Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (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: | \(7.42608738798\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.f.811.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −2.50000 | + | 4.33013i | −0.753778 | + | 1.30558i | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 0.500000 | − | 0.866025i | 0.109109 | − | 0.188982i | ||||
\(22\) | −2.50000 | + | 4.33013i | −0.533002 | + | 0.923186i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.00000 | + | 3.46410i | −0.392232 | + | 0.679366i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 3.50000 | − | 4.33013i | 0.628619 | − | 0.777714i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.00000 | 0.870388 | ||||||||
\(34\) | 1.00000 | + | 1.73205i | 0.171499 | + | 0.297044i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | 1.00000 | + | 1.73205i | 0.162221 | + | 0.280976i | ||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −2.00000 | + | 3.46410i | −0.312348 | + | 0.541002i | −0.978870 | − | 0.204483i | \(-0.934449\pi\) |
0.666523 | + | 0.745485i | \(0.267782\pi\) | |||||||
\(42\) | 0.500000 | − | 0.866025i | 0.0771517 | − | 0.133631i | ||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.50000 | − | 4.33013i | −0.337100 | − | 0.583874i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 1.00000 | − | 1.73205i | 0.132453 | − | 0.229416i | ||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 3.50000 | − | 4.33013i | 0.444500 | − | 0.549927i | ||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 5.00000 | 0.615457 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 2.00000 | + | 3.46410i | 0.240772 | + | 0.417029i | ||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −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 | ||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | −5.00000 | −0.569803 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | 0.500000 | − | 0.866025i | 0.0545545 | − | 0.0944911i | ||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | −2.50000 | + | 4.33013i | −0.266501 | + | 0.461593i | ||||
\(89\) | 18.0000 | 1.90800 | 0.953998 | − | 0.299813i | \(-0.0969242\pi\) | ||||
0.953998 | + | 0.299813i | \(0.0969242\pi\) | |||||||
\(90\) | −0.500000 | − | 0.866025i | −0.0527046 | − | 0.0912871i | ||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | −5.50000 | − | 0.866025i | −0.570323 | − | 0.0898027i | ||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 3.00000 | − | 5.19615i | 0.303046 | − | 0.524891i | ||||
\(99\) | −2.50000 | − | 4.33013i | −0.251259 | − | 0.435194i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −5.00000 | −0.497519 | −0.248759 | − | 0.968565i | \(-0.580023\pi\) | ||||
−0.248759 | + | 0.968565i | \(0.580023\pi\) | |||||||
\(102\) | 1.00000 | − | 1.73205i | 0.0990148 | − | 0.171499i | ||||
\(103\) | 2.50000 | − | 4.33013i | 0.246332 | − | 0.426660i | −0.716173 | − | 0.697923i | \(-0.754108\pi\) |
0.962505 | + | 0.271263i | \(0.0874412\pi\) | |||||||
\(104\) | −2.00000 | + | 3.46410i | −0.196116 | + | 0.339683i | ||||
\(105\) | 0.500000 | + | 0.866025i | 0.0487950 | + | 0.0845154i | ||||
\(106\) | −1.50000 | + | 2.59808i | −0.145693 | + | 0.252347i | ||||
\(107\) | −8.50000 | − | 14.7224i | −0.821726 | − | 1.42327i | −0.904396 | − | 0.426694i | \(-0.859678\pi\) |
0.0826699 | − | 0.996577i | \(-0.473655\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | −2.50000 | − | 4.33013i | −0.238366 | − | 0.412861i | ||||
\(111\) | 2.00000 | − | 3.46410i | 0.189832 | − | 0.328798i | ||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | 2.00000 | − | 3.46410i | 0.188144 | − | 0.325875i | −0.756487 | − | 0.654008i | \(-0.773086\pi\) |
0.944632 | + | 0.328133i | \(0.106419\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 2.00000 | − | 3.46410i | 0.186501 | − | 0.323029i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | −2.00000 | − | 3.46410i | −0.184900 | − | 0.320256i | ||||
\(118\) | −1.50000 | − | 2.59808i | −0.138086 | − | 0.239172i | ||||
\(119\) | −1.00000 | + | 1.73205i | −0.0916698 | + | 0.158777i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | 3.50000 | − | 4.33013i | 0.314309 | − | 0.388857i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −8.50000 | − | 14.7224i | −0.754253 | − | 1.30640i | −0.945745 | − | 0.324910i | \(-0.894666\pi\) |
0.191492 | − | 0.981494i | \(-0.438667\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | −2.00000 | − | 3.46410i | −0.175412 | − | 0.303822i | ||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | 5.00000 | 0.435194 | ||||||||
\(133\) | −1.00000 | + | 1.73205i | −0.0867110 | + | 0.150188i | ||||
\(134\) | 2.00000 | − | 3.46410i | 0.172774 | − | 0.299253i | ||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 1.00000 | + | 1.73205i | 0.0857493 | + | 0.148522i | ||||
\(137\) | −7.00000 | + | 12.1244i | −0.598050 | + | 1.03585i | 0.395058 | + | 0.918656i | \(0.370724\pi\) |
−0.993109 | + | 0.117198i | \(0.962609\pi\) | |||||||
\(138\) | 2.00000 | + | 3.46410i | 0.170251 | + | 0.294884i | ||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −1.00000 | − | 1.73205i | −0.0842152 | − | 0.145865i | ||||
\(142\) | −4.00000 | + | 6.92820i | −0.335673 | + | 0.581402i | ||||
\(143\) | −10.0000 | − | 17.3205i | −0.836242 | − | 1.44841i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.50000 | + | 2.59808i | −0.124568 | + | 0.215758i | ||||
\(146\) | −1.00000 | + | 1.73205i | −0.0827606 | + | 0.143346i | ||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | 2.00000 | + | 3.46410i | 0.164399 | + | 0.284747i | ||||
\(149\) | 5.50000 | + | 9.52628i | 0.450578 | + | 0.780423i | 0.998422 | − | 0.0561570i | \(-0.0178847\pi\) |
−0.547844 | + | 0.836580i | \(0.684551\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −5.00000 | −0.402911 | ||||||||
\(155\) | 2.00000 | + | 5.19615i | 0.160644 | + | 0.417365i | ||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | 8.00000 | 0.638470 | 0.319235 | − | 0.947676i | \(-0.396574\pi\) | ||||
0.319235 | + | 0.947676i | \(0.396574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −2.00000 | − | 3.46410i | −0.157622 | − | 0.273009i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | −2.00000 | + | 3.46410i | −0.156174 | + | 0.270501i | ||||
\(165\) | −2.50000 | + | 4.33013i | −0.194625 | + | 0.337100i | ||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | −8.00000 | − | 13.8564i | −0.619059 | − | 1.07224i | −0.989658 | − | 0.143448i | \(-0.954181\pi\) |
0.370599 | − | 0.928793i | \(-0.379152\pi\) | |||||||
\(168\) | 0.500000 | − | 0.866025i | 0.0385758 | − | 0.0668153i | ||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 1.50000 | − | 2.59808i | 0.114043 | − | 0.197528i | −0.803354 | − | 0.595502i | \(-0.796953\pi\) |
0.917397 | + | 0.397974i | \(0.130287\pi\) | |||||||
\(174\) | −1.50000 | − | 2.59808i | −0.113715 | − | 0.196960i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −2.50000 | + | 4.33013i | −0.188445 | + | 0.326396i | ||||
\(177\) | −1.50000 | + | 2.59808i | −0.112747 | + | 0.195283i | ||||
\(178\) | 18.0000 | 1.34916 | ||||||||
\(179\) | 4.50000 | + | 7.79423i | 0.336346 | + | 0.582568i | 0.983742 | − | 0.179585i | \(-0.0574756\pi\) |
−0.647397 | + | 0.762153i | \(0.724142\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 11.0000 | − | 19.0526i | 0.817624 | − | 1.41617i | −0.0898051 | − | 0.995959i | \(-0.528624\pi\) |
0.907429 | − | 0.420206i | \(-0.138042\pi\) | |||||||
\(182\) | −4.00000 | −0.296500 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | −5.50000 | − | 0.866025i | −0.403280 | − | 0.0635001i | ||||
\(187\) | −10.0000 | −0.731272 | ||||||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0.500000 | + | 0.866025i | 0.0363696 | + | 0.0629941i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 4.00000 | − | 6.92820i | 0.289430 | − | 0.501307i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.973674 | + | 0.227946i | \(0.0732010\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −0.500000 | − | 0.866025i | −0.0359908 | − | 0.0623379i | 0.847469 | − | 0.530845i | \(-0.178125\pi\) |
−0.883460 | + | 0.468507i | \(0.844792\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −2.00000 | + | 3.46410i | −0.143223 | + | 0.248069i | ||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | −13.0000 | + | 22.5167i | −0.926212 | + | 1.60425i | −0.136611 | + | 0.990625i | \(0.543621\pi\) |
−0.789601 | + | 0.613621i | \(0.789712\pi\) | |||||||
\(198\) | −2.50000 | − | 4.33013i | −0.177667 | − | 0.307729i | ||||
\(199\) | 2.50000 | − | 4.33013i | 0.177220 | − | 0.306955i | −0.763707 | − | 0.645563i | \(-0.776623\pi\) |
0.940927 | + | 0.338608i | \(0.109956\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | −5.00000 | −0.351799 | ||||||||
\(203\) | 1.50000 | + | 2.59808i | 0.105279 | + | 0.182349i | ||||
\(204\) | 1.00000 | − | 1.73205i | 0.0700140 | − | 0.121268i | ||||
\(205\) | −2.00000 | − | 3.46410i | −0.139686 | − | 0.241943i | ||||
\(206\) | 2.50000 | − | 4.33013i | 0.174183 | − | 0.301694i | ||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | −2.00000 | + | 3.46410i | −0.138675 | + | 0.240192i | ||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0.500000 | + | 0.866025i | 0.0345033 | + | 0.0597614i | ||||
\(211\) | −11.0000 | − | 19.0526i | −0.757271 | − | 1.31163i | −0.944237 | − | 0.329266i | \(-0.893199\pi\) |
0.186966 | − | 0.982366i | \(-0.440135\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | −8.50000 | − | 14.7224i | −0.581048 | − | 1.00640i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 5.50000 | + | 0.866025i | 0.373364 | + | 0.0587896i | ||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | −2.50000 | − | 4.33013i | −0.168550 | − | 0.291937i | ||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 2.00000 | − | 3.46410i | 0.134231 | − | 0.232495i | ||||
\(223\) | −1.50000 | − | 2.59808i | −0.100447 | − | 0.173980i | 0.811422 | − | 0.584461i | \(-0.198694\pi\) |
−0.911869 | + | 0.410481i | \(0.865361\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 2.00000 | − | 3.46410i | 0.133038 | − | 0.230429i | ||||
\(227\) | −2.50000 | + | 4.33013i | −0.165931 | + | 0.287401i | −0.936985 | − | 0.349368i | \(-0.886396\pi\) |
0.771055 | + | 0.636769i | \(0.219730\pi\) | |||||||
\(228\) | 1.00000 | − | 1.73205i | 0.0662266 | − | 0.114708i | ||||
\(229\) | 14.0000 | + | 24.2487i | 0.925146 | + | 1.60240i | 0.791326 | + | 0.611394i | \(0.209391\pi\) |
0.133820 | + | 0.991006i | \(0.457276\pi\) | |||||||
\(230\) | 2.00000 | − | 3.46410i | 0.131876 | − | 0.228416i | ||||
\(231\) | 2.50000 | + | 4.33013i | 0.164488 | + | 0.284901i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | −2.00000 | − | 3.46410i | −0.130744 | − | 0.226455i | ||||
\(235\) | −1.00000 | + | 1.73205i | −0.0652328 | + | 0.112987i | ||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.00000 | + | 1.73205i | −0.0648204 | + | 0.112272i | ||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | −7.00000 | − | 12.1244i | −0.449977 | − | 0.779383i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | + | 5.19615i | 0.191663 | + | 0.331970i | ||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | −8.00000 | −0.509028 | ||||||||
\(248\) | 3.50000 | − | 4.33013i | 0.222250 | − | 0.274963i | ||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.0000 | + | 24.2487i | 0.883672 | + | 1.53057i | 0.847228 | + | 0.531229i | \(0.178270\pi\) |
0.0364441 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 10.0000 | − | 17.3205i | 0.628695 | − | 1.08893i | ||||
\(254\) | −8.50000 | − | 14.7224i | −0.533337 | − | 0.923768i | ||||
\(255\) | 1.00000 | + | 1.73205i | 0.0626224 | + | 0.108465i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.00000 | + | 10.3923i | −0.374270 | + | 0.648254i | −0.990217 | − | 0.139533i | \(-0.955440\pi\) |
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(258\) | 2.00000 | − | 3.46410i | 0.124515 | − | 0.215666i | ||||
\(259\) | −2.00000 | + | 3.46410i | −0.124274 | + | 0.215249i | ||||
\(260\) | −2.00000 | − | 3.46410i | −0.124035 | − | 0.214834i | ||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | −2.00000 | − | 3.46410i | −0.123560 | − | 0.214013i | ||||
\(263\) | −14.0000 | −0.863277 | −0.431638 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431638 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(264\) | 5.00000 | 0.307729 | ||||||||
\(265\) | −1.50000 | − | 2.59808i | −0.0921443 | − | 0.159599i | ||||
\(266\) | −1.00000 | + | 1.73205i | −0.0613139 | + | 0.106199i | ||||
\(267\) | −9.00000 | − | 15.5885i | −0.550791 | − | 0.953998i | ||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | −5.00000 | + | 8.66025i | −0.304855 | + | 0.528025i | −0.977229 | − | 0.212187i | \(-0.931941\pi\) |
0.672374 | + | 0.740212i | \(0.265275\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | 15.0000 | 0.911185 | 0.455593 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455593 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(272\) | 1.00000 | + | 1.73205i | 0.0606339 | + | 0.105021i | ||||
\(273\) | 2.00000 | + | 3.46410i | 0.121046 | + | 0.209657i | ||||
\(274\) | −7.00000 | + | 12.1244i | −0.422885 | + | 0.732459i | ||||
\(275\) | 5.00000 | 0.301511 | ||||||||
\(276\) | 2.00000 | + | 3.46410i | 0.120386 | + | 0.208514i | ||||
\(277\) | 18.0000 | 1.08152 | 0.540758 | − | 0.841178i | \(-0.318138\pi\) | ||||
0.540758 | + | 0.841178i | \(0.318138\pi\) | |||||||
\(278\) | 10.0000 | 0.599760 | ||||||||
\(279\) | 2.00000 | + | 5.19615i | 0.119737 | + | 0.311086i | ||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | −1.00000 | − | 1.73205i | −0.0595491 | − | 0.103142i | ||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | −4.00000 | + | 6.92820i | −0.237356 | + | 0.411113i | ||||
\(285\) | 1.00000 | + | 1.73205i | 0.0592349 | + | 0.102598i | ||||
\(286\) | −10.0000 | − | 17.3205i | −0.591312 | − | 1.02418i | ||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | −1.50000 | + | 2.59808i | −0.0880830 | + | 0.152564i | ||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | −9.50000 | − | 16.4545i | −0.554996 | − | 0.961281i | −0.997904 | − | 0.0647140i | \(-0.979386\pi\) |
0.442908 | − | 0.896567i | \(-0.353947\pi\) | |||||||
\(294\) | −6.00000 | −0.349927 | ||||||||
\(295\) | 3.00000 | 0.174667 | ||||||||
\(296\) | 2.00000 | + | 3.46410i | 0.116248 | + | 0.201347i | ||||
\(297\) | −2.50000 | + | 4.33013i | −0.145065 | + | 0.251259i | ||||
\(298\) | 5.50000 | + | 9.52628i | 0.318606 | + | 0.551843i | ||||
\(299\) | 8.00000 | − | 13.8564i | 0.462652 | − | 0.801337i | ||||
\(300\) | −0.500000 | + | 0.866025i | −0.0288675 | + | 0.0500000i | ||||
\(301\) | −2.00000 | + | 3.46410i | −0.115278 | + | 0.199667i | ||||
\(302\) | −5.00000 | −0.287718 | ||||||||
\(303\) | 2.50000 | + | 4.33013i | 0.143621 | + | 0.248759i | ||||
\(304\) | 1.00000 | + | 1.73205i | 0.0573539 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.00000 | −0.114332 | ||||||||
\(307\) | −1.00000 | − | 1.73205i | −0.0570730 | − | 0.0988534i | 0.836077 | − | 0.548612i | \(-0.184843\pi\) |
−0.893150 | + | 0.449758i | \(0.851510\pi\) | |||||||
\(308\) | −5.00000 | −0.284901 | ||||||||
\(309\) | −5.00000 | −0.284440 | ||||||||
\(310\) | 2.00000 | + | 5.19615i | 0.113592 | + | 0.295122i | ||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | 4.00000 | 0.226455 | ||||||||
\(313\) | 17.5000 | + | 30.3109i | 0.989158 | + | 1.71327i | 0.621757 | + | 0.783210i | \(0.286419\pi\) |
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 0.500000 | − | 0.866025i | 0.0281718 | − | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.500000 | + | 0.866025i | 0.0280828 | + | 0.0486408i | 0.879725 | − | 0.475482i | \(-0.157726\pi\) |
−0.851642 | + | 0.524123i | \(0.824393\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −8.50000 | + | 14.7224i | −0.474424 | + | 0.821726i | ||||
\(322\) | −2.00000 | − | 3.46410i | −0.111456 | − | 0.193047i | ||||
\(323\) | −2.00000 | + | 3.46410i | −0.111283 | + | 0.192748i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | −7.00000 | − | 12.1244i | −0.387101 | − | 0.670478i | ||||
\(328\) | −2.00000 | + | 3.46410i | −0.110432 | + | 0.191273i | ||||
\(329\) | 1.00000 | + | 1.73205i | 0.0551318 | + | 0.0954911i | ||||
\(330\) | −2.50000 | + | 4.33013i | −0.137620 | + | 0.238366i | ||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | −8.00000 | − | 13.8564i | −0.437741 | − | 0.758189i | ||||
\(335\) | 2.00000 | + | 3.46410i | 0.109272 | + | 0.189264i | ||||
\(336\) | 0.500000 | − | 0.866025i | 0.0272772 | − | 0.0472456i | ||||
\(337\) | −3.00000 | −0.163420 | −0.0817102 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817102 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(338\) | −1.50000 | − | 2.59808i | −0.0815892 | − | 0.141317i | ||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | 10.0000 | + | 25.9808i | 0.541530 | + | 1.40694i | ||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 2.00000 | + | 3.46410i | 0.107833 | + | 0.186772i | ||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 1.50000 | − | 2.59808i | 0.0806405 | − | 0.139673i | ||||
\(347\) | 0.500000 | + | 0.866025i | 0.0268414 | + | 0.0464907i | 0.879134 | − | 0.476575i | \(-0.158122\pi\) |
−0.852293 | + | 0.523065i | \(0.824788\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | 34.0000 | 1.81998 | 0.909989 | − | 0.414632i | \(-0.136090\pi\) | ||||
0.909989 | + | 0.414632i | \(0.136090\pi\) | |||||||
\(350\) | 0.500000 | − | 0.866025i | 0.0267261 | − | 0.0462910i | ||||
\(351\) | −2.00000 | + | 3.46410i | −0.106752 | + | 0.184900i | ||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | 7.00000 | + | 12.1244i | 0.372572 | + | 0.645314i | 0.989960 | − | 0.141344i | \(-0.0451425\pi\) |
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(354\) | −1.50000 | + | 2.59808i | −0.0797241 | + | 0.138086i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 2.00000 | 0.105851 | ||||||||
\(358\) | 4.50000 | + | 7.79423i | 0.237832 | + | 0.411938i | ||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 11.0000 | − | 19.0526i | 0.578147 | − | 1.00138i | ||||
\(363\) | −7.00000 | + | 12.1244i | −0.367405 | + | 0.636364i | ||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | −1.00000 | − | 1.73205i | −0.0523424 | − | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0000 | − | 20.7846i | 0.626395 | − | 1.08495i | −0.361874 | − | 0.932227i | \(-0.617863\pi\) |
0.988269 | − | 0.152721i | \(-0.0488036\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | −2.00000 | − | 3.46410i | −0.104116 | − | 0.180334i | ||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | −3.00000 | −0.155752 | ||||||||
\(372\) | −5.50000 | − | 0.866025i | −0.285162 | − | 0.0449013i | ||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | −10.0000 | −0.517088 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | −6.00000 | + | 10.3923i | −0.309016 | + | 0.535231i | ||||
\(378\) | 0.500000 | + | 0.866025i | 0.0257172 | + | 0.0445435i | ||||
\(379\) | −1.00000 | − | 1.73205i | −0.0513665 | − | 0.0889695i | 0.839199 | − | 0.543825i | \(-0.183024\pi\) |
−0.890565 | + | 0.454855i | \(0.849691\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | −8.50000 | + | 14.7224i | −0.435468 | + | 0.754253i | ||||
\(382\) | 4.00000 | − | 6.92820i | 0.204658 | − | 0.354478i | ||||
\(383\) | 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 | ||||
\(385\) | 2.50000 | − | 4.33013i | 0.127412 | − | 0.220684i | ||||
\(386\) | −0.500000 | − | 0.866025i | −0.0254493 | − | 0.0440795i | ||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | −2.00000 | + | 3.46410i | −0.101274 | + | 0.175412i | ||||
\(391\) | −4.00000 | − | 6.92820i | −0.202289 | − | 0.350374i | ||||
\(392\) | 3.00000 | − | 5.19615i | 0.151523 | − | 0.262445i | ||||
\(393\) | −2.00000 | + | 3.46410i | −0.100887 | + | 0.174741i | ||||
\(394\) | −13.0000 | + | 22.5167i | −0.654931 | + | 1.13437i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.50000 | − | 4.33013i | −0.125630 | − | 0.217597i | ||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | 2.50000 | − | 4.33013i | 0.125314 | − | 0.217050i | ||||
\(399\) | 2.00000 | 0.100125 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | 8.00000 | + | 20.7846i | 0.398508 | + | 1.03536i | ||||
\(404\) | −5.00000 | −0.248759 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 1.50000 | + | 2.59808i | 0.0744438 | + | 0.128940i | ||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 1.00000 | − | 1.73205i | 0.0495074 | − | 0.0857493i | ||||
\(409\) | 8.50000 | + | 14.7224i | 0.420298 | + | 0.727977i | 0.995968 | − | 0.0897044i | \(-0.0285922\pi\) |
−0.575670 | + | 0.817682i | \(0.695259\pi\) | |||||||
\(410\) | −2.00000 | − | 3.46410i | −0.0987730 | − | 0.171080i | ||||
\(411\) | 14.0000 | 0.690569 | ||||||||
\(412\) | 2.50000 | − | 4.33013i | 0.123166 | − | 0.213330i | ||||
\(413\) | 1.50000 | − | 2.59808i | 0.0738102 | − | 0.127843i | ||||
\(414\) | 2.00000 | − | 3.46410i | 0.0982946 | − | 0.170251i | ||||
\(415\) | −4.50000 | − | 7.79423i | −0.220896 | − | 0.382604i | ||||
\(416\) | −2.00000 | + | 3.46410i | −0.0980581 | + | 0.169842i | ||||
\(417\) | −5.00000 | − | 8.66025i | −0.244851 | − | 0.424094i | ||||
\(418\) | −10.0000 | −0.489116 | ||||||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | 0.500000 | + | 0.866025i | 0.0243975 | + | 0.0422577i | ||||
\(421\) | −10.0000 | + | 17.3205i | −0.487370 | + | 0.844150i | −0.999895 | − | 0.0145228i | \(-0.995377\pi\) |
0.512524 | + | 0.858673i | \(0.328710\pi\) | |||||||
\(422\) | −11.0000 | − | 19.0526i | −0.535472 | − | 0.927464i | ||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | −1.50000 | + | 2.59808i | −0.0728464 | + | 0.126174i | ||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.50000 | − | 14.7224i | −0.410863 | − | 0.711636i | ||||
\(429\) | −10.0000 | + | 17.3205i | −0.482805 | + | 0.836242i | ||||
\(430\) | −4.00000 | −0.192897 | ||||||||
\(431\) | 11.0000 | + | 19.0526i | 0.529851 | + | 0.917729i | 0.999394 | + | 0.0348195i | \(0.0110856\pi\) |
−0.469542 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 5.50000 | + | 0.866025i | 0.264008 | + | 0.0415705i | ||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −4.00000 | − | 6.92820i | −0.191346 | − | 0.331421i | ||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 4.50000 | − | 7.79423i | 0.214773 | − | 0.371998i | −0.738429 | − | 0.674331i | \(-0.764432\pi\) |
0.953202 | + | 0.302333i | \(0.0977654\pi\) | |||||||
\(440\) | −2.50000 | − | 4.33013i | −0.119183 | − | 0.206431i | ||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | −8.00000 | −0.380521 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | 2.00000 | − | 3.46410i | 0.0949158 | − | 0.164399i | ||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | −1.50000 | − | 2.59808i | −0.0710271 | − | 0.123022i | ||||
\(447\) | 5.50000 | − | 9.52628i | 0.260141 | − | 0.450578i | ||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 2.00000 | − | 3.46410i | 0.0940721 | − | 0.162938i | ||||
\(453\) | 2.50000 | + | 4.33013i | 0.117460 | + | 0.203447i | ||||
\(454\) | −2.50000 | + | 4.33013i | −0.117331 | + | 0.203223i | ||||
\(455\) | 2.00000 | − | 3.46410i | 0.0937614 | − | 0.162400i | ||||
\(456\) | 1.00000 | − | 1.73205i | 0.0468293 | − | 0.0811107i | ||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 14.0000 | + | 24.2487i | 0.654177 | + | 1.13307i | ||||
\(459\) | 1.00000 | + | 1.73205i | 0.0466760 | + | 0.0808452i | ||||
\(460\) | 2.00000 | − | 3.46410i | 0.0932505 | − | 0.161515i | ||||
\(461\) | 21.0000 | 0.978068 | 0.489034 | − | 0.872265i | \(-0.337349\pi\) | ||||
0.489034 | + | 0.872265i | \(0.337349\pi\) | |||||||
\(462\) | 2.50000 | + | 4.33013i | 0.116311 | + | 0.201456i | ||||
\(463\) | 5.00000 | 0.232370 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 3.50000 | − | 4.33013i | 0.162309 | − | 0.200805i | ||||
\(466\) | 4.00000 | 0.185296 | ||||||||
\(467\) | 33.0000 | 1.52706 | 0.763529 | − | 0.645774i | \(-0.223465\pi\) | ||||
0.763529 | + | 0.645774i | \(0.223465\pi\) | |||||||
\(468\) | −2.00000 | − | 3.46410i | −0.0924500 | − | 0.160128i | ||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | −1.00000 | + | 1.73205i | −0.0461266 | + | 0.0798935i | ||||
\(471\) | −4.00000 | − | 6.92820i | −0.184310 | − | 0.319235i | ||||
\(472\) | −1.50000 | − | 2.59808i | −0.0690431 | − | 0.119586i | ||||
\(473\) | −20.0000 | −0.919601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | − | 1.73205i | 0.0458831 | − | 0.0794719i | ||||
\(476\) | −1.00000 | + | 1.73205i | −0.0458349 | + | 0.0793884i | ||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | 12.0000 | − | 20.7846i | 0.548867 | − | 0.950666i | ||||
\(479\) | −7.00000 | − | 12.1244i | −0.319838 | − | 0.553976i | 0.660616 | − | 0.750724i | \(-0.270295\pi\) |
−0.980454 | + | 0.196748i | \(0.936962\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | −3.50000 | − | 6.06218i | −0.159421 | − | 0.276125i | ||||
\(483\) | −2.00000 | + | 3.46410i | −0.0910032 | + | 0.157622i | ||||
\(484\) | −7.00000 | − | 12.1244i | −0.318182 | − | 0.551107i | ||||
\(485\) | 0.500000 | − | 0.866025i | 0.0227038 | − | 0.0393242i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −21.5000 | + | 37.2391i | −0.974258 | + | 1.68746i | −0.291896 | + | 0.956450i | \(0.594286\pi\) |
−0.682362 | + | 0.731014i | \(0.739047\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | + | 6.92820i | 0.180886 | + | 0.313304i | ||||
\(490\) | 3.00000 | + | 5.19615i | 0.135526 | + | 0.234738i | ||||
\(491\) | 7.50000 | − | 12.9904i | 0.338470 | − | 0.586248i | −0.645675 | − | 0.763612i | \(-0.723424\pi\) |
0.984145 | + | 0.177365i | \(0.0567572\pi\) | |||||||
\(492\) | 4.00000 | 0.180334 | ||||||||
\(493\) | 3.00000 | + | 5.19615i | 0.135113 | + | 0.234023i | ||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 5.00000 | 0.224733 | ||||||||
\(496\) | 3.50000 | − | 4.33013i | 0.157155 | − | 0.194428i | ||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 9.00000 | 0.403300 | ||||||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.00000 | + | 13.8564i | −0.357414 | + | 0.619059i | ||||
\(502\) | 14.0000 | + | 24.2487i | 0.624851 | + | 1.08227i | ||||
\(503\) | −18.0000 | − | 31.1769i | −0.802580 | − | 1.39011i | −0.917912 | − | 0.396783i | \(-0.870127\pi\) |
0.115332 | − | 0.993327i | \(-0.463207\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 2.50000 | − | 4.33013i | 0.111249 | − | 0.192688i | ||||
\(506\) | 10.0000 | − | 17.3205i | 0.444554 | − | 0.769991i | ||||
\(507\) | −1.50000 | + | 2.59808i | −0.0666173 | + | 0.115385i | ||||
\(508\) | −8.50000 | − | 14.7224i | −0.377127 | − | 0.653202i | ||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | 1.00000 | + | 1.73205i | 0.0442807 | + | 0.0766965i | ||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | + | 1.73205i | 0.0441511 | + | 0.0764719i | ||||
\(514\) | −6.00000 | + | 10.3923i | −0.264649 | + | 0.458385i | ||||
\(515\) | 2.50000 | + | 4.33013i | 0.110163 | + | 0.190808i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | −5.00000 | + | 8.66025i | −0.219900 | + | 0.380878i | ||||
\(518\) | −2.00000 | + | 3.46410i | −0.0878750 | + | 0.152204i | ||||
\(519\) | −3.00000 | −0.131685 | ||||||||
\(520\) | −2.00000 | − | 3.46410i | −0.0877058 | − | 0.151911i | ||||
\(521\) | 14.0000 | + | 24.2487i | 0.613351 | + | 1.06236i | 0.990671 | + | 0.136272i | \(0.0435123\pi\) |
−0.377320 | + | 0.926083i | \(0.623154\pi\) | |||||||
\(522\) | −1.50000 | + | 2.59808i | −0.0656532 | + | 0.113715i | ||||
\(523\) | −24.0000 | −1.04945 | −0.524723 | − | 0.851273i | \(-0.675831\pi\) | ||||
−0.524723 | + | 0.851273i | \(0.675831\pi\) | |||||||
\(524\) | −2.00000 | − | 3.46410i | −0.0873704 | − | 0.151330i | ||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −14.0000 | −0.610429 | ||||||||
\(527\) | 11.0000 | + | 1.73205i | 0.479168 | + | 0.0754493i | ||||
\(528\) | 5.00000 | 0.217597 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.50000 | − | 2.59808i | −0.0651558 | − | 0.112853i | ||||
\(531\) | 3.00000 | 0.130189 | ||||||||
\(532\) | −1.00000 | + | 1.73205i | −0.0433555 | + | 0.0750939i | ||||
\(533\) | −8.00000 | − | 13.8564i | −0.346518 | − | 0.600188i | ||||
\(534\) | −9.00000 | − | 15.5885i | −0.389468 | − | 0.674579i | ||||
\(535\) | 17.0000 | 0.734974 | ||||||||
\(536\) | 2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | ||||
\(537\) | 4.50000 | − | 7.79423i | 0.194189 | − | 0.336346i | ||||
\(538\) | −5.00000 | + | 8.66025i | −0.215565 | + | 0.373370i | ||||
\(539\) | 15.0000 | + | 25.9808i | 0.646096 | + | 1.11907i | ||||
\(540\) | −0.500000 | + | 0.866025i | −0.0215166 | + | 0.0372678i | ||||
\(541\) | −16.0000 | − | 27.7128i | −0.687894 | − | 1.19147i | −0.972518 | − | 0.232828i | \(-0.925202\pi\) |
0.284624 | − | 0.958639i | \(-0.408131\pi\) | |||||||
\(542\) | 15.0000 | 0.644305 | ||||||||
\(543\) | −22.0000 | −0.944110 | ||||||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | −7.00000 | + | 12.1244i | −0.299847 | + | 0.519350i | ||||
\(546\) | 2.00000 | + | 3.46410i | 0.0855921 | + | 0.148250i | ||||
\(547\) | −21.0000 | + | 36.3731i | −0.897895 | + | 1.55520i | −0.0677151 | + | 0.997705i | \(0.521571\pi\) |
−0.830180 | + | 0.557495i | \(0.811762\pi\) | |||||||
\(548\) | −7.00000 | + | 12.1244i | −0.299025 | + | 0.517927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.00000 | 0.213201 | ||||||||
\(551\) | 3.00000 | + | 5.19615i | 0.127804 | + | 0.221364i | ||||
\(552\) | 2.00000 | + | 3.46410i | 0.0851257 | + | 0.147442i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.0000 | 0.764747 | ||||||||
\(555\) | 2.00000 | + | 3.46410i | 0.0848953 | + | 0.147043i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | 13.0000 | 0.550828 | 0.275414 | − | 0.961326i | \(-0.411185\pi\) | ||||
0.275414 | + | 0.961326i | \(0.411185\pi\) | |||||||
\(558\) | 2.00000 | + | 5.19615i | 0.0846668 | + | 0.219971i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 5.00000 | + | 8.66025i | 0.211100 | + | 0.365636i | ||||
\(562\) | −10.0000 | −0.421825 | ||||||||
\(563\) | 8.50000 | − | 14.7224i | 0.358232 | − | 0.620477i | −0.629433 | − | 0.777055i | \(-0.716713\pi\) |
0.987666 | + | 0.156578i | \(0.0500463\pi\) | |||||||
\(564\) | −1.00000 | − | 1.73205i | −0.0421076 | − | 0.0729325i | ||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0.500000 | − | 0.866025i | 0.0209980 | − | 0.0363696i | ||||
\(568\) | −4.00000 | + | 6.92820i | −0.167836 | + | 0.290701i | ||||
\(569\) | 12.0000 | − | 20.7846i | 0.503066 | − | 0.871336i | −0.496928 | − | 0.867792i | \(-0.665539\pi\) |
0.999994 | − | 0.00354413i | \(-0.00112814\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | 15.0000 | − | 25.9808i | 0.627730 | − | 1.08726i | −0.360276 | − | 0.932846i | \(-0.617317\pi\) |
0.988006 | − | 0.154415i | \(-0.0493493\pi\) | |||||||
\(572\) | −10.0000 | − | 17.3205i | −0.418121 | − | 0.724207i | ||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −4.00000 | −0.166957 | ||||||||
\(575\) | 2.00000 | + | 3.46410i | 0.0834058 | + | 0.144463i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 9.00000 | + | 15.5885i | 0.374675 | + | 0.648956i | 0.990278 | − | 0.139100i | \(-0.0444210\pi\) |
−0.615603 | + | 0.788056i | \(0.711088\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | −0.500000 | + | 0.866025i | −0.0207793 | + | 0.0359908i | ||||
\(580\) | −1.50000 | + | 2.59808i | −0.0622841 | + | 0.107879i | ||||
\(581\) | −9.00000 | −0.373383 | ||||||||
\(582\) | 0.500000 | + | 0.866025i | 0.0207257 | + | 0.0358979i | ||||
\(583\) | −7.50000 | − | 12.9904i | −0.310618 | − | 0.538007i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | 4.00000 | 0.165380 | ||||||||
\(586\) | −9.50000 | − | 16.4545i | −0.392441 | − | 0.679728i | ||||
\(587\) | 27.0000 | 1.11441 | 0.557205 | − | 0.830375i | \(-0.311874\pi\) | ||||
0.557205 | + | 0.830375i | \(0.311874\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 11.0000 | + | 1.73205i | 0.453247 | + | 0.0713679i | ||||
\(590\) | 3.00000 | 0.123508 | ||||||||
\(591\) | 26.0000 | 1.06950 | ||||||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | −2.50000 | + | 4.33013i | −0.102576 | + | 0.177667i | ||||
\(595\) | −1.00000 | − | 1.73205i | −0.0409960 | − | 0.0710072i | ||||
\(596\) | 5.50000 | + | 9.52628i | 0.225289 | + | 0.390212i | ||||
\(597\) | −5.00000 | −0.204636 | ||||||||
\(598\) | 8.00000 | − | 13.8564i | 0.327144 | − | 0.566631i | ||||
\(599\) | 18.0000 | − | 31.1769i | 0.735460 | − | 1.27385i | −0.219061 | − | 0.975711i | \(-0.570299\pi\) |
0.954521 | − | 0.298143i | \(-0.0963673\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 21.0000 | + | 36.3731i | 0.856608 | + | 1.48369i | 0.875145 | + | 0.483860i | \(0.160766\pi\) |
−0.0185374 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(602\) | −2.00000 | + | 3.46410i | −0.0815139 | + | 0.141186i | ||||
\(603\) | 2.00000 | + | 3.46410i | 0.0814463 | + | 0.141069i | ||||
\(604\) | −5.00000 | −0.203447 | ||||||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | 2.50000 | + | 4.33013i | 0.101556 | + | 0.175899i | ||||
\(607\) | −24.0000 | + | 41.5692i | −0.974130 | + | 1.68724i | −0.291353 | + | 0.956616i | \(0.594105\pi\) |
−0.682777 | + | 0.730627i | \(0.739228\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 1.50000 | − | 2.59808i | 0.0607831 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | + | 6.92820i | −0.161823 | + | 0.280285i | ||||
\(612\) | −2.00000 | −0.0808452 | ||||||||
\(613\) | −12.0000 | − | 20.7846i | −0.484675 | − | 0.839482i | 0.515170 | − | 0.857088i | \(-0.327729\pi\) |
−0.999845 | + | 0.0176058i | \(0.994396\pi\) | |||||||
\(614\) | −1.00000 | − | 1.73205i | −0.0403567 | − | 0.0698999i | ||||
\(615\) | −2.00000 | + | 3.46410i | −0.0806478 | + | 0.139686i | ||||
\(616\) | −5.00000 | −0.201456 | ||||||||
\(617\) | −6.00000 | − | 10.3923i | −0.241551 | − | 0.418378i | 0.719605 | − | 0.694383i | \(-0.244323\pi\) |
−0.961156 | + | 0.276005i | \(0.910989\pi\) | |||||||
\(618\) | −5.00000 | −0.201129 | ||||||||
\(619\) | −34.0000 | −1.36658 | −0.683288 | − | 0.730149i | \(-0.739451\pi\) | ||||
−0.683288 | + | 0.730149i | \(0.739451\pi\) | |||||||
\(620\) | 2.00000 | + | 5.19615i | 0.0803219 | + | 0.208683i | ||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 20.0000 | 0.801927 | ||||||||
\(623\) | 9.00000 | + | 15.5885i | 0.360577 | + | 0.624538i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 17.5000 | + | 30.3109i | 0.699441 | + | 1.21147i | ||||
\(627\) | 5.00000 | + | 8.66025i | 0.199681 | + | 0.345857i | ||||
\(628\) | 8.00000 | 0.319235 | ||||||||
\(629\) | −4.00000 | + | 6.92820i | −0.159490 | + | 0.276246i | ||||
\(630\) | 0.500000 | − | 0.866025i | 0.0199205 | − | 0.0345033i | ||||
\(631\) | −5.50000 | + | 9.52628i | −0.218952 | + | 0.379235i | −0.954488 | − | 0.298250i | \(-0.903597\pi\) |
0.735536 | + | 0.677485i | \(0.236930\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0000 | + | 19.0526i | −0.437211 | + | 0.757271i | ||||
\(634\) | 0.500000 | + | 0.866025i | 0.0198575 | + | 0.0343943i | ||||
\(635\) | 17.0000 | 0.674624 | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 12.0000 | + | 20.7846i | 0.475457 | + | 0.823516i | ||||
\(638\) | −7.50000 | + | 12.9904i | −0.296928 | + | 0.514294i | ||||
\(639\) | −4.00000 | − | 6.92820i | −0.158238 | − | 0.274075i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −6.00000 | + | 10.3923i | −0.236986 | + | 0.410471i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
0.722862 | + | 0.690992i | \(0.242826\pi\) | |||||||
\(642\) | −8.50000 | + | 14.7224i | −0.335468 | + | 0.581048i | ||||
\(643\) | −16.0000 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(644\) | −2.00000 | − | 3.46410i | −0.0788110 | − | 0.136505i | ||||
\(645\) | 2.00000 | + | 3.46410i | 0.0787499 | + | 0.136399i | ||||
\(646\) | −2.00000 | + | 3.46410i | −0.0786889 | + | 0.136293i | ||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 15.0000 | 0.588802 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | −2.00000 | − | 5.19615i | −0.0783862 | − | 0.203653i | ||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | 21.0000 | 0.821794 | 0.410897 | − | 0.911682i | \(-0.365216\pi\) | ||||
0.410897 | + | 0.911682i | \(0.365216\pi\) | |||||||
\(654\) | −7.00000 | − | 12.1244i | −0.273722 | − | 0.474100i | ||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | −2.00000 | + | 3.46410i | −0.0780869 | + | 0.135250i | ||||
\(657\) | −1.00000 | − | 1.73205i | −0.0390137 | − | 0.0675737i | ||||
\(658\) | 1.00000 | + | 1.73205i | 0.0389841 | + | 0.0675224i | ||||
\(659\) | 15.0000 | 0.584317 | 0.292159 | − | 0.956370i | \(-0.405627\pi\) | ||||
0.292159 | + | 0.956370i | \(0.405627\pi\) | |||||||
\(660\) | −2.50000 | + | 4.33013i | −0.0973124 | + | 0.168550i | ||||
\(661\) | 18.0000 | − | 31.1769i | 0.700119 | − | 1.21264i | −0.268306 | − | 0.963334i | \(-0.586464\pi\) |
0.968424 | − | 0.249308i | \(-0.0802030\pi\) | |||||||
\(662\) | −2.00000 | + | 3.46410i | −0.0777322 | + | 0.134636i | ||||
\(663\) | 4.00000 | + | 6.92820i | 0.155347 | + | 0.269069i | ||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | −1.00000 | − | 1.73205i | −0.0387783 | − | 0.0671660i | ||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −12.0000 | −0.464642 | ||||||||
\(668\) | −8.00000 | − | 13.8564i | −0.309529 | − | 0.536120i | ||||
\(669\) | −1.50000 | + | 2.59808i | −0.0579934 | + | 0.100447i | ||||
\(670\) | 2.00000 | + | 3.46410i | 0.0772667 | + | 0.133830i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | −16.5000 | + | 28.5788i | −0.636028 | + | 1.10163i | 0.350268 | + | 0.936650i | \(0.386091\pi\) |
−0.986296 | + | 0.164984i | \(0.947243\pi\) | |||||||
\(674\) | −3.00000 | −0.115556 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | 23.5000 | − | 40.7032i | 0.903178 | − | 1.56435i | 0.0798344 | − | 0.996808i | \(-0.474561\pi\) |
0.823344 | − | 0.567543i | \(-0.192106\pi\) | |||||||
\(678\) | −4.00000 | −0.153619 | ||||||||
\(679\) | −0.500000 | − | 0.866025i | −0.0191882 | − | 0.0332350i | ||||
\(680\) | −2.00000 | −0.0766965 | ||||||||
\(681\) | 5.00000 | 0.191600 | ||||||||
\(682\) | 10.0000 | + | 25.9808i | 0.382920 | + | 0.994855i | ||||
\(683\) | −9.00000 | −0.344375 | −0.172188 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172188 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | −7.00000 | − | 12.1244i | −0.267456 | − | 0.463248i | ||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | 14.0000 | − | 24.2487i | 0.534133 | − | 0.925146i | ||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | −4.00000 | −0.152277 | ||||||||
\(691\) | −5.00000 | + | 8.66025i | −0.190209 | + | 0.329452i | −0.945319 | − | 0.326146i | \(-0.894250\pi\) |
0.755110 | + | 0.655598i | \(0.227583\pi\) | |||||||
\(692\) | 1.50000 | − | 2.59808i | 0.0570214 | − | 0.0987640i | ||||
\(693\) | 2.50000 | − | 4.33013i | 0.0949671 | − | 0.164488i | ||||
\(694\) | 0.500000 | + | 0.866025i | 0.0189797 | + | 0.0328739i | ||||
\(695\) | −5.00000 | + | 8.66025i | −0.189661 | + | 0.328502i | ||||
\(696\) | −1.50000 | − | 2.59808i | −0.0568574 | − | 0.0984798i | ||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | 34.0000 | 1.28692 | ||||||||
\(699\) | −2.00000 | − | 3.46410i | −0.0756469 | − | 0.131024i | ||||
\(700\) | 0.500000 | − | 0.866025i | 0.0188982 | − | 0.0327327i | ||||
\(701\) | 4.50000 | + | 7.79423i | 0.169963 | + | 0.294384i | 0.938406 | − | 0.345533i | \(-0.112302\pi\) |
−0.768444 | + | 0.639917i | \(0.778969\pi\) | |||||||
\(702\) | −2.00000 | + | 3.46410i | −0.0754851 | + | 0.130744i | ||||
\(703\) | −4.00000 | + | 6.92820i | −0.150863 | + | 0.261302i | ||||
\(704\) | −2.50000 | + | 4.33013i | −0.0942223 | + | 0.163198i | ||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | 7.00000 | + | 12.1244i | 0.263448 | + | 0.456306i | ||||
\(707\) | −2.50000 | − | 4.33013i | −0.0940222 | − | 0.162851i | ||||
\(708\) | −1.50000 | + | 2.59808i | −0.0563735 | + | 0.0976417i | ||||
\(709\) | 12.0000 | 0.450669 | 0.225335 | − | 0.974281i | \(-0.427652\pi\) | ||||
0.225335 | + | 0.974281i | \(0.427652\pi\) | |||||||
\(710\) | −4.00000 | − | 6.92820i | −0.150117 | − | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.0000 | 0.674579 | ||||||||
\(713\) | −14.0000 | + | 17.3205i | −0.524304 | + | 0.648658i | ||||
\(714\) | 2.00000 | 0.0748481 | ||||||||
\(715\) | 20.0000 | 0.747958 | ||||||||
\(716\) | 4.50000 | + | 7.79423i | 0.168173 | + | 0.291284i | ||||
\(717\) | −24.0000 | −0.896296 | ||||||||
\(718\) | −10.0000 | + | 17.3205i | −0.373197 | + | 0.646396i | ||||
\(719\) | −21.0000 | − | 36.3731i | −0.783168 | − | 1.35649i | −0.930087 | − | 0.367338i | \(-0.880269\pi\) |
0.146920 | − | 0.989148i | \(-0.453064\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.0186339 | − | 0.0322749i | ||||
\(721\) | 5.00000 | 0.186210 | ||||||||
\(722\) | 7.50000 | − | 12.9904i | 0.279121 | − | 0.483452i | ||||
\(723\) | −3.50000 | + | 6.06218i | −0.130166 | + | 0.225455i | ||||
\(724\) | 11.0000 | − | 19.0526i | 0.408812 | − | 0.708083i | ||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | −7.00000 | + | 12.1244i | −0.259794 | + | 0.449977i | ||||
\(727\) | 13.5000 | + | 23.3827i | 0.500687 | + | 0.867216i | 1.00000 | 0.000793791i | \(0.000252672\pi\) | |
−0.499312 | + | 0.866422i | \(0.666414\pi\) | |||||||
\(728\) | −4.00000 | −0.148250 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | − | 1.73205i | −0.0370117 | − | 0.0641061i | ||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | − | 19.0526i | 0.406294 | − | 0.703722i | −0.588177 | − | 0.808732i | \(-0.700154\pi\) |
0.994471 | + | 0.105010i | \(0.0334875\pi\) | |||||||
\(734\) | 12.0000 | − | 20.7846i | 0.442928 | − | 0.767174i | ||||
\(735\) | 3.00000 | − | 5.19615i | 0.110657 | − | 0.191663i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 10.0000 | + | 17.3205i | 0.368355 | + | 0.638009i | ||||
\(738\) | −2.00000 | − | 3.46410i | −0.0736210 | − | 0.127515i | ||||
\(739\) | −21.0000 | + | 36.3731i | −0.772497 | + | 1.33800i | 0.163693 | + | 0.986511i | \(0.447659\pi\) |
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 4.00000 | + | 6.92820i | 0.146944 | + | 0.254514i | ||||
\(742\) | −3.00000 | −0.110133 | ||||||||
\(743\) | −46.0000 | −1.68758 | −0.843788 | − | 0.536676i | \(-0.819680\pi\) | ||||
−0.843788 | + | 0.536676i | \(0.819680\pi\) | |||||||
\(744\) | −5.50000 | − | 0.866025i | −0.201640 | − | 0.0317500i | ||||
\(745\) | −11.0000 | −0.403009 | ||||||||
\(746\) | 2.00000 | 0.0732252 | ||||||||
\(747\) | −4.50000 | − | 7.79423i | −0.164646 | − | 0.285176i | ||||
\(748\) | −10.0000 | −0.365636 | ||||||||
\(749\) | 8.50000 | − | 14.7224i | 0.310583 | − | 0.537946i | ||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | −7.50000 | − | 12.9904i | −0.273679 | − | 0.474026i | 0.696122 | − | 0.717923i | \(-0.254907\pi\) |
−0.969801 | + | 0.243898i | \(0.921574\pi\) | |||||||
\(752\) | 2.00000 | 0.0729325 | ||||||||
\(753\) | 14.0000 | − | 24.2487i | 0.510188 | − | 0.883672i | ||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | 2.50000 | − | 4.33013i | 0.0909843 | − | 0.157589i | ||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | 10.0000 | − | 17.3205i | 0.363456 | − | 0.629525i | −0.625071 | − | 0.780568i | \(-0.714930\pi\) |
0.988527 | + | 0.151043i | \(0.0482633\pi\) | |||||||
\(758\) | −1.00000 | − | 1.73205i | −0.0363216 | − | 0.0629109i | ||||
\(759\) | −20.0000 | −0.725954 | ||||||||
\(760\) | −2.00000 | −0.0725476 | ||||||||
\(761\) | −25.0000 | − | 43.3013i | −0.906249 | − | 1.56967i | −0.819231 | − | 0.573463i | \(-0.805600\pi\) |
−0.0870179 | − | 0.996207i | \(-0.527734\pi\) | |||||||
\(762\) | −8.50000 | + | 14.7224i | −0.307923 | + | 0.533337i | ||||
\(763\) | 7.00000 | + | 12.1244i | 0.253417 | + | 0.438931i | ||||
\(764\) | 4.00000 | − | 6.92820i | 0.144715 | − | 0.250654i | ||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | 14.0000 | − | 24.2487i | 0.505841 | − | 0.876142i | ||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 11.5000 | + | 19.9186i | 0.414701 | + | 0.718283i | 0.995397 | − | 0.0958377i | \(-0.0305530\pi\) |
−0.580696 | + | 0.814120i | \(0.697220\pi\) | |||||||
\(770\) | 2.50000 | − | 4.33013i | 0.0900937 | − | 0.156047i | ||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | −0.500000 | − | 0.866025i | −0.0179954 | − | 0.0311689i | ||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | −5.50000 | − | 0.866025i | −0.197566 | − | 0.0311086i | ||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 9.00000 | + | 15.5885i | 0.322666 | + | 0.558873i | ||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | −2.00000 | + | 3.46410i | −0.0716115 | + | 0.124035i | ||||
\(781\) | −20.0000 | − | 34.6410i | −0.715656 | − | 1.23955i | ||||
\(782\) | −4.00000 | − | 6.92820i | −0.143040 | − | 0.247752i | ||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | −4.00000 | + | 6.92820i | −0.142766 | + | 0.247278i | ||||
\(786\) | −2.00000 | + | 3.46410i | −0.0713376 | + | 0.123560i | ||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | −13.0000 | + | 22.5167i | −0.463106 | + | 0.802123i | ||||
\(789\) | 7.00000 | + | 12.1244i | 0.249207 | + | 0.431638i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | −2.50000 | − | 4.33013i | −0.0888336 | − | 0.153864i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | −1.50000 | + | 2.59808i | −0.0531995 | + | 0.0921443i | ||||
\(796\) | 2.50000 | − | 4.33013i | 0.0886102 | − | 0.153477i | ||||
\(797\) | −6.50000 | + | 11.2583i | −0.230242 | + | 0.398791i | −0.957879 | − | 0.287171i | \(-0.907285\pi\) |
0.727637 | + | 0.685962i | \(0.240618\pi\) | |||||||
\(798\) | 2.00000 | 0.0707992 | ||||||||
\(799\) | 2.00000 | + | 3.46410i | 0.0707549 | + | 0.122551i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −9.00000 | + | 15.5885i | −0.317999 | + | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.00000 | − | 8.66025i | −0.176446 | − | 0.305614i | ||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 8.00000 | + | 20.7846i | 0.281788 | + | 0.732107i | ||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | −5.00000 | −0.175899 | ||||||||
\(809\) | −27.0000 | − | 46.7654i | −0.949269 | − | 1.64418i | −0.746968 | − | 0.664860i | \(-0.768491\pi\) |
−0.202301 | − | 0.979323i | \(-0.564842\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −3.00000 | + | 5.19615i | −0.105344 | + | 0.182462i | −0.913879 | − | 0.405987i | \(-0.866928\pi\) |
0.808535 | + | 0.588449i | \(0.200261\pi\) | |||||||
\(812\) | 1.50000 | + | 2.59808i | 0.0526397 | + | 0.0911746i | ||||
\(813\) | −7.50000 | − | 12.9904i | −0.263036 | − | 0.455593i | ||||
\(814\) | −20.0000 | −0.701000 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 1.00000 | − | 1.73205i | 0.0350070 | − | 0.0606339i | ||||
\(817\) | −4.00000 | + | 6.92820i | −0.139942 | + | 0.242387i | ||||
\(818\) | 8.50000 | + | 14.7224i | 0.297196 | + | 0.514758i | ||||
\(819\) | 2.00000 | − | 3.46410i | 0.0698857 | − | 0.121046i | ||||
\(820\) | −2.00000 | − | 3.46410i | −0.0698430 | − | 0.120972i | ||||
\(821\) | −45.0000 | −1.57051 | −0.785255 | − | 0.619172i | \(-0.787468\pi\) | ||||
−0.785255 | + | 0.619172i | \(0.787468\pi\) | |||||||
\(822\) | 14.0000 | 0.488306 | ||||||||
\(823\) | 5.50000 | + | 9.52628i | 0.191718 | + | 0.332065i | 0.945820 | − | 0.324692i | \(-0.105261\pi\) |
−0.754102 | + | 0.656758i | \(0.771927\pi\) | |||||||
\(824\) | 2.50000 | − | 4.33013i | 0.0870916 | − | 0.150847i | ||||
\(825\) | −2.50000 | − | 4.33013i | −0.0870388 | − | 0.150756i | ||||
\(826\) | 1.50000 | − | 2.59808i | 0.0521917 | − | 0.0903986i | ||||
\(827\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | −10.0000 | −0.347314 | −0.173657 | − | 0.984806i | \(-0.555558\pi\) | ||||
−0.173657 | + | 0.984806i | \(0.555558\pi\) | |||||||
\(830\) | −4.50000 | − | 7.79423i | −0.156197 | − | 0.270542i | ||||
\(831\) | −9.00000 | − | 15.5885i | −0.312207 | − | 0.540758i | ||||
\(832\) | −2.00000 | + | 3.46410i | −0.0693375 | + | 0.120096i | ||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | −5.00000 | − | 8.66025i | −0.173136 | − | 0.299880i | ||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | −10.0000 | −0.345857 | ||||||||
\(837\) | 3.50000 | − | 4.33013i | 0.120978 | − | 0.149671i | ||||
\(838\) | 9.00000 | 0.310900 | ||||||||
\(839\) | −26.0000 | −0.897620 | −0.448810 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448810 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(840\) | 0.500000 | + | 0.866025i | 0.0172516 | + | 0.0298807i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −10.0000 | + | 17.3205i | −0.344623 | + | 0.596904i | ||||
\(843\) | 5.00000 | + | 8.66025i | 0.172209 | + | 0.298275i | ||||
\(844\) | −11.0000 | − | 19.0526i | −0.378636 | − | 0.655816i | ||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | −1.00000 | + | 1.73205i | −0.0343807 | + | 0.0595491i | ||||
\(847\) | 7.00000 | − | 12.1244i | 0.240523 | − | 0.416598i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | −6.00000 | − | 10.3923i | −0.205919 | − | 0.356663i | ||||
\(850\) | 1.00000 | − | 1.73205i | 0.0342997 | − | 0.0594089i | ||||
\(851\) | −8.00000 | − | 13.8564i | −0.274236 | − | 0.474991i | ||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −12.0000 | −0.410872 | −0.205436 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205436 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | − | 1.73205i | 0.0341993 | − | 0.0592349i | ||||
\(856\) | −8.50000 | − | 14.7224i | −0.290524 | − | 0.503202i | ||||
\(857\) | 14.0000 | − | 24.2487i | 0.478231 | − | 0.828320i | −0.521458 | − | 0.853277i | \(-0.674612\pi\) |
0.999689 | + | 0.0249570i | \(0.00794488\pi\) | |||||||
\(858\) | −10.0000 | + | 17.3205i | −0.341394 | + | 0.591312i | ||||
\(859\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 2.00000 | + | 3.46410i | 0.0681598 | + | 0.118056i | ||||
\(862\) | 11.0000 | + | 19.0526i | 0.374661 | + | 0.648933i | ||||
\(863\) | 24.0000 | − | 41.5692i | 0.816970 | − | 1.41503i | −0.0909355 | − | 0.995857i | \(-0.528986\pi\) |
0.907905 | − | 0.419176i | \(-0.137681\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.50000 | + | 2.59808i | 0.0510015 | + | 0.0883372i | ||||
\(866\) | −22.0000 | −0.747590 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 5.50000 | + | 0.866025i | 0.186682 | + | 0.0293948i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.00000 | 0.101710 | ||||||||
\(871\) | 8.00000 | + | 13.8564i | 0.271070 | + | 0.469506i | ||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | 0.500000 | − | 0.866025i | 0.0169224 | − | 0.0293105i | ||||
\(874\) | −4.00000 | − | 6.92820i | −0.135302 | − | 0.234350i | ||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 20.0000 | − | 34.6410i | 0.675352 | − | 1.16974i | −0.301014 | − | 0.953620i | \(-0.597325\pi\) |
0.976366 | − | 0.216124i | \(-0.0693416\pi\) | |||||||
\(878\) | 4.50000 | − | 7.79423i | 0.151868 | − | 0.263042i | ||||
\(879\) | −9.50000 | + | 16.4545i | −0.320427 | + | 0.554996i | ||||
\(880\) | −2.50000 | − | 4.33013i | −0.0842750 | − | 0.145969i | ||||
\(881\) | 10.0000 | − | 17.3205i | 0.336909 | − | 0.583543i | −0.646941 | − | 0.762540i | \(-0.723952\pi\) |
0.983850 | + | 0.178997i | \(0.0572853\pi\) | |||||||
\(882\) | 3.00000 | + | 5.19615i | 0.101015 | + | 0.174964i | ||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | −1.50000 | − | 2.59808i | −0.0504219 | − | 0.0873334i | ||||
\(886\) | −2.00000 | + | 3.46410i | −0.0671913 | + | 0.116379i | ||||
\(887\) | −19.0000 | − | 32.9090i | −0.637958 | − | 1.10497i | −0.985880 | − | 0.167452i | \(-0.946446\pi\) |
0.347923 | − | 0.937523i | \(-0.386887\pi\) | |||||||
\(888\) | 2.00000 | − | 3.46410i | 0.0671156 | − | 0.116248i | ||||
\(889\) | 8.50000 | − | 14.7224i | 0.285081 | − | 0.493775i | ||||
\(890\) | −9.00000 | + | 15.5885i | −0.301681 | + | 0.522526i | ||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | −1.50000 | − | 2.59808i | −0.0502237 | − | 0.0869900i | ||||
\(893\) | 2.00000 | + | 3.46410i | 0.0669274 | + | 0.115922i | ||||
\(894\) | 5.50000 | − | 9.52628i | 0.183948 | − | 0.318606i | ||||
\(895\) | −9.00000 | −0.300837 | ||||||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −34.0000 | −1.13459 | ||||||||
\(899\) | 10.5000 | − | 12.9904i | 0.350195 | − | 0.433253i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −6.00000 | −0.199889 | ||||||||
\(902\) | −10.0000 | − | 17.3205i | −0.332964 | − | 0.576710i | ||||
\(903\) | 4.00000 | 0.133112 | ||||||||
\(904\) | 2.00000 | − | 3.46410i | 0.0665190 | − | 0.115214i | ||||
\(905\) | 11.0000 | + | 19.0526i | 0.365652 | + | 0.633328i | ||||
\(906\) | 2.50000 | + | 4.33013i | 0.0830569 | + | 0.143859i | ||||
\(907\) | 48.0000 | 1.59381 | 0.796907 | − | 0.604102i | \(-0.206468\pi\) | ||||
0.796907 | + | 0.604102i | \(0.206468\pi\) | |||||||
\(908\) | −2.50000 | + | 4.33013i | −0.0829654 | + | 0.143700i | ||||
\(909\) | 2.50000 | − | 4.33013i | 0.0829198 | − | 0.143621i | ||||
\(910\) | 2.00000 | − | 3.46410i | 0.0662994 | − | 0.114834i | ||||
\(911\) | −11.0000 | − | 19.0526i | −0.364446 | − | 0.631239i | 0.624241 | − | 0.781232i | \(-0.285408\pi\) |
−0.988687 | + | 0.149992i | \(0.952075\pi\) | |||||||
\(912\) | 1.00000 | − | 1.73205i | 0.0331133 | − | 0.0573539i | ||||
\(913\) | −22.5000 | − | 38.9711i | −0.744641 | − | 1.28976i | ||||
\(914\) | −18.0000 | −0.595387 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | + | 24.2487i | 0.462573 | + | 0.801200i | ||||
\(917\) | 2.00000 | − | 3.46410i | 0.0660458 | − | 0.114395i | ||||
\(918\) | 1.00000 | + | 1.73205i | 0.0330049 | + | 0.0571662i | ||||
\(919\) | 21.5000 | − | 37.2391i | 0.709220 | − | 1.22840i | −0.255927 | − | 0.966696i | \(-0.582381\pi\) |
0.965147 | − | 0.261708i | \(-0.0842858\pi\) | |||||||
\(920\) | 2.00000 | − | 3.46410i | 0.0659380 | − | 0.114208i | ||||
\(921\) | −1.00000 | + | 1.73205i | −0.0329511 | + | 0.0570730i | ||||
\(922\) | 21.0000 | 0.691598 | ||||||||
\(923\) | −16.0000 | − | 27.7128i | −0.526646 | − | 0.912178i | ||||
\(924\) | 2.50000 | + | 4.33013i | 0.0822440 | + | 0.142451i | ||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 5.00000 | 0.164310 | ||||||||
\(927\) | 2.50000 | + | 4.33013i | 0.0821108 | + | 0.142220i | ||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | 42.0000 | 1.37798 | 0.688988 | − | 0.724773i | \(-0.258055\pi\) | ||||
0.688988 | + | 0.724773i | \(0.258055\pi\) | |||||||
\(930\) | 3.50000 | − | 4.33013i | 0.114770 | − | 0.141990i | ||||
\(931\) | 12.0000 | 0.393284 | ||||||||
\(932\) | 4.00000 | 0.131024 | ||||||||
\(933\) | −10.0000 | − | 17.3205i | −0.327385 | − | 0.567048i | ||||
\(934\) | 33.0000 | 1.07979 | ||||||||
\(935\) | 5.00000 | − | 8.66025i | 0.163517 | − | 0.283221i | ||||
\(936\) | −2.00000 | − | 3.46410i | −0.0653720 | − | 0.113228i | ||||
\(937\) | 5.00000 | + | 8.66025i | 0.163343 | + | 0.282918i | 0.936066 | − | 0.351826i | \(-0.114439\pi\) |
−0.772723 | + | 0.634744i | \(0.781106\pi\) | |||||||
\(938\) | 4.00000 | 0.130605 | ||||||||
\(939\) | 17.5000 | − | 30.3109i | 0.571091 | − | 0.989158i | ||||
\(940\) | −1.00000 | + | 1.73205i | −0.0326164 | + | 0.0564933i | ||||
\(941\) | −10.5000 | + | 18.1865i | −0.342290 | + | 0.592864i | −0.984858 | − | 0.173365i | \(-0.944536\pi\) |
0.642567 | + | 0.766229i | \(0.277869\pi\) | |||||||
\(942\) | −4.00000 | − | 6.92820i | −0.130327 | − | 0.225733i | ||||
\(943\) | 8.00000 | − | 13.8564i | 0.260516 | − | 0.451227i | ||||
\(944\) | −1.50000 | − | 2.59808i | −0.0488208 | − | 0.0845602i | ||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −20.0000 | −0.650256 | ||||||||
\(947\) | 6.00000 | + | 10.3923i | 0.194974 | + | 0.337705i | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 1.00000 | − | 1.73205i | 0.0324443 | − | 0.0561951i | ||||
\(951\) | 0.500000 | − | 0.866025i | 0.0162136 | − | 0.0280828i | ||||
\(952\) | −1.00000 | + | 1.73205i | −0.0324102 | + | 0.0561361i | ||||
\(953\) | −8.00000 | −0.259145 | −0.129573 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129573 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(954\) | −1.50000 | − | 2.59808i | −0.0485643 | − | 0.0841158i | ||||
\(955\) | 4.00000 | + | 6.92820i | 0.129437 | + | 0.224191i | ||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 15.0000 | 0.484881 | ||||||||
\(958\) | −7.00000 | − | 12.1244i | −0.226160 | − | 0.391720i | ||||
\(959\) | −14.0000 | −0.452084 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −6.50000 | − | 30.3109i | −0.209677 | − | 0.977771i | ||||
\(962\) | −16.0000 | −0.515861 | ||||||||
\(963\) | 17.0000 | 0.547817 | ||||||||
\(964\) | −3.50000 | − | 6.06218i | −0.112727 | − | 0.195250i | ||||
\(965\) | 1.00000 | 0.0321911 | ||||||||
\(966\) | −2.00000 | + | 3.46410i | −0.0643489 | + | 0.111456i | ||||
\(967\) | −28.0000 | − | 48.4974i | −0.900419 | − | 1.55957i | −0.826951 | − | 0.562274i | \(-0.809926\pi\) |
−0.0734686 | − | 0.997298i | \(-0.523407\pi\) | |||||||
\(968\) | −7.00000 | − | 12.1244i | −0.224989 | − | 0.389692i | ||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | 0.500000 | − | 0.866025i | 0.0160540 | − | 0.0278064i | ||||
\(971\) | −1.50000 | + | 2.59808i | −0.0481373 | + | 0.0833762i | −0.889090 | − | 0.457732i | \(-0.848662\pi\) |
0.840953 | + | 0.541108i | \(0.181995\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 5.00000 | + | 8.66025i | 0.160293 | + | 0.277635i | ||||
\(974\) | −21.5000 | + | 37.2391i | −0.688904 | + | 1.19322i | ||||
\(975\) | −2.00000 | − | 3.46410i | −0.0640513 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.0000 | 1.79160 | 0.895799 | − | 0.444459i | \(-0.146604\pi\) | ||||
0.895799 | + | 0.444459i | \(0.146604\pi\) | |||||||
\(978\) | 4.00000 | + | 6.92820i | 0.127906 | + | 0.221540i | ||||
\(979\) | −45.0000 | + | 77.9423i | −1.43821 | + | 2.49105i | ||||
\(980\) | 3.00000 | + | 5.19615i | 0.0958315 | + | 0.165985i | ||||
\(981\) | −7.00000 | + | 12.1244i | −0.223493 | + | 0.387101i | ||||
\(982\) | 7.50000 | − | 12.9904i | 0.239335 | − | 0.414540i | ||||
\(983\) | 17.0000 | − | 29.4449i | 0.542216 | − | 0.939145i | −0.456561 | − | 0.889692i | \(-0.650919\pi\) |
0.998776 | − | 0.0494530i | \(-0.0157478\pi\) | |||||||
\(984\) | 4.00000 | 0.127515 | ||||||||
\(985\) | −13.0000 | − | 22.5167i | −0.414214 | − | 0.717440i | ||||
\(986\) | 3.00000 | + | 5.19615i | 0.0955395 | + | 0.165479i | ||||
\(987\) | 1.00000 | − | 1.73205i | 0.0318304 | − | 0.0551318i | ||||
\(988\) | −8.00000 | −0.254514 | ||||||||
\(989\) | −8.00000 | − | 13.8564i | −0.254385 | − | 0.440608i | ||||
\(990\) | 5.00000 | 0.158910 | ||||||||
\(991\) | −44.0000 | −1.39771 | −0.698853 | − | 0.715265i | \(-0.746306\pi\) | ||||
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 3.50000 | − | 4.33013i | 0.111125 | − | 0.137482i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 2.50000 | + | 4.33013i | 0.0792553 | + | 0.137274i | ||||
\(996\) | 9.00000 | 0.285176 | ||||||||
\(997\) | 6.00000 | − | 10.3923i | 0.190022 | − | 0.329128i | −0.755235 | − | 0.655454i | \(-0.772477\pi\) |
0.945257 | + | 0.326326i | \(0.105811\pi\) | |||||||
\(998\) | 16.0000 | + | 27.7128i | 0.506471 | + | 0.877234i | ||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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 | 930.2.i.f.211.1 | ✓ | 2 | |
31.5 | even | 3 | inner | 930.2.i.f.811.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.f.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
930.2.i.f.811.1 | yes | 2 | 31.5 | even | 3 | inner |