Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.b.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | −2.00000 | − | 3.46410i | −0.603023 | − | 1.04447i | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.50000 | + | 2.59808i | 0.387298 | + | 0.670820i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.00000 | + | 3.46410i | −0.426401 | + | 0.738549i | ||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | −2.50000 | − | 2.59808i | −0.490290 | − | 0.509525i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 2.50000 | + | 2.59808i | 0.400320 | + | 0.416025i | ||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −3.50000 | − | 6.06218i | −0.546608 | − | 0.946753i | −0.998504 | − | 0.0546823i | \(-0.982585\pi\) |
0.451896 | − | 0.892071i | \(-0.350748\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | −1.00000 | + | 3.46410i | −0.138675 | + | 0.480384i | ||||
\(53\) | 7.00000 | 0.961524 | 0.480762 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480762 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −6.00000 | − | 10.3923i | −0.809040 | − | 1.40130i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | 4.00000 | − | 6.92820i | 0.520756 | − | 0.901975i | −0.478953 | − | 0.877841i | \(-0.658984\pi\) |
0.999709 | − | 0.0241347i | \(-0.00768307\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5000 | − | 2.59808i | 1.30236 | − | 0.322252i | ||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | 2.50000 | + | 4.33013i | 0.303170 | + | 0.525105i | ||||
\(69\) | −2.00000 | + | 3.46410i | −0.240772 | + | 0.417029i | ||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | −6.00000 | + | 10.3923i | −0.712069 | + | 1.23334i | 0.252010 | + | 0.967725i | \(0.418908\pi\) |
−0.964079 | + | 0.265615i | \(0.914425\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −3.50000 | + | 6.06218i | −0.406867 | + | 0.704714i | ||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | −2.00000 | − | 3.46410i | −0.229416 | − | 0.397360i | ||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 1.00000 | − | 3.46410i | 0.113228 | − | 0.392232i | ||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.50000 | + | 6.06218i | −0.386510 | + | 0.669456i | ||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | 7.50000 | − | 12.9904i | 0.813489 | − | 1.40900i | ||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | −4.50000 | + | 7.79423i | −0.482451 | + | 0.835629i | ||||
\(88\) | −2.00000 | − | 3.46410i | −0.213201 | − | 0.369274i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 3.00000 | 0.316228 | ||||||||
\(91\) | 1.00000 | − | 3.46410i | 0.104828 | − | 0.363137i | ||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | − | 10.3923i | −0.618853 | − | 1.07188i | ||||
\(95\) | −6.00000 | + | 10.3923i | −0.615587 | + | 1.06623i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −9.00000 | + | 15.5885i | −0.913812 | + | 1.58277i | −0.105180 | + | 0.994453i | \(0.533542\pi\) |
−0.808632 | + | 0.588315i | \(0.799792\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | −2.50000 | − | 4.33013i | −0.247537 | − | 0.428746i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | −3.50000 | − | 6.06218i | −0.339950 | − | 0.588811i | ||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | −6.00000 | + | 10.3923i | −0.572078 | + | 0.990867i | ||||
\(111\) | 3.50000 | − | 6.06218i | 0.332205 | − | 0.575396i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.50000 | − | 4.33013i | 0.235180 | − | 0.407344i | −0.724145 | − | 0.689648i | \(-0.757765\pi\) |
0.959325 | + | 0.282304i | \(0.0910986\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | 6.00000 | + | 10.3923i | 0.559503 | + | 0.969087i | ||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | −1.00000 | + | 3.46410i | −0.0924500 | + | 0.320256i | ||||
\(118\) | −8.00000 | −0.736460 | ||||||||
\(119\) | −2.50000 | − | 4.33013i | −0.229175 | − | 0.396942i | ||||
\(120\) | 1.50000 | + | 2.59808i | 0.136931 | + | 0.237171i | ||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 7.00000 | 0.633750 | ||||||||
\(123\) | 3.50000 | − | 6.06218i | 0.315584 | − | 0.546608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | 4.00000 | + | 6.92820i | 0.354943 | + | 0.614779i | 0.987108 | − | 0.160055i | \(-0.0511671\pi\) |
−0.632166 | + | 0.774833i | \(0.717834\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | −7.50000 | − | 7.79423i | −0.657794 | − | 0.683599i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 2.00000 | + | 3.46410i | 0.174078 | + | 0.301511i | ||||
\(133\) | 2.00000 | + | 3.46410i | 0.173422 | + | 0.300376i | ||||
\(134\) | −6.00000 | + | 10.3923i | −0.518321 | + | 0.897758i | ||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 2.50000 | − | 4.33013i | 0.214373 | − | 0.371305i | ||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | 4.00000 | 0.340503 | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | 1.50000 | + | 2.59808i | 0.126773 | + | 0.219578i | ||||
\(141\) | 6.00000 | + | 10.3923i | 0.505291 | + | 0.875190i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | −10.0000 | − | 10.3923i | −0.836242 | − | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 13.5000 | + | 23.3827i | 1.12111 | + | 1.94183i | ||||
\(146\) | 0.500000 | + | 0.866025i | 0.0413803 | + | 0.0716728i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | −3.50000 | + | 6.06218i | −0.286731 | + | 0.496633i | −0.973028 | − | 0.230689i | \(-0.925902\pi\) |
0.686296 | + | 0.727322i | \(0.259235\pi\) | |||||||
\(150\) | 2.00000 | − | 3.46410i | 0.163299 | − | 0.282843i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −2.00000 | + | 3.46410i | −0.162221 | + | 0.280976i | ||||
\(153\) | 2.50000 | + | 4.33013i | 0.202113 | + | 0.350070i | ||||
\(154\) | 2.00000 | + | 3.46410i | 0.161165 | + | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.50000 | + | 0.866025i | −0.280224 | + | 0.0693375i | ||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 8.00000 | + | 13.8564i | 0.636446 | + | 1.10236i | ||||
\(159\) | 3.50000 | + | 6.06218i | 0.277568 | + | 0.480762i | ||||
\(160\) | −1.50000 | + | 2.59808i | −0.118585 | + | 0.205396i | ||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | 7.00000 | 0.546608 | ||||||||
\(165\) | 6.00000 | − | 10.3923i | 0.467099 | − | 0.809040i | ||||
\(166\) | 4.00000 | + | 6.92820i | 0.310460 | + | 0.537733i | ||||
\(167\) | 4.00000 | + | 6.92820i | 0.309529 | + | 0.536120i | 0.978259 | − | 0.207385i | \(-0.0664952\pi\) |
−0.668730 | + | 0.743505i | \(0.733162\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −15.0000 | −1.15045 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | −7.00000 | + | 12.1244i | −0.532200 | + | 0.921798i | 0.467093 | + | 0.884208i | \(0.345301\pi\) |
−0.999293 | + | 0.0375896i | \(0.988032\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | −2.00000 | + | 3.46410i | −0.150756 | + | 0.261116i | ||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −10.0000 | − | 17.3205i | −0.747435 | − | 1.29460i | −0.949048 | − | 0.315130i | \(-0.897952\pi\) |
0.201613 | − | 0.979465i | \(-0.435382\pi\) | |||||||
\(180\) | −1.50000 | − | 2.59808i | −0.111803 | − | 0.193649i | ||||
\(181\) | −5.00000 | −0.371647 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(182\) | −3.50000 | + | 0.866025i | −0.259437 | + | 0.0641941i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 2.00000 | + | 3.46410i | 0.147442 | + | 0.255377i | ||||
\(185\) | −10.5000 | − | 18.1865i | −0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0000 | −1.46254 | ||||||||
\(188\) | −6.00000 | + | 10.3923i | −0.437595 | + | 0.757937i | ||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | 12.0000 | 0.870572 | ||||||||
\(191\) | 12.0000 | − | 20.7846i | 0.868290 | − | 1.50392i | 0.00454614 | − | 0.999990i | \(-0.498553\pi\) |
0.863743 | − | 0.503932i | \(-0.168114\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −9.50000 | − | 16.4545i | −0.683825 | − | 1.18442i | −0.973805 | − | 0.227387i | \(-0.926982\pi\) |
0.289980 | − | 0.957033i | \(-0.406351\pi\) | |||||||
\(194\) | 18.0000 | 1.29232 | ||||||||
\(195\) | 7.50000 | + | 7.79423i | 0.537086 | + | 0.558156i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −11.0000 | − | 19.0526i | −0.783718 | − | 1.35744i | −0.929762 | − | 0.368161i | \(-0.879988\pi\) |
0.146045 | − | 0.989278i | \(-0.453346\pi\) | |||||||
\(198\) | −2.00000 | − | 3.46410i | −0.142134 | − | 0.246183i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 6.00000 | − | 10.3923i | 0.423207 | − | 0.733017i | ||||
\(202\) | −1.50000 | + | 2.59808i | −0.105540 | + | 0.182800i | ||||
\(203\) | 9.00000 | 0.631676 | ||||||||
\(204\) | −2.50000 | + | 4.33013i | −0.175035 | + | 0.303170i | ||||
\(205\) | −10.5000 | − | 18.1865i | −0.733352 | − | 1.27020i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | −2.50000 | − | 2.59808i | −0.173344 | − | 0.180144i | ||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | −1.50000 | − | 2.59808i | −0.103510 | − | 0.179284i | ||||
\(211\) | 4.00000 | + | 6.92820i | 0.275371 | + | 0.476957i | 0.970229 | − | 0.242190i | \(-0.0778659\pi\) |
−0.694857 | + | 0.719148i | \(0.744533\pi\) | |||||||
\(212\) | −3.50000 | + | 6.06218i | −0.240381 | + | 0.416352i | ||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | + | 20.7846i | −0.818393 | + | 1.41750i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.00000 | − | 12.1244i | −0.474100 | − | 0.821165i | ||||
\(219\) | −0.500000 | − | 0.866025i | −0.0337869 | − | 0.0585206i | ||||
\(220\) | 12.0000 | 0.809040 | ||||||||
\(221\) | 5.00000 | − | 17.3205i | 0.336336 | − | 1.16510i | ||||
\(222\) | −7.00000 | −0.469809 | ||||||||
\(223\) | 14.0000 | + | 24.2487i | 0.937509 | + | 1.62381i | 0.770097 | + | 0.637927i | \(0.220208\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | −2.00000 | + | 3.46410i | −0.133333 | + | 0.230940i | ||||
\(226\) | −5.00000 | −0.332595 | ||||||||
\(227\) | −12.0000 | + | 20.7846i | −0.796468 | + | 1.37952i | 0.125435 | + | 0.992102i | \(0.459967\pi\) |
−0.921903 | + | 0.387421i | \(0.873366\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 6.00000 | − | 10.3923i | 0.395628 | − | 0.685248i | ||||
\(231\) | −2.00000 | − | 3.46410i | −0.131590 | − | 0.227921i | ||||
\(232\) | 4.50000 | + | 7.79423i | 0.295439 | + | 0.511716i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 3.50000 | − | 0.866025i | 0.228802 | − | 0.0566139i | ||||
\(235\) | 36.0000 | 2.34838 | ||||||||
\(236\) | 4.00000 | + | 6.92820i | 0.260378 | + | 0.450988i | ||||
\(237\) | −8.00000 | − | 13.8564i | −0.519656 | − | 0.900070i | ||||
\(238\) | −2.50000 | + | 4.33013i | −0.162051 | + | 0.280680i | ||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 1.50000 | − | 2.59808i | 0.0968246 | − | 0.167705i | ||||
\(241\) | 4.50000 | − | 7.79423i | 0.289870 | − | 0.502070i | −0.683908 | − | 0.729568i | \(-0.739721\pi\) |
0.973779 | + | 0.227498i | \(0.0730544\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.50000 | − | 6.06218i | −0.224065 | − | 0.388091i | ||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | −7.00000 | −0.446304 | ||||||||
\(247\) | −4.00000 | + | 13.8564i | −0.254514 | + | 0.881662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | − | 6.92820i | −0.253490 | − | 0.439057i | ||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 8.00000 | − | 13.8564i | 0.502956 | − | 0.871145i | ||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | 15.0000 | 0.939336 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.50000 | − | 6.06218i | −0.218324 | − | 0.378148i | 0.735972 | − | 0.677012i | \(-0.236726\pi\) |
−0.954296 | + | 0.298864i | \(0.903392\pi\) | |||||||
\(258\) | 4.00000 | + | 6.92820i | 0.249029 | + | 0.431331i | ||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | −3.00000 | + | 10.3923i | −0.186052 | + | 0.644503i | ||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | −4.00000 | − | 6.92820i | −0.246651 | − | 0.427211i | 0.715944 | − | 0.698158i | \(-0.245997\pi\) |
−0.962594 | + | 0.270947i | \(0.912663\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | 21.0000 | 1.29002 | ||||||||
\(266\) | 2.00000 | − | 3.46410i | 0.122628 | − | 0.212398i | ||||
\(267\) | −3.00000 | + | 5.19615i | −0.183597 | + | 0.317999i | ||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −7.00000 | + | 12.1244i | −0.426798 | + | 0.739235i | −0.996586 | − | 0.0825561i | \(-0.973692\pi\) |
0.569789 | + | 0.821791i | \(0.307025\pi\) | |||||||
\(270\) | 1.50000 | + | 2.59808i | 0.0912871 | + | 0.158114i | ||||
\(271\) | −12.0000 | − | 20.7846i | −0.728948 | − | 1.26258i | −0.957328 | − | 0.289003i | \(-0.906676\pi\) |
0.228380 | − | 0.973572i | \(-0.426657\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 3.50000 | − | 0.866025i | 0.211830 | − | 0.0524142i | ||||
\(274\) | 3.00000 | 0.181237 | ||||||||
\(275\) | −8.00000 | − | 13.8564i | −0.482418 | − | 0.835573i | ||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | −9.50000 | + | 16.4545i | −0.570800 | + | 0.988654i | 0.425684 | + | 0.904872i | \(0.360033\pi\) |
−0.996484 | + | 0.0837823i | \(0.973300\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.50000 | − | 2.59808i | 0.0896421 | − | 0.155265i | ||||
\(281\) | 15.0000 | 0.894825 | 0.447412 | − | 0.894328i | \(-0.352346\pi\) | ||||
0.447412 | + | 0.894328i | \(0.352346\pi\) | |||||||
\(282\) | 6.00000 | − | 10.3923i | 0.357295 | − | 0.618853i | ||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | −4.00000 | + | 13.8564i | −0.236525 | + | 0.819346i | ||||
\(287\) | −7.00000 | −0.413197 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | 13.5000 | − | 23.3827i | 0.792747 | − | 1.37308i | ||||
\(291\) | −18.0000 | −1.05518 | ||||||||
\(292\) | 0.500000 | − | 0.866025i | 0.0292603 | − | 0.0506803i | ||||
\(293\) | 16.5000 | − | 28.5788i | 0.963940 | − | 1.66959i | 0.251505 | − | 0.967856i | \(-0.419075\pi\) |
0.712436 | − | 0.701737i | \(-0.247592\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 12.0000 | − | 20.7846i | 0.698667 | − | 1.21013i | ||||
\(296\) | −3.50000 | − | 6.06218i | −0.203433 | − | 0.352357i | ||||
\(297\) | 2.00000 | + | 3.46410i | 0.116052 | + | 0.201008i | ||||
\(298\) | 7.00000 | 0.405499 | ||||||||
\(299\) | 10.0000 | + | 10.3923i | 0.578315 | + | 0.601003i | ||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 4.00000 | + | 6.92820i | 0.230556 | + | 0.399335i | ||||
\(302\) | 4.00000 | + | 6.92820i | 0.230174 | + | 0.398673i | ||||
\(303\) | 1.50000 | − | 2.59808i | 0.0861727 | − | 0.149256i | ||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −10.5000 | + | 18.1865i | −0.601228 | + | 1.04136i | ||||
\(306\) | 2.50000 | − | 4.33013i | 0.142915 | − | 0.247537i | ||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | −2.00000 | − | 3.46410i | −0.113776 | − | 0.197066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 2.50000 | + | 2.59808i | 0.141535 | + | 0.147087i | ||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 6.50000 | + | 11.2583i | 0.366816 | + | 0.635344i | ||||
\(315\) | 1.50000 | + | 2.59808i | 0.0845154 | + | 0.146385i | ||||
\(316\) | 8.00000 | − | 13.8564i | 0.450035 | − | 0.779484i | ||||
\(317\) | 35.0000 | 1.96580 | 0.982898 | − | 0.184151i | \(-0.0589536\pi\) | ||||
0.982898 | + | 0.184151i | \(0.0589536\pi\) | |||||||
\(318\) | 3.50000 | − | 6.06218i | 0.196270 | − | 0.339950i | ||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | − | 3.46410i | −0.111456 | − | 0.193047i | ||||
\(323\) | 10.0000 | + | 17.3205i | 0.556415 | + | 0.963739i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 14.0000 | − | 3.46410i | 0.776580 | − | 0.192154i | ||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 7.00000 | + | 12.1244i | 0.387101 | + | 0.670478i | ||||
\(328\) | −3.50000 | − | 6.06218i | −0.193255 | − | 0.334728i | ||||
\(329\) | 6.00000 | − | 10.3923i | 0.330791 | − | 0.572946i | ||||
\(330\) | −12.0000 | −0.660578 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 4.00000 | − | 6.92820i | 0.219529 | − | 0.380235i | ||||
\(333\) | 7.00000 | 0.383598 | ||||||||
\(334\) | 4.00000 | − | 6.92820i | 0.218870 | − | 0.379094i | ||||
\(335\) | −18.0000 | − | 31.1769i | −0.983445 | − | 1.70338i | ||||
\(336\) | −0.500000 | − | 0.866025i | −0.0272772 | − | 0.0472456i | ||||
\(337\) | −9.00000 | −0.490261 | −0.245131 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245131 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(338\) | −11.0000 | − | 6.92820i | −0.598321 | − | 0.376845i | ||||
\(339\) | 5.00000 | 0.271563 | ||||||||
\(340\) | 7.50000 | + | 12.9904i | 0.406745 | + | 0.704502i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.00000 | + | 3.46410i | −0.108148 | + | 0.187317i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −4.00000 | + | 6.92820i | −0.215666 | + | 0.373544i | ||||
\(345\) | −6.00000 | + | 10.3923i | −0.323029 | + | 0.559503i | ||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | −10.0000 | + | 17.3205i | −0.536828 | + | 0.929814i | 0.462244 | + | 0.886753i | \(0.347044\pi\) |
−0.999072 | + | 0.0430610i | \(0.986289\pi\) | |||||||
\(348\) | −4.50000 | − | 7.79423i | −0.241225 | − | 0.417815i | ||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | −3.50000 | + | 0.866025i | −0.186816 | + | 0.0462250i | ||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | 12.5000 | + | 21.6506i | 0.665308 | + | 1.15235i | 0.979202 | + | 0.202889i | \(0.0650330\pi\) |
−0.313894 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(354\) | −4.00000 | − | 6.92820i | −0.212598 | − | 0.368230i | ||||
\(355\) | −18.0000 | + | 31.1769i | −0.955341 | + | 1.65470i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 2.50000 | − | 4.33013i | 0.132314 | − | 0.229175i | ||||
\(358\) | −10.0000 | + | 17.3205i | −0.528516 | + | 0.915417i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | −1.50000 | + | 2.59808i | −0.0790569 | + | 0.136931i | ||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 2.50000 | + | 4.33013i | 0.131397 | + | 0.227586i | ||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 2.50000 | + | 2.59808i | 0.131036 | + | 0.136176i | ||||
\(365\) | −3.00000 | −0.157027 | ||||||||
\(366\) | 3.50000 | + | 6.06218i | 0.182948 | + | 0.316875i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 2.00000 | − | 3.46410i | 0.104257 | − | 0.180579i | ||||
\(369\) | 7.00000 | 0.364405 | ||||||||
\(370\) | −10.5000 | + | 18.1865i | −0.545869 | + | 0.945473i | ||||
\(371\) | 3.50000 | − | 6.06218i | 0.181711 | − | 0.314733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.50000 | + | 12.9904i | −0.388335 | + | 0.672616i | −0.992226 | − | 0.124451i | \(-0.960283\pi\) |
0.603890 | + | 0.797067i | \(0.293616\pi\) | |||||||
\(374\) | 10.0000 | + | 17.3205i | 0.517088 | + | 0.895622i | ||||
\(375\) | −1.50000 | − | 2.59808i | −0.0774597 | − | 0.134164i | ||||
\(376\) | 12.0000 | 0.618853 | ||||||||
\(377\) | 22.5000 | + | 23.3827i | 1.15881 | + | 1.20427i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 14.0000 | + | 24.2487i | 0.719132 | + | 1.24557i | 0.961344 | + | 0.275349i | \(0.0887935\pi\) |
−0.242213 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(380\) | −6.00000 | − | 10.3923i | −0.307794 | − | 0.533114i | ||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | −24.0000 | −1.22795 | ||||||||
\(383\) | 14.0000 | − | 24.2487i | 0.715367 | − | 1.23905i | −0.247451 | − | 0.968900i | \(-0.579593\pi\) |
0.962818 | − | 0.270151i | \(-0.0870736\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | −9.50000 | + | 16.4545i | −0.483537 | + | 0.837511i | ||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | −9.00000 | − | 15.5885i | −0.456906 | − | 0.791384i | ||||
\(389\) | 7.00000 | 0.354914 | 0.177457 | − | 0.984129i | \(-0.443213\pi\) | ||||
0.177457 | + | 0.984129i | \(0.443213\pi\) | |||||||
\(390\) | 3.00000 | − | 10.3923i | 0.151911 | − | 0.526235i | ||||
\(391\) | 20.0000 | 1.01144 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | −6.00000 | − | 10.3923i | −0.302660 | − | 0.524222i | ||||
\(394\) | −11.0000 | + | 19.0526i | −0.554172 | + | 0.959854i | ||||
\(395\) | −48.0000 | −2.41514 | ||||||||
\(396\) | −2.00000 | + | 3.46410i | −0.100504 | + | 0.174078i | ||||
\(397\) | 1.00000 | − | 1.73205i | 0.0501886 | − | 0.0869291i | −0.839840 | − | 0.542834i | \(-0.817351\pi\) |
0.890028 | + | 0.455905i | \(0.150684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 8.50000 | + | 14.7224i | 0.424470 | + | 0.735203i | 0.996371 | − | 0.0851195i | \(-0.0271272\pi\) |
−0.571901 | + | 0.820323i | \(0.693794\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.00000 | 0.149256 | ||||||||
\(405\) | −1.50000 | − | 2.59808i | −0.0745356 | − | 0.129099i | ||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | −14.0000 | + | 24.2487i | −0.693954 | + | 1.20196i | ||||
\(408\) | 5.00000 | 0.247537 | ||||||||
\(409\) | 6.50000 | − | 11.2583i | 0.321404 | − | 0.556689i | −0.659374 | − | 0.751815i | \(-0.729178\pi\) |
0.980778 | + | 0.195127i | \(0.0625118\pi\) | |||||||
\(410\) | −10.5000 | + | 18.1865i | −0.518558 | + | 0.898169i | ||||
\(411\) | −3.00000 | −0.147979 | ||||||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | −4.00000 | − | 6.92820i | −0.196827 | − | 0.340915i | ||||
\(414\) | 2.00000 | + | 3.46410i | 0.0982946 | + | 0.170251i | ||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | −1.00000 | + | 3.46410i | −0.0490290 | + | 0.169842i | ||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | −8.00000 | − | 13.8564i | −0.391293 | − | 0.677739i | ||||
\(419\) | 8.00000 | + | 13.8564i | 0.390826 | + | 0.676930i | 0.992559 | − | 0.121768i | \(-0.0388562\pi\) |
−0.601733 | + | 0.798697i | \(0.705523\pi\) | |||||||
\(420\) | −1.50000 | + | 2.59808i | −0.0731925 | + | 0.126773i | ||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 4.00000 | − | 6.92820i | 0.194717 | − | 0.337260i | ||||
\(423\) | −6.00000 | + | 10.3923i | −0.291730 | + | 0.505291i | ||||
\(424\) | 7.00000 | 0.339950 | ||||||||
\(425\) | 10.0000 | − | 17.3205i | 0.485071 | − | 0.840168i | ||||
\(426\) | 6.00000 | + | 10.3923i | 0.290701 | + | 0.503509i | ||||
\(427\) | 3.50000 | + | 6.06218i | 0.169377 | + | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | − | 13.8564i | 0.193122 | − | 0.668994i | ||||
\(430\) | 24.0000 | 1.15738 | ||||||||
\(431\) | 2.00000 | + | 3.46410i | 0.0963366 | + | 0.166860i | 0.910166 | − | 0.414244i | \(-0.135954\pi\) |
−0.813829 | + | 0.581104i | \(0.802621\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −15.5000 | + | 26.8468i | −0.744882 | + | 1.29017i | 0.205367 | + | 0.978685i | \(0.434161\pi\) |
−0.950250 | + | 0.311489i | \(0.899172\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.5000 | + | 23.3827i | −0.647275 | + | 1.12111i | ||||
\(436\) | −7.00000 | + | 12.1244i | −0.335239 | + | 0.580651i | ||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | −0.500000 | + | 0.866025i | −0.0238909 | + | 0.0413803i | ||||
\(439\) | 8.00000 | + | 13.8564i | 0.381819 | + | 0.661330i | 0.991322 | − | 0.131453i | \(-0.0419644\pi\) |
−0.609503 | + | 0.792784i | \(0.708631\pi\) | |||||||
\(440\) | −6.00000 | − | 10.3923i | −0.286039 | − | 0.495434i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −17.5000 | + | 4.33013i | −0.832390 | + | 0.205963i | ||||
\(443\) | −16.0000 | −0.760183 | −0.380091 | − | 0.924949i | \(-0.624107\pi\) | ||||
−0.380091 | + | 0.924949i | \(0.624107\pi\) | |||||||
\(444\) | 3.50000 | + | 6.06218i | 0.166103 | + | 0.287698i | ||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | 14.0000 | − | 24.2487i | 0.662919 | − | 1.14821i | ||||
\(447\) | −7.00000 | −0.331089 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | 7.00000 | − | 12.1244i | 0.330350 | − | 0.572184i | −0.652230 | − | 0.758021i | \(-0.726166\pi\) |
0.982581 | + | 0.185837i | \(0.0594997\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | −14.0000 | + | 24.2487i | −0.659234 | + | 1.14183i | ||||
\(452\) | 2.50000 | + | 4.33013i | 0.117590 | + | 0.203672i | ||||
\(453\) | −4.00000 | − | 6.92820i | −0.187936 | − | 0.325515i | ||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 3.00000 | − | 10.3923i | 0.140642 | − | 0.487199i | ||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | −3.00000 | − | 5.19615i | −0.140181 | − | 0.242800i | ||||
\(459\) | −2.50000 | + | 4.33013i | −0.116690 | + | 0.202113i | ||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | −9.50000 | + | 16.4545i | −0.442459 | + | 0.766362i | −0.997871 | − | 0.0652135i | \(-0.979227\pi\) |
0.555412 | + | 0.831575i | \(0.312560\pi\) | |||||||
\(462\) | −2.00000 | + | 3.46410i | −0.0930484 | + | 0.161165i | ||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −2.50000 | − | 2.59808i | −0.115563 | − | 0.120096i | ||||
\(469\) | −12.0000 | −0.554109 | ||||||||
\(470\) | −18.0000 | − | 31.1769i | −0.830278 | − | 1.43808i | ||||
\(471\) | −6.50000 | − | 11.2583i | −0.299504 | − | 0.518756i | ||||
\(472\) | 4.00000 | − | 6.92820i | 0.184115 | − | 0.318896i | ||||
\(473\) | 32.0000 | 1.47136 | ||||||||
\(474\) | −8.00000 | + | 13.8564i | −0.367452 | + | 0.636446i | ||||
\(475\) | −8.00000 | + | 13.8564i | −0.367065 | + | 0.635776i | ||||
\(476\) | 5.00000 | 0.229175 | ||||||||
\(477\) | −3.50000 | + | 6.06218i | −0.160254 | + | 0.277568i | ||||
\(478\) | 2.00000 | + | 3.46410i | 0.0914779 | + | 0.158444i | ||||
\(479\) | −14.0000 | − | 24.2487i | −0.639676 | − | 1.10795i | −0.985504 | − | 0.169654i | \(-0.945735\pi\) |
0.345827 | − | 0.938298i | \(-0.387598\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | −17.5000 | − | 18.1865i | −0.797931 | − | 0.829235i | ||||
\(482\) | −9.00000 | −0.409939 | ||||||||
\(483\) | 2.00000 | + | 3.46410i | 0.0910032 | + | 0.157622i | ||||
\(484\) | −2.50000 | − | 4.33013i | −0.113636 | − | 0.196824i | ||||
\(485\) | −27.0000 | + | 46.7654i | −1.22601 | + | 2.12351i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.00000 | + | 3.46410i | −0.0906287 | + | 0.156973i | −0.907776 | − | 0.419456i | \(-0.862221\pi\) |
0.817147 | + | 0.576429i | \(0.195554\pi\) | |||||||
\(488\) | −3.50000 | + | 6.06218i | −0.158438 | + | 0.274422i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −1.50000 | + | 2.59808i | −0.0677631 | + | 0.117369i | ||||
\(491\) | −10.0000 | − | 17.3205i | −0.451294 | − | 0.781664i | 0.547173 | − | 0.837020i | \(-0.315704\pi\) |
−0.998467 | + | 0.0553560i | \(0.982371\pi\) | |||||||
\(492\) | 3.50000 | + | 6.06218i | 0.157792 | + | 0.273304i | ||||
\(493\) | 45.0000 | 2.02670 | ||||||||
\(494\) | 14.0000 | − | 3.46410i | 0.629890 | − | 0.155857i | ||||
\(495\) | 12.0000 | 0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.00000 | + | 10.3923i | 0.269137 | + | 0.466159i | ||||
\(498\) | −4.00000 | + | 6.92820i | −0.179244 | + | 0.310460i | ||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | −4.00000 | + | 6.92820i | −0.178707 | + | 0.309529i | ||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 12.0000 | − | 20.7846i | 0.535054 | − | 0.926740i | −0.464107 | − | 0.885779i | \(-0.653625\pi\) |
0.999161 | − | 0.0409609i | \(-0.0130419\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | −4.50000 | − | 7.79423i | −0.200247 | − | 0.346839i | ||||
\(506\) | −16.0000 | −0.711287 | ||||||||
\(507\) | 11.0000 | + | 6.92820i | 0.488527 | + | 0.307692i | ||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | −7.50000 | − | 12.9904i | −0.332432 | − | 0.575789i | 0.650556 | − | 0.759458i | \(-0.274536\pi\) |
−0.982988 | + | 0.183669i | \(0.941202\pi\) | |||||||
\(510\) | −7.50000 | − | 12.9904i | −0.332106 | − | 0.575224i | ||||
\(511\) | −0.500000 | + | 0.866025i | −0.0221187 | + | 0.0383107i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.00000 | − | 3.46410i | 0.0883022 | − | 0.152944i | ||||
\(514\) | −3.50000 | + | 6.06218i | −0.154378 | + | 0.267391i | ||||
\(515\) | −12.0000 | −0.528783 | ||||||||
\(516\) | 4.00000 | − | 6.92820i | 0.176090 | − | 0.304997i | ||||
\(517\) | −24.0000 | − | 41.5692i | −1.05552 | − | 1.82821i | ||||
\(518\) | 3.50000 | + | 6.06218i | 0.153781 | + | 0.266357i | ||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 10.5000 | − | 2.59808i | 0.460455 | − | 0.113933i | ||||
\(521\) | −17.0000 | −0.744784 | −0.372392 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372392 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(522\) | 4.50000 | + | 7.79423i | 0.196960 | + | 0.341144i | ||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | 6.00000 | − | 10.3923i | 0.262111 | − | 0.453990i | ||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −4.00000 | + | 6.92820i | −0.174408 | + | 0.302084i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −10.5000 | − | 18.1865i | −0.456091 | − | 0.789973i | ||||
\(531\) | 4.00000 | + | 6.92820i | 0.173585 | + | 0.300658i | ||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | −17.5000 | − | 18.1865i | −0.758009 | − | 0.787746i | ||||
\(534\) | 6.00000 | 0.259645 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | 10.0000 | − | 17.3205i | 0.431532 | − | 0.747435i | ||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | −2.00000 | + | 3.46410i | −0.0861461 | + | 0.149209i | ||||
\(540\) | 1.50000 | − | 2.59808i | 0.0645497 | − | 0.111803i | ||||
\(541\) | 43.0000 | 1.84871 | 0.924357 | − | 0.381528i | \(-0.124602\pi\) | ||||
0.924357 | + | 0.381528i | \(0.124602\pi\) | |||||||
\(542\) | −12.0000 | + | 20.7846i | −0.515444 | + | 0.892775i | ||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | 2.50000 | + | 4.33013i | 0.107187 | + | 0.185653i | ||||
\(545\) | 42.0000 | 1.79908 | ||||||||
\(546\) | −2.50000 | − | 2.59808i | −0.106990 | − | 0.111187i | ||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | −1.50000 | − | 2.59808i | −0.0640768 | − | 0.110984i | ||||
\(549\) | −3.50000 | − | 6.06218i | −0.149376 | − | 0.258727i | ||||
\(550\) | −8.00000 | + | 13.8564i | −0.341121 | + | 0.590839i | ||||
\(551\) | −36.0000 | −1.53365 | ||||||||
\(552\) | −2.00000 | + | 3.46410i | −0.0851257 | + | 0.147442i | ||||
\(553\) | −8.00000 | + | 13.8564i | −0.340195 | + | 0.589234i | ||||
\(554\) | 19.0000 | 0.807233 | ||||||||
\(555\) | 10.5000 | − | 18.1865i | 0.445700 | − | 0.771975i | ||||
\(556\) | −2.00000 | − | 3.46410i | −0.0848189 | − | 0.146911i | ||||
\(557\) | 16.5000 | + | 28.5788i | 0.699127 | + | 1.21092i | 0.968769 | + | 0.247964i | \(0.0797613\pi\) |
−0.269642 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | + | 27.7128i | −0.338364 | + | 1.17213i | ||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −10.0000 | − | 17.3205i | −0.422200 | − | 0.731272i | ||||
\(562\) | −7.50000 | − | 12.9904i | −0.316368 | − | 0.547966i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | −12.0000 | −0.505291 | ||||||||
\(565\) | 7.50000 | − | 12.9904i | 0.315527 | − | 0.546509i | ||||
\(566\) | 2.00000 | − | 3.46410i | 0.0840663 | − | 0.145607i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | 11.0000 | + | 19.0526i | 0.461144 | + | 0.798725i | 0.999018 | − | 0.0443003i | \(-0.0141058\pi\) |
−0.537874 | + | 0.843025i | \(0.680772\pi\) | |||||||
\(570\) | 6.00000 | + | 10.3923i | 0.251312 | + | 0.435286i | ||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 14.0000 | − | 3.46410i | 0.585369 | − | 0.144841i | ||||
\(573\) | 24.0000 | 1.00261 | ||||||||
\(574\) | 3.50000 | + | 6.06218i | 0.146087 | + | 0.253030i | ||||
\(575\) | 8.00000 | + | 13.8564i | 0.333623 | + | 0.577852i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −5.00000 | −0.208153 | −0.104076 | − | 0.994569i | \(-0.533189\pi\) | ||||
−0.104076 | + | 0.994569i | \(0.533189\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | 9.50000 | − | 16.4545i | 0.394807 | − | 0.683825i | ||||
\(580\) | −27.0000 | −1.12111 | ||||||||
\(581\) | −4.00000 | + | 6.92820i | −0.165948 | + | 0.287430i | ||||
\(582\) | 9.00000 | + | 15.5885i | 0.373062 | + | 0.646162i | ||||
\(583\) | −14.0000 | − | 24.2487i | −0.579821 | − | 1.00428i | ||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | −3.00000 | + | 10.3923i | −0.124035 | + | 0.429669i | ||||
\(586\) | −33.0000 | −1.36322 | ||||||||
\(587\) | 12.0000 | + | 20.7846i | 0.495293 | + | 0.857873i | 0.999985 | − | 0.00542667i | \(-0.00172737\pi\) |
−0.504692 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −24.0000 | −0.988064 | ||||||||
\(591\) | 11.0000 | − | 19.0526i | 0.452480 | − | 0.783718i | ||||
\(592\) | −3.50000 | + | 6.06218i | −0.143849 | + | 0.249154i | ||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | 2.00000 | − | 3.46410i | 0.0820610 | − | 0.142134i | ||||
\(595\) | −7.50000 | − | 12.9904i | −0.307470 | − | 0.532554i | ||||
\(596\) | −3.50000 | − | 6.06218i | −0.143366 | − | 0.248316i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.00000 | − | 13.8564i | 0.163572 | − | 0.566631i | ||||
\(599\) | −4.00000 | −0.163436 | −0.0817178 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817178 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(600\) | 2.00000 | + | 3.46410i | 0.0816497 | + | 0.141421i | ||||
\(601\) | 8.50000 | + | 14.7224i | 0.346722 | + | 0.600541i | 0.985665 | − | 0.168714i | \(-0.0539613\pi\) |
−0.638943 | + | 0.769254i | \(0.720628\pi\) | |||||||
\(602\) | 4.00000 | − | 6.92820i | 0.163028 | − | 0.282372i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | −7.50000 | + | 12.9904i | −0.304918 | + | 0.528134i | ||||
\(606\) | −3.00000 | −0.121867 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | −2.00000 | − | 3.46410i | −0.0811107 | − | 0.140488i | ||||
\(609\) | 4.50000 | + | 7.79423i | 0.182349 | + | 0.315838i | ||||
\(610\) | 21.0000 | 0.850265 | ||||||||
\(611\) | 42.0000 | − | 10.3923i | 1.69914 | − | 0.420428i | ||||
\(612\) | −5.00000 | −0.202113 | ||||||||
\(613\) | 0.500000 | + | 0.866025i | 0.0201948 | + | 0.0349784i | 0.875946 | − | 0.482409i | \(-0.160238\pi\) |
−0.855751 | + | 0.517387i | \(0.826905\pi\) | |||||||
\(614\) | −2.00000 | − | 3.46410i | −0.0807134 | − | 0.139800i | ||||
\(615\) | 10.5000 | − | 18.1865i | 0.423401 | − | 0.733352i | ||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 16.5000 | − | 28.5788i | 0.664265 | − | 1.15054i | −0.315219 | − | 0.949019i | \(-0.602078\pi\) |
0.979484 | − | 0.201522i | \(-0.0645887\pi\) | |||||||
\(618\) | −2.00000 | + | 3.46410i | −0.0804518 | + | 0.139347i | ||||
\(619\) | −32.0000 | −1.28619 | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||||
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | −4.00000 | − | 6.92820i | −0.160385 | − | 0.277796i | ||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 1.00000 | − | 3.46410i | 0.0400320 | − | 0.138675i | ||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 8.00000 | + | 13.8564i | 0.319489 | + | 0.553372i | ||||
\(628\) | 6.50000 | − | 11.2583i | 0.259378 | − | 0.449256i | ||||
\(629\) | −35.0000 | −1.39554 | ||||||||
\(630\) | 1.50000 | − | 2.59808i | 0.0597614 | − | 0.103510i | ||||
\(631\) | 20.0000 | − | 34.6410i | 0.796187 | − | 1.37904i | −0.125895 | − | 0.992044i | \(-0.540180\pi\) |
0.922082 | − | 0.386994i | \(-0.126486\pi\) | |||||||
\(632\) | −16.0000 | −0.636446 | ||||||||
\(633\) | −4.00000 | + | 6.92820i | −0.158986 | + | 0.275371i | ||||
\(634\) | −17.5000 | − | 30.3109i | −0.695014 | − | 1.20380i | ||||
\(635\) | 12.0000 | + | 20.7846i | 0.476205 | + | 0.824812i | ||||
\(636\) | −7.00000 | −0.277568 | ||||||||
\(637\) | −2.50000 | − | 2.59808i | −0.0990536 | − | 0.102940i | ||||
\(638\) | −36.0000 | −1.42525 | ||||||||
\(639\) | −6.00000 | − | 10.3923i | −0.237356 | − | 0.411113i | ||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | + | 10.3923i | −0.236617 | + | 0.409832i | −0.959741 | − | 0.280885i | \(-0.909372\pi\) |
0.723124 | + | 0.690718i | \(0.242705\pi\) | |||||||
\(644\) | −2.00000 | + | 3.46410i | −0.0788110 | + | 0.136505i | ||||
\(645\) | −24.0000 | −0.944999 | ||||||||
\(646\) | 10.0000 | − | 17.3205i | 0.393445 | − | 0.681466i | ||||
\(647\) | −6.00000 | − | 10.3923i | −0.235884 | − | 0.408564i | 0.723645 | − | 0.690172i | \(-0.242465\pi\) |
−0.959529 | + | 0.281609i | \(0.909132\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | −10.0000 | − | 10.3923i | −0.392232 | − | 0.407620i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | − | 3.46410i | −0.0783260 | − | 0.135665i | ||||
\(653\) | 17.0000 | + | 29.4449i | 0.665261 | + | 1.15227i | 0.979214 | + | 0.202828i | \(0.0650132\pi\) |
−0.313953 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(654\) | 7.00000 | − | 12.1244i | 0.273722 | − | 0.474100i | ||||
\(655\) | −36.0000 | −1.40664 | ||||||||
\(656\) | −3.50000 | + | 6.06218i | −0.136652 | + | 0.236688i | ||||
\(657\) | 0.500000 | − | 0.866025i | 0.0195069 | − | 0.0337869i | ||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 6.00000 | + | 10.3923i | 0.233550 | + | 0.404520i | ||||
\(661\) | 0.500000 | + | 0.866025i | 0.0194477 | + | 0.0336845i | 0.875585 | − | 0.483063i | \(-0.160476\pi\) |
−0.856138 | + | 0.516748i | \(0.827143\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 17.5000 | − | 4.33013i | 0.679644 | − | 0.168168i | ||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 6.00000 | + | 10.3923i | 0.232670 | + | 0.402996i | ||||
\(666\) | −3.50000 | − | 6.06218i | −0.135622 | − | 0.234905i | ||||
\(667\) | −18.0000 | + | 31.1769i | −0.696963 | + | 1.20717i | ||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | −14.0000 | + | 24.2487i | −0.541271 | + | 0.937509i | ||||
\(670\) | −18.0000 | + | 31.1769i | −0.695401 | + | 1.20447i | ||||
\(671\) | 28.0000 | 1.08093 | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | −9.50000 | − | 16.4545i | −0.366198 | − | 0.634274i | 0.622770 | − | 0.782405i | \(-0.286007\pi\) |
−0.988968 | + | 0.148132i | \(0.952674\pi\) | |||||||
\(674\) | 4.50000 | + | 7.79423i | 0.173334 | + | 0.300222i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | −0.500000 | + | 12.9904i | −0.0192308 | + | 0.499630i | ||||
\(677\) | 22.0000 | 0.845529 | 0.422764 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422764 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(678\) | −2.50000 | − | 4.33013i | −0.0960119 | − | 0.166298i | ||||
\(679\) | 9.00000 | + | 15.5885i | 0.345388 | + | 0.598230i | ||||
\(680\) | 7.50000 | − | 12.9904i | 0.287612 | − | 0.498158i | ||||
\(681\) | −24.0000 | −0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0000 | + | 17.3205i | −0.382639 | + | 0.662751i | −0.991439 | − | 0.130573i | \(-0.958318\pi\) |
0.608799 | + | 0.793324i | \(0.291651\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −4.50000 | + | 7.79423i | −0.171936 | + | 0.297802i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 3.00000 | + | 5.19615i | 0.114457 | + | 0.198246i | ||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 24.5000 | − | 6.06218i | 0.933376 | − | 0.230951i | ||||
\(690\) | 12.0000 | 0.456832 | ||||||||
\(691\) | 20.0000 | + | 34.6410i | 0.760836 | + | 1.31781i | 0.942420 | + | 0.334431i | \(0.108544\pi\) |
−0.181584 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(692\) | −7.00000 | − | 12.1244i | −0.266100 | − | 0.460899i | ||||
\(693\) | 2.00000 | − | 3.46410i | 0.0759737 | − | 0.131590i | ||||
\(694\) | 20.0000 | 0.759190 | ||||||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | −4.50000 | + | 7.79423i | −0.170572 | + | 0.295439i | ||||
\(697\) | −35.0000 | −1.32572 | ||||||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 2.00000 | + | 3.46410i | 0.0755929 | + | 0.130931i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 2.50000 | + | 2.59808i | 0.0943564 | + | 0.0980581i | ||||
\(703\) | 28.0000 | 1.05604 | ||||||||
\(704\) | −2.00000 | − | 3.46410i | −0.0753778 | − | 0.130558i | ||||
\(705\) | 18.0000 | + | 31.1769i | 0.677919 | + | 1.17419i | ||||
\(706\) | 12.5000 | − | 21.6506i | 0.470444 | − | 0.814832i | ||||
\(707\) | −3.00000 | −0.112827 | ||||||||
\(708\) | −4.00000 | + | 6.92820i | −0.150329 | + | 0.260378i | ||||
\(709\) | 0.500000 | − | 0.866025i | 0.0187779 | − | 0.0325243i | −0.856484 | − | 0.516174i | \(-0.827356\pi\) |
0.875262 | + | 0.483650i | \(0.160689\pi\) | |||||||
\(710\) | 36.0000 | 1.35106 | ||||||||
\(711\) | 8.00000 | − | 13.8564i | 0.300023 | − | 0.519656i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −5.00000 | −0.187120 | ||||||||
\(715\) | −30.0000 | − | 31.1769i | −1.12194 | − | 1.16595i | ||||
\(716\) | 20.0000 | 0.747435 | ||||||||
\(717\) | −2.00000 | − | 3.46410i | −0.0746914 | − | 0.129369i | ||||
\(718\) | 6.00000 | + | 10.3923i | 0.223918 | + | 0.387837i | ||||
\(719\) | 24.0000 | − | 41.5692i | 0.895049 | − | 1.55027i | 0.0613050 | − | 0.998119i | \(-0.480474\pi\) |
0.833744 | − | 0.552151i | \(-0.186193\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | −2.00000 | + | 3.46410i | −0.0744839 | + | 0.129010i | ||||
\(722\) | 1.50000 | − | 2.59808i | 0.0558242 | − | 0.0966904i | ||||
\(723\) | 9.00000 | 0.334714 | ||||||||
\(724\) | 2.50000 | − | 4.33013i | 0.0929118 | − | 0.160928i | ||||
\(725\) | 18.0000 | + | 31.1769i | 0.668503 | + | 1.15788i | ||||
\(726\) | 2.50000 | + | 4.33013i | 0.0927837 | + | 0.160706i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 1.00000 | − | 3.46410i | 0.0370625 | − | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.50000 | + | 2.59808i | 0.0555175 | + | 0.0961591i | ||||
\(731\) | 20.0000 | + | 34.6410i | 0.739727 | + | 1.28124i | ||||
\(732\) | 3.50000 | − | 6.06218i | 0.129364 | − | 0.224065i | ||||
\(733\) | 23.0000 | 0.849524 | 0.424762 | − | 0.905305i | \(-0.360358\pi\) | ||||
0.424762 | + | 0.905305i | \(0.360358\pi\) | |||||||
\(734\) | 2.00000 | − | 3.46410i | 0.0738213 | − | 0.127862i | ||||
\(735\) | 1.50000 | − | 2.59808i | 0.0553283 | − | 0.0958315i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −24.0000 | + | 41.5692i | −0.884051 | + | 1.53122i | ||||
\(738\) | −3.50000 | − | 6.06218i | −0.128837 | − | 0.223152i | ||||
\(739\) | −4.00000 | − | 6.92820i | −0.147142 | − | 0.254858i | 0.783028 | − | 0.621987i | \(-0.213674\pi\) |
−0.930170 | + | 0.367129i | \(0.880341\pi\) | |||||||
\(740\) | 21.0000 | 0.771975 | ||||||||
\(741\) | −14.0000 | + | 3.46410i | −0.514303 | + | 0.127257i | ||||
\(742\) | −7.00000 | −0.256978 | ||||||||
\(743\) | −8.00000 | − | 13.8564i | −0.293492 | − | 0.508342i | 0.681141 | − | 0.732152i | \(-0.261484\pi\) |
−0.974633 | + | 0.223810i | \(0.928151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5000 | + | 18.1865i | −0.384690 | + | 0.666303i | ||||
\(746\) | 15.0000 | 0.549189 | ||||||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | 10.0000 | − | 17.3205i | 0.365636 | − | 0.633300i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50000 | + | 2.59808i | −0.0547723 | + | 0.0948683i | ||||
\(751\) | 20.0000 | + | 34.6410i | 0.729810 | + | 1.26407i | 0.956963 | + | 0.290209i | \(0.0937250\pi\) |
−0.227153 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(752\) | −6.00000 | − | 10.3923i | −0.218797 | − | 0.378968i | ||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 9.00000 | − | 31.1769i | 0.327761 | − | 1.13540i | ||||
\(755\) | −24.0000 | −0.873449 | ||||||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | −19.0000 | − | 32.9090i | −0.690567 | − | 1.19610i | −0.971652 | − | 0.236414i | \(-0.924028\pi\) |
0.281086 | − | 0.959683i | \(-0.409305\pi\) | |||||||
\(758\) | 14.0000 | − | 24.2487i | 0.508503 | − | 0.880753i | ||||
\(759\) | 16.0000 | 0.580763 | ||||||||
\(760\) | −6.00000 | + | 10.3923i | −0.217643 | + | 0.376969i | ||||
\(761\) | −5.00000 | + | 8.66025i | −0.181250 | + | 0.313934i | −0.942306 | − | 0.334752i | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | 7.00000 | − | 12.1244i | 0.253417 | − | 0.438931i | ||||
\(764\) | 12.0000 | + | 20.7846i | 0.434145 | + | 0.751961i | ||||
\(765\) | 7.50000 | + | 12.9904i | 0.271163 | + | 0.469668i | ||||
\(766\) | −28.0000 | −1.01168 | ||||||||
\(767\) | 8.00000 | − | 27.7128i | 0.288863 | − | 1.00065i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −25.0000 | − | 43.3013i | −0.901523 | − | 1.56148i | −0.825518 | − | 0.564376i | \(-0.809117\pi\) |
−0.0760054 | − | 0.997107i | \(-0.524217\pi\) | |||||||
\(770\) | 6.00000 | + | 10.3923i | 0.216225 | + | 0.374513i | ||||
\(771\) | 3.50000 | − | 6.06218i | 0.126049 | − | 0.218324i | ||||
\(772\) | 19.0000 | 0.683825 | ||||||||
\(773\) | −19.0000 | + | 32.9090i | −0.683383 | + | 1.18365i | 0.290560 | + | 0.956857i | \(0.406159\pi\) |
−0.973942 | + | 0.226796i | \(0.927175\pi\) | |||||||
\(774\) | −4.00000 | + | 6.92820i | −0.143777 | + | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.00000 | + | 15.5885i | −0.323081 | + | 0.559593i | ||||
\(777\) | −3.50000 | − | 6.06218i | −0.125562 | − | 0.217479i | ||||
\(778\) | −3.50000 | − | 6.06218i | −0.125481 | − | 0.217340i | ||||
\(779\) | 28.0000 | 1.00320 | ||||||||
\(780\) | −10.5000 | + | 2.59808i | −0.375960 | + | 0.0930261i | ||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | −10.0000 | − | 17.3205i | −0.357599 | − | 0.619380i | ||||
\(783\) | −4.50000 | − | 7.79423i | −0.160817 | − | 0.278543i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | −39.0000 | −1.39197 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | 20.0000 | − | 34.6410i | 0.712923 | − | 1.23482i | −0.250832 | − | 0.968031i | \(-0.580704\pi\) |
0.963755 | − | 0.266788i | \(-0.0859624\pi\) | |||||||
\(788\) | 22.0000 | 0.783718 | ||||||||
\(789\) | 4.00000 | − | 6.92820i | 0.142404 | − | 0.246651i | ||||
\(790\) | 24.0000 | + | 41.5692i | 0.853882 | + | 1.47897i | ||||
\(791\) | −2.50000 | − | 4.33013i | −0.0888898 | − | 0.153962i | ||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | −7.00000 | + | 24.2487i | −0.248577 | + | 0.861097i | ||||
\(794\) | −2.00000 | −0.0709773 | ||||||||
\(795\) | 10.5000 | + | 18.1865i | 0.372397 | + | 0.645010i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0000 | + | 25.9808i | −0.531327 | + | 0.920286i | 0.468004 | + | 0.883726i | \(0.344973\pi\) |
−0.999331 | + | 0.0365596i | \(0.988360\pi\) | |||||||
\(798\) | 4.00000 | 0.141598 | ||||||||
\(799\) | 30.0000 | − | 51.9615i | 1.06132 | − | 1.83827i | ||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 8.50000 | − | 14.7224i | 0.300145 | − | 0.519867i | ||||
\(803\) | 2.00000 | + | 3.46410i | 0.0705785 | + | 0.122245i | ||||
\(804\) | 6.00000 | + | 10.3923i | 0.211604 | + | 0.366508i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | −1.50000 | − | 2.59808i | −0.0527698 | − | 0.0914000i | ||||
\(809\) | 2.50000 | + | 4.33013i | 0.0878953 | + | 0.152239i | 0.906621 | − | 0.421945i | \(-0.138653\pi\) |
−0.818726 | + | 0.574184i | \(0.805319\pi\) | |||||||
\(810\) | −1.50000 | + | 2.59808i | −0.0527046 | + | 0.0912871i | ||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | −4.50000 | + | 7.79423i | −0.157919 | + | 0.273524i | ||||
\(813\) | 12.0000 | − | 20.7846i | 0.420858 | − | 0.728948i | ||||
\(814\) | 28.0000 | 0.981399 | ||||||||
\(815\) | −6.00000 | + | 10.3923i | −0.210171 | + | 0.364027i | ||||
\(816\) | −2.50000 | − | 4.33013i | −0.0875175 | − | 0.151585i | ||||
\(817\) | −16.0000 | − | 27.7128i | −0.559769 | − | 0.969549i | ||||
\(818\) | −13.0000 | −0.454534 | ||||||||
\(819\) | 2.50000 | + | 2.59808i | 0.0873571 | + | 0.0907841i | ||||
\(820\) | 21.0000 | 0.733352 | ||||||||
\(821\) | −11.0000 | − | 19.0526i | −0.383903 | − | 0.664939i | 0.607714 | − | 0.794156i | \(-0.292087\pi\) |
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(822\) | 1.50000 | + | 2.59808i | 0.0523185 | + | 0.0906183i | ||||
\(823\) | 22.0000 | − | 38.1051i | 0.766872 | − | 1.32826i | −0.172379 | − | 0.985031i | \(-0.555146\pi\) |
0.939251 | − | 0.343230i | \(-0.111521\pi\) | |||||||
\(824\) | −4.00000 | −0.139347 | ||||||||
\(825\) | 8.00000 | − | 13.8564i | 0.278524 | − | 0.482418i | ||||
\(826\) | −4.00000 | + | 6.92820i | −0.139178 | + | 0.241063i | ||||
\(827\) | −24.0000 | −0.834562 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | −15.5000 | − | 26.8468i | −0.538337 | − | 0.932427i | −0.998994 | − | 0.0448490i | \(-0.985719\pi\) |
0.460657 | − | 0.887578i | \(-0.347614\pi\) | |||||||
\(830\) | 12.0000 | + | 20.7846i | 0.416526 | + | 0.721444i | ||||
\(831\) | −19.0000 | −0.659103 | ||||||||
\(832\) | 3.50000 | − | 0.866025i | 0.121341 | − | 0.0300240i | ||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | 2.00000 | + | 3.46410i | 0.0692543 | + | 0.119952i | ||||
\(835\) | 12.0000 | + | 20.7846i | 0.415277 | + | 0.719281i | ||||
\(836\) | −8.00000 | + | 13.8564i | −0.276686 | + | 0.479234i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000 | − | 13.8564i | 0.276355 | − | 0.478662i | ||||
\(839\) | 20.0000 | − | 34.6410i | 0.690477 | − | 1.19594i | −0.281205 | − | 0.959648i | \(-0.590734\pi\) |
0.971682 | − | 0.236293i | \(-0.0759325\pi\) | |||||||
\(840\) | 3.00000 | 0.103510 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 0.500000 | + | 0.866025i | 0.0172311 | + | 0.0298452i | ||||
\(843\) | 7.50000 | + | 12.9904i | 0.258314 | + | 0.447412i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 34.5000 | − | 18.1865i | 1.18684 | − | 0.625636i | ||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 2.50000 | + | 4.33013i | 0.0859010 | + | 0.148785i | ||||
\(848\) | −3.50000 | − | 6.06218i | −0.120190 | − | 0.208176i | ||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | −20.0000 | −0.685994 | ||||||||
\(851\) | 14.0000 | − | 24.2487i | 0.479914 | − | 0.831235i | ||||
\(852\) | 6.00000 | − | 10.3923i | 0.205557 | − | 0.356034i | ||||
\(853\) | −49.0000 | −1.67773 | −0.838864 | − | 0.544341i | \(-0.816780\pi\) | ||||
−0.838864 | + | 0.544341i | \(0.816780\pi\) | |||||||
\(854\) | 3.50000 | − | 6.06218i | 0.119768 | − | 0.207443i | ||||
\(855\) | −6.00000 | − | 10.3923i | −0.205196 | − | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.0000 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(858\) | −14.0000 | + | 3.46410i | −0.477952 | + | 0.118262i | ||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | −12.0000 | − | 20.7846i | −0.409197 | − | 0.708749i | ||||
\(861\) | −3.50000 | − | 6.06218i | −0.119280 | − | 0.206598i | ||||
\(862\) | 2.00000 | − | 3.46410i | 0.0681203 | − | 0.117988i | ||||
\(863\) | 12.0000 | 0.408485 | 0.204242 | − | 0.978920i | \(-0.434527\pi\) | ||||
0.204242 | + | 0.978920i | \(0.434527\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −21.0000 | + | 36.3731i | −0.714021 | + | 1.23672i | ||||
\(866\) | 31.0000 | 1.05342 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | + | 55.4256i | 1.08553 | + | 1.88019i | ||||
\(870\) | 27.0000 | 0.915386 | ||||||||
\(871\) | −30.0000 | − | 31.1769i | −1.01651 | − | 1.05639i | ||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | −9.00000 | − | 15.5885i | −0.304604 | − | 0.527589i | ||||
\(874\) | 8.00000 | + | 13.8564i | 0.270604 | + | 0.468700i | ||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 1.00000 | 0.0337869 | ||||||||
\(877\) | −1.50000 | + | 2.59808i | −0.0506514 | + | 0.0877308i | −0.890239 | − | 0.455493i | \(-0.849463\pi\) |
0.839588 | + | 0.543224i | \(0.182796\pi\) | |||||||
\(878\) | 8.00000 | − | 13.8564i | 0.269987 | − | 0.467631i | ||||
\(879\) | 33.0000 | 1.11306 | ||||||||
\(880\) | −6.00000 | + | 10.3923i | −0.202260 | + | 0.350325i | ||||
\(881\) | 20.5000 | + | 35.5070i | 0.690663 | + | 1.19626i | 0.971621 | + | 0.236543i | \(0.0760143\pi\) |
−0.280959 | + | 0.959720i | \(0.590652\pi\) | |||||||
\(882\) | −0.500000 | − | 0.866025i | −0.0168359 | − | 0.0291606i | ||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 12.5000 | + | 12.9904i | 0.420420 | + | 0.436914i | ||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 8.00000 | + | 13.8564i | 0.268765 | + | 0.465515i | ||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | 3.50000 | − | 6.06218i | 0.117452 | − | 0.203433i | ||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 9.00000 | − | 15.5885i | 0.301681 | − | 0.522526i | ||||
\(891\) | −2.00000 | + | 3.46410i | −0.0670025 | + | 0.116052i | ||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | −24.0000 | + | 41.5692i | −0.803129 | + | 1.39106i | ||||
\(894\) | 3.50000 | + | 6.06218i | 0.117058 | + | 0.202750i | ||||
\(895\) | −30.0000 | − | 51.9615i | −1.00279 | − | 1.73688i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −4.00000 | + | 13.8564i | −0.133556 | + | 0.462652i | ||||
\(898\) | −14.0000 | −0.467186 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 17.5000 | − | 30.3109i | 0.583010 | − | 1.00980i | ||||
\(902\) | 28.0000 | 0.932298 | ||||||||
\(903\) | −4.00000 | + | 6.92820i | −0.133112 | + | 0.230556i | ||||
\(904\) | 2.50000 | − | 4.33013i | 0.0831488 | − | 0.144018i | ||||
\(905\) | −15.0000 | −0.498617 | ||||||||
\(906\) | −4.00000 | + | 6.92820i | −0.132891 | + | 0.230174i | ||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | −12.0000 | − | 20.7846i | −0.398234 | − | 0.689761i | ||||
\(909\) | 3.00000 | 0.0995037 | ||||||||
\(910\) | −10.5000 | + | 2.59808i | −0.348072 | + | 0.0861254i | ||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 2.00000 | + | 3.46410i | 0.0662266 | + | 0.114708i | ||||
\(913\) | 16.0000 | + | 27.7128i | 0.529523 | + | 0.917160i | ||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | −21.0000 | −0.694239 | ||||||||
\(916\) | −3.00000 | + | 5.19615i | −0.0991228 | + | 0.171686i | ||||
\(917\) | −6.00000 | + | 10.3923i | −0.198137 | + | 0.343184i | ||||
\(918\) | 5.00000 | 0.165025 | ||||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | 6.00000 | + | 10.3923i | 0.197814 | + | 0.342624i | ||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | 19.0000 | 0.625732 | ||||||||
\(923\) | −12.0000 | + | 41.5692i | −0.394985 | + | 1.36827i | ||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | −14.0000 | − | 24.2487i | −0.460317 | − | 0.797293i | ||||
\(926\) | −16.0000 | − | 27.7128i | −0.525793 | − | 0.910700i | ||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | −9.00000 | −0.295439 | ||||||||
\(929\) | 10.5000 | − | 18.1865i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | 4.00000 | + | 6.92820i | 0.130954 | + | 0.226819i | ||||
\(934\) | 6.00000 | + | 10.3923i | 0.196326 | + | 0.340047i | ||||
\(935\) | −60.0000 | −1.96221 | ||||||||
\(936\) | −1.00000 | + | 3.46410i | −0.0326860 | + | 0.113228i | ||||
\(937\) | −49.0000 | −1.60076 | −0.800380 | − | 0.599493i | \(-0.795369\pi\) | ||||
−0.800380 | + | 0.599493i | \(0.795369\pi\) | |||||||
\(938\) | 6.00000 | + | 10.3923i | 0.195907 | + | 0.339321i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | −18.0000 | + | 31.1769i | −0.587095 | + | 1.01688i | ||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | −6.50000 | + | 11.2583i | −0.211781 | + | 0.366816i | ||||
\(943\) | 14.0000 | − | 24.2487i | 0.455903 | − | 0.789647i | ||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | −1.50000 | + | 2.59808i | −0.0487950 | + | 0.0845154i | ||||
\(946\) | −16.0000 | − | 27.7128i | −0.520205 | − | 0.901021i | ||||
\(947\) | −2.00000 | − | 3.46410i | −0.0649913 | − | 0.112568i | 0.831699 | − | 0.555227i | \(-0.187369\pi\) |
−0.896690 | + | 0.442659i | \(0.854035\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | −3.50000 | + | 0.866025i | −0.113615 | + | 0.0281124i | ||||
\(950\) | 16.0000 | 0.519109 | ||||||||
\(951\) | 17.5000 | + | 30.3109i | 0.567476 | + | 0.982898i | ||||
\(952\) | −2.50000 | − | 4.33013i | −0.0810255 | − | 0.140340i | ||||
\(953\) | 3.00000 | − | 5.19615i | 0.0971795 | − | 0.168320i | −0.813337 | − | 0.581793i | \(-0.802351\pi\) |
0.910516 | + | 0.413473i | \(0.135685\pi\) | |||||||
\(954\) | 7.00000 | 0.226633 | ||||||||
\(955\) | 36.0000 | − | 62.3538i | 1.16493 | − | 2.01772i | ||||
\(956\) | 2.00000 | − | 3.46410i | 0.0646846 | − | 0.112037i | ||||
\(957\) | 36.0000 | 1.16371 | ||||||||
\(958\) | −14.0000 | + | 24.2487i | −0.452319 | + | 0.783440i | ||||
\(959\) | 1.50000 | + | 2.59808i | 0.0484375 | + | 0.0838963i | ||||
\(960\) | 1.50000 | + | 2.59808i | 0.0484123 | + | 0.0838525i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −7.00000 | + | 24.2487i | −0.225689 | + | 0.781810i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.50000 | + | 7.79423i | 0.144935 | + | 0.251035i | ||||
\(965\) | −28.5000 | − | 49.3634i | −0.917447 | − | 1.58907i | ||||
\(966\) | 2.00000 | − | 3.46410i | 0.0643489 | − | 0.111456i | ||||
\(967\) | 40.0000 | 1.28631 | 0.643157 | − | 0.765735i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765735i | \(0.277624\pi\) | |||||||
\(968\) | −2.50000 | + | 4.33013i | −0.0803530 | + | 0.139176i | ||||
\(969\) | −10.0000 | + | 17.3205i | −0.321246 | + | 0.556415i | ||||
\(970\) | 54.0000 | 1.73384 | ||||||||
\(971\) | 12.0000 | − | 20.7846i | 0.385098 | − | 0.667010i | −0.606685 | − | 0.794943i | \(-0.707501\pi\) |
0.991783 | + | 0.127933i | \(0.0408342\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 2.00000 | + | 3.46410i | 0.0641171 | + | 0.111054i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 10.0000 | + | 10.3923i | 0.320256 | + | 0.332820i | ||||
\(976\) | 7.00000 | 0.224065 | ||||||||
\(977\) | −23.5000 | − | 40.7032i | −0.751832 | − | 1.30221i | −0.946934 | − | 0.321428i | \(-0.895837\pi\) |
0.195103 | − | 0.980783i | \(-0.437496\pi\) | |||||||
\(978\) | 2.00000 | + | 3.46410i | 0.0639529 | + | 0.110770i | ||||
\(979\) | 12.0000 | − | 20.7846i | 0.383522 | − | 0.664279i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | −7.00000 | + | 12.1244i | −0.223493 | + | 0.387101i | ||||
\(982\) | −10.0000 | + | 17.3205i | −0.319113 | + | 0.552720i | ||||
\(983\) | −28.0000 | −0.893061 | −0.446531 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446531 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(984\) | 3.50000 | − | 6.06218i | 0.111576 | − | 0.193255i | ||||
\(985\) | −33.0000 | − | 57.1577i | −1.05147 | − | 1.82120i | ||||
\(986\) | −22.5000 | − | 38.9711i | −0.716546 | − | 1.24109i | ||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | −10.0000 | − | 10.3923i | −0.318142 | − | 0.330623i | ||||
\(989\) | −32.0000 | −1.01754 | ||||||||
\(990\) | −6.00000 | − | 10.3923i | −0.190693 | − | 0.330289i | ||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 6.00000 | − | 10.3923i | 0.190308 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.00000 | 0.253490 | ||||||||
\(997\) | −19.5000 | + | 33.7750i | −0.617571 | + | 1.06966i | 0.372356 | + | 0.928090i | \(0.378550\pi\) |
−0.989928 | + | 0.141575i | \(0.954783\pi\) | |||||||
\(998\) | −2.00000 | − | 3.46410i | −0.0633089 | − | 0.109654i | ||||
\(999\) | 3.50000 | + | 6.06218i | 0.110735 | + | 0.191799i |
(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 | 546.2.l.b.211.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.r.o.757.1 | 2 | |||
13.3 | even | 3 | 7098.2.a.v.1.1 | 1 | |||
13.9 | even | 3 | inner | 546.2.l.b.295.1 | yes | 2 | |
13.10 | even | 6 | 7098.2.a.a.1.1 | 1 | |||
39.35 | odd | 6 | 1638.2.r.o.1387.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.b.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.l.b.295.1 | yes | 2 | 13.9 | even | 3 | inner | |
1638.2.r.o.757.1 | 2 | 3.2 | odd | 2 | |||
1638.2.r.o.1387.1 | 2 | 39.35 | odd | 6 | |||
7098.2.a.a.1.1 | 1 | 13.10 | even | 6 | |||
7098.2.a.v.1.1 | 1 | 13.3 | even | 3 |