Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 34 x^{10} + 124 x^{9} + 671 x^{8} - 1984 x^{7} - 5452 x^{6} + 8264 x^{5} + \cdots + 300356 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.1 | ||
Root | \(4.15292 + 1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.e.288.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.15292 | −1.11472 | −0.557362 | − | 0.830269i | \(-0.688187\pi\) | ||||
−0.557362 | + | 0.830269i | \(0.688187\pi\) | |||||||
\(3\) | − 1.99138i | − 0.383242i | −0.981469 | − | 0.191621i | \(-0.938626\pi\) | ||||
0.981469 | − | 0.191621i | \(-0.0613744\pi\) | |||||||
\(4\) | 1.94089 | 0.242611 | ||||||||
\(5\) | 5.00761i | 0.447894i | 0.974601 | + | 0.223947i | \(0.0718943\pi\) | ||||
−0.974601 | + | 0.223947i | \(0.928106\pi\) | |||||||
\(6\) | 6.27866i | 0.427209i | ||||||||
\(7\) | 2.78516i | 0.150385i | 0.997169 | + | 0.0751924i | \(0.0239571\pi\) | ||||
−0.997169 | + | 0.0751924i | \(0.976043\pi\) | |||||||
\(8\) | 19.1039 | 0.844280 | ||||||||
\(9\) | 23.0344 | 0.853126 | ||||||||
\(10\) | − 15.7886i | − 0.499279i | ||||||||
\(11\) | − 27.2453i | − 0.746798i | −0.927671 | − | 0.373399i | \(-0.878192\pi\) | ||||
0.927671 | − | 0.373399i | \(-0.121808\pi\) | |||||||
\(12\) | − 3.86505i | − 0.0929787i | ||||||||
\(13\) | −59.7352 | −1.27443 | −0.637214 | − | 0.770687i | \(-0.719913\pi\) | ||||
−0.637214 | + | 0.770687i | \(0.719913\pi\) | |||||||
\(14\) | − 8.78140i | − 0.167638i | ||||||||
\(15\) | 9.97206 | 0.171652 | ||||||||
\(16\) | −75.7601 | −1.18375 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −72.6256 | −0.951000 | ||||||||
\(19\) | −33.2605 | −0.401604 | −0.200802 | − | 0.979632i | \(-0.564355\pi\) | ||||
−0.200802 | + | 0.979632i | \(0.564355\pi\) | |||||||
\(20\) | 9.71922i | 0.108664i | ||||||||
\(21\) | 5.54633 | 0.0576337 | ||||||||
\(22\) | 85.9023i | 0.832475i | ||||||||
\(23\) | 210.884i | 1.91184i | 0.293630 | + | 0.955919i | \(0.405137\pi\) | ||||
−0.293630 | + | 0.955919i | \(0.594863\pi\) | |||||||
\(24\) | − 38.0431i | − 0.323563i | ||||||||
\(25\) | 99.9239 | 0.799391 | ||||||||
\(26\) | 188.340 | 1.42064 | ||||||||
\(27\) | − 99.6376i | − 0.710195i | ||||||||
\(28\) | 5.40570i | 0.0364850i | ||||||||
\(29\) | 20.0521i | 0.128400i | 0.997937 | + | 0.0641998i | \(0.0204495\pi\) | ||||
−0.997937 | + | 0.0641998i | \(0.979551\pi\) | |||||||
\(30\) | −31.4411 | −0.191344 | ||||||||
\(31\) | − 133.659i | − 0.774385i | −0.921999 | − | 0.387192i | \(-0.873445\pi\) | ||||
0.921999 | − | 0.387192i | \(-0.126555\pi\) | |||||||
\(32\) | 86.0343 | 0.475277 | ||||||||
\(33\) | −54.2559 | −0.286204 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.9470 | −0.0673565 | ||||||||
\(36\) | 44.7072 | 0.206978 | ||||||||
\(37\) | 152.772i | 0.678800i | 0.940642 | + | 0.339400i | \(0.110224\pi\) | ||||
−0.940642 | + | 0.339400i | \(0.889776\pi\) | |||||||
\(38\) | 104.868 | 0.447678 | ||||||||
\(39\) | 118.956i | 0.488414i | ||||||||
\(40\) | 95.6647i | 0.378148i | ||||||||
\(41\) | − 261.840i | − 0.997377i | −0.866781 | − | 0.498689i | \(-0.833815\pi\) | ||||
0.866781 | − | 0.498689i | \(-0.166185\pi\) | |||||||
\(42\) | −17.4871 | −0.0642457 | ||||||||
\(43\) | 316.820 | 1.12359 | 0.561797 | − | 0.827275i | \(-0.310110\pi\) | ||||
0.561797 | + | 0.827275i | \(0.310110\pi\) | |||||||
\(44\) | − 52.8802i | − 0.181182i | ||||||||
\(45\) | 115.347i | 0.382110i | ||||||||
\(46\) | − 664.899i | − 2.13117i | ||||||||
\(47\) | 329.443 | 1.02243 | 0.511215 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511215 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(48\) | 150.867i | 0.453663i | ||||||||
\(49\) | 335.243 | 0.977384 | ||||||||
\(50\) | −315.052 | −0.891101 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −115.939 | −0.309190 | ||||||||
\(53\) | 310.540 | 0.804829 | 0.402415 | − | 0.915458i | \(-0.368171\pi\) | ||||
0.402415 | + | 0.915458i | \(0.368171\pi\) | |||||||
\(54\) | 314.149i | 0.791672i | ||||||||
\(55\) | 136.434 | 0.334487 | ||||||||
\(56\) | 53.2074i | 0.126967i | ||||||||
\(57\) | 66.2344i | 0.153911i | ||||||||
\(58\) | − 63.2227i | − 0.143130i | ||||||||
\(59\) | 54.7388 | 0.120786 | 0.0603931 | − | 0.998175i | \(-0.480765\pi\) | ||||
0.0603931 | + | 0.998175i | \(0.480765\pi\) | |||||||
\(60\) | 19.3547 | 0.0416446 | ||||||||
\(61\) | 818.751i | 1.71853i | 0.511531 | + | 0.859265i | \(0.329079\pi\) | ||||
−0.511531 | + | 0.859265i | \(0.670921\pi\) | |||||||
\(62\) | 421.417i | 0.863226i | ||||||||
\(63\) | 64.1546i | 0.128297i | ||||||||
\(64\) | 334.822 | 0.653948 | ||||||||
\(65\) | − 299.130i | − 0.570808i | ||||||||
\(66\) | 171.064 | 0.319039 | ||||||||
\(67\) | 731.181 | 1.33325 | 0.666627 | − | 0.745392i | \(-0.267738\pi\) | ||||
0.666627 | + | 0.745392i | \(0.267738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 419.950 | 0.732696 | ||||||||
\(70\) | 43.9738 | 0.0750839 | ||||||||
\(71\) | 629.179i | 1.05169i | 0.850581 | + | 0.525844i | \(0.176250\pi\) | ||||
−0.850581 | + | 0.525844i | \(0.823750\pi\) | |||||||
\(72\) | 440.046 | 0.720277 | ||||||||
\(73\) | 496.481i | 0.796010i | 0.917383 | + | 0.398005i | \(0.130297\pi\) | ||||
−0.917383 | + | 0.398005i | \(0.869703\pi\) | |||||||
\(74\) | − 481.678i | − 0.756675i | ||||||||
\(75\) | − 198.987i | − 0.306360i | ||||||||
\(76\) | −64.5550 | −0.0974337 | ||||||||
\(77\) | 75.8828 | 0.112307 | ||||||||
\(78\) | − 375.057i | − 0.544447i | ||||||||
\(79\) | 90.0262i | 0.128212i | 0.997943 | + | 0.0641059i | \(0.0204196\pi\) | ||||
−0.997943 | + | 0.0641059i | \(0.979580\pi\) | |||||||
\(80\) | − 379.377i | − 0.530195i | ||||||||
\(81\) | 423.512 | 0.580950 | ||||||||
\(82\) | 825.559i | 1.11180i | ||||||||
\(83\) | −364.025 | −0.481409 | −0.240704 | − | 0.970599i | \(-0.577378\pi\) | ||||
−0.240704 | + | 0.970599i | \(0.577378\pi\) | |||||||
\(84\) | 10.7648 | 0.0139826 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −998.907 | −1.25250 | ||||||||
\(87\) | 39.9315 | 0.0492081 | ||||||||
\(88\) | − 520.492i | − 0.630507i | ||||||||
\(89\) | −192.079 | −0.228767 | −0.114384 | − | 0.993437i | \(-0.536489\pi\) | ||||
−0.114384 | + | 0.993437i | \(0.536489\pi\) | |||||||
\(90\) | − 363.680i | − 0.425948i | ||||||||
\(91\) | − 166.372i | − 0.191654i | ||||||||
\(92\) | 409.302i | 0.463833i | ||||||||
\(93\) | −266.167 | −0.296776 | ||||||||
\(94\) | −1038.71 | −1.13973 | ||||||||
\(95\) | − 166.556i | − 0.179876i | ||||||||
\(96\) | − 171.327i | − 0.182146i | ||||||||
\(97\) | 1350.20i | 1.41332i | 0.707554 | + | 0.706659i | \(0.249798\pi\) | ||||
−0.707554 | + | 0.706659i | \(0.750202\pi\) | |||||||
\(98\) | −1056.99 | −1.08951 | ||||||||
\(99\) | − 627.580i | − 0.637113i | ||||||||
\(100\) | 193.941 | 0.193941 | ||||||||
\(101\) | −304.020 | −0.299516 | −0.149758 | − | 0.988723i | \(-0.547850\pi\) | ||||
−0.149758 | + | 0.988723i | \(0.547850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 988.515 | 0.945643 | 0.472822 | − | 0.881158i | \(-0.343236\pi\) | ||||
0.472822 | + | 0.881158i | \(0.343236\pi\) | |||||||
\(104\) | −1141.17 | −1.07597 | ||||||||
\(105\) | 27.7738i | 0.0258138i | ||||||||
\(106\) | −979.107 | −0.897163 | ||||||||
\(107\) | − 1175.01i | − 1.06162i | −0.847492 | − | 0.530808i | \(-0.821889\pi\) | ||||
0.847492 | − | 0.530808i | \(-0.178111\pi\) | |||||||
\(108\) | − 193.386i | − 0.172301i | ||||||||
\(109\) | 838.865i | 0.737144i | 0.929599 | + | 0.368572i | \(0.120153\pi\) | ||||
−0.929599 | + | 0.368572i | \(0.879847\pi\) | |||||||
\(110\) | −430.165 | −0.372860 | ||||||||
\(111\) | 304.228 | 0.260144 | ||||||||
\(112\) | − 211.004i | − 0.178018i | ||||||||
\(113\) | − 2026.81i | − 1.68731i | −0.536885 | − | 0.843655i | \(-0.680399\pi\) | ||||
0.536885 | − | 0.843655i | \(-0.319601\pi\) | |||||||
\(114\) | − 208.831i | − 0.171569i | ||||||||
\(115\) | −1056.02 | −0.856301 | ||||||||
\(116\) | 38.9190i | 0.0311512i | ||||||||
\(117\) | −1375.96 | −1.08725 | ||||||||
\(118\) | −172.587 | −0.134643 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 190.505 | 0.144922 | ||||||||
\(121\) | 588.691 | 0.442292 | ||||||||
\(122\) | − 2581.45i | − 1.91569i | ||||||||
\(123\) | −521.423 | −0.382237 | ||||||||
\(124\) | − 259.418i | − 0.187874i | ||||||||
\(125\) | 1126.33i | 0.805937i | ||||||||
\(126\) | − 202.274i | − 0.143016i | ||||||||
\(127\) | 1600.30 | 1.11814 | 0.559070 | − | 0.829120i | \(-0.311158\pi\) | ||||
0.559070 | + | 0.829120i | \(0.311158\pi\) | |||||||
\(128\) | −1743.94 | −1.20425 | ||||||||
\(129\) | − 630.909i | − 0.430608i | ||||||||
\(130\) | 943.133i | 0.636294i | ||||||||
\(131\) | 2615.07i | 1.74412i | 0.489397 | + | 0.872061i | \(0.337217\pi\) | ||||
−0.489397 | + | 0.872061i | \(0.662783\pi\) | |||||||
\(132\) | −105.305 | −0.0694364 | ||||||||
\(133\) | − 92.6360i | − 0.0603952i | ||||||||
\(134\) | −2305.35 | −1.48621 | ||||||||
\(135\) | 498.946 | 0.318092 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 745.711 | 0.465039 | 0.232520 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232520 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(138\) | −1324.07 | −0.816754 | ||||||||
\(139\) | − 2532.45i | − 1.54532i | −0.634818 | − | 0.772661i | \(-0.718925\pi\) | ||||
0.634818 | − | 0.772661i | \(-0.281075\pi\) | |||||||
\(140\) | −27.0696 | −0.0163414 | ||||||||
\(141\) | − 656.047i | − 0.391837i | ||||||||
\(142\) | − 1983.75i | − 1.17234i | ||||||||
\(143\) | 1627.51i | 0.951740i | ||||||||
\(144\) | −1745.09 | −1.00989 | ||||||||
\(145\) | −100.413 | −0.0575094 | ||||||||
\(146\) | − 1565.36i | − 0.887332i | ||||||||
\(147\) | − 667.597i | − 0.374574i | ||||||||
\(148\) | 296.514i | 0.164684i | ||||||||
\(149\) | −1816.70 | −0.998858 | −0.499429 | − | 0.866355i | \(-0.666457\pi\) | ||||
−0.499429 | + | 0.866355i | \(0.666457\pi\) | |||||||
\(150\) | 627.388i | 0.341507i | ||||||||
\(151\) | 2120.50 | 1.14280 | 0.571402 | − | 0.820670i | \(-0.306400\pi\) | ||||
0.571402 | + | 0.820670i | \(0.306400\pi\) | |||||||
\(152\) | −635.404 | −0.339066 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −239.252 | −0.125191 | ||||||||
\(155\) | 669.314 | 0.346842 | ||||||||
\(156\) | 230.880i | 0.118495i | ||||||||
\(157\) | −1607.82 | −0.817314 | −0.408657 | − | 0.912688i | \(-0.634003\pi\) | ||||
−0.408657 | + | 0.912688i | \(0.634003\pi\) | |||||||
\(158\) | − 283.845i | − 0.142921i | ||||||||
\(159\) | − 618.404i | − 0.308444i | ||||||||
\(160\) | 430.826i | 0.212874i | ||||||||
\(161\) | −587.346 | −0.287511 | ||||||||
\(162\) | −1335.30 | −0.647599 | ||||||||
\(163\) | 2278.00i | 1.09464i | 0.836922 | + | 0.547322i | \(0.184353\pi\) | ||||
−0.836922 | + | 0.547322i | \(0.815647\pi\) | |||||||
\(164\) | − 508.202i | − 0.241975i | ||||||||
\(165\) | − 271.692i | − 0.128189i | ||||||||
\(166\) | 1147.74 | 0.536638 | ||||||||
\(167\) | − 1652.12i | − 0.765538i | −0.923844 | − | 0.382769i | \(-0.874971\pi\) | ||||
0.923844 | − | 0.382769i | \(-0.125029\pi\) | |||||||
\(168\) | 105.956 | 0.0486590 | ||||||||
\(169\) | 1371.29 | 0.624165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −766.135 | −0.342619 | ||||||||
\(172\) | 614.912 | 0.272597 | ||||||||
\(173\) | 2210.82i | 0.971595i | 0.874071 | + | 0.485797i | \(0.161471\pi\) | ||||
−0.874071 | + | 0.485797i | \(0.838529\pi\) | |||||||
\(174\) | −125.901 | −0.0548534 | ||||||||
\(175\) | 278.304i | 0.120216i | ||||||||
\(176\) | 2064.11i | 0.884023i | ||||||||
\(177\) | − 109.006i | − 0.0462903i | ||||||||
\(178\) | 605.608 | 0.255013 | ||||||||
\(179\) | −20.7548 | −0.00866640 | −0.00433320 | − | 0.999991i | \(-0.501379\pi\) | ||||
−0.00433320 | + | 0.999991i | \(0.501379\pi\) | |||||||
\(180\) | 223.876i | 0.0927042i | ||||||||
\(181\) | 436.498i | 0.179252i | 0.995975 | + | 0.0896262i | \(0.0285672\pi\) | ||||
−0.995975 | + | 0.0896262i | \(0.971433\pi\) | |||||||
\(182\) | 524.558i | 0.213642i | ||||||||
\(183\) | 1630.45 | 0.658612 | ||||||||
\(184\) | 4028.69i | 1.61413i | ||||||||
\(185\) | −765.023 | −0.304030 | ||||||||
\(186\) | 839.202 | 0.330824 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 639.412 | 0.248053 | ||||||||
\(189\) | 277.507 | 0.106803 | ||||||||
\(190\) | 525.136i | 0.200512i | ||||||||
\(191\) | 787.808 | 0.298449 | 0.149225 | − | 0.988803i | \(-0.452322\pi\) | ||||
0.149225 | + | 0.988803i | \(0.452322\pi\) | |||||||
\(192\) | − 666.758i | − 0.250620i | ||||||||
\(193\) | − 3726.86i | − 1.38998i | −0.719021 | − | 0.694988i | \(-0.755410\pi\) | ||||
0.719021 | − | 0.694988i | \(-0.244590\pi\) | |||||||
\(194\) | − 4257.06i | − 1.57546i | ||||||||
\(195\) | −595.683 | −0.218758 | ||||||||
\(196\) | 650.669 | 0.237124 | ||||||||
\(197\) | − 451.885i | − 0.163429i | −0.996656 | − | 0.0817144i | \(-0.973960\pi\) | ||||
0.996656 | − | 0.0817144i | \(-0.0260395\pi\) | |||||||
\(198\) | 1978.71i | 0.710206i | ||||||||
\(199\) | − 3480.16i | − 1.23971i | −0.784716 | − | 0.619855i | \(-0.787191\pi\) | ||||
0.784716 | − | 0.619855i | \(-0.212809\pi\) | |||||||
\(200\) | 1908.93 | 0.674910 | ||||||||
\(201\) | − 1456.06i | − 0.510958i | ||||||||
\(202\) | 958.551 | 0.333878 | ||||||||
\(203\) | −55.8485 | −0.0193093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1311.19 | 0.446719 | ||||||||
\(206\) | −3116.71 | −1.05413 | ||||||||
\(207\) | 4857.58i | 1.63104i | ||||||||
\(208\) | 4525.54 | 1.50860 | ||||||||
\(209\) | 906.194i | 0.299917i | ||||||||
\(210\) | − 87.5686i | − 0.0287753i | ||||||||
\(211\) | 1818.51i | 0.593323i | 0.954983 | + | 0.296661i | \(0.0958732\pi\) | ||||
−0.954983 | + | 0.296661i | \(0.904127\pi\) | |||||||
\(212\) | 602.724 | 0.195261 | ||||||||
\(213\) | 1252.94 | 0.403051 | ||||||||
\(214\) | 3704.72i | 1.18341i | ||||||||
\(215\) | 1586.51i | 0.503251i | ||||||||
\(216\) | − 1903.46i | − 0.599603i | ||||||||
\(217\) | 372.263 | 0.116456 | ||||||||
\(218\) | − 2644.87i | − 0.821712i | ||||||||
\(219\) | 988.684 | 0.305064 | ||||||||
\(220\) | 264.803 | 0.0811502 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −959.205 | −0.289989 | ||||||||
\(223\) | 6507.83 | 1.95425 | 0.977123 | − | 0.212676i | \(-0.0682178\pi\) | ||||
0.977123 | + | 0.212676i | \(0.0682178\pi\) | |||||||
\(224\) | 239.620i | 0.0714744i | ||||||||
\(225\) | 2301.69 | 0.681981 | ||||||||
\(226\) | 6390.36i | 1.88089i | ||||||||
\(227\) | 2427.16i | 0.709676i | 0.934928 | + | 0.354838i | \(0.115464\pi\) | ||||
−0.934928 | + | 0.354838i | \(0.884536\pi\) | |||||||
\(228\) | 128.554i | 0.0373407i | ||||||||
\(229\) | −655.706 | −0.189215 | −0.0946076 | − | 0.995515i | \(-0.530160\pi\) | ||||
−0.0946076 | + | 0.995515i | \(0.530160\pi\) | |||||||
\(230\) | 3329.55 | 0.954540 | ||||||||
\(231\) | − 151.112i | − 0.0430408i | ||||||||
\(232\) | 383.073i | 0.108405i | ||||||||
\(233\) | − 1171.70i | − 0.329445i | −0.986340 | − | 0.164723i | \(-0.947327\pi\) | ||||
0.986340 | − | 0.164723i | \(-0.0526729\pi\) | |||||||
\(234\) | 4338.30 | 1.21198 | ||||||||
\(235\) | 1649.72i | 0.457940i | ||||||||
\(236\) | 106.242 | 0.0293041 | ||||||||
\(237\) | 179.277 | 0.0491361 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5281.06 | −1.42930 | −0.714651 | − | 0.699481i | \(-0.753415\pi\) | ||||
−0.714651 | + | 0.699481i | \(0.753415\pi\) | |||||||
\(240\) | −755.484 | −0.203193 | ||||||||
\(241\) | 1327.84i | 0.354912i | 0.984129 | + | 0.177456i | \(0.0567867\pi\) | ||||
−0.984129 | + | 0.177456i | \(0.943213\pi\) | |||||||
\(242\) | −1856.09 | −0.493034 | ||||||||
\(243\) | − 3533.59i | − 0.932839i | ||||||||
\(244\) | 1589.11i | 0.416935i | ||||||||
\(245\) | 1678.77i | 0.437765i | ||||||||
\(246\) | 1644.00 | 0.426089 | ||||||||
\(247\) | 1986.82 | 0.511815 | ||||||||
\(248\) | − 2553.41i | − 0.653797i | ||||||||
\(249\) | 724.912i | 0.184496i | ||||||||
\(250\) | − 3551.23i | − 0.898397i | ||||||||
\(251\) | −4280.39 | −1.07640 | −0.538198 | − | 0.842818i | \(-0.680895\pi\) | ||||
−0.538198 | + | 0.842818i | \(0.680895\pi\) | |||||||
\(252\) | 124.517i | 0.0311263i | ||||||||
\(253\) | 5745.60 | 1.42776 | ||||||||
\(254\) | −5045.62 | −1.24642 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2819.92 | 0.688458 | ||||||||
\(257\) | −242.890 | −0.0589536 | −0.0294768 | − | 0.999565i | \(-0.509384\pi\) | ||||
−0.0294768 | + | 0.999565i | \(0.509384\pi\) | |||||||
\(258\) | 1989.20i | 0.480010i | ||||||||
\(259\) | −425.496 | −0.102081 | ||||||||
\(260\) | − 580.579i | − 0.138485i | ||||||||
\(261\) | 461.889i | 0.109541i | ||||||||
\(262\) | − 8245.11i | − 1.94422i | ||||||||
\(263\) | 3153.49 | 0.739364 | 0.369682 | − | 0.929158i | \(-0.379467\pi\) | ||||
0.369682 | + | 0.929158i | \(0.379467\pi\) | |||||||
\(264\) | −1036.50 | −0.241636 | ||||||||
\(265\) | 1555.06i | 0.360478i | ||||||||
\(266\) | 292.074i | 0.0673240i | ||||||||
\(267\) | 382.502i | 0.0876732i | ||||||||
\(268\) | 1419.14 | 0.323462 | ||||||||
\(269\) | 210.898i | 0.0478018i | 0.999714 | + | 0.0239009i | \(0.00760862\pi\) | ||||
−0.999714 | + | 0.0239009i | \(0.992391\pi\) | |||||||
\(270\) | −1573.14 | −0.354585 | ||||||||
\(271\) | −1627.36 | −0.364780 | −0.182390 | − | 0.983226i | \(-0.558383\pi\) | ||||
−0.182390 | + | 0.983226i | \(0.558383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −331.311 | −0.0734500 | ||||||||
\(274\) | −2351.16 | −0.518391 | ||||||||
\(275\) | − 2722.46i | − 0.596984i | ||||||||
\(276\) | 815.076 | 0.177760 | ||||||||
\(277\) | 4626.89i | 1.00362i | 0.864978 | + | 0.501810i | \(0.167332\pi\) | ||||
−0.864978 | + | 0.501810i | \(0.832668\pi\) | |||||||
\(278\) | 7984.62i | 1.72261i | ||||||||
\(279\) | − 3078.76i | − 0.660648i | ||||||||
\(280\) | −266.442 | −0.0568677 | ||||||||
\(281\) | 5076.28 | 1.07767 | 0.538836 | − | 0.842411i | \(-0.318864\pi\) | ||||
0.538836 | + | 0.842411i | \(0.318864\pi\) | |||||||
\(282\) | 2068.46i | 0.436791i | ||||||||
\(283\) | − 2437.04i | − 0.511898i | −0.966690 | − | 0.255949i | \(-0.917612\pi\) | ||||
0.966690 | − | 0.255949i | \(-0.0823879\pi\) | |||||||
\(284\) | 1221.17i | 0.255151i | ||||||||
\(285\) | −331.676 | −0.0689360 | ||||||||
\(286\) | − 5131.39i | − 1.06093i | ||||||||
\(287\) | 729.266 | 0.149990 | ||||||||
\(288\) | 1981.75 | 0.405471 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 316.595 | 0.0641072 | ||||||||
\(291\) | 2688.76 | 0.541642 | ||||||||
\(292\) | 963.616i | 0.193121i | ||||||||
\(293\) | −3300.30 | −0.658041 | −0.329020 | − | 0.944323i | \(-0.606718\pi\) | ||||
−0.329020 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(294\) | 2104.88i | 0.417547i | ||||||||
\(295\) | 274.111i | 0.0540994i | ||||||||
\(296\) | 2918.54i | 0.573097i | ||||||||
\(297\) | −2714.66 | −0.530372 | ||||||||
\(298\) | 5727.91 | 1.11345 | ||||||||
\(299\) | − 12597.2i | − 2.43650i | ||||||||
\(300\) | − 386.211i | − 0.0743263i | ||||||||
\(301\) | 882.395i | 0.168971i | ||||||||
\(302\) | −6685.75 | −1.27391 | ||||||||
\(303\) | 605.420i | 0.114787i | ||||||||
\(304\) | 2519.82 | 0.475399 | ||||||||
\(305\) | −4099.98 | −0.769719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1186.40 | −0.220558 | −0.110279 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110279 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(308\) | 147.280 | 0.0272470 | ||||||||
\(309\) | − 1968.51i | − 0.362410i | ||||||||
\(310\) | −2110.29 | −0.386634 | ||||||||
\(311\) | − 657.473i | − 0.119877i | −0.998202 | − | 0.0599387i | \(-0.980909\pi\) | ||||
0.998202 | − | 0.0599387i | \(-0.0190905\pi\) | |||||||
\(312\) | 2272.51i | 0.412358i | ||||||||
\(313\) | 6073.66i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(314\) | 5069.34 | 0.911080 | ||||||||
\(315\) | −321.261 | −0.0574635 | ||||||||
\(316\) | 174.731i | 0.0311056i | ||||||||
\(317\) | − 5753.26i | − 1.01935i | −0.860366 | − | 0.509677i | \(-0.829765\pi\) | ||||
0.860366 | − | 0.509677i | \(-0.170235\pi\) | |||||||
\(318\) | 1949.78i | 0.343830i | ||||||||
\(319\) | 546.327 | 0.0958886 | ||||||||
\(320\) | 1676.66i | 0.292900i | ||||||||
\(321\) | −2339.90 | −0.406855 | ||||||||
\(322\) | 1851.85 | 0.320496 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 821.991 | 0.140945 | ||||||||
\(325\) | −5968.97 | −1.01877 | ||||||||
\(326\) | − 7182.35i | − 1.22023i | ||||||||
\(327\) | 1670.50 | 0.282504 | ||||||||
\(328\) | − 5002.15i | − 0.842066i | ||||||||
\(329\) | 917.553i | 0.153758i | ||||||||
\(330\) | 856.623i | 0.142896i | ||||||||
\(331\) | 89.8427 | 0.0149190 | 0.00745952 | − | 0.999972i | \(-0.497626\pi\) | ||||
0.00745952 | + | 0.999972i | \(0.497626\pi\) | |||||||
\(332\) | −706.532 | −0.116795 | ||||||||
\(333\) | 3519.01i | 0.579101i | ||||||||
\(334\) | 5209.00i | 0.853364i | ||||||||
\(335\) | 3661.47i | 0.597156i | ||||||||
\(336\) | −420.190 | −0.0682240 | ||||||||
\(337\) | − 847.308i | − 0.136961i | −0.997652 | − | 0.0684804i | \(-0.978185\pi\) | ||||
0.997652 | − | 0.0684804i | \(-0.0218151\pi\) | |||||||
\(338\) | −4323.56 | −0.695772 | ||||||||
\(339\) | −4036.15 | −0.646648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3641.60 | −0.578309 | ||||||||
\(342\) | 2415.56 | 0.381926 | ||||||||
\(343\) | 1889.02i | 0.297369i | ||||||||
\(344\) | 6052.48 | 0.948628 | ||||||||
\(345\) | 2102.94i | 0.328170i | ||||||||
\(346\) | − 6970.55i | − 1.08306i | ||||||||
\(347\) | − 590.322i | − 0.0913260i | −0.998957 | − | 0.0456630i | \(-0.985460\pi\) | ||||
0.998957 | − | 0.0456630i | \(-0.0145400\pi\) | |||||||
\(348\) | 77.5026 | 0.0119384 | ||||||||
\(349\) | −9387.68 | −1.43986 | −0.719930 | − | 0.694047i | \(-0.755826\pi\) | ||||
−0.719930 | + | 0.694047i | \(0.755826\pi\) | |||||||
\(350\) | − 877.471i | − 0.134008i | ||||||||
\(351\) | 5951.87i | 0.905092i | ||||||||
\(352\) | − 2344.03i | − 0.354936i | ||||||||
\(353\) | −6176.09 | −0.931218 | −0.465609 | − | 0.884990i | \(-0.654165\pi\) | ||||
−0.465609 | + | 0.884990i | \(0.654165\pi\) | |||||||
\(354\) | 343.687i | 0.0516009i | ||||||||
\(355\) | −3150.68 | −0.471045 | ||||||||
\(356\) | −372.804 | −0.0555015 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 65.4382 | 0.00966066 | ||||||||
\(359\) | −7151.14 | −1.05132 | −0.525658 | − | 0.850696i | \(-0.676181\pi\) | ||||
−0.525658 | + | 0.850696i | \(0.676181\pi\) | |||||||
\(360\) | 2203.58i | 0.322608i | ||||||||
\(361\) | −5752.74 | −0.838714 | ||||||||
\(362\) | − 1376.24i | − 0.199817i | ||||||||
\(363\) | − 1172.31i | − 0.169505i | ||||||||
\(364\) | − 322.910i | − 0.0464975i | ||||||||
\(365\) | −2486.18 | −0.356528 | ||||||||
\(366\) | −5140.66 | −0.734171 | ||||||||
\(367\) | 3358.05i | 0.477626i | 0.971066 | + | 0.238813i | \(0.0767583\pi\) | ||||
−0.971066 | + | 0.238813i | \(0.923242\pi\) | |||||||
\(368\) | − 15976.6i | − 2.26314i | ||||||||
\(369\) | − 6031.32i | − 0.850888i | ||||||||
\(370\) | 2412.05 | 0.338910 | ||||||||
\(371\) | 864.905i | 0.121034i | ||||||||
\(372\) | −516.600 | −0.0720013 | ||||||||
\(373\) | 8379.14 | 1.16315 | 0.581576 | − | 0.813492i | \(-0.302436\pi\) | ||||
0.581576 | + | 0.813492i | \(0.302436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2242.95 | 0.308868 | ||||||||
\(376\) | 6293.64 | 0.863217 | ||||||||
\(377\) | − 1197.82i | − 0.163636i | ||||||||
\(378\) | −874.957 | −0.119055 | ||||||||
\(379\) | − 6395.71i | − 0.866821i | −0.901196 | − | 0.433411i | \(-0.857310\pi\) | ||||
0.901196 | − | 0.433411i | \(-0.142690\pi\) | |||||||
\(380\) | − 323.266i | − 0.0436400i | ||||||||
\(381\) | − 3186.81i | − 0.428518i | ||||||||
\(382\) | −2483.89 | −0.332689 | ||||||||
\(383\) | 204.687 | 0.0273081 | 0.0136541 | − | 0.999907i | \(-0.495654\pi\) | ||||
0.0136541 | + | 0.999907i | \(0.495654\pi\) | |||||||
\(384\) | 3472.85i | 0.461518i | ||||||||
\(385\) | 379.991i | 0.0503017i | ||||||||
\(386\) | 11750.5i | 1.54944i | ||||||||
\(387\) | 7297.75 | 0.958567 | ||||||||
\(388\) | 2620.59i | 0.342887i | ||||||||
\(389\) | −5770.56 | −0.752131 | −0.376066 | − | 0.926593i | \(-0.622723\pi\) | ||||
−0.376066 | + | 0.926593i | \(0.622723\pi\) | |||||||
\(390\) | 1878.14 | 0.243854 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6404.44 | 0.825186 | ||||||||
\(393\) | 5207.61 | 0.668420 | ||||||||
\(394\) | 1424.76i | 0.182178i | ||||||||
\(395\) | −450.816 | −0.0574253 | ||||||||
\(396\) | − 1218.06i | − 0.154571i | ||||||||
\(397\) | − 7144.37i | − 0.903188i | −0.892223 | − | 0.451594i | \(-0.850855\pi\) | ||||
0.892223 | − | 0.451594i | \(-0.149145\pi\) | |||||||
\(398\) | 10972.7i | 1.38194i | ||||||||
\(399\) | −184.474 | −0.0231459 | ||||||||
\(400\) | −7570.24 | −0.946280 | ||||||||
\(401\) | 6364.52i | 0.792591i | 0.918123 | + | 0.396296i | \(0.129704\pi\) | ||||
−0.918123 | + | 0.396296i | \(0.870296\pi\) | |||||||
\(402\) | 4590.84i | 0.569578i | ||||||||
\(403\) | 7984.16i | 0.986897i | ||||||||
\(404\) | −590.070 | −0.0726660 | ||||||||
\(405\) | 2120.78i | 0.260204i | ||||||||
\(406\) | 176.086 | 0.0215246 | ||||||||
\(407\) | 4162.33 | 0.506926 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2997.87 | 0.362433 | 0.181217 | − | 0.983443i | \(-0.441997\pi\) | ||||
0.181217 | + | 0.983443i | \(0.441997\pi\) | |||||||
\(410\) | −4134.07 | −0.497969 | ||||||||
\(411\) | − 1485.00i | − 0.178222i | ||||||||
\(412\) | 1918.60 | 0.229424 | ||||||||
\(413\) | 152.457i | 0.0181644i | ||||||||
\(414\) | − 15315.5i | − 1.81816i | ||||||||
\(415\) | − 1822.89i | − 0.215620i | ||||||||
\(416\) | −5139.27 | −0.605705 | ||||||||
\(417\) | −5043.08 | −0.592232 | ||||||||
\(418\) | − 2857.15i | − 0.334325i | ||||||||
\(419\) | 11747.3i | 1.36967i | 0.728698 | + | 0.684835i | \(0.240126\pi\) | ||||
−0.728698 | + | 0.684835i | \(0.759874\pi\) | |||||||
\(420\) | 53.9060i | 0.00626272i | ||||||||
\(421\) | 8842.15 | 1.02361 | 0.511805 | − | 0.859102i | \(-0.328977\pi\) | ||||
0.511805 | + | 0.859102i | \(0.328977\pi\) | |||||||
\(422\) | − 5733.60i | − 0.661391i | ||||||||
\(423\) | 7588.52 | 0.872261 | ||||||||
\(424\) | 5932.52 | 0.679501 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3950.41 | −0.449291 | ||||||||
\(427\) | −2280.36 | −0.258441 | ||||||||
\(428\) | − 2280.57i | − 0.257560i | ||||||||
\(429\) | 3240.98 | 0.364746 | ||||||||
\(430\) | − 5002.13i | − 0.560987i | ||||||||
\(431\) | − 3099.38i | − 0.346385i | −0.984888 | − | 0.173192i | \(-0.944592\pi\) | ||||
0.984888 | − | 0.173192i | \(-0.0554082\pi\) | |||||||
\(432\) | 7548.55i | 0.840694i | ||||||||
\(433\) | −10072.8 | −1.11794 | −0.558970 | − | 0.829188i | \(-0.688803\pi\) | ||||
−0.558970 | + | 0.829188i | \(0.688803\pi\) | |||||||
\(434\) | −1173.72 | −0.129816 | ||||||||
\(435\) | 199.961i | 0.0220400i | ||||||||
\(436\) | 1628.14i | 0.178839i | ||||||||
\(437\) | − 7014.09i | − 0.767802i | ||||||||
\(438\) | −3117.24 | −0.340063 | ||||||||
\(439\) | 17357.9i | 1.88712i | 0.331199 | + | 0.943561i | \(0.392547\pi\) | ||||
−0.331199 | + | 0.943561i | \(0.607453\pi\) | |||||||
\(440\) | 2606.42 | 0.282400 | ||||||||
\(441\) | 7722.12 | 0.833832 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6979.90 | 0.748589 | 0.374295 | − | 0.927310i | \(-0.377885\pi\) | ||||
0.374295 | + | 0.927310i | \(0.377885\pi\) | |||||||
\(444\) | 590.472 | 0.0631139 | ||||||||
\(445\) | − 961.855i | − 0.102464i | ||||||||
\(446\) | −20518.7 | −2.17845 | ||||||||
\(447\) | 3617.74i | 0.382804i | ||||||||
\(448\) | 932.533i | 0.0983439i | ||||||||
\(449\) | − 9230.50i | − 0.970188i | −0.874462 | − | 0.485094i | \(-0.838785\pi\) | ||||
0.874462 | − | 0.485094i | \(-0.161215\pi\) | |||||||
\(450\) | −7257.03 | −0.760221 | ||||||||
\(451\) | −7133.91 | −0.744840 | ||||||||
\(452\) | − 3933.81i | − 0.409361i | ||||||||
\(453\) | − 4222.72i | − 0.437970i | ||||||||
\(454\) | − 7652.64i | − 0.791093i | ||||||||
\(455\) | 833.127 | 0.0858409 | ||||||||
\(456\) | 1265.33i | 0.129944i | ||||||||
\(457\) | −12250.6 | −1.25396 | −0.626979 | − | 0.779036i | \(-0.715709\pi\) | ||||
−0.626979 | + | 0.779036i | \(0.715709\pi\) | |||||||
\(458\) | 2067.39 | 0.210923 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2049.62 | −0.207748 | ||||||||
\(461\) | −6259.50 | −0.632395 | −0.316198 | − | 0.948693i | \(-0.602406\pi\) | ||||
−0.316198 | + | 0.948693i | \(0.602406\pi\) | |||||||
\(462\) | 476.442i | 0.0479786i | ||||||||
\(463\) | 10195.0 | 1.02333 | 0.511665 | − | 0.859185i | \(-0.329029\pi\) | ||||
0.511665 | + | 0.859185i | \(0.329029\pi\) | |||||||
\(464\) | − 1519.15i | − 0.151993i | ||||||||
\(465\) | − 1332.86i | − 0.132924i | ||||||||
\(466\) | 3694.28i | 0.367241i | ||||||||
\(467\) | 14783.0 | 1.46483 | 0.732417 | − | 0.680856i | \(-0.238392\pi\) | ||||
0.732417 | + | 0.680856i | \(0.238392\pi\) | |||||||
\(468\) | −2670.59 | −0.263778 | ||||||||
\(469\) | 2036.46i | 0.200501i | ||||||||
\(470\) | − 5201.43i | − 0.510477i | ||||||||
\(471\) | 3201.79i | 0.313229i | ||||||||
\(472\) | 1045.72 | 0.101977 | ||||||||
\(473\) | − 8631.86i | − 0.839098i | ||||||||
\(474\) | −565.244 | −0.0547732 | ||||||||
\(475\) | −3323.52 | −0.321039 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7153.10 | 0.686620 | ||||||||
\(478\) | 16650.7 | 1.59328 | ||||||||
\(479\) | − 16370.0i | − 1.56152i | −0.624834 | − | 0.780758i | \(-0.714833\pi\) | ||||
0.624834 | − | 0.780758i | \(-0.285167\pi\) | |||||||
\(480\) | 857.939 | 0.0815820 | ||||||||
\(481\) | − 9125.87i | − 0.865081i | ||||||||
\(482\) | − 4186.57i | − 0.395629i | ||||||||
\(483\) | 1169.63i | 0.110186i | ||||||||
\(484\) | 1142.58 | 0.107305 | ||||||||
\(485\) | −6761.26 | −0.633017 | ||||||||
\(486\) | 11141.1i | 1.03986i | ||||||||
\(487\) | 4106.31i | 0.382084i | 0.981582 | + | 0.191042i | \(0.0611866\pi\) | ||||
−0.981582 | + | 0.191042i | \(0.938813\pi\) | |||||||
\(488\) | 15641.3i | 1.45092i | ||||||||
\(489\) | 4536.37 | 0.419513 | ||||||||
\(490\) | − 5293.01i | − 0.487987i | ||||||||
\(491\) | 878.001 | 0.0806999 | 0.0403499 | − | 0.999186i | \(-0.487153\pi\) | ||||
0.0403499 | + | 0.999186i | \(0.487153\pi\) | |||||||
\(492\) | −1012.02 | −0.0927349 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −6264.28 | −0.570533 | ||||||||
\(495\) | 3142.68 | 0.285359 | ||||||||
\(496\) | 10126.0i | 0.916679i | ||||||||
\(497\) | −1752.37 | −0.158158 | ||||||||
\(498\) | − 2285.59i | − 0.205662i | ||||||||
\(499\) | 13819.6i | 1.23978i | 0.784687 | + | 0.619892i | \(0.212824\pi\) | ||||
−0.784687 | + | 0.619892i | \(0.787176\pi\) | |||||||
\(500\) | 2186.08i | 0.195529i | ||||||||
\(501\) | −3290.00 | −0.293386 | ||||||||
\(502\) | 13495.7 | 1.19989 | ||||||||
\(503\) | − 4721.43i | − 0.418525i | −0.977859 | − | 0.209263i | \(-0.932894\pi\) | ||||
0.977859 | − | 0.209263i | \(-0.0671063\pi\) | |||||||
\(504\) | 1225.60i | 0.108319i | ||||||||
\(505\) | − 1522.41i | − 0.134152i | ||||||||
\(506\) | −18115.4 | −1.59156 | ||||||||
\(507\) | − 2730.76i | − 0.239206i | ||||||||
\(508\) | 3106.01 | 0.271273 | ||||||||
\(509\) | −16554.3 | −1.44156 | −0.720782 | − | 0.693161i | \(-0.756217\pi\) | ||||
−0.720782 | + | 0.693161i | \(0.756217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1382.78 | −0.119708 | ||||||||
\(512\) | 5060.53 | 0.436808 | ||||||||
\(513\) | 3314.00i | 0.285217i | ||||||||
\(514\) | 765.813 | 0.0657171 | ||||||||
\(515\) | 4950.09i | 0.423548i | ||||||||
\(516\) | − 1224.53i | − 0.104470i | ||||||||
\(517\) | − 8975.79i | − 0.763548i | ||||||||
\(518\) | 1341.55 | 0.113792 | ||||||||
\(519\) | 4402.60 | 0.372356 | ||||||||
\(520\) | − 5714.55i | − 0.481922i | ||||||||
\(521\) | − 14755.5i | − 1.24079i | −0.784290 | − | 0.620394i | \(-0.786973\pi\) | ||||
0.784290 | − | 0.620394i | \(-0.213027\pi\) | |||||||
\(522\) | − 1456.30i | − 0.122108i | ||||||||
\(523\) | 7800.86 | 0.652214 | 0.326107 | − | 0.945333i | \(-0.394263\pi\) | ||||
0.326107 | + | 0.945333i | \(0.394263\pi\) | |||||||
\(524\) | 5075.57i | 0.423144i | ||||||||
\(525\) | 554.210 | 0.0460719 | ||||||||
\(526\) | −9942.71 | −0.824188 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4110.43 | 0.338795 | ||||||||
\(529\) | −32304.9 | −2.65512 | ||||||||
\(530\) | − 4902.98i | − 0.401834i | ||||||||
\(531\) | 1260.88 | 0.103046 | ||||||||
\(532\) | − 179.796i | − 0.0146525i | ||||||||
\(533\) | 15641.0i | 1.27108i | ||||||||
\(534\) | − 1206.00i | − 0.0977315i | ||||||||
\(535\) | 5884.01 | 0.475491 | ||||||||
\(536\) | 13968.4 | 1.12564 | ||||||||
\(537\) | 41.3307i | 0.00332133i | ||||||||
\(538\) | − 664.944i | − 0.0532859i | ||||||||
\(539\) | − 9133.81i | − 0.729909i | ||||||||
\(540\) | 968.399 | 0.0771727 | ||||||||
\(541\) | − 23028.5i | − 1.83007i | −0.403369 | − | 0.915037i | \(-0.632161\pi\) | ||||
0.403369 | − | 0.915037i | \(-0.367839\pi\) | |||||||
\(542\) | 5130.95 | 0.406629 | ||||||||
\(543\) | 869.235 | 0.0686970 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4200.71 | −0.330162 | ||||||||
\(546\) | 1044.60 | 0.0818765 | ||||||||
\(547\) | − 2641.77i | − 0.206497i | −0.994656 | − | 0.103249i | \(-0.967076\pi\) | ||||
0.994656 | − | 0.103249i | \(-0.0329238\pi\) | |||||||
\(548\) | 1447.34 | 0.112824 | ||||||||
\(549\) | 18859.4i | 1.46612i | ||||||||
\(550\) | 8583.69i | 0.665473i | ||||||||
\(551\) | − 666.944i | − 0.0515658i | ||||||||
\(552\) | 8022.67 | 0.618601 | ||||||||
\(553\) | −250.738 | −0.0192811 | ||||||||
\(554\) | − 14588.2i | − 1.11876i | ||||||||
\(555\) | 1523.45i | 0.116517i | ||||||||
\(556\) | − 4915.21i | − 0.374913i | ||||||||
\(557\) | −19800.8 | −1.50626 | −0.753129 | − | 0.657873i | \(-0.771456\pi\) | ||||
−0.753129 | + | 0.657873i | \(0.771456\pi\) | |||||||
\(558\) | 9707.08i | 0.736440i | ||||||||
\(559\) | −18925.3 | −1.43194 | ||||||||
\(560\) | 1056.63 | 0.0797333 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16005.1 | −1.20131 | ||||||||
\(563\) | 9733.93 | 0.728661 | 0.364331 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364331 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(564\) | − 1273.31i | − 0.0950642i | ||||||||
\(565\) | 10149.5 | 0.755736 | ||||||||
\(566\) | 7683.80i | 0.570626i | ||||||||
\(567\) | 1179.55i | 0.0873660i | ||||||||
\(568\) | 12019.8i | 0.887919i | ||||||||
\(569\) | −6340.67 | −0.467161 | −0.233581 | − | 0.972337i | \(-0.575044\pi\) | ||||
−0.233581 | + | 0.972337i | \(0.575044\pi\) | |||||||
\(570\) | 1045.75 | 0.0768447 | ||||||||
\(571\) | − 12377.7i | − 0.907166i | −0.891214 | − | 0.453583i | \(-0.850146\pi\) | ||||
0.891214 | − | 0.453583i | \(-0.149854\pi\) | |||||||
\(572\) | 3158.81i | 0.230903i | ||||||||
\(573\) | − 1568.83i | − 0.114378i | ||||||||
\(574\) | −2299.32 | −0.167198 | ||||||||
\(575\) | 21072.3i | 1.52831i | ||||||||
\(576\) | 7712.41 | 0.557900 | ||||||||
\(577\) | −36.6040 | −0.00264098 | −0.00132049 | − | 0.999999i | \(-0.500420\pi\) | ||||
−0.00132049 | + | 0.999999i | \(0.500420\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7421.61 | −0.532697 | ||||||||
\(580\) | −194.891 | −0.0139524 | ||||||||
\(581\) | − 1013.87i | − 0.0723965i | ||||||||
\(582\) | −8477.44 | −0.603782 | ||||||||
\(583\) | − 8460.77i | − 0.601045i | ||||||||
\(584\) | 9484.72i | 0.672055i | ||||||||
\(585\) | − 6890.29i | − 0.486971i | ||||||||
\(586\) | 10405.6 | 0.733534 | ||||||||
\(587\) | 20350.4 | 1.43092 | 0.715462 | − | 0.698651i | \(-0.246216\pi\) | ||||
0.715462 | + | 0.698651i | \(0.246216\pi\) | |||||||
\(588\) | − 1295.73i | − 0.0908760i | ||||||||
\(589\) | 4445.58i | 0.310996i | ||||||||
\(590\) | − 864.248i | − 0.0603060i | ||||||||
\(591\) | −899.876 | −0.0626328 | ||||||||
\(592\) | − 11574.0i | − 0.803530i | ||||||||
\(593\) | 20387.4 | 1.41182 | 0.705910 | − | 0.708301i | \(-0.250538\pi\) | ||||
0.705910 | + | 0.708301i | \(0.250538\pi\) | |||||||
\(594\) | 8559.10 | 0.591219 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3526.02 | −0.242334 | ||||||||
\(597\) | −6930.33 | −0.475108 | ||||||||
\(598\) | 39717.8i | 2.71603i | ||||||||
\(599\) | 316.417 | 0.0215834 | 0.0107917 | − | 0.999942i | \(-0.496565\pi\) | ||||
0.0107917 | + | 0.999942i | \(0.496565\pi\) | |||||||
\(600\) | − 3801.41i | − 0.258653i | ||||||||
\(601\) | − 1331.85i | − 0.0903950i | −0.998978 | − | 0.0451975i | \(-0.985608\pi\) | ||||
0.998978 | − | 0.0451975i | \(-0.0143917\pi\) | |||||||
\(602\) | − 2782.12i | − 0.188357i | ||||||||
\(603\) | 16842.3 | 1.13743 | ||||||||
\(604\) | 4115.65 | 0.277257 | ||||||||
\(605\) | 2947.93i | 0.198100i | ||||||||
\(606\) | − 1908.84i | − 0.127956i | ||||||||
\(607\) | 13873.2i | 0.927668i | 0.885922 | + | 0.463834i | \(0.153527\pi\) | ||||
−0.885922 | + | 0.463834i | \(0.846473\pi\) | |||||||
\(608\) | −2861.54 | −0.190873 | ||||||||
\(609\) | 111.216i | 0.00740014i | ||||||||
\(610\) | 12926.9 | 0.858025 | ||||||||
\(611\) | −19679.3 | −1.30301 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15297.0 | 1.00790 | 0.503948 | − | 0.863734i | \(-0.331880\pi\) | ||||
0.503948 | + | 0.863734i | \(0.331880\pi\) | |||||||
\(614\) | 3740.61 | 0.245861 | ||||||||
\(615\) | − 2611.08i | − 0.171201i | ||||||||
\(616\) | 1449.66 | 0.0948186 | ||||||||
\(617\) | 15116.8i | 0.986354i | 0.869929 | + | 0.493177i | \(0.164165\pi\) | ||||
−0.869929 | + | 0.493177i | \(0.835835\pi\) | |||||||
\(618\) | 6206.55i | 0.403987i | ||||||||
\(619\) | − 22412.1i | − 1.45528i | −0.685960 | − | 0.727639i | \(-0.740618\pi\) | ||||
0.685960 | − | 0.727639i | \(-0.259382\pi\) | |||||||
\(620\) | 1299.06 | 0.0841479 | ||||||||
\(621\) | 21011.9 | 1.35778 | ||||||||
\(622\) | 2072.96i | 0.133630i | ||||||||
\(623\) | − 534.971i | − 0.0344031i | ||||||||
\(624\) | − 9012.08i | − 0.578160i | ||||||||
\(625\) | 6850.26 | 0.438417 | ||||||||
\(626\) | − 19149.7i | − 1.22265i | ||||||||
\(627\) | 1804.58 | 0.114941 | ||||||||
\(628\) | −3120.61 | −0.198290 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1012.91 | 0.0640560 | ||||||||
\(631\) | 4830.94 | 0.304781 | 0.152390 | − | 0.988320i | \(-0.451303\pi\) | ||||
0.152390 | + | 0.988320i | \(0.451303\pi\) | |||||||
\(632\) | 1719.85i | 0.108247i | ||||||||
\(633\) | 3621.34 | 0.227386 | ||||||||
\(634\) | 18139.6i | 1.13630i | ||||||||
\(635\) | 8013.68i | 0.500808i | ||||||||
\(636\) | − 1200.25i | − 0.0748320i | ||||||||
\(637\) | −20025.8 | −1.24561 | ||||||||
\(638\) | −1722.53 | −0.106889 | ||||||||
\(639\) | 14492.8i | 0.897222i | ||||||||
\(640\) | − 8732.96i | − 0.539376i | ||||||||
\(641\) | − 23007.3i | − 1.41768i | −0.705370 | − | 0.708839i | \(-0.749219\pi\) | ||||
0.705370 | − | 0.708839i | \(-0.250781\pi\) | |||||||
\(642\) | 7377.52 | 0.453532 | ||||||||
\(643\) | 5689.90i | 0.348970i | 0.984660 | + | 0.174485i | \(0.0558260\pi\) | ||||
−0.984660 | + | 0.174485i | \(0.944174\pi\) | |||||||
\(644\) | −1139.97 | −0.0697535 | ||||||||
\(645\) | 3159.35 | 0.192867 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15949.0 | −0.969122 | −0.484561 | − | 0.874758i | \(-0.661021\pi\) | ||||
−0.484561 | + | 0.874758i | \(0.661021\pi\) | |||||||
\(648\) | 8090.72 | 0.490484 | ||||||||
\(649\) | − 1491.38i | − 0.0902029i | ||||||||
\(650\) | 18819.7 | 1.13564 | ||||||||
\(651\) | − 741.318i | − 0.0446307i | ||||||||
\(652\) | 4421.35i | 0.265573i | ||||||||
\(653\) | 10764.6i | 0.645101i | 0.946552 | + | 0.322550i | \(0.104540\pi\) | ||||
−0.946552 | + | 0.322550i | \(0.895460\pi\) | |||||||
\(654\) | −5266.95 | −0.314914 | ||||||||
\(655\) | −13095.3 | −0.781182 | ||||||||
\(656\) | 19837.0i | 1.18065i | ||||||||
\(657\) | 11436.1i | 0.679097i | ||||||||
\(658\) | − 2892.97i | − 0.171398i | ||||||||
\(659\) | 25208.2 | 1.49010 | 0.745048 | − | 0.667011i | \(-0.232427\pi\) | ||||
0.745048 | + | 0.667011i | \(0.232427\pi\) | |||||||
\(660\) | − 527.325i | − 0.0311001i | ||||||||
\(661\) | −14419.5 | −0.848492 | −0.424246 | − | 0.905547i | \(-0.639461\pi\) | ||||
−0.424246 | + | 0.905547i | \(0.639461\pi\) | |||||||
\(662\) | −283.267 | −0.0166306 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6954.28 | −0.406444 | ||||||||
\(665\) | 463.885 | 0.0270506 | ||||||||
\(666\) | − 11095.2i | − 0.645539i | ||||||||
\(667\) | −4228.67 | −0.245479 | ||||||||
\(668\) | − 3206.58i | − 0.185728i | ||||||||
\(669\) | − 12959.6i | − 0.748948i | ||||||||
\(670\) | − 11544.3i | − 0.665665i | ||||||||
\(671\) | 22307.2 | 1.28339 | ||||||||
\(672\) | 477.174 | 0.0273920 | ||||||||
\(673\) | 2110.64i | 0.120890i | 0.998172 | + | 0.0604451i | \(0.0192520\pi\) | ||||
−0.998172 | + | 0.0604451i | \(0.980748\pi\) | |||||||
\(674\) | 2671.49i | 0.152674i | ||||||||
\(675\) | − 9956.17i | − 0.567723i | ||||||||
\(676\) | 2661.52 | 0.151429 | ||||||||
\(677\) | 11944.5i | 0.678087i | 0.940771 | + | 0.339043i | \(0.110103\pi\) | ||||
−0.940771 | + | 0.339043i | \(0.889897\pi\) | |||||||
\(678\) | 12725.6 | 0.720834 | ||||||||
\(679\) | −3760.52 | −0.212541 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4833.41 | 0.271977 | ||||||||
\(682\) | 11481.6 | 0.644656 | ||||||||
\(683\) | 19085.8i | 1.06925i | 0.845089 | + | 0.534626i | \(0.179547\pi\) | ||||
−0.845089 | + | 0.534626i | \(0.820453\pi\) | |||||||
\(684\) | −1486.98 | −0.0831232 | ||||||||
\(685\) | 3734.23i | 0.208288i | ||||||||
\(686\) | − 5955.92i | − 0.331484i | ||||||||
\(687\) | 1305.76i | 0.0725152i | ||||||||
\(688\) | −24002.3 | −1.33006 | ||||||||
\(689\) | −18550.2 | −1.02570 | ||||||||
\(690\) | − 6630.41i | − 0.365819i | ||||||||
\(691\) | 28316.8i | 1.55893i | 0.626445 | + | 0.779465i | \(0.284509\pi\) | ||||
−0.626445 | + | 0.779465i | \(0.715491\pi\) | |||||||
\(692\) | 4290.97i | 0.235720i | ||||||||
\(693\) | 1747.91 | 0.0958121 | ||||||||
\(694\) | 1861.24i | 0.101803i | ||||||||
\(695\) | 12681.5 | 0.692141 | ||||||||
\(696\) | 762.846 | 0.0415454 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 29598.6 | 1.60505 | ||||||||
\(699\) | −2333.31 | −0.126257 | ||||||||
\(700\) | 540.158i | 0.0291658i | ||||||||
\(701\) | −5916.75 | −0.318791 | −0.159396 | − | 0.987215i | \(-0.550955\pi\) | ||||
−0.159396 | + | 0.987215i | \(0.550955\pi\) | |||||||
\(702\) | − 18765.8i | − 1.00893i | ||||||||
\(703\) | − 5081.28i | − 0.272609i | ||||||||
\(704\) | − 9122.33i | − 0.488368i | ||||||||
\(705\) | 3285.22 | 0.175502 | ||||||||
\(706\) | 19472.7 | 1.03805 | ||||||||
\(707\) | − 846.747i | − 0.0450427i | ||||||||
\(708\) | − 211.568i | − 0.0112305i | ||||||||
\(709\) | − 18499.8i | − 0.979936i | −0.871740 | − | 0.489968i | \(-0.837008\pi\) | ||||
0.871740 | − | 0.489968i | \(-0.162992\pi\) | |||||||
\(710\) | 9933.85 | 0.525085 | ||||||||
\(711\) | 2073.70i | 0.109381i | ||||||||
\(712\) | −3669.45 | −0.193144 | ||||||||
\(713\) | 28186.6 | 1.48050 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8149.91 | −0.426279 | ||||||||
\(716\) | −40.2828 | −0.00210257 | ||||||||
\(717\) | 10516.6i | 0.547768i | ||||||||
\(718\) | 22546.9 | 1.17193 | ||||||||
\(719\) | − 22206.5i | − 1.15182i | −0.817511 | − | 0.575912i | \(-0.804647\pi\) | ||||
0.817511 | − | 0.575912i | \(-0.195353\pi\) | |||||||
\(720\) | − 8738.72i | − 0.452323i | ||||||||
\(721\) | 2753.18i | 0.142210i | ||||||||
\(722\) | 18137.9 | 0.934935 | ||||||||
\(723\) | 2644.24 | 0.136017 | ||||||||
\(724\) | 847.195i | 0.0434886i | ||||||||
\(725\) | 2003.69i | 0.102641i | ||||||||
\(726\) | 3696.19i | 0.188951i | ||||||||
\(727\) | 3777.02 | 0.192685 | 0.0963424 | − | 0.995348i | \(-0.469286\pi\) | ||||
0.0963424 | + | 0.995348i | \(0.469286\pi\) | |||||||
\(728\) | − 3178.36i | − 0.161810i | ||||||||
\(729\) | 4398.10 | 0.223447 | ||||||||
\(730\) | 7838.73 | 0.397431 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3164.52 | 0.159787 | ||||||||
\(733\) | 19956.4 | 1.00560 | 0.502801 | − | 0.864402i | \(-0.332303\pi\) | ||||
0.502801 | + | 0.864402i | \(0.332303\pi\) | |||||||
\(734\) | − 10587.7i | − 0.532422i | ||||||||
\(735\) | 3343.06 | 0.167770 | ||||||||
\(736\) | 18143.2i | 0.908652i | ||||||||
\(737\) | − 19921.3i | − 0.995671i | ||||||||
\(738\) | 19016.2i | 0.948506i | ||||||||
\(739\) | −23268.4 | −1.15824 | −0.579121 | − | 0.815241i | \(-0.696604\pi\) | ||||
−0.579121 | + | 0.815241i | \(0.696604\pi\) | |||||||
\(740\) | −1484.83 | −0.0737612 | ||||||||
\(741\) | − 3956.52i | − 0.196149i | ||||||||
\(742\) | − 2726.97i | − 0.134920i | ||||||||
\(743\) | 12587.1i | 0.621502i | 0.950491 | + | 0.310751i | \(0.100580\pi\) | ||||
−0.950491 | + | 0.310751i | \(0.899420\pi\) | |||||||
\(744\) | −5084.82 | −0.250562 | ||||||||
\(745\) | − 9097.32i | − 0.447383i | ||||||||
\(746\) | −26418.7 | −1.29659 | ||||||||
\(747\) | −8385.09 | −0.410702 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3272.61 | 0.159651 | ||||||||
\(750\) | −7071.85 | −0.344303 | ||||||||
\(751\) | 2662.79i | 0.129383i | 0.997905 | + | 0.0646914i | \(0.0206063\pi\) | ||||
−0.997905 | + | 0.0646914i | \(0.979394\pi\) | |||||||
\(752\) | −24958.6 | −1.21030 | ||||||||
\(753\) | 8523.89i | 0.412520i | ||||||||
\(754\) | 3776.62i | 0.182409i | ||||||||
\(755\) | 10618.6i | 0.511855i | ||||||||
\(756\) | 538.611 | 0.0259115 | ||||||||
\(757\) | −26430.2 | −1.26899 | −0.634493 | − | 0.772929i | \(-0.718791\pi\) | ||||
−0.634493 | + | 0.772929i | \(0.718791\pi\) | |||||||
\(758\) | 20165.1i | 0.966267i | ||||||||
\(759\) | − 11441.7i | − 0.547176i | ||||||||
\(760\) | − 3181.86i | − 0.151866i | ||||||||
\(761\) | −8469.75 | −0.403454 | −0.201727 | − | 0.979442i | \(-0.564655\pi\) | ||||
−0.201727 | + | 0.979442i | \(0.564655\pi\) | |||||||
\(762\) | 10047.8i | 0.477680i | ||||||||
\(763\) | −2336.38 | −0.110855 | ||||||||
\(764\) | 1529.05 | 0.0724071 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −645.361 | −0.0304410 | ||||||||
\(767\) | −3269.83 | −0.153933 | ||||||||
\(768\) | − 5615.54i | − 0.263846i | ||||||||
\(769\) | −8452.54 | −0.396367 | −0.198184 | − | 0.980165i | \(-0.563504\pi\) | ||||
−0.198184 | + | 0.980165i | \(0.563504\pi\) | |||||||
\(770\) | − 1198.08i | − 0.0560725i | ||||||||
\(771\) | 483.687i | 0.0225935i | ||||||||
\(772\) | − 7233.43i | − 0.337224i | ||||||||
\(773\) | −33936.2 | −1.57904 | −0.789521 | − | 0.613724i | \(-0.789671\pi\) | ||||
−0.789521 | + | 0.613724i | \(0.789671\pi\) | |||||||
\(774\) | −23009.2 | −1.06854 | ||||||||
\(775\) | − 13355.8i | − 0.619036i | ||||||||
\(776\) | 25794.0i | 1.19324i | ||||||||
\(777\) | 847.324i | 0.0391217i | ||||||||
\(778\) | 18194.1 | 0.838419 | ||||||||
\(779\) | 8708.91i | 0.400551i | ||||||||
\(780\) | −1156.15 | −0.0530730 | ||||||||
\(781\) | 17142.2 | 0.785399 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1997.95 | 0.0911887 | ||||||||
\(784\) | −25398.0 | −1.15698 | ||||||||
\(785\) | − 8051.35i | − 0.366070i | ||||||||
\(786\) | −16419.2 | −0.745105 | ||||||||
\(787\) | − 34379.1i | − 1.55716i | −0.627547 | − | 0.778578i | \(-0.715941\pi\) | ||||
0.627547 | − | 0.778578i | \(-0.284059\pi\) | |||||||
\(788\) | − 877.059i | − 0.0396497i | ||||||||
\(789\) | − 6279.81i | − 0.283355i | ||||||||
\(790\) | 1421.39 | 0.0640134 | ||||||||
\(791\) | 5645.00 | 0.253746 | ||||||||
\(792\) | − 11989.2i | − 0.537902i | ||||||||
\(793\) | − 48908.2i | − 2.19014i | ||||||||
\(794\) | 22525.6i | 1.00681i | ||||||||
\(795\) | 3096.72 | 0.138150 | ||||||||
\(796\) | − 6754.61i | − 0.300768i | ||||||||
\(797\) | 3329.26 | 0.147965 | 0.0739826 | − | 0.997260i | \(-0.476429\pi\) | ||||
0.0739826 | + | 0.997260i | \(0.476429\pi\) | |||||||
\(798\) | 581.630 | 0.0258014 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 8596.87 | 0.379932 | ||||||||
\(801\) | −4424.42 | −0.195167 | ||||||||
\(802\) | − 20066.8i | − 0.883521i | ||||||||
\(803\) | 13526.8 | 0.594459 | ||||||||
\(804\) | − 2826.05i | − 0.123964i | ||||||||
\(805\) | − 2941.20i | − 0.128775i | ||||||||
\(806\) | − 25173.4i | − 1.10012i | ||||||||
\(807\) | 419.979 | 0.0183196 | ||||||||
\(808\) | −5807.97 | −0.252876 | ||||||||
\(809\) | 7217.64i | 0.313670i | 0.987625 | + | 0.156835i | \(0.0501290\pi\) | ||||
−0.987625 | + | 0.156835i | \(0.949871\pi\) | |||||||
\(810\) | − 6686.66i | − 0.290056i | ||||||||
\(811\) | 36564.1i | 1.58316i | 0.611067 | + | 0.791579i | \(0.290741\pi\) | ||||
−0.611067 | + | 0.791579i | \(0.709259\pi\) | |||||||
\(812\) | −108.396 | −0.00468466 | ||||||||
\(813\) | 3240.70i | 0.139799i | ||||||||
\(814\) | −13123.5 | −0.565083 | ||||||||
\(815\) | −11407.3 | −0.490284 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10537.6 | −0.451240 | ||||||||
\(818\) | −9452.04 | −0.404013 | ||||||||
\(819\) | − 3832.29i | − 0.163505i | ||||||||
\(820\) | 2544.88 | 0.108379 | ||||||||
\(821\) | 23140.5i | 0.983691i | 0.870683 | + | 0.491845i | \(0.163677\pi\) | ||||
−0.870683 | + | 0.491845i | \(0.836323\pi\) | |||||||
\(822\) | 4682.07i | 0.198669i | ||||||||
\(823\) | 41287.9i | 1.74873i | 0.485269 | + | 0.874365i | \(0.338722\pi\) | ||||
−0.485269 | + | 0.874365i | \(0.661278\pi\) | |||||||
\(824\) | 18884.5 | 0.798388 | ||||||||
\(825\) | −5421.46 | −0.228789 | ||||||||
\(826\) | − 480.683i | − 0.0202483i | ||||||||
\(827\) | 10008.0i | 0.420811i | 0.977614 | + | 0.210405i | \(0.0674784\pi\) | ||||
−0.977614 | + | 0.210405i | \(0.932522\pi\) | |||||||
\(828\) | 9428.02i | 0.395708i | ||||||||
\(829\) | −44643.6 | −1.87037 | −0.935185 | − | 0.354159i | \(-0.884767\pi\) | ||||
−0.935185 | + | 0.354159i | \(0.884767\pi\) | |||||||
\(830\) | 5747.43i | 0.240357i | ||||||||
\(831\) | 9213.90 | 0.384629 | ||||||||
\(832\) | −20000.6 | −0.833410 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15900.4 | 0.660176 | ||||||||
\(835\) | 8273.17 | 0.342880 | ||||||||
\(836\) | 1758.82i | 0.0727633i | ||||||||
\(837\) | −13317.5 | −0.549964 | ||||||||
\(838\) | − 37038.2i | − 1.52681i | ||||||||
\(839\) | − 14235.3i | − 0.585765i | −0.956148 | − | 0.292882i | \(-0.905386\pi\) | ||||
0.956148 | − | 0.292882i | \(-0.0946145\pi\) | |||||||
\(840\) | 530.588i | 0.0217941i | ||||||||
\(841\) | 23986.9 | 0.983514 | ||||||||
\(842\) | −27878.6 | −1.14104 | ||||||||
\(843\) | − 10108.8i | − 0.413008i | ||||||||
\(844\) | 3529.52i | 0.143947i | ||||||||
\(845\) | 6866.88i | 0.279560i | ||||||||
\(846\) | −23926.0 | −0.972331 | ||||||||
\(847\) | 1639.60i | 0.0665140i | ||||||||
\(848\) | −23526.5 | −0.952717 | ||||||||
\(849\) | −4853.08 | −0.196181 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32217.1 | −1.29775 | ||||||||
\(852\) | 2431.81 | 0.0977846 | ||||||||
\(853\) | − 27729.0i | − 1.11304i | −0.830834 | − | 0.556520i | \(-0.812136\pi\) | ||||
0.830834 | − | 0.556520i | \(-0.187864\pi\) | |||||||
\(854\) | 7189.78 | 0.288090 | ||||||||
\(855\) | − 3836.51i | − 0.153457i | ||||||||
\(856\) | − 22447.3i | − 0.896301i | ||||||||
\(857\) | 31280.7i | 1.24682i | 0.781894 | + | 0.623411i | \(0.214254\pi\) | ||||
−0.781894 | + | 0.623411i | \(0.785746\pi\) | |||||||
\(858\) | −10218.6 | −0.406592 | ||||||||
\(859\) | 55.2890 | 0.00219608 | 0.00109804 | − | 0.999999i | \(-0.499650\pi\) | ||||
0.00109804 | + | 0.999999i | \(0.499650\pi\) | |||||||
\(860\) | 3079.24i | 0.122094i | ||||||||
\(861\) | − 1452.25i | − 0.0574826i | ||||||||
\(862\) | 9772.09i | 0.386124i | ||||||||
\(863\) | −22900.4 | −0.903291 | −0.451646 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451646 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(864\) | − 8572.25i | − 0.337539i | ||||||||
\(865\) | −11070.9 | −0.435172 | ||||||||
\(866\) | 31758.7 | 1.24620 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 722.522 | 0.0282535 | ||||||||
\(869\) | 2452.79 | 0.0957484 | ||||||||
\(870\) | − 630.461i | − 0.0245685i | ||||||||
\(871\) | −43677.2 | −1.69913 | ||||||||
\(872\) | 16025.6i | 0.622356i | ||||||||
\(873\) | 31101.0i | 1.20574i | ||||||||
\(874\) | 22114.9i | 0.855888i | ||||||||
\(875\) | −3137.02 | −0.121201 | ||||||||
\(876\) | 1918.93 | 0.0740120 | ||||||||
\(877\) | 1782.50i | 0.0686326i | 0.999411 | + | 0.0343163i | \(0.0109254\pi\) | ||||
−0.999411 | + | 0.0343163i | \(0.989075\pi\) | |||||||
\(878\) | − 54728.0i | − 2.10362i | ||||||||
\(879\) | 6572.17i | 0.252189i | ||||||||
\(880\) | −10336.3 | −0.395949 | ||||||||
\(881\) | − 17232.6i | − 0.659001i | −0.944155 | − | 0.329500i | \(-0.893120\pi\) | ||||
0.944155 | − | 0.329500i | \(-0.106880\pi\) | |||||||
\(882\) | −24347.2 | −0.929493 | ||||||||
\(883\) | 10188.2 | 0.388291 | 0.194145 | − | 0.980973i | \(-0.437807\pi\) | ||||
0.194145 | + | 0.980973i | \(0.437807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 545.859 | 0.0207332 | ||||||||
\(886\) | −22007.1 | −0.834471 | ||||||||
\(887\) | − 15671.6i | − 0.593238i | −0.954996 | − | 0.296619i | \(-0.904141\pi\) | ||||
0.954996 | − | 0.296619i | \(-0.0958592\pi\) | |||||||
\(888\) | 5811.93 | 0.219635 | ||||||||
\(889\) | 4457.10i | 0.168151i | ||||||||
\(890\) | 3032.65i | 0.114219i | ||||||||
\(891\) | − 11538.7i | − 0.433852i | ||||||||
\(892\) | 12631.0 | 0.474122 | ||||||||
\(893\) | −10957.4 | −0.410612 | ||||||||
\(894\) | − 11406.4i | − 0.426721i | ||||||||
\(895\) | − 103.932i | − 0.00388163i | ||||||||
\(896\) | − 4857.16i | − 0.181101i | ||||||||
\(897\) | −25085.8 | −0.933768 | ||||||||
\(898\) | 29103.0i | 1.08149i | ||||||||
\(899\) | 2680.15 | 0.0994307 | ||||||||
\(900\) | 4467.32 | 0.165456 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 22492.6 | 0.830291 | ||||||||
\(903\) | 1757.19 | 0.0647569 | ||||||||
\(904\) | − 38719.9i | − 1.42456i | ||||||||
\(905\) | −2185.81 | −0.0802861 | ||||||||
\(906\) | 13313.9i | 0.488216i | ||||||||
\(907\) | − 16908.3i | − 0.618999i | −0.950900 | − | 0.309500i | \(-0.899838\pi\) | ||||
0.950900 | − | 0.309500i | \(-0.100162\pi\) | |||||||
\(908\) | 4710.86i | 0.172175i | ||||||||
\(909\) | −7002.92 | −0.255525 | ||||||||
\(910\) | −2626.78 | −0.0956890 | ||||||||
\(911\) | − 36100.6i | − 1.31292i | −0.754362 | − | 0.656458i | \(-0.772054\pi\) | ||||
0.754362 | − | 0.656458i | \(-0.227946\pi\) | |||||||
\(912\) | − 5017.92i | − 0.182193i | ||||||||
\(913\) | 9917.98i | 0.359515i | ||||||||
\(914\) | 38625.1 | 1.39782 | ||||||||
\(915\) | 8164.63i | 0.294988i | ||||||||
\(916\) | −1272.65 | −0.0459057 | ||||||||
\(917\) | −7283.41 | −0.262290 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20016.2 | 0.718470 | 0.359235 | − | 0.933247i | \(-0.383038\pi\) | ||||
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(920\) | −20174.1 | −0.722958 | ||||||||
\(921\) | 2362.57i | 0.0845269i | ||||||||
\(922\) | 19735.7 | 0.704947 | ||||||||
\(923\) | − 37584.1i | − 1.34030i | ||||||||
\(924\) | − 293.291i | − 0.0104422i | ||||||||
\(925\) | 15265.6i | 0.542626i | ||||||||
\(926\) | −32144.0 | −1.14073 | ||||||||
\(927\) | 22769.8 | 0.806753 | ||||||||
\(928\) | 1725.17i | 0.0610253i | ||||||||
\(929\) | 30630.3i | 1.08175i | 0.841103 | + | 0.540875i | \(0.181907\pi\) | ||||
−0.841103 | + | 0.540875i | \(0.818093\pi\) | |||||||
\(930\) | 4202.40i | 0.148174i | ||||||||
\(931\) | −11150.3 | −0.392522 | ||||||||
\(932\) | − 2274.15i | − 0.0799272i | ||||||||
\(933\) | −1309.28 | −0.0459420 | ||||||||
\(934\) | −46609.7 | −1.63289 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −26286.2 | −0.917941 | ||||||||
\(937\) | −3883.68 | −0.135405 | −0.0677025 | − | 0.997706i | \(-0.521567\pi\) | ||||
−0.0677025 | + | 0.997706i | \(0.521567\pi\) | |||||||
\(938\) | − 6420.79i | − 0.223503i | ||||||||
\(939\) | 12095.0 | 0.420346 | ||||||||
\(940\) | 3201.93i | 0.111101i | ||||||||
\(941\) | − 21696.0i | − 0.751613i | −0.926698 | − | 0.375807i | \(-0.877366\pi\) | ||||
0.926698 | − | 0.375807i | \(-0.122634\pi\) | |||||||
\(942\) | − 10095.0i | − 0.349164i | ||||||||
\(943\) | 55217.7 | 1.90682 | ||||||||
\(944\) | −4147.02 | −0.142981 | ||||||||
\(945\) | 1389.65i | 0.0478362i | ||||||||
\(946\) | 27215.6i | 0.935364i | ||||||||
\(947\) | − 15904.8i | − 0.545763i | −0.962048 | − | 0.272882i | \(-0.912023\pi\) | ||||
0.962048 | − | 0.272882i | \(-0.0879767\pi\) | |||||||
\(948\) | 347.956 | 0.0119210 | ||||||||
\(949\) | − 29657.4i | − 1.01446i | ||||||||
\(950\) | 10478.8 | 0.357870 | ||||||||
\(951\) | −11456.9 | −0.390659 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −81.8493 | −0.00278212 | −0.00139106 | − | 0.999999i | \(-0.500443\pi\) | ||||
−0.00139106 | + | 0.999999i | \(0.500443\pi\) | |||||||
\(954\) | −22553.1 | −0.765393 | ||||||||
\(955\) | 3945.03i | 0.133674i | ||||||||
\(956\) | −10250.0 | −0.346765 | ||||||||
\(957\) | − 1087.95i | − 0.0367485i | ||||||||
\(958\) | 51613.4i | 1.74066i | ||||||||
\(959\) | 2076.93i | 0.0699348i | ||||||||
\(960\) | 3338.86 | 0.112251 | ||||||||
\(961\) | 11926.2 | 0.400328 | ||||||||
\(962\) | 28773.1i | 0.964327i | ||||||||
\(963\) | − 27065.7i | − 0.905692i | ||||||||
\(964\) | 2577.19i | 0.0861056i | ||||||||
\(965\) | 18662.7 | 0.622562 | ||||||||
\(966\) | − 3687.75i | − 0.122827i | ||||||||
\(967\) | 19279.7 | 0.641151 | 0.320576 | − | 0.947223i | \(-0.396124\pi\) | ||||
0.320576 | + | 0.947223i | \(0.396124\pi\) | |||||||
\(968\) | 11246.3 | 0.373419 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21317.7 | 0.705639 | ||||||||
\(971\) | 53776.3 | 1.77731 | 0.888653 | − | 0.458581i | \(-0.151642\pi\) | ||||
0.888653 | + | 0.458581i | \(0.151642\pi\) | |||||||
\(972\) | − 6858.31i | − 0.226317i | ||||||||
\(973\) | 7053.30 | 0.232393 | ||||||||
\(974\) | − 12946.9i | − 0.425918i | ||||||||
\(975\) | 11886.5i | 0.390433i | ||||||||
\(976\) | − 62028.6i | − 2.03431i | ||||||||
\(977\) | −54738.2 | −1.79246 | −0.896228 | − | 0.443594i | \(-0.853703\pi\) | ||||
−0.896228 | + | 0.443594i | \(0.853703\pi\) | |||||||
\(978\) | −14302.8 | −0.467641 | ||||||||
\(979\) | 5233.25i | 0.170843i | ||||||||
\(980\) | 3258.30i | 0.106207i | ||||||||
\(981\) | 19322.7i | 0.628876i | ||||||||
\(982\) | −2768.27 | −0.0899581 | ||||||||
\(983\) | 3405.32i | 0.110491i | 0.998473 | + | 0.0552456i | \(0.0175942\pi\) | ||||
−0.998473 | + | 0.0552456i | \(0.982406\pi\) | |||||||
\(984\) | −9961.19 | −0.322715 | ||||||||
\(985\) | 2262.86 | 0.0731988 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1827.20 | 0.0589264 | ||||||||
\(988\) | 3856.20 | 0.124172 | ||||||||
\(989\) | 66812.1i | 2.14813i | ||||||||
\(990\) | −9908.60 | −0.318097 | ||||||||
\(991\) | 29925.7i | 0.959256i | 0.877472 | + | 0.479628i | \(0.159228\pi\) | ||||
−0.877472 | + | 0.479628i | \(0.840772\pi\) | |||||||
\(992\) | − 11499.3i | − 0.368047i | ||||||||
\(993\) | − 178.911i | − 0.00571759i | ||||||||
\(994\) | 5525.07 | 0.176302 | ||||||||
\(995\) | 17427.3 | 0.555259 | ||||||||
\(996\) | 1406.98i | 0.0447608i | ||||||||
\(997\) | − 32714.5i | − 1.03920i | −0.854411 | − | 0.519598i | \(-0.826082\pi\) | ||||
0.854411 | − | 0.519598i | \(-0.173918\pi\) | |||||||
\(998\) | − 43572.2i | − 1.38202i | ||||||||
\(999\) | 15221.8 | 0.482080 |
(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 | 289.4.b.e.288.1 | 12 | ||
17.4 | even | 4 | 289.4.a.g.1.11 | 12 | |||
17.7 | odd | 16 | 17.4.d.a.2.3 | ✓ | 12 | ||
17.12 | odd | 16 | 17.4.d.a.9.3 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.g.1.12 | 12 | |||
17.16 | even | 2 | inner | 289.4.b.e.288.2 | 12 | ||
51.29 | even | 16 | 153.4.l.a.145.1 | 12 | |||
51.41 | even | 16 | 153.4.l.a.19.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.3 | ✓ | 12 | 17.7 | odd | 16 | ||
17.4.d.a.9.3 | yes | 12 | 17.12 | odd | 16 | ||
153.4.l.a.19.1 | 12 | 51.41 | even | 16 | |||
153.4.l.a.145.1 | 12 | 51.29 | even | 16 | |||
289.4.a.g.1.11 | 12 | 17.4 | even | 4 | |||
289.4.a.g.1.12 | 12 | 17.13 | even | 4 | |||
289.4.b.e.288.1 | 12 | 1.1 | even | 1 | trivial | ||
289.4.b.e.288.2 | 12 | 17.16 | even | 2 | inner |