Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.o.1351.4 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − 0.464102i | − 0.139932i | −0.997549 | − | 0.0699660i | \(-0.977711\pi\) | ||||
0.997549 | − | 0.0699660i | \(-0.0222891\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 0.535898i | − 0.122944i | −0.998109 | − | 0.0614718i | \(-0.980421\pi\) | ||||
0.998109 | − | 0.0614718i | \(-0.0195794\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 2.00000i | − 0.436436i | ||||||||
\(22\) | −0.464102 | −0.0989468 | ||||||||
\(23\) | 0.267949 | 0.0558713 | 0.0279356 | − | 0.999610i | \(-0.491107\pi\) | ||||
0.0279356 | + | 0.999610i | \(0.491107\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − 2.00000i | − 0.377964i | ||||||||
\(29\) | 3.73205 | 0.693024 | 0.346512 | − | 0.938045i | \(-0.387366\pi\) | ||||
0.346512 | + | 0.938045i | \(0.387366\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 1.73205i | − 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0.464102i | 0.0807897i | ||||||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 1.19615i | − 0.196646i | −0.995155 | − | 0.0983231i | \(-0.968652\pi\) | ||||
0.995155 | − | 0.0983231i | \(-0.0313479\pi\) | |||||||
\(38\) | −0.535898 | −0.0869342 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −1.92820 | −0.294048 | −0.147024 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147024 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(44\) | 0.464102i | 0.0699660i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | − 0.267949i | − 0.0395070i | ||||||||
\(47\) | 10.4641i | 1.52635i | 0.646194 | + | 0.763173i | \(0.276360\pi\) | ||||
−0.646194 | + | 0.763173i | \(0.723640\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.9282 | −1.77583 | −0.887913 | − | 0.460012i | \(-0.847845\pi\) | ||||
−0.887913 | + | 0.460012i | \(0.847845\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −0.464102 | −0.0625794 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 0.535898i | 0.0709815i | ||||||||
\(58\) | − 3.73205i | − 0.490042i | ||||||||
\(59\) | − 1.53590i | − 0.199957i | −0.994990 | − | 0.0999785i | \(-0.968123\pi\) | ||||
0.994990 | − | 0.0999785i | \(-0.0318774\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | 10.3923 | 1.33060 | 0.665299 | − | 0.746577i | \(-0.268304\pi\) | ||||
0.665299 | + | 0.746577i | \(0.268304\pi\) | |||||||
\(62\) | −1.73205 | −0.219971 | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.464102 | 0.0571270 | ||||||||
\(67\) | − 4.53590i | − 0.554148i | −0.960849 | − | 0.277074i | \(-0.910635\pi\) | ||||
0.960849 | − | 0.277074i | \(-0.0893647\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −0.267949 | −0.0322573 | ||||||||
\(70\) | − 2.00000i | − 0.239046i | ||||||||
\(71\) | − 8.39230i | − 0.995983i | −0.867182 | − | 0.497992i | \(-0.834071\pi\) | ||||
0.867182 | − | 0.497992i | \(-0.165929\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 2.00000i | − 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | −1.19615 | −0.139050 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.535898i | 0.0614718i | ||||||||
\(77\) | 0.928203 | 0.105779 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0717968 | −0.00807777 | −0.00403888 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00403888 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | 4.92820i | 0.540941i | 0.962728 | + | 0.270470i | \(0.0871792\pi\) | ||||
−0.962728 | + | 0.270470i | \(0.912821\pi\) | |||||||
\(84\) | 2.00000i | 0.218218i | ||||||||
\(85\) | 4.00000i | 0.433861i | ||||||||
\(86\) | 1.92820i | 0.207924i | ||||||||
\(87\) | −3.73205 | −0.400118 | ||||||||
\(88\) | 0.464102 | 0.0494734 | ||||||||
\(89\) | − 7.46410i | − 0.791193i | −0.918424 | − | 0.395597i | \(-0.870538\pi\) | ||||
0.918424 | − | 0.395597i | \(-0.129462\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.267949 | −0.0279356 | ||||||||
\(93\) | 1.73205i | 0.179605i | ||||||||
\(94\) | 10.4641 | 1.07929 | ||||||||
\(95\) | −0.535898 | −0.0549820 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − 7.46410i | − 0.757865i | −0.925424 | − | 0.378932i | \(-0.876291\pi\) | ||||
0.925424 | − | 0.378932i | \(-0.123709\pi\) | |||||||
\(98\) | − 3.00000i | − 0.303046i | ||||||||
\(99\) | − 0.464102i | − 0.0466440i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.9282 | −1.08740 | −0.543698 | − | 0.839281i | \(-0.682976\pi\) | ||||
−0.543698 | + | 0.839281i | \(0.682976\pi\) | |||||||
\(102\) | − 4.00000i | − 0.396059i | ||||||||
\(103\) | 15.8564 | 1.56238 | 0.781189 | − | 0.624295i | \(-0.214613\pi\) | ||||
0.781189 | + | 0.624295i | \(0.214613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 12.9282i | 1.25570i | ||||||||
\(107\) | 19.8564 | 1.91959 | 0.959796 | − | 0.280700i | \(-0.0905665\pi\) | ||||
0.959796 | + | 0.280700i | \(0.0905665\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 11.8564i | − 1.13564i | −0.823154 | − | 0.567819i | \(-0.807787\pi\) | ||||
0.823154 | − | 0.567819i | \(-0.192213\pi\) | |||||||
\(110\) | 0.464102i | 0.0442504i | ||||||||
\(111\) | 1.19615i | 0.113534i | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 11.1962 | 1.05325 | 0.526623 | − | 0.850099i | \(-0.323458\pi\) | ||||
0.526623 | + | 0.850099i | \(0.323458\pi\) | |||||||
\(114\) | 0.535898 | 0.0501915 | ||||||||
\(115\) | − 0.267949i | − 0.0249864i | ||||||||
\(116\) | −3.73205 | −0.346512 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.53590 | −0.141391 | ||||||||
\(119\) | − 8.00000i | − 0.733359i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 10.7846 | 0.980419 | ||||||||
\(122\) | − 10.3923i | − 0.940875i | ||||||||
\(123\) | − 2.00000i | − 0.180334i | ||||||||
\(124\) | 1.73205i | 0.155543i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 8.92820 | 0.792250 | 0.396125 | − | 0.918197i | \(-0.370355\pi\) | ||||
0.396125 | + | 0.918197i | \(0.370355\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 1.92820 | 0.169769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.33975 | −0.117054 | −0.0585271 | − | 0.998286i | \(-0.518640\pi\) | ||||
−0.0585271 | + | 0.998286i | \(0.518640\pi\) | |||||||
\(132\) | − 0.464102i | − 0.0403949i | ||||||||
\(133\) | 1.07180 | 0.0929366 | ||||||||
\(134\) | −4.53590 | −0.391842 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 4.00000i | − 0.342997i | ||||||||
\(137\) | − 4.46410i | − 0.381394i | −0.981649 | − | 0.190697i | \(-0.938925\pi\) | ||||
0.981649 | − | 0.190697i | \(-0.0610748\pi\) | |||||||
\(138\) | 0.267949i | 0.0228093i | ||||||||
\(139\) | 0.928203 | 0.0787292 | 0.0393646 | − | 0.999225i | \(-0.487467\pi\) | ||||
0.0393646 | + | 0.999225i | \(0.487467\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | − 10.4641i | − 0.881236i | ||||||||
\(142\) | −8.39230 | −0.704267 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 3.73205i | − 0.309930i | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 1.19615i | 0.0983231i | ||||||||
\(149\) | 20.4641i | 1.67648i | 0.545298 | + | 0.838242i | \(0.316416\pi\) | ||||
−0.545298 | + | 0.838242i | \(0.683584\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 10.3923i | − 0.845714i | −0.906196 | − | 0.422857i | \(-0.861027\pi\) | ||||
0.906196 | − | 0.422857i | \(-0.138973\pi\) | |||||||
\(152\) | 0.535898 | 0.0434671 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | − 0.928203i | − 0.0747967i | ||||||||
\(155\) | −1.73205 | −0.139122 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | −0.399043 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(158\) | 0.0717968i | 0.00571184i | ||||||||
\(159\) | 12.9282 | 1.02527 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.535898i | 0.0422347i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 23.0526i | 1.80562i | 0.430044 | + | 0.902808i | \(0.358498\pi\) | ||||
−0.430044 | + | 0.902808i | \(0.641502\pi\) | |||||||
\(164\) | − 2.00000i | − 0.156174i | ||||||||
\(165\) | 0.464102 | 0.0361303 | ||||||||
\(166\) | 4.92820 | 0.382503 | ||||||||
\(167\) | − 18.3205i | − 1.41768i | −0.705368 | − | 0.708842i | \(-0.749218\pi\) | ||||
0.705368 | − | 0.708842i | \(-0.250782\pi\) | |||||||
\(168\) | 2.00000 | 0.154303 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | − 0.535898i | − 0.0409812i | ||||||||
\(172\) | 1.92820 | 0.147024 | ||||||||
\(173\) | −2.92820 | −0.222627 | −0.111314 | − | 0.993785i | \(-0.535506\pi\) | ||||
−0.111314 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(174\) | 3.73205i | 0.282926i | ||||||||
\(175\) | − 2.00000i | − 0.151186i | ||||||||
\(176\) | − 0.464102i | − 0.0349830i | ||||||||
\(177\) | 1.53590i | 0.115445i | ||||||||
\(178\) | −7.46410 | −0.559458 | ||||||||
\(179\) | −16.2679 | −1.21592 | −0.607962 | − | 0.793966i | \(-0.708013\pi\) | ||||
−0.607962 | + | 0.793966i | \(0.708013\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 10.9282 | 0.812287 | 0.406143 | − | 0.913809i | \(-0.366873\pi\) | ||||
0.406143 | + | 0.913809i | \(0.366873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3923 | −0.768221 | ||||||||
\(184\) | 0.267949i | 0.0197535i | ||||||||
\(185\) | −1.19615 | −0.0879429 | ||||||||
\(186\) | 1.73205 | 0.127000 | ||||||||
\(187\) | 1.85641i | 0.135754i | ||||||||
\(188\) | − 10.4641i | − 0.763173i | ||||||||
\(189\) | − 2.00000i | − 0.145479i | ||||||||
\(190\) | 0.535898i | 0.0388782i | ||||||||
\(191\) | 14.5359 | 1.05178 | 0.525890 | − | 0.850552i | \(-0.323732\pi\) | ||||
0.525890 | + | 0.850552i | \(0.323732\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 23.3205i | − 1.67865i | −0.543632 | − | 0.839323i | \(-0.682951\pi\) | ||||
0.543632 | − | 0.839323i | \(-0.317049\pi\) | |||||||
\(194\) | −7.46410 | −0.535891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − 16.3923i | − 1.16790i | −0.811788 | − | 0.583952i | \(-0.801506\pi\) | ||||
0.811788 | − | 0.583952i | \(-0.198494\pi\) | |||||||
\(198\) | −0.464102 | −0.0329823 | ||||||||
\(199\) | −18.9282 | −1.34178 | −0.670892 | − | 0.741555i | \(-0.734089\pi\) | ||||
−0.670892 | + | 0.741555i | \(0.734089\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 4.53590i | 0.319938i | ||||||||
\(202\) | 10.9282i | 0.768906i | ||||||||
\(203\) | 7.46410i | 0.523877i | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | − 15.8564i | − 1.10477i | ||||||||
\(207\) | 0.267949 | 0.0186238 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.248711 | −0.0172037 | ||||||||
\(210\) | 2.00000i | 0.138013i | ||||||||
\(211\) | 23.3205 | 1.60545 | 0.802725 | − | 0.596349i | \(-0.203383\pi\) | ||||
0.802725 | + | 0.596349i | \(0.203383\pi\) | |||||||
\(212\) | 12.9282 | 0.887913 | ||||||||
\(213\) | 8.39230i | 0.575031i | ||||||||
\(214\) | − 19.8564i | − 1.35736i | ||||||||
\(215\) | 1.92820i | 0.131502i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 3.46410 | 0.235159 | ||||||||
\(218\) | −11.8564 | −0.803017 | ||||||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 0.464102 | 0.0312897 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.19615 | 0.0802805 | ||||||||
\(223\) | − 27.4641i | − 1.83913i | −0.392935 | − | 0.919566i | \(-0.628540\pi\) | ||||
0.392935 | − | 0.919566i | \(-0.371460\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 11.1962i | − 0.744757i | ||||||||
\(227\) | − 4.39230i | − 0.291528i | −0.989319 | − | 0.145764i | \(-0.953436\pi\) | ||||
0.989319 | − | 0.145764i | \(-0.0465639\pi\) | |||||||
\(228\) | − 0.535898i | − 0.0354907i | ||||||||
\(229\) | − 19.8564i | − 1.31215i | −0.754696 | − | 0.656074i | \(-0.772216\pi\) | ||||
0.754696 | − | 0.656074i | \(-0.227784\pi\) | |||||||
\(230\) | −0.267949 | −0.0176680 | ||||||||
\(231\) | −0.928203 | −0.0610713 | ||||||||
\(232\) | 3.73205i | 0.245021i | ||||||||
\(233\) | −18.1244 | −1.18737 | −0.593683 | − | 0.804699i | \(-0.702327\pi\) | ||||
−0.593683 | + | 0.804699i | \(0.702327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4641 | 0.682603 | ||||||||
\(236\) | 1.53590i | 0.0999785i | ||||||||
\(237\) | 0.0717968 | 0.00466370 | ||||||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | − 4.39230i | − 0.284115i | −0.989858 | − | 0.142057i | \(-0.954628\pi\) | ||||
0.989858 | − | 0.142057i | \(-0.0453717\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | − 14.2679i | − 0.919079i | −0.888157 | − | 0.459540i | \(-0.848014\pi\) | ||||
0.888157 | − | 0.459540i | \(-0.151986\pi\) | |||||||
\(242\) | − 10.7846i | − 0.693261i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.3923 | −0.665299 | ||||||||
\(245\) | − 3.00000i | − 0.191663i | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.73205 | 0.109985 | ||||||||
\(249\) | − 4.92820i | − 0.312312i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 12.2679 | 0.774346 | 0.387173 | − | 0.922007i | \(-0.373452\pi\) | ||||
0.387173 | + | 0.922007i | \(0.373452\pi\) | |||||||
\(252\) | − 2.00000i | − 0.125988i | ||||||||
\(253\) | − 0.124356i | − 0.00781817i | ||||||||
\(254\) | − 8.92820i | − 0.560205i | ||||||||
\(255\) | − 4.00000i | − 0.250490i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.6603 | −1.41351 | −0.706754 | − | 0.707459i | \(-0.749841\pi\) | ||||
−0.706754 | + | 0.707459i | \(0.749841\pi\) | |||||||
\(258\) | − 1.92820i | − 0.120045i | ||||||||
\(259\) | 2.39230 | 0.148651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.73205 | 0.231008 | ||||||||
\(262\) | 1.33975i | 0.0827698i | ||||||||
\(263\) | −18.1244 | −1.11760 | −0.558798 | − | 0.829304i | \(-0.688737\pi\) | ||||
−0.558798 | + | 0.829304i | \(0.688737\pi\) | |||||||
\(264\) | −0.464102 | −0.0285635 | ||||||||
\(265\) | 12.9282i | 0.794173i | ||||||||
\(266\) | − 1.07180i | − 0.0657161i | ||||||||
\(267\) | 7.46410i | 0.456796i | ||||||||
\(268\) | 4.53590i | 0.277074i | ||||||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 9.19615i | − 0.558626i | −0.960200 | − | 0.279313i | \(-0.909893\pi\) | ||||
0.960200 | − | 0.279313i | \(-0.0901068\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.46410 | −0.269686 | ||||||||
\(275\) | 0.464102i | 0.0279864i | ||||||||
\(276\) | 0.267949 | 0.0161286 | ||||||||
\(277\) | 9.92820 | 0.596528 | 0.298264 | − | 0.954483i | \(-0.403592\pi\) | ||||
0.298264 | + | 0.954483i | \(0.403592\pi\) | |||||||
\(278\) | − 0.928203i | − 0.0556699i | ||||||||
\(279\) | − 1.73205i | − 0.103695i | ||||||||
\(280\) | 2.00000i | 0.119523i | ||||||||
\(281\) | − 4.92820i | − 0.293992i | −0.989137 | − | 0.146996i | \(-0.953040\pi\) | ||||
0.989137 | − | 0.146996i | \(-0.0469604\pi\) | |||||||
\(282\) | −10.4641 | −0.623128 | ||||||||
\(283\) | 3.92820 | 0.233507 | 0.116754 | − | 0.993161i | \(-0.462751\pi\) | ||||
0.116754 | + | 0.993161i | \(0.462751\pi\) | |||||||
\(284\) | 8.39230i | 0.497992i | ||||||||
\(285\) | 0.535898 | 0.0317439 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −3.73205 | −0.219154 | ||||||||
\(291\) | 7.46410i | 0.437553i | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | 4.14359i | 0.242071i | 0.992648 | + | 0.121036i | \(0.0386215\pi\) | ||||
−0.992648 | + | 0.121036i | \(0.961378\pi\) | |||||||
\(294\) | 3.00000i | 0.174964i | ||||||||
\(295\) | −1.53590 | −0.0894235 | ||||||||
\(296\) | 1.19615 | 0.0695249 | ||||||||
\(297\) | 0.464102i | 0.0269299i | ||||||||
\(298\) | 20.4641 | 1.18545 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − 3.85641i | − 0.222280i | ||||||||
\(302\) | −10.3923 | −0.598010 | ||||||||
\(303\) | 10.9282 | 0.627809 | ||||||||
\(304\) | − 0.535898i | − 0.0307359i | ||||||||
\(305\) | − 10.3923i | − 0.595062i | ||||||||
\(306\) | 4.00000i | 0.228665i | ||||||||
\(307\) | − 12.5359i | − 0.715462i | −0.933825 | − | 0.357731i | \(-0.883551\pi\) | ||||
0.933825 | − | 0.357731i | \(-0.116449\pi\) | |||||||
\(308\) | −0.928203 | −0.0528893 | ||||||||
\(309\) | −15.8564 | −0.902039 | ||||||||
\(310\) | 1.73205i | 0.0983739i | ||||||||
\(311\) | −7.60770 | −0.431393 | −0.215696 | − | 0.976460i | \(-0.569202\pi\) | ||||
−0.215696 | + | 0.976460i | \(0.569202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0000 | −1.58265 | −0.791327 | − | 0.611393i | \(-0.790609\pi\) | ||||
−0.791327 | + | 0.611393i | \(0.790609\pi\) | |||||||
\(314\) | 5.00000i | 0.282166i | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 0.0717968 | 0.00403888 | ||||||||
\(317\) | − 21.4641i | − 1.20554i | −0.797913 | − | 0.602772i | \(-0.794063\pi\) | ||||
0.797913 | − | 0.602772i | \(-0.205937\pi\) | |||||||
\(318\) | − 12.9282i | − 0.724978i | ||||||||
\(319\) | − 1.73205i | − 0.0969762i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −19.8564 | −1.10828 | ||||||||
\(322\) | 0.535898 | 0.0298644 | ||||||||
\(323\) | 2.14359i | 0.119273i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.0526 | 1.27676 | ||||||||
\(327\) | 11.8564i | 0.655661i | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | −20.9282 | −1.15381 | ||||||||
\(330\) | − 0.464102i | − 0.0255480i | ||||||||
\(331\) | − 24.7846i | − 1.36229i | −0.732151 | − | 0.681143i | \(-0.761483\pi\) | ||||
0.732151 | − | 0.681143i | \(-0.238517\pi\) | |||||||
\(332\) | − 4.92820i | − 0.270470i | ||||||||
\(333\) | − 1.19615i | − 0.0655487i | ||||||||
\(334\) | −18.3205 | −1.00245 | ||||||||
\(335\) | −4.53590 | −0.247823 | ||||||||
\(336\) | − 2.00000i | − 0.109109i | ||||||||
\(337\) | −25.3205 | −1.37930 | −0.689648 | − | 0.724145i | \(-0.742235\pi\) | ||||
−0.689648 | + | 0.724145i | \(0.742235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.1962 | −0.608092 | ||||||||
\(340\) | − 4.00000i | − 0.216930i | ||||||||
\(341\) | −0.803848 | −0.0435308 | ||||||||
\(342\) | −0.535898 | −0.0289781 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | − 1.92820i | − 0.103962i | ||||||||
\(345\) | 0.267949i | 0.0144259i | ||||||||
\(346\) | 2.92820i | 0.157421i | ||||||||
\(347\) | 22.3923 | 1.20208 | 0.601041 | − | 0.799218i | \(-0.294753\pi\) | ||||
0.601041 | + | 0.799218i | \(0.294753\pi\) | |||||||
\(348\) | 3.73205 | 0.200059 | ||||||||
\(349\) | 14.5359i | 0.778089i | 0.921219 | + | 0.389044i | \(0.127195\pi\) | ||||
−0.921219 | + | 0.389044i | \(0.872805\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.464102 | −0.0247367 | ||||||||
\(353\) | 2.00000i | 0.106449i | 0.998583 | + | 0.0532246i | \(0.0169499\pi\) | ||||
−0.998583 | + | 0.0532246i | \(0.983050\pi\) | |||||||
\(354\) | 1.53590 | 0.0816321 | ||||||||
\(355\) | −8.39230 | −0.445417 | ||||||||
\(356\) | 7.46410i | 0.395597i | ||||||||
\(357\) | 8.00000i | 0.423405i | ||||||||
\(358\) | 16.2679i | 0.859788i | ||||||||
\(359\) | − 18.9282i | − 0.998992i | −0.866316 | − | 0.499496i | \(-0.833518\pi\) | ||||
0.866316 | − | 0.499496i | \(-0.166482\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 18.7128 | 0.984885 | ||||||||
\(362\) | − 10.9282i | − 0.574374i | ||||||||
\(363\) | −10.7846 | −0.566045 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 10.3923i | 0.543214i | ||||||||
\(367\) | 36.3923 | 1.89966 | 0.949831 | − | 0.312762i | \(-0.101254\pi\) | ||||
0.949831 | + | 0.312762i | \(0.101254\pi\) | |||||||
\(368\) | 0.267949 | 0.0139678 | ||||||||
\(369\) | 2.00000i | 0.104116i | ||||||||
\(370\) | 1.19615i | 0.0621850i | ||||||||
\(371\) | − 25.8564i | − 1.34240i | ||||||||
\(372\) | − 1.73205i | − 0.0898027i | ||||||||
\(373\) | 25.7846 | 1.33508 | 0.667538 | − | 0.744576i | \(-0.267348\pi\) | ||||
0.667538 | + | 0.744576i | \(0.267348\pi\) | |||||||
\(374\) | 1.85641 | 0.0959925 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −10.4641 | −0.539645 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 0.143594i | 0.00737590i | 0.999993 | + | 0.00368795i | \(0.00117391\pi\) | ||||
−0.999993 | + | 0.00368795i | \(0.998826\pi\) | |||||||
\(380\) | 0.535898 | 0.0274910 | ||||||||
\(381\) | −8.92820 | −0.457406 | ||||||||
\(382\) | − 14.5359i | − 0.743721i | ||||||||
\(383\) | − 4.60770i | − 0.235442i | −0.993047 | − | 0.117721i | \(-0.962441\pi\) | ||||
0.993047 | − | 0.117721i | \(-0.0375589\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 0.928203i | − 0.0473056i | ||||||||
\(386\) | −23.3205 | −1.18698 | ||||||||
\(387\) | −1.92820 | −0.0980161 | ||||||||
\(388\) | 7.46410i | 0.378932i | ||||||||
\(389\) | −20.2679 | −1.02763 | −0.513813 | − | 0.857902i | \(-0.671767\pi\) | ||||
−0.513813 | + | 0.857902i | \(0.671767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.07180 | −0.0542031 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 1.33975 | 0.0675812 | ||||||||
\(394\) | −16.3923 | −0.825832 | ||||||||
\(395\) | 0.0717968i | 0.00361249i | ||||||||
\(396\) | 0.464102i | 0.0233220i | ||||||||
\(397\) | 12.1244i | 0.608504i | 0.952592 | + | 0.304252i | \(0.0984065\pi\) | ||||
−0.952592 | + | 0.304252i | \(0.901594\pi\) | |||||||
\(398\) | 18.9282i | 0.948785i | ||||||||
\(399\) | −1.07180 | −0.0536570 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 32.0000i | − 1.59800i | −0.601329 | − | 0.799002i | \(-0.705362\pi\) | ||||
0.601329 | − | 0.799002i | \(-0.294638\pi\) | |||||||
\(402\) | 4.53590 | 0.226230 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.9282 | 0.543698 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 7.46410 | 0.370437 | ||||||||
\(407\) | −0.555136 | −0.0275171 | ||||||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | − 4.00000i | − 0.197787i | −0.995098 | − | 0.0988936i | \(-0.968470\pi\) | ||||
0.995098 | − | 0.0988936i | \(-0.0315304\pi\) | |||||||
\(410\) | − 2.00000i | − 0.0987730i | ||||||||
\(411\) | 4.46410i | 0.220198i | ||||||||
\(412\) | −15.8564 | −0.781189 | ||||||||
\(413\) | 3.07180 | 0.151153 | ||||||||
\(414\) | − 0.267949i | − 0.0131690i | ||||||||
\(415\) | 4.92820 | 0.241916 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.928203 | −0.0454543 | ||||||||
\(418\) | 0.248711i | 0.0121649i | ||||||||
\(419\) | 1.60770 | 0.0785410 | 0.0392705 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392705 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(420\) | 2.00000 | 0.0975900 | ||||||||
\(421\) | 16.3923i | 0.798912i | 0.916752 | + | 0.399456i | \(0.130801\pi\) | ||||
−0.916752 | + | 0.399456i | \(0.869199\pi\) | |||||||
\(422\) | − 23.3205i | − 1.13522i | ||||||||
\(423\) | 10.4641i | 0.508782i | ||||||||
\(424\) | − 12.9282i | − 0.627849i | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 8.39230 | 0.406608 | ||||||||
\(427\) | 20.7846i | 1.00584i | ||||||||
\(428\) | −19.8564 | −0.959796 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.92820 | 0.0929862 | ||||||||
\(431\) | 7.60770i | 0.366450i | 0.983071 | + | 0.183225i | \(0.0586537\pi\) | ||||
−0.983071 | + | 0.183225i | \(0.941346\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.3205 | −0.736257 | −0.368128 | − | 0.929775i | \(-0.620001\pi\) | ||||
−0.368128 | + | 0.929775i | \(0.620001\pi\) | |||||||
\(434\) | − 3.46410i | − 0.166282i | ||||||||
\(435\) | 3.73205i | 0.178938i | ||||||||
\(436\) | 11.8564i | 0.567819i | ||||||||
\(437\) | − 0.143594i | − 0.00686901i | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 9.85641 | 0.470421 | 0.235210 | − | 0.971945i | \(-0.424422\pi\) | ||||
0.235210 | + | 0.971945i | \(0.424422\pi\) | |||||||
\(440\) | − 0.464102i | − 0.0221252i | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.39230 | −0.208685 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(444\) | − 1.19615i | − 0.0567669i | ||||||||
\(445\) | −7.46410 | −0.353832 | ||||||||
\(446\) | −27.4641 | −1.30046 | ||||||||
\(447\) | − 20.4641i | − 0.967919i | ||||||||
\(448\) | − 2.00000i | − 0.0944911i | ||||||||
\(449\) | − 39.7128i | − 1.87416i | −0.349110 | − | 0.937082i | \(-0.613516\pi\) | ||||
0.349110 | − | 0.937082i | \(-0.386484\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 0.928203 | 0.0437074 | ||||||||
\(452\) | −11.1962 | −0.526623 | ||||||||
\(453\) | 10.3923i | 0.488273i | ||||||||
\(454\) | −4.39230 | −0.206141 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.535898 | −0.0250957 | ||||||||
\(457\) | 31.4641i | 1.47183i | 0.677075 | + | 0.735914i | \(0.263247\pi\) | ||||
−0.677075 | + | 0.735914i | \(0.736753\pi\) | |||||||
\(458\) | −19.8564 | −0.927829 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 0.267949i | 0.0124932i | ||||||||
\(461\) | 6.46410i | 0.301063i | 0.988605 | + | 0.150532i | \(0.0480985\pi\) | ||||
−0.988605 | + | 0.150532i | \(0.951901\pi\) | |||||||
\(462\) | 0.928203i | 0.0431839i | ||||||||
\(463\) | − 20.9282i | − 0.972616i | −0.873787 | − | 0.486308i | \(-0.838343\pi\) | ||||
0.873787 | − | 0.486308i | \(-0.161657\pi\) | |||||||
\(464\) | 3.73205 | 0.173256 | ||||||||
\(465\) | 1.73205 | 0.0803219 | ||||||||
\(466\) | 18.1244i | 0.839595i | ||||||||
\(467\) | 11.8564 | 0.548649 | 0.274325 | − | 0.961637i | \(-0.411546\pi\) | ||||
0.274325 | + | 0.961637i | \(0.411546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.07180 | 0.418897 | ||||||||
\(470\) | − 10.4641i | − 0.482673i | ||||||||
\(471\) | 5.00000 | 0.230388 | ||||||||
\(472\) | 1.53590 | 0.0706955 | ||||||||
\(473\) | 0.894882i | 0.0411467i | ||||||||
\(474\) | − 0.0717968i | − 0.00329773i | ||||||||
\(475\) | 0.535898i | 0.0245887i | ||||||||
\(476\) | 8.00000i | 0.366679i | ||||||||
\(477\) | −12.9282 | −0.591942 | ||||||||
\(478\) | −4.39230 | −0.200899 | ||||||||
\(479\) | − 1.46410i | − 0.0668965i | −0.999440 | − | 0.0334483i | \(-0.989351\pi\) | ||||
0.999440 | − | 0.0334483i | \(-0.0106489\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.2679 | −0.649887 | ||||||||
\(483\) | − 0.535898i | − 0.0243842i | ||||||||
\(484\) | −10.7846 | −0.490210 | ||||||||
\(485\) | −7.46410 | −0.338927 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 39.1769i | 1.77528i | 0.460542 | + | 0.887638i | \(0.347655\pi\) | ||||
−0.460542 | + | 0.887638i | \(0.652345\pi\) | |||||||
\(488\) | 10.3923i | 0.470438i | ||||||||
\(489\) | − 23.0526i | − 1.04247i | ||||||||
\(490\) | −3.00000 | −0.135526 | ||||||||
\(491\) | 17.3205 | 0.781664 | 0.390832 | − | 0.920462i | \(-0.372187\pi\) | ||||
0.390832 | + | 0.920462i | \(0.372187\pi\) | |||||||
\(492\) | 2.00000i | 0.0901670i | ||||||||
\(493\) | −14.9282 | −0.672332 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.464102 | −0.0208598 | ||||||||
\(496\) | − 1.73205i | − 0.0777714i | ||||||||
\(497\) | 16.7846 | 0.752893 | ||||||||
\(498\) | −4.92820 | −0.220838 | ||||||||
\(499\) | − 13.4641i | − 0.602736i | −0.953508 | − | 0.301368i | \(-0.902557\pi\) | ||||
0.953508 | − | 0.301368i | \(-0.0974433\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 18.3205i | 0.818500i | ||||||||
\(502\) | − 12.2679i | − 0.547545i | ||||||||
\(503\) | 31.1769 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 10.9282i | 0.486299i | ||||||||
\(506\) | −0.124356 | −0.00552828 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.92820 | −0.396125 | ||||||||
\(509\) | − 19.3923i | − 0.859549i | −0.902936 | − | 0.429774i | \(-0.858593\pi\) | ||||
0.902936 | − | 0.429774i | \(-0.141407\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0.535898i | 0.0236605i | ||||||||
\(514\) | 22.6603i | 0.999501i | ||||||||
\(515\) | − 15.8564i | − 0.698717i | ||||||||
\(516\) | −1.92820 | −0.0848844 | ||||||||
\(517\) | 4.85641 | 0.213585 | ||||||||
\(518\) | − 2.39230i | − 0.105112i | ||||||||
\(519\) | 2.92820 | 0.128534 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3205 | 0.758825 | 0.379413 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(522\) | − 3.73205i | − 0.163347i | ||||||||
\(523\) | −29.7846 | −1.30239 | −0.651195 | − | 0.758910i | \(-0.725732\pi\) | ||||
−0.651195 | + | 0.758910i | \(0.725732\pi\) | |||||||
\(524\) | 1.33975 | 0.0585271 | ||||||||
\(525\) | 2.00000i | 0.0872872i | ||||||||
\(526\) | 18.1244i | 0.790259i | ||||||||
\(527\) | 6.92820i | 0.301797i | ||||||||
\(528\) | 0.464102i | 0.0201974i | ||||||||
\(529\) | −22.9282 | −0.996878 | ||||||||
\(530\) | 12.9282 | 0.561565 | ||||||||
\(531\) | − 1.53590i | − 0.0666523i | ||||||||
\(532\) | −1.07180 | −0.0464683 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7.46410 | 0.323003 | ||||||||
\(535\) | − 19.8564i | − 0.858467i | ||||||||
\(536\) | 4.53590 | 0.195921 | ||||||||
\(537\) | 16.2679 | 0.702014 | ||||||||
\(538\) | − 12.0000i | − 0.517357i | ||||||||
\(539\) | − 1.39230i | − 0.0599708i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 13.0718i | − 0.562000i | −0.959708 | − | 0.281000i | \(-0.909334\pi\) | ||||
0.959708 | − | 0.281000i | \(-0.0906662\pi\) | |||||||
\(542\) | −9.19615 | −0.395009 | ||||||||
\(543\) | −10.9282 | −0.468974 | ||||||||
\(544\) | 4.00000i | 0.171499i | ||||||||
\(545\) | −11.8564 | −0.507873 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.07180 | 0.387882 | 0.193941 | − | 0.981013i | \(-0.437873\pi\) | ||||
0.193941 | + | 0.981013i | \(0.437873\pi\) | |||||||
\(548\) | 4.46410i | 0.190697i | ||||||||
\(549\) | 10.3923 | 0.443533 | ||||||||
\(550\) | 0.464102 | 0.0197894 | ||||||||
\(551\) | − 2.00000i | − 0.0852029i | ||||||||
\(552\) | − 0.267949i | − 0.0114047i | ||||||||
\(553\) | − 0.143594i | − 0.00610622i | ||||||||
\(554\) | − 9.92820i | − 0.421809i | ||||||||
\(555\) | 1.19615 | 0.0507738 | ||||||||
\(556\) | −0.928203 | −0.0393646 | ||||||||
\(557\) | − 37.7128i | − 1.59794i | −0.601369 | − | 0.798972i | \(-0.705378\pi\) | ||||
0.601369 | − | 0.798972i | \(-0.294622\pi\) | |||||||
\(558\) | −1.73205 | −0.0733236 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | − 1.85641i | − 0.0783775i | ||||||||
\(562\) | −4.92820 | −0.207884 | ||||||||
\(563\) | −39.3205 | −1.65716 | −0.828581 | − | 0.559869i | \(-0.810851\pi\) | ||||
−0.828581 | + | 0.559869i | \(0.810851\pi\) | |||||||
\(564\) | 10.4641i | 0.440618i | ||||||||
\(565\) | − 11.1962i | − 0.471026i | ||||||||
\(566\) | − 3.92820i | − 0.165115i | ||||||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | 8.39230 | 0.352133 | ||||||||
\(569\) | −5.32051 | −0.223047 | −0.111524 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111524 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(570\) | − 0.535898i | − 0.0224463i | ||||||||
\(571\) | 45.1769 | 1.89060 | 0.945298 | − | 0.326209i | \(-0.105771\pi\) | ||||
0.945298 | + | 0.326209i | \(0.105771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.5359 | −0.607246 | ||||||||
\(574\) | 4.00000i | 0.166957i | ||||||||
\(575\) | −0.267949 | −0.0111743 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 10.0000i | 0.416305i | 0.978096 | + | 0.208153i | \(0.0667451\pi\) | ||||
−0.978096 | + | 0.208153i | \(0.933255\pi\) | |||||||
\(578\) | 1.00000i | 0.0415945i | ||||||||
\(579\) | 23.3205i | 0.969167i | ||||||||
\(580\) | 3.73205i | 0.154965i | ||||||||
\(581\) | −9.85641 | −0.408913 | ||||||||
\(582\) | 7.46410 | 0.309397 | ||||||||
\(583\) | 6.00000i | 0.248495i | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.14359 | 0.171170 | ||||||||
\(587\) | 18.3923i | 0.759132i | 0.925165 | + | 0.379566i | \(0.123927\pi\) | ||||
−0.925165 | + | 0.379566i | \(0.876073\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | −0.928203 | −0.0382459 | ||||||||
\(590\) | 1.53590i | 0.0632319i | ||||||||
\(591\) | 16.3923i | 0.674289i | ||||||||
\(592\) | − 1.19615i | − 0.0491616i | ||||||||
\(593\) | 31.1051i | 1.27733i | 0.769483 | + | 0.638667i | \(0.220514\pi\) | ||||
−0.769483 | + | 0.638667i | \(0.779486\pi\) | |||||||
\(594\) | 0.464102 | 0.0190423 | ||||||||
\(595\) | −8.00000 | −0.327968 | ||||||||
\(596\) | − 20.4641i | − 0.838242i | ||||||||
\(597\) | 18.9282 | 0.774680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3923 | 0.424618 | 0.212309 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212309 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 21.7846 | 0.888613 | 0.444306 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444306 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(602\) | −3.85641 | −0.157175 | ||||||||
\(603\) | − 4.53590i | − 0.184716i | ||||||||
\(604\) | 10.3923i | 0.422857i | ||||||||
\(605\) | − 10.7846i | − 0.438457i | ||||||||
\(606\) | − 10.9282i | − 0.443928i | ||||||||
\(607\) | 43.1769 | 1.75250 | 0.876248 | − | 0.481860i | \(-0.160038\pi\) | ||||
0.876248 | + | 0.481860i | \(0.160038\pi\) | |||||||
\(608\) | −0.535898 | −0.0217335 | ||||||||
\(609\) | − 7.46410i | − 0.302461i | ||||||||
\(610\) | −10.3923 | −0.420772 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | − 0.947441i | − 0.0382668i | −0.999817 | − | 0.0191334i | \(-0.993909\pi\) | ||||
0.999817 | − | 0.0191334i | \(-0.00609072\pi\) | |||||||
\(614\) | −12.5359 | −0.505908 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0.928203i | 0.0373984i | ||||||||
\(617\) | 15.5359i | 0.625452i | 0.949843 | + | 0.312726i | \(0.101242\pi\) | ||||
−0.949843 | + | 0.312726i | \(0.898758\pi\) | |||||||
\(618\) | 15.8564i | 0.637838i | ||||||||
\(619\) | − 24.2487i | − 0.974638i | −0.873224 | − | 0.487319i | \(-0.837975\pi\) | ||||
0.873224 | − | 0.487319i | \(-0.162025\pi\) | |||||||
\(620\) | 1.73205 | 0.0695608 | ||||||||
\(621\) | −0.267949 | −0.0107524 | ||||||||
\(622\) | 7.60770i | 0.305041i | ||||||||
\(623\) | 14.9282 | 0.598086 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.0000i | 1.11911i | ||||||||
\(627\) | 0.248711 | 0.00993257 | ||||||||
\(628\) | 5.00000 | 0.199522 | ||||||||
\(629\) | 4.78461i | 0.190775i | ||||||||
\(630\) | − 2.00000i | − 0.0796819i | ||||||||
\(631\) | − 24.5359i | − 0.976759i | −0.872631 | − | 0.488379i | \(-0.837588\pi\) | ||||
0.872631 | − | 0.488379i | \(-0.162412\pi\) | |||||||
\(632\) | − 0.0717968i | − 0.00285592i | ||||||||
\(633\) | −23.3205 | −0.926907 | ||||||||
\(634\) | −21.4641 | −0.852448 | ||||||||
\(635\) | − 8.92820i | − 0.354305i | ||||||||
\(636\) | −12.9282 | −0.512637 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.73205 | −0.0685725 | ||||||||
\(639\) | − 8.39230i | − 0.331994i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 27.8564 | 1.10026 | 0.550131 | − | 0.835078i | \(-0.314578\pi\) | ||||
0.550131 | + | 0.835078i | \(0.314578\pi\) | |||||||
\(642\) | 19.8564i | 0.783670i | ||||||||
\(643\) | 27.4641i | 1.08308i | 0.840675 | + | 0.541539i | \(0.182158\pi\) | ||||
−0.840675 | + | 0.541539i | \(0.817842\pi\) | |||||||
\(644\) | − 0.535898i | − 0.0211174i | ||||||||
\(645\) | − 1.92820i | − 0.0759229i | ||||||||
\(646\) | 2.14359 | 0.0843386 | ||||||||
\(647\) | 21.3205 | 0.838196 | 0.419098 | − | 0.907941i | \(-0.362346\pi\) | ||||
0.419098 | + | 0.907941i | \(0.362346\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −0.712813 | −0.0279804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.46410 | −0.135769 | ||||||||
\(652\) | − 23.0526i | − 0.902808i | ||||||||
\(653\) | −44.2487 | −1.73159 | −0.865793 | − | 0.500402i | \(-0.833185\pi\) | ||||
−0.865793 | + | 0.500402i | \(0.833185\pi\) | |||||||
\(654\) | 11.8564 | 0.463622 | ||||||||
\(655\) | 1.33975i | 0.0523482i | ||||||||
\(656\) | 2.00000i | 0.0780869i | ||||||||
\(657\) | − 2.00000i | − 0.0780274i | ||||||||
\(658\) | 20.9282i | 0.815866i | ||||||||
\(659\) | −3.73205 | −0.145380 | −0.0726900 | − | 0.997355i | \(-0.523158\pi\) | ||||
−0.0726900 | + | 0.997355i | \(0.523158\pi\) | |||||||
\(660\) | −0.464102 | −0.0180651 | ||||||||
\(661\) | − 43.3205i | − 1.68497i | −0.538718 | − | 0.842486i | \(-0.681091\pi\) | ||||
0.538718 | − | 0.842486i | \(-0.318909\pi\) | |||||||
\(662\) | −24.7846 | −0.963281 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.92820 | −0.191251 | ||||||||
\(665\) | − 1.07180i | − 0.0415625i | ||||||||
\(666\) | −1.19615 | −0.0463500 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 18.3205i | 0.708842i | ||||||||
\(669\) | 27.4641i | 1.06182i | ||||||||
\(670\) | 4.53590i | 0.175237i | ||||||||
\(671\) | − 4.82309i | − 0.186193i | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | 32.0000 | 1.23351 | 0.616755 | − | 0.787155i | \(-0.288447\pi\) | ||||
0.616755 | + | 0.787155i | \(0.288447\pi\) | |||||||
\(674\) | 25.3205i | 0.975310i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6077 | 0.446120 | 0.223060 | − | 0.974805i | \(-0.428395\pi\) | ||||
0.223060 | + | 0.974805i | \(0.428395\pi\) | |||||||
\(678\) | 11.1962i | 0.429986i | ||||||||
\(679\) | 14.9282 | 0.572892 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 4.39230i | 0.168313i | ||||||||
\(682\) | 0.803848i | 0.0307809i | ||||||||
\(683\) | − 0.784610i | − 0.0300223i | −0.999887 | − | 0.0150111i | \(-0.995222\pi\) | ||||
0.999887 | − | 0.0150111i | \(-0.00477837\pi\) | |||||||
\(684\) | 0.535898i | 0.0204906i | ||||||||
\(685\) | −4.46410 | −0.170565 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | 19.8564i | 0.757569i | ||||||||
\(688\) | −1.92820 | −0.0735121 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.267949 | 0.0102007 | ||||||||
\(691\) | 35.1769i | 1.33819i | 0.743176 | + | 0.669096i | \(0.233319\pi\) | ||||
−0.743176 | + | 0.669096i | \(0.766681\pi\) | |||||||
\(692\) | 2.92820 | 0.111314 | ||||||||
\(693\) | 0.928203 | 0.0352595 | ||||||||
\(694\) | − 22.3923i | − 0.850000i | ||||||||
\(695\) | − 0.928203i | − 0.0352088i | ||||||||
\(696\) | − 3.73205i | − 0.141463i | ||||||||
\(697\) | − 8.00000i | − 0.303022i | ||||||||
\(698\) | 14.5359 | 0.550192 | ||||||||
\(699\) | 18.1244 | 0.685526 | ||||||||
\(700\) | 2.00000i | 0.0755929i | ||||||||
\(701\) | −3.73205 | −0.140958 | −0.0704788 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704788 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.641016 | −0.0241764 | ||||||||
\(704\) | 0.464102i | 0.0174915i | ||||||||
\(705\) | −10.4641 | −0.394101 | ||||||||
\(706\) | 2.00000 | 0.0752710 | ||||||||
\(707\) | − 21.8564i | − 0.821995i | ||||||||
\(708\) | − 1.53590i | − 0.0577226i | ||||||||
\(709\) | 9.07180i | 0.340698i | 0.985384 | + | 0.170349i | \(0.0544896\pi\) | ||||
−0.985384 | + | 0.170349i | \(0.945510\pi\) | |||||||
\(710\) | 8.39230i | 0.314958i | ||||||||
\(711\) | −0.0717968 | −0.00269259 | ||||||||
\(712\) | 7.46410 | 0.279729 | ||||||||
\(713\) | − 0.464102i | − 0.0173807i | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2679 | 0.607962 | ||||||||
\(717\) | 4.39230i | 0.164034i | ||||||||
\(718\) | −18.9282 | −0.706394 | ||||||||
\(719\) | 34.6410 | 1.29189 | 0.645946 | − | 0.763383i | \(-0.276463\pi\) | ||||
0.645946 | + | 0.763383i | \(0.276463\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 31.7128i | 1.18105i | ||||||||
\(722\) | − 18.7128i | − 0.696419i | ||||||||
\(723\) | 14.2679i | 0.530631i | ||||||||
\(724\) | −10.9282 | −0.406143 | ||||||||
\(725\) | −3.73205 | −0.138605 | ||||||||
\(726\) | 10.7846i | 0.400254i | ||||||||
\(727\) | 23.7128 | 0.879460 | 0.439730 | − | 0.898130i | \(-0.355074\pi\) | ||||
0.439730 | + | 0.898130i | \(0.355074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000i | 0.0740233i | ||||||||
\(731\) | 7.71281 | 0.285269 | ||||||||
\(732\) | 10.3923 | 0.384111 | ||||||||
\(733\) | 37.0718i | 1.36928i | 0.728882 | + | 0.684639i | \(0.240040\pi\) | ||||
−0.728882 | + | 0.684639i | \(0.759960\pi\) | |||||||
\(734\) | − 36.3923i | − 1.34326i | ||||||||
\(735\) | 3.00000i | 0.110657i | ||||||||
\(736\) | − 0.267949i | − 0.00987674i | ||||||||
\(737\) | −2.10512 | −0.0775430 | ||||||||
\(738\) | 2.00000 | 0.0736210 | ||||||||
\(739\) | 15.3205i | 0.563574i | 0.959477 | + | 0.281787i | \(0.0909272\pi\) | ||||
−0.959477 | + | 0.281787i | \(0.909073\pi\) | |||||||
\(740\) | 1.19615 | 0.0439714 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.8564 | −0.949219 | ||||||||
\(743\) | − 33.5359i | − 1.23031i | −0.788405 | − | 0.615156i | \(-0.789093\pi\) | ||||
0.788405 | − | 0.615156i | \(-0.210907\pi\) | |||||||
\(744\) | −1.73205 | −0.0635001 | ||||||||
\(745\) | 20.4641 | 0.749747 | ||||||||
\(746\) | − 25.7846i | − 0.944042i | ||||||||
\(747\) | 4.92820i | 0.180314i | ||||||||
\(748\) | − 1.85641i | − 0.0678769i | ||||||||
\(749\) | 39.7128i | 1.45107i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 27.9282 | 1.01911 | 0.509557 | − | 0.860437i | \(-0.329809\pi\) | ||||
0.509557 | + | 0.860437i | \(0.329809\pi\) | |||||||
\(752\) | 10.4641i | 0.381587i | ||||||||
\(753\) | −12.2679 | −0.447069 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.3923 | −0.378215 | ||||||||
\(756\) | 2.00000i | 0.0727393i | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 0.143594 | 0.00521555 | ||||||||
\(759\) | 0.124356i | 0.00451382i | ||||||||
\(760\) | − 0.535898i | − 0.0194391i | ||||||||
\(761\) | − 18.9282i | − 0.686147i | −0.939309 | − | 0.343073i | \(-0.888532\pi\) | ||||
0.939309 | − | 0.343073i | \(-0.111468\pi\) | |||||||
\(762\) | 8.92820i | 0.323435i | ||||||||
\(763\) | 23.7128 | 0.858461 | ||||||||
\(764\) | −14.5359 | −0.525890 | ||||||||
\(765\) | 4.00000i | 0.144620i | ||||||||
\(766\) | −4.60770 | −0.166483 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 19.5885i | 0.706378i | 0.935552 | + | 0.353189i | \(0.114903\pi\) | ||||
−0.935552 | + | 0.353189i | \(0.885097\pi\) | |||||||
\(770\) | −0.928203 | −0.0334501 | ||||||||
\(771\) | 22.6603 | 0.816089 | ||||||||
\(772\) | 23.3205i | 0.839323i | ||||||||
\(773\) | 27.7128i | 0.996761i | 0.866959 | + | 0.498380i | \(0.166072\pi\) | ||||
−0.866959 | + | 0.498380i | \(0.833928\pi\) | |||||||
\(774\) | 1.92820i | 0.0693078i | ||||||||
\(775\) | 1.73205i | 0.0622171i | ||||||||
\(776\) | 7.46410 | 0.267946 | ||||||||
\(777\) | −2.39230 | −0.0858235 | ||||||||
\(778\) | 20.2679i | 0.726641i | ||||||||
\(779\) | 1.07180 | 0.0384011 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.89488 | −0.139370 | ||||||||
\(782\) | 1.07180i | 0.0383274i | ||||||||
\(783\) | −3.73205 | −0.133373 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 5.00000i | 0.178458i | ||||||||
\(786\) | − 1.33975i | − 0.0477872i | ||||||||
\(787\) | 1.73205i | 0.0617409i | 0.999523 | + | 0.0308705i | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 16.3923i | 0.583952i | ||||||||
\(789\) | 18.1244 | 0.645244 | ||||||||
\(790\) | 0.0717968 | 0.00255441 | ||||||||
\(791\) | 22.3923i | 0.796179i | ||||||||
\(792\) | 0.464102 | 0.0164911 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.1244 | 0.430277 | ||||||||
\(795\) | − 12.9282i | − 0.458516i | ||||||||
\(796\) | 18.9282 | 0.670892 | ||||||||
\(797\) | −37.8564 | −1.34094 | −0.670471 | − | 0.741935i | \(-0.733908\pi\) | ||||
−0.670471 | + | 0.741935i | \(0.733908\pi\) | |||||||
\(798\) | 1.07180i | 0.0379412i | ||||||||
\(799\) | − 41.8564i | − 1.48077i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 7.46410i | − 0.263731i | ||||||||
\(802\) | −32.0000 | −1.12996 | ||||||||
\(803\) | −0.928203 | −0.0327556 | ||||||||
\(804\) | − 4.53590i | − 0.159969i | ||||||||
\(805\) | 0.535898 | 0.0188879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | − 10.9282i | − 0.384453i | ||||||||
\(809\) | −1.21539 | −0.0427308 | −0.0213654 | − | 0.999772i | \(-0.506801\pi\) | ||||
−0.0213654 | + | 0.999772i | \(0.506801\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 0.784610i | 0.0275514i | 0.999905 | + | 0.0137757i | \(0.00438508\pi\) | ||||
−0.999905 | + | 0.0137757i | \(0.995615\pi\) | |||||||
\(812\) | − 7.46410i | − 0.261939i | ||||||||
\(813\) | 9.19615i | 0.322523i | ||||||||
\(814\) | 0.555136i | 0.0194575i | ||||||||
\(815\) | 23.0526 | 0.807496 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 1.03332i | 0.0361513i | ||||||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | 35.3923i | 1.23520i | 0.786492 | + | 0.617600i | \(0.211895\pi\) | ||||
−0.786492 | + | 0.617600i | \(0.788105\pi\) | |||||||
\(822\) | 4.46410 | 0.155703 | ||||||||
\(823\) | −23.1769 | −0.807896 | −0.403948 | − | 0.914782i | \(-0.632362\pi\) | ||||
−0.403948 | + | 0.914782i | \(0.632362\pi\) | |||||||
\(824\) | 15.8564i | 0.552384i | ||||||||
\(825\) | − 0.464102i | − 0.0161579i | ||||||||
\(826\) | − 3.07180i | − 0.106881i | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | −0.267949 | −0.00931188 | ||||||||
\(829\) | 23.4641 | 0.814942 | 0.407471 | − | 0.913218i | \(-0.366411\pi\) | ||||
0.407471 | + | 0.913218i | \(0.366411\pi\) | |||||||
\(830\) | − 4.92820i | − 0.171060i | ||||||||
\(831\) | −9.92820 | −0.344406 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0000 | −0.415775 | ||||||||
\(834\) | 0.928203i | 0.0321410i | ||||||||
\(835\) | −18.3205 | −0.634007 | ||||||||
\(836\) | 0.248711 | 0.00860186 | ||||||||
\(837\) | 1.73205i | 0.0598684i | ||||||||
\(838\) | − 1.60770i | − 0.0555369i | ||||||||
\(839\) | − 39.5692i | − 1.36608i | −0.730380 | − | 0.683041i | \(-0.760657\pi\) | ||||
0.730380 | − | 0.683041i | \(-0.239343\pi\) | |||||||
\(840\) | − 2.00000i | − 0.0690066i | ||||||||
\(841\) | −15.0718 | −0.519717 | ||||||||
\(842\) | 16.3923 | 0.564916 | ||||||||
\(843\) | 4.92820i | 0.169736i | ||||||||
\(844\) | −23.3205 | −0.802725 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.4641 | 0.359763 | ||||||||
\(847\) | 21.5692i | 0.741127i | ||||||||
\(848\) | −12.9282 | −0.443956 | ||||||||
\(849\) | −3.92820 | −0.134816 | ||||||||
\(850\) | − 4.00000i | − 0.137199i | ||||||||
\(851\) | − 0.320508i | − 0.0109869i | ||||||||
\(852\) | − 8.39230i | − 0.287516i | ||||||||
\(853\) | 35.8372i | 1.22704i | 0.789679 | + | 0.613521i | \(0.210247\pi\) | ||||
−0.789679 | + | 0.613521i | \(0.789753\pi\) | |||||||
\(854\) | 20.7846 | 0.711235 | ||||||||
\(855\) | −0.535898 | −0.0183273 | ||||||||
\(856\) | 19.8564i | 0.678678i | ||||||||
\(857\) | −20.5167 | −0.700836 | −0.350418 | − | 0.936593i | \(-0.613960\pi\) | ||||
−0.350418 | + | 0.936593i | \(0.613960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.1769 | 0.927264 | 0.463632 | − | 0.886028i | \(-0.346546\pi\) | ||||
0.463632 | + | 0.886028i | \(0.346546\pi\) | |||||||
\(860\) | − 1.92820i | − 0.0657512i | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 7.60770 | 0.259119 | ||||||||
\(863\) | − 42.4641i | − 1.44549i | −0.691112 | − | 0.722747i | \(-0.742879\pi\) | ||||
0.691112 | − | 0.722747i | \(-0.257121\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 2.92820i | 0.0995619i | ||||||||
\(866\) | 15.3205i | 0.520612i | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −3.46410 | −0.117579 | ||||||||
\(869\) | 0.0333210i | 0.00113034i | ||||||||
\(870\) | 3.73205 | 0.126528 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11.8564 | 0.401509 | ||||||||
\(873\) | − 7.46410i | − 0.252622i | ||||||||
\(874\) | −0.143594 | −0.00485712 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | − 2.00000i | − 0.0675737i | ||||||||
\(877\) | 28.1244i | 0.949692i | 0.880069 | + | 0.474846i | \(0.157496\pi\) | ||||
−0.880069 | + | 0.474846i | \(0.842504\pi\) | |||||||
\(878\) | − 9.85641i | − 0.332638i | ||||||||
\(879\) | − 4.14359i | − 0.139760i | ||||||||
\(880\) | −0.464102 | −0.0156449 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | − 3.00000i | − 0.101015i | ||||||||
\(883\) | 16.0718 | 0.540859 | 0.270430 | − | 0.962740i | \(-0.412834\pi\) | ||||
0.270430 | + | 0.962740i | \(0.412834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.53590 | 0.0516287 | ||||||||
\(886\) | 4.39230i | 0.147562i | ||||||||
\(887\) | −10.1244 | −0.339943 | −0.169971 | − | 0.985449i | \(-0.554368\pi\) | ||||
−0.169971 | + | 0.985449i | \(0.554368\pi\) | |||||||
\(888\) | −1.19615 | −0.0401402 | ||||||||
\(889\) | 17.8564i | 0.598885i | ||||||||
\(890\) | 7.46410i | 0.250197i | ||||||||
\(891\) | − 0.464102i | − 0.0155480i | ||||||||
\(892\) | 27.4641i | 0.919566i | ||||||||
\(893\) | 5.60770 | 0.187654 | ||||||||
\(894\) | −20.4641 | −0.684422 | ||||||||
\(895\) | 16.2679i | 0.543778i | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.7128 | −1.32523 | ||||||||
\(899\) | − 6.46410i | − 0.215590i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 51.7128 | 1.72280 | ||||||||
\(902\) | − 0.928203i | − 0.0309058i | ||||||||
\(903\) | 3.85641i | 0.128333i | ||||||||
\(904\) | 11.1962i | 0.372378i | ||||||||
\(905\) | − 10.9282i | − 0.363266i | ||||||||
\(906\) | 10.3923 | 0.345261 | ||||||||
\(907\) | 6.85641 | 0.227663 | 0.113832 | − | 0.993500i | \(-0.463688\pi\) | ||||
0.113832 | + | 0.993500i | \(0.463688\pi\) | |||||||
\(908\) | 4.39230i | 0.145764i | ||||||||
\(909\) | −10.9282 | −0.362466 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2487 | −0.803396 | −0.401698 | − | 0.915772i | \(-0.631580\pi\) | ||||
−0.401698 | + | 0.915772i | \(0.631580\pi\) | |||||||
\(912\) | 0.535898i | 0.0177454i | ||||||||
\(913\) | 2.28719 | 0.0756948 | ||||||||
\(914\) | 31.4641 | 1.04074 | ||||||||
\(915\) | 10.3923i | 0.343559i | ||||||||
\(916\) | 19.8564i | 0.656074i | ||||||||
\(917\) | − 2.67949i | − 0.0884846i | ||||||||
\(918\) | − 4.00000i | − 0.132020i | ||||||||
\(919\) | −54.6410 | −1.80244 | −0.901220 | − | 0.433361i | \(-0.857328\pi\) | ||||
−0.901220 | + | 0.433361i | \(0.857328\pi\) | |||||||
\(920\) | 0.267949 | 0.00883402 | ||||||||
\(921\) | 12.5359i | 0.413072i | ||||||||
\(922\) | 6.46410 | 0.212884 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.928203 | 0.0305356 | ||||||||
\(925\) | 1.19615i | 0.0393292i | ||||||||
\(926\) | −20.9282 | −0.687743 | ||||||||
\(927\) | 15.8564 | 0.520793 | ||||||||
\(928\) | − 3.73205i | − 0.122511i | ||||||||
\(929\) | 33.8564i | 1.11079i | 0.831586 | + | 0.555396i | \(0.187433\pi\) | ||||
−0.831586 | + | 0.555396i | \(0.812567\pi\) | |||||||
\(930\) | − 1.73205i | − 0.0567962i | ||||||||
\(931\) | − 1.60770i | − 0.0526901i | ||||||||
\(932\) | 18.1244 | 0.593683 | ||||||||
\(933\) | 7.60770 | 0.249065 | ||||||||
\(934\) | − 11.8564i | − 0.387953i | ||||||||
\(935\) | 1.85641 | 0.0607110 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.6410 | 1.45836 | 0.729179 | − | 0.684323i | \(-0.239902\pi\) | ||||
0.729179 | + | 0.684323i | \(0.239902\pi\) | |||||||
\(938\) | − 9.07180i | − 0.296205i | ||||||||
\(939\) | 28.0000 | 0.913745 | ||||||||
\(940\) | −10.4641 | −0.341301 | ||||||||
\(941\) | − 26.7846i | − 0.873153i | −0.899667 | − | 0.436577i | \(-0.856191\pi\) | ||||
0.899667 | − | 0.436577i | \(-0.143809\pi\) | |||||||
\(942\) | − 5.00000i | − 0.162909i | ||||||||
\(943\) | 0.535898i | 0.0174513i | ||||||||
\(944\) | − 1.53590i | − 0.0499892i | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | 0.894882 | 0.0290951 | ||||||||
\(947\) | 2.53590i | 0.0824056i | 0.999151 | + | 0.0412028i | \(0.0131190\pi\) | ||||
−0.999151 | + | 0.0412028i | \(0.986881\pi\) | |||||||
\(948\) | −0.0717968 | −0.00233185 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.535898 | 0.0173868 | ||||||||
\(951\) | 21.4641i | 0.696021i | ||||||||
\(952\) | 8.00000 | 0.259281 | ||||||||
\(953\) | −15.7321 | −0.509611 | −0.254806 | − | 0.966992i | \(-0.582011\pi\) | ||||
−0.254806 | + | 0.966992i | \(0.582011\pi\) | |||||||
\(954\) | 12.9282i | 0.418566i | ||||||||
\(955\) | − 14.5359i | − 0.470371i | ||||||||
\(956\) | 4.39230i | 0.142057i | ||||||||
\(957\) | 1.73205i | 0.0559893i | ||||||||
\(958\) | −1.46410 | −0.0473030 | ||||||||
\(959\) | 8.92820 | 0.288307 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.8564 | 0.639864 | ||||||||
\(964\) | 14.2679i | 0.459540i | ||||||||
\(965\) | −23.3205 | −0.750714 | ||||||||
\(966\) | −0.535898 | −0.0172422 | ||||||||
\(967\) | 34.5359i | 1.11060i | 0.831650 | + | 0.555300i | \(0.187396\pi\) | ||||
−0.831650 | + | 0.555300i | \(0.812604\pi\) | |||||||
\(968\) | 10.7846i | 0.346630i | ||||||||
\(969\) | − 2.14359i | − 0.0688621i | ||||||||
\(970\) | 7.46410i | 0.239658i | ||||||||
\(971\) | 11.4641 | 0.367901 | 0.183950 | − | 0.982936i | \(-0.441111\pi\) | ||||
0.183950 | + | 0.982936i | \(0.441111\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.85641i | 0.0595137i | ||||||||
\(974\) | 39.1769 | 1.25531 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.3923 | 0.332650 | ||||||||
\(977\) | 33.3923i | 1.06831i | 0.845385 | + | 0.534157i | \(0.179371\pi\) | ||||
−0.845385 | + | 0.534157i | \(0.820629\pi\) | |||||||
\(978\) | −23.0526 | −0.737140 | ||||||||
\(979\) | −3.46410 | −0.110713 | ||||||||
\(980\) | 3.00000i | 0.0958315i | ||||||||
\(981\) | − 11.8564i | − 0.378546i | ||||||||
\(982\) | − 17.3205i | − 0.552720i | ||||||||
\(983\) | 57.3923i | 1.83053i | 0.402852 | + | 0.915265i | \(0.368019\pi\) | ||||
−0.402852 | + | 0.915265i | \(0.631981\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | −16.3923 | −0.522302 | ||||||||
\(986\) | 14.9282i | 0.475411i | ||||||||
\(987\) | 20.9282 | 0.666152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.516660 | −0.0164288 | ||||||||
\(990\) | 0.464102i | 0.0147501i | ||||||||
\(991\) | −25.1436 | −0.798713 | −0.399356 | − | 0.916796i | \(-0.630766\pi\) | ||||
−0.399356 | + | 0.916796i | \(0.630766\pi\) | |||||||
\(992\) | −1.73205 | −0.0549927 | ||||||||
\(993\) | 24.7846i | 0.786516i | ||||||||
\(994\) | − 16.7846i | − 0.532375i | ||||||||
\(995\) | 18.9282i | 0.600064i | ||||||||
\(996\) | 4.92820i | 0.156156i | ||||||||
\(997\) | −47.5692 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(998\) | −13.4641 | −0.426199 | ||||||||
\(999\) | 1.19615i | 0.0378446i |
(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 | 5070.2.b.o.1351.1 | 4 | ||
13.3 | even | 3 | 390.2.bb.b.121.2 | ✓ | 4 | ||
13.4 | even | 6 | 390.2.bb.b.361.2 | yes | 4 | ||
13.5 | odd | 4 | 5070.2.a.y.1.2 | 2 | |||
13.8 | odd | 4 | 5070.2.a.bg.1.1 | 2 | |||
13.12 | even | 2 | inner | 5070.2.b.o.1351.4 | 4 | ||
39.17 | odd | 6 | 1170.2.bs.e.361.1 | 4 | |||
39.29 | odd | 6 | 1170.2.bs.e.901.1 | 4 | |||
65.3 | odd | 12 | 1950.2.y.f.199.2 | 4 | |||
65.4 | even | 6 | 1950.2.bc.b.751.1 | 4 | |||
65.17 | odd | 12 | 1950.2.y.f.49.2 | 4 | |||
65.29 | even | 6 | 1950.2.bc.b.901.1 | 4 | |||
65.42 | odd | 12 | 1950.2.y.c.199.1 | 4 | |||
65.43 | odd | 12 | 1950.2.y.c.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.2 | ✓ | 4 | 13.3 | even | 3 | ||
390.2.bb.b.361.2 | yes | 4 | 13.4 | even | 6 | ||
1170.2.bs.e.361.1 | 4 | 39.17 | odd | 6 | |||
1170.2.bs.e.901.1 | 4 | 39.29 | odd | 6 | |||
1950.2.y.c.49.1 | 4 | 65.43 | odd | 12 | |||
1950.2.y.c.199.1 | 4 | 65.42 | odd | 12 | |||
1950.2.y.f.49.2 | 4 | 65.17 | odd | 12 | |||
1950.2.y.f.199.2 | 4 | 65.3 | odd | 12 | |||
1950.2.bc.b.751.1 | 4 | 65.4 | even | 6 | |||
1950.2.bc.b.901.1 | 4 | 65.29 | even | 6 | |||
5070.2.a.y.1.2 | 2 | 13.5 | odd | 4 | |||
5070.2.a.bg.1.1 | 2 | 13.8 | odd | 4 | |||
5070.2.b.o.1351.1 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.b.o.1351.4 | 4 | 13.12 | even | 2 | inner |