Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.19 | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.5.f.a.91.19 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.28826 | + | 2.27757i | 0.822066 | + | 0.569392i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.62536 | + | 14.9785i | 0.351585 | + | 0.936156i | ||||
\(5\) | 2.83091 | + | 4.90328i | 0.113236 | + | 0.196131i | 0.917073 | − | 0.398718i | \(-0.130545\pi\) |
−0.803837 | + | 0.594850i | \(0.797212\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 45.1595 | + | 26.0728i | 0.921621 | + | 0.532098i | 0.884152 | − | 0.467199i | \(-0.154737\pi\) |
0.0374695 | + | 0.999298i | \(0.488070\pi\) | |||||||
\(8\) | −15.6169 | + | 62.0654i | −0.244014 | + | 0.969772i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.85878 | + | 22.5709i | −0.0185878 | + | 0.225709i | ||||
\(11\) | −92.3736 | − | 53.3319i | −0.763418 | − | 0.440760i | 0.0671034 | − | 0.997746i | \(-0.478624\pi\) |
−0.830522 | + | 0.556986i | \(0.811958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.0686 | + | 105.774i | 0.361352 | + | 0.625881i | 0.988184 | − | 0.153274i | \(-0.0489818\pi\) |
−0.626831 | + | 0.779155i | \(0.715648\pi\) | |||||||
\(14\) | 89.1136 | + | 188.588i | 0.454661 | + | 0.962184i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −192.711 | + | 168.519i | −0.752776 | + | 0.658277i | ||||
\(17\) | 122.675 | 0.424481 | 0.212240 | − | 0.977217i | \(-0.431924\pi\) | ||||
0.212240 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 593.624i | 1.64439i | 0.569207 | + | 0.822194i | \(0.307250\pi\) | ||||
−0.569207 | + | 0.822194i | \(0.692750\pi\) | |||||||
\(20\) | −57.5188 | + | 69.9855i | −0.143797 | + | 0.174964i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −182.282 | − | 385.757i | −0.376615 | − | 0.797018i | ||||
\(23\) | −473.649 | + | 273.461i | −0.895366 | + | 0.516940i | −0.875694 | − | 0.482867i | \(-0.839596\pi\) |
−0.0196720 | + | 0.999806i | \(0.506262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 296.472 | − | 513.504i | 0.474355 | − | 0.821607i | ||||
\(26\) | −40.0976 | + | 486.900i | −0.0593160 | + | 0.720266i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −136.493 | + | 823.090i | −0.174099 | + | 1.04986i | ||||
\(29\) | 367.933 | − | 637.279i | 0.437495 | − | 0.757763i | −0.560001 | − | 0.828492i | \(-0.689199\pi\) |
0.997496 | + | 0.0707290i | \(0.0225326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 507.427 | − | 292.963i | 0.528020 | − | 0.304853i | −0.212190 | − | 0.977228i | \(-0.568059\pi\) |
0.740210 | + | 0.672376i | \(0.234726\pi\) | |||||||
\(32\) | −1017.50 | + | 115.223i | −0.993649 | + | 0.112523i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 403.388 | + | 279.401i | 0.348951 | + | 0.241696i | ||||
\(35\) | 295.239i | 0.241012i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2289.29 | 1.67223 | 0.836117 | − | 0.548551i | \(-0.184820\pi\) | ||||
0.836117 | + | 0.548551i | \(0.184820\pi\) | |||||||
\(38\) | −1352.02 | + | 1951.99i | −0.936302 | + | 1.35180i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −348.534 | + | 99.1276i | −0.217834 | + | 0.0619548i | ||||
\(41\) | −1434.13 | − | 2483.99i | −0.853142 | − | 1.47769i | −0.878358 | − | 0.478004i | \(-0.841360\pi\) |
0.0252152 | − | 0.999682i | \(-0.491973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1943.81 | − | 1122.26i | −1.05128 | − | 0.606955i | −0.128270 | − | 0.991739i | \(-0.540943\pi\) |
−0.923007 | + | 0.384784i | \(0.874276\pi\) | |||||||
\(44\) | 279.197 | − | 1683.63i | 0.144213 | − | 0.869643i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2180.31 | − | 179.555i | −1.03039 | − | 0.0848557i | ||||
\(47\) | 913.531 | + | 527.427i | 0.413550 | + | 0.238763i | 0.692314 | − | 0.721597i | \(-0.256591\pi\) |
−0.278764 | + | 0.960360i | \(0.589925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 159.084 | + | 275.542i | 0.0662574 | + | 0.114761i | ||||
\(50\) | 2144.42 | − | 1013.30i | 0.857768 | − | 0.405321i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1240.80 | + | 1509.73i | −0.458876 | + | 0.558333i | ||||
\(53\) | 4752.60 | 1.69192 | 0.845960 | − | 0.533246i | \(-0.179028\pi\) | ||||
0.845960 | + | 0.533246i | \(0.179028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 603.911i | − | 0.199640i | ||||||
\(56\) | −2323.47 | + | 2395.66i | −0.740902 | + | 0.763923i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2661.31 | − | 1257.55i | 0.791114 | − | 0.373825i | ||||
\(59\) | 1864.25 | − | 1076.32i | 0.535549 | − | 0.309200i | −0.207724 | − | 0.978188i | \(-0.566606\pi\) |
0.743273 | + | 0.668988i | \(0.233272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.1660 | − | 57.4451i | 0.00891319 | − | 0.0154381i | −0.861534 | − | 0.507699i | \(-0.830496\pi\) |
0.870448 | + | 0.492261i | \(0.163829\pi\) | |||||||
\(62\) | 2335.80 | + | 192.360i | 0.607648 | + | 0.0500416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3608.23 | − | 1938.53i | −0.880915 | − | 0.473275i | ||||
\(65\) | −345.759 | + | 598.872i | −0.0818365 | + | 0.141745i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3554.82 | − | 2052.38i | 0.791897 | − | 0.457202i | −0.0487331 | − | 0.998812i | \(-0.515518\pi\) |
0.840630 | + | 0.541610i | \(0.182185\pi\) | |||||||
\(68\) | 690.091 | + | 1837.49i | 0.149241 | + | 0.397380i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −672.427 | + | 970.824i | −0.137230 | + | 0.198127i | ||||
\(71\) | − | 5031.65i | − | 0.998145i | −0.866560 | − | 0.499072i | \(-0.833674\pi\) | ||
0.866560 | − | 0.499072i | \(-0.166326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2705.16 | 0.507631 | 0.253815 | − | 0.967253i | \(-0.418314\pi\) | ||||
0.253815 | + | 0.967253i | \(0.418314\pi\) | |||||||
\(74\) | 7527.78 | + | 5214.01i | 1.37469 | + | 0.952157i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8891.60 | + | 3339.35i | −1.53940 | + | 0.578143i | ||||
\(77\) | −2781.03 | − | 4816.88i | −0.469055 | − | 0.812427i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1196.02 | − | 690.524i | −0.191639 | − | 0.110643i | 0.401110 | − | 0.916030i | \(-0.368624\pi\) |
−0.592750 | + | 0.805387i | \(0.701958\pi\) | |||||||
\(80\) | −1371.84 | − | 467.852i | −0.214350 | − | 0.0731019i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 941.652 | − | 11434.4i | 0.140043 | − | 1.70053i | ||||
\(83\) | −2605.31 | − | 1504.18i | −0.378184 | − | 0.218345i | 0.298844 | − | 0.954302i | \(-0.403399\pi\) |
−0.677028 | + | 0.735957i | \(0.736732\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 347.282 | + | 601.509i | 0.0480667 | + | 0.0832539i | ||||
\(86\) | −3835.74 | − | 8117.45i | −0.518624 | − | 1.09755i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4752.65 | − | 4900.33i | 0.613721 | − | 0.632790i | ||||
\(89\) | −3186.35 | −0.402267 | −0.201133 | − | 0.979564i | \(-0.564462\pi\) | ||||
−0.201133 | + | 0.979564i | \(0.564462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6368.92i | 0.769100i | ||||||||
\(92\) | −6760.48 | − | 5556.22i | −0.798734 | − | 0.656454i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1802.68 | + | 3814.95i | 0.204015 | + | 0.431751i | ||||
\(95\) | −2910.71 | + | 1680.50i | −0.322516 | + | 0.186205i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2407.03 | − | 4169.10i | 0.255822 | − | 0.443097i | −0.709296 | − | 0.704910i | \(-0.750987\pi\) |
0.965118 | + | 0.261814i | \(0.0843206\pi\) | |||||||
\(98\) | −104.455 | + | 1268.38i | −0.0108762 | + | 0.132068i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9359.28 | + | 1552.05i | 0.935928 | + | 0.155205i | ||||
\(101\) | −3510.47 | + | 6080.30i | −0.344130 | + | 0.596050i | −0.985195 | − | 0.171436i | \(-0.945159\pi\) |
0.641066 | + | 0.767486i | \(0.278493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1858.85 | + | 1073.21i | −0.175214 | + | 0.101160i | −0.585042 | − | 0.811003i | \(-0.698922\pi\) |
0.409828 | + | 0.912163i | \(0.365589\pi\) | |||||||
\(104\) | −7518.59 | + | 2138.39i | −0.695136 | + | 0.197706i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15627.8 | + | 10824.4i | 1.39087 | + | 0.963366i | ||||
\(107\) | 13846.7i | 1.20943i | 0.796443 | + | 0.604713i | \(0.206712\pi\) | ||||
−0.796443 | + | 0.604713i | \(0.793288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19384.9 | −1.63159 | −0.815793 | − | 0.578344i | \(-0.803699\pi\) | ||||
−0.815793 | + | 0.578344i | \(0.803699\pi\) | |||||||
\(110\) | 1375.45 | − | 1985.82i | 0.113674 | − | 0.164117i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13096.5 | + | 2585.71i | −1.04404 | + | 0.206132i | ||||
\(113\) | 6817.20 | + | 11807.7i | 0.533887 | + | 0.924719i | 0.999216 | + | 0.0395818i | \(0.0126026\pi\) |
−0.465329 | + | 0.885138i | \(0.654064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2681.71 | − | 1548.29i | −0.202776 | − | 0.117073i | ||||
\(116\) | 11615.2 | + | 1926.16i | 0.863201 | + | 0.143145i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8581.54 | + | 706.715i | 0.616313 | + | 0.0507551i | ||||
\(119\) | 5539.93 | + | 3198.48i | 0.391211 | + | 0.225866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1631.91 | − | 2826.55i | −0.111462 | − | 0.193057i | ||||
\(122\) | 239.894 | − | 113.357i | 0.0161176 | − | 0.00761603i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7242.61 | + | 5952.47i | 0.471034 | + | 0.387128i | ||||
\(125\) | 6895.78 | 0.441330 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15689.6i | 0.972754i | 0.873749 | + | 0.486377i | \(0.161682\pi\) | ||||
−0.873749 | + | 0.486377i | \(0.838318\pi\) | |||||||
\(128\) | −7449.66 | − | 14592.4i | −0.454691 | − | 0.890649i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2500.92 | + | 1181.76i | −0.147983 | + | 0.0699266i | ||||
\(131\) | −7250.25 | + | 4185.93i | −0.422484 | + | 0.243921i | −0.696140 | − | 0.717907i | \(-0.745101\pi\) |
0.273656 | + | 0.961828i | \(0.411767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15477.5 | + | 26807.7i | −0.874977 | + | 1.51550i | ||||
\(134\) | 16363.6 | + | 1347.59i | 0.911319 | + | 0.0750497i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1915.80 | + | 7613.87i | −0.103579 | + | 0.411650i | ||||
\(137\) | −14965.1 | + | 25920.4i | −0.797333 | + | 1.38102i | 0.124014 | + | 0.992280i | \(0.460423\pi\) |
−0.921347 | + | 0.388741i | \(0.872910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20651.8 | − | 11923.3i | 1.06888 | − | 0.617118i | 0.141005 | − | 0.990009i | \(-0.454967\pi\) |
0.927875 | + | 0.372891i | \(0.121633\pi\) | |||||||
\(140\) | −4422.24 | + | 1660.83i | −0.225624 | + | 0.0847361i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11459.9 | − | 16545.4i | 0.568336 | − | 0.820541i | ||||
\(143\) | − | 13027.6i | − | 0.637078i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4166.34 | 0.198161 | ||||||||
\(146\) | 8895.30 | + | 6161.20i | 0.417306 | + | 0.289041i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12878.1 | + | 34290.1i | 0.587933 | + | 1.56547i | ||||
\(149\) | 2636.98 | + | 4567.39i | 0.118778 | + | 0.205729i | 0.919284 | − | 0.393596i | \(-0.128769\pi\) |
−0.800506 | + | 0.599325i | \(0.795436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −28946.1 | − | 16712.0i | −1.26951 | − | 0.732951i | −0.294614 | − | 0.955616i | \(-0.595191\pi\) |
−0.974895 | + | 0.222665i | \(0.928524\pi\) | |||||||
\(152\) | −36843.5 | − | 9270.55i | −1.59468 | − | 0.401253i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1826.02 | − | 22173.2i | 0.0769954 | − | 0.934945i | ||||
\(155\) | 2872.96 | + | 1658.71i | 0.119582 | + | 0.0690408i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8500.73 | − | 14723.7i | −0.344871 | − | 0.597334i | 0.640459 | − | 0.767992i | \(-0.278744\pi\) |
−0.985330 | + | 0.170658i | \(0.945411\pi\) | |||||||
\(158\) | −2360.12 | − | 4994.65i | −0.0945410 | − | 0.200074i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3445.41 | − | 4662.88i | −0.134586 | − | 0.182144i | ||||
\(161\) | −28519.6 | −1.10025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 30843.8i | 1.16089i | 0.814298 | + | 0.580447i | \(0.197122\pi\) | ||||
−0.814298 | + | 0.580447i | \(0.802878\pi\) | |||||||
\(164\) | 29138.9 | − | 35454.5i | 1.08339 | − | 1.31821i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5141.09 | − | 10879.9i | −0.186569 | − | 0.394829i | ||||
\(167\) | 13682.1 | − | 7899.35i | 0.490591 | − | 0.283243i | −0.234229 | − | 0.972181i | \(-0.575257\pi\) |
0.724819 | + | 0.688939i | \(0.241923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6821.76 | − | 11815.6i | 0.238849 | − | 0.413698i | ||||
\(170\) | −228.025 | + | 2768.88i | −0.00789015 | + | 0.0958090i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5875.12 | − | 35428.5i | 0.198591 | − | 1.19756i | ||||
\(173\) | 23531.4 | − | 40757.6i | 0.786241 | − | 1.36181i | −0.142015 | − | 0.989865i | \(-0.545358\pi\) |
0.928255 | − | 0.371944i | \(-0.121309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26777.0 | − | 15459.7i | 0.874352 | − | 0.504807i | ||||
\(176\) | 26788.8 | − | 5289.07i | 0.864825 | − | 0.170747i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10477.6 | − | 7257.14i | −0.330690 | − | 0.229047i | ||||
\(179\) | − | 2545.69i | − | 0.0794511i | −0.999211 | − | 0.0397256i | \(-0.987352\pi\) | ||
0.999211 | − | 0.0397256i | \(-0.0126484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5676.58 | 0.173272 | 0.0866362 | − | 0.996240i | \(-0.472388\pi\) | ||||
0.0866362 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(182\) | −14505.6 | + | 20942.7i | −0.437920 | + | 0.632251i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9575.56 | − | 33667.8i | −0.282832 | − | 0.994441i | ||||
\(185\) | 6480.77 | + | 11225.0i | 0.189358 | + | 0.327977i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11331.9 | − | 6542.49i | −0.324056 | − | 0.187094i | ||||
\(188\) | −2761.12 | + | 16650.3i | −0.0781214 | + | 0.471092i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13398.6 | − | 1103.41i | −0.371153 | − | 0.0305655i | ||||
\(191\) | −28127.2 | − | 16239.2i | −0.771009 | − | 0.445142i | 0.0622257 | − | 0.998062i | \(-0.480180\pi\) |
−0.833234 | + | 0.552920i | \(0.813513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −393.717 | − | 681.937i | −0.0105699 | − | 0.0183075i | 0.860692 | − | 0.509126i | \(-0.170031\pi\) |
−0.871262 | + | 0.490818i | \(0.836698\pi\) | |||||||
\(194\) | 17410.3 | − | 8226.92i | 0.462598 | − | 0.218592i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3232.29 | + | 3932.86i | −0.0841393 | + | 0.102376i | ||||
\(197\) | −24825.9 | −0.639694 | −0.319847 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319847 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12008.5i | − | 0.303237i | −0.988439 | − | 0.151619i | \(-0.951551\pi\) | ||
0.988439 | − | 0.151619i | \(-0.0484485\pi\) | |||||||
\(200\) | 27240.9 | + | 26420.0i | 0.681022 | + | 0.660499i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −25391.6 | + | 11998.3i | −0.622283 | + | 0.294048i | ||||
\(203\) | 33231.3 | − | 19186.1i | 0.806409 | − | 0.465580i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8119.80 | − | 14063.9i | 0.193213 | − | 0.334656i | ||||
\(206\) | −8556.69 | − | 704.668i | −0.201638 | − | 0.0166054i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −29593.5 | − | 10092.5i | −0.684020 | − | 0.233278i | ||||
\(209\) | 31659.1 | − | 54835.2i | 0.724780 | − | 1.25536i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25764.7 | − | 14875.2i | 0.578708 | − | 0.334117i | −0.181912 | − | 0.983315i | \(-0.558229\pi\) |
0.760620 | + | 0.649198i | \(0.224895\pi\) | |||||||
\(212\) | 26735.1 | + | 71186.9i | 0.594854 | + | 1.58390i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31536.9 | + | 45531.7i | −0.688638 | + | 0.994228i | ||||
\(215\) | − | 12708.1i | − | 0.274917i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30553.5 | 0.648846 | ||||||||
\(218\) | −63742.6 | − | 44150.4i | −1.34127 | − | 0.929012i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9045.68 | − | 3397.22i | 0.186894 | − | 0.0701905i | ||||
\(221\) | 7491.58 | + | 12975.8i | 0.153387 | + | 0.265674i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −45854.8 | − | 26474.3i | −0.922093 | − | 0.532371i | −0.0377910 | − | 0.999286i | \(-0.512032\pi\) |
−0.884302 | + | 0.466915i | \(0.845365\pi\) | |||||||
\(224\) | −48953.8 | − | 21325.6i | −0.975642 | − | 0.425016i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4476.18 | + | 54353.6i | −0.0876376 | + | 1.06417i | ||||
\(227\) | 32593.5 | + | 18817.9i | 0.632528 | + | 0.365190i | 0.781730 | − | 0.623616i | \(-0.214337\pi\) |
−0.149203 | + | 0.988807i | \(0.547671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28619.2 | + | 49569.9i | 0.545741 | + | 0.945251i | 0.998560 | + | 0.0536486i | \(0.0170851\pi\) |
−0.452819 | + | 0.891603i | \(0.649582\pi\) | |||||||
\(230\) | −5291.85 | − | 11199.0i | −0.100035 | − | 0.211701i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 33807.0 | + | 32788.2i | 0.628102 | + | 0.609174i | ||||
\(233\) | 36468.7 | 0.671751 | 0.335876 | − | 0.941906i | \(-0.390968\pi\) | ||||
0.335876 | + | 0.941906i | \(0.390968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5972.39i | 0.108147i | ||||||||
\(236\) | 26608.8 | + | 21868.9i | 0.477750 | + | 0.392648i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10932.0 | + | 23135.0i | 0.192995 | + | 0.408429i | ||||
\(239\) | −45342.6 | + | 26178.6i | −0.793799 | + | 0.458300i | −0.841298 | − | 0.540571i | \(-0.818208\pi\) |
0.0474993 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6755.56 | − | 11701.0i | 0.116313 | − | 0.201460i | −0.801991 | − | 0.597336i | \(-0.796226\pi\) |
0.918304 | + | 0.395877i | \(0.129559\pi\) | |||||||
\(242\) | 1071.51 | − | 13011.2i | 0.0182964 | − | 0.222171i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1047.01 | + | 173.627i | 0.0175862 | + | 0.00291633i | ||||
\(245\) | −900.705 | + | 1560.07i | −0.0150055 | + | 0.0259903i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −62789.9 | + | 36251.8i | −1.02919 | + | 0.594204i | ||||
\(248\) | 10258.5 | + | 36068.9i | 0.166793 | + | 0.586447i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22675.1 | + | 15705.6i | 0.362802 | + | 0.251290i | ||||
\(251\) | 111309.i | 1.76678i | 0.468635 | + | 0.883392i | \(0.344746\pi\) | ||||
−0.468635 | + | 0.883392i | \(0.655254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58336.8 | 0.911385 | ||||||||
\(254\) | −35734.0 | + | 51591.4i | −0.553879 | + | 0.799668i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8738.74 | − | 64950.8i | 0.133343 | − | 0.991070i | ||||
\(257\) | −36956.5 | − | 64010.6i | −0.559532 | − | 0.969138i | −0.997535 | − | 0.0701645i | \(-0.977648\pi\) |
0.438003 | − | 0.898973i | \(-0.355686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 103383. | + | 59688.2i | 1.54117 | + | 0.889793i | ||||
\(260\) | −10915.2 | − | 1810.08i | −0.161468 | − | 0.0267763i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −33374.5 | − | 2748.48i | −0.486197 | − | 0.0400397i | ||||
\(263\) | −6380.84 | − | 3683.98i | −0.0922500 | − | 0.0532606i | 0.453165 | − | 0.891426i | \(-0.350295\pi\) |
−0.545415 | + | 0.838166i | \(0.683628\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13454.2 | + | 23303.3i | 0.191587 | + | 0.331838i | ||||
\(266\) | −111950. | + | 52900.0i | −1.58220 | + | 0.747639i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 50738.7 | + | 41700.5i | 0.706431 | + | 0.580593i | ||||
\(269\) | 38604.8 | 0.533502 | 0.266751 | − | 0.963765i | \(-0.414050\pi\) | ||||
0.266751 | + | 0.963765i | \(0.414050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12540.3i | − | 0.170753i | −0.996349 | − | 0.0853767i | \(-0.972791\pi\) | ||
0.996349 | − | 0.0853767i | \(-0.0272094\pi\) | |||||||
\(272\) | −23640.8 | + | 20673.1i | −0.319539 | + | 0.279426i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −108245. | + | 51148.9i | −1.44180 | + | 0.681295i | ||||
\(275\) | −54772.4 | + | 31622.8i | −0.724263 | + | 0.418153i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 46052.4 | − | 79765.0i | 0.600195 | − | 1.03957i | −0.392596 | − | 0.919711i | \(-0.628423\pi\) |
0.992791 | − | 0.119857i | \(-0.0382436\pi\) | |||||||
\(278\) | 95064.9 | + | 7828.87i | 1.23007 | + | 0.101300i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18324.1 | − | 4610.71i | −0.233726 | − | 0.0588101i | ||||
\(281\) | 11148.0 | − | 19308.8i | 0.141183 | − | 0.244537i | −0.786759 | − | 0.617260i | \(-0.788243\pi\) |
0.927942 | + | 0.372723i | \(0.121576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21648.6 | + | 12498.8i | −0.270307 | + | 0.156062i | −0.629027 | − | 0.777383i | \(-0.716547\pi\) |
0.358720 | + | 0.933445i | \(0.383213\pi\) | |||||||
\(284\) | 75366.5 | − | 28304.8i | 0.934419 | − | 0.350933i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29671.3 | − | 42838.2i | 0.362747 | − | 0.523720i | ||||
\(287\) | − | 149568.i | − | 1.81582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68471.9 | −0.819816 | ||||||||
\(290\) | 13700.0 | + | 9489.12i | 0.162902 | + | 0.112831i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15217.5 | + | 40519.3i | 0.178475 | + | 0.475222i | ||||
\(293\) | −11748.6 | − | 20349.1i | −0.136852 | − | 0.237034i | 0.789452 | − | 0.613813i | \(-0.210365\pi\) |
−0.926303 | + | 0.376779i | \(0.877032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10555.0 | + | 6093.95i | 0.121287 | + | 0.0700253i | ||||
\(296\) | −35751.5 | + | 142086.i | −0.408048 | + | 1.62169i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1731.44 | + | 21024.7i | −0.0194974 | + | 0.236754i | ||||
\(299\) | −57850.1 | − | 33399.7i | −0.647085 | − | 0.373595i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −58521.0 | − | 101361.i | −0.645920 | − | 1.11877i | ||||
\(302\) | −57119.6 | − | 120880.i | −0.626283 | − | 1.32538i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −100037. | − | 114398.i | −1.08246 | − | 1.23786i | ||||
\(305\) | 375.559 | 0.00403719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32060.0i | − | 0.340163i | −0.985430 | − | 0.170082i | \(-0.945597\pi\) | ||
0.985430 | − | 0.170082i | \(-0.0544031\pi\) | |||||||
\(308\) | 56505.3 | − | 68752.3i | 0.595646 | − | 0.724746i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5669.24 | + | 11997.6i | 0.0589931 | + | 0.124845i | ||||
\(311\) | 61441.4 | − | 35473.2i | 0.635244 | − | 0.366758i | −0.147536 | − | 0.989057i | \(-0.547134\pi\) |
0.782780 | + | 0.622298i | \(0.213801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −59259.6 | + | 102641.i | −0.604882 | + | 1.04769i | 0.387189 | + | 0.922001i | \(0.373446\pi\) |
−0.992070 | + | 0.125685i | \(0.959887\pi\) | |||||||
\(314\) | 5581.58 | − | 67776.4i | 0.0566106 | − | 0.687415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3614.95 | − | 21799.1i | 0.0362016 | − | 0.218305i | ||||
\(317\) | −67390.6 | + | 116724.i | −0.670626 | + | 1.16156i | 0.307100 | + | 0.951677i | \(0.400641\pi\) |
−0.977727 | + | 0.209882i | \(0.932692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −67974.6 | + | 39245.2i | −0.667983 | + | 0.385660i | ||||
\(320\) | −709.388 | − | 23180.0i | −0.00692762 | − | 0.226367i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −93780.0 | − | 64955.4i | −0.904479 | − | 0.626474i | ||||
\(323\) | 72822.8i | 0.698011i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 72420.4 | 0.685637 | ||||||||
\(326\) | −70248.8 | + | 101422.i | −0.661003 | + | 0.954331i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 176567. | − | 50217.8i | 1.64120 | − | 0.466778i | ||||
\(329\) | 27503.0 | + | 47636.7i | 0.254091 | + | 0.440098i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 133143. | + | 76870.2i | 1.21524 | + | 0.701620i | 0.963896 | − | 0.266278i | \(-0.0857939\pi\) |
0.251345 | + | 0.967898i | \(0.419127\pi\) | |||||||
\(332\) | 7874.49 | − | 47485.2i | 0.0714408 | − | 0.430806i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62981.6 | + | 5186.72i | 0.564574 | + | 0.0464943i | ||||
\(335\) | 20126.8 | + | 11620.2i | 0.179343 | + | 0.103544i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11471.8 | + | 19869.8i | 0.101012 | + | 0.174958i | 0.912102 | − | 0.409964i | \(-0.134459\pi\) |
−0.811090 | + | 0.584922i | \(0.801125\pi\) | |||||||
\(338\) | 49342.7 | − | 23315.9i | 0.431906 | − | 0.204089i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7056.12 | + | 8585.46i | −0.0610391 | + | 0.0742687i | ||||
\(341\) | −62497.2 | −0.537467 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 108611.i | − | 0.923175i | ||||||
\(344\) | 100010. | − | 103117.i | 0.845134 | − | 0.871393i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 170206. | − | 80427.3i | 1.42174 | − | 0.671817i | ||||
\(347\) | −6260.87 | + | 3614.72i | −0.0519967 | + | 0.0300203i | −0.525773 | − | 0.850625i | \(-0.676224\pi\) |
0.473776 | + | 0.880645i | \(0.342891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −55282.6 | + | 95752.3i | −0.453877 | + | 0.786137i | −0.998623 | − | 0.0524636i | \(-0.983293\pi\) |
0.544746 | + | 0.838601i | \(0.316626\pi\) | |||||||
\(350\) | 123260. | + | 10150.9i | 1.00621 | + | 0.0828641i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 100135. | + | 43621.5i | 0.808165 | + | 0.352059i | ||||
\(353\) | −30801.7 | + | 53350.1i | −0.247187 | + | 0.428140i | −0.962744 | − | 0.270414i | \(-0.912840\pi\) |
0.715557 | + | 0.698554i | \(0.246173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24671.6 | − | 14244.1i | 0.195767 | − | 0.113026i | ||||
\(356\) | −17924.4 | − | 47726.8i | −0.141431 | − | 0.376584i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5797.99 | − | 8370.91i | 0.0452388 | − | 0.0653141i | ||||
\(359\) | − | 84462.7i | − | 0.655354i | −0.944790 | − | 0.327677i | \(-0.893734\pi\) | ||
0.944790 | − | 0.327677i | \(-0.106266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −222069. | −1.70401 | ||||||||
\(362\) | 18666.1 | + | 12928.8i | 0.142441 | + | 0.0986600i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −95396.8 | + | 35827.5i | −0.719998 | + | 0.270404i | ||||
\(365\) | 7658.07 | + | 13264.2i | 0.0574823 | + | 0.0995622i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −161018. | − | 92963.9i | −1.19548 | − | 0.690212i | −0.235937 | − | 0.971768i | \(-0.575816\pi\) |
−0.959545 | + | 0.281556i | \(0.909149\pi\) | |||||||
\(368\) | 45193.7 | − | 132518.i | 0.333720 | − | 0.978538i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4255.27 | + | 51671.2i | −0.0310831 | + | 0.377438i | ||||
\(371\) | 214625. | + | 123914.i | 1.55931 | + | 0.900268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 42545.6 | + | 73691.2i | 0.305800 | + | 0.529661i | 0.977439 | − | 0.211217i | \(-0.0677428\pi\) |
−0.671639 | + | 0.740878i | \(0.734409\pi\) | |||||||
\(374\) | −22361.4 | − | 47322.7i | −0.159866 | − | 0.338319i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −47001.5 | + | 48461.9i | −0.332457 | + | 0.342787i | ||||
\(377\) | 89876.5 | 0.632359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 146982.i | − | 1.02326i | −0.859206 | − | 0.511630i | \(-0.829042\pi\) | ||
0.859206 | − | 0.511630i | \(-0.170958\pi\) | |||||||
\(380\) | −41545.1 | − | 34144.6i | −0.287708 | − | 0.236458i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −55503.6 | − | 117460.i | −0.380360 | − | 0.804942i | ||||
\(383\) | 161253. | − | 93099.7i | 1.09929 | − | 0.634674i | 0.163254 | − | 0.986584i | \(-0.447801\pi\) |
0.936034 | + | 0.351910i | \(0.114468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15745.7 | − | 27272.3i | 0.106228 | − | 0.183993i | ||||
\(386\) | 258.515 | − | 3139.11i | 0.00173504 | − | 0.0210684i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 75987.2 | + | 12601.0i | 0.504751 | + | 0.0837030i | ||||
\(389\) | −128002. | + | 221706.i | −0.845897 | + | 1.46514i | 0.0389437 | + | 0.999241i | \(0.487601\pi\) |
−0.884840 | + | 0.465894i | \(0.845733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −58104.8 | + | 33546.8i | −0.380066 | + | 0.219431i | ||||
\(392\) | −19586.0 | + | 5570.52i | −0.127460 | + | 0.0362513i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −81634.1 | − | 56542.7i | −0.525871 | − | 0.364237i | ||||
\(395\) | − | 7819.24i | − | 0.0501153i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260735. | −1.65432 | −0.827159 | − | 0.561968i | \(-0.810044\pi\) | ||||
−0.827159 | + | 0.561968i | \(0.810044\pi\) | |||||||
\(398\) | 27350.2 | − | 39487.1i | 0.172661 | − | 0.249281i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 29401.9 | + | 148919.i | 0.183762 | + | 0.930743i | ||||
\(401\) | 26507.0 | + | 45911.4i | 0.164843 | + | 0.285517i | 0.936600 | − | 0.350401i | \(-0.113955\pi\) |
−0.771756 | + | 0.635918i | \(0.780621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 61975.7 | + | 35781.7i | 0.381603 | + | 0.220318i | ||||
\(404\) | −110821. | − | 18377.6i | −0.678986 | − | 0.112597i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 152971. | + | 12597.6i | 0.928019 | + | 0.0764251i | ||||
\(407\) | −211470. | − | 122092.i | −1.27661 | − | 0.737053i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −73697.8 | − | 127648.i | −0.440563 | − | 0.763078i | 0.557168 | − | 0.830400i | \(-0.311888\pi\) |
−0.997731 | + | 0.0673220i | \(0.978555\pi\) | |||||||
\(410\) | 58731.5 | − | 27752.4i | 0.349385 | − | 0.165095i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26531.7 | − | 21805.6i | −0.156304 | − | 0.128462i | ||||
\(413\) | 112251. | 0.658099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 17032.8i | − | 0.0988983i | ||||||
\(416\) | −74324.7 | − | 100588.i | −0.429483 | − | 0.581246i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 228995. | − | 108207.i | 1.31061 | − | 0.619302i | ||||
\(419\) | −201431. | + | 116296.i | −1.14736 | + | 0.662426i | −0.948242 | − | 0.317550i | \(-0.897140\pi\) |
−0.199115 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34900.8 | − | 60449.9i | 0.196911 | − | 0.341060i | −0.750614 | − | 0.660741i | \(-0.770242\pi\) |
0.947525 | + | 0.319680i | \(0.103576\pi\) | |||||||
\(422\) | 118600. | + | 9767.08i | 0.665980 | + | 0.0548454i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −74220.8 | + | 294972.i | −0.412852 | + | 1.64078i | ||||
\(425\) | 36369.7 | − | 62994.1i | 0.201355 | − | 0.348756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2995.51 | − | 1729.46i | 0.0164292 | − | 0.00948539i | ||||
\(428\) | −207403. | + | 77892.8i | −1.13221 | + | 0.425216i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 28943.5 | − | 41787.5i | 0.156536 | − | 0.226000i | ||||
\(431\) | 147873.i | 0.796037i | 0.917377 | + | 0.398019i | \(0.130302\pi\) | ||||
−0.917377 | + | 0.398019i | \(0.869698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 294850. | 1.57262 | 0.786312 | − | 0.617830i | \(-0.211988\pi\) | ||||
0.786312 | + | 0.617830i | \(0.211988\pi\) | |||||||
\(434\) | 100468. | + | 69587.7i | 0.533395 | + | 0.369448i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −109047. | − | 290356.i | −0.573641 | − | 1.52742i | ||||
\(437\) | −162333. | − | 281169.i | −0.850050 | − | 1.47233i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 62468.0 | + | 36065.9i | 0.324137 | + | 0.187140i | 0.653235 | − | 0.757155i | \(-0.273411\pi\) |
−0.329098 | + | 0.944296i | \(0.606745\pi\) | |||||||
\(440\) | 37482.0 | + | 9431.20i | 0.193605 | + | 0.0487149i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4918.98 | + | 59730.5i | −0.0251785 | + | 0.305739i | ||||
\(443\) | 165331. | + | 95453.7i | 0.842453 | + | 0.486391i | 0.858097 | − | 0.513487i | \(-0.171647\pi\) |
−0.0156440 | + | 0.999878i | \(0.504980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9020.28 | − | 15623.6i | −0.0455512 | − | 0.0788970i | ||||
\(446\) | −90485.7 | − | 191492.i | −0.454894 | − | 0.962677i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −112402. | − | 181620.i | −0.560041 | − | 0.904914i | ||||
\(449\) | −192859. | −0.956639 | −0.478319 | − | 0.878186i | \(-0.658754\pi\) | ||||
−0.478319 | + | 0.878186i | \(0.658754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 305940.i | 1.50412i | ||||||||
\(452\) | −138513. | + | 168534.i | −0.677975 | + | 0.824919i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 64317.1 | + | 136112.i | 0.312043 | + | 0.660367i | ||||
\(455\) | −31228.6 | + | 18029.8i | −0.150844 | + | 0.0870901i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2962.66 | − | 5131.48i | 0.0141857 | − | 0.0245703i | −0.858845 | − | 0.512235i | \(-0.828818\pi\) |
0.873031 | + | 0.487665i | \(0.162151\pi\) | |||||||
\(458\) | −18791.4 | + | 228181.i | −0.0895834 | + | 1.08780i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8105.41 | − | 48877.7i | 0.0383053 | − | 0.230991i | ||||
\(461\) | 63341.9 | − | 109711.i | 0.298050 | − | 0.516238i | −0.677640 | − | 0.735394i | \(-0.736997\pi\) |
0.975690 | + | 0.219156i | \(0.0703304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −204011. | + | 117786.i | −0.951682 | + | 0.549454i | −0.893603 | − | 0.448858i | \(-0.851831\pi\) |
−0.0580790 | + | 0.998312i | \(0.518498\pi\) | |||||||
\(464\) | 36488.9 | + | 184814.i | 0.169483 | + | 0.858418i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 119919. | + | 83060.0i | 0.552224 | + | 0.382490i | ||||
\(467\) | 97776.2i | 0.448332i | 0.974551 | + | 0.224166i | \(0.0719658\pi\) | ||||
−0.974551 | + | 0.224166i | \(0.928034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 214045. | 0.973105 | ||||||||
\(470\) | −13602.5 | + | 19638.8i | −0.0615778 | + | 0.0889036i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 37688.8 | + | 132514.i | 0.169172 | + | 0.594810i | ||||
\(473\) | 119705. | + | 207334.i | 0.535043 | + | 0.926721i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 304829. | + | 175993.i | 1.35104 | + | 0.780024i | ||||
\(476\) | −16744.3 | + | 100972.i | −0.0739015 | + | 0.445645i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −208722. | − | 17188.8i | −0.913508 | − | 0.0752300i | ||||
\(479\) | −349162. | − | 201589.i | −1.52179 | − | 0.878608i | −0.999669 | − | 0.0257398i | \(-0.991806\pi\) |
−0.522126 | − | 0.852869i | \(-0.674861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 139803. | + | 242147.i | 0.604266 | + | 1.04662i | ||||
\(482\) | 48863.8 | − | 23089.6i | 0.210326 | − | 0.0993855i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 33157.4 | − | 40344.0i | 0.141543 | − | 0.172222i | ||||
\(485\) | 27256.3 | 0.115873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 195207.i | − | 0.823071i | −0.911394 | − | 0.411536i | \(-0.864993\pi\) | ||
0.911394 | − | 0.411536i | \(-0.135007\pi\) | |||||||
\(488\) | 3047.41 | + | 2955.57i | 0.0127965 | + | 0.0124109i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6514.92 | + | 3078.49i | −0.0271342 | + | 0.0128217i | ||||
\(491\) | −65937.1 | + | 38068.8i | −0.273506 | + | 0.157909i | −0.630480 | − | 0.776206i | \(-0.717142\pi\) |
0.356974 | + | 0.934114i | \(0.383809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45136.2 | − | 78178.1i | 0.185708 | − | 0.321656i | ||||
\(494\) | −289036. | − | 23802.9i | −1.18440 | − | 0.0975386i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48416.8 | + | 141968.i | −0.196803 | + | 0.577069i | ||||
\(497\) | 131189. | − | 227226.i | 0.531111 | − | 0.919912i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12618.3 | − | 7285.17i | 0.0506757 | − | 0.0292576i | −0.474448 | − | 0.880283i | \(-0.657352\pi\) |
0.525124 | + | 0.851026i | \(0.324019\pi\) | |||||||
\(500\) | 38791.2 | + | 103288.i | 0.155165 | + | 0.413153i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −253514. | + | 366014.i | −1.00599 | + | 1.45241i | ||||
\(503\) | − | 280154.i | − | 1.10729i | −0.832753 | − | 0.553645i | \(-0.813236\pi\) | ||
0.832753 | − | 0.553645i | \(-0.186764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39751.2 | −0.155872 | ||||||||
\(506\) | 191827. | + | 132866.i | 0.749219 | + | 0.518935i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −235006. | + | 88259.4i | −0.910650 | + | 0.342006i | ||||
\(509\) | 101505. | + | 175811.i | 0.391787 | + | 0.678595i | 0.992685 | − | 0.120731i | \(-0.0385238\pi\) |
−0.600899 | + | 0.799325i | \(0.705190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 122164. | + | 70531.3i | 0.467843 | + | 0.270110i | ||||
\(512\) | 176665. | − | 193672.i | 0.673924 | − | 0.738801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24265.7 | − | 294655.i | 0.0918472 | − | 1.11529i | ||||
\(515\) | −10524.5 | − | 6076.30i | −0.0396813 | − | 0.0229100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56257.4 | − | 97440.7i | −0.210474 | − | 0.364552i | ||||
\(518\) | 204007. | + | 431732.i | 0.760300 | + | 1.60900i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −31769.6 | − | 30812.2i | −0.117491 | − | 0.113950i | ||||
\(521\) | 30822.1 | 0.113550 | 0.0567749 | − | 0.998387i | \(-0.481918\pi\) | ||||
0.0567749 | + | 0.998387i | \(0.481918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 94412.3i | − | 0.345164i | −0.984995 | − | 0.172582i | \(-0.944789\pi\) | ||
0.984995 | − | 0.172582i | \(-0.0552109\pi\) | |||||||
\(524\) | −103484. | − | 85050.4i | −0.376887 | − | 0.309752i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12591.4 | − | 26646.7i | −0.0455095 | − | 0.0963101i | ||||
\(527\) | 62248.6 | − | 35939.3i | 0.224134 | − | 0.129404i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9641.45 | − | 16699.5i | 0.0344533 | − | 0.0596749i | ||||
\(530\) | −8834.03 | + | 107270.i | −0.0314490 | + | 0.381881i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −488606. | − | 81025.8i | −1.72638 | − | 0.286286i | ||||
\(533\) | 175161. | − | 303387.i | 0.616570 | − | 1.06793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −67894.3 | + | 39198.8i | −0.237206 | + | 0.136951i | ||||
\(536\) | 71866.5 | + | 252683.i | 0.250148 | + | 0.879523i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 126943. | + | 87925.0i | 0.438574 | + | 0.303772i | ||||
\(539\) | − | 33937.0i | − | 0.116814i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 166561. | 0.569087 | 0.284544 | − | 0.958663i | \(-0.408158\pi\) | ||||
0.284544 | + | 0.958663i | \(0.408158\pi\) | |||||||
\(542\) | 28561.4 | − | 41235.8i | 0.0972257 | − | 0.140371i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −124821. | + | 14135.0i | −0.421785 | + | 0.0477637i | ||||
\(545\) | −54876.8 | − | 95049.4i | −0.184755 | − | 0.320005i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −256245. | − | 147943.i | −0.856410 | − | 0.494448i | 0.00639865 | − | 0.999980i | \(-0.497963\pi\) |
−0.862808 | + | 0.505531i | \(0.831297\pi\) | |||||||
\(548\) | −472433. | − | 78343.7i | −1.57318 | − | 0.260881i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −252129. | − | 20763.6i | −0.833485 | − | 0.0686399i | ||||
\(551\) | 378304. | + | 218414.i | 1.24606 | + | 0.719411i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36007.8 | − | 62367.3i | −0.117746 | − | 0.203942i | ||||
\(554\) | 333103. | − | 157401.i | 1.08532 | − | 0.512847i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 294768. | + | 242260.i | 0.953521 | + | 0.783669i | ||||
\(557\) | 30600.2 | 0.0986312 | 0.0493156 | − | 0.998783i | \(-0.484296\pi\) | ||||
0.0493156 | + | 0.998783i | \(0.484296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 274139.i | − | 0.877298i | ||||||
\(560\) | −49753.4 | − | 56895.7i | −0.158652 | − | 0.181428i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 80634.7 | − | 38102.3i | 0.255299 | − | 0.120637i | ||||
\(563\) | 210267. | − | 121398.i | 0.663369 | − | 0.382996i | −0.130191 | − | 0.991489i | \(-0.541559\pi\) |
0.793559 | + | 0.608493i | \(0.208226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38597.8 | + | 66853.3i | −0.120911 | + | 0.209424i | ||||
\(566\) | −99653.3 | − | 8206.73i | −0.311070 | − | 0.0256175i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 312291. | + | 78578.6i | 0.967973 | + | 0.243561i | ||||
\(569\) | 148459. | − | 257138.i | 0.458545 | − | 0.794223i | −0.540339 | − | 0.841447i | \(-0.681704\pi\) |
0.998884 | + | 0.0472242i | \(0.0150375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 228446. | − | 131893.i | 0.700665 | − | 0.404529i | −0.106930 | − | 0.994267i | \(-0.534102\pi\) |
0.807595 | + | 0.589737i | \(0.200769\pi\) | |||||||
\(572\) | 195134. | − | 73285.1i | 0.596405 | − | 0.223987i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 340650. | − | 491818.i | 1.03392 | − | 1.49273i | ||||
\(575\) | 324294.i | 0.980852i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 350367. | 1.05238 | 0.526188 | − | 0.850368i | \(-0.323621\pi\) | ||||
0.526188 | + | 0.850368i | \(0.323621\pi\) | |||||||
\(578\) | −225154. | − | 155949.i | −0.673943 | − | 0.466797i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23437.2 | + | 62405.5i | 0.0696705 | + | 0.185510i | ||||
\(581\) | −78436.3 | − | 135856.i | −0.232362 | − | 0.402463i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −439015. | − | 253466.i | −1.29164 | − | 0.745730i | ||||
\(584\) | −42246.2 | + | 167897.i | −0.123869 | + | 0.492286i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7714.12 | − | 93671.5i | 0.0224642 | − | 0.272780i | ||||
\(587\) | 5965.76 | + | 3444.33i | 0.0173137 | + | 0.00999606i | 0.508632 | − | 0.860984i | \(-0.330151\pi\) |
−0.491318 | + | 0.870980i | \(0.663485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 173910. | + | 301221.i | 0.501296 | + | 0.868270i | ||||
\(590\) | 20828.3 | + | 44078.3i | 0.0598344 | + | 0.126625i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −441170. | + | 385788.i | −1.25882 | + | 1.10079i | ||||
\(593\) | −544416. | −1.54818 | −0.774090 | − | 0.633076i | \(-0.781792\pi\) | ||||
−0.774090 | + | 0.633076i | \(0.781792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36218.4i | 0.102305i | ||||||||
\(596\) | −53578.6 | + | 65191.2i | −0.150834 | + | 0.183526i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −114156. | − | 241585.i | −0.319225 | − | 0.675565i | ||||
\(599\) | 122771. | − | 70881.9i | 0.342170 | − | 0.197552i | −0.319061 | − | 0.947734i | \(-0.603367\pi\) |
0.661231 | + | 0.750182i | \(0.270034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 265380. | − | 459652.i | 0.734715 | − | 1.27256i | −0.220133 | − | 0.975470i | \(-0.570649\pi\) |
0.954848 | − | 0.297094i | \(-0.0960176\pi\) | |||||||
\(602\) | 38424.9 | − | 466588.i | 0.106028 | − | 1.28748i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 87488.8 | − | 527580.i | 0.239816 | − | 1.44615i | ||||
\(605\) | 9239.58 | − | 16003.4i | 0.0252430 | − | 0.0437222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35215.7 | − | 20331.8i | 0.0955782 | − | 0.0551821i | −0.451449 | − | 0.892297i | \(-0.649093\pi\) |
0.547027 | + | 0.837115i | \(0.315759\pi\) | |||||||
\(608\) | −68399.3 | − | 604011.i | −0.185031 | − | 1.63395i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1234.94 | + | 855.362i | 0.00331883 | + | 0.00229874i | ||||
\(611\) | 128837.i | 0.345110i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −498556. | −1.32676 | −0.663382 | − | 0.748281i | \(-0.730879\pi\) | ||||
−0.663382 | + | 0.748281i | \(0.730879\pi\) | |||||||
\(614\) | 73018.9 | − | 105422.i | 0.193686 | − | 0.279636i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 342393. | − | 97381.0i | 0.902325 | − | 0.256633i | ||||
\(617\) | −45030.4 | − | 77995.0i | −0.118287 | − | 0.204879i | 0.800802 | − | 0.598929i | \(-0.204407\pi\) |
−0.919089 | + | 0.394050i | \(0.871074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −149379. | − | 86244.1i | −0.389860 | − | 0.225086i | 0.292240 | − | 0.956345i | \(-0.405600\pi\) |
−0.682099 | + | 0.731259i | \(0.738933\pi\) | |||||||
\(620\) | −8683.45 | + | 52363.5i | −0.0225896 | + | 0.136221i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 282828. | + | 23291.7i | 0.731042 | + | 0.0602034i | ||||
\(623\) | −143894. | − | 83077.2i | −0.370738 | − | 0.214045i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −165774. | − | 287128.i | −0.424380 | − | 0.735049i | ||||
\(626\) | −428633. | + | 202542.i | −1.09380 | + | 0.516852i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 172719. | − | 210154.i | 0.437946 | − | 0.532867i | ||||
\(629\) | 280838. | 0.709831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 210621.i | 0.528985i | 0.964388 | + | 0.264492i | \(0.0852044\pi\) | ||||
−0.964388 | + | 0.264492i | \(0.914796\pi\) | |||||||
\(632\) | 61535.7 | − | 63447.8i | 0.154061 | − | 0.158848i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −487445. | + | 230332.i | −1.21268 | + | 0.573029i | ||||
\(635\) | −76930.2 | + | 44415.7i | −0.190787 | + | 0.110151i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19430.1 | + | 33653.9i | −0.0478846 | + | 0.0829385i | ||||
\(638\) | −312902. | − | 25768.4i | −0.768718 | − | 0.0633061i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50461.3 | − | 77837.5i | 0.123196 | − | 0.190033i | ||||
\(641\) | −232262. | + | 402289.i | −0.565278 | + | 0.979089i | 0.431746 | + | 0.901995i | \(0.357898\pi\) |
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 361978. | − | 208988.i | 0.875509 | − | 0.505476i | 0.00633423 | − | 0.999980i | \(-0.497984\pi\) |
0.869175 | + | 0.494504i | \(0.164650\pi\) | |||||||
\(644\) | −160433. | − | 427181.i | −0.386832 | − | 1.03001i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −165859. | + | 239461.i | −0.397442 | + | 0.573811i | ||||
\(647\) | − | 825841.i | − | 1.97282i | −0.164299 | − | 0.986411i | \(-0.552536\pi\) | ||
0.164299 | − | 0.986411i | \(-0.447464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −229610. | −0.545131 | ||||||||
\(650\) | 238138. | + | 164943.i | 0.563639 | + | 0.390397i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −461993. | + | 173507.i | −1.08678 | + | 0.408153i | ||||
\(653\) | 164273. | + | 284529.i | 0.385247 | + | 0.667267i | 0.991803 | − | 0.127773i | \(-0.0407830\pi\) |
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41049.6 | − | 23700.0i | −0.0956811 | − | 0.0552415i | ||||
\(656\) | 694972. | + | 237013.i | 1.61495 | + | 0.550762i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18058.5 | + | 219282.i | −0.0417090 | + | 0.506467i | ||||
\(659\) | −144939. | − | 83680.3i | −0.333744 | − | 0.192687i | 0.323758 | − | 0.946140i | \(-0.395054\pi\) |
−0.657502 | + | 0.753453i | \(0.728387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 152616. | + | 264339.i | 0.349300 | + | 0.605005i | 0.986125 | − | 0.166003i | \(-0.0530862\pi\) |
−0.636826 | + | 0.771008i | \(0.719753\pi\) | |||||||
\(662\) | 262732. | + | 556012.i | 0.599512 | + | 1.26873i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 134044. | − | 138209.i | 0.304027 | − | 0.313473i | ||||
\(665\) | −175261. | −0.396317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 402461.i | 0.904633i | ||||||||
\(668\) | 195287. | + | 160500.i | 0.437644 | + | 0.359685i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 39716.3 | + | 84050.4i | 0.0884748 | + | 0.187236i | ||||
\(671\) | −6127.32 | + | 3537.61i | −0.0136090 | + | 0.00785715i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −403032. | + | 698073.i | −0.889836 | + | 1.54124i | −0.0497671 | + | 0.998761i | \(0.515848\pi\) |
−0.840069 | + | 0.542480i | \(0.817485\pi\) | |||||||
\(674\) | −7532.41 | + | 91465.0i | −0.0165811 | + | 0.201342i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 215355. | + | 35712.5i | 0.471262 | + | 0.0781496i | ||||
\(677\) | −183117. | + | 317169.i | −0.399533 | + | 0.692011i | −0.993668 | − | 0.112354i | \(-0.964161\pi\) |
0.594136 | + | 0.804365i | \(0.297494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 217400. | − | 125516.i | 0.471542 | − | 0.272245i | ||||
\(680\) | −42756.4 | + | 12160.5i | −0.0924662 | + | 0.0262986i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −205507. | − | 142342.i | −0.441833 | − | 0.306029i | ||||
\(683\) | 398332.i | 0.853894i | 0.904277 | + | 0.426947i | \(0.140411\pi\) | ||||
−0.904277 | + | 0.426947i | \(0.859589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −169460. | −0.361148 | ||||||||
\(686\) | 247368. | − | 357140.i | 0.525649 | − | 0.758911i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 563715. | − | 111298.i | 1.19092 | − | 0.235130i | ||||
\(689\) | 290235. | + | 502701.i | 0.611379 | + | 1.05894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 304679. | + | 175906.i | 0.638096 | + | 0.368405i | 0.783881 | − | 0.620912i | \(-0.213237\pi\) |
−0.145785 | + | 0.989316i | \(0.546571\pi\) | |||||||
\(692\) | 742860. | + | 123189.i | 1.55130 | + | 0.257252i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28820.2 | − | 2373.42i | −0.0598381 | − | 0.00492784i | ||||
\(695\) | 116927. | + | 67507.8i | 0.242072 | + | 0.139760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −175932. | − | 304723.i | −0.362143 | − | 0.627249i | ||||
\(698\) | −399866. | + | 188949.i | −0.820737 | + | 0.387823i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 382194. | + | 314113.i | 0.779987 | + | 0.641047i | ||||
\(701\) | 620142. | 1.26199 | 0.630994 | − | 0.775788i | \(-0.282647\pi\) | ||||
0.630994 | + | 0.775788i | \(0.282647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.35898e6i | 2.74980i | ||||||||
\(704\) | 229919. | + | 371503.i | 0.463906 | + | 0.749579i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −222793. | + | 105276.i | −0.446984 | + | 0.211213i | ||||
\(707\) | −317061. | + | 183055.i | −0.634314 | + | 0.366222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −157448. | + | 272708.i | −0.313217 | + | 0.542508i | −0.979057 | − | 0.203587i | \(-0.934740\pi\) |
0.665840 | + | 0.746095i | \(0.268073\pi\) | |||||||
\(710\) | 113569. | + | 9352.70i | 0.225290 | + | 0.0185533i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49760.9 | − | 197762.i | 0.0981585 | − | 0.390107i | ||||
\(713\) | −160228. | + | 277523.i | −0.315181 | + | 0.545909i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 63878.0 | − | 36880.0i | 0.124951 | − | 0.0721404i | ||||
\(716\) | 38130.7 | − | 14320.4i | 0.0743786 | − | 0.0279338i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 192370. | − | 277736.i | 0.373154 | − | 0.538745i | ||||
\(719\) | 361941.i | 0.700132i | 0.936725 | + | 0.350066i | \(0.113841\pi\) | ||||
−0.936725 | + | 0.350066i | \(0.886159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −111926. | −0.215308 | ||||||||
\(722\) | −730221. | − | 505777.i | −1.40081 | − | 0.970252i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31932.8 | + | 85026.6i | 0.0609200 | + | 0.162210i | ||||
\(725\) | −218164. | − | 377870.i | −0.415056 | − | 0.718897i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −267542. | − | 154465.i | −0.506200 | − | 0.292255i | 0.225070 | − | 0.974343i | \(-0.427739\pi\) |
−0.731270 | + | 0.682088i | \(0.761072\pi\) | |||||||
\(728\) | −395289. | − | 99462.6i | −0.745852 | − | 0.187671i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5028.29 | + | 61057.9i | −0.00943572 | + | 0.114577i | ||||
\(731\) | −238457. | − | 137673.i | −0.446247 | − | 0.257641i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −441272. | − | 764305.i | −0.821293 | − | 1.42252i | −0.904719 | − | 0.426008i | \(-0.859920\pi\) |
0.0834259 | − | 0.996514i | \(-0.473414\pi\) | |||||||
\(734\) | −317739. | − | 672420.i | −0.589764 | − | 1.24810i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 450427. | − | 332821.i | 0.831512 | − | 0.614406i | ||||
\(737\) | −437829. | −0.806065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 396910.i | 0.726781i | 0.931637 | + | 0.363390i | \(0.118381\pi\) | ||||
−0.931637 | + | 0.363390i | \(0.881619\pi\) | |||||||
\(740\) | −131677. | + | 160217.i | −0.240462 | + | 0.292580i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 423522. | + | 896284.i | 0.769250 | + | 1.62794i | ||||
\(743\) | −831366. | + | 479989.i | −1.50596 | + | 0.869469i | −0.505988 | + | 0.862541i | \(0.668872\pi\) |
−0.999976 | + | 0.00692819i | \(0.997795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14930.1 | + | 25859.7i | −0.0268999 | + | 0.0465920i | ||||
\(746\) | −27935.5 | + | 339217.i | −0.0501971 | + | 0.609536i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34250.5 | − | 206539.i | 0.0612158 | − | 0.369147i | ||||
\(749\) | −361023. | + | 625310.i | −0.643534 | + | 1.11463i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 572212. | − | 330367.i | 1.01456 | − | 0.585756i | 0.102036 | − | 0.994781i | \(-0.467464\pi\) |
0.912523 | + | 0.409025i | \(0.134131\pi\) | |||||||
\(752\) | −264929. | + | 52306.4i | −0.468482 | + | 0.0924952i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 295538. | + | 204700.i | 0.519841 | + | 0.360060i | ||||
\(755\) | − | 189241.i | − | 0.331987i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 326842. | 0.570356 | 0.285178 | − | 0.958475i | \(-0.407947\pi\) | ||||
0.285178 | + | 0.958475i | \(0.407947\pi\) | |||||||
\(758\) | 334762. | − | 483316.i | 0.582636 | − | 0.841187i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −58844.6 | − | 206898.i | −0.101878 | − | 0.358203i | ||||
\(761\) | 164813. | + | 285464.i | 0.284591 | + | 0.492927i | 0.972510 | − | 0.232861i | \(-0.0748088\pi\) |
−0.687919 | + | 0.725788i | \(0.741475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −875410. | − | 505418.i | −1.50370 | − | 0.868164i | ||||
\(764\) | 85013.7 | − | 512654.i | 0.145647 | − | 0.878290i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 742285. | + | 61129.3i | 1.26507 | + | 0.104182i | ||||
\(767\) | 227694. | + | 131459.i | 0.387044 | + | 0.223460i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 299738. | + | 519162.i | 0.506862 | + | 0.877910i | 0.999968 | + | 0.00794129i | \(0.00252782\pi\) |
−0.493107 | + | 0.869969i | \(0.664139\pi\) | |||||||
\(770\) | 113890. | − | 53816.7i | 0.192091 | − | 0.0907686i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7999.60 | − | 9733.43i | 0.0134225 | − | 0.0163317i | ||||
\(773\) | 58555.0 | 0.0979952 | 0.0489976 | − | 0.998799i | \(-0.484397\pi\) | ||||
0.0489976 | + | 0.998799i | \(0.484397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 347422.i | − | 0.578433i | ||||||
\(776\) | 221166. | + | 214501.i | 0.367279 | + | 0.356211i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −925854. | + | 437494.i | −1.52962 | + | 0.722792i | ||||
\(779\) | 1.47456e6 | − | 851336.i | 2.42989 | − | 1.40290i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −268347. | + | 464791.i | −0.439942 | + | 0.762002i | ||||
\(782\) | −267469. | − | 22026.9i | −0.437381 | − | 0.0360196i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −77091.2 | − | 26291.1i | −0.125422 | − | 0.0427737i | ||||
\(785\) | 48129.6 | − | 83362.8i | 0.0781039 | − | 0.135280i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −553254. | + | 319421.i | −0.893254 | + | 0.515720i | −0.875005 | − | 0.484113i | \(-0.839142\pi\) |
−0.0182482 | + | 0.999833i | \(0.505809\pi\) | |||||||
\(788\) | −139655. | − | 371855.i | −0.224907 | − | 0.598854i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17808.9 | − | 25711.7i | 0.0285353 | − | 0.0411981i | ||||
\(791\) | 710975.i | 1.13632i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8101.59 | 0.0128832 | ||||||||
\(794\) | −857367. | − | 593843.i | −1.35996 | − | 0.941955i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 179869. | − | 67552.1i | 0.283877 | − | 0.106614i | ||||
\(797\) | −587628. | − | 1.01780e6i | −0.925095 | − | 1.60231i | −0.791409 | − | 0.611287i | \(-0.790652\pi\) |
−0.133686 | − | 0.991024i | \(-0.542681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 112067. | + | 64702.1i | 0.175544 | + | 0.101350i | ||||
\(800\) | −242492. | + | 556649.i | −0.378893 | + | 0.869765i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17404.5 | + | 211340.i | −0.0270591 | + | 0.328574i | ||||
\(803\) | −249886. | − | 144272.i | −0.387535 | − | 0.223743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −80736.4 | − | 139840.i | −0.124588 | − | 0.215793i | ||||
\(806\) | 122297. | + | 258814.i | 0.188255 | + | 0.398398i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −322554. | − | 312834.i | −0.494060 | − | 0.479171i | ||||
\(809\) | 215543. | 0.329334 | 0.164667 | − | 0.986349i | \(-0.447345\pi\) | ||||
0.164667 | + | 0.986349i | \(0.447345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.05773e6i | − | 1.60817i | −0.594512 | − | 0.804087i | \(-0.702655\pi\) | ||
0.594512 | − | 0.804087i | \(-0.297345\pi\) | |||||||
\(812\) | 474317. | + | 389826.i | 0.719377 | + | 0.591233i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −417295. | − | 883108.i | −0.629788 | − | 1.33280i | ||||
\(815\) | −151236. | + | 87315.9i | −0.227687 | + | 0.131455i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 666201. | − | 1.15389e6i | 0.998070 | − | 1.72871i | ||||
\(818\) | 48390.0 | − | 587594.i | 0.0723185 | − | 0.878153i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 256333. | + | 42507.8i | 0.381221 | + | 0.0632180i | ||||
\(821\) | −37925.7 | + | 65689.3i | −0.0562662 | + | 0.0974559i | −0.892787 | − | 0.450480i | \(-0.851253\pi\) |
0.836520 | + | 0.547936i | \(0.184586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 569508. | − | 328806.i | 0.840815 | − | 0.485445i | −0.0167265 | − | 0.999860i | \(-0.505324\pi\) |
0.857541 | + | 0.514416i | \(0.171991\pi\) | |||||||
\(824\) | −37579.6 | − | 132130.i | −0.0553475 | − | 0.194602i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 369112. | + | 255660.i | 0.541000 | + | 0.374716i | ||||
\(827\) | − | 669017.i | − | 0.978196i | −0.872229 | − | 0.489098i | \(-0.837326\pi\) | ||
0.872229 | − | 0.489098i | \(-0.162674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −637042. | −0.926955 | −0.463478 | − | 0.886109i | \(-0.653399\pi\) | ||||
−0.463478 | + | 0.886109i | \(0.653399\pi\) | |||||||
\(830\) | 38793.3 | − | 56008.2i | 0.0563119 | − | 0.0813010i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15303.0 | − | 500039.i | −0.0221070 | − | 0.722367i | ||||
\(833\) | 19515.6 | + | 33802.1i | 0.0281250 | + | 0.0487139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 77465.4 | + | 44724.7i | 0.111105 | + | 0.0641467i | ||||
\(836\) | 999443. | + | 165738.i | 1.43003 | + | 0.237143i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −927231. | − | 76360.1i | −1.32038 | − | 0.108737i | ||||
\(839\) | 872716. | + | 503863.i | 1.23979 | + | 0.715795i | 0.969052 | − | 0.246858i | \(-0.0793980\pi\) |
0.270741 | + | 0.962652i | \(0.412731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82891.1 | + | 143572.i | 0.117197 | + | 0.202991i | ||||
\(842\) | 252442. | − | 119286.i | 0.356071 | − | 0.168254i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 367744. | + | 302237.i | 0.516251 | + | 0.424290i | ||||
\(845\) | 77247.2 | 0.108186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 170194.i | − | 0.237234i | ||||||
\(848\) | −915877. | + | 800904.i | −1.27364 | + | 1.11375i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 263067. | − | 124307.i | 0.364106 | − | 0.172051i | ||||
\(851\) | −1.08432e6 | + | 626031.i | −1.49726 | + | 0.864444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 96790.1 | − | 167645.i | 0.133025 | − | 0.230406i | −0.791816 | − | 0.610759i | \(-0.790864\pi\) |
0.924841 | + | 0.380353i | \(0.124198\pi\) | |||||||
\(854\) | 13789.0 | + | 1135.56i | 0.0189068 | + | 0.00155703i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −859402. | − | 216242.i | −1.17287 | − | 0.295116i | ||||
\(857\) | 461864. | − | 799972.i | 0.628858 | − | 1.08921i | −0.358923 | − | 0.933367i | \(-0.616856\pi\) |
0.987781 | − | 0.155847i | \(-0.0498107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −628431. | + | 362825.i | −0.851670 | + | 0.491712i | −0.861214 | − | 0.508243i | \(-0.830295\pi\) |
0.00954418 | + | 0.999954i | \(0.496962\pi\) | |||||||
\(860\) | 190348. | − | 71487.4i | 0.257366 | − | 0.0966569i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −336790. | + | 486244.i | −0.453257 | + | 0.654395i | ||||
\(863\) | − | 444700.i | − | 0.597097i | −0.954394 | − | 0.298549i | \(-0.903497\pi\) | ||
0.954394 | − | 0.298549i | \(-0.0965025\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 266461. | 0.356124 | ||||||||
\(866\) | 969543. | + | 671540.i | 1.29280 | + | 0.895439i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 171875. | + | 457646.i | 0.228125 | + | 0.607421i | ||||
\(869\) | 73653.9 | + | 127572.i | 0.0975341 | + | 0.168934i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 434176. | + | 250672.i | 0.572308 | + | 0.330422i | ||||
\(872\) | 302731. | − | 1.20313e6i | 0.398129 | − | 1.58227i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 106588. | − | 1.29428e6i | 0.139536 | − | 1.69436i | ||||
\(875\) | 311409. | + | 179792.i | 0.406739 | + | 0.234831i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 288301. | + | 499353.i | 0.374841 | + | 0.649244i | 0.990303 | − | 0.138922i | \(-0.0443638\pi\) |
−0.615462 | + | 0.788167i | \(0.711031\pi\) | |||||||
\(878\) | 123269. | + | 260869.i | 0.159906 | + | 0.338403i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 101770. | + | 116380.i | 0.131419 | + | 0.150284i | ||||
\(881\) | 1.16458e6 | 1.50044 | 0.750219 | − | 0.661190i | \(-0.229948\pi\) | ||||
0.750219 | + | 0.661190i | \(0.229948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12142.2i | − | 0.0155731i | −0.999970 | − | 0.00778655i | \(-0.997521\pi\) | ||
0.999970 | − | 0.00778655i | \(-0.00247856\pi\) | |||||||
\(884\) | −152215. | + | 185206.i | −0.194784 | + | 0.237001i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 326248. | + | 690429.i | 0.415605 | + | 0.879532i | ||||
\(887\) | 1.12130e6 | − | 647385.i | 1.42520 | − | 0.822840i | 0.428464 | − | 0.903559i | \(-0.359055\pi\) |
0.996737 | + | 0.0807193i | \(0.0257217\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −409071. | + | 708532.i | −0.517601 | + | 0.896511i | ||||
\(890\) | 5922.72 | − | 71918.8i | 0.00747723 | − | 0.0907951i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 138595. | − | 835763.i | 0.174188 | − | 1.05040i | ||||
\(893\) | −313094. | + | 542294.i | −0.392619 | + | 0.680036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12482.2 | − | 7206.63i | 0.0155828 | − | 0.00899676i | ||||
\(896\) | 44042.5 | − | 853218.i | 0.0548600 | − | 1.06278i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −634173. | − | 439250.i | −0.786420 | − | 0.544703i | ||||
\(899\) | − | 431164.i | − | 0.533485i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 583026. | 0.718188 | ||||||||
\(902\) | −696800. | + | 1.00601e6i | −0.856436 | + | 1.23649i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −839316. | + | 238712.i | −1.02704 | + | 0.292104i | ||||
\(905\) | 16069.9 | + | 27833.8i | 0.0196207 | + | 0.0339841i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −593065. | − | 342406.i | −0.720921 | − | 0.416224i | 0.0941708 | − | 0.995556i | \(-0.469980\pi\) |
−0.815091 | + | 0.579332i | \(0.803313\pi\) | |||||||
\(908\) | −98513.1 | + | 594059.i | −0.119487 | + | 0.720540i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −143752. | − | 11838.4i | −0.173593 | − | 0.0142958i | ||||
\(911\) | −621519. | − | 358834.i | −0.748890 | − | 0.432372i | 0.0764028 | − | 0.997077i | \(-0.475657\pi\) |
−0.825293 | + | 0.564705i | \(0.808990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 160441. | + | 277893.i | 0.192475 | + | 0.333377i | ||||
\(914\) | 21429.3 | − | 10126.0i | 0.0256517 | − | 0.0121212i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −581489. | + | 707521.i | −0.693028 | + | 0.843235i | ||||
\(917\) | −436556. | −0.519160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 441444.i | − | 0.522691i | −0.965245 | − | 0.261345i | \(-0.915834\pi\) | ||
0.965245 | − | 0.261345i | \(-0.0841661\pi\) | |||||||
\(920\) | 137975. | − | 142262.i | 0.163014 | − | 0.168079i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 458160. | − | 216495.i | 0.538959 | − | 0.254674i | ||||
\(923\) | 532217. | − | 307275.i | 0.624720 | − | 0.360682i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 678710. | − | 1.17556e6i | 0.793232 | − | 1.37392i | ||||
\(926\) | −939108. | − | 77338.2i | −1.09520 | − | 0.0901929i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −300941. | + | 690823.i | −0.349451 | + | 0.802179i | ||||
\(929\) | 633285. | − | 1.09688e6i | 0.733783 | − | 1.27095i | −0.221472 | − | 0.975167i | \(-0.571086\pi\) |
0.955255 | − | 0.295783i | \(-0.0955804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −163568. | + | 94436.2i | −0.188712 | + | 0.108953i | ||||
\(932\) | 205150. | + | 546246.i | 0.236178 | + | 0.628864i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −222692. | + | 321514.i | −0.255277 | + | 0.368558i | ||||
\(935\) | − | 74084.8i | − | 0.0847434i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 377258. | 0.429694 | 0.214847 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214847 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(938\) | 703837. | + | 487503.i | 0.799957 | + | 0.554079i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −89457.5 | + | 33596.9i | −0.101242 | + | 0.0380227i | ||||
\(941\) | −645770. | − | 1.11851e6i | −0.729288 | − | 1.26316i | −0.957185 | − | 0.289478i | \(-0.906518\pi\) |
0.227897 | − | 0.973685i | \(-0.426815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.35855e6 | + | 784359.i | 1.52775 | + | 0.882046i | ||||
\(944\) | −177879. | + | 521580.i | −0.199610 | + | 0.585298i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −78598.0 | + | 954405.i | −0.0878273 | + | 1.06647i | ||||
\(947\) | −1.02088e6 | − | 589403.i | −1.13834 | − | 0.657222i | −0.192322 | − | 0.981332i | \(-0.561602\pi\) |
−0.946019 | + | 0.324110i | \(0.894935\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 165200. | + | 286136.i | 0.183434 | + | 0.317716i | ||||
\(950\) | 601521. | + | 1.27298e6i | 0.666506 | + | 1.41050i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −285031. | + | 293888.i | −0.314499 | + | 0.324271i | ||||
\(953\) | −613396. | −0.675391 | −0.337695 | − | 0.941255i | \(-0.609647\pi\) | ||||
−0.337695 | + | 0.941255i | \(0.609647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 183887.i | − | 0.201625i | ||||||
\(956\) | −647184. | − | 531900.i | −0.708128 | − | 0.581988i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −689005. | − | 1.45812e6i | −0.750743 | − | 1.58877i | ||||
\(959\) | −1.35163e6 | + | 780367.i | −1.46968 | + | 0.848519i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −290105. | + | 502477.i | −0.314130 | + | 0.544089i | ||||
\(962\) | −91795.0 | + | 1.11465e6i | −0.0991903 | + | 1.20445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 213265. | + | 35365.9i | 0.229491 | + | 0.0380567i | ||||
\(965\) | 2229.15 | − | 3861.01i | 0.00239379 | − | 0.00414616i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41063.4 | + | 23708.0i | −0.0439139 | + | 0.0253537i | −0.521796 | − | 0.853070i | \(-0.674738\pi\) |
0.477882 | + | 0.878424i | \(0.341405\pi\) | |||||||
\(968\) | 200916. | − | 57143.3i | 0.214420 | − | 0.0609838i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 89626.0 | + | 62078.1i | 0.0952556 | + | 0.0659774i | ||||
\(971\) | − | 746340.i | − | 0.791586i | −0.918340 | − | 0.395793i | \(-0.870470\pi\) | ||
0.918340 | − | 0.395793i | \(-0.129530\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.24350e6 | 1.31347 | ||||||||
\(974\) | 444597. | − | 641892.i | 0.468650 | − | 0.676619i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3289.16 | + | 16659.4i | 0.00345291 | + | 0.0174888i | ||||
\(977\) | −143356. | − | 248299.i | −0.150185 | − | 0.260128i | 0.781111 | − | 0.624393i | \(-0.214654\pi\) |
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 294335. | + | 169934.i | 0.307098 | + | 0.177303i | ||||
\(980\) | −28434.2 | − | 4715.26i | −0.0296067 | − | 0.00490969i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −303523. | − | 24996.0i | −0.314752 | − | 0.0259208i | ||||
\(983\) | 504643. | + | 291356.i | 0.522249 | + | 0.301521i | 0.737854 | − | 0.674960i | \(-0.235839\pi\) |
−0.215605 | + | 0.976481i | \(0.569172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70279.8 | − | 121728.i | −0.0724366 | − | 0.125464i | ||||
\(986\) | 326476. | − | 154270.i | 0.335813 | − | 0.158682i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −896213. | − | 736569.i | −0.918116 | − | 0.754570i | ||||
\(989\) | 1.22758e6 | 1.25504 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 918794.i | 0.935558i | 0.883845 | + | 0.467779i | \(0.154946\pi\) | ||||
−0.883845 | + | 0.467779i | \(0.845054\pi\) | |||||||
\(992\) | −482550. | + | 356557.i | −0.490364 | + | 0.362331i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 948909. | − | 448388.i | 0.960399 | − | 0.453818i | ||||
\(995\) | 58881.0 | − | 33995.0i | 0.0594742 | − | 0.0343375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 697626. | − | 1.20832e6i | 0.701830 | − | 1.21561i | −0.265993 | − | 0.963975i | \(-0.585700\pi\) |
0.967823 | − | 0.251631i | \(-0.0809668\pi\) | |||||||
\(998\) | 58084.7 | + | 4783.45i | 0.0583178 | + | 0.00480264i | ||||
\(999\) | 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 | 108.5.f.a.19.19 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.7.4 | ✓ | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.19.4 | 44 | ||
9.2 | odd | 6 | 324.5.d.f.163.12 | 22 | |||
9.4 | even | 3 | inner | 108.5.f.a.91.4 | 44 | ||
9.5 | odd | 6 | 36.5.f.a.31.19 | yes | 44 | ||
9.7 | even | 3 | 324.5.d.e.163.11 | 22 | |||
12.11 | even | 2 | 36.5.f.a.7.19 | yes | 44 | ||
36.7 | odd | 6 | 324.5.d.e.163.12 | 22 | |||
36.11 | even | 6 | 324.5.d.f.163.11 | 22 | |||
36.23 | even | 6 | 36.5.f.a.31.4 | yes | 44 | ||
36.31 | odd | 6 | inner | 108.5.f.a.91.19 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.4 | ✓ | 44 | 3.2 | odd | 2 | ||
36.5.f.a.7.19 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.4 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.19 | yes | 44 | 9.5 | odd | 6 | ||
108.5.f.a.19.4 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.19.19 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.4 | 44 | 9.4 | even | 3 | inner | ||
108.5.f.a.91.19 | 44 | 36.31 | odd | 6 | inner | ||
324.5.d.e.163.11 | 22 | 9.7 | even | 3 | |||
324.5.d.e.163.12 | 22 | 36.7 | odd | 6 | |||
324.5.d.f.163.11 | 22 | 36.11 | even | 6 | |||
324.5.d.f.163.12 | 22 | 9.2 | odd | 6 |