Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,6,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.55");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (of order \(2\), degree \(1\), 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: | \(40.4167225929\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 674 x^{14} + 3404 x^{13} + 173721 x^{12} - 919512 x^{11} - 21981508 x^{10} + \cdots + 224266997486896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{46}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Root | \(-7.16085 + 2.48366i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.6.b.d.55.7 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70662 | − | 4.96731i | −0.478467 | − | 0.878105i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −17.3484 | + | 26.8893i | −0.542138 | + | 0.840289i | ||||
\(5\) | 28.3847i | 0.507761i | 0.967236 | + | 0.253880i | \(0.0817070\pi\) | ||||
−0.967236 | + | 0.253880i | \(0.918293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −117.282 | − | 55.2436i | −0.904665 | − | 0.426125i | ||||
\(8\) | 180.523 | + | 13.3961i | 0.997258 | + | 0.0740037i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 140.996 | − | 76.8266i | 0.445868 | − | 0.242947i | ||||
\(11\) | − | 271.548i | − | 0.676651i | −0.941029 | − | 0.338326i | \(-0.890139\pi\) | ||
0.941029 | − | 0.338326i | \(-0.109861\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 180.279i | 0.295861i | 0.988998 | + | 0.147930i | \(0.0472612\pi\) | ||||
−0.988998 | + | 0.147930i | \(0.952739\pi\) | |||||||
\(14\) | 43.0265 | + | 732.102i | 0.0586700 | + | 0.998277i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −422.064 | − | 932.973i | −0.412172 | − | 0.911106i | ||||
\(17\) | − | 2098.19i | − | 1.76085i | −0.474185 | − | 0.880425i | \(-0.657257\pi\) | ||
0.474185 | − | 0.880425i | \(-0.342743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1445.92 | −0.918882 | −0.459441 | − | 0.888208i | \(-0.651950\pi\) | ||||
−0.459441 | + | 0.888208i | \(0.651950\pi\) | |||||||
\(20\) | −763.243 | − | 492.430i | −0.426666 | − | 0.275277i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1348.86 | + | 734.977i | −0.594171 | + | 0.323755i | ||||
\(23\) | 1665.96i | 0.656668i | 0.944562 | + | 0.328334i | \(0.106487\pi\) | ||||
−0.944562 | + | 0.328334i | \(0.893513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2319.31 | 0.742179 | ||||||||
\(26\) | 895.504 | − | 487.948i | 0.259797 | − | 0.141560i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3520.12 | − | 2195.25i | 0.848521 | − | 0.529161i | ||||
\(29\) | 4202.58 | 0.927943 | 0.463971 | − | 0.885850i | \(-0.346424\pi\) | ||||
0.463971 | + | 0.885850i | \(0.346424\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1810.94 | −0.338454 | −0.169227 | − | 0.985577i | \(-0.554127\pi\) | ||||
−0.169227 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(32\) | −3492.00 | + | 4621.73i | −0.602836 | + | 0.797865i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10422.4 | + | 5679.00i | −1.54621 | + | 0.842509i | ||||
\(35\) | 1568.07 | − | 3329.02i | 0.216369 | − | 0.459353i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8532.29 | −1.02462 | −0.512308 | − | 0.858802i | \(-0.671209\pi\) | ||||
−0.512308 | + | 0.858802i | \(0.671209\pi\) | |||||||
\(38\) | 3913.55 | + | 7182.33i | 0.439655 | + | 0.806875i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −380.244 | + | 5124.09i | −0.0375762 | + | 0.506369i | ||||
\(41\) | 20646.9i | 1.91821i | 0.283058 | + | 0.959103i | \(0.408651\pi\) | ||||
−0.283058 | + | 0.959103i | \(0.591349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10894.2i | 0.898511i | 0.893403 | + | 0.449256i | \(0.148311\pi\) | ||||
−0.893403 | + | 0.449256i | \(0.851689\pi\) | |||||||
\(44\) | 7301.72 | + | 4710.93i | 0.568583 | + | 0.366838i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8275.37 | − | 4509.13i | 0.576624 | − | 0.314194i | ||||
\(47\) | −15279.9 | −1.00897 | −0.504483 | − | 0.863422i | \(-0.668317\pi\) | ||||
−0.504483 | + | 0.863422i | \(0.668317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10703.3 | + | 12958.2i | 0.636836 | + | 0.771000i | ||||
\(50\) | −6277.49 | − | 11520.7i | −0.355108 | − | 0.651711i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4847.58 | − | 3127.56i | −0.248609 | − | 0.160398i | ||||
\(53\) | 20297.1 | 0.992529 | 0.496265 | − | 0.868171i | \(-0.334705\pi\) | ||||
0.496265 | + | 0.868171i | \(0.334705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7707.80 | 0.343577 | ||||||||
\(56\) | −20432.1 | − | 11543.9i | −0.870649 | − | 0.491905i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11374.8 | − | 20875.5i | −0.443990 | − | 0.814832i | ||||
\(59\) | 14318.9 | 0.535523 | 0.267762 | − | 0.963485i | \(-0.413716\pi\) | ||||
0.267762 | + | 0.963485i | \(0.413716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18947.4i | 0.651968i | 0.945375 | + | 0.325984i | \(0.105695\pi\) | ||||
−0.945375 | + | 0.325984i | \(0.894305\pi\) | |||||||
\(62\) | 4901.53 | + | 8995.51i | 0.161939 | + | 0.297199i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32409.1 | + | 4836.61i | 0.989047 | + | 0.147602i | ||||
\(65\) | −5117.17 | −0.150227 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 58173.5i | 1.58321i | 0.611035 | + | 0.791604i | \(0.290754\pi\) | ||||
−0.611035 | + | 0.791604i | \(0.709246\pi\) | |||||||
\(68\) | 56418.8 | + | 36400.3i | 1.47962 | + | 0.954624i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20780.5 | + | 1221.29i | −0.506886 | + | 0.0297903i | ||||
\(71\) | − | 45807.8i | − | 1.07843i | −0.842167 | − | 0.539216i | \(-0.818720\pi\) | ||
0.842167 | − | 0.539216i | \(-0.181280\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 25714.9i | 0.564777i | 0.959300 | + | 0.282389i | \(0.0911268\pi\) | ||||
−0.959300 | + | 0.282389i | \(0.908873\pi\) | |||||||
\(74\) | 23093.7 | + | 42382.6i | 0.490245 | + | 0.899721i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 25084.4 | − | 38879.7i | 0.498161 | − | 0.772126i | ||||
\(77\) | −15001.3 | + | 31847.8i | −0.288338 | + | 0.612142i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 89207.5i | − | 1.60818i | −0.594510 | − | 0.804088i | \(-0.702654\pi\) | ||
0.594510 | − | 0.804088i | \(-0.297346\pi\) | |||||||
\(80\) | 26482.1 | − | 11980.2i | 0.462624 | − | 0.209285i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 102560. | − | 55883.3i | 1.68439 | − | 0.917799i | ||||
\(83\) | 68687.3 | 1.09441 | 0.547206 | − | 0.836998i | \(-0.315691\pi\) | ||||
0.547206 | + | 0.836998i | \(0.315691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59556.5 | 0.894091 | ||||||||
\(86\) | 54114.8 | − | 29486.4i | 0.788988 | − | 0.429908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3637.68 | − | 49020.6i | 0.0500747 | − | 0.674796i | ||||
\(89\) | 31947.0i | 0.427519i | 0.976886 | + | 0.213759i | \(0.0685709\pi\) | ||||
−0.976886 | + | 0.213759i | \(0.931429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9959.27 | − | 21143.6i | 0.126074 | − | 0.267655i | ||||
\(92\) | −44796.5 | − | 28901.9i | −0.551791 | − | 0.356005i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 41356.9 | + | 75900.1i | 0.482757 | + | 0.885978i | ||||
\(95\) | − | 41041.9i | − | 0.466572i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 111178.i | 1.19975i | 0.800095 | + | 0.599874i | \(0.204782\pi\) | ||||
−0.800095 | + | 0.599874i | \(0.795218\pi\) | |||||||
\(98\) | 35397.6 | − | 88239.5i | 0.372314 | − | 0.928107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −40236.4 | + | 62364.5i | −0.402364 | + | 0.623645i | ||||
\(101\) | 90187.0i | 0.879712i | 0.898068 | + | 0.439856i | \(0.144971\pi\) | ||||
−0.898068 | + | 0.439856i | \(0.855029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26036.4 | 0.241817 | 0.120909 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(104\) | −2415.04 | + | 32544.6i | −0.0218948 | + | 0.295050i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −54936.4 | − | 100822.i | −0.474893 | − | 0.871545i | ||||
\(107\) | 27241.7i | 0.230025i | 0.993364 | + | 0.115012i | \(0.0366908\pi\) | ||||
−0.993364 | + | 0.115012i | \(0.963309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −48187.3 | −0.388478 | −0.194239 | − | 0.980954i | \(-0.562224\pi\) | ||||
−0.194239 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(110\) | −20862.1 | − | 38287.1i | −0.164390 | − | 0.301697i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2040.03 | + | 132738.i | −0.0153671 | + | 0.999882i | ||||
\(113\) | 218602. | 1.61049 | 0.805245 | − | 0.592942i | \(-0.202034\pi\) | ||||
0.805245 | + | 0.592942i | \(0.202034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −47287.9 | −0.333430 | ||||||||
\(116\) | −72908.2 | + | 113004.i | −0.503073 | + | 0.779741i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −38755.7 | − | 71126.3i | −0.256230 | − | 0.470246i | ||||
\(119\) | −115911. | + | 246081.i | −0.750342 | + | 1.59298i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87312.7 | 0.542143 | ||||||||
\(122\) | 94117.9 | − | 51283.5i | 0.572496 | − | 0.311945i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 31417.0 | − | 48694.9i | 0.183489 | − | 0.284400i | ||||
\(125\) | 154535.i | 0.884610i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 70206.5i | − | 0.386250i | −0.981174 | − | 0.193125i | \(-0.938138\pi\) | ||
0.981174 | − | 0.193125i | \(-0.0618622\pi\) | |||||||
\(128\) | −63694.1 | − | 174077.i | −0.343617 | − | 0.939110i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13850.2 | + | 25418.6i | 0.0718785 | + | 0.131915i | ||||
\(131\) | 63299.6 | 0.322272 | 0.161136 | − | 0.986932i | \(-0.448484\pi\) | ||||
0.161136 | + | 0.986932i | \(0.448484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 169581. | + | 79877.6i | 0.831280 | + | 0.391558i | ||||
\(134\) | 288966. | − | 157453.i | 1.39022 | − | 0.757513i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28107.6 | − | 378771.i | 0.130309 | − | 1.75602i | ||||
\(137\) | 749.523 | 0.00341180 | 0.00170590 | − | 0.999999i | \(-0.499457\pi\) | ||||
0.00170590 | + | 0.999999i | \(0.499457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −338690. | −1.48685 | −0.743423 | − | 0.668822i | \(-0.766799\pi\) | ||||
−0.743423 | + | 0.668822i | \(0.766799\pi\) | |||||||
\(140\) | 62311.4 | + | 99917.6i | 0.268687 | + | 0.430846i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −227542. | + | 123984.i | −0.946978 | + | 0.515995i | ||||
\(143\) | 48954.5 | 0.200195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 119289.i | 0.471173i | ||||||||
\(146\) | 127734. | − | 69600.4i | 0.495934 | − | 0.270228i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 148022. | − | 229427.i | 0.555484 | − | 0.860974i | ||||
\(149\) | −339997. | −1.25461 | −0.627305 | − | 0.778773i | \(-0.715842\pi\) | ||||
−0.627305 | + | 0.778773i | \(0.715842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 338495.i | 1.20812i | 0.796938 | + | 0.604061i | \(0.206452\pi\) | ||||
−0.796938 | + | 0.604061i | \(0.793548\pi\) | |||||||
\(152\) | −261021. | − | 19369.7i | −0.916362 | − | 0.0680006i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 198801. | − | 11683.8i | 0.675486 | − | 0.0396991i | ||||
\(155\) | − | 51403.0i | − | 0.171854i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 592002.i | 1.91679i | 0.285449 | + | 0.958394i | \(0.407857\pi\) | ||||
−0.285449 | + | 0.958394i | \(0.592143\pi\) | |||||||
\(158\) | −443122. | + | 241451.i | −1.41215 | + | 0.769459i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −131186. | − | 99119.4i | −0.405125 | − | 0.306097i | ||||
\(161\) | 92033.8 | − | 195388.i | 0.279822 | − | 0.594064i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 255977.i | 0.754625i | 0.926086 | + | 0.377313i | \(0.123152\pi\) | ||||
−0.926086 | + | 0.377313i | \(0.876848\pi\) | |||||||
\(164\) | −555180. | − | 358191.i | −1.61185 | − | 1.03993i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −185910. | − | 341191.i | −0.523641 | − | 0.961010i | ||||
\(167\) | −515543. | −1.43045 | −0.715227 | − | 0.698892i | \(-0.753677\pi\) | ||||
−0.715227 | + | 0.698892i | \(0.753677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 338792. | 0.912466 | ||||||||
\(170\) | −161197. | − | 295836.i | −0.427793 | − | 0.785106i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −292937. | − | 188997.i | −0.755010 | − | 0.487117i | ||||
\(173\) | − | 37150.1i | − | 0.0943723i | −0.998886 | − | 0.0471861i | \(-0.984975\pi\) | ||
0.998886 | − | 0.0471861i | \(-0.0150254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −272014. | − | 128127.i | −0.671423 | − | 0.316261i | ||||
\(176\) | −253347. | + | 114611.i | −0.616501 | + | 0.278897i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 158691. | − | 86468.4i | 0.375407 | − | 0.204554i | ||||
\(179\) | 143168.i | 0.333975i | 0.985959 | + | 0.166987i | \(0.0534039\pi\) | ||||
−0.985959 | + | 0.166987i | \(0.946596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 470966.i | − | 1.06855i | −0.845312 | − | 0.534273i | \(-0.820585\pi\) | ||
0.845312 | − | 0.534273i | \(-0.179415\pi\) | |||||||
\(182\) | −131983. | + | 7756.80i | −0.295351 | + | 0.0173582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22317.4 | + | 300745.i | −0.0485959 | + | 0.654868i | ||||
\(185\) | − | 242186.i | − | 0.520260i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −569759. | −1.19148 | ||||||||
\(188\) | 265082. | − | 410865.i | 0.546999 | − | 0.847823i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −203868. | + | 111085.i | −0.409699 | + | 0.223239i | ||||
\(191\) | 22686.0i | 0.0449961i | 0.999747 | + | 0.0224981i | \(0.00716196\pi\) | ||||
−0.999747 | + | 0.0224981i | \(0.992838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −191865. | −0.370768 | −0.185384 | − | 0.982666i | \(-0.559353\pi\) | ||||
−0.185384 | + | 0.982666i | \(0.559353\pi\) | |||||||
\(194\) | 552256. | − | 300917.i | 1.05350 | − | 0.574040i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −534121. | + | 62999.6i | −0.993116 | + | 0.117138i | ||||
\(197\) | −126782. | −0.232751 | −0.116376 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116376 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 47757.2 | 0.0854881 | 0.0427441 | − | 0.999086i | \(-0.486390\pi\) | ||||
0.0427441 | + | 0.999086i | \(0.486390\pi\) | |||||||
\(200\) | 418689. | + | 31069.7i | 0.740144 | + | 0.0549240i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 447987. | − | 244102.i | 0.772480 | − | 0.420913i | ||||
\(203\) | −492889. | − | 232166.i | −0.839477 | − | 0.395419i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −586056. | −0.973990 | ||||||||
\(206\) | −70470.5 | − | 129331.i | −0.115702 | − | 0.212341i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 168196. | − | 76089.5i | 0.269561 | − | 0.121946i | ||||
\(209\) | 392636.i | 0.621762i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 317222.i | 0.490521i | 0.969457 | + | 0.245261i | \(0.0788735\pi\) | ||||
−0.969457 | + | 0.245261i | \(0.921126\pi\) | |||||||
\(212\) | −352122. | + | 545773.i | −0.538088 | + | 0.834012i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 135318. | − | 73732.9i | 0.201986 | − | 0.110059i | ||||
\(215\) | −309228. | −0.456229 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 212391. | + | 100043.i | 0.306188 | + | 0.144224i | ||||
\(218\) | 130425. | + | 239361.i | 0.185874 | + | 0.341124i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −133718. | + | 207257.i | −0.186266 | + | 0.288704i | ||||
\(221\) | 378260. | 0.520967 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 422350. | 0.568736 | 0.284368 | − | 0.958715i | \(-0.408216\pi\) | ||||
0.284368 | + | 0.958715i | \(0.408216\pi\) | |||||||
\(224\) | 664871. | − | 349137.i | 0.885354 | − | 0.464917i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −591672. | − | 1.08586e6i | −0.770567 | − | 1.41418i | ||||
\(227\) | −383018. | −0.493349 | −0.246675 | − | 0.969098i | \(-0.579338\pi\) | ||||
−0.246675 | + | 0.969098i | \(0.579338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 856224.i | 1.07894i | 0.842004 | + | 0.539472i | \(0.181376\pi\) | ||||
−0.842004 | + | 0.539472i | \(0.818624\pi\) | |||||||
\(230\) | 127990. | + | 234894.i | 0.159536 | + | 0.292787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 758663. | + | 56298.2i | 0.925398 | + | 0.0686712i | ||||
\(233\) | 324537. | 0.391629 | 0.195814 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195814 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 433716.i | − | 0.512313i | ||||||
\(236\) | −248410. | + | 385023.i | −0.290328 | + | 0.449994i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.53609e6 | − | 90277.8i | 1.75782 | − | 0.103309i | ||||
\(239\) | − | 214134.i | − | 0.242489i | −0.992623 | − | 0.121244i | \(-0.961312\pi\) | ||
0.992623 | − | 0.121244i | \(-0.0386885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 437254.i | − | 0.484944i | −0.970158 | − | 0.242472i | \(-0.922042\pi\) | ||
0.970158 | − | 0.242472i | \(-0.0779582\pi\) | |||||||
\(242\) | −236322. | − | 433710.i | −0.259398 | − | 0.476059i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −509483. | − | 328708.i | −0.547841 | − | 0.353457i | ||||
\(245\) | −367814. | + | 303810.i | −0.391483 | + | 0.323360i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 260669.i | − | 0.271861i | ||||||
\(248\) | −326916. | − | 24259.5i | −0.337526 | − | 0.0250469i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 767624. | − | 418268.i | 0.776781 | − | 0.423257i | ||||
\(251\) | 1.50647e6 | 1.50930 | 0.754650 | − | 0.656128i | \(-0.227807\pi\) | ||||
0.754650 | + | 0.656128i | \(0.227807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 452389. | 0.444335 | ||||||||
\(254\) | −348738. | + | 190022.i | −0.339168 | + | 0.184808i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −692299. | + | 787549.i | −0.660228 | + | 0.751065i | ||||
\(257\) | − | 1.17493e6i | − | 1.10963i | −0.831973 | − | 0.554817i | \(-0.812788\pi\) | ||
0.831973 | − | 0.554817i | \(-0.187212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00069e6 | + | 471354.i | 0.926934 | + | 0.436614i | ||||
\(260\) | 88774.9 | − | 137597.i | 0.0814436 | − | 0.126234i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −171328. | − | 314429.i | −0.154197 | − | 0.282989i | ||||
\(263\) | 1.59797e6i | 1.42456i | 0.701897 | + | 0.712278i | \(0.252337\pi\) | ||||
−0.701897 | + | 0.712278i | \(0.747663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 576126.i | 0.503967i | ||||||||
\(266\) | −62212.8 | − | 1.05856e6i | −0.0539108 | − | 0.917299i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.56424e6 | − | 1.00922e6i | −1.33035 | − | 0.858318i | ||||
\(269\) | 201541.i | 0.169818i | 0.996389 | + | 0.0849090i | \(0.0270599\pi\) | ||||
−0.996389 | + | 0.0849090i | \(0.972940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −988629. | −0.817730 | −0.408865 | − | 0.912595i | \(-0.634075\pi\) | ||||
−0.408865 | + | 0.912595i | \(0.634075\pi\) | |||||||
\(272\) | −1.95755e6 | + | 885571.i | −1.60432 | + | 0.725774i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2028.67 | − | 3723.12i | −0.00163244 | − | 0.00299592i | ||||
\(275\) | − | 629804.i | − | 0.502196i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.53035e6 | 1.19837 | 0.599187 | − | 0.800609i | \(-0.295491\pi\) | ||||
0.599187 | + | 0.800609i | \(0.295491\pi\) | |||||||
\(278\) | 916706. | + | 1.68238e6i | 0.711407 | + | 1.30561i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 327669. | − | 579959.i | 0.249770 | − | 0.442081i | ||||
\(281\) | 456987. | 0.345253 | 0.172627 | − | 0.984987i | \(-0.444775\pi\) | ||||
0.172627 | + | 0.984987i | \(0.444775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.62201e6 | 1.20389 | 0.601946 | − | 0.798537i | \(-0.294392\pi\) | ||||
0.601946 | + | 0.798537i | \(0.294392\pi\) | |||||||
\(284\) | 1.23174e6 | + | 794692.i | 0.906196 | + | 0.584660i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −132501. | − | 243172.i | −0.0957866 | − | 0.175792i | ||||
\(287\) | 1.14061e6 | − | 2.42152e6i | 0.817395 | − | 1.73533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.98254e6 | −2.10059 | ||||||||
\(290\) | 592546. | − | 322870.i | 0.413740 | − | 0.225441i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −691454. | − | 446113.i | −0.474576 | − | 0.306187i | ||||
\(293\) | 543908.i | 0.370132i | 0.982726 | + | 0.185066i | \(0.0592499\pi\) | ||||
−0.982726 | + | 0.185066i | \(0.940750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 406436.i | 0.271918i | ||||||||
\(296\) | −1.54027e6 | − | 114299.i | −1.02181 | − | 0.0758254i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 920242. | + | 1.68887e6i | 0.600290 | + | 1.10168i | ||||
\(299\) | −300339. | −0.194283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 601834. | − | 1.27770e6i | 0.382878 | − | 0.812851i | ||||
\(302\) | 1.68141e6 | − | 916178.i | 1.06086 | − | 0.578046i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 610270. | + | 1.34900e6i | 0.378737 | + | 0.837199i | ||||
\(305\) | −537817. | −0.331044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 483324. | 0.292680 | 0.146340 | − | 0.989234i | \(-0.453251\pi\) | ||||
0.146340 | + | 0.989234i | \(0.453251\pi\) | |||||||
\(308\) | −596115. | − | 955882.i | −0.358058 | − | 0.574153i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −255335. | + | 139128.i | −0.150906 | + | 0.0822264i | ||||
\(311\) | 1.48235e6 | 0.869059 | 0.434529 | − | 0.900658i | \(-0.356915\pi\) | ||||
0.434529 | + | 0.900658i | \(0.356915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 874317.i | − | 0.504438i | −0.967670 | − | 0.252219i | \(-0.918840\pi\) | ||
0.967670 | − | 0.252219i | \(-0.0811604\pi\) | |||||||
\(314\) | 2.94066e6 | − | 1.60232e6i | 1.68314 | − | 0.917120i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.39872e6 | + | 1.54761e6i | 1.35133 | + | 0.871854i | ||||
\(317\) | −1.32505e6 | −0.740598 | −0.370299 | − | 0.928913i | \(-0.620745\pi\) | ||||
−0.370299 | + | 0.928913i | \(0.620745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.14120e6i | − | 0.627894i | ||||||
\(320\) | −137286. | + | 919922.i | −0.0749463 | + | 0.502199i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.21965e6 | + | 71680.6i | −0.655537 | + | 0.0385267i | ||||
\(323\) | 3.03381e6i | 1.61801i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 418124.i | 0.219582i | ||||||||
\(326\) | 1.27152e6 | − | 692831.i | 0.662640 | − | 0.361063i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −276588. | + | 3.72724e6i | −0.141954 | + | 1.91295i | ||||
\(329\) | 1.79206e6 | + | 844117.i | 0.912775 | + | 0.429945i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26134.3i | 0.0131112i | 0.999979 | + | 0.00655558i | \(0.00208672\pi\) | ||||
−0.999979 | + | 0.00655558i | \(0.997913\pi\) | |||||||
\(332\) | −1.19162e6 | + | 1.84695e6i | −0.593323 | + | 0.919623i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.39538e6 | + | 2.56087e6i | 0.684425 | + | 1.25609i | ||||
\(335\) | −1.65124e6 | −0.803891 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.18182e6 | 0.566863 | 0.283431 | − | 0.958993i | \(-0.408527\pi\) | ||||
0.283431 | + | 0.958993i | \(0.408527\pi\) | |||||||
\(338\) | −916982. | − | 1.68289e6i | −0.436585 | − | 0.801242i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.03321e6 | + | 1.60143e6i | −0.484721 | + | 0.751295i | ||||
\(341\) | 491757.i | 0.229015i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −539451. | − | 2.11106e6i | −0.247581 | − | 0.968867i | ||||
\(344\) | −145940. | + | 1.96665e6i | −0.0664932 | + | 0.896048i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −184536. | + | 100551.i | −0.0828688 | + | 0.0451540i | ||||
\(347\) | 541674.i | 0.241499i | 0.992683 | + | 0.120749i | \(0.0385297\pi\) | ||||
−0.992683 | + | 0.120749i | \(0.961470\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.74079e6i | − | 1.64399i | −0.569494 | − | 0.821996i | \(-0.692861\pi\) | ||
0.569494 | − | 0.821996i | \(-0.307139\pi\) | |||||||
\(350\) | 99791.8 | + | 1.69797e6i | 0.0435437 | + | 0.740901i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.25502e6 | + | 948245.i | 0.539876 | + | 0.407910i | ||||
\(353\) | 416451.i | 0.177880i | 0.996037 | + | 0.0889399i | \(0.0283479\pi\) | ||||
−0.996037 | + | 0.0889399i | \(0.971652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.30024e6 | 0.547586 | ||||||||
\(356\) | −859032. | − | 554230.i | −0.359240 | − | 0.231774i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 711161. | − | 387501.i | 0.293265 | − | 0.159796i | ||||
\(359\) | − | 2.78304e6i | − | 1.13968i | −0.821755 | − | 0.569840i | \(-0.807005\pi\) | ||
0.821755 | − | 0.569840i | \(-0.192995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −385421. | −0.155656 | ||||||||
\(362\) | −2.33944e6 | + | 1.27473e6i | −0.938297 | + | 0.511265i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 395758. | + | 634605.i | 0.156558 | + | 0.251044i | ||||
\(365\) | −729909. | −0.286772 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.80251e6 | −1.86124 | −0.930622 | − | 0.365982i | \(-0.880733\pi\) | ||||
−0.930622 | + | 0.365982i | \(0.880733\pi\) | |||||||
\(368\) | 1.55430e6 | − | 703144.i | 0.598294 | − | 0.270660i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.20302e6 | + | 655507.i | −0.456843 | + | 0.248927i | ||||
\(371\) | −2.38049e6 | − | 1.12128e6i | −0.897906 | − | 0.422941i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −285751. | −0.106345 | −0.0531723 | − | 0.998585i | \(-0.516933\pi\) | ||||
−0.0531723 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(374\) | 1.54212e6 | + | 2.83017e6i | 0.570085 | + | 1.04625i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.75838e6 | − | 204691.i | −1.00620 | − | 0.0746671i | ||||
\(377\) | 757639.i | 0.274542i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 220006.i | − | 0.0786749i | −0.999226 | − | 0.0393374i | \(-0.987475\pi\) | ||
0.999226 | − | 0.0393374i | \(-0.0125247\pi\) | |||||||
\(380\) | 1.10359e6 | + | 712013.i | 0.392056 | + | 0.252947i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 112689. | − | 61402.5i | 0.0395113 | − | 0.0215292i | ||||
\(383\) | 3.72820e6 | 1.29868 | 0.649341 | − | 0.760498i | \(-0.275045\pi\) | ||||
0.649341 | + | 0.760498i | \(0.275045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −903989. | − | 425807.i | −0.310822 | − | 0.146407i | ||||
\(386\) | 519305. | + | 953053.i | 0.177400 | + | 0.325573i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.98950e6 | − | 1.92876e6i | −1.00813 | − | 0.650429i | ||||
\(389\) | 2.84417e6 | 0.952975 | 0.476488 | − | 0.879181i | \(-0.341910\pi\) | ||||
0.476488 | + | 0.879181i | \(0.341910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.49551e6 | 1.15629 | ||||||||
\(392\) | 1.75860e6 | + | 2.48263e6i | 0.578033 | + | 0.816014i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 343151. | + | 629766.i | 0.111364 | + | 0.204380i | ||||
\(395\) | 2.53213e6 | 0.816569 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.69596e6i | 0.540056i | 0.962852 | + | 0.270028i | \(0.0870330\pi\) | ||||
−0.962852 | + | 0.270028i | \(0.912967\pi\) | |||||||
\(398\) | −129260. | − | 237225.i | −0.0409033 | − | 0.0750676i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −978898. | − | 2.16385e6i | −0.305906 | − | 0.676204i | ||||
\(401\) | −4.51541e6 | −1.40229 | −0.701143 | − | 0.713021i | \(-0.747326\pi\) | ||||
−0.701143 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 326475.i | − | 0.100135i | ||||||
\(404\) | −2.42506e6 | − | 1.56460e6i | −0.739213 | − | 0.476926i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 180823. | + | 3.07672e6i | 0.0544424 | + | 0.926344i | ||||
\(407\) | 2.31693e6i | 0.693308i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 911330.i | − | 0.269381i | −0.990888 | − | 0.134691i | \(-0.956996\pi\) | ||
0.990888 | − | 0.134691i | \(-0.0430041\pi\) | |||||||
\(410\) | 1.58623e6 | + | 2.91112e6i | 0.466022 | + | 0.855266i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −451690. | + | 700098.i | −0.131098 | + | 0.203196i | ||||
\(413\) | −1.67935e6 | − | 791025.i | −0.484469 | − | 0.228200i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.94967e6i | 0.555700i | ||||||||
\(416\) | −833202. | − | 629536.i | −0.236057 | − | 0.178356i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.95035e6 | − | 1.06272e6i | 0.545973 | − | 0.297493i | ||||
\(419\) | 69632.2 | 0.0193765 | 0.00968824 | − | 0.999953i | \(-0.496916\pi\) | ||||
0.00968824 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.62044e6 | −0.995533 | −0.497767 | − | 0.867311i | \(-0.665846\pi\) | ||||
−0.497767 | + | 0.867311i | \(0.665846\pi\) | |||||||
\(422\) | 1.57574e6 | − | 858600.i | 0.430729 | − | 0.234698i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.66408e6 | + | 271901.i | 0.989808 | + | 0.0734508i | ||||
\(425\) | − | 4.86635e6i | − | 1.30687i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04672e6 | − | 2.22220e6i | 0.277819 | − | 0.589812i | ||||
\(428\) | −732509. | − | 472600.i | −0.193287 | − | 0.124705i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 836963. | + | 1.53603e6i | 0.218291 | + | 0.400617i | ||||
\(431\) | 791654.i | 0.205278i | 0.994719 | + | 0.102639i | \(0.0327286\pi\) | ||||
−0.994719 | + | 0.102639i | \(0.967271\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 329131.i | 0.0843625i | 0.999110 | + | 0.0421812i | \(0.0134307\pi\) | ||||
−0.999110 | + | 0.0421812i | \(0.986569\pi\) | |||||||
\(434\) | −77918.5 | − | 1.32579e6i | −0.0198571 | − | 0.337871i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 835973. | − | 1.29572e6i | 0.210609 | − | 0.326434i | ||||
\(437\) | − | 2.40885e6i | − | 0.603400i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.71306e6 | 1.16719 | 0.583595 | − | 0.812045i | \(-0.301646\pi\) | ||||
0.583595 | + | 0.812045i | \(0.301646\pi\) | |||||||
\(440\) | 1.39144e6 | + | 103255.i | 0.342635 | + | 0.0254260i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.02381e6 | − | 1.87894e6i | −0.249266 | − | 0.457464i | ||||
\(443\) | − | 2.41380e6i | − | 0.584377i | −0.956361 | − | 0.292188i | \(-0.905617\pi\) | ||
0.956361 | − | 0.292188i | \(-0.0943834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −906806. | −0.217077 | ||||||||
\(446\) | −1.14314e6 | − | 2.09795e6i | −0.272122 | − | 0.499410i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.53382e6 | − | 2.35764e6i | −0.831859 | − | 0.554987i | ||||
\(449\) | 2.88865e6 | 0.676205 | 0.338103 | − | 0.941109i | \(-0.390215\pi\) | ||||
0.338103 | + | 0.941109i | \(0.390215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.60662e6 | 1.29796 | ||||||||
\(452\) | −3.79240e6 | + | 5.87805e6i | −0.873108 | + | 1.35328i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.03668e6 | + | 1.90257e6i | 0.236051 | + | 0.433213i | ||||
\(455\) | 600154. | + | 282691.i | 0.135905 | + | 0.0640152i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.81000e6 | −0.853365 | −0.426682 | − | 0.904402i | \(-0.640318\pi\) | ||||
−0.426682 | + | 0.904402i | \(0.640318\pi\) | |||||||
\(458\) | 4.25313e6 | − | 2.31747e6i | 0.947426 | − | 0.516239i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 820370. | − | 1.27154e6i | 0.180765 | − | 0.280178i | ||||
\(461\) | − | 5.30428e6i | − | 1.16245i | −0.813743 | − | 0.581224i | \(-0.802574\pi\) | ||
0.813743 | − | 0.581224i | \(-0.197426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63705e6i | 1.00529i | 0.864494 | + | 0.502643i | \(0.167639\pi\) | ||||
−0.864494 | + | 0.502643i | \(0.832361\pi\) | |||||||
\(464\) | −1.77376e6 | − | 3.92089e6i | −0.382472 | − | 0.845454i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −878398. | − | 1.61208e6i | −0.187381 | − | 0.343891i | ||||
\(467\) | 1.92138e6 | 0.407682 | 0.203841 | − | 0.979004i | \(-0.434658\pi\) | ||||
0.203841 | + | 0.979004i | \(0.434658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.21371e6 | − | 6.82272e6i | 0.674644 | − | 1.43227i | ||||
\(470\) | −2.15440e6 | + | 1.17390e6i | −0.449865 | + | 0.245125i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.58488e6 | + | 191817.i | 0.534055 | + | 0.0396307i | ||||
\(473\) | 2.95829e6 | 0.607979 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.35353e6 | −0.681975 | ||||||||
\(476\) | −4.60604e6 | − | 7.38588e6i | −0.931774 | − | 1.49412i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.06367e6 | + | 579580.i | −0.212931 | + | 0.116023i | ||||
\(479\) | −5.23498e6 | −1.04250 | −0.521250 | − | 0.853404i | \(-0.674534\pi\) | ||||
−0.521250 | + | 0.853404i | \(0.674534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.53820e6i | − | 0.303144i | ||||||
\(482\) | −2.17198e6 | + | 1.18348e6i | −0.425832 | + | 0.232030i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.51474e6 | + | 2.34777e6i | −0.293917 | + | 0.455557i | ||||
\(485\) | −3.15576e6 | −0.609185 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.98270e6i | 0.952012i | 0.879442 | + | 0.476006i | \(0.157916\pi\) | ||||
−0.879442 | + | 0.476006i | \(0.842084\pi\) | |||||||
\(488\) | −253822. | + | 3.42045e6i | −0.0482480 | + | 0.650180i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.50465e6 | + | 1.00475e6i | 0.471256 | + | 0.189046i | ||||
\(491\) | − | 4.48170e6i | − | 0.838956i | −0.907766 | − | 0.419478i | \(-0.862213\pi\) | ||
0.907766 | − | 0.419478i | \(-0.137787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.81782e6i | − | 1.63397i | ||||||
\(494\) | −1.29483e6 | + | 705532.i | −0.238723 | + | 0.130077i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 764334. | + | 1.68956e6i | 0.139501 | + | 0.308368i | ||||
\(497\) | −2.53058e6 | + | 5.37244e6i | −0.459547 | + | 0.975620i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.74642e6i | − | 1.57246i | −0.617935 | − | 0.786229i | \(-0.712031\pi\) | ||
0.617935 | − | 0.786229i | \(-0.287969\pi\) | |||||||
\(500\) | −4.15533e6 | − | 2.68094e6i | −0.743328 | − | 0.479581i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.07743e6 | − | 7.48310e6i | −0.722150 | − | 1.32532i | ||||
\(503\) | −7.16489e6 | −1.26267 | −0.631335 | − | 0.775511i | \(-0.717493\pi\) | ||||
−0.631335 | + | 0.775511i | \(0.717493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.55993e6 | −0.446683 | ||||||||
\(506\) | −1.22445e6 | − | 2.24716e6i | −0.212600 | − | 0.390173i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.88780e6 | + | 1.21797e6i | 0.324562 | + | 0.209401i | ||||
\(509\) | − | 509493.i | − | 0.0871654i | −0.999050 | − | 0.0435827i | \(-0.986123\pi\) | ||
0.999050 | − | 0.0435827i | \(-0.0138772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.42058e6 | − | 3.01590e6i | 0.240666 | − | 0.510934i | ||||
\(512\) | 5.78579e6 | + | 1.30727e6i | 0.975412 | + | 0.220390i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.83625e6 | + | 3.18009e6i | −0.974375 | + | 0.530923i | ||||
\(515\) | 739034.i | 0.122785i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.14923e6i | 0.682717i | ||||||||
\(518\) | −367115. | − | 6.24650e6i | −0.0601143 | − | 1.02285i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −923768. | − | 68550.2i | −0.149815 | − | 0.0111173i | ||||
\(521\) | − | 2.24559e6i | − | 0.362441i | −0.983443 | − | 0.181220i | \(-0.941995\pi\) | ||
0.983443 | − | 0.181220i | \(-0.0580047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.67986e6 | −1.06786 | −0.533929 | − | 0.845529i | \(-0.679285\pi\) | ||||
−0.533929 | + | 0.845529i | \(0.679285\pi\) | |||||||
\(524\) | −1.09815e6 | + | 1.70208e6i | −0.174716 | + | 0.270802i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.93763e6 | − | 4.32510e6i | 1.25091 | − | 0.681604i | ||||
\(527\) | 3.79970e6i | 0.595967i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.66091e6 | 0.568787 | ||||||||
\(530\) | 2.86180e6 | − | 1.55935e6i | 0.442537 | − | 0.241132i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.08981e6 | + | 3.17415e6i | −0.779691 | + | 0.486237i | ||||
\(533\) | −3.72221e6 | −0.567522 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −773247. | −0.116798 | ||||||||
\(536\) | −779297. | + | 1.05016e7i | −0.117163 | + | 1.57887i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.00112e6 | − | 545496.i | 0.149118 | − | 0.0812523i | ||||
\(539\) | 3.51877e6 | − | 2.90646e6i | 0.521698 | − | 0.430916i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.39309e6 | 1.23290 | 0.616451 | − | 0.787393i | \(-0.288570\pi\) | ||||
0.616451 | + | 0.787393i | \(0.288570\pi\) | |||||||
\(542\) | 2.67584e6 | + | 4.91083e6i | 0.391257 | + | 0.718053i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.69726e6 | + | 7.32688e6i | 1.40492 | + | 1.06150i | ||||
\(545\) | − | 1.36778e6i | − | 0.197254i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.21277e6i | 1.31650i | 0.752798 | + | 0.658251i | \(0.228704\pi\) | ||||
−0.752798 | + | 0.658251i | \(0.771296\pi\) | |||||||
\(548\) | −13003.1 | + | 20154.1i | −0.00184967 | + | 0.00286690i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.12843e6 | + | 1.70464e6i | −0.440981 | + | 0.240284i | ||||
\(551\) | −6.07659e6 | −0.852670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.92814e6 | + | 1.04625e7i | −0.685283 | + | 1.45486i | ||||
\(554\) | −4.14208e6 | − | 7.60175e6i | −0.573383 | − | 1.05230i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.87574e6 | − | 9.10713e6i | 0.806076 | − | 1.24938i | ||||
\(557\) | 7.30468e6 | 0.997616 | 0.498808 | − | 0.866713i | \(-0.333771\pi\) | ||||
0.498808 | + | 0.866713i | \(0.333771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.96400e6 | −0.265834 | ||||||||
\(560\) | −3.76771e6 | − | 57905.6i | −0.507701 | − | 0.00780279i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.23689e6 | − | 2.27000e6i | −0.165192 | − | 0.303169i | ||||
\(563\) | −41121.0 | −0.00546754 | −0.00273377 | − | 0.999996i | \(-0.500870\pi\) | ||||
−0.00273377 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.20495e6i | 0.817744i | ||||||||
\(566\) | −4.39016e6 | − | 8.05703e6i | −0.576023 | − | 1.05714i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 613645. | − | 8.26935e6i | 0.0798080 | − | 1.07548i | ||||
\(569\) | 5.94994e6 | 0.770428 | 0.385214 | − | 0.922827i | \(-0.374128\pi\) | ||||
0.385214 | + | 0.922827i | \(0.374128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.93009e6i | 0.632797i | 0.948626 | + | 0.316399i | \(0.102474\pi\) | ||||
−0.948626 | + | 0.316399i | \(0.897526\pi\) | |||||||
\(572\) | −849283. | + | 1.31635e6i | −0.108533 | + | 0.168221i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.51156e7 | + | 888364.i | −1.91490 | + | 0.112541i | ||||
\(575\) | 3.86389e6i | 0.487365i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.17226e6i | 0.896843i | 0.893822 | + | 0.448422i | \(0.148014\pi\) | ||||
−0.893822 | + | 0.448422i | \(0.851986\pi\) | |||||||
\(578\) | 8.07261e6 | + | 1.48152e7i | 1.00507 | + | 1.84454i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.20759e6 | − | 2.06948e6i | −0.395922 | − | 0.255441i | ||||
\(581\) | −8.05581e6 | − | 3.79453e6i | −0.990076 | − | 0.466356i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.51162e6i | − | 0.671596i | ||||||
\(584\) | −344479. | + | 4.64213e6i | −0.0417956 | + | 0.563229i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.70176e6 | − | 1.47215e6i | 0.325015 | − | 0.177096i | ||||
\(587\) | 6.02358e6 | 0.721538 | 0.360769 | − | 0.932655i | \(-0.382514\pi\) | ||||
0.360769 | + | 0.932655i | \(0.382514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.61847e6 | 0.310999 | ||||||||
\(590\) | 2.01890e6 | − | 1.10007e6i | 0.238772 | − | 0.130104i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.60118e6 | + | 7.96039e6i | 0.422318 | + | 0.933534i | ||||
\(593\) | 1.29430e6i | 0.151146i | 0.997140 | + | 0.0755731i | \(0.0240786\pi\) | ||||
−0.997140 | + | 0.0755731i | \(0.975921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.98492e6 | − | 3.29011e6i | −0.808852 | − | 0.380994i | ||||
\(596\) | 5.89841e6 | − | 9.14226e6i | 0.680172 | − | 1.05424i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 812903. | + | 1.49188e6i | 0.0929578 | + | 0.170601i | ||||
\(599\) | 1.32740e7i | 1.51159i | 0.654810 | + | 0.755794i | \(0.272749\pi\) | ||||
−0.654810 | + | 0.755794i | \(0.727251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.50249e6i | − | 0.282609i | −0.989966 | − | 0.141304i | \(-0.954870\pi\) | ||
0.989966 | − | 0.141304i | \(-0.0451297\pi\) | |||||||
\(602\) | −7.97565e6 | + | 468739.i | −0.896964 | + | 0.0527157i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.10189e6 | − | 5.87236e6i | −1.01517 | − | 0.654969i | ||||
\(605\) | 2.47834e6i | 0.275279i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.09850e6 | −0.781978 | −0.390989 | − | 0.920395i | \(-0.627867\pi\) | ||||
−0.390989 | + | 0.920395i | \(0.627867\pi\) | |||||||
\(608\) | 5.04915e6 | − | 6.68264e6i | 0.553935 | − | 0.733144i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.45567e6 | + | 2.67151e6i | 0.158394 | + | 0.290691i | ||||
\(611\) | − | 2.75465e6i | − | 0.298513i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11324.6 | 0.00121722 | 0.000608612 | − | 1.00000i | \(-0.499806\pi\) | ||||
0.000608612 | 1.00000i | \(0.499806\pi\) | ||||||||
\(614\) | −1.30818e6 | − | 2.40082e6i | −0.140038 | − | 0.257004i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.13471e6 | + | 5.54830e6i | −0.332848 | + | 0.589126i | ||||
\(617\) | −6.35901e6 | −0.672476 | −0.336238 | − | 0.941777i | \(-0.609155\pi\) | ||||
−0.336238 | + | 0.941777i | \(0.609155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.53359e7 | −1.60873 | −0.804365 | − | 0.594135i | \(-0.797494\pi\) | ||||
−0.804365 | + | 0.594135i | \(0.797494\pi\) | |||||||
\(620\) | 1.38219e6 | + | 891761.i | 0.144407 | + | 0.0931685i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.01215e6 | − | 7.36329e6i | −0.415816 | − | 0.763125i | ||||
\(623\) | 1.76487e6 | − | 3.74682e6i | 0.182176 | − | 0.386761i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.86141e6 | 0.293009 | ||||||||
\(626\) | −4.34301e6 | + | 2.36644e6i | −0.442950 | + | 0.241357i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.59185e7 | − | 1.02703e7i | −1.61066 | − | 1.03916i | ||||
\(629\) | 1.79024e7i | 1.80420i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.80461e6i | 0.280413i | 0.990122 | + | 0.140207i | \(0.0447767\pi\) | ||||
−0.990122 | + | 0.140207i | \(0.955223\pi\) | |||||||
\(632\) | 1.19503e6 | − | 1.61040e7i | 0.119011 | − | 1.60377i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.58639e6 | + | 6.58192e6i | 0.354352 | + | 0.650324i | ||||
\(635\) | 1.99279e6 | 0.196122 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.33609e6 | + | 1.92958e6i | −0.228109 | + | 0.188415i | ||||
\(638\) | −5.66871e6 | + | 3.08880e6i | −0.551357 | + | 0.300427i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.94112e6 | − | 1.80794e6i | 0.476843 | − | 0.174475i | ||||
\(641\) | 6.37046e6 | 0.612386 | 0.306193 | − | 0.951969i | \(-0.400945\pi\) | ||||
0.306193 | + | 0.951969i | \(0.400945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.01925e7 | 0.972198 | 0.486099 | − | 0.873904i | \(-0.338419\pi\) | ||||
0.486099 | + | 0.873904i | \(0.338419\pi\) | |||||||
\(644\) | 3.65720e6 | + | 5.86440e6i | 0.347484 | + | 0.557197i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50699e7 | − | 8.21137e6i | 1.42079 | − | 0.774166i | ||||
\(647\) | −1.45811e7 | −1.36940 | −0.684698 | − | 0.728827i | \(-0.740066\pi\) | ||||
−0.684698 | + | 0.728827i | \(0.740066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.88826e6i | − | 0.362362i | ||||||
\(650\) | 2.07695e6 | − | 1.13170e6i | 0.192816 | − | 0.105063i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.88302e6 | − | 4.44079e6i | −0.634103 | − | 0.409111i | ||||
\(653\) | −1.59522e6 | −0.146399 | −0.0731996 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731996 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.79674e6i | 0.163637i | ||||||||
\(656\) | 1.92630e7 | − | 8.71432e6i | 1.74769 | − | 0.790631i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −657442. | − | 1.11864e7i | −0.0591960 | − | 1.00723i | ||||
\(659\) | 5.66808e6i | 0.508419i | 0.967149 | + | 0.254210i | \(0.0818154\pi\) | ||||
−0.967149 | + | 0.254210i | \(0.918185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.08220e7i | 1.85361i | 0.375541 | + | 0.926806i | \(0.377457\pi\) | ||||
−0.375541 | + | 0.926806i | \(0.622543\pi\) | |||||||
\(662\) | 129817. | − | 70735.6i | 0.0115130 | − | 0.00627326i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.23996e7 | + | 920142.i | 1.09141 | + | 0.0809906i | ||||
\(665\) | −2.26730e6 | + | 4.81349e6i | −0.198818 | + | 0.422091i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.00135e6i | 0.609351i | ||||||||
\(668\) | 8.94386e6 | − | 1.38626e7i | 0.775504 | − | 1.20200i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.46927e6 | + | 8.20221e6i | 0.384635 | + | 0.705901i | ||||
\(671\) | 5.14514e6 | 0.441155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.63494e7 | −1.39144 | −0.695720 | − | 0.718313i | \(-0.744915\pi\) | ||||
−0.695720 | + | 0.718313i | \(0.744915\pi\) | |||||||
\(674\) | −3.19875e6 | − | 5.87049e6i | −0.271225 | − | 0.497765i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.87751e6 | + | 9.10987e6i | −0.494683 | + | 0.766736i | ||||
\(677\) | 1.27172e7i | 1.06640i | 0.845991 | + | 0.533198i | \(0.179010\pi\) | ||||
−0.845991 | + | 0.533198i | \(0.820990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.14187e6 | − | 1.30392e7i | 0.511242 | − | 1.08537i | ||||
\(680\) | 1.07513e7 | + | 797824.i | 0.891639 | + | 0.0661660i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.44271e6 | − | 1.33100e6i | 0.201100 | − | 0.109576i | ||||
\(683\) | 5.60180e6i | 0.459490i | 0.973251 | + | 0.229745i | \(0.0737891\pi\) | ||||
−0.973251 | + | 0.229745i | \(0.926211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21275.0i | 0.00173238i | ||||||||
\(686\) | −9.02618e6 | + | 8.39345e6i | −0.732308 | + | 0.680973i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.01640e7 | − | 4.59805e6i | 0.818639 | − | 0.370341i | ||||
\(689\) | 3.65914e6i | 0.293651i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.62765e6 | 0.607709 | 0.303855 | − | 0.952718i | \(-0.401726\pi\) | ||||
0.303855 | + | 0.952718i | \(0.401726\pi\) | |||||||
\(692\) | 998938. | + | 644495.i | 0.0793000 | + | 0.0511628i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.69067e6 | − | 1.46611e6i | 0.212061 | − | 0.115549i | ||||
\(695\) | − | 9.61362e6i | − | 0.754962i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.33211e7 | 3.37767 | ||||||||
\(698\) | −1.85817e7 | + | 1.01249e7i | −1.44360 | + | 0.786596i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.16425e6 | − | 5.09146e6i | 0.629755 | − | 0.392733i | ||||
\(701\) | 1.48602e7 | 1.14217 | 0.571083 | − | 0.820893i | \(-0.306524\pi\) | ||||
0.571083 | + | 0.820893i | \(0.306524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.23370e7 | 0.941501 | ||||||||
\(704\) | 1.31337e6 | − | 8.80062e6i | 0.0998747 | − | 0.669240i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.06864e6 | − | 1.12717e6i | 0.156197 | − | 0.0851097i | ||||
\(707\) | 4.98225e6 | − | 1.05773e7i | 0.374867 | − | 0.795844i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.36416e7 | 1.01917 | 0.509587 | − | 0.860419i | \(-0.329798\pi\) | ||||
0.509587 | + | 0.860419i | \(0.329798\pi\) | |||||||
\(710\) | −3.51925e6 | − | 6.45870e6i | −0.262002 | − | 0.480838i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −427965. | + | 5.76717e6i | −0.0316380 | + | 0.426347i | ||||
\(713\) | − | 3.01696e6i | − | 0.222252i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.38956e6i | 0.101651i | ||||||||
\(716\) | −3.84968e6 | − | 2.48374e6i | −0.280635 | − | 0.181060i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.38242e7 | + | 7.53263e6i | −1.00076 | + | 0.545300i | ||||
\(719\) | 2.34845e6 | 0.169418 | 0.0847088 | − | 0.996406i | \(-0.473004\pi\) | ||||
0.0847088 | + | 0.996406i | \(0.473004\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05361e6 | − | 1.43834e6i | −0.218763 | − | 0.103044i | ||||
\(722\) | 1.04319e6 | + | 1.91451e6i | 0.0744765 | + | 0.136683i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.26639e7 | + | 8.17053e6i | 0.897888 | + | 0.579300i | ||||
\(725\) | 9.74709e6 | 0.688700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.45752e7 | −1.72449 | −0.862246 | − | 0.506490i | \(-0.830943\pi\) | ||||
−0.862246 | + | 0.506490i | \(0.830943\pi\) | |||||||
\(728\) | 2.08112e6 | − | 3.68349e6i | 0.145535 | − | 0.257591i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.97559e6 | + | 3.62569e6i | 0.137211 | + | 0.251816i | ||||
\(731\) | 2.28581e7 | 1.58214 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.80954e7i | 1.24396i | 0.783032 | + | 0.621982i | \(0.213672\pi\) | ||||
−0.783032 | + | 0.621982i | \(0.786328\pi\) | |||||||
\(734\) | 1.29986e7 | + | 2.38556e7i | 0.890544 | + | 1.63437i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.69963e6 | − | 5.81755e6i | −0.523933 | − | 0.395863i | ||||
\(737\) | 1.57969e7 | 1.07128 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.37056e7i | − | 1.59676i | −0.602151 | − | 0.798382i | \(-0.705690\pi\) | ||
0.602151 | − | 0.798382i | \(-0.294310\pi\) | |||||||
\(740\) | 6.51221e6 | + | 4.20155e6i | 0.437169 | + | 0.282053i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 873312. | + | 1.48595e7i | 0.0582317 | + | 0.990819i | ||||
\(743\) | 7.66583e6i | 0.509433i | 0.967016 | + | 0.254717i | \(0.0819822\pi\) | ||||
−0.967016 | + | 0.254717i | \(0.918018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.65070e6i | − | 0.637042i | ||||||
\(746\) | 773419. | + | 1.41941e6i | 0.0508824 | + | 0.0933818i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.88442e6 | − | 1.53204e7i | 0.645948 | − | 1.00119i | ||||
\(749\) | 1.50493e6 | − | 3.19497e6i | 0.0980192 | − | 0.208095i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.68186e7i | 1.73515i | 0.497310 | + | 0.867573i | \(0.334321\pi\) | ||||
−0.497310 | + | 0.867573i | \(0.665679\pi\) | |||||||
\(752\) | 6.44911e6 | + | 1.42557e7i | 0.415867 | + | 0.919274i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.76343e6 | − | 2.05064e6i | 0.241077 | − | 0.131359i | ||||
\(755\) | −9.60809e6 | −0.613437 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.38220e7 | −0.876661 | −0.438330 | − | 0.898814i | \(-0.644430\pi\) | ||||
−0.438330 | + | 0.898814i | \(0.644430\pi\) | |||||||
\(758\) | −1.09284e6 | + | 595472.i | −0.0690848 | + | 0.0376433i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 549802. | − | 7.40901e6i | 0.0345281 | − | 0.465293i | ||||
\(761\) | 8.75585e6i | 0.548071i | 0.961720 | + | 0.274035i | \(0.0883585\pi\) | ||||
−0.961720 | + | 0.274035i | \(0.911641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.65152e6 | + | 2.66204e6i | 0.351442 | + | 0.165540i | ||||
\(764\) | −610011. | − | 393567.i | −0.0378098 | − | 0.0243941i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.00908e7 | − | 1.85192e7i | −0.621376 | − | 1.14038i | ||||
\(767\) | 2.58139e6i | 0.158440i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.57987e7i | 1.57319i | 0.617466 | + | 0.786597i | \(0.288159\pi\) | ||||
−0.617466 | + | 0.786597i | \(0.711841\pi\) | |||||||
\(770\) | 331640. | + | 5.64290e6i | 0.0201577 | + | 0.342985i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.32855e6 | − | 5.15910e6i | 0.201007 | − | 0.311552i | ||||
\(773\) | 1.88397e7i | 1.13403i | 0.823706 | + | 0.567017i | \(0.191903\pi\) | ||||
−0.823706 | + | 0.567017i | \(0.808097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.20013e6 | −0.251194 | ||||||||
\(776\) | −1.48935e6 | + | 2.00702e7i | −0.0887857 | + | 1.19646i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.69809e6 | − | 1.41279e7i | −0.455967 | − | 0.836813i | ||||
\(779\) | − | 2.98537e7i | − | 1.76260i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.24390e7 | −0.729723 | ||||||||
\(782\) | −9.46101e6 | − | 1.73633e7i | −0.553249 | − | 1.01535i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.57215e6 | − | 1.54551e7i | 0.439976 | − | 0.898009i | ||||
\(785\) | −1.68038e7 | −0.973270 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.08065e6 | 0.522613 | 0.261306 | − | 0.965256i | \(-0.415847\pi\) | ||||
0.261306 | + | 0.965256i | \(0.415847\pi\) | |||||||
\(788\) | 2.19947e6 | − | 3.40907e6i | 0.126183 | − | 0.195578i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.85350e6 | − | 1.25779e7i | −0.390701 | − | 0.717033i | ||||
\(791\) | −2.56382e7 | − | 1.20764e7i | −1.45695 | − | 0.686269i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.41583e6 | −0.192892 | ||||||||
\(794\) | 8.42436e6 | − | 4.59031e6i | 0.474226 | − | 0.258399i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −828512. | + | 1.28415e6i | −0.0463464 | + | 0.0718348i | ||||
\(797\) | − | 1.78683e7i | − | 0.996409i | −0.867060 | − | 0.498204i | \(-0.833993\pi\) | ||
0.867060 | − | 0.498204i | \(-0.166007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.20602e7i | 1.77664i | ||||||||
\(800\) | −8.09903e6 | + | 1.07192e7i | −0.447412 | + | 0.592159i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.22215e7 | + | 2.24295e7i | 0.670948 | + | 1.23135i | ||||
\(803\) | 6.98282e6 | 0.382157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.54603e6 | + | 2.61235e6i | 0.301643 | + | 0.142083i | ||||
\(806\) | −1.62171e6 | + | 883644.i | −0.0879294 | + | 0.0479115i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.20815e6 | + | 1.62808e7i | −0.0651019 | + | 0.877300i | ||||
\(809\) | −7.98209e6 | −0.428790 | −0.214395 | − | 0.976747i | \(-0.568778\pi\) | ||||
−0.214395 | + | 0.976747i | \(0.568778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.67840e6 | 0.409939 | 0.204969 | − | 0.978768i | \(-0.434291\pi\) | ||||
0.204969 | + | 0.978768i | \(0.434291\pi\) | |||||||
\(812\) | 1.47936e7 | − | 9.22570e6i | 0.787379 | − | 0.491032i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.15089e7 | − | 6.27104e6i | 0.608797 | − | 0.331725i | ||||
\(815\) | −7.26582e6 | −0.383169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.57521e7i | − | 0.825626i | ||||||
\(818\) | −4.52686e6 | + | 2.46662e6i | −0.236545 | + | 0.128890i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.01671e7 | − | 1.57586e7i | 0.528037 | − | 0.818433i | ||||
\(821\) | −2.51595e7 | −1.30270 | −0.651350 | − | 0.758778i | \(-0.725797\pi\) | ||||
−0.651350 | + | 0.758778i | \(0.725797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.68144e7i | − | 1.37997i | −0.723826 | − | 0.689983i | \(-0.757618\pi\) | ||
0.723826 | − | 0.689983i | \(-0.242382\pi\) | |||||||
\(824\) | 4.70016e6 | + | 348786.i | 0.241154 | + | 0.0178954i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 616091. | + | 1.04829e7i | 0.0314192 | + | 0.534601i | ||||
\(827\) | 3.63867e7i | 1.85003i | 0.379932 | + | 0.925014i | \(0.375947\pi\) | ||||
−0.379932 | + | 0.925014i | \(0.624053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.21755e6i | 0.0615318i | 0.999527 | + | 0.0307659i | \(0.00979464\pi\) | ||||
−0.999527 | + | 0.0307659i | \(0.990205\pi\) | |||||||
\(830\) | 9.68461e6 | − | 5.27701e6i | 0.487963 | − | 0.265884i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −871940. | + | 5.84269e6i | −0.0436695 | + | 0.292620i | ||||
\(833\) | 2.71887e7 | − | 2.24576e7i | 1.35761 | − | 1.12137i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.46335e7i | − | 0.726329i | ||||||
\(836\) | −1.05577e7 | − | 6.81162e6i | −0.522460 | − | 0.337081i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −188468. | − | 345885.i | −0.00927101 | − | 0.0170146i | ||||
\(839\) | 2.09675e7 | 1.02835 | 0.514176 | − | 0.857684i | \(-0.328098\pi\) | ||||
0.514176 | + | 0.857684i | \(0.328098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.84945e6 | −0.138922 | ||||||||
\(842\) | 9.79915e6 | + | 1.79839e7i | 0.476330 | + | 0.874183i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.52987e6 | − | 5.50331e6i | −0.412180 | − | 0.265930i | ||||
\(845\) | 9.61652e6i | 0.463315i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.02402e7 | − | 4.82347e6i | −0.490458 | − | 0.231021i | ||||
\(848\) | −8.56666e6 | − | 1.89366e7i | −0.409093 | − | 0.904299i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.41727e7 | + | 1.31714e7i | −1.14757 | + | 0.625293i | ||||
\(851\) | − | 1.42145e7i | − | 0.672833i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.70557e7i | − | 0.802598i | −0.915947 | − | 0.401299i | \(-0.868559\pi\) | ||
0.915947 | − | 0.401299i | \(-0.131441\pi\) | |||||||
\(854\) | −1.38715e7 | + | 815243.i | −0.650845 | + | 0.0382510i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −364932. | + | 4.91775e6i | −0.0170227 | + | 0.229394i | ||||
\(857\) | − | 2.25388e7i | − | 1.04828i | −0.851631 | − | 0.524142i | \(-0.824386\pi\) | ||
0.851631 | − | 0.524142i | \(-0.175614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.25330e7 | 1.50433 | 0.752163 | − | 0.658977i | \(-0.229011\pi\) | ||||
0.752163 | + | 0.658977i | \(0.229011\pi\) | |||||||
\(860\) | 5.36462e6 | − | 8.31491e6i | 0.247339 | − | 0.383364i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.93239e6 | − | 2.14271e6i | 0.180256 | − | 0.0982187i | ||||
\(863\) | 2.91580e7i | 1.33270i | 0.745641 | + | 0.666348i | \(0.232143\pi\) | ||||
−0.745641 | + | 0.666348i | \(0.767857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.05449e6 | 0.0479185 | ||||||||
\(866\) | 1.63490e6 | − | 890833.i | 0.0740792 | − | 0.0403647i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.37473e6 | + | 3.97546e6i | −0.287186 | + | 0.179097i | ||||
\(869\) | −2.42241e7 | −1.08817 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04875e7 | −0.468409 | ||||||||
\(872\) | −8.69891e6 | − | 645522.i | −0.387413 | − | 0.0287488i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.19655e7 | + | 6.51983e6i | −0.529849 | + | 0.288707i | ||||
\(875\) | 8.53707e6 | − | 1.81242e7i | 0.376954 | − | 0.800275i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.01593e7 | −0.885068 | −0.442534 | − | 0.896752i | \(-0.645920\pi\) | ||||
−0.442534 | + | 0.896752i | \(0.645920\pi\) | |||||||
\(878\) | −1.27565e7 | − | 2.34113e7i | −0.558462 | − | 1.02492i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.25319e6 | − | 7.19117e6i | −0.141613 | − | 0.313035i | ||||
\(881\) | 1.13630e7i | 0.493235i | 0.969113 | + | 0.246618i | \(0.0793192\pi\) | ||||
−0.969113 | + | 0.246618i | \(0.920681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.80949e7i | 1.64424i | 0.569314 | + | 0.822120i | \(0.307209\pi\) | ||||
−0.569314 | + | 0.822120i | \(0.692791\pi\) | |||||||
\(884\) | −6.56222e6 | + | 1.01711e7i | −0.282436 | + | 0.437763i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.19901e7 | + | 6.53325e6i | −0.513144 | + | 0.279605i | ||||
\(887\) | −2.78544e7 | −1.18873 | −0.594366 | − | 0.804195i | \(-0.702597\pi\) | ||||
−0.594366 | + | 0.804195i | \(0.702597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.87846e6 | + | 8.23399e6i | −0.164590 | + | 0.349426i | ||||
\(890\) | 2.45438e6 | + | 4.50439e6i | 0.103864 | + | 0.190617i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.32712e6 | + | 1.13567e7i | −0.308334 | + | 0.477903i | ||||
\(893\) | 2.20935e7 | 0.927120 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.06378e6 | −0.169579 | ||||||||
\(896\) | −2.14644e6 | + | 2.39348e7i | −0.0893199 | + | 0.996003i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.81846e6 | − | 1.43488e7i | −0.323542 | − | 0.593779i | ||||
\(899\) | −7.61063e6 | −0.314066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 4.25871e7i | − | 1.74770i | ||||||
\(902\) | −1.51750e7 | − | 2.78499e7i | −0.621029 | − | 1.13974i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.94627e7 | + | 2.92841e6i | 1.60607 | + | 0.119182i | ||||
\(905\) | 1.33682e7 | 0.542566 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.46521e7i | − | 0.995028i | −0.867456 | − | 0.497514i | \(-0.834246\pi\) | ||
0.867456 | − | 0.497514i | \(-0.165754\pi\) | |||||||
\(908\) | 6.64476e6 | − | 1.02991e7i | 0.267463 | − | 0.414556i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −220174. | − | 3.74629e6i | −0.00881380 | − | 0.149968i | ||||
\(911\) | 7.97197e6i | 0.318251i | 0.987258 | + | 0.159125i | \(0.0508674\pi\) | ||||
−0.987258 | + | 0.159125i | \(0.949133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.86519e7i | − | 0.740536i | ||||||
\(914\) | 1.03122e7 | + | 1.89255e7i | 0.408307 | + | 0.749344i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.30232e7 | − | 1.48541e7i | −0.906625 | − | 0.584937i | ||||
\(917\) | −7.42392e6 | − | 3.49689e6i | −0.291548 | − | 0.137328i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.11031e7i | 0.824248i | 0.911128 | + | 0.412124i | \(0.135213\pi\) | ||||
−0.911128 | + | 0.412124i | \(0.864787\pi\) | |||||||
\(920\) | −8.53655e6 | − | 633473.i | −0.332516 | − | 0.0246751i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.63480e7 | + | 1.43567e7i | −1.02075 | + | 0.556194i | ||||
\(923\) | 8.25819e6 | 0.319066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.97890e7 | −0.760449 | ||||||||
\(926\) | 2.30337e7 | − | 1.25507e7i | 0.882746 | − | 0.480996i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.46754e7 | + | 1.94232e7i | −0.559398 | + | 0.740373i | ||||
\(929\) | − | 8.47045e6i | − | 0.322009i | −0.986954 | − | 0.161004i | \(-0.948527\pi\) | ||
0.986954 | − | 0.161004i | \(-0.0514733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.54761e7 | − | 1.87365e7i | −0.585177 | − | 0.708457i | ||||
\(932\) | −5.63020e6 | + | 8.72656e6i | −0.212317 | + | 0.329081i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.20044e6 | − | 9.54410e6i | −0.195062 | − | 0.357987i | ||||
\(935\) | − | 1.61724e7i | − | 0.604988i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.95834e7i | − | 1.10077i | −0.834909 | − | 0.550387i | \(-0.814480\pi\) | ||
0.834909 | − | 0.550387i | \(-0.185520\pi\) | |||||||
\(938\) | −4.25889e7 | + | 2.50300e6i | −1.58048 | + | 0.0928868i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.16623e7 | + | 7.52428e6i | 0.430491 | + | 0.277744i | ||||
\(941\) | − | 3.62480e7i | − | 1.33447i | −0.744846 | − | 0.667237i | \(-0.767477\pi\) | ||
0.744846 | − | 0.667237i | \(-0.232523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.43970e7 | −1.25962 | ||||||||
\(944\) | −6.04348e6 | − | 1.33591e7i | −0.220728 | − | 0.487918i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00697e6 | − | 1.46948e7i | −0.290898 | − | 0.533869i | ||||
\(947\) | 2.19768e7i | 0.796322i | 0.917316 | + | 0.398161i | \(0.130351\pi\) | ||||
−0.917316 | + | 0.398161i | \(0.869649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.63586e6 | −0.167096 | ||||||||
\(950\) | 9.07673e6 | + | 1.66580e7i | 0.326303 | + | 0.598846i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.42212e7 | + | 4.28704e7i | −0.866170 | + | 1.53308i | ||||
\(953\) | −2.02983e7 | −0.723982 | −0.361991 | − | 0.932182i | \(-0.617903\pi\) | ||||
−0.361991 | + | 0.932182i | \(0.617903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −643936. | −0.0228473 | ||||||||
\(956\) | 5.75792e6 | + | 3.71489e6i | 0.203761 | + | 0.131462i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.41691e7 | + | 2.60038e7i | 0.498802 | + | 0.915425i | ||||
\(959\) | −87905.9 | − | 41406.3i | −0.00308654 | − | 0.00145385i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.53496e7 | −0.885449 | ||||||||
\(962\) | −7.64070e6 | + | 4.16331e6i | −0.266192 | + | 0.145044i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.17574e7 | + | 7.58567e6i | 0.407493 | + | 0.262906i | ||||
\(965\) | − | 5.44602e6i | − | 0.188261i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.30270e6i | 0.285531i | 0.989757 | + | 0.142765i | \(0.0455995\pi\) | ||||
−0.989757 | + | 0.142765i | \(0.954401\pi\) | |||||||
\(968\) | 1.57620e7 | + | 1.16965e6i | 0.540657 | + | 0.0401206i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.54143e6 | + | 1.56756e7i | 0.291475 | + | 0.534928i | ||||
\(971\) | −3.20554e7 | −1.09107 | −0.545536 | − | 0.838088i | \(-0.683674\pi\) | ||||
−0.545536 | + | 0.838088i | \(0.683674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.97224e7 | + | 1.87105e7i | 1.34510 | + | 0.633581i | ||||
\(974\) | 2.47506e7 | − | 1.34863e7i | 0.835967 | − | 0.455507i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.76774e7 | − | 7.99704e6i | 0.594012 | − | 0.268723i | ||||
\(977\) | −5.73398e7 | −1.92185 | −0.960926 | − | 0.276806i | \(-0.910724\pi\) | ||||
−0.960926 | + | 0.276806i | \(0.910724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.67515e6 | 0.289281 | ||||||||
\(980\) | −1.78822e6 | − | 1.51609e7i | −0.0594780 | − | 0.504265i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.22620e7 | + | 1.21303e7i | −0.736692 | + | 0.401413i | ||||
\(983\) | 2.32471e7 | 0.767335 | 0.383668 | − | 0.923471i | \(-0.374661\pi\) | ||||
0.383668 | + | 0.923471i | \(0.374661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.59867e6i | − | 0.118182i | ||||||
\(986\) | −4.38009e7 | + | 2.38665e7i | −1.43480 | + | 0.781800i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00920e6 | + | 4.52220e6i | 0.228442 | + | 0.147386i | ||||
\(989\) | −1.81493e7 | −0.590024 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.54996e7i | − | 0.501343i | −0.968072 | − | 0.250672i | \(-0.919349\pi\) | ||
0.968072 | − | 0.250672i | \(-0.0806515\pi\) | |||||||
\(992\) | 6.32381e6 | − | 8.36968e6i | 0.204033 | − | 0.270041i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.35359e7 | − | 1.97095e6i | 1.07658 | − | 0.0632717i | ||||
\(995\) | 1.35557e6i | 0.0434075i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.02461e7i | − | 0.326452i | −0.986589 | − | 0.163226i | \(-0.947810\pi\) | ||
0.986589 | − | 0.163226i | \(-0.0521900\pi\) | |||||||
\(998\) | −4.34462e7 | + | 2.36732e7i | −1.38078 | + | 0.752370i | ||||
\(999\) | 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 | 252.6.b.d.55.6 | 16 | ||
3.2 | odd | 2 | 28.6.d.b.27.11 | yes | 16 | ||
4.3 | odd | 2 | inner | 252.6.b.d.55.8 | 16 | ||
7.6 | odd | 2 | inner | 252.6.b.d.55.5 | 16 | ||
12.11 | even | 2 | 28.6.d.b.27.10 | yes | 16 | ||
21.20 | even | 2 | 28.6.d.b.27.12 | yes | 16 | ||
24.5 | odd | 2 | 448.6.f.d.447.14 | 16 | |||
24.11 | even | 2 | 448.6.f.d.447.4 | 16 | |||
28.27 | even | 2 | inner | 252.6.b.d.55.7 | 16 | ||
84.83 | odd | 2 | 28.6.d.b.27.9 | ✓ | 16 | ||
168.83 | odd | 2 | 448.6.f.d.447.13 | 16 | |||
168.125 | even | 2 | 448.6.f.d.447.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.d.b.27.9 | ✓ | 16 | 84.83 | odd | 2 | ||
28.6.d.b.27.10 | yes | 16 | 12.11 | even | 2 | ||
28.6.d.b.27.11 | yes | 16 | 3.2 | odd | 2 | ||
28.6.d.b.27.12 | yes | 16 | 21.20 | even | 2 | ||
252.6.b.d.55.5 | 16 | 7.6 | odd | 2 | inner | ||
252.6.b.d.55.6 | 16 | 1.1 | even | 1 | trivial | ||
252.6.b.d.55.7 | 16 | 28.27 | even | 2 | inner | ||
252.6.b.d.55.8 | 16 | 4.3 | odd | 2 | inner | ||
448.6.f.d.447.3 | 16 | 168.125 | even | 2 | |||
448.6.f.d.447.4 | 16 | 24.11 | even | 2 | |||
448.6.f.d.447.13 | 16 | 168.83 | odd | 2 | |||
448.6.f.d.447.14 | 16 | 24.5 | odd | 2 |