Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(221,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
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 | 221.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.221 |
Dual form | 770.2.i.i.331.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 1.50000 | + | 2.59808i | 0.433013 | + | 0.750000i | ||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.00000 | − | 6.92820i | 0.970143 | − | 1.68034i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
0.695113 | − | 0.718900i | \(-0.255354\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.707107 | − | 1.22474i | ||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.50000 | − | 7.79423i | 0.327327 | − | 1.70084i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | −1.50000 | + | 2.59808i | −0.306186 | + | 0.530330i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −3.00000 | − | 5.19615i | −0.588348 | − | 1.01905i | ||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | −1.50000 | − | 2.59808i | −0.273861 | − | 0.474342i | ||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 8.00000 | 1.37199 | ||||||||
\(35\) | −2.00000 | − | 1.73205i | −0.338062 | − | 0.292770i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | −9.00000 | + | 15.5885i | −1.44115 | + | 2.49615i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 7.50000 | − | 2.59808i | 1.15728 | − | 0.400892i | ||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | −3.50000 | + | 6.06218i | −0.516047 | + | 0.893819i | ||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −12.0000 | − | 20.7846i | −1.68034 | − | 2.91043i | ||||
\(52\) | 3.00000 | − | 5.19615i | 0.416025 | − | 0.720577i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | 12.0000 | 1.58944 | ||||||||
\(58\) | −4.50000 | − | 7.79423i | −0.590879 | − | 1.02343i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 1.50000 | − | 2.59808i | 0.193649 | − | 0.335410i | ||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −12.0000 | − | 10.3923i | −1.51186 | − | 1.30931i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | + | 5.19615i | 0.372104 | + | 0.644503i | ||||
\(66\) | 1.50000 | − | 2.59808i | 0.184637 | − | 0.319801i | ||||
\(67\) | −0.500000 | + | 0.866025i | −0.0610847 | + | 0.105802i | −0.894951 | − | 0.446165i | \(-0.852789\pi\) |
0.833866 | + | 0.551967i | \(0.186123\pi\) | |||||||
\(68\) | 4.00000 | + | 6.92820i | 0.485071 | + | 0.840168i | ||||
\(69\) | 21.0000 | 2.52810 | ||||||||
\(70\) | 0.500000 | − | 2.59808i | 0.0597614 | − | 0.310530i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 3.00000 | + | 5.19615i | 0.353553 | + | 0.612372i | ||||
\(73\) | −4.00000 | + | 6.92820i | −0.468165 | + | 0.810885i | −0.999338 | − | 0.0363782i | \(-0.988418\pi\) |
0.531174 | + | 0.847263i | \(0.321751\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 1.50000 | + | 2.59808i | 0.173205 | + | 0.300000i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0.500000 | − | 2.59808i | 0.0569803 | − | 0.296078i | ||||
\(78\) | −18.0000 | −2.03810 | ||||||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | 9.00000 | 0.987878 | 0.493939 | − | 0.869496i | \(-0.335557\pi\) | ||||
0.493939 | + | 0.869496i | \(0.335557\pi\) | |||||||
\(84\) | 6.00000 | + | 5.19615i | 0.654654 | + | 0.566947i | ||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | −0.500000 | − | 0.866025i | −0.0539164 | − | 0.0933859i | ||||
\(87\) | −13.5000 | + | 23.3827i | −1.44735 | + | 2.50689i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −0.500000 | − | 0.866025i | −0.0529999 | − | 0.0917985i | 0.838308 | − | 0.545197i | \(-0.183545\pi\) |
−0.891308 | + | 0.453398i | \(0.850212\pi\) | |||||||
\(90\) | −6.00000 | −0.632456 | ||||||||
\(91\) | −15.0000 | + | 5.19615i | −1.57243 | + | 0.544705i | ||||
\(92\) | −7.00000 | −0.729800 | ||||||||
\(93\) | −9.00000 | − | 15.5885i | −0.933257 | − | 1.61645i | ||||
\(94\) | −4.00000 | + | 6.92820i | −0.412568 | + | 0.714590i | ||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | −1.50000 | − | 2.59808i | −0.153093 | − | 0.265165i | ||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 6.50000 | + | 2.59808i | 0.656599 | + | 0.262445i | ||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −2.50000 | + | 4.33013i | −0.248759 | + | 0.430864i | −0.963182 | − | 0.268851i | \(-0.913356\pi\) |
0.714423 | + | 0.699715i | \(0.246689\pi\) | |||||||
\(102\) | 12.0000 | − | 20.7846i | 1.18818 | − | 2.05798i | ||||
\(103\) | 6.50000 | + | 11.2583i | 0.640464 | + | 1.10932i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | −7.50000 | + | 2.59808i | −0.731925 | + | 0.253546i | ||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 8.50000 | + | 14.7224i | 0.821726 | + | 1.42327i | 0.904396 | + | 0.426694i | \(0.140322\pi\) |
−0.0826699 | + | 0.996577i | \(0.526345\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | −0.500000 | − | 0.866025i | −0.0476731 | − | 0.0825723i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 6.00000 | + | 10.3923i | 0.561951 | + | 0.973329i | ||||
\(115\) | 3.50000 | − | 6.06218i | 0.326377 | − | 0.565301i | ||||
\(116\) | 4.50000 | − | 7.79423i | 0.417815 | − | 0.723676i | ||||
\(117\) | 18.0000 | + | 31.1769i | 1.66410 | + | 2.88231i | ||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 4.00000 | − | 20.7846i | 0.366679 | − | 1.90532i | ||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −2.50000 | + | 4.33013i | −0.226339 | + | 0.392031i | ||||
\(123\) | 4.50000 | − | 7.79423i | 0.405751 | − | 0.702782i | ||||
\(124\) | 3.00000 | + | 5.19615i | 0.269408 | + | 0.466628i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.00000 | − | 15.5885i | 0.267261 | − | 1.38873i | ||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.50000 | + | 2.59808i | −0.132068 | + | 0.228748i | ||||
\(130\) | −3.00000 | + | 5.19615i | −0.263117 | + | 0.455733i | ||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 8.00000 | + | 6.92820i | 0.693688 | + | 0.600751i | ||||
\(134\) | −1.00000 | −0.0863868 | ||||||||
\(135\) | 4.50000 | + | 7.79423i | 0.387298 | + | 0.670820i | ||||
\(136\) | −4.00000 | + | 6.92820i | −0.342997 | + | 0.594089i | ||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 10.5000 | + | 18.1865i | 0.893819 | + | 1.54814i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 2.50000 | − | 0.866025i | 0.211289 | − | 0.0731925i | ||||
\(141\) | 24.0000 | 2.02116 | ||||||||
\(142\) | 2.00000 | + | 3.46410i | 0.167836 | + | 0.290701i | ||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | 4.50000 | + | 7.79423i | 0.373705 | + | 0.647275i | ||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | −3.00000 | − | 20.7846i | −0.247436 | − | 1.71429i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 7.50000 | + | 12.9904i | 0.614424 | + | 1.06421i | 0.990485 | + | 0.137619i | \(0.0439449\pi\) |
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(150\) | −1.50000 | + | 2.59808i | −0.122474 | + | 0.212132i | ||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | −2.00000 | − | 3.46410i | −0.162221 | − | 0.280976i | ||||
\(153\) | −48.0000 | −3.88057 | ||||||||
\(154\) | 2.50000 | − | 0.866025i | 0.201456 | − | 0.0697863i | ||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −9.00000 | − | 15.5885i | −0.720577 | − | 1.24808i | ||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 5.00000 | − | 8.66025i | 0.397779 | − | 0.688973i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 14.0000 | + | 12.1244i | 1.10335 | + | 0.955533i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −4.00000 | − | 6.92820i | −0.313304 | − | 0.542659i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | 4.50000 | + | 7.79423i | 0.349268 | + | 0.604949i | ||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | −1.50000 | + | 7.79423i | −0.115728 | + | 0.601338i | ||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | −4.00000 | − | 6.92820i | −0.306786 | − | 0.531369i | ||||
\(171\) | 12.0000 | − | 20.7846i | 0.917663 | − | 1.58944i | ||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | −5.00000 | − | 8.66025i | −0.380143 | − | 0.658427i | 0.610939 | − | 0.791677i | \(-0.290792\pi\) |
−0.991082 | + | 0.133250i | \(0.957459\pi\) | |||||||
\(174\) | −27.0000 | −2.04686 | ||||||||
\(175\) | −0.500000 | + | 2.59808i | −0.0377964 | + | 0.196396i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −9.00000 | − | 15.5885i | −0.676481 | − | 1.17170i | ||||
\(178\) | 0.500000 | − | 0.866025i | 0.0374766 | − | 0.0649113i | ||||
\(179\) | −4.00000 | + | 6.92820i | −0.298974 | + | 0.517838i | −0.975901 | − | 0.218212i | \(-0.929978\pi\) |
0.676927 | + | 0.736050i | \(0.263311\pi\) | |||||||
\(180\) | −3.00000 | − | 5.19615i | −0.223607 | − | 0.387298i | ||||
\(181\) | 3.00000 | 0.222988 | 0.111494 | − | 0.993765i | \(-0.464436\pi\) | ||||
0.111494 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(182\) | −12.0000 | − | 10.3923i | −0.889499 | − | 0.770329i | ||||
\(183\) | 15.0000 | 1.10883 | ||||||||
\(184\) | −3.50000 | − | 6.06218i | −0.258023 | − | 0.446910i | ||||
\(185\) | 1.00000 | − | 1.73205i | 0.0735215 | − | 0.127343i | ||||
\(186\) | 9.00000 | − | 15.5885i | 0.659912 | − | 1.14300i | ||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | −22.5000 | + | 7.79423i | −1.63663 | + | 0.566947i | ||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 8.00000 | + | 13.8564i | 0.578860 | + | 1.00261i | 0.995610 | + | 0.0935936i | \(0.0298354\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(192\) | 1.50000 | − | 2.59808i | 0.108253 | − | 0.187500i | ||||
\(193\) | −9.00000 | + | 15.5885i | −0.647834 | + | 1.12208i | 0.335805 | + | 0.941932i | \(0.390992\pi\) |
−0.983639 | + | 0.180150i | \(0.942342\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.0000 | 1.28901 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 1.50000 | + | 2.59808i | 0.105802 | + | 0.183254i | ||||
\(202\) | −5.00000 | −0.351799 | ||||||||
\(203\) | −22.5000 | + | 7.79423i | −1.57919 | + | 0.547048i | ||||
\(204\) | 24.0000 | 1.68034 | ||||||||
\(205\) | −1.50000 | − | 2.59808i | −0.104765 | − | 0.181458i | ||||
\(206\) | −6.50000 | + | 11.2583i | −0.452876 | + | 0.784405i | ||||
\(207\) | 21.0000 | − | 36.3731i | 1.45960 | − | 2.52810i | ||||
\(208\) | 3.00000 | + | 5.19615i | 0.208013 | + | 0.360288i | ||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | −6.00000 | − | 5.19615i | −0.414039 | − | 0.358569i | ||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 1.00000 | + | 1.73205i | 0.0686803 | + | 0.118958i | ||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | −8.50000 | + | 14.7224i | −0.581048 | + | 1.00640i | ||||
\(215\) | 0.500000 | + | 0.866025i | 0.0340997 | + | 0.0590624i | ||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 3.00000 | − | 15.5885i | 0.203653 | − | 1.05821i | ||||
\(218\) | −5.00000 | −0.338643 | ||||||||
\(219\) | 12.0000 | + | 20.7846i | 0.810885 | + | 1.40449i | ||||
\(220\) | 0.500000 | − | 0.866025i | 0.0337100 | − | 0.0583874i | ||||
\(221\) | −24.0000 | + | 41.5692i | −1.61441 | + | 2.79625i | ||||
\(222\) | 3.00000 | + | 5.19615i | 0.201347 | + | 0.348743i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | 6.00000 | 0.400000 | ||||||||
\(226\) | 6.00000 | + | 10.3923i | 0.399114 | + | 0.691286i | ||||
\(227\) | 10.0000 | − | 17.3205i | 0.663723 | − | 1.14960i | −0.315906 | − | 0.948790i | \(-0.602309\pi\) |
0.979630 | − | 0.200812i | \(-0.0643581\pi\) | |||||||
\(228\) | −6.00000 | + | 10.3923i | −0.397360 | + | 0.688247i | ||||
\(229\) | 3.00000 | + | 5.19615i | 0.198246 | + | 0.343371i | 0.947960 | − | 0.318390i | \(-0.103142\pi\) |
−0.749714 | + | 0.661762i | \(0.769809\pi\) | |||||||
\(230\) | 7.00000 | 0.461566 | ||||||||
\(231\) | −6.00000 | − | 5.19615i | −0.394771 | − | 0.341882i | ||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | −13.0000 | − | 22.5167i | −0.851658 | − | 1.47512i | −0.879711 | − | 0.475509i | \(-0.842264\pi\) |
0.0280525 | − | 0.999606i | \(-0.491069\pi\) | |||||||
\(234\) | −18.0000 | + | 31.1769i | −1.17670 | + | 2.03810i | ||||
\(235\) | 4.00000 | − | 6.92820i | 0.260931 | − | 0.451946i | ||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | −30.0000 | −1.94871 | ||||||||
\(238\) | 20.0000 | − | 6.92820i | 1.29641 | − | 0.449089i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 1.50000 | + | 2.59808i | 0.0968246 | + | 0.167705i | ||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | −6.50000 | − | 2.59808i | −0.415270 | − | 0.165985i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | −12.0000 | − | 20.7846i | −0.763542 | − | 1.32249i | ||||
\(248\) | −3.00000 | + | 5.19615i | −0.190500 | + | 0.329956i | ||||
\(249\) | 13.5000 | − | 23.3827i | 0.855528 | − | 1.48182i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 2.00000 | 0.126239 | 0.0631194 | − | 0.998006i | \(-0.479895\pi\) | ||||
0.0631194 | + | 0.998006i | \(0.479895\pi\) | |||||||
\(252\) | 15.0000 | − | 5.19615i | 0.944911 | − | 0.327327i | ||||
\(253\) | 7.00000 | 0.440086 | ||||||||
\(254\) | −10.0000 | − | 17.3205i | −0.627456 | − | 1.08679i | ||||
\(255\) | −12.0000 | + | 20.7846i | −0.751469 | + | 1.30158i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | −3.00000 | −0.186772 | ||||||||
\(259\) | 4.00000 | + | 3.46410i | 0.248548 | + | 0.215249i | ||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | 27.0000 | + | 46.7654i | 1.67126 | + | 2.89470i | ||||
\(262\) | −9.00000 | + | 15.5885i | −0.556022 | + | 0.963058i | ||||
\(263\) | −6.50000 | + | 11.2583i | −0.400807 | + | 0.694218i | −0.993824 | − | 0.110972i | \(-0.964604\pi\) |
0.593016 | + | 0.805190i | \(0.297937\pi\) | |||||||
\(264\) | 1.50000 | + | 2.59808i | 0.0923186 | + | 0.159901i | ||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | −2.00000 | + | 10.3923i | −0.122628 | + | 0.637193i | ||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | −0.500000 | − | 0.866025i | −0.0305424 | − | 0.0529009i | ||||
\(269\) | −3.50000 | + | 6.06218i | −0.213399 | + | 0.369618i | −0.952776 | − | 0.303674i | \(-0.901787\pi\) |
0.739377 | + | 0.673291i | \(0.235120\pi\) | |||||||
\(270\) | −4.50000 | + | 7.79423i | −0.273861 | + | 0.474342i | ||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | −9.00000 | + | 46.7654i | −0.544705 | + | 2.83037i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | −10.5000 | + | 18.1865i | −0.632026 | + | 1.09470i | ||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | −1.00000 | − | 1.73205i | −0.0599760 | − | 0.103882i | ||||
\(279\) | −36.0000 | −2.15526 | ||||||||
\(280\) | 2.00000 | + | 1.73205i | 0.119523 | + | 0.103510i | ||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 12.0000 | + | 20.7846i | 0.714590 | + | 1.23771i | ||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | −6.00000 | − | 10.3923i | −0.355409 | − | 0.615587i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 7.50000 | − | 2.59808i | 0.442711 | − | 0.153360i | ||||
\(288\) | −6.00000 | −0.353553 | ||||||||
\(289\) | −23.5000 | − | 40.7032i | −1.38235 | − | 2.39431i | ||||
\(290\) | −4.50000 | + | 7.79423i | −0.264249 | + | 0.457693i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00000 | − | 6.92820i | −0.234082 | − | 0.405442i | ||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 16.5000 | − | 12.9904i | 0.962300 | − | 0.757614i | ||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | −7.50000 | + | 12.9904i | −0.434463 | + | 0.752513i | ||||
\(299\) | −21.0000 | − | 36.3731i | −1.21446 | − | 2.10351i | ||||
\(300\) | −3.00000 | −0.173205 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | 16.0000 | 0.920697 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 2.50000 | − | 4.33013i | 0.143150 | − | 0.247942i | ||||
\(306\) | −24.0000 | − | 41.5692i | −1.37199 | − | 2.37635i | ||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 2.00000 | + | 1.73205i | 0.113961 | + | 0.0986928i | ||||
\(309\) | 39.0000 | 2.21863 | ||||||||
\(310\) | −3.00000 | − | 5.19615i | −0.170389 | − | 0.295122i | ||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | 9.00000 | − | 15.5885i | 0.509525 | − | 0.882523i | ||||
\(313\) | −8.00000 | − | 13.8564i | −0.452187 | − | 0.783210i | 0.546335 | − | 0.837567i | \(-0.316023\pi\) |
−0.998522 | + | 0.0543564i | \(0.982689\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | −3.00000 | + | 15.5885i | −0.169031 | + | 0.878310i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −4.00000 | − | 6.92820i | −0.224662 | − | 0.389127i | 0.731556 | − | 0.681782i | \(-0.238795\pi\) |
−0.956218 | + | 0.292655i | \(0.905461\pi\) | |||||||
\(318\) | 3.00000 | − | 5.19615i | 0.168232 | − | 0.291386i | ||||
\(319\) | −4.50000 | + | 7.79423i | −0.251952 | + | 0.436393i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 51.0000 | 2.84654 | ||||||||
\(322\) | −3.50000 | + | 18.1865i | −0.195047 | + | 1.01350i | ||||
\(323\) | 32.0000 | 1.78053 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | 4.00000 | − | 6.92820i | 0.221540 | − | 0.383718i | ||||
\(327\) | 7.50000 | + | 12.9904i | 0.414751 | + | 0.718370i | ||||
\(328\) | −3.00000 | −0.165647 | ||||||||
\(329\) | 16.0000 | + | 13.8564i | 0.882109 | + | 0.763928i | ||||
\(330\) | −3.00000 | −0.165145 | ||||||||
\(331\) | −16.0000 | − | 27.7128i | −0.879440 | − | 1.52323i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
−0.0274825 | − | 0.999622i | \(-0.508749\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | 6.00000 | − | 10.3923i | 0.328798 | − | 0.569495i | ||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | 1.00000 | 0.0546358 | ||||||||
\(336\) | −7.50000 | + | 2.59808i | −0.409159 | + | 0.141737i | ||||
\(337\) | −20.0000 | −1.08947 | −0.544735 | − | 0.838608i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(338\) | 11.5000 | + | 19.9186i | 0.625518 | + | 1.08343i | ||||
\(339\) | 18.0000 | − | 31.1769i | 0.977626 | − | 1.69330i | ||||
\(340\) | 4.00000 | − | 6.92820i | 0.216930 | − | 0.375735i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 24.0000 | 1.29777 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −10.5000 | − | 18.1865i | −0.565301 | − | 0.979130i | ||||
\(346\) | 5.00000 | − | 8.66025i | 0.268802 | − | 0.465578i | ||||
\(347\) | 6.50000 | − | 11.2583i | 0.348938 | − | 0.604379i | −0.637123 | − | 0.770762i | \(-0.719876\pi\) |
0.986061 | + | 0.166383i | \(0.0532089\pi\) | |||||||
\(348\) | −13.5000 | − | 23.3827i | −0.723676 | − | 1.25344i | ||||
\(349\) | −13.0000 | −0.695874 | −0.347937 | − | 0.937518i | \(-0.613118\pi\) | ||||
−0.347937 | + | 0.937518i | \(0.613118\pi\) | |||||||
\(350\) | −2.50000 | + | 0.866025i | −0.133631 | + | 0.0462910i | ||||
\(351\) | 54.0000 | 2.88231 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 4.00000 | − | 6.92820i | 0.212899 | − | 0.368751i | −0.739722 | − | 0.672913i | \(-0.765043\pi\) |
0.952620 | + | 0.304162i | \(0.0983763\pi\) | |||||||
\(354\) | 9.00000 | − | 15.5885i | 0.478345 | − | 0.828517i | ||||
\(355\) | −2.00000 | − | 3.46410i | −0.106149 | − | 0.183855i | ||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | −48.0000 | − | 41.5692i | −2.54043 | − | 2.20008i | ||||
\(358\) | −8.00000 | −0.422813 | ||||||||
\(359\) | 8.00000 | + | 13.8564i | 0.422224 | + | 0.731313i | 0.996157 | − | 0.0875892i | \(-0.0279163\pi\) |
−0.573933 | + | 0.818902i | \(0.694583\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 1.50000 | + | 2.59808i | 0.0788382 | + | 0.136552i | ||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | 3.00000 | − | 15.5885i | 0.157243 | − | 0.817057i | ||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 7.50000 | + | 12.9904i | 0.392031 | + | 0.679018i | ||||
\(367\) | −5.50000 | + | 9.52628i | −0.287098 | + | 0.497268i | −0.973116 | − | 0.230317i | \(-0.926024\pi\) |
0.686018 | + | 0.727585i | \(0.259357\pi\) | |||||||
\(368\) | 3.50000 | − | 6.06218i | 0.182450 | − | 0.316013i | ||||
\(369\) | −9.00000 | − | 15.5885i | −0.468521 | − | 0.811503i | ||||
\(370\) | 2.00000 | 0.103975 | ||||||||
\(371\) | 1.00000 | − | 5.19615i | 0.0519174 | − | 0.269771i | ||||
\(372\) | 18.0000 | 0.933257 | ||||||||
\(373\) | 16.0000 | + | 27.7128i | 0.828449 | + | 1.43492i | 0.899255 | + | 0.437425i | \(0.144109\pi\) |
−0.0708063 | + | 0.997490i | \(0.522557\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 1.50000 | − | 2.59808i | 0.0774597 | − | 0.134164i | ||||
\(376\) | −4.00000 | − | 6.92820i | −0.206284 | − | 0.357295i | ||||
\(377\) | 54.0000 | 2.78114 | ||||||||
\(378\) | −18.0000 | − | 15.5885i | −0.925820 | − | 0.801784i | ||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 2.00000 | + | 3.46410i | 0.102598 | + | 0.177705i | ||||
\(381\) | −30.0000 | + | 51.9615i | −1.53695 | + | 2.66207i | ||||
\(382\) | −8.00000 | + | 13.8564i | −0.409316 | + | 0.708955i | ||||
\(383\) | 3.50000 | + | 6.06218i | 0.178842 | + | 0.309763i | 0.941484 | − | 0.337058i | \(-0.109432\pi\) |
−0.762642 | + | 0.646820i | \(0.776098\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | −2.50000 | + | 0.866025i | −0.127412 | + | 0.0441367i | ||||
\(386\) | −18.0000 | −0.916176 | ||||||||
\(387\) | 3.00000 | + | 5.19615i | 0.152499 | + | 0.264135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 9.00000 | + | 15.5885i | 0.455733 | + | 0.789352i | ||||
\(391\) | 56.0000 | 2.83204 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 54.0000 | 2.72394 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | −5.00000 | + | 8.66025i | −0.251577 | + | 0.435745i | ||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | −10.0000 | − | 17.3205i | −0.501886 | − | 0.869291i | −0.999998 | − | 0.00217869i | \(-0.999307\pi\) |
0.498112 | − | 0.867113i | \(-0.334027\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0000 | − | 10.3923i | 1.50188 | − | 0.520266i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 2.50000 | + | 4.33013i | 0.124844 | + | 0.216236i | 0.921672 | − | 0.387970i | \(-0.126824\pi\) |
−0.796828 | + | 0.604206i | \(0.793490\pi\) | |||||||
\(402\) | −1.50000 | + | 2.59808i | −0.0748132 | + | 0.129580i | ||||
\(403\) | −18.0000 | + | 31.1769i | −0.896644 | + | 1.55303i | ||||
\(404\) | −2.50000 | − | 4.33013i | −0.124380 | − | 0.215432i | ||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | −18.0000 | − | 15.5885i | −0.893325 | − | 0.773642i | ||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 12.0000 | + | 20.7846i | 0.594089 | + | 1.02899i | ||||
\(409\) | −6.50000 | + | 11.2583i | −0.321404 | + | 0.556689i | −0.980778 | − | 0.195127i | \(-0.937488\pi\) |
0.659374 | + | 0.751815i | \(0.270822\pi\) | |||||||
\(410\) | 1.50000 | − | 2.59808i | 0.0740797 | − | 0.128310i | ||||
\(411\) | 9.00000 | + | 15.5885i | 0.443937 | + | 0.768922i | ||||
\(412\) | −13.0000 | −0.640464 | ||||||||
\(413\) | 3.00000 | − | 15.5885i | 0.147620 | − | 0.767058i | ||||
\(414\) | 42.0000 | 2.06419 | ||||||||
\(415\) | −4.50000 | − | 7.79423i | −0.220896 | − | 0.382604i | ||||
\(416\) | −3.00000 | + | 5.19615i | −0.147087 | + | 0.254762i | ||||
\(417\) | −3.00000 | + | 5.19615i | −0.146911 | + | 0.254457i | ||||
\(418\) | 2.00000 | + | 3.46410i | 0.0978232 | + | 0.169435i | ||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 1.50000 | − | 7.79423i | 0.0731925 | − | 0.380319i | ||||
\(421\) | 25.0000 | 1.21843 | 0.609213 | − | 0.793007i | \(-0.291486\pi\) | ||||
0.609213 | + | 0.793007i | \(0.291486\pi\) | |||||||
\(422\) | −7.00000 | − | 12.1244i | −0.340755 | − | 0.590204i | ||||
\(423\) | 24.0000 | − | 41.5692i | 1.16692 | − | 2.02116i | ||||
\(424\) | −1.00000 | + | 1.73205i | −0.0485643 | + | 0.0841158i | ||||
\(425\) | 4.00000 | + | 6.92820i | 0.194029 | + | 0.336067i | ||||
\(426\) | 12.0000 | 0.581402 | ||||||||
\(427\) | 10.0000 | + | 8.66025i | 0.483934 | + | 0.419099i | ||||
\(428\) | −17.0000 | −0.821726 | ||||||||
\(429\) | 9.00000 | + | 15.5885i | 0.434524 | + | 0.752618i | ||||
\(430\) | −0.500000 | + | 0.866025i | −0.0241121 | + | 0.0417635i | ||||
\(431\) | 2.00000 | − | 3.46410i | 0.0963366 | − | 0.166860i | −0.813829 | − | 0.581104i | \(-0.802621\pi\) |
0.910166 | + | 0.414244i | \(0.135954\pi\) | |||||||
\(432\) | 4.50000 | + | 7.79423i | 0.216506 | + | 0.375000i | ||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 15.0000 | − | 5.19615i | 0.720023 | − | 0.249423i | ||||
\(435\) | 27.0000 | 1.29455 | ||||||||
\(436\) | −2.50000 | − | 4.33013i | −0.119728 | − | 0.207375i | ||||
\(437\) | −14.0000 | + | 24.2487i | −0.669711 | + | 1.15997i | ||||
\(438\) | −12.0000 | + | 20.7846i | −0.573382 | + | 0.993127i | ||||
\(439\) | −15.0000 | − | 25.9808i | −0.715911 | − | 1.23999i | −0.962607 | − | 0.270901i | \(-0.912678\pi\) |
0.246696 | − | 0.969093i | \(-0.420655\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −39.0000 | − | 15.5885i | −1.85714 | − | 0.742307i | ||||
\(442\) | −48.0000 | −2.28313 | ||||||||
\(443\) | −6.50000 | − | 11.2583i | −0.308824 | − | 0.534899i | 0.669281 | − | 0.743009i | \(-0.266602\pi\) |
−0.978105 | + | 0.208110i | \(0.933269\pi\) | |||||||
\(444\) | −3.00000 | + | 5.19615i | −0.142374 | + | 0.246598i | ||||
\(445\) | −0.500000 | + | 0.866025i | −0.0237023 | + | 0.0410535i | ||||
\(446\) | −8.00000 | − | 13.8564i | −0.378811 | − | 0.656120i | ||||
\(447\) | 45.0000 | 2.12843 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | −25.0000 | −1.17982 | −0.589911 | − | 0.807468i | \(-0.700837\pi\) | ||||
−0.589911 | + | 0.807468i | \(0.700837\pi\) | |||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | 1.50000 | − | 2.59808i | 0.0706322 | − | 0.122339i | ||||
\(452\) | −6.00000 | + | 10.3923i | −0.282216 | + | 0.488813i | ||||
\(453\) | −24.0000 | − | 41.5692i | −1.12762 | − | 1.95309i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 12.0000 | + | 10.3923i | 0.562569 | + | 0.487199i | ||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | 4.00000 | + | 6.92820i | 0.187112 | + | 0.324088i | 0.944286 | − | 0.329125i | \(-0.106754\pi\) |
−0.757174 | + | 0.653213i | \(0.773421\pi\) | |||||||
\(458\) | −3.00000 | + | 5.19615i | −0.140181 | + | 0.242800i | ||||
\(459\) | −36.0000 | + | 62.3538i | −1.68034 | + | 2.91043i | ||||
\(460\) | 3.50000 | + | 6.06218i | 0.163188 | + | 0.282650i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 1.50000 | − | 7.79423i | 0.0697863 | − | 0.362620i | ||||
\(463\) | 11.0000 | 0.511213 | 0.255607 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255607 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(464\) | 4.50000 | + | 7.79423i | 0.208907 | + | 0.361838i | ||||
\(465\) | −9.00000 | + | 15.5885i | −0.417365 | + | 0.722897i | ||||
\(466\) | 13.0000 | − | 22.5167i | 0.602213 | − | 1.04306i | ||||
\(467\) | 13.5000 | + | 23.3827i | 0.624705 | + | 1.08202i | 0.988598 | + | 0.150581i | \(0.0481143\pi\) |
−0.363892 | + | 0.931441i | \(0.618552\pi\) | |||||||
\(468\) | −36.0000 | −1.66410 | ||||||||
\(469\) | −0.500000 | + | 2.59808i | −0.0230879 | + | 0.119968i | ||||
\(470\) | 8.00000 | 0.369012 | ||||||||
\(471\) | 6.00000 | + | 10.3923i | 0.276465 | + | 0.478852i | ||||
\(472\) | −3.00000 | + | 5.19615i | −0.138086 | + | 0.239172i | ||||
\(473\) | −0.500000 | + | 0.866025i | −0.0229900 | + | 0.0398199i | ||||
\(474\) | −15.0000 | − | 25.9808i | −0.688973 | − | 1.19334i | ||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 16.0000 | + | 13.8564i | 0.733359 | + | 0.635107i | ||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | 21.0000 | − | 36.3731i | 0.959514 | − | 1.66193i | 0.235833 | − | 0.971794i | \(-0.424218\pi\) |
0.723681 | − | 0.690134i | \(-0.242449\pi\) | |||||||
\(480\) | −1.50000 | + | 2.59808i | −0.0684653 | + | 0.118585i | ||||
\(481\) | −6.00000 | − | 10.3923i | −0.273576 | − | 0.473848i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 52.5000 | − | 18.1865i | 2.38883 | − | 0.827516i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | − | 3.46410i | 0.0906287 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(488\) | −2.50000 | − | 4.33013i | −0.113170 | − | 0.196016i | ||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | −1.00000 | − | 6.92820i | −0.0451754 | − | 0.312984i | ||||
\(491\) | −22.0000 | −0.992846 | −0.496423 | − | 0.868081i | \(-0.665354\pi\) | ||||
−0.496423 | + | 0.868081i | \(0.665354\pi\) | |||||||
\(492\) | 4.50000 | + | 7.79423i | 0.202876 | + | 0.351391i | ||||
\(493\) | −36.0000 | + | 62.3538i | −1.62136 | + | 2.80828i | ||||
\(494\) | 12.0000 | − | 20.7846i | 0.539906 | − | 0.935144i | ||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 10.0000 | − | 3.46410i | 0.448561 | − | 0.155386i | ||||
\(498\) | 27.0000 | 1.20990 | ||||||||
\(499\) | −2.00000 | − | 3.46410i | −0.0895323 | − | 0.155074i | 0.817781 | − | 0.575529i | \(-0.195204\pi\) |
−0.907314 | + | 0.420455i | \(0.861871\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 4.50000 | − | 7.79423i | 0.201045 | − | 0.348220i | ||||
\(502\) | 1.00000 | + | 1.73205i | 0.0446322 | + | 0.0773052i | ||||
\(503\) | 19.0000 | 0.847168 | 0.423584 | − | 0.905857i | \(-0.360772\pi\) | ||||
0.423584 | + | 0.905857i | \(0.360772\pi\) | |||||||
\(504\) | 12.0000 | + | 10.3923i | 0.534522 | + | 0.462910i | ||||
\(505\) | 5.00000 | 0.222497 | ||||||||
\(506\) | 3.50000 | + | 6.06218i | 0.155594 | + | 0.269497i | ||||
\(507\) | 34.5000 | − | 59.7558i | 1.53220 | − | 2.65385i | ||||
\(508\) | 10.0000 | − | 17.3205i | 0.443678 | − | 0.768473i | ||||
\(509\) | 11.5000 | + | 19.9186i | 0.509729 | + | 0.882876i | 0.999936 | + | 0.0112702i | \(0.00358750\pi\) |
−0.490208 | + | 0.871606i | \(0.663079\pi\) | |||||||
\(510\) | −24.0000 | −1.06274 | ||||||||
\(511\) | −4.00000 | + | 20.7846i | −0.176950 | + | 0.919457i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −18.0000 | − | 31.1769i | −0.794719 | − | 1.37649i | ||||
\(514\) | −3.00000 | + | 5.19615i | −0.132324 | + | 0.229192i | ||||
\(515\) | 6.50000 | − | 11.2583i | 0.286424 | − | 0.496101i | ||||
\(516\) | −1.50000 | − | 2.59808i | −0.0660338 | − | 0.114374i | ||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | −1.00000 | + | 5.19615i | −0.0439375 | + | 0.228306i | ||||
\(519\) | −30.0000 | −1.31685 | ||||||||
\(520\) | −3.00000 | − | 5.19615i | −0.131559 | − | 0.227866i | ||||
\(521\) | −7.00000 | + | 12.1244i | −0.306676 | + | 0.531178i | −0.977633 | − | 0.210318i | \(-0.932550\pi\) |
0.670957 | + | 0.741496i | \(0.265883\pi\) | |||||||
\(522\) | −27.0000 | + | 46.7654i | −1.18176 | + | 2.04686i | ||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 6.00000 | + | 5.19615i | 0.261861 | + | 0.226779i | ||||
\(526\) | −13.0000 | −0.566827 | ||||||||
\(527\) | −24.0000 | − | 41.5692i | −1.04546 | − | 1.81078i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | −1.00000 | − | 1.73205i | −0.0434372 | − | 0.0752355i | ||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | −10.0000 | + | 3.46410i | −0.433555 | + | 0.150188i | ||||
\(533\) | −18.0000 | −0.779667 | ||||||||
\(534\) | −1.50000 | − | 2.59808i | −0.0649113 | − | 0.112430i | ||||
\(535\) | 8.50000 | − | 14.7224i | 0.367487 | − | 0.636506i | ||||
\(536\) | 0.500000 | − | 0.866025i | 0.0215967 | − | 0.0374066i | ||||
\(537\) | 12.0000 | + | 20.7846i | 0.517838 | + | 0.896922i | ||||
\(538\) | −7.00000 | −0.301791 | ||||||||
\(539\) | −1.00000 | − | 6.92820i | −0.0430730 | − | 0.298419i | ||||
\(540\) | −9.00000 | −0.387298 | ||||||||
\(541\) | 7.50000 | + | 12.9904i | 0.322450 | + | 0.558500i | 0.980993 | − | 0.194043i | \(-0.0621602\pi\) |
−0.658543 | + | 0.752543i | \(0.728827\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.50000 | − | 7.79423i | 0.193113 | − | 0.334482i | ||||
\(544\) | −4.00000 | − | 6.92820i | −0.171499 | − | 0.297044i | ||||
\(545\) | 5.00000 | 0.214176 | ||||||||
\(546\) | −45.0000 | + | 15.5885i | −1.92582 | + | 0.667124i | ||||
\(547\) | −45.0000 | −1.92406 | −0.962031 | − | 0.272942i | \(-0.912003\pi\) | ||||
−0.962031 | + | 0.272942i | \(0.912003\pi\) | |||||||
\(548\) | −3.00000 | − | 5.19615i | −0.128154 | − | 0.221969i | ||||
\(549\) | 15.0000 | − | 25.9808i | 0.640184 | − | 1.10883i | ||||
\(550\) | −0.500000 | + | 0.866025i | −0.0213201 | + | 0.0369274i | ||||
\(551\) | −18.0000 | − | 31.1769i | −0.766826 | − | 1.32818i | ||||
\(552\) | −21.0000 | −0.893819 | ||||||||
\(553\) | −20.0000 | − | 17.3205i | −0.850487 | − | 0.736543i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | −3.00000 | − | 5.19615i | −0.127343 | − | 0.220564i | ||||
\(556\) | 1.00000 | − | 1.73205i | 0.0424094 | − | 0.0734553i | ||||
\(557\) | 6.00000 | − | 10.3923i | 0.254228 | − | 0.440336i | −0.710457 | − | 0.703740i | \(-0.751512\pi\) |
0.964686 | + | 0.263404i | \(0.0848453\pi\) | |||||||
\(558\) | −18.0000 | − | 31.1769i | −0.762001 | − | 1.31982i | ||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | −0.500000 | + | 2.59808i | −0.0211289 | + | 0.109789i | ||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 15.0000 | + | 25.9808i | 0.632737 | + | 1.09593i | ||||
\(563\) | −20.5000 | + | 35.5070i | −0.863972 | + | 1.49644i | 0.00409232 | + | 0.999992i | \(0.498697\pi\) |
−0.868064 | + | 0.496452i | \(0.834636\pi\) | |||||||
\(564\) | −12.0000 | + | 20.7846i | −0.505291 | + | 0.875190i | ||||
\(565\) | −6.00000 | − | 10.3923i | −0.252422 | − | 0.437208i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −4.50000 | + | 23.3827i | −0.188982 | + | 0.981981i | ||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 6.00000 | − | 10.3923i | 0.251312 | − | 0.435286i | ||||
\(571\) | −5.00000 | + | 8.66025i | −0.209243 | + | 0.362420i | −0.951476 | − | 0.307722i | \(-0.900433\pi\) |
0.742233 | + | 0.670142i | \(0.233767\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | 48.0000 | 2.00523 | ||||||||
\(574\) | 6.00000 | + | 5.19615i | 0.250435 | + | 0.216883i | ||||
\(575\) | −7.00000 | −0.291920 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | 1.00000 | − | 1.73205i | 0.0416305 | − | 0.0721062i | −0.844459 | − | 0.535620i | \(-0.820078\pi\) |
0.886090 | + | 0.463513i | \(0.153411\pi\) | |||||||
\(578\) | 23.5000 | − | 40.7032i | 0.977471 | − | 1.69303i | ||||
\(579\) | 27.0000 | + | 46.7654i | 1.12208 | + | 1.94350i | ||||
\(580\) | −9.00000 | −0.373705 | ||||||||
\(581\) | 22.5000 | − | 7.79423i | 0.933457 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.00000 | − | 1.73205i | −0.0414158 | − | 0.0717342i | ||||
\(584\) | 4.00000 | − | 6.92820i | 0.165521 | − | 0.286691i | ||||
\(585\) | 18.0000 | − | 31.1769i | 0.744208 | − | 1.28901i | ||||
\(586\) | −13.0000 | − | 22.5167i | −0.537025 | − | 0.930155i | ||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 19.5000 | + | 7.79423i | 0.804166 | + | 0.321429i | ||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | −3.00000 | − | 5.19615i | −0.123508 | − | 0.213922i | ||||
\(591\) | −27.0000 | + | 46.7654i | −1.11063 | + | 1.92367i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | −9.00000 | −0.369274 | ||||||||
\(595\) | −20.0000 | + | 6.92820i | −0.819920 | + | 0.284029i | ||||
\(596\) | −15.0000 | −0.614424 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.0000 | − | 36.3731i | 0.858754 | − | 1.48741i | ||||
\(599\) | 17.0000 | − | 29.4449i | 0.694601 | − | 1.20308i | −0.275714 | − | 0.961240i | \(-0.588914\pi\) |
0.970315 | − | 0.241845i | \(-0.0777525\pi\) | |||||||
\(600\) | −1.50000 | − | 2.59808i | −0.0612372 | − | 0.106066i | ||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | −2.00000 | − | 1.73205i | −0.0815139 | − | 0.0705931i | ||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | 8.00000 | + | 13.8564i | 0.325515 | + | 0.563809i | ||||
\(605\) | −0.500000 | + | 0.866025i | −0.0203279 | + | 0.0352089i | ||||
\(606\) | −7.50000 | + | 12.9904i | −0.304667 | + | 0.527698i | ||||
\(607\) | 5.50000 | + | 9.52628i | 0.223238 | + | 0.386660i | 0.955789 | − | 0.294052i | \(-0.0950039\pi\) |
−0.732551 | + | 0.680712i | \(0.761671\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | −13.5000 | + | 70.1481i | −0.547048 | + | 2.84254i | ||||
\(610\) | 5.00000 | 0.202444 | ||||||||
\(611\) | −24.0000 | − | 41.5692i | −0.970936 | − | 1.68171i | ||||
\(612\) | 24.0000 | − | 41.5692i | 0.970143 | − | 1.68034i | ||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 3.50000 | + | 6.06218i | 0.141249 | + | 0.244650i | ||||
\(615\) | −9.00000 | −0.362915 | ||||||||
\(616\) | −0.500000 | + | 2.59808i | −0.0201456 | + | 0.104679i | ||||
\(617\) | 28.0000 | 1.12724 | 0.563619 | − | 0.826035i | \(-0.309409\pi\) | ||||
0.563619 | + | 0.826035i | \(0.309409\pi\) | |||||||
\(618\) | 19.5000 | + | 33.7750i | 0.784405 | + | 1.35863i | ||||
\(619\) | −5.00000 | + | 8.66025i | −0.200967 | + | 0.348085i | −0.948840 | − | 0.315757i | \(-0.897742\pi\) |
0.747873 | + | 0.663842i | \(0.231075\pi\) | |||||||
\(620\) | 3.00000 | − | 5.19615i | 0.120483 | − | 0.208683i | ||||
\(621\) | −31.5000 | − | 54.5596i | −1.26405 | − | 2.18940i | ||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | −2.00000 | − | 1.73205i | −0.0801283 | − | 0.0693932i | ||||
\(624\) | 18.0000 | 0.720577 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 8.00000 | − | 13.8564i | 0.319744 | − | 0.553813i | ||||
\(627\) | 6.00000 | − | 10.3923i | 0.239617 | − | 0.415029i | ||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | −15.0000 | + | 5.19615i | −0.597614 | + | 0.207020i | ||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 5.00000 | + | 8.66025i | 0.198889 | + | 0.344486i | ||||
\(633\) | −21.0000 | + | 36.3731i | −0.834675 | + | 1.44570i | ||||
\(634\) | 4.00000 | − | 6.92820i | 0.158860 | − | 0.275154i | ||||
\(635\) | 10.0000 | + | 17.3205i | 0.396838 | + | 0.687343i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −33.0000 | + | 25.9808i | −1.30751 | + | 1.02940i | ||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 25.5000 | + | 44.1673i | 1.00640 | + | 1.74314i | ||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | −17.5000 | + | 6.06218i | −0.689597 | + | 0.238883i | ||||
\(645\) | 3.00000 | 0.118125 | ||||||||
\(646\) | 16.0000 | + | 27.7128i | 0.629512 | + | 1.09035i | ||||
\(647\) | −19.5000 | + | 33.7750i | −0.766624 | + | 1.32783i | 0.172760 | + | 0.984964i | \(0.444732\pi\) |
−0.939384 | + | 0.342868i | \(0.888602\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | −3.00000 | − | 5.19615i | −0.117760 | − | 0.203967i | ||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | −36.0000 | − | 31.1769i | −1.41095 | − | 1.22192i | ||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | −7.50000 | + | 12.9904i | −0.293273 | + | 0.507964i | ||||
\(655\) | 9.00000 | − | 15.5885i | 0.351659 | − | 0.609091i | ||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 48.0000 | 1.87266 | ||||||||
\(658\) | −4.00000 | + | 20.7846i | −0.155936 | + | 0.810268i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | −1.50000 | − | 2.59808i | −0.0583874 | − | 0.101130i | ||||
\(661\) | −12.5000 | + | 21.6506i | −0.486194 | + | 0.842112i | −0.999874 | − | 0.0158695i | \(-0.994948\pi\) |
0.513680 | + | 0.857982i | \(0.328282\pi\) | |||||||
\(662\) | 16.0000 | − | 27.7128i | 0.621858 | − | 1.07709i | ||||
\(663\) | 72.0000 | + | 124.708i | 2.79625 | + | 4.84324i | ||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 2.00000 | − | 10.3923i | 0.0775567 | − | 0.402996i | ||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | −31.5000 | − | 54.5596i | −1.21968 | − | 2.11256i | ||||
\(668\) | −1.50000 | + | 2.59808i | −0.0580367 | + | 0.100523i | ||||
\(669\) | −24.0000 | + | 41.5692i | −0.927894 | + | 1.60716i | ||||
\(670\) | 0.500000 | + | 0.866025i | 0.0193167 | + | 0.0334575i | ||||
\(671\) | 5.00000 | 0.193023 | ||||||||
\(672\) | −6.00000 | − | 5.19615i | −0.231455 | − | 0.200446i | ||||
\(673\) | 26.0000 | 1.00223 | 0.501113 | − | 0.865382i | \(-0.332924\pi\) | ||||
0.501113 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(674\) | −10.0000 | − | 17.3205i | −0.385186 | − | 0.667161i | ||||
\(675\) | 4.50000 | − | 7.79423i | 0.173205 | − | 0.300000i | ||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | 16.0000 | + | 27.7128i | 0.614930 | + | 1.06509i | 0.990397 | + | 0.138254i | \(0.0441491\pi\) |
−0.375467 | + | 0.926836i | \(0.622518\pi\) | |||||||
\(678\) | 36.0000 | 1.38257 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | −30.0000 | − | 51.9615i | −1.14960 | − | 1.99117i | ||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | 1.50000 | − | 2.59808i | 0.0573959 | − | 0.0994126i | −0.835900 | − | 0.548882i | \(-0.815054\pi\) |
0.893296 | + | 0.449469i | \(0.148387\pi\) | |||||||
\(684\) | 12.0000 | + | 20.7846i | 0.458831 | + | 0.794719i | ||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 18.5000 | + | 0.866025i | 0.706333 | + | 0.0330650i | ||||
\(687\) | 18.0000 | 0.686743 | ||||||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 10.5000 | − | 18.1865i | 0.399728 | − | 0.692349i | ||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 10.0000 | 0.380143 | ||||||||
\(693\) | −15.0000 | + | 5.19615i | −0.569803 | + | 0.197386i | ||||
\(694\) | 13.0000 | 0.493473 | ||||||||
\(695\) | 1.00000 | + | 1.73205i | 0.0379322 | + | 0.0657004i | ||||
\(696\) | 13.5000 | − | 23.3827i | 0.511716 | − | 0.886318i | ||||
\(697\) | 12.0000 | − | 20.7846i | 0.454532 | − | 0.787273i | ||||
\(698\) | −6.50000 | − | 11.2583i | −0.246029 | − | 0.426134i | ||||
\(699\) | −78.0000 | −2.95023 | ||||||||
\(700\) | −2.00000 | − | 1.73205i | −0.0755929 | − | 0.0654654i | ||||
\(701\) | −21.0000 | −0.793159 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(702\) | 27.0000 | + | 46.7654i | 1.01905 | + | 1.76505i | ||||
\(703\) | −4.00000 | + | 6.92820i | −0.150863 | + | 0.261302i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −12.0000 | − | 20.7846i | −0.451946 | − | 0.782794i | ||||
\(706\) | 8.00000 | 0.301084 | ||||||||
\(707\) | −2.50000 | + | 12.9904i | −0.0940222 | + | 0.488554i | ||||
\(708\) | 18.0000 | 0.676481 | ||||||||
\(709\) | −0.500000 | − | 0.866025i | −0.0187779 | − | 0.0325243i | 0.856484 | − | 0.516174i | \(-0.172644\pi\) |
−0.875262 | + | 0.483650i | \(0.839311\pi\) | |||||||
\(710\) | 2.00000 | − | 3.46410i | 0.0750587 | − | 0.130005i | ||||
\(711\) | −30.0000 | + | 51.9615i | −1.12509 | + | 1.94871i | ||||
\(712\) | 0.500000 | + | 0.866025i | 0.0187383 | + | 0.0324557i | ||||
\(713\) | 42.0000 | 1.57291 | ||||||||
\(714\) | 12.0000 | − | 62.3538i | 0.449089 | − | 2.33353i | ||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | −4.00000 | − | 6.92820i | −0.149487 | − | 0.258919i | ||||
\(717\) | −9.00000 | + | 15.5885i | −0.336111 | + | 0.582162i | ||||
\(718\) | −8.00000 | + | 13.8564i | −0.298557 | + | 0.517116i | ||||
\(719\) | −22.0000 | − | 38.1051i | −0.820462 | − | 1.42108i | −0.905339 | − | 0.424690i | \(-0.860383\pi\) |
0.0848774 | − | 0.996391i | \(-0.472950\pi\) | |||||||
\(720\) | 6.00000 | 0.223607 | ||||||||
\(721\) | 26.0000 | + | 22.5167i | 0.968291 | + | 0.838564i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | −15.0000 | − | 25.9808i | −0.557856 | − | 0.966235i | ||||
\(724\) | −1.50000 | + | 2.59808i | −0.0557471 | + | 0.0965567i | ||||
\(725\) | 4.50000 | − | 7.79423i | 0.167126 | − | 0.289470i | ||||
\(726\) | −1.50000 | − | 2.59808i | −0.0556702 | − | 0.0964237i | ||||
\(727\) | 21.0000 | 0.778847 | 0.389423 | − | 0.921059i | \(-0.372674\pi\) | ||||
0.389423 | + | 0.921059i | \(0.372674\pi\) | |||||||
\(728\) | 15.0000 | − | 5.19615i | 0.555937 | − | 0.192582i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 4.00000 | + | 6.92820i | 0.148047 | + | 0.256424i | ||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | −7.50000 | + | 12.9904i | −0.277208 | + | 0.480138i | ||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | −11.0000 | −0.406017 | ||||||||
\(735\) | −16.5000 | + | 12.9904i | −0.608612 | + | 0.479157i | ||||
\(736\) | 7.00000 | 0.258023 | ||||||||
\(737\) | 0.500000 | + | 0.866025i | 0.0184177 | + | 0.0319005i | ||||
\(738\) | 9.00000 | − | 15.5885i | 0.331295 | − | 0.573819i | ||||
\(739\) | 6.00000 | − | 10.3923i | 0.220714 | − | 0.382287i | −0.734311 | − | 0.678813i | \(-0.762495\pi\) |
0.955025 | + | 0.296526i | \(0.0958281\pi\) | |||||||
\(740\) | 1.00000 | + | 1.73205i | 0.0367607 | + | 0.0636715i | ||||
\(741\) | −72.0000 | −2.64499 | ||||||||
\(742\) | 5.00000 | − | 1.73205i | 0.183556 | − | 0.0635856i | ||||
\(743\) | −39.0000 | −1.43077 | −0.715386 | − | 0.698730i | \(-0.753749\pi\) | ||||
−0.715386 | + | 0.698730i | \(0.753749\pi\) | |||||||
\(744\) | 9.00000 | + | 15.5885i | 0.329956 | + | 0.571501i | ||||
\(745\) | 7.50000 | − | 12.9904i | 0.274779 | − | 0.475931i | ||||
\(746\) | −16.0000 | + | 27.7128i | −0.585802 | + | 1.01464i | ||||
\(747\) | −27.0000 | − | 46.7654i | −0.987878 | − | 1.71106i | ||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 34.0000 | + | 29.4449i | 1.24233 | + | 1.07589i | ||||
\(750\) | 3.00000 | 0.109545 | ||||||||
\(751\) | 7.00000 | + | 12.1244i | 0.255434 | + | 0.442424i | 0.965013 | − | 0.262201i | \(-0.0844484\pi\) |
−0.709580 | + | 0.704625i | \(0.751115\pi\) | |||||||
\(752\) | 4.00000 | − | 6.92820i | 0.145865 | − | 0.252646i | ||||
\(753\) | 3.00000 | − | 5.19615i | 0.109326 | − | 0.189358i | ||||
\(754\) | 27.0000 | + | 46.7654i | 0.983282 | + | 1.70309i | ||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 4.50000 | − | 23.3827i | 0.163663 | − | 0.850420i | ||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | −12.0000 | − | 20.7846i | −0.435860 | − | 0.754931i | ||||
\(759\) | 10.5000 | − | 18.1865i | 0.381126 | − | 0.660129i | ||||
\(760\) | −2.00000 | + | 3.46410i | −0.0725476 | + | 0.125656i | ||||
\(761\) | −17.0000 | − | 29.4449i | −0.616250 | − | 1.06738i | −0.990164 | − | 0.139912i | \(-0.955318\pi\) |
0.373914 | − | 0.927463i | \(-0.378015\pi\) | |||||||
\(762\) | −60.0000 | −2.17357 | ||||||||
\(763\) | −2.50000 | + | 12.9904i | −0.0905061 | + | 0.470283i | ||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 24.0000 | + | 41.5692i | 0.867722 | + | 1.50294i | ||||
\(766\) | −3.50000 | + | 6.06218i | −0.126460 | + | 0.219035i | ||||
\(767\) | −18.0000 | + | 31.1769i | −0.649942 | + | 1.12573i | ||||
\(768\) | 1.50000 | + | 2.59808i | 0.0541266 | + | 0.0937500i | ||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | −2.00000 | − | 1.73205i | −0.0720750 | − | 0.0624188i | ||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | −9.00000 | − | 15.5885i | −0.323917 | − | 0.561041i | ||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | −3.00000 | + | 5.19615i | −0.107833 | + | 0.186772i | ||||
\(775\) | 3.00000 | + | 5.19615i | 0.107763 | + | 0.186651i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.0000 | − | 5.19615i | 0.538122 | − | 0.186411i | ||||
\(778\) | 30.0000 | 1.07555 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | −9.00000 | + | 15.5885i | −0.322252 | + | 0.558156i | ||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 28.0000 | + | 48.4974i | 1.00128 | + | 1.73426i | ||||
\(783\) | 81.0000 | 2.89470 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | 4.00000 | 0.142766 | ||||||||
\(786\) | 27.0000 | + | 46.7654i | 0.963058 | + | 1.66807i | ||||
\(787\) | 8.50000 | − | 14.7224i | 0.302992 | − | 0.524798i | −0.673820 | − | 0.738896i | \(-0.735348\pi\) |
0.976812 | + | 0.214097i | \(0.0686810\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 19.5000 | + | 33.7750i | 0.694218 | + | 1.20242i | ||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | 30.0000 | − | 10.3923i | 1.06668 | − | 0.369508i | ||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | −15.0000 | − | 25.9808i | −0.532666 | − | 0.922604i | ||||
\(794\) | 10.0000 | − | 17.3205i | 0.354887 | − | 0.614682i | ||||
\(795\) | −3.00000 | + | 5.19615i | −0.106399 | + | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000 | 0.283375 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(798\) | 24.0000 | + | 20.7846i | 0.849591 | + | 0.735767i | ||||
\(799\) | 64.0000 | 2.26416 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | −2.50000 | + | 4.33013i | −0.0882781 | + | 0.152902i | ||||
\(803\) | 4.00000 | + | 6.92820i | 0.141157 | + | 0.244491i | ||||
\(804\) | −3.00000 | −0.105802 | ||||||||
\(805\) | 3.50000 | − | 18.1865i | 0.123359 | − | 0.640991i | ||||
\(806\) | −36.0000 | −1.26805 | ||||||||
\(807\) | 10.5000 | + | 18.1865i | 0.369618 | + | 0.640196i | ||||
\(808\) | 2.50000 | − | 4.33013i | 0.0879497 | − | 0.152333i | ||||
\(809\) | 6.50000 | − | 11.2583i | 0.228528 | − | 0.395822i | −0.728844 | − | 0.684680i | \(-0.759942\pi\) |
0.957372 | + | 0.288858i | \(0.0932755\pi\) | |||||||
\(810\) | 4.50000 | + | 7.79423i | 0.158114 | + | 0.273861i | ||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 4.50000 | − | 23.3827i | 0.157919 | − | 0.820571i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | −12.0000 | + | 20.7846i | −0.420084 | + | 0.727607i | ||||
\(817\) | −2.00000 | − | 3.46410i | −0.0699711 | − | 0.121194i | ||||
\(818\) | −13.0000 | −0.454534 | ||||||||
\(819\) | 72.0000 | + | 62.3538i | 2.51588 | + | 2.17882i | ||||
\(820\) | 3.00000 | 0.104765 | ||||||||
\(821\) | 15.0000 | + | 25.9808i | 0.523504 | + | 0.906735i | 0.999626 | + | 0.0273557i | \(0.00870868\pi\) |
−0.476122 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(822\) | −9.00000 | + | 15.5885i | −0.313911 | + | 0.543710i | ||||
\(823\) | −6.50000 | + | 11.2583i | −0.226576 | + | 0.392441i | −0.956791 | − | 0.290776i | \(-0.906086\pi\) |
0.730215 | + | 0.683217i | \(0.239420\pi\) | |||||||
\(824\) | −6.50000 | − | 11.2583i | −0.226438 | − | 0.392203i | ||||
\(825\) | 3.00000 | 0.104447 | ||||||||
\(826\) | 15.0000 | − | 5.19615i | 0.521917 | − | 0.180797i | ||||
\(827\) | −27.0000 | −0.938882 | −0.469441 | − | 0.882964i | \(-0.655545\pi\) | ||||
−0.469441 | + | 0.882964i | \(0.655545\pi\) | |||||||
\(828\) | 21.0000 | + | 36.3731i | 0.729800 | + | 1.26405i | ||||
\(829\) | 27.0000 | − | 46.7654i | 0.937749 | − | 1.62423i | 0.168091 | − | 0.985771i | \(-0.446240\pi\) |
0.769657 | − | 0.638457i | \(-0.220427\pi\) | |||||||
\(830\) | 4.50000 | − | 7.79423i | 0.156197 | − | 0.270542i | ||||
\(831\) | 3.00000 | + | 5.19615i | 0.104069 | + | 0.180253i | ||||
\(832\) | −6.00000 | −0.208013 | ||||||||
\(833\) | −8.00000 | − | 55.4256i | −0.277184 | − | 1.92038i | ||||
\(834\) | −6.00000 | −0.207763 | ||||||||
\(835\) | −1.50000 | − | 2.59808i | −0.0519096 | − | 0.0899101i | ||||
\(836\) | −2.00000 | + | 3.46410i | −0.0691714 | + | 0.119808i | ||||
\(837\) | −27.0000 | + | 46.7654i | −0.933257 | + | 1.61645i | ||||
\(838\) | 15.0000 | + | 25.9808i | 0.518166 | + | 0.897491i | ||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 7.50000 | − | 2.59808i | 0.258775 | − | 0.0896421i | ||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 12.5000 | + | 21.6506i | 0.430778 | + | 0.746130i | ||||
\(843\) | 45.0000 | − | 77.9423i | 1.54988 | − | 2.68447i | ||||
\(844\) | 7.00000 | − | 12.1244i | 0.240950 | − | 0.417338i | ||||
\(845\) | −11.5000 | − | 19.9186i | −0.395612 | − | 0.685220i | ||||
\(846\) | 48.0000 | 1.65027 | ||||||||
\(847\) | −2.00000 | − | 1.73205i | −0.0687208 | − | 0.0595140i | ||||
\(848\) | −2.00000 | −0.0686803 | ||||||||
\(849\) | 6.00000 | + | 10.3923i | 0.205919 | + | 0.356663i | ||||
\(850\) | −4.00000 | + | 6.92820i | −0.137199 | + | 0.237635i | ||||
\(851\) | −7.00000 | + | 12.1244i | −0.239957 | + | 0.415618i | ||||
\(852\) | 6.00000 | + | 10.3923i | 0.205557 | + | 0.356034i | ||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | −2.50000 | + | 12.9904i | −0.0855482 | + | 0.444522i | ||||
\(855\) | −24.0000 | −0.820783 | ||||||||
\(856\) | −8.50000 | − | 14.7224i | −0.290524 | − | 0.503202i | ||||
\(857\) | 12.0000 | − | 20.7846i | 0.409912 | − | 0.709989i | −0.584967 | − | 0.811057i | \(-0.698893\pi\) |
0.994880 | + | 0.101068i | \(0.0322260\pi\) | |||||||
\(858\) | −9.00000 | + | 15.5885i | −0.307255 | + | 0.532181i | ||||
\(859\) | 1.00000 | + | 1.73205i | 0.0341196 | + | 0.0590968i | 0.882581 | − | 0.470160i | \(-0.155804\pi\) |
−0.848461 | + | 0.529257i | \(0.822471\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 4.50000 | − | 23.3827i | 0.153360 | − | 0.796880i | ||||
\(862\) | 4.00000 | 0.136241 | ||||||||
\(863\) | 12.5000 | + | 21.6506i | 0.425505 | + | 0.736996i | 0.996467 | − | 0.0839800i | \(-0.0267632\pi\) |
−0.570962 | + | 0.820976i | \(0.693430\pi\) | |||||||
\(864\) | −4.50000 | + | 7.79423i | −0.153093 | + | 0.265165i | ||||
\(865\) | −5.00000 | + | 8.66025i | −0.170005 | + | 0.294457i | ||||
\(866\) | −15.0000 | − | 25.9808i | −0.509721 | − | 0.882862i | ||||
\(867\) | −141.000 | −4.78861 | ||||||||
\(868\) | 12.0000 | + | 10.3923i | 0.407307 | + | 0.352738i | ||||
\(869\) | −10.0000 | −0.339227 | ||||||||
\(870\) | 13.5000 | + | 23.3827i | 0.457693 | + | 0.792747i | ||||
\(871\) | 3.00000 | − | 5.19615i | 0.101651 | − | 0.176065i | ||||
\(872\) | 2.50000 | − | 4.33013i | 0.0846607 | − | 0.146637i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.0000 | −0.947114 | ||||||||
\(875\) | 2.50000 | − | 0.866025i | 0.0845154 | − | 0.0292770i | ||||
\(876\) | −24.0000 | −0.810885 | ||||||||
\(877\) | 10.0000 | + | 17.3205i | 0.337676 | + | 0.584872i | 0.983995 | − | 0.178195i | \(-0.0570259\pi\) |
−0.646319 | + | 0.763067i | \(0.723693\pi\) | |||||||
\(878\) | 15.0000 | − | 25.9808i | 0.506225 | − | 0.876808i | ||||
\(879\) | −39.0000 | + | 67.5500i | −1.31544 | + | 2.27840i | ||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | 29.0000 | 0.977035 | 0.488517 | − | 0.872554i | \(-0.337538\pi\) | ||||
0.488517 | + | 0.872554i | \(0.337538\pi\) | |||||||
\(882\) | −6.00000 | − | 41.5692i | −0.202031 | − | 1.39971i | ||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | −24.0000 | − | 41.5692i | −0.807207 | − | 1.39812i | ||||
\(885\) | −9.00000 | + | 15.5885i | −0.302532 | + | 0.524000i | ||||
\(886\) | 6.50000 | − | 11.2583i | 0.218372 | − | 0.378231i | ||||
\(887\) | 13.5000 | + | 23.3827i | 0.453286 | + | 0.785114i | 0.998588 | − | 0.0531258i | \(-0.0169184\pi\) |
−0.545302 | + | 0.838240i | \(0.683585\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | −50.0000 | + | 17.3205i | −1.67695 | + | 0.580911i | ||||
\(890\) | −1.00000 | −0.0335201 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | −16.0000 | + | 27.7128i | −0.535420 | + | 0.927374i | ||||
\(894\) | 22.5000 | + | 38.9711i | 0.752513 | + | 1.30339i | ||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | −126.000 | −4.20702 | ||||||||
\(898\) | −12.5000 | − | 21.6506i | −0.417130 | − | 0.722491i | ||||
\(899\) | −27.0000 | + | 46.7654i | −0.900500 | + | 1.55971i | ||||
\(900\) | −3.00000 | + | 5.19615i | −0.100000 | + | 0.173205i | ||||
\(901\) | −8.00000 | − | 13.8564i | −0.266519 | − | 0.461624i | ||||
\(902\) | 3.00000 | 0.0998891 | ||||||||
\(903\) | −1.50000 | + | 7.79423i | −0.0499169 | + | 0.259376i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | −1.50000 | − | 2.59808i | −0.0498617 | − | 0.0863630i | ||||
\(906\) | 24.0000 | − | 41.5692i | 0.797347 | − | 1.38104i | ||||
\(907\) | 0.500000 | − | 0.866025i | 0.0166022 | − | 0.0287559i | −0.857605 | − | 0.514309i | \(-0.828048\pi\) |
0.874207 | + | 0.485553i | \(0.161382\pi\) | |||||||
\(908\) | 10.0000 | + | 17.3205i | 0.331862 | + | 0.574801i | ||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | −3.00000 | + | 15.5885i | −0.0994490 | + | 0.516752i | ||||
\(911\) | −34.0000 | −1.12647 | −0.563235 | − | 0.826297i | \(-0.690443\pi\) | ||||
−0.563235 | + | 0.826297i | \(0.690443\pi\) | |||||||
\(912\) | −6.00000 | − | 10.3923i | −0.198680 | − | 0.344124i | ||||
\(913\) | 4.50000 | − | 7.79423i | 0.148928 | − | 0.257951i | ||||
\(914\) | −4.00000 | + | 6.92820i | −0.132308 | + | 0.229165i | ||||
\(915\) | −7.50000 | − | 12.9904i | −0.247942 | − | 0.429449i | ||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | 36.0000 | + | 31.1769i | 1.18882 | + | 1.02955i | ||||
\(918\) | −72.0000 | −2.37635 | ||||||||
\(919\) | 2.00000 | + | 3.46410i | 0.0659739 | + | 0.114270i | 0.897126 | − | 0.441776i | \(-0.145651\pi\) |
−0.831152 | + | 0.556046i | \(0.812318\pi\) | |||||||
\(920\) | −3.50000 | + | 6.06218i | −0.115392 | + | 0.199864i | ||||
\(921\) | 10.5000 | − | 18.1865i | 0.345987 | − | 0.599267i | ||||
\(922\) | −9.00000 | − | 15.5885i | −0.296399 | − | 0.513378i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | 7.50000 | − | 2.59808i | 0.246732 | − | 0.0854704i | ||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 5.50000 | + | 9.52628i | 0.180741 | + | 0.313053i | ||||
\(927\) | 39.0000 | − | 67.5500i | 1.28093 | − | 2.21863i | ||||
\(928\) | −4.50000 | + | 7.79423i | −0.147720 | + | 0.255858i | ||||
\(929\) | −13.5000 | − | 23.3827i | −0.442921 | − | 0.767161i | 0.554984 | − | 0.831861i | \(-0.312724\pi\) |
−0.997905 | + | 0.0646999i | \(0.979391\pi\) | |||||||
\(930\) | −18.0000 | −0.590243 | ||||||||
\(931\) | 26.0000 | + | 10.3923i | 0.852116 | + | 0.340594i | ||||
\(932\) | 26.0000 | 0.851658 | ||||||||
\(933\) | −27.0000 | − | 46.7654i | −0.883940 | − | 1.53103i | ||||
\(934\) | −13.5000 | + | 23.3827i | −0.441733 | + | 0.765105i | ||||
\(935\) | −4.00000 | + | 6.92820i | −0.130814 | + | 0.226576i | ||||
\(936\) | −18.0000 | − | 31.1769i | −0.588348 | − | 1.01905i | ||||
\(937\) | 28.0000 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(938\) | −2.50000 | + | 0.866025i | −0.0816279 | + | 0.0282767i | ||||
\(939\) | −48.0000 | −1.56642 | ||||||||
\(940\) | 4.00000 | + | 6.92820i | 0.130466 | + | 0.225973i | ||||
\(941\) | 5.00000 | − | 8.66025i | 0.162995 | − | 0.282316i | −0.772946 | − | 0.634472i | \(-0.781218\pi\) |
0.935942 | + | 0.352155i | \(0.114551\pi\) | |||||||
\(942\) | −6.00000 | + | 10.3923i | −0.195491 | + | 0.338600i | ||||
\(943\) | 10.5000 | + | 18.1865i | 0.341927 | + | 0.592235i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 18.0000 | + | 15.5885i | 0.585540 | + | 0.507093i | ||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 25.5000 | + | 44.1673i | 0.828639 | + | 1.43524i | 0.899106 | + | 0.437730i | \(0.144217\pi\) |
−0.0704677 | + | 0.997514i | \(0.522449\pi\) | |||||||
\(948\) | 15.0000 | − | 25.9808i | 0.487177 | − | 0.843816i | ||||
\(949\) | 24.0000 | − | 41.5692i | 0.779073 | − | 1.34939i | ||||
\(950\) | −2.00000 | − | 3.46410i | −0.0648886 | − | 0.112390i | ||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | −4.00000 | + | 20.7846i | −0.129641 | + | 0.673633i | ||||
\(953\) | −14.0000 | −0.453504 | −0.226752 | − | 0.973952i | \(-0.572811\pi\) | ||||
−0.226752 | + | 0.973952i | \(0.572811\pi\) | |||||||
\(954\) | −6.00000 | − | 10.3923i | −0.194257 | − | 0.336463i | ||||
\(955\) | 8.00000 | − | 13.8564i | 0.258874 | − | 0.448383i | ||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | 13.5000 | + | 23.3827i | 0.436393 | + | 0.755855i | ||||
\(958\) | 42.0000 | 1.35696 | ||||||||
\(959\) | −3.00000 | + | 15.5885i | −0.0968751 | + | 0.503378i | ||||
\(960\) | −3.00000 | −0.0968246 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 6.00000 | − | 10.3923i | 0.193448 | − | 0.335061i | ||||
\(963\) | 51.0000 | − | 88.3346i | 1.64345 | − | 2.84654i | ||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | 18.0000 | 0.579441 | ||||||||
\(966\) | 42.0000 | + | 36.3731i | 1.35133 | + | 1.17028i | ||||
\(967\) | −59.0000 | −1.89731 | −0.948656 | − | 0.316310i | \(-0.897556\pi\) | ||||
−0.948656 | + | 0.316310i | \(0.897556\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 48.0000 | − | 83.1384i | 1.54198 | − | 2.67079i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0000 | − | 27.7128i | −0.513464 | − | 0.889346i | −0.999878 | − | 0.0156178i | \(-0.995028\pi\) |
0.486414 | − | 0.873729i | \(-0.338305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.00000 | + | 1.73205i | −0.160293 | + | 0.0555270i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | −9.00000 | − | 15.5885i | −0.288231 | − | 0.499230i | ||||
\(976\) | 2.50000 | − | 4.33013i | 0.0800230 | − | 0.138604i | ||||
\(977\) | −12.0000 | + | 20.7846i | −0.383914 | + | 0.664959i | −0.991618 | − | 0.129205i | \(-0.958757\pi\) |
0.607704 | + | 0.794164i | \(0.292091\pi\) | |||||||
\(978\) | −12.0000 | − | 20.7846i | −0.383718 | − | 0.664619i | ||||
\(979\) | −1.00000 | −0.0319601 | ||||||||
\(980\) | 5.50000 | − | 4.33013i | 0.175691 | − | 0.138321i | ||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | −11.0000 | − | 19.0526i | −0.351024 | − | 0.607992i | ||||
\(983\) | 18.5000 | − | 32.0429i | 0.590058 | − | 1.02201i | −0.404166 | − | 0.914686i | \(-0.632438\pi\) |
0.994224 | − | 0.107325i | \(-0.0342286\pi\) | |||||||
\(984\) | −4.50000 | + | 7.79423i | −0.143455 | + | 0.248471i | ||||
\(985\) | 9.00000 | + | 15.5885i | 0.286764 | + | 0.496690i | ||||
\(986\) | −72.0000 | −2.29295 | ||||||||
\(987\) | 60.0000 | − | 20.7846i | 1.90982 | − | 0.661581i | ||||
\(988\) | 24.0000 | 0.763542 | ||||||||
\(989\) | −3.50000 | − | 6.06218i | −0.111294 | − | 0.192766i | ||||
\(990\) | −3.00000 | + | 5.19615i | −0.0953463 | + | 0.165145i | ||||
\(991\) | −10.0000 | + | 17.3205i | −0.317660 | + | 0.550204i | −0.979999 | − | 0.199000i | \(-0.936231\pi\) |
0.662339 | + | 0.749204i | \(0.269564\pi\) | |||||||
\(992\) | −3.00000 | − | 5.19615i | −0.0952501 | − | 0.164978i | ||||
\(993\) | −96.0000 | −3.04647 | ||||||||
\(994\) | 8.00000 | + | 6.92820i | 0.253745 | + | 0.219749i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 13.5000 | + | 23.3827i | 0.427764 | + | 0.740909i | ||||
\(997\) | −14.0000 | + | 24.2487i | −0.443384 | + | 0.767964i | −0.997938 | − | 0.0641836i | \(-0.979556\pi\) |
0.554554 | + | 0.832148i | \(0.312889\pi\) | |||||||
\(998\) | 2.00000 | − | 3.46410i | 0.0633089 | − | 0.109654i | ||||
\(999\) | −9.00000 | − | 15.5885i | −0.284747 | − | 0.493197i |
(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 | 770.2.i.i.221.1 | ✓ | 2 | |
7.2 | even | 3 | inner | 770.2.i.i.331.1 | yes | 2 | |
7.3 | odd | 6 | 5390.2.a.s.1.1 | 1 | |||
7.4 | even | 3 | 5390.2.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.i.i.221.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
770.2.i.i.331.1 | yes | 2 | 7.2 | even | 3 | inner | |
5390.2.a.b.1.1 | 1 | 7.4 | even | 3 | |||
5390.2.a.s.1.1 | 1 | 7.3 | odd | 6 |