Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,4,Mod(31,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.31");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.6492835239\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.17 | ||
Character | \(\chi\) | \(=\) | 672.31 |
Dual form | 672.4.bl.a.607.17 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.11284 | − | 4.10660i | 0.636192 | − | 0.367306i | −0.146954 | − | 0.989143i | \(-0.546947\pi\) |
0.783146 | + | 0.621838i | \(0.213614\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.3102 | + | 2.78176i | 0.988655 | + | 0.150201i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −40.8910 | − | 23.6084i | −1.12083 | − | 0.647109i | −0.179214 | − | 0.983810i | \(-0.557356\pi\) |
−0.941612 | + | 0.336701i | \(0.890689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 81.4016i | 1.73667i | 0.495976 | + | 0.868336i | \(0.334810\pi\) | ||||
−0.495976 | + | 0.868336i | \(0.665190\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.6396i | 0.424128i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −94.4919 | − | 54.5549i | −1.34810 | − | 0.778324i | −0.360118 | − | 0.932907i | \(-0.617263\pi\) |
−0.987980 | + | 0.154582i | \(0.950597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.4730 | − | 38.9245i | −0.271351 | − | 0.469994i | 0.697857 | − | 0.716237i | \(-0.254137\pi\) |
−0.969208 | + | 0.246243i | \(0.920804\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −34.6925 | + | 43.3985i | −0.360501 | + | 0.450968i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.3244 | − | 12.3117i | 0.193324 | − | 0.111616i | −0.400214 | − | 0.916422i | \(-0.631064\pi\) |
0.593538 | + | 0.804806i | \(0.297731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −28.7716 | + | 49.8339i | −0.230173 | + | 0.398671i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −184.406 | −1.18080 | −0.590402 | − | 0.807109i | \(-0.701031\pi\) | ||||
−0.590402 | + | 0.807109i | \(0.701031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.55767 | + | 4.43001i | −0.0148184 | + | 0.0256662i | −0.873340 | − | 0.487112i | \(-0.838050\pi\) |
0.858521 | + | 0.512778i | \(0.171384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 122.673 | − | 70.8252i | 0.647109 | − | 0.373609i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 141.661 | − | 55.4063i | 0.684145 | − | 0.267582i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 197.154 | + | 341.481i | 0.875998 | + | 1.51727i | 0.855696 | + | 0.517479i | \(0.173129\pi\) |
0.0203019 | + | 0.999794i | \(0.493537\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −211.488 | − | 122.102i | −0.868336 | − | 0.501334i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 220.708i | 0.840701i | 0.907362 | + | 0.420350i | \(0.138093\pi\) | ||||
−0.907362 | + | 0.420350i | \(0.861907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 140.609i | 0.498667i | 0.968418 | + | 0.249334i | \(0.0802116\pi\) | ||||
−0.968418 | + | 0.249334i | \(0.919788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −64.0156 | − | 36.9594i | −0.212064 | − | 0.122435i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −56.9367 | − | 98.6172i | −0.176704 | − | 0.306060i | 0.764046 | − | 0.645162i | \(-0.223210\pi\) |
−0.940750 | + | 0.339102i | \(0.889877\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 327.524 | + | 101.869i | 0.954879 | + | 0.296994i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 283.476 | − | 163.665i | 0.778324 | − | 0.449366i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −60.9847 | + | 105.629i | −0.158055 | + | 0.273759i | −0.934167 | − | 0.356836i | \(-0.883856\pi\) |
0.776112 | + | 0.630594i | \(0.217189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −387.801 | −0.950748 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 134.838 | 0.313329 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −51.9763 | + | 90.0257i | −0.114691 | + | 0.198650i | −0.917656 | − | 0.397376i | \(-0.869921\pi\) |
0.802965 | + | 0.596026i | \(0.203254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.8213 | + | 33.3831i | −0.121365 | + | 0.0700700i | −0.559453 | − | 0.828862i | \(-0.688989\pi\) |
0.438089 | + | 0.898932i | \(0.355656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −60.7140 | − | 155.231i | −0.121417 | − | 0.310434i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 334.284 | + | 578.997i | 0.637890 | + | 1.10486i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −635.240 | − | 366.756i | −1.15831 | − | 0.668752i | −0.207414 | − | 0.978253i | \(-0.566505\pi\) |
−0.950899 | + | 0.309501i | \(0.899838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 73.8700i | 0.128883i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 259.891i | 0.434413i | 0.976126 | + | 0.217207i | \(0.0696946\pi\) | ||||
−0.976126 | + | 0.217207i | \(0.930305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −956.279 | − | 552.108i | −1.53321 | − | 0.885197i | −0.999211 | − | 0.0397089i | \(-0.987357\pi\) |
−0.533995 | − | 0.845488i | \(-0.679310\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −86.3149 | − | 149.502i | −0.132890 | − | 0.230173i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −683.047 | − | 546.022i | −1.01091 | − | 0.808117i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 328.369 | − | 189.584i | 0.467650 | − | 0.269998i | −0.247605 | − | 0.968861i | \(-0.579644\pi\) |
0.715256 | + | 0.698863i | \(0.246310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −693.821 | −0.917552 | −0.458776 | − | 0.888552i | \(-0.651712\pi\) | ||||
−0.458776 | + | 0.888552i | \(0.651712\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −896.142 | −1.14353 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 276.609 | − | 479.101i | 0.340869 | − | 0.590402i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −557.497 | + | 321.871i | −0.663984 | + | 0.383351i | −0.793793 | − | 0.608188i | \(-0.791897\pi\) |
0.129809 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −226.440 | + | 1490.48i | −0.260850 | + | 1.71697i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.67300 | − | 13.2900i | −0.00855541 | − | 0.0148184i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −319.695 | − | 184.576i | −0.345263 | − | 0.199338i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 345.596i | 0.361752i | 0.983506 | + | 0.180876i | \(0.0578933\pi\) | ||||
−0.983506 | + | 0.180876i | \(0.942107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 424.951i | 0.431406i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 901.580 | + | 520.528i | 0.888224 | + | 0.512816i | 0.873361 | − | 0.487073i | \(-0.161936\pi\) |
0.0148626 | + | 0.999890i | \(0.495269\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −766.154 | − | 1327.02i | −0.732927 | − | 1.26947i | −0.955627 | − | 0.294579i | \(-0.904821\pi\) |
0.222701 | − | 0.974887i | \(-0.428513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −68.5415 | + | 451.155i | −0.0637044 | + | 0.419317i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1818.71 | + | 1050.03i | −1.64319 | + | 0.948697i | −0.663502 | + | 0.748174i | \(0.730931\pi\) |
−0.979689 | + | 0.200522i | \(0.935736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1059.81 | + | 1835.64i | −0.931294 | + | 1.61305i | −0.150182 | + | 0.988658i | \(0.547986\pi\) |
−0.781113 | + | 0.624390i | \(0.785348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1182.92 | −1.01152 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 269.039 | 0.223974 | 0.111987 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111987 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 101.118 | − | 175.142i | 0.0819942 | − | 0.142018i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 634.463 | − | 366.307i | 0.501334 | − | 0.289445i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1578.40 | − | 1261.76i | −1.21590 | − | 0.971980i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 449.214 | + | 778.061i | 0.337501 | + | 0.584568i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −573.415 | − | 331.061i | −0.420350 | − | 0.242689i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1499.27i | 1.07279i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1326.96i | − | 0.927156i | −0.886056 | − | 0.463578i | \(-0.846565\pi\) | ||
0.886056 | − | 0.463578i | \(-0.153435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −365.313 | − | 210.914i | −0.249334 | − | 0.143953i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −767.720 | − | 1329.73i | −0.512031 | − | 0.886863i | −0.999903 | − | 0.0139481i | \(-0.995560\pi\) |
0.487872 | − | 0.872915i | \(-0.337773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −303.206 | − | 775.227i | −0.197679 | − | 0.505419i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 192.047 | − | 110.878i | 0.122435 | − | 0.0706880i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 880.026 | − | 1524.25i | 0.548800 | − | 0.950550i | −0.449557 | − | 0.893252i | \(-0.648418\pi\) |
0.998357 | − | 0.0572984i | \(-0.0182486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2717.18 | 1.65805 | 0.829023 | − | 0.559214i | \(-0.188897\pi\) | ||||
0.829023 | + | 0.559214i | \(0.188897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 341.620 | 0.204040 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1921.76 | − | 3328.59i | 1.12382 | − | 1.94651i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1311.65 | + | 757.282i | −0.751219 | + | 0.433716i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −755.949 | + | 698.128i | −0.424147 | + | 0.391705i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −857.940 | − | 1486.00i | −0.471713 | − | 0.817030i | 0.527764 | − | 0.849391i | \(-0.323031\pi\) |
−0.999476 | + | 0.0323610i | \(0.989697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 876.950 | + | 506.307i | 0.472617 | + | 0.272866i | 0.717335 | − | 0.696729i | \(-0.245362\pi\) |
−0.244717 | + | 0.969594i | \(0.578695\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 981.989i | 0.518883i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0133i | 0.0217715i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2204.53 | + | 1272.79i | 1.12064 | + | 0.647003i | 0.941565 | − | 0.336832i | \(-0.109355\pi\) |
0.179078 | + | 0.983835i | \(0.442689\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −182.954 | − | 316.886i | −0.0912529 | − | 0.158055i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 424.702 | − | 166.109i | 0.207896 | − | 0.0813120i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1609.94 | + | 929.496i | −0.773619 | + | 0.446649i | −0.834164 | − | 0.551516i | \(-0.814049\pi\) |
0.0605453 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 581.702 | − | 1007.54i | 0.274457 | − | 0.475374i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1181.19 | −0.547326 | −0.273663 | − | 0.961826i | \(-0.588235\pi\) | ||||
−0.273663 | + | 0.961826i | \(0.588235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4429.22 | −2.01603 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −202.257 | + | 350.320i | −0.0904504 | + | 0.156665i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3762.06 | + | 2172.03i | −1.65332 | + | 0.954544i | −0.677625 | + | 0.735407i | \(0.736991\pi\) |
−0.975694 | + | 0.219137i | \(0.929676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −665.439 | + | 832.431i | −0.287443 | + | 0.359576i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −155.929 | − | 270.077i | −0.0662166 | − | 0.114691i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3960.64 | + | 2286.68i | 1.65381 | + | 0.954829i | 0.975484 | + | 0.220069i | \(0.0706282\pi\) |
0.678327 | + | 0.734760i | \(0.262705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 478.812i | − | 0.196629i | −0.995155 | − | 0.0983144i | \(-0.968655\pi\) | ||
0.995155 | − | 0.0983144i | \(-0.0313451\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 200.299i | − | 0.0809099i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2804.65 | + | 1619.27i | 1.11461 | + | 0.643518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2575.91 | + | 4461.61i | 1.00732 | + | 1.74473i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 494.374 | + | 75.1075i | 0.190267 | + | 0.0289062i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1459.86 | − | 842.853i | 0.553048 | − | 0.319302i | −0.197303 | − | 0.980343i | \(-0.563218\pi\) |
0.750350 | + | 0.661040i | \(0.229885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 60.0489 | − | 104.008i | 0.0223959 | − | 0.0387909i | −0.854610 | − | 0.519270i | \(-0.826204\pi\) |
0.877006 | + | 0.480479i | \(0.159537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2005.70 | −0.736571 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2577.93 | 0.932334 | 0.466167 | − | 0.884697i | \(-0.345635\pi\) | ||||
0.466167 | + | 0.884697i | \(0.345635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1386.88 | + | 2402.15i | −0.494038 | + | 0.855698i | −0.999976 | − | 0.00687102i | \(-0.997813\pi\) |
0.505939 | + | 0.862569i | \(0.331146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1905.72 | − | 1100.27i | 0.668752 | − | 0.386104i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3376.50 | − | 512.973i | −1.16741 | − | 0.177358i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 906.358 | + | 1569.86i | 0.308794 | + | 0.534847i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −191.920 | − | 110.805i | −0.0644413 | − | 0.0372052i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2122.21i | 0.702375i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2599.69i | 0.848200i | 0.905615 | + | 0.424100i | \(0.139410\pi\) | ||||
−0.905615 | + | 0.424100i | \(0.860590\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −675.216 | − | 389.836i | −0.217207 | − | 0.125404i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 577.426 | + | 1000.13i | 0.183163 | + | 0.317248i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −59.1545 | + | 73.9994i | −0.0185054 | + | 0.0231493i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2868.84 | − | 1656.32i | 0.885197 | − | 0.511069i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4440.86 | − | 7691.79i | 1.35169 | − | 2.34120i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1922.13 | 0.577198 | 0.288599 | − | 0.957450i | \(-0.406811\pi\) | ||||
0.288599 | + | 0.957450i | \(0.406811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 517.889 | 0.153449 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −685.559 | + | 1187.42i | −0.200450 | + | 0.347190i | −0.948673 | − | 0.316257i | \(-0.897574\pi\) |
0.748224 | + | 0.663447i | \(0.230907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2574.44 | + | 1486.36i | −0.742900 | + | 0.428913i | −0.823123 | − | 0.567864i | \(-0.807770\pi\) |
0.0802229 | + | 0.996777i | \(0.474437\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2443.18 | − | 955.574i | 0.695884 | − | 0.272174i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −63.5321 | − | 110.041i | −0.0178632 | − | 0.0309400i | 0.856956 | − | 0.515390i | \(-0.172353\pi\) |
−0.874819 | + | 0.484450i | \(0.839020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −809.963 | − | 467.633i | −0.224835 | − | 0.129808i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1137.50i | 0.311767i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6394.34i | − | 1.73061i | −0.501246 | − | 0.865305i | \(-0.667125\pi\) | ||
0.501246 | − | 0.865305i | \(-0.332875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5791.82 | − | 3343.91i | −1.54807 | − | 0.893776i | −0.998289 | − | 0.0584649i | \(-0.981379\pi\) |
−0.549777 | − | 0.835312i | \(-0.685287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2747.96 | − | 620.432i | 0.716574 | − | 0.161787i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3168.51 | − | 1829.34i | 0.816225 | − | 0.471248i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1040.73 | − | 1802.60i | 0.264874 | − | 0.458776i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5459.52 | 1.37292 | 0.686458 | − | 0.727169i | \(-0.259164\pi\) | ||||
0.686458 | + | 0.727169i | \(0.259164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1162.64 | −0.288910 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1344.21 | − | 2328.24i | 0.330109 | − | 0.571766i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3473.96 | − | 2005.69i | 0.843190 | − | 0.486816i | −0.0151575 | − | 0.999885i | \(-0.504825\pi\) |
0.858347 | + | 0.513069i | \(0.171492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2660.00 | + | 6801.00i | 0.638164 | + | 1.63164i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 829.827 | + | 1437.30i | 0.196801 | + | 0.340869i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4992.70 | − | 2882.54i | −1.17058 | − | 0.675836i | −0.216765 | − | 0.976224i | \(-0.569551\pi\) |
−0.953817 | + | 0.300388i | \(0.902884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1001.76i | 0.232217i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1931.23i | − | 0.442656i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2355.68 | − | 1360.05i | −0.533933 | − | 0.308266i | 0.208683 | − | 0.977983i | \(-0.433082\pi\) |
−0.742617 | + | 0.669717i | \(0.766416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1282.56 | + | 2221.46i | 0.287491 | + | 0.497949i | 0.973210 | − | 0.229917i | \(-0.0738455\pi\) |
−0.685719 | + | 0.727866i | \(0.740512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3532.71 | − | 2824.02i | −0.783184 | − | 0.626072i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2353.00 | − | 1358.50i | 0.515968 | − | 0.297894i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1506.83 | − | 2609.90i | 0.326847 | − | 0.566115i | −0.655038 | − | 0.755596i | \(-0.727347\pi\) |
0.981884 | + | 0.189481i | \(0.0606806\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46.0380 | 0.00987894 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2758.53 | 0.585623 | 0.292811 | − | 0.956170i | \(-0.405409\pi\) | ||||
0.292811 | + | 0.956170i | \(0.405409\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 288.776 | − | 500.175i | 0.0606571 | − | 0.105061i | −0.834102 | − | 0.551610i | \(-0.814014\pi\) |
0.894759 | + | 0.446549i | \(0.147347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 959.084 | − | 553.727i | 0.199338 | − | 0.115088i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −613.955 | + | 4041.19i | −0.126274 | + | 0.831163i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3495.98 | + | 6055.22i | 0.711578 | + | 1.23249i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −897.885 | − | 518.394i | −0.180876 | − | 0.104429i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3660.64i | − | 0.729886i | −0.931030 | − | 0.364943i | \(-0.881088\pi\) | ||
0.931030 | − | 0.364943i | \(-0.118912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 853.785i | 0.168506i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1104.06 | − | 637.427i | −0.215703 | − | 0.124536i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1002.19 | + | 1735.84i | 0.193840 | + | 0.335740i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −391.141 | + | 2574.58i | −0.0749003 | + | 0.493010i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2704.74 | + | 1561.58i | −0.512816 | + | 0.296075i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −274.183 | + | 474.898i | −0.0514743 | + | 0.0891560i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2883.84 | −0.536121 | −0.268061 | − | 0.963402i | \(-0.586383\pi\) | ||||
−0.268061 | + | 0.963402i | \(0.586383\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4596.93 | 0.846311 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1528.53 | + | 2647.49i | −0.278697 | + | 0.482718i | −0.971061 | − | 0.238831i | \(-0.923236\pi\) |
0.692364 | + | 0.721548i | \(0.256569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 367.070 | − | 211.928i | 0.0662876 | − | 0.0382712i | −0.466490 | − | 0.884527i | \(-0.654482\pi\) |
0.532777 | + | 0.846255i | \(0.321148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1069.32 | − | 854.809i | −0.191268 | − | 0.152898i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2544.92 | − | 4407.94i | −0.450906 | − | 0.780992i | 0.547537 | − | 0.836782i | \(-0.315566\pi\) |
−0.998443 | + | 0.0557900i | \(0.982232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7540.54 | + | 4353.53i | 1.32348 | + | 0.764110i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6300.20i | − | 1.09546i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4904.06i | 0.844797i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4056.56 | − | 2342.06i | −0.692361 | − | 0.399735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3179.42 | − | 5506.92i | −0.537683 | − | 0.931294i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −768.190 | − | 1964.08i | −0.128729 | − | 0.329128i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3465.52 | − | 2000.82i | 0.575474 | − | 0.332250i | −0.183859 | − | 0.982953i | \(-0.558859\pi\) |
0.759333 | + | 0.650703i | \(0.225525\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1774.39 | − | 3073.33i | 0.291999 | − | 0.505758i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6024.49 | −0.982546 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6215.04 | 1.00461 | 0.502307 | − | 0.864689i | \(-0.332485\pi\) | ||||
0.502307 | + | 0.864689i | \(0.332485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −403.558 | + | 698.983i | −0.0646557 | + | 0.111987i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 209.171 | − | 120.765i | 0.0332177 | − | 0.0191783i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5713.63 | + | 2776.33i | 0.899438 | + | 0.437048i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 303.355 | + | 525.426i | 0.0473394 | + | 0.0819942i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1959.90 | + | 1131.55i | 0.303207 | + | 0.175057i | 0.643883 | − | 0.765124i | \(-0.277323\pi\) |
−0.340676 | + | 0.940181i | \(0.610656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3056.05i | − | 0.468730i | −0.972149 | − | 0.234365i | \(-0.924699\pi\) | ||
0.972149 | − | 0.234365i | \(-0.0753011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2197.84i | 0.334223i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2799.56 | + | 1616.33i | 0.422113 | + | 0.243707i | 0.695981 | − | 0.718060i | \(-0.254970\pi\) |
−0.273868 | + | 0.961767i | \(0.588303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1067.27 | + | 1848.56i | 0.159563 | + | 0.276370i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5645.76 | − | 2208.17i | 0.836990 | − | 0.327363i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7704.11 | − | 4447.97i | 1.13261 | − | 0.653913i | 0.188021 | − | 0.982165i | \(-0.439793\pi\) |
0.944590 | + | 0.328252i | \(0.106459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2419.42 | − | 4190.57i | 0.352737 | − | 0.610959i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2695.28 | −0.389712 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9069.16 | −1.30055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4855.36 | − | 8409.73i | 0.690593 | − | 1.19614i | −0.281051 | − | 0.959693i | \(-0.590683\pi\) |
0.971644 | − | 0.236449i | \(-0.0759837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1720.24 | − | 993.184i | 0.242689 | − | 0.140117i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1410.47 | + | 1764.43i | −0.197380 | + | 0.246913i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −589.352 | − | 1020.79i | −0.0818109 | − | 0.141701i | 0.822217 | − | 0.569174i | \(-0.192737\pi\) |
−0.904028 | + | 0.427474i | \(0.859404\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3895.21 | − | 2248.90i | −0.536393 | − | 0.309687i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15010.9i | − | 2.05067i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12717.5i | 1.72362i | 0.507228 | + | 0.861812i | \(0.330670\pi\) | ||||
−0.507228 | + | 0.861812i | \(0.669330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3447.55 | + | 1990.44i | 0.463578 | + | 0.267647i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7240.04 | + | 12540.1i | 0.965924 | + | 1.67303i | 0.707112 | + | 0.707101i | \(0.249998\pi\) |
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7100.70 | − | 1078.77i | −0.939962 | − | 0.142803i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1095.94 | − | 632.741i | 0.143953 | − | 0.0831112i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −118.125 | + | 204.599i | −0.0153964 | + | 0.0266673i | −0.873621 | − | 0.486607i | \(-0.838234\pi\) |
0.858225 | + | 0.513274i | \(0.171568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2686.65 | −0.347493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4606.32 | 0.591242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1557.09 | − | 2696.96i | 0.198344 | − | 0.343541i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10069.8 | + | 5813.82i | −1.27302 | + | 0.734980i | −0.975556 | − | 0.219752i | \(-0.929475\pi\) |
−0.297468 | + | 0.954732i | \(0.596142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2468.91 | + | 375.088i | 0.309775 | + | 0.0470623i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6163.99 | + | 10676.3i | 0.767618 | + | 1.32955i | 0.938851 | + | 0.344323i | \(0.111891\pi\) |
−0.171234 | + | 0.985230i | \(0.554775\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −360.610 | − | 208.198i | −0.0445738 | − | 0.0257347i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 665.270i | 0.0816235i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18618.0i | − | 2.26747i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7142.52 | − | 4123.74i | −0.863509 | − | 0.498547i | 0.00167708 | − | 0.999999i | \(-0.499466\pi\) |
−0.865186 | + | 0.501452i | \(0.832800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2640.08 | + | 4572.75i | 0.316850 | + | 0.548800i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1202.12 | + | 1503.80i | −0.143227 | + | 0.179170i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4935.04 | + | 2849.25i | −0.583739 | + | 0.337022i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4075.77 | + | 7059.45i | −0.478637 | + | 0.829023i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11595.5 | −1.35197 | −0.675986 | − | 0.736914i | \(-0.736282\pi\) | ||||
−0.675986 | + | 0.736914i | \(0.736282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12667.9 | 1.46649 | 0.733246 | − | 0.679963i | \(-0.238004\pi\) | ||||
0.733246 | + | 0.679963i | \(0.238004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −512.430 | + | 887.555i | −0.0589012 | + | 0.102020i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5437.37 | − | 3139.27i | 0.620591 | − | 0.358299i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1151.58 | + | 450.405i | −0.130513 | + | 0.0510460i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5765.28 | + | 9985.77i | 0.648836 | + | 1.12382i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1601.91 | − | 924.863i | −0.179028 | − | 0.103362i | 0.407808 | − | 0.913068i | \(-0.366293\pi\) |
−0.586836 | + | 0.809706i | \(0.699627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1481.53i | − | 0.164429i | −0.996615 | − | 0.0822147i | \(-0.973801\pi\) | ||
0.996615 | − | 0.0822147i | \(-0.0261993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4543.69i | − | 0.500813i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −958.450 | − | 553.361i | −0.104917 | − | 0.0605741i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6660.84 | + | 11536.9i | 0.724156 | + | 1.25428i | 0.959320 | + | 0.282319i | \(0.0911038\pi\) |
−0.235164 | + | 0.971956i | \(0.575563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −679.867 | − | 3011.20i | −0.0734118 | − | 0.325149i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3682.77 | − | 2126.25i | 0.394974 | − | 0.228039i | −0.289339 | − | 0.957227i | \(-0.593435\pi\) |
0.684313 | + | 0.729188i | \(0.260102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2643.59 | + | 4578.84i | −0.281614 | + | 0.487770i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5147.64 | 0.544687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11588.4 | 1.21802 | 0.609010 | − | 0.793163i | \(-0.291567\pi\) | ||||
0.609010 | + | 0.793163i | \(0.291567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5210.55 | − | 9024.94i | 0.544025 | − | 0.942279i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2630.85 | + | 1518.92i | −0.272866 | + | 0.157539i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4510.16 | + | 11531.4i | 0.464702 | + | 1.18813i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1519.63 | − | 2632.08i | −0.155548 | − | 0.269417i | 0.777710 | − | 0.628623i | \(-0.216381\pi\) |
−0.933258 | + | 0.359206i | \(0.883048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2551.28 | − | 1472.98i | −0.259441 | − | 0.149789i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7884.53i | 0.796571i | 0.917261 | + | 0.398286i | \(0.130395\pi\) | ||||
−0.917261 | + | 0.398286i | \(0.869605\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6854.97i | 0.688073i | 0.938956 | + | 0.344036i | \(0.111794\pi\) | ||||
−0.938956 | + | 0.344036i | \(0.888206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −109.154 | − | 63.0200i | −0.0108858 | − | 0.00628490i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2688.66 | − | 4656.90i | −0.266417 | − | 0.461447i | 0.701517 | − | 0.712653i | \(-0.252506\pi\) |
−0.967934 | + | 0.251205i | \(0.919173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10611.1 | − | 8482.45i | −1.04473 | − | 0.835145i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6613.60 | + | 3818.36i | −0.647003 | + | 0.373548i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3319.56 | − | 5749.64i | 0.322692 | − | 0.558920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2586.34 | 0.249831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1097.72 | 0.105370 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2570.92 | + | 4452.96i | −0.245237 | + | 0.424762i | −0.962198 | − | 0.272351i | \(-0.912199\pi\) |
0.716962 | + | 0.697113i | \(0.245532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27797.1 | + | 16048.6i | −2.63501 | + | 1.52132i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −205.489 | + | 1352.57i | −0.0193583 | + | 0.127421i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1419.23 | + | 2458.17i | 0.132874 | + | 0.230144i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6760.47 | − | 3903.16i | −0.629047 | − | 0.363181i | 0.151336 | − | 0.988482i | \(-0.451643\pi\) |
−0.780383 | + | 0.625302i | \(0.784976\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5576.98i | − | 0.515746i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15179.4i | − | 1.39519i | −0.716493 | − | 0.697595i | \(-0.754254\pi\) | ||
0.716493 | − | 0.697595i | \(-0.245746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17424.9 | + | 10060.3i | 1.59184 | + | 0.919049i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1745.11 | + | 3022.61i | 0.158458 | + | 0.274457i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −722.954 | + | 4758.64i | −0.0652493 | + | 0.429485i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17185.6 | − | 9922.10i | 1.54175 | − | 0.890129i | 0.543019 | − | 0.839720i | \(-0.317281\pi\) |
0.998729 | − | 0.0504084i | \(-0.0160523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1771.79 | − | 3068.83i | 0.158000 | − | 0.273663i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3894.11 | −0.345189 | −0.172594 | − | 0.984993i | \(-0.555215\pi\) | ||||
−0.172594 | + | 0.984993i | \(0.555215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8550.40 | 0.753441 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6643.83 | − | 11507.4i | 0.581978 | − | 1.00801i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14465.8 | + | 8351.85i | −1.25970 | + | 0.727287i | −0.973016 | − | 0.230739i | \(-0.925886\pi\) |
−0.286682 | + | 0.958026i | \(0.592552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15973.8 | − | 12769.3i | −1.38286 | − | 1.10544i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −606.772 | − | 1050.96i | −0.0522215 | − | 0.0904504i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10899.1 | − | 6292.58i | −0.932564 | − | 0.538416i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5376.74i | 0.457386i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13032.2i | − | 1.10221i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12739.7 | + | 7355.29i | 1.07128 | + | 0.618505i | 0.928531 | − | 0.371254i | \(-0.121072\pi\) |
0.142750 | + | 0.989759i | \(0.454405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3021.64 | + | 5233.63i | 0.252633 | + | 0.437573i | 0.964250 | − | 0.264995i | \(-0.0853702\pi\) |
−0.711617 | + | 0.702568i | \(0.752037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1164.56 | − | 2977.51i | −0.0968107 | − | 0.247522i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 483.358 | − | 279.067i | 0.0399533 | − | 0.0230671i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5780.35 | + | 10011.9i | −0.475084 | + | 0.822869i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 935.574 | 0.0764604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17965.9 | −1.46002 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8624.14 | + | 14937.4i | −0.696924 | + | 1.20711i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11881.9 | + | 6860.03i | −0.954829 | + | 0.551271i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10987.8 | − | 11897.8i | −0.878066 | − | 0.950790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −101.020 | − | 174.972i | −0.00802808 | − | 0.0139050i | 0.861983 | − | 0.506936i | \(-0.169222\pi\) |
−0.870012 | + | 0.493031i | \(0.835889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1243.99 | + | 718.218i | 0.0983144 | + | 0.0567619i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17408.8i | 1.36828i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14260.6i | − | 1.11470i | −0.830279 | − | 0.557348i | \(-0.811819\pi\) | ||
0.830279 | − | 0.557348i | \(-0.188181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 520.392 | + | 300.448i | 0.0404550 | + | 0.0233567i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4144.16 | + | 7177.90i | 0.320413 | + | 0.554971i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6539.86 | − | 2557.87i | 0.502899 | − | 0.196694i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8413.96 | + | 4857.80i | −0.643518 | + | 0.371535i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9396.60 | − | 16275.4i | 0.714805 | − | 1.23808i | −0.248229 | − | 0.968701i | \(-0.579849\pi\) |
0.963035 | − | 0.269378i | \(-0.0868180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11445.8 | −0.866022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15455.5 | −1.16316 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3498.08 | + | 6058.86i | −0.261859 | + | 0.453553i | −0.966736 | − | 0.255777i | \(-0.917669\pi\) |
0.704877 | + | 0.709330i | \(0.251002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1913.63 | − | 1104.84i | 0.142490 | − | 0.0822669i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −936.696 | + | 1171.76i | −0.0693784 | + | 0.0867889i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9179.23 | + | 15898.9i | 0.676298 | + | 1.17138i | 0.976088 | + | 0.217377i | \(0.0697501\pi\) |
−0.299790 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18813.8 | − | 10862.2i | −1.37887 | − | 0.796090i | −0.386844 | − | 0.922145i | \(-0.626435\pi\) |
−0.992023 | + | 0.126055i | \(0.959768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5057.12i | 0.368698i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1416.91i | 0.102764i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13148.6 | − | 7591.34i | −0.948671 | − | 0.547715i | −0.0560028 | − | 0.998431i | \(-0.517836\pi\) |
−0.892668 | + | 0.450715i | \(0.851169\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 180.147 | + | 312.023i | 0.0129303 | + | 0.0223959i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12704.0 | − | 1930.04i | −0.907143 | − | 0.137817i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4987.45 | − | 2879.50i | 0.354303 | − | 0.204557i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3008.56 | − | 5210.97i | 0.212630 | − | 0.368286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3428.94 | 0.241103 | 0.120551 | − | 0.992707i | \(-0.461534\pi\) | ||||
0.120551 | + | 0.992707i | \(0.461534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 229.914 | 0.0160840 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3866.89 | + | 6697.65i | −0.269142 | + | 0.466167i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13768.6 | + | 7949.31i | −0.953472 | + | 0.550487i | −0.894158 | − | 0.447752i | \(-0.852225\pi\) |
−0.0593141 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16408.5 | − | 2492.85i | −1.13056 | − | 0.171760i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4160.65 | − | 7206.45i | −0.285233 | − | 0.494038i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1577.37 | + | 910.697i | 0.107596 | + | 0.0621203i | 0.552832 | − | 0.833293i | \(-0.313547\pi\) |
−0.445237 | + | 0.895413i | \(0.646880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9901.30i | 0.672018i | 0.941859 | + | 0.336009i | \(0.109077\pi\) | ||||
−0.941859 | + | 0.336009i | \(0.890923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6601.61i | 0.445835i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6390.37 | + | 3689.48i | 0.429431 | + | 0.247932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8454.27 | + | 14643.2i | 0.565319 | + | 0.979161i | 0.997020 | + | 0.0771439i | \(0.0245801\pi\) |
−0.431701 | + | 0.902017i | \(0.642087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6397.50 | − | 8002.95i | 0.425681 | − | 0.532506i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8027.60 | − | 4634.74i | 0.531525 | − | 0.306876i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 740.944 | − | 1283.35i | 0.0488196 | − | 0.0845581i | −0.840583 | − | 0.541683i | \(-0.817787\pi\) |
0.889403 | + | 0.457125i | \(0.151121\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5438.15 | −0.356565 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3569.43 | 0.232901 | 0.116450 | − | 0.993197i | \(-0.462848\pi\) | ||||
0.116450 | + | 0.993197i | \(0.462848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3046.20 | + | 5276.18i | −0.197799 | + | 0.342597i | −0.947814 | − | 0.318823i | \(-0.896713\pi\) |
0.750016 | + | 0.661420i | \(0.230046\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 575.760 | − | 332.415i | 0.0372052 | − | 0.0214804i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11103.2 | + | 4342.69i | −0.714031 | + | 0.279271i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2560.43 | + | 4434.80i | 0.163868 | + | 0.283827i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5513.67 | − | 3183.32i | −0.351188 | − | 0.202758i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 43022.9i | − | 2.72724i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12560.5i | 0.792431i | 0.918158 | + | 0.396215i | \(0.129677\pi\) | ||||
−0.918158 | + | 0.396215i | \(0.870323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6754.20 | − | 3899.54i | −0.424100 | − | 0.244854i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5449.30 | − | 9438.47i | −0.340550 | − | 0.589849i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8292.29 | + | 26660.9i | −0.515781 | + | 1.65831i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2025.65 | − | 1169.51i | 0.125404 | − | 0.0724022i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5147.70 | + | 8916.07i | −0.317195 | + | 0.549397i | −0.979902 | − | 0.199482i | \(-0.936074\pi\) |
0.662707 | + | 0.748879i | \(0.269408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7660.53 | 0.469832 | 0.234916 | − | 0.972016i | \(-0.424519\pi\) | ||||
0.234916 | + | 0.972016i | \(0.424519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3464.56 | −0.211499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12532.7 | + | 21707.2i | −0.761530 | + | 1.31901i | 0.180531 | + | 0.983569i | \(0.442218\pi\) |
−0.942062 | + | 0.335440i | \(0.891115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4250.72 | − | 2454.16i | 0.257096 | − | 0.148435i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −103.524 | − | 264.687i | −0.00623262 | − | 0.0159353i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3393.47 | + | 5877.67i | 0.203364 | + | 0.352237i | 0.949610 | − | 0.313433i | \(-0.101479\pi\) |
−0.746246 | + | 0.665670i | \(0.768146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10921.3 | − | 6305.44i | −0.651500 | − | 0.376144i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9937.95i | 0.590131i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11856.9i | − | 0.700877i | −0.936586 | − | 0.350438i | \(-0.886033\pi\) | ||
0.936586 | − | 0.350438i | \(-0.113967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24659.1 | + | 14236.9i | 1.45103 | + | 0.837750i | 0.998540 | − | 0.0540209i | \(-0.0172038\pi\) |
0.452486 | + | 0.891771i | \(0.350537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13322.6 | + | 23075.4i | 0.780401 | + | 1.35169i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5340.21 | − | 4268.92i | −0.311405 | − | 0.248935i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3932.36 | + | 2270.35i | −0.228278 | + | 0.131796i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2883.19 | + | 4993.83i | −0.166623 | + | 0.288599i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3152.49 | 0.181372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6474.43 | 0.370834 | 0.185417 | − | 0.982660i | \(-0.440636\pi\) | ||||
0.185417 | + | 0.982660i | \(0.440636\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −776.834 | + | 1345.52i | −0.0442968 | + | 0.0767243i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 999.203 | − | 576.890i | 0.0567245 | − | 0.0327499i | −0.471370 | − | 0.881936i | \(-0.656240\pi\) |
0.528094 | + | 0.849186i | \(0.322907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −961.366 | + | 6327.92i | −0.0543355 | + | 0.357648i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2056.68 | − | 3562.27i | −0.115730 | − | 0.200450i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17174.4 | − | 9915.66i | −0.962169 | − | 0.555508i | −0.0653288 | − | 0.997864i | \(-0.520810\pi\) |
−0.896840 | + | 0.442355i | \(0.854143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14455.7i | − | 0.806310i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8918.14i | − | 0.495267i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8598.34 | − | 4964.25i | −0.475429 | − | 0.274489i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9852.12 | − | 17064.4i | −0.542391 | − | 0.939449i | −0.998766 | − | 0.0496613i | \(-0.984186\pi\) |
0.456375 | − | 0.889787i | \(-0.349148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1182.11 | + | 7780.92i | −0.0647976 | + | 0.426512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19326.9 | − | 11158.4i | 1.05484 | − | 0.609010i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12040.7 | − | 20855.1i | 0.654338 | − | 1.13335i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 381.192 | 0.0206266 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14049.5 | −0.756976 | −0.378488 | − | 0.925606i | \(-0.623556\pi\) | ||||
−0.378488 | + | 0.925606i | \(0.623556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8861.30 | − | 15348.2i | 0.475406 | − | 0.823427i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2429.89 | − | 1402.90i | 0.129808 | − | 0.0749450i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15060.1 | + | 12038.9i | 0.801122 | + | 0.640411i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7451.93 | + | 12907.1i | 0.394729 | + | 0.683691i | 0.993067 | − | 0.117553i | \(-0.0375051\pi\) |
−0.598337 | + | 0.801244i | \(0.704172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2955.32 | − | 1706.25i | −0.155883 | − | 0.0899994i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 125.957i | 0.00661587i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 31567.6i | − | 1.65114i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16613.0 | + | 9591.52i | 0.865305 | + | 0.499584i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15722.5 | − | 27232.1i | −0.815507 | − | 1.41250i | −0.908963 | − | 0.416876i | \(-0.863125\pi\) |
0.0934560 | − | 0.995623i | \(-0.470209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10337.0 | − | 26429.2i | −0.533937 | − | 1.36515i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17375.5 | − | 10031.7i | 0.893776 | − | 0.516022i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5305.66 | − | 9189.67i | 0.271789 | − | 0.470753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25428.5 | −1.29724 | −0.648618 | − | 0.761114i | \(-0.724653\pi\) | ||||
−0.648618 | + | 0.761114i | \(0.724653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7670.93 | − | 13286.4i | 0.388125 | − | 0.672252i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4287.96 | + | 2475.66i | −0.216070 | + | 0.124748i | −0.604129 | − | 0.796886i | \(-0.706479\pi\) |
0.388059 | + | 0.921634i | \(0.373146\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2510.01 | + | 8070.06i | −0.125963 | + | 0.404991i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17317.1 | + | 29994.0i | 0.865512 | + | 1.49911i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17783.4 | − | 10267.3i | −0.885215 | − | 0.511079i | −0.0128407 | − | 0.999918i | \(-0.504087\pi\) |
−0.872374 | + | 0.488838i | \(0.837421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10976.0i | 0.544150i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19070.6i | 0.941634i | 0.882231 | + | 0.470817i | \(0.156041\pi\) | ||||
−0.882231 | + | 0.470817i | \(0.843959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12204.8 | − | 7046.44i | −0.600200 | − | 0.346526i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3122.20 | + | 5407.80i | 0.152925 | + | 0.264874i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36221.8 | + | 14167.1i | −1.76705 | + | 0.691126i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26097.3 | − | 15067.3i | 1.26805 | − | 0.732107i | 0.293428 | − | 0.955981i | \(-0.405204\pi\) |
0.974618 | + | 0.223874i | \(0.0718705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8189.29 | + | 14184.3i | −0.396327 | + | 0.686458i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8316.81 | 0.400900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34967.7 | 1.67889 | 0.839446 | − | 0.543443i | \(-0.182880\pi\) | ||||
0.839446 | + | 0.543443i | \(0.182880\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1743.95 | − | 3020.62i | 0.0834012 | − | 0.144455i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3501.17 | + | 2021.40i | −0.166777 | + | 0.0962887i | −0.581065 | − | 0.813857i | \(-0.697364\pi\) |
0.414288 | + | 0.910146i | \(0.364031\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24511.5 | + | 30662.7i | −1.16301 | + | 1.45487i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4032.64 | + | 6984.73i | 0.190589 | + | 0.330109i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7328.23 | − | 4230.96i | −0.344990 | − | 0.199180i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17771.8i | − | 0.833378i | −0.909049 | − | 0.416689i | \(-0.863190\pi\) | ||
0.909049 | − | 0.416689i | \(-0.136810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12034.2i | 0.562126i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4512.24 | + | 2605.14i | 0.209953 | + | 0.121217i | 0.601290 | − | 0.799031i | \(-0.294654\pi\) |
−0.391336 | + | 0.920248i | \(0.627987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −147.177 | − | 254.917i | −0.00682160 | − | 0.0118154i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21659.5 | − | 3290.61i | −1.00004 | − | 0.151931i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8590.92 | − | 4959.97i | 0.395124 | − | 0.228125i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6135.61 | − | 10627.2i | 0.281113 | − | 0.486902i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4978.96 | −0.227246 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20907.3 | 0.950592 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −959.889 | + | 1662.58i | −0.0434769 | + | 0.0753042i | −0.886945 | − | 0.461875i | \(-0.847177\pi\) |
0.843468 | + | 0.537179i | \(0.180510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14978.1 | − | 8647.61i | 0.675836 | − | 0.390194i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4926.14 | + | 748.401i | 0.221433 | + | 0.0336411i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2717.44 | − | 4706.74i | −0.121689 | − | 0.210771i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2602.65 | − | 1502.64i | −0.116109 | − | 0.0670354i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6915.49i | 0.307352i | 0.988121 | + | 0.153676i | \(0.0491112\pi\) | ||||
−0.988121 | + | 0.153676i | \(0.950889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12424.7i | 0.550131i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5017.47 | + | 2896.84i | 0.221328 | + | 0.127784i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26068.8 | + | 45152.5i | 1.14564 | + | 1.98430i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2338.69 | − | 2925.59i | 0.102395 | − | 0.128091i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7067.03 | − | 4080.15i | 0.308266 | − | 0.177978i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6054.09 | − | 10486.0i | 0.263103 | − | 0.455708i | −0.703962 | − | 0.710238i | \(-0.748587\pi\) |
0.967065 | + | 0.254530i | \(0.0819208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37167.6 | 1.60928 | 0.804642 | − | 0.593760i | \(-0.202357\pi\) | ||||
0.804642 | + | 0.593760i | \(0.202357\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7695.37 | −0.331966 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7634.15 | + | 13222.7i | −0.328113 | + | 0.568309i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5473.14 | − | 3159.92i | 0.234371 | − | 0.135314i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12636.1 | − | 4942.22i | 0.539122 | − | 0.210861i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2040.21 | + | 3533.75i | 0.0867283 | + | 0.150218i | 0.906126 | − | 0.423007i | \(-0.139025\pi\) |
−0.819398 | + | 0.573225i | \(0.805692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18704.5 | − | 10799.0i | −0.792221 | − | 0.457389i | 0.0485231 | − | 0.998822i | \(-0.484549\pi\) |
−0.840744 | + | 0.541433i | \(0.817882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8151.03i | 0.343979i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23867.6i | 1.00358i | 0.864991 | + | 0.501788i | \(0.167324\pi\) | ||||
−0.864991 | + | 0.501788i | \(0.832676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14730.1 | − | 8504.44i | −0.617127 | − | 0.356298i | 0.158623 | − | 0.987339i | \(-0.449295\pi\) |
−0.775750 | + | 0.631041i | \(0.782628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4520.49 | + | 7829.71i | 0.188705 | + | 0.326847i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25390.9 | − | 27493.8i | −1.05611 | − | 1.14358i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8401.65 | + | 4850.69i | −0.348205 | + | 0.201036i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −69.0570 | + | 119.610i | −0.00285180 | + | 0.00493947i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2200.67 | 0.0905551 | 0.0452775 | − | 0.998974i | \(-0.485583\pi\) | ||||
0.0452775 | + | 0.998974i | \(0.485583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9616.58 | 0.394300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4137.79 | + | 7166.86i | −0.169055 | + | 0.292811i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31504.3 | + | 18189.0i | −1.28258 | + | 0.740499i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6060.79 | + | 15496.0i | 0.245869 | + | 0.628630i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 866.328 | + | 1500.52i | 0.0350204 | + | 0.0606571i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8408.40 | + | 4854.59i | 0.338703 | + | 0.195550i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35822.1i | − | 1.43789i | −0.695065 | − | 0.718947i | \(-0.744624\pi\) | ||
0.695065 | − | 0.718947i | \(-0.255376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3322.36i | 0.132892i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14010.3 | + | 8088.82i | 0.558438 | + | 0.322414i | 0.752518 | − | 0.658571i | \(-0.228839\pi\) |
−0.194080 | + | 0.980986i | \(0.562172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16698.0 | − | 28921.7i | −0.663245 | − | 1.14877i | −0.979758 | − | 0.200185i | \(-0.935846\pi\) |
0.316513 | − | 0.948588i | \(-0.397488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9578.38 | − | 7656.89i | −0.379129 | − | 0.303073i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13338.4 | + | 7700.94i | −0.526124 | + | 0.303758i | −0.739437 | − | 0.673226i | \(-0.764908\pi\) |
0.213312 | + | 0.976984i | \(0.431575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17839.3 | + | 30898.6i | −0.701219 | + | 1.21455i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20975.9 | −0.821660 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17903.1 | −0.698873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29854.5 | − | 51709.6i | 1.16140 | − | 2.01161i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2693.66 | − | 1555.18i | 0.104429 | − | 0.0602921i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4170.60 | + | 27451.8i | −0.161134 | + | 1.06062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11494.2 | + | 19908.5i | 0.442567 | + | 0.766548i | 0.997879 | − | 0.0650939i | \(-0.0207347\pi\) |
−0.555313 | + | 0.831642i | \(0.687401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9510.61 | + | 5490.95i | 0.364943 | + | 0.210700i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44097.1i | 1.68635i | 0.537643 | + | 0.843173i | \(0.319315\pi\) | ||||
−0.537643 | + | 0.843173i | \(0.680685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21367.6i | − | 0.814355i | −0.913349 | − | 0.407178i | \(-0.866513\pi\) | ||
0.913349 | − | 0.407178i | \(-0.133487\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2218.20 | − | 1280.68i | −0.0842530 | − | 0.0486435i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17222.8 | + | 29830.7i | 0.651956 | + | 1.12922i | 0.982648 | + | 0.185482i | \(0.0593845\pi\) |
−0.330692 | + | 0.943739i | \(0.607282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3691.29 | − | 24296.9i | 0.139260 | − | 0.916638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3312.17 | − | 1912.28i | 0.124536 | − | 0.0719010i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2559.08 | + | 4432.46i | −0.0958974 | + | 0.166099i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37561.9 | 1.40286 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6013.14 | −0.223827 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 471.649 | − | 816.921i | 0.0174976 | − | 0.0303068i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11525.1 | − | 6654.03i | 0.426146 | − | 0.246036i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6102.23 | − | 4878.08i | −0.224883 | − | 0.179770i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1966.29 | − | 3405.72i | −0.0722229 | − | 0.125094i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5854.66 | + | 3380.19i | 0.214334 | + | 0.123746i | 0.603324 | − | 0.797496i | \(-0.293843\pi\) |
−0.388990 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 9369.50i | − | 0.341877i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17345.6i | 0.630830i | 0.948954 | + | 0.315415i | \(0.102144\pi\) | ||||
−0.948954 | + | 0.315415i | \(0.897856\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28371.0 | + | 16380.0i | 1.02842 | + | 0.593756i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −822.548 | − | 1424.69i | −0.0297187 | − | 0.0514743i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10358.1 | − | 26483.2i | −0.373014 | − | 0.953710i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27620.4 | − | 15946.7i | 0.991418 | − | 0.572396i | 0.0857205 | − | 0.996319i | \(-0.472681\pi\) |
0.905698 | + | 0.423923i | \(0.139347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4325.76 | − | 7492.43i | 0.154765 | − | 0.268061i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21155.5 | −0.754434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22689.8 | −0.806524 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6895.39 | + | 11943.2i | −0.244309 | + | 0.423155i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34785.7 | − | 20083.6i | 1.22851 | − | 0.709279i | 0.261790 | − | 0.965125i | \(-0.415687\pi\) |
0.966718 | + | 0.255846i | \(0.0823540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3395.26 | − | 15038.0i | −0.119522 | − | 0.529377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4585.58 | − | 7942.46i | −0.160906 | − | 0.278697i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36644.1 | + | 21156.5i | 1.28170 | + | 0.739990i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53552.4i | − | 1.86711i | −0.358437 | − | 0.933554i | \(-0.616690\pi\) | ||
0.358437 | − | 0.933554i | \(-0.383310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1271.57i | 0.0441917i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12878.3 | − | 7435.29i | −0.446143 | − | 0.257581i | 0.260057 | − | 0.965593i | \(-0.416259\pi\) |
−0.706200 | + | 0.708013i | \(0.749592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2717.28 | + | 4706.46i | 0.0938354 | + | 0.162528i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3824.84 | − | 1495.97i | 0.131664 | − | 0.0514962i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27577.0 | − | 15921.6i | 0.946284 | − | 0.546338i | 0.0543597 | − | 0.998521i | \(-0.482688\pi\) |
0.891925 | + | 0.452184i | \(0.149355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44942.5 | − | 77842.6i | 1.53730 | − | 2.66268i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15269.5 | 0.520661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27066.7 | 0.920016 | 0.460008 | − | 0.887915i | \(-0.347846\pi\) | ||||
0.460008 | + | 0.887915i | \(0.347846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6922.53 | − | 11990.2i | 0.234563 | − | 0.406275i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22621.6 | + | 13060.6i | −0.764110 | + | 0.441159i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20353.5 | − | 25461.2i | 0.685348 | − | 0.857336i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14882.4 | + | 25777.1i | 0.499561 | + | 0.865265i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16368.4 | + | 9450.30i | 0.547730 | + | 0.316232i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 986.388i | − | 0.0329046i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13564.1i | − | 0.451077i | −0.974234 | − | 0.225538i | \(-0.927586\pi\) | ||
0.974234 | − | 0.225538i | \(-0.0724141\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12741.1 | − | 7356.09i | −0.422398 | − | 0.243872i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26845.6 | + | 46497.9i | 0.887245 | + | 1.53675i | 0.843118 | + | 0.537728i | \(0.180717\pi\) |
0.0441269 | + | 0.999026i | \(0.485949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49752.0 | + | 7558.55i | 1.63924 | + | 0.249040i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12169.7 | − | 7026.17i | 0.399735 | − | 0.230787i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10299.0 | + | 17838.3i | −0.337250 | + | 0.584134i | −0.983914 | − | 0.178640i | \(-0.942830\pi\) |
0.646664 | + | 0.762775i | \(0.276163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30395.5 | 0.992281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19076.5 | 0.620863 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12478.0 | − | 21612.5i | 0.404868 | − | 0.701251i | −0.589438 | − | 0.807813i | \(-0.700651\pi\) |
0.994306 | + | 0.106562i | \(0.0339842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18336.4 | − | 10586.5i | 0.593144 | − | 0.342452i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6255.12 | + | 950.305i | 0.201725 | + | 0.0306470i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1731.13 | + | 2998.41i | 0.0556591 | + | 0.0964044i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50408.0 | − | 29103.1i | −1.61580 | − | 0.932885i | −0.987989 | − | 0.154522i | \(-0.950616\pi\) |
−0.627815 | − | 0.778363i | \(-0.716050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12004.9i | 0.383649i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22781.5i | 0.725852i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15421.5 | + | 8903.61i | 0.489874 | + | 0.282829i | 0.724522 | − | 0.689252i | \(-0.242061\pi\) |
−0.234648 | + | 0.972080i | \(0.575394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5323.16 | + | 9219.98i | 0.168586 | + | 0.291999i |
(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 | 672.4.bl.a.31.17 | ✓ | 48 | |
4.3 | odd | 2 | 672.4.bl.b.31.17 | yes | 48 | ||
7.5 | odd | 6 | 672.4.bl.b.607.17 | yes | 48 | ||
28.19 | even | 6 | inner | 672.4.bl.a.607.17 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.bl.a.31.17 | ✓ | 48 | 1.1 | even | 1 | trivial | |
672.4.bl.a.607.17 | yes | 48 | 28.19 | even | 6 | inner | |
672.4.bl.b.31.17 | yes | 48 | 4.3 | odd | 2 | ||
672.4.bl.b.607.17 | yes | 48 | 7.5 | odd | 6 |