Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(143,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.143");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.i (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: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 143.12 | ||
Character | \(\chi\) | \(=\) | 189.143 |
Dual form | 189.4.i.a.152.11 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.257625i | 0.0910841i | 0.998962 | + | 0.0455421i | \(0.0145015\pi\) | ||||
−0.998962 | + | 0.0455421i | \(0.985498\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.93363 | 0.991704 | ||||||||
\(5\) | −3.19386 | + | 5.53193i | −0.285668 | + | 0.494791i | −0.972771 | − | 0.231769i | \(-0.925549\pi\) |
0.687103 | + | 0.726560i | \(0.258882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.2112 | + | 10.5650i | −0.821328 | + | 0.570456i | ||||
\(8\) | 4.10490i | 0.181413i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.42516 | − | 0.822818i | −0.0450676 | − | 0.0260198i | ||||
\(11\) | −52.8984 | + | 30.5409i | −1.44995 | + | 0.837130i | −0.998478 | − | 0.0551546i | \(-0.982435\pi\) |
−0.451474 | + | 0.892284i | \(0.649102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.78677 | + | 5.07304i | −0.187462 | + | 0.108231i | −0.590794 | − | 0.806822i | \(-0.701185\pi\) |
0.403332 | + | 0.915054i | \(0.367852\pi\) | |||||||
\(14\) | −2.72180 | − | 3.91879i | −0.0519595 | − | 0.0748100i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.4115 | 0.975180 | ||||||||
\(17\) | 22.5082 | − | 38.9853i | 0.321120 | − | 0.556196i | −0.659599 | − | 0.751617i | \(-0.729274\pi\) |
0.980719 | + | 0.195421i | \(0.0626074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −69.6373 | + | 40.2051i | −0.840837 | + | 0.485457i | −0.857549 | − | 0.514403i | \(-0.828014\pi\) |
0.0167118 | + | 0.999860i | \(0.494680\pi\) | |||||||
\(20\) | −25.3389 | + | 43.8883i | −0.283298 | + | 0.490686i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.86810 | − | 13.6279i | −0.0762493 | − | 0.132068i | ||||
\(23\) | −23.9716 | − | 13.8400i | −0.217323 | − | 0.125471i | 0.387387 | − | 0.921917i | \(-0.373378\pi\) |
−0.604710 | + | 0.796446i | \(0.706711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.0985 | + | 72.9167i | 0.336788 | + | 0.583334i | ||||
\(26\) | −1.30694 | − | 2.26369i | −0.00985817 | − | 0.0170749i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −120.680 | + | 83.8187i | −0.814514 | + | 0.565723i | ||||
\(29\) | −48.9383 | − | 28.2545i | −0.313366 | − | 0.180922i | 0.335066 | − | 0.942195i | \(-0.391241\pi\) |
−0.648432 | + | 0.761273i | \(0.724575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 106.409i | 0.616502i | 0.951305 | + | 0.308251i | \(0.0997436\pi\) | ||||
−0.951305 | + | 0.308251i | \(0.900256\pi\) | |||||||
\(32\) | 48.9180i | 0.270236i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0436 | + | 5.79867i | 0.0506607 | + | 0.0292489i | ||||
\(35\) | −9.86226 | − | 117.890i | −0.0476293 | − | 0.569347i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 95.6403 | + | 165.654i | 0.424951 | + | 0.736036i | 0.996416 | − | 0.0845902i | \(-0.0269581\pi\) |
−0.571465 | + | 0.820626i | \(0.693625\pi\) | |||||||
\(38\) | −10.3578 | − | 17.9403i | −0.0442175 | − | 0.0765869i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −22.7080 | − | 13.1105i | −0.0897613 | − | 0.0518237i | ||||
\(41\) | −15.0856 | − | 26.1289i | −0.0574626 | − | 0.0995282i | 0.835863 | − | 0.548938i | \(-0.184968\pi\) |
−0.893326 | + | 0.449410i | \(0.851634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −185.062 | + | 320.536i | −0.656317 | + | 1.13678i | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(44\) | −419.676 | + | 242.300i | −1.43792 | + | 0.830185i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.56553 | − | 6.17569i | 0.0114285 | − | 0.0197947i | ||||
\(47\) | −496.082 | −1.53960 | −0.769798 | − | 0.638288i | \(-0.779643\pi\) | ||||
−0.769798 | + | 0.638288i | \(0.779643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 119.762 | − | 321.413i | 0.349161 | − | 0.937063i | ||||
\(50\) | −18.7852 | + | 10.8456i | −0.0531325 | + | 0.0306760i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −69.7110 | + | 40.2476i | −0.185907 | + | 0.107334i | ||||
\(53\) | 601.424 | + | 347.232i | 1.55871 | + | 0.899924i | 0.997380 | + | 0.0723355i | \(0.0230452\pi\) |
0.561335 | + | 0.827589i | \(0.310288\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 390.174i | − | 0.956564i | ||||||
\(56\) | −43.3682 | − | 62.4405i | −0.103488 | − | 0.148999i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.27907 | − | 12.6077i | 0.0164791 | − | 0.0285427i | ||||
\(59\) | 635.340 | 1.40194 | 0.700968 | − | 0.713193i | \(-0.252752\pi\) | ||||
0.700968 | + | 0.713193i | \(0.252752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 747.913i | − | 1.56984i | −0.619595 | − | 0.784922i | \(-0.712703\pi\) | ||
0.619595 | − | 0.784922i | \(-0.287297\pi\) | |||||||
\(62\) | −27.4135 | −0.0561536 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 486.690 | 0.950566 | ||||||||
\(65\) | − | 64.8104i | − | 0.123673i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 164.786 | 0.300475 | 0.150237 | − | 0.988650i | \(-0.451996\pi\) | ||||
0.150237 | + | 0.988650i | \(0.451996\pi\) | |||||||
\(68\) | 178.572 | − | 309.295i | 0.318456 | − | 0.551582i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 30.3715 | − | 2.54076i | 0.0518584 | − | 0.00433828i | ||||
\(71\) | 278.490i | 0.465502i | 0.972536 | + | 0.232751i | \(0.0747728\pi\) | ||||
−0.972536 | + | 0.232751i | \(0.925227\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −313.876 | − | 181.216i | −0.503238 | − | 0.290545i | 0.226812 | − | 0.973939i | \(-0.427170\pi\) |
−0.730050 | + | 0.683394i | \(0.760503\pi\) | |||||||
\(74\) | −42.6766 | + | 24.6393i | −0.0670412 | + | 0.0387063i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −552.477 | + | 318.973i | −0.833861 | + | 0.481430i | ||||
\(77\) | 481.985 | − | 1023.44i | 0.713341 | − | 1.51469i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 557.480 | 0.793942 | 0.396971 | − | 0.917831i | \(-0.370061\pi\) | ||||
0.396971 | + | 0.917831i | \(0.370061\pi\) | |||||||
\(80\) | −199.334 | + | 345.256i | −0.278577 | + | 0.482510i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.73147 | − | 3.88641i | 0.00906544 | − | 0.00523393i | ||||
\(83\) | 514.684 | − | 891.459i | 0.680650 | − | 1.17892i | −0.294133 | − | 0.955765i | \(-0.595031\pi\) |
0.974783 | − | 0.223156i | \(-0.0716358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 143.776 | + | 249.028i | 0.183467 | + | 0.317775i | ||||
\(86\) | −82.5781 | − | 47.6765i | −0.103542 | − | 0.0597801i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −125.367 | − | 217.143i | −0.151866 | − | 0.263040i | ||||
\(89\) | 730.130 | + | 1264.62i | 0.869591 | + | 1.50618i | 0.862415 | + | 0.506201i | \(0.168951\pi\) |
0.00717569 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 80.0608 | − | 169.999i | 0.0922269 | − | 0.195833i | ||||
\(92\) | −190.182 | − | 109.802i | −0.215520 | − | 0.124431i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 127.803i | − | 0.140233i | ||||||
\(95\) | − | 513.638i | − | 0.554718i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −878.164 | − | 507.008i | −0.919217 | − | 0.530710i | −0.0358320 | − | 0.999358i | \(-0.511408\pi\) |
−0.883385 | + | 0.468647i | \(0.844741\pi\) | |||||||
\(98\) | 82.8039 | + | 30.8537i | 0.0853516 | + | 0.0318030i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 333.994 | + | 578.494i | 0.333994 | + | 0.578494i | ||||
\(101\) | −71.8520 | − | 124.451i | −0.0707875 | − | 0.122608i | 0.828459 | − | 0.560050i | \(-0.189218\pi\) |
−0.899247 | + | 0.437442i | \(0.855885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 473.681 | + | 273.480i | 0.453138 | + | 0.261619i | 0.709155 | − | 0.705053i | \(-0.249077\pi\) |
−0.256017 | + | 0.966672i | \(0.582410\pi\) | |||||||
\(104\) | −20.8243 | − | 36.0688i | −0.0196346 | − | 0.0340080i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −89.4556 | + | 154.942i | −0.0819689 | + | 0.141974i | ||||
\(107\) | 1153.06 | − | 665.722i | 1.04178 | − | 0.601475i | 0.121447 | − | 0.992598i | \(-0.461247\pi\) |
0.920338 | + | 0.391123i | \(0.127913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 527.013 | − | 912.813i | 0.463107 | − | 0.802125i | −0.536007 | − | 0.844214i | \(-0.680068\pi\) |
0.999114 | + | 0.0420888i | \(0.0134013\pi\) | |||||||
\(110\) | 100.518 | 0.0871278 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −949.355 | + | 659.377i | −0.800943 | + | 0.556297i | ||||
\(113\) | −804.987 | + | 464.760i | −0.670149 | + | 0.386911i | −0.796133 | − | 0.605122i | \(-0.793125\pi\) |
0.125984 | + | 0.992032i | \(0.459791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 153.124 | − | 88.4062i | 0.124164 | − | 0.0716863i | ||||
\(116\) | −388.258 | − | 224.161i | −0.310766 | − | 0.179421i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 163.679i | 0.127694i | ||||||||
\(119\) | 69.5026 | + | 830.813i | 0.0535403 | + | 0.640004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1199.99 | − | 2078.45i | 0.901573 | − | 1.56157i | ||||
\(122\) | 192.681 | 0.142988 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 844.207i | 0.611387i | ||||||||
\(125\) | −1336.29 | −0.956173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1387.22 | −0.969259 | −0.484629 | − | 0.874720i | \(-0.661046\pi\) | ||||
−0.484629 | + | 0.874720i | \(0.661046\pi\) | |||||||
\(128\) | 516.727i | 0.356818i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 16.6968 | 0.0112646 | ||||||||
\(131\) | −196.378 | + | 340.137i | −0.130974 | + | 0.226854i | −0.924052 | − | 0.382266i | \(-0.875144\pi\) |
0.793078 | + | 0.609120i | \(0.208477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 634.502 | − | 1347.29i | 0.413671 | − | 0.878380i | ||||
\(134\) | 42.4530i | 0.0273685i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 160.031 | + | 92.3939i | 0.100901 | + | 0.0582552i | ||||
\(137\) | −1802.86 | + | 1040.88i | −1.12430 | + | 0.649112i | −0.942494 | − | 0.334223i | \(-0.891526\pi\) |
−0.181801 | + | 0.983335i | \(0.558193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1088.49 | + | 628.441i | −0.664206 | + | 0.383479i | −0.793878 | − | 0.608078i | \(-0.791941\pi\) |
0.129672 | + | 0.991557i | \(0.458608\pi\) | |||||||
\(140\) | −78.2435 | − | 935.299i | −0.0472342 | − | 0.564623i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −71.7459 | −0.0423999 | ||||||||
\(143\) | 309.871 | − | 536.712i | 0.181208 | − | 0.313861i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 312.604 | − | 180.482i | 0.179037 | − | 0.103367i | ||||
\(146\) | 46.6858 | − | 80.8622i | 0.0264640 | − | 0.0458370i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 758.775 | + | 1314.24i | 0.421425 | + | 0.729930i | ||||
\(149\) | 2604.69 | + | 1503.82i | 1.43211 | + | 0.826830i | 0.997282 | − | 0.0736835i | \(-0.0234755\pi\) |
0.434829 | + | 0.900513i | \(0.356809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1435.11 | + | 2485.69i | 0.773428 | + | 1.33962i | 0.935674 | + | 0.352867i | \(0.114793\pi\) |
−0.162245 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(152\) | −165.038 | − | 285.854i | −0.0880681 | − | 0.152538i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 263.662 | + | 124.171i | 0.137964 | + | 0.0649740i | ||||
\(155\) | −588.645 | − | 339.855i | −0.305040 | − | 0.176115i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 917.702i | − | 0.466501i | −0.972417 | − | 0.233250i | \(-0.925064\pi\) | ||
0.972417 | − | 0.233250i | \(-0.0749361\pi\) | |||||||
\(158\) | 143.621i | 0.0723155i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −270.611 | − | 156.237i | −0.133710 | − | 0.0771977i | ||||
\(161\) | 510.857 | − | 42.7363i | 0.250069 | − | 0.0209198i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −806.536 | − | 1396.96i | −0.387563 | − | 0.671279i | 0.604558 | − | 0.796561i | \(-0.293350\pi\) |
−0.992121 | + | 0.125282i | \(0.960016\pi\) | |||||||
\(164\) | −119.683 | − | 207.297i | −0.0569859 | − | 0.0987025i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 229.662 | + | 132.595i | 0.107381 | + | 0.0619964i | ||||
\(167\) | −922.384 | − | 1597.62i | −0.427402 | − | 0.740282i | 0.569239 | − | 0.822172i | \(-0.307238\pi\) |
−0.996641 | + | 0.0818896i | \(0.973905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1047.03 | + | 1813.51i | −0.476572 | + | 0.825447i | ||||
\(170\) | −64.1557 | + | 37.0403i | −0.0289442 | + | 0.0167110i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1468.21 | + | 2543.02i | −0.650872 | + | 1.12734i | ||||
\(173\) | −2005.80 | −0.881494 | −0.440747 | − | 0.897631i | \(-0.645286\pi\) | ||||
−0.440747 | + | 0.897631i | \(0.645286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1410.73 | − | 664.382i | −0.609380 | − | 0.286986i | ||||
\(176\) | −3301.47 | + | 1906.10i | −1.41396 | + | 0.816352i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −325.798 | + | 188.100i | −0.137189 | + | 0.0792060i | ||||
\(179\) | 1424.92 | + | 822.678i | 0.594992 | + | 0.343519i | 0.767069 | − | 0.641565i | \(-0.221714\pi\) |
−0.172077 | + | 0.985083i | \(0.555048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3394.40i | 1.39394i | 0.717099 | + | 0.696971i | \(0.245469\pi\) | ||||
−0.717099 | + | 0.696971i | \(0.754531\pi\) | |||||||
\(182\) | 43.7960 | + | 20.6256i | 0.0178372 | + | 0.00840041i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 56.8119 | − | 98.4011i | 0.0227621 | − | 0.0394251i | ||||
\(185\) | −1221.85 | −0.485579 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2749.68i | 1.07528i | ||||||||
\(188\) | −3935.73 | −1.52682 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 132.326 | 0.0505260 | ||||||||
\(191\) | − | 113.285i | − | 0.0429165i | −0.999770 | − | 0.0214582i | \(-0.993169\pi\) | ||
0.999770 | − | 0.0214582i | \(-0.00683090\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −875.800 | −0.326640 | −0.163320 | − | 0.986573i | \(-0.552220\pi\) | ||||
−0.163320 | + | 0.986573i | \(0.552220\pi\) | |||||||
\(194\) | 130.618 | − | 226.237i | 0.0483393 | − | 0.0837261i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 950.148 | − | 2549.97i | 0.346264 | − | 0.929289i | ||||
\(197\) | − | 1004.09i | − | 0.363140i | −0.983378 | − | 0.181570i | \(-0.941882\pi\) | ||
0.983378 | − | 0.181570i | \(-0.0581179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1451.86 | + | 838.230i | 0.517183 | + | 0.298596i | 0.735781 | − | 0.677219i | \(-0.236815\pi\) |
−0.218598 | + | 0.975815i | \(0.570148\pi\) | |||||||
\(200\) | −299.316 | + | 172.810i | −0.105824 | + | 0.0610976i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.0618 | − | 18.5109i | 0.0111676 | − | 0.00644762i | ||||
\(203\) | 1042.92 | − | 87.2466i | 0.360584 | − | 0.0301651i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 192.725 | 0.0656608 | ||||||||
\(206\) | −70.4553 | + | 122.032i | −0.0238294 | + | 0.0412737i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −548.396 | + | 316.616i | −0.182810 | + | 0.105545i | ||||
\(209\) | 2455.80 | − | 4253.57i | 0.812782 | − | 1.40778i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1528.10 | + | 2646.75i | 0.498572 | + | 0.863552i | 0.999999 | − | 0.00164804i | \(-0.000524587\pi\) |
−0.501427 | + | 0.865200i | \(0.667191\pi\) | |||||||
\(212\) | 4771.47 | + | 2754.81i | 1.54578 | + | 0.892458i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 171.507 | + | 297.058i | 0.0547848 | + | 0.0948901i | ||||
\(215\) | −1182.12 | − | 2047.50i | −0.374977 | − | 0.649480i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1124.21 | − | 1618.60i | −0.351687 | − | 0.506351i | ||||
\(218\) | 235.163 | + | 135.772i | 0.0730608 | + | 0.0421817i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 3095.49i | − | 0.948628i | ||||||
\(221\) | 456.740i | 0.139021i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3580.72 | − | 2067.33i | −1.07526 | − | 0.620801i | −0.145645 | − | 0.989337i | \(-0.546526\pi\) |
−0.929613 | + | 0.368536i | \(0.879859\pi\) | |||||||
\(224\) | −516.818 | − | 744.101i | −0.154158 | − | 0.221953i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −119.734 | − | 207.385i | −0.0352414 | − | 0.0610400i | ||||
\(227\) | 2220.58 | + | 3846.16i | 0.649274 | + | 1.12458i | 0.983297 | + | 0.182010i | \(0.0582605\pi\) |
−0.334023 | + | 0.942565i | \(0.608406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1125.72 | + | 649.933i | 0.324845 | + | 0.187549i | 0.653550 | − | 0.756883i | \(-0.273279\pi\) |
−0.328705 | + | 0.944433i | \(0.606612\pi\) | |||||||
\(230\) | 22.7756 | + | 39.4486i | 0.00652948 | + | 0.0113094i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 115.982 | − | 200.887i | 0.0328215 | − | 0.0568485i | ||||
\(233\) | 1741.16 | − | 1005.26i | 0.489559 | − | 0.282647i | −0.234832 | − | 0.972036i | \(-0.575454\pi\) |
0.724392 | + | 0.689389i | \(0.242121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1584.42 | − | 2744.29i | 0.439813 | − | 0.761778i | ||||
\(236\) | 5040.55 | 1.39031 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −214.038 | + | 17.9056i | −0.0582943 | + | 0.00487667i | ||||
\(239\) | −4499.21 | + | 2597.62i | −1.21770 | + | 0.703038i | −0.964425 | − | 0.264356i | \(-0.914840\pi\) |
−0.253273 | + | 0.967395i | \(0.581507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5836.81 | − | 3369.88i | 1.56009 | − | 0.900719i | 0.562845 | − | 0.826563i | \(-0.309707\pi\) |
0.997247 | − | 0.0741564i | \(-0.0236264\pi\) | |||||||
\(242\) | 535.460 | + | 309.148i | 0.142234 | + | 0.0821190i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5933.67i | − | 1.55682i | ||||||
\(245\) | 1395.53 | + | 1689.06i | 0.363906 | + | 0.440450i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 407.925 | − | 706.546i | 0.105084 | − | 0.182010i | ||||
\(248\) | −436.797 | −0.111841 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 344.262i | − | 0.0870922i | ||||||
\(251\) | −1818.28 | −0.457246 | −0.228623 | − | 0.973515i | \(-0.573422\pi\) | ||||
−0.228623 | + | 0.973515i | \(0.573422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1690.75 | 0.420144 | ||||||||
\(254\) | − | 357.382i | − | 0.0882841i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3760.40 | 0.918065 | ||||||||
\(257\) | 232.027 | − | 401.882i | 0.0563168 | − | 0.0975435i | −0.836493 | − | 0.547978i | \(-0.815398\pi\) |
0.892809 | + | 0.450435i | \(0.148731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3204.94 | − | 1509.36i | −0.768900 | − | 0.362112i | ||||
\(260\) | − | 514.182i | − | 0.122647i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −87.6278 | − | 50.5919i | −0.0206628 | − | 0.0119297i | ||||
\(263\) | 326.067 | − | 188.255i | 0.0764492 | − | 0.0441380i | −0.461288 | − | 0.887250i | \(-0.652613\pi\) |
0.537737 | + | 0.843112i | \(0.319279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3841.73 | + | 2218.02i | −0.890549 | + | 0.514159i | ||||
\(266\) | 347.094 | + | 163.463i | 0.0800065 | + | 0.0376789i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1307.35 | 0.297982 | ||||||||
\(269\) | 1998.09 | − | 3460.80i | 0.452885 | − | 0.784419i | −0.545679 | − | 0.837994i | \(-0.683728\pi\) |
0.998564 | + | 0.0535750i | \(0.0170616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −729.622 | + | 421.248i | −0.163548 | + | 0.0944242i | −0.579540 | − | 0.814944i | \(-0.696768\pi\) |
0.415992 | + | 0.909368i | \(0.363434\pi\) | |||||||
\(272\) | 1404.77 | − | 2433.13i | 0.313150 | − | 0.542391i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −268.157 | − | 464.461i | −0.0591238 | − | 0.102405i | ||||
\(275\) | −4453.89 | − | 2571.45i | −0.976653 | − | 0.563871i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2083.09 | − | 3608.02i | −0.451844 | − | 0.782616i | 0.546657 | − | 0.837357i | \(-0.315900\pi\) |
−0.998501 | + | 0.0547404i | \(0.982567\pi\) | |||||||
\(278\) | −161.902 | − | 280.422i | −0.0349289 | − | 0.0604986i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 483.929 | − | 40.4836i | 0.103287 | − | 0.00864056i | ||||
\(281\) | 4478.35 | + | 2585.58i | 0.950733 | + | 0.548906i | 0.893309 | − | 0.449444i | \(-0.148378\pi\) |
0.0574244 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6019.50i | 1.26439i | 0.774810 | + | 0.632195i | \(0.217846\pi\) | ||||
−0.774810 | + | 0.632195i | \(0.782154\pi\) | |||||||
\(284\) | 2209.44i | 0.461640i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 138.270 | + | 79.8304i | 0.0285877 | + | 0.0165051i | ||||
\(287\) | 505.521 | + | 238.074i | 0.103972 | + | 0.0489654i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1443.26 | + | 2499.80i | 0.293764 | + | 0.508814i | ||||
\(290\) | 46.4967 | + | 80.5346i | 0.00941510 | + | 0.0163074i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2490.17 | − | 1437.70i | −0.499063 | − | 0.288134i | ||||
\(293\) | −2243.89 | − | 3886.53i | −0.447404 | − | 0.774926i | 0.550812 | − | 0.834629i | \(-0.314318\pi\) |
−0.998216 | + | 0.0597027i | \(0.980985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2029.19 | + | 3514.66i | −0.400488 | + | 0.693665i | ||||
\(296\) | −679.993 | + | 392.594i | −0.133526 | + | 0.0770914i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −387.421 | + | 671.033i | −0.0753111 | + | 0.130443i | ||||
\(299\) | 280.844 | 0.0543198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −571.449 | − | 6830.92i | −0.109428 | − | 1.30807i | ||||
\(302\) | −640.374 | + | 369.720i | −0.122018 | + | 0.0704471i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4346.17 | + | 2509.26i | −0.819967 | + | 0.473408i | ||||
\(305\) | 4137.40 | + | 2388.73i | 0.776744 | + | 0.448454i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 263.461i | 0.0489789i | 0.999700 | + | 0.0244895i | \(0.00779602\pi\) | ||||
−0.999700 | + | 0.0244895i | \(0.992204\pi\) | |||||||
\(308\) | 3823.89 | − | 8119.55i | 0.707423 | − | 1.50213i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 87.5550 | − | 151.650i | 0.0160413 | − | 0.0277843i | ||||
\(311\) | −4852.47 | −0.884753 | −0.442377 | − | 0.896829i | \(-0.645865\pi\) | ||||
−0.442377 | + | 0.896829i | \(0.645865\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2738.54i | − | 0.494542i | −0.968946 | − | 0.247271i | \(-0.920466\pi\) | ||
0.968946 | − | 0.247271i | \(-0.0795337\pi\) | |||||||
\(314\) | 236.423 | 0.0424908 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4422.84 | 0.787355 | ||||||||
\(317\) | 7417.18i | 1.31417i | 0.753819 | + | 0.657083i | \(0.228210\pi\) | ||||
−0.753819 | + | 0.657083i | \(0.771790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3451.67 | 0.605820 | ||||||||
\(320\) | −1554.42 | + | 2692.33i | −0.271546 | + | 0.470331i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.0099 | + | 131.609i | 0.00190547 | + | 0.0227774i | ||||
\(323\) | 3619.78i | 0.623560i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −739.820 | − | 427.135i | −0.126270 | − | 0.0729021i | ||||
\(326\) | 359.892 | − | 207.784i | 0.0611429 | − | 0.0353009i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 107.257 | − | 61.9247i | 0.0180557 | − | 0.0104244i | ||||
\(329\) | 7546.01 | − | 5241.10i | 1.26451 | − | 0.878271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4172.12 | 0.692811 | 0.346406 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346406 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(332\) | 4083.31 | − | 7072.51i | 0.675003 | − | 1.16914i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 411.585 | − | 237.629i | 0.0674280 | − | 0.0389296i | ||||
\(335\) | −526.303 | + | 911.584i | −0.0858359 | + | 0.148672i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −528.671 | − | 915.685i | −0.0854556 | − | 0.148013i | 0.820130 | − | 0.572178i | \(-0.193901\pi\) |
−0.905585 | + | 0.424164i | \(0.860568\pi\) | |||||||
\(338\) | −467.204 | − | 269.741i | −0.0751851 | − | 0.0434081i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1140.67 | + | 1975.69i | 0.181945 | + | 0.315138i | ||||
\(341\) | −3249.82 | − | 5628.85i | −0.516092 | − | 0.893898i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1573.99 | + | 6154.36i | 0.247777 | + | 0.968817i | ||||
\(344\) | −1315.77 | − | 759.660i | −0.206225 | − | 0.119064i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 516.745i | − | 0.0802901i | ||||||
\(347\) | − | 4780.66i | − | 0.739594i | −0.929113 | − | 0.369797i | \(-0.879427\pi\) | ||
0.929113 | − | 0.369797i | \(-0.120573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2180.04 | + | 1258.65i | 0.334370 | + | 0.193048i | 0.657780 | − | 0.753211i | \(-0.271496\pi\) |
−0.323410 | + | 0.946259i | \(0.604829\pi\) | |||||||
\(350\) | 171.161 | − | 363.440i | 0.0261399 | − | 0.0555048i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1494.00 | − | 2587.68i | −0.226223 | − | 0.391829i | ||||
\(353\) | 3002.91 | + | 5201.18i | 0.452772 | + | 0.784224i | 0.998557 | − | 0.0537011i | \(-0.0171018\pi\) |
−0.545785 | + | 0.837925i | \(0.683768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1540.59 | − | 889.458i | −0.230326 | − | 0.132979i | ||||
\(356\) | 5792.58 | + | 10033.0i | 0.862377 | + | 1.49368i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −211.942 | + | 367.095i | −0.0312891 | + | 0.0541943i | ||||
\(359\) | −5772.63 | + | 3332.83i | −0.848656 | + | 0.489972i | −0.860197 | − | 0.509961i | \(-0.829660\pi\) |
0.0115408 | + | 0.999933i | \(0.496326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −196.595 | + | 340.513i | −0.0286624 | + | 0.0496447i | ||||
\(362\) | −874.481 | −0.126966 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 635.173 | − | 1348.71i | 0.0914618 | − | 0.194208i | ||||
\(365\) | 2004.95 | − | 1157.56i | 0.287518 | − | 0.165998i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1394.22 | + | 804.953i | −0.198304 | + | 0.114491i | −0.595864 | − | 0.803085i | \(-0.703190\pi\) |
0.397560 | + | 0.917576i | \(0.369857\pi\) | |||||||
\(368\) | −1496.10 | − | 863.777i | −0.211929 | − | 0.122357i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 314.778i | − | 0.0442285i | ||||||
\(371\) | −12816.9 | + | 1072.21i | −1.79358 | + | 0.150044i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2605.53 | + | 4512.91i | −0.361687 | + | 0.626460i | −0.988239 | − | 0.152920i | \(-0.951132\pi\) |
0.626552 | + | 0.779380i | \(0.284466\pi\) | |||||||
\(374\) | −708.387 | −0.0979407 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2036.37i | − | 0.279302i | ||||||
\(377\) | 573.346 | 0.0783257 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9946.69 | −1.34809 | −0.674046 | − | 0.738689i | \(-0.735445\pi\) | ||||
−0.674046 | + | 0.738689i | \(0.735445\pi\) | |||||||
\(380\) | − | 4075.02i | − | 0.550116i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.1852 | 0.00390901 | ||||||||
\(383\) | −7224.48 | + | 12513.2i | −0.963848 | + | 1.66943i | −0.251170 | + | 0.967943i | \(0.580815\pi\) |
−0.712678 | + | 0.701491i | \(0.752518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4122.18 | + | 5935.01i | 0.545677 | + | 0.785653i | ||||
\(386\) | − | 225.628i | − | 0.0297517i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6967.03 | − | 4022.42i | −0.911591 | − | 0.526307i | ||||
\(389\) | −7862.92 | + | 4539.66i | −1.02485 | + | 0.591696i | −0.915505 | − | 0.402308i | \(-0.868208\pi\) |
−0.109344 | + | 0.994004i | \(0.534875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1079.12 | + | 623.028i | −0.139574 | + | 0.0805828i | ||||
\(392\) | 1319.37 | + | 491.611i | 0.169995 | + | 0.0633421i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 258.679 | 0.0330763 | ||||||||
\(395\) | −1780.51 | + | 3083.94i | −0.226803 | + | 0.392835i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1879.14 | − | 1084.92i | 0.237559 | − | 0.137155i | −0.376495 | − | 0.926419i | \(-0.622871\pi\) |
0.614055 | + | 0.789264i | \(0.289537\pi\) | |||||||
\(398\) | −215.949 | + | 374.035i | −0.0271973 | + | 0.0471072i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2627.43 | + | 4550.84i | 0.328429 | + | 0.568855i | ||||
\(401\) | 260.757 | + | 150.548i | 0.0324728 | + | 0.0187482i | 0.516149 | − | 0.856499i | \(-0.327365\pi\) |
−0.483676 | + | 0.875247i | \(0.660699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −539.816 | − | 934.988i | −0.0667249 | − | 0.115571i | ||||
\(404\) | −570.047 | − | 987.351i | −0.0702003 | − | 0.121590i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.4769 | + | 268.682i | 0.00274756 | + | 0.0328435i | ||||
\(407\) | −10118.4 | − | 5841.88i | −1.23232 | − | 0.711478i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4548.11i | − | 0.549853i | −0.961465 | − | 0.274926i | \(-0.911347\pi\) | ||
0.961465 | − | 0.274926i | \(-0.0886535\pi\) | |||||||
\(410\) | 49.6507i | 0.00598066i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3758.01 | + | 2169.69i | 0.449379 | + | 0.259449i | ||||
\(413\) | −9664.29 | + | 6712.36i | −1.15145 | + | 0.799743i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3287.66 | + | 5694.40i | 0.388879 | + | 0.673559i | ||||
\(416\) | −248.163 | − | 429.831i | −0.0292480 | − | 0.0506591i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1095.83 | + | 632.676i | 0.128226 | + | 0.0740315i | ||||
\(419\) | 687.732 | + | 1191.19i | 0.0801859 | + | 0.138886i | 0.903330 | − | 0.428947i | \(-0.141115\pi\) |
−0.823144 | + | 0.567833i | \(0.807782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1505.07 | + | 2606.85i | −0.174234 | + | 0.301782i | −0.939896 | − | 0.341461i | \(-0.889078\pi\) |
0.765662 | + | 0.643243i | \(0.222412\pi\) | |||||||
\(422\) | −681.868 | + | 393.676i | −0.0786559 | + | 0.0454120i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1425.35 | + | 2468.78i | −0.163258 | + | 0.282771i | ||||
\(425\) | 3790.25 | 0.432597 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7901.69 | + | 11376.7i | 0.895526 | + | 1.28936i | ||||
\(428\) | 9147.99 | − | 5281.59i | 1.03314 | − | 0.596485i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 527.486 | − | 304.544i | 0.0591573 | − | 0.0341545i | ||||
\(431\) | 2888.94 | + | 1667.93i | 0.322867 | + | 0.186407i | 0.652670 | − | 0.757643i | \(-0.273649\pi\) |
−0.329803 | + | 0.944050i | \(0.606982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3574.98i | 0.396772i | 0.980124 | + | 0.198386i | \(0.0635700\pi\) | ||||
−0.980124 | + | 0.198386i | \(0.936430\pi\) | |||||||
\(434\) | 416.993 | − | 289.623i | 0.0461205 | − | 0.0320331i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4181.12 | − | 7241.92i | 0.459265 | − | 0.795470i | ||||
\(437\) | 2225.76 | 0.243644 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6057.88i | 0.658603i | 0.944225 | + | 0.329301i | \(0.106813\pi\) | ||||
−0.944225 | + | 0.329301i | \(0.893187\pi\) | |||||||
\(440\) | 1601.62 | 0.173533 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −117.668 | −0.0126626 | ||||||||
\(443\) | − | 15905.0i | − | 1.70580i | −0.522071 | − | 0.852902i | \(-0.674841\pi\) | ||
0.522071 | − | 0.852902i | \(-0.325159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9327.73 | −0.993656 | ||||||||
\(446\) | 532.595 | − | 922.482i | 0.0565451 | − | 0.0979390i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7403.14 | + | 5141.87i | −0.780727 | + | 0.542256i | ||||
\(449\) | − | 3388.65i | − | 0.356169i | −0.984015 | − | 0.178085i | \(-0.943010\pi\) | ||
0.984015 | − | 0.178085i | \(-0.0569901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1596.00 | + | 921.453i | 0.166636 | + | 0.0962073i | ||||
\(452\) | −6386.47 | + | 3687.23i | −0.664589 | + | 0.383701i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −990.867 | + | 572.077i | −0.102431 | + | 0.0591386i | ||||
\(455\) | 684.721 | + | 985.845i | 0.0705499 | + | 0.101576i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2281.48 | 0.233530 | 0.116765 | − | 0.993160i | \(-0.462748\pi\) | ||||
0.116765 | + | 0.993160i | \(0.462748\pi\) | |||||||
\(458\) | −167.439 | + | 290.013i | −0.0170828 | + | 0.0295882i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1214.83 | − | 701.382i | 0.123134 | − | 0.0710915i | ||||
\(461\) | −2730.79 | + | 4729.87i | −0.275891 | + | 0.477856i | −0.970359 | − | 0.241666i | \(-0.922306\pi\) |
0.694469 | + | 0.719523i | \(0.255639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5628.16 | − | 9748.26i | −0.564931 | − | 0.978488i | −0.997056 | − | 0.0766749i | \(-0.975570\pi\) |
0.432126 | − | 0.901813i | \(-0.357764\pi\) | |||||||
\(464\) | −3054.31 | − | 1763.41i | −0.305588 | − | 0.176431i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 258.980 | + | 448.567i | 0.0257447 | + | 0.0445911i | ||||
\(467\) | 8118.96 | + | 14062.5i | 0.804498 | + | 1.39343i | 0.916629 | + | 0.399738i | \(0.130899\pi\) |
−0.112131 | + | 0.993693i | \(0.535768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2506.59 | + | 1740.96i | −0.246788 | + | 0.171407i | ||||
\(470\) | 706.998 | + | 408.185i | 0.0693859 | + | 0.0400600i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2608.01i | 0.254329i | ||||||||
\(473\) | − | 22607.8i | − | 2.19769i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5863.25 | − | 3385.15i | −0.566367 | − | 0.326992i | ||||
\(476\) | 551.408 | + | 6591.37i | 0.0530961 | + | 0.634695i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −669.212 | − | 1159.11i | −0.0640356 | − | 0.110913i | ||||
\(479\) | 3133.26 | + | 5426.96i | 0.298877 | + | 0.517670i | 0.975879 | − | 0.218311i | \(-0.0700546\pi\) |
−0.677002 | + | 0.735981i | \(0.736721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1680.74 | − | 970.375i | −0.159325 | − | 0.0919861i | ||||
\(482\) | 868.166 | + | 1503.71i | 0.0820412 | + | 0.142100i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9520.30 | − | 16489.6i | 0.894093 | − | 1.54861i | ||||
\(485\) | 5609.47 | − | 3238.63i | 0.525181 | − | 0.303214i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 262.826 | − | 455.227i | 0.0244554 | − | 0.0423580i | −0.853539 | − | 0.521029i | \(-0.825548\pi\) |
0.877994 | + | 0.478671i | \(0.158882\pi\) | |||||||
\(488\) | 3070.11 | 0.284790 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −435.145 | + | 359.523i | −0.0401180 | + | 0.0331461i | ||||
\(491\) | 13426.5 | − | 7751.78i | 1.23407 | − | 0.712491i | 0.266194 | − | 0.963919i | \(-0.414234\pi\) |
0.967876 | + | 0.251429i | \(0.0809004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2203.02 | + | 1271.92i | −0.201256 | + | 0.116195i | ||||
\(494\) | 182.024 | + | 105.092i | 0.0165782 | + | 0.00957144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6641.13i | 0.601200i | ||||||||
\(497\) | −2942.24 | − | 4236.17i | −0.265548 | − | 0.382330i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4660.34 | + | 8071.95i | −0.418087 | + | 0.724148i | −0.995747 | − | 0.0921292i | \(-0.970633\pi\) |
0.577660 | + | 0.816278i | \(0.303966\pi\) | |||||||
\(500\) | −10601.6 | −0.948240 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 468.434i | − | 0.0416479i | ||||||
\(503\) | 1065.29 | 0.0944311 | 0.0472155 | − | 0.998885i | \(-0.484965\pi\) | ||||
0.0472155 | + | 0.998885i | \(0.484965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 917.941 | 0.0808868 | ||||||||
\(506\) | 435.578i | 0.0382684i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11005.7 | −0.961218 | ||||||||
\(509\) | 4693.68 | − | 8129.69i | 0.408730 | − | 0.707941i | −0.586018 | − | 0.810298i | \(-0.699305\pi\) |
0.994748 | + | 0.102357i | \(0.0326384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6688.98 | − | 559.574i | 0.579066 | − | 0.0484425i | ||||
\(512\) | 5102.59i | 0.440439i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 103.535 | + | 59.7758i | 0.00888467 | + | 0.00512957i | ||||
\(515\) | −3025.74 | + | 1746.91i | −0.258894 | + | 0.149472i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26241.9 | − | 15150.8i | 2.23234 | − | 1.28884i | ||||
\(518\) | 388.848 | − | 825.672i | 0.0329827 | − | 0.0700346i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 266.040 | 0.0224358 | ||||||||
\(521\) | 10087.0 | − | 17471.2i | 0.848216 | − | 1.46915i | −0.0345837 | − | 0.999402i | \(-0.511011\pi\) |
0.882799 | − | 0.469751i | \(-0.155656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13914.0 | − | 8033.23i | 1.16332 | − | 0.671642i | 0.211221 | − | 0.977438i | \(-0.432256\pi\) |
0.952097 | + | 0.305797i | \(0.0989227\pi\) | |||||||
\(524\) | −1557.99 | + | 2698.52i | −0.129888 | + | 0.224972i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.4991 | + | 84.0029i | 0.00402027 | + | 0.00696331i | ||||
\(527\) | 4148.38 | + | 2395.07i | 0.342896 | + | 0.197971i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5700.41 | − | 9873.40i | −0.468514 | − | 0.811490i | ||||
\(530\) | −571.418 | − | 989.725i | −0.0468317 | − | 0.0811149i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5033.90 | − | 10688.9i | 0.410239 | − | 0.871093i | ||||
\(533\) | 265.106 | + | 153.059i | 0.0215442 | + | 0.0124385i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8504.90i | 0.687288i | ||||||||
\(536\) | 676.430i | 0.0545099i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 891.588 | + | 514.759i | 0.0714482 | + | 0.0412506i | ||||
\(539\) | 3481.01 | + | 20659.9i | 0.278177 | + | 1.65099i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12174.8 | − | 21087.4i | −0.967535 | − | 1.67582i | −0.702645 | − | 0.711541i | \(-0.747998\pi\) |
−0.264890 | − | 0.964279i | \(-0.585336\pi\) | |||||||
\(542\) | −108.524 | − | 187.969i | −0.00860055 | − | 0.0148966i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1907.08 | + | 1101.06i | 0.150304 | + | 0.0867782i | ||||
\(545\) | 3366.41 | + | 5830.79i | 0.264589 | + | 0.458282i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5442.16 | − | 9426.10i | 0.425393 | − | 0.736802i | −0.571064 | − | 0.820906i | \(-0.693469\pi\) |
0.996457 | + | 0.0841031i | \(0.0268025\pi\) | |||||||
\(548\) | −14303.2 | + | 8257.96i | −1.11497 | + | 0.643727i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 662.470 | − | 1147.43i | 0.0513597 | − | 0.0889576i | ||||
\(551\) | 4543.91 | 0.351319 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8479.95 | + | 5889.77i | −0.652087 | + | 0.452908i | ||||
\(554\) | 929.515 | − | 536.656i | 0.0712839 | − | 0.0411558i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8635.69 | + | 4985.82i | −0.658695 | + | 0.380298i | ||||
\(557\) | 21701.2 | + | 12529.2i | 1.65082 | + | 0.953104i | 0.976734 | + | 0.214455i | \(0.0687975\pi\) |
0.674090 | + | 0.738649i | \(0.264536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3755.31i | − | 0.284137i | ||||||
\(560\) | −615.519 | − | 7357.72i | −0.0464472 | − | 0.555215i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −666.109 | + | 1153.73i | −0.0499966 | + | 0.0865967i | ||||
\(563\) | −17896.2 | −1.33967 | −0.669836 | − | 0.742509i | \(-0.733635\pi\) | ||||
−0.669836 | + | 0.742509i | \(0.733635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5937.51i | − | 0.442112i | ||||||
\(566\) | −1550.77 | −0.115166 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1143.17 | −0.0844480 | ||||||||
\(569\) | − | 883.312i | − | 0.0650797i | −0.999470 | − | 0.0325399i | \(-0.989640\pi\) | ||
0.999470 | − | 0.0325399i | \(-0.0103596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10459.5 | 0.766579 | 0.383290 | − | 0.923628i | \(-0.374791\pi\) | ||||
0.383290 | + | 0.923628i | \(0.374791\pi\) | |||||||
\(572\) | 2458.40 | − | 4258.07i | 0.179704 | − | 0.311257i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −61.3339 | + | 130.235i | −0.00445998 | + | 0.00947021i | ||||
\(575\) | − | 2330.58i | − | 0.169029i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17098.4 | + | 9871.79i | 1.23365 | + | 0.712249i | 0.967789 | − | 0.251762i | \(-0.0810099\pi\) |
0.265863 | + | 0.964011i | \(0.414343\pi\) | |||||||
\(578\) | −644.011 | + | 371.820i | −0.0463449 | + | 0.0267572i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2480.08 | − | 1431.88i | 0.177552 | − | 0.102509i | ||||
\(581\) | 1589.28 | + | 18997.8i | 0.113485 | + | 1.35656i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42419.1 | −3.01341 | ||||||||
\(584\) | 743.874 | − | 1288.43i | 0.0527084 | − | 0.0912937i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1001.27 | − | 578.082i | 0.0705835 | − | 0.0407514i | ||||
\(587\) | 4130.99 | − | 7155.09i | 0.290467 | − | 0.503104i | −0.683453 | − | 0.729995i | \(-0.739523\pi\) |
0.973920 | + | 0.226890i | \(0.0728559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4278.17 | − | 7410.01i | −0.299285 | − | 0.518377i | ||||
\(590\) | −905.463 | − | 522.769i | −0.0631819 | − | 0.0364781i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5969.06 | + | 10338.7i | 0.414403 | + | 0.717768i | ||||
\(593\) | −13435.3 | − | 23270.7i | −0.930392 | − | 1.61149i | −0.782652 | − | 0.622460i | \(-0.786133\pi\) |
−0.147741 | − | 0.989026i | \(-0.547200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4817.98 | − | 2269.02i | −0.331963 | − | 0.156337i | ||||
\(596\) | 20664.6 | + | 11930.7i | 1.42023 | + | 0.819970i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 72.3524i | 0.00494768i | ||||||||
\(599\) | − | 16691.0i | − | 1.13852i | −0.822156 | − | 0.569262i | \(-0.807229\pi\) | ||
0.822156 | − | 0.569262i | \(-0.192771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16426.9 | + | 9484.10i | 1.11492 | + | 0.643702i | 0.940100 | − | 0.340898i | \(-0.110731\pi\) |
0.174824 | + | 0.984600i | \(0.444064\pi\) | |||||||
\(602\) | 1759.82 | − | 147.219i | 0.119144 | − | 0.00996713i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11385.6 | + | 19720.5i | 0.767012 | + | 1.32850i | ||||
\(605\) | 7665.23 | + | 13276.6i | 0.515100 | + | 0.892180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4464.29 | − | 2577.46i | −0.298517 | − | 0.172349i | 0.343260 | − | 0.939241i | \(-0.388469\pi\) |
−0.641776 | + | 0.766892i | \(0.721802\pi\) | |||||||
\(608\) | −1966.75 | − | 3406.52i | −0.131188 | − | 0.227224i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −615.397 | + | 1065.90i | −0.0408470 | + | 0.0707491i | ||||
\(611\) | 4358.96 | − | 2516.65i | 0.288616 | − | 0.166633i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4050.42 | − | 7015.53i | 0.266876 | − | 0.462242i | −0.701178 | − | 0.712987i | \(-0.747342\pi\) |
0.968053 | + | 0.250744i | \(0.0806754\pi\) | |||||||
\(614\) | −67.8742 | −0.00446120 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4201.10 | + | 1978.50i | 0.274784 | + | 0.129409i | ||||
\(617\) | 6750.27 | − | 3897.27i | 0.440447 | − | 0.254292i | −0.263340 | − | 0.964703i | \(-0.584824\pi\) |
0.703787 | + | 0.710411i | \(0.251491\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15171.1 | − | 8759.06i | 0.985104 | − | 0.568750i | 0.0812970 | − | 0.996690i | \(-0.474094\pi\) |
0.903807 | + | 0.427940i | \(0.140760\pi\) | |||||||
\(620\) | −4670.09 | − | 2696.28i | −0.302509 | − | 0.174654i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1250.12i | − | 0.0805870i | ||||||
\(623\) | −24466.9 | − | 11522.6i | −1.57343 | − | 0.741002i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −994.380 | + | 1722.32i | −0.0636403 | + | 0.110228i | ||||
\(626\) | 705.516 | 0.0450449 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7280.71i | − | 0.462630i | ||||||
\(629\) | 8610.77 | 0.545841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8636.00 | 0.544839 | 0.272420 | − | 0.962179i | \(-0.412176\pi\) | ||||
0.272420 | + | 0.962179i | \(0.412176\pi\) | |||||||
\(632\) | 2288.40i | 0.144031i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1910.85 | −0.119700 | ||||||||
\(635\) | 4430.59 | − | 7674.00i | 0.276886 | − | 0.479580i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 578.218 | + | 3431.74i | 0.0359652 | + | 0.213454i | ||||
\(638\) | 889.237i | 0.0551806i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2858.50 | − | 1650.35i | −0.176550 | − | 0.101931i | ||||
\(641\) | 13306.7 | − | 7682.65i | 0.819945 | − | 0.473396i | −0.0304525 | − | 0.999536i | \(-0.509695\pi\) |
0.850398 | + | 0.526141i | \(0.176361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6869.74 | + | 3966.25i | −0.421332 | + | 0.243256i | −0.695647 | − | 0.718384i | \(-0.744882\pi\) |
0.274315 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(644\) | 4052.95 | − | 339.054i | 0.247995 | − | 0.0207463i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −932.546 | −0.0567965 | ||||||||
\(647\) | −9673.35 | + | 16754.7i | −0.587788 | + | 1.01808i | 0.406734 | + | 0.913547i | \(0.366668\pi\) |
−0.994522 | + | 0.104531i | \(0.966666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33608.5 | + | 19403.9i | −2.03274 | + | 1.17360i | ||||
\(650\) | 110.041 | − | 190.596i | 0.00664023 | − | 0.0115012i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6398.76 | − | 11083.0i | −0.384348 | − | 0.665710i | ||||
\(653\) | −16717.4 | − | 9651.81i | −1.00184 | − | 0.578414i | −0.0930501 | − | 0.995661i | \(-0.529662\pi\) |
−0.908793 | + | 0.417247i | \(0.862995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1254.41 | − | 2172.70i | −0.0748303 | − | 0.129610i | ||||
\(656\) | −941.512 | − | 1630.75i | −0.0560364 | − | 0.0970579i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1350.24 | + | 1944.04i | 0.0799966 | + | 0.115177i | ||||
\(659\) | −6426.97 | − | 3710.61i | −0.379908 | − | 0.219340i | 0.297870 | − | 0.954606i | \(-0.403724\pi\) |
−0.677778 | + | 0.735266i | \(0.737057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 14146.3i | − | 0.832415i | −0.909270 | − | 0.416208i | \(-0.863359\pi\) | ||
0.909270 | − | 0.416208i | \(-0.136641\pi\) | |||||||
\(662\) | 1074.84i | 0.0631041i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3659.35 | + | 2112.73i | 0.213871 | + | 0.123478i | ||||
\(665\) | 5426.58 | + | 7813.06i | 0.316442 | + | 0.455605i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 782.086 | + | 1354.61i | 0.0454011 | + | 0.0786369i | ||||
\(668\) | −7317.85 | − | 12674.9i | −0.423856 | − | 0.734141i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −234.847 | − | 135.589i | −0.0135417 | − | 0.00781829i | ||||
\(671\) | 22841.9 | + | 39563.4i | 1.31416 | + | 2.27620i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4164.46 | − | 7213.05i | 0.238526 | − | 0.413139i | −0.721766 | − | 0.692138i | \(-0.756669\pi\) |
0.960292 | + | 0.278998i | \(0.0900024\pi\) | |||||||
\(674\) | 235.903 | − | 136.199i | 0.0134817 | − | 0.00778365i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8306.74 | + | 14387.7i | −0.472618 | + | 0.818599i | ||||
\(677\) | 4479.59 | 0.254305 | 0.127153 | − | 0.991883i | \(-0.459416\pi\) | ||||
0.127153 | + | 0.991883i | \(0.459416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18714.5 | − | 1565.58i | 1.05773 | − | 0.0884853i | ||||
\(680\) | −1022.23 | + | 590.187i | −0.0576483 | + | 0.0332833i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1450.13 | − | 837.234i | 0.0814199 | − | 0.0470078i | ||||
\(683\) | −2140.00 | − | 1235.53i | −0.119890 | − | 0.0692184i | 0.438856 | − | 0.898557i | \(-0.355384\pi\) |
−0.558746 | + | 0.829339i | \(0.688717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13297.7i | − | 0.741721i | ||||||
\(686\) | −1585.52 | + | 405.500i | −0.0882439 | + | 0.0225686i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11550.0 | + | 20005.2i | −0.640028 | + | 1.10856i | ||||
\(689\) | −7046.09 | −0.389601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23174.9i | 1.27585i | 0.770097 | + | 0.637926i | \(0.220208\pi\) | ||||
−0.770097 | + | 0.637926i | \(0.779792\pi\) | |||||||
\(692\) | −15913.3 | −0.874181 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1231.62 | 0.0673653 | ||||||||
\(695\) | − | 8028.61i | − | 0.438191i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1358.19 | −0.0738096 | ||||||||
\(698\) | −324.259 | + | 561.633i | −0.0175837 | + | 0.0304558i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11192.2 | − | 5270.96i | −0.604324 | − | 0.284605i | ||||
\(701\) | − | 21807.9i | − | 1.17500i | −0.809225 | − | 0.587498i | \(-0.800113\pi\) | ||
0.809225 | − | 0.587498i | \(-0.199887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13320.3 | − | 7690.46i | −0.714628 | − | 0.412591i | ||||
\(704\) | −25745.1 | + | 14863.9i | −1.37827 | + | 0.795747i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1339.95 | + | 773.623i | −0.0714304 | + | 0.0412404i | ||||
\(707\) | 2407.78 | + | 1133.94i | 0.128082 | + | 0.0603200i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12974.7 | 0.687270 | 0.343635 | − | 0.939103i | \(-0.388342\pi\) | ||||
0.343635 | + | 0.939103i | \(0.388342\pi\) | |||||||
\(710\) | 229.147 | − | 396.893i | 0.0121123 | − | 0.0209791i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5191.14 | + | 2997.11i | −0.273239 | + | 0.157755i | ||||
\(713\) | 1472.70 | − | 2550.79i | 0.0773534 | − | 0.133980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1979.37 | + | 3428.37i | 0.103530 | + | 0.179320i | ||||
\(716\) | 11304.8 | + | 6526.82i | 0.590056 | + | 0.340669i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −858.620 | − | 1487.17i | −0.0446287 | − | 0.0772992i | ||||
\(719\) | −8416.91 | − | 14578.5i | −0.436575 | − | 0.756171i | 0.560847 | − | 0.827919i | \(-0.310475\pi\) |
−0.997423 | + | 0.0717486i | \(0.977142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10094.6 | + | 844.474i | −0.521417 | + | 0.0436197i | ||||
\(722\) | −87.7246 | − | 50.6478i | −0.00452184 | − | 0.00261069i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26929.9i | 1.38238i | ||||||||
\(725\) | − | 4757.89i | − | 0.243729i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28354.9 | + | 16370.7i | 1.44653 | + | 0.835152i | 0.998272 | − | 0.0587547i | \(-0.0187130\pi\) |
0.448253 | + | 0.893907i | \(0.352046\pi\) | |||||||
\(728\) | 697.830 | + | 328.641i | 0.0355265 | + | 0.0167311i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 298.216 | + | 516.525i | 0.0151198 | + | 0.0261883i | ||||
\(731\) | 8330.81 | + | 14429.4i | 0.421513 | + | 0.730083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6413.52 | + | 3702.85i | 0.323177 | + | 0.186586i | 0.652808 | − | 0.757524i | \(-0.273591\pi\) |
−0.329631 | + | 0.944110i | \(0.606924\pi\) | |||||||
\(734\) | −207.376 | − | 359.186i | −0.0104283 | − | 0.0180624i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 677.025 | − | 1172.64i | 0.0339069 | − | 0.0587285i | ||||
\(737\) | −8716.91 | + | 5032.71i | −0.435674 | + | 0.251536i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6333.95 | − | 10970.7i | 0.315288 | − | 0.546095i | −0.664210 | − | 0.747546i | \(-0.731232\pi\) |
0.979499 | + | 0.201450i | \(0.0645655\pi\) | |||||||
\(740\) | −9693.69 | −0.481550 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −276.228 | − | 3301.95i | −0.0136667 | − | 0.163367i | ||||
\(743\) | −16940.8 | + | 9780.78i | −0.836471 | + | 0.482937i | −0.856063 | − | 0.516871i | \(-0.827097\pi\) |
0.0195919 | + | 0.999808i | \(0.493763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16638.0 | + | 9605.97i | −0.818215 | + | 0.472397i | ||||
\(746\) | −1162.64 | − | 671.249i | −0.0570605 | − | 0.0329439i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21815.0i | 1.06636i | ||||||||
\(749\) | −10506.2 | + | 22308.6i | −0.512533 | + | 1.08830i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1163.24 | − | 2014.80i | 0.0565211 | − | 0.0978975i | −0.836380 | − | 0.548149i | \(-0.815333\pi\) |
0.892902 | + | 0.450252i | \(0.148666\pi\) | |||||||
\(752\) | −30961.2 | −1.50138 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 147.708i | 0.00713423i | ||||||||
\(755\) | −18334.2 | −0.883774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5811.77 | 0.279039 | 0.139519 | − | 0.990219i | \(-0.455444\pi\) | ||||
0.139519 | + | 0.990219i | \(0.455444\pi\) | |||||||
\(758\) | − | 2562.52i | − | 0.122790i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2108.43 | 0.100633 | ||||||||
\(761\) | −13299.7 | + | 23035.7i | −0.633526 | + | 1.09730i | 0.353299 | + | 0.935510i | \(0.385060\pi\) |
−0.986825 | + | 0.161789i | \(0.948274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1627.35 | + | 19452.9i | 0.0772138 | + | 0.922990i | ||||
\(764\) | − | 898.765i | − | 0.0425604i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3223.70 | − | 1861.21i | −0.152059 | − | 0.0877913i | ||||
\(767\) | −5582.59 | + | 3223.11i | −0.262810 | + | 0.151734i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5505.13 | − | 3178.39i | 0.258153 | − | 0.149045i | −0.365339 | − | 0.930875i | \(-0.619047\pi\) |
0.623492 | + | 0.781830i | \(0.285713\pi\) | |||||||
\(770\) | −1529.01 | + | 1061.98i | −0.0715605 | + | 0.0497025i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6948.27 | −0.323930 | ||||||||
\(773\) | 3466.39 | − | 6003.96i | 0.161290 | − | 0.279363i | −0.774041 | − | 0.633135i | \(-0.781768\pi\) |
0.935332 | + | 0.353772i | \(0.115101\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7758.97 | + | 4479.64i | −0.359626 | + | 0.207630i | ||||
\(776\) | 2081.22 | − | 3604.78i | 0.0962776 | − | 0.166758i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1169.53 | − | 2025.68i | −0.0538942 | − | 0.0933474i | ||||
\(779\) | 2101.03 | + | 1213.03i | 0.0966334 | + | 0.0557913i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8505.33 | − | 14731.7i | −0.389686 | − | 0.674956i | ||||
\(782\) | −160.507 | − | 278.007i | −0.00733982 | − | 0.0127129i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7474.53 | − | 20059.8i | 0.340494 | − | 0.913805i | ||||
\(785\) | 5076.66 | + | 2931.01i | 0.230820 | + | 0.133264i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33309.9i | − | 1.50873i | −0.656455 | − | 0.754365i | \(-0.727945\pi\) | ||
0.656455 | − | 0.754365i | \(-0.272055\pi\) | |||||||
\(788\) | − | 7966.09i | − | 0.360127i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −794.500 | − | 458.705i | −0.0357810 | − | 0.0206582i | ||||
\(791\) | 7334.66 | − | 15574.2i | 0.329697 | − | 0.700071i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3794.20 | + | 6571.74i | 0.169907 | + | 0.294287i | ||||
\(794\) | 279.502 | + | 484.112i | 0.0124926 | + | 0.0216379i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11518.5 | + | 6650.21i | 0.512892 | + | 0.296119i | ||||
\(797\) | 17597.8 | + | 30480.4i | 0.782117 | + | 1.35467i | 0.930706 | + | 0.365768i | \(0.119194\pi\) |
−0.148589 | + | 0.988899i | \(0.547473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11165.9 | + | 19339.9i | −0.494395 | + | 0.856318i | ||||
\(800\) | −3566.94 | + | 2059.37i | −0.157638 | + | 0.0910123i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −38.7850 | + | 67.1775i | −0.00170766 | + | 0.00295776i | ||||
\(803\) | 22138.0 | 0.972894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1395.19 | + | 2962.52i | −0.0610858 | + | 0.129708i | ||||
\(806\) | 240.876 | − | 139.070i | 0.0105267 | − | 0.00607758i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 510.860 | − | 294.945i | 0.0222426 | − | 0.0128418i | ||||
\(809\) | 17121.2 | + | 9884.94i | 0.744067 | + | 0.429587i | 0.823546 | − | 0.567249i | \(-0.191992\pi\) |
−0.0794792 | + | 0.996837i | \(0.525326\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20597.9i | − | 0.891848i | −0.895071 | − | 0.445924i | \(-0.852875\pi\) | ||
0.895071 | − | 0.445924i | \(-0.147125\pi\) | |||||||
\(812\) | 8274.13 | − | 692.182i | 0.357593 | − | 0.0299148i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1505.01 | − | 2606.76i | 0.0648044 | − | 0.112244i | ||||
\(815\) | 10303.9 | 0.442857 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29761.7i | − | 1.27446i | ||||||
\(818\) | 1171.71 | 0.0500829 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1529.01 | 0.0651161 | ||||||||
\(821\) | 4298.25i | 0.182716i | 0.995818 | + | 0.0913581i | \(0.0291208\pi\) | ||||
−0.995818 | + | 0.0913581i | \(0.970879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9618.81 | −0.407401 | −0.203700 | − | 0.979033i | \(-0.565297\pi\) | ||||
−0.203700 | + | 0.979033i | \(0.565297\pi\) | |||||||
\(824\) | −1122.61 | + | 1944.41i | −0.0474610 | + | 0.0822049i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1729.27 | − | 2489.76i | −0.0728439 | − | 0.104879i | ||||
\(827\) | − | 28304.7i | − | 1.19015i | −0.803672 | − | 0.595073i | \(-0.797123\pi\) | ||
0.803672 | − | 0.595073i | \(-0.202877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24753.6 | + | 14291.5i | 1.03707 | + | 0.598750i | 0.919001 | − | 0.394256i | \(-0.128998\pi\) |
0.118065 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(830\) | −1467.02 | + | 846.983i | −0.0613505 | + | 0.0354207i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4276.43 | + | 2469.00i | −0.178195 | + | 0.102881i | ||||
\(833\) | −9834.75 | − | 11903.4i | −0.409068 | − | 0.495111i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11783.9 | 0.488380 | ||||||||
\(836\) | 19483.4 | − | 33746.3i | 0.806039 | − | 1.39610i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −306.879 | + | 177.177i | −0.0126503 | + | 0.00730366i | ||||
\(839\) | 16920.3 | − | 29306.9i | 0.696251 | − | 1.20594i | −0.273506 | − | 0.961870i | \(-0.588183\pi\) |
0.969757 | − | 0.244072i | \(-0.0784835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10597.9 | − | 18356.0i | −0.434535 | − | 0.752636i | ||||
\(842\) | −671.590 | − | 387.743i | −0.0274876 | − | 0.0158700i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12123.4 | + | 20998.3i | 0.494436 | + | 0.856388i | ||||
\(845\) | −6688.13 | − | 11584.2i | −0.272282 | − | 0.471607i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3705.44 | + | 44293.7i | 0.150319 | + | 1.79687i | ||||
\(848\) | 37535.8 | + | 21671.3i | 1.52003 | + | 0.877588i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 976.462i | 0.0394028i | ||||||||
\(851\) | − | 5294.66i | − | 0.213277i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20134.3 | − | 11624.6i | −0.808191 | − | 0.466609i | 0.0381363 | − | 0.999273i | \(-0.487858\pi\) |
−0.846327 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(854\) | −2930.91 | + | 2035.67i | −0.117440 | + | 0.0815683i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2732.72 | + | 4733.22i | 0.109115 | + | 0.188993i | ||||
\(857\) | 10798.5 | + | 18703.5i | 0.430418 | + | 0.745506i | 0.996909 | − | 0.0785619i | \(-0.0250328\pi\) |
−0.566491 | + | 0.824068i | \(0.691699\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11823.9 | − | 6826.55i | −0.469648 | − | 0.271151i | 0.246445 | − | 0.969157i | \(-0.420738\pi\) |
−0.716092 | + | 0.698006i | \(0.754071\pi\) | |||||||
\(860\) | −9378.53 | − | 16244.1i | −0.371866 | − | 0.644092i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −429.701 | + | 744.264i | −0.0169787 | + | 0.0294080i | ||||
\(863\) | −9232.02 | + | 5330.11i | −0.364150 | + | 0.210242i | −0.670900 | − | 0.741548i | \(-0.734092\pi\) |
0.306750 | + | 0.951790i | \(0.400759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6406.26 | − | 11096.0i | 0.251814 | − | 0.436155i | ||||
\(866\) | −921.003 | −0.0361397 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8919.03 | − | 12841.4i | −0.348769 | − | 0.502150i | ||||
\(869\) | −29489.8 | + | 17025.9i | −1.15118 | + | 0.664632i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1447.94 | + | 835.966i | −0.0563277 | + | 0.0325208i | ||||
\(872\) | 3747.00 | + | 2163.33i | 0.145516 | + | 0.0840134i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 573.411i | 0.0221921i | ||||||||
\(875\) | 20326.6 | − | 14117.9i | 0.785332 | − | 0.545454i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 764.513 | − | 1324.17i | 0.0294364 | − | 0.0509854i | −0.850932 | − | 0.525276i | \(-0.823962\pi\) |
0.880368 | + | 0.474291i | \(0.157295\pi\) | |||||||
\(878\) | −1560.66 | −0.0599883 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 24351.3i | − | 0.932822i | ||||||
\(881\) | −22496.2 | −0.860292 | −0.430146 | − | 0.902759i | \(-0.641538\pi\) | ||||
−0.430146 | + | 0.902759i | \(0.641538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1745.87 | −0.0665381 | −0.0332691 | − | 0.999446i | \(-0.510592\pi\) | ||||
−0.0332691 | + | 0.999446i | \(0.510592\pi\) | |||||||
\(884\) | 3623.61i | 0.137868i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4097.53 | 0.155372 | ||||||||
\(887\) | −4586.51 | + | 7944.07i | −0.173619 | + | 0.300717i | −0.939682 | − | 0.342048i | \(-0.888879\pi\) |
0.766064 | + | 0.642765i | \(0.222213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21101.3 | − | 14656.0i | 0.796080 | − | 0.552919i | ||||
\(890\) | − | 2403.06i | − | 0.0905063i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28408.1 | − | 16401.4i | −1.06634 | − | 0.615650i | ||||
\(893\) | 34545.8 | − | 19945.0i | 1.29455 | − | 0.747408i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9101.99 | + | 5255.04i | −0.339940 | + | 0.196264i | ||||
\(896\) | −5459.21 | − | 7860.04i | −0.203549 | − | 0.293064i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 872.999 | 0.0324414 | ||||||||
\(899\) | 3006.53 | − | 5207.46i | 0.111539 | − | 0.193191i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27073.9 | − | 15631.1i | 1.00107 | − | 0.577968i | ||||
\(902\) | −237.389 | + | 411.170i | −0.00876296 | + | 0.0151779i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1907.79 | − | 3304.39i | −0.0701905 | − | 0.121574i | ||||
\(905\) | −18777.6 | − | 10841.2i | −0.689710 | − | 0.398204i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7220.71 | − | 12506.6i | −0.264344 | − | 0.457857i | 0.703048 | − | 0.711143i | \(-0.251822\pi\) |
−0.967391 | + | 0.253286i | \(0.918489\pi\) | |||||||
\(908\) | 17617.3 | + | 30514.0i | 0.643887 | + | 1.11525i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −253.978 | + | 176.401i | −0.00925197 | + | 0.00642598i | ||||
\(911\) | 6737.06 | + | 3889.65i | 0.245015 | + | 0.141460i | 0.617480 | − | 0.786587i | \(-0.288154\pi\) |
−0.372464 | + | 0.928046i | \(0.621487\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62875.7i | 2.27917i | ||||||||
\(914\) | 587.766i | 0.0212709i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8931.03 | + | 5156.33i | 0.322150 | + | 0.185993i | ||||
\(917\) | −606.392 | − | 7248.63i | −0.0218373 | − | 0.261037i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18628.7 | − | 32265.9i | −0.668667 | − | 1.15817i | −0.978277 | − | 0.207302i | \(-0.933532\pi\) |
0.309610 | − | 0.950864i | \(-0.399801\pi\) | |||||||
\(920\) | 362.899 | + | 628.559i | 0.0130048 | + | 0.0225250i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1218.53 | − | 703.519i | −0.0435252 | − | 0.0251293i | ||||
\(923\) | −1412.79 | − | 2447.03i | −0.0503820 | − | 0.0872642i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8052.63 | + | 13947.6i | −0.286237 | + | 0.495776i | ||||
\(926\) | 2511.39 | − | 1449.95i | 0.0891248 | − | 0.0514562i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1382.15 | − | 2393.96i | 0.0488916 | − | 0.0846827i | ||||
\(929\) | 5028.76 | 0.177598 | 0.0887989 | − | 0.996050i | \(-0.471697\pi\) | ||||
0.0887989 | + | 0.996050i | \(0.471697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4582.52 | + | 27197.4i | 0.161317 | + | 0.957419i | ||||
\(932\) | 13813.7 | − | 7975.37i | 0.485498 | − | 0.280302i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3622.84 | + | 2091.65i | −0.126920 | + | 0.0732770i | ||||
\(935\) | −15211.1 | − | 8782.11i | −0.532037 | − | 0.307172i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4765.66i | − | 0.166155i | −0.996543 | − | 0.0830776i | \(-0.973525\pi\) | ||
0.996543 | − | 0.0830776i | \(-0.0264749\pi\) | |||||||
\(938\) | −448.515 | − | 645.761i | −0.0156125 | − | 0.0224785i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12570.2 | − | 21772.2i | 0.436164 | − | 0.755458i | ||||
\(941\) | 20633.4 | 0.714804 | 0.357402 | − | 0.933951i | \(-0.383663\pi\) | ||||
0.357402 | + | 0.933951i | \(0.383663\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 835.137i | 0.0288397i | ||||||||
\(944\) | 39652.5 | 1.36714 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5824.33 | 0.200175 | ||||||||
\(947\) | − | 19798.6i | − | 0.679374i | −0.940539 | − | 0.339687i | \(-0.889679\pi\) | ||
0.940539 | − | 0.339687i | \(-0.110321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3677.27 | 0.125784 | ||||||||
\(950\) | 872.099 | − | 1510.52i | 0.0297838 | − | 0.0515871i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3410.41 | + | 285.301i | −0.116105 | + | 0.00971289i | ||||
\(953\) | 14437.1i | 0.490726i | 0.969431 | + | 0.245363i | \(0.0789072\pi\) | ||||
−0.969431 | + | 0.245363i | \(0.921093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 626.687 | + | 361.818i | 0.0212347 | + | 0.0122599i | ||||
\(956\) | −35695.1 | + | 20608.6i | −1.20760 | + | 0.697206i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1398.12 | + | 807.205i | −0.0471516 | + | 0.0272230i | ||||
\(959\) | 16426.8 | − | 34880.2i | 0.553126 | − | 1.17450i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18468.2 | 0.619925 | ||||||||
\(962\) | 249.993 | − | 433.000i | 0.00837847 | − | 0.0145119i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46307.1 | − | 26735.4i | 1.54715 | − | 0.893246i | ||||
\(965\) | 2797.18 | − | 4844.87i | 0.0933104 | − | 0.161618i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24854.3 | + | 43049.0i | 0.826537 | + | 1.43160i | 0.900739 | + | 0.434362i | \(0.143026\pi\) |
−0.0742011 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(968\) | 8531.83 | + | 4925.85i | 0.283289 | + | 0.163557i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 834.351 | + | 1445.14i | 0.0276179 | + | 0.0478357i | ||||
\(971\) | 25649.0 | + | 44425.3i | 0.847698 | + | 1.46826i | 0.883258 | + | 0.468888i | \(0.155345\pi\) |
−0.0355601 | + | 0.999368i | \(0.511322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9917.81 | − | 21059.2i | 0.326773 | − | 0.693863i | ||||
\(974\) | 117.278 | + | 67.7104i | 0.00385814 | + | 0.00222750i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 46678.4i | − | 1.53088i | ||||||
\(977\) | 10042.8i | 0.328862i | 0.986389 | + | 0.164431i | \(0.0525788\pi\) | ||||
−0.986389 | + | 0.164431i | \(0.947421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −77245.4 | − | 44597.6i | −2.52173 | − | 1.45592i | ||||
\(980\) | 11071.6 | + | 13400.4i | 0.360887 | + | 0.436796i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1997.05 | + | 3458.99i | 0.0648966 | + | 0.112404i | ||||
\(983\) | −3538.32 | − | 6128.55i | −0.114807 | − | 0.198851i | 0.802896 | − | 0.596119i | \(-0.203291\pi\) |
−0.917702 | + | 0.397269i | \(0.869958\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5554.57 | + | 3206.93i | 0.179678 | + | 0.103737i | ||||
\(986\) | −327.677 | − | 567.554i | −0.0105835 | − | 0.0183312i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3236.32 | − | 5605.48i | 0.104212 | − | 0.180500i | ||||
\(989\) | 8872.46 | − | 5122.52i | 0.285266 | − | 0.164698i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13272.9 | + | 22989.4i | −0.425457 | + | 0.736913i | −0.996463 | − | 0.0840327i | \(-0.973220\pi\) |
0.571006 | + | 0.820946i | \(0.306553\pi\) | |||||||
\(992\) | −5205.29 | −0.166601 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1091.34 | − | 757.995i | 0.0348242 | − | 0.0241873i | ||||
\(995\) | −9274.06 | + | 5354.38i | −0.295485 | + | 0.170598i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23812.9 | − | 13748.4i | 0.756431 | − | 0.436726i | −0.0715818 | − | 0.997435i | \(-0.522805\pi\) |
0.828013 | + | 0.560709i | \(0.189471\pi\) | |||||||
\(998\) | −2079.54 | − | 1200.62i | −0.0659584 | − | 0.0380811i | ||||
\(999\) | 0 | 0 |
(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 | 189.4.i.a.143.12 | 44 | ||
3.2 | odd | 2 | 63.4.i.a.38.11 | yes | 44 | ||
7.5 | odd | 6 | 189.4.s.a.89.12 | 44 | |||
9.4 | even | 3 | 63.4.s.a.59.11 | yes | 44 | ||
9.5 | odd | 6 | 189.4.s.a.17.12 | 44 | |||
21.5 | even | 6 | 63.4.s.a.47.11 | yes | 44 | ||
63.5 | even | 6 | inner | 189.4.i.a.152.11 | 44 | ||
63.40 | odd | 6 | 63.4.i.a.5.12 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.12 | ✓ | 44 | 63.40 | odd | 6 | ||
63.4.i.a.38.11 | yes | 44 | 3.2 | odd | 2 | ||
63.4.s.a.47.11 | yes | 44 | 21.5 | even | 6 | ||
63.4.s.a.59.11 | yes | 44 | 9.4 | even | 3 | ||
189.4.i.a.143.12 | 44 | 1.1 | even | 1 | trivial | ||
189.4.i.a.152.11 | 44 | 63.5 | even | 6 | inner | ||
189.4.s.a.17.12 | 44 | 9.5 | odd | 6 | |||
189.4.s.a.89.12 | 44 | 7.5 | odd | 6 |