Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(165,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.e (of order \(3\), degree \(2\), not 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: | \(10.1729412175\) |
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: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.165 |
Dual form | 1274.2.e.d.471.1 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | 2.50000 | − | 2.59808i | 0.693375 | − | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50000 | + | 2.59808i | −0.387298 | + | 0.670820i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | −1.00000 | + | 1.73205i | −0.235702 | + | 0.408248i | ||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | 0.625543 | 0.312772 | − | 0.949828i | \(-0.398743\pi\) | ||||
0.312772 | + | 0.949828i | \(0.398743\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | −2.50000 | + | 2.59808i | −0.490290 | + | 0.509525i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | 5.00000 | − | 8.66025i | 0.898027 | − | 1.55543i | 0.0680129 | − | 0.997684i | \(-0.478334\pi\) |
0.830014 | − | 0.557743i | \(-0.188333\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | − | 1.73205i | 0.166667 | − | 0.288675i | ||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | −3.50000 | − | 0.866025i | −0.560449 | − | 0.138675i | ||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.00000 | − | 3.46410i | 0.282843 | − | 0.489898i | ||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 2.50000 | − | 2.59808i | 0.346688 | − | 0.360288i | ||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | 3.00000 | 0.390567 | 0.195283 | − | 0.980747i | \(-0.437437\pi\) | ||||
0.195283 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | −5.50000 | + | 9.52628i | −0.704203 | + | 1.21972i | 0.262776 | + | 0.964857i | \(0.415362\pi\) |
−0.966978 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(62\) | −5.00000 | + | 8.66025i | −0.635001 | + | 1.09985i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.5000 | − | 2.59808i | −1.30236 | − | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | −1.50000 | − | 2.59808i | −0.180579 | − | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | + | 2.59808i | 0.178017 | + | 0.308335i | 0.941201 | − | 0.337846i | \(-0.109698\pi\) |
−0.763184 | + | 0.646181i | \(0.776365\pi\) | |||||||
\(72\) | −1.00000 | + | 1.73205i | −0.117851 | + | 0.204124i | ||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.50000 | + | 0.866025i | 0.396297 | + | 0.0980581i | ||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | − | 15.5885i | −0.976187 | − | 1.69081i | ||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 6.00000 | 0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.00000 | 0.312772 | ||||||||
\(93\) | −10.0000 | −1.03695 | ||||||||
\(94\) | 3.00000 | + | 5.19615i | 0.309426 | + | 0.535942i | ||||
\(95\) | −12.0000 | −1.23117 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 3.00000 | + | 5.19615i | 0.297044 | + | 0.514496i | ||||
\(103\) | −7.00000 | − | 12.1244i | −0.689730 | − | 1.19465i | −0.971925 | − | 0.235291i | \(-0.924396\pi\) |
0.282194 | − | 0.959357i | \(-0.408938\pi\) | |||||||
\(104\) | −2.50000 | + | 2.59808i | −0.245145 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | − | 10.3923i | 0.582772 | − | 1.00939i | ||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | 8.00000 | − | 13.8564i | 0.766261 | − | 1.32720i | −0.173316 | − | 0.984866i | \(-0.555448\pi\) |
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | − | 6.92820i | −0.379663 | − | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | + | 15.5885i | 0.846649 | + | 1.46644i | 0.884182 | + | 0.467143i | \(0.154717\pi\) |
−0.0375328 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | −2.00000 | − | 6.92820i | −0.184900 | − | 0.640513i | ||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.50000 | − | 2.59808i | 0.136931 | − | 0.237171i | ||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 5.50000 | − | 9.52628i | 0.497947 | − | 0.862469i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.50000 | + | 9.52628i | −0.488046 | + | 0.845321i | −0.999905 | − | 0.0137486i | \(-0.995624\pi\) |
0.511859 | + | 0.859069i | \(0.328957\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 10.5000 | + | 2.59808i | 0.920911 | + | 0.227866i | ||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.00000 | + | 1.73205i | 0.0863868 | + | 0.149626i | ||||
\(135\) | 7.50000 | + | 12.9904i | 0.645497 | + | 1.11803i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 3.00000 | 0.256307 | 0.128154 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(138\) | 1.50000 | + | 2.59808i | 0.127688 | + | 0.221163i | ||||
\(139\) | 8.00000 | + | 13.8564i | 0.678551 | + | 1.17529i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | + | 5.19615i | −0.252646 | + | 0.437595i | ||||
\(142\) | −1.50000 | − | 2.59808i | −0.125877 | − | 0.218026i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | 0.500000 | − | 0.866025i | 0.0406894 | − | 0.0704761i | −0.844963 | − | 0.534824i | \(-0.820378\pi\) |
0.885653 | + | 0.464348i | \(0.153711\pi\) | |||||||
\(152\) | −2.00000 | + | 3.46410i | −0.162221 | + | 0.280976i | ||||
\(153\) | 6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.0000 | −2.40966 | ||||||||
\(156\) | −3.50000 | − | 0.866025i | −0.280224 | − | 0.0693375i | ||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | −2.00000 | − | 3.46410i | −0.159111 | − | 0.275589i | ||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 1.50000 | + | 2.59808i | 0.118585 | + | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 9.00000 | + | 15.5885i | 0.690268 | + | 1.19558i | ||||
\(171\) | −4.00000 | − | 6.92820i | −0.305888 | − | 0.529813i | ||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | − | 2.59808i | −0.112747 | − | 0.195283i | ||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | −6.00000 | −0.447214 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | −3.00000 | −0.221163 | ||||||||
\(185\) | −12.0000 | − | 20.7846i | −0.882258 | − | 1.52811i | ||||
\(186\) | 10.0000 | 0.733236 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.00000 | − | 5.19615i | −0.218797 | − | 0.378968i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | 0.870572 | ||||||||
\(191\) | 12.0000 | − | 20.7846i | 0.868290 | − | 1.50392i | 0.00454614 | − | 0.999990i | \(-0.498553\pi\) |
0.863743 | − | 0.503932i | \(-0.168114\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 1.00000 | + | 1.73205i | 0.0717958 | + | 0.124354i | ||||
\(195\) | 3.00000 | + | 10.3923i | 0.214834 | + | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | + | 10.3923i | −0.427482 | + | 0.740421i | −0.996649 | − | 0.0818013i | \(-0.973933\pi\) |
0.569166 | + | 0.822222i | \(0.307266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 2.00000 | − | 3.46410i | 0.141421 | − | 0.244949i | ||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | −3.00000 | − | 5.19615i | −0.211079 | − | 0.365600i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.00000 | + | 12.1244i | 0.487713 | + | 0.844744i | ||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | 2.50000 | − | 2.59808i | 0.173344 | − | 0.180144i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | −6.00000 | + | 10.3923i | −0.412082 | + | 0.713746i | ||||
\(213\) | 1.50000 | − | 2.59808i | 0.102778 | − | 0.178017i | ||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | −12.0000 | + | 20.7846i | −0.818393 | + | 1.41750i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.00000 | + | 13.8564i | −0.541828 | + | 0.938474i | ||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | − | 15.5885i | 1.00901 | − | 1.04859i | ||||
\(222\) | 4.00000 | + | 6.92820i | 0.268462 | + | 0.464991i | ||||
\(223\) | −4.00000 | + | 6.92820i | −0.267860 | + | 0.463947i | −0.968309 | − | 0.249756i | \(-0.919650\pi\) |
0.700449 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | + | 6.92820i | 0.266667 | + | 0.461880i | ||||
\(226\) | −9.00000 | − | 15.5885i | −0.598671 | − | 1.03693i | ||||
\(227\) | −15.0000 | −0.995585 | −0.497792 | − | 0.867296i | \(-0.665856\pi\) | ||||
−0.497792 | + | 0.867296i | \(0.665856\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | 11.0000 | + | 19.0526i | 0.726900 | + | 1.25903i | 0.958187 | + | 0.286143i | \(0.0923732\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 4.50000 | + | 7.79423i | 0.296721 | + | 0.513936i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 1.50000 | + | 2.59808i | 0.0982683 | + | 0.170206i | 0.910968 | − | 0.412477i | \(-0.135336\pi\) |
−0.812700 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(234\) | 2.00000 | + | 6.92820i | 0.130744 | + | 0.452911i | ||||
\(235\) | −9.00000 | + | 15.5885i | −0.587095 | + | 1.01688i | ||||
\(236\) | 3.00000 | 0.195283 | ||||||||
\(237\) | 2.00000 | − | 3.46410i | 0.129914 | − | 0.225018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0000 | 1.35838 | 0.679189 | − | 0.733964i | \(-0.262332\pi\) | ||||
0.679189 | + | 0.733964i | \(0.262332\pi\) | |||||||
\(240\) | −1.50000 | + | 2.59808i | −0.0968246 | + | 0.167705i | ||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | −5.50000 | + | 9.52628i | −0.353553 | + | 0.612372i | ||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −5.50000 | + | 9.52628i | −0.352101 | + | 0.609858i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | − | 13.8564i | −0.254514 | − | 0.881662i | ||||
\(248\) | −5.00000 | + | 8.66025i | −0.317500 | + | 0.549927i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.00000 | 0.189737 | ||||||||
\(251\) | −1.50000 | − | 2.59808i | −0.0946792 | − | 0.163989i | 0.814795 | − | 0.579748i | \(-0.196849\pi\) |
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.50000 | − | 9.52628i | 0.345101 | − | 0.597732i | ||||
\(255\) | −9.00000 | + | 15.5885i | −0.563602 | + | 0.976187i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 4.00000 | − | 6.92820i | 0.249029 | − | 0.431331i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.5000 | − | 2.59808i | −0.651182 | − | 0.161126i | ||||
\(261\) | 6.00000 | + | 10.3923i | 0.371391 | + | 0.643268i | ||||
\(262\) | 7.50000 | + | 12.9904i | 0.463352 | + | 0.802548i | ||||
\(263\) | 13.5000 | + | 23.3827i | 0.832446 | + | 1.44184i | 0.896093 | + | 0.443866i | \(0.146393\pi\) |
−0.0636476 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.0000 | 2.21146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.00000 | + | 5.19615i | 0.183597 | + | 0.317999i | ||||
\(268\) | −1.00000 | − | 1.73205i | −0.0610847 | − | 0.105802i | ||||
\(269\) | 9.00000 | 0.548740 | 0.274370 | − | 0.961624i | \(-0.411531\pi\) | ||||
0.274370 | + | 0.961624i | \(0.411531\pi\) | |||||||
\(270\) | −7.50000 | − | 12.9904i | −0.456435 | − | 0.790569i | ||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | −0.181237 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | − | 2.59808i | −0.0902894 | − | 0.156386i | ||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −8.00000 | − | 13.8564i | −0.479808 | − | 0.831052i | ||||
\(279\) | −10.0000 | − | 17.3205i | −0.598684 | − | 1.03695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | 15.5000 | + | 26.8468i | 0.921379 | + | 1.59588i | 0.797283 | + | 0.603606i | \(0.206270\pi\) |
0.124096 | + | 0.992270i | \(0.460397\pi\) | |||||||
\(284\) | 1.50000 | + | 2.59808i | 0.0890086 | + | 0.154167i | ||||
\(285\) | 6.00000 | + | 10.3923i | 0.355409 | + | 0.615587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | + | 1.73205i | −0.0589256 | + | 0.102062i | ||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | −18.0000 | −1.05700 | ||||||||
\(291\) | −1.00000 | + | 1.73205i | −0.0586210 | + | 0.101535i | ||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | 3.00000 | + | 5.19615i | 0.175262 | + | 0.303562i | 0.940252 | − | 0.340480i | \(-0.110589\pi\) |
−0.764990 | + | 0.644042i | \(0.777256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.50000 | − | 7.79423i | −0.262000 | − | 0.453798i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.50000 | − | 7.79423i | 0.433736 | − | 0.450752i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.500000 | + | 0.866025i | −0.0287718 | + | 0.0498342i | ||||
\(303\) | 3.00000 | − | 5.19615i | 0.172345 | − | 0.298511i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 33.0000 | 1.88957 | ||||||||
\(306\) | −6.00000 | + | 10.3923i | −0.342997 | + | 0.594089i | ||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | + | 12.1244i | −0.398216 | + | 0.689730i | ||||
\(310\) | 30.0000 | 1.70389 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 3.50000 | + | 0.866025i | 0.198148 | + | 0.0490290i | ||||
\(313\) | −4.00000 | − | 6.92820i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(314\) | 1.00000 | − | 1.73205i | 0.0564333 | − | 0.0977453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | + | 3.46410i | 0.112509 | + | 0.194871i | ||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | −12.0000 | −0.672927 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | − | 2.59808i | −0.0838525 | − | 0.145237i | ||||
\(321\) | 9.00000 | + | 15.5885i | 0.502331 | + | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | − | 20.7846i | 0.667698 | − | 1.15649i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4.00000 | + | 13.8564i | 0.221880 | + | 0.768615i | ||||
\(326\) | 10.0000 | − | 17.3205i | 0.553849 | − | 0.959294i | ||||
\(327\) | −16.0000 | −0.884802 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | − | 13.8564i | 0.438397 | − | 0.759326i | ||||
\(334\) | −6.00000 | + | 10.3923i | −0.328305 | + | 0.568642i | ||||
\(335\) | −3.00000 | + | 5.19615i | −0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0.500000 | + | 12.9904i | 0.0271964 | + | 0.706584i | ||||
\(339\) | 9.00000 | − | 15.5885i | 0.488813 | − | 0.846649i | ||||
\(340\) | −9.00000 | − | 15.5885i | −0.488094 | − | 0.845403i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000 | + | 6.92820i | 0.216295 | + | 0.374634i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | + | 6.92820i | 0.215666 | + | 0.373544i | ||||
\(345\) | −4.50000 | + | 7.79423i | −0.242272 | + | 0.419627i | ||||
\(346\) | 4.50000 | − | 7.79423i | 0.241921 | − | 0.419020i | ||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 6.00000 | 0.321634 | ||||||||
\(349\) | −14.5000 | + | 25.1147i | −0.776167 | + | 1.34436i | 0.157969 | + | 0.987444i | \(0.449505\pi\) |
−0.934136 | + | 0.356917i | \(0.883828\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.5000 | + | 12.9904i | −0.667201 | + | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | 1.50000 | + | 2.59808i | 0.0797241 | + | 0.138086i | ||||
\(355\) | 4.50000 | − | 7.79423i | 0.238835 | − | 0.413675i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.00000 | + | 5.19615i | 0.158555 | + | 0.274625i | ||||
\(359\) | 4.50000 | + | 7.79423i | 0.237501 | + | 0.411364i | 0.959997 | − | 0.280012i | \(-0.0903384\pi\) |
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(360\) | 6.00000 | 0.316228 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −5.00000 | −0.262794 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | −11.0000 | −0.574979 | ||||||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | 3.00000 | 0.156386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.0000 | + | 20.7846i | 0.623850 | + | 1.08054i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | −16.0000 | + | 27.7128i | −0.828449 | + | 1.43492i | 0.0708063 | + | 0.997490i | \(0.477443\pi\) |
−0.899255 | + | 0.437425i | \(0.855891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | + | 2.59808i | 0.0774597 | + | 0.134164i | ||||
\(376\) | 3.00000 | + | 5.19615i | 0.154713 | + | 0.267971i | ||||
\(377\) | 6.00000 | + | 20.7846i | 0.309016 | + | 1.07046i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000 | − | 24.2487i | 0.719132 | − | 1.24557i | −0.242213 | − | 0.970223i | \(-0.577873\pi\) |
0.961344 | − | 0.275349i | \(-0.0887935\pi\) | |||||||
\(380\) | −12.0000 | −0.615587 | ||||||||
\(381\) | 11.0000 | 0.563547 | ||||||||
\(382\) | −12.0000 | + | 20.7846i | −0.613973 | + | 1.06343i | ||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.50000 | + | 4.33013i | 0.127247 | + | 0.220398i | ||||
\(387\) | −16.0000 | −0.813326 | ||||||||
\(388\) | −1.00000 | − | 1.73205i | −0.0507673 | − | 0.0879316i | ||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | −3.00000 | − | 10.3923i | −0.151911 | − | 0.526235i | ||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.50000 | + | 12.9904i | −0.378325 | + | 0.655278i | ||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | 6.00000 | − | 10.3923i | 0.301893 | − | 0.522894i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.50000 | − | 6.06218i | 0.175660 | − | 0.304252i | −0.764730 | − | 0.644351i | \(-0.777127\pi\) |
0.940389 | + | 0.340099i | \(0.110461\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | 1.00000 | − | 1.73205i | 0.0498755 | − | 0.0863868i | ||||
\(403\) | −10.0000 | − | 34.6410i | −0.498135 | − | 1.72559i | ||||
\(404\) | 3.00000 | + | 5.19615i | 0.149256 | + | 0.258518i | ||||
\(405\) | −1.50000 | + | 2.59808i | −0.0745356 | + | 0.129099i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00000 | + | 5.19615i | 0.148522 | + | 0.257248i | ||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50000 | − | 2.59808i | −0.0739895 | − | 0.128154i | ||||
\(412\) | −7.00000 | − | 12.1244i | −0.344865 | − | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.00000 | + | 5.19615i | −0.147442 | + | 0.255377i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | 8.00000 | − | 13.8564i | 0.391762 | − | 0.678551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | −2.00000 | + | 3.46410i | −0.0973585 | + | 0.168630i | ||||
\(423\) | −12.0000 | −0.583460 | ||||||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | −12.0000 | + | 20.7846i | −0.582086 | + | 1.00820i | ||||
\(426\) | −1.50000 | + | 2.59808i | −0.0726752 | + | 0.125877i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | − | 20.7846i | 0.578691 | − | 1.00232i | ||||
\(431\) | 16.5000 | + | 28.5788i | 0.794777 | + | 1.37659i | 0.922981 | + | 0.384846i | \(0.125746\pi\) |
−0.128204 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | 2.00000 | + | 3.46410i | 0.0961139 | + | 0.166474i | 0.910073 | − | 0.414448i | \(-0.136025\pi\) |
−0.813959 | + | 0.580922i | \(0.802692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.00000 | − | 15.5885i | −0.431517 | − | 0.747409i | ||||
\(436\) | 8.00000 | − | 13.8564i | 0.383131 | − | 0.663602i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.0000 | + | 15.5885i | −0.713477 | + | 0.741467i | ||||
\(443\) | −9.00000 | − | 15.5885i | −0.427603 | − | 0.740630i | 0.569057 | − | 0.822298i | \(-0.307309\pi\) |
−0.996660 | + | 0.0816684i | \(0.973975\pi\) | |||||||
\(444\) | −4.00000 | − | 6.92820i | −0.189832 | − | 0.328798i | ||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.50000 | − | 7.79423i | −0.212368 | − | 0.367832i | 0.740087 | − | 0.672511i | \(-0.234784\pi\) |
−0.952455 | + | 0.304679i | \(0.901451\pi\) | |||||||
\(450\) | −4.00000 | − | 6.92820i | −0.188562 | − | 0.326599i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000 | + | 15.5885i | 0.423324 | + | 0.733219i | ||||
\(453\) | −1.00000 | −0.0469841 | ||||||||
\(454\) | 15.0000 | 0.703985 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 29.0000 | 1.35656 | 0.678281 | − | 0.734802i | \(-0.262725\pi\) | ||||
0.678281 | + | 0.734802i | \(0.262725\pi\) | |||||||
\(458\) | −11.0000 | − | 19.0526i | −0.513996 | − | 0.890268i | ||||
\(459\) | −30.0000 | −1.40028 | ||||||||
\(460\) | −4.50000 | − | 7.79423i | −0.209814 | − | 0.363408i | ||||
\(461\) | −10.5000 | − | 18.1865i | −0.489034 | − | 0.847031i | 0.510887 | − | 0.859648i | \(-0.329317\pi\) |
−0.999920 | + | 0.0126168i | \(0.995984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 15.0000 | + | 25.9808i | 0.695608 | + | 1.20483i | ||||
\(466\) | −1.50000 | − | 2.59808i | −0.0694862 | − | 0.120354i | ||||
\(467\) | 1.50000 | + | 2.59808i | 0.0694117 | + | 0.120225i | 0.898642 | − | 0.438682i | \(-0.144554\pi\) |
−0.829231 | + | 0.558906i | \(0.811221\pi\) | |||||||
\(468\) | −2.00000 | − | 6.92820i | −0.0924500 | − | 0.320256i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.00000 | − | 15.5885i | 0.415139 | − | 0.719042i | ||||
\(471\) | 2.00000 | 0.0921551 | ||||||||
\(472\) | −3.00000 | −0.138086 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.00000 | + | 3.46410i | −0.0918630 | + | 0.159111i | ||||
\(475\) | 8.00000 | + | 13.8564i | 0.367065 | + | 0.635776i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | + | 20.7846i | 0.549442 | + | 0.951662i | ||||
\(478\) | −21.0000 | −0.960518 | ||||||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 1.50000 | − | 2.59808i | 0.0684653 | − | 0.118585i | ||||
\(481\) | 20.0000 | − | 20.7846i | 0.911922 | − | 0.947697i | ||||
\(482\) | 28.0000 | 1.27537 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50000 | − | 9.52628i | 0.250000 | − | 0.433013i | ||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 8.00000 | − | 13.8564i | 0.362887 | − | 0.628539i | ||||
\(487\) | −13.0000 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(488\) | 5.50000 | − | 9.52628i | 0.248973 | − | 0.431234i | ||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | + | 10.3923i | −0.270776 | + | 0.468998i | −0.969061 | − | 0.246822i | \(-0.920614\pi\) |
0.698285 | + | 0.715820i | \(0.253947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | + | 31.1769i | −0.810679 | + | 1.40414i | ||||
\(494\) | 4.00000 | + | 13.8564i | 0.179969 | + | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | − | 8.66025i | 0.224507 | − | 0.388857i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0000 | + | 19.0526i | 0.492428 | + | 0.852910i | 0.999962 | − | 0.00872186i | \(-0.00277629\pi\) |
−0.507534 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | −21.0000 | − | 36.3731i | −0.936344 | − | 1.62179i | −0.772220 | − | 0.635355i | \(-0.780854\pi\) |
−0.164124 | − | 0.986440i | \(-0.552480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | − | 15.5885i | 0.400495 | − | 0.693677i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | + | 6.92820i | −0.488527 | + | 0.307692i | ||||
\(508\) | −5.50000 | + | 9.52628i | −0.244023 | + | 0.422660i | ||||
\(509\) | −15.0000 | −0.664863 | −0.332432 | − | 0.943127i | \(-0.607869\pi\) | ||||
−0.332432 | + | 0.943127i | \(0.607869\pi\) | |||||||
\(510\) | 9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.0000 | + | 17.3205i | −0.441511 | + | 0.764719i | ||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | −21.0000 | + | 36.3731i | −0.925371 | + | 1.60279i | ||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 10.5000 | + | 2.59808i | 0.460455 | + | 0.113933i | ||||
\(521\) | 18.0000 | − | 31.1769i | 0.788594 | − | 1.36589i | −0.138234 | − | 0.990400i | \(-0.544143\pi\) |
0.926828 | − | 0.375486i | \(-0.122524\pi\) | |||||||
\(522\) | −6.00000 | − | 10.3923i | −0.262613 | − | 0.454859i | ||||
\(523\) | −1.00000 | −0.0437269 | −0.0218635 | − | 0.999761i | \(-0.506960\pi\) | ||||
−0.0218635 | + | 0.999761i | \(0.506960\pi\) | |||||||
\(524\) | −7.50000 | − | 12.9904i | −0.327639 | − | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.5000 | − | 23.3827i | −0.588628 | − | 1.01953i | ||||
\(527\) | 30.0000 | − | 51.9615i | 1.30682 | − | 2.26348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −36.0000 | −1.56374 | ||||||||
\(531\) | 3.00000 | − | 5.19615i | 0.130189 | − | 0.225494i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.00000 | − | 5.19615i | −0.129823 | − | 0.224860i | ||||
\(535\) | 27.0000 | + | 46.7654i | 1.16731 | + | 2.02184i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | −9.00000 | −0.388018 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.50000 | + | 12.9904i | 0.322749 | + | 0.559017i | ||||
\(541\) | −19.0000 | − | 32.9090i | −0.816874 | − | 1.41487i | −0.907975 | − | 0.419025i | \(-0.862372\pi\) |
0.0911008 | − | 0.995842i | \(-0.470961\pi\) | |||||||
\(542\) | −2.00000 | −0.0859074 | ||||||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | −48.0000 | −2.05609 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 3.00000 | 0.128154 | ||||||||
\(549\) | 11.0000 | + | 19.0526i | 0.469469 | + | 0.813143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | + | 20.7846i | 0.511217 | + | 0.885454i | ||||
\(552\) | 1.50000 | + | 2.59808i | 0.0638442 | + | 0.110581i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | −12.0000 | + | 20.7846i | −0.509372 | + | 0.882258i | ||||
\(556\) | 8.00000 | + | 13.8564i | 0.339276 | + | 0.587643i | ||||
\(557\) | −12.0000 | − | 20.7846i | −0.508456 | − | 0.880672i | −0.999952 | − | 0.00979220i | \(-0.996883\pi\) |
0.491496 | − | 0.870880i | \(-0.336450\pi\) | |||||||
\(558\) | 10.0000 | + | 17.3205i | 0.423334 | + | 0.733236i | ||||
\(559\) | −28.0000 | − | 6.92820i | −1.18427 | − | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | −36.0000 | −1.51722 | −0.758610 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758610 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 27.0000 | − | 46.7654i | 1.13590 | − | 1.96743i | ||||
\(566\) | −15.5000 | − | 26.8468i | −0.651514 | − | 1.12845i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | ||||
\(569\) | −45.0000 | −1.88650 | −0.943249 | − | 0.332086i | \(-0.892248\pi\) | ||||
−0.943249 | + | 0.332086i | \(0.892248\pi\) | |||||||
\(570\) | −6.00000 | − | 10.3923i | −0.251312 | − | 0.435286i | ||||
\(571\) | −4.00000 | + | 6.92820i | −0.167395 | + | 0.289936i | −0.937503 | − | 0.347977i | \(-0.886869\pi\) |
0.770108 | + | 0.637913i | \(0.220202\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | + | 10.3923i | −0.250217 | + | 0.433389i | ||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | 14.0000 | − | 24.2487i | 0.582828 | − | 1.00949i | −0.412315 | − | 0.911041i | \(-0.635280\pi\) |
0.995142 | − | 0.0984456i | \(-0.0313871\pi\) | |||||||
\(578\) | −19.0000 | −0.790296 | ||||||||
\(579\) | −2.50000 | + | 4.33013i | −0.103896 | + | 0.179954i | ||||
\(580\) | 18.0000 | 0.747409 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.00000 | − | 1.73205i | 0.0414513 | − | 0.0717958i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.00000 | − | 1.73205i | 0.0413803 | − | 0.0716728i | ||||
\(585\) | −15.0000 | + | 15.5885i | −0.620174 | + | 0.644503i | ||||
\(586\) | −3.00000 | − | 5.19615i | −0.123929 | − | 0.214651i | ||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | − | 34.6410i | −0.824086 | − | 1.42736i | ||||
\(590\) | 4.50000 | + | 7.79423i | 0.185262 | + | 0.320883i | ||||
\(591\) | 12.0000 | 0.493614 | ||||||||
\(592\) | 8.00000 | 0.328798 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.00000 | − | 12.1244i | −0.286491 | − | 0.496217i | ||||
\(598\) | −7.50000 | + | 7.79423i | −0.306698 | + | 0.318730i | ||||
\(599\) | −1.50000 | + | 2.59808i | −0.0612883 | + | 0.106155i | −0.895042 | − | 0.445983i | \(-0.852854\pi\) |
0.833753 | + | 0.552137i | \(0.186188\pi\) | |||||||
\(600\) | −4.00000 | −0.163299 | ||||||||
\(601\) | −13.0000 | + | 22.5167i | −0.530281 | + | 0.918474i | 0.469095 | + | 0.883148i | \(0.344580\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0.500000 | − | 0.866025i | 0.0203447 | − | 0.0352381i | ||||
\(605\) | −33.0000 | −1.34164 | ||||||||
\(606\) | −3.00000 | + | 5.19615i | −0.121867 | + | 0.211079i | ||||
\(607\) | 5.00000 | − | 8.66025i | 0.202944 | − | 0.351509i | −0.746532 | − | 0.665350i | \(-0.768282\pi\) |
0.949476 | + | 0.313841i | \(0.101616\pi\) | |||||||
\(608\) | −2.00000 | + | 3.46410i | −0.0811107 | + | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33.0000 | −1.33613 | ||||||||
\(611\) | −21.0000 | − | 5.19615i | −0.849569 | − | 0.210214i | ||||
\(612\) | 6.00000 | − | 10.3923i | 0.242536 | − | 0.420084i | ||||
\(613\) | 11.0000 | + | 19.0526i | 0.444286 | + | 0.769526i | 0.998002 | − | 0.0631797i | \(-0.0201241\pi\) |
−0.553716 | + | 0.832705i | \(0.686791\pi\) | |||||||
\(614\) | 13.0000 | 0.524637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | + | 2.59808i | 0.0603877 | + | 0.104595i | 0.894639 | − | 0.446790i | \(-0.147433\pi\) |
−0.834251 | + | 0.551385i | \(0.814100\pi\) | |||||||
\(618\) | 7.00000 | − | 12.1244i | 0.281581 | − | 0.487713i | ||||
\(619\) | 18.5000 | − | 32.0429i | 0.743578 | − | 1.28791i | −0.207279 | − | 0.978282i | \(-0.566461\pi\) |
0.950856 | − | 0.309633i | \(-0.100206\pi\) | |||||||
\(620\) | −30.0000 | −1.20483 | ||||||||
\(621\) | −15.0000 | −0.601929 | ||||||||
\(622\) | −3.00000 | + | 5.19615i | −0.120289 | + | 0.208347i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.50000 | − | 0.866025i | −0.140112 | − | 0.0346688i | ||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 4.00000 | + | 6.92820i | 0.159872 | + | 0.276907i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | + | 1.73205i | −0.0399043 | + | 0.0691164i | ||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.50000 | − | 4.33013i | −0.0995234 | − | 0.172380i | 0.811964 | − | 0.583707i | \(-0.198398\pi\) |
−0.911487 | + | 0.411328i | \(0.865065\pi\) | |||||||
\(632\) | −2.00000 | − | 3.46410i | −0.0795557 | − | 0.137795i | ||||
\(633\) | −4.00000 | −0.158986 | ||||||||
\(634\) | −6.00000 | − | 10.3923i | −0.238290 | − | 0.412731i | ||||
\(635\) | 33.0000 | 1.30957 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | −9.00000 | −0.355479 | −0.177739 | − | 0.984078i | \(-0.556878\pi\) | ||||
−0.177739 | + | 0.984078i | \(0.556878\pi\) | |||||||
\(642\) | −9.00000 | − | 15.5885i | −0.355202 | − | 0.615227i | ||||
\(643\) | −20.5000 | − | 35.5070i | −0.808441 | − | 1.40026i | −0.913943 | − | 0.405842i | \(-0.866978\pi\) |
0.105502 | − | 0.994419i | \(-0.466355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | 0.944999 | ||||||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | 18.0000 | + | 31.1769i | 0.707653 | + | 1.22569i | 0.965726 | + | 0.259565i | \(0.0835793\pi\) |
−0.258073 | + | 0.966126i | \(0.583087\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | − | 13.8564i | −0.156893 | − | 0.543493i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0000 | + | 17.3205i | −0.391630 | + | 0.678323i | ||||
\(653\) | 30.0000 | 1.17399 | 0.586995 | − | 0.809590i | \(-0.300311\pi\) | ||||
0.586995 | + | 0.809590i | \(0.300311\pi\) | |||||||
\(654\) | 16.0000 | 0.625650 | ||||||||
\(655\) | −22.5000 | + | 38.9711i | −0.879148 | + | 1.52273i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | + | 3.46410i | 0.0780274 | + | 0.135147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | − | 5.19615i | −0.116863 | − | 0.202413i | 0.801660 | − | 0.597781i | \(-0.203951\pi\) |
−0.918523 | + | 0.395367i | \(0.870617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5000 | − | 19.9186i | −0.447298 | − | 0.774743i | 0.550911 | − | 0.834564i | \(-0.314280\pi\) |
−0.998209 | + | 0.0598209i | \(0.980947\pi\) | |||||||
\(662\) | −5.00000 | + | 8.66025i | −0.194331 | + | 0.336590i | ||||
\(663\) | −21.0000 | − | 5.19615i | −0.815572 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | + | 13.8564i | −0.309994 | + | 0.536925i | ||||
\(667\) | −9.00000 | + | 15.5885i | −0.348481 | + | 0.603587i | ||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | 3.00000 | − | 5.19615i | 0.115900 | − | 0.200745i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | −14.0000 | −0.539260 | ||||||||
\(675\) | 10.0000 | − | 17.3205i | 0.384900 | − | 0.666667i | ||||
\(676\) | −0.500000 | − | 12.9904i | −0.0192308 | − | 0.499630i | ||||
\(677\) | 25.5000 | + | 44.1673i | 0.980045 | + | 1.69749i | 0.662169 | + | 0.749355i | \(0.269636\pi\) |
0.317876 | + | 0.948132i | \(0.397030\pi\) | |||||||
\(678\) | −9.00000 | + | 15.5885i | −0.345643 | + | 0.598671i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.00000 | + | 15.5885i | 0.345134 | + | 0.597790i | ||||
\(681\) | 7.50000 | + | 12.9904i | 0.287401 | + | 0.497792i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | −4.00000 | − | 6.92820i | −0.152944 | − | 0.264906i | ||||
\(685\) | −4.50000 | − | 7.79423i | −0.171936 | − | 0.297802i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0000 | − | 19.0526i | 0.419676 | − | 0.726900i | ||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | 12.0000 | + | 41.5692i | 0.457164 | + | 1.58366i | ||||
\(690\) | 4.50000 | − | 7.79423i | 0.171312 | − | 0.296721i | ||||
\(691\) | −1.00000 | −0.0380418 | −0.0190209 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190209 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(692\) | −4.50000 | + | 7.79423i | −0.171064 | + | 0.296292i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 24.0000 | − | 41.5692i | 0.910372 | − | 1.57681i | ||||
\(696\) | −6.00000 | −0.227429 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 14.5000 | − | 25.1147i | 0.548833 | − | 0.950607i | ||||
\(699\) | 1.50000 | − | 2.59808i | 0.0567352 | − | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | 12.5000 | − | 12.9904i | 0.471782 | − | 0.490290i | ||||
\(703\) | 16.0000 | − | 27.7128i | 0.603451 | − | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.0000 | 0.677919 | ||||||||
\(706\) | −3.00000 | − | 5.19615i | −0.112906 | − | 0.195560i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.50000 | − | 2.59808i | −0.0563735 | − | 0.0976417i | ||||
\(709\) | 5.00000 | − | 8.66025i | 0.187779 | − | 0.325243i | −0.756730 | − | 0.653727i | \(-0.773204\pi\) |
0.944509 | + | 0.328484i | \(0.106538\pi\) | |||||||
\(710\) | −4.50000 | + | 7.79423i | −0.168882 | + | 0.292512i | ||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 15.0000 | − | 25.9808i | 0.561754 | − | 0.972987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.00000 | − | 5.19615i | −0.112115 | − | 0.194189i | ||||
\(717\) | −10.5000 | − | 18.1865i | −0.392130 | − | 0.679189i | ||||
\(718\) | −4.50000 | − | 7.79423i | −0.167939 | − | 0.290878i | ||||
\(719\) | 24.0000 | − | 41.5692i | 0.895049 | − | 1.55027i | 0.0613050 | − | 0.998119i | \(-0.480474\pi\) |
0.833744 | − | 0.552151i | \(-0.186193\pi\) | |||||||
\(720\) | −6.00000 | −0.223607 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.50000 | − | 2.59808i | −0.0558242 | − | 0.0966904i | ||||
\(723\) | 14.0000 | + | 24.2487i | 0.520666 | + | 0.901819i | ||||
\(724\) | 5.00000 | 0.185824 | ||||||||
\(725\) | −12.0000 | − | 20.7846i | −0.445669 | − | 0.771921i | ||||
\(726\) | 11.0000 | 0.408248 | ||||||||
\(727\) | −52.0000 | −1.92857 | −0.964287 | − | 0.264861i | \(-0.914674\pi\) | ||||
−0.964287 | + | 0.264861i | \(0.914674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | −24.0000 | − | 41.5692i | −0.887672 | − | 1.53749i | ||||
\(732\) | 11.0000 | 0.406572 | ||||||||
\(733\) | −17.5000 | − | 30.3109i | −0.646377 | − | 1.11956i | −0.983982 | − | 0.178270i | \(-0.942950\pi\) |
0.337604 | − | 0.941288i | \(-0.390383\pi\) | |||||||
\(734\) | −5.00000 | − | 8.66025i | −0.184553 | − | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | + | 13.8564i | 0.294285 | + | 0.509716i | 0.974818 | − | 0.223001i | \(-0.0715853\pi\) |
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | −12.0000 | − | 20.7846i | −0.441129 | − | 0.764057i | ||||
\(741\) | −10.0000 | + | 10.3923i | −0.367359 | + | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | + | 41.5692i | −0.880475 | + | 1.52503i | −0.0296605 | + | 0.999560i | \(0.509443\pi\) |
−0.850814 | + | 0.525467i | \(0.823891\pi\) | |||||||
\(744\) | 10.0000 | 0.366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.0000 | − | 27.7128i | 0.585802 | − | 1.01464i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50000 | − | 2.59808i | −0.0547723 | − | 0.0948683i | ||||
\(751\) | 17.0000 | 0.620339 | 0.310169 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310169 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(752\) | −3.00000 | − | 5.19615i | −0.109399 | − | 0.189484i | ||||
\(753\) | −1.50000 | + | 2.59808i | −0.0546630 | + | 0.0946792i | ||||
\(754\) | −6.00000 | − | 20.7846i | −0.218507 | − | 0.756931i | ||||
\(755\) | −3.00000 | −0.109181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | − | 45.0333i | 0.944986 | − | 1.63676i | 0.189207 | − | 0.981937i | \(-0.439408\pi\) |
0.755779 | − | 0.654827i | \(-0.227258\pi\) | |||||||
\(758\) | −14.0000 | + | 24.2487i | −0.508503 | + | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | −6.00000 | + | 10.3923i | −0.217500 | + | 0.376721i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(762\) | −11.0000 | −0.398488 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.0000 | − | 20.7846i | 0.434145 | − | 0.751961i | ||||
\(765\) | −36.0000 | −1.30158 | ||||||||
\(766\) | −3.00000 | + | 5.19615i | −0.108394 | + | 0.187745i | ||||
\(767\) | 7.50000 | − | 7.79423i | 0.270809 | − | 0.281433i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | + | 5.19615i | 0.108042 | + | 0.187135i | ||||
\(772\) | −2.50000 | − | 4.33013i | −0.0899770 | − | 0.155845i | ||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | 16.0000 | 0.575108 | ||||||||
\(775\) | 20.0000 | + | 34.6410i | 0.718421 | + | 1.24434i | ||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0000 | + | 25.9808i | −0.537776 | + | 0.931455i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.00000 | + | 10.3923i | 0.107417 | + | 0.372104i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 15.0000 | − | 25.9808i | 0.536056 | − | 0.928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.00000 | 0.214149 | ||||||||
\(786\) | 7.50000 | − | 12.9904i | 0.267516 | − | 0.463352i | ||||
\(787\) | 53.0000 | 1.88925 | 0.944623 | − | 0.328158i | \(-0.106428\pi\) | ||||
0.944623 | + | 0.328158i | \(0.106428\pi\) | |||||||
\(788\) | −6.00000 | + | 10.3923i | −0.213741 | + | 0.370211i | ||||
\(789\) | 13.5000 | − | 23.3827i | 0.480613 | − | 0.832446i | ||||
\(790\) | −6.00000 | + | 10.3923i | −0.213470 | + | 0.369742i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.0000 | + | 38.1051i | 0.390621 | + | 1.35315i | ||||
\(794\) | −3.50000 | + | 6.06218i | −0.124210 | + | 0.215139i | ||||
\(795\) | −18.0000 | − | 31.1769i | −0.638394 | − | 1.10573i | ||||
\(796\) | 14.0000 | 0.496217 | ||||||||
\(797\) | 7.50000 | + | 12.9904i | 0.265664 | + | 0.460143i | 0.967737 | − | 0.251961i | \(-0.0810756\pi\) |
−0.702074 | + | 0.712104i | \(0.747742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 2.00000 | − | 3.46410i | 0.0707107 | − | 0.122474i | ||||
\(801\) | −6.00000 | + | 10.3923i | −0.212000 | + | 0.367194i | ||||
\(802\) | −6.00000 | −0.211867 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.00000 | + | 1.73205i | −0.0352673 | + | 0.0610847i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0000 | + | 34.6410i | 0.352235 | + | 1.22018i | ||||
\(807\) | −4.50000 | − | 7.79423i | −0.158408 | − | 0.274370i | ||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | 21.0000 | + | 36.3731i | 0.738321 | + | 1.27881i | 0.953251 | + | 0.302180i | \(0.0977142\pi\) |
−0.214930 | + | 0.976629i | \(0.568952\pi\) | |||||||
\(810\) | 1.50000 | − | 2.59808i | 0.0527046 | − | 0.0912871i | ||||
\(811\) | −19.0000 | −0.667180 | −0.333590 | − | 0.942718i | \(-0.608260\pi\) | ||||
−0.333590 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.00000 | − | 1.73205i | −0.0350715 | − | 0.0607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60.0000 | 2.10171 | ||||||||
\(816\) | −3.00000 | − | 5.19615i | −0.105021 | − | 0.181902i | ||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | 0.418803 | 0.209401 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209401 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(822\) | 1.50000 | + | 2.59808i | 0.0523185 | + | 0.0906183i | ||||
\(823\) | −13.0000 | −0.453152 | −0.226576 | − | 0.973994i | \(-0.572753\pi\) | ||||
−0.226576 | + | 0.973994i | \(0.572753\pi\) | |||||||
\(824\) | 7.00000 | + | 12.1244i | 0.243857 | + | 0.422372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0000 | 0.834562 | 0.417281 | − | 0.908778i | \(-0.362983\pi\) | ||||
0.417281 | + | 0.908778i | \(0.362983\pi\) | |||||||
\(828\) | 3.00000 | − | 5.19615i | 0.104257 | − | 0.180579i | ||||
\(829\) | 12.5000 | + | 21.6506i | 0.434143 | + | 0.751958i | 0.997225 | − | 0.0744432i | \(-0.0237179\pi\) |
−0.563082 | + | 0.826401i | \(0.690385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.0000 | − | 22.5167i | −0.450965 | − | 0.781094i | ||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.00000 | + | 13.8564i | −0.277017 | + | 0.479808i | ||||
\(835\) | −36.0000 | −1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0000 | + | 43.3013i | −0.864126 | + | 1.49671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0000 | + | 46.7654i | 0.932144 | + | 1.61452i | 0.779650 | + | 0.626215i | \(0.215397\pi\) |
0.152493 | + | 0.988304i | \(0.451270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −26.0000 | −0.896019 | ||||||||
\(843\) | −9.00000 | − | 15.5885i | −0.309976 | − | 0.536895i | ||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | −33.0000 | + | 20.7846i | −1.13523 | + | 0.715012i | ||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | + | 10.3923i | −0.206041 | + | 0.356873i | ||||
\(849\) | 15.5000 | − | 26.8468i | 0.531959 | − | 0.921379i | ||||
\(850\) | 12.0000 | − | 20.7846i | 0.411597 | − | 0.712906i | ||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 1.50000 | − | 2.59808i | 0.0513892 | − | 0.0890086i | ||||
\(853\) | 17.0000 | 0.582069 | 0.291034 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291034 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | + | 20.7846i | −0.410391 | + | 0.710819i | ||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | −12.0000 | + | 20.7846i | −0.409197 | + | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.5000 | − | 28.5788i | −0.561992 | − | 0.973399i | ||||
\(863\) | 28.5000 | + | 49.3634i | 0.970151 | + | 1.68035i | 0.695087 | + | 0.718925i | \(0.255366\pi\) |
0.275064 | + | 0.961426i | \(0.411301\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 27.0000 | 0.918028 | ||||||||
\(866\) | −2.00000 | − | 3.46410i | −0.0679628 | − | 0.117715i | ||||
\(867\) | −9.50000 | − | 16.4545i | −0.322637 | − | 0.558824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 9.00000 | + | 15.5885i | 0.305129 | + | 0.528498i | ||||
\(871\) | −7.00000 | − | 1.73205i | −0.237186 | − | 0.0586883i | ||||
\(872\) | −8.00000 | + | 13.8564i | −0.270914 | + | 0.469237i | ||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | −6.00000 | + | 10.3923i | −0.202953 | + | 0.351525i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 11.0000 | − | 19.0526i | 0.371444 | − | 0.643359i | −0.618344 | − | 0.785907i | \(-0.712196\pi\) |
0.989788 | + | 0.142548i | \(0.0455296\pi\) | |||||||
\(878\) | −14.0000 | −0.472477 | ||||||||
\(879\) | 3.00000 | − | 5.19615i | 0.101187 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.00000 | − | 5.19615i | 0.101073 | − | 0.175063i | −0.811054 | − | 0.584971i | \(-0.801106\pi\) |
0.912127 | + | 0.409908i | \(0.134439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 15.0000 | − | 15.5885i | 0.504505 | − | 0.524297i | ||||
\(885\) | −4.50000 | + | 7.79423i | −0.151266 | + | 0.262000i | ||||
\(886\) | 9.00000 | + | 15.5885i | 0.302361 | + | 0.523704i | ||||
\(887\) | 12.0000 | 0.402921 | 0.201460 | − | 0.979497i | \(-0.435431\pi\) | ||||
0.201460 | + | 0.979497i | \(0.435431\pi\) | |||||||
\(888\) | 4.00000 | + | 6.92820i | 0.134231 | + | 0.232495i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.00000 | − | 15.5885i | −0.301681 | − | 0.522526i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | + | 6.92820i | −0.133930 | + | 0.231973i | ||||
\(893\) | −24.0000 | −0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00000 | + | 15.5885i | −0.300837 | + | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.5000 | − | 2.59808i | −0.350585 | − | 0.0867472i | ||||
\(898\) | 4.50000 | + | 7.79423i | 0.150167 | + | 0.260097i | ||||
\(899\) | 30.0000 | + | 51.9615i | 1.00056 | + | 1.73301i | ||||
\(900\) | 4.00000 | + | 6.92820i | 0.133333 | + | 0.230940i | ||||
\(901\) | −36.0000 | + | 62.3538i | −1.19933 | + | 2.07731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.00000 | − | 15.5885i | −0.299336 | − | 0.518464i | ||||
\(905\) | −7.50000 | − | 12.9904i | −0.249308 | − | 0.431815i | ||||
\(906\) | 1.00000 | 0.0332228 | ||||||||
\(907\) | −7.00000 | − | 12.1244i | −0.232431 | − | 0.402583i | 0.726092 | − | 0.687598i | \(-0.241335\pi\) |
−0.958523 | + | 0.285015i | \(0.908001\pi\) | |||||||
\(908\) | −15.0000 | −0.497792 | ||||||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.0000 | 0.695761 | 0.347881 | − | 0.937539i | \(-0.386901\pi\) | ||||
0.347881 | + | 0.937539i | \(0.386901\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −29.0000 | −0.959235 | ||||||||
\(915\) | −16.5000 | − | 28.5788i | −0.545473 | − | 0.944787i | ||||
\(916\) | 11.0000 | + | 19.0526i | 0.363450 | + | 0.629514i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 30.0000 | 0.990148 | ||||||||
\(919\) | 3.50000 | − | 6.06218i | 0.115454 | − | 0.199973i | −0.802507 | − | 0.596643i | \(-0.796501\pi\) |
0.917961 | + | 0.396670i | \(0.129834\pi\) | |||||||
\(920\) | 4.50000 | + | 7.79423i | 0.148361 | + | 0.256968i | ||||
\(921\) | 6.50000 | + | 11.2583i | 0.214182 | + | 0.370975i | ||||
\(922\) | 10.5000 | + | 18.1865i | 0.345799 | + | 0.598942i | ||||
\(923\) | 10.5000 | + | 2.59808i | 0.345612 | + | 0.0855167i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | + | 27.7128i | −0.526077 | + | 0.911192i | ||||
\(926\) | 31.0000 | 1.01872 | ||||||||
\(927\) | −28.0000 | −0.919641 | ||||||||
\(928\) | 3.00000 | − | 5.19615i | 0.0984798 | − | 0.170572i | ||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | −15.0000 | − | 25.9808i | −0.491869 | − | 0.851943i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | + | 2.59808i | 0.0491341 | + | 0.0851028i | ||||
\(933\) | −6.00000 | −0.196431 | ||||||||
\(934\) | −1.50000 | − | 2.59808i | −0.0490815 | − | 0.0850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | + | 6.92820i | 0.0653720 | + | 0.226455i | ||||
\(937\) | 8.00000 | 0.261349 | 0.130674 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130674 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.00000 | + | 6.92820i | −0.130535 | + | 0.226093i | ||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | −7.50000 | + | 12.9904i | −0.244493 | + | 0.423474i | −0.961989 | − | 0.273088i | \(-0.911955\pi\) |
0.717496 | + | 0.696563i | \(0.245288\pi\) | |||||||
\(942\) | −2.00000 | −0.0651635 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0000 | −1.36482 | −0.682408 | − | 0.730971i | \(-0.739067\pi\) | ||||
−0.682408 | + | 0.730971i | \(0.739067\pi\) | |||||||
\(948\) | 2.00000 | − | 3.46410i | 0.0649570 | − | 0.112509i | ||||
\(949\) | 2.00000 | + | 6.92820i | 0.0649227 | + | 0.224899i | ||||
\(950\) | −8.00000 | − | 13.8564i | −0.259554 | − | 0.449561i | ||||
\(951\) | 6.00000 | − | 10.3923i | 0.194563 | − | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.50000 | + | 12.9904i | 0.242949 | + | 0.420800i | 0.961553 | − | 0.274620i | \(-0.0885520\pi\) |
−0.718604 | + | 0.695419i | \(0.755219\pi\) | |||||||
\(954\) | −12.0000 | − | 20.7846i | −0.388514 | − | 0.672927i | ||||
\(955\) | −72.0000 | −2.32987 | ||||||||
\(956\) | 21.0000 | 0.679189 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.0000 | + | 25.9808i | 0.484628 | + | 0.839400i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.50000 | + | 2.59808i | −0.0484123 | + | 0.0838525i | ||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | −20.0000 | + | 20.7846i | −0.644826 | + | 0.670123i | ||||
\(963\) | −18.0000 | + | 31.1769i | −0.580042 | + | 1.00466i | ||||
\(964\) | −28.0000 | −0.901819 | ||||||||
\(965\) | −7.50000 | + | 12.9904i | −0.241434 | + | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | −5.50000 | + | 9.52628i | −0.176777 | + | 0.306186i | ||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 3.00000 | − | 5.19615i | 0.0963242 | − | 0.166838i | ||||
\(971\) | −1.50000 | + | 2.59808i | −0.0481373 | + | 0.0833762i | −0.889090 | − | 0.457732i | \(-0.848662\pi\) |
0.840953 | + | 0.541108i | \(0.181995\pi\) | |||||||
\(972\) | −8.00000 | + | 13.8564i | −0.256600 | + | 0.444444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.0000 | 0.416547 | ||||||||
\(975\) | 10.0000 | − | 10.3923i | 0.320256 | − | 0.332820i | ||||
\(976\) | −5.50000 | + | 9.52628i | −0.176051 | + | 0.304929i | ||||
\(977\) | −19.5000 | − | 33.7750i | −0.623860 | − | 1.08056i | −0.988760 | − | 0.149511i | \(-0.952230\pi\) |
0.364900 | − | 0.931047i | \(-0.381103\pi\) | |||||||
\(978\) | −20.0000 | −0.639529 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | − | 27.7128i | −0.510841 | − | 0.884802i | ||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | 15.0000 | − | 25.9808i | 0.478426 | − | 0.828658i | −0.521268 | − | 0.853393i | \(-0.674541\pi\) |
0.999694 | + | 0.0247352i | \(0.00787426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | 1.14706 | ||||||||
\(986\) | 18.0000 | − | 31.1769i | 0.573237 | − | 0.992875i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.00000 | − | 13.8564i | −0.127257 | − | 0.440831i | ||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.50000 | − | 14.7224i | −0.270011 | − | 0.467673i | 0.698853 | − | 0.715265i | \(-0.253694\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | −5.00000 | + | 8.66025i | −0.158750 | + | 0.274963i | ||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | − | 36.3731i | −0.665745 | − | 1.15310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.0000 | 1.10846 | 0.554231 | − | 0.832363i | \(-0.313013\pi\) | ||||
0.554231 | + | 0.832363i | \(0.313013\pi\) | |||||||
\(998\) | −11.0000 | − | 19.0526i | −0.348199 | − | 0.603098i | ||||
\(999\) | −40.0000 | −1.26554 |
(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 | 1274.2.e.d.165.1 | 2 | ||
7.2 | even | 3 | 1274.2.h.j.373.1 | 2 | |||
7.3 | odd | 6 | 1274.2.g.g.295.1 | 2 | |||
7.4 | even | 3 | 182.2.g.b.113.1 | yes | 2 | ||
7.5 | odd | 6 | 1274.2.h.i.373.1 | 2 | |||
7.6 | odd | 2 | 1274.2.e.i.165.1 | 2 | |||
13.3 | even | 3 | 1274.2.h.j.263.1 | 2 | |||
21.11 | odd | 6 | 1638.2.r.c.1387.1 | 2 | |||
28.11 | odd | 6 | 1456.2.s.e.113.1 | 2 | |||
91.3 | odd | 6 | 1274.2.g.g.393.1 | 2 | |||
91.4 | even | 6 | 2366.2.a.n.1.1 | 1 | |||
91.16 | even | 3 | inner | 1274.2.e.d.471.1 | 2 | ||
91.32 | odd | 12 | 2366.2.d.f.337.2 | 2 | |||
91.46 | odd | 12 | 2366.2.d.f.337.1 | 2 | |||
91.55 | odd | 6 | 1274.2.h.i.263.1 | 2 | |||
91.68 | odd | 6 | 1274.2.e.i.471.1 | 2 | |||
91.74 | even | 3 | 2366.2.a.f.1.1 | 1 | |||
91.81 | even | 3 | 182.2.g.b.29.1 | ✓ | 2 | ||
273.263 | odd | 6 | 1638.2.r.c.757.1 | 2 | |||
364.263 | odd | 6 | 1456.2.s.e.1121.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.g.b.29.1 | ✓ | 2 | 91.81 | even | 3 | ||
182.2.g.b.113.1 | yes | 2 | 7.4 | even | 3 | ||
1274.2.e.d.165.1 | 2 | 1.1 | even | 1 | trivial | ||
1274.2.e.d.471.1 | 2 | 91.16 | even | 3 | inner | ||
1274.2.e.i.165.1 | 2 | 7.6 | odd | 2 | |||
1274.2.e.i.471.1 | 2 | 91.68 | odd | 6 | |||
1274.2.g.g.295.1 | 2 | 7.3 | odd | 6 | |||
1274.2.g.g.393.1 | 2 | 91.3 | odd | 6 | |||
1274.2.h.i.263.1 | 2 | 91.55 | odd | 6 | |||
1274.2.h.i.373.1 | 2 | 7.5 | odd | 6 | |||
1274.2.h.j.263.1 | 2 | 13.3 | even | 3 | |||
1274.2.h.j.373.1 | 2 | 7.2 | even | 3 | |||
1456.2.s.e.113.1 | 2 | 28.11 | odd | 6 | |||
1456.2.s.e.1121.1 | 2 | 364.263 | odd | 6 | |||
1638.2.r.c.757.1 | 2 | 273.263 | odd | 6 | |||
1638.2.r.c.1387.1 | 2 | 21.11 | odd | 6 | |||
2366.2.a.f.1.1 | 1 | 91.74 | even | 3 | |||
2366.2.a.n.1.1 | 1 | 91.4 | even | 6 | |||
2366.2.d.f.337.1 | 2 | 91.46 | odd | 12 | |||
2366.2.d.f.337.2 | 2 | 91.32 | odd | 12 |