Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(81,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.k (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: | \(8.02425976078\) |
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: | \( x^{14} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.5 | ||
Root | \(3.07347i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.89 |
Dual form | 136.4.k.a.81.5 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.07347 | − | 3.07347i | 0.591489 | − | 0.591489i | −0.346544 | − | 0.938034i | \(-0.612645\pi\) |
0.938034 | + | 0.346544i | \(0.112645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.67626 | + | 8.67626i | −0.776028 | + | 0.776028i | −0.979153 | − | 0.203125i | \(-0.934890\pi\) |
0.203125 | + | 0.979153i | \(0.434890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.02315 | + | 9.02315i | 0.487204 | + | 0.487204i | 0.907423 | − | 0.420219i | \(-0.138047\pi\) |
−0.420219 | + | 0.907423i | \(0.638047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.10760i | 0.300281i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.0636 | + | 39.0636i | 1.07074 | + | 1.07074i | 0.997300 | + | 0.0734374i | \(0.0233969\pi\) |
0.0734374 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.868393 | −0.0185268 | −0.00926342 | − | 0.999957i | \(-0.502949\pi\) | ||||
−0.00926342 | + | 0.999957i | \(0.502949\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 53.3324i | 0.918024i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 69.8166 | − | 6.21656i | 0.996059 | − | 0.0886904i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 50.0440i | − | 0.604256i | −0.953267 | − | 0.302128i | \(-0.902303\pi\) | ||
0.953267 | − | 0.302128i | \(-0.0976971\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 55.4647 | 0.576352 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −34.6437 | − | 34.6437i | −0.314074 | − | 0.314074i | 0.532412 | − | 0.846486i | \(-0.321286\pi\) |
−0.846486 | + | 0.532412i | \(0.821286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 25.5549i | − | 0.204439i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 107.902 | + | 107.902i | 0.769102 | + | 0.769102i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 100.912 | − | 100.912i | 0.646166 | − | 0.646166i | −0.305898 | − | 0.952064i | \(-0.598957\pi\) |
0.952064 | + | 0.305898i | \(0.0989567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −208.341 | + | 208.341i | −1.20707 | + | 1.20707i | −0.235095 | + | 0.971972i | \(0.575540\pi\) |
−0.971972 | + | 0.235095i | \(0.924460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 240.121 | 1.26666 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −156.574 | −0.756168 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −92.7068 | + | 92.7068i | −0.411916 | + | 0.411916i | −0.882406 | − | 0.470489i | \(-0.844077\pi\) |
0.470489 | + | 0.882406i | \(0.344077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.66898 | + | 2.66898i | −0.0109584 | + | 0.0109584i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 127.219 | + | 127.219i | 0.484590 | + | 0.484590i | 0.906594 | − | 0.422004i | \(-0.138673\pi\) |
−0.422004 | + | 0.906594i | \(0.638673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 274.357i | 0.973001i | 0.873680 | + | 0.486500i | \(0.161727\pi\) | ||||
−0.873680 | + | 0.486500i | \(0.838273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −70.3436 | − | 70.3436i | −0.233027 | − | 0.233027i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −92.6014 | −0.287389 | −0.143695 | − | 0.989622i | \(-0.545898\pi\) | ||||
−0.143695 | + | 0.989622i | \(0.545898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 180.166i | − | 0.525264i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 195.473 | − | 233.685i | 0.536699 | − | 0.641618i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 460.648i | − | 1.19386i | −0.802292 | − | 0.596932i | \(-0.796386\pi\) | ||
0.802292 | − | 0.596932i | \(-0.203614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −677.851 | −1.66184 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −153.808 | − | 153.808i | −0.357411 | − | 0.357411i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 539.280i | − | 1.18997i | −0.803736 | − | 0.594986i | \(-0.797158\pi\) | ||
0.803736 | − | 0.594986i | \(-0.202842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −456.343 | − | 456.343i | −0.957849 | − | 0.957849i | 0.0412984 | − | 0.999147i | \(-0.486851\pi\) |
−0.999147 | + | 0.0412984i | \(0.986851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −73.1561 | + | 73.1561i | −0.146298 | + | 0.146298i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.53440 | − | 7.53440i | 0.0143773 | − | 0.0143773i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −105.099 | −0.191640 | −0.0958200 | − | 0.995399i | \(-0.530547\pi\) | ||||
−0.0958200 | + | 0.995399i | \(0.530547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −212.952 | −0.371543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −57.5002 | + | 57.5002i | −0.0961129 | + | 0.0961129i | −0.753528 | − | 0.657415i | \(-0.771650\pi\) |
0.657415 | + | 0.753528i | \(0.271650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 636.819 | − | 636.819i | 1.02101 | − | 1.02101i | 0.0212391 | − | 0.999774i | \(-0.493239\pi\) |
0.999774 | − | 0.0212391i | \(-0.00676113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −78.5421 | − | 78.5421i | −0.120923 | − | 0.120923i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 704.953i | 1.04334i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 448.664 | + | 448.664i | 0.638970 | + | 0.638970i | 0.950301 | − | 0.311332i | \(-0.100775\pi\) |
−0.311332 | + | 0.950301i | \(0.600775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 444.362 | 0.609550 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 264.124i | − | 0.349293i | −0.984631 | − | 0.174647i | \(-0.944122\pi\) | ||
0.984631 | − | 0.174647i | \(-0.0558783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −551.810 | + | 659.683i | −0.704144 | + | 0.841796i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 620.297i | − | 0.764400i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1573.69 | −1.87428 | −0.937141 | − | 0.348951i | \(-0.886538\pi\) | ||||
−0.937141 | + | 0.348951i | \(0.886538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.83564 | − | 7.83564i | −0.00902636 | − | 0.00902636i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1280.66i | 1.42793i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 434.194 | + | 434.194i | 0.468920 | + | 0.468920i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 224.583 | − | 224.583i | 0.235082 | − | 0.235082i | −0.579728 | − | 0.814810i | \(-0.696841\pi\) |
0.814810 | + | 0.579728i | \(0.196841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −316.712 | + | 316.712i | −0.321522 | + | 0.321522i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1692.20 | 1.66713 | 0.833564 | − | 0.552423i | \(-0.186296\pi\) | ||||
0.833564 | + | 0.552423i | \(0.186296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 642.624 | 0.614753 | 0.307377 | − | 0.951588i | \(-0.400549\pi\) | ||||
0.307377 | + | 0.951588i | \(0.400549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −481.226 | + | 481.226i | −0.447265 | + | 0.447265i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1188.35 | − | 1188.35i | 1.07366 | − | 1.07366i | 0.0765994 | − | 0.997062i | \(-0.475594\pi\) |
0.997062 | − | 0.0765994i | \(-0.0244062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −526.566 | − | 526.566i | −0.462714 | − | 0.462714i | 0.436830 | − | 0.899544i | \(-0.356101\pi\) |
−0.899544 | + | 0.436830i | \(0.856101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 569.862i | 0.487288i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 204.185 | + | 204.185i | 0.169983 | + | 0.169983i | 0.786972 | − | 0.616989i | \(-0.211648\pi\) |
−0.616989 | + | 0.786972i | \(0.711648\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 601.155 | 0.487460 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.04058i | − | 0.00556327i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 686.058 | + | 573.873i | 0.528495 | + | 0.442074i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1720.93i | 1.29296i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 782.004 | 0.573260 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −862.811 | − | 862.811i | −0.617378 | − | 0.617378i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 955.662i | 0.667726i | 0.942622 | + | 0.333863i | \(0.108352\pi\) | ||||
−0.942622 | + | 0.333863i | \(0.891648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 843.227 | + | 843.227i | 0.575519 | + | 0.575519i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 775.731 | − | 775.731i | 0.517374 | − | 0.517374i | −0.399402 | − | 0.916776i | \(-0.630782\pi\) |
0.916776 | + | 0.399402i | \(0.130782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 451.554 | − | 451.554i | 0.294396 | − | 0.294396i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1872.37 | −1.19369 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −535.781 | −0.334123 | −0.167061 | − | 0.985946i | \(-0.553428\pi\) | ||||
−0.167061 | + | 0.985946i | \(0.553428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 555.349 | − | 555.349i | 0.338878 | − | 0.338878i | −0.517067 | − | 0.855945i | \(-0.672976\pi\) |
0.855945 | + | 0.517067i | \(0.172976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −284.607 | + | 284.607i | −0.169988 | + | 0.169988i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.9225 | − | 33.9225i | −0.0198374 | − | 0.0198374i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1751.07i | 1.00289i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −553.733 | − | 553.733i | −0.310688 | − | 0.310688i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2846.15 | 1.56487 | 0.782435 | − | 0.622733i | \(-0.213978\pi\) | ||||
0.782435 | + | 0.622733i | \(0.213978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 311.072i | 0.167647i | 0.996481 | + | 0.0838235i | \(0.0267132\pi\) | ||||
−0.996481 | + | 0.0838235i | \(0.973287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 50.4013 | + | 566.045i | 0.0266321 | + | 0.299098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3615.24i | − | 1.87344i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −294.137 | −0.149521 | −0.0747603 | − | 0.997202i | \(-0.523819\pi\) | ||||
−0.0747603 | + | 0.997202i | \(0.523819\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1415.79 | − | 1415.79i | −0.706158 | − | 0.706158i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 625.190i | − | 0.306036i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1717.64 | + | 1717.64i | 0.825372 | + | 0.825372i | 0.986873 | − | 0.161500i | \(-0.0516333\pi\) |
−0.161500 | + | 0.986873i | \(0.551633\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2083.35 | + | 2083.35i | −0.982963 | + | 0.982963i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1974.22 | + | 1974.22i | −0.914790 | + | 0.914790i | −0.996644 | − | 0.0818543i | \(-0.973916\pi\) |
0.0818543 | + | 0.996644i | \(0.473916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.25 | −0.999657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 405.736 | 0.181447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3015.57 | − | 3015.57i | 1.32526 | − | 1.32526i | 0.415804 | − | 0.909454i | \(-0.363500\pi\) |
0.909454 | − | 0.415804i | \(-0.136500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 230.585 | − | 230.585i | 0.0996036 | − | 0.0996036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1657.46 | − | 1657.46i | −0.703855 | − | 0.703855i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 891.459i | − | 0.372239i | −0.982527 | − | 0.186120i | \(-0.940409\pi\) | ||
0.982527 | − | 0.186120i | \(-0.0595912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1545.68 | − | 1545.68i | −0.634748 | − | 0.634748i | 0.314507 | − | 0.949255i | \(-0.398161\pi\) |
−0.949255 | + | 0.314507i | \(0.898161\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2805.11 | −1.13311 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1608.70i | − | 0.639317i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2970.13 | + | 2484.44i | 1.16148 | + | 0.971554i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1947.23i | 0.749420i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1937.35 | 0.733937 | 0.366968 | − | 0.930233i | \(-0.380396\pi\) | ||||
0.366968 | + | 0.930233i | \(0.380396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1909.84 | − | 1909.84i | −0.712298 | − | 0.712298i | 0.254718 | − | 0.967015i | \(-0.418017\pi\) |
−0.967015 | + | 0.254718i | \(0.918017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 46.3135i | − | 0.0170081i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 399.215 | + | 399.215i | 0.144380 | + | 0.144380i | 0.775602 | − | 0.631222i | \(-0.217446\pi\) |
−0.631222 | + | 0.775602i | \(0.717446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3648.28 | + | 3648.28i | −1.29960 | + | 1.29960i | −0.370941 | + | 0.928656i | \(0.620965\pi\) |
−0.928656 | + | 0.370941i | \(0.879035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −323.018 | + | 323.018i | −0.113353 | + | 0.113353i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1821.08 | 0.629630 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2207.56 | −0.752111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 280.877 | − | 280.877i | 0.0943106 | − | 0.0943106i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1954.90 | − | 1954.90i | 0.647000 | − | 0.647000i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3555.86 | − | 3555.86i | −1.16017 | − | 1.16017i | −0.984439 | − | 0.175728i | \(-0.943772\pi\) |
−0.175728 | − | 0.984439i | \(-0.556228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 353.450i | 0.113699i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2380.39 | − | 2380.39i | −0.755076 | − | 0.755076i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3759.78 | −1.17618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3914.48i | − | 1.20784i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −60.6282 | + | 5.39842i | −0.0184538 | + | 0.00164315i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 485.861i | − | 0.145900i | −0.997336 | − | 0.0729499i | \(-0.976759\pi\) | ||
0.997336 | − | 0.0729499i | \(-0.0232413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 207.189 | 0.0613892 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1690.16 | + | 1690.16i | 0.494183 | + | 0.494183i | 0.909621 | − | 0.415438i | \(-0.136372\pi\) |
−0.415438 | + | 0.909621i | \(0.636372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 187.996i | 0.0542493i | 0.999632 | + | 0.0271247i | \(0.00863511\pi\) | ||||
−0.999632 | + | 0.0271247i | \(0.991365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2166.65 | + | 2166.65i | 0.617122 | + | 0.617122i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3789.41 | − | 3789.41i | 1.06546 | − | 1.06546i | 0.0677606 | − | 0.997702i | \(-0.478415\pi\) |
0.997702 | − | 0.0677606i | \(-0.0215854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 803.433 | − | 803.433i | 0.223022 | − | 0.223022i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2757.91 | 0.755887 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4249.16 | −1.15002 | −0.575011 | − | 0.818146i | \(-0.695002\pi\) | ||||
−0.575011 | + | 0.818146i | \(0.695002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4536.47 | − | 4536.47i | 1.21253 | − | 1.21253i | 0.242338 | − | 0.970192i | \(-0.422086\pi\) |
0.970192 | − | 0.242338i | \(-0.0779143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1547.62 | + | 1547.62i | −0.408560 | + | 0.408560i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1563.16 | + | 1563.16i | 0.407620 | + | 0.407620i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.4578i | 0.0111950i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −811.775 | − | 811.775i | −0.206603 | − | 0.206603i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 529.038 | 0.133038 | 0.0665191 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665191 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2706.61i | − | 0.672582i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 331.544 | + | 3723.48i | 0.0814199 | + | 0.914407i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4391.33i | 1.06585i | 0.846162 | + | 0.532926i | \(0.178907\pi\) | ||||
−0.846162 | + | 0.532926i | \(0.821093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1673.01 | −0.401375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 818.151 | + | 818.151i | 0.194032 | + | 0.194032i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6530.80i | 1.53120i | 0.643315 | + | 0.765601i | \(0.277558\pi\) | ||||
−0.643315 | + | 0.765601i | \(0.722442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3996.70 | + | 3996.70i | 0.926472 | + | 0.926472i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4836.69 | + | 4836.69i | −1.10862 | + | 1.10862i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5185.75 | − | 5185.75i | 1.17539 | − | 1.17539i | 0.194488 | − | 0.980905i | \(-0.437695\pi\) |
0.980905 | − | 0.194488i | \(-0.0623047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3156.92 | −0.707635 | −0.353818 | − | 0.935314i | \(-0.615117\pi\) | ||||
−0.353818 | + | 0.935314i | \(0.615117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −48.1652 | −0.0106780 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 998.265 | − | 998.265i | 0.218900 | − | 0.218900i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2386.93 | + | 2386.93i | −0.517749 | + | 0.517749i | −0.916890 | − | 0.399141i | \(-0.869308\pi\) |
0.399141 | + | 0.916890i | \(0.369308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1689.14 | − | 1689.14i | −0.362460 | − | 0.362460i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5791.03i | 1.22941i | 0.788758 | + | 0.614704i | \(0.210725\pi\) | ||||
−0.788758 | + | 0.614704i | \(0.789275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5454.87 | + | 5454.87i | 1.14579 | + | 1.14579i | 0.987372 | + | 0.158416i | \(0.0506386\pi\) |
0.158416 | + | 0.987372i | \(0.449361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2668.96 | 0.554722 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2295.82i | 0.472189i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4835.71 | − | 868.038i | 0.984268 | − | 0.176682i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1380.50i | − | 0.278097i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4992.55 | −0.995453 | −0.497727 | − | 0.867334i | \(-0.665832\pi\) | ||||
−0.497727 | + | 0.867334i | \(0.665832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4678.94 | + | 4678.94i | 0.923451 | + | 0.923451i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8430.08i | 1.64701i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.0843 | + | 30.0843i | 0.00581880 | + | 0.00581880i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2475.56 | + | 2475.56i | −0.474050 | + | 0.474050i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5200.92 | − | 5200.92i | 0.986088 | − | 0.986088i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7918.70 | 1.48663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7425.89 | −1.38051 | −0.690257 | − | 0.723564i | \(-0.742503\pi\) | ||||
−0.690257 | + | 0.723564i | \(0.742503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1975.08 | − | 1975.08i | 0.363620 | − | 0.363620i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6145.92 | − | 6145.92i | 1.12059 | − | 1.12059i | 0.128935 | − | 0.991653i | \(-0.458844\pi\) |
0.991653 | − | 0.128935i | \(-0.0411559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2545.72 | − | 2545.72i | −0.459720 | − | 0.459720i | 0.438843 | − | 0.898564i | \(-0.355388\pi\) |
−0.898564 | + | 0.438843i | \(0.855388\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 1269.44i | − | 0.227063i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2469.84 | − | 2469.84i | −0.437603 | − | 0.437603i | 0.453602 | − | 0.891204i | \(-0.350139\pi\) |
−0.891204 | + | 0.453602i | \(0.850139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7883.94 | 1.38375 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 7304.69i | − | 1.27012i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −311.101 | − | 3493.90i | −0.0535917 | − | 0.601875i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.1917i | 0.00378761i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3236.76 | −0.547381 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −835.556 | − | 835.556i | −0.140017 | − | 0.140017i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5092.63i | 0.845669i | 0.906207 | + | 0.422834i | \(0.138965\pi\) | ||||
−0.906207 | + | 0.422834i | \(0.861035\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −751.629 | − | 751.629i | −0.123691 | − | 0.123691i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 911.865 | − | 911.865i | 0.148718 | − | 0.148718i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6369.59 | + | 6369.59i | −1.02960 | + | 1.02960i | −0.0300466 | + | 0.999548i | \(0.509566\pi\) |
−0.999548 | + | 0.0300466i | \(0.990434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1255.11 | 0.201086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16277.1 | −2.58490 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4720.60 | − | 4720.60i | 0.743115 | − | 0.743115i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1847.63 | − | 1847.63i | 0.288328 | − | 0.288328i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3438.43 | − | 3438.43i | −0.531943 | − | 0.531943i | 0.389207 | − | 0.921150i | \(-0.372749\pi\) |
−0.921150 | + | 0.389207i | \(0.872749\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2937.29i | − | 0.450514i | −0.974299 | − | 0.225257i | \(-0.927678\pi\) | ||
0.974299 | − | 0.225257i | \(-0.0723221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93.7014 | − | 93.7014i | −0.0142490 | − | 0.0142490i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11318.3 | −1.70655 | −0.853274 | − | 0.521462i | \(-0.825387\pi\) | ||||
−0.853274 | + | 0.521462i | \(0.825387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 997.772i | − | 0.149173i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3872.36 | − | 344.800i | 0.574081 | − | 0.0511169i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10060.7i | − | 1.47906i | −0.673124 | − | 0.739530i | \(-0.735048\pi\) | ||
0.673124 | − | 0.739530i | \(-0.264952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4354.60 | 0.634874 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5289.21 | + | 5289.21i | 0.764770 | + | 0.764770i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11050.4i | 1.58467i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1489.62 | + | 1489.62i | 0.211873 | + | 0.211873i | 0.805063 | − | 0.593190i | \(-0.202132\pi\) |
−0.593190 | + | 0.805063i | \(0.702132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1031.44 | + | 1031.44i | −0.145513 | + | 0.145513i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4156.49 | − | 4156.49i | 0.581656 | − | 0.581656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1001.78 | 0.139062 | 0.0695312 | − | 0.997580i | \(-0.477850\pi\) | ||||
0.0695312 | + | 0.997580i | \(0.477850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5303.65 | −0.730344 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −87.6310 | + | 87.6310i | −0.0119714 | + | 0.0119714i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2198.89 | − | 2198.89i | 0.298020 | − | 0.298020i | −0.542218 | − | 0.840238i | \(-0.682415\pi\) |
0.840238 | + | 0.542218i | \(0.182415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2937.19 | + | 2937.19i | 0.394953 | + | 0.394953i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3039.84i | 0.405558i | 0.979225 | + | 0.202779i | \(0.0649972\pi\) | ||||
−0.979225 | + | 0.202779i | \(0.935003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6116.35 | − | 6116.35i | −0.809658 | − | 0.809658i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2224.37 | −0.292174 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7047.01i | 0.918503i | 0.888306 | + | 0.459252i | \(0.151882\pi\) | ||||
−0.888306 | + | 0.459252i | \(0.848118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2634.07 | − | 2203.34i | −0.340692 | − | 0.284981i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4768.37i | − | 0.612042i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7785.44 | −0.991717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2938.84 | − | 2938.84i | −0.371527 | − | 0.371527i | 0.496506 | − | 0.868033i | \(-0.334616\pi\) |
−0.868033 | + | 0.496506i | \(0.834616\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2775.67i | − | 0.348264i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7877.17 | + | 7877.17i | 0.980965 | + | 0.980965i | 0.999822 | − | 0.0188573i | \(-0.00600283\pi\) |
−0.0188573 | + | 0.999822i | \(0.506003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 180.922 | − | 180.922i | 0.0223632 | − | 0.0223632i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3855.40 | + | 3855.40i | −0.473028 | + | 0.473028i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7242.91 | −0.882108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6227.41 | −0.752874 | −0.376437 | − | 0.926442i | \(-0.622851\pi\) | ||||
−0.376437 | + | 0.926442i | \(0.622851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1646.70 | + | 1646.70i | −0.197630 | + | 0.197630i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4866.01 | − | 4866.01i | 0.579759 | − | 0.579759i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2291.60 | + | 2291.60i | 0.271061 | + | 0.271061i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3413.69i | − | 0.400886i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1855.27 | − | 1855.27i | −0.216315 | − | 0.216315i | 0.590629 | − | 0.806943i | \(-0.298880\pi\) |
−0.806943 | + | 0.590629i | \(0.798880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13594.4 | −1.57376 | −0.786878 | − | 0.617109i | \(-0.788304\pi\) | ||||
−0.786878 | + | 0.617109i | \(0.788304\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 750.774i | − | 0.0862976i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −158.863 | − | 1784.15i | −0.0181318 | − | 0.203633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8235.31i | − | 0.933336i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −208.520 | −0.0234672 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5094.94 | − | 5094.94i | −0.569408 | − | 0.569408i | 0.362555 | − | 0.931962i | \(-0.381905\pi\) |
−0.931962 | + | 0.362555i | \(0.881905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7430.53i | − | 0.824684i | −0.911029 | − | 0.412342i | \(-0.864711\pi\) | ||
0.911029 | − | 0.412342i | \(-0.135289\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5381.86 | + | 5381.86i | 0.593196 | + | 0.593196i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1733.71 | + | 1733.71i | −0.189781 | + | 0.189781i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10536.6 | − | 10536.6i | 1.14553 | − | 1.14553i | 0.158103 | − | 0.987423i | \(-0.449462\pi\) |
0.987423 | − | 0.158103i | \(-0.0505380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1460.71 | 0.157727 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17733.7 | −1.90193 | −0.950964 | − | 0.309302i | \(-0.899904\pi\) | ||||
−0.950964 | + | 0.309302i | \(0.899904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13653.8 | − | 13653.8i | 1.45450 | − | 1.45450i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8747.54 | − | 8747.54i | 0.925603 | − | 0.925603i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10516.0 | + | 10516.0i | 1.10530 | + | 1.10530i | 0.993759 | + | 0.111544i | \(0.0355797\pi\) |
0.111544 | + | 0.993759i | \(0.464420\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9939.22i | 1.03774i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 956.070 | + | 956.070i | 0.0991614 | + | 0.0991614i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 135.968 | 0.0140094 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6104.30i | 0.624829i | 0.949946 | + | 0.312415i | \(0.101138\pi\) | ||||
−0.949946 | + | 0.312415i | \(0.898862\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8204.13 | + | 6862.57i | 0.834283 | + | 0.697859i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4495.32i | 0.454160i | 0.973876 | + | 0.227080i | \(0.0729179\pi\) | ||||
−0.973876 | + | 0.227080i | \(0.927082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4964.24 | −0.498289 | −0.249144 | − | 0.968466i | \(-0.580149\pi\) | ||||
−0.249144 | + | 0.968466i | \(0.580149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11111.3 | − | 11111.3i | −1.10812 | − | 1.10812i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 789.079i | 0.0781889i | 0.999236 | + | 0.0390944i | \(0.0124473\pi\) | ||||
−0.999236 | + | 0.0390944i | \(0.987553\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −948.323 | − | 948.323i | −0.0933678 | − | 0.0933678i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −904.022 | + | 904.022i | −0.0884398 | + | 0.0884398i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10717.4 | + | 10717.4i | −1.04183 | + | 1.04183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1278.87 | −0.123534 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3734.74 | 0.358495 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2956.32 | − | 2956.32i | 0.281999 | − | 0.281999i | −0.551907 | − | 0.833906i | \(-0.686100\pi\) |
0.833906 | + | 0.551907i | \(0.186100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 80.5059 | − | 80.5059i | 0.00763151 | − | 0.00763151i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1921.50 | − | 1921.50i | −0.181017 | − | 0.181017i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3897.08i | 0.364861i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1159.43 | + | 1159.43i | 0.107883 | + | 0.107883i | 0.758988 | − | 0.651105i | \(-0.225694\pi\) |
−0.651105 | + | 0.758988i | \(0.725694\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10558.2 | 0.976398 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 765.124i | − | 0.0703249i | −0.999382 | − | 0.0351625i | \(-0.988805\pi\) | ||
0.999382 | − | 0.0351625i | \(-0.0111949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6417.98 | − | 7672.63i | 0.586311 | − | 0.700928i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5495.74i | − | 0.499021i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1037.67 | −0.0936532 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11036.9 | + | 11036.9i | 0.990142 | + | 0.990142i | 0.999952 | − | 0.00980984i | \(-0.00312262\pi\) |
−0.00980984 | + | 0.999952i | \(0.503123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12135.4i | 1.08218i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14656.0 | + | 14656.0i | 1.29917 | + | 1.29917i | 0.928943 | + | 0.370224i | \(0.120719\pi\) |
0.370224 | + | 0.928943i | \(0.379281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14681.9 | + | 14681.9i | −1.29374 | + | 1.29374i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6750.09 | + | 6750.09i | −0.591286 | + | 0.591286i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20332.9 | 1.77061 | 0.885304 | − | 0.465012i | \(-0.153950\pi\) | ||||
0.885304 | + | 0.465012i | \(0.153950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11492.2 | 0.994884 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5399.85 | − | 5399.85i | 0.464735 | − | 0.464735i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5575.57 | + | 5575.57i | −0.477066 | + | 0.477066i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3617.34 | − | 3617.34i | −0.307718 | − | 0.307718i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18536.5i | − | 1.56775i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1124.38 | + | 1124.38i | 0.0945490 | + | 0.0945490i | 0.752799 | − | 0.658250i | \(-0.228703\pi\) |
−0.658250 | + | 0.752799i | \(0.728703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8009.53 | 0.669660 | 0.334830 | − | 0.942278i | \(-0.391321\pi\) | ||||
0.334830 | + | 0.942278i | \(0.391321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1417.39i | − | 0.117829i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13250.5 | + | 15840.8i | −1.09526 | + | 1.30937i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9766.63i | − | 0.802715i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4372.27 | 0.357326 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −110.476 | − | 110.476i | −0.00897793 | − | 0.00897793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20620.8i | 1.66638i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2739.87 | − | 2739.87i | −0.220175 | − | 0.220175i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7037.91 | − | 7037.91i | 0.562420 | − | 0.562420i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4328.20 | − | 4328.20i | 0.343963 | − | 0.343963i | −0.513892 | − | 0.857855i | \(-0.671797\pi\) |
0.857855 | + | 0.513892i | \(0.171797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9501.18 | −0.750893 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9137.24 | 0.718158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12109.7 | + | 12109.7i | −0.946573 | + | 0.946573i | −0.998643 | − | 0.0520704i | \(-0.983418\pi\) |
0.0520704 | + | 0.998643i | \(0.483418\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3699.85 | − | 3699.85i | 0.287624 | − | 0.287624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5050.02 | − | 5050.02i | −0.390450 | − | 0.390450i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8096.72i | 0.622618i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4944.27 | − | 4944.27i | −0.378149 | − | 0.378149i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1702.39 | −0.129502 | −0.0647509 | − | 0.997901i | \(-0.520625\pi\) | ||||
−0.0647509 | + | 0.997901i | \(0.520625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 238.250i | − | 0.0180266i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16764.4 | − | 1492.73i | 1.26167 | − | 0.112340i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19262.1i | 1.44192i | 0.692976 | + | 0.720961i | \(0.256299\pi\) | ||||
−0.692976 | + | 0.720961i | \(0.743701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3543.12 | −0.263823 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4009.54 | + | 4009.54i | 0.296975 | + | 0.296975i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4320.59i | − | 0.318328i | −0.987252 | − | 0.159164i | \(-0.949120\pi\) | ||
0.987252 | − | 0.159164i | \(-0.0508799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3305.73 | − | 3305.73i | −0.242277 | − | 0.242277i | 0.575514 | − | 0.817792i | \(-0.304802\pi\) |
−0.817792 | + | 0.575514i | \(0.804802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5954.39 | − | 5954.39i | 0.434116 | − | 0.434116i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −885.314 | + | 885.314i | −0.0642090 | + | 0.0642090i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4858.52 | −0.350542 | −0.175271 | − | 0.984520i | \(-0.556080\pi\) | ||||
−0.175271 | + | 0.984520i | \(0.556080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11739.7 | −0.842633 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2383.23 | − | 2383.23i | 0.170177 | − | 0.170177i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17994.5 | − | 17994.5i | 1.27832 | − | 1.27832i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 61.0859 | + | 61.0859i | 0.00431725 | + | 0.00431725i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27354.2i | 1.92339i | 0.274125 | + | 0.961694i | \(0.411612\pi\) | ||||
−0.274125 | + | 0.961694i | \(0.588388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10426.2 | + | 10426.2i | 0.729378 | + | 0.729378i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2453.95 | 0.170799 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13606.3i | − | 0.942233i | −0.882071 | − | 0.471117i | \(-0.843851\pi\) | ||
0.882071 | − | 0.471117i | \(-0.156149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10931.5 | + | 973.353i | −0.753189 | + | 0.0670649i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22425.8i | 1.53740i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17513.3 | 1.19461 | 0.597307 | − | 0.802013i | \(-0.296238\pi\) | ||||
0.597307 | + | 0.802013i | \(0.296238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13737.7 | − | 13737.7i | −0.932399 | − | 0.932399i | 0.0654564 | − | 0.997855i | \(-0.479150\pi\) |
−0.997855 | + | 0.0654564i | \(0.979150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 852.099i | − | 0.0575459i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14931.2 | − | 14931.2i | −1.00337 | − | 1.00337i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4673.11 | − | 4673.11i | 0.312480 | − | 0.312480i | −0.533389 | − | 0.845870i | \(-0.679082\pi\) |
0.845870 | + | 0.533389i | \(0.179082\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5597.03 | − | 5597.03i | 0.372419 | − | 0.372419i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 80.4144 | 0.00532442 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24289.4 | 1.60039 | 0.800196 | − | 0.599739i | \(-0.204729\pi\) | ||||
0.800196 | + | 0.599739i | \(0.204729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6784.87 | + | 6784.87i | −0.444866 | + | 0.444866i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19700.6 | + | 19700.6i | −1.28544 | + | 1.28544i | −0.347915 | + | 0.937526i | \(0.613110\pi\) |
−0.937526 | + | 0.347915i | \(0.886890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21044.4 | − | 21044.4i | −1.36647 | − | 1.36647i | −0.865415 | − | 0.501055i | \(-0.832945\pi\) |
−0.501055 | − | 0.865415i | \(-0.667055\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 7476.24i | − | 0.483110i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14199.7 | − | 14199.7i | −0.913158 | − | 0.913158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18166.3 | 1.16264 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 12016.6i | − | 0.765387i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5896.15 | + | 7048.79i | −0.373760 | + | 0.446826i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3117.99i | − | 0.196712i | −0.995151 | − | 0.0983559i | \(-0.968642\pi\) | ||
0.995151 | − | 0.0983559i | \(-0.0313584\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21857.6 | −1.37245 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8291.56 | − | 8291.56i | −0.518174 | − | 0.518174i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 156.455i | 0.00973148i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −466.188 | − | 466.188i | −0.0288609 | − | 0.0288609i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1391.32 | + | 1391.32i | −0.0857314 | + | 0.0857314i | −0.748672 | − | 0.662941i | \(-0.769308\pi\) |
0.662941 | + | 0.748672i | \(0.269308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3638.34 | − | 3638.34i | 0.223145 | − | 0.223145i | −0.586676 | − | 0.809821i | \(-0.699564\pi\) |
0.809821 | + | 0.586676i | \(0.199564\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14632.1 | −0.893238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3564.67 | −0.216602 | −0.108301 | − | 0.994118i | \(-0.534541\pi\) | ||||
−0.108301 | + | 0.994118i | \(0.534541\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21066.2 | − | 21066.2i | 1.27415 | − | 1.27415i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11555.6 | + | 11555.6i | −0.695696 | + | 0.695696i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19594.4 | − | 19594.4i | −1.17425 | − | 1.17425i | −0.981185 | − | 0.193070i | \(-0.938156\pi\) |
−0.193070 | − | 0.981185i | \(-0.561844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13460.9i | 0.802993i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5163.07 | + | 5163.07i | 0.306591 | + | 0.306591i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3093.29 | 0.182849 | 0.0914245 | − | 0.995812i | \(-0.470858\pi\) | ||||
0.0914245 | + | 0.995812i | \(0.470858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 26602.2i | − | 1.56537i | −0.622420 | − | 0.782683i | \(-0.713851\pi\) | ||
0.622420 | − | 0.782683i | \(-0.286149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −169.747 | + | 202.931i | −0.00994333 | + | 0.0118871i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7835.60i | 0.456920i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6991.90 | −0.405888 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1493.28 | − | 1493.28i | −0.0862981 | − | 0.0862981i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 35652.8i | − | 2.05121i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11937.4 | − | 11937.4i | −0.683736 | − | 0.683736i | 0.277104 | − | 0.960840i | \(-0.410625\pi\) |
−0.960840 | + | 0.277104i | \(0.910625\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2757.42 | − | 2757.42i | 0.157234 | − | 0.157234i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2726.21 | − | 2726.21i | 0.154766 | − | 0.154766i | −0.625477 | − | 0.780243i | \(-0.715095\pi\) |
0.780243 | + | 0.625477i | \(0.215095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4052.89 | 0.229066 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10389.3 | 0.584608 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16602.4 | + | 16602.4i | −0.930123 | + | 0.930123i | −0.997713 | − | 0.0675904i | \(-0.978469\pi\) |
0.0675904 | + | 0.997713i | \(0.478469\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4648.57 | − | 4648.57i | 0.259289 | − | 0.259289i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 577.798 | + | 577.798i | 0.0320879 | + | 0.0320879i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 400.023i | 0.0221185i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10570.1 | + | 10570.1i | 0.581920 | + | 0.581920i | 0.935431 | − | 0.353511i | \(-0.115012\pi\) |
−0.353511 | + | 0.935431i | \(0.615012\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5715.47 | −0.313294 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9636.70i | 0.525958i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9672.83 | + | 8091.10i | 0.525659 | + | 0.439702i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 23293.3i | − | 1.26042i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8204.92 | −0.442076 | −0.221038 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221038 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4639.41 | + | 4639.41i | 0.248903 | + | 0.248903i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4938.65i | − | 0.263830i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15269.0 | + | 15269.0i | 0.812232 | + | 0.812232i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15750.5 | + | 15750.5i | −0.834304 | + | 0.834304i | −0.988102 | − | 0.153798i | \(-0.950849\pi\) |
0.153798 | + | 0.988102i | \(0.450849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3637.58 | + | 3637.58i | −0.191871 | + | 0.191871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14435.4 | 0.758217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 588.641 | 0.0307887 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13059.6 | + | 13059.6i | −0.680225 | + | 0.680225i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10899.1 | + | 10899.1i | −0.565326 | + | 0.565326i | −0.930816 | − | 0.365489i | \(-0.880902\pi\) |
0.365489 | + | 0.930816i | \(0.380902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5798.49 | + | 5798.49i | 0.299511 | + | 0.299511i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 27885.4i | − | 1.43440i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2578.78 | − | 2578.78i | −0.132102 | − | 0.132102i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −597.129 | −0.0304626 | −0.0152313 | − | 0.999884i | \(-0.504848\pi\) | ||||
−0.0152313 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21510.9i | 1.09287i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1705.56 | + | 19154.7i | 0.0862958 | + | 0.969166i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16993.0i | 0.856274i | 0.903714 | + | 0.428137i | \(0.140830\pi\) | ||||
−0.903714 | + | 0.428137i | \(0.859170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9608.66 | 0.482205 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4105.54 | − | 4105.54i | −0.205196 | − | 0.205196i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37983.6i | − | 1.89073i | −0.326017 | − | 0.945364i | \(-0.605707\pi\) | ||
0.326017 | − | 0.945364i | \(-0.394293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 133.566 | + | 133.566i | 0.00662170 | + | 0.00662170i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2340.76 | − | 2340.76i | 0.115578 | − | 0.115578i | −0.646953 | − | 0.762530i | \(-0.723957\pi\) |
0.762530 | + | 0.646953i | \(0.223957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24693.9 | + | 24693.9i | −1.21438 | + | 1.21438i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2141.41 | 0.104886 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21445.3 | 1.04618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13570.6 | + | 13570.6i | −0.659383 | + | 0.659383i | −0.955234 | − | 0.295851i | \(-0.904397\pi\) |
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1625.98 | − | 1625.98i | 0.0786907 | − | 0.0786907i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2698.94 | − | 2698.94i | −0.130099 | − | 0.130099i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2949.36i | 0.141607i | 0.997490 | + | 0.0708035i | \(0.0225563\pi\) | ||||
−0.997490 | + | 0.0708035i | \(0.977444\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8318.68 | − | 8318.68i | −0.397825 | − | 0.397825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21295.1 | −1.01438 | −0.507192 | − | 0.861833i | \(-0.669317\pi\) | ||||
−0.507192 | + | 0.861833i | \(0.669317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9502.56i | − | 0.450873i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5348.44 | − | 4473.85i | −0.252776 | − | 0.211441i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 468.308i | 0.0220464i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27668.1 | 1.29745 | 0.648724 | − | 0.761024i | \(-0.275303\pi\) | ||||
0.648724 | + | 0.761024i | \(0.275303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13496.6 | + | 13496.6i | 0.630439 | + | 0.630439i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19775.2i | 0.920133i | 0.887884 | + | 0.460067i | \(0.152174\pi\) | ||||
−0.887884 | + | 0.460067i | \(0.847826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5324.12 | + | 5324.12i | 0.246772 | + | 0.246772i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5141.95 | + | 5141.95i | −0.237409 | + | 0.237409i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6366.52 | − | 6366.52i | 0.292817 | − | 0.292817i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4492.32 | −0.205823 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21777.1 | 0.993936 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2552.01 | − | 2552.01i | 0.116032 | − | 0.116032i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3947.52 | + | 3947.52i | −0.178798 | + | 0.178798i | −0.790832 | − | 0.612034i | \(-0.790352\pi\) |
0.612034 | + | 0.790832i | \(0.290352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20072.2 | + | 20072.2i | 0.905690 | + | 0.905690i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3684.78i | 0.165633i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 396.285 | + | 396.285i | 0.0177459 | + | 0.0177459i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24567.4 | 1.09600 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 16897.8i | − | 0.751006i | −0.926821 | − | 0.375503i | \(-0.877470\pi\) | ||
0.926821 | − | 0.375503i | \(-0.122530\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6465.11 | + | 575.662i | −0.286257 | + | 0.0254887i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12758.9i | − | 0.562812i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49752.8 | 2.18647 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5424.31 | + | 5424.31i | 0.237493 | + | 0.237493i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 31876.5i | − | 1.39046i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21479.4 | − | 21479.4i | −0.933467 | − | 0.933467i | 0.0644539 | − | 0.997921i | \(-0.479469\pi\) |
−0.997921 | + | 0.0644539i | \(0.979469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29914.5 | − | 29914.5i | 1.29524 | − | 1.29524i | 0.363740 | − | 0.931501i | \(-0.381500\pi\) |
0.931501 | − | 0.363740i | \(-0.118500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9702.69 | + | 9702.69i | −0.418559 | + | 0.418559i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29805.3 | −1.28102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13729.9 | 0.587942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 63.5282 | − | 63.5282i | 0.00271045 | − | 0.00271045i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9116.42 | + | 9116.42i | −0.387534 | + | 0.387534i | −0.873807 | − | 0.486273i | \(-0.838356\pi\) |
0.486273 | + | 0.873807i | \(0.338356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26462.2 | + | 26462.2i | 1.12079 | + | 1.12079i | 0.991622 | + | 0.129171i | \(0.0412316\pi\) |
0.129171 | + | 0.991622i | \(0.458768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6136.27i | − | 0.258954i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9620.86 | + | 9620.86i | 0.404535 | + | 0.404535i | 0.879828 | − | 0.475293i | \(-0.157658\pi\) |
−0.475293 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14740.5 | −0.617562 | −0.308781 | − | 0.951133i | \(-0.599921\pi\) | ||||
−0.308781 | + | 0.951133i | \(0.599921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14672.3i | 0.612486i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1120.01 | − | 12578.5i | −0.0465859 | − | 0.523194i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 34257.7i | − | 1.41981i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44960.8 | −1.85672 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8464.19 | − | 8464.19i | −0.348291 | − | 0.348291i | 0.511182 | − | 0.859473i | \(-0.329208\pi\) |
−0.859473 | + | 0.511182i | \(0.829208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4022.69i | 0.164939i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17798.5 | + | 17798.5i | 0.727182 | + | 0.727182i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19055.2 | − | 19055.2i | 0.775762 | − | 0.775762i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15528.2 | + | 15528.2i | −0.629934 | + | 0.629934i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33530.7 | 1.35544 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6423.40 | 0.258744 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19959.8 | + | 19959.8i | −0.801185 | + | 0.801185i | −0.983281 | − | 0.182096i | \(-0.941712\pi\) |
0.182096 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3520.27 | + | 3520.27i | −0.140808 | + | 0.140808i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2185.79 | + | 2185.79i | 0.0871238 | + | 0.0871238i | 0.749326 | − | 0.662202i | \(-0.230378\pi\) |
−0.662202 | + | 0.749326i | \(0.730378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21827.6i | 0.866994i | 0.901155 | + | 0.433497i | \(0.142720\pi\) | ||||
−0.901155 | + | 0.433497i | \(0.857280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7056.14 | + | 7056.14i | 0.279295 | + | 0.279295i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12268.5 | 0.483921 | 0.241960 | − | 0.970286i | \(-0.422210\pi\) | ||||
0.241960 | + | 0.970286i | \(0.422210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52327.7i | 2.05687i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12194.5 | − | 17530.3i | 0.477678 | − | 0.686689i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35052.8i | 1.36834i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 91.2672 | 0.00355048 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1820.83 | + | 1820.83i | 0.0705908 | + | 0.0705908i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 15570.6i | − | 0.601578i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13528.2 | − | 13528.2i | −0.520883 | − | 0.520883i | 0.396955 | − | 0.917838i | \(-0.370067\pi\) |
−0.917838 | + | 0.396955i | \(0.870067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15344.4 | + | 15344.4i | −0.588800 | + | 0.588800i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4803.46 | + | 4803.46i | −0.183692 | + | 0.183692i | −0.792962 | − | 0.609270i | \(-0.791462\pi\) |
0.609270 | + | 0.792962i | \(0.291462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28197.9 | −1.07467 | −0.537335 | − | 0.843369i | \(-0.680569\pi\) | ||||
−0.537335 | + | 0.843369i | \(0.680569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28761.1 | 1.09242 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16408.3 | − | 16408.3i | 0.621126 | − | 0.621126i | −0.324694 | − | 0.945819i | \(-0.605261\pi\) |
0.945819 | + | 0.324694i | \(0.105261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8623.08 | + | 8623.08i | −0.325319 | + | 0.325319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17358.4 | + | 17358.4i | 0.652668 | + | 0.652668i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4634.14i | 0.173657i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7734.53 | + | 7734.53i | 0.288868 | + | 0.288868i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 184.926 | 0.00688351 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42048.0i | 1.55993i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2863.64 | − | 32160.8i | −0.105884 | − | 1.18916i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15217.1i | 0.560791i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26821.4 | 0.985164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10692.8 | − | 10692.8i | −0.391455 | − | 0.391455i | 0.483751 | − | 0.875206i | \(-0.339274\pi\) |
−0.875206 | + | 0.483751i | \(0.839274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13719.7i | 0.500608i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2425.45 | + | 2425.45i | 0.0882095 | + | 0.0882095i | 0.749835 | − | 0.661625i | \(-0.230133\pi\) |
−0.661625 | + | 0.749835i | \(0.730133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10317.6 | − | 10317.6i | 0.374001 | − | 0.374001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24337.9 | − | 24337.9i | 0.879328 | − | 0.879328i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13999.1 | 0.504133 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53382.8 | −1.91614 | −0.958071 | − | 0.286530i | \(-0.907498\pi\) | ||||
−0.958071 | + | 0.286530i | \(0.907498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22823.2 | + | 22823.2i | −0.816559 | + | 0.816559i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.9328 | − | 49.9328i | 0.00178067 | − | 0.00178067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2369.11 | + | 2369.11i | 0.0842117 | + | 0.0842117i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5210.13i | 0.184599i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1215.07 | − | 1215.07i | −0.0429119 | − | 0.0429119i | 0.685325 | − | 0.728237i | \(-0.259660\pi\) |
−0.728237 | + | 0.685325i | \(0.759660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9016.20 | −0.317394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 37778.5i | − | 1.32563i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −47325.2 | + | 4213.90i | −1.65530 | + | 0.147390i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11129.8i | 0.388040i | 0.980998 | + | 0.194020i | \(0.0621527\pi\) | ||||
−0.980998 | + | 0.194020i | \(0.937847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15648.4 | −0.543839 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2133.89 | + | 2133.89i | 0.0739242 | + | 0.0739242i | 0.743102 | − | 0.669178i | \(-0.233354\pi\) |
−0.669178 | + | 0.743102i | \(0.733354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8814.63i | − | 0.304394i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16894.7 | − | 16894.7i | −0.581571 | − | 0.581571i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13784.2 | − | 13784.2i | 0.472994 | − | 0.472994i | −0.429888 | − | 0.902882i | \(-0.641447\pi\) |
0.902882 | + | 0.429888i | \(0.141447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −553.009 | + | 553.009i | −0.0189162 | + | 0.0189162i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15181.9 | −0.517674 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4535.38 | −0.154161 | −0.0770805 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770805 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16809.0 | + | 16809.0i | −0.569555 | + | 0.569555i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24231.0 | − | 24231.0i | 0.818472 | − | 0.818472i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4834.43 | − | 4834.43i | −0.162786 | − | 0.162786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 57020.7i | − | 1.91402i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9634.63 | + | 9634.63i | 0.322400 | + | 0.322400i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33140.6 | 1.10553 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52772.2i | 1.75495i | 0.479620 | + | 0.877476i | \(0.340774\pi\) | ||||
−0.479620 | + | 0.877476i | \(0.659226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11694.5 | − | 9782.22i | −0.387701 | − | 0.324304i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 16848.4i | − | 0.556839i | −0.960460 | − | 0.278420i | \(-0.910189\pi\) | ||
0.960460 | − | 0.278420i | \(-0.0898106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10022.0 | 0.330206 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 68.2054 | + | 68.2054i | 0.00224033 | + | 0.00224033i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 24152.4i | − | 0.790893i | −0.918489 | − | 0.395447i | \(-0.870590\pi\) | ||
0.918489 | − | 0.395447i | \(-0.129410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61474.1 | − | 61474.1i | −2.00686 | − | 2.00686i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4269.18 | − | 4269.18i | 0.138944 | − | 0.138944i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22057.4 | − | 22057.4i | 0.715689 | − | 0.715689i | −0.252030 | − | 0.967719i | \(-0.581098\pi\) |
0.967719 | + | 0.252030i | \(0.0810982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6927.38 | −0.224086 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5136.11 | −0.165637 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9504.73 | − | 9504.73i | 0.305594 | − | 0.305594i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8193.28 | − | 8193.28i | 0.262632 | − | 0.262632i | −0.563491 | − | 0.826122i | \(-0.690542\pi\) |
0.826122 | + | 0.563491i | \(0.190542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15652.0 | + | 15652.0i | 0.500204 | + | 0.500204i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 63306.9i | − | 2.01705i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −347.648 | − | 347.648i | −0.0110432 | − | 0.0110432i | 0.701564 | − | 0.712607i | \(-0.252486\pi\) |
−0.712607 | + | 0.701564i | \(0.752486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20006.5 | −0.633611 |
(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 | 136.4.k.a.89.5 | yes | 14 | |
4.3 | odd | 2 | 272.4.o.g.225.3 | 14 | |||
17.8 | even | 8 | 2312.4.a.m.1.5 | 14 | |||
17.9 | even | 8 | 2312.4.a.m.1.10 | 14 | |||
17.13 | even | 4 | inner | 136.4.k.a.81.5 | ✓ | 14 | |
68.47 | odd | 4 | 272.4.o.g.81.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.k.a.81.5 | ✓ | 14 | 17.13 | even | 4 | inner | |
136.4.k.a.89.5 | yes | 14 | 1.1 | even | 1 | trivial | |
272.4.o.g.81.3 | 14 | 68.47 | odd | 4 | |||
272.4.o.g.225.3 | 14 | 4.3 | odd | 2 | |||
2312.4.a.m.1.5 | 14 | 17.8 | even | 8 | |||
2312.4.a.m.1.10 | 14 | 17.9 | even | 8 |