Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (of order \(2\), degree \(1\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 152x^{10} + 8222x^{8} + 194132x^{6} + 1882697x^{4} + 5152508x^{2} + 4008004 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.8 | ||
Root | \(5.90052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.a.239.7 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.18705 | + | 4.71347i | 0.420898 | + | 0.907108i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.5852i | 1.30454i | 0.757986 | + | 0.652270i | \(0.226183\pi\) | ||||
−0.757986 | + | 0.652270i | \(0.773817\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17.4336 | + | 20.6172i | −0.645689 | + | 0.763600i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.0233 | −0.850353 | −0.425177 | − | 0.905110i | \(-0.639788\pi\) | ||||
−0.425177 | + | 0.905110i | \(0.639788\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −55.7458 | −1.18932 | −0.594658 | − | 0.803979i | \(-0.702713\pi\) | ||||
−0.594658 | + | 0.803979i | \(0.702713\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −68.7469 | + | 31.8986i | −1.18336 | + | 0.549079i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 86.4384i | − | 1.23320i | −0.787277 | − | 0.616600i | \(-0.788510\pi\) | ||
0.787277 | − | 0.616600i | \(-0.211490\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 96.8558i | 1.16949i | 0.811218 | + | 0.584743i | \(0.198805\pi\) | ||||
−0.811218 | + | 0.584743i | \(0.801195\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 32.9943 | − | 15.3094i | 0.342855 | − | 0.159085i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 115.219 | 1.04456 | 0.522278 | − | 0.852775i | \(-0.325082\pi\) | ||||
0.522278 | + | 0.852775i | \(0.325082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −87.7283 | −0.701826 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −135.307 | − | 37.0818i | −0.964437 | − | 0.264311i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 49.1735i | − | 0.314872i | −0.987529 | − | 0.157436i | \(-0.949677\pi\) | ||
0.987529 | − | 0.157436i | \(-0.0503228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 12.5750i | − | 0.0728558i | −0.999336 | − | 0.0364279i | \(-0.988402\pi\) | ||
0.999336 | − | 0.0364279i | \(-0.0115979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −67.8496 | − | 146.228i | −0.357912 | − | 0.771362i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 102.096 | 0.493070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −296.822 | −1.31884 | −0.659421 | − | 0.751774i | \(-0.729199\pi\) | ||||
−0.659421 | + | 0.751774i | \(0.729199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −121.919 | − | 262.756i | −0.500581 | − | 1.07884i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 213.956i | − | 0.814982i | −0.913209 | − | 0.407491i | \(-0.866404\pi\) | ||
0.913209 | − | 0.407491i | \(-0.133596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 165.680i | 0.587581i | 0.955870 | + | 0.293790i | \(0.0949168\pi\) | ||||
−0.955870 | + | 0.293790i | \(0.905083\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −300.706 | − | 254.273i | −0.996148 | − | 0.842328i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 426.135 | 1.32251 | 0.661257 | − | 0.750159i | \(-0.270023\pi\) | ||||
0.661257 | + | 0.750159i | \(0.270023\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 407.425 | − | 189.045i | 1.11864 | − | 0.519052i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 460.767i | 1.19417i | 0.802177 | + | 0.597087i | \(0.203675\pi\) | ||||
−0.802177 | + | 0.597087i | \(0.796325\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 452.482i | − | 1.10932i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −456.527 | + | 211.829i | −1.06085 | + | 0.492235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −686.382 | −1.51456 | −0.757282 | − | 0.653088i | \(-0.773473\pi\) | ||||
−0.757282 | + | 0.653088i | \(0.773473\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −583.424 | −1.22459 | −0.612293 | − | 0.790631i | \(-0.709753\pi\) | ||||
−0.612293 | + | 0.790631i | \(0.709753\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 144.320 | + | 122.035i | 0.288614 | + | 0.244048i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 813.064i | − | 1.55151i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 589.155i | 1.07428i | 0.843493 | + | 0.537140i | \(0.180495\pi\) | ||||
−0.843493 | + | 0.537140i | \(0.819505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 251.989 | + | 543.080i | 0.439652 | + | 0.947524i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 766.330 | 1.28094 | 0.640469 | − | 0.767984i | \(-0.278740\pi\) | ||||
0.640469 | + | 0.767984i | \(0.278740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −904.778 | −1.45063 | −0.725317 | − | 0.688415i | \(-0.758307\pi\) | ||||
−0.725317 | + | 0.688415i | \(0.758307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −191.866 | − | 413.505i | −0.295397 | − | 0.636632i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 217.163i | 0.321403i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 459.440i | 0.654317i | 0.944969 | + | 0.327159i | \(0.106091\pi\) | ||||
−0.944969 | + | 0.327159i | \(0.893909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −121.139 | − | 718.865i | −0.166171 | − | 0.986097i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1115.25 | −1.47487 | −0.737436 | − | 0.675417i | \(-0.763964\pi\) | ||||
−0.737436 | + | 0.675417i | \(0.763964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1260.72 | 1.60876 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 231.778 | − | 107.545i | 0.285623 | − | 0.132529i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 119.900i | 0.142802i | 0.997448 | + | 0.0714011i | \(0.0227470\pi\) | ||||
−0.997448 | + | 0.0714011i | \(0.977253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 390.221i | 0.449519i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 59.2717 | − | 27.5021i | 0.0660881 | − | 0.0306649i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1412.66 | −1.52564 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −331.017 | −0.346491 | −0.173246 | − | 0.984879i | \(-0.555425\pi\) | ||||
−0.173246 | + | 0.984879i | \(0.555425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 540.848 | − | 639.614i | 0.549064 | − | 0.649330i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1609.16i | − | 1.58532i | −0.609662 | − | 0.792661i | \(-0.708695\pi\) | ||
0.609662 | − | 0.792661i | \(-0.291305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.96i | 1.32872i | 0.747411 | + | 0.664362i | \(0.231297\pi\) | ||||
−0.747411 | + | 0.664362i | \(0.768703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 223.290 | + | 481.229i | 0.207532 | + | 0.447268i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 502.365 | 0.453883 | 0.226941 | − | 0.973908i | \(-0.427127\pi\) | ||||
0.226941 | + | 0.973908i | \(0.427127\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1599.88 | 1.40588 | 0.702938 | − | 0.711251i | \(-0.251871\pi\) | ||||
0.702938 | + | 0.711251i | \(0.251871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −649.164 | − | 1399.06i | −0.555099 | − | 1.19633i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 934.016i | 0.777565i | 0.921330 | + | 0.388782i | \(0.127104\pi\) | ||||
−0.921330 | + | 0.388782i | \(0.872896\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1680.49i | 1.36266i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 971.851 | − | 1149.32i | 0.767928 | − | 0.908162i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −605.069 | −0.466105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −368.553 | −0.276900 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1008.47 | − | 467.932i | 0.739277 | − | 0.343025i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 543.616i | 0.388980i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 301.355i | 0.210558i | 0.994443 | + | 0.105279i | \(0.0335736\pi\) | ||||
−0.994443 | + | 0.105279i | \(0.966426\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −780.928 | + | 362.351i | −0.532999 | + | 0.247312i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −389.347 | −0.259675 | −0.129837 | − | 0.991535i | \(-0.541445\pi\) | ||||
−0.129837 | + | 0.991535i | \(0.541445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 677.991 | 0.442024 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 540.846 | − | 1973.48i | 0.344805 | − | 1.25815i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3037.04i | 1.89395i | 0.321302 | + | 0.946977i | \(0.395880\pi\) | ||||
−0.321302 | + | 0.946977i | \(0.604120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1287.18i | 0.785445i | 0.919657 | + | 0.392723i | \(0.128467\pi\) | ||||
−0.919657 | + | 0.392723i | \(0.871533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 931.979 | + | 2008.57i | 0.556644 | + | 1.19966i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1729.42 | 1.01134 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 717.205 | 0.410763 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −107.166 | − | 230.960i | −0.0601283 | − | 0.129587i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2051.44i | 1.12792i | 0.825801 | + | 0.563961i | \(0.190723\pi\) | ||||
−0.825801 | + | 0.563961i | \(0.809277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 473.535i | 0.255204i | 0.991825 | + | 0.127602i | \(0.0407280\pi\) | ||||
−0.991825 | + | 0.127602i | \(0.959272\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1782.12 | + | 1506.93i | 0.941671 | + | 0.796263i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 183.409 | 0.0950434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1184.81 | 0.602280 | 0.301140 | − | 0.953580i | \(-0.402633\pi\) | ||||
0.301140 | + | 0.953580i | \(0.402633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2171.81 | + | 1007.72i | −1.08324 | + | 0.502626i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 806.531i | − | 0.394805i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4055.24i | − | 1.94866i | −0.225132 | − | 0.974328i | \(-0.572281\pi\) | ||
0.225132 | − | 0.974328i | \(-0.427719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2132.76 | − | 989.601i | 1.00627 | − | 0.466911i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3681.23 | 1.70576 | 0.852881 | − | 0.522105i | \(-0.174853\pi\) | ||||
0.852881 | + | 0.522105i | \(0.174853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 910.598 | 0.414473 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1996.90 | − | 1688.55i | −0.893020 | − | 0.755125i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1069.27i | 0.469914i | 0.972006 | + | 0.234957i | \(0.0754949\pi\) | ||||
−0.972006 | + | 0.234957i | \(0.924505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 614.098i | 0.265265i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1501.15 | − | 3235.24i | −0.637478 | − | 1.37387i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2666.57 | 1.11346 | 0.556728 | − | 0.830695i | \(-0.312056\pi\) | ||||
0.556728 | + | 0.830695i | \(0.312056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2648.47 | 1.08762 | 0.543810 | − | 0.839208i | \(-0.316981\pi\) | ||||
0.543810 | + | 0.839208i | \(0.316981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1275.98 | − | 2749.95i | −0.515427 | − | 1.11083i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4329.20i | − | 1.72048i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2681.61i | 1.04865i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −259.573 | + | 947.148i | −0.0999003 | + | 0.364523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 864.174 | 0.327379 | 0.163690 | − | 0.986512i | \(-0.447660\pi\) | ||||
0.163690 | + | 0.986512i | \(0.447660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1133.69 | −0.422822 | −0.211411 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211411 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3832.36 | − | 1778.21i | 1.40739 | − | 0.653029i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1642.58i | − | 0.594056i | −0.954869 | − | 0.297028i | \(-0.904004\pi\) | ||
0.954869 | − | 0.297028i | \(-0.0959955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4912.39i | 1.74990i | 0.484213 | + | 0.874950i | \(0.339106\pi\) | ||||
−0.484213 | + | 0.874950i | \(0.660894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2776.96 | + | 1288.51i | −0.974487 | + | 0.452162i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −344.214 | −0.119010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3120.59 | 1.06318 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2008.68 | + | 2375.49i | −0.674458 | + | 0.797623i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3004.79i | − | 0.994476i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 928.566i | 0.302963i | 0.988460 | + | 0.151481i | \(0.0484043\pi\) | ||||
−0.988460 | + | 0.151481i | \(0.951596\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1676.00 | + | 3612.07i | 0.539145 | + | 1.16195i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2416.48 | −0.766523 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −88.0248 | −0.0275369 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1978.80 | − | 4264.64i | −0.610569 | − | 1.31588i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4818.58i | 1.46666i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 208.318i | − | 0.0625561i | −0.999511 | − | 0.0312781i | \(-0.990042\pi\) | ||
0.999511 | − | 0.0312781i | \(-0.00995774\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1529.42 | − | 1808.71i | 0.453161 | − | 0.535915i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6151.95 | −1.79876 | −0.899382 | − | 0.437165i | \(-0.855983\pi\) | ||||
−0.899382 | + | 0.437165i | \(0.855983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1493.71 | 0.431035 | 0.215518 | − | 0.976500i | \(-0.430856\pi\) | ||||
0.215518 | + | 0.976500i | \(0.430856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1023.59 | + | 474.947i | −0.291547 | + | 0.135278i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1003.48i | 0.282146i | 0.989999 | + | 0.141073i | \(0.0450552\pi\) | ||||
−0.989999 | + | 0.141073i | \(0.954945\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6215.27i | 1.72527i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2165.56 | + | 1004.82i | −0.593536 | + | 0.275401i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6048.49 | −1.63701 | −0.818503 | − | 0.574502i | \(-0.805196\pi\) | ||||
−0.818503 | + | 0.574502i | \(0.805196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5619.61 | −1.50204 | −0.751018 | − | 0.660282i | \(-0.770437\pi\) | ||||
−0.751018 | + | 0.660282i | \(0.770437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3123.41 | − | 2143.18i | 0.824555 | − | 0.565782i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 714.675i | − | 0.186363i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5399.31i | − | 1.39089i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2439.11 | − | 5256.69i | −0.620771 | − | 1.33787i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6402.41 | 1.61003 | 0.805013 | − | 0.593257i | \(-0.202158\pi\) | ||||
0.805013 | + | 0.593257i | \(0.202158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3574.47 | −0.888241 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2757.26 | + | 5942.37i | 0.677124 | + | 1.45932i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1609.20i | 0.390580i | 0.980746 | + | 0.195290i | \(0.0625648\pi\) | ||||
−0.980746 | + | 0.195290i | \(0.937435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2077.75i | 0.498475i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1013.82 | + | 857.271i | 0.240436 | + | 0.203309i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1897.73 | −0.444940 | −0.222470 | − | 0.974940i | \(-0.571412\pi\) | ||||
−0.222470 | + | 0.974940i | \(0.571412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6720.38 | −1.55785 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −565.146 | + | 262.228i | −0.129537 | + | 0.0601053i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3874.72i | 0.878238i | 0.898429 | + | 0.439119i | \(0.144709\pi\) | ||||
−0.898429 | + | 0.439119i | \(0.855291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1292.92i | 0.289813i | 0.989445 | + | 0.144906i | \(0.0462881\pi\) | ||||
−0.989445 | + | 0.144906i | \(0.953712\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1839.29 | + | 853.433i | −0.407762 | + | 0.189202i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2721.62 | 0.596800 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5644.74 | −1.22440 | −0.612202 | − | 0.790702i | \(-0.709716\pi\) | ||||
−0.612202 | + | 0.790702i | \(0.709716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 259.261 | + | 219.227i | 0.0556328 | + | 0.0470422i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1146.55i | − | 0.243407i | −0.992566 | − | 0.121704i | \(-0.961164\pi\) | ||
0.992566 | − | 0.121704i | \(-0.0388357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5222.40i | 1.09696i | 0.836164 | + | 0.548479i | \(0.184793\pi\) | ||||
−0.836164 | + | 0.548479i | \(0.815207\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3089.57 | − | 6658.54i | −0.642141 | − | 1.38392i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1497.69 | −0.308034 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2558.59 | −0.520780 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −723.951 | − | 1560.24i | −0.145838 | − | 0.314305i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4783.47i | − | 0.953765i | −0.878967 | − | 0.476883i | \(-0.841767\pi\) | ||
0.878967 | − | 0.476883i | \(-0.158233\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10011.0i | − | 1.97581i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4197.67 | + | 1150.40i | 0.820112 | + | 0.224758i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6422.97 | −1.24231 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1159.76 | 0.222085 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7584.74 | − | 3519.32i | 1.43806 | − | 0.667260i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8509.36i | − | 1.59752i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9710.23i | − | 1.80519i | −0.430494 | − | 0.902593i | \(-0.641661\pi\) | ||
0.430494 | − | 0.902593i | \(-0.358339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6546.84 | + | 3037.74i | −1.20530 | + | 0.559258i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3463.09 | 0.631427 | 0.315713 | − | 0.948855i | \(-0.397756\pi\) | ||||
0.315713 | + | 0.948855i | \(0.397756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2972.44 | 0.536780 | 0.268390 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268390 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1779.91 | + | 2104.94i | −0.318370 | + | 0.376508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1056.65i | − | 0.187217i | −0.995609 | − | 0.0936083i | \(-0.970160\pi\) | ||
0.995609 | − | 0.0936083i | \(-0.0298401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1525.52i | 0.267752i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1098.70 | + | 2367.88i | 0.191038 | + | 0.411720i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8372.06 | 1.44221 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4890.48 | 0.834693 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3499.02 | + | 7540.97i | 0.591731 | + | 1.27528i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2982.94i | − | 0.499863i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 11409.6i | − | 1.89465i | −0.320279 | − | 0.947323i | \(-0.603777\pi\) | ||
0.320279 | − | 0.947323i | \(-0.396223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5174.67 | − | 6119.63i | 0.851562 | − | 1.00707i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8592.94 | −1.40144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6052.69 | −0.978371 | −0.489185 | − | 0.872180i | \(-0.662706\pi\) | ||||
−0.489185 | + | 0.872180i | \(0.662706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4402.45 | + | 2042.74i | −0.705335 | + | 0.327276i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 390.117i | 0.0619532i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7920.94 | + | 3675.32i | −1.23608 | + | 0.573543i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1661.68 | −0.257071 | −0.128535 | − | 0.991705i | \(-0.541028\pi\) | ||||
−0.128535 | + | 0.991705i | \(0.541028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5890.92 | −0.903535 | −0.451768 | − | 0.892136i | \(-0.649206\pi\) | ||||
−0.451768 | + | 0.892136i | \(0.649206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7542.79 | + | 2067.16i | 1.14702 | + | 0.314350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4847.63i | 0.730916i | 0.930828 | + | 0.365458i | \(0.119088\pi\) | ||||
−0.930828 | + | 0.365458i | \(0.880912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11177.1i | 1.67104i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1323.32 | − | 2851.97i | −0.196183 | − | 0.422808i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9508.69 | 1.39791 | 0.698954 | − | 0.715166i | \(-0.253649\pi\) | ||||
0.698954 | + | 0.715166i | \(0.253649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2522.04 | −0.367699 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −806.046 | − | 1737.17i | −0.116547 | − | 0.251178i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13196.4i | − | 1.89241i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3663.26i | − | 0.521037i | −0.965469 | − | 0.260518i | \(-0.916106\pi\) | ||
0.965469 | − | 0.260518i | \(-0.0838935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4411.17 | + | 3730.02i | 0.622321 | + | 0.526225i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3225.37 | 0.451355 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6227.72 | 0.864502 | 0.432251 | − | 0.901753i | \(-0.357720\pi\) | ||||
0.432251 | + | 0.901753i | \(0.357720\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2562.32 | + | 1188.92i | −0.352847 | + | 0.163721i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2741.22i | 0.374482i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5881.91i | 0.797186i | 0.917128 | + | 0.398593i | \(0.130501\pi\) | ||||
−0.917128 | + | 0.398593i | \(0.869499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1420.43 | + | 659.079i | −0.190999 | + | 0.0886237i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3238.56 | −0.432069 | −0.216035 | − | 0.976386i | \(-0.569312\pi\) | ||||
−0.216035 | + | 0.976386i | \(0.569312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3167.37 | −0.419284 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3415.86 | − | 2888.40i | −0.448677 | − | 0.379395i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7962.71i | 1.03785i | 0.854818 | + | 0.518927i | \(0.173668\pi\) | ||||
−0.854818 | + | 0.518927i | \(0.826332\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9959.32i | − | 1.28814i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −851.521 | − | 1835.17i | −0.109297 | − | 0.235553i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6701.03 | −0.853583 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5784.53 | −0.731277 | −0.365639 | − | 0.930757i | \(-0.619149\pi\) | ||||
−0.365639 | + | 0.930757i | \(0.619149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1482.80 | + | 3195.69i | 0.186047 | + | 0.400964i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2460.74i | 0.306443i | 0.988192 | + | 0.153221i | \(0.0489647\pi\) | ||||
−0.988192 | + | 0.153221i | \(0.951035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 701.002i | 0.0866486i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10484.8 | − | 1766.84i | 1.28640 | − | 0.216777i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9208.39 | 1.12148 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12763.1 | 1.54301 | 0.771507 | − | 0.636221i | \(-0.219503\pi\) | ||||
0.771507 | + | 0.636221i | \(0.219503\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14315.0 | + | 6642.16i | −1.71802 | + | 0.797162i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4804.67i | 0.572452i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 16266.1i | − | 1.92403i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6067.07 | + | 2815.12i | −0.712483 | + | 0.330593i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7332.36 | −0.854915 | −0.427457 | − | 0.904035i | \(-0.640591\pi\) | ||||
−0.427457 | + | 0.904035i | \(0.640591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11584.3 | 1.34106 | 0.670528 | − | 0.741885i | \(-0.266068\pi\) | ||||
0.670528 | + | 0.741885i | \(0.266068\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7429.07 | + | 8785.71i | −0.853933 | + | 1.00987i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7583.09i | 0.865491i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4083.97i | 0.462850i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3782.33 | + | 8151.57i | 0.425671 | + | 0.917393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −973.251 | −0.108770 | −0.0543850 | − | 0.998520i | \(-0.517320\pi\) | ||||
−0.0543850 | + | 0.998520i | \(0.517320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6021.08 | −0.668256 | −0.334128 | − | 0.942528i | \(-0.608442\pi\) | ||||
−0.334128 | + | 0.942528i | \(0.608442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1568.56 | + | 3380.52i | 0.172890 | + | 0.372606i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11159.6i | 1.22159i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4643.72i | 0.504858i | 0.967615 | + | 0.252429i | \(0.0812295\pi\) | ||||
−0.967615 | + | 0.252429i | \(0.918771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 854.247 | − | 1010.24i | 0.0922413 | − | 0.109086i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14381.2 | 1.54238 | 0.771189 | − | 0.636606i | \(-0.219662\pi\) | ||||
0.771189 | + | 0.636606i | \(0.219662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1748.77 | −0.186291 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9669.40 | + | 4486.61i | −1.02315 | + | 0.474741i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10241.0i | 1.07639i | 0.842819 | + | 0.538197i | \(0.180894\pi\) | ||||
−0.842819 | + | 0.538197i | \(0.819106\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6637.62i | 0.693023i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2231.99 | + | 1035.65i | −0.231497 | + | 0.107415i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5691.45 | −0.586416 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18144.7 | 1.85728 | 0.928638 | − | 0.370988i | \(-0.120981\pi\) | ||||
0.928638 | + | 0.370988i | \(0.120981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3205.29 | + | 11695.7i | −0.325948 | + | 1.18934i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10005.2i | − | 1.01083i | −0.862877 | − | 0.505413i | \(-0.831340\pi\) | ||
0.862877 | − | 0.505413i | \(-0.168660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13659.6i | − | 1.37109i | −0.728031 | − | 0.685544i | \(-0.759564\pi\) | ||
0.728031 | − | 0.685544i | \(-0.240436\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 401.124 | + | 864.491i | 0.0400036 | + | 0.0862146i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11500.9 | 1.13961 | 0.569804 | − | 0.821781i | \(-0.307019\pi\) | ||||
0.569804 | + | 0.821781i | \(0.307019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4124.08 | 0.406039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2591.24 | + | 5584.56i | 0.253499 | + | 0.546333i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5139.95i | − | 0.499651i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8496.99i | − | 0.820776i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9499.73 | − | 8032.83i | −0.911871 | − | 0.771065i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3223.54 | −0.307489 | −0.153745 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153745 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16546.6 | 1.56852 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3801.56 | − | 1763.93i | 0.358131 | − | 0.166173i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4827.95i | − | 0.452012i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13316.6i | − | 1.23908i | −0.784964 | − | 0.619542i | \(-0.787318\pi\) | ||
0.784964 | − | 0.619542i | \(-0.212682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19114.3 | − | 8869.03i | 1.76764 | − | 0.820187i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4229.41 | −0.388739 | −0.194369 | − | 0.980928i | \(-0.562266\pi\) | ||||
−0.194369 | + | 0.980928i | \(0.562266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4250.47 | −0.388300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9328.91 | + | 7888.38i | 0.847077 | + | 0.716276i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5364.31i | − | 0.484149i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2412.58i | − | 0.216437i | −0.994127 | − | 0.108219i | \(-0.965485\pi\) | ||
0.994127 | − | 0.108219i | \(-0.0345146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8051.05 | + | 17351.4i | 0.717953 | + | 1.54731i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6942.70 | 0.615427 | 0.307714 | − | 0.951479i | \(-0.400436\pi\) | ||||
0.307714 | + | 0.951479i | \(0.400436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23470.0 | 2.06812 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1991.52 | + | 4292.07i | 0.174451 | + | 0.375972i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5335.45i | − | 0.464616i | −0.972642 | − | 0.232308i | \(-0.925372\pi\) | ||
0.972642 | − | 0.232308i | \(-0.0746278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6333.44i | 0.548288i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3591.59 | − | 13105.2i | 0.309108 | − | 1.12790i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20258.3 | −1.73337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13220.1 | −1.12460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5039.97 | + | 2338.55i | −0.426262 | + | 0.197786i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4804.38i | − | 0.404000i | −0.979386 | − | 0.202000i | \(-0.935256\pi\) | ||
0.979386 | − | 0.202000i | \(-0.0647440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20692.5i | − | 1.73006i | −0.501722 | − | 0.865029i | \(-0.667300\pi\) | ||
0.501722 | − | 0.865029i | \(-0.332700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2894.53 | + | 1343.06i | −0.240624 | + | 0.111650i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1086.96 | −0.0898458 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1108.36 | 0.0910959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11966.1 | − | 14151.3i | 0.977938 | − | 1.15652i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11927.1i | 0.969271i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7327.09i | 0.592108i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5831.93 | + | 12568.8i | 0.468652 | + | 1.01003i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1520.14 | 0.121479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5176.25 | −0.411357 | −0.205679 | − | 0.978620i | \(-0.565940\pi\) | ||||
−0.205679 | + | 0.978620i | \(0.565940\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5792.34 | + | 12483.5i | 0.457777 | + | 0.986588i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23334.5i | 1.83402i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 439.585i | 0.0343607i | 0.999852 | + | 0.0171804i | \(0.00546895\pi\) | ||||
−0.999852 | + | 0.0171804i | \(0.994531\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10171.2 | − | 12028.6i | 0.790702 | − | 0.935095i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4762.73 | 0.368238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3216.08 | 0.247309 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20405.6 | − | 9468.20i | 1.56066 | − | 0.724149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19663.7i | − | 1.49583i | −0.663795 | − | 0.747914i | \(-0.731055\pi\) | ||
0.663795 | − | 0.747914i | \(-0.268945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9235.97i | − | 0.698819i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12639.7 | + | 5864.81i | −0.951243 | + | 0.441377i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3268.52 | 0.244675 | 0.122337 | − | 0.992489i | \(-0.460961\pi\) | ||||
0.122337 | + | 0.992489i | \(0.460961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13622.8 | −1.01436 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5032.05 | + | 847.973i | −0.372710 | + | 0.0628069i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12364.5i | 0.910980i | 0.890241 | + | 0.455490i | \(0.150536\pi\) | ||||
−0.890241 | + | 0.455490i | \(0.849464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12593.6i | 0.922990i | 0.887143 | + | 0.461495i | \(0.152687\pi\) | ||||
−0.887143 | + | 0.461495i | \(0.847313\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1889.99 | + | 4073.26i | 0.137793 | + | 0.296968i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10107.9 | −0.733096 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13016.7 | −0.939156 | −0.469578 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469578 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2479.43 | − | 5343.60i | −0.177965 | − | 0.383545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7806.74i | 0.557449i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14294.5i | − | 1.01547i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16763.1 | + | 14174.6i | 1.18473 | + | 1.00179i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16247.0 | 1.14240 | 0.571199 | − | 0.820812i | \(-0.306479\pi\) | ||||
0.571199 | + | 0.820812i | \(0.306479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1217.96 | 0.0852039 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7742.26 | − | 3592.41i | 0.538873 | − | 0.250037i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17711.4i | − | 1.22651i | −0.789885 | − | 0.613256i | \(-0.789860\pi\) | ||
0.789885 | − | 0.613256i | \(-0.210140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 8825.05i | − | 0.608053i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23154.4 | + | 10743.7i | −1.58735 | + | 0.736530i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8240.46 | 0.562097 | 0.281048 | − | 0.959694i | \(-0.409318\pi\) | ||||
0.281048 | + | 0.959694i | \(0.409318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5366.47 | 0.364231 | 0.182116 | − | 0.983277i | \(-0.441706\pi\) | ||||
0.182116 | + | 0.983277i | \(0.441706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12146.7 | − | 10271.1i | −0.820320 | − | 0.693650i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 5375.43i | − | 0.361227i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7742.72i | 0.517739i | 0.965912 | + | 0.258869i | \(0.0833499\pi\) | ||||
−0.965912 | + | 0.258869i | \(0.916650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −752.814 | − | 1622.44i | −0.0500913 | − | 0.107955i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23755.2 | −1.57289 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2581.09 | 0.170064 | 0.0850320 | − | 0.996378i | \(-0.472901\pi\) | ||||
0.0850320 | + | 0.996378i | \(0.472901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6824.89 | + | 14708.8i | 0.447490 | + | 0.964416i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5974.41i | 0.389823i | 0.980821 | + | 0.194911i | \(0.0624419\pi\) | ||||
−0.980821 | + | 0.194911i | \(0.937558\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6142.33i | 0.398839i | 0.979914 | + | 0.199419i | \(0.0639056\pi\) | ||||
−0.979914 | + | 0.199419i | \(0.936094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15589.9 | − | 4272.52i | −1.00741 | − | 0.276088i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 839.302 | 0.0539742 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18894.8 | −1.20927 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14163.0 | − | 6571.63i | 0.902097 | − | 0.418574i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25656.8i | 1.62639i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4185.65i | − | 0.264070i | −0.991245 | − | 0.132035i | \(-0.957849\pi\) | ||
0.991245 | − | 0.132035i | \(-0.0421511\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4376.77 | + | 2030.82i | −0.274820 | + | 0.127517i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4395.32 | −0.274682 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2731.55 | 0.169902 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13359.9 | + | 15799.6i | −0.827088 | + | 0.978125i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11627.2i | − | 0.716452i | −0.933635 | − | 0.358226i | \(-0.883382\pi\) | ||
0.933635 | − | 0.358226i | \(-0.116618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30093.1i | 1.84565i | 0.385215 | + | 0.922827i | \(0.374127\pi\) | ||||
−0.385215 | + | 0.922827i | \(0.625873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5284.96 | − | 11390.0i | −0.322628 | − | 0.695319i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23676.7 | −1.43868 | −0.719340 | − | 0.694659i | \(-0.755555\pi\) | ||||
−0.719340 | + | 0.694659i | \(0.755555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21293.8 | 1.28791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −192.515 | − | 414.902i | −0.0115902 | − | 0.0249790i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13535.0i | − | 0.811126i | −0.914067 | − | 0.405563i | \(-0.867076\pi\) | ||
0.914067 | − | 0.405563i | \(-0.132924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5678.70i | − | 0.338756i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15773.5 | − | 18654.0i | 0.936658 | − | 1.10770i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4587.12 | −0.271152 | −0.135576 | − | 0.990767i | \(-0.543288\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22014.3 | −1.29540 | −0.647698 | − | 0.761897i | \(-0.724268\pi\) | ||||
−0.647698 | + | 0.761897i | \(0.724268\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22712.2 | + | 10538.5i | −1.33042 | + | 0.617316i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9888.63i | 0.576639i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5665.70i | − | 0.328901i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 981.902 | − | 455.603i | 0.0567452 | − | 0.0263298i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18099.8 | 1.04133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5312.83 | 0.304301 | 0.152150 | − | 0.988357i | \(-0.451380\pi\) | ||||
0.152150 | + | 0.988357i | \(0.451380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11870.2 | + | 3253.13i | 0.676867 | + | 0.185501i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 31630.1i | − | 1.79563i | −0.440372 | − | 0.897815i | \(-0.645154\pi\) | ||
0.440372 | − | 0.897815i | \(-0.354846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2317.12i | 0.130961i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13454.6 | − | 28997.0i | −0.757097 | − | 1.63167i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16304.5 | 0.913435 | 0.456718 | − | 0.889612i | \(-0.349025\pi\) | ||||
0.456718 | + | 0.889612i | \(0.349025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44295.8 | −2.47074 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3266.82 | + | 7040.55i | 0.181422 | + | 0.390995i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 25685.8i | − | 1.42025i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9225.62i | 0.507900i | 0.967217 | + | 0.253950i | \(0.0817299\pi\) | ||||
−0.967217 | + | 0.253950i | \(0.918270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4477.30 | − | 3785.94i | −0.245424 | − | 0.207527i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18773.7 | −1.02464 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18494.0 | −1.00504 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4729.86 | + | 2194.66i | −0.255937 | + | 0.118755i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4759.97i | 0.256464i | 0.991744 | + | 0.128232i | \(0.0409303\pi\) | ||||
−0.991744 | + | 0.128232i | \(0.959070\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28748.9i | − | 1.54237i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29295.5 | + | 13593.1i | −1.56501 | + | 0.726165i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11264.1 | −0.599196 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29605.9 | 1.56823 | 0.784114 | − | 0.620617i | \(-0.213118\pi\) | ||||
0.784114 | + | 0.620617i | \(0.213118\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9472.38 | − | 8009.70i | −0.499637 | − | 0.422485i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1448.87i | − | 0.0761020i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25224.0i | 1.31933i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13228.4 | − | 28509.4i | −0.689013 | − | 1.48494i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34086.2 | −1.76801 | −0.884007 | − | 0.467474i | \(-0.845164\pi\) | ||||
−0.884007 | + | 0.467474i | \(0.845164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9722.74 | 0.502211 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12290.4 | − | 26487.8i | −0.632204 | − | 1.36251i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4313.90i | 0.220985i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15552.2i | 0.793396i | 0.917949 | + | 0.396698i | \(0.129844\pi\) | ||||
−0.917949 | + | 0.396698i | \(0.870156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16932.9 | + | 10034.9i | 0.860279 | + | 0.509823i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14321.1 | 0.724604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1511.48 | −0.0761636 | −0.0380818 | − | 0.999275i | \(-0.512125\pi\) | ||||
−0.0380818 | + | 0.999275i | \(0.512125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3368.60 | − | 1563.03i | 0.169051 | − | 0.0784399i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18277.5i | − | 0.913517i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6749.94i | 0.335995i | 0.985787 | + | 0.167998i | \(0.0537301\pi\) | ||||
−0.985787 | + | 0.167998i | \(0.946270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25449.5 | − | 11808.6i | 1.26169 | − | 0.585423i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24008.4 | 1.18544 | 0.592719 | − | 0.805409i | \(-0.298054\pi\) | ||||
0.592719 | + | 0.805409i | \(0.298054\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29920.7 | −1.47142 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19442.8 | − | 22993.3i | 0.952309 | − | 1.12621i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3516.55i | − | 0.171552i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35758.5i | 1.73748i | 0.495272 | + | 0.868738i | \(0.335069\pi\) | ||||
−0.495272 | + | 0.868738i | \(0.664931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14002.4 | + | 30177.6i | 0.677658 | + | 1.46047i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6906.61 | −0.332924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12640.7 | −0.606916 | −0.303458 | − | 0.952845i | \(-0.598141\pi\) | ||||
−0.303458 | + | 0.952845i | \(0.598141\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7817.55 | − | 16848.2i | −0.373859 | − | 0.805730i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28346.1i | 1.35026i | 0.737699 | + | 0.675129i | \(0.235912\pi\) | ||||
−0.737699 | + | 0.675129i | \(0.764088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11199.1i | − | 0.531371i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21978.9 | + | 25992.6i | −1.03876 | + | 1.22845i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38262.9 | 1.80130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15226.0 | −0.713999 | −0.356999 | − | 0.934105i | \(-0.616200\pi\) | ||||
−0.356999 | + | 0.934105i | \(0.616200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7584.91 | + | 3519.40i | −0.354298 | + | 0.164395i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20084.4i | 0.934522i | 0.884119 | + | 0.467261i | \(0.154759\pi\) | ||||
−0.884119 | + | 0.467261i | \(0.845241\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1103.18i | 0.0511321i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9793.42 | + | 4544.15i | −0.452171 | + | 0.209808i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20722.8 | 0.953110 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23774.1 | −1.08925 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1823.44 | + | 6653.50i | −0.0832242 | + | 0.303674i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17280.7i | 0.785699i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18800.0i | 0.851522i | 0.904836 | + | 0.425761i | \(0.139994\pi\) | ||||
−0.904836 | + | 0.425761i | \(0.860006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4150.44 | − | 8944.91i | −0.187275 | − | 0.403609i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6538.11 | 0.293892 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32523.5 | 1.45642 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14697.8 | − | 31676.3i | −0.655696 | − | 1.41314i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 28103.9i | − | 1.24905i | −0.781005 | − | 0.624524i | \(-0.785293\pi\) | ||
0.781005 | − | 0.624524i | \(-0.214707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36834.4i | − | 1.63092i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2472.01 | − | 2090.29i | −0.109044 | − | 0.0922059i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28069.2 | 1.23355 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11763.4 | 0.515039 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18263.4 | + | 8474.22i | −0.796656 | + | 0.369649i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7958.95i | − | 0.345886i | −0.984932 | − | 0.172943i | \(-0.944672\pi\) | ||
0.984932 | − | 0.172943i | \(-0.0553276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18626.6i | − | 0.806494i | −0.915091 | − | 0.403247i | \(-0.867882\pi\) | ||
0.915091 | − | 0.403247i | \(-0.132118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6094.14 | + | 2827.68i | −0.262892 | + | 0.121982i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 59146.5 | 2.54210 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16047.1 | −0.687168 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8045.27 | − | 6802.95i | −0.343253 | − | 0.290250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 34766.7i | − | 1.47791i | −0.673753 | − | 0.738957i | \(-0.735319\pi\) | ||
0.673753 | − | 0.738957i | \(-0.264681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22756.3i | 0.963832i | 0.876217 | + | 0.481916i | \(0.160059\pi\) | ||||
−0.876217 | + | 0.481916i | \(0.839941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5952.33 | + | 12828.3i | 0.251192 | + | 0.541362i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25960.0 | −1.09156 | −0.545778 | − | 0.837930i | \(-0.683766\pi\) | ||||
−0.545778 | + | 0.837930i | \(0.683766\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9264.02 | −0.388121 | −0.194061 | − | 0.980990i | \(-0.562166\pi\) | ||||
−0.194061 | + | 0.980990i | \(0.562166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12345.3 | − | 26606.3i | −0.515349 | − | 1.11067i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4235.48i | 0.176171i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53691.6i | 2.22524i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −466.303 | + | 1701.48i | −0.0192566 | + | 0.0702649i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16620.6 | −0.683917 | −0.341959 | − | 0.939715i | \(-0.611090\pi\) | ||||
−0.341959 | + | 0.939715i | \(0.611090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21971.0 | 0.900856 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5404.23 | − | 2507.56i | 0.220797 | − | 0.102450i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13281.3i | 0.540697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2579.87i | 0.104658i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24615.6 | + | 11421.7i | −0.995060 | + | 0.461708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34199.4 | −1.37760 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18494.8 | 0.742379 | 0.371190 | − | 0.928557i | \(-0.378950\pi\) | ||||
0.371190 | + | 0.928557i | \(0.378950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24627.8 | − | 29125.1i | 0.985091 | − | 1.16498i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 293.990i | 0.0117182i | 0.999983 | + | 0.00585910i | \(0.00186502\pi\) | ||||
−0.999983 | + | 0.00585910i | \(0.998135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 11212.2i | − | 0.445351i | −0.974893 | − | 0.222675i | \(-0.928521\pi\) | ||
0.974893 | − | 0.222675i | \(-0.0714790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3275.53 | − | 7059.32i | −0.129651 | − | 0.279420i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17496.3 | −0.690129 | −0.345064 | − | 0.938579i | \(-0.612143\pi\) | ||||
−0.345064 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15595.5 | −0.613021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5595.77 | − | 12059.8i | −0.219195 | − | 0.472403i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 14253.4i | − | 0.556401i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 32842.9i | − | 1.27766i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5770.81 | − | 6824.64i | 0.223726 | − | 0.264581i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3805.31 | 0.147021 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15209.2 | −0.585607 | −0.292804 | − | 0.956173i | \(-0.594588\pi\) | ||||
−0.292804 | + | 0.956173i | \(0.594588\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22546.7 | − | 10461.7i | 0.865168 | − | 0.401438i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23485.7i | 0.898132i | 0.893499 | + | 0.449066i | \(0.148243\pi\) | ||||
−0.893499 | + | 0.449066i | \(0.851757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38770.5i | 1.47761i | 0.673919 | + | 0.738805i | \(0.264610\pi\) | ||||
−0.673919 | + | 0.738805i | \(0.735390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 47186.7 | − | 21894.6i | 1.79227 | − | 0.831616i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24491.0 | 0.927089 | 0.463544 | − | 0.886074i | \(-0.346578\pi\) | ||||
0.463544 | + | 0.886074i | \(0.346578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2109.48 | 0.0795836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3758.13 | + | 22301.6i | 0.141304 | + | 0.838531i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41273.6i | 1.54666i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38892.5i | 1.45255i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14047.4 | − | 30274.5i | −0.522885 | − | 1.12691i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −618.355 | −0.0229402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39827.9 | 1.47265 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2536.46 | + | 5466.50i | 0.0934751 | + | 0.201455i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38628.5i | 1.41884i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16043.5i | − | 0.587339i | −0.955907 | − | 0.293670i | \(-0.905123\pi\) | ||
0.955907 | − | 0.293670i | \(-0.0948765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33176.4 | + | 28053.5i | 1.21055 | + | 1.02363i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20367.3 | 0.740723 | 0.370362 | − | 0.928888i | \(-0.379234\pi\) | ||||
0.370362 | + | 0.928888i | \(0.379234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34598.7 | 1.25416 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40108.6 | − | 18610.4i | 1.44913 | − | 0.672395i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2725.43i | 0.0981478i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27011.0i | 0.969542i | 0.874641 | + | 0.484771i | \(0.161097\pi\) | ||||
−0.874641 | + | 0.484771i | \(0.838903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45768.9 | − | 21236.8i | 1.63750 | − | 0.759800i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42719.7 | −1.52344 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26039.6 | 0.925598 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28636.6 | − | 24214.6i | −1.01461 | − | 0.857943i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29191.8i | − | 1.03095i | −0.856905 | − | 0.515474i | \(-0.827616\pi\) | ||
0.856905 | − | 0.515474i | \(-0.172384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4745.93i | − | 0.167069i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7573.96 | + | 16323.2i | 0.265767 | + | 0.572772i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39111.8 | −1.36801 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44629.5 | −1.55601 | −0.778006 | − | 0.628257i | \(-0.783769\pi\) | ||||
−0.778006 | + | 0.628257i | \(0.783769\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6500.88 | + | 14010.5i | 0.225930 | + | 0.486918i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5317.21i | 0.184204i | 0.995750 | + | 0.0921021i | \(0.0293586\pi\) | ||||
−0.995750 | + | 0.0921021i | \(0.970641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 24651.7i | − | 0.851294i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13814.3 | − | 3785.92i | −0.475535 | − | 0.130324i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7403.69 | 0.254052 | 0.127026 | − | 0.991899i | \(-0.459457\pi\) | ||||
0.127026 | + | 0.991899i | \(0.459457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50437.6 | 1.72526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4980.51 | − | 2310.96i | 0.169826 | − | 0.0787992i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30007.8i | − | 1.01999i | −0.860178 | − | 0.509993i | \(-0.829648\pi\) | ||
0.860178 | − | 0.509993i | \(-0.170352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12604.2i | 0.427080i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7190.51 | + | 3336.40i | −0.242880 | + | 0.112696i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21259.3 | 0.715847 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29632.9 | 0.994692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8758.03 | + | 10357.4i | −0.293067 | + | 0.346585i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 16535.1i | − | 0.551588i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44735.5i | 1.48769i | 0.668352 | + | 0.743846i | \(0.267000\pi\) | ||||
−0.668352 | + | 0.743846i | \(0.733000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18310.1 | + | 39461.4i | 0.607024 | + | 1.30824i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9285.42 | −0.306883 | −0.153441 | − | 0.988158i | \(-0.549036\pi\) | ||||
−0.153441 | + | 0.988158i | \(0.549036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9010.23 | 0.296870 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10695.7 | + | 23051.2i | 0.351321 | + | 0.757157i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 17486.1i | − | 0.572600i | −0.958140 | − | 0.286300i | \(-0.907575\pi\) | ||
0.958140 | − | 0.286300i | \(-0.0924254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3719.71i | − | 0.121432i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27891.6 | + | 32985.0i | −0.907759 | + | 1.07353i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51426.1 | −1.66860 | −0.834302 | − | 0.551307i | \(-0.814129\pi\) | ||||
−0.834302 | + | 0.551307i | \(0.814129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23957.4 | 0.774971 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14060.0 | − | 6523.85i | 0.453430 | − | 0.210392i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19089.5i | 0.613761i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29365.3i | − | 0.941290i | −0.882323 | − | 0.470645i | \(-0.844021\pi\) | ||
0.882323 | − | 0.470645i | \(-0.155979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 53778.8 | − | 24953.4i | 1.71865 | − | 0.797454i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71648.3 | −2.28282 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8452.97 | −0.268514 | −0.134257 | − | 0.990947i | \(-0.542865\pi\) | ||||
−0.134257 | + | 0.990947i | \(0.542865\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40162.0 | + | 11006.7i | 1.27194 | + | 0.348585i |
(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 | 336.4.h.a.239.8 | yes | 12 | |
3.2 | odd | 2 | inner | 336.4.h.a.239.6 | yes | 12 | |
4.3 | odd | 2 | inner | 336.4.h.a.239.5 | ✓ | 12 | |
12.11 | even | 2 | inner | 336.4.h.a.239.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.a.239.5 | ✓ | 12 | 4.3 | odd | 2 | inner | |
336.4.h.a.239.6 | yes | 12 | 3.2 | odd | 2 | inner | |
336.4.h.a.239.7 | yes | 12 | 12.11 | even | 2 | inner | |
336.4.h.a.239.8 | yes | 12 | 1.1 | even | 1 | trivial |