Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 112 x^{16} + 5026 x^{14} + 114847 x^{12} + 1397921 x^{10} + 8545747 x^{8} + 21033277 x^{6} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 13^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.14 | ||
Root | \(2.37150i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.k.337.5 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.17344i | 1.12198i | 0.827822 | + | 0.560991i | \(0.189580\pi\) | ||||
−0.827822 | + | 0.560991i | \(0.810420\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −2.07074 | −0.258842 | ||||||||
\(5\) | − 6.74147i | − 0.602975i | −0.953470 | − | 0.301488i | \(-0.902517\pi\) | ||||
0.953470 | − | 0.301488i | \(-0.0974832\pi\) | |||||||
\(6\) | 9.52033i | 0.647776i | ||||||||
\(7\) | − 14.1726i | − 0.765251i | −0.923904 | − | 0.382625i | \(-0.875020\pi\) | ||||
0.923904 | − | 0.382625i | \(-0.124980\pi\) | |||||||
\(8\) | 18.8162i | 0.831565i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 21.3937 | 0.676527 | ||||||||
\(11\) | 62.4956i | 1.71301i | 0.516136 | + | 0.856507i | \(0.327370\pi\) | ||||
−0.516136 | + | 0.856507i | \(0.672630\pi\) | |||||||
\(12\) | −6.21221 | −0.149442 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 44.9761 | 0.858597 | ||||||||
\(15\) | − 20.2244i | − 0.348128i | ||||||||
\(16\) | −76.2779 | −1.19184 | ||||||||
\(17\) | 58.6172 | 0.836280 | 0.418140 | − | 0.908383i | \(-0.362682\pi\) | ||||
0.418140 | + | 0.908383i | \(0.362682\pi\) | |||||||
\(18\) | 28.5610i | 0.373994i | ||||||||
\(19\) | − 64.1652i | − 0.774764i | −0.921919 | − | 0.387382i | \(-0.873380\pi\) | ||||
0.921919 | − | 0.387382i | \(-0.126620\pi\) | |||||||
\(20\) | 13.9598i | 0.156075i | ||||||||
\(21\) | − 42.5179i | − 0.441818i | ||||||||
\(22\) | −198.326 | −1.92197 | ||||||||
\(23\) | −10.9221 | −0.0990177 | −0.0495088 | − | 0.998774i | \(-0.515766\pi\) | ||||
−0.0495088 | + | 0.998774i | \(0.515766\pi\) | |||||||
\(24\) | 56.4485i | 0.480105i | ||||||||
\(25\) | 79.5526 | 0.636421 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 29.3478i | 0.198079i | ||||||||
\(29\) | 216.316 | 1.38514 | 0.692568 | − | 0.721353i | \(-0.256479\pi\) | ||||
0.692568 | + | 0.721353i | \(0.256479\pi\) | |||||||
\(30\) | 64.1810 | 0.390593 | ||||||||
\(31\) | 38.6271i | 0.223795i | 0.993720 | + | 0.111897i | \(0.0356928\pi\) | ||||
−0.993720 | + | 0.111897i | \(0.964307\pi\) | |||||||
\(32\) | − 91.5342i | − 0.505660i | ||||||||
\(33\) | 187.487i | 0.989009i | ||||||||
\(34\) | 186.018i | 0.938290i | ||||||||
\(35\) | −95.5445 | −0.461427 | ||||||||
\(36\) | −18.6366 | −0.0862807 | ||||||||
\(37\) | 423.770i | 1.88290i | 0.337147 | + | 0.941452i | \(0.390538\pi\) | ||||
−0.337147 | + | 0.941452i | \(0.609462\pi\) | |||||||
\(38\) | 203.625 | 0.869270 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 126.849 | 0.501414 | ||||||||
\(41\) | 366.126i | 1.39461i | 0.716772 | + | 0.697307i | \(0.245619\pi\) | ||||
−0.716772 | + | 0.697307i | \(0.754381\pi\) | |||||||
\(42\) | 134.928 | 0.495711 | ||||||||
\(43\) | 128.297 | 0.455001 | 0.227501 | − | 0.973778i | \(-0.426945\pi\) | ||||
0.227501 | + | 0.973778i | \(0.426945\pi\) | |||||||
\(44\) | − 129.412i | − 0.443400i | ||||||||
\(45\) | − 60.6732i | − 0.200992i | ||||||||
\(46\) | − 34.6605i | − 0.111096i | ||||||||
\(47\) | − 93.1169i | − 0.288989i | −0.989506 | − | 0.144495i | \(-0.953844\pi\) | ||||
0.989506 | − | 0.144495i | \(-0.0461556\pi\) | |||||||
\(48\) | −228.834 | −0.688111 | ||||||||
\(49\) | 142.136 | 0.414391 | ||||||||
\(50\) | 252.455i | 0.714052i | ||||||||
\(51\) | 175.852 | 0.482826 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 131.909 | 0.341869 | 0.170934 | − | 0.985282i | \(-0.445321\pi\) | ||||
0.170934 | + | 0.985282i | \(0.445321\pi\) | |||||||
\(54\) | 85.6829i | 0.215925i | ||||||||
\(55\) | 421.313 | 1.03290 | ||||||||
\(56\) | 266.675 | 0.636356 | ||||||||
\(57\) | − 192.496i | − 0.447310i | ||||||||
\(58\) | 686.467i | 1.55410i | ||||||||
\(59\) | 386.729i | 0.853353i | 0.904404 | + | 0.426677i | \(0.140316\pi\) | ||||
−0.904404 | + | 0.426677i | \(0.859684\pi\) | |||||||
\(60\) | 41.8794i | 0.0901102i | ||||||||
\(61\) | −621.077 | −1.30362 | −0.651810 | − | 0.758382i | \(-0.725990\pi\) | ||||
−0.651810 | + | 0.758382i | \(0.725990\pi\) | |||||||
\(62\) | −122.581 | −0.251094 | ||||||||
\(63\) | − 127.554i | − 0.255084i | ||||||||
\(64\) | −319.745 | −0.624502 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −594.979 | −1.10965 | ||||||||
\(67\) | − 865.273i | − 1.57776i | −0.614547 | − | 0.788880i | \(-0.710661\pi\) | ||||
0.614547 | − | 0.788880i | \(-0.289339\pi\) | |||||||
\(68\) | −121.381 | −0.216464 | ||||||||
\(69\) | −32.7662 | −0.0571679 | ||||||||
\(70\) | − 303.205i | − 0.517713i | ||||||||
\(71\) | 607.506i | 1.01546i | 0.861516 | + | 0.507730i | \(0.169515\pi\) | ||||
−0.861516 | + | 0.507730i | \(0.830485\pi\) | |||||||
\(72\) | 169.346i | 0.277188i | ||||||||
\(73\) | 980.958i | 1.57277i | 0.617735 | + | 0.786387i | \(0.288051\pi\) | ||||
−0.617735 | + | 0.786387i | \(0.711949\pi\) | |||||||
\(74\) | −1344.81 | −2.11258 | ||||||||
\(75\) | 238.658 | 0.367438 | ||||||||
\(76\) | 132.869i | 0.200541i | ||||||||
\(77\) | 885.728 | 1.31088 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1331.91 | 1.89685 | 0.948425 | − | 0.317003i | \(-0.102676\pi\) | ||||
0.948425 | + | 0.317003i | \(0.102676\pi\) | |||||||
\(80\) | 514.226i | 0.718652i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1161.88 | −1.56473 | ||||||||
\(83\) | − 907.633i | − 1.20031i | −0.799884 | − | 0.600155i | \(-0.795106\pi\) | ||||
0.799884 | − | 0.600155i | \(-0.204894\pi\) | |||||||
\(84\) | 88.0434i | 0.114361i | ||||||||
\(85\) | − 395.166i | − 0.504256i | ||||||||
\(86\) | 407.142i | 0.510503i | ||||||||
\(87\) | 648.949 | 0.799708 | ||||||||
\(88\) | −1175.93 | −1.42448 | ||||||||
\(89\) | − 1033.67i | − 1.23110i | −0.788096 | − | 0.615552i | \(-0.788933\pi\) | ||||
0.788096 | − | 0.615552i | \(-0.211067\pi\) | |||||||
\(90\) | 192.543 | 0.225509 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22.6167 | 0.0256299 | ||||||||
\(93\) | 115.881i | 0.129208i | ||||||||
\(94\) | 295.501 | 0.324240 | ||||||||
\(95\) | −432.568 | −0.467163 | ||||||||
\(96\) | − 274.603i | − 0.291943i | ||||||||
\(97\) | − 1046.17i | − 1.09508i | −0.836781 | − | 0.547538i | \(-0.815565\pi\) | ||||
0.836781 | − | 0.547538i | \(-0.184435\pi\) | |||||||
\(98\) | 451.061i | 0.464939i | ||||||||
\(99\) | 562.461i | 0.571004i | ||||||||
\(100\) | −164.732 | −0.164732 | ||||||||
\(101\) | −1416.64 | −1.39566 | −0.697828 | − | 0.716265i | \(-0.745850\pi\) | ||||
−0.697828 | + | 0.716265i | \(0.745850\pi\) | |||||||
\(102\) | 558.055i | 0.541722i | ||||||||
\(103\) | −387.629 | −0.370818 | −0.185409 | − | 0.982661i | \(-0.559361\pi\) | ||||
−0.185409 | + | 0.982661i | \(0.559361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −286.633 | −0.266405 | ||||||||
\(106\) | 418.605i | 0.383570i | ||||||||
\(107\) | 86.4526 | 0.0781092 | 0.0390546 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390546 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(108\) | −55.9099 | −0.0498142 | ||||||||
\(109\) | 940.072i | 0.826079i | 0.910713 | + | 0.413039i | \(0.135533\pi\) | ||||
−0.910713 | + | 0.413039i | \(0.864467\pi\) | |||||||
\(110\) | 1337.01i | 1.15890i | ||||||||
\(111\) | 1271.31i | 1.08709i | ||||||||
\(112\) | 1081.06i | 0.912059i | ||||||||
\(113\) | 960.499 | 0.799612 | 0.399806 | − | 0.916600i | \(-0.369078\pi\) | ||||
0.399806 | + | 0.916600i | \(0.369078\pi\) | |||||||
\(114\) | 610.874 | 0.501873 | ||||||||
\(115\) | 73.6307i | 0.0597052i | ||||||||
\(116\) | −447.934 | −0.358531 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1227.26 | −0.957447 | ||||||||
\(119\) | − 830.760i | − 0.639964i | ||||||||
\(120\) | 380.546 | 0.289491 | ||||||||
\(121\) | −2574.71 | −1.93441 | ||||||||
\(122\) | − 1970.95i | − 1.46264i | ||||||||
\(123\) | 1098.38i | 0.805181i | ||||||||
\(124\) | − 79.9866i | − 0.0579275i | ||||||||
\(125\) | − 1378.99i | − 0.986721i | ||||||||
\(126\) | 404.785 | 0.286199 | ||||||||
\(127\) | −2022.18 | −1.41291 | −0.706456 | − | 0.707757i | \(-0.749707\pi\) | ||||
−0.706456 | + | 0.707757i | \(0.749707\pi\) | |||||||
\(128\) | − 1746.97i | − 1.20634i | ||||||||
\(129\) | 384.890 | 0.262695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1857.90 | 1.23912 | 0.619561 | − | 0.784948i | \(-0.287310\pi\) | ||||
0.619561 | + | 0.784948i | \(0.287310\pi\) | |||||||
\(132\) | − 388.236i | − 0.255997i | ||||||||
\(133\) | −909.390 | −0.592888 | ||||||||
\(134\) | 2745.90 | 1.77022 | ||||||||
\(135\) | − 182.020i | − 0.116043i | ||||||||
\(136\) | 1102.95i | 0.695421i | ||||||||
\(137\) | 1894.12i | 1.18121i | 0.806961 | + | 0.590604i | \(0.201110\pi\) | ||||
−0.806961 | + | 0.590604i | \(0.798890\pi\) | |||||||
\(138\) | − 103.982i | − 0.0641413i | ||||||||
\(139\) | −1226.08 | −0.748165 | −0.374082 | − | 0.927395i | \(-0.622042\pi\) | ||||
−0.374082 | + | 0.927395i | \(0.622042\pi\) | |||||||
\(140\) | 197.847 | 0.119437 | ||||||||
\(141\) | − 279.351i | − 0.166848i | ||||||||
\(142\) | −1927.89 | −1.13933 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −686.501 | −0.397281 | ||||||||
\(145\) | − 1458.29i | − 0.835203i | ||||||||
\(146\) | −3113.01 | −1.76462 | ||||||||
\(147\) | 426.409 | 0.239249 | ||||||||
\(148\) | − 877.517i | − 0.487375i | ||||||||
\(149\) | − 3195.65i | − 1.75703i | −0.477711 | − | 0.878517i | \(-0.658533\pi\) | ||||
0.477711 | − | 0.878517i | \(-0.341467\pi\) | |||||||
\(150\) | 757.366i | 0.412258i | ||||||||
\(151\) | 508.232i | 0.273903i | 0.990578 | + | 0.136951i | \(0.0437304\pi\) | ||||
−0.990578 | + | 0.136951i | \(0.956270\pi\) | |||||||
\(152\) | 1207.34 | 0.644267 | ||||||||
\(153\) | 527.555 | 0.278760 | ||||||||
\(154\) | 2810.81i | 1.47079i | ||||||||
\(155\) | 260.404 | 0.134943 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1243.08 | −0.631900 | −0.315950 | − | 0.948776i | \(-0.602323\pi\) | ||||
−0.315950 | + | 0.948776i | \(0.602323\pi\) | |||||||
\(158\) | 4226.73i | 2.12823i | ||||||||
\(159\) | 395.726 | 0.197378 | ||||||||
\(160\) | −617.075 | −0.304901 | ||||||||
\(161\) | 154.794i | 0.0757734i | ||||||||
\(162\) | 257.049i | 0.124665i | ||||||||
\(163\) | − 33.9996i | − 0.0163378i | −0.999967 | − | 0.00816888i | \(-0.997400\pi\) | ||||
0.999967 | − | 0.00816888i | \(-0.00260026\pi\) | |||||||
\(164\) | − 758.149i | − 0.360985i | ||||||||
\(165\) | 1263.94 | 0.596348 | ||||||||
\(166\) | 2880.32 | 1.34673 | ||||||||
\(167\) | − 2210.67i | − 1.02435i | −0.858880 | − | 0.512176i | \(-0.828839\pi\) | ||||
0.858880 | − | 0.512176i | \(-0.171161\pi\) | |||||||
\(168\) | 800.025 | 0.367400 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1254.04 | 0.565766 | ||||||||
\(171\) | − 577.487i | − 0.258255i | ||||||||
\(172\) | −265.668 | −0.117773 | ||||||||
\(173\) | 661.307 | 0.290626 | 0.145313 | − | 0.989386i | \(-0.453581\pi\) | ||||
0.145313 | + | 0.989386i | \(0.453581\pi\) | |||||||
\(174\) | 2059.40i | 0.897258i | ||||||||
\(175\) | − 1127.47i | − 0.487021i | ||||||||
\(176\) | − 4767.04i | − 2.04164i | ||||||||
\(177\) | 1160.19i | 0.492684i | ||||||||
\(178\) | 3280.28 | 1.38128 | ||||||||
\(179\) | 2325.05 | 0.970850 | 0.485425 | − | 0.874278i | \(-0.338665\pi\) | ||||
0.485425 | + | 0.874278i | \(0.338665\pi\) | |||||||
\(180\) | 125.638i | 0.0520251i | ||||||||
\(181\) | −2122.20 | −0.871503 | −0.435752 | − | 0.900067i | \(-0.643517\pi\) | ||||
−0.435752 | + | 0.900067i | \(0.643517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1863.23 | −0.752645 | ||||||||
\(184\) | − 205.511i | − 0.0823397i | ||||||||
\(185\) | 2856.84 | 1.13534 | ||||||||
\(186\) | −367.743 | −0.144969 | ||||||||
\(187\) | 3663.32i | 1.43256i | ||||||||
\(188\) | 192.820i | 0.0748025i | ||||||||
\(189\) | − 382.661i | − 0.147273i | ||||||||
\(190\) | − 1372.73i | − 0.524149i | ||||||||
\(191\) | −2484.37 | −0.941166 | −0.470583 | − | 0.882356i | \(-0.655956\pi\) | ||||
−0.470583 | + | 0.882356i | \(0.655956\pi\) | |||||||
\(192\) | −959.235 | −0.360556 | ||||||||
\(193\) | − 266.771i | − 0.0994955i | −0.998762 | − | 0.0497478i | \(-0.984158\pi\) | ||||
0.998762 | − | 0.0497478i | \(-0.0158417\pi\) | |||||||
\(194\) | 3319.95 | 1.22865 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −294.327 | −0.107262 | ||||||||
\(197\) | 1231.03i | 0.445216i | 0.974908 | + | 0.222608i | \(0.0714569\pi\) | ||||
−0.974908 | + | 0.222608i | \(0.928543\pi\) | |||||||
\(198\) | −1784.94 | −0.640656 | ||||||||
\(199\) | 3246.14 | 1.15635 | 0.578173 | − | 0.815914i | \(-0.303766\pi\) | ||||
0.578173 | + | 0.815914i | \(0.303766\pi\) | |||||||
\(200\) | 1496.88i | 0.529225i | ||||||||
\(201\) | − 2595.82i | − 0.910921i | ||||||||
\(202\) | − 4495.63i | − 1.56590i | ||||||||
\(203\) | − 3065.77i | − 1.05998i | ||||||||
\(204\) | −364.142 | −0.124976 | ||||||||
\(205\) | 2468.23 | 0.840919 | ||||||||
\(206\) | − 1230.12i | − 0.416051i | ||||||||
\(207\) | −98.2985 | −0.0330059 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4010.05 | 1.32718 | ||||||||
\(210\) | − 909.614i | − 0.298902i | ||||||||
\(211\) | 330.708 | 0.107900 | 0.0539500 | − | 0.998544i | \(-0.482819\pi\) | ||||
0.0539500 | + | 0.998544i | \(0.482819\pi\) | |||||||
\(212\) | −273.148 | −0.0884900 | ||||||||
\(213\) | 1822.52i | 0.586277i | ||||||||
\(214\) | 274.352i | 0.0876371i | ||||||||
\(215\) | − 864.908i | − 0.274355i | ||||||||
\(216\) | 508.037i | 0.160035i | ||||||||
\(217\) | 547.449 | 0.171259 | ||||||||
\(218\) | −2983.26 | −0.926845 | ||||||||
\(219\) | 2942.87i | 0.908041i | ||||||||
\(220\) | −872.427 | −0.267359 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4034.43 | −1.21970 | ||||||||
\(223\) | − 5785.86i | − 1.73744i | −0.495300 | − | 0.868722i | \(-0.664942\pi\) | ||||
0.495300 | − | 0.868722i | \(-0.335058\pi\) | |||||||
\(224\) | −1297.28 | −0.386957 | ||||||||
\(225\) | 715.973 | 0.212140 | ||||||||
\(226\) | 3048.09i | 0.897149i | ||||||||
\(227\) | − 2945.35i | − 0.861189i | −0.902545 | − | 0.430595i | \(-0.858304\pi\) | ||||
0.902545 | − | 0.430595i | \(-0.141696\pi\) | |||||||
\(228\) | 398.608i | 0.115783i | ||||||||
\(229\) | − 3541.26i | − 1.02189i | −0.859613 | − | 0.510945i | \(-0.829296\pi\) | ||||
0.859613 | − | 0.510945i | \(-0.170704\pi\) | |||||||
\(230\) | −233.663 | −0.0669882 | ||||||||
\(231\) | 2657.18 | 0.756840 | ||||||||
\(232\) | 4070.25i | 1.15183i | ||||||||
\(233\) | −2340.76 | −0.658148 | −0.329074 | − | 0.944304i | \(-0.606737\pi\) | ||||
−0.329074 | + | 0.944304i | \(0.606737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −627.745 | −0.174253 | ||||||||
\(236\) | − 800.814i | − 0.220884i | ||||||||
\(237\) | 3995.72 | 1.09515 | ||||||||
\(238\) | 2636.37 | 0.718027 | ||||||||
\(239\) | 1515.70i | 0.410218i | 0.978739 | + | 0.205109i | \(0.0657549\pi\) | ||||
−0.978739 | + | 0.205109i | \(0.934245\pi\) | |||||||
\(240\) | 1542.68i | 0.414914i | ||||||||
\(241\) | 2392.47i | 0.639472i | 0.947507 | + | 0.319736i | \(0.103594\pi\) | ||||
−0.947507 | + | 0.319736i | \(0.896406\pi\) | |||||||
\(242\) | − 8170.68i | − 2.17038i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1286.09 | 0.337432 | ||||||||
\(245\) | − 958.207i | − 0.249868i | ||||||||
\(246\) | −3485.64 | −0.903398 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −726.815 | −0.186100 | ||||||||
\(249\) | − 2722.90i | − 0.692999i | ||||||||
\(250\) | 4376.13 | 1.10708 | ||||||||
\(251\) | 2198.78 | 0.552931 | 0.276465 | − | 0.961024i | \(-0.410837\pi\) | ||||
0.276465 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(252\) | 264.130i | 0.0660263i | ||||||||
\(253\) | − 682.581i | − 0.169619i | ||||||||
\(254\) | − 6417.29i | − 1.58526i | ||||||||
\(255\) | − 1185.50i | − 0.291132i | ||||||||
\(256\) | 2985.94 | 0.728988 | ||||||||
\(257\) | 6194.26 | 1.50345 | 0.751727 | − | 0.659475i | \(-0.229221\pi\) | ||||
0.751727 | + | 0.659475i | \(0.229221\pi\) | |||||||
\(258\) | 1221.43i | 0.294739i | ||||||||
\(259\) | 6005.95 | 1.44089 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1946.85 | 0.461712 | ||||||||
\(262\) | 5895.92i | 1.39027i | ||||||||
\(263\) | −4181.74 | −0.980445 | −0.490222 | − | 0.871597i | \(-0.663084\pi\) | ||||
−0.490222 | + | 0.871597i | \(0.663084\pi\) | |||||||
\(264\) | −3527.79 | −0.822425 | ||||||||
\(265\) | − 889.258i | − 0.206139i | ||||||||
\(266\) | − 2885.90i | − 0.665210i | ||||||||
\(267\) | − 3101.00i | − 0.710778i | ||||||||
\(268\) | 1791.75i | 0.408391i | ||||||||
\(269\) | 2767.69 | 0.627320 | 0.313660 | − | 0.949535i | \(-0.398445\pi\) | ||||
0.313660 | + | 0.949535i | \(0.398445\pi\) | |||||||
\(270\) | 577.629 | 0.130198 | ||||||||
\(271\) | − 7191.36i | − 1.61197i | −0.591935 | − | 0.805986i | \(-0.701636\pi\) | ||||
0.591935 | − | 0.805986i | \(-0.298364\pi\) | |||||||
\(272\) | −4471.20 | −0.996714 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6010.88 | −1.32529 | ||||||||
\(275\) | 4971.69i | 1.09020i | ||||||||
\(276\) | 67.8501 | 0.0147974 | ||||||||
\(277\) | −1317.27 | −0.285729 | −0.142864 | − | 0.989742i | \(-0.545631\pi\) | ||||
−0.142864 | + | 0.989742i | \(0.545631\pi\) | |||||||
\(278\) | − 3890.90i | − 0.839427i | ||||||||
\(279\) | 347.644i | 0.0745983i | ||||||||
\(280\) | − 1797.78i | − 0.383707i | ||||||||
\(281\) | − 3948.92i | − 0.838338i | −0.907908 | − | 0.419169i | \(-0.862321\pi\) | ||||
0.907908 | − | 0.419169i | \(-0.137679\pi\) | |||||||
\(282\) | 886.503 | 0.187200 | ||||||||
\(283\) | 4981.52 | 1.04636 | 0.523181 | − | 0.852221i | \(-0.324745\pi\) | ||||
0.523181 | + | 0.852221i | \(0.324745\pi\) | |||||||
\(284\) | − 1257.99i | − 0.262844i | ||||||||
\(285\) | −1297.70 | −0.269717 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5188.97 | 1.06723 | ||||||||
\(288\) | − 823.808i | − 0.168553i | ||||||||
\(289\) | −1477.03 | −0.300636 | ||||||||
\(290\) | 4627.80 | 0.937082 | ||||||||
\(291\) | − 3138.50i | − 0.632242i | ||||||||
\(292\) | − 2031.31i | − 0.407100i | ||||||||
\(293\) | − 3203.02i | − 0.638644i | −0.947646 | − | 0.319322i | \(-0.896545\pi\) | ||||
0.947646 | − | 0.319322i | \(-0.103455\pi\) | |||||||
\(294\) | 1353.18i | 0.268433i | ||||||||
\(295\) | 2607.12 | 0.514551 | ||||||||
\(296\) | −7973.74 | −1.56576 | ||||||||
\(297\) | 1687.38i | 0.329670i | ||||||||
\(298\) | 10141.2 | 1.97136 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −494.197 | −0.0951083 | ||||||||
\(301\) | − 1818.30i | − 0.348190i | ||||||||
\(302\) | −1612.84 | −0.307314 | ||||||||
\(303\) | −4249.93 | −0.805782 | ||||||||
\(304\) | 4894.39i | 0.923396i | ||||||||
\(305\) | 4186.97i | 0.786051i | ||||||||
\(306\) | 1674.16i | 0.312763i | ||||||||
\(307\) | 4795.67i | 0.891542i | 0.895147 | + | 0.445771i | \(0.147070\pi\) | ||||
−0.895147 | + | 0.445771i | \(0.852930\pi\) | |||||||
\(308\) | −1834.11 | −0.339312 | ||||||||
\(309\) | −1162.89 | −0.214092 | ||||||||
\(310\) | 826.376i | 0.151403i | ||||||||
\(311\) | −630.213 | −0.114907 | −0.0574535 | − | 0.998348i | \(-0.518298\pi\) | ||||
−0.0574535 | + | 0.998348i | \(0.518298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9314.73 | −1.68211 | −0.841054 | − | 0.540952i | \(-0.818064\pi\) | ||||
−0.841054 | + | 0.540952i | \(0.818064\pi\) | |||||||
\(314\) | − 3944.83i | − 0.708980i | ||||||||
\(315\) | −859.900 | −0.153809 | ||||||||
\(316\) | −2758.02 | −0.490984 | ||||||||
\(317\) | − 576.333i | − 0.102114i | −0.998696 | − | 0.0510569i | \(-0.983741\pi\) | ||||
0.998696 | − | 0.0510569i | \(-0.0162590\pi\) | |||||||
\(318\) | 1255.81i | 0.221455i | ||||||||
\(319\) | 13518.8i | 2.37275i | ||||||||
\(320\) | 2155.55i | 0.376559i | ||||||||
\(321\) | 259.358 | 0.0450964 | ||||||||
\(322\) | −491.231 | −0.0850163 | ||||||||
\(323\) | − 3761.18i | − 0.647919i | ||||||||
\(324\) | −167.730 | −0.0287602 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 107.896 | 0.0183307 | ||||||||
\(327\) | 2820.22i | 0.476937i | ||||||||
\(328\) | −6889.08 | −1.15971 | ||||||||
\(329\) | −1319.71 | −0.221149 | ||||||||
\(330\) | 4011.03i | 0.669091i | ||||||||
\(331\) | − 1575.95i | − 0.261699i | −0.991402 | − | 0.130849i | \(-0.958230\pi\) | ||||
0.991402 | − | 0.130849i | \(-0.0417704\pi\) | |||||||
\(332\) | 1879.47i | 0.310691i | ||||||||
\(333\) | 3813.93i | 0.627635i | ||||||||
\(334\) | 7015.44 | 1.14930 | ||||||||
\(335\) | −5833.22 | −0.951351 | ||||||||
\(336\) | 3243.18i | 0.526577i | ||||||||
\(337\) | −9289.32 | −1.50155 | −0.750774 | − | 0.660559i | \(-0.770319\pi\) | ||||
−0.750774 | + | 0.660559i | \(0.770319\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2881.50 | 0.461656 | ||||||||
\(340\) | 818.284i | 0.130523i | ||||||||
\(341\) | −2414.03 | −0.383363 | ||||||||
\(342\) | 1832.62 | 0.289757 | ||||||||
\(343\) | − 6875.66i | − 1.08236i | ||||||||
\(344\) | 2414.05i | 0.378363i | ||||||||
\(345\) | 220.892i | 0.0344708i | ||||||||
\(346\) | 2098.62i | 0.326077i | ||||||||
\(347\) | −7701.82 | −1.19151 | −0.595757 | − | 0.803164i | \(-0.703148\pi\) | ||||
−0.595757 | + | 0.803164i | \(0.703148\pi\) | |||||||
\(348\) | −1343.80 | −0.206998 | ||||||||
\(349\) | − 4972.89i | − 0.762730i | −0.924425 | − | 0.381365i | \(-0.875454\pi\) | ||||
0.924425 | − | 0.381365i | \(-0.124546\pi\) | |||||||
\(350\) | 3577.96 | 0.546429 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5720.49 | 0.866202 | ||||||||
\(353\) | − 1575.34i | − 0.237526i | −0.992923 | − | 0.118763i | \(-0.962107\pi\) | ||||
0.992923 | − | 0.118763i | \(-0.0378929\pi\) | |||||||
\(354\) | −3681.79 | −0.552782 | ||||||||
\(355\) | 4095.49 | 0.612298 | ||||||||
\(356\) | 2140.45i | 0.318661i | ||||||||
\(357\) | − 2492.28i | − 0.369483i | ||||||||
\(358\) | 7378.41i | 1.08928i | ||||||||
\(359\) | 7567.42i | 1.11252i | 0.831010 | + | 0.556258i | \(0.187763\pi\) | ||||
−0.831010 | + | 0.556258i | \(0.812237\pi\) | |||||||
\(360\) | 1141.64 | 0.167138 | ||||||||
\(361\) | 2741.83 | 0.399741 | ||||||||
\(362\) | − 6734.69i | − 0.977810i | ||||||||
\(363\) | −7724.12 | −1.11683 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6613.10 | 0.948344 | ||||||||
\(366\) | − 5912.86i | − 0.844454i | ||||||||
\(367\) | 4368.25 | 0.621310 | 0.310655 | − | 0.950523i | \(-0.399452\pi\) | ||||
0.310655 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(368\) | 833.112 | 0.118014 | ||||||||
\(369\) | 3295.13i | 0.464872i | ||||||||
\(370\) | 9066.01i | 1.27384i | ||||||||
\(371\) | − 1869.49i | − 0.261615i | ||||||||
\(372\) | − 239.960i | − 0.0334445i | ||||||||
\(373\) | −801.944 | −0.111322 | −0.0556610 | − | 0.998450i | \(-0.517727\pi\) | ||||
−0.0556610 | + | 0.998450i | \(0.517727\pi\) | |||||||
\(374\) | −11625.3 | −1.60730 | ||||||||
\(375\) | − 4136.96i | − 0.569684i | ||||||||
\(376\) | 1752.10 | 0.240313 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1214.35 | 0.165237 | ||||||||
\(379\) | − 68.0819i | − 0.00922727i | −0.999989 | − | 0.00461363i | \(-0.998531\pi\) | ||||
0.999989 | − | 0.00461363i | \(-0.00146857\pi\) | |||||||
\(380\) | 895.734 | 0.120922 | ||||||||
\(381\) | −6066.55 | −0.815745 | ||||||||
\(382\) | − 7884.01i | − 1.05597i | ||||||||
\(383\) | − 1549.01i | − 0.206659i | −0.994647 | − | 0.103330i | \(-0.967050\pi\) | ||||
0.994647 | − | 0.103330i | \(-0.0329497\pi\) | |||||||
\(384\) | − 5240.90i | − 0.696480i | ||||||||
\(385\) | − 5971.11i | − 0.790431i | ||||||||
\(386\) | 846.584 | 0.111632 | ||||||||
\(387\) | 1154.67 | 0.151667 | ||||||||
\(388\) | 2166.34i | 0.283451i | ||||||||
\(389\) | −7300.51 | −0.951544 | −0.475772 | − | 0.879569i | \(-0.657831\pi\) | ||||
−0.475772 | + | 0.879569i | \(0.657831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −640.220 | −0.0828065 | ||||||||
\(392\) | 2674.46i | 0.344594i | ||||||||
\(393\) | 5573.69 | 0.715408 | ||||||||
\(394\) | −3906.61 | −0.499524 | ||||||||
\(395\) | − 8979.00i | − 1.14375i | ||||||||
\(396\) | − 1164.71i | − 0.147800i | ||||||||
\(397\) | 6096.27i | 0.770688i | 0.922773 | + | 0.385344i | \(0.125917\pi\) | ||||
−0.922773 | + | 0.385344i | \(0.874083\pi\) | |||||||
\(398\) | 10301.4i | 1.29740i | ||||||||
\(399\) | −2728.17 | −0.342304 | ||||||||
\(400\) | −6068.11 | −0.758513 | ||||||||
\(401\) | 7592.37i | 0.945498i | 0.881197 | + | 0.472749i | \(0.156738\pi\) | ||||
−0.881197 | + | 0.472749i | \(0.843262\pi\) | |||||||
\(402\) | 8237.69 | 1.02204 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2933.49 | 0.361254 | ||||||||
\(405\) | − 546.059i | − 0.0669973i | ||||||||
\(406\) | 9729.05 | 1.18927 | ||||||||
\(407\) | −26483.8 | −3.22544 | ||||||||
\(408\) | 3308.85i | 0.401502i | ||||||||
\(409\) | 7233.86i | 0.874551i | 0.899328 | + | 0.437275i | \(0.144057\pi\) | ||||
−0.899328 | + | 0.437275i | \(0.855943\pi\) | |||||||
\(410\) | 7832.77i | 0.943495i | ||||||||
\(411\) | 5682.36i | 0.681971i | ||||||||
\(412\) | 802.678 | 0.0959832 | ||||||||
\(413\) | 5480.97 | 0.653029 | ||||||||
\(414\) | − 311.945i | − 0.0370320i | ||||||||
\(415\) | −6118.78 | −0.723757 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3678.25 | −0.431953 | ||||||||
\(418\) | 12725.6i | 1.48907i | ||||||||
\(419\) | −5312.55 | −0.619416 | −0.309708 | − | 0.950832i | \(-0.600231\pi\) | ||||
−0.309708 | + | 0.950832i | \(0.600231\pi\) | |||||||
\(420\) | 593.542 | 0.0689569 | ||||||||
\(421\) | − 15028.1i | − 1.73973i | −0.493290 | − | 0.869865i | \(-0.664206\pi\) | ||||
0.493290 | − | 0.869865i | \(-0.335794\pi\) | |||||||
\(422\) | 1049.48i | 0.121062i | ||||||||
\(423\) | − 838.052i | − 0.0963297i | ||||||||
\(424\) | 2482.02i | 0.284286i | ||||||||
\(425\) | 4663.15 | 0.532226 | ||||||||
\(426\) | −5783.66 | −0.657791 | ||||||||
\(427\) | 8802.31i | 0.997596i | ||||||||
\(428\) | −179.020 | −0.0202179 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2744.73 | 0.307821 | ||||||||
\(431\) | 7154.66i | 0.799600i | 0.916602 | + | 0.399800i | \(0.130920\pi\) | ||||
−0.916602 | + | 0.399800i | \(0.869080\pi\) | |||||||
\(432\) | −2059.50 | −0.229370 | ||||||||
\(433\) | 9542.58 | 1.05909 | 0.529546 | − | 0.848281i | \(-0.322362\pi\) | ||||
0.529546 | + | 0.848281i | \(0.322362\pi\) | |||||||
\(434\) | 1737.30i | 0.192150i | ||||||||
\(435\) | − 4374.87i | − 0.482204i | ||||||||
\(436\) | − 1946.64i | − 0.213824i | ||||||||
\(437\) | 700.816i | 0.0767153i | ||||||||
\(438\) | −9339.04 | −1.01881 | ||||||||
\(439\) | −7070.70 | −0.768715 | −0.384358 | − | 0.923184i | \(-0.625577\pi\) | ||||
−0.384358 | + | 0.923184i | \(0.625577\pi\) | |||||||
\(440\) | 7927.49i | 0.858928i | ||||||||
\(441\) | 1279.23 | 0.138130 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2092.58 | 0.224428 | 0.112214 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112214 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(444\) | − 2632.55i | − 0.281386i | ||||||||
\(445\) | −6968.42 | −0.742326 | ||||||||
\(446\) | 18361.1 | 1.94938 | ||||||||
\(447\) | − 9586.96i | − 1.01442i | ||||||||
\(448\) | 4531.63i | 0.477901i | ||||||||
\(449\) | 5842.05i | 0.614038i | 0.951703 | + | 0.307019i | \(0.0993316\pi\) | ||||
−0.951703 | + | 0.307019i | \(0.900668\pi\) | |||||||
\(450\) | 2272.10i | 0.238017i | ||||||||
\(451\) | −22881.3 | −2.38899 | ||||||||
\(452\) | −1988.94 | −0.206973 | ||||||||
\(453\) | 1524.69i | 0.158138i | ||||||||
\(454\) | 9346.91 | 0.966238 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3622.03 | 0.371967 | ||||||||
\(457\) | − 5954.40i | − 0.609486i | −0.952435 | − | 0.304743i | \(-0.901429\pi\) | ||||
0.952435 | − | 0.304743i | \(-0.0985705\pi\) | |||||||
\(458\) | 11238.0 | 1.14654 | ||||||||
\(459\) | 1582.66 | 0.160942 | ||||||||
\(460\) | − 152.470i | − 0.0154542i | ||||||||
\(461\) | 1865.94i | 0.188515i | 0.995548 | + | 0.0942576i | \(0.0300477\pi\) | ||||
−0.995548 | + | 0.0942576i | \(0.969952\pi\) | |||||||
\(462\) | 8432.42i | 0.849160i | ||||||||
\(463\) | − 6700.05i | − 0.672522i | −0.941769 | − | 0.336261i | \(-0.890838\pi\) | ||||
0.941769 | − | 0.336261i | \(-0.109162\pi\) | |||||||
\(464\) | −16500.2 | −1.65086 | ||||||||
\(465\) | 781.211 | 0.0779093 | ||||||||
\(466\) | − 7428.28i | − 0.738430i | ||||||||
\(467\) | 16585.8 | 1.64347 | 0.821734 | − | 0.569871i | \(-0.193007\pi\) | ||||
0.821734 | + | 0.569871i | \(0.193007\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12263.2 | −1.20738 | ||||||||
\(470\) | − 1992.11i | − 0.195509i | ||||||||
\(471\) | −3729.23 | −0.364828 | ||||||||
\(472\) | −7276.77 | −0.709619 | ||||||||
\(473\) | 8017.98i | 0.779423i | ||||||||
\(474\) | 12680.2i | 1.22873i | ||||||||
\(475\) | − 5104.51i | − 0.493075i | ||||||||
\(476\) | 1720.29i | 0.165649i | ||||||||
\(477\) | 1187.18 | 0.113956 | ||||||||
\(478\) | −4809.97 | −0.460257 | ||||||||
\(479\) | − 6166.88i | − 0.588250i | −0.955767 | − | 0.294125i | \(-0.904972\pi\) | ||||
0.955767 | − | 0.294125i | \(-0.0950282\pi\) | |||||||
\(480\) | −1851.23 | −0.176034 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −7592.38 | −0.717476 | ||||||||
\(483\) | 464.383i | 0.0437478i | ||||||||
\(484\) | 5331.53 | 0.500708 | ||||||||
\(485\) | −7052.71 | −0.660303 | ||||||||
\(486\) | 771.146i | 0.0719751i | ||||||||
\(487\) | − 5718.51i | − 0.532095i | −0.963960 | − | 0.266047i | \(-0.914282\pi\) | ||||
0.963960 | − | 0.266047i | \(-0.0857178\pi\) | |||||||
\(488\) | − 11686.3i | − 1.08405i | ||||||||
\(489\) | − 101.999i | − 0.00943261i | ||||||||
\(490\) | 3040.82 | 0.280347 | ||||||||
\(491\) | 21060.9 | 1.93578 | 0.967888 | − | 0.251383i | \(-0.0808854\pi\) | ||||
0.967888 | + | 0.251383i | \(0.0808854\pi\) | |||||||
\(492\) | − 2274.45i | − 0.208415i | ||||||||
\(493\) | 12679.8 | 1.15836 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3791.81 | 0.344302 | ||||||||
\(496\) | − 2946.40i | − 0.266728i | ||||||||
\(497\) | 8609.97 | 0.777082 | ||||||||
\(498\) | 8640.97 | 0.777532 | ||||||||
\(499\) | 7863.87i | 0.705481i | 0.935721 | + | 0.352741i | \(0.114750\pi\) | ||||
−0.935721 | + | 0.352741i | \(0.885250\pi\) | |||||||
\(500\) | 2855.51i | 0.255405i | ||||||||
\(501\) | − 6632.01i | − 0.591410i | ||||||||
\(502\) | 6977.70i | 0.620378i | ||||||||
\(503\) | −6504.06 | −0.576544 | −0.288272 | − | 0.957549i | \(-0.593081\pi\) | ||||
−0.288272 | + | 0.957549i | \(0.593081\pi\) | |||||||
\(504\) | 2400.07 | 0.212119 | ||||||||
\(505\) | 9550.26i | 0.841546i | ||||||||
\(506\) | 2166.13 | 0.190309 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4187.41 | 0.365721 | ||||||||
\(509\) | − 14799.3i | − 1.28873i | −0.764717 | − | 0.644367i | \(-0.777121\pi\) | ||||
0.764717 | − | 0.644367i | \(-0.222879\pi\) | |||||||
\(510\) | 3762.11 | 0.326645 | ||||||||
\(511\) | 13902.8 | 1.20357 | ||||||||
\(512\) | − 4500.03i | − 0.388428i | ||||||||
\(513\) | − 1732.46i | − 0.149103i | ||||||||
\(514\) | 19657.1i | 1.68685i | ||||||||
\(515\) | 2613.19i | 0.223594i | ||||||||
\(516\) | −797.005 | −0.0679965 | ||||||||
\(517\) | 5819.40 | 0.495042 | ||||||||
\(518\) | 19059.5i | 1.61666i | ||||||||
\(519\) | 1983.92 | 0.167793 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6633.65 | −0.557822 | −0.278911 | − | 0.960317i | \(-0.589974\pi\) | ||||
−0.278911 | + | 0.960317i | \(0.589974\pi\) | |||||||
\(522\) | 6178.20i | 0.518032i | ||||||||
\(523\) | 4527.41 | 0.378527 | 0.189264 | − | 0.981926i | \(-0.439390\pi\) | ||||
0.189264 | + | 0.981926i | \(0.439390\pi\) | |||||||
\(524\) | −3847.21 | −0.320737 | ||||||||
\(525\) | − 3382.41i | − 0.281182i | ||||||||
\(526\) | − 13270.5i | − 1.10004i | ||||||||
\(527\) | 2264.21i | 0.187155i | ||||||||
\(528\) | − 14301.1i | − 1.17874i | ||||||||
\(529\) | −12047.7 | −0.990195 | ||||||||
\(530\) | 2822.01 | 0.231284 | ||||||||
\(531\) | 3480.56i | 0.284451i | ||||||||
\(532\) | 1883.11 | 0.153464 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9840.83 | 0.797480 | ||||||||
\(535\) | − 582.818i | − 0.0470980i | ||||||||
\(536\) | 16281.1 | 1.31201 | ||||||||
\(537\) | 6975.14 | 0.560521 | ||||||||
\(538\) | 8783.11i | 0.703841i | ||||||||
\(539\) | 8882.89i | 0.709858i | ||||||||
\(540\) | 376.915i | 0.0300367i | ||||||||
\(541\) | 8685.42i | 0.690232i | 0.938560 | + | 0.345116i | \(0.112160\pi\) | ||||
−0.938560 | + | 0.345116i | \(0.887840\pi\) | |||||||
\(542\) | 22821.4 | 1.80860 | ||||||||
\(543\) | −6366.61 | −0.503162 | ||||||||
\(544\) | − 5365.48i | − 0.422873i | ||||||||
\(545\) | 6337.47 | 0.498105 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24656.6 | 1.92731 | 0.963657 | − | 0.267142i | \(-0.0860793\pi\) | ||||
0.963657 | + | 0.267142i | \(0.0860793\pi\) | |||||||
\(548\) | − 3922.22i | − 0.305746i | ||||||||
\(549\) | −5589.70 | −0.434540 | ||||||||
\(550\) | −15777.4 | −1.22318 | ||||||||
\(551\) | − 13880.0i | − 1.07315i | ||||||||
\(552\) | − 616.534i | − 0.0475388i | ||||||||
\(553\) | − 18876.6i | − 1.45157i | ||||||||
\(554\) | − 4180.27i | − 0.320582i | ||||||||
\(555\) | 8570.51 | 0.655492 | ||||||||
\(556\) | 2538.89 | 0.193656 | ||||||||
\(557\) | 9215.90i | 0.701059i | 0.936552 | + | 0.350530i | \(0.113998\pi\) | ||||
−0.936552 | + | 0.350530i | \(0.886002\pi\) | |||||||
\(558\) | −1103.23 | −0.0836979 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7287.93 | 0.549949 | ||||||||
\(561\) | 10990.0i | 0.827088i | ||||||||
\(562\) | 12531.7 | 0.940600 | ||||||||
\(563\) | 19686.7 | 1.47370 | 0.736850 | − | 0.676056i | \(-0.236312\pi\) | ||||
0.736850 | + | 0.676056i | \(0.236312\pi\) | |||||||
\(564\) | 578.461i | 0.0431873i | ||||||||
\(565\) | − 6475.17i | − 0.482146i | ||||||||
\(566\) | 15808.6i | 1.17400i | ||||||||
\(567\) | − 1147.98i | − 0.0850279i | ||||||||
\(568\) | −11430.9 | −0.844422 | ||||||||
\(569\) | 3559.36 | 0.262243 | 0.131121 | − | 0.991366i | \(-0.458142\pi\) | ||||
0.131121 | + | 0.991366i | \(0.458142\pi\) | |||||||
\(570\) | − 4118.19i | − 0.302617i | ||||||||
\(571\) | 710.968 | 0.0521070 | 0.0260535 | − | 0.999661i | \(-0.491706\pi\) | ||||
0.0260535 | + | 0.999661i | \(0.491706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7453.11 | −0.543383 | ||||||||
\(574\) | 16466.9i | 1.19741i | ||||||||
\(575\) | −868.878 | −0.0630169 | ||||||||
\(576\) | −2877.70 | −0.208167 | ||||||||
\(577\) | 8041.67i | 0.580206i | 0.956995 | + | 0.290103i | \(0.0936896\pi\) | ||||
−0.956995 | + | 0.290103i | \(0.906310\pi\) | |||||||
\(578\) | − 4687.26i | − 0.337308i | ||||||||
\(579\) | − 800.314i | − 0.0574438i | ||||||||
\(580\) | 3019.73i | 0.216186i | ||||||||
\(581\) | −12863.6 | −0.918538 | ||||||||
\(582\) | 9959.86 | 0.709364 | ||||||||
\(583\) | 8243.72i | 0.585626i | ||||||||
\(584\) | −18457.9 | −1.30786 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10164.6 | 0.716546 | ||||||||
\(587\) | 14641.3i | 1.02949i | 0.857344 | + | 0.514744i | \(0.172113\pi\) | ||||
−0.857344 | + | 0.514744i | \(0.827887\pi\) | |||||||
\(588\) | −882.980 | −0.0619277 | ||||||||
\(589\) | 2478.52 | 0.173388 | ||||||||
\(590\) | 8273.56i | 0.577317i | ||||||||
\(591\) | 3693.10i | 0.257045i | ||||||||
\(592\) | − 32324.3i | − 2.24413i | ||||||||
\(593\) | 5735.76i | 0.397200i | 0.980081 | + | 0.198600i | \(0.0636394\pi\) | ||||
−0.980081 | + | 0.198600i | \(0.936361\pi\) | |||||||
\(594\) | −5354.81 | −0.369883 | ||||||||
\(595\) | −5600.55 | −0.385882 | ||||||||
\(596\) | 6617.35i | 0.454794i | ||||||||
\(597\) | 9738.43 | 0.667617 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16109.3 | −1.09884 | −0.549422 | − | 0.835545i | \(-0.685152\pi\) | ||||
−0.549422 | + | 0.835545i | \(0.685152\pi\) | |||||||
\(600\) | 4490.63i | 0.305548i | ||||||||
\(601\) | −21005.4 | −1.42567 | −0.712837 | − | 0.701330i | \(-0.752590\pi\) | ||||
−0.712837 | + | 0.701330i | \(0.752590\pi\) | |||||||
\(602\) | 5770.28 | 0.390663 | ||||||||
\(603\) | − 7787.46i | − 0.525920i | ||||||||
\(604\) | − 1052.41i | − 0.0708975i | ||||||||
\(605\) | 17357.3i | 1.16640i | ||||||||
\(606\) | − 13486.9i | − 0.904073i | ||||||||
\(607\) | 7478.16 | 0.500048 | 0.250024 | − | 0.968240i | \(-0.419561\pi\) | ||||
0.250024 | + | 0.968240i | \(0.419561\pi\) | |||||||
\(608\) | −5873.31 | −0.391767 | ||||||||
\(609\) | − 9197.32i | − 0.611977i | ||||||||
\(610\) | −13287.1 | −0.881934 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1092.43 | −0.0721548 | ||||||||
\(613\) | − 16435.5i | − 1.08291i | −0.840730 | − | 0.541455i | \(-0.817874\pi\) | ||||
0.840730 | − | 0.541455i | \(-0.182126\pi\) | |||||||
\(614\) | −15218.8 | −1.00029 | ||||||||
\(615\) | 7404.68 | 0.485505 | ||||||||
\(616\) | 16666.0i | 1.09009i | ||||||||
\(617\) | − 1290.89i | − 0.0842289i | −0.999113 | − | 0.0421145i | \(-0.986591\pi\) | ||||
0.999113 | − | 0.0421145i | \(-0.0134094\pi\) | |||||||
\(618\) | − 3690.36i | − 0.240207i | ||||||||
\(619\) | − 26719.0i | − 1.73494i | −0.497490 | − | 0.867470i | \(-0.665745\pi\) | ||||
0.497490 | − | 0.867470i | \(-0.334255\pi\) | |||||||
\(620\) | −539.227 | −0.0349289 | ||||||||
\(621\) | −294.896 | −0.0190560 | ||||||||
\(622\) | − 1999.94i | − 0.128924i | ||||||||
\(623\) | −14649.8 | −0.942103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 647.683 | 0.0414517 | ||||||||
\(626\) | − 29559.8i | − 1.88729i | ||||||||
\(627\) | 12030.1 | 0.766248 | ||||||||
\(628\) | 2574.08 | 0.163562 | ||||||||
\(629\) | 24840.2i | 1.57463i | ||||||||
\(630\) | − 2728.84i | − 0.172571i | ||||||||
\(631\) | − 10697.4i | − 0.674893i | −0.941345 | − | 0.337447i | \(-0.890437\pi\) | ||||
0.941345 | − | 0.337447i | \(-0.109563\pi\) | |||||||
\(632\) | 25061.4i | 1.57735i | ||||||||
\(633\) | 992.125 | 0.0622961 | ||||||||
\(634\) | 1828.96 | 0.114570 | ||||||||
\(635\) | 13632.5i | 0.851951i | ||||||||
\(636\) | −819.444 | −0.0510897 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −42901.2 | −2.66219 | ||||||||
\(639\) | 5467.56i | 0.338487i | ||||||||
\(640\) | −11777.1 | −0.727393 | ||||||||
\(641\) | −23572.8 | −1.45253 | −0.726264 | − | 0.687416i | \(-0.758745\pi\) | ||||
−0.726264 | + | 0.687416i | \(0.758745\pi\) | |||||||
\(642\) | 823.057i | 0.0505973i | ||||||||
\(643\) | 14000.3i | 0.858661i | 0.903147 | + | 0.429331i | \(0.141250\pi\) | ||||
−0.903147 | + | 0.429331i | \(0.858750\pi\) | |||||||
\(644\) | − 320.538i | − 0.0196133i | ||||||||
\(645\) | − 2594.72i | − 0.158399i | ||||||||
\(646\) | 11935.9 | 0.726953 | ||||||||
\(647\) | −614.196 | −0.0373207 | −0.0186604 | − | 0.999826i | \(-0.505940\pi\) | ||||
−0.0186604 | + | 0.999826i | \(0.505940\pi\) | |||||||
\(648\) | 1524.11i | 0.0923962i | ||||||||
\(649\) | −24168.9 | −1.46181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1642.35 | 0.0988765 | ||||||||
\(652\) | 70.4042i | 0.00422890i | ||||||||
\(653\) | −5333.42 | −0.319622 | −0.159811 | − | 0.987148i | \(-0.551088\pi\) | ||||
−0.159811 | + | 0.987148i | \(0.551088\pi\) | |||||||
\(654\) | −8949.79 | −0.535114 | ||||||||
\(655\) | − 12524.9i | − 0.747161i | ||||||||
\(656\) | − 27927.3i | − 1.66216i | ||||||||
\(657\) | 8828.62i | 0.524258i | ||||||||
\(658\) | − 4188.03i | − 0.248125i | ||||||||
\(659\) | 21396.8 | 1.26480 | 0.632398 | − | 0.774644i | \(-0.282071\pi\) | ||||
0.632398 | + | 0.774644i | \(0.282071\pi\) | |||||||
\(660\) | −2617.28 | −0.154360 | ||||||||
\(661\) | − 16107.9i | − 0.947841i | −0.880568 | − | 0.473921i | \(-0.842838\pi\) | ||||
0.880568 | − | 0.473921i | \(-0.157162\pi\) | |||||||
\(662\) | 5001.20 | 0.293621 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17078.2 | 0.998136 | ||||||||
\(665\) | 6130.63i | 0.357497i | ||||||||
\(666\) | −12103.3 | −0.704194 | ||||||||
\(667\) | −2362.62 | −0.137153 | ||||||||
\(668\) | 4577.72i | 0.265145i | ||||||||
\(669\) | − 17357.6i | − 1.00311i | ||||||||
\(670\) | − 18511.4i | − 1.06740i | ||||||||
\(671\) | − 38814.6i | − 2.23312i | ||||||||
\(672\) | −3891.85 | −0.223410 | ||||||||
\(673\) | −20329.9 | −1.16443 | −0.582213 | − | 0.813036i | \(-0.697813\pi\) | ||||
−0.582213 | + | 0.813036i | \(0.697813\pi\) | |||||||
\(674\) | − 29479.1i | − 1.68471i | ||||||||
\(675\) | 2147.92 | 0.122479 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24883.5 | −1.41263 | −0.706314 | − | 0.707899i | \(-0.749643\pi\) | ||||
−0.706314 | + | 0.707899i | \(0.749643\pi\) | |||||||
\(678\) | 9144.26i | 0.517969i | ||||||||
\(679\) | −14827.0 | −0.838007 | ||||||||
\(680\) | 7435.51 | 0.419322 | ||||||||
\(681\) | − 8836.06i | − 0.497208i | ||||||||
\(682\) | − 7660.78i | − 0.430127i | ||||||||
\(683\) | − 258.953i | − 0.0145074i | −0.999974 | − | 0.00725369i | \(-0.997691\pi\) | ||||
0.999974 | − | 0.00725369i | \(-0.00230894\pi\) | |||||||
\(684\) | 1195.82i | 0.0668471i | ||||||||
\(685\) | 12769.1 | 0.712240 | ||||||||
\(686\) | 21819.5 | 1.21439 | ||||||||
\(687\) | − 10623.8i | − 0.589989i | ||||||||
\(688\) | −9786.20 | −0.542290 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −700.989 | −0.0386756 | ||||||||
\(691\) | 658.193i | 0.0362357i | 0.999836 | + | 0.0181178i | \(0.00576740\pi\) | ||||
−0.999836 | + | 0.0181178i | \(0.994233\pi\) | |||||||
\(692\) | −1369.39 | −0.0752262 | ||||||||
\(693\) | 7971.55 | 0.436962 | ||||||||
\(694\) | − 24441.3i | − 1.33686i | ||||||||
\(695\) | 8265.60i | 0.451125i | ||||||||
\(696\) | 12210.7i | 0.665010i | ||||||||
\(697\) | 21461.2i | 1.16629i | ||||||||
\(698\) | 15781.2 | 0.855768 | ||||||||
\(699\) | −7022.29 | −0.379982 | ||||||||
\(700\) | 2334.69i | 0.126062i | ||||||||
\(701\) | 8222.16 | 0.443005 | 0.221503 | − | 0.975160i | \(-0.428904\pi\) | ||||
0.221503 | + | 0.975160i | \(0.428904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27191.3 | 1.45881 | ||||||||
\(704\) | − 19982.7i | − 1.06978i | ||||||||
\(705\) | −1883.23 | −0.100605 | ||||||||
\(706\) | 4999.25 | 0.266500 | ||||||||
\(707\) | 20077.6i | 1.06803i | ||||||||
\(708\) | − 2402.44i | − 0.127527i | ||||||||
\(709\) | 6817.51i | 0.361124i | 0.983564 | + | 0.180562i | \(0.0577917\pi\) | ||||
−0.983564 | + | 0.180562i | \(0.942208\pi\) | |||||||
\(710\) | 12996.8i | 0.686987i | ||||||||
\(711\) | 11987.2 | 0.632283 | ||||||||
\(712\) | 19449.6 | 1.02374 | ||||||||
\(713\) | − 421.888i | − 0.0221596i | ||||||||
\(714\) | 7909.11 | 0.414553 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4814.56 | −0.251297 | ||||||||
\(717\) | 4547.09i | 0.236840i | ||||||||
\(718\) | −24014.8 | −1.24822 | ||||||||
\(719\) | −23385.7 | −1.21299 | −0.606496 | − | 0.795087i | \(-0.707425\pi\) | ||||
−0.606496 | + | 0.795087i | \(0.707425\pi\) | |||||||
\(720\) | 4628.03i | 0.239551i | ||||||||
\(721\) | 5493.73i | 0.283769i | ||||||||
\(722\) | 8701.03i | 0.448502i | ||||||||
\(723\) | 7177.42i | 0.369199i | ||||||||
\(724\) | 4394.52 | 0.225582 | ||||||||
\(725\) | 17208.5 | 0.881529 | ||||||||
\(726\) | − 24512.0i | − 1.25307i | ||||||||
\(727\) | −20488.6 | −1.04523 | −0.522613 | − | 0.852570i | \(-0.675043\pi\) | ||||
−0.522613 | + | 0.852570i | \(0.675043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 20986.3i | 1.06402i | ||||||||
\(731\) | 7520.38 | 0.380508 | ||||||||
\(732\) | 3858.26 | 0.194816 | ||||||||
\(733\) | 16993.4i | 0.856299i | 0.903708 | + | 0.428149i | \(0.140834\pi\) | ||||
−0.903708 | + | 0.428149i | \(0.859166\pi\) | |||||||
\(734\) | 13862.4i | 0.697099i | ||||||||
\(735\) | − 2874.62i | − 0.144261i | ||||||||
\(736\) | 999.742i | 0.0500693i | ||||||||
\(737\) | 54075.8 | 2.70272 | ||||||||
\(738\) | −10456.9 | −0.521577 | ||||||||
\(739\) | − 14014.3i | − 0.697600i | −0.937197 | − | 0.348800i | \(-0.886589\pi\) | ||||
0.937197 | − | 0.348800i | \(-0.113411\pi\) | |||||||
\(740\) | −5915.75 | −0.293875 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5932.73 | 0.293528 | ||||||||
\(743\) | 141.560i | 0.00698971i | 0.999994 | + | 0.00349485i | \(0.00111245\pi\) | ||||
−0.999994 | + | 0.00349485i | \(0.998888\pi\) | |||||||
\(744\) | −2180.45 | −0.107445 | ||||||||
\(745\) | −21543.4 | −1.05945 | ||||||||
\(746\) | − 2544.92i | − 0.124901i | ||||||||
\(747\) | − 8168.70i | − 0.400103i | ||||||||
\(748\) | − 7585.76i | − 0.370806i | ||||||||
\(749\) | − 1225.26i | − 0.0597731i | ||||||||
\(750\) | 13128.4 | 0.639175 | ||||||||
\(751\) | −20734.3 | −1.00746 | −0.503732 | − | 0.863860i | \(-0.668040\pi\) | ||||
−0.503732 | + | 0.863860i | \(0.668040\pi\) | |||||||
\(752\) | 7102.76i | 0.344430i | ||||||||
\(753\) | 6596.34 | 0.319235 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3426.23 | 0.165157 | ||||||||
\(756\) | 792.391i | 0.0381203i | ||||||||
\(757\) | 17449.8 | 0.837812 | 0.418906 | − | 0.908030i | \(-0.362414\pi\) | ||||
0.418906 | + | 0.908030i | \(0.362414\pi\) | |||||||
\(758\) | 216.054 | 0.0103528 | ||||||||
\(759\) | − 2047.74i | − 0.0979293i | ||||||||
\(760\) | − 8139.27i | − 0.388477i | ||||||||
\(761\) | − 424.121i | − 0.0202028i | −0.999949 | − | 0.0101014i | \(-0.996785\pi\) | ||||
0.999949 | − | 0.0101014i | \(-0.00321544\pi\) | |||||||
\(762\) | − 19251.9i | − 0.915251i | ||||||||
\(763\) | 13323.3 | 0.632157 | ||||||||
\(764\) | 5144.48 | 0.243613 | ||||||||
\(765\) | − 3556.49i | − 0.168085i | ||||||||
\(766\) | 4915.68 | 0.231868 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8957.81 | 0.420882 | ||||||||
\(769\) | − 38060.7i | − 1.78479i | −0.451252 | − | 0.892396i | \(-0.649023\pi\) | ||||
0.451252 | − | 0.892396i | \(-0.350977\pi\) | |||||||
\(770\) | 18949.0 | 0.886849 | ||||||||
\(771\) | 18582.8 | 0.868019 | ||||||||
\(772\) | 552.413i | 0.0257536i | ||||||||
\(773\) | 16683.3i | 0.776268i | 0.921603 | + | 0.388134i | \(0.126880\pi\) | ||||
−0.921603 | + | 0.388134i | \(0.873120\pi\) | |||||||
\(774\) | 3664.28i | 0.170168i | ||||||||
\(775\) | 3072.89i | 0.142428i | ||||||||
\(776\) | 19684.9 | 0.910627 | ||||||||
\(777\) | 18017.8 | 0.831900 | ||||||||
\(778\) | − 23167.7i | − 1.06761i | ||||||||
\(779\) | 23492.5 | 1.08050 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37966.5 | −1.73950 | ||||||||
\(782\) | − 2031.70i | − 0.0929073i | ||||||||
\(783\) | 5840.54 | 0.266569 | ||||||||
\(784\) | −10841.9 | −0.493889 | ||||||||
\(785\) | 8380.17i | 0.381020i | ||||||||
\(786\) | 17687.8i | 0.802674i | ||||||||
\(787\) | − 39105.2i | − 1.77122i | −0.464432 | − | 0.885609i | \(-0.653741\pi\) | ||||
0.464432 | − | 0.885609i | \(-0.346259\pi\) | |||||||
\(788\) | − 2549.14i | − 0.115240i | ||||||||
\(789\) | −12545.2 | −0.566060 | ||||||||
\(790\) | 28494.3 | 1.28327 | ||||||||
\(791\) | − 13612.8i | − 0.611903i | ||||||||
\(792\) | −10583.4 | −0.474827 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19346.2 | −0.864697 | ||||||||
\(795\) | − 2667.78i | − 0.119014i | ||||||||
\(796\) | −6721.90 | −0.299311 | ||||||||
\(797\) | 4346.93 | 0.193195 | 0.0965974 | − | 0.995324i | \(-0.469204\pi\) | ||||
0.0965974 | + | 0.995324i | \(0.469204\pi\) | |||||||
\(798\) | − 8657.69i | − 0.384059i | ||||||||
\(799\) | − 5458.25i | − 0.241676i | ||||||||
\(800\) | − 7281.78i | − 0.321812i | ||||||||
\(801\) | − 9302.99i | − 0.410368i | ||||||||
\(802\) | −24093.9 | −1.06083 | ||||||||
\(803\) | −61305.6 | −2.69418 | ||||||||
\(804\) | 5375.26i | 0.235784i | ||||||||
\(805\) | 1043.54 | 0.0456895 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8303.07 | 0.362183 | ||||||||
\(808\) | − 26655.8i | − 1.16058i | ||||||||
\(809\) | −23030.2 | −1.00086 | −0.500432 | − | 0.865776i | \(-0.666826\pi\) | ||||
−0.500432 | + | 0.865776i | \(0.666826\pi\) | |||||||
\(810\) | 1732.89 | 0.0751697 | ||||||||
\(811\) | − 7898.11i | − 0.341973i | −0.985273 | − | 0.170987i | \(-0.945305\pi\) | ||||
0.985273 | − | 0.170987i | \(-0.0546955\pi\) | |||||||
\(812\) | 6348.41i | 0.274366i | ||||||||
\(813\) | − 21574.1i | − 0.930672i | ||||||||
\(814\) | − 84044.8i | − 3.61888i | ||||||||
\(815\) | −229.207 | −0.00985127 | ||||||||
\(816\) | −13413.6 | −0.575453 | ||||||||
\(817\) | − 8232.18i | − 0.352518i | ||||||||
\(818\) | −22956.2 | −0.981230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5111.04 | −0.217665 | ||||||||
\(821\) | 3939.61i | 0.167471i | 0.996488 | + | 0.0837353i | \(0.0266850\pi\) | ||||
−0.996488 | + | 0.0837353i | \(0.973315\pi\) | |||||||
\(822\) | −18032.6 | −0.765159 | ||||||||
\(823\) | 17599.8 | 0.745430 | 0.372715 | − | 0.927946i | \(-0.378427\pi\) | ||||
0.372715 | + | 0.927946i | \(0.378427\pi\) | |||||||
\(824\) | − 7293.70i | − 0.308359i | ||||||||
\(825\) | 14915.1i | 0.629425i | ||||||||
\(826\) | 17393.6i | 0.732687i | ||||||||
\(827\) | 12510.6i | 0.526042i | 0.964790 | + | 0.263021i | \(0.0847189\pi\) | ||||
−0.964790 | + | 0.263021i | \(0.915281\pi\) | |||||||
\(828\) | 203.550 | 0.00854331 | ||||||||
\(829\) | −28630.8 | −1.19950 | −0.599752 | − | 0.800186i | \(-0.704734\pi\) | ||||
−0.599752 | + | 0.800186i | \(0.704734\pi\) | |||||||
\(830\) | − 19417.6i | − 0.812042i | ||||||||
\(831\) | −3951.80 | −0.164966 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8331.62 | 0.346547 | ||||||||
\(834\) | − 11672.7i | − 0.484643i | ||||||||
\(835\) | −14903.2 | −0.617660 | ||||||||
\(836\) | −8303.75 | −0.343530 | ||||||||
\(837\) | 1042.93i | 0.0430693i | ||||||||
\(838\) | − 16859.1i | − 0.694973i | ||||||||
\(839\) | 21250.3i | 0.874426i | 0.899358 | + | 0.437213i | \(0.144034\pi\) | ||||
−0.899358 | + | 0.437213i | \(0.855966\pi\) | |||||||
\(840\) | − 5393.34i | − 0.221533i | ||||||||
\(841\) | 22403.7 | 0.918600 | ||||||||
\(842\) | 47690.9 | 1.95194 | ||||||||
\(843\) | − 11846.8i | − 0.484015i | ||||||||
\(844\) | −684.810 | −0.0279291 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2659.51 | 0.108080 | ||||||||
\(847\) | 36490.4i | 1.48031i | ||||||||
\(848\) | −10061.7 | −0.407454 | ||||||||
\(849\) | 14944.6 | 0.604118 | ||||||||
\(850\) | 14798.2i | 0.597147i | ||||||||
\(851\) | − 4628.45i | − 0.186441i | ||||||||
\(852\) | − 3773.96i | − 0.151753i | ||||||||
\(853\) | 34721.1i | 1.39370i | 0.717215 | + | 0.696852i | \(0.245416\pi\) | ||||
−0.717215 | + | 0.696852i | \(0.754584\pi\) | |||||||
\(854\) | −27933.6 | −1.11928 | ||||||||
\(855\) | −3893.11 | −0.155721 | ||||||||
\(856\) | 1626.71i | 0.0649529i | ||||||||
\(857\) | −4898.06 | −0.195233 | −0.0976163 | − | 0.995224i | \(-0.531122\pi\) | ||||
−0.0976163 | + | 0.995224i | \(0.531122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12564.2 | −0.499051 | −0.249526 | − | 0.968368i | \(-0.580275\pi\) | ||||
−0.249526 | + | 0.968368i | \(0.580275\pi\) | |||||||
\(860\) | 1791.00i | 0.0710145i | ||||||||
\(861\) | 15566.9 | 0.616166 | ||||||||
\(862\) | −22704.9 | −0.897137 | ||||||||
\(863\) | 22826.6i | 0.900380i | 0.892933 | + | 0.450190i | \(0.148644\pi\) | ||||
−0.892933 | + | 0.450190i | \(0.851356\pi\) | |||||||
\(864\) | − 2471.42i | − 0.0973143i | ||||||||
\(865\) | − 4458.18i | − 0.175240i | ||||||||
\(866\) | 30282.8i | 1.18828i | ||||||||
\(867\) | −4431.08 | −0.173572 | ||||||||
\(868\) | −1133.62 | −0.0443291 | ||||||||
\(869\) | 83238.3i | 3.24933i | ||||||||
\(870\) | 13883.4 | 0.541024 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17688.6 | −0.686939 | ||||||||
\(873\) | − 9415.51i | − 0.365025i | ||||||||
\(874\) | −2224.00 | −0.0860731 | ||||||||
\(875\) | −19543.9 | −0.755089 | ||||||||
\(876\) | − 6093.92i | − 0.235039i | ||||||||
\(877\) | − 25212.7i | − 0.970776i | −0.874299 | − | 0.485388i | \(-0.838678\pi\) | ||||
0.874299 | − | 0.485388i | \(-0.161322\pi\) | |||||||
\(878\) | − 22438.5i | − 0.862484i | ||||||||
\(879\) | − 9609.07i | − 0.368721i | ||||||||
\(880\) | −32136.9 | −1.23106 | ||||||||
\(881\) | 18026.2 | 0.689352 | 0.344676 | − | 0.938722i | \(-0.387989\pi\) | ||||
0.344676 | + | 0.938722i | \(0.387989\pi\) | |||||||
\(882\) | 4059.55i | 0.154980i | ||||||||
\(883\) | 18833.1 | 0.717764 | 0.358882 | − | 0.933383i | \(-0.383158\pi\) | ||||
0.358882 | + | 0.933383i | \(0.383158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7821.37 | 0.297076 | ||||||||
\(886\) | 6640.68i | 0.251803i | ||||||||
\(887\) | 38451.4 | 1.45555 | 0.727775 | − | 0.685816i | \(-0.240555\pi\) | ||||
0.727775 | + | 0.685816i | \(0.240555\pi\) | |||||||
\(888\) | −23921.2 | −0.903991 | ||||||||
\(889\) | 28659.7i | 1.08123i | ||||||||
\(890\) | − 22113.9i | − 0.832876i | ||||||||
\(891\) | 5062.15i | 0.190335i | ||||||||
\(892\) | 11981.0i | 0.449723i | ||||||||
\(893\) | −5974.86 | −0.223898 | ||||||||
\(894\) | 30423.7 | 1.13816 | ||||||||
\(895\) | − 15674.2i | − 0.585399i | ||||||||
\(896\) | −24759.1 | −0.923152 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18539.4 | −0.688940 | ||||||||
\(899\) | 8355.68i | 0.309986i | ||||||||
\(900\) | −1482.59 | −0.0549108 | ||||||||
\(901\) | 7732.11 | 0.285898 | ||||||||
\(902\) | − 72612.3i | − 2.68041i | ||||||||
\(903\) | − 5454.91i | − 0.201028i | ||||||||
\(904\) | 18072.9i | 0.664929i | ||||||||
\(905\) | 14306.8i | 0.525495i | ||||||||
\(906\) | −4838.53 | −0.177428 | ||||||||
\(907\) | 5531.31 | 0.202496 | 0.101248 | − | 0.994861i | \(-0.467716\pi\) | ||||
0.101248 | + | 0.994861i | \(0.467716\pi\) | |||||||
\(908\) | 6099.05i | 0.222912i | ||||||||
\(909\) | −12749.8 | −0.465219 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15695.2 | 0.570806 | 0.285403 | − | 0.958408i | \(-0.407872\pi\) | ||||
0.285403 | + | 0.958408i | \(0.407872\pi\) | |||||||
\(912\) | 14683.2i | 0.533123i | ||||||||
\(913\) | 56723.1 | 2.05615 | ||||||||
\(914\) | 18895.9 | 0.683832 | ||||||||
\(915\) | 12560.9i | 0.453827i | ||||||||
\(916\) | 7333.01i | 0.264508i | ||||||||
\(917\) | − 26331.3i | − 0.948240i | ||||||||
\(918\) | 5022.49i | 0.180574i | ||||||||
\(919\) | −51503.5 | −1.84869 | −0.924344 | − | 0.381561i | \(-0.875386\pi\) | ||||
−0.924344 | + | 0.381561i | \(0.875386\pi\) | |||||||
\(920\) | −1385.45 | −0.0496488 | ||||||||
\(921\) | 14387.0i | 0.514732i | ||||||||
\(922\) | −5921.45 | −0.211510 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5502.33 | −0.195902 | ||||||||
\(925\) | 33712.0i | 1.19832i | ||||||||
\(926\) | 21262.2 | 0.754557 | ||||||||
\(927\) | −3488.66 | −0.123606 | ||||||||
\(928\) | − 19800.3i | − 0.700407i | ||||||||
\(929\) | 42927.0i | 1.51603i | 0.652238 | + | 0.758014i | \(0.273830\pi\) | ||||
−0.652238 | + | 0.758014i | \(0.726170\pi\) | |||||||
\(930\) | 2479.13i | 0.0874127i | ||||||||
\(931\) | − 9120.20i | − 0.321055i | ||||||||
\(932\) | 4847.10 | 0.170356 | ||||||||
\(933\) | −1890.64 | −0.0663416 | ||||||||
\(934\) | 52634.1i | 1.84394i | ||||||||
\(935\) | 24696.2 | 0.863797 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44206.6 | 1.54127 | 0.770633 | − | 0.637280i | \(-0.219940\pi\) | ||||
0.770633 | + | 0.637280i | \(0.219940\pi\) | |||||||
\(938\) | − 38916.6i | − 1.35466i | ||||||||
\(939\) | −27944.2 | −0.971165 | ||||||||
\(940\) | 1299.89 | 0.0451041 | ||||||||
\(941\) | 44067.7i | 1.52664i | 0.646022 | + | 0.763319i | \(0.276432\pi\) | ||||
−0.646022 | + | 0.763319i | \(0.723568\pi\) | |||||||
\(942\) | − 11834.5i | − 0.409330i | ||||||||
\(943\) | − 3998.85i | − 0.138092i | ||||||||
\(944\) | − 29498.9i | − 1.01706i | ||||||||
\(945\) | −2579.70 | −0.0888017 | ||||||||
\(946\) | −25444.6 | −0.874498 | ||||||||
\(947\) | − 44402.5i | − 1.52364i | −0.647789 | − | 0.761820i | \(-0.724306\pi\) | ||||
0.647789 | − | 0.761820i | \(-0.275694\pi\) | |||||||
\(948\) | −8274.07 | −0.283470 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 16198.9 | 0.553221 | ||||||||
\(951\) | − 1729.00i | − 0.0589554i | ||||||||
\(952\) | 15631.7 | 0.532172 | ||||||||
\(953\) | 10361.7 | 0.352202 | 0.176101 | − | 0.984372i | \(-0.443651\pi\) | ||||
0.176101 | + | 0.984372i | \(0.443651\pi\) | |||||||
\(954\) | 3767.44i | 0.127857i | ||||||||
\(955\) | 16748.3i | 0.567500i | ||||||||
\(956\) | − 3138.60i | − 0.106182i | ||||||||
\(957\) | 40556.5i | 1.36991i | ||||||||
\(958\) | 19570.2 | 0.660006 | ||||||||
\(959\) | 26844.7 | 0.903920 | ||||||||
\(960\) | 6466.65i | 0.217407i | ||||||||
\(961\) | 28298.9 | 0.949916 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 778.073 | 0.0260364 | ||||||||
\(964\) | − 4954.18i | − 0.165522i | ||||||||
\(965\) | −1798.43 | −0.0599933 | ||||||||
\(966\) | −1473.69 | −0.0490842 | ||||||||
\(967\) | − 8432.54i | − 0.280426i | −0.990121 | − | 0.140213i | \(-0.955221\pi\) | ||||
0.990121 | − | 0.140213i | \(-0.0447788\pi\) | |||||||
\(968\) | − 48446.1i | − 1.60859i | ||||||||
\(969\) | − 11283.5i | − 0.374076i | ||||||||
\(970\) | − 22381.4i | − 0.740848i | ||||||||
\(971\) | −36917.1 | −1.22011 | −0.610055 | − | 0.792359i | \(-0.708853\pi\) | ||||
−0.610055 | + | 0.792359i | \(0.708853\pi\) | |||||||
\(972\) | −503.189 | −0.0166047 | ||||||||
\(973\) | 17376.8i | 0.572534i | ||||||||
\(974\) | 18147.4 | 0.597001 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 47374.5 | 1.55371 | ||||||||
\(977\) | 38306.9i | 1.25440i | 0.778859 | + | 0.627199i | \(0.215799\pi\) | ||||
−0.778859 | + | 0.627199i | \(0.784201\pi\) | |||||||
\(978\) | 323.687 | 0.0105832 | ||||||||
\(979\) | 64599.6 | 2.10890 | ||||||||
\(980\) | 1984.19i | 0.0646763i | ||||||||
\(981\) | 8460.65i | 0.275360i | ||||||||
\(982\) | 66835.6i | 2.17190i | ||||||||
\(983\) | − 18810.9i | − 0.610350i | −0.952296 | − | 0.305175i | \(-0.901285\pi\) | ||||
0.952296 | − | 0.305175i | \(-0.0987149\pi\) | |||||||
\(984\) | −20667.3 | −0.669561 | ||||||||
\(985\) | 8298.97 | 0.268454 | ||||||||
\(986\) | 40238.8i | 1.29966i | ||||||||
\(987\) | −3959.14 | −0.127681 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1401.26 | −0.0450532 | ||||||||
\(990\) | 12033.1i | 0.386300i | ||||||||
\(991\) | −6492.09 | −0.208101 | −0.104051 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104051 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(992\) | 3535.71 | 0.113164 | ||||||||
\(993\) | − 4727.86i | − 0.151092i | ||||||||
\(994\) | 27323.2i | 0.871872i | ||||||||
\(995\) | − 21883.8i | − 0.697249i | ||||||||
\(996\) | 5638.41i | 0.179377i | ||||||||
\(997\) | 48552.1 | 1.54229 | 0.771143 | − | 0.636662i | \(-0.219685\pi\) | ||||
0.771143 | + | 0.636662i | \(0.219685\pi\) | |||||||
\(998\) | −24955.5 | −0.791537 | ||||||||
\(999\) | 11441.8i | 0.362365i |
(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 | 507.4.b.k.337.14 | 18 | ||
13.5 | odd | 4 | 507.4.a.o.1.8 | ✓ | 9 | ||
13.8 | odd | 4 | 507.4.a.p.1.2 | yes | 9 | ||
13.12 | even | 2 | inner | 507.4.b.k.337.5 | 18 | ||
39.5 | even | 4 | 1521.4.a.bi.1.2 | 9 | |||
39.8 | even | 4 | 1521.4.a.bf.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.8 | ✓ | 9 | 13.5 | odd | 4 | ||
507.4.a.p.1.2 | yes | 9 | 13.8 | odd | 4 | ||
507.4.b.k.337.5 | 18 | 13.12 | even | 2 | inner | ||
507.4.b.k.337.14 | 18 | 1.1 | even | 1 | trivial | ||
1521.4.a.bf.1.8 | 9 | 39.8 | even | 4 | |||
1521.4.a.bi.1.2 | 9 | 39.5 | even | 4 |