Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Root | \(13.3074i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.5.d.a.43.2 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | − | 2.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 12.3074i | 1.36749i | 0.729721 | + | 0.683745i | \(0.239650\pi\) | ||||
−0.729721 | + | 0.683745i | \(0.760350\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | 10.7621 | − | 10.7621i | 0.430483 | − | 0.430483i | −0.458309 | − | 0.888793i | \(-0.651545\pi\) |
0.888793 | + | 0.458309i | \(0.151545\pi\) | |||||||
\(6\) | 24.6148 | − | 24.6148i | 0.683745 | − | 0.683745i | ||||
\(7\) | 35.0611 | 0.715534 | 0.357767 | − | 0.933811i | \(-0.383538\pi\) | ||||
0.357767 | + | 0.933811i | \(0.383538\pi\) | |||||||
\(8\) | 16.0000 | − | 16.0000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −70.4723 | −0.870028 | ||||||||
\(10\) | −43.0483 | −0.430483 | ||||||||
\(11\) | 142.240i | 1.17553i | 0.809030 | + | 0.587767i | \(0.199993\pi\) | ||||
−0.809030 | + | 0.587767i | \(0.800007\pi\) | |||||||
\(12\) | −98.4593 | −0.683745 | ||||||||
\(13\) | −181.910 | + | 181.910i | −1.07639 | + | 1.07639i | −0.0795603 | + | 0.996830i | \(0.525352\pi\) |
−0.996830 | + | 0.0795603i | \(0.974648\pi\) | |||||||
\(14\) | −70.1223 | − | 70.1223i | −0.357767 | − | 0.357767i | ||||
\(15\) | 132.453 | + | 132.453i | 0.588681 | + | 0.588681i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −88.0634 | + | 88.0634i | −0.304718 | + | 0.304718i | −0.842856 | − | 0.538139i | \(-0.819128\pi\) |
0.538139 | + | 0.842856i | \(0.319128\pi\) | |||||||
\(18\) | 140.945 | + | 140.945i | 0.435014 | + | 0.435014i | ||||
\(19\) | 13.8864 | − | 13.8864i | 0.0384665 | − | 0.0384665i | −0.687612 | − | 0.726078i | \(-0.741341\pi\) |
0.726078 | + | 0.687612i | \(0.241341\pi\) | |||||||
\(20\) | 86.0967 | + | 86.0967i | 0.215242 | + | 0.215242i | ||||
\(21\) | 431.512i | 0.978485i | ||||||||
\(22\) | 284.479 | − | 284.479i | 0.587767 | − | 0.587767i | ||||
\(23\) | 79.7242 | − | 79.7242i | 0.150707 | − | 0.150707i | −0.627727 | − | 0.778434i | \(-0.716014\pi\) |
0.778434 | + | 0.627727i | \(0.216014\pi\) | |||||||
\(24\) | 196.919 | + | 196.919i | 0.341872 | + | 0.341872i | ||||
\(25\) | 393.355i | 0.629368i | ||||||||
\(26\) | 727.640 | 1.07639 | ||||||||
\(27\) | 129.569i | 0.177735i | ||||||||
\(28\) | 280.489i | 0.357767i | ||||||||
\(29\) | 420.383 | + | 420.383i | 0.499861 | + | 0.499861i | 0.911395 | − | 0.411534i | \(-0.135007\pi\) |
−0.411534 | + | 0.911395i | \(0.635007\pi\) | |||||||
\(30\) | − | 529.813i | − | 0.588681i | ||||||
\(31\) | −624.657 | − | 624.657i | −0.650007 | − | 0.650007i | 0.302987 | − | 0.952995i | \(-0.402016\pi\) |
−0.952995 | + | 0.302987i | \(0.902016\pi\) | |||||||
\(32\) | 128.000 | + | 128.000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1750.60 | −1.60753 | ||||||||
\(34\) | 352.253 | 0.304718 | ||||||||
\(35\) | 377.331 | − | 377.331i | 0.308025 | − | 0.308025i | ||||
\(36\) | − | 563.778i | − | 0.435014i | ||||||
\(37\) | −7.65345 | − | 1368.98i | −0.00559054 | − | 0.999984i | ||||
\(38\) | −55.5457 | −0.0384665 | ||||||||
\(39\) | −2238.84 | − | 2238.84i | −1.47195 | − | 1.47195i | ||||
\(40\) | − | 344.387i | − | 0.215242i | ||||||
\(41\) | 1239.16i | 0.737154i | 0.929597 | + | 0.368577i | \(0.120155\pi\) | ||||
−0.929597 | + | 0.368577i | \(0.879845\pi\) | |||||||
\(42\) | 863.024 | − | 863.024i | 0.489242 | − | 0.489242i | ||||
\(43\) | 607.562 | − | 607.562i | 0.328590 | − | 0.328590i | −0.523460 | − | 0.852050i | \(-0.675359\pi\) |
0.852050 | + | 0.523460i | \(0.175359\pi\) | |||||||
\(44\) | −1137.92 | −0.587767 | ||||||||
\(45\) | −758.428 | + | 758.428i | −0.374533 | + | 0.374533i | ||||
\(46\) | −318.897 | −0.150707 | ||||||||
\(47\) | 2971.58 | 1.34521 | 0.672607 | − | 0.740000i | \(-0.265175\pi\) | ||||
0.672607 | + | 0.740000i | \(0.265175\pi\) | |||||||
\(48\) | − | 787.674i | − | 0.341872i | ||||||
\(49\) | −1171.72 | −0.488012 | ||||||||
\(50\) | 786.710 | − | 786.710i | 0.314684 | − | 0.314684i | ||||
\(51\) | −1083.83 | − | 1083.83i | −0.416698 | − | 0.416698i | ||||
\(52\) | −1455.28 | − | 1455.28i | −0.538195 | − | 0.538195i | ||||
\(53\) | 1041.64 | 0.370822 | 0.185411 | − | 0.982661i | \(-0.440638\pi\) | ||||
0.185411 | + | 0.982661i | \(0.440638\pi\) | |||||||
\(54\) | 259.138 | − | 259.138i | 0.0888676 | − | 0.0888676i | ||||
\(55\) | 1530.80 | + | 1530.80i | 0.506048 | + | 0.506048i | ||||
\(56\) | 560.978 | − | 560.978i | 0.178883 | − | 0.178883i | ||||
\(57\) | 170.906 | + | 170.906i | 0.0526026 | + | 0.0526026i | ||||
\(58\) | − | 1681.53i | − | 0.499861i | ||||||
\(59\) | 1896.67 | − | 1896.67i | 0.544863 | − | 0.544863i | −0.380087 | − | 0.924951i | \(-0.624106\pi\) |
0.924951 | + | 0.380087i | \(0.124106\pi\) | |||||||
\(60\) | −1059.63 | + | 1059.63i | −0.294341 | + | 0.294341i | ||||
\(61\) | 4012.39 | + | 4012.39i | 1.07831 | + | 1.07831i | 0.996661 | + | 0.0816497i | \(0.0260189\pi\) |
0.0816497 | + | 0.996661i | \(0.473981\pi\) | |||||||
\(62\) | 2498.63i | 0.650007i | ||||||||
\(63\) | −2470.84 | −0.622534 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 3915.46i | 0.926736i | ||||||||
\(66\) | 3501.20 | + | 3501.20i | 0.803766 | + | 0.803766i | ||||
\(67\) | 2338.93i | 0.521037i | 0.965469 | + | 0.260518i | \(0.0838934\pi\) | ||||
−0.965469 | + | 0.260518i | \(0.916107\pi\) | |||||||
\(68\) | −704.507 | − | 704.507i | −0.152359 | − | 0.152359i | ||||
\(69\) | 981.198 | + | 981.198i | 0.206091 | + | 0.206091i | ||||
\(70\) | −1509.32 | −0.308025 | ||||||||
\(71\) | 3648.82 | 0.723830 | 0.361915 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361915 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(72\) | −1127.56 | + | 1127.56i | −0.217507 | + | 0.217507i | ||||
\(73\) | − | 9943.51i | − | 1.86592i | −0.359976 | − | 0.932962i | \(-0.617215\pi\) | ||
0.359976 | − | 0.932962i | \(-0.382785\pi\) | |||||||
\(74\) | −2722.65 | + | 2753.26i | −0.497197 | + | 0.502787i | ||||
\(75\) | −4841.18 | −0.860655 | ||||||||
\(76\) | 111.091 | + | 111.091i | 0.0192333 | + | 0.0192333i | ||||
\(77\) | 4987.09i | 0.841135i | ||||||||
\(78\) | 8955.36i | 1.47195i | ||||||||
\(79\) | 6403.03 | − | 6403.03i | 1.02596 | − | 1.02596i | 0.0263085 | − | 0.999654i | \(-0.491625\pi\) |
0.999654 | − | 0.0263085i | \(-0.00837522\pi\) | |||||||
\(80\) | −688.773 | + | 688.773i | −0.107621 | + | 0.107621i | ||||
\(81\) | −7302.91 | −1.11308 | ||||||||
\(82\) | 2478.31 | − | 2478.31i | 0.368577 | − | 0.368577i | ||||
\(83\) | −7154.52 | −1.03854 | −0.519271 | − | 0.854610i | \(-0.673797\pi\) | ||||
−0.519271 | + | 0.854610i | \(0.673797\pi\) | |||||||
\(84\) | −3452.09 | −0.489242 | ||||||||
\(85\) | 1895.49i | 0.262352i | ||||||||
\(86\) | −2430.25 | −0.328590 | ||||||||
\(87\) | −5173.82 | + | 5173.82i | −0.683555 | + | 0.683555i | ||||
\(88\) | 2275.84 | + | 2275.84i | 0.293884 | + | 0.293884i | ||||
\(89\) | 2259.76 | + | 2259.76i | 0.285287 | + | 0.285287i | 0.835213 | − | 0.549926i | \(-0.185344\pi\) |
−0.549926 | + | 0.835213i | \(0.685344\pi\) | |||||||
\(90\) | 3033.71 | 0.374533 | ||||||||
\(91\) | −6377.97 | + | 6377.97i | −0.770193 | + | 0.770193i | ||||
\(92\) | 637.794 | + | 637.794i | 0.0753537 | + | 0.0753537i | ||||
\(93\) | 7687.91 | − | 7687.91i | 0.888878 | − | 0.888878i | ||||
\(94\) | −5943.15 | − | 5943.15i | −0.672607 | − | 0.672607i | ||||
\(95\) | − | 298.893i | − | 0.0331184i | ||||||
\(96\) | −1575.35 | + | 1575.35i | −0.170936 | + | 0.170936i | ||||
\(97\) | 8558.26 | − | 8558.26i | 0.909583 | − | 0.909583i | −0.0866556 | − | 0.996238i | \(-0.527618\pi\) |
0.996238 | + | 0.0866556i | \(0.0276180\pi\) | |||||||
\(98\) | 2343.43 | + | 2343.43i | 0.244006 | + | 0.244006i | ||||
\(99\) | − | 10024.0i | − | 1.02275i | ||||||
\(100\) | −3146.84 | −0.314684 | ||||||||
\(101\) | 12369.2i | 1.21255i | 0.795256 | + | 0.606274i | \(0.207336\pi\) | ||||
−0.795256 | + | 0.606274i | \(0.792664\pi\) | |||||||
\(102\) | 4335.33i | 0.416698i | ||||||||
\(103\) | −5805.26 | − | 5805.26i | −0.547202 | − | 0.547202i | 0.378429 | − | 0.925630i | \(-0.376465\pi\) |
−0.925630 | + | 0.378429i | \(0.876465\pi\) | |||||||
\(104\) | 5821.12i | 0.538195i | ||||||||
\(105\) | 4643.97 | + | 4643.97i | 0.421221 | + | 0.421221i | ||||
\(106\) | −2083.28 | − | 2083.28i | −0.185411 | − | 0.185411i | ||||
\(107\) | 3685.46 | 0.321903 | 0.160951 | − | 0.986962i | \(-0.448544\pi\) | ||||
0.160951 | + | 0.986962i | \(0.448544\pi\) | |||||||
\(108\) | −1036.55 | −0.0888676 | ||||||||
\(109\) | 9605.82 | − | 9605.82i | 0.808502 | − | 0.808502i | −0.175905 | − | 0.984407i | \(-0.556285\pi\) |
0.984407 | + | 0.175905i | \(0.0562851\pi\) | |||||||
\(110\) | − | 6123.18i | − | 0.506048i | ||||||
\(111\) | 16848.6 | − | 94.1941i | 1.36747 | − | 0.00764500i | ||||
\(112\) | −2243.91 | −0.178883 | ||||||||
\(113\) | 4922.36 | + | 4922.36i | 0.385493 | + | 0.385493i | 0.873076 | − | 0.487583i | \(-0.162121\pi\) |
−0.487583 | + | 0.873076i | \(0.662121\pi\) | |||||||
\(114\) | − | 683.623i | − | 0.0526026i | ||||||
\(115\) | − | 1716.00i | − | 0.129754i | ||||||
\(116\) | −3363.06 | + | 3363.06i | −0.249930 | + | 0.249930i | ||||
\(117\) | 12819.6 | − | 12819.6i | 0.936490 | − | 0.936490i | ||||
\(118\) | −7586.67 | −0.544863 | ||||||||
\(119\) | −3087.60 | + | 3087.60i | −0.218036 | + | 0.218036i | ||||
\(120\) | 4238.51 | 0.294341 | ||||||||
\(121\) | −5591.14 | −0.381882 | ||||||||
\(122\) | − | 16049.6i | − | 1.07831i | ||||||
\(123\) | −15250.8 | −1.00805 | ||||||||
\(124\) | 4997.26 | − | 4997.26i | 0.325004 | − | 0.325004i | ||||
\(125\) | 10959.6 | + | 10959.6i | 0.701416 | + | 0.701416i | ||||
\(126\) | 4941.68 | + | 4941.68i | 0.311267 | + | 0.311267i | ||||
\(127\) | −23426.1 | −1.45242 | −0.726211 | − | 0.687472i | \(-0.758721\pi\) | ||||
−0.726211 | + | 0.687472i | \(0.758721\pi\) | |||||||
\(128\) | −1024.00 | + | 1024.00i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 7477.51 | + | 7477.51i | 0.449343 | + | 0.449343i | ||||
\(130\) | 7830.92 | − | 7830.92i | 0.463368 | − | 0.463368i | ||||
\(131\) | −4160.42 | − | 4160.42i | −0.242435 | − | 0.242435i | 0.575422 | − | 0.817857i | \(-0.304838\pi\) |
−0.817857 | + | 0.575422i | \(0.804838\pi\) | |||||||
\(132\) | − | 14004.8i | − | 0.803766i | ||||||
\(133\) | 486.874 | − | 486.874i | 0.0275241 | − | 0.0275241i | ||||
\(134\) | 4677.87 | − | 4677.87i | 0.260518 | − | 0.260518i | ||||
\(135\) | 1394.43 | + | 1394.43i | 0.0765121 | + | 0.0765121i | ||||
\(136\) | 2818.03i | 0.152359i | ||||||||
\(137\) | −22901.6 | −1.22018 | −0.610092 | − | 0.792331i | \(-0.708867\pi\) | ||||
−0.610092 | + | 0.792331i | \(0.708867\pi\) | |||||||
\(138\) | − | 3924.79i | − | 0.206091i | ||||||
\(139\) | − | 30870.3i | − | 1.59776i | −0.601492 | − | 0.798879i | \(-0.705427\pi\) | ||
0.601492 | − | 0.798879i | \(-0.294573\pi\) | |||||||
\(140\) | 3018.65 | + | 3018.65i | 0.154013 | + | 0.154013i | ||||
\(141\) | 36572.4i | 1.83957i | ||||||||
\(142\) | −7297.65 | − | 7297.65i | −0.361915 | − | 0.361915i | ||||
\(143\) | −25874.8 | − | 25874.8i | −1.26533 | − | 1.26533i | ||||
\(144\) | 4510.23 | 0.217507 | ||||||||
\(145\) | 9048.39 | 0.430364 | ||||||||
\(146\) | −19887.0 | + | 19887.0i | −0.932962 | + | 0.932962i | ||||
\(147\) | − | 14420.8i | − | 0.667351i | ||||||
\(148\) | 10951.8 | − | 61.2276i | 0.499992 | − | 0.00279527i | ||||
\(149\) | 23301.1 | 1.04955 | 0.524776 | − | 0.851240i | \(-0.324149\pi\) | ||||
0.524776 | + | 0.851240i | \(0.324149\pi\) | |||||||
\(150\) | 9682.37 | + | 9682.37i | 0.430327 | + | 0.430327i | ||||
\(151\) | 20776.6i | 0.911214i | 0.890181 | + | 0.455607i | \(0.150578\pi\) | ||||
−0.890181 | + | 0.455607i | \(0.849422\pi\) | |||||||
\(152\) | − | 444.365i | − | 0.0192333i | ||||||
\(153\) | 6206.03 | − | 6206.03i | 0.265113 | − | 0.265113i | ||||
\(154\) | 9974.17 | − | 9974.17i | 0.420567 | − | 0.420567i | ||||
\(155\) | −13445.2 | −0.559635 | ||||||||
\(156\) | 17910.7 | − | 17910.7i | 0.735976 | − | 0.735976i | ||||
\(157\) | −44450.2 | −1.80333 | −0.901663 | − | 0.432440i | \(-0.857653\pi\) | ||||
−0.901663 | + | 0.432440i | \(0.857653\pi\) | |||||||
\(158\) | −25612.1 | −1.02596 | ||||||||
\(159\) | 12819.9i | 0.507096i | ||||||||
\(160\) | 2755.09 | 0.107621 | ||||||||
\(161\) | 2795.22 | − | 2795.22i | 0.107836 | − | 0.107836i | ||||
\(162\) | 14605.8 | + | 14605.8i | 0.556540 | + | 0.556540i | ||||
\(163\) | 9806.05 | + | 9806.05i | 0.369079 | + | 0.369079i | 0.867141 | − | 0.498063i | \(-0.165955\pi\) |
−0.498063 | + | 0.867141i | \(0.665955\pi\) | |||||||
\(164\) | −9913.25 | −0.368577 | ||||||||
\(165\) | −18840.1 | + | 18840.1i | −0.692016 | + | 0.692016i | ||||
\(166\) | 14309.0 | + | 14309.0i | 0.519271 | + | 0.519271i | ||||
\(167\) | 25412.6 | − | 25412.6i | 0.911207 | − | 0.911207i | −0.0851606 | − | 0.996367i | \(-0.527140\pi\) |
0.996367 | + | 0.0851606i | \(0.0271403\pi\) | |||||||
\(168\) | 6904.19 | + | 6904.19i | 0.244621 | + | 0.244621i | ||||
\(169\) | − | 37621.5i | − | 1.31723i | ||||||
\(170\) | 3790.98 | − | 3790.98i | 0.131176 | − | 0.131176i | ||||
\(171\) | −978.607 | + | 978.607i | −0.0334669 | + | 0.0334669i | ||||
\(172\) | 4860.50 | + | 4860.50i | 0.164295 | + | 0.164295i | ||||
\(173\) | 26725.9i | 0.892977i | 0.894789 | + | 0.446489i | \(0.147326\pi\) | ||||
−0.894789 | + | 0.446489i | \(0.852674\pi\) | |||||||
\(174\) | 20695.3 | 0.683555 | ||||||||
\(175\) | 13791.5i | 0.450334i | ||||||||
\(176\) | − | 9103.34i | − | 0.293884i | ||||||
\(177\) | 23343.1 | + | 23343.1i | 0.745095 | + | 0.745095i | ||||
\(178\) | − | 9039.02i | − | 0.285287i | ||||||
\(179\) | 29943.6 | + | 29943.6i | 0.934542 | + | 0.934542i | 0.997985 | − | 0.0634438i | \(-0.0202084\pi\) |
−0.0634438 | + | 0.997985i | \(0.520208\pi\) | |||||||
\(180\) | −6067.43 | − | 6067.43i | −0.187266 | − | 0.187266i | ||||
\(181\) | 36299.1 | 1.10800 | 0.553999 | − | 0.832518i | \(-0.313101\pi\) | ||||
0.553999 | + | 0.832518i | \(0.313101\pi\) | |||||||
\(182\) | 25511.9 | 0.770193 | ||||||||
\(183\) | −49382.2 | + | 49382.2i | −1.47458 | + | 1.47458i | ||||
\(184\) | − | 2551.18i | − | 0.0753537i | ||||||
\(185\) | −14815.4 | − | 14650.7i | −0.432883 | − | 0.428070i | ||||
\(186\) | −30751.6 | −0.888878 | ||||||||
\(187\) | −12526.1 | − | 12526.1i | −0.358206 | − | 0.358206i | ||||
\(188\) | 23772.6i | 0.672607i | ||||||||
\(189\) | 4542.84i | 0.127176i | ||||||||
\(190\) | −597.787 | + | 597.787i | −0.0165592 | + | 0.0165592i | ||||
\(191\) | 1331.07 | − | 1331.07i | 0.0364867 | − | 0.0364867i | −0.688628 | − | 0.725115i | \(-0.741787\pi\) |
0.725115 | + | 0.688628i | \(0.241787\pi\) | |||||||
\(192\) | 6301.39 | 0.170936 | ||||||||
\(193\) | −47495.0 | + | 47495.0i | −1.27507 | + | 1.27507i | −0.331675 | + | 0.943394i | \(0.607614\pi\) |
−0.943394 | + | 0.331675i | \(0.892386\pi\) | |||||||
\(194\) | −34233.1 | −0.909583 | ||||||||
\(195\) | −48189.2 | −1.26730 | ||||||||
\(196\) | − | 9373.73i | − | 0.244006i | ||||||
\(197\) | 22672.3 | 0.584202 | 0.292101 | − | 0.956388i | \(-0.405646\pi\) | ||||
0.292101 | + | 0.956388i | \(0.405646\pi\) | |||||||
\(198\) | −20047.9 | + | 20047.9i | −0.511374 | + | 0.511374i | ||||
\(199\) | −26429.3 | − | 26429.3i | −0.667389 | − | 0.667389i | 0.289722 | − | 0.957111i | \(-0.406437\pi\) |
−0.957111 | + | 0.289722i | \(0.906437\pi\) | |||||||
\(200\) | 6293.68 | + | 6293.68i | 0.157342 | + | 0.157342i | ||||
\(201\) | −28786.2 | −0.712512 | ||||||||
\(202\) | 24738.4 | − | 24738.4i | 0.606274 | − | 0.606274i | ||||
\(203\) | 14739.1 | + | 14739.1i | 0.357667 | + | 0.357667i | ||||
\(204\) | 8670.65 | − | 8670.65i | 0.208349 | − | 0.208349i | ||||
\(205\) | 13335.9 | + | 13335.9i | 0.317333 | + | 0.317333i | ||||
\(206\) | 23221.1i | 0.547202i | ||||||||
\(207\) | −5618.35 | + | 5618.35i | −0.131120 | + | 0.131120i | ||||
\(208\) | 11642.2 | − | 11642.2i | 0.269098 | − | 0.269098i | ||||
\(209\) | 1975.20 | + | 1975.20i | 0.0452187 | + | 0.0452187i | ||||
\(210\) | − | 18575.9i | − | 0.421221i | ||||||
\(211\) | 48508.7 | 1.08957 | 0.544784 | − | 0.838576i | \(-0.316612\pi\) | ||||
0.544784 | + | 0.838576i | \(0.316612\pi\) | |||||||
\(212\) | 8333.12i | 0.185411i | ||||||||
\(213\) | 44907.6i | 0.989829i | ||||||||
\(214\) | −7370.93 | − | 7370.93i | −0.160951 | − | 0.160951i | ||||
\(215\) | − | 13077.3i | − | 0.282905i | ||||||
\(216\) | 2073.10 | + | 2073.10i | 0.0444338 | + | 0.0444338i | ||||
\(217\) | −21901.2 | − | 21901.2i | −0.465102 | − | 0.465102i | ||||
\(218\) | −38423.3 | −0.808502 | ||||||||
\(219\) | 122379. | 2.55163 | ||||||||
\(220\) | −12246.4 | + | 12246.4i | −0.253024 | + | 0.253024i | ||||
\(221\) | − | 32039.2i | − | 0.655990i | ||||||
\(222\) | −33885.5 | − | 33508.8i | −0.687557 | − | 0.679912i | ||||
\(223\) | 37090.7 | 0.745856 | 0.372928 | − | 0.927860i | \(-0.378354\pi\) | ||||
0.372928 | + | 0.927860i | \(0.378354\pi\) | |||||||
\(224\) | 4487.83 | + | 4487.83i | 0.0894417 | + | 0.0894417i | ||||
\(225\) | − | 27720.6i | − | 0.547568i | ||||||
\(226\) | − | 19689.4i | − | 0.385493i | ||||||
\(227\) | 38853.5 | − | 38853.5i | 0.754012 | − | 0.754012i | −0.221214 | − | 0.975225i | \(-0.571002\pi\) |
0.975225 | + | 0.221214i | \(0.0710018\pi\) | |||||||
\(228\) | −1367.25 | + | 1367.25i | −0.0263013 | + | 0.0263013i | ||||
\(229\) | −22098.2 | −0.421391 | −0.210695 | − | 0.977552i | \(-0.567573\pi\) | ||||
−0.210695 | + | 0.977552i | \(0.567573\pi\) | |||||||
\(230\) | −3431.99 | + | 3431.99i | −0.0648770 | + | 0.0648770i | ||||
\(231\) | −61378.1 | −1.15024 | ||||||||
\(232\) | 13452.3 | 0.249930 | ||||||||
\(233\) | − | 45800.4i | − | 0.843641i | −0.906679 | − | 0.421821i | \(-0.861391\pi\) | ||
0.906679 | − | 0.421821i | \(-0.138609\pi\) | |||||||
\(234\) | −51278.4 | −0.936490 | ||||||||
\(235\) | 31980.3 | − | 31980.3i | 0.579092 | − | 0.579092i | ||||
\(236\) | 15173.3 | + | 15173.3i | 0.272432 | + | 0.272432i | ||||
\(237\) | 78804.7 | + | 78804.7i | 1.40299 | + | 1.40299i | ||||
\(238\) | 12350.4 | 0.218036 | ||||||||
\(239\) | 36004.7 | − | 36004.7i | 0.630323 | − | 0.630323i | −0.317826 | − | 0.948149i | \(-0.602953\pi\) |
0.948149 | + | 0.317826i | \(0.102953\pi\) | |||||||
\(240\) | −8477.01 | − | 8477.01i | −0.147170 | − | 0.147170i | ||||
\(241\) | 34717.3 | − | 34717.3i | 0.597739 | − | 0.597739i | −0.341971 | − | 0.939710i | \(-0.611095\pi\) |
0.939710 | + | 0.341971i | \(0.111095\pi\) | |||||||
\(242\) | 11182.3 | + | 11182.3i | 0.190941 | + | 0.190941i | ||||
\(243\) | − | 79384.8i | − | 1.34439i | ||||||
\(244\) | −32099.2 | + | 32099.2i | −0.539155 | + | 0.539155i | ||||
\(245\) | −12610.1 | + | 12610.1i | −0.210081 | + | 0.210081i | ||||
\(246\) | 30501.6 | + | 30501.6i | 0.504025 | + | 0.504025i | ||||
\(247\) | 5052.15i | 0.0828100i | ||||||||
\(248\) | −19989.0 | −0.325004 | ||||||||
\(249\) | − | 88053.6i | − | 1.42020i | ||||||
\(250\) | − | 43838.5i | − | 0.701416i | ||||||
\(251\) | −43521.6 | − | 43521.6i | −0.690807 | − | 0.690807i | 0.271602 | − | 0.962410i | \(-0.412447\pi\) |
−0.962410 | + | 0.271602i | \(0.912447\pi\) | |||||||
\(252\) | − | 19766.7i | − | 0.311267i | ||||||
\(253\) | 11340.0 | + | 11340.0i | 0.177162 | + | 0.177162i | ||||
\(254\) | 46852.2 | + | 46852.2i | 0.726211 | + | 0.726211i | ||||
\(255\) | −23328.6 | −0.358763 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −53578.0 | + | 53578.0i | −0.811185 | + | 0.811185i | −0.984812 | − | 0.173627i | \(-0.944451\pi\) |
0.173627 | + | 0.984812i | \(0.444451\pi\) | |||||||
\(258\) | − | 29910.1i | − | 0.449343i | ||||||
\(259\) | −268.339 | − | 47998.0i | −0.00400022 | − | 0.715522i | ||||
\(260\) | −31323.7 | −0.463368 | ||||||||
\(261\) | −29625.3 | − | 29625.3i | −0.434893 | − | 0.434893i | ||||
\(262\) | 16641.7i | 0.242435i | ||||||||
\(263\) | − | 26433.1i | − | 0.382153i | −0.981575 | − | 0.191077i | \(-0.938802\pi\) | ||
0.981575 | − | 0.191077i | \(-0.0611979\pi\) | |||||||
\(264\) | −28009.6 | + | 28009.6i | −0.401883 | + | 0.401883i | ||||
\(265\) | 11210.2 | − | 11210.2i | 0.159633 | − | 0.159633i | ||||
\(266\) | −1947.49 | −0.0275241 | ||||||||
\(267\) | −27811.7 | + | 27811.7i | −0.390127 | + | 0.390127i | ||||
\(268\) | −18711.5 | −0.260518 | ||||||||
\(269\) | −120348. | −1.66316 | −0.831578 | − | 0.555408i | \(-0.812562\pi\) | ||||
−0.831578 | + | 0.555408i | \(0.812562\pi\) | |||||||
\(270\) | − | 5577.73i | − | 0.0765121i | ||||||
\(271\) | 12124.6 | 0.165093 | 0.0825464 | − | 0.996587i | \(-0.473695\pi\) | ||||
0.0825464 | + | 0.996587i | \(0.473695\pi\) | |||||||
\(272\) | 5636.06 | − | 5636.06i | 0.0761794 | − | 0.0761794i | ||||
\(273\) | −78496.3 | − | 78496.3i | −1.05323 | − | 1.05323i | ||||
\(274\) | 45803.2 | + | 45803.2i | 0.610092 | + | 0.610092i | ||||
\(275\) | −55950.7 | −0.739844 | ||||||||
\(276\) | −7849.59 | + | 7849.59i | −0.103045 | + | 0.103045i | ||||
\(277\) | 4822.15 | + | 4822.15i | 0.0628465 | + | 0.0628465i | 0.737831 | − | 0.674985i | \(-0.235850\pi\) |
−0.674985 | + | 0.737831i | \(0.735850\pi\) | |||||||
\(278\) | −61740.6 | + | 61740.6i | −0.798879 | + | 0.798879i | ||||
\(279\) | 44021.0 | + | 44021.0i | 0.565525 | + | 0.565525i | ||||
\(280\) | − | 12074.6i | − | 0.154013i | ||||||
\(281\) | 75002.5 | − | 75002.5i | 0.949868 | − | 0.949868i | −0.0489341 | − | 0.998802i | \(-0.515582\pi\) |
0.998802 | + | 0.0489341i | \(0.0155824\pi\) | |||||||
\(282\) | 73144.8 | − | 73144.8i | 0.919783 | − | 0.919783i | ||||
\(283\) | 23758.4 | + | 23758.4i | 0.296650 | + | 0.296650i | 0.839700 | − | 0.543050i | \(-0.182731\pi\) |
−0.543050 | + | 0.839700i | \(0.682731\pi\) | |||||||
\(284\) | 29190.6i | 0.361915i | ||||||||
\(285\) | 3678.60 | 0.0452890 | ||||||||
\(286\) | 103499.i | 1.26533i | ||||||||
\(287\) | 43446.2i | 0.527459i | ||||||||
\(288\) | −9020.45 | − | 9020.45i | −0.108754 | − | 0.108754i | ||||
\(289\) | 68010.7i | 0.814294i | ||||||||
\(290\) | −18096.8 | − | 18096.8i | −0.215182 | − | 0.215182i | ||||
\(291\) | 105330. | + | 105330.i | 1.24384 | + | 1.24384i | ||||
\(292\) | 79548.0 | 0.932962 | ||||||||
\(293\) | 108751. | 1.26677 | 0.633384 | − | 0.773837i | \(-0.281665\pi\) | ||||
0.633384 | + | 0.773837i | \(0.281665\pi\) | |||||||
\(294\) | −28841.6 | + | 28841.6i | −0.333675 | + | 0.333675i | ||||
\(295\) | − | 40824.2i | − | 0.469109i | ||||||
\(296\) | −22026.1 | − | 21781.2i | −0.251394 | − | 0.248598i | ||||
\(297\) | −18429.9 | −0.208934 | ||||||||
\(298\) | −46602.2 | − | 46602.2i | −0.524776 | − | 0.524776i | ||||
\(299\) | 29005.3i | 0.324440i | ||||||||
\(300\) | − | 38729.5i | − | 0.430327i | ||||||
\(301\) | 21301.8 | − | 21301.8i | 0.235117 | − | 0.235117i | ||||
\(302\) | 41553.2 | − | 41553.2i | 0.455607 | − | 0.455607i | ||||
\(303\) | −152233. | −1.65815 | ||||||||
\(304\) | −888.730 | + | 888.730i | −0.00961663 | + | 0.00961663i | ||||
\(305\) | 86363.4 | 0.928389 | ||||||||
\(306\) | −24824.1 | −0.265113 | ||||||||
\(307\) | 162258.i | 1.72159i | 0.508952 | + | 0.860795i | \(0.330033\pi\) | ||||
−0.508952 | + | 0.860795i | \(0.669967\pi\) | |||||||
\(308\) | −39896.7 | −0.420567 | ||||||||
\(309\) | 71447.7 | − | 71447.7i | 0.748293 | − | 0.748293i | ||||
\(310\) | 26890.4 | + | 26890.4i | 0.279817 | + | 0.279817i | ||||
\(311\) | 88112.7 | + | 88112.7i | 0.910999 | + | 0.910999i | 0.996351 | − | 0.0853518i | \(-0.0272014\pi\) |
−0.0853518 | + | 0.996351i | \(0.527201\pi\) | |||||||
\(312\) | −71642.9 | −0.735976 | ||||||||
\(313\) | −88253.8 | + | 88253.8i | −0.900834 | + | 0.900834i | −0.995508 | − | 0.0946740i | \(-0.969819\pi\) |
0.0946740 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(314\) | 88900.3 | + | 88900.3i | 0.901663 | + | 0.901663i | ||||
\(315\) | −26591.4 | + | 26591.4i | −0.267991 | + | 0.267991i | ||||
\(316\) | 51224.2 | + | 51224.2i | 0.512981 | + | 0.512981i | ||||
\(317\) | − | 34320.2i | − | 0.341532i | −0.985312 | − | 0.170766i | \(-0.945376\pi\) | ||
0.985312 | − | 0.170766i | \(-0.0546242\pi\) | |||||||
\(318\) | 25639.8 | − | 25639.8i | 0.253548 | − | 0.253548i | ||||
\(319\) | −59795.2 | + | 59795.2i | −0.587604 | + | 0.587604i | ||||
\(320\) | −5510.19 | − | 5510.19i | −0.0538104 | − | 0.0538104i | ||||
\(321\) | 45358.5i | 0.440199i | ||||||||
\(322\) | −11180.9 | −0.107836 | ||||||||
\(323\) | 2445.77i | 0.0234428i | ||||||||
\(324\) | − | 58423.3i | − | 0.556540i | ||||||
\(325\) | −71555.2 | − | 71555.2i | −0.677446 | − | 0.677446i | ||||
\(326\) | − | 39224.2i | − | 0.369079i | ||||||
\(327\) | 118223. | + | 118223.i | 1.10562 | + | 1.10562i | ||||
\(328\) | 19826.5 | + | 19826.5i | 0.184289 | + | 0.184289i | ||||
\(329\) | 104187. | 0.962545 | ||||||||
\(330\) | 75360.5 | 0.692016 | ||||||||
\(331\) | 27326.2 | − | 27326.2i | 0.249415 | − | 0.249415i | −0.571316 | − | 0.820731i | \(-0.693567\pi\) |
0.820731 | + | 0.571316i | \(0.193567\pi\) | |||||||
\(332\) | − | 57236.1i | − | 0.519271i | ||||||
\(333\) | 539.356 | + | 96475.0i | 0.00486393 | + | 0.870014i | ||||
\(334\) | −101651. | −0.911207 | ||||||||
\(335\) | 25171.8 | + | 25171.8i | 0.224298 | + | 0.224298i | ||||
\(336\) | − | 27616.8i | − | 0.244621i | ||||||
\(337\) | 129267.i | 1.13822i | 0.822261 | + | 0.569110i | \(0.192712\pi\) | ||||
−0.822261 | + | 0.569110i | \(0.807288\pi\) | |||||||
\(338\) | −75242.9 | + | 75242.9i | −0.658616 | + | 0.658616i | ||||
\(339\) | −60581.5 | + | 60581.5i | −0.527158 | + | 0.527158i | ||||
\(340\) | −15163.9 | −0.131176 | ||||||||
\(341\) | 88851.0 | − | 88851.0i | 0.764106 | − | 0.764106i | ||||
\(342\) | 3914.43 | 0.0334669 | ||||||||
\(343\) | −125264. | −1.06472 | ||||||||
\(344\) | − | 19442.0i | − | 0.164295i | ||||||
\(345\) | 21119.5 | 0.177437 | ||||||||
\(346\) | 53451.8 | − | 53451.8i | 0.446489 | − | 0.446489i | ||||
\(347\) | −58943.9 | − | 58943.9i | −0.489531 | − | 0.489531i | 0.418627 | − | 0.908158i | \(-0.362511\pi\) |
−0.908158 | + | 0.418627i | \(0.862511\pi\) | |||||||
\(348\) | −41390.6 | − | 41390.6i | −0.341777 | − | 0.341777i | ||||
\(349\) | −199349. | −1.63668 | −0.818340 | − | 0.574734i | \(-0.805105\pi\) | ||||
−0.818340 | + | 0.574734i | \(0.805105\pi\) | |||||||
\(350\) | 27583.0 | − | 27583.0i | 0.225167 | − | 0.225167i | ||||
\(351\) | −23569.9 | − | 23569.9i | −0.191313 | − | 0.191313i | ||||
\(352\) | −18206.7 | + | 18206.7i | −0.146942 | + | 0.146942i | ||||
\(353\) | −134420. | − | 134420.i | −1.07873 | − | 1.07873i | −0.996623 | − | 0.0821094i | \(-0.973834\pi\) |
−0.0821094 | − | 0.996623i | \(-0.526166\pi\) | |||||||
\(354\) | − | 93372.3i | − | 0.745095i | ||||||
\(355\) | 39268.9 | − | 39268.9i | 0.311596 | − | 0.311596i | ||||
\(356\) | −18078.0 | + | 18078.0i | −0.142643 | + | 0.142643i | ||||
\(357\) | −38000.4 | − | 38000.4i | −0.298161 | − | 0.298161i | ||||
\(358\) | − | 119775.i | − | 0.934542i | ||||||
\(359\) | 237450. | 1.84240 | 0.921199 | − | 0.389091i | \(-0.127211\pi\) | ||||
0.921199 | + | 0.389091i | \(0.127211\pi\) | |||||||
\(360\) | 24269.7i | 0.187266i | ||||||||
\(361\) | 129935.i | 0.997041i | ||||||||
\(362\) | −72598.2 | − | 72598.2i | −0.553999 | − | 0.553999i | ||||
\(363\) | − | 68812.4i | − | 0.522220i | ||||||
\(364\) | −51023.8 | − | 51023.8i | −0.385097 | − | 0.385097i | ||||
\(365\) | −107013. | − | 107013.i | −0.803249 | − | 0.803249i | ||||
\(366\) | 197529. | 1.47458 | ||||||||
\(367\) | −204541. | −1.51862 | −0.759309 | − | 0.650730i | \(-0.774463\pi\) | ||||
−0.759309 | + | 0.650730i | \(0.774463\pi\) | |||||||
\(368\) | −5102.35 | + | 5102.35i | −0.0376769 | + | 0.0376769i | ||||
\(369\) | − | 87326.2i | − | 0.641345i | ||||||
\(370\) | 329.468 | + | 58932.2i | 0.00240663 | + | 0.430477i | ||||
\(371\) | 36521.1 | 0.265336 | ||||||||
\(372\) | 61503.3 | + | 61503.3i | 0.444439 | + | 0.444439i | ||||
\(373\) | − | 10556.7i | − | 0.0758767i | −0.999280 | − | 0.0379384i | \(-0.987921\pi\) | ||
0.999280 | − | 0.0379384i | \(-0.0120791\pi\) | |||||||
\(374\) | 50104.4i | 0.358206i | ||||||||
\(375\) | −134885. | + | 134885.i | −0.959179 | + | 0.959179i | ||||
\(376\) | 47545.2 | − | 47545.2i | 0.336303 | − | 0.336303i | ||||
\(377\) | −152944. | −1.07609 | ||||||||
\(378\) | 9085.68 | − | 9085.68i | 0.0635878 | − | 0.0635878i | ||||
\(379\) | 130955. | 0.911682 | 0.455841 | − | 0.890061i | \(-0.349339\pi\) | ||||
0.455841 | + | 0.890061i | \(0.349339\pi\) | |||||||
\(380\) | 2391.15 | 0.0165592 | ||||||||
\(381\) | − | 288315.i | − | 1.98617i | ||||||
\(382\) | −5324.29 | −0.0364867 | ||||||||
\(383\) | −152787. | + | 152787.i | −1.04157 | + | 1.04157i | −0.0424733 | + | 0.999098i | \(0.513524\pi\) |
−0.999098 | + | 0.0424733i | \(0.986476\pi\) | |||||||
\(384\) | −12602.8 | − | 12602.8i | −0.0854681 | − | 0.0854681i | ||||
\(385\) | 53671.4 | + | 53671.4i | 0.362094 | + | 0.362094i | ||||
\(386\) | 189980. | 1.27507 | ||||||||
\(387\) | −42816.3 | + | 42816.3i | −0.285882 | + | 0.285882i | ||||
\(388\) | 68466.1 | + | 68466.1i | 0.454791 | + | 0.454791i | ||||
\(389\) | −112269. | + | 112269.i | −0.741929 | + | 0.741929i | −0.972949 | − | 0.231020i | \(-0.925794\pi\) |
0.231020 | + | 0.972949i | \(0.425794\pi\) | |||||||
\(390\) | 96378.3 | + | 96378.3i | 0.633651 | + | 0.633651i | ||||
\(391\) | 14041.6i | 0.0918464i | ||||||||
\(392\) | −18747.5 | + | 18747.5i | −0.122003 | + | 0.122003i | ||||
\(393\) | 51204.0 | − | 51204.0i | 0.331527 | − | 0.331527i | ||||
\(394\) | −45344.6 | − | 45344.6i | −0.292101 | − | 0.292101i | ||||
\(395\) | − | 137820.i | − | 0.883319i | ||||||
\(396\) | 80191.6 | 0.511374 | ||||||||
\(397\) | − | 157029.i | − | 0.996319i | −0.867085 | − | 0.498160i | \(-0.834009\pi\) | ||
0.867085 | − | 0.498160i | \(-0.165991\pi\) | |||||||
\(398\) | 105717.i | 0.667389i | ||||||||
\(399\) | 5992.15 | + | 5992.15i | 0.0376389 | + | 0.0376389i | ||||
\(400\) | − | 25174.7i | − | 0.157342i | ||||||
\(401\) | 15819.3 | + | 15819.3i | 0.0983779 | + | 0.0983779i | 0.754583 | − | 0.656205i | \(-0.227839\pi\) |
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(402\) | 57572.4 | + | 57572.4i | 0.356256 | + | 0.356256i | ||||
\(403\) | 227263. | 1.39932 | ||||||||
\(404\) | −98953.6 | −0.606274 | ||||||||
\(405\) | −78594.5 | + | 78594.5i | −0.479162 | + | 0.479162i | ||||
\(406\) | − | 58956.4i | − | 0.357667i | ||||||
\(407\) | 194723. | − | 1088.62i | 1.17552 | − | 0.00657187i | ||||
\(408\) | −34682.6 | −0.208349 | ||||||||
\(409\) | 38105.9 | + | 38105.9i | 0.227795 | + | 0.227795i | 0.811771 | − | 0.583976i | \(-0.198504\pi\) |
−0.583976 | + | 0.811771i | \(0.698504\pi\) | |||||||
\(410\) | − | 53343.6i | − | 0.317333i | ||||||
\(411\) | − | 281860.i | − | 1.66859i | ||||||
\(412\) | 46442.1 | − | 46442.1i | 0.273601 | − | 0.273601i | ||||
\(413\) | 66499.4 | − | 66499.4i | 0.389868 | − | 0.389868i | ||||
\(414\) | 22473.4 | 0.131120 | ||||||||
\(415\) | −76997.5 | + | 76997.5i | −0.447075 | + | 0.447075i | ||||
\(416\) | −46569.0 | −0.269098 | ||||||||
\(417\) | 379933. | 2.18492 | ||||||||
\(418\) | − | 7900.80i | − | 0.0452187i | ||||||
\(419\) | 260486. | 1.48374 | 0.741868 | − | 0.670546i | \(-0.233940\pi\) | ||||
0.741868 | + | 0.670546i | \(0.233940\pi\) | |||||||
\(420\) | −37151.7 | + | 37151.7i | −0.210611 | + | 0.210611i | ||||
\(421\) | −94783.8 | − | 94783.8i | −0.534774 | − | 0.534774i | 0.387216 | − | 0.921989i | \(-0.373437\pi\) |
−0.921989 | + | 0.387216i | \(0.873437\pi\) | |||||||
\(422\) | −97017.3 | − | 97017.3i | −0.544784 | − | 0.544784i | ||||
\(423\) | −209414. | −1.17037 | ||||||||
\(424\) | 16666.2 | − | 16666.2i | 0.0927056 | − | 0.0927056i | ||||
\(425\) | −34640.2 | − | 34640.2i | −0.191780 | − | 0.191780i | ||||
\(426\) | 89815.1 | − | 89815.1i | 0.494915 | − | 0.494915i | ||||
\(427\) | 140679. | + | 140679.i | 0.771568 | + | 0.771568i | ||||
\(428\) | 29483.7i | 0.160951i | ||||||||
\(429\) | 318452. | − | 318452.i | 1.73033 | − | 1.73033i | ||||
\(430\) | −26154.5 | + | 26154.5i | −0.141452 | + | 0.141452i | ||||
\(431\) | −67577.5 | − | 67577.5i | −0.363788 | − | 0.363788i | 0.501418 | − | 0.865205i | \(-0.332812\pi\) |
−0.865205 | + | 0.501418i | \(0.832812\pi\) | |||||||
\(432\) | − | 8292.42i | − | 0.0444338i | ||||||
\(433\) | −236655. | −1.26224 | −0.631118 | − | 0.775687i | \(-0.717404\pi\) | ||||
−0.631118 | + | 0.775687i | \(0.717404\pi\) | |||||||
\(434\) | 87604.8i | 0.465102i | ||||||||
\(435\) | 111362.i | 0.588518i | ||||||||
\(436\) | 76846.5 | + | 76846.5i | 0.404251 | + | 0.404251i | ||||
\(437\) | − | 2214.17i | − | 0.0115944i | ||||||
\(438\) | −244758. | − | 244758.i | −1.27582 | − | 1.27582i | ||||
\(439\) | 131517. | + | 131517.i | 0.682424 | + | 0.682424i | 0.960546 | − | 0.278122i | \(-0.0897120\pi\) |
−0.278122 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(440\) | 48985.5 | 0.253024 | ||||||||
\(441\) | 82573.5 | 0.424584 | ||||||||
\(442\) | −64078.4 | + | 64078.4i | −0.327995 | + | 0.327995i | ||||
\(443\) | − | 190133.i | − | 0.968835i | −0.874837 | − | 0.484418i | \(-0.839032\pi\) | ||
0.874837 | − | 0.484418i | \(-0.160968\pi\) | |||||||
\(444\) | 753.553 | + | 134789.i | 0.00382250 | + | 0.683734i | ||||
\(445\) | 48639.4 | 0.245622 | ||||||||
\(446\) | −74181.4 | − | 74181.4i | −0.372928 | − | 0.372928i | ||||
\(447\) | 286776.i | 1.43525i | ||||||||
\(448\) | − | 17951.3i | − | 0.0894417i | ||||||
\(449\) | −201365. | + | 201365.i | −0.998831 | + | 0.998831i | −0.999999 | − | 0.00116876i | \(-0.999628\pi\) |
0.00116876 | + | 0.999999i | \(0.499628\pi\) | |||||||
\(450\) | −55441.3 | + | 55441.3i | −0.273784 | + | 0.273784i | ||||
\(451\) | −176257. | −0.866550 | ||||||||
\(452\) | −39378.9 | + | 39378.9i | −0.192747 | + | 0.192747i | ||||
\(453\) | −255706. | −1.24608 | ||||||||
\(454\) | −155414. | −0.754012 | ||||||||
\(455\) | 137281.i | 0.663111i | ||||||||
\(456\) | 5468.98 | 0.0263013 | ||||||||
\(457\) | −88971.9 | + | 88971.9i | −0.426011 | + | 0.426011i | −0.887267 | − | 0.461256i | \(-0.847399\pi\) |
0.461256 | + | 0.887267i | \(0.347399\pi\) | |||||||
\(458\) | 44196.3 | + | 44196.3i | 0.210695 | + | 0.210695i | ||||
\(459\) | −11410.3 | − | 11410.3i | −0.0541591 | − | 0.0541591i | ||||
\(460\) | 13728.0 | 0.0648770 | ||||||||
\(461\) | −222424. | + | 222424.i | −1.04660 | + | 1.04660i | −0.0477366 | + | 0.998860i | \(0.515201\pi\) |
−0.998860 | + | 0.0477366i | \(0.984799\pi\) | |||||||
\(462\) | 122756. | + | 122756.i | 0.575121 | + | 0.575121i | ||||
\(463\) | −164606. | + | 164606.i | −0.767861 | + | 0.767861i | −0.977730 | − | 0.209868i | \(-0.932696\pi\) |
0.209868 | + | 0.977730i | \(0.432696\pi\) | |||||||
\(464\) | −26904.5 | − | 26904.5i | −0.124965 | − | 0.124965i | ||||
\(465\) | − | 165476.i | − | 0.765295i | ||||||
\(466\) | −91600.9 | + | 91600.9i | −0.421821 | + | 0.421821i | ||||
\(467\) | 209613. | − | 209613.i | 0.961134 | − | 0.961134i | −0.0381387 | − | 0.999272i | \(-0.512143\pi\) |
0.999272 | + | 0.0381387i | \(0.0121429\pi\) | |||||||
\(468\) | 102557. | + | 102557.i | 0.468245 | + | 0.468245i | ||||
\(469\) | 82005.7i | 0.372819i | ||||||||
\(470\) | −127921. | −0.579092 | ||||||||
\(471\) | − | 547066.i | − | 2.46603i | ||||||
\(472\) | − | 60693.4i | − | 0.272432i | ||||||
\(473\) | 86419.4 | + | 86419.4i | 0.386268 | + | 0.386268i | ||||
\(474\) | − | 315219.i | − | 1.40299i | ||||||
\(475\) | 5462.29 | + | 5462.29i | 0.0242096 | + | 0.0242096i | ||||
\(476\) | −24700.8 | − | 24700.8i | −0.109018 | − | 0.109018i | ||||
\(477\) | −73406.7 | −0.322626 | ||||||||
\(478\) | −144019. | −0.630323 | ||||||||
\(479\) | −157711. | + | 157711.i | −0.687373 | + | 0.687373i | −0.961650 | − | 0.274278i | \(-0.911561\pi\) |
0.274278 | + | 0.961650i | \(0.411561\pi\) | |||||||
\(480\) | 33908.1i | 0.147170i | ||||||||
\(481\) | 250423. | + | 247639.i | 1.08239 | + | 1.07036i | ||||
\(482\) | −138869. | −0.597739 | ||||||||
\(483\) | 34401.9 | + | 34401.9i | 0.147465 | + | 0.147465i | ||||
\(484\) | − | 44729.1i | − | 0.190941i | ||||||
\(485\) | − | 184209.i | − | 0.783120i | ||||||
\(486\) | −158770. | + | 158770.i | −0.672195 | + | 0.672195i | ||||
\(487\) | 13375.5 | − | 13375.5i | 0.0563966 | − | 0.0563966i | −0.678346 | − | 0.734743i | \(-0.737303\pi\) |
0.734743 | + | 0.678346i | \(0.237303\pi\) | |||||||
\(488\) | 128397. | 0.539155 | ||||||||
\(489\) | −120687. | + | 120687.i | −0.504711 | + | 0.504711i | ||||
\(490\) | 50440.4 | 0.210081 | ||||||||
\(491\) | 386204. | 1.60197 | 0.800984 | − | 0.598686i | \(-0.204310\pi\) | ||||
0.800984 | + | 0.598686i | \(0.204310\pi\) | |||||||
\(492\) | − | 122006.i | − | 0.504025i | ||||||
\(493\) | −74040.7 | −0.304633 | ||||||||
\(494\) | 10104.3 | − | 10104.3i | 0.0414050 | − | 0.0414050i | ||||
\(495\) | −107879. | − | 107879.i | −0.440276 | − | 0.440276i | ||||
\(496\) | 39978.1 | + | 39978.1i | 0.162502 | + | 0.162502i | ||||
\(497\) | 127932. | 0.517924 | ||||||||
\(498\) | −176107. | + | 176107.i | −0.710098 | + | 0.710098i | ||||
\(499\) | −22816.0 | − | 22816.0i | −0.0916303 | − | 0.0916303i | 0.659806 | − | 0.751436i | \(-0.270639\pi\) |
−0.751436 | + | 0.659806i | \(0.770639\pi\) | |||||||
\(500\) | −87677.0 | + | 87677.0i | −0.350708 | + | 0.350708i | ||||
\(501\) | 312764. | + | 312764.i | 1.24607 | + | 1.24607i | ||||
\(502\) | 174086.i | 0.690807i | ||||||||
\(503\) | 310068. | − | 310068.i | 1.22552 | − | 1.22552i | 0.259882 | − | 0.965640i | \(-0.416316\pi\) |
0.965640 | − | 0.259882i | \(-0.0836837\pi\) | |||||||
\(504\) | −39533.4 | + | 39533.4i | −0.155634 | + | 0.155634i | ||||
\(505\) | 133118. | + | 133118.i | 0.521981 | + | 0.521981i | ||||
\(506\) | − | 45359.8i | − | 0.177162i | ||||||
\(507\) | 463023. | 1.80130 | ||||||||
\(508\) | − | 187409.i | − | 0.726211i | ||||||
\(509\) | 308422.i | 1.19045i | 0.803560 | + | 0.595224i | \(0.202937\pi\) | ||||
−0.803560 | + | 0.595224i | \(0.797063\pi\) | |||||||
\(510\) | 46657.1 | + | 46657.1i | 0.179382 | + | 0.179382i | ||||
\(511\) | − | 348631.i | − | 1.33513i | ||||||
\(512\) | −8192.00 | − | 8192.00i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 1799.25 | + | 1799.25i | 0.00683686 | + | 0.00683686i | ||||
\(514\) | 214312. | 0.811185 | ||||||||
\(515\) | −124953. | −0.471122 | ||||||||
\(516\) | −59820.1 | + | 59820.1i | −0.224671 | + | 0.224671i | ||||
\(517\) | 422676.i | 1.58135i | ||||||||
\(518\) | −95459.2 | + | 96532.6i | −0.355761 | + | 0.359761i | ||||
\(519\) | −328927. | −1.22114 | ||||||||
\(520\) | 62647.4 | + | 62647.4i | 0.231684 | + | 0.231684i | ||||
\(521\) | − | 312647.i | − | 1.15181i | −0.817518 | − | 0.575903i | \(-0.804651\pi\) | ||
0.817518 | − | 0.575903i | \(-0.195349\pi\) | |||||||
\(522\) | 118501.i | 0.434893i | ||||||||
\(523\) | 206955. | − | 206955.i | 0.756611 | − | 0.756611i | −0.219093 | − | 0.975704i | \(-0.570310\pi\) |
0.975704 | + | 0.219093i | \(0.0703098\pi\) | |||||||
\(524\) | 33283.4 | − | 33283.4i | 0.121217 | − | 0.121217i | ||||
\(525\) | −169737. | −0.615827 | ||||||||
\(526\) | −52866.3 | + | 52866.3i | −0.191077 | + | 0.191077i | ||||
\(527\) | 110019. | 0.396137 | ||||||||
\(528\) | 112039. | 0.401883 | ||||||||
\(529\) | 267129.i | 0.954575i | ||||||||
\(530\) | −44840.8 | −0.159633 | ||||||||
\(531\) | −133663. | + | 133663.i | −0.474046 | + | 0.474046i | ||||
\(532\) | 3894.99 | + | 3894.99i | 0.0137620 | + | 0.0137620i | ||||
\(533\) | −225415. | − | 225415.i | −0.793466 | − | 0.793466i | ||||
\(534\) | 111247. | 0.390127 | ||||||||
\(535\) | 39663.3 | − | 39663.3i | 0.138574 | − | 0.138574i | ||||
\(536\) | 37422.9 | + | 37422.9i | 0.130259 | + | 0.130259i | ||||
\(537\) | −368529. | + | 368529.i | −1.27798 | + | 1.27798i | ||||
\(538\) | 240695. | + | 240695.i | 0.831578 | + | 0.831578i | ||||
\(539\) | − | 166665.i | − | 0.573675i | ||||||
\(540\) | −11155.5 | + | 11155.5i | −0.0382560 | + | 0.0382560i | ||||
\(541\) | 52416.1 | − | 52416.1i | 0.179089 | − | 0.179089i | −0.611869 | − | 0.790959i | \(-0.709582\pi\) |
0.790959 | + | 0.611869i | \(0.209582\pi\) | |||||||
\(542\) | −24249.2 | − | 24249.2i | −0.0825464 | − | 0.0825464i | ||||
\(543\) | 446748.i | 1.51517i | ||||||||
\(544\) | −22544.2 | −0.0761794 | ||||||||
\(545\) | − | 206757.i | − | 0.696093i | ||||||
\(546\) | 313985.i | 1.05323i | ||||||||
\(547\) | −270647. | − | 270647.i | −0.904543 | − | 0.904543i | 0.0912822 | − | 0.995825i | \(-0.470903\pi\) |
−0.995825 | + | 0.0912822i | \(0.970903\pi\) | |||||||
\(548\) | − | 183213.i | − | 0.610092i | ||||||
\(549\) | −282763. | − | 282763.i | −0.938161 | − | 0.938161i | ||||
\(550\) | 111901. | + | 111901.i | 0.369922 | + | 0.369922i | ||||
\(551\) | 11675.2 | 0.0384558 | ||||||||
\(552\) | 31398.4 | 0.103045 | ||||||||
\(553\) | 224498. | − | 224498.i | 0.734111 | − | 0.734111i | ||||
\(554\) | − | 19288.6i | − | 0.0628465i | ||||||
\(555\) | 180312. | − | 182339.i | 0.585381 | − | 0.591963i | ||||
\(556\) | 246962. | 0.798879 | ||||||||
\(557\) | 312727. | + | 312727.i | 1.00799 | + | 1.00799i | 0.999968 | + | 0.00801789i | \(0.00255220\pi\) |
0.00801789 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(558\) | − | 176084.i | − | 0.565525i | ||||||
\(559\) | 221043.i | 0.707381i | ||||||||
\(560\) | −24149.2 | + | 24149.2i | −0.0770063 | + | 0.0770063i | ||||
\(561\) | 154164. | − | 154164.i | 0.489843 | − | 0.489843i | ||||
\(562\) | −300010. | −0.949868 | ||||||||
\(563\) | −262229. | + | 262229.i | −0.827303 | + | 0.827303i | −0.987143 | − | 0.159840i | \(-0.948902\pi\) |
0.159840 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(564\) | −292579. | −0.919783 | ||||||||
\(565\) | 105950. | 0.331897 | ||||||||
\(566\) | − | 95033.6i | − | 0.296650i | ||||||
\(567\) | −256048. | −0.796446 | ||||||||
\(568\) | 58381.2 | − | 58381.2i | 0.180957 | − | 0.180957i | ||||
\(569\) | 72427.4 | + | 72427.4i | 0.223706 | + | 0.223706i | 0.810057 | − | 0.586351i | \(-0.199436\pi\) |
−0.586351 | + | 0.810057i | \(0.699436\pi\) | |||||||
\(570\) | −7357.21 | − | 7357.21i | −0.0226445 | − | 0.0226445i | ||||
\(571\) | 187442. | 0.574902 | 0.287451 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287451 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(572\) | 206999. | − | 206999.i | 0.632667 | − | 0.632667i | ||||
\(573\) | 16382.0 | + | 16382.0i | 0.0498952 | + | 0.0498952i | ||||
\(574\) | 86892.5 | − | 86892.5i | 0.263729 | − | 0.263729i | ||||
\(575\) | 31359.9 | + | 31359.9i | 0.0948505 | + | 0.0948505i | ||||
\(576\) | 36081.8i | 0.108754i | ||||||||
\(577\) | 440676. | − | 440676.i | 1.32363 | − | 1.32363i | 0.412820 | − | 0.910813i | \(-0.364544\pi\) |
0.910813 | − | 0.412820i | \(-0.135456\pi\) | |||||||
\(578\) | 136021. | − | 136021.i | 0.407147 | − | 0.407147i | ||||
\(579\) | −584541. | − | 584541.i | −1.74364 | − | 1.74364i | ||||
\(580\) | 72387.1i | 0.215182i | ||||||||
\(581\) | −250846. | −0.743112 | ||||||||
\(582\) | − | 421320.i | − | 1.24384i | ||||||
\(583\) | 148163.i | 0.435914i | ||||||||
\(584\) | −159096. | − | 159096.i | −0.466481 | − | 0.466481i | ||||
\(585\) | − | 275931.i | − | 0.806286i | ||||||
\(586\) | −217502. | − | 217502.i | −0.633384 | − | 0.633384i | ||||
\(587\) | −254904. | − | 254904.i | −0.739777 | − | 0.739777i | 0.232758 | − | 0.972535i | \(-0.425225\pi\) |
−0.972535 | + | 0.232758i | \(0.925225\pi\) | |||||||
\(588\) | 115366. | 0.333675 | ||||||||
\(589\) | −17348.5 | −0.0500070 | ||||||||
\(590\) | −81648.4 | + | 81648.4i | −0.234554 | + | 0.234554i | ||||
\(591\) | 279037.i | 0.798890i | ||||||||
\(592\) | 489.821 | + | 87614.6i | 0.00139763 | + | 0.249996i | ||||
\(593\) | −67949.6 | −0.193231 | −0.0966156 | − | 0.995322i | \(-0.530802\pi\) | ||||
−0.0966156 | + | 0.995322i | \(0.530802\pi\) | |||||||
\(594\) | 36859.7 | + | 36859.7i | 0.104467 | + | 0.104467i | ||||
\(595\) | 66458.1i | 0.187721i | ||||||||
\(596\) | 186409.i | 0.524776i | ||||||||
\(597\) | 325276. | − | 325276.i | 0.912648 | − | 0.912648i | ||||
\(598\) | 58010.5 | − | 58010.5i | 0.162220 | − | 0.162220i | ||||
\(599\) | 288040. | 0.802785 | 0.401393 | − | 0.915906i | \(-0.368526\pi\) | ||||
0.401393 | + | 0.915906i | \(0.368526\pi\) | |||||||
\(600\) | −77458.9 | + | 77458.9i | −0.215164 | + | 0.215164i | ||||
\(601\) | 117937. | 0.326513 | 0.163257 | − | 0.986584i | \(-0.447800\pi\) | ||||
0.163257 | + | 0.986584i | \(0.447800\pi\) | |||||||
\(602\) | −85207.3 | −0.235117 | ||||||||
\(603\) | − | 164830.i | − | 0.453316i | ||||||
\(604\) | −166213. | −0.455607 | ||||||||
\(605\) | −60172.3 | + | 60172.3i | −0.164394 | + | 0.164394i | ||||
\(606\) | 304465. | + | 304465.i | 0.829073 | + | 0.829073i | ||||
\(607\) | −93551.7 | − | 93551.7i | −0.253907 | − | 0.253907i | 0.568663 | − | 0.822570i | \(-0.307461\pi\) |
−0.822570 | + | 0.568663i | \(0.807461\pi\) | |||||||
\(608\) | 3554.92 | 0.00961663 | ||||||||
\(609\) | −181400. | + | 181400.i | −0.489106 | + | 0.489106i | ||||
\(610\) | −172727. | − | 172727.i | −0.464195 | − | 0.464195i | ||||
\(611\) | −540559. | + | 540559.i | −1.44797 | + | 1.44797i | ||||
\(612\) | 49648.2 | + | 49648.2i | 0.132556 | + | 0.132556i | ||||
\(613\) | − | 268669.i | − | 0.714983i | −0.933916 | − | 0.357492i | \(-0.883632\pi\) | ||
0.933916 | − | 0.357492i | \(-0.116368\pi\) | |||||||
\(614\) | 324516. | − | 324516.i | 0.860795 | − | 0.860795i | ||||
\(615\) | −164130. | + | 164130.i | −0.433949 | + | 0.433949i | ||||
\(616\) | 79793.4 | + | 79793.4i | 0.210284 | + | 0.210284i | ||||
\(617\) | − | 484519.i | − | 1.27274i | −0.771383 | − | 0.636371i | \(-0.780435\pi\) | ||
0.771383 | − | 0.636371i | \(-0.219565\pi\) | |||||||
\(618\) | −285791. | −0.748293 | ||||||||
\(619\) | − | 172756.i | − | 0.450870i | −0.974258 | − | 0.225435i | \(-0.927620\pi\) | ||
0.974258 | − | 0.225435i | \(-0.0723804\pi\) | |||||||
\(620\) | − | 107562.i | − | 0.279817i | ||||||
\(621\) | 10329.8 | + | 10329.8i | 0.0267860 | + | 0.0267860i | ||||
\(622\) | − | 352451.i | − | 0.910999i | ||||||
\(623\) | 79229.6 | + | 79229.6i | 0.204132 | + | 0.204132i | ||||
\(624\) | 143286. | + | 143286.i | 0.367988 | + | 0.367988i | ||||
\(625\) | −9950.31 | −0.0254728 | ||||||||
\(626\) | 353015. | 0.900834 | ||||||||
\(627\) | −24309.6 | + | 24309.6i | −0.0618361 | + | 0.0618361i | ||||
\(628\) | − | 355601.i | − | 0.901663i | ||||||
\(629\) | 121231. | + | 119883.i | 0.306416 | + | 0.303009i | ||||
\(630\) | 106365. | 0.267991 | ||||||||
\(631\) | −170631. | − | 170631.i | −0.428549 | − | 0.428549i | 0.459585 | − | 0.888134i | \(-0.347998\pi\) |
−0.888134 | + | 0.459585i | \(0.847998\pi\) | |||||||
\(632\) | − | 204897.i | − | 0.512981i | ||||||
\(633\) | 597016.i | 1.48997i | ||||||||
\(634\) | −68640.4 | + | 68640.4i | −0.170766 | + | 0.170766i | ||||
\(635\) | −252114. | + | 252114.i | −0.625243 | + | 0.625243i | ||||
\(636\) | −102559. | −0.253548 | ||||||||
\(637\) | 213147. | − | 213147.i | 0.525291 | − | 0.525291i | ||||
\(638\) | 239181. | 0.587604 | ||||||||
\(639\) | −257141. | −0.629752 | ||||||||
\(640\) | 22040.7i | 0.0538104i | ||||||||
\(641\) | 300030. | 0.730211 | 0.365105 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365105 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(642\) | 90717.0 | − | 90717.0i | 0.220099 | − | 0.220099i | ||||
\(643\) | −131810. | − | 131810.i | −0.318806 | − | 0.318806i | 0.529502 | − | 0.848309i | \(-0.322379\pi\) |
−0.848309 | + | 0.529502i | \(0.822379\pi\) | |||||||
\(644\) | 22361.8 | + | 22361.8i | 0.0539181 | + | 0.0539181i | ||||
\(645\) | 160947. | 0.386869 | ||||||||
\(646\) | 4891.54 | − | 4891.54i | 0.0117214 | − | 0.0117214i | ||||
\(647\) | 164840. | + | 164840.i | 0.393780 | + | 0.393780i | 0.876032 | − | 0.482253i | \(-0.160181\pi\) |
−0.482253 | + | 0.876032i | \(0.660181\pi\) | |||||||
\(648\) | −116847. | + | 116847.i | −0.278270 | + | 0.278270i | ||||
\(649\) | 269782. | + | 269782.i | 0.640505 | + | 0.640505i | ||||
\(650\) | 286221.i | 0.677446i | ||||||||
\(651\) | 269547. | − | 269547.i | 0.636022 | − | 0.636022i | ||||
\(652\) | −78448.4 | + | 78448.4i | −0.184539 | + | 0.184539i | ||||
\(653\) | −398531. | − | 398531.i | −0.934622 | − | 0.934622i | 0.0633679 | − | 0.997990i | \(-0.479816\pi\) |
−0.997990 | + | 0.0633679i | \(0.979816\pi\) | |||||||
\(654\) | − | 472891.i | − | 1.10562i | ||||||
\(655\) | −89549.5 | −0.208728 | ||||||||
\(656\) | − | 79306.0i | − | 0.184289i | ||||||
\(657\) | 700741.i | 1.62341i | ||||||||
\(658\) | −208374. | − | 208374.i | −0.481273 | − | 0.481273i | ||||
\(659\) | 282645.i | 0.650833i | 0.945571 | + | 0.325417i | \(0.105505\pi\) | ||||
−0.945571 | + | 0.325417i | \(0.894495\pi\) | |||||||
\(660\) | −150721. | − | 150721.i | −0.346008 | − | 0.346008i | ||||
\(661\) | 411076. | + | 411076.i | 0.940848 | + | 0.940848i | 0.998346 | − | 0.0574980i | \(-0.0183123\pi\) |
−0.0574980 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(662\) | −109305. | −0.249415 | ||||||||
\(663\) | 394320. | 0.897060 | ||||||||
\(664\) | −114472. | + | 114472.i | −0.259636 | + | 0.259636i | ||||
\(665\) | − | 10479.5i | − | 0.0236973i | ||||||
\(666\) | 191871. | − | 194029.i | 0.432575 | − | 0.437439i | ||||
\(667\) | 67029.4 | 0.150665 | ||||||||
\(668\) | 203301. | + | 203301.i | 0.455603 | + | 0.455603i | ||||
\(669\) | 456490.i | 1.01995i | ||||||||
\(670\) | − | 100687.i | − | 0.224298i | ||||||
\(671\) | −570722. | + | 570722.i | −1.26759 | + | 1.26759i | ||||
\(672\) | −55233.5 | + | 55233.5i | −0.122311 | + | 0.122311i | ||||
\(673\) | −550661. | −1.21578 | −0.607889 | − | 0.794022i | \(-0.707983\pi\) | ||||
−0.607889 | + | 0.794022i | \(0.707983\pi\) | |||||||
\(674\) | 258533. | − | 258533.i | 0.569110 | − | 0.569110i | ||||
\(675\) | −50966.6 | −0.111861 | ||||||||
\(676\) | 300972. | 0.658616 | ||||||||
\(677\) | − | 37674.3i | − | 0.0821992i | −0.999155 | − | 0.0410996i | \(-0.986914\pi\) | ||
0.999155 | − | 0.0410996i | \(-0.0130861\pi\) | |||||||
\(678\) | 242326. | 0.527158 | ||||||||
\(679\) | 300063. | − | 300063.i | 0.650837 | − | 0.650837i | ||||
\(680\) | 30327.8 | + | 30327.8i | 0.0655879 | + | 0.0655879i | ||||
\(681\) | 478185. | + | 478185.i | 1.03110 | + | 1.03110i | ||||
\(682\) | −355404. | −0.764106 | ||||||||
\(683\) | 57341.0 | − | 57341.0i | 0.122920 | − | 0.122920i | −0.642971 | − | 0.765891i | \(-0.722298\pi\) |
0.765891 | + | 0.642971i | \(0.222298\pi\) | |||||||
\(684\) | −7828.86 | − | 7828.86i | −0.0167335 | − | 0.0167335i | ||||
\(685\) | −246469. | + | 246469.i | −0.525269 | + | 0.525269i | ||||
\(686\) | 250527. | + | 250527.i | 0.532361 | + | 0.532361i | ||||
\(687\) | − | 271971.i | − | 0.576247i | ||||||
\(688\) | −38884.0 | + | 38884.0i | −0.0821474 | + | 0.0821474i | ||||
\(689\) | −189485. | + | 189485.i | −0.399150 | + | 0.399150i | ||||
\(690\) | −42239.0 | − | 42239.0i | −0.0887187 | − | 0.0887187i | ||||
\(691\) | − | 360431.i | − | 0.754859i | −0.926038 | − | 0.377429i | \(-0.876808\pi\) | ||
0.926038 | − | 0.377429i | \(-0.123192\pi\) | |||||||
\(692\) | −213807. | −0.446489 | ||||||||
\(693\) | − | 351451.i | − | 0.731811i | ||||||
\(694\) | 235776.i | 0.489531i | ||||||||
\(695\) | −332228. | − | 332228.i | −0.687808 | − | 0.687808i | ||||
\(696\) | 165562.i | 0.341777i | ||||||||
\(697\) | −109124. | − | 109124.i | −0.224624 | − | 0.224624i | ||||
\(698\) | 398699. | + | 398699.i | 0.818340 | + | 0.818340i | ||||
\(699\) | 563685. | 1.15367 | ||||||||
\(700\) | −110332. | −0.225167 | ||||||||
\(701\) | −26111.7 | + | 26111.7i | −0.0531373 | + | 0.0531373i | −0.733176 | − | 0.680039i | \(-0.761963\pi\) |
0.680039 | + | 0.733176i | \(0.261963\pi\) | |||||||
\(702\) | 94279.6i | 0.191313i | ||||||||
\(703\) | −19116.5 | − | 18903.9i | −0.0386810 | − | 0.0382509i | ||||
\(704\) | 72826.7 | 0.146942 | ||||||||
\(705\) | 393595. | + | 393595.i | 0.791902 | + | 0.791902i | ||||
\(706\) | 537679.i | 1.07873i | ||||||||
\(707\) | 433678.i | 0.867618i | ||||||||
\(708\) | −186745. | + | 186745.i | −0.372547 | + | 0.372547i | ||||
\(709\) | −17996.5 | + | 17996.5i | −0.0358010 | + | 0.0358010i | −0.724781 | − | 0.688980i | \(-0.758059\pi\) |
0.688980 | + | 0.724781i | \(0.258059\pi\) | |||||||
\(710\) | −157076. | −0.311596 | ||||||||
\(711\) | −451236. | + | 451236.i | −0.892616 | + | 0.892616i | ||||
\(712\) | 72312.2 | 0.142643 | ||||||||
\(713\) | −99600.6 | −0.195922 | ||||||||
\(714\) | 152002.i | 0.298161i | ||||||||
\(715\) | −556934. | −1.08941 | ||||||||
\(716\) | −239549. | + | 239549.i | −0.467271 | + | 0.467271i | ||||
\(717\) | 443124. | + | 443124.i | 0.861960 | + | 0.861960i | ||||
\(718\) | −474900. | − | 474900.i | −0.921199 | − | 0.921199i | ||||
\(719\) | −838819. | −1.62260 | −0.811298 | − | 0.584633i | \(-0.801238\pi\) | ||||
−0.811298 | + | 0.584633i | \(0.801238\pi\) | |||||||
\(720\) | 48539.4 | − | 48539.4i | 0.0936331 | − | 0.0936331i | ||||
\(721\) | −203539. | − | 203539.i | −0.391541 | − | 0.391541i | ||||
\(722\) | 259871. | − | 259871.i | 0.498520 | − | 0.498520i | ||||
\(723\) | 427280. | + | 427280.i | 0.817402 | + | 0.817402i | ||||
\(724\) | 290393.i | 0.553999i | ||||||||
\(725\) | −165360. | + | 165360.i | −0.314597 | + | 0.314597i | ||||
\(726\) | −137625. | + | 137625.i | −0.261110 | + | 0.261110i | ||||
\(727\) | −653992. | − | 653992.i | −1.23738 | − | 1.23738i | −0.961068 | − | 0.276314i | \(-0.910887\pi\) |
−0.276314 | − | 0.961068i | \(-0.589113\pi\) | |||||||
\(728\) | 204095.i | 0.385097i | ||||||||
\(729\) | 385486. | 0.725359 | ||||||||
\(730\) | 428051.i | 0.803249i | ||||||||
\(731\) | 107008.i | 0.200254i | ||||||||
\(732\) | −395057. | − | 395057.i | −0.737289 | − | 0.737289i | ||||
\(733\) | 199044.i | 0.370460i | 0.982695 | + | 0.185230i | \(0.0593029\pi\) | ||||
−0.982695 | + | 0.185230i | \(0.940697\pi\) | |||||||
\(734\) | 409082. | + | 409082.i | 0.759309 | + | 0.759309i | ||||
\(735\) | −155198. | − | 155198.i | −0.287283 | − | 0.287283i | ||||
\(736\) | 20409.4 | 0.0376769 | ||||||||
\(737\) | −332689. | −0.612497 | ||||||||
\(738\) | −174652. | + | 174652.i | −0.320672 | + | 0.320672i | ||||
\(739\) | − | 637184.i | − | 1.16674i | −0.812205 | − | 0.583372i | \(-0.801733\pi\) | ||
0.812205 | − | 0.583372i | \(-0.198267\pi\) | |||||||
\(740\) | 117206. | − | 118523.i | 0.214035 | − | 0.216442i | ||||
\(741\) | −62178.9 | −0.113242 | ||||||||
\(742\) | −73042.2 | − | 73042.2i | −0.132668 | − | 0.132668i | ||||
\(743\) | 296206.i | 0.536557i | 0.963341 | + | 0.268279i | \(0.0864548\pi\) | ||||
−0.963341 | + | 0.268279i | \(0.913545\pi\) | |||||||
\(744\) | − | 246013.i | − | 0.444439i | ||||||
\(745\) | 250768. | − | 250768.i | 0.451815 | − | 0.451815i | ||||
\(746\) | −21113.3 | + | 21113.3i | −0.0379384 | + | 0.0379384i | ||||
\(747\) | 504195. | 0.903561 | ||||||||
\(748\) | 100209. | − | 100209.i | 0.179103 | − | 0.179103i | ||||
\(749\) | 129217. | 0.230332 | ||||||||
\(750\) | 539538. | 0.959179 | ||||||||
\(751\) | − | 318219.i | − | 0.564218i | −0.959382 | − | 0.282109i | \(-0.908966\pi\) | ||
0.959382 | − | 0.282109i | \(-0.0910339\pi\) | |||||||
\(752\) | −190181. | −0.336303 | ||||||||
\(753\) | 535638. | − | 535638.i | 0.944672 | − | 0.944672i | ||||
\(754\) | 305887. | + | 305887.i | 0.538045 | + | 0.538045i | ||||
\(755\) | 223599. | + | 223599.i | 0.392263 | + | 0.392263i | ||||
\(756\) | −36342.7 | −0.0635878 | ||||||||
\(757\) | 690801. | − | 690801.i | 1.20548 | − | 1.20548i | 0.233009 | − | 0.972475i | \(-0.425143\pi\) |
0.972475 | − | 0.233009i | \(-0.0748570\pi\) | |||||||
\(758\) | −261910. | − | 261910.i | −0.455841 | − | 0.455841i | ||||
\(759\) | −139565. | + | 139565.i | −0.242267 | + | 0.242267i | ||||
\(760\) | −4782.29 | − | 4782.29i | −0.00827960 | − | 0.00827960i | ||||
\(761\) | − | 483055.i | − | 0.834117i | −0.908880 | − | 0.417059i | \(-0.863061\pi\) | ||
0.908880 | − | 0.417059i | \(-0.136939\pi\) | |||||||
\(762\) | −576630. | + | 576630.i | −0.993086 | + | 0.993086i | ||||
\(763\) | 336791. | − | 336791.i | 0.578511 | − | 0.578511i | ||||
\(764\) | 10648.6 | + | 10648.6i | 0.0182434 | + | 0.0182434i | ||||
\(765\) | − | 133580.i | − | 0.228253i | ||||||
\(766\) | 611148. | 1.04157 | ||||||||
\(767\) | 690046.i | 1.17297i | ||||||||
\(768\) | 50411.1i | 0.0854681i | ||||||||
\(769\) | −346196. | − | 346196.i | −0.585422 | − | 0.585422i | 0.350966 | − | 0.936388i | \(-0.385853\pi\) |
−0.936388 | + | 0.350966i | \(0.885853\pi\) | |||||||
\(770\) | − | 214686.i | − | 0.362094i | ||||||
\(771\) | −659406. | − | 659406.i | −1.10929 | − | 1.10929i | ||||
\(772\) | −379960. | − | 379960.i | −0.637534 | − | 0.637534i | ||||
\(773\) | −124294. | −0.208014 | −0.104007 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104007 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(774\) | 171265. | 0.285882 | ||||||||
\(775\) | 245712. | − | 245712.i | 0.409094 | − | 0.409094i | ||||
\(776\) | − | 273864.i | − | 0.454791i | ||||||
\(777\) | 590730. | − | 3302.55i | 0.978470 | − | 0.00547026i | ||||
\(778\) | 449078. | 0.741929 | ||||||||
\(779\) | 17207.4 | + | 17207.4i | 0.0283558 | + | 0.0283558i | ||||
\(780\) | − | 385513.i | − | 0.633651i | ||||||
\(781\) | 519008.i | 0.850887i | ||||||||
\(782\) | 28083.1 | − | 28083.1i | 0.0459232 | − | 0.0459232i | ||||
\(783\) | −54468.6 | + | 54468.6i | −0.0888429 | + | 0.0888429i | ||||
\(784\) | 74989.8 | 0.122003 | ||||||||
\(785\) | −478376. | + | 478376.i | −0.776301 | + | 0.776301i | ||||
\(786\) | −204816. | −0.331527 | ||||||||
\(787\) | 708117. | 1.14329 | 0.571644 | − | 0.820502i | \(-0.306306\pi\) | ||||
0.571644 | + | 0.820502i | \(0.306306\pi\) | |||||||
\(788\) | 181378.i | 0.292101i | ||||||||
\(789\) | 325323. | 0.522590 | ||||||||
\(790\) | −275640. | + | 275640.i | −0.441660 | + | 0.441660i | ||||
\(791\) | 172584. | + | 172584.i | 0.275833 | + | 0.275833i | ||||
\(792\) | −160383. | − | 160383.i | −0.255687 | − | 0.255687i | ||||
\(793\) | −1.45979e6 | −2.32137 | ||||||||
\(794\) | −314058. | + | 314058.i | −0.498160 | + | 0.498160i | ||||
\(795\) | 137969. | + | 137969.i | 0.218296 | + | 0.218296i | ||||
\(796\) | 211434. | − | 211434.i | 0.333695 | − | 0.333695i | ||||
\(797\) | 564747. | + | 564747.i | 0.889073 | + | 0.889073i | 0.994434 | − | 0.105361i | \(-0.0335997\pi\) |
−0.105361 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(798\) | − | 23968.6i | − | 0.0376389i | ||||||
\(799\) | −261687. | + | 261687.i | −0.409910 | + | 0.409910i | ||||
\(800\) | −50349.5 | + | 50349.5i | −0.0786710 | + | 0.0786710i | ||||
\(801\) | −159250. | − | 159250.i | −0.248207 | − | 0.248207i | ||||
\(802\) | − | 63277.1i | − | 0.0983779i | ||||||
\(803\) | 1.41436e6 | 2.19346 | ||||||||
\(804\) | − | 230290.i | − | 0.356256i | ||||||
\(805\) | − | 60164.8i | − | 0.0928434i | ||||||
\(806\) | −454525. | − | 454525.i | −0.699662 | − | 0.699662i | ||||
\(807\) | − | 1.48117e6i | − | 2.27435i | ||||||
\(808\) | 197907. | + | 197907.i | 0.303137 | + | 0.303137i | ||||
\(809\) | −527837. | − | 527837.i | −0.806497 | − | 0.806497i | 0.177605 | − | 0.984102i | \(-0.443165\pi\) |
−0.984102 | + | 0.177605i | \(0.943165\pi\) | |||||||
\(810\) | 314378. | 0.479162 | ||||||||
\(811\) | −74359.6 | −0.113056 | −0.0565282 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565282 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(812\) | −117913. | + | 117913.i | −0.178834 | + | 0.178834i | ||||
\(813\) | 149222.i | 0.225763i | ||||||||
\(814\) | −391623. | − | 387269.i | −0.591044 | − | 0.584472i | ||||
\(815\) | 211067. | 0.317764 | ||||||||
\(816\) | 69365.2 | + | 69365.2i | 0.104175 | + | 0.104175i | ||||
\(817\) | − | 16873.7i | − | 0.0252794i | ||||||
\(818\) | − | 152423.i | − | 0.227795i | ||||||
\(819\) | 449470. | − | 449470.i | 0.670090 | − | 0.670090i | ||||
\(820\) | −106687. | + | 106687.i | −0.158666 | + | 0.158666i | ||||
\(821\) | −546995. | −0.811516 | −0.405758 | − | 0.913980i | \(-0.632992\pi\) | ||||
−0.405758 | + | 0.913980i | \(0.632992\pi\) | |||||||
\(822\) | −563719. | + | 563719.i | −0.834294 | + | 0.834294i | ||||
\(823\) | 182458. | 0.269379 | 0.134690 | − | 0.990888i | \(-0.456996\pi\) | ||||
0.134690 | + | 0.990888i | \(0.456996\pi\) | |||||||
\(824\) | −185768. | −0.273601 | ||||||||
\(825\) | − | 688608.i | − | 1.01173i | ||||||
\(826\) | −265997. | −0.389868 | ||||||||
\(827\) | 647411. | − | 647411.i | 0.946606 | − | 0.946606i | −0.0520393 | − | 0.998645i | \(-0.516572\pi\) |
0.998645 | + | 0.0520393i | \(0.0165721\pi\) | |||||||
\(828\) | −44946.8 | − | 44946.8i | −0.0655598 | − | 0.0655598i | ||||
\(829\) | 172830. | + | 172830.i | 0.251484 | + | 0.251484i | 0.821579 | − | 0.570095i | \(-0.193094\pi\) |
−0.570095 | + | 0.821579i | \(0.693094\pi\) | |||||||
\(830\) | 307990. | 0.447075 | ||||||||
\(831\) | −59348.1 | + | 59348.1i | −0.0859419 | + | 0.0859419i | ||||
\(832\) | 93137.9 | + | 93137.9i | 0.134549 | + | 0.134549i | ||||
\(833\) | 103185. | − | 103185.i | 0.148706 | − | 0.148706i | ||||
\(834\) | −759866. | − | 759866.i | −1.09246 | − | 1.09246i | ||||
\(835\) | − | 546986.i | − | 0.784518i | ||||||
\(836\) | −15801.6 | + | 15801.6i | −0.0226094 | + | 0.0226094i | ||||
\(837\) | 80936.2 | − | 80936.2i | 0.115529 | − | 0.115529i | ||||
\(838\) | −520973. | − | 520973.i | −0.741868 | − | 0.741868i | ||||
\(839\) | − | 163602.i | − | 0.232415i | −0.993225 | − | 0.116208i | \(-0.962926\pi\) | ||
0.993225 | − | 0.116208i | \(-0.0370738\pi\) | |||||||
\(840\) | 148607. | 0.210611 | ||||||||
\(841\) | − | 353837.i | − | 0.500278i | ||||||
\(842\) | 379135.i | 0.534774i | ||||||||
\(843\) | 923087. | + | 923087.i | 1.29893 | + | 1.29893i | ||||
\(844\) | 388069.i | 0.544784i | ||||||||
\(845\) | −404885. | − | 404885.i | −0.567046 | − | 0.567046i | ||||
\(846\) | 418828. | + | 418828.i | 0.585187 | + | 0.585187i | ||||
\(847\) | −196032. | −0.273249 | ||||||||
\(848\) | −66664.9 | −0.0927056 | ||||||||
\(849\) | −292404. | + | 292404.i | −0.405666 | + | 0.405666i | ||||
\(850\) | 138561.i | 0.191780i | ||||||||
\(851\) | −109751. | − | 108531.i | −0.151548 | − | 0.149863i | ||||
\(852\) | −359261. | −0.494915 | ||||||||
\(853\) | −18724.3 | − | 18724.3i | −0.0257341 | − | 0.0257341i | 0.694123 | − | 0.719857i | \(-0.255793\pi\) |
−0.719857 | + | 0.694123i | \(0.755793\pi\) | |||||||
\(854\) | − | 562717.i | − | 0.771568i | ||||||
\(855\) | 21063.7i | 0.0288139i | ||||||||
\(856\) | 58967.4 | − | 58967.4i | 0.0804757 | − | 0.0804757i | ||||
\(857\) | 346059. | − | 346059.i | 0.471181 | − | 0.471181i | −0.431116 | − | 0.902297i | \(-0.641880\pi\) |
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(858\) | −1.27381e6 | −1.73033 | ||||||||
\(859\) | 51923.0 | − | 51923.0i | 0.0703677 | − | 0.0703677i | −0.671047 | − | 0.741415i | \(-0.734155\pi\) |
0.741415 | + | 0.671047i | \(0.234155\pi\) | |||||||
\(860\) | 104618. | 0.141452 | ||||||||
\(861\) | −534711. | −0.721294 | ||||||||
\(862\) | 270310.i | 0.363788i | ||||||||
\(863\) | −157762. | −0.211826 | −0.105913 | − | 0.994375i | \(-0.533777\pi\) | ||||
−0.105913 | + | 0.994375i | \(0.533777\pi\) | |||||||
\(864\) | −16584.8 | + | 16584.8i | −0.0222169 | + | 0.0222169i | ||||
\(865\) | 287626. | + | 287626.i | 0.384412 | + | 0.384412i | ||||
\(866\) | 473311. | + | 473311.i | 0.631118 | + | 0.631118i | ||||
\(867\) | −837035. | −1.11354 | ||||||||
\(868\) | 175210. | − | 175210.i | 0.232551 | − | 0.232551i | ||||
\(869\) | 910765. | + | 910765.i | 1.20605 | + | 1.20605i | ||||
\(870\) | 222725. | − | 222725.i | 0.294259 | − | 0.294259i | ||||
\(871\) | −425475. | − | 425475.i | −0.560839 | − | 0.560839i | ||||
\(872\) | − | 307386.i | − | 0.404251i | ||||||
\(873\) | −603120. | + | 603120.i | −0.791362 | + | 0.791362i | ||||
\(874\) | −4428.33 | + | 4428.33i | −0.00579719 | + | 0.00579719i | ||||
\(875\) | 384257. | + | 384257.i | 0.501887 | + | 0.501887i | ||||
\(876\) | 979030.i | 1.27582i | ||||||||
\(877\) | −76468.4 | −0.0994220 | −0.0497110 | − | 0.998764i | \(-0.515830\pi\) | ||||
−0.0497110 | + | 0.998764i | \(0.515830\pi\) | |||||||
\(878\) | − | 526069.i | − | 0.682424i | ||||||
\(879\) | 1.33844e6i | 1.73229i | ||||||||
\(880\) | −97970.9 | − | 97970.9i | −0.126512 | − | 0.126512i | ||||
\(881\) | 906881.i | 1.16842i | 0.811603 | + | 0.584209i | \(0.198595\pi\) | ||||
−0.811603 | + | 0.584209i | \(0.801405\pi\) | |||||||
\(882\) | −165147. | − | 165147.i | −0.212292 | − | 0.212292i | ||||
\(883\) | 57834.1 | + | 57834.1i | 0.0741759 | + | 0.0741759i | 0.743221 | − | 0.669046i | \(-0.233297\pi\) |
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(884\) | 256314. | 0.327995 | ||||||||
\(885\) | 502440. | 0.641502 | ||||||||
\(886\) | −380266. | + | 380266.i | −0.484418 | + | 0.484418i | ||||
\(887\) | 461248.i | 0.586256i | 0.956073 | + | 0.293128i | \(0.0946962\pi\) | ||||
−0.956073 | + | 0.293128i | \(0.905304\pi\) | |||||||
\(888\) | 268070. | − | 271084.i | 0.339956 | − | 0.343778i | ||||
\(889\) | −821347. | −1.03926 | ||||||||
\(890\) | −97278.7 | − | 97278.7i | −0.122811 | − | 0.122811i | ||||
\(891\) | − | 1.03876e6i | − | 1.30846i | ||||||
\(892\) | 296726.i | 0.372928i | ||||||||
\(893\) | 41264.5 | − | 41264.5i | 0.0517457 | − | 0.0517457i | ||||
\(894\) | 573552. | − | 573552.i | 0.717626 | − | 0.717626i | ||||
\(895\) | 644512. | 0.804609 | ||||||||
\(896\) | −35902.6 | + | 35902.6i | −0.0447208 | + | 0.0447208i | ||||
\(897\) | −356980. | −0.443668 | ||||||||
\(898\) | 805461. | 0.998831 | ||||||||
\(899\) | − | 525190.i | − | 0.649827i | ||||||
\(900\) | 221765. | 0.273784 | ||||||||
\(901\) | −91730.3 | + | 91730.3i | −0.112996 | + | 0.112996i | ||||
\(902\) | 352514. | + | 352514.i | 0.433275 | + | 0.433275i | ||||
\(903\) | 262170. | + | 262170.i | 0.321520 | + | 0.321520i | ||||
\(904\) | 157516. | 0.192747 | ||||||||
\(905\) | 390654. | − | 390654.i | 0.476974 | − | 0.476974i | ||||
\(906\) | 511412. | + | 511412.i | 0.623038 | + | 0.623038i | ||||
\(907\) | 301412. | − | 301412.i | 0.366392 | − | 0.366392i | −0.499768 | − | 0.866160i | \(-0.666581\pi\) |
0.866160 | + | 0.499768i | \(0.166581\pi\) | |||||||
\(908\) | 310828. | + | 310828.i | 0.377006 | + | 0.377006i | ||||
\(909\) | − | 871685.i | − | 1.05495i | ||||||
\(910\) | 274561. | − | 274561.i | 0.331555 | − | 0.331555i | ||||
\(911\) | 683769. | − | 683769.i | 0.823896 | − | 0.823896i | −0.162768 | − | 0.986664i | \(-0.552042\pi\) |
0.986664 | + | 0.162768i | \(0.0520423\pi\) | |||||||
\(912\) | −10938.0 | − | 10938.0i | −0.0131506 | − | 0.0131506i | ||||
\(913\) | − | 1.01766e6i | − | 1.22084i | ||||||
\(914\) | 355888. | 0.426011 | ||||||||
\(915\) | 1.06291e6i | 1.26956i | ||||||||
\(916\) | − | 176785.i | − | 0.210695i | ||||||
\(917\) | −145869. | − | 145869.i | −0.173470 | − | 0.173470i | ||||
\(918\) | 45641.1i | 0.0541591i | ||||||||
\(919\) | 1.04857e6 | + | 1.04857e6i | 1.24155 | + | 1.24155i | 0.959356 | + | 0.282198i | \(0.0910635\pi\) |
0.282198 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(920\) | −27456.0 | − | 27456.0i | −0.0324385 | − | 0.0324385i | ||||
\(921\) | −1.99698e6 | −2.35426 | ||||||||
\(922\) | 889695. | 1.04660 | ||||||||
\(923\) | −663758. | + | 663758.i | −0.779123 | + | 0.779123i | ||||
\(924\) | − | 491025.i | − | 0.575121i | ||||||
\(925\) | 538495. | − | 3010.52i | 0.629358 | − | 0.00351851i | ||||
\(926\) | 658423. | 0.767861 | ||||||||
\(927\) | 409110. | + | 409110.i | 0.476081 | + | 0.476081i | ||||
\(928\) | 107618.i | 0.124965i | ||||||||
\(929\) | − | 42411.1i | − | 0.0491414i | −0.999698 | − | 0.0245707i | \(-0.992178\pi\) | ||
0.999698 | − | 0.0245707i | \(-0.00782189\pi\) | |||||||
\(930\) | −330952. | + | 330952.i | −0.382647 | + | 0.382647i | ||||
\(931\) | −16270.9 | + | 16270.9i | −0.0187721 | + | 0.0187721i | ||||
\(932\) | 366403. | 0.421821 | ||||||||
\(933\) | −1.08444e6 | + | 1.08444e6i | −1.24578 | + | 1.24578i | ||||
\(934\) | −838451. | −0.961134 | ||||||||
\(935\) | −269614. | −0.308403 | ||||||||
\(936\) | − | 410227.i | − | 0.468245i | ||||||
\(937\) | 15225.0 | 0.0173411 | 0.00867057 | − | 0.999962i | \(-0.497240\pi\) | ||||
0.00867057 | + | 0.999962i | \(0.497240\pi\) | |||||||
\(938\) | 164011. | − | 164011.i | 0.186410 | − | 0.186410i | ||||
\(939\) | −1.08618e6 | − | 1.08618e6i | −1.23188 | − | 1.23188i | ||||
\(940\) | 255843. | + | 255843.i | 0.289546 | + | 0.289546i | ||||
\(941\) | −46311.6 | −0.0523011 | −0.0261505 | − | 0.999658i | \(-0.508325\pi\) | ||||
−0.0261505 | + | 0.999658i | \(0.508325\pi\) | |||||||
\(942\) | −1.09413e6 | + | 1.09413e6i | −1.23301 | + | 1.23301i | ||||
\(943\) | 98790.8 | + | 98790.8i | 0.111095 | + | 0.111095i | ||||
\(944\) | −121387. | + | 121387.i | −0.136216 | + | 0.136216i | ||||
\(945\) | 48890.4 | + | 48890.4i | 0.0547469 | + | 0.0547469i | ||||
\(946\) | − | 345678.i | − | 0.386268i | ||||||
\(947\) | −1.05701e6 | + | 1.05701e6i | −1.17864 | + | 1.17864i | −0.198546 | + | 0.980092i | \(0.563622\pi\) |
−0.980092 | + | 0.198546i | \(0.936378\pi\) | |||||||
\(948\) | −630438. | + | 630438.i | −0.701496 | + | 0.701496i | ||||
\(949\) | 1.80882e6 | + | 1.80882e6i | 2.00846 | + | 2.00846i | ||||
\(950\) | − | 21849.2i | − | 0.0242096i | ||||||
\(951\) | 422393. | 0.467041 | ||||||||
\(952\) | 98803.3i | 0.109018i | ||||||||
\(953\) | − | 1.71773e6i | − | 1.89134i | −0.325125 | − | 0.945671i | \(-0.605406\pi\) | ||
0.325125 | − | 0.945671i | \(-0.394594\pi\) | |||||||
\(954\) | 146813. | + | 146813.i | 0.161313 | + | 0.161313i | ||||
\(955\) | − | 28650.2i | − | 0.0314139i | ||||||
\(956\) | 288038. | + | 288038.i | 0.315162 | + | 0.315162i | ||||
\(957\) | −735923. | − | 735923.i | −0.803542 | − | 0.803542i | ||||
\(958\) | 630846. | 0.687373 | ||||||||
\(959\) | −802957. | −0.873082 | ||||||||
\(960\) | 67816.1 | − | 67816.1i | 0.0735852 | − | 0.0735852i | ||||
\(961\) | − | 143128.i | − | 0.154981i | ||||||
\(962\) | −5568.95 | − | 996123.i | −0.00601760 | − | 1.07637i | ||||
\(963\) | −259723. | −0.280064 | ||||||||
\(964\) | 277738. | + | 277738.i | 0.298869 | + | 0.298869i | ||||
\(965\) | 1.02229e6i | 1.09779i | ||||||||
\(966\) | − | 137608.i | − | 0.147465i | ||||||
\(967\) | −671054. | + | 671054.i | −0.717637 | + | 0.717637i | −0.968121 | − | 0.250484i | \(-0.919410\pi\) |
0.250484 | + | 0.968121i | \(0.419410\pi\) | |||||||
\(968\) | −89458.2 | + | 89458.2i | −0.0954705 | + | 0.0954705i | ||||
\(969\) | −30101.1 | −0.0320578 | ||||||||
\(970\) | −368419. | + | 368419.i | −0.391560 | + | 0.391560i | ||||
\(971\) | −238177. | −0.252616 | −0.126308 | − | 0.991991i | \(-0.540313\pi\) | ||||
−0.126308 | + | 0.991991i | \(0.540313\pi\) | |||||||
\(972\) | 635079. | 0.672195 | ||||||||
\(973\) | − | 1.08235e6i | − | 1.14325i | ||||||
\(974\) | −53502.1 | −0.0563966 | ||||||||
\(975\) | 880659. | − | 880659.i | 0.926400 | − | 0.926400i | ||||
\(976\) | −256793. | − | 256793.i | −0.269578 | − | 0.269578i | ||||
\(977\) | 108059. | + | 108059.i | 0.113206 | + | 0.113206i | 0.761441 | − | 0.648234i | \(-0.224492\pi\) |
−0.648234 | + | 0.761441i | \(0.724492\pi\) | |||||||
\(978\) | 482748. | 0.504711 | ||||||||
\(979\) | −321427. | + | 321427.i | −0.335364 | + | 0.335364i | ||||
\(980\) | −100881. | − | 100881.i | −0.105040 | − | 0.105040i | ||||
\(981\) | −676944. | + | 676944.i | −0.703420 | + | 0.703420i | ||||
\(982\) | −772408. | − | 772408.i | −0.800984 | − | 0.800984i | ||||
\(983\) | 1.48107e6i | 1.53274i | 0.642397 | + | 0.766372i | \(0.277940\pi\) | ||||
−0.642397 | + | 0.766372i | \(0.722060\pi\) | |||||||
\(984\) | −244013. | + | 244013.i | −0.252013 | + | 0.252013i | ||||
\(985\) | 244001. | − | 244001.i | 0.251489 | − | 0.251489i | ||||
\(986\) | 148081. | + | 148081.i | 0.152316 | + | 0.152316i | ||||
\(987\) | 1.28227e6i | 1.31627i | ||||||||
\(988\) | −40417.2 | −0.0414050 | ||||||||
\(989\) | − | 96874.8i | − | 0.0990417i | ||||||
\(990\) | 431515.i | 0.440276i | ||||||||
\(991\) | −921056. | − | 921056.i | −0.937861 | − | 0.937861i | 0.0603181 | − | 0.998179i | \(-0.480788\pi\) |
−0.998179 | + | 0.0603181i | \(0.980788\pi\) | |||||||
\(992\) | − | 159912.i | − | 0.162502i | ||||||
\(993\) | 336314. | + | 336314.i | 0.341072 | + | 0.341072i | ||||
\(994\) | −255864. | − | 255864.i | −0.258962 | − | 0.258962i | ||||
\(995\) | −568868. | −0.574600 | ||||||||
\(996\) | 704428. | 0.710098 | ||||||||
\(997\) | 151297. | − | 151297.i | 0.152209 | − | 0.152209i | −0.626895 | − | 0.779104i | \(-0.715674\pi\) |
0.779104 | + | 0.626895i | \(0.215674\pi\) | |||||||
\(998\) | 91264.1i | 0.0916303i | ||||||||
\(999\) | 177377. | − | 991.650i | 0.177732 | − | 0.000993636i |
(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 | 74.5.d.a.31.6 | ✓ | 14 | |
37.6 | odd | 4 | inner | 74.5.d.a.43.2 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.d.a.31.6 | ✓ | 14 | 1.1 | even | 1 | trivial | |
74.5.d.a.43.2 | yes | 14 | 37.6 | odd | 4 | inner |