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.c.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 | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 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 | ||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | + | 1.73205i | 0.258199 | + | 0.447214i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.50000 | − | 6.06218i | 0.848875 | − | 1.47029i | −0.0333386 | − | 0.999444i | \(-0.510614\pi\) |
0.882213 | − | 0.470850i | \(-0.156053\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 7.00000 | 1.20049 | ||||||||
\(35\) | −1.00000 | + | 1.73205i | −0.169031 | + | 0.292770i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 5.00000 | 0.811107 | ||||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | 2.50000 | + | 4.33013i | 0.390434 | + | 0.676252i | 0.992507 | − | 0.122189i | \(-0.0389915\pi\) |
−0.602072 | + | 0.798441i | \(0.705658\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 1.00000 | − | 1.73205i | 0.149071 | − | 0.258199i | ||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | −1.00000 | −0.145865 | −0.0729325 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729325 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | −7.00000 | −0.980196 | ||||||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | −5.00000 | −0.662266 | ||||||||
\(58\) | 2.50000 | − | 4.33013i | 0.328266 | − | 0.568574i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | −1.00000 | − | 1.73205i | −0.127000 | − | 0.219971i | ||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.00000 | − | 1.73205i | −0.868243 | − | 0.214834i | ||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 3.50000 | + | 6.06218i | 0.424437 | + | 0.735147i | ||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −4.00000 | + | 6.92820i | −0.474713 | + | 0.822226i | −0.999581 | − | 0.0289572i | \(-0.990781\pi\) |
0.524868 | + | 0.851184i | \(0.324115\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 2.50000 | + | 4.33013i | 0.286770 | + | 0.496700i | ||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 2.50000 | − | 2.59808i | 0.283069 | − | 0.294174i | ||||
\(79\) | 3.00000 | 0.337526 | 0.168763 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(80\) | 1.00000 | + | 1.73205i | 0.111803 | + | 0.193649i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.50000 | + | 4.33013i | −0.276079 | + | 0.478183i | ||||
\(83\) | −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 | ||||
\(85\) | −7.00000 | + | 12.1244i | −0.759257 | + | 1.31507i | ||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −2.50000 | + | 4.33013i | −0.268028 | + | 0.464238i | ||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | 5.50000 | + | 9.52628i | 0.582999 | + | 1.00978i | 0.995122 | + | 0.0986553i | \(0.0314541\pi\) |
−0.412123 | + | 0.911128i | \(0.635213\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 2.50000 | − | 2.59808i | 0.262071 | − | 0.272352i | ||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | −0.500000 | − | 0.866025i | −0.0515711 | − | 0.0893237i | ||||
\(95\) | −5.00000 | + | 8.66025i | −0.512989 | + | 0.888523i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | 0.500000 | − | 0.866025i | 0.0505076 | − | 0.0874818i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −7.00000 | − | 12.1244i | −0.696526 | − | 1.20642i | −0.969664 | − | 0.244443i | \(-0.921395\pi\) |
0.273138 | − | 0.961975i | \(-0.411939\pi\) | |||||||
\(102\) | −3.50000 | − | 6.06218i | −0.346552 | − | 0.600245i | ||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | −3.50000 | − | 0.866025i | −0.343203 | − | 0.0849208i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 1.50000 | + | 2.59808i | 0.145693 | + | 0.252347i | ||||
\(107\) | −7.50000 | − | 12.9904i | −0.725052 | − | 1.25583i | −0.958952 | − | 0.283567i | \(-0.908482\pi\) |
0.233900 | − | 0.972261i | \(-0.424851\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | −3.00000 | + | 5.19615i | −0.286039 | + | 0.495434i | ||||
\(111\) | 1.00000 | − | 1.73205i | 0.0949158 | − | 0.164399i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | −2.50000 | − | 4.33013i | −0.234146 | − | 0.405554i | ||||
\(115\) | 6.00000 | + | 10.3923i | 0.559503 | + | 0.969087i | ||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | −2.50000 | + | 2.59808i | −0.231125 | + | 0.240192i | ||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | −3.50000 | − | 6.06218i | −0.320844 | − | 0.555719i | ||||
\(120\) | −1.00000 | − | 1.73205i | −0.0912871 | − | 0.158114i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −7.00000 | −0.633750 | ||||||||
\(123\) | 2.50000 | − | 4.33013i | 0.225417 | − | 0.390434i | ||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | 6.00000 | + | 10.3923i | 0.532414 | + | 0.922168i | 0.999284 | + | 0.0378419i | \(0.0120483\pi\) |
−0.466870 | + | 0.884326i | \(0.654618\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | −2.00000 | − | 6.92820i | −0.175412 | − | 0.607644i | ||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | −1.50000 | − | 2.59808i | −0.130558 | − | 0.226134i | ||||
\(133\) | −2.50000 | − | 4.33013i | −0.216777 | − | 0.375470i | ||||
\(134\) | 1.00000 | − | 1.73205i | 0.0863868 | − | 0.149626i | ||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | −3.50000 | + | 6.06218i | −0.300123 | + | 0.519827i | ||||
\(137\) | −9.00000 | + | 15.5885i | −0.768922 | + | 1.33181i | 0.169226 | + | 0.985577i | \(0.445873\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | 9.50000 | − | 16.4545i | 0.805779 | − | 1.39565i | −0.109984 | − | 0.993933i | \(-0.535080\pi\) |
0.915764 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(140\) | −1.00000 | − | 1.73205i | −0.0845154 | − | 0.146385i | ||||
\(141\) | 0.500000 | + | 0.866025i | 0.0421076 | + | 0.0729325i | ||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | −3.00000 | − | 10.3923i | −0.250873 | − | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.00000 | + | 8.66025i | 0.415227 | + | 0.719195i | ||||
\(146\) | 6.00000 | + | 10.3923i | 0.496564 | + | 0.860073i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −7.00000 | + | 12.1244i | −0.573462 | + | 0.993266i | 0.422744 | + | 0.906249i | \(0.361067\pi\) |
−0.996207 | + | 0.0870170i | \(0.972267\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 13.0000 | 1.05792 | 0.528962 | − | 0.848645i | \(-0.322581\pi\) | ||||
0.528962 | + | 0.848645i | \(0.322581\pi\) | |||||||
\(152\) | −2.50000 | + | 4.33013i | −0.202777 | + | 0.351220i | ||||
\(153\) | 3.50000 | + | 6.06218i | 0.282958 | + | 0.490098i | ||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 3.50000 | + | 0.866025i | 0.280224 | + | 0.0693375i | ||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 1.50000 | + | 2.59808i | 0.119334 | + | 0.206692i | ||||
\(159\) | −1.50000 | − | 2.59808i | −0.118958 | − | 0.206041i | ||||
\(160\) | −1.00000 | + | 1.73205i | −0.0790569 | + | 0.136931i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 7.00000 | − | 12.1244i | 0.548282 | − | 0.949653i | −0.450110 | − | 0.892973i | \(-0.648615\pi\) |
0.998392 | − | 0.0566798i | \(-0.0180514\pi\) | |||||||
\(164\) | −5.00000 | −0.390434 | ||||||||
\(165\) | 3.00000 | − | 5.19615i | 0.233550 | − | 0.404520i | ||||
\(166\) | −4.00000 | − | 6.92820i | −0.310460 | − | 0.537733i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | −14.0000 | −1.07375 | ||||||||
\(171\) | 2.50000 | + | 4.33013i | 0.191180 | + | 0.331133i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −6.00000 | + | 10.3923i | −0.456172 | + | 0.790112i | −0.998755 | − | 0.0498898i | \(-0.984113\pi\) |
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | −5.50000 | + | 9.52628i | −0.412242 | + | 0.714025i | ||||
\(179\) | −10.0000 | − | 17.3205i | −0.747435 | − | 1.29460i | −0.949048 | − | 0.315130i | \(-0.897952\pi\) |
0.201613 | − | 0.979465i | \(-0.435382\pi\) | |||||||
\(180\) | 1.00000 | + | 1.73205i | 0.0745356 | + | 0.129099i | ||||
\(181\) | −9.00000 | −0.668965 | −0.334482 | − | 0.942402i | \(-0.608561\pi\) | ||||
−0.334482 | + | 0.942402i | \(0.608561\pi\) | |||||||
\(182\) | 3.50000 | + | 0.866025i | 0.259437 | + | 0.0641941i | ||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −21.0000 | −1.53567 | ||||||||
\(188\) | 0.500000 | − | 0.866025i | 0.0364662 | − | 0.0631614i | ||||
\(189\) | 0.500000 | − | 0.866025i | 0.0363696 | − | 0.0629941i | ||||
\(190\) | −10.0000 | −0.725476 | ||||||||
\(191\) | 2.00000 | − | 3.46410i | 0.144715 | − | 0.250654i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) |
0.929267 | + | 0.369410i | \(0.120440\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 2.00000 | + | 6.92820i | 0.143223 | + | 0.496139i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 4.50000 | + | 7.79423i | 0.320612 | + | 0.555316i | 0.980614 | − | 0.195947i | \(-0.0627782\pi\) |
−0.660003 | + | 0.751263i | \(0.729445\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | 13.0000 | − | 22.5167i | 0.921546 | − | 1.59616i | 0.124521 | − | 0.992217i | \(-0.460261\pi\) |
0.797025 | − | 0.603947i | \(-0.206406\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | 7.00000 | − | 12.1244i | 0.492518 | − | 0.853067i | ||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 3.50000 | − | 6.06218i | 0.245049 | − | 0.424437i | ||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 1.00000 | + | 1.73205i | 0.0690066 | + | 0.119523i | ||||
\(211\) | 5.00000 | + | 8.66025i | 0.344214 | + | 0.596196i | 0.985211 | − | 0.171347i | \(-0.0548120\pi\) |
−0.640996 | + | 0.767544i | \(0.721479\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 7.50000 | − | 12.9904i | 0.512689 | − | 0.888004i | ||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.00000 | + | 1.73205i | −0.0678844 | + | 0.117579i | ||||
\(218\) | −8.00000 | − | 13.8564i | −0.541828 | − | 0.938474i | ||||
\(219\) | −6.00000 | − | 10.3923i | −0.405442 | − | 0.702247i | ||||
\(220\) | −6.00000 | −0.404520 | ||||||||
\(221\) | 17.5000 | − | 18.1865i | 1.17718 | − | 1.22336i | ||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −7.00000 | + | 12.1244i | −0.464606 | + | 0.804722i | −0.999184 | − | 0.0403978i | \(-0.987137\pi\) |
0.534577 | + | 0.845120i | \(0.320471\pi\) | |||||||
\(228\) | 2.50000 | − | 4.33013i | 0.165567 | − | 0.286770i | ||||
\(229\) | 27.0000 | 1.78421 | 0.892105 | − | 0.451828i | \(-0.149228\pi\) | ||||
0.892105 | + | 0.451828i | \(0.149228\pi\) | |||||||
\(230\) | −6.00000 | + | 10.3923i | −0.395628 | + | 0.685248i | ||||
\(231\) | 1.50000 | + | 2.59808i | 0.0986928 | + | 0.170941i | ||||
\(232\) | 2.50000 | + | 4.33013i | 0.164133 | + | 0.284287i | ||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | −3.50000 | − | 0.866025i | −0.228802 | − | 0.0566139i | ||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | 3.50000 | − | 6.06218i | 0.226871 | − | 0.392953i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 1.00000 | − | 1.73205i | 0.0645497 | − | 0.111803i | ||||
\(241\) | −14.0000 | + | 24.2487i | −0.901819 | + | 1.56200i | −0.0766885 | + | 0.997055i | \(0.524435\pi\) |
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.50000 | − | 6.06218i | −0.224065 | − | 0.388091i | ||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | 5.00000 | 0.318788 | ||||||||
\(247\) | 12.5000 | − | 12.9904i | 0.795356 | − | 0.826558i | ||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 4.00000 | + | 6.92820i | 0.253490 | + | 0.439057i | ||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | 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 | ||||||||
\(253\) | −9.00000 | + | 15.5885i | −0.565825 | + | 0.980038i | ||||
\(254\) | −6.00000 | + | 10.3923i | −0.376473 | + | 0.652071i | ||||
\(255\) | 14.0000 | 0.876714 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.50000 | + | 12.9904i | 0.467837 | + | 0.810318i | 0.999325 | − | 0.0367485i | \(-0.0117000\pi\) |
−0.531487 | + | 0.847066i | \(0.678367\pi\) | |||||||
\(258\) | 1.00000 | + | 1.73205i | 0.0622573 | + | 0.107833i | ||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 5.00000 | − | 5.19615i | 0.310087 | − | 0.322252i | ||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 4.00000 | + | 6.92820i | 0.247121 | + | 0.428026i | ||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 1.50000 | − | 2.59808i | 0.0923186 | − | 0.159901i | ||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 2.50000 | − | 4.33013i | 0.153285 | − | 0.265497i | ||||
\(267\) | 5.50000 | − | 9.52628i | 0.336595 | − | 0.582999i | ||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | −1.00000 | − | 1.73205i | −0.0608581 | − | 0.105409i | ||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | −7.00000 | −0.424437 | ||||||||
\(273\) | −3.50000 | − | 0.866025i | −0.211830 | − | 0.0524142i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 1.50000 | + | 2.59808i | 0.0904534 | + | 0.156670i | ||||
\(276\) | −3.00000 | − | 5.19615i | −0.180579 | − | 0.312772i | ||||
\(277\) | −3.00000 | + | 5.19615i | −0.180253 | + | 0.312207i | −0.941966 | − | 0.335707i | \(-0.891025\pi\) |
0.761714 | + | 0.647913i | \(0.224358\pi\) | |||||||
\(278\) | 19.0000 | 1.13954 | ||||||||
\(279\) | 1.00000 | − | 1.73205i | 0.0598684 | − | 0.103695i | ||||
\(280\) | 1.00000 | − | 1.73205i | 0.0597614 | − | 0.103510i | ||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | −0.500000 | + | 0.866025i | −0.0297746 | + | 0.0515711i | ||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | −4.00000 | − | 6.92820i | −0.237356 | − | 0.411113i | ||||
\(285\) | 10.0000 | 0.592349 | ||||||||
\(286\) | 7.50000 | − | 7.79423i | 0.443484 | − | 0.460882i | ||||
\(287\) | 5.00000 | 0.295141 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | −5.00000 | + | 8.66025i | −0.293610 | + | 0.508548i | ||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | −6.00000 | + | 10.3923i | −0.350524 | + | 0.607125i | −0.986341 | − | 0.164714i | \(-0.947330\pi\) |
0.635818 | + | 0.771839i | \(0.280663\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −1.50000 | − | 2.59808i | −0.0870388 | − | 0.150756i | ||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | −6.00000 | − | 20.7846i | −0.346989 | − | 1.20201i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 1.00000 | + | 1.73205i | 0.0576390 | + | 0.0998337i | ||||
\(302\) | 6.50000 | + | 11.2583i | 0.374033 | + | 0.647844i | ||||
\(303\) | −7.00000 | + | 12.1244i | −0.402139 | + | 0.696526i | ||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | 7.00000 | − | 12.1244i | 0.400819 | − | 0.694239i | ||||
\(306\) | −3.50000 | + | 6.06218i | −0.200082 | + | 0.346552i | ||||
\(307\) | 9.00000 | 0.513657 | 0.256829 | − | 0.966457i | \(-0.417322\pi\) | ||||
0.256829 | + | 0.966457i | \(0.417322\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | −5.00000 | − | 8.66025i | −0.284440 | − | 0.492665i | ||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | 23.0000 | 1.30421 | 0.652105 | − | 0.758129i | \(-0.273886\pi\) | ||||
0.652105 | + | 0.758129i | \(0.273886\pi\) | |||||||
\(312\) | 1.00000 | + | 3.46410i | 0.0566139 | + | 0.196116i | ||||
\(313\) | 28.0000 | 1.58265 | 0.791327 | − | 0.611393i | \(-0.209391\pi\) | ||||
0.791327 | + | 0.611393i | \(0.209391\pi\) | |||||||
\(314\) | −9.00000 | − | 15.5885i | −0.507899 | − | 0.879708i | ||||
\(315\) | −1.00000 | − | 1.73205i | −0.0563436 | − | 0.0975900i | ||||
\(316\) | −1.50000 | + | 2.59808i | −0.0843816 | + | 0.146153i | ||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 1.50000 | − | 2.59808i | 0.0841158 | − | 0.145693i | ||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | −7.50000 | + | 12.9904i | −0.418609 | + | 0.725052i | ||||
\(322\) | −3.00000 | − | 5.19615i | −0.167183 | − | 0.289570i | ||||
\(323\) | −17.5000 | − | 30.3109i | −0.973726 | − | 1.68654i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.50000 | − | 0.866025i | −0.194145 | − | 0.0480384i | ||||
\(326\) | 14.0000 | 0.775388 | ||||||||
\(327\) | 8.00000 | + | 13.8564i | 0.442401 | + | 0.766261i | ||||
\(328\) | −2.50000 | − | 4.33013i | −0.138039 | − | 0.239091i | ||||
\(329\) | −0.500000 | + | 0.866025i | −0.0275659 | + | 0.0477455i | ||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | −11.0000 | + | 19.0526i | −0.604615 | + | 1.04722i | 0.387498 | + | 0.921871i | \(0.373340\pi\) |
−0.992112 | + | 0.125353i | \(0.959994\pi\) | |||||||
\(332\) | 4.00000 | − | 6.92820i | 0.219529 | − | 0.380235i | ||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | + | 3.46410i | 0.109272 | + | 0.189264i | ||||
\(336\) | 0.500000 | + | 0.866025i | 0.0272772 | + | 0.0472456i | ||||
\(337\) | −17.0000 | −0.926049 | −0.463025 | − | 0.886345i | \(-0.653236\pi\) | ||||
−0.463025 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(338\) | 0.500000 | + | 12.9904i | 0.0271964 | + | 0.706584i | ||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | −7.00000 | − | 12.1244i | −0.379628 | − | 0.657536i | ||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | −2.50000 | + | 4.33013i | −0.135185 | + | 0.234146i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.00000 | − | 1.73205i | 0.0539164 | − | 0.0933859i | ||||
\(345\) | 6.00000 | − | 10.3923i | 0.323029 | − | 0.559503i | ||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | −8.50000 | + | 14.7224i | −0.456304 | + | 0.790342i | −0.998762 | − | 0.0497412i | \(-0.984160\pi\) |
0.542458 | + | 0.840083i | \(0.317494\pi\) | |||||||
\(348\) | −2.50000 | − | 4.33013i | −0.134014 | − | 0.232119i | ||||
\(349\) | 9.00000 | + | 15.5885i | 0.481759 | + | 0.834431i | 0.999781 | − | 0.0209364i | \(-0.00666475\pi\) |
−0.518022 | + | 0.855367i | \(0.673331\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 3.50000 | + | 0.866025i | 0.186816 | + | 0.0462250i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −7.00000 | − | 12.1244i | −0.372572 | − | 0.645314i | 0.617388 | − | 0.786659i | \(-0.288191\pi\) |
−0.989960 | + | 0.141344i | \(0.954858\pi\) | |||||||
\(354\) | −3.00000 | − | 5.19615i | −0.159448 | − | 0.276172i | ||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | −11.0000 | −0.582999 | ||||||||
\(357\) | −3.50000 | + | 6.06218i | −0.185240 | + | 0.320844i | ||||
\(358\) | 10.0000 | − | 17.3205i | 0.528516 | − | 0.915417i | ||||
\(359\) | 18.0000 | 0.950004 | 0.475002 | − | 0.879985i | \(-0.342447\pi\) | ||||
0.475002 | + | 0.879985i | \(0.342447\pi\) | |||||||
\(360\) | −1.00000 | + | 1.73205i | −0.0527046 | + | 0.0912871i | ||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | −4.50000 | − | 7.79423i | −0.236515 | − | 0.409656i | ||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 1.00000 | + | 3.46410i | 0.0524142 | + | 0.181568i | ||||
\(365\) | −24.0000 | −1.25622 | ||||||||
\(366\) | 3.50000 | + | 6.06218i | 0.182948 | + | 0.316875i | ||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | −5.00000 | −0.260290 | ||||||||
\(370\) | 2.00000 | − | 3.46410i | 0.103975 | − | 0.180090i | ||||
\(371\) | 1.50000 | − | 2.59808i | 0.0778761 | − | 0.134885i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | −2.00000 | + | 3.46410i | −0.103556 | + | 0.179364i | −0.913147 | − | 0.407630i | \(-0.866355\pi\) |
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(374\) | −10.5000 | − | 18.1865i | −0.542942 | − | 0.940403i | ||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 1.00000 | 0.0515711 | ||||||||
\(377\) | −5.00000 | − | 17.3205i | −0.257513 | − | 0.892052i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 10.0000 | + | 17.3205i | 0.513665 | + | 0.889695i | 0.999874 | + | 0.0158521i | \(0.00504609\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(380\) | −5.00000 | − | 8.66025i | −0.256495 | − | 0.444262i | ||||
\(381\) | 6.00000 | − | 10.3923i | 0.307389 | − | 0.532414i | ||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | −15.5000 | + | 26.8468i | −0.792013 | + | 1.37181i | 0.132706 | + | 0.991155i | \(0.457633\pi\) |
−0.924719 | + | 0.380651i | \(0.875700\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 6.00000 | 0.305788 | ||||||||
\(386\) | 6.50000 | − | 11.2583i | 0.330841 | − | 0.573034i | ||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 1.00000 | + | 1.73205i | 0.0507673 | + | 0.0879316i | ||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | −5.00000 | + | 5.19615i | −0.253185 | + | 0.263117i | ||||
\(391\) | −42.0000 | −2.12403 | ||||||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | −4.00000 | − | 6.92820i | −0.201773 | − | 0.349482i | ||||
\(394\) | −4.50000 | + | 7.79423i | −0.226707 | + | 0.392668i | ||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | 7.50000 | − | 12.9904i | 0.376414 | − | 0.651969i | −0.614123 | − | 0.789210i | \(-0.710490\pi\) |
0.990538 | + | 0.137241i | \(0.0438236\pi\) | |||||||
\(398\) | 26.0000 | 1.30326 | ||||||||
\(399\) | −2.50000 | + | 4.33013i | −0.125157 | + | 0.216777i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | −7.00000 | − | 1.73205i | −0.348695 | − | 0.0862796i | ||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 1.00000 | + | 1.73205i | 0.0496904 | + | 0.0860663i | ||||
\(406\) | −2.50000 | − | 4.33013i | −0.124073 | − | 0.214901i | ||||
\(407\) | 3.00000 | − | 5.19615i | 0.148704 | − | 0.257564i | ||||
\(408\) | 7.00000 | 0.346552 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 5.00000 | − | 8.66025i | 0.246932 | − | 0.427699i | ||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | −5.00000 | + | 8.66025i | −0.246332 | + | 0.426660i | ||||
\(413\) | −3.00000 | − | 5.19615i | −0.147620 | − | 0.255686i | ||||
\(414\) | 3.00000 | + | 5.19615i | 0.147442 | + | 0.255377i | ||||
\(415\) | 16.0000 | 0.785409 | ||||||||
\(416\) | 2.50000 | − | 2.59808i | 0.122573 | − | 0.127381i | ||||
\(417\) | −19.0000 | −0.930434 | ||||||||
\(418\) | −7.50000 | − | 12.9904i | −0.366837 | − | 0.635380i | ||||
\(419\) | −2.00000 | − | 3.46410i | −0.0977064 | − | 0.169232i | 0.813029 | − | 0.582224i | \(-0.197817\pi\) |
−0.910735 | + | 0.412991i | \(0.864484\pi\) | |||||||
\(420\) | −1.00000 | + | 1.73205i | −0.0487950 | + | 0.0845154i | ||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | −5.00000 | + | 8.66025i | −0.243396 | + | 0.421575i | ||||
\(423\) | 0.500000 | − | 0.866025i | 0.0243108 | − | 0.0421076i | ||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | −3.50000 | + | 6.06218i | −0.169775 | + | 0.294059i | ||||
\(426\) | 4.00000 | + | 6.92820i | 0.193801 | + | 0.335673i | ||||
\(427\) | 3.50000 | + | 6.06218i | 0.169377 | + | 0.293369i | ||||
\(428\) | 15.0000 | 0.725052 | ||||||||
\(429\) | −7.50000 | + | 7.79423i | −0.362103 | + | 0.376309i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | 4.00000 | + | 6.92820i | 0.192673 | + | 0.333720i | 0.946135 | − | 0.323772i | \(-0.104951\pi\) |
−0.753462 | + | 0.657491i | \(0.771618\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −13.0000 | + | 22.5167i | −0.624740 | + | 1.08208i | 0.363851 | + | 0.931457i | \(0.381462\pi\) |
−0.988591 | + | 0.150624i | \(0.951872\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 5.00000 | − | 8.66025i | 0.239732 | − | 0.415227i | ||||
\(436\) | 8.00000 | − | 13.8564i | 0.383131 | − | 0.663602i | ||||
\(437\) | −30.0000 | −1.43509 | ||||||||
\(438\) | 6.00000 | − | 10.3923i | 0.286691 | − | 0.496564i | ||||
\(439\) | −2.00000 | − | 3.46410i | −0.0954548 | − | 0.165333i | 0.814344 | − | 0.580383i | \(-0.197097\pi\) |
−0.909798 | + | 0.415051i | \(0.863764\pi\) | |||||||
\(440\) | −3.00000 | − | 5.19615i | −0.143019 | − | 0.247717i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 24.5000 | + | 6.06218i | 1.16535 | + | 0.288348i | ||||
\(443\) | 15.0000 | 0.712672 | 0.356336 | − | 0.934358i | \(-0.384026\pi\) | ||||
0.356336 | + | 0.934358i | \(0.384026\pi\) | |||||||
\(444\) | 1.00000 | + | 1.73205i | 0.0474579 | + | 0.0821995i | ||||
\(445\) | −11.0000 | − | 19.0526i | −0.521450 | − | 0.903178i | ||||
\(446\) | −2.00000 | + | 3.46410i | −0.0947027 | + | 0.164030i | ||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | 19.0000 | − | 32.9090i | 0.896665 | − | 1.55307i | 0.0649356 | − | 0.997889i | \(-0.479316\pi\) |
0.831730 | − | 0.555181i | \(-0.187351\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 7.50000 | − | 12.9904i | 0.353161 | − | 0.611693i | ||||
\(452\) | −3.00000 | − | 5.19615i | −0.141108 | − | 0.244406i | ||||
\(453\) | −6.50000 | − | 11.2583i | −0.305397 | − | 0.528962i | ||||
\(454\) | −14.0000 | −0.657053 | ||||||||
\(455\) | −5.00000 | + | 5.19615i | −0.234404 | + | 0.243599i | ||||
\(456\) | 5.00000 | 0.234146 | ||||||||
\(457\) | −13.0000 | − | 22.5167i | −0.608114 | − | 1.05328i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.383437 | − | 0.923567i | \(-0.374740\pi\) | |||||||
\(458\) | 13.5000 | + | 23.3827i | 0.630814 | + | 1.09260i | ||||
\(459\) | 3.50000 | − | 6.06218i | 0.163366 | − | 0.282958i | ||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | −4.00000 | + | 6.92820i | −0.186299 | + | 0.322679i | −0.944013 | − | 0.329907i | \(-0.892983\pi\) |
0.757715 | + | 0.652586i | \(0.226316\pi\) | |||||||
\(462\) | −1.50000 | + | 2.59808i | −0.0697863 | + | 0.120873i | ||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | −2.50000 | + | 4.33013i | −0.116060 | + | 0.201021i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | 13.0000 | + | 22.5167i | 0.602213 | + | 1.04306i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −1.00000 | − | 3.46410i | −0.0462250 | − | 0.160128i | ||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 1.00000 | + | 1.73205i | 0.0461266 | + | 0.0798935i | ||||
\(471\) | 9.00000 | + | 15.5885i | 0.414698 | + | 0.718278i | ||||
\(472\) | −3.00000 | + | 5.19615i | −0.138086 | + | 0.239172i | ||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 1.50000 | − | 2.59808i | 0.0688973 | − | 0.119334i | ||||
\(475\) | −2.50000 | + | 4.33013i | −0.114708 | + | 0.198680i | ||||
\(476\) | 7.00000 | 0.320844 | ||||||||
\(477\) | −1.50000 | + | 2.59808i | −0.0686803 | + | 0.118958i | ||||
\(478\) | 6.00000 | + | 10.3923i | 0.274434 | + | 0.475333i | ||||
\(479\) | −10.5000 | − | 18.1865i | −0.479757 | − | 0.830964i | 0.519973 | − | 0.854183i | \(-0.325942\pi\) |
−0.999730 | + | 0.0232187i | \(0.992609\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | 2.00000 | + | 6.92820i | 0.0911922 | + | 0.315899i | ||||
\(482\) | −28.0000 | −1.27537 | ||||||||
\(483\) | 3.00000 | + | 5.19615i | 0.136505 | + | 0.236433i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −2.00000 | + | 3.46410i | −0.0908153 | + | 0.157297i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −17.5000 | + | 30.3109i | −0.793001 | + | 1.37352i | 0.131100 | + | 0.991369i | \(0.458149\pi\) |
−0.924101 | + | 0.382148i | \(0.875184\pi\) | |||||||
\(488\) | 3.50000 | − | 6.06218i | 0.158438 | − | 0.274422i | ||||
\(489\) | −14.0000 | −0.633102 | ||||||||
\(490\) | −1.00000 | + | 1.73205i | −0.0451754 | + | 0.0782461i | ||||
\(491\) | 4.00000 | + | 6.92820i | 0.180517 | + | 0.312665i | 0.942057 | − | 0.335453i | \(-0.108889\pi\) |
−0.761539 | + | 0.648119i | \(0.775556\pi\) | |||||||
\(492\) | 2.50000 | + | 4.33013i | 0.112709 | + | 0.195217i | ||||
\(493\) | −35.0000 | −1.57632 | ||||||||
\(494\) | 17.5000 | + | 4.33013i | 0.787362 | + | 0.194822i | ||||
\(495\) | −6.00000 | −0.269680 | ||||||||
\(496\) | 1.00000 | + | 1.73205i | 0.0449013 | + | 0.0777714i | ||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | −4.00000 | + | 6.92820i | −0.179244 | + | 0.310460i | ||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | −6.00000 | + | 10.3923i | −0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | −12.0000 | + | 20.7846i | −0.535054 | + | 0.926740i | 0.464107 | + | 0.885779i | \(0.346375\pi\) |
−0.999161 | + | 0.0409609i | \(0.986958\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | 14.0000 | + | 24.2487i | 0.622992 | + | 1.07905i | ||||
\(506\) | −18.0000 | −0.800198 | ||||||||
\(507\) | −0.500000 | − | 12.9904i | −0.0222058 | − | 0.576923i | ||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | 20.0000 | + | 34.6410i | 0.886484 | + | 1.53544i | 0.844003 | + | 0.536339i | \(0.180193\pi\) |
0.0424816 | + | 0.999097i | \(0.486474\pi\) | |||||||
\(510\) | 7.00000 | + | 12.1244i | 0.309965 | + | 0.536875i | ||||
\(511\) | 6.00000 | − | 10.3923i | 0.265424 | − | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.50000 | − | 4.33013i | 0.110378 | − | 0.191180i | ||||
\(514\) | −7.50000 | + | 12.9904i | −0.330811 | + | 0.572981i | ||||
\(515\) | −20.0000 | −0.881305 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | 1.50000 | + | 2.59808i | 0.0659699 | + | 0.114263i | ||||
\(518\) | 1.00000 | + | 1.73205i | 0.0439375 | + | 0.0761019i | ||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 7.00000 | + | 1.73205i | 0.306970 | + | 0.0759555i | ||||
\(521\) | 21.0000 | 0.920027 | 0.460013 | − | 0.887912i | \(-0.347845\pi\) | ||||
0.460013 | + | 0.887912i | \(0.347845\pi\) | |||||||
\(522\) | 2.50000 | + | 4.33013i | 0.109422 | + | 0.189525i | ||||
\(523\) | −19.5000 | − | 33.7750i | −0.852675 | − | 1.47688i | −0.878785 | − | 0.477218i | \(-0.841645\pi\) |
0.0261094 | − | 0.999659i | \(-0.491688\pi\) | |||||||
\(524\) | −4.00000 | + | 6.92820i | −0.174741 | + | 0.302660i | ||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | −7.00000 | + | 12.1244i | −0.304925 | + | 0.528145i | ||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −3.00000 | − | 5.19615i | −0.130312 | − | 0.225706i | ||||
\(531\) | 3.00000 | + | 5.19615i | 0.130189 | + | 0.225494i | ||||
\(532\) | 5.00000 | 0.216777 | ||||||||
\(533\) | 5.00000 | + | 17.3205i | 0.216574 | + | 0.750234i | ||||
\(534\) | 11.0000 | 0.476017 | ||||||||
\(535\) | 15.0000 | + | 25.9808i | 0.648507 | + | 1.12325i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −10.0000 | + | 17.3205i | −0.431532 | + | 0.747435i | ||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | −1.50000 | + | 2.59808i | −0.0646096 | + | 0.111907i | ||||
\(540\) | 1.00000 | − | 1.73205i | 0.0430331 | − | 0.0745356i | ||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 1.00000 | − | 1.73205i | 0.0429537 | − | 0.0743980i | ||||
\(543\) | 4.50000 | + | 7.79423i | 0.193113 | + | 0.334482i | ||||
\(544\) | −3.50000 | − | 6.06218i | −0.150061 | − | 0.259914i | ||||
\(545\) | 32.0000 | 1.37073 | ||||||||
\(546\) | −1.00000 | − | 3.46410i | −0.0427960 | − | 0.148250i | ||||
\(547\) | −32.0000 | −1.36822 | −0.684111 | − | 0.729378i | \(-0.739809\pi\) | ||||
−0.684111 | + | 0.729378i | \(0.739809\pi\) | |||||||
\(548\) | −9.00000 | − | 15.5885i | −0.384461 | − | 0.665906i | ||||
\(549\) | −3.50000 | − | 6.06218i | −0.149376 | − | 0.258727i | ||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | −25.0000 | −1.06504 | ||||||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | 1.50000 | − | 2.59808i | 0.0637865 | − | 0.110481i | ||||
\(554\) | −6.00000 | −0.254916 | ||||||||
\(555\) | −2.00000 | + | 3.46410i | −0.0848953 | + | 0.147043i | ||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | 7.50000 | + | 12.9904i | 0.317785 | + | 0.550420i | 0.980026 | − | 0.198871i | \(-0.0637276\pi\) |
−0.662240 | + | 0.749291i | \(0.730394\pi\) | |||||||
\(558\) | 2.00000 | 0.0846668 | ||||||||
\(559\) | −5.00000 | + | 5.19615i | −0.211477 | + | 0.219774i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 10.5000 | + | 18.1865i | 0.443310 | + | 0.767836i | ||||
\(562\) | 8.00000 | + | 13.8564i | 0.337460 | + | 0.584497i | ||||
\(563\) | −15.0000 | + | 25.9808i | −0.632175 | + | 1.09496i | 0.354932 | + | 0.934892i | \(0.384504\pi\) |
−0.987106 | + | 0.160066i | \(0.948829\pi\) | |||||||
\(564\) | −1.00000 | −0.0421076 | ||||||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | 14.0000 | − | 24.2487i | 0.588464 | − | 1.01925i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 4.00000 | − | 6.92820i | 0.167836 | − | 0.290701i | ||||
\(569\) | 22.0000 | + | 38.1051i | 0.922288 | + | 1.59745i | 0.795866 | + | 0.605473i | \(0.207016\pi\) |
0.126422 | + | 0.991977i | \(0.459651\pi\) | |||||||
\(570\) | 5.00000 | + | 8.66025i | 0.209427 | + | 0.362738i | ||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 10.5000 | + | 2.59808i | 0.439027 | + | 0.108631i | ||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 2.50000 | + | 4.33013i | 0.104348 | + | 0.180736i | ||||
\(575\) | 3.00000 | + | 5.19615i | 0.125109 | + | 0.216695i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | 16.0000 | − | 27.7128i | 0.665512 | − | 1.15270i | ||||
\(579\) | −6.50000 | + | 11.2583i | −0.270131 | + | 0.467880i | ||||
\(580\) | −10.0000 | −0.415227 | ||||||||
\(581\) | −4.00000 | + | 6.92820i | −0.165948 | + | 0.287430i | ||||
\(582\) | −1.00000 | − | 1.73205i | −0.0414513 | − | 0.0717958i | ||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 5.00000 | − | 5.19615i | 0.206725 | − | 0.214834i | ||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | −5.00000 | − | 8.66025i | −0.206372 | − | 0.357447i | 0.744197 | − | 0.667960i | \(-0.232832\pi\) |
−0.950569 | + | 0.310513i | \(0.899499\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | −12.0000 | −0.494032 | ||||||||
\(591\) | 4.50000 | − | 7.79423i | 0.185105 | − | 0.320612i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −13.0000 | −0.533846 | −0.266923 | − | 0.963718i | \(-0.586007\pi\) | ||||
−0.266923 | + | 0.963718i | \(0.586007\pi\) | |||||||
\(594\) | 1.50000 | − | 2.59808i | 0.0615457 | − | 0.106600i | ||||
\(595\) | 7.00000 | + | 12.1244i | 0.286972 | + | 0.497050i | ||||
\(596\) | −7.00000 | − | 12.1244i | −0.286731 | − | 0.496633i | ||||
\(597\) | −26.0000 | −1.06411 | ||||||||
\(598\) | 15.0000 | − | 15.5885i | 0.613396 | − | 0.637459i | ||||
\(599\) | −26.0000 | −1.06233 | −0.531166 | − | 0.847268i | \(-0.678246\pi\) | ||||
−0.531166 | + | 0.847268i | \(0.678246\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | −19.0000 | − | 32.9090i | −0.775026 | − | 1.34238i | −0.934780 | − | 0.355228i | \(-0.884403\pi\) |
0.159754 | − | 0.987157i | \(-0.448930\pi\) | |||||||
\(602\) | −1.00000 | + | 1.73205i | −0.0407570 | + | 0.0705931i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | −6.50000 | + | 11.2583i | −0.264481 | + | 0.458095i | ||||
\(605\) | −2.00000 | + | 3.46410i | −0.0813116 | + | 0.140836i | ||||
\(606\) | −14.0000 | −0.568711 | ||||||||
\(607\) | 15.0000 | − | 25.9808i | 0.608831 | − | 1.05453i | −0.382602 | − | 0.923913i | \(-0.624972\pi\) |
0.991433 | − | 0.130613i | \(-0.0416947\pi\) | |||||||
\(608\) | −2.50000 | − | 4.33013i | −0.101388 | − | 0.175610i | ||||
\(609\) | 2.50000 | + | 4.33013i | 0.101305 | + | 0.175466i | ||||
\(610\) | 14.0000 | 0.566843 | ||||||||
\(611\) | −3.50000 | − | 0.866025i | −0.141595 | − | 0.0350356i | ||||
\(612\) | −7.00000 | −0.282958 | ||||||||
\(613\) | 14.0000 | + | 24.2487i | 0.565455 | + | 0.979396i | 0.997007 | + | 0.0773084i | \(0.0246326\pi\) |
−0.431553 | + | 0.902088i | \(0.642034\pi\) | |||||||
\(614\) | 4.50000 | + | 7.79423i | 0.181605 | + | 0.314549i | ||||
\(615\) | −5.00000 | + | 8.66025i | −0.201619 | + | 0.349215i | ||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | 10.0000 | − | 17.3205i | 0.402585 | − | 0.697297i | −0.591452 | − | 0.806340i | \(-0.701445\pi\) |
0.994037 | + | 0.109043i | \(0.0347785\pi\) | |||||||
\(618\) | 5.00000 | − | 8.66025i | 0.201129 | − | 0.348367i | ||||
\(619\) | 41.0000 | 1.64793 | 0.823965 | − | 0.566641i | \(-0.191757\pi\) | ||||
0.823965 | + | 0.566641i | \(0.191757\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | 11.5000 | + | 19.9186i | 0.461108 | + | 0.798662i | ||||
\(623\) | 11.0000 | 0.440706 | ||||||||
\(624\) | −2.50000 | + | 2.59808i | −0.100080 | + | 0.104006i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 14.0000 | + | 24.2487i | 0.559553 | + | 0.969173i | ||||
\(627\) | 7.50000 | + | 12.9904i | 0.299521 | + | 0.518786i | ||||
\(628\) | 9.00000 | − | 15.5885i | 0.359139 | − | 0.622047i | ||||
\(629\) | 14.0000 | 0.558217 | ||||||||
\(630\) | 1.00000 | − | 1.73205i | 0.0398410 | − | 0.0690066i | ||||
\(631\) | −7.50000 | + | 12.9904i | −0.298570 | + | 0.517139i | −0.975809 | − | 0.218624i | \(-0.929843\pi\) |
0.677239 | + | 0.735763i | \(0.263176\pi\) | |||||||
\(632\) | −3.00000 | −0.119334 | ||||||||
\(633\) | 5.00000 | − | 8.66025i | 0.198732 | − | 0.344214i | ||||
\(634\) | 15.0000 | + | 25.9808i | 0.595726 | + | 1.03183i | ||||
\(635\) | −12.0000 | − | 20.7846i | −0.476205 | − | 0.824812i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | −1.00000 | − | 3.46410i | −0.0396214 | − | 0.137253i | ||||
\(638\) | −15.0000 | −0.593856 | ||||||||
\(639\) | −4.00000 | − | 6.92820i | −0.158238 | − | 0.274075i | ||||
\(640\) | −1.00000 | − | 1.73205i | −0.0395285 | − | 0.0684653i | ||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | −15.0000 | −0.592003 | ||||||||
\(643\) | 24.5000 | − | 42.4352i | 0.966186 | − | 1.67348i | 0.259791 | − | 0.965665i | \(-0.416346\pi\) |
0.706395 | − | 0.707818i | \(-0.250320\pi\) | |||||||
\(644\) | 3.00000 | − | 5.19615i | 0.118217 | − | 0.204757i | ||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 17.5000 | − | 30.3109i | 0.688528 | − | 1.19257i | ||||
\(647\) | −0.500000 | − | 0.866025i | −0.0196570 | − | 0.0340470i | 0.856030 | − | 0.516927i | \(-0.172924\pi\) |
−0.875687 | + | 0.482880i | \(0.839591\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −18.0000 | −0.706562 | ||||||||
\(650\) | −1.00000 | − | 3.46410i | −0.0392232 | − | 0.135873i | ||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | 7.00000 | + | 12.1244i | 0.274141 | + | 0.474826i | ||||
\(653\) | −13.5000 | − | 23.3827i | −0.528296 | − | 0.915035i | −0.999456 | − | 0.0329874i | \(-0.989498\pi\) |
0.471160 | − | 0.882048i | \(-0.343835\pi\) | |||||||
\(654\) | −8.00000 | + | 13.8564i | −0.312825 | + | 0.541828i | ||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | 2.50000 | − | 4.33013i | 0.0976086 | − | 0.169063i | ||||
\(657\) | −6.00000 | + | 10.3923i | −0.234082 | + | 0.405442i | ||||
\(658\) | −1.00000 | −0.0389841 | ||||||||
\(659\) | 13.5000 | − | 23.3827i | 0.525885 | − | 0.910860i | −0.473660 | − | 0.880708i | \(-0.657067\pi\) |
0.999545 | − | 0.0301523i | \(-0.00959924\pi\) | |||||||
\(660\) | 3.00000 | + | 5.19615i | 0.116775 | + | 0.202260i | ||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | −22.0000 | −0.855054 | ||||||||
\(663\) | −24.5000 | − | 6.06218i | −0.951501 | − | 0.235435i | ||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 5.00000 | + | 8.66025i | 0.193892 | + | 0.335830i | ||||
\(666\) | −1.00000 | − | 1.73205i | −0.0387492 | − | 0.0671156i | ||||
\(667\) | −15.0000 | + | 25.9808i | −0.580802 | + | 1.00598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.00000 | − | 3.46410i | 0.0773245 | − | 0.133930i | ||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | 21.0000 | 0.810696 | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | −11.5000 | − | 19.9186i | −0.443292 | − | 0.767805i | 0.554639 | − | 0.832091i | \(-0.312856\pi\) |
−0.997932 | + | 0.0642860i | \(0.979523\pi\) | |||||||
\(674\) | −8.50000 | − | 14.7224i | −0.327408 | − | 0.567087i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 3.00000 | + | 5.19615i | 0.115214 | + | 0.199557i | ||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | 7.00000 | − | 12.1244i | 0.268438 | − | 0.464948i | ||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | −3.00000 | + | 5.19615i | −0.114876 | + | 0.198971i | ||||
\(683\) | −18.0000 | + | 31.1769i | −0.688751 | + | 1.19295i | 0.283491 | + | 0.958975i | \(0.408507\pi\) |
−0.972242 | + | 0.233977i | \(0.924826\pi\) | |||||||
\(684\) | −5.00000 | −0.191180 | ||||||||
\(685\) | 18.0000 | − | 31.1769i | 0.687745 | − | 1.19121i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −13.5000 | − | 23.3827i | −0.515057 | − | 0.892105i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | 10.5000 | + | 2.59808i | 0.400018 | + | 0.0989788i | ||||
\(690\) | 12.0000 | 0.456832 | ||||||||
\(691\) | −20.0000 | − | 34.6410i | −0.760836 | − | 1.31781i | −0.942420 | − | 0.334431i | \(-0.891456\pi\) |
0.181584 | − | 0.983375i | \(-0.441877\pi\) | |||||||
\(692\) | −6.00000 | − | 10.3923i | −0.228086 | − | 0.395056i | ||||
\(693\) | 1.50000 | − | 2.59808i | 0.0569803 | − | 0.0986928i | ||||
\(694\) | −17.0000 | −0.645311 | ||||||||
\(695\) | −19.0000 | + | 32.9090i | −0.720711 | + | 1.24831i | ||||
\(696\) | 2.50000 | − | 4.33013i | 0.0947623 | − | 0.164133i | ||||
\(697\) | 35.0000 | 1.32572 | ||||||||
\(698\) | −9.00000 | + | 15.5885i | −0.340655 | + | 0.590032i | ||||
\(699\) | −13.0000 | − | 22.5167i | −0.491705 | − | 0.851658i | ||||
\(700\) | −0.500000 | − | 0.866025i | −0.0188982 | − | 0.0327327i | ||||
\(701\) | 13.0000 | 0.491003 | 0.245502 | − | 0.969396i | \(-0.421047\pi\) | ||||
0.245502 | + | 0.969396i | \(0.421047\pi\) | |||||||
\(702\) | 1.00000 | + | 3.46410i | 0.0377426 | + | 0.130744i | ||||
\(703\) | 10.0000 | 0.377157 | ||||||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | −1.00000 | − | 1.73205i | −0.0376622 | − | 0.0652328i | ||||
\(706\) | 7.00000 | − | 12.1244i | 0.263448 | − | 0.456306i | ||||
\(707\) | −14.0000 | −0.526524 | ||||||||
\(708\) | 3.00000 | − | 5.19615i | 0.112747 | − | 0.195283i | ||||
\(709\) | 14.0000 | − | 24.2487i | 0.525781 | − | 0.910679i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) |
0.999549 | − | 0.0300298i | \(-0.00956021\pi\) | |||||||
\(710\) | 16.0000 | 0.600469 | ||||||||
\(711\) | −1.50000 | + | 2.59808i | −0.0562544 | + | 0.0974355i | ||||
\(712\) | −5.50000 | − | 9.52628i | −0.206121 | − | 0.357012i | ||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | −7.00000 | −0.261968 | ||||||||
\(715\) | 6.00000 | + | 20.7846i | 0.224387 | + | 0.777300i | ||||
\(716\) | 20.0000 | 0.747435 | ||||||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | 9.00000 | + | 15.5885i | 0.335877 | + | 0.581756i | ||||
\(719\) | 7.50000 | − | 12.9904i | 0.279703 | − | 0.484459i | −0.691608 | − | 0.722273i | \(-0.743097\pi\) |
0.971311 | + | 0.237814i | \(0.0764307\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 5.00000 | − | 8.66025i | 0.186210 | − | 0.322525i | ||||
\(722\) | 3.00000 | − | 5.19615i | 0.111648 | − | 0.193381i | ||||
\(723\) | 28.0000 | 1.04133 | ||||||||
\(724\) | 4.50000 | − | 7.79423i | 0.167241 | − | 0.289670i | ||||
\(725\) | 2.50000 | + | 4.33013i | 0.0928477 | + | 0.160817i | ||||
\(726\) | −1.00000 | − | 1.73205i | −0.0371135 | − | 0.0642824i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −2.50000 | + | 2.59808i | −0.0926562 | + | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.0000 | − | 20.7846i | −0.444140 | − | 0.769273i | ||||
\(731\) | 7.00000 | + | 12.1244i | 0.258904 | + | 0.448435i | ||||
\(732\) | −3.50000 | + | 6.06218i | −0.129364 | + | 0.224065i | ||||
\(733\) | −7.00000 | −0.258551 | −0.129275 | − | 0.991609i | \(-0.541265\pi\) | ||||
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | −5.00000 | + | 8.66025i | −0.184553 | + | 0.319656i | ||||
\(735\) | 1.00000 | − | 1.73205i | 0.0368856 | − | 0.0638877i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | −3.00000 | + | 5.19615i | −0.110506 | + | 0.191403i | ||||
\(738\) | −2.50000 | − | 4.33013i | −0.0920263 | − | 0.159394i | ||||
\(739\) | 7.00000 | + | 12.1244i | 0.257499 | + | 0.446002i | 0.965571 | − | 0.260138i | \(-0.0837682\pi\) |
−0.708072 | + | 0.706140i | \(0.750435\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | −17.5000 | − | 4.33013i | −0.642879 | − | 0.159071i | ||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | 14.0000 | − | 24.2487i | 0.512920 | − | 0.888404i | ||||
\(746\) | −4.00000 | −0.146450 | ||||||||
\(747\) | 4.00000 | − | 6.92820i | 0.146352 | − | 0.253490i | ||||
\(748\) | 10.5000 | − | 18.1865i | 0.383918 | − | 0.664966i | ||||
\(749\) | −15.0000 | −0.548088 | ||||||||
\(750\) | 6.00000 | − | 10.3923i | 0.219089 | − | 0.379473i | ||||
\(751\) | 16.5000 | + | 28.5788i | 0.602094 | + | 1.04286i | 0.992504 | + | 0.122216i | \(0.0389999\pi\) |
−0.390410 | + | 0.920641i | \(0.627667\pi\) | |||||||
\(752\) | 0.500000 | + | 0.866025i | 0.0182331 | + | 0.0315807i | ||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 12.5000 | − | 12.9904i | 0.455223 | − | 0.473082i | ||||
\(755\) | −26.0000 | −0.946237 | ||||||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | −16.0000 | − | 27.7128i | −0.581530 | − | 1.00724i | −0.995298 | − | 0.0968571i | \(-0.969121\pi\) |
0.413768 | − | 0.910382i | \(-0.364212\pi\) | |||||||
\(758\) | −10.0000 | + | 17.3205i | −0.363216 | + | 0.629109i | ||||
\(759\) | 18.0000 | 0.653359 | ||||||||
\(760\) | 5.00000 | − | 8.66025i | 0.181369 | − | 0.314140i | ||||
\(761\) | 9.00000 | − | 15.5885i | 0.326250 | − | 0.565081i | −0.655515 | − | 0.755182i | \(-0.727548\pi\) |
0.981764 | + | 0.190101i | \(0.0608816\pi\) | |||||||
\(762\) | 12.0000 | 0.434714 | ||||||||
\(763\) | −8.00000 | + | 13.8564i | −0.289619 | + | 0.501636i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | −7.00000 | − | 12.1244i | −0.253086 | − | 0.438357i | ||||
\(766\) | −31.0000 | −1.12008 | ||||||||
\(767\) | 15.0000 | − | 15.5885i | 0.541619 | − | 0.562867i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −23.0000 | − | 39.8372i | −0.829401 | − | 1.43657i | −0.898509 | − | 0.438956i | \(-0.855348\pi\) |
0.0691074 | − | 0.997609i | \(-0.477985\pi\) | |||||||
\(770\) | 3.00000 | + | 5.19615i | 0.108112 | + | 0.187256i | ||||
\(771\) | 7.50000 | − | 12.9904i | 0.270106 | − | 0.467837i | ||||
\(772\) | 13.0000 | 0.467880 | ||||||||
\(773\) | 5.00000 | − | 8.66025i | 0.179838 | − | 0.311488i | −0.761987 | − | 0.647592i | \(-0.775776\pi\) |
0.941825 | + | 0.336104i | \(0.109109\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −1.00000 | + | 1.73205i | −0.0358979 | + | 0.0621770i | ||||
\(777\) | −1.00000 | − | 1.73205i | −0.0358748 | − | 0.0621370i | ||||
\(778\) | 3.00000 | + | 5.19615i | 0.107555 | + | 0.186291i | ||||
\(779\) | 25.0000 | 0.895718 | ||||||||
\(780\) | −7.00000 | − | 1.73205i | −0.250640 | − | 0.0620174i | ||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | −21.0000 | − | 36.3731i | −0.750958 | − | 1.30070i | ||||
\(783\) | −2.50000 | − | 4.33013i | −0.0893427 | − | 0.154746i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | 36.0000 | 1.28490 | ||||||||
\(786\) | 4.00000 | − | 6.92820i | 0.142675 | − | 0.247121i | ||||
\(787\) | −12.5000 | + | 21.6506i | −0.445577 | + | 0.771762i | −0.998092 | − | 0.0617409i | \(-0.980335\pi\) |
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(788\) | −9.00000 | −0.320612 | ||||||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | −3.00000 | − | 5.19615i | −0.106735 | − | 0.184871i | ||||
\(791\) | 3.00000 | + | 5.19615i | 0.106668 | + | 0.184754i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | −17.5000 | + | 18.1865i | −0.621443 | + | 0.645823i | ||||
\(794\) | 15.0000 | 0.532330 | ||||||||
\(795\) | 3.00000 | + | 5.19615i | 0.106399 | + | 0.184289i | ||||
\(796\) | 13.0000 | + | 22.5167i | 0.460773 | + | 0.798082i | ||||
\(797\) | −28.0000 | + | 48.4974i | −0.991811 | + | 1.71787i | −0.385301 | + | 0.922791i | \(0.625902\pi\) |
−0.606510 | + | 0.795076i | \(0.707431\pi\) | |||||||
\(798\) | −5.00000 | −0.176998 | ||||||||
\(799\) | −3.50000 | + | 6.06218i | −0.123821 | + | 0.214464i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −11.0000 | −0.388666 | ||||||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | −18.0000 | − | 31.1769i | −0.635206 | − | 1.10021i | ||||
\(804\) | −1.00000 | − | 1.73205i | −0.0352673 | − | 0.0610847i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | −2.00000 | − | 6.92820i | −0.0704470 | − | 0.244036i | ||||
\(807\) | −24.0000 | −0.844840 | ||||||||
\(808\) | 7.00000 | + | 12.1244i | 0.246259 | + | 0.426533i | ||||
\(809\) | −26.0000 | − | 45.0333i | −0.914111 | − | 1.58329i | −0.808197 | − | 0.588912i | \(-0.799556\pi\) |
−0.105914 | − | 0.994375i | \(-0.533777\pi\) | |||||||
\(810\) | −1.00000 | + | 1.73205i | −0.0351364 | + | 0.0608581i | ||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 2.50000 | − | 4.33013i | 0.0877328 | − | 0.151958i | ||||
\(813\) | −1.00000 | + | 1.73205i | −0.0350715 | + | 0.0607457i | ||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | −14.0000 | + | 24.2487i | −0.490399 | + | 0.849395i | ||||
\(816\) | 3.50000 | + | 6.06218i | 0.122525 | + | 0.212219i | ||||
\(817\) | 5.00000 | + | 8.66025i | 0.174928 | + | 0.302984i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.00000 | + | 3.46410i | 0.0349428 | + | 0.121046i | ||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | −7.50000 | − | 12.9904i | −0.261752 | − | 0.453367i | 0.704956 | − | 0.709251i | \(-0.250967\pi\) |
−0.966708 | + | 0.255884i | \(0.917634\pi\) | |||||||
\(822\) | 9.00000 | + | 15.5885i | 0.313911 | + | 0.543710i | ||||
\(823\) | 24.0000 | − | 41.5692i | 0.836587 | − | 1.44901i | −0.0561440 | − | 0.998423i | \(-0.517881\pi\) |
0.892731 | − | 0.450589i | \(-0.148786\pi\) | |||||||
\(824\) | −10.0000 | −0.348367 | ||||||||
\(825\) | 1.50000 | − | 2.59808i | 0.0522233 | − | 0.0904534i | ||||
\(826\) | 3.00000 | − | 5.19615i | 0.104383 | − | 0.180797i | ||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | 3.50000 | + | 6.06218i | 0.121560 | + | 0.210548i | 0.920383 | − | 0.391018i | \(-0.127877\pi\) |
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 8.00000 | + | 13.8564i | 0.277684 | + | 0.480963i | ||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 3.50000 | + | 0.866025i | 0.121341 | + | 0.0300240i | ||||
\(833\) | −7.00000 | −0.242536 | ||||||||
\(834\) | −9.50000 | − | 16.4545i | −0.328958 | − | 0.569772i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.50000 | − | 12.9904i | 0.259393 | − | 0.449282i | ||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 2.00000 | − | 3.46410i | 0.0690889 | − | 0.119665i | ||||
\(839\) | 12.0000 | − | 20.7846i | 0.414286 | − | 0.717564i | −0.581067 | − | 0.813856i | \(-0.697365\pi\) |
0.995353 | + | 0.0962912i | \(0.0306980\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | −11.0000 | − | 19.0526i | −0.379085 | − | 0.656595i | ||||
\(843\) | −8.00000 | − | 13.8564i | −0.275535 | − | 0.477240i | ||||
\(844\) | −10.0000 | −0.344214 | ||||||||
\(845\) | −23.0000 | − | 12.1244i | −0.791224 | − | 0.417091i | ||||
\(846\) | 1.00000 | 0.0343807 | ||||||||
\(847\) | −1.00000 | − | 1.73205i | −0.0343604 | − | 0.0595140i | ||||
\(848\) | −1.50000 | − | 2.59808i | −0.0515102 | − | 0.0892183i | ||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | −7.00000 | −0.240098 | ||||||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | −4.00000 | + | 6.92820i | −0.137038 | + | 0.237356i | ||||
\(853\) | 41.0000 | 1.40381 | 0.701907 | − | 0.712269i | \(-0.252332\pi\) | ||||
0.701907 | + | 0.712269i | \(0.252332\pi\) | |||||||
\(854\) | −3.50000 | + | 6.06218i | −0.119768 | + | 0.207443i | ||||
\(855\) | −5.00000 | − | 8.66025i | −0.170996 | − | 0.296174i | ||||
\(856\) | 7.50000 | + | 12.9904i | 0.256345 | + | 0.444002i | ||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | −10.5000 | − | 2.59808i | −0.358464 | − | 0.0886969i | ||||
\(859\) | 35.0000 | 1.19418 | 0.597092 | − | 0.802173i | \(-0.296323\pi\) | ||||
0.597092 | + | 0.802173i | \(0.296323\pi\) | |||||||
\(860\) | 2.00000 | + | 3.46410i | 0.0681994 | + | 0.118125i | ||||
\(861\) | −2.50000 | − | 4.33013i | −0.0851998 | − | 0.147570i | ||||
\(862\) | −4.00000 | + | 6.92820i | −0.136241 | + | 0.235976i | ||||
\(863\) | 34.0000 | 1.15737 | 0.578687 | − | 0.815550i | \(-0.303565\pi\) | ||||
0.578687 | + | 0.815550i | \(0.303565\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 12.0000 | − | 20.7846i | 0.408012 | − | 0.706698i | ||||
\(866\) | −26.0000 | −0.883516 | ||||||||
\(867\) | −16.0000 | + | 27.7128i | −0.543388 | + | 0.941176i | ||||
\(868\) | −1.00000 | − | 1.73205i | −0.0339422 | − | 0.0587896i | ||||
\(869\) | −4.50000 | − | 7.79423i | −0.152652 | − | 0.264401i | ||||
\(870\) | 10.0000 | 0.339032 | ||||||||
\(871\) | −2.00000 | − | 6.92820i | −0.0677674 | − | 0.234753i | ||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | 1.00000 | + | 1.73205i | 0.0338449 | + | 0.0586210i | ||||
\(874\) | −15.0000 | − | 25.9808i | −0.507383 | − | 0.878812i | ||||
\(875\) | 6.00000 | − | 10.3923i | 0.202837 | − | 0.351324i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | −20.0000 | + | 34.6410i | −0.675352 | + | 1.16974i | 0.301014 | + | 0.953620i | \(0.402675\pi\) |
−0.976366 | + | 0.216124i | \(0.930658\pi\) | |||||||
\(878\) | 2.00000 | − | 3.46410i | 0.0674967 | − | 0.116908i | ||||
\(879\) | 12.0000 | 0.404750 | ||||||||
\(880\) | 3.00000 | − | 5.19615i | 0.101130 | − | 0.175162i | ||||
\(881\) | 13.0000 | + | 22.5167i | 0.437981 | + | 0.758606i | 0.997534 | − | 0.0701893i | \(-0.0223603\pi\) |
−0.559553 | + | 0.828795i | \(0.689027\pi\) | |||||||
\(882\) | 0.500000 | + | 0.866025i | 0.0168359 | + | 0.0291606i | ||||
\(883\) | −14.0000 | −0.471138 | −0.235569 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235569 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(884\) | 7.00000 | + | 24.2487i | 0.235435 | + | 0.815572i | ||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | 7.50000 | + | 12.9904i | 0.251967 | + | 0.436420i | ||||
\(887\) | −18.5000 | − | 32.0429i | −0.621169 | − | 1.07590i | −0.989268 | − | 0.146110i | \(-0.953325\pi\) |
0.368099 | − | 0.929787i | \(-0.380009\pi\) | |||||||
\(888\) | −1.00000 | + | 1.73205i | −0.0335578 | + | 0.0581238i | ||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 11.0000 | − | 19.0526i | 0.368721 | − | 0.638643i | ||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | −2.50000 | + | 4.33013i | −0.0836593 | + | 0.144902i | ||||
\(894\) | 7.00000 | + | 12.1244i | 0.234115 | + | 0.405499i | ||||
\(895\) | 20.0000 | + | 34.6410i | 0.668526 | + | 1.15792i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −15.0000 | + | 15.5885i | −0.500835 | + | 0.520483i | ||||
\(898\) | 38.0000 | 1.26808 | ||||||||
\(899\) | 5.00000 | + | 8.66025i | 0.166759 | + | 0.288836i | ||||
\(900\) | 0.500000 | + | 0.866025i | 0.0166667 | + | 0.0288675i | ||||
\(901\) | 10.5000 | − | 18.1865i | 0.349806 | − | 0.605881i | ||||
\(902\) | 15.0000 | 0.499445 | ||||||||
\(903\) | 1.00000 | − | 1.73205i | 0.0332779 | − | 0.0576390i | ||||
\(904\) | 3.00000 | − | 5.19615i | 0.0997785 | − | 0.172821i | ||||
\(905\) | 18.0000 | 0.598340 | ||||||||
\(906\) | 6.50000 | − | 11.2583i | 0.215948 | − | 0.374033i | ||||
\(907\) | 19.0000 | + | 32.9090i | 0.630885 | + | 1.09272i | 0.987371 | + | 0.158424i | \(0.0506412\pi\) |
−0.356487 | + | 0.934300i | \(0.616025\pi\) | |||||||
\(908\) | −7.00000 | − | 12.1244i | −0.232303 | − | 0.402361i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | −7.00000 | − | 1.73205i | −0.232048 | − | 0.0574169i | ||||
\(911\) | −52.0000 | −1.72284 | −0.861418 | − | 0.507896i | \(-0.830423\pi\) | ||||
−0.861418 | + | 0.507896i | \(0.830423\pi\) | |||||||
\(912\) | 2.50000 | + | 4.33013i | 0.0827833 | + | 0.143385i | ||||
\(913\) | 12.0000 | + | 20.7846i | 0.397142 | + | 0.687870i | ||||
\(914\) | 13.0000 | − | 22.5167i | 0.430002 | − | 0.744785i | ||||
\(915\) | −14.0000 | −0.462826 | ||||||||
\(916\) | −13.5000 | + | 23.3827i | −0.446053 | + | 0.772586i | ||||
\(917\) | 4.00000 | − | 6.92820i | 0.132092 | − | 0.228789i | ||||
\(918\) | 7.00000 | 0.231034 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | −6.00000 | − | 10.3923i | −0.197814 | − | 0.342624i | ||||
\(921\) | −4.50000 | − | 7.79423i | −0.148280 | − | 0.256829i | ||||
\(922\) | −8.00000 | −0.263466 | ||||||||
\(923\) | −20.0000 | + | 20.7846i | −0.658308 | + | 0.684134i | ||||
\(924\) | −3.00000 | −0.0986928 | ||||||||
\(925\) | −1.00000 | − | 1.73205i | −0.0328798 | − | 0.0569495i | ||||
\(926\) | −15.5000 | − | 26.8468i | −0.509362 | − | 0.882240i | ||||
\(927\) | −5.00000 | + | 8.66025i | −0.164222 | + | 0.284440i | ||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | 6.50000 | − | 11.2583i | 0.213258 | − | 0.369374i | −0.739474 | − | 0.673185i | \(-0.764926\pi\) |
0.952732 | + | 0.303811i | \(0.0982592\pi\) | |||||||
\(930\) | 2.00000 | − | 3.46410i | 0.0655826 | − | 0.113592i | ||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | −13.0000 | + | 22.5167i | −0.425829 | + | 0.737558i | ||||
\(933\) | −11.5000 | − | 19.9186i | −0.376493 | − | 0.652105i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 42.0000 | 1.37355 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 52.0000 | 1.69877 | 0.849383 | − | 0.527777i | \(-0.176974\pi\) | ||||
0.849383 | + | 0.527777i | \(0.176974\pi\) | |||||||
\(938\) | −1.00000 | − | 1.73205i | −0.0326512 | − | 0.0565535i | ||||
\(939\) | −14.0000 | − | 24.2487i | −0.456873 | − | 0.791327i | ||||
\(940\) | −1.00000 | + | 1.73205i | −0.0326164 | + | 0.0564933i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | −9.00000 | + | 15.5885i | −0.293236 | + | 0.507899i | ||||
\(943\) | 15.0000 | − | 25.9808i | 0.488467 | − | 0.846050i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | −1.00000 | + | 1.73205i | −0.0325300 | + | 0.0563436i | ||||
\(946\) | 3.00000 | + | 5.19615i | 0.0975384 | + | 0.168941i | ||||
\(947\) | 15.5000 | + | 26.8468i | 0.503682 | + | 0.872403i | 0.999991 | + | 0.00425721i | \(0.00135512\pi\) |
−0.496309 | + | 0.868146i | \(0.665312\pi\) | |||||||
\(948\) | 3.00000 | 0.0974355 | ||||||||
\(949\) | 42.0000 | + | 10.3923i | 1.36338 | + | 0.337348i | ||||
\(950\) | −5.00000 | −0.162221 | ||||||||
\(951\) | −15.0000 | − | 25.9808i | −0.486408 | − | 0.842484i | ||||
\(952\) | 3.50000 | + | 6.06218i | 0.113436 | + | 0.196476i | ||||
\(953\) | 7.00000 | − | 12.1244i | 0.226752 | − | 0.392746i | −0.730091 | − | 0.683349i | \(-0.760523\pi\) |
0.956844 | + | 0.290603i | \(0.0938559\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | −4.00000 | + | 6.92820i | −0.129437 | + | 0.224191i | ||||
\(956\) | −6.00000 | + | 10.3923i | −0.194054 | + | 0.336111i | ||||
\(957\) | 15.0000 | 0.484881 | ||||||||
\(958\) | 10.5000 | − | 18.1865i | 0.339240 | − | 0.587580i | ||||
\(959\) | 9.00000 | + | 15.5885i | 0.290625 | + | 0.503378i | ||||
\(960\) | 1.00000 | + | 1.73205i | 0.0322749 | + | 0.0559017i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −5.00000 | + | 5.19615i | −0.161206 | + | 0.167531i | ||||
\(963\) | 15.0000 | 0.483368 | ||||||||
\(964\) | −14.0000 | − | 24.2487i | −0.450910 | − | 0.780998i | ||||
\(965\) | 13.0000 | + | 22.5167i | 0.418485 | + | 0.724837i | ||||
\(966\) | −3.00000 | + | 5.19615i | −0.0965234 | + | 0.167183i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | −17.5000 | + | 30.3109i | −0.562181 | + | 0.973726i | ||||
\(970\) | −4.00000 | −0.128432 | ||||||||
\(971\) | −11.0000 | + | 19.0526i | −0.353007 | + | 0.611426i | −0.986775 | − | 0.162098i | \(-0.948174\pi\) |
0.633768 | + | 0.773523i | \(0.281507\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −9.50000 | − | 16.4545i | −0.304556 | − | 0.527506i | ||||
\(974\) | −35.0000 | −1.12147 | ||||||||
\(975\) | 1.00000 | + | 3.46410i | 0.0320256 | + | 0.110940i | ||||
\(976\) | 7.00000 | 0.224065 | ||||||||
\(977\) | −4.00000 | − | 6.92820i | −0.127971 | − | 0.221653i | 0.794919 | − | 0.606715i | \(-0.207513\pi\) |
−0.922890 | + | 0.385063i | \(0.874180\pi\) | |||||||
\(978\) | −7.00000 | − | 12.1244i | −0.223835 | − | 0.387694i | ||||
\(979\) | 16.5000 | − | 28.5788i | 0.527342 | − | 0.913384i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 8.00000 | − | 13.8564i | 0.255420 | − | 0.442401i | ||||
\(982\) | −4.00000 | + | 6.92820i | −0.127645 | + | 0.221088i | ||||
\(983\) | −32.0000 | −1.02064 | −0.510321 | − | 0.859984i | \(-0.670473\pi\) | ||||
−0.510321 | + | 0.859984i | \(0.670473\pi\) | |||||||
\(984\) | −2.50000 | + | 4.33013i | −0.0796971 | + | 0.138039i | ||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | −17.5000 | − | 30.3109i | −0.557314 | − | 0.965295i | ||||
\(987\) | 1.00000 | 0.0318304 | ||||||||
\(988\) | 5.00000 | + | 17.3205i | 0.159071 | + | 0.551039i | ||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | −3.00000 | − | 5.19615i | −0.0953463 | − | 0.165145i | ||||
\(991\) | 1.50000 | + | 2.59808i | 0.0476491 | + | 0.0825306i | 0.888866 | − | 0.458167i | \(-0.151494\pi\) |
−0.841217 | + | 0.540697i | \(0.818160\pi\) | |||||||
\(992\) | −1.00000 | + | 1.73205i | −0.0317500 | + | 0.0549927i | ||||
\(993\) | 22.0000 | 0.698149 | ||||||||
\(994\) | −4.00000 | + | 6.92820i | −0.126872 | + | 0.219749i | ||||
\(995\) | −26.0000 | + | 45.0333i | −0.824255 | + | 1.42765i | ||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | −3.50000 | + | 6.06218i | −0.110846 | + | 0.191991i | −0.916112 | − | 0.400923i | \(-0.868689\pi\) |
0.805266 | + | 0.592914i | \(0.202023\pi\) | |||||||
\(998\) | 7.00000 | + | 12.1244i | 0.221581 | + | 0.383790i | ||||
\(999\) | 1.00000 | + | 1.73205i | 0.0316386 | + | 0.0547997i |
(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.c.211.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.r.l.757.1 | 2 | |||
13.3 | even | 3 | 7098.2.a.i.1.1 | 1 | |||
13.9 | even | 3 | inner | 546.2.l.c.295.1 | yes | 2 | |
13.10 | even | 6 | 7098.2.a.bd.1.1 | 1 | |||
39.35 | odd | 6 | 1638.2.r.l.1387.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.c.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.l.c.295.1 | yes | 2 | 13.9 | even | 3 | inner | |
1638.2.r.l.757.1 | 2 | 3.2 | odd | 2 | |||
1638.2.r.l.1387.1 | 2 | 39.35 | odd | 6 | |||
7098.2.a.i.1.1 | 1 | 13.3 | even | 3 | |||
7098.2.a.bd.1.1 | 1 | 13.10 | even | 6 |