | \(-0.614904\pi\) | ||||
−0.353194 | + | 0.935550i | \(0.614904\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.3275 | 1.28850 | ||||||||
\(226\) | 4.93831 | + | 8.55340i | 0.328491 | + | 0.568964i | ||||
\(227\) | 3.47556 | − | 6.01985i | 0.230681 | − | 0.399551i | −0.727328 | − | 0.686290i | \(-0.759238\pi\) |
0.958009 | + | 0.286739i | \(0.0925712\pi\) | |||||||
\(228\) | 1.62721 | − | 2.81842i | 0.107765 | − | 0.186654i | ||||
\(229\) | 10.5436 | + | 18.2620i | 0.696740 | + | 1.20679i | 0.969590 | + | 0.244733i | \(0.0787003\pi\) |
−0.272850 | + | 0.962057i | \(0.587966\pi\) | |||||||
\(230\) | −37.4444 | −2.46901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.6861 | 0.701579 | ||||||||
\(233\) | −3.04181 | − | 5.26857i | −0.199276 | − | 0.345155i | 0.749018 | − | 0.662549i | \(-0.230526\pi\) |
−0.948294 | + | 0.317394i | \(0.897192\pi\) | |||||||
\(234\) | 6.00958 | − | 10.4089i | 0.392858 | − | 0.680451i | ||||
\(235\) | 8.39901 | − | 14.5475i | 0.547891 | − | 0.948975i | ||||
\(236\) | 2.88164 | + | 4.99115i | 0.187579 | + | 0.324896i | ||||
\(237\) | 42.0227 | 2.72967 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2056 | −0.918881 | −0.459440 | − | 0.888209i | \(-0.651950\pi\) | ||||
−0.459440 | + | 0.888209i | \(0.651950\pi\) | |||||||
\(240\) | −21.4600 | − | 37.1698i | −1.38524 | − | 2.39930i | ||||
\(241\) | −4.22041 | + | 7.30996i | −0.271860 | + | 0.470876i | −0.969338 | − | 0.245730i | \(-0.920972\pi\) |
0.697478 | + | 0.716606i | \(0.254306\pi\) | |||||||
\(242\) | −1.24485 | + | 2.15614i | −0.0800218 | + | 0.138602i | ||||
\(243\) | 6.44861 | + | 11.1693i | 0.413679 | + | 0.716512i | ||||
\(244\) | −2.57834 | −0.165061 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −23.6655 | −1.50886 | ||||||||
\(247\) | −0.406803 | − | 0.704604i | −0.0258843 | − | 0.0448329i | ||||
\(248\) | −0.897225 | + | 1.55404i | −0.0569738 | + | 0.0986816i | ||||
\(249\) | 25.5655 | − | 44.2808i | 1.62015 | − | 2.80618i | ||||
\(250\) | −5.31612 | − | 9.20779i | −0.336221 | − | 0.582352i | ||||
\(251\) | −23.9844 | −1.51388 | −0.756941 | − | 0.653483i | \(-0.773307\pi\) | ||||
−0.756941 | + | 0.653483i | \(0.773307\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7683 | 1.43143 | ||||||||
\(254\) | −11.6811 | − | 20.2323i | −0.732938 | − | 1.26949i | ||||
\(255\) | −2.28917 | + | 3.96496i | −0.143353 | + | 0.248295i | ||||
\(256\) | −10.4234 | + | 18.0539i | −0.651466 | + | 1.12837i | ||||
\(257\) | −7.80581 | − | 13.5201i | −0.486913 | − | 0.843359i | 0.512974 | − | 0.858404i | \(-0.328544\pi\) |
−0.999887 | + | 0.0150459i | \(0.995211\pi\) | |||||||
\(258\) | 38.0383 | 2.36816 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.62721 | 0.224950 | ||||||||
\(261\) | −27.4670 | − | 47.5743i | −1.70017 | − | 2.94478i | ||||
\(262\) | 8.20555 | − | 14.2124i | 0.506941 | − | 0.878047i | ||||
\(263\) | 7.58540 | − | 13.1383i | 0.467736 | − | 0.810143i | −0.531584 | − | 0.847005i | \(-0.678403\pi\) |
0.999320 | + | 0.0368628i | \(0.0117365\pi\) | |||||||
\(264\) | 6.20555 | + | 10.7483i | 0.381925 | + | 0.661514i | ||||
\(265\) | −7.01916 | −0.431183 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.0333 | 2.02160 | ||||||||
\(268\) | −6.47054 | − | 11.2073i | −0.395251 | − | 0.684595i | ||||
\(269\) | −11.6464 | + | 20.1721i | −0.710092 | + | 1.22991i | 0.254731 | + | 0.967012i | \(0.418013\pi\) |
−0.964822 | + | 0.262903i | \(0.915320\pi\) | |||||||
\(270\) | −28.7144 | + | 49.7348i | −1.74750 | + | 3.02676i | ||||
\(271\) | −6.37279 | − | 11.0380i | −0.387119 | − | 0.670510i | 0.604941 | − | 0.796270i | \(-0.293196\pi\) |
−0.992061 | + | 0.125760i | \(0.959863\pi\) | |||||||
\(272\) | 2.57834 | 0.156335 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3522 | 0.685810 | ||||||||
\(275\) | −4.52444 | − | 7.83656i | −0.272834 | − | 0.472562i | ||||
\(276\) | 14.6761 | − | 25.4197i | 0.883397 | − | 1.53009i | ||||
\(277\) | −4.06097 | + | 7.03380i | −0.244000 | + | 0.422620i | −0.961850 | − | 0.273578i | \(-0.911793\pi\) |
0.717850 | + | 0.696198i | \(0.245126\pi\) | |||||||
\(278\) | −10.4947 | − | 18.1774i | −0.629431 | − | 1.09021i | ||||
\(279\) | 9.22471 | 0.552269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0333 | 1.13543 | 0.567715 | − | 0.823225i | \(-0.307827\pi\) | ||||
0.567715 | + | 0.823225i | \(0.307827\pi\) | |||||||
\(282\) | 16.7980 | + | 29.0950i | 1.00031 | + | 1.73258i | ||||
\(283\) | −5.57331 | + | 9.65326i | −0.331299 | + | 0.573827i | −0.982767 | − | 0.184849i | \(-0.940820\pi\) |
0.651468 | + | 0.758676i | \(0.274154\pi\) | |||||||
\(284\) | 5.62721 | − | 9.74662i | 0.333914 | − | 0.578355i | ||||
\(285\) | 3.55139 | + | 6.15118i | 0.210366 | + | 0.364365i | ||||
\(286\) | −5.62721 | −0.332744 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 42.0036 | 2.47508 | ||||||||
\(289\) | 8.36248 | + | 14.4842i | 0.491911 | + | 0.852014i | ||||
\(290\) | 21.1489 | − | 36.6309i | 1.24191 | − | 2.15104i | ||||
\(291\) | −1.84056 | + | 3.18794i | −0.107895 | + | 0.186880i | ||||
\(292\) | 1.51030 | + | 2.61592i | 0.0883839 | + | 0.153085i | ||||
\(293\) | −14.1758 | −0.828161 | −0.414080 | − | 0.910240i | \(-0.635897\pi\) | ||||
−0.414080 | + | 0.910240i | \(0.635897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5783 | −0.732339 | ||||||||
\(296\) | 3.96526 | + | 6.86803i | 0.230476 | + | 0.399196i | ||||
\(297\) | 17.4600 | − | 30.2416i | 1.01313 | − | 1.75479i | ||||
\(298\) | 7.72999 | − | 13.3887i | 0.447786 | − | 0.775588i | ||||
\(299\) | −3.66902 | − | 6.35493i | −0.212185 | − | 0.367515i | ||||
\(300\) | −11.6655 | −0.673509 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 21.7350 | 1.25071 | ||||||||
\(303\) | 20.3275 | + | 35.2082i | 1.16778 | + | 2.02266i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 2.81361 | − | 4.87331i | 0.161107 | − | 0.279045i | ||||
\(306\) | −3.15165 | − | 5.45882i | −0.180168 | − | 0.312060i | ||||
\(307\) | 13.5592 | 0.773863 | 0.386932 | − | 0.922108i | \(-0.373535\pi\) | ||||
0.386932 | + | 0.922108i | \(0.373535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6867 | −0.778606 | ||||||||
\(310\) | 3.55139 | + | 6.15118i | 0.201705 | + | 0.349364i | ||||
\(311\) | −0.213343 | + | 0.369521i | −0.0120976 | + | 0.0209536i | −0.872011 | − | 0.489487i | \(-0.837184\pi\) |
0.859913 | + | 0.510440i | \(0.170518\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 9.07583 | + | 15.7198i | 0.512996 | + | 0.888535i | 0.999886 | + | 0.0150721i | \(0.00479777\pi\) |
−0.486890 | + | 0.873463i | \(0.661869\pi\) | |||||||
\(314\) | 23.2645 | 1.31289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.4600 | −0.982200 | ||||||||
\(317\) | −4.71083 | − | 8.15940i | −0.264587 | − | 0.458278i | 0.702869 | − | 0.711320i | \(-0.251902\pi\) |
−0.967455 | + | 0.253042i | \(0.918569\pi\) | |||||||
\(318\) | 7.01916 | − | 12.1575i | 0.393615 | − | 0.681761i | ||||
\(319\) | −12.8597 | + | 22.2737i | −0.720006 | + | 1.24709i | ||||
\(320\) | 2.33804 | + | 4.04961i | 0.130701 | + | 0.226380i | ||||
\(321\) | −1.79445 | −0.100156 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.426686 | −0.0237415 | ||||||||
\(324\) | −9.69346 | − | 16.7896i | −0.538526 | − | 0.932754i | ||||
\(325\) | −1.45819 | + | 2.52566i | −0.0808859 | + | 0.140098i | ||||
\(326\) | −12.2056 | + | 21.1406i | −0.676003 | + | 1.17087i | ||||
\(327\) | 8.64637 | + | 14.9760i | 0.478145 | + | 0.828172i | ||||
\(328\) | −5.42166 | −0.299361 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 49.1255 | 2.70427 | ||||||||
\(331\) | 8.70027 | + | 15.0693i | 0.478210 | + | 0.828284i | 0.999688 | − | 0.0249807i | \(-0.00795244\pi\) |
−0.521478 | + | 0.853265i | \(0.674619\pi\) | |||||||
\(332\) | −10.6222 | + | 18.3982i | −0.582968 | + | 1.00973i | ||||
\(333\) | 20.3842 | − | 35.3064i | 1.11704 | − | 1.93478i | ||||
\(334\) | −1.84056 | − | 3.18794i | −0.100711 | − | 0.174436i | ||||
\(335\) | 28.2439 | 1.54313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0524 | 1.20127 | 0.600637 | − | 0.799522i | \(-0.294914\pi\) | ||||
0.600637 | + | 0.799522i | \(0.294914\pi\) | |||||||
\(338\) | 0.906803 | + | 1.57063i | 0.0493236 | + | 0.0854310i | ||||
\(339\) | 8.44861 | − | 14.6334i | 0.458866 | − | 0.794779i | ||||
\(340\) | 0.951124 | − | 1.64740i | 0.0515819 | − | 0.0893426i | ||||
\(341\) | −2.15944 | − | 3.74027i | −0.116940 | − | 0.202547i | ||||
\(342\) | −9.77886 | −0.528780 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.71440 | 0.469849 | ||||||||
\(345\) | 32.0305 | + | 55.4785i | 1.72447 | + | 2.98686i | ||||
\(346\) | 18.4061 | − | 31.8803i | 0.989517 | − | 1.71389i | ||||
\(347\) | −12.6761 | + | 21.9556i | −0.680488 | + | 1.17864i | 0.294344 | + | 0.955700i | \(0.404899\pi\) |
−0.974832 | + | 0.222940i | \(0.928434\pi\) | |||||||
\(348\) | 16.5783 | + | 28.7145i | 0.888692 | + | 1.53926i | ||||
\(349\) | −5.70529 | −0.305397 | −0.152699 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152699 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.2544 | −0.600717 | ||||||||
\(352\) | −9.83276 | − | 17.0308i | −0.524088 | − | 0.907747i | ||||
\(353\) | 14.3380 | − | 24.8342i | 0.763137 | − | 1.32179i | −0.178089 | − | 0.984014i | \(-0.556991\pi\) |
0.941226 | − | 0.337778i | \(-0.109675\pi\) | |||||||
\(354\) | 12.5783 | − | 21.7863i | 0.668531 | − | 1.15793i | ||||
\(355\) | 12.2814 | + | 21.2720i | 0.651828 | + | 1.12900i | ||||
\(356\) | −13.7250 | −0.727422 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.9561 | 1.05472 | ||||||||
\(359\) | −5.52167 | − | 9.56381i | −0.291423 | − | 0.504759i | 0.682724 | − | 0.730677i | \(-0.260795\pi\) |
−0.974146 | + | 0.225918i | \(0.927462\pi\) | |||||||
\(360\) | −12.0192 | + | 20.8178i | −0.633465 | + | 1.09719i | ||||
\(361\) | 9.16902 | − | 15.8812i | 0.482580 | − | 0.835853i | ||||
\(362\) | 0.627213 | + | 1.08636i | 0.0329656 | + | 0.0570981i | ||||
\(363\) | 4.25945 | 0.223563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.59247 | −0.345066 | ||||||||
\(366\) | 5.62721 | + | 9.74662i | 0.294139 | + | 0.509464i | ||||
\(367\) | −13.6733 | + | 23.6829i | −0.713741 | + | 1.23624i | 0.249701 | + | 0.968323i | \(0.419668\pi\) |
−0.963443 | + | 0.267914i | \(0.913666\pi\) | |||||||
\(368\) | 18.0383 | − | 31.2433i | 0.940312 | − | 1.62867i | ||||
\(369\) | 13.9355 | + | 24.1371i | 0.725455 | + | 1.25653i | ||||
\(370\) | 31.3905 | 1.63191 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.56777 | −0.288676 | ||||||||
\(373\) | −8.07306 | − | 13.9829i | −0.418007 | − | 0.724009i | 0.577732 | − | 0.816227i | \(-0.303938\pi\) |
−0.995739 | + | 0.0922172i | \(0.970605\pi\) | |||||||
\(374\) | −1.47556 | + | 2.55575i | −0.0762995 | + | 0.132155i | ||||
\(375\) | −9.09498 | + | 15.7530i | −0.469663 | + | 0.813480i | ||||
\(376\) | 3.84835 | + | 6.66554i | 0.198463 | + | 0.343749i | ||||
\(377\) | 8.28917 | 0.426914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1305 | 1.34223 | 0.671117 | − | 0.741351i | \(-0.265815\pi\) | ||||
0.671117 | + | 0.741351i | \(0.265815\pi\) | |||||||
\(380\) | −1.47556 | − | 2.55575i | −0.0756947 | − | 0.131107i | ||||
\(381\) | −19.9844 | + | 34.6140i | −1.02383 | + | 1.77333i | ||||
\(382\) | 7.10278 | − | 12.3024i | 0.363410 | − | 0.629444i | ||||
\(383\) | 10.5244 | + | 18.2289i | 0.537774 | + | 0.931451i | 0.999024 | + | 0.0441810i | \(0.0140678\pi\) |
−0.461250 | + | 0.887270i | \(0.652599\pi\) | |||||||
\(384\) | 29.9789 | 1.52985 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.1361 | 1.12670 | ||||||||
\(387\) | −22.3990 | − | 38.7962i | −1.13861 | − | 1.97212i | ||||
\(388\) | 0.764731 | − | 1.32455i | 0.0388233 | − | 0.0672440i | ||||
\(389\) | 10.8030 | − | 18.7114i | 0.547736 | − | 0.948707i | −0.450693 | − | 0.892679i | \(-0.648823\pi\) |
0.998429 | − | 0.0560278i | \(-0.0178435\pi\) | |||||||
\(390\) | −7.91638 | − | 13.7116i | −0.400862 | − | 0.694313i | ||||
\(391\) | −3.84835 | −0.194619 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.0766 | −1.41628 | ||||||||
\(394\) | −17.0680 | − | 29.5627i | −0.859875 | − | 1.48935i | ||||
\(395\) | 19.0532 | − | 33.0011i | 0.958669 | − | 1.66046i | ||||
\(396\) | −13.2544 | + | 22.9573i | −0.666060 | + | 1.15365i | ||||
\(397\) | 13.8476 | + | 23.9848i | 0.694992 | + | 1.20376i | 0.970183 | + | 0.242372i | \(0.0779256\pi\) |
−0.275191 | + | 0.961390i | \(0.588741\pi\) | |||||||
\(398\) | −39.1950 | −1.96467 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.3380 | −0.716902 | ||||||||
\(401\) | 1.28917 | + | 2.23291i | 0.0643780 | + | 0.111506i | 0.896418 | − | 0.443210i | \(-0.146160\pi\) |
−0.832040 | + | 0.554716i | \(0.812827\pi\) | |||||||
\(402\) | −28.2439 | + | 48.9198i | −1.40868 | + | 2.43990i | ||||
\(403\) | −0.695972 | + | 1.20546i | −0.0346688 | + | 0.0600482i | ||||
\(404\) | −8.44584 | − | 14.6286i | −0.420196 | − | 0.727801i | ||||
\(405\) | 42.3119 | 2.10250 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.0872 | −0.946117 | ||||||||
\(408\) | −1.04888 | − | 1.81671i | −0.0519271 | − | 0.0899404i | ||||
\(409\) | −7.55845 | + | 13.0916i | −0.373742 | + | 0.647339i | −0.990138 | − | 0.140097i | \(-0.955259\pi\) |
0.616396 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(410\) | −10.7300 | + | 18.5849i | −0.529916 | + | 0.917842i | ||||
\(411\) | −9.71083 | − | 16.8197i | −0.479000 | − | 0.829652i | ||||
\(412\) | 5.68665 | 0.280161 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −88.1971 | −4.33465 | ||||||||
\(415\) | −23.1829 | − | 40.1540i | −1.13800 | − | 1.97108i | ||||
\(416\) | −3.16902 | + | 5.48891i | −0.155374 | + | 0.269116i | ||||
\(417\) | −17.9547 | + | 31.0984i | −0.879245 | + | 1.52290i | ||||
\(418\) | 2.28917 | + | 3.96496i | 0.111967 | + | 0.193932i | ||||
\(419\) | −9.99446 | −0.488261 | −0.244131 | − | 0.969742i | \(-0.578503\pi\) | ||||
−0.244131 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9250 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(422\) | −15.7569 | − | 27.2918i | −0.767036 | − | 1.32854i | ||||
\(423\) | 19.7832 | − | 34.2654i | 0.961890 | − | 1.66604i | ||||
\(424\) | 1.60806 | − | 2.78524i | 0.0780941 | − | 0.135263i | ||||
\(425\) | 0.764731 | + | 1.32455i | 0.0370949 | + | 0.0642502i | ||||
\(426\) | −49.1255 | −2.38014 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.745574 | 0.0360387 | ||||||||
\(429\) | 4.81361 | + | 8.33741i | 0.232403 | + | 0.402534i | ||||
\(430\) | 17.2466 | − | 29.8720i | 0.831706 | − | 1.44056i | ||||
\(431\) | −15.3380 | + | 26.5663i | −0.738808 | + | 1.27965i | 0.214225 | + | 0.976784i | \(0.431277\pi\) |
−0.953033 | + | 0.302868i | \(0.902056\pi\) | |||||||
\(432\) | −27.6655 | − | 47.9181i | −1.33106 | − | 2.30546i | ||||
\(433\) | −3.51941 | −0.169132 | −0.0845661 | − | 0.996418i | \(-0.526950\pi\) | ||||
−0.0845661 | + | 0.996418i | \(0.526950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.3643 | −3.46960 | ||||||||
\(436\) | −3.59247 | − | 6.22234i | −0.172048 | − | 0.297996i | ||||
\(437\) | −2.98514 | + | 5.17041i | −0.142799 | + | 0.247334i | ||||
\(438\) | 6.59247 | − | 11.4185i | 0.315000 | − | 0.545597i | ||||
\(439\) | −16.1758 | − | 28.0174i | −0.772030 | − | 1.33720i | −0.936449 | − | 0.350805i | \(-0.885908\pi\) |
0.164418 | − | 0.986391i | \(-0.447425\pi\) | |||||||
\(440\) | 11.2544 | 0.536534 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.951124 | 0.0452404 | ||||||||
\(443\) | −7.72292 | − | 13.3765i | −0.366927 | − | 0.635536i | 0.622156 | − | 0.782893i | \(-0.286257\pi\) |
−0.989083 | + | 0.147357i | \(0.952923\pi\) | |||||||
\(444\) | −12.3033 | + | 21.3099i | −0.583889 | + | 1.01133i | ||||
\(445\) | 14.9773 | − | 25.9415i | 0.709994 | − | 1.22975i | ||||
\(446\) | −9.56552 | − | 16.5680i | −0.452941 | − | 0.784516i | ||||
\(447\) | −26.4494 | −1.25101 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.4705 | −0.682907 | −0.341453 | − | 0.939899i | \(-0.610919\pi\) | ||||
−0.341453 | + | 0.939899i | \(0.610919\pi\) | |||||||
\(450\) | 17.5262 | + | 30.3563i | 0.826194 | + | 1.43101i | ||||
\(451\) | 6.52444 | − | 11.3007i | 0.307224 | − | 0.532127i | ||||
\(452\) | −3.51030 | + | 6.08003i | −0.165111 | + | 0.285980i | ||||
\(453\) | −18.5925 | − | 32.2031i | −0.873550 | − | 1.51303i | ||||
\(454\) | 12.6066 | 0.591657 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.25443 | −0.152402 | ||||||||
\(457\) | 17.3353 | + | 30.0256i | 0.810910 | + | 1.40454i | 0.912228 | + | 0.409683i | \(0.134361\pi\) |
−0.101318 | + | 0.994854i | \(0.532306\pi\) | |||||||
\(458\) | −19.1219 | + | 33.1202i | −0.893509 | + | 1.54760i | ||||
\(459\) | −2.95112 | + | 5.11150i | −0.137747 | + | 0.238584i | ||||
\(460\) | −13.3083 | − | 23.0507i | −0.620504 | − | 1.07474i | ||||
\(461\) | 12.5400 | 0.584047 | 0.292024 | − | 0.956411i | \(-0.405671\pi\) | ||||
0.292024 | + | 0.956411i | \(0.405671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1517 | 0.564735 | 0.282368 | − | 0.959306i | \(-0.408880\pi\) | ||||
0.282368 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(464\) | 20.3764 | + | 35.2929i | 0.945949 | + | 1.63843i | ||||
\(465\) | 6.07583 | − | 10.5236i | 0.281760 | − | 0.488022i | ||||
\(466\) | 5.51664 | − | 9.55511i | 0.255554 | − | 0.442632i | ||||
\(467\) | 18.5166 | + | 32.0718i | 0.856848 | + | 1.48410i | 0.874920 | + | 0.484268i | \(0.160914\pi\) |
−0.0180717 | + | 0.999837i | \(0.505753\pi\) | |||||||
\(468\) | 8.54359 | 0.394928 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 30.4650 | 1.40525 | ||||||||
\(471\) | −19.9008 | − | 34.4692i | −0.916980 | − | 1.58826i | ||||
\(472\) | 2.88164 | − | 4.99115i | 0.132638 | − | 0.229736i | ||||
\(473\) | −10.4869 | + | 18.1639i | −0.482189 | + | 0.835176i | ||||
\(474\) | 38.1063 | + | 66.0021i | 1.75028 | + | 3.03158i | ||||
\(475\) | 2.37279 | 0.108871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.5330 | −0.756996 | ||||||||
\(478\) | −12.8816 | − | 22.3117i | −0.589192 | − | 1.02051i | ||||
\(479\) | −6.00430 | + | 10.3997i | −0.274343 | + | 0.475177i | −0.969969 | − | 0.243228i | \(-0.921794\pi\) |
0.695626 | + | 0.718404i | \(0.255127\pi\) | |||||||
\(480\) | 27.6655 | − | 47.9181i | 1.26275 | − | 2.18715i | ||||
\(481\) | 3.07583 | + | 5.32749i | 0.140246 | + | 0.242912i | ||||
\(482\) | −15.3083 | −0.697275 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.76975 | −0.0804434 | ||||||||
\(485\) | 1.66902 | + | 2.89083i | 0.0757864 | + | 0.131266i | ||||
\(486\) | −11.6952 | + | 20.2568i | −0.530507 | + | 0.918865i | ||||
\(487\) | −5.55918 | + | 9.62878i | −0.251911 | + | 0.436322i | −0.964052 | − | 0.265714i | \(-0.914392\pi\) |
0.712141 | + | 0.702036i | \(0.247726\pi\) | |||||||
\(488\) | 1.28917 | + | 2.23291i | 0.0583579 | + | 0.101079i | ||||
\(489\) | 41.7633 | 1.88860 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0594386 | 0.00268243 | 0.00134121 | − | 0.999999i | \(-0.499573\pi\) | ||||
0.00134121 | + | 0.999999i | \(0.499573\pi\) | |||||||
\(492\) | −8.41110 | − | 14.5685i | −0.379202 | − | 0.656797i | ||||
\(493\) | 2.17358 | − | 3.76475i | 0.0978930 | − | 0.169556i | ||||
\(494\) | 0.737781 | − | 1.27787i | 0.0331943 | − | 0.0574943i | ||||
\(495\) | −28.9277 | − | 50.1043i | −1.30021 | − | 2.25202i | ||||
\(496\) | −6.84333 | −0.307274 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 92.7316 | 4.15540 | ||||||||
\(499\) | −5.14888 | − | 8.91812i | −0.230496 | − | 0.399230i | 0.727458 | − | 0.686152i | \(-0.240701\pi\) |
−0.957954 | + | 0.286922i | \(0.907368\pi\) | |||||||
\(500\) | 3.77886 | − | 6.54518i | 0.168996 | − | 0.292710i | ||||
\(501\) | −3.14888 | + | 5.45402i | −0.140682 | + | 0.243668i | ||||
\(502\) | −21.7491 | − | 37.6706i | −0.970712 | − | 1.68132i | ||||
\(503\) | −9.32391 | −0.415733 | −0.207866 | − | 0.978157i | \(-0.566652\pi\) | ||||
−0.207866 | + | 0.978157i | \(0.566652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.8661 | 1.64052 | ||||||||
\(506\) | 20.6464 | + | 35.7606i | 0.917843 | + | 1.58975i | ||||
\(507\) | 1.55139 | − | 2.68708i | 0.0688995 | − | 0.119338i | ||||
\(508\) | 8.30330 | − | 14.3817i | 0.368399 | − | 0.638087i | ||||
\(509\) | −19.8476 | − | 34.3771i | −0.879730 | − | 1.52374i | −0.851637 | − | 0.524132i | \(-0.824390\pi\) |
−0.0280937 | − | 0.999605i | \(-0.508944\pi\) | |||||||
\(510\) | −8.30330 | −0.367676 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.4842 | −0.816892 | ||||||||
\(513\) | 4.57834 | + | 7.92991i | 0.202139 | + | 0.350114i | ||||
\(514\) | 14.1567 | − | 24.5201i | 0.624424 | − | 1.08153i | ||||
\(515\) | −6.20555 | + | 10.7483i | −0.273449 | + | 0.473628i | ||||
\(516\) | 13.5194 | + | 23.4163i | 0.595159 | + | 1.03085i | ||||
\(517\) | −18.5244 | −0.814704 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −62.9794 | −2.76449 | ||||||||
\(520\) | −1.81361 | − | 3.14126i | −0.0795319 | − | 0.137753i | ||||
\(521\) | −11.1814 | + | 19.3667i | −0.489865 | + | 0.848471i | −0.999932 | − | 0.0116639i | \(-0.996287\pi\) |
0.510067 | + | 0.860135i | \(0.329621\pi\) | |||||||
\(522\) | 49.8144 | − | 86.2811i | 2.18032 | − | 3.77642i | ||||
\(523\) | 10.3275 | + | 17.8877i | 0.451589 | + | 0.782176i | 0.998485 | − | 0.0550252i | \(-0.0175239\pi\) |
−0.546896 | + | 0.837201i | \(0.684191\pi\) | |||||||
\(524\) | 11.6655 | 0.509611 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.5139 | 1.19966 | ||||||||
\(527\) | 0.364994 | + | 0.632188i | 0.0158994 | + | 0.0275386i | ||||
\(528\) | −23.6655 | + | 40.9899i | −1.02991 | + | 1.78386i | ||||
\(529\) | −15.4234 | + | 26.7142i | −0.670585 | + | 1.16149i | ||||
\(530\) | −6.36499 | − | 11.0245i | −0.276478 | − | 0.478873i | ||||
\(531\) | −29.6272 | −1.28571 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.20555 | −0.182163 | ||||||||
\(534\) | 29.9547 | + | 51.8831i | 1.29627 | + | 2.24520i | ||||
\(535\) | −0.813607 | + | 1.40921i | −0.0351753 | + | 0.0609254i | ||||
\(536\) | −6.47054 | + | 11.2073i | −0.279485 | + | 0.484082i | ||||
\(537\) | −17.0708 | − | 29.5675i | −0.736659 | − | 1.27593i | ||||
\(538\) | −42.2439 | −1.82126 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −40.8222 | −1.75671 | ||||||||
\(541\) | −2.81084 | − | 4.86851i | −0.120847 | − | 0.209314i | 0.799255 | − | 0.600992i | \(-0.205228\pi\) |
−0.920102 | + | 0.391679i | \(0.871894\pi\) | |||||||
\(542\) | 11.5577 | − | 20.0186i | 0.496447 | − | 0.859871i | ||||
\(543\) | 1.07306 | − | 1.85859i | 0.0460492 | − | 0.0797596i | ||||
\(544\) | 1.66196 | + | 2.87859i | 0.0712558 | + | 0.123419i | ||||
\(545\) | 15.6811 | 0.671705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3970 | −0.444542 | −0.222271 | − | 0.974985i | \(-0.571347\pi\) | ||||
−0.222271 | + | 0.974985i | \(0.571347\pi\) | |||||||
\(548\) | 4.03474 | + | 6.98838i | 0.172356 | + | 0.298529i | ||||
\(549\) | 6.62721 | − | 11.4787i | 0.282843 | − | 0.489898i | ||||
\(550\) | 8.20555 | − | 14.2124i | 0.349886 | − | 0.606020i | ||||
\(551\) | −3.37206 | − | 5.84058i | −0.143655 | − | 0.248817i | ||||
\(552\) | −29.3522 | −1.24931 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.7300 | −0.625817 | ||||||||
\(555\) | −26.8519 | − | 46.5089i | −1.13980 | − | 1.97419i | ||||
\(556\) | 7.45998 | − | 12.9211i | 0.316373 | − | 0.547975i | ||||
\(557\) | −7.32748 | + | 12.6916i | −0.310475 | + | 0.537759i | −0.978465 | − | 0.206411i | \(-0.933822\pi\) |
0.667990 | + | 0.744170i | \(0.267155\pi\) | |||||||
\(558\) | 8.36499 | + | 14.4886i | 0.354118 | + | 0.613351i | ||||
\(559\) | 6.75971 | 0.285905 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.04888 | 0.213164 | ||||||||
\(562\) | 17.2594 | + | 29.8942i | 0.728046 | + | 1.26101i | ||||
\(563\) | 12.3728 | − | 21.4303i | 0.521451 | − | 0.903179i | −0.478238 | − | 0.878230i | \(-0.658724\pi\) |
0.999689 | − | 0.0249490i | \(-0.00794233\pi\) | |||||||
\(564\) | −11.9406 | + | 20.6817i | −0.502788 | + | 0.870855i | ||||
\(565\) | −7.66123 | − | 13.2696i | −0.322310 | − | 0.558258i | ||||
\(566\) | −20.2156 | −0.849725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.2544 | −0.472225 | ||||||||
\(569\) | 10.2665 | + | 17.7821i | 0.430395 | + | 0.745466i | 0.996907 | − | 0.0785876i | \(-0.0250410\pi\) |
−0.566512 | + | 0.824053i | \(0.691708\pi\) | |||||||
\(570\) | −6.44082 | + | 11.1558i | −0.269776 | + | 0.467266i | ||||
\(571\) | 20.9476 | − | 36.2824i | 0.876631 | − | 1.51837i | 0.0216158 | − | 0.999766i | \(-0.493119\pi\) |
0.855015 | − | 0.518603i | \(-0.173548\pi\) | |||||||
\(572\) | −2.00000 | − | 3.46410i | −0.0836242 | − | 0.144841i | ||||
\(573\) | −24.3033 | −1.01529 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.4005 | 0.892464 | ||||||||
\(576\) | 5.50707 | + | 9.53852i | 0.229461 | + | 0.397438i | ||||
\(577\) | 10.0872 | − | 17.4715i | 0.419935 | − | 0.727349i | −0.575997 | − | 0.817452i | \(-0.695386\pi\) |
0.995932 | + | 0.0901025i | \(0.0287195\pi\) | |||||||
\(578\) | −15.1663 | + | 26.2687i | −0.630833 | + | 1.09263i | ||||
\(579\) | −18.9355 | − | 32.7973i | −0.786934 | − | 1.36301i | ||||
\(580\) | 30.0666 | 1.24845 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.67609 | −0.276733 | ||||||||
\(583\) | 3.87028 | + | 6.70351i | 0.160290 | + | 0.277631i | ||||
\(584\) | 1.51030 | − | 2.61592i | 0.0624968 | − | 0.108248i | ||||
\(585\) | −9.32318 | + | 16.1482i | −0.385466 | + | 0.667647i | ||||
\(586\) | −12.8547 | − | 22.2650i | −0.531022 | − | 0.919758i | ||||
\(587\) | −18.7441 | −0.773653 | −0.386826 | − | 0.922153i | \(-0.626429\pi\) | ||||
−0.386826 | + | 0.922153i | \(0.626429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.13249 | 0.0466636 | ||||||||
\(590\) | −11.4061 | − | 19.7559i | −0.469581 | − | 0.813338i | ||||
\(591\) | −29.2005 | + | 50.5768i | −1.20115 | + | 2.08045i | ||||
\(592\) | −15.1219 | + | 26.1920i | −0.621508 | + | 1.07648i | ||||
\(593\) | 1.49042 | + | 2.58149i | 0.0612043 | + | 0.106009i | 0.895004 | − | 0.446058i | \(-0.147173\pi\) |
−0.833800 | + | 0.552067i | \(0.813839\pi\) | |||||||
\(594\) | 63.3311 | 2.59850 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.9894 | 0.450145 | ||||||||
\(597\) | 33.5280 | + | 58.0722i | 1.37221 | + | 2.37674i | ||||
\(598\) | 6.65416 | − | 11.5253i | 0.272109 | − | 0.471307i | ||||
\(599\) | −3.73705 | + | 6.47277i | −0.152692 | + | 0.264470i | −0.932216 | − | 0.361902i | \(-0.882128\pi\) |
0.779524 | + | 0.626372i | \(0.215461\pi\) | |||||||
\(600\) | 5.83276 | + | 10.1026i | 0.238122 | + | 0.412439i | ||||
\(601\) | 21.4700 | 0.875780 | 0.437890 | − | 0.899028i | \(-0.355726\pi\) | ||||
0.437890 | + | 0.899028i | \(0.355726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.5260 | 2.70915 | ||||||||
\(604\) | 7.72496 | + | 13.3800i | 0.314324 | + | 0.544426i | ||||
\(605\) | 1.93124 | − | 3.34501i | 0.0785161 | − | 0.135994i | ||||
\(606\) | −36.8661 | + | 63.8539i | −1.49758 | + | 2.59389i | ||||
\(607\) | 11.4522 | + | 19.8358i | 0.464830 | + | 0.805109i | 0.999194 | − | 0.0401456i | \(-0.0127822\pi\) |
−0.534364 | + | 0.845254i | \(0.679449\pi\) | |||||||
\(608\) | 5.15667 | 0.209131 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2056 | 0.413211 | ||||||||
\(611\) | 2.98514 | + | 5.17041i | 0.120766 | + | 0.209173i | ||||
\(612\) | 2.24029 | − | 3.88030i | 0.0905585 | − | 0.156852i | ||||
\(613\) | 10.0731 | − | 17.4470i | 0.406847 | − | 0.704679i | −0.587688 | − | 0.809088i | \(-0.699962\pi\) |
0.994535 | + | 0.104408i | \(0.0332949\pi\) | |||||||
\(614\) | 12.2955 | + | 21.2964i | 0.496206 | + | 0.859455i | ||||
\(615\) | 36.7144 | 1.48047 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7844 | −0.554939 | −0.277470 | − | 0.960734i | \(-0.589496\pi\) | ||||
−0.277470 | + | 0.960734i | \(0.589496\pi\) | |||||||
\(618\) | −12.4111 | − | 21.4967i | −0.499248 | − | 0.864722i | ||||
\(619\) | 9.83276 | − | 17.0308i | 0.395212 | − | 0.684527i | −0.597916 | − | 0.801559i | \(-0.704004\pi\) |
0.993128 | + | 0.117031i | \(0.0373378\pi\) | |||||||
\(620\) | −2.52444 | + | 4.37245i | −0.101384 | + | 0.175602i | ||||
\(621\) | 41.2927 | + | 71.5211i | 1.65702 | + | 2.87004i | ||||
\(622\) | −0.773841 | −0.0310282 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.2544 | 0.610666 | ||||||||
\(625\) | 15.5383 | + | 26.9131i | 0.621533 | + | 1.07653i | ||||
\(626\) | −16.4600 | + | 28.5095i | −0.657873 | + | 1.13947i | ||||
\(627\) | 3.91638 | − | 6.78337i | 0.156405 | − | 0.270902i | ||||
\(628\) | 8.26856 | + | 14.3216i | 0.329951 | + | 0.571493i | ||||
\(629\) | 3.22616 | 0.128635 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1672 | −0.643608 | −0.321804 | − | 0.946806i | \(-0.604289\pi\) | ||||
−0.321804 | + | 0.946806i | \(0.604289\pi\) | |||||||
\(632\) | 8.72999 | + | 15.1208i | 0.347260 | + | 0.601472i | ||||
\(633\) | −26.9575 | + | 46.6917i | −1.07146 | + | 1.85583i | ||||
\(634\) | 8.54359 | − | 14.7979i | 0.339309 | − | 0.587701i | ||||
\(635\) | 18.1219 | + | 31.3881i | 0.719147 | + | 1.24560i | ||||
\(636\) | 9.97887 | 0.395688 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −46.6449 | −1.84669 | ||||||||
\(639\) | 28.9277 | + | 50.1043i | 1.14436 | + | 1.98210i | ||||
\(640\) | 13.5925 | − | 23.5428i | 0.537290 | − | 0.930613i | ||||
\(641\) | 14.5018 | − | 25.1178i | 0.572786 | − | 0.992095i | −0.423492 | − | 0.905900i | \(-0.639196\pi\) |
0.996278 | − | 0.0861949i | \(-0.0274708\pi\) | |||||||
\(642\) | −1.62721 | − | 2.81842i | −0.0642210 | − | 0.111234i | ||||
\(643\) | −39.2233 | −1.54681 | −0.773407 | − | 0.633910i | \(-0.781449\pi\) | ||||
−0.773407 | + | 0.633910i | \(0.781449\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −59.0122 | −2.32360 | ||||||||
\(646\) | −0.386920 | − | 0.670166i | −0.0152232 | − | 0.0263673i | ||||
\(647\) | 5.99221 | − | 10.3788i | 0.235578 | − | 0.408033i | −0.723863 | − | 0.689944i | \(-0.757635\pi\) |
0.959440 | + | 0.281911i | \(0.0909684\pi\) | |||||||
\(648\) | −9.69346 | + | 16.7896i | −0.380795 | + | 0.659556i | ||||
\(649\) | 6.93554 | + | 12.0127i | 0.272244 | + | 0.471540i | ||||
\(650\) | −5.28917 | −0.207458 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.3522 | −0.679564 | ||||||||
\(653\) | −22.6655 | − | 39.2578i | −0.886971 | − | 1.53628i | −0.843438 | − | 0.537226i | \(-0.819472\pi\) |
−0.0435323 | − | 0.999052i | \(-0.513861\pi\) | |||||||
\(654\) | −15.6811 | + | 27.1605i | −0.613180 | + | 1.06206i | ||||
\(655\) | −12.7300 | + | 22.0490i | −0.497402 | + | 0.861525i | ||||
\(656\) | −10.3380 | − | 17.9060i | −0.403633 | − | 0.699113i | ||||
\(657\) | −15.5280 | −0.605805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.12193 | 0.238477 | 0.119238 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119238 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(660\) | 17.4600 | + | 30.2416i | 0.679629 | + | 1.17715i | ||||
\(661\) | 13.7640 | − | 23.8400i | 0.535358 | − | 0.927267i | −0.463788 | − | 0.885946i | \(-0.653510\pi\) |
0.999146 | − | 0.0413207i | \(-0.0131565\pi\) | |||||||
\(662\) | −15.7789 | + | 27.3298i | −0.613263 | + | 1.06220i | ||||
\(663\) | −0.813607 | − | 1.40921i | −0.0315979 | − | 0.0547291i | ||||
\(664\) | 21.2444 | 0.824442 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 73.9377 | 2.86503 | ||||||||
\(667\) | −30.4131 | − | 52.6771i | −1.17760 | − | 2.03967i | ||||
\(668\) | 1.30833 | − | 2.26609i | 0.0506206 | − | 0.0876775i | ||||
\(669\) | −16.3650 | + | 28.3450i | −0.632707 | + | 1.09588i | ||||
\(670\) | 25.6116 | + | 44.3606i | 0.989463 | + | 1.71380i | ||||
\(671\) | −6.20555 | −0.239563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9547 | 1.07757 | 0.538787 | − | 0.842442i | \(-0.318883\pi\) | ||||
0.538787 | + | 0.842442i | \(0.318883\pi\) | |||||||
\(674\) | 19.9972 | + | 34.6362i | 0.770265 | + | 1.33414i | ||||
\(675\) | 16.4111 | − | 28.4249i | 0.631664 | − | 1.09407i | ||||
\(676\) | −0.644584 | + | 1.11645i | −0.0247917 | + | 0.0429405i | ||||
\(677\) | 6.33025 | + | 10.9643i | 0.243291 | + | 0.421393i | 0.961650 | − | 0.274280i | \(-0.0884396\pi\) |
−0.718359 | + | 0.695673i | \(0.755106\pi\) | |||||||
\(678\) | 30.6449 | 1.17691 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.90225 | −0.0729479 | ||||||||
\(681\) | −10.7839 | − | 18.6782i | −0.413239 | − | 0.715752i | ||||
\(682\) | 3.91638 | − | 6.78337i | 0.149966 | − | 0.259749i | ||||
\(683\) | 14.1517 | − | 24.5114i | 0.541498 | − | 0.937902i | −0.457320 | − | 0.889302i | \(-0.651191\pi\) |
0.998818 | − | 0.0485999i | \(-0.0154759\pi\) | |||||||
\(684\) | −3.47556 | − | 6.01985i | −0.132891 | − | 0.230175i | ||||
\(685\) | −17.6116 | −0.672906 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 65.4288 | 2.49626 | ||||||||
\(688\) | 16.6167 | + | 28.7809i | 0.633504 | + | 1.09726i | ||||
\(689\) | 1.24736 | − | 2.16049i | 0.0475206 | − | 0.0823081i | ||||
\(690\) | −58.0908 | + | 100.616i | −2.21148 | + | 3.83039i | ||||
\(691\) | −6.11763 | − | 10.5961i | −0.232726 | − | 0.403093i | 0.725884 | − | 0.687818i | \(-0.241431\pi\) |
−0.958609 | + | 0.284725i | \(0.908098\pi\) | |||||||
\(692\) | 26.1672 | 0.994729 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.9789 | −1.74533 | ||||||||
\(695\) | 16.2814 | + | 28.2002i | 0.617588 | + | 1.06969i | ||||
\(696\) | 16.5783 | − | 28.7145i | 0.628400 | − | 1.08842i | ||||
\(697\) | −1.10278 | + | 1.91006i | −0.0417706 | + | 0.0723488i | ||||
\(698\) | −5.17358 | − | 8.96090i | −0.195823 | − | 0.339175i | ||||
\(699\) | −18.8761 | −0.713960 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.0419 | 1.92783 | 0.963913 | − | 0.266219i | \(-0.0857743\pi\) | ||||
0.963913 | + | 0.266219i | \(0.0857743\pi\) | |||||||
\(702\) | −10.2056 | − | 17.6765i | −0.385184 | − | 0.667158i | ||||
\(703\) | 2.50251 | − | 4.33448i | 0.0943840 | − | 0.163478i | ||||
\(704\) | 2.57834 | − | 4.46581i | 0.0971747 | − | 0.168312i | ||||
\(705\) | −26.0602 | − | 45.1377i | −0.981485 | − | 1.69998i | ||||
\(706\) | 52.0071 | 1.95731 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.8822 | 0.672053 | ||||||||
\(709\) | −21.2955 | − | 36.8849i | −0.799770 | − | 1.38524i | −0.919766 | − | 0.392467i | \(-0.871622\pi\) |
0.119996 | − | 0.992774i | \(-0.461712\pi\) | |||||||
\(710\) | −22.2736 | + | 38.5790i | −0.835913 | + | 1.44784i | ||||
\(711\) | 44.8781 | − | 77.7312i | 1.68306 | − | 2.91515i | ||||
\(712\) | 6.86248 | + | 11.8862i | 0.257182 | + | 0.445453i | ||||
\(713\) | 10.2141 | 0.382523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.72999 | 0.326483 | ||||||||
\(716\) | 7.09273 | + | 12.2850i | 0.265068 | + | 0.459111i | ||||
\(717\) | −22.0383 | + | 38.1715i | −0.823036 | + | 1.42554i | ||||
\(718\) | 10.0141 | − | 17.3450i | 0.373724 | − | 0.647309i | ||||
\(719\) | 21.2466 | + | 36.8002i | 0.792366 | + | 1.37242i | 0.924499 | + | 0.381186i | \(0.124484\pi\) |
−0.132133 | + | 0.991232i | \(0.542183\pi\) | |||||||
\(720\) | −91.6727 | −3.41644 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 33.2580 | 1.23773 | ||||||||
\(723\) | 13.0950 | + | 22.6812i | 0.487008 | + | 0.843522i | ||||
\(724\) | −0.445843 | + | 0.772222i | −0.0165696 | + | 0.0286994i | ||||
\(725\) | −12.0872 | + | 20.9356i | −0.448907 | + | 0.777530i | ||||
\(726\) | 3.86248 | + | 6.69002i | 0.143350 | + | 0.248290i | ||||
\(727\) | −3.75614 | −0.139307 | −0.0696537 | − | 0.997571i | \(-0.522189\pi\) | ||||
−0.0696537 | + | 0.997571i | \(0.522189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.09775 | −0.188806 | ||||||||
\(730\) | −5.97807 | − | 10.3543i | −0.221258 | − | 0.383231i | ||||
\(731\) | 1.77252 | − | 3.07010i | 0.0655592 | − | 0.113552i | ||||
\(732\) | −4.00000 | + | 6.92820i | −0.147844 | + | 0.256074i | ||||
\(733\) | −22.8910 | − | 39.6483i | −0.845497 | − | 1.46444i | −0.885189 | − | 0.465232i | \(-0.845971\pi\) |
0.0396921 | − | 0.999212i | \(-0.487362\pi\) | |||||||
\(734\) | −49.5960 | −1.83062 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.5089 | 1.71434 | ||||||||
\(737\) | −15.5733 | − | 26.9738i | −0.573650 | − | 0.993592i | ||||
\(738\) | −25.2736 | + | 43.7751i | −0.930333 | + | 1.61138i | ||||
\(739\) | 7.02695 | − | 12.1710i | 0.258491 | − | 0.447719i | −0.707347 | − | 0.706866i | \(-0.750108\pi\) |
0.965838 | + | 0.259148i | \(0.0834416\pi\) | |||||||
\(740\) | 11.1567 | + | 19.3239i | 0.410127 | + | 0.710362i | ||||
\(741\) | −2.52444 | −0.0927375 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.74557 | 0.174098 | 0.0870491 | − | 0.996204i | \(-0.472256\pi\) | ||||
0.0870491 | + | 0.996204i | \(0.472256\pi\) | |||||||
\(744\) | 2.78389 | + | 4.82183i | 0.102062 | + | 0.176777i | ||||
\(745\) | −11.9922 | + | 20.7711i | −0.439360 | + | 0.760995i | ||||
\(746\) | 14.6413 | − | 25.3596i | 0.536058 | − | 0.928479i | ||||
\(747\) | −54.6054 | − | 94.5793i | −1.99791 | − | 3.46047i | ||||
\(748\) | −2.09775 | −0.0767014 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −32.9894 | −1.20460 | ||||||||
\(751\) | −18.0504 | − | 31.2642i | −0.658669 | − | 1.14085i | −0.980961 | − | 0.194207i | \(-0.937787\pi\) |
0.322292 | − | 0.946640i | \(-0.395547\pi\) | |||||||
\(752\) | −14.6761 | + | 25.4197i | −0.535182 | + | 0.926962i | ||||
\(753\) | −37.2091 | + | 64.4481i | −1.35598 | + | 2.34862i | ||||
\(754\) | 7.51664 | + | 13.0192i | 0.273740 | + | 0.474132i | ||||
\(755\) | −33.7194 | −1.22718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.03474 | −0.0376084 | −0.0188042 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188042 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(758\) | 23.6952 | + | 41.0414i | 0.860650 | + | 1.49069i | ||||
\(759\) | 35.3225 | − | 61.1803i | 1.28212 | − | 2.22070i | ||||
\(760\) | −1.47556 | + | 2.55575i | −0.0535243 | + | 0.0927067i | ||||
\(761\) | −14.9207 | − | 25.8434i | −0.540874 | − | 0.936822i | −0.998854 | − | 0.0478590i | \(-0.984760\pi\) |
0.457980 | − | 0.888963i | \(-0.348573\pi\) | |||||||
\(762\) | −72.4877 | −2.62595 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.0978 | 0.365324 | ||||||||
\(765\) | 4.88943 | + | 8.46874i | 0.176778 | + | 0.306188i | ||||
\(766\) | −19.0872 | + | 33.0600i | −0.689648 | + | 1.19451i | ||||
\(767\) | 2.23527 | − | 3.87160i | 0.0807109 | − | 0.139795i | ||||
\(768\) | 32.3416 | + | 56.0173i | 1.16703 | + | 2.02135i | ||||
\(769\) | 23.6358 | 0.852329 | 0.426164 | − | 0.904646i | \(-0.359864\pi\) | ||||
0.426164 | + | 0.904646i | \(0.359864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.4394 | −1.74450 | ||||||||
\(772\) | 7.86751 | + | 13.6269i | 0.283158 | + | 0.490444i | ||||
\(773\) | −6.51388 | + | 11.2824i | −0.234288 | + | 0.405798i | −0.959065 | − | 0.283184i | \(-0.908609\pi\) |
0.724778 | + | 0.688983i | \(0.241942\pi\) | |||||||
\(774\) | 40.6230 | − | 70.3611i | 1.46016 | − | 2.52908i | ||||
\(775\) | −2.02972 | − | 3.51558i | −0.0729097 | − | 0.126283i | ||||
\(776\) | −1.52946 | −0.0549045 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.1849 | 1.40485 | ||||||||
\(779\) | 1.71083 | + | 2.96325i | 0.0612969 | + | 0.106169i | ||||
\(780\) | 5.62721 | − | 9.74662i | 0.201487 | − | 0.348985i | ||||
\(781\) | 13.5436 | − | 23.4582i | 0.484628 | − | 0.839400i | ||||
\(782\) | −3.48970 | − | 6.04433i | −0.124791 | − | 0.216145i | ||||
\(783\) | −93.2898 | −3.33391 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0922 | −1.28819 | ||||||||
\(786\) | −25.4600 | − | 44.0980i | −0.908127 | − | 1.57292i | ||||
\(787\) | −23.1071 | + | 40.0226i | −0.823678 | + | 1.42665i | 0.0792472 | + | 0.996855i | \(0.474748\pi\) |
−0.902925 | + | 0.429797i | \(0.858585\pi\) | |||||||
\(788\) | 12.1325 | − | 21.0141i | 0.432202 | − | 0.748596i | ||||
\(789\) | −23.5358 | − | 40.7652i | −0.837897 | − | 1.45128i | ||||
\(790\) | 69.1099 | 2.45882 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 26.5089 | 0.941951 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | −25.1141 | + | 43.4990i | −0.891267 | + | 1.54372i | ||||
\(795\) | −10.8894 | + | 18.8610i | −0.386208 | + | 0.668932i | ||||
\(796\) | −13.9305 | − | 24.1284i | −0.493754 | − | 0.855207i | ||||
\(797\) | 53.1155 | 1.88145 | 0.940723 | − | 0.339176i | \(-0.110148\pi\) | ||||
0.940723 | + | 0.339176i | \(0.110148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.13104 | 0.110768 | ||||||||
\(800\) | −9.24208 | − | 16.0077i | −0.326757 | − | 0.565959i | ||||
\(801\) | 35.2779 | − | 61.1031i | 1.24648 | − | 2.15897i | ||||
\(802\) | −2.33804 | + | 4.04961i | −0.0825592 | + | 0.142997i | ||||
\(803\) | 3.63501 | + | 6.29602i | 0.128277 | + | 0.222182i | ||||
\(804\) | −40.1533 | −1.41610 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.52444 | −0.0889195 | ||||||||
\(807\) | 36.1361 | + | 62.5895i | 1.27205 | + | 2.20325i | ||||
\(808\) | −8.44584 | + | 14.6286i | −0.297124 | + | 0.514633i | ||||
\(809\) | 27.2318 | − | 47.1668i | 0.957418 | − | 1.65830i | 0.228683 | − | 0.973501i | \(-0.426558\pi\) |
0.728735 | − | 0.684796i | \(-0.240109\pi\) | |||||||
\(810\) | 38.3686 | + | 66.4563i | 1.34813 | + | 2.33504i | ||||
\(811\) | 38.0978 | 1.33779 | 0.668897 | − | 0.743356i | \(-0.266767\pi\) | ||||
0.668897 | + | 0.743356i | \(0.266767\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.5466 | −1.38696 | ||||||||
\(814\) | −17.3083 | − | 29.9789i | −0.606656 | − | 1.05076i | ||||
\(815\) | 18.9355 | − | 32.7973i | 0.663283 | − | 1.14884i | ||||
\(816\) | 4.00000 | − | 6.92820i | 0.140028 | − | 0.242536i | ||||
\(817\) | −2.74987 | − | 4.76292i | −0.0962058 | − | 0.166633i | ||||
\(818\) | −27.4161 | −0.958582 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.2544 | −0.532708 | ||||||||
\(821\) | 1.15165 | + | 1.99472i | 0.0401929 | + | 0.0696161i | 0.885422 | − | 0.464788i | \(-0.153869\pi\) |
−0.845229 | + | 0.534404i | \(0.820536\pi\) | |||||||
\(822\) | 17.6116 | − | 30.5042i | 0.614276 | − | 1.06396i | ||||
\(823\) | −11.8086 | + | 20.4531i | −0.411621 | + | 0.712949i | −0.995067 | − | 0.0992029i | \(-0.968371\pi\) |
0.583446 | + | 0.812152i | \(0.301704\pi\) | |||||||
\(824\) | −2.84333 | − | 4.92478i | −0.0990519 | − | 0.171563i | ||||
\(825\) | −28.0766 | −0.977503 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.1643 | −1.67484 | −0.837419 | − | 0.546562i | \(-0.815936\pi\) | ||||
−0.837419 | + | 0.546562i | \(0.815936\pi\) | |||||||
\(828\) | −31.3466 | − | 54.2940i | −1.08937 | − | 1.88685i | ||||
\(829\) | −6.53580 | + | 11.3203i | −0.226998 | + | 0.393172i | −0.956917 | − | 0.290362i | \(-0.906224\pi\) |
0.729919 | + | 0.683533i | \(0.239558\pi\) | |||||||
\(830\) | 42.0447 | − | 72.8235i | 1.45939 | − | 2.52774i | ||||
\(831\) | 12.6003 | + | 21.8243i | 0.437098 | + | 0.757076i | ||||
\(832\) | −1.66196 | −0.0576179 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −65.1255 | −2.25511 | ||||||||
\(835\) | 2.85542 | + | 4.94573i | 0.0988157 | + | 0.171154i | ||||
\(836\) | −1.62721 | + | 2.81842i | −0.0562783 | + | 0.0974769i | ||||
\(837\) | 7.83276 | − | 13.5667i | 0.270740 | − | 0.468935i | ||||
\(838\) | −9.06301 | − | 15.6976i | −0.313076 | − | 0.542264i | ||||
\(839\) | −17.6756 | −0.610229 | −0.305114 | − | 0.952316i | \(-0.598695\pi\) | ||||
−0.305114 | + | 0.952316i | \(0.598695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.7103 | 1.36932 | ||||||||
\(842\) | −23.5089 | − | 40.7185i | −0.810169 | − | 1.40325i | ||||
\(843\) | 29.5280 | − | 51.1440i | 1.01700 | − | 1.76149i | ||||
\(844\) | 11.2005 | − | 19.3999i | 0.385538 | − | 0.667771i | ||||
\(845\) | −1.40680 | − | 2.43665i | −0.0483955 | − | 0.0838235i | ||||
\(846\) | 71.7577 | 2.46708 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.2650 | 0.421181 | ||||||||
\(849\) | 17.2927 | + | 29.9519i | 0.593485 | + | 1.02795i | ||||
\(850\) | −1.38692 | + | 2.40222i | −0.0475710 | + | 0.0823953i | ||||
\(851\) | 22.5705 | − | 39.0933i | 0.773708 | − | 1.34010i | ||||
\(852\) | −17.4600 | − | 30.2416i | −0.598169 | − | 1.03606i | ||||
\(853\) | −5.48970 | −0.187964 | −0.0939818 | − | 0.995574i | \(-0.529960\pi\) | ||||
−0.0939818 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.1708 | 0.518831 | ||||||||
\(856\) | −0.372787 | − | 0.645686i | −0.0127416 | − | 0.0220691i | ||||
\(857\) | 5.52444 | − | 9.56861i | 0.188711 | − | 0.326857i | −0.756110 | − | 0.654445i | \(-0.772902\pi\) |
0.944821 | + | 0.327588i | \(0.106236\pi\) | |||||||
\(858\) | −8.72999 | + | 15.1208i | −0.298037 | + | 0.516215i | ||||
\(859\) | −22.6308 | − | 39.1977i | −0.772152 | − | 1.33741i | −0.936381 | − | 0.350985i | \(-0.885847\pi\) |
0.164229 | − | 0.986422i | \(-0.447486\pi\) | |||||||
\(860\) | 24.5189 | 0.836087 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.6344 | −1.89491 | ||||||||
\(863\) | 2.95112 | + | 5.11150i | 0.100457 | + | 0.173997i | 0.911873 | − | 0.410472i | \(-0.134636\pi\) |
−0.811416 | + | 0.584469i | \(0.801303\pi\) | |||||||
\(864\) | 35.6655 | − | 61.7745i | 1.21337 | − | 2.10161i | ||||
\(865\) | −28.5550 | + | 49.4586i | −0.970898 | + | 1.68164i | ||||
\(866\) | −3.19142 | − | 5.52770i | −0.108449 | − | 0.187839i | ||||
\(867\) | 51.8938 | 1.76241 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0227 | −1.42552 | ||||||||
\(870\) | −65.6202 | − | 113.658i | −2.22473 | − | 3.85335i | ||||
\(871\) | −5.01916 | + | 8.69343i | −0.170068 | + | 0.294566i | ||||
\(872\) | −3.59247 | + | 6.22234i | −0.121656 | + | 0.210715i | ||||
\(873\) | 3.93124 | + | 6.80911i | 0.133052 | + | 0.230453i | ||||
\(874\) | −10.8277 | −0.366254 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.37227 | 0.316660 | ||||||||
\(877\) | 2.45364 | + | 4.24982i | 0.0828534 | + | 0.143506i | 0.904474 | − | 0.426528i | \(-0.140263\pi\) |
−0.821621 | + | 0.570034i | \(0.806930\pi\) | |||||||
\(878\) | 29.3366 | − | 50.8125i | 0.990062 | − | 1.71484i | ||||
\(879\) | −21.9922 | + | 38.0916i | −0.741779 | + | 1.28480i | ||||
\(880\) | 21.4600 | + | 37.1698i | 0.723416 | + | 1.25299i | ||||
\(881\) | 44.2822 | 1.49190 | 0.745952 | − | 0.665999i | \(-0.231995\pi\) | ||||
0.745952 | + | 0.665999i | \(0.231995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −58.8605 | −1.98081 | −0.990407 | − | 0.138181i | \(-0.955874\pi\) | ||||
−0.990407 | + | 0.138181i | \(0.955874\pi\) | |||||||
\(884\) | 0.338044 | + | 0.585510i | 0.0113697 | + | 0.0196928i | ||||
\(885\) | −19.5139 | + | 33.7990i | −0.655952 | + | 1.13614i | ||||
\(886\) | 14.0063 | − | 24.2597i | 0.470552 | − | 0.815020i | ||||
\(887\) | 5.06446 | + | 8.77191i | 0.170048 | + | 0.294532i | 0.938436 | − | 0.345452i | \(-0.112274\pi\) |
−0.768388 | + | 0.639984i | \(0.778941\pi\) | |||||||
\(888\) | 24.6066 | 0.825744 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 54.3260 | 1.82101 | ||||||||
\(891\) | −23.3303 | − | 40.4092i | −0.781593 | − | 1.35376i | ||||
\(892\) | 6.79947 | − | 11.7770i | 0.227663 | − | 0.394324i | ||||
\(893\) | 2.42873 | − | 4.20668i | 0.0812743 | − | 0.140771i | ||||
\(894\) | −23.9844 | − | 41.5422i | −0.802159 | − | 1.38938i | ||||
\(895\) | −30.9597 | −1.03487 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.7683 | −0.760211 | ||||||||
\(898\) | −13.1219 | − | 22.7279i | −0.437885 | − | 0.758438i | ||||
\(899\) | −5.76903 | + | 9.99225i | −0.192408 | + | 0.333260i | ||||
\(900\) | −12.4582 | + | 21.5782i | −0.415273 | + | 0.719274i | ||||
\(901\) | −0.654163 | − | 1.13304i | −0.0217933 | − | 0.0377471i | ||||
\(902\) | 23.6655 | 0.787976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.02061 | 0.233502 | ||||||||
\(905\) | −0.973050 | − | 1.68537i | −0.0323453 | − | 0.0560237i | ||||
\(906\) | 33.7194 | − | 58.4038i | 1.12025 | − | 1.94033i | ||||
\(907\) | −18.9773 | + | 32.8697i | −0.630132 | + | 1.09142i | 0.357392 | + | 0.933955i | \(0.383666\pi\) |
−0.987524 | + | 0.157467i | \(0.949667\pi\) | |||||||
\(908\) | 4.48059 | + | 7.76060i | 0.148693 | + | 0.257545i | ||||
\(909\) | 86.8349 | 2.88013 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.57477 | 0.184700 | 0.0923501 | − | 0.995727i | \(-0.470562\pi\) | ||||
0.0923501 | + | 0.995727i | \(0.470562\pi\) | |||||||
\(912\) | −6.20555 | − | 10.7483i | −0.205486 | − | 0.355913i | ||||
\(913\) | −25.5655 | + | 44.2808i | −0.846095 | + | 1.46548i | ||||
\(914\) | −31.4394 | + | 54.4546i | −1.03992 | + | 1.80120i | ||||
\(915\) | −8.72999 | − | 15.1208i | −0.288605 | − | 0.499878i | ||||
\(916\) | −27.1849 | −0.898216 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10.7044 | −0.353296 | ||||||||
\(919\) | −7.89220 | − | 13.6697i | −0.260340 | − | 0.450922i | 0.705992 | − | 0.708219i | \(-0.250501\pi\) |
−0.966332 | + | 0.257298i | \(0.917168\pi\) | |||||||
\(920\) | −13.3083 | + | 23.0507i | −0.438762 | + | 0.759959i | ||||
\(921\) | 21.0355 | − | 36.4346i | 0.693145 | − | 1.20056i | ||||
\(922\) | 11.3713 | + | 19.6957i | 0.374495 | + | 0.648644i | ||||
\(923\) | −8.72999 | −0.287351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9406 | −0.589882 | ||||||||
\(926\) | 11.0192 | + | 19.0857i | 0.362112 | + | 0.627196i | ||||
\(927\) | −14.6167 | + | 25.3168i | −0.480074 | + | 0.831512i | ||||
\(928\) | −26.2686 | + | 45.4985i | −0.862308 | + | 1.49356i | ||||
\(929\) | 22.6315 | + | 39.1989i | 0.742516 | + | 1.28608i | 0.951346 | + | 0.308123i | \(0.0997009\pi\) |
−0.208831 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(930\) | 22.0383 | 0.722665 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.84281 | 0.256900 | ||||||||
\(933\) | 0.661956 | + | 1.14654i | 0.0216715 | + | 0.0375361i | ||||
\(934\) | −33.5819 | + | 58.1656i | −1.09883 | + | 1.90324i | ||||
\(935\) | 2.28917 | − | 3.96496i | 0.0748638 | − | 0.129668i | ||||
\(936\) | −4.27180 | − | 7.39897i | −0.139628 | − | 0.241843i | ||||
\(937\) | 53.6188 | 1.75165 | 0.875824 | − | 0.482630i | \(-0.160318\pi\) | ||||
0.875824 | + | 0.482630i | \(0.160318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.3205 | 1.83795 | ||||||||
\(940\) | 10.8277 | + | 18.7542i | 0.353162 | + | 0.611694i | ||||
\(941\) | −10.3876 | + | 17.9919i | −0.338628 | + | 0.586520i | −0.984175 | − | 0.177200i | \(-0.943296\pi\) |
0.645547 | + | 0.763720i | \(0.276629\pi\) | |||||||
\(942\) | 36.0922 | − | 62.5135i | 1.17595 | − | 2.03680i | ||||
\(943\) | 15.4303 | + | 26.7260i | 0.502478 | + | 0.870318i | ||||
\(944\) | 21.9789 | 0.715351 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.0383 | −1.23673 | ||||||||
\(947\) | 5.43026 | + | 9.40548i | 0.176460 | + | 0.305637i | 0.940665 | − | 0.339335i | \(-0.110202\pi\) |
−0.764206 | + | 0.644972i | \(0.776869\pi\) | |||||||
\(948\) | −27.0872 | + | 46.9164i | −0.879751 | + | 1.52377i | ||||
\(949\) | 1.17153 | − | 2.02916i | 0.0380296 | − | 0.0658692i | ||||
\(950\) | 2.15165 | + | 3.72677i | 0.0698088 | + | 0.120912i | ||||
\(951\) | −29.2333 | −0.947955 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.7180 | −0.833087 | −0.416543 | − | 0.909116i | \(-0.636759\pi\) | ||||
−0.416543 | + | 0.909116i | \(0.636759\pi\) | |||||||
\(954\) | −14.9922 | − | 25.9673i | −0.485391 | − | 0.840721i | ||||
\(955\) | −11.0192 | + | 19.0857i | −0.356572 | + | 0.617600i | ||||
\(956\) | 9.15667 | − | 15.8598i | 0.296148 | − | 0.512943i | ||||
\(957\) | 39.9008 | + | 69.1102i | 1.28981 | + | 2.23402i | ||||
\(958\) | −21.7789 | −0.703643 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 14.5089 | 0.468271 | ||||||||
\(961\) | 14.5312 | + | 25.1689i | 0.468750 | + | 0.811899i | ||||
\(962\) | −5.57834 | + | 9.66196i | −0.179853 | + | 0.311514i | ||||
\(963\) | −1.91638 | + | 3.31927i | −0.0617545 | + | 0.106962i | ||||
\(964\) | −5.44082 | − | 9.42378i | −0.175237 | − | 0.303519i | ||||
\(965\) | −34.3416 | −1.10550 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.5038 | 1.07741 | 0.538705 | − | 0.842494i | \(-0.318914\pi\) | ||||
0.538705 | + | 0.842494i | \(0.318914\pi\) | |||||||
\(968\) | 0.884877 | + | 1.53265i | 0.0284410 | + | 0.0492613i | ||||
\(969\) | −0.661956 | + | 1.14654i | −0.0212651 | + | 0.0368322i | ||||
\(970\) | −3.02695 | + | 5.24283i | −0.0971895 | + | 0.168337i | ||||
\(971\) | −1.01916 | − | 1.76523i | −0.0327063 | − | 0.0566490i | 0.849209 | − | 0.528057i | \(-0.177079\pi\) |
−0.881915 | + | 0.471408i | \(0.843746\pi\) | |||||||
\(972\) | −16.6267 | −0.533302 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.1643 | −0.646107 | ||||||||
\(975\) | 4.52444 | + | 7.83656i | 0.144898 | + | 0.250971i | ||||
\(976\) | −4.91638 | + | 8.51542i | −0.157370 | + | 0.272572i | ||||
\(977\) | −7.57054 | + | 13.1126i | −0.242203 | + | 0.419508i | −0.961342 | − | 0.275359i | \(-0.911203\pi\) |
0.719138 | + | 0.694867i | \(0.244537\pi\) | |||||||
\(978\) | 37.8711 | + | 65.5946i | 1.21098 | + | 2.09748i | ||||
\(979\) | −33.0333 | −1.05575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.9355 | 1.17926 | ||||||||
\(982\) | 0.0538991 | + | 0.0933560i | 0.00171999 | + | 0.00297911i | ||||
\(983\) | −24.6562 | + | 42.7058i | −0.786411 | + | 1.36210i | 0.141742 | + | 0.989904i | \(0.454730\pi\) |
−0.928153 | + | 0.372200i | \(0.878604\pi\) | |||||||
\(984\) | −8.41110 | + | 14.5685i | −0.268136 | + | 0.464425i | ||||
\(985\) | 26.4791 | + | 45.8632i | 0.843695 | + | 1.46132i | ||||
\(986\) | 7.88403 | 0.251079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.04888 | 0.0333692 | ||||||||
\(989\) | −24.8015 | − | 42.9575i | −0.788642 | − | 1.36597i | ||||
\(990\) | 52.4635 | − | 90.8695i | 1.66740 | − | 2.88802i | ||||
\(991\) | −2.71585 | + | 4.70400i | −0.0862720 | + | 0.149427i | −0.905933 | − | 0.423422i | \(-0.860829\pi\) |
0.819661 | + | 0.572850i | \(0.194162\pi\) | |||||||
\(992\) | −4.41110 | − | 7.64025i | −0.140053 | − | 0.242578i | ||||
\(993\) | 53.9900 | 1.71332 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.8066 | 1.92770 | ||||||||
\(996\) | 32.9583 | + | 57.0854i | 1.04432 | + | 1.80882i | ||||
\(997\) | 26.8030 | − | 46.4242i | 0.848861 | − | 1.47027i | −0.0333647 | − | 0.999443i | \(-0.510622\pi\) |
0.882226 | − | 0.470827i | \(-0.156044\pi\) | |||||||
\(998\) | 9.33804 | − | 16.1740i | 0.295591 | − | 0.511978i | ||||
\(999\) | −34.6167 | − | 59.9578i | −1.09522 | − | 1.89698i |
(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 | 637.2.e.j.508.3 | 6 | ||
7.2 | even | 3 | inner | 637.2.e.j.79.3 | 6 | ||
7.3 | odd | 6 | 637.2.a.j.1.1 | 3 | |||
7.4 | even | 3 | 91.2.a.d.1.1 | ✓ | 3 | ||
7.5 | odd | 6 | 637.2.e.i.79.3 | 6 | |||
7.6 | odd | 2 | 637.2.e.i.508.3 | 6 | |||
21.11 | odd | 6 | 819.2.a.i.1.3 | 3 | |||
21.17 | even | 6 | 5733.2.a.x.1.3 | 3 | |||
28.11 | odd | 6 | 1456.2.a.t.1.3 | 3 | |||
35.4 | even | 6 | 2275.2.a.m.1.3 | 3 | |||
56.11 | odd | 6 | 5824.2.a.bs.1.1 | 3 | |||
56.53 | even | 6 | 5824.2.a.by.1.3 | 3 | |||
91.18 | odd | 12 | 1183.2.c.f.337.5 | 6 | |||
91.25 | even | 6 | 1183.2.a.i.1.3 | 3 | |||
91.38 | odd | 6 | 8281.2.a.bg.1.3 | 3 | |||
91.60 | odd | 12 | 1183.2.c.f.337.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.d.1.1 | ✓ | 3 | 7.4 | even | 3 | ||
637.2.a.j.1.1 | 3 | 7.3 | odd | 6 | |||
637.2.e.i.79.3 | 6 | 7.5 | odd | 6 | |||
637.2.e.i.508.3 | 6 | 7.6 | odd | 2 | |||
637.2.e.j.79.3 | 6 | 7.2 | even | 3 | inner | ||
637.2.e.j.508.3 | 6 | 1.1 | even | 1 | trivial | ||
819.2.a.i.1.3 | 3 | 21.11 | odd | 6 | |||
1183.2.a.i.1.3 | 3 | 91.25 | even | 6 | |||
1183.2.c.f.337.2 | 6 | 91.60 | odd | 12 | |||
1183.2.c.f.337.5 | 6 | 91.18 | odd | 12 | |||
1456.2.a.t.1.3 | 3 | 28.11 | odd | 6 | |||
2275.2.a.m.1.3 | 3 | 35.4 | even | 6 | |||
5733.2.a.x.1.3 | 3 | 21.17 | even | 6 | |||
5824.2.a.bs.1.1 | 3 | 56.11 | odd | 6 | |||
5824.2.a.by.1.3 | 3 | 56.53 | even | 6 | |||
8281.2.a.bg.1.3 | 3 | 91.38 | odd | 6 |