Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(65,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 263.2 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.263 |
Dual form | 462.2.n.d.65.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.13746 | − | 0.656712i | 0.508687 | − | 0.293691i | −0.223607 | − | 0.974679i | \(-0.571783\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | −1.13746 | + | 2.38876i | −0.429919 | + | 0.902867i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 1.13746 | + | 0.656712i | 0.359696 | + | 0.207671i | ||||
\(11\) | −2.50000 | + | 2.17945i | −0.753778 | + | 0.657129i | ||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | − | 2.62685i | − | 0.728557i | −0.931290 | − | 0.364278i | \(-0.881316\pi\) | ||
0.931290 | − | 0.364278i | \(-0.118684\pi\) | |||||||
\(14\) | −2.63746 | + | 0.209313i | −0.704890 | + | 0.0559414i | ||||
\(15\) | 2.27492 | 0.587381 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.63746 | + | 2.83616i | −0.397142 | + | 0.687870i | −0.993372 | − | 0.114943i | \(-0.963331\pi\) |
0.596230 | + | 0.802814i | \(0.296665\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | 5.63746 | − | 3.25479i | 1.29332 | − | 0.746700i | 0.314080 | − | 0.949396i | \(-0.398304\pi\) |
0.979242 | + | 0.202697i | \(0.0649706\pi\) | |||||||
\(20\) | 1.31342i | 0.293691i | ||||||||
\(21\) | −3.77492 | + | 2.59808i | −0.823754 | + | 0.566947i | ||||
\(22\) | −3.13746 | − | 1.07534i | −0.668908 | − | 0.229263i | ||||
\(23\) | 4.91238 | − | 2.83616i | 1.02430 | − | 0.591381i | 0.108954 | − | 0.994047i | \(-0.465250\pi\) |
0.915347 | + | 0.402666i | \(0.131916\pi\) | |||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | −1.63746 | + | 2.83616i | −0.327492 | + | 0.567232i | ||||
\(26\) | 2.27492 | − | 1.31342i | 0.446148 | − | 0.257584i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −1.50000 | − | 2.17945i | −0.283473 | − | 0.411877i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 1.13746 | + | 1.97014i | 0.207671 | + | 0.359696i | ||||
\(31\) | 5.13746 | − | 8.89834i | 0.922715 | − | 1.59819i | 0.127519 | − | 0.991836i | \(-0.459299\pi\) |
0.795196 | − | 0.606353i | \(-0.207368\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −5.63746 | + | 1.10411i | −0.981356 | + | 0.192201i | ||||
\(34\) | −3.27492 | −0.561644 | ||||||||
\(35\) | 0.274917 | + | 3.46410i | 0.0464695 | + | 0.585540i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 3.63746 | + | 6.30026i | 0.597995 | + | 1.03576i | 0.993117 | + | 0.117128i | \(0.0373689\pi\) |
−0.395122 | + | 0.918629i | \(0.629298\pi\) | |||||||
\(38\) | 5.63746 | + | 3.25479i | 0.914517 | + | 0.527996i | ||||
\(39\) | 2.27492 | − | 3.94027i | 0.364278 | − | 0.630949i | ||||
\(40\) | −1.13746 | + | 0.656712i | −0.179848 | + | 0.103835i | ||||
\(41\) | −6.54983 | −1.02291 | −0.511456 | − | 0.859309i | \(-0.670894\pi\) | ||||
−0.511456 | + | 0.859309i | \(0.670894\pi\) | |||||||
\(42\) | −4.13746 | − | 1.97014i | −0.638424 | − | 0.303999i | ||||
\(43\) | − | 9.97368i | − | 1.52097i | −0.649355 | − | 0.760486i | \(-0.724961\pi\) | ||
0.649355 | − | 0.760486i | \(-0.275039\pi\) | |||||||
\(44\) | −0.637459 | − | 3.25479i | −0.0961005 | − | 0.490678i | ||||
\(45\) | 3.41238 | + | 1.97014i | 0.508687 | + | 0.293691i | ||||
\(46\) | 4.91238 | + | 2.83616i | 0.724290 | + | 0.418169i | ||||
\(47\) | −1.91238 | + | 1.10411i | −0.278949 | + | 0.161051i | −0.632947 | − | 0.774195i | \(-0.718155\pi\) |
0.353999 | + | 0.935246i | \(0.384822\pi\) | |||||||
\(48\) | − | 1.73205i | − | 0.250000i | ||||||
\(49\) | −4.41238 | − | 5.43424i | −0.630339 | − | 0.776320i | ||||
\(50\) | −3.27492 | −0.463143 | ||||||||
\(51\) | −4.91238 | + | 2.83616i | −0.687870 | + | 0.397142i | ||||
\(52\) | 2.27492 | + | 1.31342i | 0.315474 | + | 0.182139i | ||||
\(53\) | −11.6873 | − | 6.74766i | −1.60537 | − | 0.926863i | −0.990387 | − | 0.138325i | \(-0.955828\pi\) |
−0.614986 | − | 0.788538i | \(-0.710838\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | −1.41238 | + | 4.12081i | −0.190445 | + | 0.555650i | ||||
\(56\) | 1.13746 | − | 2.38876i | 0.151999 | − | 0.319212i | ||||
\(57\) | 11.2749 | 1.49340 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | −1.50000 | − | 0.866025i | −0.195283 | − | 0.112747i | 0.399170 | − | 0.916877i | \(-0.369298\pi\) |
−0.594454 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(60\) | −1.13746 | + | 1.97014i | −0.146845 | + | 0.254343i | ||||
\(61\) | 6.00000 | − | 3.46410i | 0.768221 | − | 0.443533i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 10.2749 | 1.30492 | ||||||||
\(63\) | −7.91238 | + | 0.627940i | −0.996866 | + | 0.0791130i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.72508 | − | 2.98793i | −0.213970 | − | 0.370607i | ||||
\(66\) | −3.77492 | − | 4.33013i | −0.464660 | − | 0.533002i | ||||
\(67\) | 4.27492 | − | 7.40437i | 0.522264 | − | 0.904588i | −0.477400 | − | 0.878686i | \(-0.658421\pi\) |
0.999664 | − | 0.0259023i | \(-0.00824587\pi\) | |||||||
\(68\) | −1.63746 | − | 2.83616i | −0.198571 | − | 0.343935i | ||||
\(69\) | 9.82475 | 1.18276 | ||||||||
\(70\) | −2.86254 | + | 1.97014i | −0.342139 | + | 0.235476i | ||||
\(71\) | 9.97368i | 1.18366i | 0.806064 | + | 0.591829i | \(0.201594\pi\) | ||||
−0.806064 | + | 0.591829i | \(0.798406\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | 4.54983 | + | 2.62685i | 0.532518 | + | 0.307449i | 0.742041 | − | 0.670354i | \(-0.233858\pi\) |
−0.209523 | + | 0.977804i | \(0.567191\pi\) | |||||||
\(74\) | −3.63746 | + | 6.30026i | −0.422846 | + | 0.732391i | ||||
\(75\) | −4.91238 | + | 2.83616i | −0.567232 | + | 0.327492i | ||||
\(76\) | 6.50958i | 0.746700i | ||||||||
\(77\) | −2.36254 | − | 8.45094i | −0.269237 | − | 0.963074i | ||||
\(78\) | 4.54983 | 0.515167 | ||||||||
\(79\) | 1.86254 | − | 1.07534i | 0.209552 | − | 0.120985i | −0.391551 | − | 0.920156i | \(-0.628061\pi\) |
0.601103 | + | 0.799171i | \(0.294728\pi\) | |||||||
\(80\) | −1.13746 | − | 0.656712i | −0.127172 | − | 0.0734226i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −3.27492 | − | 5.67232i | −0.361654 | − | 0.626403i | ||||
\(83\) | 10.2749 | 1.12782 | 0.563909 | − | 0.825837i | \(-0.309297\pi\) | ||||
0.563909 | + | 0.825837i | \(0.309297\pi\) | |||||||
\(84\) | −0.362541 | − | 4.56821i | −0.0395565 | − | 0.498433i | ||||
\(85\) | 4.30136i | 0.466547i | ||||||||
\(86\) | 8.63746 | − | 4.98684i | 0.931401 | − | 0.537745i | ||||
\(87\) | 1.50000 | + | 0.866025i | 0.160817 | + | 0.0928477i | ||||
\(88\) | 2.50000 | − | 2.17945i | 0.266501 | − | 0.232330i | ||||
\(89\) | −2.27492 | + | 1.31342i | −0.241141 | + | 0.139223i | −0.615701 | − | 0.787980i | \(-0.711127\pi\) |
0.374560 | + | 0.927203i | \(0.377794\pi\) | |||||||
\(90\) | 3.94027i | 0.415341i | ||||||||
\(91\) | 6.27492 | + | 2.98793i | 0.657790 | + | 0.313220i | ||||
\(92\) | 5.67232i | 0.591381i | ||||||||
\(93\) | 15.4124 | − | 8.89834i | 1.59819 | − | 0.922715i | ||||
\(94\) | −1.91238 | − | 1.10411i | −0.197247 | − | 0.113880i | ||||
\(95\) | 4.27492 | − | 7.40437i | 0.438597 | − | 0.759673i | ||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | −13.5498 | −1.37578 | −0.687889 | − | 0.725816i | \(-0.741462\pi\) | ||||
−0.687889 | + | 0.725816i | \(0.741462\pi\) | |||||||
\(98\) | 2.50000 | − | 6.53835i | 0.252538 | − | 0.660473i | ||||
\(99\) | −9.41238 | − | 3.22602i | −0.945979 | − | 0.324227i | ||||
\(100\) | −1.63746 | − | 2.83616i | −0.163746 | − | 0.283616i | ||||
\(101\) | 4.91238 | − | 8.50848i | 0.488800 | − | 0.846626i | −0.511117 | − | 0.859511i | \(-0.670768\pi\) |
0.999917 | + | 0.0128851i | \(0.00410157\pi\) | |||||||
\(102\) | −4.91238 | − | 2.83616i | −0.486398 | − | 0.280822i | ||||
\(103\) | 6.54983 | + | 11.3446i | 0.645374 | + | 1.11782i | 0.984215 | + | 0.176977i | \(0.0566319\pi\) |
−0.338841 | + | 0.940844i | \(0.610035\pi\) | |||||||
\(104\) | 2.62685i | 0.257584i | ||||||||
\(105\) | −2.58762 | + | 5.43424i | −0.252526 | + | 0.530327i | ||||
\(106\) | − | 13.4953i | − | 1.31078i | ||||||
\(107\) | −7.13746 | − | 12.3624i | −0.690004 | − | 1.19512i | −0.971836 | − | 0.235658i | \(-0.924275\pi\) |
0.281832 | − | 0.959464i | \(-0.409058\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | 3.72508 | + | 2.15068i | 0.356798 | + | 0.205998i | 0.667675 | − | 0.744453i | \(-0.267289\pi\) |
−0.310877 | + | 0.950450i | \(0.600623\pi\) | |||||||
\(110\) | −4.27492 | + | 0.837253i | −0.407597 | + | 0.0798290i | ||||
\(111\) | 12.6005i | 1.19599i | ||||||||
\(112\) | 2.63746 | − | 0.209313i | 0.249216 | − | 0.0197783i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 5.63746 | + | 9.76436i | 0.527996 | + | 0.914517i | ||||
\(115\) | 3.72508 | − | 6.45203i | 0.347366 | − | 0.601655i | ||||
\(116\) | −0.500000 | + | 0.866025i | −0.0464238 | + | 0.0804084i | ||||
\(117\) | 6.82475 | − | 3.94027i | 0.630949 | − | 0.364278i | ||||
\(118\) | − | 1.73205i | − | 0.159448i | ||||||
\(119\) | −4.91238 | − | 7.13752i | −0.450317 | − | 0.654295i | ||||
\(120\) | −2.27492 | −0.207671 | ||||||||
\(121\) | 1.50000 | − | 10.8972i | 0.136364 | − | 0.990659i | ||||
\(122\) | 6.00000 | + | 3.46410i | 0.543214 | + | 0.313625i | ||||
\(123\) | −9.82475 | − | 5.67232i | −0.885868 | − | 0.511456i | ||||
\(124\) | 5.13746 | + | 8.89834i | 0.461357 | + | 0.799094i | ||||
\(125\) | 10.8685i | 0.972106i | ||||||||
\(126\) | −4.50000 | − | 6.53835i | −0.400892 | − | 0.582482i | ||||
\(127\) | 3.52165i | 0.312496i | 0.987718 | + | 0.156248i | \(0.0499398\pi\) | ||||
−0.987718 | + | 0.156248i | \(0.950060\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 8.63746 | − | 14.9605i | 0.760486 | − | 1.31720i | ||||
\(130\) | 1.72508 | − | 2.98793i | 0.151300 | − | 0.262059i | ||||
\(131\) | 5.13746 | + | 8.89834i | 0.448862 | + | 0.777452i | 0.998312 | − | 0.0580748i | \(-0.0184962\pi\) |
−0.549450 | + | 0.835526i | \(0.685163\pi\) | |||||||
\(132\) | 1.86254 | − | 5.43424i | 0.162113 | − | 0.472990i | ||||
\(133\) | 1.36254 | + | 17.1687i | 0.118147 | + | 1.48872i | ||||
\(134\) | 8.54983 | 0.738593 | ||||||||
\(135\) | 3.41238 | + | 5.91041i | 0.293691 | + | 0.508687i | ||||
\(136\) | 1.63746 | − | 2.83616i | 0.140411 | − | 0.243199i | ||||
\(137\) | −3.72508 | − | 2.15068i | −0.318255 | − | 0.183745i | 0.332359 | − | 0.943153i | \(-0.392155\pi\) |
−0.650615 | + | 0.759408i | \(0.725489\pi\) | |||||||
\(138\) | 4.91238 | + | 8.50848i | 0.418169 | + | 0.724290i | ||||
\(139\) | − | 0.418627i | − | 0.0355075i | −0.999842 | − | 0.0177537i | \(-0.994349\pi\) | ||
0.999842 | − | 0.0177537i | \(-0.00565148\pi\) | |||||||
\(140\) | −3.13746 | − | 1.49397i | −0.265164 | − | 0.126263i | ||||
\(141\) | −3.82475 | −0.322102 | ||||||||
\(142\) | −8.63746 | + | 4.98684i | −0.724839 | + | 0.418486i | ||||
\(143\) | 5.72508 | + | 6.56712i | 0.478755 | + | 0.549170i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 1.13746 | − | 0.656712i | 0.0944608 | − | 0.0545370i | ||||
\(146\) | 5.25370i | 0.434799i | ||||||||
\(147\) | −1.91238 | − | 11.9726i | −0.157730 | − | 0.987482i | ||||
\(148\) | −7.27492 | −0.597995 | ||||||||
\(149\) | −3.63746 | − | 6.30026i | −0.297992 | − | 0.516138i | 0.677684 | − | 0.735353i | \(-0.262984\pi\) |
−0.975677 | + | 0.219215i | \(0.929650\pi\) | |||||||
\(150\) | −4.91238 | − | 2.83616i | −0.401094 | − | 0.231572i | ||||
\(151\) | −10.5000 | − | 6.06218i | −0.854478 | − | 0.493333i | 0.00768132 | − | 0.999970i | \(-0.497555\pi\) |
−0.862159 | + | 0.506637i | \(0.830888\pi\) | |||||||
\(152\) | −5.63746 | + | 3.25479i | −0.457258 | + | 0.263998i | ||||
\(153\) | −9.82475 | −0.794284 | ||||||||
\(154\) | 6.13746 | − | 6.27149i | 0.494571 | − | 0.505371i | ||||
\(155\) | − | 13.4953i | − | 1.08397i | ||||||
\(156\) | 2.27492 | + | 3.94027i | 0.182139 | + | 0.315474i | ||||
\(157\) | −8.63746 | + | 14.9605i | −0.689344 | + | 1.19398i | 0.282706 | + | 0.959207i | \(0.408768\pi\) |
−0.972050 | + | 0.234773i | \(0.924565\pi\) | |||||||
\(158\) | 1.86254 | + | 1.07534i | 0.148176 | + | 0.0855494i | ||||
\(159\) | −11.6873 | − | 20.2430i | −0.926863 | − | 1.60537i | ||||
\(160\) | − | 1.31342i | − | 0.103835i | ||||||
\(161\) | 1.18729 | + | 14.9605i | 0.0935718 | + | 1.17905i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −8.27492 | − | 14.3326i | −0.648142 | − | 1.12261i | −0.983566 | − | 0.180547i | \(-0.942213\pi\) |
0.335425 | − | 0.942067i | \(-0.391120\pi\) | |||||||
\(164\) | 3.27492 | − | 5.67232i | 0.255728 | − | 0.442934i | ||||
\(165\) | −5.68729 | + | 4.95807i | −0.442755 | + | 0.385985i | ||||
\(166\) | 5.13746 | + | 8.89834i | 0.398744 | + | 0.690645i | ||||
\(167\) | 7.45017 | 0.576511 | 0.288256 | − | 0.957554i | \(-0.406925\pi\) | ||||
0.288256 | + | 0.957554i | \(0.406925\pi\) | |||||||
\(168\) | 3.77492 | − | 2.59808i | 0.291241 | − | 0.200446i | ||||
\(169\) | 6.09967 | 0.469205 | ||||||||
\(170\) | −3.72508 | + | 2.15068i | −0.285701 | + | 0.164949i | ||||
\(171\) | 16.9124 | + | 9.76436i | 1.29332 | + | 0.746700i | ||||
\(172\) | 8.63746 | + | 4.98684i | 0.658600 | + | 0.380243i | ||||
\(173\) | 7.00000 | + | 12.1244i | 0.532200 | + | 0.921798i | 0.999293 | + | 0.0375896i | \(0.0119679\pi\) |
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(174\) | 1.73205i | 0.131306i | ||||||||
\(175\) | −4.91238 | − | 7.13752i | −0.371341 | − | 0.539546i | ||||
\(176\) | 3.13746 | + | 1.07534i | 0.236495 | + | 0.0810567i | ||||
\(177\) | −1.50000 | − | 2.59808i | −0.112747 | − | 0.195283i | ||||
\(178\) | −2.27492 | − | 1.31342i | −0.170512 | − | 0.0984453i | ||||
\(179\) | −12.3625 | − | 7.13752i | −0.924020 | − | 0.533483i | −0.0391045 | − | 0.999235i | \(-0.512451\pi\) |
−0.884915 | + | 0.465752i | \(0.845784\pi\) | |||||||
\(180\) | −3.41238 | + | 1.97014i | −0.254343 | + | 0.146845i | ||||
\(181\) | −6.54983 | −0.486845 | −0.243423 | − | 0.969920i | \(-0.578270\pi\) | ||||
−0.243423 | + | 0.969920i | \(0.578270\pi\) | |||||||
\(182\) | 0.549834 | + | 6.92820i | 0.0407564 | + | 0.513553i | ||||
\(183\) | 12.0000 | 0.887066 | ||||||||
\(184\) | −4.91238 | + | 2.83616i | −0.362145 | + | 0.209085i | ||||
\(185\) | 8.27492 | + | 4.77753i | 0.608384 | + | 0.351251i | ||||
\(186\) | 15.4124 | + | 8.89834i | 1.13009 | + | 0.652458i | ||||
\(187\) | −2.08762 | − | 10.6592i | −0.152662 | − | 0.779475i | ||||
\(188\) | − | 2.20822i | − | 0.161051i | ||||||
\(189\) | −12.4124 | − | 5.91041i | −0.902867 | − | 0.429919i | ||||
\(190\) | 8.54983 | 0.620270 | ||||||||
\(191\) | 9.82475 | − | 5.67232i | 0.710894 | − | 0.410435i | −0.100498 | − | 0.994937i | \(-0.532044\pi\) |
0.811392 | + | 0.584502i | \(0.198710\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | −19.1375 | − | 11.0490i | −1.37754 | − | 0.795326i | −0.385681 | − | 0.922632i | \(-0.626033\pi\) |
−0.991863 | + | 0.127307i | \(0.959367\pi\) | |||||||
\(194\) | −6.77492 | − | 11.7345i | −0.486411 | − | 0.842488i | ||||
\(195\) | − | 5.97586i | − | 0.427940i | ||||||
\(196\) | 6.91238 | − | 1.10411i | 0.493741 | − | 0.0788650i | ||||
\(197\) | −12.7251 | −0.906625 | −0.453312 | − | 0.891352i | \(-0.649758\pi\) | ||||
−0.453312 | + | 0.891352i | \(0.649758\pi\) | |||||||
\(198\) | −1.91238 | − | 9.76436i | −0.135907 | − | 0.693923i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 1.63746 | − | 2.83616i | 0.115786 | − | 0.200547i | ||||
\(201\) | 12.8248 | − | 7.40437i | 0.904588 | − | 0.522264i | ||||
\(202\) | 9.82475 | 0.691267 | ||||||||
\(203\) | −1.13746 | + | 2.38876i | −0.0798339 | + | 0.167658i | ||||
\(204\) | − | 5.67232i | − | 0.397142i | ||||||
\(205\) | −7.45017 | + | 4.30136i | −0.520342 | + | 0.300420i | ||||
\(206\) | −6.54983 | + | 11.3446i | −0.456349 | + | 0.790419i | ||||
\(207\) | 14.7371 | + | 8.50848i | 1.02430 | + | 0.591381i | ||||
\(208\) | −2.27492 | + | 1.31342i | −0.157737 | + | 0.0910696i | ||||
\(209\) | −7.00000 | + | 20.4235i | −0.484200 | + | 1.41272i | ||||
\(210\) | −6.00000 | + | 0.476171i | −0.414039 | + | 0.0328589i | ||||
\(211\) | 19.9474i | 1.37323i | 0.727020 | + | 0.686616i | \(0.240905\pi\) | ||||
−0.727020 | + | 0.686616i | \(0.759095\pi\) | |||||||
\(212\) | 11.6873 | − | 6.74766i | 0.802687 | − | 0.463431i | ||||
\(213\) | −8.63746 | + | 14.9605i | −0.591829 | + | 1.02508i | ||||
\(214\) | 7.13746 | − | 12.3624i | 0.487907 | − | 0.845079i | ||||
\(215\) | −6.54983 | − | 11.3446i | −0.446695 | − | 0.773698i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 15.4124 | + | 22.3937i | 1.04626 | + | 1.52018i | ||||
\(218\) | 4.30136i | 0.291325i | ||||||||
\(219\) | 4.54983 | + | 7.88054i | 0.307449 | + | 0.532518i | ||||
\(220\) | −2.86254 | − | 3.28356i | −0.192993 | − | 0.221378i | ||||
\(221\) | 7.45017 | + | 4.30136i | 0.501152 | + | 0.289340i | ||||
\(222\) | −10.9124 | + | 6.30026i | −0.732391 | + | 0.422846i | ||||
\(223\) | 2.82475 | 0.189159 | 0.0945797 | − | 0.995517i | \(-0.469849\pi\) | ||||
0.0945797 | + | 0.995517i | \(0.469849\pi\) | |||||||
\(224\) | 1.50000 | + | 2.17945i | 0.100223 | + | 0.145621i | ||||
\(225\) | −9.82475 | −0.654983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6873 | + | 20.2430i | −0.775713 | + | 1.34357i | 0.158680 | + | 0.987330i | \(0.449276\pi\) |
−0.934393 | + | 0.356244i | \(0.884057\pi\) | |||||||
\(228\) | −5.63746 | + | 9.76436i | −0.373350 | + | 0.646661i | ||||
\(229\) | 3.27492 | + | 5.67232i | 0.216413 | + | 0.374838i | 0.953709 | − | 0.300732i | \(-0.0972310\pi\) |
−0.737296 | + | 0.675570i | \(0.763898\pi\) | |||||||
\(230\) | 7.45017 | 0.491249 | ||||||||
\(231\) | 3.77492 | − | 14.7224i | 0.248371 | − | 0.968665i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 8.91238 | + | 15.4367i | 0.583869 | + | 1.01129i | 0.995015 | + | 0.0997216i | \(0.0317952\pi\) |
−0.411146 | + | 0.911569i | \(0.634871\pi\) | |||||||
\(234\) | 6.82475 | + | 3.94027i | 0.446148 | + | 0.257584i | ||||
\(235\) | −1.45017 | + | 2.51176i | −0.0945984 | + | 0.163849i | ||||
\(236\) | 1.50000 | − | 0.866025i | 0.0976417 | − | 0.0563735i | ||||
\(237\) | 3.72508 | 0.241970 | ||||||||
\(238\) | 3.72508 | − | 7.82300i | 0.241461 | − | 0.507090i | ||||
\(239\) | −12.5498 | −0.811781 | −0.405891 | − | 0.913922i | \(-0.633039\pi\) | ||||
−0.405891 | + | 0.913922i | \(0.633039\pi\) | |||||||
\(240\) | −1.13746 | − | 1.97014i | −0.0734226 | − | 0.127172i | ||||
\(241\) | −3.41238 | − | 1.97014i | −0.219810 | − | 0.126908i | 0.386052 | − | 0.922477i | \(-0.373839\pi\) |
−0.605862 | + | 0.795569i | \(0.707172\pi\) | |||||||
\(242\) | 10.1873 | − | 4.14959i | 0.654864 | − | 0.266745i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 6.92820i | 0.443533i | ||||||||
\(245\) | −8.58762 | − | 3.28356i | −0.548643 | − | 0.209779i | ||||
\(246\) | − | 11.3446i | − | 0.723308i | ||||||
\(247\) | −8.54983 | − | 14.8087i | −0.544013 | − | 0.942258i | ||||
\(248\) | −5.13746 | + | 8.89834i | −0.326229 | + | 0.565045i | ||||
\(249\) | 15.4124 | + | 8.89834i | 0.976720 | + | 0.563909i | ||||
\(250\) | −9.41238 | + | 5.43424i | −0.595291 | + | 0.343691i | ||||
\(251\) | − | 0.894797i | − | 0.0564791i | −0.999601 | − | 0.0282396i | \(-0.991010\pi\) | ||
0.999601 | − | 0.0282396i | \(-0.00899012\pi\) | |||||||
\(252\) | 3.41238 | − | 7.16629i | 0.214959 | − | 0.451434i | ||||
\(253\) | −6.09967 | + | 17.7967i | −0.383483 | + | 1.11887i | ||||
\(254\) | −3.04983 | + | 1.76082i | −0.191364 | + | 0.110484i | ||||
\(255\) | −3.72508 | + | 6.45203i | −0.233274 | + | 0.404042i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −14.2749 | + | 8.24163i | −0.890445 | + | 0.514099i | −0.874088 | − | 0.485768i | \(-0.838540\pi\) |
−0.0163569 | + | 0.999866i | \(0.505207\pi\) | |||||||
\(258\) | 17.2749 | 1.07549 | ||||||||
\(259\) | −19.1873 | + | 1.52274i | −1.19224 | + | 0.0946183i | ||||
\(260\) | 3.45017 | 0.213970 | ||||||||
\(261\) | 1.50000 | + | 2.59808i | 0.0928477 | + | 0.160817i | ||||
\(262\) | −5.13746 | + | 8.89834i | −0.317393 | + | 0.549741i | ||||
\(263\) | −14.5498 | + | 25.2011i | −0.897181 | + | 1.55396i | −0.0660996 | + | 0.997813i | \(0.521056\pi\) |
−0.831082 | + | 0.556150i | \(0.812278\pi\) | |||||||
\(264\) | 5.63746 | − | 1.10411i | 0.346962 | − | 0.0679533i | ||||
\(265\) | −17.7251 | −1.08884 | ||||||||
\(266\) | −14.1873 | + | 9.76436i | −0.869879 | + | 0.598692i | ||||
\(267\) | −4.54983 | −0.278445 | ||||||||
\(268\) | 4.27492 | + | 7.40437i | 0.261132 | + | 0.452294i | ||||
\(269\) | −2.58762 | − | 1.49397i | −0.157770 | − | 0.0910887i | 0.419036 | − | 0.907969i | \(-0.362368\pi\) |
−0.576807 | + | 0.816881i | \(0.695701\pi\) | |||||||
\(270\) | −3.41238 | + | 5.91041i | −0.207671 | + | 0.359696i | ||||
\(271\) | −7.23713 | + | 4.17836i | −0.439624 | + | 0.253817i | −0.703438 | − | 0.710756i | \(-0.748353\pi\) |
0.263814 | + | 0.964574i | \(0.415019\pi\) | |||||||
\(272\) | 3.27492 | 0.198571 | ||||||||
\(273\) | 6.82475 | + | 9.91613i | 0.413053 | + | 0.600152i | ||||
\(274\) | − | 4.30136i | − | 0.259854i | ||||||
\(275\) | −2.08762 | − | 10.6592i | −0.125888 | − | 0.642772i | ||||
\(276\) | −4.91238 | + | 8.50848i | −0.295690 | + | 0.512151i | ||||
\(277\) | −7.45017 | − | 4.30136i | −0.447637 | − | 0.258443i | 0.259195 | − | 0.965825i | \(-0.416543\pi\) |
−0.706832 | + | 0.707382i | \(0.749876\pi\) | |||||||
\(278\) | 0.362541 | − | 0.209313i | 0.0217438 | − | 0.0125538i | ||||
\(279\) | 30.8248 | 1.84543 | ||||||||
\(280\) | −0.274917 | − | 3.46410i | −0.0164294 | − | 0.207020i | ||||
\(281\) | 11.2749 | 0.672605 | 0.336303 | − | 0.941754i | \(-0.390824\pi\) | ||||
0.336303 | + | 0.941754i | \(0.390824\pi\) | |||||||
\(282\) | −1.91238 | − | 3.31233i | −0.113880 | − | 0.197247i | ||||
\(283\) | −5.27492 | − | 3.04547i | −0.313561 | − | 0.181035i | 0.334958 | − | 0.942233i | \(-0.391278\pi\) |
−0.648519 | + | 0.761198i | \(0.724611\pi\) | |||||||
\(284\) | −8.63746 | − | 4.98684i | −0.512539 | − | 0.295914i | ||||
\(285\) | 12.8248 | − | 7.40437i | 0.759673 | − | 0.438597i | ||||
\(286\) | −2.82475 | + | 8.24163i | −0.167031 | + | 0.487338i | ||||
\(287\) | 7.45017 | − | 15.6460i | 0.439769 | − | 0.923554i | ||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | 3.13746 | + | 5.43424i | 0.184556 | + | 0.319661i | ||||
\(290\) | 1.13746 | + | 0.656712i | 0.0667939 | + | 0.0385635i | ||||
\(291\) | −20.3248 | − | 11.7345i | −1.19146 | − | 0.687889i | ||||
\(292\) | −4.54983 | + | 2.62685i | −0.266259 | + | 0.153725i | ||||
\(293\) | 6.09967 | 0.356346 | 0.178173 | − | 0.983999i | \(-0.442981\pi\) | ||||
0.178173 | + | 0.983999i | \(0.442981\pi\) | |||||||
\(294\) | 9.41238 | − | 7.64246i | 0.548941 | − | 0.445717i | ||||
\(295\) | −2.27492 | −0.132451 | ||||||||
\(296\) | −3.63746 | − | 6.30026i | −0.211423 | − | 0.366195i | ||||
\(297\) | −11.3248 | − | 12.9904i | −0.657129 | − | 0.753778i | ||||
\(298\) | 3.63746 | − | 6.30026i | 0.210712 | − | 0.364964i | ||||
\(299\) | −7.45017 | − | 12.9041i | −0.430854 | − | 0.746261i | ||||
\(300\) | − | 5.67232i | − | 0.327492i | ||||||
\(301\) | 23.8248 | + | 11.3446i | 1.37324 | + | 0.653895i | ||||
\(302\) | − | 12.1244i | − | 0.697678i | ||||||
\(303\) | 14.7371 | − | 8.50848i | 0.846626 | − | 0.488800i | ||||
\(304\) | −5.63746 | − | 3.25479i | −0.323330 | − | 0.186675i | ||||
\(305\) | 4.54983 | − | 7.88054i | 0.260523 | − | 0.451239i | ||||
\(306\) | −4.91238 | − | 8.50848i | −0.280822 | − | 0.486398i | ||||
\(307\) | − | 1.78959i | − | 0.102138i | −0.998695 | − | 0.0510688i | \(-0.983737\pi\) | ||
0.998695 | − | 0.0510688i | \(-0.0162628\pi\) | |||||||
\(308\) | 8.50000 | + | 2.17945i | 0.484332 | + | 0.124186i | ||||
\(309\) | 22.6893i | 1.29075i | ||||||||
\(310\) | 11.6873 | − | 6.74766i | 0.663794 | − | 0.383241i | ||||
\(311\) | 15.3625 | + | 8.86957i | 0.871130 | + | 0.502947i | 0.867724 | − | 0.497047i | \(-0.165582\pi\) |
0.00340628 | + | 0.999994i | \(0.498916\pi\) | |||||||
\(312\) | −2.27492 | + | 3.94027i | −0.128792 | + | 0.223074i | ||||
\(313\) | −3.50000 | − | 6.06218i | −0.197832 | − | 0.342655i | 0.749993 | − | 0.661445i | \(-0.230057\pi\) |
−0.947825 | + | 0.318791i | \(0.896723\pi\) | |||||||
\(314\) | −17.2749 | −0.974880 | ||||||||
\(315\) | −8.58762 | + | 5.91041i | −0.483858 | + | 0.333014i | ||||
\(316\) | 2.15068i | 0.120985i | ||||||||
\(317\) | 11.6873 | − | 6.74766i | 0.656424 | − | 0.378986i | −0.134489 | − | 0.990915i | \(-0.542939\pi\) |
0.790913 | + | 0.611929i | \(0.209606\pi\) | |||||||
\(318\) | 11.6873 | − | 20.2430i | 0.655391 | − | 1.13517i | ||||
\(319\) | −2.50000 | + | 2.17945i | −0.139973 | + | 0.122026i | ||||
\(320\) | 1.13746 | − | 0.656712i | 0.0635859 | − | 0.0367113i | ||||
\(321\) | − | 24.7249i | − | 1.38001i | ||||||
\(322\) | −12.3625 | + | 8.50848i | −0.688937 | + | 0.474159i | ||||
\(323\) | 21.3183i | 1.18618i | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 7.45017 | + | 4.30136i | 0.413261 | + | 0.238596i | ||||
\(326\) | 8.27492 | − | 14.3326i | 0.458305 | − | 0.793808i | ||||
\(327\) | 3.72508 | + | 6.45203i | 0.205998 | + | 0.356798i | ||||
\(328\) | 6.54983 | 0.361654 | ||||||||
\(329\) | −0.462210 | − | 5.82409i | −0.0254825 | − | 0.321093i | ||||
\(330\) | −7.13746 | − | 2.44631i | −0.392904 | − | 0.134665i | ||||
\(331\) | 2.54983 | + | 4.41644i | 0.140152 | + | 0.242750i | 0.927554 | − | 0.373690i | \(-0.121908\pi\) |
−0.787402 | + | 0.616440i | \(0.788574\pi\) | |||||||
\(332\) | −5.13746 | + | 8.89834i | −0.281955 | + | 0.488360i | ||||
\(333\) | −10.9124 | + | 18.9008i | −0.597995 | + | 1.03576i | ||||
\(334\) | 3.72508 | + | 6.45203i | 0.203827 | + | 0.353040i | ||||
\(335\) | − | 11.2296i | − | 0.613536i | ||||||
\(336\) | 4.13746 | + | 1.97014i | 0.225717 | + | 0.107480i | ||||
\(337\) | 9.19397i | 0.500827i | 0.968139 | + | 0.250414i | \(0.0805666\pi\) | ||||
−0.968139 | + | 0.250414i | \(0.919433\pi\) | |||||||
\(338\) | 3.04983 | + | 5.28247i | 0.165889 | + | 0.287328i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.72508 | − | 2.15068i | −0.202021 | − | 0.116637i | ||||
\(341\) | 6.54983 | + | 33.4427i | 0.354693 | + | 1.81102i | ||||
\(342\) | 19.5287i | 1.05599i | ||||||||
\(343\) | 18.0000 | − | 4.35890i | 0.971909 | − | 0.235358i | ||||
\(344\) | 9.97368i | 0.537745i | ||||||||
\(345\) | 11.1752 | − | 6.45203i | 0.601655 | − | 0.347366i | ||||
\(346\) | −7.00000 | + | 12.1244i | −0.376322 | + | 0.651809i | ||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | −1.50000 | + | 0.866025i | −0.0804084 | + | 0.0464238i | ||||
\(349\) | − | 25.3161i | − | 1.35514i | −0.735457 | − | 0.677571i | \(-0.763033\pi\) | ||
0.735457 | − | 0.677571i | \(-0.236967\pi\) | |||||||
\(350\) | 3.72508 | − | 7.82300i | 0.199114 | − | 0.418157i | ||||
\(351\) | 13.6495 | 0.728557 | ||||||||
\(352\) | 0.637459 | + | 3.25479i | 0.0339767 | + | 0.173481i | ||||
\(353\) | −31.6495 | − | 18.2728i | −1.68453 | − | 0.972566i | −0.958581 | − | 0.284820i | \(-0.908066\pi\) |
−0.725952 | − | 0.687745i | \(-0.758601\pi\) | |||||||
\(354\) | 1.50000 | − | 2.59808i | 0.0797241 | − | 0.138086i | ||||
\(355\) | 6.54983 | + | 11.3446i | 0.347629 | + | 0.602111i | ||||
\(356\) | − | 2.62685i | − | 0.139223i | ||||||
\(357\) | −1.18729 | − | 14.9605i | −0.0628382 | − | 0.791795i | ||||
\(358\) | − | 14.2750i | − | 0.754459i | ||||||
\(359\) | −12.8248 | − | 22.2131i | −0.676865 | − | 1.17236i | −0.975920 | − | 0.218128i | \(-0.930005\pi\) |
0.299056 | − | 0.954236i | \(-0.403328\pi\) | |||||||
\(360\) | −3.41238 | − | 1.97014i | −0.179848 | − | 0.103835i | ||||
\(361\) | 11.6873 | − | 20.2430i | 0.615121 | − | 1.06542i | ||||
\(362\) | −3.27492 | − | 5.67232i | −0.172126 | − | 0.298131i | ||||
\(363\) | 11.6873 | − | 15.0468i | 0.613424 | − | 0.789754i | ||||
\(364\) | −5.72508 | + | 3.94027i | −0.300076 | + | 0.206526i | ||||
\(365\) | 6.90033 | 0.361180 | ||||||||
\(366\) | 6.00000 | + | 10.3923i | 0.313625 | + | 0.543214i | ||||
\(367\) | −8.86254 | + | 15.3504i | −0.462621 | + | 0.801283i | −0.999091 | − | 0.0426367i | \(-0.986424\pi\) |
0.536470 | + | 0.843920i | \(0.319758\pi\) | |||||||
\(368\) | −4.91238 | − | 2.83616i | −0.256075 | − | 0.147845i | ||||
\(369\) | −9.82475 | − | 17.0170i | −0.511456 | − | 0.885868i | ||||
\(370\) | 9.55505i | 0.496743i | ||||||||
\(371\) | 29.4124 | − | 20.2430i | 1.52701 | − | 1.05096i | ||||
\(372\) | 17.7967i | 0.922715i | ||||||||
\(373\) | −7.45017 | + | 4.30136i | −0.385755 | + | 0.222716i | −0.680319 | − | 0.732916i | \(-0.738159\pi\) |
0.294564 | + | 0.955632i | \(0.404826\pi\) | |||||||
\(374\) | 8.18729 | − | 7.13752i | 0.423355 | − | 0.369072i | ||||
\(375\) | −9.41238 | + | 16.3027i | −0.486053 | + | 0.841868i | ||||
\(376\) | 1.91238 | − | 1.10411i | 0.0986233 | − | 0.0569402i | ||||
\(377\) | − | 2.62685i | − | 0.135290i | ||||||
\(378\) | −1.08762 | − | 13.7046i | −0.0559414 | − | 0.704890i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 4.27492 | + | 7.40437i | 0.219299 | + | 0.379836i | ||||
\(381\) | −3.04983 | + | 5.28247i | −0.156248 | + | 0.270629i | ||||
\(382\) | 9.82475 | + | 5.67232i | 0.502678 | + | 0.290221i | ||||
\(383\) | 26.0120 | − | 15.0181i | 1.32915 | − | 0.767387i | 0.343985 | − | 0.938975i | \(-0.388223\pi\) |
0.985169 | + | 0.171588i | \(0.0548899\pi\) | |||||||
\(384\) | 1.73205i | 0.0883883i | ||||||||
\(385\) | −8.23713 | − | 8.06109i | −0.419803 | − | 0.410831i | ||||
\(386\) | − | 22.0980i | − | 1.12476i | ||||||
\(387\) | 25.9124 | − | 14.9605i | 1.31720 | − | 0.760486i | ||||
\(388\) | 6.77492 | − | 11.7345i | 0.343944 | − | 0.595729i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 5.17525 | − | 2.98793i | 0.262059 | − | 0.151300i | ||||
\(391\) | 18.5764i | 0.939448i | ||||||||
\(392\) | 4.41238 | + | 5.43424i | 0.222859 | + | 0.274470i | ||||
\(393\) | 17.7967i | 0.897724i | ||||||||
\(394\) | −6.36254 | − | 11.0202i | −0.320540 | − | 0.555192i | ||||
\(395\) | 1.41238 | − | 2.44631i | 0.0710643 | − | 0.123087i | ||||
\(396\) | 7.50000 | − | 6.53835i | 0.376889 | − | 0.328564i | ||||
\(397\) | 5.36254 | + | 9.28819i | 0.269138 | + | 0.466161i | 0.968640 | − | 0.248470i | \(-0.0799278\pi\) |
−0.699501 | + | 0.714631i | \(0.746594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.8248 | + | 26.9331i | −0.642041 | + | 1.34834i | ||||
\(400\) | 3.27492 | 0.163746 | ||||||||
\(401\) | −19.6495 | + | 11.3446i | −0.981249 | + | 0.566525i | −0.902647 | − | 0.430381i | \(-0.858379\pi\) |
−0.0786023 | + | 0.996906i | \(0.525046\pi\) | |||||||
\(402\) | 12.8248 | + | 7.40437i | 0.639640 | + | 0.369297i | ||||
\(403\) | −23.3746 | − | 13.4953i | −1.16437 | − | 0.672250i | ||||
\(404\) | 4.91238 | + | 8.50848i | 0.244400 | + | 0.423313i | ||||
\(405\) | 11.8208i | 0.587381i | ||||||||
\(406\) | −2.63746 | + | 0.209313i | −0.130895 | + | 0.0103880i | ||||
\(407\) | −22.8248 | − | 7.82300i | −1.13138 | − | 0.387772i | ||||
\(408\) | 4.91238 | − | 2.83616i | 0.243199 | − | 0.140411i | ||||
\(409\) | −12.3127 | − | 7.10874i | −0.608824 | − | 0.351505i | 0.163681 | − | 0.986513i | \(-0.447663\pi\) |
−0.772505 | + | 0.635009i | \(0.780997\pi\) | |||||||
\(410\) | −7.45017 | − | 4.30136i | −0.367937 | − | 0.212429i | ||||
\(411\) | −3.72508 | − | 6.45203i | −0.183745 | − | 0.318255i | ||||
\(412\) | −13.0997 | −0.645374 | ||||||||
\(413\) | 3.77492 | − | 2.59808i | 0.185752 | − | 0.127843i | ||||
\(414\) | 17.0170i | 0.836338i | ||||||||
\(415\) | 11.6873 | − | 6.74766i | 0.573707 | − | 0.331230i | ||||
\(416\) | −2.27492 | − | 1.31342i | −0.111537 | − | 0.0643959i | ||||
\(417\) | 0.362541 | − | 0.627940i | 0.0177537 | − | 0.0307504i | ||||
\(418\) | −21.1873 | + | 4.14959i | −1.03630 | + | 0.202963i | ||||
\(419\) | − | 27.2942i | − | 1.33341i | −0.745322 | − | 0.666704i | \(-0.767704\pi\) | ||
0.745322 | − | 0.666704i | \(-0.232296\pi\) | |||||||
\(420\) | −3.41238 | − | 4.95807i | −0.166507 | − | 0.241929i | ||||
\(421\) | 22.3746 | 1.09047 | 0.545235 | − | 0.838283i | \(-0.316440\pi\) | ||||
0.545235 | + | 0.838283i | \(0.316440\pi\) | |||||||
\(422\) | −17.2749 | + | 9.97368i | −0.840930 | + | 0.485511i | ||||
\(423\) | −5.73713 | − | 3.31233i | −0.278949 | − | 0.161051i | ||||
\(424\) | 11.6873 | + | 6.74766i | 0.567585 | + | 0.327695i | ||||
\(425\) | −5.36254 | − | 9.28819i | −0.260121 | − | 0.450544i | ||||
\(426\) | −17.2749 | −0.836972 | ||||||||
\(427\) | 1.45017 | + | 18.2728i | 0.0701784 | + | 0.884285i | ||||
\(428\) | 14.2749 | 0.690004 | ||||||||
\(429\) | 2.90033 | + | 14.8087i | 0.140029 | + | 0.714973i | ||||
\(430\) | 6.54983 | − | 11.3446i | 0.315861 | − | 0.547087i | ||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 4.50000 | − | 2.59808i | 0.216506 | − | 0.125000i | ||||
\(433\) | −3.27492 | −0.157382 | −0.0786912 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786912 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(434\) | −11.6873 | + | 24.5443i | −0.561008 | + | 1.17817i | ||||
\(435\) | 2.27492 | 0.109074 | ||||||||
\(436\) | −3.72508 | + | 2.15068i | −0.178399 | + | 0.102999i | ||||
\(437\) | 18.4622 | − | 31.9775i | 0.883167 | − | 1.52969i | ||||
\(438\) | −4.54983 | + | 7.88054i | −0.217399 | + | 0.376547i | ||||
\(439\) | −2.32475 | + | 1.34220i | −0.110954 | + | 0.0640595i | −0.554450 | − | 0.832217i | \(-0.687071\pi\) |
0.443496 | + | 0.896276i | \(0.353738\pi\) | |||||||
\(440\) | 1.41238 | − | 4.12081i | 0.0673324 | − | 0.196452i | ||||
\(441\) | 7.50000 | − | 19.6150i | 0.357143 | − | 0.934050i | ||||
\(442\) | 8.60271i | 0.409189i | ||||||||
\(443\) | −3.04983 | + | 1.76082i | −0.144902 | + | 0.0836592i | −0.570698 | − | 0.821160i | \(-0.693327\pi\) |
0.425796 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(444\) | −10.9124 | − | 6.30026i | −0.517878 | − | 0.298997i | ||||
\(445\) | −1.72508 | + | 2.98793i | −0.0817768 | + | 0.141642i | ||||
\(446\) | 1.41238 | + | 2.44631i | 0.0668779 | + | 0.115836i | ||||
\(447\) | − | 12.6005i | − | 0.595984i | ||||||
\(448\) | −1.13746 | + | 2.38876i | −0.0537399 | + | 0.112858i | ||||
\(449\) | − | 4.30136i | − | 0.202993i | −0.994836 | − | 0.101497i | \(-0.967637\pi\) | ||
0.994836 | − | 0.101497i | \(-0.0323631\pi\) | |||||||
\(450\) | −4.91238 | − | 8.50848i | −0.231572 | − | 0.401094i | ||||
\(451\) | 16.3746 | − | 14.2750i | 0.771049 | − | 0.672185i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5000 | − | 18.1865i | −0.493333 | − | 0.854478i | ||||
\(454\) | −23.3746 | −1.09702 | ||||||||
\(455\) | 9.09967 | − | 0.722166i | 0.426599 | − | 0.0338557i | ||||
\(456\) | −11.2749 | −0.527996 | ||||||||
\(457\) | −31.3368 | + | 18.0923i | −1.46587 | + | 0.846322i | −0.999272 | − | 0.0381453i | \(-0.987855\pi\) |
−0.466601 | + | 0.884468i | \(0.654522\pi\) | |||||||
\(458\) | −3.27492 | + | 5.67232i | −0.153027 | + | 0.265050i | ||||
\(459\) | −14.7371 | − | 8.50848i | −0.687870 | − | 0.397142i | ||||
\(460\) | 3.72508 | + | 6.45203i | 0.173683 | + | 0.300828i | ||||
\(461\) | −9.82475 | −0.457584 | −0.228792 | − | 0.973475i | \(-0.573478\pi\) | ||||
−0.228792 | + | 0.973475i | \(0.573478\pi\) | |||||||
\(462\) | 14.6375 | − | 4.09204i | 0.680996 | − | 0.190379i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | 11.6873 | − | 20.2430i | 0.541985 | − | 0.938746i | ||||
\(466\) | −8.91238 | + | 15.4367i | −0.412858 | + | 0.715091i | ||||
\(467\) | 1.81271 | − | 1.04657i | 0.0838821 | − | 0.0484293i | −0.457472 | − | 0.889224i | \(-0.651245\pi\) |
0.541354 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(468\) | 7.88054i | 0.364278i | ||||||||
\(469\) | 12.8248 | + | 18.6339i | 0.592192 | + | 0.860435i | ||||
\(470\) | −2.90033 | −0.133782 | ||||||||
\(471\) | −25.9124 | + | 14.9605i | −1.19398 | + | 0.689344i | ||||
\(472\) | 1.50000 | + | 0.866025i | 0.0690431 | + | 0.0398621i | ||||
\(473\) | 21.7371 | + | 24.9342i | 0.999474 | + | 1.14648i | ||||
\(474\) | 1.86254 | + | 3.22602i | 0.0855494 | + | 0.148176i | ||||
\(475\) | 21.3183i | 0.978152i | ||||||||
\(476\) | 8.63746 | − | 0.685484i | 0.395897 | − | 0.0314191i | ||||
\(477\) | − | 40.4860i | − | 1.85373i | ||||||
\(478\) | −6.27492 | − | 10.8685i | −0.287008 | − | 0.497112i | ||||
\(479\) | 14.0000 | − | 24.2487i | 0.639676 | − | 1.10795i | −0.345827 | − | 0.938298i | \(-0.612402\pi\) |
0.985504 | − | 0.169654i | \(-0.0542649\pi\) | |||||||
\(480\) | 1.13746 | − | 1.97014i | 0.0519176 | − | 0.0899240i | ||||
\(481\) | 16.5498 | − | 9.55505i | 0.754607 | − | 0.435673i | ||||
\(482\) | − | 3.94027i | − | 0.179474i | ||||||
\(483\) | −11.1752 | + | 23.4690i | −0.508491 | + | 1.06788i | ||||
\(484\) | 8.68729 | + | 6.74766i | 0.394877 | + | 0.306712i | ||||
\(485\) | −15.4124 | + | 8.89834i | −0.699840 | + | 0.404053i | ||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 9.68729 | − | 16.7789i | 0.438973 | − | 0.760324i | −0.558637 | − | 0.829412i | \(-0.688676\pi\) |
0.997611 | + | 0.0690882i | \(0.0220090\pi\) | |||||||
\(488\) | −6.00000 | + | 3.46410i | −0.271607 | + | 0.156813i | ||||
\(489\) | − | 28.6652i | − | 1.29628i | ||||||
\(490\) | −1.45017 | − | 9.07888i | −0.0655118 | − | 0.410142i | ||||
\(491\) | −15.3746 | −0.693845 | −0.346923 | − | 0.937894i | \(-0.612773\pi\) | ||||
−0.346923 | + | 0.937894i | \(0.612773\pi\) | |||||||
\(492\) | 9.82475 | − | 5.67232i | 0.442934 | − | 0.255728i | ||||
\(493\) | −1.63746 | + | 2.83616i | −0.0737474 | + | 0.127734i | ||||
\(494\) | 8.54983 | − | 14.8087i | 0.384675 | − | 0.666277i | ||||
\(495\) | −12.8248 | + | 2.51176i | −0.576430 | + | 0.112895i | ||||
\(496\) | −10.2749 | −0.461357 | ||||||||
\(497\) | −23.8248 | − | 11.3446i | −1.06869 | − | 0.508877i | ||||
\(498\) | 17.7967i | 0.797488i | ||||||||
\(499\) | −1.72508 | − | 2.98793i | −0.0772253 | − | 0.133758i | 0.824827 | − | 0.565386i | \(-0.191273\pi\) |
−0.902052 | + | 0.431628i | \(0.857939\pi\) | |||||||
\(500\) | −9.41238 | − | 5.43424i | −0.420934 | − | 0.243026i | ||||
\(501\) | 11.1752 | + | 6.45203i | 0.499273 | + | 0.288256i | ||||
\(502\) | 0.774917 | − | 0.447399i | 0.0345862 | − | 0.0199684i | ||||
\(503\) | 33.6495 | 1.50036 | 0.750179 | − | 0.661235i | \(-0.229967\pi\) | ||||
0.750179 | + | 0.661235i | \(0.229967\pi\) | |||||||
\(504\) | 7.91238 | − | 0.627940i | 0.352445 | − | 0.0279707i | ||||
\(505\) | − | 12.9041i | − | 0.574223i | ||||||
\(506\) | −18.4622 | + | 3.61587i | −0.820745 | + | 0.160745i | ||||
\(507\) | 9.14950 | + | 5.28247i | 0.406344 | + | 0.234603i | ||||
\(508\) | −3.04983 | − | 1.76082i | −0.135315 | − | 0.0781239i | ||||
\(509\) | 20.5876 | − | 11.8863i | 0.912530 | − | 0.526850i | 0.0312860 | − | 0.999510i | \(-0.490040\pi\) |
0.881244 | + | 0.472661i | \(0.156706\pi\) | |||||||
\(510\) | −7.45017 | −0.329899 | ||||||||
\(511\) | −11.4502 | + | 7.88054i | −0.506526 | + | 0.348615i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.9124 | + | 29.2931i | 0.746700 | + | 1.29332i | ||||
\(514\) | −14.2749 | − | 8.24163i | −0.629640 | − | 0.363523i | ||||
\(515\) | 14.9003 | + | 8.60271i | 0.656587 | + | 0.379081i | ||||
\(516\) | 8.63746 | + | 14.9605i | 0.380243 | + | 0.658600i | ||||
\(517\) | 2.37459 | − | 6.92820i | 0.104434 | − | 0.304702i | ||||
\(518\) | −10.9124 | − | 15.8553i | −0.479462 | − | 0.696643i | ||||
\(519\) | 24.2487i | 1.06440i | ||||||||
\(520\) | 1.72508 | + | 2.98793i | 0.0756499 | + | 0.131029i | ||||
\(521\) | 15.0997 | + | 8.71780i | 0.661529 | + | 0.381934i | 0.792859 | − | 0.609405i | \(-0.208592\pi\) |
−0.131331 | + | 0.991339i | \(0.541925\pi\) | |||||||
\(522\) | −1.50000 | + | 2.59808i | −0.0656532 | + | 0.113715i | ||||
\(523\) | 24.0997 | − | 13.9140i | 1.05380 | − | 0.608415i | 0.130093 | − | 0.991502i | \(-0.458472\pi\) |
0.923712 | + | 0.383087i | \(0.125139\pi\) | |||||||
\(524\) | −10.2749 | −0.448862 | ||||||||
\(525\) | −1.18729 | − | 14.9605i | −0.0518177 | − | 0.652930i | ||||
\(526\) | −29.0997 | −1.26881 | ||||||||
\(527\) | 16.8248 | + | 29.1413i | 0.732898 | + | 1.26942i | ||||
\(528\) | 3.77492 | + | 4.33013i | 0.164282 | + | 0.188445i | ||||
\(529\) | 4.58762 | − | 7.94600i | 0.199462 | − | 0.345478i | ||||
\(530\) | −8.86254 | − | 15.3504i | −0.384964 | − | 0.666778i | ||||
\(531\) | − | 5.19615i | − | 0.225494i | ||||||
\(532\) | −15.5498 | − | 7.40437i | −0.674171 | − | 0.321020i | ||||
\(533\) | 17.2054i | 0.745249i | ||||||||
\(534\) | −2.27492 | − | 3.94027i | −0.0984453 | − | 0.170512i | ||||
\(535\) | −16.2371 | − | 9.37451i | −0.701992 | − | 0.405295i | ||||
\(536\) | −4.27492 | + | 7.40437i | −0.184648 | + | 0.319820i | ||||
\(537\) | −12.3625 | − | 21.4125i | −0.533483 | − | 0.924020i | ||||
\(538\) | − | 2.98793i | − | 0.128819i | ||||||
\(539\) | 22.8746 | + | 3.96904i | 0.985278 | + | 0.170959i | ||||
\(540\) | −6.82475 | −0.293691 | ||||||||
\(541\) | 7.45017 | − | 4.30136i | 0.320308 | − | 0.184930i | −0.331222 | − | 0.943553i | \(-0.607461\pi\) |
0.651530 | + | 0.758623i | \(0.274128\pi\) | |||||||
\(542\) | −7.23713 | − | 4.17836i | −0.310861 | − | 0.179476i | ||||
\(543\) | −9.82475 | − | 5.67232i | −0.421620 | − | 0.243423i | ||||
\(544\) | 1.63746 | + | 2.83616i | 0.0702055 | + | 0.121599i | ||||
\(545\) | 5.64950 | 0.241998 | ||||||||
\(546\) | −5.17525 | + | 10.8685i | −0.221480 | + | 0.465128i | ||||
\(547\) | 17.0170i | 0.727593i | 0.931478 | + | 0.363797i | \(0.118520\pi\) | ||||
−0.931478 | + | 0.363797i | \(0.881480\pi\) | |||||||
\(548\) | 3.72508 | − | 2.15068i | 0.159128 | − | 0.0918724i | ||||
\(549\) | 18.0000 | + | 10.3923i | 0.768221 | + | 0.443533i | ||||
\(550\) | 8.18729 | − | 7.13752i | 0.349107 | − | 0.304345i | ||||
\(551\) | 5.63746 | − | 3.25479i | 0.240164 | − | 0.138659i | ||||
\(552\) | −9.82475 | −0.418169 | ||||||||
\(553\) | 0.450166 | + | 5.67232i | 0.0191430 | + | 0.241212i | ||||
\(554\) | − | 8.60271i | − | 0.365494i | ||||||
\(555\) | 8.27492 | + | 14.3326i | 0.351251 | + | 0.608384i | ||||
\(556\) | 0.362541 | + | 0.209313i | 0.0153752 | + | 0.00887686i | ||||
\(557\) | −7.32475 | + | 12.6868i | −0.310360 | + | 0.537559i | −0.978440 | − | 0.206530i | \(-0.933783\pi\) |
0.668081 | + | 0.744089i | \(0.267116\pi\) | |||||||
\(558\) | 15.4124 | + | 26.6950i | 0.652458 | + | 1.13009i | ||||
\(559\) | −26.1993 | −1.10811 | ||||||||
\(560\) | 2.86254 | − | 1.97014i | 0.120964 | − | 0.0832534i | ||||
\(561\) | 6.09967 | − | 17.7967i | 0.257528 | − | 0.751376i | ||||
\(562\) | 5.63746 | + | 9.76436i | 0.237802 | + | 0.411885i | ||||
\(563\) | −19.1375 | + | 33.1471i | −0.806548 | + | 1.39698i | 0.108694 | + | 0.994075i | \(0.465333\pi\) |
−0.915241 | + | 0.402906i | \(0.868000\pi\) | |||||||
\(564\) | 1.91238 | − | 3.31233i | 0.0805255 | − | 0.139474i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 6.09095i | − | 0.256022i | ||||||
\(567\) | −13.5000 | − | 19.6150i | −0.566947 | − | 0.823754i | ||||
\(568\) | − | 9.97368i | − | 0.418486i | ||||||
\(569\) | −4.18729 | − | 7.25260i | −0.175540 | − | 0.304045i | 0.764808 | − | 0.644259i | \(-0.222834\pi\) |
−0.940348 | + | 0.340214i | \(0.889501\pi\) | |||||||
\(570\) | 12.8248 | + | 7.40437i | 0.537170 | + | 0.310135i | ||||
\(571\) | −18.4622 | − | 10.6592i | −0.772619 | − | 0.446072i | 0.0611888 | − | 0.998126i | \(-0.480511\pi\) |
−0.833808 | + | 0.552054i | \(0.813844\pi\) | |||||||
\(572\) | −8.54983 | + | 1.67451i | −0.357487 | + | 0.0700147i | ||||
\(573\) | 19.6495 | 0.820870 | ||||||||
\(574\) | 17.2749 | − | 1.37097i | 0.721041 | − | 0.0572231i | ||||
\(575\) | 18.5764i | 0.774689i | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | 18.6873 | − | 32.3673i | 0.777962 | − | 1.34747i | −0.155152 | − | 0.987891i | \(-0.549587\pi\) |
0.933114 | − | 0.359579i | \(-0.117080\pi\) | |||||||
\(578\) | −3.13746 | + | 5.43424i | −0.130501 | + | 0.226034i | ||||
\(579\) | −19.1375 | − | 33.1471i | −0.795326 | − | 1.37754i | ||||
\(580\) | 1.31342i | 0.0545370i | ||||||||
\(581\) | −11.6873 | + | 24.5443i | −0.484871 | + | 1.01827i | ||||
\(582\) | − | 23.4690i | − | 0.972821i | ||||||
\(583\) | 43.9244 | − | 8.60271i | 1.81916 | − | 0.356288i | ||||
\(584\) | −4.54983 | − | 2.62685i | −0.188273 | − | 0.108700i | ||||
\(585\) | 5.17525 | − | 8.96379i | 0.213970 | − | 0.370607i | ||||
\(586\) | 3.04983 | + | 5.28247i | 0.125987 | + | 0.218217i | ||||
\(587\) | 13.3802i | 0.552261i | 0.961120 | + | 0.276131i | \(0.0890523\pi\) | ||||
−0.961120 | + | 0.276131i | \(0.910948\pi\) | |||||||
\(588\) | 11.3248 | + | 4.33013i | 0.467025 | + | 0.178571i | ||||
\(589\) | − | 66.8854i | − | 2.75596i | ||||||
\(590\) | −1.13746 | − | 1.97014i | −0.0468284 | − | 0.0811092i | ||||
\(591\) | −19.0876 | − | 11.0202i | −0.785160 | − | 0.453312i | ||||
\(592\) | 3.63746 | − | 6.30026i | 0.149499 | − | 0.258939i | ||||
\(593\) | 4.91238 | + | 8.50848i | 0.201727 | + | 0.349402i | 0.949085 | − | 0.315020i | \(-0.102011\pi\) |
−0.747358 | + | 0.664422i | \(0.768678\pi\) | |||||||
\(594\) | 5.58762 | − | 16.3027i | 0.229263 | − | 0.668908i | ||||
\(595\) | −10.2749 | − | 4.89261i | −0.421231 | − | 0.200578i | ||||
\(596\) | 7.27492 | 0.297992 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.45017 | − | 12.9041i | 0.304660 | − | 0.527686i | ||||
\(599\) | 6.09967 | + | 3.52165i | 0.249226 | + | 0.143891i | 0.619410 | − | 0.785068i | \(-0.287372\pi\) |
−0.370184 | + | 0.928958i | \(0.620705\pi\) | |||||||
\(600\) | 4.91238 | − | 2.83616i | 0.200547 | − | 0.115786i | ||||
\(601\) | − | 20.4235i | − | 0.833093i | −0.909114 | − | 0.416547i | \(-0.863240\pi\) | ||
0.909114 | − | 0.416547i | \(-0.136760\pi\) | |||||||
\(602\) | 2.08762 | + | 26.3052i | 0.0850852 | + | 1.07212i | ||||
\(603\) | 25.6495 | 1.04453 | ||||||||
\(604\) | 10.5000 | − | 6.06218i | 0.427239 | − | 0.246667i | ||||
\(605\) | −5.45017 | − | 13.3802i | −0.221581 | − | 0.543984i | ||||
\(606\) | 14.7371 | + | 8.50848i | 0.598655 | + | 0.345634i | ||||
\(607\) | −22.1375 | + | 12.7811i | −0.898532 | + | 0.518768i | −0.876724 | − | 0.480995i | \(-0.840276\pi\) |
−0.0218082 | + | 0.999762i | \(0.506942\pi\) | |||||||
\(608\) | − | 6.50958i | − | 0.263998i | ||||||
\(609\) | −3.77492 | + | 2.59808i | −0.152967 | + | 0.105279i | ||||
\(610\) | 9.09967 | 0.368435 | ||||||||
\(611\) | 2.90033 | + | 5.02352i | 0.117335 | + | 0.203230i | ||||
\(612\) | 4.91238 | − | 8.50848i | 0.198571 | − | 0.343935i | ||||
\(613\) | 30.8248 | + | 17.7967i | 1.24500 | + | 0.718801i | 0.970108 | − | 0.242674i | \(-0.0780245\pi\) |
0.274892 | + | 0.961475i | \(0.411358\pi\) | |||||||
\(614\) | 1.54983 | − | 0.894797i | 0.0625462 | − | 0.0361111i | ||||
\(615\) | −14.9003 | −0.600839 | ||||||||
\(616\) | 2.36254 | + | 8.45094i | 0.0951895 | + | 0.340498i | ||||
\(617\) | − | 31.2920i | − | 1.25977i | −0.776689 | − | 0.629884i | \(-0.783102\pi\) | ||
0.776689 | − | 0.629884i | \(-0.216898\pi\) | |||||||
\(618\) | −19.6495 | + | 11.3446i | −0.790419 | + | 0.456349i | ||||
\(619\) | −6.54983 | + | 11.3446i | −0.263260 | + | 0.455980i | −0.967106 | − | 0.254373i | \(-0.918131\pi\) |
0.703846 | + | 0.710352i | \(0.251464\pi\) | |||||||
\(620\) | 11.6873 | + | 6.74766i | 0.469373 | + | 0.270993i | ||||
\(621\) | 14.7371 | + | 25.5255i | 0.591381 | + | 1.02430i | ||||
\(622\) | 17.7391i | 0.711275i | ||||||||
\(623\) | −0.549834 | − | 6.92820i | −0.0220287 | − | 0.277573i | ||||
\(624\) | −4.54983 | −0.182139 | ||||||||
\(625\) | −1.04983 | − | 1.81837i | −0.0419934 | − | 0.0727347i | ||||
\(626\) | 3.50000 | − | 6.06218i | 0.139888 | − | 0.242293i | ||||
\(627\) | −28.1873 | + | 24.5731i | −1.12569 | + | 0.981356i | ||||
\(628\) | −8.63746 | − | 14.9605i | −0.344672 | − | 0.596990i | ||||
\(629\) | −23.8248 | −0.949955 | ||||||||
\(630\) | −9.41238 | − | 4.48190i | −0.374998 | − | 0.178563i | ||||
\(631\) | −27.9244 | −1.11165 | −0.555827 | − | 0.831298i | \(-0.687598\pi\) | ||||
−0.555827 | + | 0.831298i | \(0.687598\pi\) | |||||||
\(632\) | −1.86254 | + | 1.07534i | −0.0740879 | + | 0.0427747i | ||||
\(633\) | −17.2749 | + | 29.9210i | −0.686616 | + | 1.18925i | ||||
\(634\) | 11.6873 | + | 6.74766i | 0.464162 | + | 0.267984i | ||||
\(635\) | 2.31271 | + | 4.00573i | 0.0917770 | + | 0.158962i | ||||
\(636\) | 23.3746 | 0.926863 | ||||||||
\(637\) | −14.2749 | + | 11.5906i | −0.565593 | + | 0.459238i | ||||
\(638\) | −3.13746 | − | 1.07534i | −0.124213 | − | 0.0425731i | ||||
\(639\) | −25.9124 | + | 14.9605i | −1.02508 | + | 0.591829i | ||||
\(640\) | 1.13746 | + | 0.656712i | 0.0449620 | + | 0.0259588i | ||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 21.4124 | − | 12.3624i | 0.845079 | − | 0.487907i | ||||
\(643\) | −33.6495 | −1.32701 | −0.663503 | − | 0.748173i | \(-0.730931\pi\) | ||||
−0.663503 | + | 0.748173i | \(0.730931\pi\) | |||||||
\(644\) | −13.5498 | − | 6.45203i | −0.533938 | − | 0.254246i | ||||
\(645\) | − | 22.6893i | − | 0.893390i | ||||||
\(646\) | −18.4622 | + | 10.6592i | −0.726386 | + | 0.419379i | ||||
\(647\) | −21.8248 | − | 12.6005i | −0.858020 | − | 0.495378i | 0.00532906 | − | 0.999986i | \(-0.498304\pi\) |
−0.863349 | + | 0.504608i | \(0.831637\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 5.63746 | − | 1.10411i | 0.221290 | − | 0.0433401i | ||||
\(650\) | 8.60271i | 0.337426i | ||||||||
\(651\) | 3.72508 | + | 46.9380i | 0.145998 | + | 1.83965i | ||||
\(652\) | 16.5498 | 0.648142 | ||||||||
\(653\) | −19.1375 | + | 11.0490i | −0.748907 | + | 0.432381i | −0.825299 | − | 0.564696i | \(-0.808993\pi\) |
0.0763921 | + | 0.997078i | \(0.475660\pi\) | |||||||
\(654\) | −3.72508 | + | 6.45203i | −0.145662 | + | 0.252294i | ||||
\(655\) | 11.6873 | + | 6.74766i | 0.456660 | + | 0.263653i | ||||
\(656\) | 3.27492 | + | 5.67232i | 0.127864 | + | 0.221467i | ||||
\(657\) | 15.7611i | 0.614899i | ||||||||
\(658\) | 4.81271 | − | 3.31233i | 0.187619 | − | 0.129128i | ||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | −1.45017 | − | 7.40437i | −0.0564476 | − | 0.288215i | ||||
\(661\) | 5.36254 | − | 9.28819i | 0.208579 | − | 0.361269i | −0.742688 | − | 0.669637i | \(-0.766450\pi\) |
0.951267 | + | 0.308368i | \(0.0997829\pi\) | |||||||
\(662\) | −2.54983 | + | 4.41644i | −0.0991021 | + | 0.171650i | ||||
\(663\) | 7.45017 | + | 12.9041i | 0.289340 | + | 0.501152i | ||||
\(664\) | −10.2749 | −0.398744 | ||||||||
\(665\) | 12.8248 | + | 18.6339i | 0.497323 | + | 0.722593i | ||||
\(666\) | −21.8248 | −0.845692 | ||||||||
\(667\) | 4.91238 | − | 2.83616i | 0.190208 | − | 0.109817i | ||||
\(668\) | −3.72508 | + | 6.45203i | −0.144128 | + | 0.249637i | ||||
\(669\) | 4.23713 | + | 2.44631i | 0.163817 | + | 0.0945797i | ||||
\(670\) | 9.72508 | − | 5.61478i | 0.375713 | − | 0.216918i | ||||
\(671\) | −7.45017 | + | 21.7370i | −0.287610 | + | 0.839146i | ||||
\(672\) | 0.362541 | + | 4.56821i | 0.0139853 | + | 0.176223i | ||||
\(673\) | 22.0980i | 0.851817i | 0.904766 | + | 0.425908i | \(0.140045\pi\) | ||||
−0.904766 | + | 0.425908i | \(0.859955\pi\) | |||||||
\(674\) | −7.96221 | + | 4.59698i | −0.306693 | + | 0.177069i | ||||
\(675\) | −14.7371 | − | 8.50848i | −0.567232 | − | 0.327492i | ||||
\(676\) | −3.04983 | + | 5.28247i | −0.117301 | + | 0.203172i | ||||
\(677\) | 16.5997 | + | 28.7515i | 0.637977 | + | 1.10501i | 0.985876 | + | 0.167477i | \(0.0535619\pi\) |
−0.347899 | + | 0.937532i | \(0.613105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.4124 | − | 32.3673i | 0.591473 | − | 1.24214i | ||||
\(680\) | − | 4.30136i | − | 0.164949i | ||||||
\(681\) | −35.0619 | + | 20.2430i | −1.34357 | + | 0.775713i | ||||
\(682\) | −25.6873 | + | 22.3937i | −0.983617 | + | 0.857498i | ||||
\(683\) | 41.3248 | + | 23.8589i | 1.58125 | + | 0.912934i | 0.994678 | + | 0.103035i | \(0.0328554\pi\) |
0.586570 | + | 0.809899i | \(0.300478\pi\) | |||||||
\(684\) | −16.9124 | + | 9.76436i | −0.646661 | + | 0.373350i | ||||
\(685\) | −5.64950 | −0.215856 | ||||||||
\(686\) | 12.7749 | + | 13.4090i | 0.487749 | + | 0.511958i | ||||
\(687\) | 11.3446i | 0.432825i | ||||||||
\(688\) | −8.63746 | + | 4.98684i | −0.329300 | + | 0.190121i | ||||
\(689\) | −17.7251 | + | 30.7007i | −0.675272 | + | 1.16961i | ||||
\(690\) | 11.1752 | + | 6.45203i | 0.425434 | + | 0.245625i | ||||
\(691\) | 14.0000 | + | 24.2487i | 0.532585 | + | 0.922464i | 0.999276 | + | 0.0380440i | \(0.0121127\pi\) |
−0.466691 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(692\) | −14.0000 | −0.532200 | ||||||||
\(693\) | 18.4124 | − | 18.8145i | 0.699428 | − | 0.714703i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | −0.274917 | − | 0.476171i | −0.0104282 | − | 0.0180622i | ||||
\(696\) | −1.50000 | − | 0.866025i | −0.0568574 | − | 0.0328266i | ||||
\(697\) | 10.7251 | − | 18.5764i | 0.406241 | − | 0.703631i | ||||
\(698\) | 21.9244 | − | 12.6581i | 0.829852 | − | 0.479115i | ||||
\(699\) | 30.8734i | 1.16774i | ||||||||
\(700\) | 8.63746 | − | 0.685484i | 0.326465 | − | 0.0259089i | ||||
\(701\) | −9.90033 | −0.373930 | −0.186965 | − | 0.982367i | \(-0.559865\pi\) | ||||
−0.186965 | + | 0.982367i | \(0.559865\pi\) | |||||||
\(702\) | 6.82475 | + | 11.8208i | 0.257584 | + | 0.446148i | ||||
\(703\) | 41.0120 | + | 23.6783i | 1.54680 | + | 0.893045i | ||||
\(704\) | −2.50000 | + | 2.17945i | −0.0942223 | + | 0.0821411i | ||||
\(705\) | −4.35050 | + | 2.51176i | −0.163849 | + | 0.0945984i | ||||
\(706\) | − | 36.5457i | − | 1.37542i | ||||||
\(707\) | 14.7371 | + | 21.4125i | 0.554247 | + | 0.805302i | ||||
\(708\) | 3.00000 | 0.112747 | ||||||||
\(709\) | 17.6375 | + | 30.5490i | 0.662389 | + | 1.14729i | 0.979986 | + | 0.199065i | \(0.0637906\pi\) |
−0.317598 | + | 0.948226i | \(0.602876\pi\) | |||||||
\(710\) | −6.54983 | + | 11.3446i | −0.245811 | + | 0.425757i | ||||
\(711\) | 5.58762 | + | 3.22602i | 0.209552 | + | 0.120985i | ||||
\(712\) | 2.27492 | − | 1.31342i | 0.0852561 | − | 0.0492226i | ||||
\(713\) | − | 58.2826i | − | 2.18270i | ||||||
\(714\) | 12.3625 | − | 8.50848i | 0.462656 | − | 0.318422i | ||||
\(715\) | 10.8248 | + | 3.71010i | 0.404823 | + | 0.138750i | ||||
\(716\) | 12.3625 | − | 7.13752i | 0.462010 | − | 0.266742i | ||||
\(717\) | −18.8248 | − | 10.8685i | −0.703023 | − | 0.405891i | ||||
\(718\) | 12.8248 | − | 22.2131i | 0.478615 | − | 0.828986i | ||||
\(719\) | −13.0876 | + | 7.55614i | −0.488086 | + | 0.281797i | −0.723780 | − | 0.690031i | \(-0.757597\pi\) |
0.235694 | + | 0.971827i | \(0.424264\pi\) | |||||||
\(720\) | − | 3.94027i | − | 0.146845i | ||||||
\(721\) | −34.5498 | + | 2.74194i | −1.28670 | + | 0.102115i | ||||
\(722\) | 23.3746 | 0.869912 | ||||||||
\(723\) | −3.41238 | − | 5.91041i | −0.126908 | − | 0.219810i | ||||
\(724\) | 3.27492 | − | 5.67232i | 0.121711 | − | 0.210810i | ||||
\(725\) | −1.63746 | + | 2.83616i | −0.0608137 | + | 0.105332i | ||||
\(726\) | 18.8746 | + | 2.59808i | 0.700502 | + | 0.0964237i | ||||
\(727\) | 10.2749 | 0.381076 | 0.190538 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190538 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(728\) | −6.27492 | − | 2.98793i | −0.232564 | − | 0.110740i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 3.45017 | + | 5.97586i | 0.127696 | + | 0.221177i | ||||
\(731\) | 28.2870 | + | 16.3315i | 1.04623 | + | 0.604042i | ||||
\(732\) | −6.00000 | + | 10.3923i | −0.221766 | + | 0.384111i | ||||
\(733\) | 33.0997 | − | 19.1101i | 1.22256 | − | 0.705848i | 0.257100 | − | 0.966385i | \(-0.417233\pi\) |
0.965464 | + | 0.260537i | \(0.0838996\pi\) | |||||||
\(734\) | −17.7251 | −0.654245 | ||||||||
\(735\) | −10.0378 | − | 12.3624i | −0.370249 | − | 0.455996i | ||||
\(736\) | − | 5.67232i | − | 0.209085i | ||||||
\(737\) | 5.45017 | + | 27.8279i | 0.200759 | + | 1.02505i | ||||
\(738\) | 9.82475 | − | 17.0170i | 0.361654 | − | 0.626403i | ||||
\(739\) | 6.09967 | + | 3.52165i | 0.224380 | + | 0.129546i | 0.607977 | − | 0.793955i | \(-0.291981\pi\) |
−0.383597 | + | 0.923501i | \(0.625315\pi\) | |||||||
\(740\) | −8.27492 | + | 4.77753i | −0.304192 | + | 0.175625i | ||||
\(741\) | − | 29.6175i | − | 1.08803i | ||||||
\(742\) | 32.2371 | + | 15.3504i | 1.18346 | + | 0.563530i | ||||
\(743\) | 2.35050 | 0.0862314 | 0.0431157 | − | 0.999070i | \(-0.486272\pi\) | ||||
0.0431157 | + | 0.999070i | \(0.486272\pi\) | |||||||
\(744\) | −15.4124 | + | 8.89834i | −0.565045 | + | 0.326229i | ||||
\(745\) | −8.27492 | − | 4.77753i | −0.303170 | − | 0.175035i | ||||
\(746\) | −7.45017 | − | 4.30136i | −0.272770 | − | 0.157484i | ||||
\(747\) | 15.4124 | + | 26.6950i | 0.563909 | + | 0.976720i | ||||
\(748\) | 10.2749 | + | 3.52165i | 0.375688 | + | 0.128764i | ||||
\(749\) | 37.6495 | − | 2.98793i | 1.37568 | − | 0.109177i | ||||
\(750\) | −18.8248 | −0.687383 | ||||||||
\(751\) | −17.1375 | − | 29.6829i | −0.625355 | − | 1.08315i | −0.988472 | − | 0.151403i | \(-0.951621\pi\) |
0.363117 | − | 0.931743i | \(-0.381712\pi\) | |||||||
\(752\) | 1.91238 | + | 1.10411i | 0.0697372 | + | 0.0402628i | ||||
\(753\) | 0.774917 | − | 1.34220i | 0.0282396 | − | 0.0489123i | ||||
\(754\) | 2.27492 | − | 1.31342i | 0.0828476 | − | 0.0478321i | ||||
\(755\) | −15.9244 | −0.579549 | ||||||||
\(756\) | 11.3248 | − | 7.79423i | 0.411877 | − | 0.283473i | ||||
\(757\) | 35.4743 | 1.28933 | 0.644667 | − | 0.764464i | \(-0.276996\pi\) | ||||
0.644667 | + | 0.764464i | \(0.276996\pi\) | |||||||
\(758\) | 10.0000 | + | 17.3205i | 0.363216 | + | 0.629109i | ||||
\(759\) | −24.5619 | + | 21.4125i | −0.891540 | + | 0.777226i | ||||
\(760\) | −4.27492 | + | 7.40437i | −0.155068 | + | 0.268585i | ||||
\(761\) | −20.0997 | − | 34.8136i | −0.728612 | − | 1.26199i | −0.957470 | − | 0.288534i | \(-0.906832\pi\) |
0.228857 | − | 0.973460i | \(-0.426501\pi\) | |||||||
\(762\) | −6.09967 | −0.220968 | ||||||||
\(763\) | −9.37459 | + | 6.45203i | −0.339383 | + | 0.233579i | ||||
\(764\) | 11.3446i | 0.410435i | ||||||||
\(765\) | −11.1752 | + | 6.45203i | −0.404042 | + | 0.233274i | ||||
\(766\) | 26.0120 | + | 15.0181i | 0.939853 | + | 0.542625i | ||||
\(767\) | −2.27492 | + | 3.94027i | −0.0821425 | + | 0.142275i | ||||
\(768\) | −1.50000 | + | 0.866025i | −0.0541266 | + | 0.0312500i | ||||
\(769\) | 37.8591i | 1.36523i | 0.730776 | + | 0.682617i | \(0.239158\pi\) | ||||
−0.730776 | + | 0.682617i | \(0.760842\pi\) | |||||||
\(770\) | 2.86254 | − | 11.1641i | 0.103159 | − | 0.402326i | ||||
\(771\) | −28.5498 | −1.02820 | ||||||||
\(772\) | 19.1375 | − | 11.0490i | 0.688772 | − | 0.397663i | ||||
\(773\) | −12.0000 | − | 6.92820i | −0.431610 | − | 0.249190i | 0.268422 | − | 0.963301i | \(-0.413498\pi\) |
−0.700032 | + | 0.714111i | \(0.746831\pi\) | |||||||
\(774\) | 25.9124 | + | 14.9605i | 0.931401 | + | 0.537745i | ||||
\(775\) | 16.8248 | + | 29.1413i | 0.604363 | + | 1.04679i | ||||
\(776\) | 13.5498 | 0.486411 | ||||||||
\(777\) | −30.0997 | − | 14.3326i | −1.07982 | − | 0.514178i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.9244 | + | 21.3183i | −1.32295 | + | 0.763808i | ||||
\(780\) | 5.17525 | + | 2.98793i | 0.185304 | + | 0.106985i | ||||
\(781\) | −21.7371 | − | 24.9342i | −0.777816 | − | 0.892216i | ||||
\(782\) | −16.0876 | + | 9.28819i | −0.575292 | + | 0.332145i | ||||
\(783\) | 5.19615i | 0.185695i | ||||||||
\(784\) | −2.50000 | + | 6.53835i | −0.0892857 | + | 0.233512i | ||||
\(785\) | 22.6893i | 0.809816i | ||||||||
\(786\) | −15.4124 | + | 8.89834i | −0.549741 | + | 0.317393i | ||||
\(787\) | 47.7371 | + | 27.5610i | 1.70164 | + | 0.982445i | 0.944098 | + | 0.329664i | \(0.106935\pi\) |
0.757546 | + | 0.652781i | \(0.226398\pi\) | |||||||
\(788\) | 6.36254 | − | 11.0202i | 0.226656 | − | 0.392580i | ||||
\(789\) | −43.6495 | + | 25.2011i | −1.55396 | + | 0.897181i | ||||
\(790\) | 2.82475 | 0.100500 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.41238 | + | 3.22602i | 0.334454 | + | 0.114631i | ||||
\(793\) | −9.09967 | − | 15.7611i | −0.323139 | − | 0.559693i | ||||
\(794\) | −5.36254 | + | 9.28819i | −0.190309 | + | 0.329626i | ||||
\(795\) | −26.5876 | − | 15.3504i | −0.942966 | − | 0.544422i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.7249i | 0.875800i | 0.899024 | + | 0.437900i | \(0.144278\pi\) | ||||
−0.899024 | + | 0.437900i | \(0.855722\pi\) | |||||||
\(798\) | −29.7371 | + | 2.35999i | −1.05268 | + | 0.0835428i | ||||
\(799\) | − | 7.23174i | − | 0.255841i | ||||||
\(800\) | 1.63746 | + | 2.83616i | 0.0578929 | + | 0.100273i | ||||
\(801\) | −6.82475 | − | 3.94027i | −0.241141 | − | 0.139223i | ||||
\(802\) | −19.6495 | − | 11.3446i | −0.693848 | − | 0.400593i | ||||
\(803\) | −17.0997 | + | 3.34901i | −0.603434 | + | 0.118184i | ||||
\(804\) | 14.8087i | 0.522264i | ||||||||
\(805\) | 11.1752 | + | 16.2373i | 0.393876 | + | 0.572288i | ||||
\(806\) | − | 26.9906i | − | 0.950705i | ||||||
\(807\) | −2.58762 | − | 4.48190i | −0.0910887 | − | 0.157770i | ||||
\(808\) | −4.91238 | + | 8.50848i | −0.172817 | + | 0.299327i | ||||
\(809\) | 15.8248 | − | 27.4093i | 0.556369 | − | 0.963659i | −0.441427 | − | 0.897297i | \(-0.645528\pi\) |
0.997796 | − | 0.0663616i | \(-0.0211391\pi\) | |||||||
\(810\) | −10.2371 | + | 5.91041i | −0.359696 | + | 0.207671i | ||||
\(811\) | 17.3205i | 0.608205i | 0.952639 | + | 0.304103i | \(0.0983566\pi\) | ||||
−0.952639 | + | 0.304103i | \(0.901643\pi\) | |||||||
\(812\) | −1.50000 | − | 2.17945i | −0.0526397 | − | 0.0764837i | ||||
\(813\) | −14.4743 | −0.507634 | ||||||||
\(814\) | −4.63746 | − | 23.6783i | −0.162543 | − | 0.829925i | ||||
\(815\) | −18.8248 | − | 10.8685i | −0.659402 | − | 0.380706i | ||||
\(816\) | 4.91238 | + | 2.83616i | 0.171968 | + | 0.0992855i | ||||
\(817\) | −32.4622 | − | 56.2262i | −1.13571 | − | 1.96711i | ||||
\(818\) | − | 14.2175i | − | 0.497103i | ||||||
\(819\) | 1.64950 | + | 20.7846i | 0.0576383 | + | 0.726273i | ||||
\(820\) | − | 8.60271i | − | 0.300420i | ||||||
\(821\) | 12.9622 | + | 22.4512i | 0.452384 | + | 0.783553i | 0.998534 | − | 0.0541353i | \(-0.0172402\pi\) |
−0.546149 | + | 0.837688i | \(0.683907\pi\) | |||||||
\(822\) | 3.72508 | − | 6.45203i | 0.129927 | − | 0.225040i | ||||
\(823\) | −13.4502 | + | 23.2964i | −0.468843 | + | 0.812060i | −0.999366 | − | 0.0356105i | \(-0.988662\pi\) |
0.530522 | + | 0.847671i | \(0.321996\pi\) | |||||||
\(824\) | −6.54983 | − | 11.3446i | −0.228174 | − | 0.395209i | ||||
\(825\) | 6.09967 | − | 17.7967i | 0.212363 | − | 0.619601i | ||||
\(826\) | 4.13746 | + | 1.97014i | 0.143961 | + | 0.0685498i | ||||
\(827\) | 44.4743 | 1.54652 | 0.773261 | − | 0.634088i | \(-0.218624\pi\) | ||||
0.773261 | + | 0.634088i | \(0.218624\pi\) | |||||||
\(828\) | −14.7371 | + | 8.50848i | −0.512151 | + | 0.295690i | ||||
\(829\) | 8.18729 | − | 14.1808i | 0.284356 | − | 0.492520i | −0.688096 | − | 0.725619i | \(-0.741553\pi\) |
0.972453 | + | 0.233099i | \(0.0748868\pi\) | |||||||
\(830\) | 11.6873 | + | 6.74766i | 0.405672 | + | 0.234215i | ||||
\(831\) | −7.45017 | − | 12.9041i | −0.258443 | − | 0.447637i | ||||
\(832\) | − | 2.62685i | − | 0.0910696i | ||||||
\(833\) | 22.6375 | − | 3.61587i | 0.784341 | − | 0.125283i | ||||
\(834\) | 0.725083 | 0.0251076 | ||||||||
\(835\) | 8.47425 | − | 4.89261i | 0.293264 | − | 0.169316i | ||||
\(836\) | −14.1873 | − | 16.2739i | −0.490678 | − | 0.562846i | ||||
\(837\) | 46.2371 | + | 26.6950i | 1.59819 | + | 0.922715i | ||||
\(838\) | 23.6375 | − | 13.6471i | 0.816542 | − | 0.471431i | ||||
\(839\) | − | 57.2152i | − | 1.97529i | −0.156712 | − | 0.987644i | \(-0.550089\pi\) | ||
0.156712 | − | 0.987644i | \(-0.449911\pi\) | |||||||
\(840\) | 2.58762 | − | 5.43424i | 0.0892815 | − | 0.187499i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 11.1873 | + | 19.3770i | 0.385540 | + | 0.667774i | ||||
\(843\) | 16.9124 | + | 9.76436i | 0.582493 | + | 0.336303i | ||||
\(844\) | −17.2749 | − | 9.97368i | −0.594627 | − | 0.343308i | ||||
\(845\) | 6.93812 | − | 4.00573i | 0.238679 | − | 0.137801i | ||||
\(846\) | − | 6.62466i | − | 0.227761i | ||||||
\(847\) | 24.3248 | + | 15.9783i | 0.835808 | + | 0.549021i | ||||
\(848\) | 13.4953i | 0.463431i | ||||||||
\(849\) | −5.27492 | − | 9.13642i | −0.181035 | − | 0.313561i | ||||
\(850\) | 5.36254 | − | 9.28819i | 0.183934 | − | 0.318582i | ||||
\(851\) | 35.7371 | + | 20.6328i | 1.22505 | + | 0.707285i | ||||
\(852\) | −8.63746 | − | 14.9605i | −0.295914 | − | 0.512539i | ||||
\(853\) | − | 13.1342i | − | 0.449708i | −0.974392 | − | 0.224854i | \(-0.927810\pi\) | ||
0.974392 | − | 0.224854i | \(-0.0721905\pi\) | |||||||
\(854\) | −15.0997 | + | 10.3923i | −0.516700 | + | 0.355617i | ||||
\(855\) | 25.6495 | 0.877195 | ||||||||
\(856\) | 7.13746 | + | 12.3624i | 0.243953 | + | 0.422540i | ||||
\(857\) | 8.63746 | − | 14.9605i | 0.295050 | − | 0.511042i | −0.679947 | − | 0.733262i | \(-0.737997\pi\) |
0.974997 | + | 0.222220i | \(0.0713304\pi\) | |||||||
\(858\) | −11.3746 | + | 9.91613i | −0.388322 | + | 0.338531i | ||||
\(859\) | −14.0000 | − | 24.2487i | −0.477674 | − | 0.827355i | 0.521999 | − | 0.852946i | \(-0.325187\pi\) |
−0.999672 | + | 0.0255910i | \(0.991853\pi\) | |||||||
\(860\) | 13.0997 | 0.446695 | ||||||||
\(861\) | 24.7251 | − | 17.0170i | 0.842629 | − | 0.579937i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | 33.1993 | − | 19.1676i | 1.13012 | − | 0.652474i | 0.186154 | − | 0.982521i | \(-0.440398\pi\) |
0.943965 | + | 0.330046i | \(0.107064\pi\) | |||||||
\(864\) | 4.50000 | + | 2.59808i | 0.153093 | + | 0.0883883i | ||||
\(865\) | 15.9244 | + | 9.19397i | 0.541447 | + | 0.312604i | ||||
\(866\) | −1.63746 | − | 2.83616i | −0.0556431 | − | 0.0963767i | ||||
\(867\) | 10.8685i | 0.369113i | ||||||||
\(868\) | −27.0997 | + | 2.15068i | −0.919823 | + | 0.0729988i | ||||
\(869\) | −2.31271 | + | 6.74766i | −0.0784532 | + | 0.228899i | ||||
\(870\) | 1.13746 | + | 1.97014i | 0.0385635 | + | 0.0667939i | ||||
\(871\) | −19.4502 | − | 11.2296i | −0.659044 | − | 0.380499i | ||||
\(872\) | −3.72508 | − | 2.15068i | −0.126147 | − | 0.0728311i | ||||
\(873\) | −20.3248 | − | 35.2035i | −0.687889 | − | 1.19146i | ||||
\(874\) | 36.9244 | 1.24899 | ||||||||
\(875\) | −25.9622 | − | 12.3624i | −0.877683 | − | 0.417927i | ||||
\(876\) | −9.09967 | −0.307449 | ||||||||
\(877\) | −19.6495 | + | 11.3446i | −0.663517 | + | 0.383081i | −0.793616 | − | 0.608420i | \(-0.791804\pi\) |
0.130099 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(878\) | −2.32475 | − | 1.34220i | −0.0784566 | − | 0.0452969i | ||||
\(879\) | 9.14950 | + | 5.28247i | 0.308605 | + | 0.178173i | ||||
\(880\) | 4.27492 | − | 0.837253i | 0.144107 | − | 0.0282238i | ||||
\(881\) | − | 11.4597i | − | 0.386088i | −0.981190 | − | 0.193044i | \(-0.938164\pi\) | ||
0.981190 | − | 0.193044i | \(-0.0618361\pi\) | |||||||
\(882\) | 20.7371 | − | 3.31233i | 0.698255 | − | 0.111532i | ||||
\(883\) | −34.1993 | −1.15090 | −0.575450 | − | 0.817837i | \(-0.695173\pi\) | ||||
−0.575450 | + | 0.817837i | \(0.695173\pi\) | |||||||
\(884\) | −7.45017 | + | 4.30136i | −0.250576 | + | 0.144670i | ||||
\(885\) | −3.41238 | − | 1.97014i | −0.114706 | − | 0.0662254i | ||||
\(886\) | −3.04983 | − | 1.76082i | −0.102461 | − | 0.0591560i | ||||
\(887\) | −3.72508 | − | 6.45203i | −0.125076 | − | 0.216638i | 0.796687 | − | 0.604393i | \(-0.206584\pi\) |
−0.921763 | + | 0.387755i | \(0.873251\pi\) | |||||||
\(888\) | − | 12.6005i | − | 0.422846i | ||||||
\(889\) | −8.41238 | − | 4.00573i | −0.282142 | − | 0.134348i | ||||
\(890\) | −3.45017 | −0.115650 | ||||||||
\(891\) | −5.73713 | − | 29.2931i | −0.192201 | − | 0.981356i | ||||
\(892\) | −1.41238 | + | 2.44631i | −0.0472898 | + | 0.0819084i | ||||
\(893\) | −7.18729 | + | 12.4488i | −0.240514 | + | 0.416582i | ||||
\(894\) | 10.9124 | − | 6.30026i | 0.364964 | − | 0.210712i | ||||
\(895\) | −18.7492 | −0.626716 | ||||||||
\(896\) | −2.63746 | + | 0.209313i | −0.0881113 | + | 0.00699267i | ||||
\(897\) | − | 25.8081i | − | 0.861708i | ||||||
\(898\) | 3.72508 | − | 2.15068i | 0.124308 | − | 0.0717690i | ||||
\(899\) | 5.13746 | − | 8.89834i | 0.171344 | − | 0.296776i | ||||
\(900\) | 4.91238 | − | 8.50848i | 0.163746 | − | 0.283616i | ||||
\(901\) | 38.2749 | − | 22.0980i | 1.27512 | − | 0.736192i | ||||
\(902\) | 20.5498 | + | 7.04329i | 0.684235 | + | 0.234516i | ||||
\(903\) | 25.9124 | + | 37.6498i | 0.862310 | + | 1.25291i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.45017 | + | 4.30136i | −0.247652 | + | 0.142982i | ||||
\(906\) | 10.5000 | − | 18.1865i | 0.348839 | − | 0.604207i | ||||
\(907\) | −5.72508 | + | 9.91613i | −0.190098 | + | 0.329260i | −0.945283 | − | 0.326253i | \(-0.894214\pi\) |
0.755184 | + | 0.655512i | \(0.227547\pi\) | |||||||
\(908\) | −11.6873 | − | 20.2430i | −0.387856 | − | 0.671787i | ||||
\(909\) | 29.4743 | 0.977599 | ||||||||
\(910\) | 5.17525 | + | 7.51946i | 0.171558 | + | 0.249268i | ||||
\(911\) | − | 52.6103i | − | 1.74306i | −0.490344 | − | 0.871529i | \(-0.663129\pi\) | ||
0.490344 | − | 0.871529i | \(-0.336871\pi\) | |||||||
\(912\) | −5.63746 | − | 9.76436i | −0.186675 | − | 0.323330i | ||||
\(913\) | −25.6873 | + | 22.3937i | −0.850125 | + | 0.741122i | ||||
\(914\) | −31.3368 | − | 18.0923i | −1.03653 | − | 0.598440i | ||||
\(915\) | 13.6495 | − | 7.88054i | 0.451239 | − | 0.260523i | ||||
\(916\) | −6.54983 | −0.216413 | ||||||||
\(917\) | −27.0997 | + | 2.15068i | −0.894910 | + | 0.0710216i | ||||
\(918\) | − | 17.0170i | − | 0.561644i | ||||||
\(919\) | −19.8127 | + | 11.4389i | −0.653561 | + | 0.377334i | −0.789819 | − | 0.613340i | \(-0.789826\pi\) |
0.136258 | + | 0.990673i | \(0.456492\pi\) | |||||||
\(920\) | −3.72508 | + | 6.45203i | −0.122812 | + | 0.212717i | ||||
\(921\) | 1.54983 | − | 2.68439i | 0.0510688 | − | 0.0884537i | ||||
\(922\) | −4.91238 | − | 8.50848i | −0.161780 | − | 0.280212i | ||||
\(923\) | 26.1993 | 0.862362 | ||||||||
\(924\) | 10.8625 | + | 10.6304i | 0.357351 | + | 0.349714i | ||||
\(925\) | −23.8248 | −0.783353 | ||||||||
\(926\) | 10.0000 | + | 17.3205i | 0.328620 | + | 0.569187i | ||||
\(927\) | −19.6495 | + | 34.0339i | −0.645374 | + | 1.11782i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | 16.5498 | − | 9.55505i | 0.542982 | − | 0.313491i | −0.203304 | − | 0.979116i | \(-0.565168\pi\) |
0.746287 | + | 0.665625i | \(0.231835\pi\) | |||||||
\(930\) | 23.3746 | 0.766483 | ||||||||
\(931\) | −42.5619 | − | 16.2739i | −1.39491 | − | 0.533357i | ||||
\(932\) | −17.8248 | −0.583869 | ||||||||
\(933\) | 15.3625 | + | 26.6087i | 0.502947 | + | 0.871130i | ||||
\(934\) | 1.81271 | + | 1.04657i | 0.0593136 | + | 0.0342447i | ||||
\(935\) | −9.37459 | − | 10.7534i | −0.306582 | − | 0.351673i | ||||
\(936\) | −6.82475 | + | 3.94027i | −0.223074 | + | 0.128792i | ||||
\(937\) | − | 12.5430i | − | 0.409761i | −0.978787 | − | 0.204881i | \(-0.934319\pi\) | ||
0.978787 | − | 0.204881i | \(-0.0656806\pi\) | |||||||
\(938\) | −9.72508 | + | 20.4235i | −0.317535 | + | 0.666852i | ||||
\(939\) | − | 12.1244i | − | 0.395663i | ||||||
\(940\) | −1.45017 | − | 2.51176i | −0.0472992 | − | 0.0819246i | ||||
\(941\) | 16.5997 | − | 28.7515i | 0.541134 | − | 0.937271i | −0.457706 | − | 0.889104i | \(-0.651329\pi\) |
0.998839 | − | 0.0481673i | \(-0.0153381\pi\) | |||||||
\(942\) | −25.9124 | − | 14.9605i | −0.844271 | − | 0.487440i | ||||
\(943\) | −32.1752 | + | 18.5764i | −1.04777 | + | 0.604930i | ||||
\(944\) | 1.73205i | 0.0563735i | ||||||||
\(945\) | −18.0000 | + | 1.42851i | −0.585540 | + | 0.0464695i | ||||
\(946\) | −10.7251 | + | 31.2920i | −0.348703 | + | 1.01739i | ||||
\(947\) | −14.7371 | + | 8.50848i | −0.478892 | + | 0.276489i | −0.719955 | − | 0.694021i | \(-0.755837\pi\) |
0.241062 | + | 0.970510i | \(0.422504\pi\) | |||||||
\(948\) | −1.86254 | + | 3.22602i | −0.0604925 | + | 0.104776i | ||||
\(949\) | 6.90033 | − | 11.9517i | 0.223994 | − | 0.387969i | ||||
\(950\) | −18.4622 | + | 10.6592i | −0.598993 | + | 0.345829i | ||||
\(951\) | 23.3746 | 0.757973 | ||||||||
\(952\) | 4.91238 | + | 7.13752i | 0.159211 | + | 0.231328i | ||||
\(953\) | 27.6495 | 0.895655 | 0.447828 | − | 0.894120i | \(-0.352198\pi\) | ||||
0.447828 | + | 0.894120i | \(0.352198\pi\) | |||||||
\(954\) | 35.0619 | − | 20.2430i | 1.13517 | − | 0.655391i | ||||
\(955\) | 7.45017 | − | 12.9041i | 0.241082 | − | 0.417566i | ||||
\(956\) | 6.27492 | − | 10.8685i | 0.202945 | − | 0.351512i | ||||
\(957\) | −5.63746 | + | 1.10411i | −0.182233 | + | 0.0356908i | ||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | 9.37459 | − | 6.45203i | 0.302721 | − | 0.208347i | ||||
\(960\) | 2.27492 | 0.0734226 | ||||||||
\(961\) | −37.2870 | − | 64.5829i | −1.20281 | − | 2.08332i | ||||
\(962\) | 16.5498 | + | 9.55505i | 0.533588 | + | 0.308067i | ||||
\(963\) | 21.4124 | − | 37.0873i | 0.690004 | − | 1.19512i | ||||
\(964\) | 3.41238 | − | 1.97014i | 0.109905 | − | 0.0634538i | ||||
\(965\) | −29.0241 | −0.934318 | ||||||||
\(966\) | −25.9124 | + | 2.05645i | −0.833717 | + | 0.0661653i | ||||
\(967\) | − | 27.7704i | − | 0.893034i | −0.894775 | − | 0.446517i | \(-0.852664\pi\) | ||
0.894775 | − | 0.446517i | \(-0.147336\pi\) | |||||||
\(968\) | −1.50000 | + | 10.8972i | −0.0482118 | + | 0.350251i | ||||
\(969\) | −18.4622 | + | 31.9775i | −0.593092 | + | 1.02726i | ||||
\(970\) | −15.4124 | − | 8.89834i | −0.494862 | − | 0.285708i | ||||
\(971\) | 49.2371 | − | 28.4271i | 1.58009 | − | 0.912268i | 0.585250 | − | 0.810853i | \(-0.300996\pi\) |
0.994844 | − | 0.101415i | \(-0.0323371\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | 1.00000 | + | 0.476171i | 0.0320585 | + | 0.0152653i | ||||
\(974\) | 19.3746 | 0.620802 | ||||||||
\(975\) | 7.45017 | + | 12.9041i | 0.238596 | + | 0.413261i | ||||
\(976\) | −6.00000 | − | 3.46410i | −0.192055 | − | 0.110883i | ||||
\(977\) | −27.0997 | − | 15.6460i | −0.866995 | − | 0.500560i | −0.000646664 | − | 1.00000i | \(-0.500206\pi\) |
−0.866349 | + | 0.499440i | \(0.833539\pi\) | |||||||
\(978\) | 24.8248 | − | 14.3326i | 0.793808 | − | 0.458305i | ||||
\(979\) | 2.82475 | − | 8.24163i | 0.0902795 | − | 0.263404i | ||||
\(980\) | 7.13746 | − | 5.79532i | 0.227998 | − | 0.185125i | ||||
\(981\) | 12.9041i | 0.411995i | ||||||||
\(982\) | −7.68729 | − | 13.3148i | −0.245311 | − | 0.424892i | ||||
\(983\) | −19.1873 | − | 11.0778i | −0.611980 | − | 0.353327i | 0.161760 | − | 0.986830i | \(-0.448283\pi\) |
−0.773740 | + | 0.633504i | \(0.781616\pi\) | |||||||
\(984\) | 9.82475 | + | 5.67232i | 0.313202 | + | 0.180827i | ||||
\(985\) | −14.4743 | + | 8.35671i | −0.461188 | + | 0.266267i | ||||
\(986\) | −3.27492 | −0.104295 | ||||||||
\(987\) | 4.35050 | − | 9.13642i | 0.138478 | − | 0.290816i | ||||
\(988\) | 17.0997 | 0.544013 | ||||||||
\(989\) | −28.2870 | − | 48.9945i | −0.899473 | − | 1.55793i | ||||
\(990\) | −8.58762 | − | 9.85068i | −0.272933 | − | 0.313075i | ||||
\(991\) | −7.41238 | + | 12.8386i | −0.235462 | + | 0.407832i | −0.959407 | − | 0.282026i | \(-0.908994\pi\) |
0.723945 | + | 0.689858i | \(0.242327\pi\) | |||||||
\(992\) | −5.13746 | − | 8.89834i | −0.163114 | − | 0.282523i | ||||
\(993\) | 8.83289i | 0.280303i | ||||||||
\(994\) | −2.08762 | − | 26.3052i | −0.0662154 | − | 0.834349i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.4124 | + | 8.89834i | −0.488360 | + | 0.281955i | ||||
\(997\) | −5.37459 | − | 3.10302i | −0.170215 | − | 0.0982736i | 0.412472 | − | 0.910970i | \(-0.364665\pi\) |
−0.582687 | + | 0.812697i | \(0.697999\pi\) | |||||||
\(998\) | 1.72508 | − | 2.98793i | 0.0546065 | − | 0.0945813i | ||||
\(999\) | −32.7371 | + | 18.9008i | −1.03576 | + | 0.597995i |
(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 | 462.2.n.d.263.2 | yes | 4 | |
3.2 | odd | 2 | 462.2.n.a.263.1 | yes | 4 | ||
7.2 | even | 3 | 462.2.n.c.65.1 | yes | 4 | ||
11.10 | odd | 2 | 462.2.n.b.263.2 | yes | 4 | ||
21.2 | odd | 6 | 462.2.n.b.65.2 | yes | 4 | ||
33.32 | even | 2 | 462.2.n.c.263.1 | yes | 4 | ||
77.65 | odd | 6 | 462.2.n.a.65.1 | ✓ | 4 | ||
231.65 | even | 6 | inner | 462.2.n.d.65.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.n.a.65.1 | ✓ | 4 | 77.65 | odd | 6 | ||
462.2.n.a.263.1 | yes | 4 | 3.2 | odd | 2 | ||
462.2.n.b.65.2 | yes | 4 | 21.2 | odd | 6 | ||
462.2.n.b.263.2 | yes | 4 | 11.10 | odd | 2 | ||
462.2.n.c.65.1 | yes | 4 | 7.2 | even | 3 | ||
462.2.n.c.263.1 | yes | 4 | 33.32 | even | 2 | ||
462.2.n.d.65.2 | yes | 4 | 231.65 | even | 6 | inner | |
462.2.n.d.263.2 | yes | 4 | 1.1 | even | 1 | trivial |