Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(28.3879361069\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + 3566264 x^{5} + 15496192 x^{4} - 53008480 x^{3} - 16576192 x^{2} + \cdots - 50564480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-10.7661\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7661 | 1.90320 | 0.951601 | − | 0.307335i | \(-0.0994373\pi\) | ||||
0.951601 | + | 0.307335i | \(0.0994373\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 83.9098 | 2.62218 | ||||||||
\(5\) | −60.5969 | −1.08399 | −0.541995 | − | 0.840382i | \(-0.682331\pi\) | ||||
−0.541995 | + | 0.840382i | \(0.682331\pi\) | |||||||
\(6\) | −96.8953 | −1.09881 | ||||||||
\(7\) | −233.164 | −1.79853 | −0.899263 | − | 0.437409i | \(-0.855896\pi\) | ||||
−0.899263 | + | 0.437409i | \(0.855896\pi\) | |||||||
\(8\) | 558.868 | 3.08734 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −652.394 | −2.06305 | ||||||||
\(11\) | 441.792 | 1.10087 | 0.550435 | − | 0.834878i | \(-0.314462\pi\) | ||||
0.550435 | + | 0.834878i | \(0.314462\pi\) | |||||||
\(12\) | −755.188 | −1.51392 | ||||||||
\(13\) | −615.817 | −1.01063 | −0.505316 | − | 0.862934i | \(-0.668624\pi\) | ||||
−0.505316 | + | 0.862934i | \(0.668624\pi\) | |||||||
\(14\) | −2510.28 | −3.42296 | ||||||||
\(15\) | 545.372 | 0.625842 | ||||||||
\(16\) | 3331.74 | 3.25365 | ||||||||
\(17\) | −1491.95 | −1.25208 | −0.626042 | − | 0.779789i | \(-0.715326\pi\) | ||||
−0.626042 | + | 0.779789i | \(0.715326\pi\) | |||||||
\(18\) | 872.057 | 0.634401 | ||||||||
\(19\) | −1189.53 | −0.755946 | −0.377973 | − | 0.925817i | \(-0.623379\pi\) | ||||
−0.377973 | + | 0.925817i | \(0.623379\pi\) | |||||||
\(20\) | −5084.67 | −2.84242 | ||||||||
\(21\) | 2098.48 | 1.03838 | ||||||||
\(22\) | 4756.40 | 2.09518 | ||||||||
\(23\) | −4791.05 | −1.88848 | −0.944238 | − | 0.329265i | \(-0.893199\pi\) | ||||
−0.944238 | + | 0.329265i | \(0.893199\pi\) | |||||||
\(24\) | −5029.81 | −1.78247 | ||||||||
\(25\) | 546.980 | 0.175033 | ||||||||
\(26\) | −6629.97 | −1.92344 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −19564.7 | −4.71606 | ||||||||
\(29\) | −4769.56 | −1.05313 | −0.526566 | − | 0.850134i | \(-0.676521\pi\) | ||||
−0.526566 | + | 0.850134i | \(0.676521\pi\) | |||||||
\(30\) | 5871.55 | 1.19110 | ||||||||
\(31\) | 6722.80 | 1.25645 | 0.628226 | − | 0.778031i | \(-0.283781\pi\) | ||||
0.628226 | + | 0.778031i | \(0.283781\pi\) | |||||||
\(32\) | 17986.2 | 3.10501 | ||||||||
\(33\) | −3976.13 | −0.635588 | ||||||||
\(34\) | −16062.6 | −2.38297 | ||||||||
\(35\) | 14129.0 | 1.94958 | ||||||||
\(36\) | 6796.69 | 0.874060 | ||||||||
\(37\) | 3091.95 | 0.371302 | 0.185651 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185651 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(38\) | −12806.6 | −1.43872 | ||||||||
\(39\) | 5542.35 | 0.583489 | ||||||||
\(40\) | −33865.6 | −3.34664 | ||||||||
\(41\) | 16633.3 | 1.54532 | 0.772661 | − | 0.634819i | \(-0.218925\pi\) | ||||
0.772661 | + | 0.634819i | \(0.218925\pi\) | |||||||
\(42\) | 22592.5 | 1.97625 | ||||||||
\(43\) | 16690.1 | 1.37654 | 0.688268 | − | 0.725456i | \(-0.258371\pi\) | ||||
0.688268 | + | 0.725456i | \(0.258371\pi\) | |||||||
\(44\) | 37070.7 | 2.88668 | ||||||||
\(45\) | −4908.35 | −0.361330 | ||||||||
\(46\) | −51581.1 | −3.59415 | ||||||||
\(47\) | −5195.02 | −0.343038 | −0.171519 | − | 0.985181i | \(-0.554868\pi\) | ||||
−0.171519 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(48\) | −29985.6 | −1.87849 | ||||||||
\(49\) | 37558.5 | 2.23469 | ||||||||
\(50\) | 5888.86 | 0.333124 | ||||||||
\(51\) | 13427.6 | 0.722891 | ||||||||
\(52\) | −51673.0 | −2.65006 | ||||||||
\(53\) | −4994.59 | −0.244236 | −0.122118 | − | 0.992516i | \(-0.538969\pi\) | ||||
−0.122118 | + | 0.992516i | \(0.538969\pi\) | |||||||
\(54\) | −7848.52 | −0.366272 | ||||||||
\(55\) | −26771.2 | −1.19333 | ||||||||
\(56\) | −130308. | −5.55265 | ||||||||
\(57\) | 10705.8 | 0.436446 | ||||||||
\(58\) | −51349.7 | −2.00432 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 45762.0 | 1.64107 | ||||||||
\(61\) | −41246.4 | −1.41926 | −0.709630 | − | 0.704575i | \(-0.751138\pi\) | ||||
−0.709630 | + | 0.704575i | \(0.751138\pi\) | |||||||
\(62\) | 72378.6 | 2.39128 | ||||||||
\(63\) | −18886.3 | −0.599508 | ||||||||
\(64\) | 87026.0 | 2.65582 | ||||||||
\(65\) | 37316.6 | 1.09551 | ||||||||
\(66\) | −42807.6 | −1.20965 | ||||||||
\(67\) | 41332.6 | 1.12488 | 0.562439 | − | 0.826838i | \(-0.309863\pi\) | ||||
0.562439 | + | 0.826838i | \(0.309863\pi\) | |||||||
\(68\) | −125190. | −3.28319 | ||||||||
\(69\) | 43119.5 | 1.09031 | ||||||||
\(70\) | 152115. | 3.71045 | ||||||||
\(71\) | −3791.51 | −0.0892618 | −0.0446309 | − | 0.999004i | \(-0.514211\pi\) | ||||
−0.0446309 | + | 0.999004i | \(0.514211\pi\) | |||||||
\(72\) | 45268.3 | 1.02911 | ||||||||
\(73\) | −15511.7 | −0.340685 | −0.170343 | − | 0.985385i | \(-0.554487\pi\) | ||||
−0.170343 | + | 0.985385i | \(0.554487\pi\) | |||||||
\(74\) | 33288.3 | 0.706663 | ||||||||
\(75\) | −4922.82 | −0.101056 | ||||||||
\(76\) | −99813.1 | −1.98223 | ||||||||
\(77\) | −103010. | −1.97994 | ||||||||
\(78\) | 59669.7 | 1.11050 | ||||||||
\(79\) | 6475.81 | 0.116742 | 0.0583709 | − | 0.998295i | \(-0.481409\pi\) | ||||
0.0583709 | + | 0.998295i | \(0.481409\pi\) | |||||||
\(80\) | −201893. | −3.52692 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 179076. | 2.94106 | ||||||||
\(83\) | −20354.7 | −0.324318 | −0.162159 | − | 0.986765i | \(-0.551846\pi\) | ||||
−0.162159 | + | 0.986765i | \(0.551846\pi\) | |||||||
\(84\) | 176083. | 2.72282 | ||||||||
\(85\) | 90407.8 | 1.35725 | ||||||||
\(86\) | 179688. | 2.61983 | ||||||||
\(87\) | 42926.0 | 0.608026 | ||||||||
\(88\) | 246903. | 3.39876 | ||||||||
\(89\) | 35567.6 | 0.475970 | 0.237985 | − | 0.971269i | \(-0.423513\pi\) | ||||
0.237985 | + | 0.971269i | \(0.423513\pi\) | |||||||
\(90\) | −52843.9 | −0.687684 | ||||||||
\(91\) | 143586. | 1.81765 | ||||||||
\(92\) | −402016. | −4.95192 | ||||||||
\(93\) | −60505.2 | −0.725413 | ||||||||
\(94\) | −55930.3 | −0.652871 | ||||||||
\(95\) | 72081.7 | 0.819438 | ||||||||
\(96\) | −161875. | −1.79268 | ||||||||
\(97\) | −18405.4 | −0.198616 | −0.0993082 | − | 0.995057i | \(-0.531663\pi\) | ||||
−0.0993082 | + | 0.995057i | \(0.531663\pi\) | |||||||
\(98\) | 404360. | 4.25307 | ||||||||
\(99\) | 35785.2 | 0.366957 | ||||||||
\(100\) | 45896.9 | 0.458969 | ||||||||
\(101\) | 77102.1 | 0.752078 | 0.376039 | − | 0.926604i | \(-0.377286\pi\) | ||||
0.376039 | + | 0.926604i | \(0.377286\pi\) | |||||||
\(102\) | 144563. | 1.37581 | ||||||||
\(103\) | −192261. | −1.78566 | −0.892829 | − | 0.450395i | \(-0.851283\pi\) | ||||
−0.892829 | + | 0.450395i | \(0.851283\pi\) | |||||||
\(104\) | −344160. | −3.12016 | ||||||||
\(105\) | −127161. | −1.12559 | ||||||||
\(106\) | −53772.4 | −0.464831 | ||||||||
\(107\) | −52637.5 | −0.444463 | −0.222232 | − | 0.974994i | \(-0.571334\pi\) | ||||
−0.222232 | + | 0.974994i | \(0.571334\pi\) | |||||||
\(108\) | −61170.2 | −0.504639 | ||||||||
\(109\) | −192595. | −1.55267 | −0.776334 | − | 0.630322i | \(-0.782923\pi\) | ||||
−0.776334 | + | 0.630322i | \(0.782923\pi\) | |||||||
\(110\) | −288223. | −2.27115 | ||||||||
\(111\) | −27827.5 | −0.214371 | ||||||||
\(112\) | −776841. | −5.85177 | ||||||||
\(113\) | 84620.6 | 0.623419 | 0.311709 | − | 0.950177i | \(-0.399098\pi\) | ||||
0.311709 | + | 0.950177i | \(0.399098\pi\) | |||||||
\(114\) | 115260. | 0.830645 | ||||||||
\(115\) | 290323. | 2.04709 | ||||||||
\(116\) | −400212. | −2.76150 | ||||||||
\(117\) | −49881.1 | −0.336877 | ||||||||
\(118\) | −37476.9 | −0.247776 | ||||||||
\(119\) | 347870. | 2.25190 | ||||||||
\(120\) | 304791. | 1.93218 | ||||||||
\(121\) | 34129.4 | 0.211916 | ||||||||
\(122\) | −444065. | −2.70114 | ||||||||
\(123\) | −149700. | −0.892192 | ||||||||
\(124\) | 564109. | 3.29464 | ||||||||
\(125\) | 156220. | 0.894255 | ||||||||
\(126\) | −203332. | −1.14099 | ||||||||
\(127\) | −42822.7 | −0.235594 | −0.117797 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117797 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(128\) | 361377. | 1.94955 | ||||||||
\(129\) | −150211. | −0.794744 | ||||||||
\(130\) | 401755. | 2.08499 | ||||||||
\(131\) | −165092. | −0.840519 | −0.420260 | − | 0.907404i | \(-0.638061\pi\) | ||||
−0.420260 | + | 0.907404i | \(0.638061\pi\) | |||||||
\(132\) | −333636. | −1.66663 | ||||||||
\(133\) | 277355. | 1.35959 | ||||||||
\(134\) | 444993. | 2.14087 | ||||||||
\(135\) | 44175.1 | 0.208614 | ||||||||
\(136\) | −833805. | −3.86560 | ||||||||
\(137\) | 76275.0 | 0.347201 | 0.173600 | − | 0.984816i | \(-0.444460\pi\) | ||||
0.173600 | + | 0.984816i | \(0.444460\pi\) | |||||||
\(138\) | 464230. | 2.07508 | ||||||||
\(139\) | −401114. | −1.76088 | −0.880441 | − | 0.474155i | \(-0.842754\pi\) | ||||
−0.880441 | + | 0.474155i | \(0.842754\pi\) | |||||||
\(140\) | 1.18556e6 | 5.11216 | ||||||||
\(141\) | 46755.2 | 0.198053 | ||||||||
\(142\) | −40819.9 | −0.169883 | ||||||||
\(143\) | −272063. | −1.11258 | ||||||||
\(144\) | 269871. | 1.08455 | ||||||||
\(145\) | 289020. | 1.14158 | ||||||||
\(146\) | −167002. | −0.648393 | ||||||||
\(147\) | −338026. | −1.29020 | ||||||||
\(148\) | 259444. | 0.973621 | ||||||||
\(149\) | 97892.0 | 0.361228 | 0.180614 | − | 0.983554i | \(-0.442192\pi\) | ||||
0.180614 | + | 0.983554i | \(0.442192\pi\) | |||||||
\(150\) | −52999.7 | −0.192329 | ||||||||
\(151\) | 165925. | 0.592202 | 0.296101 | − | 0.955157i | \(-0.404313\pi\) | ||||
0.296101 | + | 0.955157i | \(0.404313\pi\) | |||||||
\(152\) | −664789. | −2.33386 | ||||||||
\(153\) | −120848. | −0.417361 | ||||||||
\(154\) | −1.10902e6 | −3.76823 | ||||||||
\(155\) | −407381. | −1.36198 | ||||||||
\(156\) | 465057. | 1.53001 | ||||||||
\(157\) | −176014. | −0.569899 | −0.284950 | − | 0.958542i | \(-0.591977\pi\) | ||||
−0.284950 | + | 0.958542i | \(0.591977\pi\) | |||||||
\(158\) | 69719.4 | 0.222183 | ||||||||
\(159\) | 44951.3 | 0.141010 | ||||||||
\(160\) | −1.08990e6 | −3.36580 | ||||||||
\(161\) | 1.11710e6 | 3.39647 | ||||||||
\(162\) | 70636.6 | 0.211467 | ||||||||
\(163\) | −139166. | −0.410263 | −0.205132 | − | 0.978734i | \(-0.565762\pi\) | ||||
−0.205132 | + | 0.978734i | \(0.565762\pi\) | |||||||
\(164\) | 1.39570e6 | 4.05211 | ||||||||
\(165\) | 240941. | 0.688971 | ||||||||
\(166\) | −219142. | −0.617242 | ||||||||
\(167\) | −20633.9 | −0.0572518 | −0.0286259 | − | 0.999590i | \(-0.509113\pi\) | ||||
−0.0286259 | + | 0.999590i | \(0.509113\pi\) | |||||||
\(168\) | 1.17277e6 | 3.20583 | ||||||||
\(169\) | 7937.10 | 0.0213769 | ||||||||
\(170\) | 973343. | 2.58311 | ||||||||
\(171\) | −96351.8 | −0.251982 | ||||||||
\(172\) | 1.40046e6 | 3.60953 | ||||||||
\(173\) | −460281. | −1.16925 | −0.584626 | − | 0.811303i | \(-0.698759\pi\) | ||||
−0.584626 | + | 0.811303i | \(0.698759\pi\) | |||||||
\(174\) | 462147. | 1.15720 | ||||||||
\(175\) | −127536. | −0.314802 | ||||||||
\(176\) | 1.47193e6 | 3.58185 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | 382925. | 0.905866 | ||||||||
\(179\) | −51633.5 | −0.120448 | −0.0602239 | − | 0.998185i | \(-0.519181\pi\) | ||||
−0.0602239 | + | 0.998185i | \(0.519181\pi\) | |||||||
\(180\) | −411858. | −0.947472 | ||||||||
\(181\) | 312077. | 0.708052 | 0.354026 | − | 0.935236i | \(-0.384812\pi\) | ||||
0.354026 | + | 0.935236i | \(0.384812\pi\) | |||||||
\(182\) | 1.54587e6 | 3.45935 | ||||||||
\(183\) | 371218. | 0.819410 | ||||||||
\(184\) | −2.67756e6 | −5.83036 | ||||||||
\(185\) | −187362. | −0.402488 | ||||||||
\(186\) | −651407. | −1.38061 | ||||||||
\(187\) | −659134. | −1.37838 | ||||||||
\(188\) | −435913. | −0.899508 | ||||||||
\(189\) | 169977. | 0.346126 | ||||||||
\(190\) | 776042. | 1.55956 | ||||||||
\(191\) | −818682. | −1.62380 | −0.811899 | − | 0.583798i | \(-0.801566\pi\) | ||||
−0.811899 | + | 0.583798i | \(0.801566\pi\) | |||||||
\(192\) | −783234. | −1.53334 | ||||||||
\(193\) | −29498.1 | −0.0570034 | −0.0285017 | − | 0.999594i | \(-0.509074\pi\) | ||||
−0.0285017 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(194\) | −198155. | −0.378007 | ||||||||
\(195\) | −335849. | −0.632496 | ||||||||
\(196\) | 3.15152e6 | 5.85977 | ||||||||
\(197\) | 608501. | 1.11711 | 0.558555 | − | 0.829467i | \(-0.311356\pi\) | ||||
0.558555 | + | 0.829467i | \(0.311356\pi\) | |||||||
\(198\) | 385268. | 0.698393 | ||||||||
\(199\) | −452321. | −0.809681 | −0.404840 | − | 0.914387i | \(-0.632673\pi\) | ||||
−0.404840 | + | 0.914387i | \(0.632673\pi\) | |||||||
\(200\) | 305689. | 0.540387 | ||||||||
\(201\) | −371993. | −0.649449 | ||||||||
\(202\) | 830092. | 1.43136 | ||||||||
\(203\) | 1.11209e6 | 1.89409 | ||||||||
\(204\) | 1.12671e6 | 1.89555 | ||||||||
\(205\) | −1.00793e6 | −1.67511 | ||||||||
\(206\) | −2.06991e6 | −3.39847 | ||||||||
\(207\) | −388075. | −0.629492 | ||||||||
\(208\) | −2.05174e6 | −3.28824 | ||||||||
\(209\) | −525524. | −0.832199 | ||||||||
\(210\) | −1.36903e6 | −2.14223 | ||||||||
\(211\) | 29005.8 | 0.0448516 | 0.0224258 | − | 0.999749i | \(-0.492861\pi\) | ||||
0.0224258 | + | 0.999749i | \(0.492861\pi\) | |||||||
\(212\) | −419095. | −0.640431 | ||||||||
\(213\) | 34123.5 | 0.0515353 | ||||||||
\(214\) | −566703. | −0.845903 | ||||||||
\(215\) | −1.01137e6 | −1.49215 | ||||||||
\(216\) | −407415. | −0.594158 | ||||||||
\(217\) | −1.56752e6 | −2.25976 | ||||||||
\(218\) | −2.07350e6 | −2.95504 | ||||||||
\(219\) | 139606. | 0.196695 | ||||||||
\(220\) | −2.24637e6 | −3.12913 | ||||||||
\(221\) | 918771. | 1.26540 | ||||||||
\(222\) | −299595. | −0.407992 | ||||||||
\(223\) | 917713. | 1.23579 | 0.617895 | − | 0.786260i | \(-0.287986\pi\) | ||||
0.617895 | + | 0.786260i | \(0.287986\pi\) | |||||||
\(224\) | −4.19373e6 | −5.58444 | ||||||||
\(225\) | 44305.3 | 0.0583445 | ||||||||
\(226\) | 911037. | 1.18649 | ||||||||
\(227\) | −888321. | −1.14421 | −0.572104 | − | 0.820181i | \(-0.693873\pi\) | ||||
−0.572104 | + | 0.820181i | \(0.693873\pi\) | |||||||
\(228\) | 898318. | 1.14444 | ||||||||
\(229\) | −613349. | −0.772892 | −0.386446 | − | 0.922312i | \(-0.626297\pi\) | ||||
−0.386446 | + | 0.922312i | \(0.626297\pi\) | |||||||
\(230\) | 3.12565e6 | 3.89602 | ||||||||
\(231\) | 927091. | 1.14312 | ||||||||
\(232\) | −2.66555e6 | −3.25138 | ||||||||
\(233\) | −460846. | −0.556116 | −0.278058 | − | 0.960564i | \(-0.589691\pi\) | ||||
−0.278058 | + | 0.960564i | \(0.589691\pi\) | |||||||
\(234\) | −537027. | −0.641146 | ||||||||
\(235\) | 314802. | 0.371850 | ||||||||
\(236\) | −292090. | −0.341379 | ||||||||
\(237\) | −58282.3 | −0.0674009 | ||||||||
\(238\) | 3.74522e6 | 4.28583 | ||||||||
\(239\) | 1.00128e6 | 1.13387 | 0.566934 | − | 0.823763i | \(-0.308129\pi\) | ||||
0.566934 | + | 0.823763i | \(0.308129\pi\) | |||||||
\(240\) | 1.81703e6 | 2.03627 | ||||||||
\(241\) | −350750. | −0.389005 | −0.194502 | − | 0.980902i | \(-0.562309\pi\) | ||||
−0.194502 | + | 0.980902i | \(0.562309\pi\) | |||||||
\(242\) | 367441. | 0.403320 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −3.46098e6 | −3.72156 | ||||||||
\(245\) | −2.27593e6 | −2.42238 | ||||||||
\(246\) | −1.61169e6 | −1.69802 | ||||||||
\(247\) | 732531. | 0.763983 | ||||||||
\(248\) | 3.75716e6 | 3.87909 | ||||||||
\(249\) | 183193. | 0.187245 | ||||||||
\(250\) | 1.68189e6 | 1.70195 | ||||||||
\(251\) | 1.91311e6 | 1.91671 | 0.958353 | − | 0.285585i | \(-0.0921878\pi\) | ||||
0.958353 | + | 0.285585i | \(0.0921878\pi\) | |||||||
\(252\) | −1.58474e6 | −1.57202 | ||||||||
\(253\) | −2.11665e6 | −2.07897 | ||||||||
\(254\) | −461035. | −0.448383 | ||||||||
\(255\) | −813670. | −0.783606 | ||||||||
\(256\) | 1.10580e6 | 1.05457 | ||||||||
\(257\) | 834372. | 0.788001 | 0.394001 | − | 0.919110i | \(-0.371091\pi\) | ||||
0.394001 | + | 0.919110i | \(0.371091\pi\) | |||||||
\(258\) | −1.61719e6 | −1.51256 | ||||||||
\(259\) | −720930. | −0.667796 | ||||||||
\(260\) | 3.13122e6 | 2.87264 | ||||||||
\(261\) | −386334. | −0.351044 | ||||||||
\(262\) | −1.77740e6 | −1.59968 | ||||||||
\(263\) | −295137. | −0.263108 | −0.131554 | − | 0.991309i | \(-0.541997\pi\) | ||||
−0.131554 | + | 0.991309i | \(0.541997\pi\) | |||||||
\(264\) | −2.22213e6 | −1.96227 | ||||||||
\(265\) | 302656. | 0.264750 | ||||||||
\(266\) | 2.98605e6 | 2.58757 | ||||||||
\(267\) | −320108. | −0.274801 | ||||||||
\(268\) | 3.46821e6 | 2.94964 | ||||||||
\(269\) | 308327. | 0.259795 | 0.129897 | − | 0.991527i | \(-0.458535\pi\) | ||||
0.129897 | + | 0.991527i | \(0.458535\pi\) | |||||||
\(270\) | 475595. | 0.397034 | ||||||||
\(271\) | 1.89619e6 | 1.56840 | 0.784202 | − | 0.620506i | \(-0.213073\pi\) | ||||
0.784202 | + | 0.620506i | \(0.213073\pi\) | |||||||
\(272\) | −4.97080e6 | −4.07384 | ||||||||
\(273\) | −1.29228e6 | −1.04942 | ||||||||
\(274\) | 821187. | 0.660793 | ||||||||
\(275\) | 241651. | 0.192689 | ||||||||
\(276\) | 3.61814e6 | 2.85899 | ||||||||
\(277\) | −37822.4 | −0.0296176 | −0.0148088 | − | 0.999890i | \(-0.504714\pi\) | ||||
−0.0148088 | + | 0.999890i | \(0.504714\pi\) | |||||||
\(278\) | −4.31845e6 | −3.35132 | ||||||||
\(279\) | 544547. | 0.418817 | ||||||||
\(280\) | 7.89625e6 | 6.01902 | ||||||||
\(281\) | 1.67537e6 | 1.26574 | 0.632871 | − | 0.774258i | \(-0.281876\pi\) | ||||
0.632871 | + | 0.774258i | \(0.281876\pi\) | |||||||
\(282\) | 503373. | 0.376935 | ||||||||
\(283\) | 23322.7 | 0.0173106 | 0.00865530 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865530 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(284\) | −318144. | −0.234061 | ||||||||
\(285\) | −648735. | −0.473103 | ||||||||
\(286\) | −2.92907e6 | −2.11746 | ||||||||
\(287\) | −3.87829e6 | −2.77930 | ||||||||
\(288\) | 1.45688e6 | 1.03500 | ||||||||
\(289\) | 806072. | 0.567714 | ||||||||
\(290\) | 3.11163e6 | 2.17267 | ||||||||
\(291\) | 165648. | 0.114671 | ||||||||
\(292\) | −1.30159e6 | −0.893338 | ||||||||
\(293\) | −1.04372e6 | −0.710259 | −0.355130 | − | 0.934817i | \(-0.615563\pi\) | ||||
−0.355130 | + | 0.934817i | \(0.615563\pi\) | |||||||
\(294\) | −3.63924e6 | −2.45551 | ||||||||
\(295\) | 210938. | 0.141123 | ||||||||
\(296\) | 1.72799e6 | 1.14633 | ||||||||
\(297\) | −322067. | −0.211863 | ||||||||
\(298\) | 1.05392e6 | 0.687490 | ||||||||
\(299\) | 2.95041e6 | 1.90855 | ||||||||
\(300\) | −413072. | −0.264986 | ||||||||
\(301\) | −3.89153e6 | −2.47574 | ||||||||
\(302\) | 1.78637e6 | 1.12708 | ||||||||
\(303\) | −693919. | −0.434212 | ||||||||
\(304\) | −3.96319e6 | −2.45958 | ||||||||
\(305\) | 2.49941e6 | 1.53846 | ||||||||
\(306\) | −1.30107e6 | −0.794323 | ||||||||
\(307\) | −99932.3 | −0.0605146 | −0.0302573 | − | 0.999542i | \(-0.509633\pi\) | ||||
−0.0302573 | + | 0.999542i | \(0.509633\pi\) | |||||||
\(308\) | −8.64355e6 | −5.19177 | ||||||||
\(309\) | 1.73035e6 | 1.03095 | ||||||||
\(310\) | −4.38592e6 | −2.59213 | ||||||||
\(311\) | −1.52909e6 | −0.896460 | −0.448230 | − | 0.893918i | \(-0.647945\pi\) | ||||
−0.448230 | + | 0.893918i | \(0.647945\pi\) | |||||||
\(312\) | 3.09744e6 | 1.80143 | ||||||||
\(313\) | −975618. | −0.562884 | −0.281442 | − | 0.959578i | \(-0.590813\pi\) | ||||
−0.281442 | + | 0.959578i | \(0.590813\pi\) | |||||||
\(314\) | −1.89499e6 | −1.08463 | ||||||||
\(315\) | 1.14445e6 | 0.649861 | ||||||||
\(316\) | 543383. | 0.306118 | ||||||||
\(317\) | 302184. | 0.168897 | 0.0844487 | − | 0.996428i | \(-0.473087\pi\) | ||||
0.0844487 | + | 0.996428i | \(0.473087\pi\) | |||||||
\(318\) | 483952. | 0.268370 | ||||||||
\(319\) | −2.10715e6 | −1.15936 | ||||||||
\(320\) | −5.27350e6 | −2.87888 | ||||||||
\(321\) | 473737. | 0.256611 | ||||||||
\(322\) | 1.20269e7 | 6.46417 | ||||||||
\(323\) | 1.77472e6 | 0.946508 | ||||||||
\(324\) | 550532. | 0.291353 | ||||||||
\(325\) | −336839. | −0.176894 | ||||||||
\(326\) | −1.49828e6 | −0.780814 | ||||||||
\(327\) | 1.73335e6 | 0.896433 | ||||||||
\(328\) | 9.29582e6 | 4.77093 | ||||||||
\(329\) | 1.21129e6 | 0.616963 | ||||||||
\(330\) | 2.59400e6 | 1.31125 | ||||||||
\(331\) | −1.49800e6 | −0.751521 | −0.375760 | − | 0.926717i | \(-0.622618\pi\) | ||||
−0.375760 | + | 0.926717i | \(0.622618\pi\) | |||||||
\(332\) | −1.70796e6 | −0.850419 | ||||||||
\(333\) | 250448. | 0.123767 | ||||||||
\(334\) | −222147. | −0.108962 | ||||||||
\(335\) | −2.50463e6 | −1.21936 | ||||||||
\(336\) | 6.99157e6 | 3.37852 | ||||||||
\(337\) | −1.15647e6 | −0.554703 | −0.277352 | − | 0.960769i | \(-0.589457\pi\) | ||||
−0.277352 | + | 0.960769i | \(0.589457\pi\) | |||||||
\(338\) | 85451.9 | 0.0406846 | ||||||||
\(339\) | −761585. | −0.359931 | ||||||||
\(340\) | 7.58609e6 | 3.55894 | ||||||||
\(341\) | 2.97008e6 | 1.38319 | ||||||||
\(342\) | −1.03734e6 | −0.479573 | ||||||||
\(343\) | −4.83850e6 | −2.22063 | ||||||||
\(344\) | 9.32755e6 | 4.24983 | ||||||||
\(345\) | −2.61290e6 | −1.18189 | ||||||||
\(346\) | −4.95545e6 | −2.22532 | ||||||||
\(347\) | −3.05494e6 | −1.36200 | −0.681002 | − | 0.732281i | \(-0.738456\pi\) | ||||
−0.681002 | + | 0.732281i | \(0.738456\pi\) | |||||||
\(348\) | 3.60191e6 | 1.59435 | ||||||||
\(349\) | −1.18451e6 | −0.520566 | −0.260283 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260283 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(350\) | −1.37307e6 | −0.599132 | ||||||||
\(351\) | 448930. | 0.194496 | ||||||||
\(352\) | 7.94615e6 | 3.41822 | ||||||||
\(353\) | 1.37958e6 | 0.589266 | 0.294633 | − | 0.955610i | \(-0.404803\pi\) | ||||
0.294633 | + | 0.955610i | \(0.404803\pi\) | |||||||
\(354\) | 337292. | 0.143053 | ||||||||
\(355\) | 229753. | 0.0967589 | ||||||||
\(356\) | 2.98447e6 | 1.24808 | ||||||||
\(357\) | −3.13083e6 | −1.30014 | ||||||||
\(358\) | −555893. | −0.229237 | ||||||||
\(359\) | −1.97393e6 | −0.808341 | −0.404171 | − | 0.914684i | \(-0.632440\pi\) | ||||
−0.404171 | + | 0.914684i | \(0.632440\pi\) | |||||||
\(360\) | −2.74312e6 | −1.11555 | ||||||||
\(361\) | −1.06112e6 | −0.428545 | ||||||||
\(362\) | 3.35986e6 | 1.34757 | ||||||||
\(363\) | −307164. | −0.122350 | ||||||||
\(364\) | 1.20483e7 | 4.76620 | ||||||||
\(365\) | 939963. | 0.369299 | ||||||||
\(366\) | 3.99659e6 | 1.55950 | ||||||||
\(367\) | −2.33800e6 | −0.906107 | −0.453054 | − | 0.891483i | \(-0.649665\pi\) | ||||
−0.453054 | + | 0.891483i | \(0.649665\pi\) | |||||||
\(368\) | −1.59625e7 | −6.14443 | ||||||||
\(369\) | 1.34730e6 | 0.515107 | ||||||||
\(370\) | −2.01717e6 | −0.766016 | ||||||||
\(371\) | 1.16456e6 | 0.439265 | ||||||||
\(372\) | −5.07698e6 | −1.90216 | ||||||||
\(373\) | −1.13024e6 | −0.420627 | −0.210313 | − | 0.977634i | \(-0.567448\pi\) | ||||
−0.210313 | + | 0.977634i | \(0.567448\pi\) | |||||||
\(374\) | −7.09633e6 | −2.62334 | ||||||||
\(375\) | −1.40598e6 | −0.516298 | ||||||||
\(376\) | −2.90333e6 | −1.05907 | ||||||||
\(377\) | 2.93717e6 | 1.06433 | ||||||||
\(378\) | 1.82999e6 | 0.658748 | ||||||||
\(379\) | −3.32442e6 | −1.18883 | −0.594413 | − | 0.804160i | \(-0.702615\pi\) | ||||
−0.594413 | + | 0.804160i | \(0.702615\pi\) | |||||||
\(380\) | 6.04836e6 | 2.14871 | ||||||||
\(381\) | 385404. | 0.136020 | ||||||||
\(382\) | −8.81405e6 | −3.09042 | ||||||||
\(383\) | −844054. | −0.294018 | −0.147009 | − | 0.989135i | \(-0.546965\pi\) | ||||
−0.147009 | + | 0.989135i | \(0.546965\pi\) | |||||||
\(384\) | −3.25239e6 | −1.12558 | ||||||||
\(385\) | 6.24209e6 | 2.14624 | ||||||||
\(386\) | −317581. | −0.108489 | ||||||||
\(387\) | 1.35190e6 | 0.458845 | ||||||||
\(388\) | −1.54439e6 | −0.520808 | ||||||||
\(389\) | 2.14732e6 | 0.719485 | 0.359743 | − | 0.933052i | \(-0.382865\pi\) | ||||
0.359743 | + | 0.933052i | \(0.382865\pi\) | |||||||
\(390\) | −3.61580e6 | −1.20377 | ||||||||
\(391\) | 7.14803e6 | 2.36453 | ||||||||
\(392\) | 2.09902e7 | 6.89925 | ||||||||
\(393\) | 1.48583e6 | 0.485274 | ||||||||
\(394\) | 6.55121e6 | 2.12609 | ||||||||
\(395\) | −392413. | −0.126547 | ||||||||
\(396\) | 3.00272e6 | 0.962227 | ||||||||
\(397\) | 3.41321e6 | 1.08689 | 0.543446 | − | 0.839444i | \(-0.317119\pi\) | ||||
0.543446 | + | 0.839444i | \(0.317119\pi\) | |||||||
\(398\) | −4.86975e6 | −1.54099 | ||||||||
\(399\) | −2.49620e6 | −0.784959 | ||||||||
\(400\) | 1.82239e6 | 0.569497 | ||||||||
\(401\) | −5.32467e6 | −1.65361 | −0.826803 | − | 0.562491i | \(-0.809843\pi\) | ||||
−0.826803 | + | 0.562491i | \(0.809843\pi\) | |||||||
\(402\) | −4.00493e6 | −1.23603 | ||||||||
\(403\) | −4.14001e6 | −1.26981 | ||||||||
\(404\) | 6.46962e6 | 1.97208 | ||||||||
\(405\) | −397576. | −0.120443 | ||||||||
\(406\) | 1.19729e7 | 3.60483 | ||||||||
\(407\) | 1.36600e6 | 0.408756 | ||||||||
\(408\) | 7.50425e6 | 2.23181 | ||||||||
\(409\) | 5.35983e6 | 1.58432 | 0.792160 | − | 0.610314i | \(-0.208957\pi\) | ||||
0.792160 | + | 0.610314i | \(0.208957\pi\) | |||||||
\(410\) | −1.08515e7 | −3.18808 | ||||||||
\(411\) | −686475. | −0.200456 | ||||||||
\(412\) | −1.61326e7 | −4.68232 | ||||||||
\(413\) | 811644. | 0.234148 | ||||||||
\(414\) | −4.17807e6 | −1.19805 | ||||||||
\(415\) | 1.23343e6 | 0.351557 | ||||||||
\(416\) | −1.10762e7 | −3.13803 | ||||||||
\(417\) | 3.61002e6 | 1.01665 | ||||||||
\(418\) | −5.65787e6 | −1.58384 | ||||||||
\(419\) | 6.25129e6 | 1.73954 | 0.869770 | − | 0.493457i | \(-0.164267\pi\) | ||||
0.869770 | + | 0.493457i | \(0.164267\pi\) | |||||||
\(420\) | −1.06701e7 | −2.95150 | ||||||||
\(421\) | 1.98238e6 | 0.545106 | 0.272553 | − | 0.962141i | \(-0.412132\pi\) | ||||
0.272553 | + | 0.962141i | \(0.412132\pi\) | |||||||
\(422\) | 312280. | 0.0853618 | ||||||||
\(423\) | −420796. | −0.114346 | ||||||||
\(424\) | −2.79131e6 | −0.754040 | ||||||||
\(425\) | −816069. | −0.219157 | ||||||||
\(426\) | 367379. | 0.0980822 | ||||||||
\(427\) | 9.61719e6 | 2.55257 | ||||||||
\(428\) | −4.41680e6 | −1.16546 | ||||||||
\(429\) | 2.44857e6 | 0.642346 | ||||||||
\(430\) | −1.08885e7 | −2.83987 | ||||||||
\(431\) | 2.80610e6 | 0.727628 | 0.363814 | − | 0.931472i | \(-0.381474\pi\) | ||||
0.363814 | + | 0.931472i | \(0.381474\pi\) | |||||||
\(432\) | −2.42883e6 | −0.626165 | ||||||||
\(433\) | 171431. | 0.0439408 | 0.0219704 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219704 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(434\) | −1.68761e7 | −4.30078 | ||||||||
\(435\) | −2.60118e6 | −0.659094 | ||||||||
\(436\) | −1.61606e7 | −4.07138 | ||||||||
\(437\) | 5.69909e6 | 1.42759 | ||||||||
\(438\) | 1.50301e6 | 0.374350 | ||||||||
\(439\) | 5.47874e6 | 1.35681 | 0.678406 | − | 0.734688i | \(-0.262671\pi\) | ||||
0.678406 | + | 0.734688i | \(0.262671\pi\) | |||||||
\(440\) | −1.49616e7 | −3.68422 | ||||||||
\(441\) | 3.04224e6 | 0.744897 | ||||||||
\(442\) | 9.89161e6 | 2.40830 | ||||||||
\(443\) | −2.02077e6 | −0.489223 | −0.244611 | − | 0.969621i | \(-0.578660\pi\) | ||||
−0.244611 | + | 0.969621i | \(0.578660\pi\) | |||||||
\(444\) | −2.33500e6 | −0.562120 | ||||||||
\(445\) | −2.15528e6 | −0.515946 | ||||||||
\(446\) | 9.88023e6 | 2.35196 | ||||||||
\(447\) | −881028. | −0.208555 | ||||||||
\(448\) | −2.02913e7 | −4.77656 | ||||||||
\(449\) | 8.24886e6 | 1.93098 | 0.965491 | − | 0.260436i | \(-0.0838662\pi\) | ||||
0.965491 | + | 0.260436i | \(0.0838662\pi\) | |||||||
\(450\) | 476997. | 0.111041 | ||||||||
\(451\) | 7.34846e6 | 1.70120 | ||||||||
\(452\) | 7.10049e6 | 1.63472 | ||||||||
\(453\) | −1.49333e6 | −0.341908 | ||||||||
\(454\) | −9.56379e6 | −2.17766 | ||||||||
\(455\) | −8.70088e6 | −1.97031 | ||||||||
\(456\) | 5.98310e6 | 1.34746 | ||||||||
\(457\) | −5.70265e6 | −1.27728 | −0.638640 | − | 0.769505i | \(-0.720503\pi\) | ||||
−0.638640 | + | 0.769505i | \(0.720503\pi\) | |||||||
\(458\) | −6.60340e6 | −1.47097 | ||||||||
\(459\) | 1.08764e6 | 0.240964 | ||||||||
\(460\) | 2.43609e7 | 5.36783 | ||||||||
\(461\) | 3.39304e6 | 0.743596 | 0.371798 | − | 0.928314i | \(-0.378741\pi\) | ||||
0.371798 | + | 0.928314i | \(0.378741\pi\) | |||||||
\(462\) | 9.98119e6 | 2.17559 | ||||||||
\(463\) | −1.50634e6 | −0.326565 | −0.163283 | − | 0.986579i | \(-0.552208\pi\) | ||||
−0.163283 | + | 0.986579i | \(0.552208\pi\) | |||||||
\(464\) | −1.58909e7 | −3.42652 | ||||||||
\(465\) | 3.66643e6 | 0.786340 | ||||||||
\(466\) | −4.96153e6 | −1.05840 | ||||||||
\(467\) | −2.86503e6 | −0.607908 | −0.303954 | − | 0.952687i | \(-0.598307\pi\) | ||||
−0.303954 | + | 0.952687i | \(0.598307\pi\) | |||||||
\(468\) | −4.18551e6 | −0.883353 | ||||||||
\(469\) | −9.63728e6 | −2.02312 | ||||||||
\(470\) | 3.38920e6 | 0.707705 | ||||||||
\(471\) | 1.58413e6 | 0.329032 | ||||||||
\(472\) | −1.94542e6 | −0.401937 | ||||||||
\(473\) | 7.37355e6 | 1.51539 | ||||||||
\(474\) | −627475. | −0.128277 | ||||||||
\(475\) | −650648. | −0.132316 | ||||||||
\(476\) | 2.91897e7 | 5.90490 | ||||||||
\(477\) | −404562. | −0.0814121 | ||||||||
\(478\) | 1.07800e7 | 2.15798 | ||||||||
\(479\) | −7.27328e6 | −1.44841 | −0.724205 | − | 0.689585i | \(-0.757793\pi\) | ||||
−0.724205 | + | 0.689585i | \(0.757793\pi\) | |||||||
\(480\) | 9.80914e6 | 1.94325 | ||||||||
\(481\) | −1.90407e6 | −0.375250 | ||||||||
\(482\) | −3.77622e6 | −0.740355 | ||||||||
\(483\) | −1.00539e7 | −1.96095 | ||||||||
\(484\) | 2.86379e6 | 0.555683 | ||||||||
\(485\) | 1.11531e6 | 0.215298 | ||||||||
\(486\) | −635730. | −0.122091 | ||||||||
\(487\) | −1.00706e7 | −1.92413 | −0.962066 | − | 0.272816i | \(-0.912045\pi\) | ||||
−0.962066 | + | 0.272816i | \(0.912045\pi\) | |||||||
\(488\) | −2.30513e7 | −4.38173 | ||||||||
\(489\) | 1.25249e6 | 0.236866 | ||||||||
\(490\) | −2.45029e7 | −4.61029 | ||||||||
\(491\) | 2.30880e6 | 0.432198 | 0.216099 | − | 0.976371i | \(-0.430667\pi\) | ||||
0.216099 | + | 0.976371i | \(0.430667\pi\) | |||||||
\(492\) | −1.25613e7 | −2.33949 | ||||||||
\(493\) | 7.11596e6 | 1.31861 | ||||||||
\(494\) | 7.88654e6 | 1.45402 | ||||||||
\(495\) | −2.16847e6 | −0.397777 | ||||||||
\(496\) | 2.23986e7 | 4.08805 | ||||||||
\(497\) | 884043. | 0.160540 | ||||||||
\(498\) | 1.97228e6 | 0.356365 | ||||||||
\(499\) | −530048. | −0.0952937 | −0.0476468 | − | 0.998864i | \(-0.515172\pi\) | ||||
−0.0476468 | + | 0.998864i | \(0.515172\pi\) | |||||||
\(500\) | 1.31084e7 | 2.34490 | ||||||||
\(501\) | 185705. | 0.0330544 | ||||||||
\(502\) | 2.05968e7 | 3.64788 | ||||||||
\(503\) | 1.05998e6 | 0.186800 | 0.0934002 | − | 0.995629i | \(-0.470226\pi\) | ||||
0.0934002 | + | 0.995629i | \(0.470226\pi\) | |||||||
\(504\) | −1.05549e7 | −1.85088 | ||||||||
\(505\) | −4.67214e6 | −0.815244 | ||||||||
\(506\) | −2.27881e7 | −3.95670 | ||||||||
\(507\) | −71433.9 | −0.0123420 | ||||||||
\(508\) | −3.59324e6 | −0.617770 | ||||||||
\(509\) | 604951. | 0.103497 | 0.0517483 | − | 0.998660i | \(-0.483521\pi\) | ||||
0.0517483 | + | 0.998660i | \(0.483521\pi\) | |||||||
\(510\) | −8.76008e6 | −1.49136 | ||||||||
\(511\) | 3.61678e6 | 0.612731 | ||||||||
\(512\) | 341148. | 0.0575132 | ||||||||
\(513\) | 867166. | 0.145482 | ||||||||
\(514\) | 8.98297e6 | 1.49973 | ||||||||
\(515\) | 1.16504e7 | 1.93564 | ||||||||
\(516\) | −1.26042e7 | −2.08396 | ||||||||
\(517\) | −2.29512e6 | −0.377641 | ||||||||
\(518\) | −7.76164e6 | −1.27095 | ||||||||
\(519\) | 4.14253e6 | 0.675067 | ||||||||
\(520\) | 2.08550e7 | 3.38222 | ||||||||
\(521\) | 786658. | 0.126967 | 0.0634836 | − | 0.997983i | \(-0.479779\pi\) | ||||
0.0634836 | + | 0.997983i | \(0.479779\pi\) | |||||||
\(522\) | −4.15933e6 | −0.668108 | ||||||||
\(523\) | 4.91796e6 | 0.786196 | 0.393098 | − | 0.919497i | \(-0.371403\pi\) | ||||
0.393098 | + | 0.919497i | \(0.371403\pi\) | |||||||
\(524\) | −1.38528e7 | −2.20399 | ||||||||
\(525\) | 1.14782e6 | 0.181751 | ||||||||
\(526\) | −3.17749e6 | −0.500749 | ||||||||
\(527\) | −1.00301e7 | −1.57318 | ||||||||
\(528\) | −1.32474e7 | −2.06798 | ||||||||
\(529\) | 1.65178e7 | 2.56634 | ||||||||
\(530\) | 3.25844e6 | 0.503872 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | 2.32728e7 | 3.56508 | ||||||||
\(533\) | −1.02431e7 | −1.56175 | ||||||||
\(534\) | −3.44633e6 | −0.523002 | ||||||||
\(535\) | 3.18967e6 | 0.481793 | ||||||||
\(536\) | 2.30995e7 | 3.47288 | ||||||||
\(537\) | 464701. | 0.0695406 | ||||||||
\(538\) | 3.31949e6 | 0.494442 | ||||||||
\(539\) | 1.65930e7 | 2.46011 | ||||||||
\(540\) | 3.70672e6 | 0.547023 | ||||||||
\(541\) | 6.04007e6 | 0.887255 | 0.443628 | − | 0.896211i | \(-0.353691\pi\) | ||||
0.443628 | + | 0.896211i | \(0.353691\pi\) | |||||||
\(542\) | 2.04146e7 | 2.98499 | ||||||||
\(543\) | −2.80869e6 | −0.408794 | ||||||||
\(544\) | −2.68345e7 | −3.88774 | ||||||||
\(545\) | 1.16706e7 | 1.68308 | ||||||||
\(546\) | −1.39128e7 | −1.99726 | ||||||||
\(547\) | −7.80143e6 | −1.11482 | −0.557412 | − | 0.830236i | \(-0.688206\pi\) | ||||
−0.557412 | + | 0.830236i | \(0.688206\pi\) | |||||||
\(548\) | 6.40022e6 | 0.910423 | ||||||||
\(549\) | −3.34096e6 | −0.473087 | ||||||||
\(550\) | 2.60165e6 | 0.366727 | ||||||||
\(551\) | 5.67352e6 | 0.796112 | ||||||||
\(552\) | 2.40981e7 | 3.36616 | ||||||||
\(553\) | −1.50993e6 | −0.209963 | ||||||||
\(554\) | −407201. | −0.0563682 | ||||||||
\(555\) | 1.68626e6 | 0.232376 | ||||||||
\(556\) | −3.36573e7 | −4.61735 | ||||||||
\(557\) | 4.58897e6 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(558\) | 5.86267e6 | 0.797094 | ||||||||
\(559\) | −1.02780e7 | −1.39117 | ||||||||
\(560\) | 4.70741e7 | 6.34325 | ||||||||
\(561\) | 5.93221e6 | 0.795809 | ||||||||
\(562\) | 1.80373e7 | 2.40896 | ||||||||
\(563\) | −1.33156e7 | −1.77048 | −0.885239 | − | 0.465137i | \(-0.846005\pi\) | ||||
−0.885239 | + | 0.465137i | \(0.846005\pi\) | |||||||
\(564\) | 3.92321e6 | 0.519331 | ||||||||
\(565\) | −5.12774e6 | −0.675780 | ||||||||
\(566\) | 251095. | 0.0329456 | ||||||||
\(567\) | −1.52979e6 | −0.199836 | ||||||||
\(568\) | −2.11895e6 | −0.275581 | ||||||||
\(569\) | 8.48086e6 | 1.09814 | 0.549072 | − | 0.835775i | \(-0.314981\pi\) | ||||
0.549072 | + | 0.835775i | \(0.314981\pi\) | |||||||
\(570\) | −6.98437e6 | −0.900410 | ||||||||
\(571\) | −8.94164e6 | −1.14770 | −0.573848 | − | 0.818962i | \(-0.694550\pi\) | ||||
−0.573848 | + | 0.818962i | \(0.694550\pi\) | |||||||
\(572\) | −2.28287e7 | −2.91737 | ||||||||
\(573\) | 7.36814e6 | 0.937500 | ||||||||
\(574\) | −4.17542e7 | −5.28957 | ||||||||
\(575\) | −2.62061e6 | −0.330546 | ||||||||
\(576\) | 7.04910e6 | 0.885274 | ||||||||
\(577\) | 6.27318e6 | 0.784419 | 0.392210 | − | 0.919876i | \(-0.371711\pi\) | ||||
0.392210 | + | 0.919876i | \(0.371711\pi\) | |||||||
\(578\) | 8.67828e6 | 1.08047 | ||||||||
\(579\) | 265483. | 0.0329109 | ||||||||
\(580\) | 2.42516e7 | 2.99344 | ||||||||
\(581\) | 4.74599e6 | 0.583293 | ||||||||
\(582\) | 1.78339e6 | 0.218243 | ||||||||
\(583\) | −2.20657e6 | −0.268873 | ||||||||
\(584\) | −8.66901e6 | −1.05181 | ||||||||
\(585\) | 3.02264e6 | 0.365172 | ||||||||
\(586\) | −1.12369e7 | −1.35177 | ||||||||
\(587\) | 8.73012e6 | 1.04574 | 0.522872 | − | 0.852411i | \(-0.324861\pi\) | ||||
0.522872 | + | 0.852411i | \(0.324861\pi\) | |||||||
\(588\) | −2.83637e7 | −3.38314 | ||||||||
\(589\) | −7.99696e6 | −0.949810 | ||||||||
\(590\) | 2.27098e6 | 0.268586 | ||||||||
\(591\) | −5.47651e6 | −0.644964 | ||||||||
\(592\) | 1.03015e7 | 1.20809 | ||||||||
\(593\) | 9.23757e6 | 1.07875 | 0.539375 | − | 0.842065i | \(-0.318660\pi\) | ||||
0.539375 | + | 0.842065i | \(0.318660\pi\) | |||||||
\(594\) | −3.46741e6 | −0.403218 | ||||||||
\(595\) | −2.10798e7 | −2.44104 | ||||||||
\(596\) | 8.21409e6 | 0.947205 | ||||||||
\(597\) | 4.07089e6 | 0.467469 | ||||||||
\(598\) | 3.17645e7 | 3.63236 | ||||||||
\(599\) | −2.25499e6 | −0.256790 | −0.128395 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128395 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(600\) | −2.75120e6 | −0.311993 | ||||||||
\(601\) | −1.51694e7 | −1.71310 | −0.856549 | − | 0.516066i | \(-0.827396\pi\) | ||||
−0.856549 | + | 0.516066i | \(0.827396\pi\) | |||||||
\(602\) | −4.18968e7 | −4.71183 | ||||||||
\(603\) | 3.34794e6 | 0.374960 | ||||||||
\(604\) | 1.39227e7 | 1.55286 | ||||||||
\(605\) | −2.06813e6 | −0.229715 | ||||||||
\(606\) | −7.47083e6 | −0.826394 | ||||||||
\(607\) | 1.16631e7 | 1.28481 | 0.642407 | − | 0.766363i | \(-0.277936\pi\) | ||||
0.642407 | + | 0.766363i | \(0.277936\pi\) | |||||||
\(608\) | −2.13951e7 | −2.34722 | ||||||||
\(609\) | −1.00088e7 | −1.09355 | ||||||||
\(610\) | 2.69089e7 | 2.92801 | ||||||||
\(611\) | 3.19918e6 | 0.346685 | ||||||||
\(612\) | −1.01404e7 | −1.09440 | ||||||||
\(613\) | 1.66308e6 | 0.178756 | 0.0893780 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893780 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(614\) | −1.07589e6 | −0.115172 | ||||||||
\(615\) | 9.07133e6 | 0.967127 | ||||||||
\(616\) | −5.75690e7 | −6.11275 | ||||||||
\(617\) | 1.02503e7 | 1.08399 | 0.541994 | − | 0.840382i | \(-0.317669\pi\) | ||||
0.541994 | + | 0.840382i | \(0.317669\pi\) | |||||||
\(618\) | 1.86292e7 | 1.96211 | ||||||||
\(619\) | −1.17846e7 | −1.23619 | −0.618097 | − | 0.786102i | \(-0.712096\pi\) | ||||
−0.618097 | + | 0.786102i | \(0.712096\pi\) | |||||||
\(620\) | −3.41832e7 | −3.57136 | ||||||||
\(621\) | 3.49268e6 | 0.363437 | ||||||||
\(622\) | −1.64624e7 | −1.70615 | ||||||||
\(623\) | −8.29308e6 | −0.856043 | ||||||||
\(624\) | 1.84656e7 | 1.89847 | ||||||||
\(625\) | −1.11757e7 | −1.14440 | ||||||||
\(626\) | −1.05036e7 | −1.07128 | ||||||||
\(627\) | 4.72972e6 | 0.480470 | ||||||||
\(628\) | −1.47693e7 | −1.49438 | ||||||||
\(629\) | −4.61304e6 | −0.464901 | ||||||||
\(630\) | 1.23213e7 | 1.23682 | ||||||||
\(631\) | −1.77856e7 | −1.77826 | −0.889130 | − | 0.457654i | \(-0.848690\pi\) | ||||
−0.889130 | + | 0.457654i | \(0.848690\pi\) | |||||||
\(632\) | 3.61912e6 | 0.360421 | ||||||||
\(633\) | −261052. | −0.0258951 | ||||||||
\(634\) | 3.25335e6 | 0.321446 | ||||||||
\(635\) | 2.59492e6 | 0.255382 | ||||||||
\(636\) | 3.77185e6 | 0.369753 | ||||||||
\(637\) | −2.31291e7 | −2.25845 | ||||||||
\(638\) | −2.26859e7 | −2.20650 | ||||||||
\(639\) | −307112. | −0.0297539 | ||||||||
\(640\) | −2.18983e7 | −2.11330 | ||||||||
\(641\) | −9.51708e6 | −0.914869 | −0.457434 | − | 0.889243i | \(-0.651232\pi\) | ||||
−0.457434 | + | 0.889243i | \(0.651232\pi\) | |||||||
\(642\) | 5.10032e6 | 0.488383 | ||||||||
\(643\) | −383483. | −0.0365779 | −0.0182890 | − | 0.999833i | \(-0.505822\pi\) | ||||
−0.0182890 | + | 0.999833i | \(0.505822\pi\) | |||||||
\(644\) | 9.37357e7 | 8.90615 | ||||||||
\(645\) | 9.10231e6 | 0.861494 | ||||||||
\(646\) | 1.91069e7 | 1.80140 | ||||||||
\(647\) | 6.28292e6 | 0.590066 | 0.295033 | − | 0.955487i | \(-0.404669\pi\) | ||||
0.295033 | + | 0.955487i | \(0.404669\pi\) | |||||||
\(648\) | 3.66673e6 | 0.343037 | ||||||||
\(649\) | −1.53788e6 | −0.143321 | ||||||||
\(650\) | −3.62646e6 | −0.336666 | ||||||||
\(651\) | 1.41076e7 | 1.30467 | ||||||||
\(652\) | −1.16773e7 | −1.07578 | ||||||||
\(653\) | 4.44773e6 | 0.408184 | 0.204092 | − | 0.978952i | \(-0.434576\pi\) | ||||
0.204092 | + | 0.978952i | \(0.434576\pi\) | |||||||
\(654\) | 1.86615e7 | 1.70609 | ||||||||
\(655\) | 1.00041e7 | 0.911114 | ||||||||
\(656\) | 5.54178e7 | 5.02793 | ||||||||
\(657\) | −1.25645e6 | −0.113562 | ||||||||
\(658\) | 1.30409e7 | 1.17420 | ||||||||
\(659\) | −3.86787e6 | −0.346943 | −0.173471 | − | 0.984839i | \(-0.555498\pi\) | ||||
−0.173471 | + | 0.984839i | \(0.555498\pi\) | |||||||
\(660\) | 2.02173e7 | 1.80661 | ||||||||
\(661\) | 8.16662e6 | 0.727007 | 0.363504 | − | 0.931593i | \(-0.381580\pi\) | ||||
0.363504 | + | 0.931593i | \(0.381580\pi\) | |||||||
\(662\) | −1.61276e7 | −1.43030 | ||||||||
\(663\) | −8.26893e6 | −0.730577 | ||||||||
\(664\) | −1.13756e7 | −1.00128 | ||||||||
\(665\) | −1.68069e7 | −1.47378 | ||||||||
\(666\) | 2.69635e6 | 0.235554 | ||||||||
\(667\) | 2.28512e7 | 1.98881 | ||||||||
\(668\) | −1.73138e6 | −0.150125 | ||||||||
\(669\) | −8.25942e6 | −0.713484 | ||||||||
\(670\) | −2.69652e7 | −2.32068 | ||||||||
\(671\) | −1.82224e7 | −1.56242 | ||||||||
\(672\) | 3.77435e7 | 3.22418 | ||||||||
\(673\) | 1.90914e7 | 1.62480 | 0.812402 | − | 0.583098i | \(-0.198160\pi\) | ||||
0.812402 | + | 0.583098i | \(0.198160\pi\) | |||||||
\(674\) | −1.24507e7 | −1.05571 | ||||||||
\(675\) | −398748. | −0.0336852 | ||||||||
\(676\) | 666000. | 0.0560541 | ||||||||
\(677\) | 1.41093e7 | 1.18313 | 0.591567 | − | 0.806256i | \(-0.298509\pi\) | ||||
0.591567 | + | 0.806256i | \(0.298509\pi\) | |||||||
\(678\) | −8.19933e6 | −0.685022 | ||||||||
\(679\) | 4.29147e6 | 0.357217 | ||||||||
\(680\) | 5.05260e7 | 4.19027 | ||||||||
\(681\) | 7.99489e6 | 0.660609 | ||||||||
\(682\) | 3.19763e7 | 2.63249 | ||||||||
\(683\) | 7.16115e6 | 0.587396 | 0.293698 | − | 0.955898i | \(-0.405114\pi\) | ||||
0.293698 | + | 0.955898i | \(0.405114\pi\) | |||||||
\(684\) | −8.08486e6 | −0.660742 | ||||||||
\(685\) | −4.62202e6 | −0.376362 | ||||||||
\(686\) | −5.20919e7 | −4.22630 | ||||||||
\(687\) | 5.52014e6 | 0.446229 | ||||||||
\(688\) | 5.56070e7 | 4.47876 | ||||||||
\(689\) | 3.07575e6 | 0.246833 | ||||||||
\(690\) | −2.81309e7 | −2.24937 | ||||||||
\(691\) | 9.02513e6 | 0.719048 | 0.359524 | − | 0.933136i | \(-0.382939\pi\) | ||||
0.359524 | + | 0.933136i | \(0.382939\pi\) | |||||||
\(692\) | −3.86221e7 | −3.06599 | ||||||||
\(693\) | −8.34382e6 | −0.659981 | ||||||||
\(694\) | −3.28899e7 | −2.59217 | ||||||||
\(695\) | 2.43062e7 | 1.90878 | ||||||||
\(696\) | 2.39900e7 | 1.87718 | ||||||||
\(697\) | −2.48161e7 | −1.93487 | ||||||||
\(698\) | −1.27526e7 | −0.990743 | ||||||||
\(699\) | 4.14761e6 | 0.321074 | ||||||||
\(700\) | −1.07015e7 | −0.825468 | ||||||||
\(701\) | −5.85795e6 | −0.450247 | −0.225123 | − | 0.974330i | \(-0.572278\pi\) | ||||
−0.225123 | + | 0.974330i | \(0.572278\pi\) | |||||||
\(702\) | 4.83325e6 | 0.370166 | ||||||||
\(703\) | −3.67796e6 | −0.280684 | ||||||||
\(704\) | 3.84474e7 | 2.92372 | ||||||||
\(705\) | −2.83322e6 | −0.214688 | ||||||||
\(706\) | 1.48528e7 | 1.12149 | ||||||||
\(707\) | −1.79774e7 | −1.35263 | ||||||||
\(708\) | 2.62881e6 | 0.197095 | ||||||||
\(709\) | −941213. | −0.0703189 | −0.0351595 | − | 0.999382i | \(-0.511194\pi\) | ||||
−0.0351595 | + | 0.999382i | \(0.511194\pi\) | |||||||
\(710\) | 2.47356e6 | 0.184152 | ||||||||
\(711\) | 524540. | 0.0389139 | ||||||||
\(712\) | 1.98776e7 | 1.46948 | ||||||||
\(713\) | −3.22093e7 | −2.37278 | ||||||||
\(714\) | −3.37070e7 | −2.47442 | ||||||||
\(715\) | 1.64862e7 | 1.20602 | ||||||||
\(716\) | −4.33255e6 | −0.315836 | ||||||||
\(717\) | −9.01156e6 | −0.654639 | ||||||||
\(718\) | −2.12516e7 | −1.53844 | ||||||||
\(719\) | −1.49350e7 | −1.07741 | −0.538706 | − | 0.842494i | \(-0.681087\pi\) | ||||
−0.538706 | + | 0.842494i | \(0.681087\pi\) | |||||||
\(720\) | −1.63533e7 | −1.17564 | ||||||||
\(721\) | 4.48284e7 | 3.21155 | ||||||||
\(722\) | −1.14242e7 | −0.815609 | ||||||||
\(723\) | 3.15675e6 | 0.224592 | ||||||||
\(724\) | 2.61863e7 | 1.85664 | ||||||||
\(725\) | −2.60885e6 | −0.184333 | ||||||||
\(726\) | −3.30697e6 | −0.232857 | ||||||||
\(727\) | −6.59529e6 | −0.462805 | −0.231402 | − | 0.972858i | \(-0.574331\pi\) | ||||
−0.231402 | + | 0.972858i | \(0.574331\pi\) | |||||||
\(728\) | 8.02457e7 | 5.61169 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.01198e7 | 0.702851 | ||||||||
\(731\) | −2.49009e7 | −1.72354 | ||||||||
\(732\) | 3.11488e7 | 2.14864 | ||||||||
\(733\) | −1.07918e7 | −0.741877 | −0.370939 | − | 0.928657i | \(-0.620964\pi\) | ||||
−0.370939 | + | 0.928657i | \(0.620964\pi\) | |||||||
\(734\) | −2.51712e7 | −1.72451 | ||||||||
\(735\) | 2.04833e7 | 1.39856 | ||||||||
\(736\) | −8.61726e7 | −5.86374 | ||||||||
\(737\) | 1.82604e7 | 1.23835 | ||||||||
\(738\) | 1.45052e7 | 0.980353 | ||||||||
\(739\) | −2.62963e7 | −1.77126 | −0.885631 | − | 0.464389i | \(-0.846274\pi\) | ||||
−0.885631 | + | 0.464389i | \(0.846274\pi\) | |||||||
\(740\) | −1.57215e7 | −1.05540 | ||||||||
\(741\) | −6.59278e6 | −0.441086 | ||||||||
\(742\) | 1.25378e7 | 0.836010 | ||||||||
\(743\) | −1.79796e7 | −1.19484 | −0.597419 | − | 0.801929i | \(-0.703807\pi\) | ||||
−0.597419 | + | 0.801929i | \(0.703807\pi\) | |||||||
\(744\) | −3.38144e7 | −2.23959 | ||||||||
\(745\) | −5.93195e6 | −0.391567 | ||||||||
\(746\) | −1.21683e7 | −0.800538 | ||||||||
\(747\) | −1.64873e6 | −0.108106 | ||||||||
\(748\) | −5.53078e7 | −3.61437 | ||||||||
\(749\) | 1.22732e7 | 0.799378 | ||||||||
\(750\) | −1.51370e7 | −0.982621 | ||||||||
\(751\) | −3.69885e6 | −0.239313 | −0.119657 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119657 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(752\) | −1.73084e7 | −1.11613 | ||||||||
\(753\) | −1.72180e7 | −1.10661 | ||||||||
\(754\) | 3.16220e7 | 2.02563 | ||||||||
\(755\) | −1.00545e7 | −0.641941 | ||||||||
\(756\) | 1.42627e7 | 0.907605 | ||||||||
\(757\) | 1.89384e7 | 1.20117 | 0.600583 | − | 0.799563i | \(-0.294935\pi\) | ||||
0.600583 | + | 0.799563i | \(0.294935\pi\) | |||||||
\(758\) | −3.57912e7 | −2.26258 | ||||||||
\(759\) | 1.90498e7 | 1.20029 | ||||||||
\(760\) | 4.02841e7 | 2.52988 | ||||||||
\(761\) | −1.99494e7 | −1.24873 | −0.624365 | − | 0.781132i | \(-0.714642\pi\) | ||||
−0.624365 | + | 0.781132i | \(0.714642\pi\) | |||||||
\(762\) | 4.14931e6 | 0.258874 | ||||||||
\(763\) | 4.49062e7 | 2.79251 | ||||||||
\(764\) | −6.86954e7 | −4.25789 | ||||||||
\(765\) | 7.32303e6 | 0.452415 | ||||||||
\(766\) | −9.08721e6 | −0.559575 | ||||||||
\(767\) | 2.14366e6 | 0.131573 | ||||||||
\(768\) | −9.95220e6 | −0.608858 | ||||||||
\(769\) | 9.25313e6 | 0.564251 | 0.282126 | − | 0.959377i | \(-0.408960\pi\) | ||||
0.282126 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(770\) | 6.72032e7 | 4.08473 | ||||||||
\(771\) | −7.50935e6 | −0.454953 | ||||||||
\(772\) | −2.47518e6 | −0.149473 | ||||||||
\(773\) | 2.38372e7 | 1.43485 | 0.717424 | − | 0.696637i | \(-0.245321\pi\) | ||||
0.717424 | + | 0.696637i | \(0.245321\pi\) | |||||||
\(774\) | 1.45547e7 | 0.873276 | ||||||||
\(775\) | 3.67723e6 | 0.219921 | ||||||||
\(776\) | −1.02862e7 | −0.613196 | ||||||||
\(777\) | 6.48837e6 | 0.385552 | ||||||||
\(778\) | 2.31183e7 | 1.36933 | ||||||||
\(779\) | −1.97858e7 | −1.16818 | ||||||||
\(780\) | −2.81810e7 | −1.65852 | ||||||||
\(781\) | −1.67506e6 | −0.0982657 | ||||||||
\(782\) | 7.69567e7 | 4.50018 | ||||||||
\(783\) | 3.47701e6 | 0.202675 | ||||||||
\(784\) | 1.25135e8 | 7.27090 | ||||||||
\(785\) | 1.06659e7 | 0.617765 | ||||||||
\(786\) | 1.59966e7 | 0.923575 | ||||||||
\(787\) | 1.76172e7 | 1.01391 | 0.506956 | − | 0.861972i | \(-0.330771\pi\) | ||||
0.506956 | + | 0.861972i | \(0.330771\pi\) | |||||||
\(788\) | 5.10592e7 | 2.92926 | ||||||||
\(789\) | 2.65624e6 | 0.151906 | ||||||||
\(790\) | −4.22478e6 | −0.240844 | ||||||||
\(791\) | −1.97305e7 | −1.12123 | ||||||||
\(792\) | 1.99992e7 | 1.13292 | ||||||||
\(793\) | 2.54002e7 | 1.43435 | ||||||||
\(794\) | 3.67471e7 | 2.06858 | ||||||||
\(795\) | −2.72391e6 | −0.152853 | ||||||||
\(796\) | −3.79541e7 | −2.12313 | ||||||||
\(797\) | −3.37738e7 | −1.88336 | −0.941682 | − | 0.336504i | \(-0.890756\pi\) | ||||
−0.941682 | + | 0.336504i | \(0.890756\pi\) | |||||||
\(798\) | −2.68744e7 | −1.49394 | ||||||||
\(799\) | 7.75073e6 | 0.429512 | ||||||||
\(800\) | 9.83806e6 | 0.543481 | ||||||||
\(801\) | 2.88097e6 | 0.158657 | ||||||||
\(802\) | −5.73262e7 | −3.14715 | ||||||||
\(803\) | −6.85296e6 | −0.375050 | ||||||||
\(804\) | −3.12139e7 | −1.70297 | ||||||||
\(805\) | −6.76928e7 | −3.68174 | ||||||||
\(806\) | −4.45719e7 | −2.41671 | ||||||||
\(807\) | −2.77494e6 | −0.149993 | ||||||||
\(808\) | 4.30899e7 | 2.32192 | ||||||||
\(809\) | −3.55067e7 | −1.90739 | −0.953695 | − | 0.300776i | \(-0.902755\pi\) | ||||
−0.953695 | + | 0.300776i | \(0.902755\pi\) | |||||||
\(810\) | −4.28036e6 | −0.229228 | ||||||||
\(811\) | 6.18290e6 | 0.330096 | 0.165048 | − | 0.986286i | \(-0.447222\pi\) | ||||
0.165048 | + | 0.986286i | \(0.447222\pi\) | |||||||
\(812\) | 9.33151e7 | 4.96663 | ||||||||
\(813\) | −1.70657e7 | −0.905518 | ||||||||
\(814\) | 1.47065e7 | 0.777945 | ||||||||
\(815\) | 8.43300e6 | 0.444721 | ||||||||
\(816\) | 4.47372e7 | 2.35203 | ||||||||
\(817\) | −1.98533e7 | −1.04059 | ||||||||
\(818\) | 5.77047e7 | 3.01528 | ||||||||
\(819\) | 1.16305e7 | 0.605882 | ||||||||
\(820\) | −8.45748e7 | −4.39245 | ||||||||
\(821\) | 2.77015e7 | 1.43432 | 0.717159 | − | 0.696909i | \(-0.245442\pi\) | ||||
0.717159 | + | 0.696909i | \(0.245442\pi\) | |||||||
\(822\) | −7.39068e6 | −0.381509 | ||||||||
\(823\) | 1.16521e7 | 0.599660 | 0.299830 | − | 0.953993i | \(-0.403070\pi\) | ||||
0.299830 | + | 0.953993i | \(0.403070\pi\) | |||||||
\(824\) | −1.07449e8 | −5.51293 | ||||||||
\(825\) | −2.17486e6 | −0.111249 | ||||||||
\(826\) | 8.73827e6 | 0.445631 | ||||||||
\(827\) | 1.70280e7 | 0.865764 | 0.432882 | − | 0.901450i | \(-0.357497\pi\) | ||||
0.432882 | + | 0.901450i | \(0.357497\pi\) | |||||||
\(828\) | −3.25633e7 | −1.65064 | ||||||||
\(829\) | 4.16981e6 | 0.210732 | 0.105366 | − | 0.994434i | \(-0.466399\pi\) | ||||
0.105366 | + | 0.994434i | \(0.466399\pi\) | |||||||
\(830\) | 1.32793e7 | 0.669084 | ||||||||
\(831\) | 340401. | 0.0170997 | ||||||||
\(832\) | −5.35920e7 | −2.68406 | ||||||||
\(833\) | −5.60355e7 | −2.79802 | ||||||||
\(834\) | 3.88660e7 | 1.93488 | ||||||||
\(835\) | 1.25035e6 | 0.0620604 | ||||||||
\(836\) | −4.40966e7 | −2.18218 | ||||||||
\(837\) | −4.90092e6 | −0.241804 | ||||||||
\(838\) | 6.73023e7 | 3.31070 | ||||||||
\(839\) | 2.01150e6 | 0.0986539 | 0.0493269 | − | 0.998783i | \(-0.484292\pi\) | ||||
0.0493269 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(840\) | −7.10662e7 | −3.47508 | ||||||||
\(841\) | 2.23752e6 | 0.109088 | ||||||||
\(842\) | 2.13425e7 | 1.03745 | ||||||||
\(843\) | −1.50783e7 | −0.730776 | ||||||||
\(844\) | 2.43387e6 | 0.117609 | ||||||||
\(845\) | −480963. | −0.0231724 | ||||||||
\(846\) | −4.53035e6 | −0.217624 | ||||||||
\(847\) | −7.95774e6 | −0.381137 | ||||||||
\(848\) | −1.66406e7 | −0.794659 | ||||||||
\(849\) | −209904. | −0.00999428 | ||||||||
\(850\) | −8.78591e6 | −0.417099 | ||||||||
\(851\) | −1.48137e7 | −0.701195 | ||||||||
\(852\) | 2.86330e6 | 0.135135 | ||||||||
\(853\) | 1.07451e7 | 0.505634 | 0.252817 | − | 0.967514i | \(-0.418643\pi\) | ||||
0.252817 | + | 0.967514i | \(0.418643\pi\) | |||||||
\(854\) | 1.03540e8 | 4.85807 | ||||||||
\(855\) | 5.83862e6 | 0.273146 | ||||||||
\(856\) | −2.94174e7 | −1.37221 | ||||||||
\(857\) | −2.35618e6 | −0.109586 | −0.0547931 | − | 0.998498i | \(-0.517450\pi\) | ||||
−0.0547931 | + | 0.998498i | \(0.517450\pi\) | |||||||
\(858\) | 2.63616e7 | 1.22251 | ||||||||
\(859\) | 3.64884e6 | 0.168722 | 0.0843611 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843611 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(860\) | −8.48636e7 | −3.91269 | ||||||||
\(861\) | 3.49046e7 | 1.60463 | ||||||||
\(862\) | 3.02108e7 | 1.38482 | ||||||||
\(863\) | 3.09382e7 | 1.41406 | 0.707029 | − | 0.707184i | \(-0.250035\pi\) | ||||
0.707029 | + | 0.707184i | \(0.250035\pi\) | |||||||
\(864\) | −1.31119e7 | −0.597560 | ||||||||
\(865\) | 2.78916e7 | 1.26746 | ||||||||
\(866\) | 1.84564e6 | 0.0836283 | ||||||||
\(867\) | −7.25465e6 | −0.327770 | ||||||||
\(868\) | −1.31530e8 | −5.92550 | ||||||||
\(869\) | 2.86096e6 | 0.128518 | ||||||||
\(870\) | −2.80047e7 | −1.25439 | ||||||||
\(871\) | −2.54533e7 | −1.13684 | ||||||||
\(872\) | −1.07635e8 | −4.79361 | ||||||||
\(873\) | −1.49083e6 | −0.0662055 | ||||||||
\(874\) | 6.13572e7 | 2.71698 | ||||||||
\(875\) | −3.64249e7 | −1.60834 | ||||||||
\(876\) | 1.17143e7 | 0.515769 | ||||||||
\(877\) | 1.80640e7 | 0.793075 | 0.396538 | − | 0.918018i | \(-0.370212\pi\) | ||||
0.396538 | + | 0.918018i | \(0.370212\pi\) | |||||||
\(878\) | 5.89849e7 | 2.58229 | ||||||||
\(879\) | 9.39352e6 | 0.410068 | ||||||||
\(880\) | −8.91946e7 | −3.88268 | ||||||||
\(881\) | −2.41533e7 | −1.04842 | −0.524211 | − | 0.851588i | \(-0.675640\pi\) | ||||
−0.524211 | + | 0.851588i | \(0.675640\pi\) | |||||||
\(882\) | 3.27531e7 | 1.41769 | ||||||||
\(883\) | −3.60339e7 | −1.55528 | −0.777642 | − | 0.628708i | \(-0.783584\pi\) | ||||
−0.777642 | + | 0.628708i | \(0.783584\pi\) | |||||||
\(884\) | 7.70938e7 | 3.31810 | ||||||||
\(885\) | −1.89844e6 | −0.0814776 | ||||||||
\(886\) | −2.17559e7 | −0.931090 | ||||||||
\(887\) | −6.17290e6 | −0.263439 | −0.131719 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131719 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(888\) | −1.55519e7 | −0.661837 | ||||||||
\(889\) | 9.98471e6 | 0.423722 | ||||||||
\(890\) | −2.32041e7 | −0.981950 | ||||||||
\(891\) | 2.89860e6 | 0.122319 | ||||||||
\(892\) | 7.70051e7 | 3.24047 | ||||||||
\(893\) | 6.17962e6 | 0.259318 | ||||||||
\(894\) | −9.48527e6 | −0.396923 | ||||||||
\(895\) | 3.12883e6 | 0.130564 | ||||||||
\(896\) | −8.42600e7 | −3.50632 | ||||||||
\(897\) | −2.65537e7 | −1.10190 | ||||||||
\(898\) | 8.88084e7 | 3.67505 | ||||||||
\(899\) | −3.20648e7 | −1.32321 | ||||||||
\(900\) | 3.71765e6 | 0.152990 | ||||||||
\(901\) | 7.45170e6 | 0.305804 | ||||||||
\(902\) | 7.91146e7 | 3.23773 | ||||||||
\(903\) | 3.50238e7 | 1.42937 | ||||||||
\(904\) | 4.72917e7 | 1.92470 | ||||||||
\(905\) | −1.89109e7 | −0.767521 | ||||||||
\(906\) | −1.60774e7 | −0.650720 | ||||||||
\(907\) | −3.72640e7 | −1.50408 | −0.752041 | − | 0.659116i | \(-0.770931\pi\) | ||||
−0.752041 | + | 0.659116i | \(0.770931\pi\) | |||||||
\(908\) | −7.45388e7 | −3.00032 | ||||||||
\(909\) | 6.24527e6 | 0.250693 | ||||||||
\(910\) | −9.36749e7 | −3.74990 | ||||||||
\(911\) | −502464. | −0.0200590 | −0.0100295 | − | 0.999950i | \(-0.503193\pi\) | ||||
−0.0100295 | + | 0.999950i | \(0.503193\pi\) | |||||||
\(912\) | 3.56687e7 | 1.42004 | ||||||||
\(913\) | −8.99257e6 | −0.357032 | ||||||||
\(914\) | −6.13956e7 | −2.43092 | ||||||||
\(915\) | −2.24946e7 | −0.888232 | ||||||||
\(916\) | −5.14659e7 | −2.02666 | ||||||||
\(917\) | 3.84935e7 | 1.51170 | ||||||||
\(918\) | 1.17096e7 | 0.458603 | ||||||||
\(919\) | −4.73641e7 | −1.84995 | −0.924976 | − | 0.380025i | \(-0.875916\pi\) | ||||
−0.924976 | + | 0.380025i | \(0.875916\pi\) | |||||||
\(920\) | 1.62252e8 | 6.32005 | ||||||||
\(921\) | 899391. | 0.0349381 | ||||||||
\(922\) | 3.65300e7 | 1.41521 | ||||||||
\(923\) | 2.33487e6 | 0.0902109 | ||||||||
\(924\) | 7.77919e7 | 2.99747 | ||||||||
\(925\) | 1.69123e6 | 0.0649903 | ||||||||
\(926\) | −1.62174e7 | −0.621520 | ||||||||
\(927\) | −1.55732e7 | −0.595220 | ||||||||
\(928\) | −8.57860e7 | −3.26999 | ||||||||
\(929\) | −2.27180e7 | −0.863635 | −0.431817 | − | 0.901961i | \(-0.642127\pi\) | ||||
−0.431817 | + | 0.901961i | \(0.642127\pi\) | |||||||
\(930\) | 3.94732e7 | 1.49656 | ||||||||
\(931\) | −4.46769e7 | −1.68931 | ||||||||
\(932\) | −3.86694e7 | −1.45824 | ||||||||
\(933\) | 1.37618e7 | 0.517572 | ||||||||
\(934\) | −3.08454e7 | −1.15697 | ||||||||
\(935\) | 3.99415e7 | 1.49415 | ||||||||
\(936\) | −2.78770e7 | −1.04005 | ||||||||
\(937\) | 1.02685e7 | 0.382082 | 0.191041 | − | 0.981582i | \(-0.438814\pi\) | ||||
0.191041 | + | 0.981582i | \(0.438814\pi\) | |||||||
\(938\) | −1.03756e8 | −3.85041 | ||||||||
\(939\) | 8.78056e6 | 0.324981 | ||||||||
\(940\) | 2.64149e7 | 0.975057 | ||||||||
\(941\) | 2.02021e7 | 0.743741 | 0.371871 | − | 0.928285i | \(-0.378716\pi\) | ||||
0.371871 | + | 0.928285i | \(0.378716\pi\) | |||||||
\(942\) | 1.70549e7 | 0.626214 | ||||||||
\(943\) | −7.96910e7 | −2.91830 | ||||||||
\(944\) | −1.15978e7 | −0.423589 | ||||||||
\(945\) | −1.03000e7 | −0.375197 | ||||||||
\(946\) | 7.93847e7 | 2.88409 | ||||||||
\(947\) | 4.57833e7 | 1.65895 | 0.829473 | − | 0.558547i | \(-0.188641\pi\) | ||||
0.829473 | + | 0.558547i | \(0.188641\pi\) | |||||||
\(948\) | −4.89045e6 | −0.176737 | ||||||||
\(949\) | 9.55238e6 | 0.344307 | ||||||||
\(950\) | −7.00496e6 | −0.251824 | ||||||||
\(951\) | −2.71965e6 | −0.0975129 | ||||||||
\(952\) | 1.94413e8 | 6.95239 | ||||||||
\(953\) | 1.44135e7 | 0.514087 | 0.257043 | − | 0.966400i | \(-0.417252\pi\) | ||||
0.257043 | + | 0.966400i | \(0.417252\pi\) | |||||||
\(954\) | −4.35557e6 | −0.154944 | ||||||||
\(955\) | 4.96096e7 | 1.76018 | ||||||||
\(956\) | 8.40175e7 | 2.97321 | ||||||||
\(957\) | 1.89644e7 | 0.669358 | ||||||||
\(958\) | −7.83051e7 | −2.75662 | ||||||||
\(959\) | −1.77846e7 | −0.624449 | ||||||||
\(960\) | 4.74615e7 | 1.66212 | ||||||||
\(961\) | 1.65669e7 | 0.578672 | ||||||||
\(962\) | −2.04995e7 | −0.714176 | ||||||||
\(963\) | −4.26364e6 | −0.148154 | ||||||||
\(964\) | −2.94313e7 | −1.02004 | ||||||||
\(965\) | 1.78749e6 | 0.0617911 | ||||||||
\(966\) | −1.08242e8 | −3.73209 | ||||||||
\(967\) | −3.29498e7 | −1.13315 | −0.566574 | − | 0.824011i | \(-0.691732\pi\) | ||||
−0.566574 | + | 0.824011i | \(0.691732\pi\) | |||||||
\(968\) | 1.90738e7 | 0.654257 | ||||||||
\(969\) | −1.59725e7 | −0.546467 | ||||||||
\(970\) | 1.20076e7 | 0.409756 | ||||||||
\(971\) | 4.05011e7 | 1.37854 | 0.689269 | − | 0.724506i | \(-0.257932\pi\) | ||||
0.689269 | + | 0.724506i | \(0.257932\pi\) | |||||||
\(972\) | −4.95479e6 | −0.168213 | ||||||||
\(973\) | 9.35253e7 | 3.16699 | ||||||||
\(974\) | −1.08422e8 | −3.66201 | ||||||||
\(975\) | 3.03155e6 | 0.102130 | ||||||||
\(976\) | −1.37422e8 | −4.61777 | ||||||||
\(977\) | −8.62455e6 | −0.289068 | −0.144534 | − | 0.989500i | \(-0.546168\pi\) | ||||
−0.144534 | + | 0.989500i | \(0.546168\pi\) | |||||||
\(978\) | 1.34845e7 | 0.450803 | ||||||||
\(979\) | 1.57135e7 | 0.523981 | ||||||||
\(980\) | −1.90972e8 | −6.35193 | ||||||||
\(981\) | −1.56002e7 | −0.517556 | ||||||||
\(982\) | 2.48569e7 | 0.822561 | ||||||||
\(983\) | 5.74597e7 | 1.89662 | 0.948309 | − | 0.317349i | \(-0.102793\pi\) | ||||
0.948309 | + | 0.317349i | \(0.102793\pi\) | |||||||
\(984\) | −8.36623e7 | −2.75450 | ||||||||
\(985\) | −3.68733e7 | −1.21094 | ||||||||
\(986\) | 7.66115e7 | 2.50958 | ||||||||
\(987\) | −1.09016e7 | −0.356204 | ||||||||
\(988\) | 6.14665e7 | 2.00330 | ||||||||
\(989\) | −7.99631e7 | −2.59955 | ||||||||
\(990\) | −2.33460e7 | −0.757051 | ||||||||
\(991\) | −447099. | −0.0144617 | −0.00723086 | − | 0.999974i | \(-0.502302\pi\) | ||||
−0.00723086 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(992\) | 1.20917e8 | 3.90130 | ||||||||
\(993\) | 1.34820e7 | 0.433891 | ||||||||
\(994\) | 9.51773e6 | 0.305539 | ||||||||
\(995\) | 2.74092e7 | 0.877685 | ||||||||
\(996\) | 1.53717e7 | 0.490990 | ||||||||
\(997\) | 2.65036e7 | 0.844437 | 0.422218 | − | 0.906494i | \(-0.361252\pi\) | ||||
0.422218 | + | 0.906494i | \(0.361252\pi\) | |||||||
\(998\) | −5.70657e6 | −0.181363 | ||||||||
\(999\) | −2.25403e6 | −0.0714571 |
(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 | 177.6.a.b.1.12 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.d.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.b.1.12 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.d.1.1 | 12 | 3.2 | odd | 2 |