Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(79,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.79");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.j (of order \(6\), degree \(2\), 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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 214.12 | ||
Character | \(\chi\) | \(=\) | 245.214 |
Dual form | 245.4.j.g.79.12 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.20246 | − | 2.42629i | 1.48580 | − | 0.857824i | 0.485926 | − | 0.874000i | \(-0.338482\pi\) |
0.999869 | + | 0.0161753i | \(0.00514900\pi\) | |||||||
\(3\) | 0.991781 | + | 0.572605i | 0.190868 | + | 0.110198i | 0.592389 | − | 0.805652i | \(-0.298185\pi\) |
−0.401521 | + | 0.915850i | \(0.631518\pi\) | |||||||
\(4\) | 7.77380 | − | 13.4646i | 0.971726 | − | 1.68308i | ||||
\(5\) | −6.75158 | − | 8.91157i | −0.603880 | − | 0.797075i | ||||
\(6\) | 5.55723 | 0.378122 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 36.6254i | − | 1.61863i | ||||||
\(9\) | −12.8442 | − | 22.2469i | −0.475713 | − | 0.823959i | ||||
\(10\) | −49.9954 | − | 21.0693i | −1.58099 | − | 0.666268i | ||||
\(11\) | 19.8919 | − | 34.4537i | 0.545238 | − | 0.944380i | −0.453354 | − | 0.891331i | \(-0.649773\pi\) |
0.998592 | − | 0.0530495i | \(-0.0168941\pi\) | |||||||
\(12\) | 15.4198 | − | 8.90264i | 0.370943 | − | 0.214164i | ||||
\(13\) | 61.1016i | 1.30358i | 0.758400 | + | 0.651789i | \(0.225981\pi\) | ||||
−0.758400 | + | 0.651789i | \(0.774019\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.59328 | − | 12.7043i | −0.0274255 | − | 0.218683i | ||||
\(16\) | −26.6736 | − | 46.2001i | −0.416775 | − | 0.721876i | ||||
\(17\) | −68.4751 | − | 39.5341i | −0.976920 | − | 0.564025i | −0.0755812 | − | 0.997140i | \(-0.524081\pi\) |
−0.901339 | + | 0.433115i | \(0.857415\pi\) | |||||||
\(18\) | −107.955 | − | 62.3278i | −1.41362 | − | 0.816156i | ||||
\(19\) | 1.17292 | + | 2.03156i | 0.0141624 | + | 0.0245300i | 0.873020 | − | 0.487685i | \(-0.162158\pi\) |
−0.858857 | + | 0.512215i | \(0.828825\pi\) | |||||||
\(20\) | −172.476 | + | 21.6307i | −1.92835 | + | 0.241838i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 193.054i | − | 1.87087i | ||||||
\(23\) | 161.523 | − | 93.2555i | 1.46434 | − | 0.845440i | 0.465137 | − | 0.885239i | \(-0.346005\pi\) |
0.999208 | + | 0.0397987i | \(0.0126717\pi\) | |||||||
\(24\) | 20.9719 | − | 36.3244i | 0.178370 | − | 0.308945i | ||||
\(25\) | −33.8323 | + | 120.334i | −0.270659 | + | 0.962675i | ||||
\(26\) | 148.250 | + | 256.777i | 1.11824 | + | 1.93685i | ||||
\(27\) | − | 60.3394i | − | 0.430086i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −62.5696 | −0.400651 | −0.200325 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200325 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(30\) | −37.5201 | − | 49.5237i | −0.228340 | − | 0.301392i | ||||
\(31\) | 104.569 | − | 181.119i | 0.605843 | − | 1.04935i | −0.386075 | − | 0.922468i | \(-0.626169\pi\) |
0.991918 | − | 0.126883i | \(-0.0404974\pi\) | |||||||
\(32\) | 29.5585 | + | 17.0656i | 0.163289 | + | 0.0942751i | ||||
\(33\) | 39.4567 | − | 22.7804i | 0.208137 | − | 0.120168i | ||||
\(34\) | −383.685 | −1.93534 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −399.395 | −1.84905 | ||||||||
\(37\) | −179.660 | + | 103.727i | −0.798270 | + | 0.460881i | −0.842866 | − | 0.538124i | \(-0.819133\pi\) |
0.0445962 | + | 0.999005i | \(0.485800\pi\) | |||||||
\(38\) | 9.85830 | + | 5.69169i | 0.0420849 | + | 0.0242977i | ||||
\(39\) | −34.9871 | + | 60.5994i | −0.143652 | + | 0.248812i | ||||
\(40\) | −326.390 | + | 247.280i | −1.29017 | + | 0.977458i | ||||
\(41\) | 346.718 | 1.32069 | 0.660344 | − | 0.750964i | \(-0.270411\pi\) | ||||
0.660344 | + | 0.750964i | \(0.270411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 271.573i | 0.963129i | 0.876411 | + | 0.481564i | \(0.159931\pi\) | ||||
−0.876411 | + | 0.481564i | \(0.840069\pi\) | |||||||
\(44\) | −309.271 | − | 535.673i | −1.05964 | − | 1.83536i | ||||
\(45\) | −111.536 | + | 264.664i | −0.369484 | + | 0.876751i | ||||
\(46\) | 452.531 | − | 783.806i | 1.45048 | − | 2.51230i | ||||
\(47\) | 467.335 | − | 269.816i | 1.45038 | − | 0.837377i | 0.451877 | − | 0.892080i | \(-0.350754\pi\) |
0.998503 | + | 0.0547029i | \(0.0174212\pi\) | |||||||
\(48\) | − | 61.0938i | − | 0.183711i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 149.788 | + | 587.788i | 0.423663 | + | 1.66252i | ||||
\(51\) | −45.2749 | − | 78.4183i | −0.124309 | − | 0.215309i | ||||
\(52\) | 822.710 | + | 474.992i | 2.19402 | + | 1.26672i | ||||
\(53\) | 514.798 | + | 297.219i | 1.33421 | + | 0.770305i | 0.985941 | − | 0.167091i | \(-0.0534375\pi\) |
0.348265 | + | 0.937396i | \(0.386771\pi\) | |||||||
\(54\) | −146.401 | − | 253.574i | −0.368938 | − | 0.639020i | ||||
\(55\) | −441.338 | + | 55.3492i | −1.08200 | + | 0.135696i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.68648i | 0.00624268i | ||||||||
\(58\) | −262.946 | + | 151.812i | −0.595285 | + | 0.343688i | ||||
\(59\) | −112.336 | + | 194.571i | −0.247879 | + | 0.429339i | −0.962937 | − | 0.269726i | \(-0.913067\pi\) |
0.715058 | + | 0.699065i | \(0.246400\pi\) | |||||||
\(60\) | −183.445 | − | 77.3080i | −0.394710 | − | 0.166340i | ||||
\(61\) | −7.75441 | − | 13.4310i | −0.0162762 | − | 0.0281913i | 0.857773 | − | 0.514029i | \(-0.171848\pi\) |
−0.874049 | + | 0.485838i | \(0.838514\pi\) | |||||||
\(62\) | − | 1014.86i | − | 2.07883i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 592.403 | 1.15704 | ||||||||
\(65\) | 544.511 | − | 412.532i | 1.03905 | − | 0.787205i | ||||
\(66\) | 110.544 | − | 191.467i | 0.206166 | − | 0.357091i | ||||
\(67\) | 435.985 | + | 251.716i | 0.794986 | + | 0.458985i | 0.841715 | − | 0.539922i | \(-0.181546\pi\) |
−0.0467288 | + | 0.998908i | \(0.514880\pi\) | |||||||
\(68\) | −1064.62 | + | 614.661i | −1.89860 | + | 1.09616i | ||||
\(69\) | 213.594 | 0.372663 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −660.472 | −1.10399 | −0.551997 | − | 0.833846i | \(-0.686134\pi\) | ||||
−0.551997 | + | 0.833846i | \(0.686134\pi\) | |||||||
\(72\) | −814.802 | + | 470.426i | −1.33368 | + | 0.770003i | ||||
\(73\) | −601.156 | − | 347.078i | −0.963836 | − | 0.556471i | −0.0664843 | − | 0.997787i | \(-0.521178\pi\) |
−0.897351 | + | 0.441317i | \(0.854512\pi\) | |||||||
\(74\) | −503.344 | + | 871.817i | −0.790710 | + | 1.36955i | ||||
\(75\) | −102.458 | + | 99.9729i | −0.157745 | + | 0.153918i | ||||
\(76\) | 36.4722 | 0.0550480 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 339.556i | 0.492912i | ||||||||
\(79\) | 84.6277 | + | 146.580i | 0.120524 | + | 0.208753i | 0.919974 | − | 0.391979i | \(-0.128209\pi\) |
−0.799451 | + | 0.600732i | \(0.794876\pi\) | |||||||
\(80\) | −231.626 | + | 549.628i | −0.323708 | + | 0.768128i | ||||
\(81\) | −312.244 | + | 540.822i | −0.428318 | + | 0.741869i | ||||
\(82\) | 1457.07 | − | 841.239i | 1.96227 | − | 1.13292i | ||||
\(83\) | 335.518i | 0.443709i | 0.975080 | + | 0.221854i | \(0.0712110\pi\) | ||||
−0.975080 | + | 0.221854i | \(0.928789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 110.004 | + | 877.138i | 0.140372 | + | 1.11928i | ||||
\(86\) | 658.917 | + | 1141.28i | 0.826196 | + | 1.43101i | ||||
\(87\) | −62.0553 | − | 35.8276i | −0.0764716 | − | 0.0441509i | ||||
\(88\) | −1261.88 | − | 728.548i | −1.52860 | − | 0.882539i | ||||
\(89\) | 136.809 | + | 236.961i | 0.162941 | + | 0.282222i | 0.935922 | − | 0.352207i | \(-0.114569\pi\) |
−0.772981 | + | 0.634429i | \(0.781235\pi\) | |||||||
\(90\) | 173.428 | + | 1382.86i | 0.203121 | + | 1.61963i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2899.80i | − | 3.28614i | ||||||
\(93\) | 207.419 | − | 119.753i | 0.231273 | − | 0.133525i | ||||
\(94\) | 1309.31 | − | 2267.79i | 1.43665 | − | 2.48834i | ||||
\(95\) | 10.1853 | − | 24.1688i | 0.0109999 | − | 0.0261017i | ||||
\(96\) | 19.5437 | + | 33.8507i | 0.0207778 | + | 0.0359883i | ||||
\(97\) | 251.125i | 0.262865i | 0.991325 | + | 0.131433i | \(0.0419577\pi\) | ||||
−0.991325 | + | 0.131433i | \(0.958042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1021.98 | −1.03751 | ||||||||
\(100\) | 1357.25 | + | 1391.00i | 1.35725 | + | 1.39100i | ||||
\(101\) | −701.493 | + | 1215.02i | −0.691101 | + | 1.19702i | 0.280376 | + | 0.959890i | \(0.409541\pi\) |
−0.971477 | + | 0.237132i | \(0.923793\pi\) | |||||||
\(102\) | −380.532 | − | 219.700i | −0.369395 | − | 0.213270i | ||||
\(103\) | 348.656 | − | 201.297i | 0.333535 | − | 0.192566i | −0.323875 | − | 0.946100i | \(-0.604986\pi\) |
0.657409 | + | 0.753534i | \(0.271652\pi\) | |||||||
\(104\) | 2237.87 | 2.11001 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2884.56 | 2.64314 | ||||||||
\(107\) | 391.024 | − | 225.758i | 0.353287 | − | 0.203971i | −0.312845 | − | 0.949804i | \(-0.601282\pi\) |
0.666132 | + | 0.745834i | \(0.267949\pi\) | |||||||
\(108\) | −812.447 | − | 469.067i | −0.723868 | − | 0.417926i | ||||
\(109\) | 187.530 | − | 324.812i | 0.164790 | − | 0.285425i | −0.771790 | − | 0.635877i | \(-0.780639\pi\) |
0.936581 | + | 0.350452i | \(0.113972\pi\) | |||||||
\(110\) | −1720.41 | + | 1303.42i | −1.49123 | + | 1.12978i | ||||
\(111\) | −237.578 | −0.203153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 892.024i | − | 0.742607i | −0.928512 | − | 0.371303i | \(-0.878911\pi\) | ||
0.928512 | − | 0.371303i | \(-0.121089\pi\) | |||||||
\(114\) | 6.51818 | + | 11.2898i | 0.00535512 | + | 0.00927534i | ||||
\(115\) | −1921.59 | − | 809.805i | −1.55817 | − | 0.656649i | ||||
\(116\) | −486.403 | + | 842.475i | −0.389323 | + | 0.674327i | ||||
\(117\) | 1359.32 | − | 784.804i | 1.07410 | − | 0.620129i | ||||
\(118\) | 1090.24i | 0.850548i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −465.301 | + | 58.3545i | −0.353967 | + | 0.0443918i | ||||
\(121\) | −125.872 | − | 218.016i | −0.0945693 | − | 0.163799i | ||||
\(122\) | −65.1752 | − | 37.6289i | −0.0483663 | − | 0.0279243i | ||||
\(123\) | 343.868 | + | 198.532i | 0.252077 | + | 0.145537i | ||||
\(124\) | −1625.80 | − | 2815.96i | −1.17743 | − | 2.03936i | ||||
\(125\) | 1300.79 | − | 510.948i | 0.930770 | − | 0.365605i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1203.39i | − | 0.840813i | −0.907336 | − | 0.420407i | \(-0.861887\pi\) | ||
0.907336 | − | 0.420407i | \(-0.138113\pi\) | |||||||
\(128\) | 2253.08 | − | 1300.82i | 1.55583 | − | 0.898259i | ||||
\(129\) | −155.504 | + | 269.341i | −0.106135 | + | 0.183831i | ||||
\(130\) | 1287.36 | − | 3054.80i | 0.868533 | − | 2.06095i | ||||
\(131\) | −852.373 | − | 1476.35i | −0.568490 | − | 0.984653i | −0.996716 | − | 0.0809815i | \(-0.974195\pi\) |
0.428226 | − | 0.903672i | \(-0.359139\pi\) | |||||||
\(132\) | − | 708.360i | − | 0.467082i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2442.95 | 1.57492 | ||||||||
\(135\) | −537.719 | + | 407.386i | −0.342811 | + | 0.259720i | ||||
\(136\) | −1447.95 | + | 2507.93i | −0.912948 | + | 1.58127i | ||||
\(137\) | −465.784 | − | 268.921i | −0.290472 | − | 0.167704i | 0.347683 | − | 0.937612i | \(-0.386969\pi\) |
−0.638155 | + | 0.769908i | \(0.720302\pi\) | |||||||
\(138\) | 897.623 | − | 518.243i | 0.553701 | − | 0.319679i | ||||
\(139\) | 1587.63 | 0.968786 | 0.484393 | − | 0.874851i | \(-0.339041\pi\) | ||||
0.484393 | + | 0.874851i | \(0.339041\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 617.992 | 0.369109 | ||||||||
\(142\) | −2775.61 | + | 1602.50i | −1.64031 | + | 0.947034i | ||||
\(143\) | 2105.18 | + | 1215.42i | 1.23107 | + | 0.710761i | ||||
\(144\) | −685.205 | + | 1186.81i | −0.396531 | + | 0.686812i | ||||
\(145\) | 422.443 | + | 557.593i | 0.241945 | + | 0.319349i | ||||
\(146\) | −3368.45 | −1.90942 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3225.41i | 1.79140i | ||||||||
\(149\) | −876.296 | − | 1517.79i | −0.481805 | − | 0.834511i | 0.517977 | − | 0.855395i | \(-0.326685\pi\) |
−0.999782 | + | 0.0208837i | \(0.993352\pi\) | |||||||
\(150\) | −188.014 | + | 668.726i | −0.102342 | + | 0.364009i | ||||
\(151\) | −1036.50 | + | 1795.26i | −0.558602 | + | 0.967526i | 0.439012 | + | 0.898481i | \(0.355329\pi\) |
−0.997614 | + | 0.0690451i | \(0.978005\pi\) | |||||||
\(152\) | 74.4066 | − | 42.9587i | 0.0397051 | − | 0.0229237i | ||||
\(153\) | 2031.14i | 1.07326i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2320.06 | + | 290.964i | −1.20227 | + | 0.150779i | ||||
\(156\) | 543.965 | + | 942.175i | 0.279180 | + | 0.483554i | ||||
\(157\) | 944.904 | + | 545.541i | 0.480328 | + | 0.277318i | 0.720553 | − | 0.693399i | \(-0.243888\pi\) |
−0.240225 | + | 0.970717i | \(0.577221\pi\) | |||||||
\(158\) | 711.290 | + | 410.663i | 0.358147 | + | 0.206776i | ||||
\(159\) | 340.378 | + | 589.552i | 0.169772 | + | 0.294054i | ||||
\(160\) | −47.4852 | − | 378.633i | −0.0234627 | − | 0.187085i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3030.38i | 1.46969i | ||||||||
\(163\) | −968.260 | + | 559.025i | −0.465276 | + | 0.268627i | −0.714260 | − | 0.699880i | \(-0.753237\pi\) |
0.248984 | + | 0.968508i | \(0.419903\pi\) | |||||||
\(164\) | 2695.31 | − | 4668.42i | 1.28335 | − | 2.22282i | ||||
\(165\) | −469.404 | − | 197.818i | −0.221473 | − | 0.0933341i | ||||
\(166\) | 814.064 | + | 1410.00i | 0.380624 | + | 0.659261i | ||||
\(167\) | − | 3355.23i | − | 1.55470i | −0.629066 | − | 0.777352i | \(-0.716562\pi\) | ||
0.629066 | − | 0.777352i | \(-0.283438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1536.40 | −0.699318 | ||||||||
\(170\) | 2590.48 | + | 3419.24i | 1.16871 | + | 1.54261i | ||||
\(171\) | 30.1305 | − | 52.1876i | 0.0134745 | − | 0.0233385i | ||||
\(172\) | 3656.63 | + | 2111.16i | 1.62102 | + | 0.935897i | ||||
\(173\) | −2831.07 | + | 1634.52i | −1.24417 | + | 0.718323i | −0.969941 | − | 0.243340i | \(-0.921757\pi\) |
−0.274232 | + | 0.961664i | \(0.588424\pi\) | |||||||
\(174\) | −347.714 | −0.151495 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2122.35 | −0.908967 | ||||||||
\(177\) | −222.825 | + | 128.648i | −0.0946246 | + | 0.0546316i | ||||
\(178\) | 1149.87 | + | 663.879i | 0.484194 | + | 0.279550i | ||||
\(179\) | −1064.02 | + | 1842.93i | −0.444293 | + | 0.769539i | −0.998003 | − | 0.0631715i | \(-0.979879\pi\) |
0.553709 | + | 0.832710i | \(0.313212\pi\) | |||||||
\(180\) | 2696.55 | + | 3559.23i | 1.11660 | + | 1.47383i | ||||
\(181\) | −922.343 | −0.378769 | −0.189385 | − | 0.981903i | \(-0.560649\pi\) | ||||
−0.189385 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 17.7609i | − | 0.00717443i | ||||||
\(184\) | −3415.52 | − | 5915.86i | −1.36845 | − | 2.37023i | ||||
\(185\) | 2137.36 | + | 900.736i | 0.849416 | + | 0.357964i | ||||
\(186\) | 581.114 | − | 1006.52i | 0.229082 | − | 0.396782i | ||||
\(187\) | −2724.19 | + | 1572.81i | −1.06531 | + | 0.615056i | ||||
\(188\) | − | 8389.99i | − | 3.25480i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.8372 | − | 126.281i | −0.00604710 | − | 0.0482178i | ||||
\(191\) | 554.086 | + | 959.705i | 0.209907 | + | 0.363570i | 0.951685 | − | 0.307076i | \(-0.0993505\pi\) |
−0.741778 | + | 0.670646i | \(0.766017\pi\) | |||||||
\(192\) | 587.534 | + | 339.213i | 0.220842 | + | 0.127503i | ||||
\(193\) | 241.661 | + | 139.523i | 0.0901304 | + | 0.0520368i | 0.544388 | − | 0.838834i | \(-0.316762\pi\) |
−0.454257 | + | 0.890870i | \(0.650095\pi\) | |||||||
\(194\) | 609.304 | + | 1055.35i | 0.225492 | + | 0.390564i | ||||
\(195\) | 776.254 | − | 97.3518i | 0.285070 | − | 0.0357513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1232.54i | 0.445759i | 0.974846 | + | 0.222879i | \(0.0715456\pi\) | ||||
−0.974846 | + | 0.222879i | \(0.928454\pi\) | |||||||
\(198\) | −4294.85 | + | 2479.63i | −1.54152 | + | 0.889999i | ||||
\(199\) | −750.322 | + | 1299.60i | −0.267281 | + | 0.462944i | −0.968159 | − | 0.250337i | \(-0.919459\pi\) |
0.700878 | + | 0.713281i | \(0.252792\pi\) | |||||||
\(200\) | 4407.30 | + | 1239.12i | 1.55822 | + | 0.438096i | ||||
\(201\) | 288.268 | + | 499.295i | 0.101158 | + | 0.175212i | ||||
\(202\) | 6808.12i | 2.37137i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1407.83 | −0.483176 | ||||||||
\(205\) | −2340.89 | − | 3089.80i | −0.797536 | − | 1.05269i | ||||
\(206\) | 976.810 | − | 1691.88i | 0.330376 | − | 0.572229i | ||||
\(207\) | −4149.29 | − | 2395.59i | −1.39322 | − | 0.804373i | ||||
\(208\) | 2822.90 | − | 1629.80i | 0.941023 | − | 0.543300i | ||||
\(209\) | 93.3261 | 0.0308876 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3971.90 | −1.29591 | −0.647955 | − | 0.761679i | \(-0.724376\pi\) | ||||
−0.647955 | + | 0.761679i | \(0.724376\pi\) | |||||||
\(212\) | 8003.88 | − | 4621.04i | 2.59297 | − | 1.49705i | ||||
\(213\) | −655.044 | − | 378.190i | −0.210718 | − | 0.121658i | ||||
\(214\) | 1095.51 | − | 1897.48i | 0.349942 | − | 0.606117i | ||||
\(215\) | 2420.15 | − | 1833.55i | 0.767686 | − | 0.581614i | ||||
\(216\) | −2209.96 | −0.696150 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 1820.01i | − | 0.565445i | ||||||
\(219\) | −397.477 | − | 688.450i | −0.122644 | − | 0.212425i | ||||
\(220\) | −2685.62 | + | 6372.73i | −0.823020 | + | 1.95295i | ||||
\(221\) | 2415.60 | − | 4183.93i | 0.735251 | − | 1.27349i | ||||
\(222\) | −998.414 | + | 576.435i | −0.301843 | + | 0.174269i | ||||
\(223\) | 2861.98i | 0.859429i | 0.902965 | + | 0.429715i | \(0.141386\pi\) | ||||
−0.902965 | + | 0.429715i | \(0.858614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3111.62 | − | 792.941i | 0.921961 | − | 0.234946i | ||||
\(226\) | −2164.31 | − | 3748.70i | −0.637026 | − | 1.10336i | ||||
\(227\) | −1793.50 | − | 1035.48i | −0.524400 | − | 0.302763i | 0.214333 | − | 0.976761i | \(-0.431242\pi\) |
−0.738733 | + | 0.673998i | \(0.764576\pi\) | |||||||
\(228\) | 36.1724 | + | 20.8842i | 0.0105069 | + | 0.00606617i | ||||
\(229\) | −2879.11 | − | 4986.76i | −0.830816 | − | 1.43902i | −0.897392 | − | 0.441234i | \(-0.854541\pi\) |
0.0665762 | − | 0.997781i | \(-0.478792\pi\) | |||||||
\(230\) | −10040.2 | + | 1259.17i | −2.87841 | + | 0.360988i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2291.64i | 0.648506i | ||||||||
\(233\) | −1428.93 | + | 824.995i | −0.401771 | + | 0.231962i | −0.687248 | − | 0.726423i | \(-0.741181\pi\) |
0.285477 | + | 0.958386i | \(0.407848\pi\) | |||||||
\(234\) | 3808.33 | − | 6596.22i | 1.06392 | − | 1.84277i | ||||
\(235\) | −5559.74 | − | 2343.01i | −1.54331 | − | 0.650387i | ||||
\(236\) | 1746.55 | + | 3025.12i | 0.481741 | + | 0.834400i | ||||
\(237\) | 193.833i | 0.0531258i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4008.31 | 1.08484 | 0.542419 | − | 0.840108i | \(-0.317509\pi\) | ||||
0.542419 | + | 0.840108i | \(0.317509\pi\) | |||||||
\(240\) | −544.442 | + | 412.480i | −0.146432 | + | 0.110939i | ||||
\(241\) | −1575.61 | + | 2729.03i | −0.421136 | + | 0.729428i | −0.996051 | − | 0.0887847i | \(-0.971702\pi\) |
0.574915 | + | 0.818213i | \(0.305035\pi\) | |||||||
\(242\) | −1057.94 | − | 610.804i | −0.281021 | − | 0.162248i | ||||
\(243\) | −2030.25 | + | 1172.17i | −0.535970 | + | 0.309443i | ||||
\(244\) | −241.125 | −0.0632641 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1926.79 | 0.499381 | ||||||||
\(247\) | −124.131 | + | 71.6672i | −0.0319768 | + | 0.0184618i | ||||
\(248\) | −6633.55 | − | 3829.88i | −1.69851 | − | 0.980636i | ||||
\(249\) | −192.119 | + | 332.760i | −0.0488958 | + | 0.0846900i | ||||
\(250\) | 4226.82 | − | 5303.34i | 1.06931 | − | 1.34165i | ||||
\(251\) | 3531.54 | 0.888084 | 0.444042 | − | 0.896006i | \(-0.353544\pi\) | ||||
0.444042 | + | 0.896006i | \(0.353544\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7420.10i | − | 1.84386i | ||||||
\(254\) | −2919.77 | − | 5057.19i | −0.721270 | − | 1.24928i | ||||
\(255\) | −393.154 | + | 932.918i | −0.0965501 | + | 0.229104i | ||||
\(256\) | 3942.72 | − | 6829.00i | 0.962579 | − | 1.66724i | ||||
\(257\) | −4923.81 | + | 2842.76i | −1.19509 | + | 0.689987i | −0.959457 | − | 0.281854i | \(-0.909050\pi\) |
−0.235636 | + | 0.971841i | \(0.575717\pi\) | |||||||
\(258\) | 1509.20i | 0.364180i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1321.67 | − | 10538.6i | −0.315255 | − | 2.51375i | ||||
\(261\) | 803.659 | + | 1391.98i | 0.190595 | + | 0.330120i | ||||
\(262\) | −7164.13 | − | 4136.21i | −1.68932 | − | 0.975329i | ||||
\(263\) | 3846.85 | + | 2220.98i | 0.901927 | + | 0.520728i | 0.877825 | − | 0.478982i | \(-0.158994\pi\) |
0.0241019 | + | 0.999710i | \(0.492327\pi\) | |||||||
\(264\) | −834.340 | − | 1445.12i | −0.194508 | − | 0.336898i | ||||
\(265\) | −827.013 | − | 6594.36i | −0.191710 | − | 1.52863i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 313.351i | 0.0718230i | ||||||||
\(268\) | 6778.53 | − | 3913.58i | 1.54502 | − | 0.892016i | ||||
\(269\) | −839.565 | + | 1454.17i | −0.190294 | + | 0.329599i | −0.945348 | − | 0.326064i | \(-0.894278\pi\) |
0.755053 | + | 0.655663i | \(0.227611\pi\) | |||||||
\(270\) | −1271.31 | + | 3016.69i | −0.286553 | + | 0.679963i | ||||
\(271\) | 570.883 | + | 988.799i | 0.127966 | + | 0.221643i | 0.922888 | − | 0.385068i | \(-0.125822\pi\) |
−0.794923 | + | 0.606711i | \(0.792489\pi\) | |||||||
\(272\) | 4218.07i | 0.940287i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2609.92 | −0.575442 | ||||||||
\(275\) | 3472.98 | + | 3559.32i | 0.761558 | + | 0.780492i | ||||
\(276\) | 1660.44 | − | 2875.97i | 0.362126 | − | 0.627221i | ||||
\(277\) | −2350.93 | − | 1357.31i | −0.509940 | − | 0.294414i | 0.222869 | − | 0.974848i | \(-0.428458\pi\) |
−0.732809 | + | 0.680434i | \(0.761791\pi\) | |||||||
\(278\) | 6671.97 | − | 3852.06i | 1.43942 | − | 0.831048i | ||||
\(279\) | −5372.44 | −1.15283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5343.68 | −1.13444 | −0.567219 | − | 0.823567i | \(-0.691981\pi\) | ||||
−0.567219 | + | 0.823567i | \(0.691981\pi\) | |||||||
\(282\) | 2597.09 | − | 1499.43i | 0.548420 | − | 0.316631i | ||||
\(283\) | 5887.65 | + | 3399.24i | 1.23669 | + | 0.714006i | 0.968417 | − | 0.249336i | \(-0.0802123\pi\) |
0.268277 | + | 0.963342i | \(0.413546\pi\) | |||||||
\(284\) | −5134.38 | + | 8893.01i | −1.07278 | + | 1.85811i | ||||
\(285\) | 23.9407 | − | 18.1380i | 0.00497589 | − | 0.00376983i | ||||
\(286\) | 11795.9 | 2.43883 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 876.780i | − | 0.179391i | ||||||
\(289\) | 669.389 | + | 1159.42i | 0.136249 | + | 0.235990i | ||||
\(290\) | 3128.19 | + | 1318.29i | 0.633426 | + | 0.266941i | ||||
\(291\) | −143.796 | + | 249.061i | −0.0289672 | + | 0.0501726i | ||||
\(292\) | −9346.54 | + | 5396.23i | −1.87317 | + | 1.08147i | ||||
\(293\) | 5119.59i | 1.02078i | 0.859942 | + | 0.510392i | \(0.170500\pi\) | ||||
−0.859942 | + | 0.510392i | \(0.829500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2492.38 | − | 312.575i | 0.491905 | − | 0.0616909i | ||||
\(296\) | 3799.04 | + | 6580.14i | 0.745996 | + | 1.29210i | ||||
\(297\) | −2078.92 | − | 1200.26i | −0.406165 | − | 0.234499i | ||||
\(298\) | −7365.21 | − | 4252.30i | −1.43173 | − | 0.826608i | ||||
\(299\) | 5698.06 | + | 9869.33i | 1.10210 | + | 1.90889i | ||||
\(300\) | 549.606 | + | 2156.73i | 0.105772 | + | 0.415063i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10059.4i | 1.91673i | ||||||||
\(303\) | −1391.46 | + | 803.357i | −0.263819 | + | 0.152316i | ||||
\(304\) | 62.5720 | − | 108.378i | 0.0118051 | − | 0.0204470i | ||||
\(305\) | −67.3371 | + | 159.785i | −0.0126417 | + | 0.0299975i | ||||
\(306\) | 4928.15 | + | 8535.80i | 0.920665 | + | 1.59464i | ||||
\(307\) | 4188.66i | 0.778695i | 0.921091 | + | 0.389347i | \(0.127299\pi\) | ||||
−0.921091 | + | 0.389347i | \(0.872701\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 461.054 | 0.0848817 | ||||||||
\(310\) | −9044.00 | + | 6851.91i | −1.65698 | + | 1.25536i | ||||
\(311\) | 4879.59 | − | 8451.70i | 0.889699 | − | 1.54100i | 0.0494671 | − | 0.998776i | \(-0.484248\pi\) |
0.840232 | − | 0.542228i | \(-0.182419\pi\) | |||||||
\(312\) | 2219.48 | + | 1281.42i | 0.402735 | + | 0.232519i | ||||
\(313\) | 5162.12 | − | 2980.35i | 0.932205 | − | 0.538209i | 0.0446970 | − | 0.999001i | \(-0.485768\pi\) |
0.887508 | + | 0.460792i | \(0.152434\pi\) | |||||||
\(314\) | 5294.57 | 0.951560 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2631.52 | 0.468463 | ||||||||
\(317\) | −2357.62 | + | 1361.18i | −0.417720 | + | 0.241171i | −0.694102 | − | 0.719877i | \(-0.744198\pi\) |
0.276381 | + | 0.961048i | \(0.410865\pi\) | |||||||
\(318\) | 2860.85 | + | 1651.71i | 0.504493 | + | 0.291269i | ||||
\(319\) | −1244.62 | + | 2155.75i | −0.218450 | + | 0.378367i | ||||
\(320\) | −3999.66 | − | 5279.24i | −0.698711 | − | 0.922246i | ||||
\(321\) | 517.081 | 0.0899085 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 185.481i | − | 0.0319519i | ||||||
\(324\) | 4854.65 | + | 8408.50i | 0.832416 | + | 1.44179i | ||||
\(325\) | −7352.62 | − | 2067.21i | −1.25492 | − | 0.352825i | ||||
\(326\) | −2712.72 | + | 4698.57i | −0.460870 | + | 0.798250i | ||||
\(327\) | 371.978 | − | 214.762i | 0.0629065 | − | 0.0363191i | ||||
\(328\) | − | 12698.7i | − | 2.13771i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2452.62 | + | 307.588i | −0.409128 | + | 0.0513097i | ||||
\(331\) | −189.377 | − | 328.010i | −0.0314474 | − | 0.0544684i | 0.849873 | − | 0.526987i | \(-0.176678\pi\) |
−0.881321 | + | 0.472518i | \(0.843345\pi\) | |||||||
\(332\) | 4517.62 | + | 2608.25i | 0.746797 | + | 0.431163i | ||||
\(333\) | 4615.20 | + | 2664.59i | 0.759494 | + | 0.438494i | ||||
\(334\) | −8140.78 | − | 14100.2i | −1.33366 | − | 2.30997i | ||||
\(335\) | −700.402 | − | 5584.80i | −0.114230 | − | 0.910836i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8031.54i | 1.29824i | 0.760687 | + | 0.649118i | \(0.224862\pi\) | ||||
−0.760687 | + | 0.649118i | \(0.775138\pi\) | |||||||
\(338\) | −6456.67 | + | 3727.76i | −1.03904 | + | 0.599892i | ||||
\(339\) | 510.777 | − | 884.693i | 0.0818337 | − | 0.141740i | ||||
\(340\) | 12665.5 | + | 5337.54i | 2.02024 | + | 0.851379i | ||||
\(341\) | −4160.14 | − | 7205.57i | −0.660658 | − | 1.14429i | ||||
\(342\) | − | 292.422i | − | 0.0462350i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9946.49 | 1.55895 | ||||||||
\(345\) | −1442.10 | − | 1903.46i | −0.225044 | − | 0.297040i | ||||
\(346\) | −7931.63 | + | 13738.0i | −1.23239 | + | 2.13456i | ||||
\(347\) | 563.035 | + | 325.069i | 0.0871047 | + | 0.0502899i | 0.542920 | − | 0.839785i | \(-0.317319\pi\) |
−0.455815 | + | 0.890075i | \(0.650652\pi\) | |||||||
\(348\) | −964.812 | + | 557.034i | −0.148619 | + | 0.0858051i | ||||
\(349\) | 1240.68 | 0.190292 | 0.0951462 | − | 0.995463i | \(-0.469668\pi\) | ||||
0.0951462 | + | 0.995463i | \(0.469668\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3686.83 | 0.560651 | ||||||||
\(352\) | 1175.95 | − | 678.933i | 0.178063 | − | 0.102805i | ||||
\(353\) | 6818.95 | + | 3936.92i | 1.02815 | + | 0.593601i | 0.916453 | − | 0.400141i | \(-0.131039\pi\) |
0.111694 | + | 0.993743i | \(0.464372\pi\) | |||||||
\(354\) | −624.276 | + | 1081.28i | −0.0937286 | + | 0.162343i | ||||
\(355\) | 4459.23 | + | 5885.85i | 0.666680 | + | 0.879967i | ||||
\(356\) | 4254.11 | 0.633336 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10326.5i | 1.52450i | ||||||||
\(359\) | −203.360 | − | 352.231i | −0.0298968 | − | 0.0517828i | 0.850690 | − | 0.525668i | \(-0.176185\pi\) |
−0.880587 | + | 0.473885i | \(0.842851\pi\) | |||||||
\(360\) | 9693.44 | + | 4085.05i | 1.41914 | + | 0.598058i | ||||
\(361\) | 3426.75 | − | 5935.30i | 0.499599 | − | 0.865331i | ||||
\(362\) | −3876.11 | + | 2237.88i | −0.562774 | + | 0.324917i | ||||
\(363\) | − | 288.299i | − | 0.0416854i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 965.746 | + | 7700.57i | 0.138492 | + | 1.10429i | ||||
\(366\) | −43.0930 | − | 74.6393i | −0.00615440 | − | 0.0106597i | ||||
\(367\) | −566.619 | − | 327.138i | −0.0805920 | − | 0.0465298i | 0.459162 | − | 0.888352i | \(-0.348150\pi\) |
−0.539754 | + | 0.841822i | \(0.681483\pi\) | |||||||
\(368\) | −8616.82 | − | 4974.93i | −1.22061 | − | 0.704717i | ||||
\(369\) | −4453.33 | − | 7713.39i | −0.628268 | − | 1.08819i | ||||
\(370\) | 11167.6 | − | 1400.56i | 1.56913 | − | 0.196788i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 3723.76i | − | 0.519000i | ||||||
\(373\) | 4763.50 | − | 2750.21i | 0.661245 | − | 0.381770i | −0.131506 | − | 0.991315i | \(-0.541981\pi\) |
0.792751 | + | 0.609545i | \(0.208648\pi\) | |||||||
\(374\) | −7632.21 | + | 13219.4i | −1.05522 | + | 1.82769i | ||||
\(375\) | 1582.67 | + | 238.090i | 0.217943 | + | 0.0327865i | ||||
\(376\) | −9882.13 | − | 17116.4i | −1.35540 | − | 2.34763i | ||||
\(377\) | − | 3823.10i | − | 0.522280i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1771.48 | 0.240091 | 0.120046 | − | 0.992768i | \(-0.461696\pi\) | ||||
0.120046 | + | 0.992768i | \(0.461696\pi\) | |||||||
\(380\) | −246.245 | − | 325.024i | −0.0332423 | − | 0.0438774i | ||||
\(381\) | 689.065 | − | 1193.50i | 0.0926559 | − | 0.160485i | ||||
\(382\) | 4657.05 | + | 2688.75i | 0.623758 | + | 0.360127i | ||||
\(383\) | −7712.17 | + | 4452.62i | −1.02891 | + | 0.594043i | −0.916673 | − | 0.399638i | \(-0.869136\pi\) |
−0.112240 | + | 0.993681i | \(0.535802\pi\) | |||||||
\(384\) | 2979.42 | 0.395945 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1354.10 | 0.178554 | ||||||||
\(387\) | 6041.66 | − | 3488.15i | 0.793579 | − | 0.458173i | ||||
\(388\) | 3381.31 | + | 1952.20i | 0.442422 | + | 0.255433i | ||||
\(389\) | 4686.74 | − | 8117.67i | 0.610866 | − | 1.05805i | −0.380228 | − | 0.924893i | \(-0.624155\pi\) |
0.991095 | − | 0.133159i | \(-0.0425121\pi\) | |||||||
\(390\) | 3025.98 | − | 2292.54i | 0.392888 | − | 0.297659i | ||||
\(391\) | −14747.1 | −1.90740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1952.29i | − | 0.250586i | ||||||
\(394\) | 2990.49 | + | 5179.68i | 0.382383 | + | 0.662306i | ||||
\(395\) | 734.883 | − | 1743.81i | 0.0936101 | − | 0.222128i | ||||
\(396\) | −7944.70 | + | 13760.6i | −1.00817 | + | 1.74621i | ||||
\(397\) | 9092.24 | − | 5249.41i | 1.14944 | − | 0.663628i | 0.200687 | − | 0.979655i | \(-0.435683\pi\) |
0.948750 | + | 0.316027i | \(0.102349\pi\) | |||||||
\(398\) | 7282.01i | 0.917121i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6461.89 | − | 1646.70i | 0.807736 | − | 0.205837i | ||||
\(401\) | 1399.27 | + | 2423.60i | 0.174255 | + | 0.301818i | 0.939903 | − | 0.341441i | \(-0.110915\pi\) |
−0.765648 | + | 0.643259i | \(0.777582\pi\) | |||||||
\(402\) | 2422.87 | + | 1398.85i | 0.300602 | + | 0.173552i | ||||
\(403\) | 11066.6 | + | 6389.33i | 1.36791 | + | 0.789764i | ||||
\(404\) | 10906.5 | + | 18890.7i | 1.34312 | + | 2.32635i | ||||
\(405\) | 6927.72 | − | 868.821i | 0.849978 | − | 0.106598i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8253.28i | 1.00516i | ||||||||
\(408\) | −2872.11 | + | 1658.21i | −0.348506 | + | 0.201210i | ||||
\(409\) | 3795.09 | − | 6573.29i | 0.458815 | − | 0.794690i | −0.540084 | − | 0.841611i | \(-0.681608\pi\) |
0.998899 | + | 0.0469208i | \(0.0149408\pi\) | |||||||
\(410\) | −17334.3 | − | 7305.08i | −2.08800 | − | 0.879932i | ||||
\(411\) | −307.971 | − | 533.421i | −0.0369612 | − | 0.0640187i | ||||
\(412\) | − | 6259.36i | − | 0.748487i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −23249.7 | −2.76004 | ||||||||
\(415\) | 2989.99 | − | 2265.27i | 0.353669 | − | 0.267947i | ||||
\(416\) | −1042.74 | + | 1806.07i | −0.122895 | + | 0.212860i | ||||
\(417\) | 1574.58 | + | 909.086i | 0.184911 | + | 0.106758i | ||||
\(418\) | 392.200 | − | 226.437i | 0.0458926 | − | 0.0264961i | ||||
\(419\) | 11070.5 | 1.29076 | 0.645382 | − | 0.763860i | \(-0.276698\pi\) | ||||
0.645382 | + | 0.763860i | \(0.276698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8891.82 | 1.02936 | 0.514680 | − | 0.857382i | \(-0.327911\pi\) | ||||
0.514680 | + | 0.857382i | \(0.327911\pi\) | |||||||
\(422\) | −16691.8 | + | 9637.00i | −1.92546 | + | 1.11166i | ||||
\(423\) | −12005.1 | − | 6931.17i | −1.37993 | − | 0.796702i | ||||
\(424\) | 10885.8 | − | 18854.7i | 1.24684 | − | 2.15959i | ||||
\(425\) | 7073.98 | − | 6902.38i | 0.807385 | − | 0.787799i | ||||
\(426\) | −3670.40 | −0.417444 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 7019.99i | − | 0.792814i | ||||||
\(429\) | 1391.92 | + | 2410.87i | 0.156649 | + | 0.271324i | ||||
\(430\) | 5721.85 | − | 13577.4i | 0.641702 | − | 1.52270i | ||||
\(431\) | −7619.87 | + | 13198.0i | −0.851592 | + | 1.47500i | 0.0281792 | + | 0.999603i | \(0.491029\pi\) |
−0.879771 | + | 0.475398i | \(0.842304\pi\) | |||||||
\(432\) | −2787.68 | + | 1609.47i | −0.310469 | + | 0.179249i | ||||
\(433\) | 15959.0i | 1.77123i | 0.464421 | + | 0.885615i | \(0.346263\pi\) | ||||
−0.464421 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 99.6907 | + | 794.904i | 0.0109880 | + | 0.0876154i | ||||
\(436\) | −2915.65 | − | 5050.05i | −0.320262 | − | 0.554710i | ||||
\(437\) | 378.907 | + | 218.762i | 0.0414774 | + | 0.0239470i | ||||
\(438\) | −3340.77 | − | 1928.79i | −0.364447 | − | 0.210414i | ||||
\(439\) | 5417.23 | + | 9382.92i | 0.588953 | + | 1.02010i | 0.994370 | + | 0.105964i | \(0.0337930\pi\) |
−0.405417 | + | 0.914132i | \(0.632874\pi\) | |||||||
\(440\) | 2027.19 | + | 16164.2i | 0.219642 | + | 1.75136i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 23443.8i | − | 2.52287i | ||||||
\(443\) | −7147.51 | + | 4126.62i | −0.766565 | + | 0.442577i | −0.831648 | − | 0.555303i | \(-0.812602\pi\) |
0.0650828 | + | 0.997880i | \(0.479269\pi\) | |||||||
\(444\) | −1846.89 | + | 3198.90i | −0.197409 | + | 0.341922i | ||||
\(445\) | 1188.01 | − | 2819.04i | 0.126556 | − | 0.300304i | ||||
\(446\) | 6944.02 | + | 12027.4i | 0.737239 | + | 1.27694i | ||||
\(447\) | − | 2007.09i | − | 0.212376i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11022.5 | 1.15853 | 0.579267 | − | 0.815138i | \(-0.303339\pi\) | ||||
0.579267 | + | 0.815138i | \(0.303339\pi\) | |||||||
\(450\) | 11152.6 | − | 10882.0i | 1.16830 | − | 1.13996i | ||||
\(451\) | 6896.85 | − | 11945.7i | 0.720089 | − | 1.24723i | ||||
\(452\) | −12010.8 | − | 6934.42i | −1.24986 | − | 0.721610i | ||||
\(453\) | −2055.95 | + | 1187.01i | −0.213239 | + | 0.123113i | ||||
\(454\) | −10049.5 | −1.03887 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 98.3934 | 0.0101046 | ||||||||
\(457\) | 8078.79 | − | 4664.29i | 0.826936 | − | 0.477432i | −0.0258662 | − | 0.999665i | \(-0.508234\pi\) |
0.852803 | + | 0.522234i | \(0.174901\pi\) | |||||||
\(458\) | −24198.7 | − | 13971.1i | −2.46885 | − | 1.42539i | ||||
\(459\) | −2385.46 | + | 4131.74i | −0.242579 | + | 0.420160i | ||||
\(460\) | −25841.8 | + | 19578.2i | −2.61930 | + | 1.98443i | ||||
\(461\) | −16806.4 | −1.69794 | −0.848972 | − | 0.528438i | \(-0.822778\pi\) | ||||
−0.848972 | + | 0.528438i | \(0.822778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8238.55i | − | 0.826950i | −0.910515 | − | 0.413475i | \(-0.864315\pi\) | ||
0.910515 | − | 0.413475i | \(-0.135685\pi\) | |||||||
\(464\) | 1668.96 | + | 2890.72i | 0.166981 | + | 0.289220i | ||||
\(465\) | −2467.60 | − | 1039.90i | −0.246091 | − | 0.103708i | ||||
\(466\) | −4003.36 | + | 6934.03i | −0.397966 | + | 0.689297i | ||||
\(467\) | 16943.0 | − | 9782.06i | 1.67886 | − | 0.969293i | 0.716478 | − | 0.697610i | \(-0.245753\pi\) |
0.962387 | − | 0.271683i | \(-0.0875802\pi\) | |||||||
\(468\) | − | 24403.6i | − | 2.41038i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −29049.4 | + | 3643.15i | −2.85096 | + | 0.357545i | ||||
\(471\) | 624.759 | + | 1082.11i | 0.0611197 | + | 0.105862i | ||||
\(472\) | 7126.26 | + | 4114.35i | 0.694942 | + | 0.401225i | ||||
\(473\) | 9356.71 | + | 5402.10i | 0.909560 | + | 0.525135i | ||||
\(474\) | 470.296 | + | 814.577i | 0.0455726 | + | 0.0789341i | ||||
\(475\) | −284.149 | + | 72.4103i | −0.0274476 | + | 0.00699455i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 15270.2i | − | 1.46578i | ||||||
\(478\) | 16844.8 | − | 9725.35i | 1.61185 | − | 0.930601i | ||||
\(479\) | 626.668 | − | 1085.42i | 0.0597770 | − | 0.103537i | −0.834588 | − | 0.550874i | \(-0.814294\pi\) |
0.894365 | + | 0.447337i | \(0.147628\pi\) | |||||||
\(480\) | 169.712 | − | 402.711i | 0.0161380 | − | 0.0382941i | ||||
\(481\) | −6337.88 | − | 10977.5i | −0.600795 | − | 1.04061i | ||||
\(482\) | 15291.5i | 1.44504i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3914.01 | −0.367582 | ||||||||
\(485\) | 2237.92 | − | 1695.49i | 0.209523 | − | 0.158739i | ||||
\(486\) | −5688.04 | + | 9851.98i | −0.530895 | + | 0.919537i | ||||
\(487\) | −3085.94 | − | 1781.67i | −0.287141 | − | 0.165781i | 0.349511 | − | 0.936932i | \(-0.386348\pi\) |
−0.636652 | + | 0.771152i | \(0.719681\pi\) | |||||||
\(488\) | −491.917 | + | 284.008i | −0.0456312 | + | 0.0263452i | ||||
\(489\) | −1280.40 | −0.118409 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10148.4 | −0.932774 | −0.466387 | − | 0.884581i | \(-0.654445\pi\) | ||||
−0.466387 | + | 0.884581i | \(0.654445\pi\) | |||||||
\(492\) | 5346.32 | − | 3086.70i | 0.489900 | − | 0.282844i | ||||
\(493\) | 4284.45 | + | 2473.63i | 0.391404 | + | 0.225977i | ||||
\(494\) | −347.771 | + | 602.358i | −0.0316740 | + | 0.0548610i | ||||
\(495\) | 6900.00 | + | 9107.48i | 0.626530 | + | 0.826972i | ||||
\(496\) | −11156.9 | −1.01000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1864.55i | 0.167776i | ||||||||
\(499\) | 4105.28 | + | 7110.55i | 0.368292 | + | 0.637900i | 0.989299 | − | 0.145905i | \(-0.0466095\pi\) |
−0.621007 | + | 0.783805i | \(0.713276\pi\) | |||||||
\(500\) | 3232.36 | − | 21486.7i | 0.289112 | − | 1.92183i | ||||
\(501\) | 1921.22 | − | 3327.66i | 0.171325 | − | 0.296744i | ||||
\(502\) | 14841.2 | − | 8568.56i | 1.31951 | − | 0.761820i | ||||
\(503\) | 8479.88i | 0.751688i | 0.926683 | + | 0.375844i | \(0.122647\pi\) | ||||
−0.926683 | + | 0.375844i | \(0.877353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15564.0 | − | 1951.91i | 1.37146 | − | 0.171998i | ||||
\(506\) | −18003.3 | − | 31182.7i | −1.58171 | − | 2.73961i | ||||
\(507\) | −1523.77 | − | 879.751i | −0.133478 | − | 0.0770634i | ||||
\(508\) | −16203.1 | − | 9354.89i | −1.41515 | − | 0.817040i | ||||
\(509\) | 3511.50 | + | 6082.10i | 0.305785 | + | 0.529636i | 0.977436 | − | 0.211232i | \(-0.0677477\pi\) |
−0.671651 | + | 0.740868i | \(0.734414\pi\) | |||||||
\(510\) | 611.317 | + | 4874.46i | 0.0530776 | + | 0.423225i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 17451.7i | − | 1.50638i | ||||||
\(513\) | 122.583 | − | 70.7732i | 0.0105500 | − | 0.00609106i | ||||
\(514\) | −13794.8 | + | 23893.2i | −1.18378 | + | 2.05036i | ||||
\(515\) | −4147.85 | − | 1748.00i | −0.354905 | − | 0.149565i | ||||
\(516\) | 2417.72 | + | 4187.61i | 0.206268 | + | 0.357266i | ||||
\(517\) | − | 21468.6i | − | 1.82628i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3743.73 | −0.316631 | ||||||||
\(520\) | −15109.2 | − | 19943.0i | −1.27419 | − | 1.68184i | ||||
\(521\) | −3279.25 | + | 5679.82i | −0.275751 | + | 0.477615i | −0.970324 | − | 0.241807i | \(-0.922260\pi\) |
0.694573 | + | 0.719422i | \(0.255593\pi\) | |||||||
\(522\) | 6754.69 | + | 3899.82i | 0.566370 | + | 0.326994i | ||||
\(523\) | 91.9094 | − | 53.0639i | 0.00768435 | − | 0.00443656i | −0.496153 | − | 0.868235i | \(-0.665254\pi\) |
0.503837 | + | 0.863799i | \(0.331921\pi\) | |||||||
\(524\) | −26504.7 | −2.20966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21555.0 | 1.78677 | ||||||||
\(527\) | −14320.7 | + | 8268.08i | −1.18372 | + | 0.683421i | ||||
\(528\) | −2104.91 | − | 1215.27i | −0.173493 | − | 0.100166i | ||||
\(529\) | 11309.7 | − | 19588.9i | 0.929537 | − | 1.61001i | ||||
\(530\) | −19475.3 | − | 25706.0i | −1.59614 | − | 2.10679i | ||||
\(531\) | 5771.48 | 0.471677 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21185.0i | 1.72162i | ||||||||
\(534\) | 760.281 | + | 1316.84i | 0.0616115 | + | 0.106714i | ||||
\(535\) | −4651.89 | − | 1960.42i | −0.375923 | − | 0.158423i | ||||
\(536\) | 9219.21 | − | 15968.1i | 0.742928 | − | 1.28679i | ||||
\(537\) | −2110.55 | + | 1218.53i | −0.169603 | + | 0.0979204i | ||||
\(538\) | 8148.12i | 0.652956i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1305.18 | + | 10407.1i | 0.104011 | + | 0.829354i | ||||
\(541\) | 685.454 | + | 1187.24i | 0.0544732 | + | 0.0943503i | 0.891976 | − | 0.452082i | \(-0.149319\pi\) |
−0.837503 | + | 0.546433i | \(0.815985\pi\) | |||||||
\(542\) | 4798.23 | + | 2770.26i | 0.380262 | + | 0.219544i | ||||
\(543\) | −914.763 | − | 528.138i | −0.0722951 | − | 0.0417396i | ||||
\(544\) | −1349.35 | − | 2337.14i | −0.106347 | − | 0.184198i | ||||
\(545\) | −4160.71 | + | 521.804i | −0.327019 | + | 0.0410122i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5324.93i | − | 0.416229i | −0.978104 | − | 0.208115i | \(-0.933267\pi\) | ||
0.978104 | − | 0.208115i | \(-0.0667327\pi\) | |||||||
\(548\) | −7241.83 | + | 4181.07i | −0.564517 | + | 0.325924i | ||||
\(549\) | −199.199 | + | 345.023i | −0.0154856 | + | 0.0268219i | ||||
\(550\) | 23231.0 | + | 6531.46i | 1.80104 | + | 0.506368i | ||||
\(551\) | −73.3890 | − | 127.114i | −0.00567419 | − | 0.00982798i | ||||
\(552\) | − | 7822.98i | − | 0.603203i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13172.9 | −1.01022 | ||||||||
\(555\) | 1604.03 | + | 2117.20i | 0.122680 | + | 0.161928i | ||||
\(556\) | 12341.9 | − | 21376.9i | 0.941394 | − | 1.63054i | ||||
\(557\) | 13757.7 | + | 7942.99i | 1.04655 | + | 0.604229i | 0.921683 | − | 0.387944i | \(-0.126815\pi\) |
0.124872 | + | 0.992173i | \(0.460148\pi\) | |||||||
\(558\) | −22577.5 | + | 13035.1i | −1.71287 | + | 0.988925i | ||||
\(559\) | −16593.6 | −1.25551 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3602.40 | −0.271112 | ||||||||
\(562\) | −22456.6 | + | 12965.3i | −1.68554 | + | 0.973148i | ||||
\(563\) | 15538.1 | + | 8970.95i | 1.16315 | + | 0.671546i | 0.952057 | − | 0.305919i | \(-0.0989638\pi\) |
0.211095 | + | 0.977466i | \(0.432297\pi\) | |||||||
\(564\) | 4804.15 | − | 8321.04i | 0.358673 | − | 0.621239i | ||||
\(565\) | −7949.34 | + | 6022.57i | −0.591914 | + | 0.448445i | ||||
\(566\) | 32990.2 | 2.44997 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24190.1i | 1.78696i | ||||||||
\(569\) | −9403.52 | − | 16287.4i | −0.692823 | − | 1.20000i | −0.970909 | − | 0.239448i | \(-0.923033\pi\) |
0.278086 | − | 0.960556i | \(-0.410300\pi\) | |||||||
\(570\) | 56.6021 | − | 134.311i | 0.00415930 | − | 0.00986963i | ||||
\(571\) | 2965.75 | − | 5136.83i | 0.217360 | − | 0.376479i | −0.736640 | − | 0.676285i | \(-0.763589\pi\) |
0.954000 | + | 0.299806i | \(0.0969220\pi\) | |||||||
\(572\) | 32730.4 | − | 18896.9i | 2.39253 | − | 1.38133i | ||||
\(573\) | 1269.09i | 0.0925253i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5757.14 | + | 22591.9i | 0.417547 | + | 1.63851i | ||||
\(576\) | −7608.97 | − | 13179.1i | −0.550417 | − | 0.953351i | ||||
\(577\) | −9949.81 | − | 5744.53i | −0.717879 | − | 0.414467i | 0.0960927 | − | 0.995372i | \(-0.469365\pi\) |
−0.813971 | + | 0.580905i | \(0.802699\pi\) | |||||||
\(578\) | 5626.17 | + | 3248.27i | 0.404875 | + | 0.233755i | ||||
\(579\) | 159.784 | + | 276.753i | 0.0114687 | + | 0.0198644i | ||||
\(580\) | 10791.8 | − | 1353.42i | 0.772593 | − | 0.0968926i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1395.56i | 0.0993950i | ||||||||
\(583\) | 20480.6 | − | 11824.5i | 1.45492 | − | 0.839999i | ||||
\(584\) | −12711.9 | + | 22017.6i | −0.900721 | + | 1.56009i | ||||
\(585\) | −16171.4 | − | 6815.01i | −1.14291 | − | 0.481652i | ||||
\(586\) | 12421.6 | + | 21514.9i | 0.875653 | + | 1.51668i | ||||
\(587\) | − | 4853.49i | − | 0.341269i | −0.985334 | − | 0.170634i | \(-0.945418\pi\) | ||
0.985334 | − | 0.170634i | \(-0.0545817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 490.604 | 0.0343208 | ||||||||
\(590\) | 9715.74 | − | 7360.84i | 0.677951 | − | 0.513628i | ||||
\(591\) | −705.756 | + | 1222.41i | −0.0491217 | + | 0.0850813i | ||||
\(592\) | 9584.38 | + | 5533.55i | 0.665398 | + | 0.384168i | ||||
\(593\) | −2327.99 | + | 1344.07i | −0.161213 | + | 0.0930762i | −0.578436 | − | 0.815728i | \(-0.696337\pi\) |
0.417223 | + | 0.908804i | \(0.363003\pi\) | |||||||
\(594\) | −11648.8 | −0.804637 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27248.6 | −1.87273 | ||||||||
\(597\) | −1488.31 | + | 859.277i | −0.102031 | + | 0.0589076i | ||||
\(598\) | 47891.8 | + | 27650.3i | 3.27498 | + | 1.89081i | ||||
\(599\) | −11479.1 | + | 19882.3i | −0.783008 | + | 1.35621i | 0.147174 | + | 0.989111i | \(0.452982\pi\) |
−0.930182 | + | 0.367099i | \(0.880351\pi\) | |||||||
\(600\) | 3661.55 | + | 3752.58i | 0.249137 | + | 0.255331i | ||||
\(601\) | 7566.12 | 0.513525 | 0.256762 | − | 0.966475i | \(-0.417344\pi\) | ||||
0.256762 | + | 0.966475i | \(0.417344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12932.4i | − | 0.873381i | ||||||
\(604\) | 16115.0 | + | 27912.1i | 1.08561 | + | 1.88034i | ||||
\(605\) | −1093.04 | + | 2593.67i | −0.0734516 | + | 0.174294i | ||||
\(606\) | −3898.36 | + | 6752.16i | −0.261320 | + | 0.452620i | ||||
\(607\) | −20087.6 | + | 11597.6i | −1.34321 | + | 0.775505i | −0.987278 | − | 0.159004i | \(-0.949172\pi\) |
−0.355937 | + | 0.934510i | \(0.615838\pi\) | |||||||
\(608\) | 80.0663i | 0.00534065i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 104.703 | + | 834.869i | 0.00694966 | + | 0.0554145i | ||||
\(611\) | 16486.2 | + | 28554.9i | 1.09159 | + | 1.89068i | ||||
\(612\) | 27348.6 | + | 15789.7i | 1.80637 | + | 1.04291i | ||||
\(613\) | −8163.80 | − | 4713.37i | −0.537900 | − | 0.310557i | 0.206328 | − | 0.978483i | \(-0.433849\pi\) |
−0.744227 | + | 0.667926i | \(0.767182\pi\) | |||||||
\(614\) | 10162.9 | + | 17602.7i | 0.667983 | + | 1.15698i | ||||
\(615\) | −552.417 | − | 4404.81i | −0.0362205 | − | 0.288812i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 811.353i | 0.0529398i | 0.999650 | + | 0.0264699i | \(0.00842662\pi\) | ||||
−0.999650 | + | 0.0264699i | \(0.991573\pi\) | |||||||
\(618\) | 1937.56 | − | 1118.65i | 0.126117 | − | 0.0728136i | ||||
\(619\) | 4641.44 | − | 8039.20i | 0.301381 | − | 0.522008i | −0.675068 | − | 0.737756i | \(-0.735886\pi\) |
0.976449 | + | 0.215748i | \(0.0692189\pi\) | |||||||
\(620\) | −14118.0 | + | 33500.6i | −0.914502 | + | 2.17003i | ||||
\(621\) | −5626.98 | − | 9746.22i | −0.363612 | − | 0.629794i | ||||
\(622\) | − | 47357.3i | − | 3.05282i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3732.93 | 0.239482 | ||||||||
\(625\) | −13335.7 | − | 8142.38i | −0.853488 | − | 0.521113i | ||||
\(626\) | 14462.4 | − | 25049.6i | 0.923378 | − | 1.59934i | ||||
\(627\) | 92.5591 | + | 53.4390i | 0.00589546 | + | 0.00340375i | ||||
\(628\) | 14691.0 | − | 8481.85i | 0.933495 | − | 0.538954i | ||||
\(629\) | 16403.0 | 1.03979 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26078.4 | −1.64527 | −0.822634 | − | 0.568572i | \(-0.807496\pi\) | ||||
−0.822634 | + | 0.568572i | \(0.807496\pi\) | |||||||
\(632\) | 5368.54 | − | 3099.53i | 0.337894 | − | 0.195083i | ||||
\(633\) | −3939.26 | − | 2274.33i | −0.247348 | − | 0.142807i | ||||
\(634\) | −6605.22 | + | 11440.6i | −0.413765 | + | 0.716662i | ||||
\(635\) | −10724.1 | + | 8124.76i | −0.670192 | + | 0.507750i | ||||
\(636\) | 10584.1 | 0.659887 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12079.3i | 0.749567i | ||||||||
\(639\) | 8483.27 | + | 14693.4i | 0.525184 | + | 0.909646i | ||||
\(640\) | −26804.2 | − | 11295.9i | −1.65551 | − | 0.697674i | ||||
\(641\) | 15485.7 | − | 26822.0i | 0.954210 | − | 1.65274i | 0.218046 | − | 0.975939i | \(-0.430032\pi\) |
0.736165 | − | 0.676802i | \(-0.236635\pi\) | |||||||
\(642\) | 2173.01 | − | 1254.59i | 0.133586 | − | 0.0771257i | ||||
\(643\) | 7482.92i | 0.458939i | 0.973316 | + | 0.229469i | \(0.0736990\pi\) | ||||
−0.973316 | + | 0.229469i | \(0.926301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3450.15 | − | 432.692i | 0.210620 | − | 0.0264143i | ||||
\(646\) | −450.032 | − | 779.478i | −0.0274091 | − | 0.0474739i | ||||
\(647\) | 23400.2 | + | 13510.1i | 1.42188 | + | 0.820925i | 0.996460 | − | 0.0840701i | \(-0.0267920\pi\) |
0.425423 | + | 0.904995i | \(0.360125\pi\) | |||||||
\(648\) | 19807.9 | + | 11436.1i | 1.20081 | + | 0.693289i | ||||
\(649\) | 4469.14 | + | 7740.77i | 0.270306 | + | 0.468185i | ||||
\(650\) | −35914.8 | + | 9152.26i | −2.16722 | + | 0.552279i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17383.0i | 1.04413i | ||||||||
\(653\) | −27125.2 | + | 15660.7i | −1.62556 | + | 0.938518i | −0.640165 | + | 0.768237i | \(0.721134\pi\) |
−0.985396 | + | 0.170280i | \(0.945533\pi\) | |||||||
\(654\) | 1042.15 | − | 1805.06i | 0.0623108 | − | 0.107926i | ||||
\(655\) | −7401.77 | + | 17563.7i | −0.441543 | + | 1.04774i | ||||
\(656\) | −9248.21 | − | 16018.4i | −0.550430 | − | 0.953373i | ||||
\(657\) | 17831.8i | 1.05888i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14051.9 | 0.830627 | 0.415314 | − | 0.909678i | \(-0.363672\pi\) | ||||
0.415314 | + | 0.909678i | \(0.363672\pi\) | |||||||
\(660\) | −6312.60 | + | 4782.55i | −0.372300 | + | 0.282061i | ||||
\(661\) | 598.051 | − | 1035.86i | 0.0351914 | − | 0.0609533i | −0.847893 | − | 0.530167i | \(-0.822129\pi\) |
0.883085 | + | 0.469214i | \(0.155463\pi\) | |||||||
\(662\) | −1591.70 | − | 918.966i | −0.0934487 | − | 0.0539526i | ||||
\(663\) | 4791.48 | − | 2766.36i | 0.280672 | − | 0.162046i | ||||
\(664\) | 12288.5 | 0.718201 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25860.3 | 1.50460 | ||||||||
\(667\) | −10106.4 | + | 5834.96i | −0.586691 | + | 0.338726i | ||||
\(668\) | −45176.9 | − | 26082.9i | −2.61669 | − | 1.51075i | ||||
\(669\) | −1638.79 | + | 2838.46i | −0.0947073 | + | 0.164038i | ||||
\(670\) | −16493.8 | − | 21770.5i | −0.951060 | − | 1.25533i | ||||
\(671\) | −616.998 | −0.0354977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4801.54i | − | 0.275016i | −0.990501 | − | 0.137508i | \(-0.956091\pi\) | ||
0.990501 | − | 0.137508i | \(-0.0439093\pi\) | |||||||
\(674\) | 19486.9 | + | 33752.3i | 1.11366 | + | 1.92891i | ||||
\(675\) | 7260.91 | + | 2041.42i | 0.414033 | + | 0.116406i | ||||
\(676\) | −11943.7 | + | 20687.1i | −0.679545 | + | 1.17701i | ||||
\(677\) | −1252.62 | + | 723.199i | −0.0711108 | + | 0.0410558i | −0.535134 | − | 0.844767i | \(-0.679739\pi\) |
0.464023 | + | 0.885823i | \(0.346405\pi\) | |||||||
\(678\) | − | 4957.18i | − | 0.280796i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 32125.6 | − | 4028.94i | 1.81170 | − | 0.227210i | ||||
\(681\) | −1185.84 | − | 2053.94i | −0.0667276 | − | 0.115576i | ||||
\(682\) | −34965.7 | − | 20187.4i | −1.96320 | − | 1.13346i | ||||
\(683\) | −11612.3 | − | 6704.37i | −0.650560 | − | 0.375601i | 0.138111 | − | 0.990417i | \(-0.455897\pi\) |
−0.788671 | + | 0.614816i | \(0.789230\pi\) | |||||||
\(684\) | −468.458 | − | 811.392i | −0.0261870 | − | 0.0453573i | ||||
\(685\) | 748.273 | + | 5966.51i | 0.0417373 | + | 0.332801i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6594.37i | − | 0.366217i | ||||||
\(688\) | 12546.7 | − | 7243.85i | 0.695260 | − | 0.401408i | ||||
\(689\) | −18160.5 | + | 31455.0i | −1.00415 | + | 1.73924i | ||||
\(690\) | −10678.7 | − | 4500.27i | −0.589177 | − | 0.248293i | ||||
\(691\) | 1306.74 | + | 2263.34i | 0.0719403 | + | 0.124604i | 0.899752 | − | 0.436402i | \(-0.143748\pi\) |
−0.827811 | + | 0.561007i | \(0.810414\pi\) | |||||||
\(692\) | 50825.6i | 2.79205i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3154.85 | 0.172560 | ||||||||
\(695\) | −10719.0 | − | 14148.3i | −0.585030 | − | 0.772195i | ||||
\(696\) | −1312.20 | + | 2272.80i | −0.0714640 | + | 0.123779i | ||||
\(697\) | −23741.5 | − | 13707.2i | −1.29021 | − | 0.744901i | ||||
\(698\) | 5213.91 | − | 3010.25i | 0.282736 | − | 0.163237i | ||||
\(699\) | −1889.59 | −0.102247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4957.94 | −0.267131 | −0.133566 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133566 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(702\) | 15493.8 | − | 8945.34i | 0.833013 | − | 0.480940i | ||||
\(703\) | −421.454 | − | 243.327i | −0.0226109 | − | 0.0130544i | ||||
\(704\) | 11784.0 | − | 20410.5i | 0.630861 | − | 1.09268i | ||||
\(705\) | −4172.43 | − | 5507.29i | −0.222897 | − | 0.294208i | ||||
\(706\) | 38208.5 | 2.03682 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4000.34i | 0.212347i | ||||||||
\(709\) | −15870.8 | − | 27489.0i | −0.840676 | − | 1.45609i | −0.889324 | − | 0.457277i | \(-0.848825\pi\) |
0.0486488 | − | 0.998816i | \(-0.484508\pi\) | |||||||
\(710\) | 33020.6 | + | 13915.7i | 1.74541 | + | 0.735557i | ||||
\(711\) | 2173.96 | − | 3765.41i | 0.114669 | − | 0.198613i | ||||
\(712\) | 8678.78 | − | 5010.70i | 0.456813 | − | 0.263741i | ||||
\(713\) | − | 39006.5i | − | 2.04882i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3381.92 | − | 26966.5i | −0.176891 | − | 1.41047i | ||||
\(716\) | 16542.9 | + | 28653.2i | 0.863462 | + | 1.49556i | ||||
\(717\) | 3975.37 | + | 2295.18i | 0.207061 | + | 0.119547i | ||||
\(718\) | −1709.23 | − | 986.824i | −0.0888411 | − | 0.0512924i | ||||
\(719\) | −12439.5 | − | 21545.9i | −0.645224 | − | 1.11756i | −0.984250 | − | 0.176784i | \(-0.943431\pi\) |
0.339026 | − | 0.940777i | \(-0.389903\pi\) | |||||||
\(720\) | 15202.6 | − | 1906.59i | 0.786898 | − | 0.0986866i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 33257.2i | − | 1.71427i | ||||||
\(723\) | −3125.31 | + | 1804.40i | −0.160763 | + | 0.0928165i | ||||
\(724\) | −7170.11 | + | 12419.0i | −0.368060 | + | 0.637498i | ||||
\(725\) | 2116.87 | − | 7529.27i | 0.108440 | − | 0.385697i | ||||
\(726\) | −699.499 | − | 1211.57i | −0.0357587 | − | 0.0619359i | ||||
\(727\) | 5429.27i | 0.276974i | 0.990364 | + | 0.138487i | \(0.0442240\pi\) | ||||
−0.990364 | + | 0.138487i | \(0.955776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14176.4 | 0.720237 | ||||||||
\(730\) | 22742.4 | + | 30018.2i | 1.15306 | + | 1.52195i | ||||
\(731\) | 10736.4 | − | 18596.0i | 0.543229 | − | 0.940900i | ||||
\(732\) | −239.143 | − | 138.069i | −0.0120751 | − | 0.00697157i | ||||
\(733\) | −10730.6 | + | 6195.34i | −0.540716 | + | 0.312183i | −0.745369 | − | 0.666652i | \(-0.767727\pi\) |
0.204653 | + | 0.978835i | \(0.434393\pi\) | |||||||
\(734\) | −3174.93 | −0.159658 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6365.85 | 0.318816 | ||||||||
\(737\) | 17345.1 | − | 10014.2i | 0.866914 | − | 0.500513i | ||||
\(738\) | −37429.9 | − | 21610.2i | −1.86696 | − | 1.07789i | ||||
\(739\) | −4087.22 | + | 7079.27i | −0.203452 | + | 0.352389i | −0.949638 | − | 0.313348i | \(-0.898549\pi\) |
0.746187 | + | 0.665737i | \(0.231883\pi\) | |||||||
\(740\) | 28743.5 | − | 21776.6i | 1.42788 | − | 1.08179i | ||||
\(741\) | −164.148 | −0.00813782 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17213.0i | − | 0.849911i | −0.905214 | − | 0.424956i | \(-0.860290\pi\) | ||
0.905214 | − | 0.424956i | \(-0.139710\pi\) | |||||||
\(744\) | −4386.02 | − | 7596.81i | −0.216128 | − | 0.374345i | ||||
\(745\) | −7609.51 | + | 18056.7i | −0.374216 | + | 0.887979i | ||||
\(746\) | 13345.6 | − | 23115.3i | 0.654983 | − | 1.13446i | ||||
\(747\) | 7464.22 | − | 4309.47i | 0.365598 | − | 0.211078i | ||||
\(748\) | 48907.0i | 2.39066i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7228.80 | − | 2839.46i | 0.351945 | − | 0.138243i | ||||
\(751\) | −1487.50 | − | 2576.42i | −0.0722763 | − | 0.125186i | 0.827622 | − | 0.561285i | \(-0.189693\pi\) |
−0.899899 | + | 0.436099i | \(0.856360\pi\) | |||||||
\(752\) | −24931.1 | − | 14394.0i | −1.20897 | − | 0.697996i | ||||
\(753\) | 3502.52 | + | 2022.18i | 0.169507 | + | 0.0978650i | ||||
\(754\) | −9275.96 | − | 16066.4i | −0.448025 | − | 0.776001i | ||||
\(755\) | 22996.6 | − | 2884.06i | 1.10852 | − | 0.139022i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1108.45i | 0.0532198i | 0.999646 | + | 0.0266099i | \(0.00847120\pi\) | ||||
−0.999646 | + | 0.0266099i | \(0.991529\pi\) | |||||||
\(758\) | 7444.56 | − | 4298.12i | 0.356726 | − | 0.205956i | ||||
\(759\) | 4248.79 | − | 7359.12i | 0.203190 | − | 0.351935i | ||||
\(760\) | −885.191 | − | 373.041i | −0.0422490 | − | 0.0178048i | ||||
\(761\) | −13462.1 | − | 23317.1i | −0.641264 | − | 1.11070i | −0.985151 | − | 0.171691i | \(-0.945077\pi\) |
0.343886 | − | 0.939011i | \(-0.388256\pi\) | |||||||
\(762\) | − | 6687.50i | − | 0.317930i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17229.4 | 0.815888 | ||||||||
\(765\) | 18100.7 | − | 13713.4i | 0.855466 | − | 0.648118i | ||||
\(766\) | −21606.7 | + | 37424.0i | −1.01917 | + | 1.76525i | ||||
\(767\) | −11888.6 | − | 6863.89i | −0.559678 | − | 0.323130i | ||||
\(768\) | 7820.64 | − | 4515.25i | 0.367452 | − | 0.212148i | ||||
\(769\) | 15160.3 | 0.710914 | 0.355457 | − | 0.934693i | \(-0.384325\pi\) | ||||
0.355457 | + | 0.934693i | \(0.384325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6511.12 | −0.304141 | ||||||||
\(772\) | 3757.26 | − | 2169.25i | 0.175164 | − | 0.101131i | ||||
\(773\) | −8006.82 | − | 4622.74i | −0.372556 | − | 0.215095i | 0.302019 | − | 0.953302i | \(-0.402339\pi\) |
−0.674574 | + | 0.738207i | \(0.735673\pi\) | |||||||
\(774\) | 16926.6 | − | 29317.7i | 0.786064 | − | 1.36150i | ||||
\(775\) | 18257.0 | + | 18710.9i | 0.846208 | + | 0.867246i | ||||
\(776\) | 9197.57 | 0.425481 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 45485.6i | − | 2.09606i | ||||||
\(779\) | 406.672 | + | 704.376i | 0.0187041 | + | 0.0323965i | ||||
\(780\) | 4723.64 | − | 11208.8i | 0.216838 | − | 0.514536i | ||||
\(781\) | −13138.0 | + | 22755.7i | −0.601940 | + | 1.04259i | ||||
\(782\) | −61974.1 | + | 35780.8i | −2.83400 | + | 1.63621i | ||||
\(783\) | 3775.41i | 0.172314i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1517.97 | − | 12103.8i | −0.0690174 | − | 0.550325i | ||||
\(786\) | −4736.83 | − | 8204.44i | −0.214958 | − | 0.372319i | ||||
\(787\) | −26128.4 | − | 15085.2i | −1.18345 | − | 0.683266i | −0.226641 | − | 0.973978i | \(-0.572775\pi\) |
−0.956811 | + | 0.290712i | \(0.906108\pi\) | |||||||
\(788\) | 16595.6 | + | 9581.49i | 0.750247 | + | 0.433155i | ||||
\(789\) | 2543.49 | + | 4405.45i | 0.114766 | + | 0.198781i | ||||
\(790\) | −1142.67 | − | 9111.34i | −0.0514614 | − | 0.410338i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 37430.6i | 1.67934i | ||||||||
\(793\) | 820.657 | − | 473.806i | 0.0367495 | − | 0.0212174i | ||||
\(794\) | 25473.2 | − | 44120.9i | 1.13855 | − | 1.97203i | ||||
\(795\) | 2955.75 | − | 7013.71i | 0.131861 | − | 0.312894i | ||||
\(796\) | 11665.7 | + | 20205.6i | 0.519448 | + | 0.899710i | ||||
\(797\) | 14025.3i | 0.623340i | 0.950190 | + | 0.311670i | \(0.100888\pi\) | ||||
−0.950190 | + | 0.311670i | \(0.899112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42667.8 | −1.88921 | ||||||||
\(800\) | −3053.61 | + | 2979.54i | −0.134952 | + | 0.131678i | ||||
\(801\) | 3514.42 | − | 6087.16i | 0.155026 | − | 0.268513i | ||||
\(802\) | 11760.8 | + | 6790.07i | 0.517814 | + | 0.298960i | ||||
\(803\) | −23916.2 | + | 13808.0i | −1.05104 | + | 0.606818i | ||||
\(804\) | 8963.75 | 0.393193 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 62009.5 | 2.70992 | ||||||||
\(807\) | −1665.33 | + | 961.478i | −0.0726423 | + | 0.0419401i | ||||
\(808\) | 44500.7 | + | 25692.5i | 1.93754 | + | 1.11864i | ||||
\(809\) | −4213.27 | + | 7297.60i | −0.183104 | + | 0.317145i | −0.942936 | − | 0.332974i | \(-0.891948\pi\) |
0.759832 | + | 0.650119i | \(0.225281\pi\) | |||||||
\(810\) | 27005.5 | − | 20459.9i | 1.17145 | − | 0.887514i | ||||
\(811\) | −16791.3 | −0.727031 | −0.363515 | − | 0.931588i | \(-0.618424\pi\) | ||||
−0.363515 | + | 0.931588i | \(0.618424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1307.56i | 0.0564062i | ||||||||
\(814\) | 20024.9 | + | 34684.1i | 0.862251 | + | 1.49346i | ||||
\(815\) | 11519.1 | + | 4854.42i | 0.495087 | + | 0.208642i | ||||
\(816\) | −2415.29 | + | 4183.40i | −0.103618 | + | 0.179471i | ||||
\(817\) | −551.716 | + | 318.534i | −0.0236256 | + | 0.0136402i | ||||
\(818\) | − | 36832.0i | − | 1.57433i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −59800.6 | + | 7499.73i | −2.54674 | + | 0.319393i | ||||
\(821\) | −5254.05 | − | 9100.29i | −0.223347 | − | 0.386848i | 0.732475 | − | 0.680794i | \(-0.238365\pi\) |
−0.955822 | + | 0.293946i | \(0.905032\pi\) | |||||||
\(822\) | −2588.47 | − | 1494.45i | −0.109834 | − | 0.0634125i | ||||
\(823\) | −29431.5 | − | 16992.3i | −1.24656 | − | 0.719701i | −0.276137 | − | 0.961118i | \(-0.589054\pi\) |
−0.970421 | + | 0.241418i | \(0.922388\pi\) | |||||||
\(824\) | −7372.58 | − | 12769.7i | −0.311694 | − | 0.539870i | ||||
\(825\) | 1406.35 | + | 5518.72i | 0.0593488 | + | 0.232893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31679.9i | 1.33207i | 0.745922 | + | 0.666033i | \(0.232009\pi\) | ||||
−0.745922 | + | 0.666033i | \(0.767991\pi\) | |||||||
\(828\) | −64511.5 | + | 37245.8i | −2.70765 | + | 1.56326i | ||||
\(829\) | −6342.91 | + | 10986.2i | −0.265740 | + | 0.460275i | −0.967757 | − | 0.251885i | \(-0.918950\pi\) |
0.702017 | + | 0.712160i | \(0.252283\pi\) | |||||||
\(830\) | 7069.11 | − | 16774.3i | 0.295629 | − | 0.701501i | ||||
\(831\) | −1554.40 | − | 2692.30i | −0.0648876 | − | 0.112389i | ||||
\(832\) | 36196.7i | 1.50829i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8822.84 | 0.366319 | ||||||||
\(835\) | −29900.4 | + | 22653.1i | −1.23922 | + | 0.938854i | ||||
\(836\) | 725.499 | − | 1256.60i | 0.0300142 | − | 0.0519862i | ||||
\(837\) | −10928.6 | − | 6309.63i | −0.451311 | − | 0.260565i | ||||
\(838\) | 46523.4 | − | 26860.3i | 1.91781 | − | 1.10725i | ||||
\(839\) | −31557.8 | −1.29857 | −0.649283 | − | 0.760547i | \(-0.724931\pi\) | ||||
−0.649283 | + | 0.760547i | \(0.724931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20474.1 | −0.839479 | ||||||||
\(842\) | 37367.5 | − | 21574.2i | 1.52942 | − | 0.883010i | ||||
\(843\) | −5299.76 | − | 3059.82i | −0.216528 | − | 0.125013i | ||||
\(844\) | −30876.8 | + | 53480.2i | −1.25927 | + | 2.18112i | ||||
\(845\) | 10373.1 | + | 13691.8i | 0.422304 | + | 0.557409i | ||||
\(846\) | −67268.2 | −2.73372 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 31711.6i | − | 1.28418i | ||||||
\(849\) | 3892.84 | + | 6742.60i | 0.157364 | + | 0.272562i | ||||
\(850\) | 12981.0 | − | 46170.6i | 0.523816 | − | 1.86310i | ||||
\(851\) | −19346.2 | + | 33508.6i | −0.779295 | + | 1.34978i | ||||
\(852\) | −10184.4 | + | 5879.95i | −0.409519 | + | 0.236436i | ||||
\(853\) | 5455.96i | 0.219002i | 0.993987 | + | 0.109501i | \(0.0349252\pi\) | ||||
−0.993987 | + | 0.109501i | \(0.965075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −668.502 | + | 83.8384i | −0.0267395 | + | 0.00335346i | ||||
\(856\) | −8268.48 | − | 14321.4i | −0.330153 | − | 0.571842i | ||||
\(857\) | 22801.2 | + | 13164.3i | 0.908836 | + | 0.524717i | 0.880056 | − | 0.474869i | \(-0.157505\pi\) |
0.0287796 | + | 0.999586i | \(0.490838\pi\) | |||||||
\(858\) | 11699.0 | + | 6754.39i | 0.465496 | + | 0.268754i | ||||
\(859\) | 13244.5 | + | 22940.1i | 0.526072 | + | 0.911183i | 0.999539 | + | 0.0303717i | \(0.00966909\pi\) |
−0.473467 | + | 0.880812i | \(0.656998\pi\) | |||||||
\(860\) | −5874.31 | − | 46840.0i | −0.232921 | − | 1.85725i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 73952.2i | 2.92207i | ||||||||
\(863\) | 7073.39 | − | 4083.83i | 0.279005 | − | 0.161083i | −0.353968 | − | 0.935258i | \(-0.615168\pi\) |
0.632973 | + | 0.774174i | \(0.281835\pi\) | |||||||
\(864\) | 1029.73 | − | 1783.54i | 0.0405464 | − | 0.0702284i | ||||
\(865\) | 33680.3 | + | 14193.7i | 1.32389 | + | 0.557919i | ||||
\(866\) | 38721.3 | + | 67067.3i | 1.51940 | + | 2.63168i | ||||
\(867\) | 1533.18i | 0.0600573i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6733.61 | 0.262856 | ||||||||
\(870\) | 2347.62 | + | 3098.68i | 0.0914847 | + | 0.120753i | ||||
\(871\) | −15380.3 | + | 26639.4i | −0.598324 | + | 1.03633i | ||||
\(872\) | −11896.4 | − | 6868.38i | −0.461998 | − | 0.266735i | ||||
\(873\) | 5586.76 | − | 3225.52i | 0.216590 | − | 0.125048i | ||||
\(874\) | 2123.13 | 0.0821691 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12359.6 | −0.476705 | ||||||||
\(877\) | −4480.15 | + | 2586.62i | −0.172502 | + | 0.0995939i | −0.583765 | − | 0.811923i | \(-0.698421\pi\) |
0.411263 | + | 0.911517i | \(0.365088\pi\) | |||||||
\(878\) | 45531.4 | + | 26287.6i | 1.75013 | + | 1.01044i | ||||
\(879\) | −2931.50 | + | 5077.51i | −0.112488 | + | 0.194835i | ||||
\(880\) | 14329.2 | + | 18913.5i | 0.548907 | + | 0.724516i | ||||
\(881\) | 8713.88 | 0.333233 | 0.166616 | − | 0.986022i | \(-0.446716\pi\) | ||||
0.166616 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32124.1i | 1.22431i | 0.790740 | + | 0.612153i | \(0.209696\pi\) | ||||
−0.790740 | + | 0.612153i | \(0.790304\pi\) | |||||||
\(884\) | −37556.7 | − | 65050.2i | −1.42892 | − | 2.47497i | ||||
\(885\) | 2650.88 | + | 1117.14i | 0.100687 | + | 0.0424321i | ||||
\(886\) | −20024.8 | + | 34683.9i | −0.759306 | + | 1.31516i | ||||
\(887\) | −13441.5 | + | 7760.43i | −0.508816 | + | 0.293765i | −0.732347 | − | 0.680932i | \(-0.761575\pi\) |
0.223531 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(888\) | 8701.41i | 0.328829i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1847.25 | − | 14729.4i | −0.0695729 | − | 0.554753i | ||||
\(891\) | 12422.2 | + | 21515.9i | 0.467071 | + | 0.808991i | ||||
\(892\) | 38535.5 | + | 22248.5i | 1.44649 | + | 0.835129i | ||||
\(893\) | 1096.29 | + | 632.945i | 0.0410818 | + | 0.0237186i | ||||
\(894\) | −4869.78 | − | 8434.71i | −0.182181 | − | 0.315547i | ||||
\(895\) | 23607.3 | − | 2960.64i | 0.881680 | − | 0.110573i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13050.9i | 0.485795i | ||||||||
\(898\) | 46321.5 | − | 26743.7i | 1.72134 | − | 0.993819i | ||||
\(899\) | −6542.83 | + | 11332.5i | −0.242732 | + | 0.420423i | ||||
\(900\) | 13512.4 | − | 48060.9i | 0.500461 | − | 1.78003i | ||||
\(901\) | −23500.6 | − | 40704.2i | −0.868942 | − | 1.50505i | ||||
\(902\) | − | 66935.2i | − | 2.47084i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32670.8 | −1.20201 | ||||||||
\(905\) | 6227.27 | + | 8219.53i | 0.228731 | + | 0.301908i | ||||
\(906\) | −5760.05 | + | 9976.70i | −0.211219 | + | 0.365843i | ||||
\(907\) | 45614.0 | + | 26335.2i | 1.66989 | + | 0.964109i | 0.967696 | + | 0.252120i | \(0.0811277\pi\) |
0.702190 | + | 0.711989i | \(0.252206\pi\) | |||||||
\(908\) | −27884.6 | + | 16099.2i | −1.01915 | + | 0.588404i | ||||
\(909\) | 36040.6 | 1.31506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19502.8 | −0.709283 | −0.354641 | − | 0.935002i | \(-0.615397\pi\) | ||||
−0.354641 | + | 0.935002i | \(0.615397\pi\) | |||||||
\(912\) | 124.115 | − | 71.6581i | 0.00450644 | − | 0.00260179i | ||||
\(913\) | 11559.8 | + | 6674.07i | 0.419030 | + | 0.241927i | ||||
\(914\) | 22633.9 | − | 39203.0i | 0.819106 | − | 1.41873i | ||||
\(915\) | −158.277 | + | 119.914i | −0.00571856 | + | 0.00433249i | ||||
\(916\) | −89526.5 | −3.22930 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 23151.3i | 0.832362i | ||||||||
\(919\) | −22640.2 | − | 39214.0i | −0.812656 | − | 1.40756i | −0.910999 | − | 0.412410i | \(-0.864687\pi\) |
0.0983421 | − | 0.995153i | \(-0.468646\pi\) | |||||||
\(920\) | −29659.4 | + | 70379.1i | −1.06287 | + | 2.52210i | ||||
\(921\) | −2398.45 | + | 4154.23i | −0.0858105 | + | 0.148628i | ||||
\(922\) | −70628.3 | + | 40777.3i | −2.52280 | + | 1.45654i | ||||
\(923\) | − | 40355.9i | − | 1.43914i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6403.60 | − | 25128.6i | −0.227620 | − | 0.893216i | ||||
\(926\) | −19989.1 | − | 34622.2i | −0.709378 | − | 1.22868i | ||||
\(927\) | −8956.45 | − | 5171.01i | −0.317334 | − | 0.183213i | ||||
\(928\) | −1849.46 | − | 1067.79i | −0.0654220 | − | 0.0377714i | ||||
\(929\) | −1600.78 | − | 2772.63i | −0.0565337 | − | 0.0979192i | 0.836374 | − | 0.548160i | \(-0.184672\pi\) |
−0.892907 | + | 0.450241i | \(0.851338\pi\) | |||||||
\(930\) | −12893.1 | + | 1616.95i | −0.454604 | + | 0.0570129i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25653.4i | 0.901615i | ||||||||
\(933\) | 9678.98 | − | 5588.16i | 0.339631 | − | 0.196086i | ||||
\(934\) | 47468.3 | − | 82217.5i | 1.66297 | − | 2.88034i | ||||
\(935\) | 32408.8 | + | 13657.9i | 1.13356 | + | 0.477711i | ||||
\(936\) | −28743.8 | − | 49785.7i | −1.00376 | − | 1.73856i | ||||
\(937\) | 23678.3i | 0.825546i | 0.910834 | + | 0.412773i | \(0.135440\pi\) | ||||
−0.910834 | + | 0.412773i | \(0.864560\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6826.26 | 0.237238 | ||||||||
\(940\) | −74768.0 | + | 56645.7i | −2.59432 | + | 1.96551i | ||||
\(941\) | −17363.3 | + | 30074.2i | −0.601518 | + | 1.04186i | 0.391073 | + | 0.920360i | \(0.372104\pi\) |
−0.992591 | + | 0.121501i | \(0.961229\pi\) | |||||||
\(942\) | 5251.05 | + | 3031.70i | 0.181623 | + | 0.104860i | ||||
\(943\) | 56003.0 | − | 32333.3i | 1.93394 | − | 1.11656i | ||||
\(944\) | 11985.6 | 0.413240 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52428.3 | 1.80189 | ||||||||
\(947\) | 25366.7 | − | 14645.5i | 0.870440 | − | 0.502549i | 0.00294538 | − | 0.999996i | \(-0.499062\pi\) |
0.867494 | + | 0.497447i | \(0.165729\pi\) | |||||||
\(948\) | 2609.89 | + | 1506.82i | 0.0894148 | + | 0.0516237i | ||||
\(949\) | 21207.0 | − | 36731.6i | 0.725404 | − | 1.25644i | ||||
\(950\) | −1018.44 | + | 993.730i | −0.0347815 | + | 0.0339377i | ||||
\(951\) | −3117.66 | −0.106306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23209.3i | 0.788900i | 0.918917 | + | 0.394450i | \(0.129065\pi\) | ||||
−0.918917 | + | 0.394450i | \(0.870935\pi\) | |||||||
\(954\) | −37050.0 | − | 64172.5i | −1.25738 | − | 2.17784i | ||||
\(955\) | 4811.53 | − | 11417.3i | 0.163034 | − | 0.386864i | ||||
\(956\) | 31159.9 | − | 53970.4i | 1.05416 | − | 1.82587i | ||||
\(957\) | −2468.79 | + | 1425.36i | −0.0833904 | + | 0.0481455i | ||||
\(958\) | − | 6081.93i | − | 0.205113i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −943.862 | − | 7526.08i | −0.0317323 | − | 0.253024i | ||||
\(961\) | −6973.82 | − | 12079.0i | −0.234092 | − | 0.405459i | ||||
\(962\) | −53269.4 | − | 30755.1i | −1.78532 | − | 1.03075i | ||||
\(963\) | −10044.8 | − | 5799.38i | −0.336127 | − | 0.194063i | ||||
\(964\) | 24496.9 | + | 42429.9i | 0.818457 | + | 1.41761i | ||||
\(965\) | −388.224 | − | 3095.59i | −0.0129507 | − | 0.103265i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25503.9i | − | 0.848140i | −0.905629 | − | 0.424070i | \(-0.860601\pi\) | ||
0.905629 | − | 0.424070i | \(-0.139399\pi\) | |||||||
\(968\) | −7984.94 | + | 4610.11i | −0.265130 | + | 0.153073i | ||||
\(969\) | 106.207 | − | 183.957i | 0.00352103 | − | 0.00609860i | ||||
\(970\) | 5291.02 | − | 12555.1i | 0.175139 | − | 0.415588i | ||||
\(971\) | −6915.82 | − | 11978.6i | −0.228568 | − | 0.395891i | 0.728816 | − | 0.684709i | \(-0.240071\pi\) |
−0.957384 | + | 0.288819i | \(0.906738\pi\) | |||||||
\(972\) | 36448.8i | 1.20277i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17291.4 | −0.568843 | ||||||||
\(975\) | −6108.50 | − | 6260.37i | −0.200645 | − | 0.205633i | ||||
\(976\) | −413.676 | + | 716.508i | −0.0135671 | + | 0.0234988i | ||||
\(977\) | 33487.9 | + | 19334.3i | 1.09659 | + | 0.633119i | 0.935324 | − | 0.353791i | \(-0.115108\pi\) |
0.161270 | + | 0.986910i | \(0.448441\pi\) | |||||||
\(978\) | −5380.85 | + | 3106.63i | −0.175931 | + | 0.101574i | ||||
\(979\) | 10885.6 | 0.355367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9634.74 | −0.313572 | ||||||||
\(982\) | −42648.4 | + | 24623.1i | −1.38591 | + | 0.800157i | ||||
\(983\) | −24374.2 | − | 14072.4i | −0.790860 | − | 0.456603i | 0.0494050 | − | 0.998779i | \(-0.484268\pi\) |
−0.840265 | + | 0.542175i | \(0.817601\pi\) | |||||||
\(984\) | 7271.33 | − | 12594.3i | 0.235571 | − | 0.408020i | ||||
\(985\) | 10983.8 | − | 8321.56i | 0.355303 | − | 0.269185i | ||||
\(986\) | 24007.0 | 0.775395 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2228.51i | 0.0717594i | ||||||||
\(989\) | 25325.7 | + | 43865.4i | 0.814268 | + | 1.41035i | ||||
\(990\) | 51094.5 | + | 21532.4i | 1.64029 | + | 0.691258i | ||||
\(991\) | 15598.9 | − | 27018.2i | 0.500017 | − | 0.866055i | −0.499983 | − | 0.866035i | \(-0.666660\pi\) |
1.00000 | 1.95269e-5i | \(-6.21562e-6\pi\) | ||||||||
\(992\) | 6181.80 | − | 3569.07i | 0.197855 | − | 0.114232i | ||||
\(993\) | − | 433.752i | − | 0.0138617i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16647.3 | − | 2087.78i | 0.530407 | − | 0.0665195i | ||||
\(996\) | 2986.99 | + | 5173.62i | 0.0950266 | + | 0.164591i | ||||
\(997\) | −35534.4 | − | 20515.8i | −1.12877 | − | 0.651696i | −0.185146 | − | 0.982711i | \(-0.559276\pi\) |
−0.943626 | + | 0.331015i | \(0.892609\pi\) | |||||||
\(998\) | 34504.6 | + | 19921.2i | 1.09441 | + | 0.631859i | ||||
\(999\) | 6258.82 | + | 10840.6i | 0.198219 | + | 0.343325i |
(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 | 245.4.j.g.214.12 | 24 | ||
5.4 | even | 2 | inner | 245.4.j.g.214.1 | 24 | ||
7.2 | even | 3 | inner | 245.4.j.g.79.1 | 24 | ||
7.3 | odd | 6 | 245.4.b.g.99.12 | yes | 12 | ||
7.4 | even | 3 | 245.4.b.g.99.11 | yes | 12 | ||
7.5 | odd | 6 | inner | 245.4.j.g.79.2 | 24 | ||
7.6 | odd | 2 | inner | 245.4.j.g.214.11 | 24 | ||
35.3 | even | 12 | 1225.4.a.bs.1.11 | 12 | |||
35.4 | even | 6 | 245.4.b.g.99.2 | yes | 12 | ||
35.9 | even | 6 | inner | 245.4.j.g.79.12 | 24 | ||
35.17 | even | 12 | 1225.4.a.bs.1.2 | 12 | |||
35.18 | odd | 12 | 1225.4.a.bs.1.12 | 12 | |||
35.19 | odd | 6 | inner | 245.4.j.g.79.11 | 24 | ||
35.24 | odd | 6 | 245.4.b.g.99.1 | ✓ | 12 | ||
35.32 | odd | 12 | 1225.4.a.bs.1.1 | 12 | |||
35.34 | odd | 2 | inner | 245.4.j.g.214.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.b.g.99.1 | ✓ | 12 | 35.24 | odd | 6 | ||
245.4.b.g.99.2 | yes | 12 | 35.4 | even | 6 | ||
245.4.b.g.99.11 | yes | 12 | 7.4 | even | 3 | ||
245.4.b.g.99.12 | yes | 12 | 7.3 | odd | 6 | ||
245.4.j.g.79.1 | 24 | 7.2 | even | 3 | inner | ||
245.4.j.g.79.2 | 24 | 7.5 | odd | 6 | inner | ||
245.4.j.g.79.11 | 24 | 35.19 | odd | 6 | inner | ||
245.4.j.g.79.12 | 24 | 35.9 | even | 6 | inner | ||
245.4.j.g.214.1 | 24 | 5.4 | even | 2 | inner | ||
245.4.j.g.214.2 | 24 | 35.34 | odd | 2 | inner | ||
245.4.j.g.214.11 | 24 | 7.6 | odd | 2 | inner | ||
245.4.j.g.214.12 | 24 | 1.1 | even | 1 | trivial | ||
1225.4.a.bs.1.1 | 12 | 35.32 | odd | 12 | |||
1225.4.a.bs.1.2 | 12 | 35.17 | even | 12 | |||
1225.4.a.bs.1.11 | 12 | 35.3 | even | 12 | |||
1225.4.a.bs.1.12 | 12 | 35.18 | odd | 12 |