Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.307532.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 76x + 168 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-9.21967\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.21967 | −1.27627 | −0.638134 | − | 0.769925i | \(-0.720294\pi\) | ||||
−0.638134 | + | 0.769925i | \(0.720294\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 20.1236 | 0.628862 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 64.9770 | 0.736854 | ||||||||
\(7\) | 147.570 | 1.13829 | 0.569144 | − | 0.822238i | \(-0.307275\pi\) | ||||
0.569144 | + | 0.822238i | \(0.307275\pi\) | |||||||
\(8\) | 85.7438 | 0.473672 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 180.492 | 0.570765 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −181.112 | −0.363074 | ||||||||
\(13\) | −1124.39 | −1.84526 | −0.922628 | − | 0.385690i | \(-0.873963\pi\) | ||||
−0.922628 | + | 0.385690i | \(0.873963\pi\) | |||||||
\(14\) | −1065.40 | −1.45276 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | −1263.00 | −1.23339 | ||||||||
\(17\) | 1019.99 | 0.855996 | 0.427998 | − | 0.903780i | \(-0.359219\pi\) | ||||
0.427998 | + | 0.903780i | \(0.359219\pi\) | |||||||
\(18\) | −584.793 | −0.425423 | ||||||||
\(19\) | −13.7131 | −0.00871467 | −0.00435734 | − | 0.999991i | \(-0.501387\pi\) | ||||
−0.00435734 | + | 0.999991i | \(0.501387\pi\) | |||||||
\(20\) | −503.090 | −0.281236 | ||||||||
\(21\) | −1328.13 | −0.657191 | ||||||||
\(22\) | −873.580 | −0.384810 | ||||||||
\(23\) | −2116.94 | −0.834430 | −0.417215 | − | 0.908808i | \(-0.636994\pi\) | ||||
−0.417215 | + | 0.908808i | \(0.636994\pi\) | |||||||
\(24\) | −771.694 | −0.273475 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 8117.69 | 2.35504 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2969.63 | 0.715826 | ||||||||
\(29\) | 3120.98 | 0.689122 | 0.344561 | − | 0.938764i | \(-0.388028\pi\) | ||||
0.344561 | + | 0.938764i | \(0.388028\pi\) | |||||||
\(30\) | −1624.42 | −0.329531 | ||||||||
\(31\) | −9628.99 | −1.79960 | −0.899801 | − | 0.436301i | \(-0.856288\pi\) | ||||
−0.899801 | + | 0.436301i | \(0.856288\pi\) | |||||||
\(32\) | 6374.61 | 1.10047 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −7363.96 | −1.09248 | ||||||||
\(35\) | −3689.24 | −0.509058 | ||||||||
\(36\) | 1630.01 | 0.209621 | ||||||||
\(37\) | −3121.52 | −0.374854 | −0.187427 | − | 0.982279i | \(-0.560015\pi\) | ||||
−0.187427 | + | 0.982279i | \(0.560015\pi\) | |||||||
\(38\) | 99.0039 | 0.0111223 | ||||||||
\(39\) | 10119.5 | 1.06536 | ||||||||
\(40\) | −2143.59 | −0.211832 | ||||||||
\(41\) | −5884.38 | −0.546690 | −0.273345 | − | 0.961916i | \(-0.588130\pi\) | ||||
−0.273345 | + | 0.961916i | \(0.588130\pi\) | |||||||
\(42\) | 9588.63 | 0.838752 | ||||||||
\(43\) | 20522.3 | 1.69260 | 0.846302 | − | 0.532704i | \(-0.178824\pi\) | ||||
0.846302 | + | 0.532704i | \(0.178824\pi\) | |||||||
\(44\) | 2434.95 | 0.189609 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 15283.6 | 1.06496 | ||||||||
\(47\) | 24718.5 | 1.63222 | 0.816108 | − | 0.577899i | \(-0.196127\pi\) | ||||
0.816108 | + | 0.577899i | \(0.196127\pi\) | |||||||
\(48\) | 11367.0 | 0.712101 | ||||||||
\(49\) | 4969.81 | 0.295699 | ||||||||
\(50\) | −4512.29 | −0.255254 | ||||||||
\(51\) | −9179.87 | −0.494210 | ||||||||
\(52\) | −22626.7 | −1.16041 | ||||||||
\(53\) | 22761.1 | 1.11302 | 0.556511 | − | 0.830840i | \(-0.312140\pi\) | ||||
0.556511 | + | 0.830840i | \(0.312140\pi\) | |||||||
\(54\) | 5263.14 | 0.245618 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 12653.2 | 0.539175 | ||||||||
\(57\) | 123.418 | 0.00503142 | ||||||||
\(58\) | −22532.4 | −0.879505 | ||||||||
\(59\) | −14533.5 | −0.543553 | −0.271776 | − | 0.962360i | \(-0.587611\pi\) | ||||
−0.271776 | + | 0.962360i | \(0.587611\pi\) | |||||||
\(60\) | 4527.81 | 0.162371 | ||||||||
\(61\) | 43984.9 | 1.51349 | 0.756743 | − | 0.653712i | \(-0.226789\pi\) | ||||
0.756743 | + | 0.653712i | \(0.226789\pi\) | |||||||
\(62\) | 69518.1 | 2.29677 | ||||||||
\(63\) | 11953.1 | 0.379429 | ||||||||
\(64\) | −5606.68 | −0.171102 | ||||||||
\(65\) | 28109.6 | 0.825224 | ||||||||
\(66\) | 7862.22 | 0.222170 | ||||||||
\(67\) | −31488.3 | −0.856964 | −0.428482 | − | 0.903550i | \(-0.640951\pi\) | ||||
−0.428482 | + | 0.903550i | \(0.640951\pi\) | |||||||
\(68\) | 20525.8 | 0.538303 | ||||||||
\(69\) | 19052.5 | 0.481758 | ||||||||
\(70\) | 26635.1 | 0.649694 | ||||||||
\(71\) | −29173.2 | −0.686812 | −0.343406 | − | 0.939187i | \(-0.611581\pi\) | ||||
−0.343406 | + | 0.939187i | \(0.611581\pi\) | |||||||
\(72\) | 6945.24 | 0.157891 | ||||||||
\(73\) | 49583.0 | 1.08899 | 0.544497 | − | 0.838763i | \(-0.316721\pi\) | ||||
0.544497 | + | 0.838763i | \(0.316721\pi\) | |||||||
\(74\) | 22536.3 | 0.478414 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | −275.956 | −0.00548033 | ||||||||
\(77\) | 17855.9 | 0.343207 | ||||||||
\(78\) | −73059.2 | −1.35968 | ||||||||
\(79\) | −85075.4 | −1.53369 | −0.766843 | − | 0.641835i | \(-0.778174\pi\) | ||||
−0.766843 | + | 0.641835i | \(0.778174\pi\) | |||||||
\(80\) | 31574.9 | 0.551591 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 42483.3 | 0.697724 | ||||||||
\(83\) | 77321.9 | 1.23199 | 0.615995 | − | 0.787750i | \(-0.288754\pi\) | ||||
0.615995 | + | 0.787750i | \(0.288754\pi\) | |||||||
\(84\) | −26726.7 | −0.413282 | ||||||||
\(85\) | −25499.6 | −0.382813 | ||||||||
\(86\) | −148164. | −2.16022 | ||||||||
\(87\) | −28088.8 | −0.397865 | ||||||||
\(88\) | 10375.0 | 0.142817 | ||||||||
\(89\) | 70217.7 | 0.939661 | 0.469831 | − | 0.882757i | \(-0.344315\pi\) | ||||
0.469831 | + | 0.882757i | \(0.344315\pi\) | |||||||
\(90\) | 14619.8 | 0.190255 | ||||||||
\(91\) | −165925. | −2.10043 | ||||||||
\(92\) | −42600.5 | −0.524741 | ||||||||
\(93\) | 86660.9 | 1.03900 | ||||||||
\(94\) | −178459. | −2.08315 | ||||||||
\(95\) | 342.827 | 0.00389732 | ||||||||
\(96\) | −57371.5 | −0.635357 | ||||||||
\(97\) | −21080.0 | −0.227479 | −0.113739 | − | 0.993511i | \(-0.536283\pi\) | ||||
−0.113739 | + | 0.993511i | \(0.536283\pi\) | |||||||
\(98\) | −35880.4 | −0.377391 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 12577.2 | 0.125772 | ||||||||
\(101\) | −60279.4 | −0.587984 | −0.293992 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293992 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(102\) | 66275.6 | 0.630744 | ||||||||
\(103\) | 83535.5 | 0.775851 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(104\) | −96409.0 | −0.874046 | ||||||||
\(105\) | 33203.2 | 0.293905 | ||||||||
\(106\) | −164328. | −1.42052 | ||||||||
\(107\) | 159288. | 1.34500 | 0.672502 | − | 0.740095i | \(-0.265219\pi\) | ||||
0.672502 | + | 0.740095i | \(0.265219\pi\) | |||||||
\(108\) | −14670.1 | −0.121025 | ||||||||
\(109\) | −31166.3 | −0.251258 | −0.125629 | − | 0.992077i | \(-0.540095\pi\) | ||||
−0.125629 | + | 0.992077i | \(0.540095\pi\) | |||||||
\(110\) | 21839.5 | 0.172092 | ||||||||
\(111\) | 28093.7 | 0.216422 | ||||||||
\(112\) | −186380. | −1.40396 | ||||||||
\(113\) | 141850. | 1.04504 | 0.522521 | − | 0.852626i | \(-0.324992\pi\) | ||||
0.522521 | + | 0.852626i | \(0.324992\pi\) | |||||||
\(114\) | −891.035 | −0.00642144 | ||||||||
\(115\) | 52923.6 | 0.373168 | ||||||||
\(116\) | 62805.3 | 0.433363 | ||||||||
\(117\) | −91075.2 | −0.615086 | ||||||||
\(118\) | 104927. | 0.693719 | ||||||||
\(119\) | 150519. | 0.974370 | ||||||||
\(120\) | 19292.3 | 0.122302 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −317556. | −1.93162 | ||||||||
\(123\) | 52959.5 | 0.315632 | ||||||||
\(124\) | −193770. | −1.13170 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −86297.7 | −0.484254 | ||||||||
\(127\) | −92350.0 | −0.508075 | −0.254037 | − | 0.967194i | \(-0.581759\pi\) | ||||
−0.254037 | + | 0.967194i | \(0.581759\pi\) | |||||||
\(128\) | −163509. | −0.882098 | ||||||||
\(129\) | −184701. | −0.977225 | ||||||||
\(130\) | −202942. | −1.05321 | ||||||||
\(131\) | 210539. | 1.07190 | 0.535949 | − | 0.844250i | \(-0.319954\pi\) | ||||
0.535949 | + | 0.844250i | \(0.319954\pi\) | |||||||
\(132\) | −21914.6 | −0.109471 | ||||||||
\(133\) | −2023.64 | −0.00991981 | ||||||||
\(134\) | 227335. | 1.09372 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 87457.4 | 0.405461 | ||||||||
\(137\) | 23859.0 | 0.108605 | 0.0543027 | − | 0.998525i | \(-0.482706\pi\) | ||||
0.0543027 | + | 0.998525i | \(0.482706\pi\) | |||||||
\(138\) | −137553. | −0.614853 | ||||||||
\(139\) | 292430. | 1.28377 | 0.641883 | − | 0.766803i | \(-0.278154\pi\) | ||||
0.641883 | + | 0.766803i | \(0.278154\pi\) | |||||||
\(140\) | −74240.8 | −0.320127 | ||||||||
\(141\) | −222467. | −0.942361 | ||||||||
\(142\) | 210621. | 0.876557 | ||||||||
\(143\) | −136051. | −0.556366 | ||||||||
\(144\) | −102303. | −0.411132 | ||||||||
\(145\) | −78024.5 | −0.308185 | ||||||||
\(146\) | −357973. | −1.38985 | ||||||||
\(147\) | −44728.3 | −0.170722 | ||||||||
\(148\) | −62816.2 | −0.235731 | ||||||||
\(149\) | 350530. | 1.29348 | 0.646740 | − | 0.762710i | \(-0.276132\pi\) | ||||
0.646740 | + | 0.762710i | \(0.276132\pi\) | |||||||
\(150\) | 40610.6 | 0.147371 | ||||||||
\(151\) | −513284. | −1.83196 | −0.915979 | − | 0.401225i | \(-0.868584\pi\) | ||||
−0.915979 | + | 0.401225i | \(0.868584\pi\) | |||||||
\(152\) | −1175.81 | −0.00412790 | ||||||||
\(153\) | 82618.8 | 0.285332 | ||||||||
\(154\) | −128914. | −0.438024 | ||||||||
\(155\) | 240725. | 0.804806 | ||||||||
\(156\) | 203640. | 0.669964 | ||||||||
\(157\) | 154810. | 0.501244 | 0.250622 | − | 0.968085i | \(-0.419365\pi\) | ||||
0.250622 | + | 0.968085i | \(0.419365\pi\) | |||||||
\(158\) | 614216. | 1.95740 | ||||||||
\(159\) | −204850. | −0.642604 | ||||||||
\(160\) | −159365. | −0.492146 | ||||||||
\(161\) | −312397. | −0.949821 | ||||||||
\(162\) | −47368.2 | −0.141808 | ||||||||
\(163\) | 184152. | 0.542883 | 0.271442 | − | 0.962455i | \(-0.412500\pi\) | ||||
0.271442 | + | 0.962455i | \(0.412500\pi\) | |||||||
\(164\) | −118415. | −0.343793 | ||||||||
\(165\) | 27225.0 | 0.0778499 | ||||||||
\(166\) | −558238. | −1.57235 | ||||||||
\(167\) | −72082.3 | −0.200003 | −0.100002 | − | 0.994987i | \(-0.531885\pi\) | ||||
−0.100002 | + | 0.994987i | \(0.531885\pi\) | |||||||
\(168\) | −113879. | −0.311293 | ||||||||
\(169\) | 892949. | 2.40497 | ||||||||
\(170\) | 184099. | 0.488572 | ||||||||
\(171\) | −1110.76 | −0.00290489 | ||||||||
\(172\) | 412983. | 1.06441 | ||||||||
\(173\) | −374895. | −0.952345 | −0.476173 | − | 0.879352i | \(-0.657976\pi\) | ||||
−0.476173 | + | 0.879352i | \(0.657976\pi\) | |||||||
\(174\) | 202792. | 0.507782 | ||||||||
\(175\) | 92231.0 | 0.227658 | ||||||||
\(176\) | −152823. | −0.371882 | ||||||||
\(177\) | 130802. | 0.313820 | ||||||||
\(178\) | −506948. | −1.19926 | ||||||||
\(179\) | 354545. | 0.827064 | 0.413532 | − | 0.910490i | \(-0.364295\pi\) | ||||
0.413532 | + | 0.910490i | \(0.364295\pi\) | |||||||
\(180\) | −40750.3 | −0.0937452 | ||||||||
\(181\) | 403999. | 0.916609 | 0.458305 | − | 0.888795i | \(-0.348457\pi\) | ||||
0.458305 | + | 0.888795i | \(0.348457\pi\) | |||||||
\(182\) | 1.19792e6 | 2.68072 | ||||||||
\(183\) | −395864. | −0.873812 | ||||||||
\(184\) | −181515. | −0.395246 | ||||||||
\(185\) | 78038.0 | 0.167640 | ||||||||
\(186\) | −625663. | −1.32604 | ||||||||
\(187\) | 123418. | 0.258093 | ||||||||
\(188\) | 497425. | 1.02644 | ||||||||
\(189\) | −107578. | −0.219064 | ||||||||
\(190\) | −2475.10 | −0.00497403 | ||||||||
\(191\) | 181282. | 0.359560 | 0.179780 | − | 0.983707i | \(-0.442461\pi\) | ||||
0.179780 | + | 0.983707i | \(0.442461\pi\) | |||||||
\(192\) | 50460.2 | 0.0987860 | ||||||||
\(193\) | 683762. | 1.32133 | 0.660665 | − | 0.750681i | \(-0.270274\pi\) | ||||
0.660665 | + | 0.750681i | \(0.270274\pi\) | |||||||
\(194\) | 152190. | 0.290324 | ||||||||
\(195\) | −252987. | −0.476443 | ||||||||
\(196\) | 100010. | 0.185954 | ||||||||
\(197\) | −442098. | −0.811620 | −0.405810 | − | 0.913958i | \(-0.633010\pi\) | ||||
−0.405810 | + | 0.913958i | \(0.633010\pi\) | |||||||
\(198\) | −70760.0 | −0.128270 | ||||||||
\(199\) | 925615. | 1.65691 | 0.828453 | − | 0.560059i | \(-0.189222\pi\) | ||||
0.828453 | + | 0.560059i | \(0.189222\pi\) | |||||||
\(200\) | 53589.8 | 0.0947344 | ||||||||
\(201\) | 283395. | 0.494768 | ||||||||
\(202\) | 435197. | 0.750425 | ||||||||
\(203\) | 460562. | 0.784419 | ||||||||
\(204\) | −184732. | −0.310790 | ||||||||
\(205\) | 147110. | 0.244487 | ||||||||
\(206\) | −603099. | −0.990194 | ||||||||
\(207\) | −171472. | −0.278143 | ||||||||
\(208\) | 1.42009e6 | 2.27593 | ||||||||
\(209\) | −1659.28 | −0.00262757 | ||||||||
\(210\) | −239716. | −0.375101 | ||||||||
\(211\) | 605880. | 0.936873 | 0.468436 | − | 0.883497i | \(-0.344818\pi\) | ||||
0.468436 | + | 0.883497i | \(0.344818\pi\) | |||||||
\(212\) | 458035. | 0.699938 | ||||||||
\(213\) | 262559. | 0.396531 | ||||||||
\(214\) | −1.15001e6 | −1.71659 | ||||||||
\(215\) | −513058. | −0.756955 | ||||||||
\(216\) | −62507.2 | −0.0911582 | ||||||||
\(217\) | −1.42095e6 | −2.04846 | ||||||||
\(218\) | 225011. | 0.320673 | ||||||||
\(219\) | −446247. | −0.628731 | ||||||||
\(220\) | −60873.8 | −0.0847957 | ||||||||
\(221\) | −1.14686e6 | −1.57953 | ||||||||
\(222\) | −202827. | −0.276213 | ||||||||
\(223\) | 581147. | 0.782571 | 0.391286 | − | 0.920269i | \(-0.372030\pi\) | ||||
0.391286 | + | 0.920269i | \(0.372030\pi\) | |||||||
\(224\) | 940699. | 1.25265 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −1.02411e6 | −1.33376 | ||||||||
\(227\) | 1.51651e6 | 1.95335 | 0.976674 | − | 0.214726i | \(-0.0688859\pi\) | ||||
0.976674 | + | 0.214726i | \(0.0688859\pi\) | |||||||
\(228\) | 2483.61 | 0.00316407 | ||||||||
\(229\) | 916540. | 1.15495 | 0.577474 | − | 0.816409i | \(-0.304038\pi\) | ||||
0.577474 | + | 0.816409i | \(0.304038\pi\) | |||||||
\(230\) | −382091. | −0.476263 | ||||||||
\(231\) | −160703. | −0.198150 | ||||||||
\(232\) | 267605. | 0.326418 | ||||||||
\(233\) | −650940. | −0.785509 | −0.392755 | − | 0.919643i | \(-0.628478\pi\) | ||||
−0.392755 | + | 0.919643i | \(0.628478\pi\) | |||||||
\(234\) | 657533. | 0.785014 | ||||||||
\(235\) | −617963. | −0.729950 | ||||||||
\(236\) | −292467. | −0.341820 | ||||||||
\(237\) | 765679. | 0.885474 | ||||||||
\(238\) | −1.08670e6 | −1.24356 | ||||||||
\(239\) | −1.06473e6 | −1.20572 | −0.602860 | − | 0.797847i | \(-0.705972\pi\) | ||||
−0.602860 | + | 0.797847i | \(0.705972\pi\) | |||||||
\(240\) | −284174. | −0.318461 | ||||||||
\(241\) | −1.21958e6 | −1.35259 | −0.676297 | − | 0.736629i | \(-0.736417\pi\) | ||||
−0.676297 | + | 0.736629i | \(0.736417\pi\) | |||||||
\(242\) | −105703. | −0.116024 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 885133. | 0.951774 | ||||||||
\(245\) | −124245. | −0.132240 | ||||||||
\(246\) | −382350. | −0.402831 | ||||||||
\(247\) | 15418.8 | 0.0160808 | ||||||||
\(248\) | −825625. | −0.852420 | ||||||||
\(249\) | −695897. | −0.711290 | ||||||||
\(250\) | 112807. | 0.114153 | ||||||||
\(251\) | 1.82454e6 | 1.82797 | 0.913987 | − | 0.405743i | \(-0.132987\pi\) | ||||
0.913987 | + | 0.405743i | \(0.132987\pi\) | |||||||
\(252\) | 240540. | 0.238609 | ||||||||
\(253\) | −256150. | −0.251590 | ||||||||
\(254\) | 666736. | 0.648440 | ||||||||
\(255\) | 229497. | 0.221017 | ||||||||
\(256\) | 1.35990e6 | 1.29690 | ||||||||
\(257\) | −475038. | −0.448637 | −0.224319 | − | 0.974516i | \(-0.572016\pi\) | ||||
−0.224319 | + | 0.974516i | \(0.572016\pi\) | |||||||
\(258\) | 1.33348e6 | 1.24720 | ||||||||
\(259\) | −460642. | −0.426691 | ||||||||
\(260\) | 565667. | 0.518952 | ||||||||
\(261\) | 252799. | 0.229707 | ||||||||
\(262\) | −1.52002e6 | −1.36803 | ||||||||
\(263\) | −1.07504e6 | −0.958376 | −0.479188 | − | 0.877712i | \(-0.659069\pi\) | ||||
−0.479188 | + | 0.877712i | \(0.659069\pi\) | |||||||
\(264\) | −93375.0 | −0.0824557 | ||||||||
\(265\) | −569028. | −0.497759 | ||||||||
\(266\) | 14610.0 | 0.0126603 | ||||||||
\(267\) | −631959. | −0.542514 | ||||||||
\(268\) | −633658. | −0.538912 | ||||||||
\(269\) | 180662. | 0.152225 | 0.0761126 | − | 0.997099i | \(-0.475749\pi\) | ||||
0.0761126 | + | 0.997099i | \(0.475749\pi\) | |||||||
\(270\) | −131578. | −0.109844 | ||||||||
\(271\) | 302884. | 0.250526 | 0.125263 | − | 0.992124i | \(-0.460023\pi\) | ||||
0.125263 | + | 0.992124i | \(0.460023\pi\) | |||||||
\(272\) | −1.28824e6 | −1.05578 | ||||||||
\(273\) | 1.49333e6 | 1.21269 | ||||||||
\(274\) | −172254. | −0.138610 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 383404. | 0.302959 | ||||||||
\(277\) | 1.08898e6 | 0.852745 | 0.426372 | − | 0.904548i | \(-0.359791\pi\) | ||||
0.426372 | + | 0.904548i | \(0.359791\pi\) | |||||||
\(278\) | −2.11125e6 | −1.63843 | ||||||||
\(279\) | −779948. | −0.599867 | ||||||||
\(280\) | −316329. | −0.241126 | ||||||||
\(281\) | −942590. | −0.712127 | −0.356063 | − | 0.934462i | \(-0.615881\pi\) | ||||
−0.356063 | + | 0.934462i | \(0.615881\pi\) | |||||||
\(282\) | 1.60614e6 | 1.20271 | ||||||||
\(283\) | 848952. | 0.630111 | 0.315055 | − | 0.949073i | \(-0.397977\pi\) | ||||
0.315055 | + | 0.949073i | \(0.397977\pi\) | |||||||
\(284\) | −587069. | −0.431910 | ||||||||
\(285\) | −3085.44 | −0.00225012 | ||||||||
\(286\) | 982240. | 0.710072 | ||||||||
\(287\) | −868357. | −0.622291 | ||||||||
\(288\) | 516343. | 0.366824 | ||||||||
\(289\) | −379486. | −0.267271 | ||||||||
\(290\) | 563311. | 0.393327 | ||||||||
\(291\) | 189720. | 0.131335 | ||||||||
\(292\) | 997788. | 0.684827 | ||||||||
\(293\) | 628367. | 0.427606 | 0.213803 | − | 0.976877i | \(-0.431415\pi\) | ||||
0.213803 | + | 0.976877i | \(0.431415\pi\) | |||||||
\(294\) | 322923. | 0.217887 | ||||||||
\(295\) | 363339. | 0.243084 | ||||||||
\(296\) | −267651. | −0.177558 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −2.53071e6 | −1.65083 | ||||||||
\(299\) | 2.38026e6 | 1.53974 | ||||||||
\(300\) | −113195. | −0.0726147 | ||||||||
\(301\) | 3.02847e6 | 1.92667 | ||||||||
\(302\) | 3.70574e6 | 2.33807 | ||||||||
\(303\) | 542514. | 0.339473 | ||||||||
\(304\) | 17319.6 | 0.0107486 | ||||||||
\(305\) | −1.09962e6 | −0.676852 | ||||||||
\(306\) | −596480. | −0.364160 | ||||||||
\(307\) | 1.88248e6 | 1.13994 | 0.569972 | − | 0.821664i | \(-0.306954\pi\) | ||||
0.569972 | + | 0.821664i | \(0.306954\pi\) | |||||||
\(308\) | 359325. | 0.215830 | ||||||||
\(309\) | −751820. | −0.447938 | ||||||||
\(310\) | −1.73795e6 | −1.02715 | ||||||||
\(311\) | −1.53497e6 | −0.899908 | −0.449954 | − | 0.893052i | \(-0.648560\pi\) | ||||
−0.449954 | + | 0.893052i | \(0.648560\pi\) | |||||||
\(312\) | 867681. | 0.504631 | ||||||||
\(313\) | −2.22901e6 | −1.28603 | −0.643015 | − | 0.765854i | \(-0.722317\pi\) | ||||
−0.643015 | + | 0.765854i | \(0.722317\pi\) | |||||||
\(314\) | −1.11767e6 | −0.639722 | ||||||||
\(315\) | −298829. | −0.169686 | ||||||||
\(316\) | −1.71202e6 | −0.964477 | ||||||||
\(317\) | 1.00659e6 | 0.562605 | 0.281303 | − | 0.959619i | \(-0.409234\pi\) | ||||
0.281303 | + | 0.959619i | \(0.409234\pi\) | |||||||
\(318\) | 1.47895e6 | 0.820135 | ||||||||
\(319\) | 377639. | 0.207778 | ||||||||
\(320\) | 140167. | 0.0765193 | ||||||||
\(321\) | −1.43359e6 | −0.776539 | ||||||||
\(322\) | 2.25540e6 | 1.21223 | ||||||||
\(323\) | −13987.2 | −0.00745973 | ||||||||
\(324\) | 132031. | 0.0698736 | ||||||||
\(325\) | −702741. | −0.369051 | ||||||||
\(326\) | −1.32951e6 | −0.692865 | ||||||||
\(327\) | 280497. | 0.145064 | ||||||||
\(328\) | −504549. | −0.258952 | ||||||||
\(329\) | 3.64770e6 | 1.85793 | ||||||||
\(330\) | −196555. | −0.0993574 | ||||||||
\(331\) | −2.96963e6 | −1.48982 | −0.744908 | − | 0.667167i | \(-0.767507\pi\) | ||||
−0.744908 | + | 0.667167i | \(0.767507\pi\) | |||||||
\(332\) | 1.55599e6 | 0.774752 | ||||||||
\(333\) | −252843. | −0.124951 | ||||||||
\(334\) | 520410. | 0.255258 | ||||||||
\(335\) | 787208. | 0.383246 | ||||||||
\(336\) | 1.67742e6 | 0.810575 | ||||||||
\(337\) | 69782.5 | 0.0334712 | 0.0167356 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167356 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(338\) | −6.44680e6 | −3.06939 | ||||||||
\(339\) | −1.27665e6 | −0.603356 | ||||||||
\(340\) | −513144. | −0.240737 | ||||||||
\(341\) | −1.16511e6 | −0.542600 | ||||||||
\(342\) | 8019.32 | 0.00370742 | ||||||||
\(343\) | −1.74681e6 | −0.801697 | ||||||||
\(344\) | 1.75966e6 | 0.801739 | ||||||||
\(345\) | −476312. | −0.215449 | ||||||||
\(346\) | 2.70662e6 | 1.21545 | ||||||||
\(347\) | −1.04233e6 | −0.464708 | −0.232354 | − | 0.972631i | \(-0.574643\pi\) | ||||
−0.232354 | + | 0.972631i | \(0.574643\pi\) | |||||||
\(348\) | −565248. | −0.250202 | ||||||||
\(349\) | −3.75012e6 | −1.64809 | −0.824047 | − | 0.566522i | \(-0.808289\pi\) | ||||
−0.824047 | + | 0.566522i | \(0.808289\pi\) | |||||||
\(350\) | −665877. | −0.290552 | ||||||||
\(351\) | 819677. | 0.355120 | ||||||||
\(352\) | 771328. | 0.331805 | ||||||||
\(353\) | 800792. | 0.342045 | 0.171022 | − | 0.985267i | \(-0.445293\pi\) | ||||
0.171022 | + | 0.985267i | \(0.445293\pi\) | |||||||
\(354\) | −944346. | −0.400519 | ||||||||
\(355\) | 729330. | 0.307152 | ||||||||
\(356\) | 1.41303e6 | 0.590917 | ||||||||
\(357\) | −1.35467e6 | −0.562553 | ||||||||
\(358\) | −2.55970e6 | −1.05556 | ||||||||
\(359\) | 267422. | 0.109512 | 0.0547559 | − | 0.998500i | \(-0.482562\pi\) | ||||
0.0547559 | + | 0.998500i | \(0.482562\pi\) | |||||||
\(360\) | −173631. | −0.0706108 | ||||||||
\(361\) | −2.47591e6 | −0.999924 | ||||||||
\(362\) | −2.91674e6 | −1.16984 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −3.33901e6 | −1.32088 | ||||||||
\(365\) | −1.23957e6 | −0.487013 | ||||||||
\(366\) | 2.85800e6 | 1.11522 | ||||||||
\(367\) | 2.63334e6 | 1.02057 | 0.510283 | − | 0.860007i | \(-0.329541\pi\) | ||||
0.510283 | + | 0.860007i | \(0.329541\pi\) | |||||||
\(368\) | 2.67369e6 | 1.02918 | ||||||||
\(369\) | −476635. | −0.182230 | ||||||||
\(370\) | −563408. | −0.213953 | ||||||||
\(371\) | 3.35885e6 | 1.26694 | ||||||||
\(372\) | 1.74393e6 | 0.653388 | ||||||||
\(373\) | −3.93389e6 | −1.46403 | −0.732015 | − | 0.681289i | \(-0.761420\pi\) | ||||
−0.732015 | + | 0.681289i | \(0.761420\pi\) | |||||||
\(374\) | −891039. | −0.329395 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | 2.11946e6 | 0.773135 | ||||||||
\(377\) | −3.50918e6 | −1.27161 | ||||||||
\(378\) | 776679. | 0.279584 | ||||||||
\(379\) | −1.80355e6 | −0.644956 | −0.322478 | − | 0.946577i | \(-0.604516\pi\) | ||||
−0.322478 | + | 0.946577i | \(0.604516\pi\) | |||||||
\(380\) | 6898.91 | 0.00245088 | ||||||||
\(381\) | 831150. | 0.293337 | ||||||||
\(382\) | −1.30880e6 | −0.458895 | ||||||||
\(383\) | 2.19398e6 | 0.764252 | 0.382126 | − | 0.924110i | \(-0.375192\pi\) | ||||
0.382126 | + | 0.924110i | \(0.375192\pi\) | |||||||
\(384\) | 1.47158e6 | 0.509280 | ||||||||
\(385\) | −446398. | −0.153487 | ||||||||
\(386\) | −4.93653e6 | −1.68637 | ||||||||
\(387\) | 1.66231e6 | 0.564201 | ||||||||
\(388\) | −424204. | −0.143053 | ||||||||
\(389\) | 354221. | 0.118686 | 0.0593430 | − | 0.998238i | \(-0.481099\pi\) | ||||
0.0593430 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(390\) | 1.82648e6 | 0.608070 | ||||||||
\(391\) | −2.15925e6 | −0.714268 | ||||||||
\(392\) | 426130. | 0.140064 | ||||||||
\(393\) | −1.89485e6 | −0.618861 | ||||||||
\(394\) | 3.19180e6 | 1.03584 | ||||||||
\(395\) | 2.12689e6 | 0.685885 | ||||||||
\(396\) | 197231. | 0.0632030 | ||||||||
\(397\) | 168373. | 0.0536162 | 0.0268081 | − | 0.999641i | \(-0.491466\pi\) | ||||
0.0268081 | + | 0.999641i | \(0.491466\pi\) | |||||||
\(398\) | −6.68263e6 | −2.11466 | ||||||||
\(399\) | 18212.7 | 0.00572720 | ||||||||
\(400\) | −789373. | −0.246679 | ||||||||
\(401\) | −4.59458e6 | −1.42687 | −0.713436 | − | 0.700721i | \(-0.752862\pi\) | ||||
−0.713436 | + | 0.700721i | \(0.752862\pi\) | |||||||
\(402\) | −2.04602e6 | −0.631457 | ||||||||
\(403\) | 1.08267e7 | 3.32073 | ||||||||
\(404\) | −1.21304e6 | −0.369761 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −3.32510e6 | −1.00113 | ||||||||
\(407\) | −377704. | −0.113023 | ||||||||
\(408\) | −787117. | −0.234093 | ||||||||
\(409\) | 3.59299e6 | 1.06206 | 0.531028 | − | 0.847354i | \(-0.321806\pi\) | ||||
0.531028 | + | 0.847354i | \(0.321806\pi\) | |||||||
\(410\) | −1.06208e6 | −0.312032 | ||||||||
\(411\) | −214731. | −0.0627033 | ||||||||
\(412\) | 1.68103e6 | 0.487903 | ||||||||
\(413\) | −2.14471e6 | −0.618719 | ||||||||
\(414\) | 1.23797e6 | 0.354986 | ||||||||
\(415\) | −1.93305e6 | −0.550963 | ||||||||
\(416\) | −7.16752e6 | −2.03065 | ||||||||
\(417\) | −2.63187e6 | −0.741182 | ||||||||
\(418\) | 11979.5 | 0.00335349 | ||||||||
\(419\) | −4.10701e6 | −1.14285 | −0.571427 | − | 0.820653i | \(-0.693610\pi\) | ||||
−0.571427 | + | 0.820653i | \(0.693610\pi\) | |||||||
\(420\) | 668167. | 0.184825 | ||||||||
\(421\) | 5.36278e6 | 1.47464 | 0.737318 | − | 0.675546i | \(-0.236092\pi\) | ||||
0.737318 | + | 0.675546i | \(0.236092\pi\) | |||||||
\(422\) | −4.37425e6 | −1.19570 | ||||||||
\(423\) | 2.00220e6 | 0.544072 | ||||||||
\(424\) | 1.95162e6 | 0.527208 | ||||||||
\(425\) | 637491. | 0.171199 | ||||||||
\(426\) | −1.89559e6 | −0.506081 | ||||||||
\(427\) | 6.49083e6 | 1.72278 | ||||||||
\(428\) | 3.20545e6 | 0.845822 | ||||||||
\(429\) | 1.22446e6 | 0.321218 | ||||||||
\(430\) | 3.70411e6 | 0.966078 | ||||||||
\(431\) | 2.52160e6 | 0.653857 | 0.326929 | − | 0.945049i | \(-0.393986\pi\) | ||||
0.326929 | + | 0.945049i | \(0.393986\pi\) | |||||||
\(432\) | 920724. | 0.237367 | ||||||||
\(433\) | 2.99694e6 | 0.768171 | 0.384085 | − | 0.923298i | \(-0.374517\pi\) | ||||
0.384085 | + | 0.923298i | \(0.374517\pi\) | |||||||
\(434\) | 1.02588e7 | 2.61439 | ||||||||
\(435\) | 702221. | 0.177931 | ||||||||
\(436\) | −627179. | −0.158007 | ||||||||
\(437\) | 29029.8 | 0.00727178 | ||||||||
\(438\) | 3.22175e6 | 0.802430 | ||||||||
\(439\) | 1.93618e6 | 0.479495 | 0.239748 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239748 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(440\) | −259375. | −0.0638699 | ||||||||
\(441\) | 402554. | 0.0985662 | ||||||||
\(442\) | 8.27992e6 | 2.01591 | ||||||||
\(443\) | −7.28132e6 | −1.76279 | −0.881395 | − | 0.472380i | \(-0.843395\pi\) | ||||
−0.881395 | + | 0.472380i | \(0.843395\pi\) | |||||||
\(444\) | 565346. | 0.136100 | ||||||||
\(445\) | −1.75544e6 | −0.420229 | ||||||||
\(446\) | −4.19569e6 | −0.998771 | ||||||||
\(447\) | −3.15477e6 | −0.746791 | ||||||||
\(448\) | −827377. | −0.194764 | ||||||||
\(449\) | 6.15007e6 | 1.43967 | 0.719837 | − | 0.694143i | \(-0.244216\pi\) | ||||
0.719837 | + | 0.694143i | \(0.244216\pi\) | |||||||
\(450\) | −365496. | −0.0850846 | ||||||||
\(451\) | −712011. | −0.164833 | ||||||||
\(452\) | 2.85454e6 | 0.657188 | ||||||||
\(453\) | 4.61956e6 | 1.05768 | ||||||||
\(454\) | −1.09487e7 | −2.49300 | ||||||||
\(455\) | 4.14813e6 | 0.939342 | ||||||||
\(456\) | 10582.3 | 0.00238324 | ||||||||
\(457\) | −5.60231e6 | −1.25481 | −0.627403 | − | 0.778695i | \(-0.715882\pi\) | ||||
−0.627403 | + | 0.778695i | \(0.715882\pi\) | |||||||
\(458\) | −6.61711e6 | −1.47402 | ||||||||
\(459\) | −743570. | −0.164737 | ||||||||
\(460\) | 1.06501e6 | 0.234671 | ||||||||
\(461\) | 2.85697e6 | 0.626113 | 0.313057 | − | 0.949734i | \(-0.398647\pi\) | ||||
0.313057 | + | 0.949734i | \(0.398647\pi\) | |||||||
\(462\) | 1.16022e6 | 0.252893 | ||||||||
\(463\) | 2.42615e6 | 0.525976 | 0.262988 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262988 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(464\) | −3.94179e6 | −0.849959 | ||||||||
\(465\) | −2.16652e6 | −0.464655 | ||||||||
\(466\) | 4.69957e6 | 1.00252 | ||||||||
\(467\) | 167522. | 0.0355451 | 0.0177726 | − | 0.999842i | \(-0.494343\pi\) | ||||
0.0177726 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(468\) | −1.83276e6 | −0.386804 | ||||||||
\(469\) | −4.64672e6 | −0.975471 | ||||||||
\(470\) | 4.46149e6 | 0.931612 | ||||||||
\(471\) | −1.39329e6 | −0.289393 | ||||||||
\(472\) | −1.24616e6 | −0.257466 | ||||||||
\(473\) | 2.48320e6 | 0.510339 | ||||||||
\(474\) | −5.52795e6 | −1.13010 | ||||||||
\(475\) | −8570.68 | −0.00174293 | ||||||||
\(476\) | 3.02898e6 | 0.612744 | ||||||||
\(477\) | 1.84365e6 | 0.371008 | ||||||||
\(478\) | 7.68702e6 | 1.53882 | ||||||||
\(479\) | 5.39034e6 | 1.07344 | 0.536719 | − | 0.843761i | \(-0.319663\pi\) | ||||
0.536719 | + | 0.843761i | \(0.319663\pi\) | |||||||
\(480\) | 1.43429e6 | 0.284140 | ||||||||
\(481\) | 3.50979e6 | 0.691701 | ||||||||
\(482\) | 8.80496e6 | 1.72627 | ||||||||
\(483\) | 2.81157e6 | 0.548379 | ||||||||
\(484\) | 294629. | 0.0571693 | ||||||||
\(485\) | 526999. | 0.101732 | ||||||||
\(486\) | 426314. | 0.0818727 | ||||||||
\(487\) | 1.38574e6 | 0.264764 | 0.132382 | − | 0.991199i | \(-0.457737\pi\) | ||||
0.132382 | + | 0.991199i | \(0.457737\pi\) | |||||||
\(488\) | 3.77143e6 | 0.716896 | ||||||||
\(489\) | −1.65736e6 | −0.313434 | ||||||||
\(490\) | 897009. | 0.168774 | ||||||||
\(491\) | −3.39592e6 | −0.635703 | −0.317851 | − | 0.948141i | \(-0.602961\pi\) | ||||
−0.317851 | + | 0.948141i | \(0.602961\pi\) | |||||||
\(492\) | 1.06573e6 | 0.198489 | ||||||||
\(493\) | 3.18336e6 | 0.589886 | ||||||||
\(494\) | −111319. | −0.0205234 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | 1.21614e7 | 2.21962 | ||||||||
\(497\) | −4.30508e6 | −0.781790 | ||||||||
\(498\) | 5.02414e6 | 0.907797 | ||||||||
\(499\) | 2.83293e6 | 0.509313 | 0.254657 | − | 0.967032i | \(-0.418038\pi\) | ||||
0.254657 | + | 0.967032i | \(0.418038\pi\) | |||||||
\(500\) | −314431. | −0.0562471 | ||||||||
\(501\) | 648741. | 0.115472 | ||||||||
\(502\) | −1.31726e7 | −2.33299 | ||||||||
\(503\) | 9.23328e6 | 1.62718 | 0.813591 | − | 0.581437i | \(-0.197509\pi\) | ||||
0.813591 | + | 0.581437i | \(0.197509\pi\) | |||||||
\(504\) | 1.02491e6 | 0.179725 | ||||||||
\(505\) | 1.50698e6 | 0.262954 | ||||||||
\(506\) | 1.84932e6 | 0.321096 | ||||||||
\(507\) | −8.03654e6 | −1.38851 | ||||||||
\(508\) | −1.85841e6 | −0.319509 | ||||||||
\(509\) | −5.70039e6 | −0.975238 | −0.487619 | − | 0.873057i | \(-0.662134\pi\) | ||||
−0.487619 | + | 0.873057i | \(0.662134\pi\) | |||||||
\(510\) | −1.65689e6 | −0.282077 | ||||||||
\(511\) | 7.31695e6 | 1.23959 | ||||||||
\(512\) | −4.58570e6 | −0.773091 | ||||||||
\(513\) | 9996.84 | 0.00167714 | ||||||||
\(514\) | 3.42961e6 | 0.572582 | ||||||||
\(515\) | −2.08839e6 | −0.346971 | ||||||||
\(516\) | −3.71684e6 | −0.614540 | ||||||||
\(517\) | 2.99094e6 | 0.492132 | ||||||||
\(518\) | 3.32568e6 | 0.544573 | ||||||||
\(519\) | 3.37406e6 | 0.549837 | ||||||||
\(520\) | 2.41023e6 | 0.390885 | ||||||||
\(521\) | −1.35063e6 | −0.217994 | −0.108997 | − | 0.994042i | \(-0.534764\pi\) | ||||
−0.108997 | + | 0.994042i | \(0.534764\pi\) | |||||||
\(522\) | −1.82513e6 | −0.293168 | ||||||||
\(523\) | 440837. | 0.0704731 | 0.0352366 | − | 0.999379i | \(-0.488782\pi\) | ||||
0.0352366 | + | 0.999379i | \(0.488782\pi\) | |||||||
\(524\) | 4.23679e6 | 0.674076 | ||||||||
\(525\) | −830079. | −0.131438 | ||||||||
\(526\) | 7.76144e6 | 1.22314 | ||||||||
\(527\) | −9.82143e6 | −1.54045 | ||||||||
\(528\) | 1.37540e6 | 0.214706 | ||||||||
\(529\) | −1.95489e6 | −0.303727 | ||||||||
\(530\) | 4.10819e6 | 0.635274 | ||||||||
\(531\) | −1.17722e6 | −0.181184 | ||||||||
\(532\) | −40722.8 | −0.00623819 | ||||||||
\(533\) | 6.61632e6 | 1.00878 | ||||||||
\(534\) | 4.56253e6 | 0.692393 | ||||||||
\(535\) | −3.98220e6 | −0.601504 | ||||||||
\(536\) | −2.69993e6 | −0.405919 | ||||||||
\(537\) | −3.19091e6 | −0.477506 | ||||||||
\(538\) | −1.30432e6 | −0.194280 | ||||||||
\(539\) | 601347. | 0.0891565 | ||||||||
\(540\) | 366752. | 0.0541238 | ||||||||
\(541\) | 7.01375e6 | 1.03028 | 0.515142 | − | 0.857105i | \(-0.327739\pi\) | ||||
0.515142 | + | 0.857105i | \(0.327739\pi\) | |||||||
\(542\) | −2.18672e6 | −0.319738 | ||||||||
\(543\) | −3.63599e6 | −0.529205 | ||||||||
\(544\) | 6.50201e6 | 0.941999 | ||||||||
\(545\) | 779159. | 0.112366 | ||||||||
\(546\) | −1.07813e7 | −1.54771 | ||||||||
\(547\) | −1.01822e7 | −1.45503 | −0.727517 | − | 0.686090i | \(-0.759326\pi\) | ||||
−0.727517 | + | 0.686090i | \(0.759326\pi\) | |||||||
\(548\) | 480129. | 0.0682978 | ||||||||
\(549\) | 3.56277e6 | 0.504496 | ||||||||
\(550\) | −545987. | −0.0769619 | ||||||||
\(551\) | −42798.3 | −0.00600547 | ||||||||
\(552\) | 1.63363e6 | 0.228195 | ||||||||
\(553\) | −1.25546e7 | −1.74578 | ||||||||
\(554\) | −7.86205e6 | −1.08833 | ||||||||
\(555\) | −702342. | −0.0967868 | ||||||||
\(556\) | 5.88475e6 | 0.807311 | ||||||||
\(557\) | −1.09154e7 | −1.49074 | −0.745371 | − | 0.666650i | \(-0.767728\pi\) | ||||
−0.745371 | + | 0.666650i | \(0.767728\pi\) | |||||||
\(558\) | 5.63096e6 | 0.765592 | ||||||||
\(559\) | −2.30750e7 | −3.12329 | ||||||||
\(560\) | 4.65950e6 | 0.627869 | ||||||||
\(561\) | −1.11076e6 | −0.149010 | ||||||||
\(562\) | 6.80519e6 | 0.908865 | ||||||||
\(563\) | 1.25187e6 | 0.166452 | 0.0832261 | − | 0.996531i | \(-0.473478\pi\) | ||||
0.0832261 | + | 0.996531i | \(0.473478\pi\) | |||||||
\(564\) | −4.47683e6 | −0.592615 | ||||||||
\(565\) | −3.54626e6 | −0.467357 | ||||||||
\(566\) | −6.12915e6 | −0.804191 | ||||||||
\(567\) | 968205. | 0.126476 | ||||||||
\(568\) | −2.50142e6 | −0.325324 | ||||||||
\(569\) | 3.75381e6 | 0.486061 | 0.243031 | − | 0.970019i | \(-0.421858\pi\) | ||||
0.243031 | + | 0.970019i | \(0.421858\pi\) | |||||||
\(570\) | 22275.9 | 0.00287176 | ||||||||
\(571\) | −7.39573e6 | −0.949273 | −0.474636 | − | 0.880182i | \(-0.657420\pi\) | ||||
−0.474636 | + | 0.880182i | \(0.657420\pi\) | |||||||
\(572\) | −2.73783e6 | −0.349877 | ||||||||
\(573\) | −1.63154e6 | −0.207592 | ||||||||
\(574\) | 6.26925e6 | 0.794210 | ||||||||
\(575\) | −1.32309e6 | −0.166886 | ||||||||
\(576\) | −454141. | −0.0570341 | ||||||||
\(577\) | −6.45181e6 | −0.806755 | −0.403378 | − | 0.915034i | \(-0.632164\pi\) | ||||
−0.403378 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(578\) | 2.73976e6 | 0.341109 | ||||||||
\(579\) | −6.15386e6 | −0.762871 | ||||||||
\(580\) | −1.57013e6 | −0.193806 | ||||||||
\(581\) | 1.14104e7 | 1.40236 | ||||||||
\(582\) | −1.36971e6 | −0.167619 | ||||||||
\(583\) | 2.75410e6 | 0.335589 | ||||||||
\(584\) | 4.25143e6 | 0.515826 | ||||||||
\(585\) | 2.27688e6 | 0.275075 | ||||||||
\(586\) | −4.53660e6 | −0.545741 | ||||||||
\(587\) | 5.91956e6 | 0.709078 | 0.354539 | − | 0.935041i | \(-0.384638\pi\) | ||||
0.354539 | + | 0.935041i | \(0.384638\pi\) | |||||||
\(588\) | −900093. | −0.107360 | ||||||||
\(589\) | 132043. | 0.0156829 | ||||||||
\(590\) | −2.62318e6 | −0.310241 | ||||||||
\(591\) | 3.97888e6 | 0.468589 | ||||||||
\(592\) | 3.94247e6 | 0.462343 | ||||||||
\(593\) | −2.54171e6 | −0.296817 | −0.148409 | − | 0.988926i | \(-0.547415\pi\) | ||||
−0.148409 | + | 0.988926i | \(0.547415\pi\) | |||||||
\(594\) | 636840. | 0.0740566 | ||||||||
\(595\) | −3.76297e6 | −0.435751 | ||||||||
\(596\) | 7.05393e6 | 0.813421 | ||||||||
\(597\) | −8.33053e6 | −0.956615 | ||||||||
\(598\) | −1.71847e7 | −1.96512 | ||||||||
\(599\) | 1.17309e7 | 1.33587 | 0.667935 | − | 0.744220i | \(-0.267179\pi\) | ||||
0.667935 | + | 0.744220i | \(0.267179\pi\) | |||||||
\(600\) | −482309. | −0.0546949 | ||||||||
\(601\) | −2.88018e6 | −0.325262 | −0.162631 | − | 0.986687i | \(-0.551998\pi\) | ||||
−0.162631 | + | 0.986687i | \(0.551998\pi\) | |||||||
\(602\) | −2.18646e7 | −2.45895 | ||||||||
\(603\) | −2.55055e6 | −0.285655 | ||||||||
\(604\) | −1.03291e7 | −1.15205 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | −3.91677e6 | −0.433258 | ||||||||
\(607\) | −1.33207e7 | −1.46742 | −0.733712 | − | 0.679460i | \(-0.762214\pi\) | ||||
−0.733712 | + | 0.679460i | \(0.762214\pi\) | |||||||
\(608\) | −87415.6 | −0.00959025 | ||||||||
\(609\) | −4.14506e6 | −0.452885 | ||||||||
\(610\) | 7.93890e6 | 0.863845 | ||||||||
\(611\) | −2.77931e7 | −3.01186 | ||||||||
\(612\) | 1.66259e6 | 0.179434 | ||||||||
\(613\) | −8.85926e6 | −0.952239 | −0.476120 | − | 0.879381i | \(-0.657957\pi\) | ||||
−0.476120 | + | 0.879381i | \(0.657957\pi\) | |||||||
\(614\) | −1.35908e7 | −1.45487 | ||||||||
\(615\) | −1.32399e6 | −0.141155 | ||||||||
\(616\) | 1.53103e6 | 0.162567 | ||||||||
\(617\) | 1.75148e7 | 1.85222 | 0.926110 | − | 0.377253i | \(-0.123131\pi\) | ||||
0.926110 | + | 0.377253i | \(0.123131\pi\) | |||||||
\(618\) | 5.42789e6 | 0.571689 | ||||||||
\(619\) | 3.94768e6 | 0.414109 | 0.207055 | − | 0.978329i | \(-0.433612\pi\) | ||||
0.207055 | + | 0.978329i | \(0.433612\pi\) | |||||||
\(620\) | 4.84424e6 | 0.506112 | ||||||||
\(621\) | 1.54325e6 | 0.160586 | ||||||||
\(622\) | 1.10820e7 | 1.14852 | ||||||||
\(623\) | 1.03620e7 | 1.06960 | ||||||||
\(624\) | −1.27808e7 | −1.31401 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.60927e7 | 1.64132 | ||||||||
\(627\) | 14933.6 | 0.00151703 | ||||||||
\(628\) | 3.11533e6 | 0.315213 | ||||||||
\(629\) | −3.18391e6 | −0.320873 | ||||||||
\(630\) | 2.15744e6 | 0.216565 | ||||||||
\(631\) | −5.78181e6 | −0.578083 | −0.289042 | − | 0.957317i | \(-0.593337\pi\) | ||||
−0.289042 | + | 0.957317i | \(0.593337\pi\) | |||||||
\(632\) | −7.29469e6 | −0.726464 | ||||||||
\(633\) | −5.45292e6 | −0.540904 | ||||||||
\(634\) | −7.26723e6 | −0.718035 | ||||||||
\(635\) | 2.30875e6 | 0.227218 | ||||||||
\(636\) | −4.12232e6 | −0.404109 | ||||||||
\(637\) | −5.58798e6 | −0.545640 | ||||||||
\(638\) | −2.72643e6 | −0.265181 | ||||||||
\(639\) | −2.36303e6 | −0.228937 | ||||||||
\(640\) | 4.08773e6 | 0.394486 | ||||||||
\(641\) | −4.31966e6 | −0.415245 | −0.207623 | − | 0.978209i | \(-0.566573\pi\) | ||||
−0.207623 | + | 0.978209i | \(0.566573\pi\) | |||||||
\(642\) | 1.03501e7 | 0.991072 | ||||||||
\(643\) | 1.95083e7 | 1.86076 | 0.930381 | − | 0.366593i | \(-0.119476\pi\) | ||||
0.930381 | + | 0.366593i | \(0.119476\pi\) | |||||||
\(644\) | −6.28654e6 | −0.597306 | ||||||||
\(645\) | 4.61752e6 | 0.437028 | ||||||||
\(646\) | 100983. | 0.00952062 | ||||||||
\(647\) | −1.08322e7 | −1.01732 | −0.508660 | − | 0.860967i | \(-0.669859\pi\) | ||||
−0.508660 | + | 0.860967i | \(0.669859\pi\) | |||||||
\(648\) | 562565. | 0.0526302 | ||||||||
\(649\) | −1.75856e6 | −0.163887 | ||||||||
\(650\) | 5.07355e6 | 0.471009 | ||||||||
\(651\) | 1.27885e7 | 1.18268 | ||||||||
\(652\) | 3.70579e6 | 0.341399 | ||||||||
\(653\) | 1.83320e6 | 0.168239 | 0.0841197 | − | 0.996456i | \(-0.473192\pi\) | ||||
0.0841197 | + | 0.996456i | \(0.473192\pi\) | |||||||
\(654\) | −2.02510e6 | −0.185140 | ||||||||
\(655\) | −5.26346e6 | −0.479367 | ||||||||
\(656\) | 7.43195e6 | 0.674285 | ||||||||
\(657\) | 4.01622e6 | 0.362998 | ||||||||
\(658\) | −2.63352e7 | −2.37122 | ||||||||
\(659\) | 1.77259e7 | 1.58999 | 0.794994 | − | 0.606618i | \(-0.207474\pi\) | ||||
0.794994 | + | 0.606618i | \(0.207474\pi\) | |||||||
\(660\) | 547865. | 0.0489568 | ||||||||
\(661\) | −5.89810e6 | −0.525060 | −0.262530 | − | 0.964924i | \(-0.584557\pi\) | ||||
−0.262530 | + | 0.964924i | \(0.584557\pi\) | |||||||
\(662\) | 2.14398e7 | 1.90141 | ||||||||
\(663\) | 1.03217e7 | 0.911943 | ||||||||
\(664\) | 6.62987e6 | 0.583559 | ||||||||
\(665\) | 50590.9 | 0.00443627 | ||||||||
\(666\) | 1.82544e6 | 0.159471 | ||||||||
\(667\) | −6.60694e6 | −0.575024 | ||||||||
\(668\) | −1.45055e6 | −0.125775 | ||||||||
\(669\) | −5.23032e6 | −0.451818 | ||||||||
\(670\) | −5.68338e6 | −0.489125 | ||||||||
\(671\) | 5.32217e6 | 0.456333 | ||||||||
\(672\) | −8.46629e6 | −0.723219 | ||||||||
\(673\) | −6.98177e6 | −0.594193 | −0.297097 | − | 0.954847i | \(-0.596018\pi\) | ||||
−0.297097 | + | 0.954847i | \(0.596018\pi\) | |||||||
\(674\) | −503806. | −0.0427183 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 1.79693e7 | 1.51240 | ||||||||
\(677\) | 5.68896e6 | 0.477047 | 0.238524 | − | 0.971137i | \(-0.423337\pi\) | ||||
0.238524 | + | 0.971137i | \(0.423337\pi\) | |||||||
\(678\) | 9.21700e6 | 0.770044 | ||||||||
\(679\) | −3.11076e6 | −0.258936 | ||||||||
\(680\) | −2.18644e6 | −0.181328 | ||||||||
\(681\) | −1.36486e7 | −1.12777 | ||||||||
\(682\) | 8.41169e6 | 0.692504 | ||||||||
\(683\) | 1.65539e6 | 0.135784 | 0.0678920 | − | 0.997693i | \(-0.478373\pi\) | ||||
0.0678920 | + | 0.997693i | \(0.478373\pi\) | |||||||
\(684\) | −22352.5 | −0.00182678 | ||||||||
\(685\) | −596475. | −0.0485698 | ||||||||
\(686\) | 1.26114e7 | 1.02318 | ||||||||
\(687\) | −8.24886e6 | −0.666810 | ||||||||
\(688\) | −2.59196e7 | −2.08765 | ||||||||
\(689\) | −2.55923e7 | −2.05381 | ||||||||
\(690\) | 3.43882e6 | 0.274971 | ||||||||
\(691\) | −8.36041e6 | −0.666090 | −0.333045 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333045 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(692\) | −7.54423e6 | −0.598894 | ||||||||
\(693\) | 1.44633e6 | 0.114402 | ||||||||
\(694\) | 7.52524e6 | 0.593092 | ||||||||
\(695\) | −7.31076e6 | −0.574117 | ||||||||
\(696\) | −2.40844e6 | −0.188457 | ||||||||
\(697\) | −6.00199e6 | −0.467965 | ||||||||
\(698\) | 2.70746e7 | 2.10341 | ||||||||
\(699\) | 5.85846e6 | 0.453514 | ||||||||
\(700\) | 1.85602e6 | 0.143165 | ||||||||
\(701\) | 1.07851e7 | 0.828948 | 0.414474 | − | 0.910061i | \(-0.363966\pi\) | ||||
0.414474 | + | 0.910061i | \(0.363966\pi\) | |||||||
\(702\) | −5.91779e6 | −0.453228 | ||||||||
\(703\) | 42805.7 | 0.00326673 | ||||||||
\(704\) | −678409. | −0.0515893 | ||||||||
\(705\) | 5.56167e6 | 0.421437 | ||||||||
\(706\) | −5.78145e6 | −0.436541 | ||||||||
\(707\) | −8.89541e6 | −0.669295 | ||||||||
\(708\) | 2.63220e6 | 0.197350 | ||||||||
\(709\) | −1.37457e7 | −1.02695 | −0.513476 | − | 0.858104i | \(-0.671642\pi\) | ||||
−0.513476 | + | 0.858104i | \(0.671642\pi\) | |||||||
\(710\) | −5.26552e6 | −0.392008 | ||||||||
\(711\) | −6.89111e6 | −0.511229 | ||||||||
\(712\) | 6.02073e6 | 0.445091 | ||||||||
\(713\) | 2.03840e7 | 1.50164 | ||||||||
\(714\) | 9.78027e6 | 0.717968 | ||||||||
\(715\) | 3.40127e6 | 0.248814 | ||||||||
\(716\) | 7.13472e6 | 0.520109 | ||||||||
\(717\) | 9.58260e6 | 0.696122 | ||||||||
\(718\) | −1.93070e6 | −0.139767 | ||||||||
\(719\) | 2.23290e6 | 0.161082 | 0.0805409 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805409 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(720\) | 2.55757e6 | 0.183864 | ||||||||
\(721\) | 1.23273e7 | 0.883141 | ||||||||
\(722\) | 1.78753e7 | 1.27617 | ||||||||
\(723\) | 1.09762e7 | 0.780921 | ||||||||
\(724\) | 8.12991e6 | 0.576421 | ||||||||
\(725\) | 1.95061e6 | 0.137824 | ||||||||
\(726\) | 951328. | 0.0669867 | ||||||||
\(727\) | 7.70500e6 | 0.540675 | 0.270338 | − | 0.962766i | \(-0.412865\pi\) | ||||
0.270338 | + | 0.962766i | \(0.412865\pi\) | |||||||
\(728\) | −1.42270e7 | −0.994916 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 8.94932e6 | 0.621560 | ||||||||
\(731\) | 2.09325e7 | 1.44886 | ||||||||
\(732\) | −7.96620e6 | −0.549507 | ||||||||
\(733\) | −5.23205e6 | −0.359676 | −0.179838 | − | 0.983696i | \(-0.557557\pi\) | ||||
−0.179838 | + | 0.983696i | \(0.557557\pi\) | |||||||
\(734\) | −1.90118e7 | −1.30252 | ||||||||
\(735\) | 1.11821e6 | 0.0763491 | ||||||||
\(736\) | −1.34947e7 | −0.918266 | ||||||||
\(737\) | −3.81009e6 | −0.258384 | ||||||||
\(738\) | 3.44115e6 | 0.232575 | ||||||||
\(739\) | 1.90698e7 | 1.28450 | 0.642252 | − | 0.766494i | \(-0.278000\pi\) | ||||
0.642252 | + | 0.766494i | \(0.278000\pi\) | |||||||
\(740\) | 1.57040e6 | 0.105422 | ||||||||
\(741\) | −138769. | −0.00928426 | ||||||||
\(742\) | −2.42498e7 | −1.61696 | ||||||||
\(743\) | 2.31407e7 | 1.53781 | 0.768907 | − | 0.639361i | \(-0.220801\pi\) | ||||
0.768907 | + | 0.639361i | \(0.220801\pi\) | |||||||
\(744\) | 7.43063e6 | 0.492145 | ||||||||
\(745\) | −8.76326e6 | −0.578462 | ||||||||
\(746\) | 2.84013e7 | 1.86849 | ||||||||
\(747\) | 6.26307e6 | 0.410663 | ||||||||
\(748\) | 2.48362e6 | 0.162305 | ||||||||
\(749\) | 2.35061e7 | 1.53100 | ||||||||
\(750\) | −1.01527e6 | −0.0659062 | ||||||||
\(751\) | 1.96879e7 | 1.27380 | 0.636898 | − | 0.770948i | \(-0.280217\pi\) | ||||
0.636898 | + | 0.770948i | \(0.280217\pi\) | |||||||
\(752\) | −3.12194e7 | −2.01317 | ||||||||
\(753\) | −1.64209e7 | −1.05538 | ||||||||
\(754\) | 2.53351e7 | 1.62291 | ||||||||
\(755\) | 1.28321e7 | 0.819277 | ||||||||
\(756\) | −2.16486e6 | −0.137761 | ||||||||
\(757\) | −8.22162e6 | −0.521456 | −0.260728 | − | 0.965412i | \(-0.583963\pi\) | ||||
−0.260728 | + | 0.965412i | \(0.583963\pi\) | |||||||
\(758\) | 1.30210e7 | 0.823137 | ||||||||
\(759\) | 2.30535e6 | 0.145256 | ||||||||
\(760\) | 29395.3 | 0.00184605 | ||||||||
\(761\) | 2.18719e6 | 0.136907 | 0.0684534 | − | 0.997654i | \(-0.478194\pi\) | ||||
0.0684534 | + | 0.997654i | \(0.478194\pi\) | |||||||
\(762\) | −6.00063e6 | −0.374377 | ||||||||
\(763\) | −4.59921e6 | −0.286004 | ||||||||
\(764\) | 3.64805e6 | 0.226114 | ||||||||
\(765\) | −2.06547e6 | −0.127604 | ||||||||
\(766\) | −1.58398e7 | −0.975391 | ||||||||
\(767\) | 1.63413e7 | 1.00299 | ||||||||
\(768\) | −1.22391e7 | −0.748764 | ||||||||
\(769\) | 3.97950e6 | 0.242668 | 0.121334 | − | 0.992612i | \(-0.461283\pi\) | ||||
0.121334 | + | 0.992612i | \(0.461283\pi\) | |||||||
\(770\) | 3.22285e6 | 0.195890 | ||||||||
\(771\) | 4.27534e6 | 0.259021 | ||||||||
\(772\) | 1.37597e7 | 0.830935 | ||||||||
\(773\) | −1.92979e7 | −1.16161 | −0.580807 | − | 0.814042i | \(-0.697263\pi\) | ||||
−0.580807 | + | 0.814042i | \(0.697263\pi\) | |||||||
\(774\) | −1.20013e7 | −0.720072 | ||||||||
\(775\) | −6.01812e6 | −0.359920 | ||||||||
\(776\) | −1.80748e6 | −0.107750 | ||||||||
\(777\) | 4.14578e6 | 0.246350 | ||||||||
\(778\) | −2.55735e6 | −0.151475 | ||||||||
\(779\) | 80693.1 | 0.00476423 | ||||||||
\(780\) | −5.09100e6 | −0.299617 | ||||||||
\(781\) | −3.52996e6 | −0.207082 | ||||||||
\(782\) | 1.55891e7 | 0.911599 | ||||||||
\(783\) | −2.27519e6 | −0.132622 | ||||||||
\(784\) | −6.27685e6 | −0.364713 | ||||||||
\(785\) | −3.87024e6 | −0.224163 | ||||||||
\(786\) | 1.36802e7 | 0.789832 | ||||||||
\(787\) | −1.54391e7 | −0.888556 | −0.444278 | − | 0.895889i | \(-0.646540\pi\) | ||||
−0.444278 | + | 0.895889i | \(0.646540\pi\) | |||||||
\(788\) | −8.89659e6 | −0.510397 | ||||||||
\(789\) | 9.67537e6 | 0.553318 | ||||||||
\(790\) | −1.53554e7 | −0.875374 | ||||||||
\(791\) | 2.09328e7 | 1.18956 | ||||||||
\(792\) | 840375. | 0.0476058 | ||||||||
\(793\) | −4.94559e7 | −2.79277 | ||||||||
\(794\) | −1.21560e6 | −0.0684287 | ||||||||
\(795\) | 5.12125e6 | 0.287381 | ||||||||
\(796\) | 1.86267e7 | 1.04196 | ||||||||
\(797\) | 2.66071e7 | 1.48372 | 0.741860 | − | 0.670555i | \(-0.233944\pi\) | ||||
0.741860 | + | 0.670555i | \(0.233944\pi\) | |||||||
\(798\) | −131490. | −0.00730945 | ||||||||
\(799\) | 2.52125e7 | 1.39717 | ||||||||
\(800\) | 3.98413e6 | 0.220094 | ||||||||
\(801\) | 5.68763e6 | 0.313220 | ||||||||
\(802\) | 3.31713e7 | 1.82107 | ||||||||
\(803\) | 5.99954e6 | 0.328344 | ||||||||
\(804\) | 5.70292e6 | 0.311141 | ||||||||
\(805\) | 7.80992e6 | 0.424773 | ||||||||
\(806\) | −7.81651e7 | −4.23814 | ||||||||
\(807\) | −1.62596e6 | −0.0878872 | ||||||||
\(808\) | −5.16858e6 | −0.278511 | ||||||||
\(809\) | −3.15651e7 | −1.69565 | −0.847825 | − | 0.530276i | \(-0.822088\pi\) | ||||
−0.847825 | + | 0.530276i | \(0.822088\pi\) | |||||||
\(810\) | 1.18421e6 | 0.0634183 | ||||||||
\(811\) | 3.50230e7 | 1.86982 | 0.934912 | − | 0.354880i | \(-0.115478\pi\) | ||||
0.934912 | + | 0.354880i | \(0.115478\pi\) | |||||||
\(812\) | 9.26816e6 | 0.493291 | ||||||||
\(813\) | −2.72595e6 | −0.144641 | ||||||||
\(814\) | 2.72690e6 | 0.144247 | ||||||||
\(815\) | −4.60379e6 | −0.242785 | ||||||||
\(816\) | 1.15941e7 | 0.609555 | ||||||||
\(817\) | −281424. | −0.0147505 | ||||||||
\(818\) | −2.59402e7 | −1.35547 | ||||||||
\(819\) | −1.34399e7 | −0.700144 | ||||||||
\(820\) | 2.96037e6 | 0.153749 | ||||||||
\(821\) | −6.00202e6 | −0.310770 | −0.155385 | − | 0.987854i | \(-0.549662\pi\) | ||||
−0.155385 | + | 0.987854i | \(0.549662\pi\) | |||||||
\(822\) | 1.55029e6 | 0.0800263 | ||||||||
\(823\) | −2.98462e7 | −1.53599 | −0.767996 | − | 0.640455i | \(-0.778746\pi\) | ||||
−0.767996 | + | 0.640455i | \(0.778746\pi\) | |||||||
\(824\) | 7.16265e6 | 0.367499 | ||||||||
\(825\) | −680625. | −0.0348155 | ||||||||
\(826\) | 1.54841e7 | 0.789652 | ||||||||
\(827\) | −3.81477e6 | −0.193956 | −0.0969782 | − | 0.995287i | \(-0.530918\pi\) | ||||
−0.0969782 | + | 0.995287i | \(0.530918\pi\) | |||||||
\(828\) | −3.45064e6 | −0.174914 | ||||||||
\(829\) | 7.23404e6 | 0.365590 | 0.182795 | − | 0.983151i | \(-0.441486\pi\) | ||||
0.182795 | + | 0.983151i | \(0.441486\pi\) | |||||||
\(830\) | 1.39560e7 | 0.703177 | ||||||||
\(831\) | −9.80079e6 | −0.492332 | ||||||||
\(832\) | 6.30407e6 | 0.315728 | ||||||||
\(833\) | 5.06913e6 | 0.253117 | ||||||||
\(834\) | 1.90013e7 | 0.945948 | ||||||||
\(835\) | 1.80206e6 | 0.0894442 | ||||||||
\(836\) | −33390.7 | −0.00165238 | ||||||||
\(837\) | 7.01953e6 | 0.346333 | ||||||||
\(838\) | 2.96512e7 | 1.45859 | ||||||||
\(839\) | −2.18515e6 | −0.107171 | −0.0535853 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535853 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(840\) | 2.84697e6 | 0.139214 | ||||||||
\(841\) | −1.07706e7 | −0.525111 | ||||||||
\(842\) | −3.87175e7 | −1.88203 | ||||||||
\(843\) | 8.48331e6 | 0.411146 | ||||||||
\(844\) | 1.21925e7 | 0.589164 | ||||||||
\(845\) | −2.23237e7 | −1.07554 | ||||||||
\(846\) | −1.44552e7 | −0.694383 | ||||||||
\(847\) | 2.16057e6 | 0.103481 | ||||||||
\(848\) | −2.87472e7 | −1.37280 | ||||||||
\(849\) | −7.64056e6 | −0.363795 | ||||||||
\(850\) | −4.60247e6 | −0.218496 | ||||||||
\(851\) | 6.60808e6 | 0.312789 | ||||||||
\(852\) | 5.28362e6 | 0.249363 | ||||||||
\(853\) | −1.41107e7 | −0.664014 | −0.332007 | − | 0.943277i | \(-0.607726\pi\) | ||||
−0.332007 | + | 0.943277i | \(0.607726\pi\) | |||||||
\(854\) | −4.68616e7 | −2.19873 | ||||||||
\(855\) | 27769.0 | 0.00129911 | ||||||||
\(856\) | 1.36580e7 | 0.637091 | ||||||||
\(857\) | 3.50068e7 | 1.62817 | 0.814087 | − | 0.580743i | \(-0.197238\pi\) | ||||
0.814087 | + | 0.580743i | \(0.197238\pi\) | |||||||
\(858\) | −8.84016e6 | −0.409960 | ||||||||
\(859\) | 2.72242e6 | 0.125885 | 0.0629423 | − | 0.998017i | \(-0.479952\pi\) | ||||
0.0629423 | + | 0.998017i | \(0.479952\pi\) | |||||||
\(860\) | −1.03246e7 | −0.476020 | ||||||||
\(861\) | 7.81521e6 | 0.359280 | ||||||||
\(862\) | −1.82051e7 | −0.834498 | ||||||||
\(863\) | 976336. | 0.0446244 | 0.0223122 | − | 0.999751i | \(-0.492897\pi\) | ||||
0.0223122 | + | 0.999751i | \(0.492897\pi\) | |||||||
\(864\) | −4.64709e6 | −0.211786 | ||||||||
\(865\) | 9.37238e6 | 0.425902 | ||||||||
\(866\) | −2.16369e7 | −0.980392 | ||||||||
\(867\) | 3.41538e6 | 0.154309 | ||||||||
\(868\) | −2.85945e7 | −1.28820 | ||||||||
\(869\) | −1.02941e7 | −0.462424 | ||||||||
\(870\) | −5.06980e6 | −0.227087 | ||||||||
\(871\) | 3.54050e7 | 1.58132 | ||||||||
\(872\) | −2.67232e6 | −0.119014 | ||||||||
\(873\) | −1.70748e6 | −0.0758262 | ||||||||
\(874\) | −209586. | −0.00928075 | ||||||||
\(875\) | −2.30578e6 | −0.101812 | ||||||||
\(876\) | −8.98009e6 | −0.395385 | ||||||||
\(877\) | 3.04885e7 | 1.33856 | 0.669279 | − | 0.743011i | \(-0.266603\pi\) | ||||
0.669279 | + | 0.743011i | \(0.266603\pi\) | |||||||
\(878\) | −1.39786e7 | −0.611965 | ||||||||
\(879\) | −5.65530e6 | −0.246879 | ||||||||
\(880\) | 3.82056e6 | 0.166311 | ||||||||
\(881\) | 3.54112e7 | 1.53710 | 0.768548 | − | 0.639792i | \(-0.220980\pi\) | ||||
0.768548 | + | 0.639792i | \(0.220980\pi\) | |||||||
\(882\) | −2.90631e6 | −0.125797 | ||||||||
\(883\) | 7.34069e6 | 0.316836 | 0.158418 | − | 0.987372i | \(-0.449361\pi\) | ||||
0.158418 | + | 0.987372i | \(0.449361\pi\) | |||||||
\(884\) | −2.30789e7 | −0.993308 | ||||||||
\(885\) | −3.27005e6 | −0.140345 | ||||||||
\(886\) | 5.25687e7 | 2.24979 | ||||||||
\(887\) | 8.51565e6 | 0.363420 | 0.181710 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181710 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(888\) | 2.40886e6 | 0.102513 | ||||||||
\(889\) | −1.36281e7 | −0.578335 | ||||||||
\(890\) | 1.26737e7 | 0.536326 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.16948e7 | 0.492129 | ||||||||
\(893\) | −338967. | −0.0142242 | ||||||||
\(894\) | 2.27764e7 | 0.953107 | ||||||||
\(895\) | −8.86363e6 | −0.369874 | ||||||||
\(896\) | −2.41290e7 | −1.00408 | ||||||||
\(897\) | −2.14223e7 | −0.888967 | ||||||||
\(898\) | −4.44015e7 | −1.83741 | ||||||||
\(899\) | −3.00519e7 | −1.24014 | ||||||||
\(900\) | 1.01876e6 | 0.0419241 | ||||||||
\(901\) | 2.32160e7 | 0.952743 | ||||||||
\(902\) | 5.14048e6 | 0.210372 | ||||||||
\(903\) | −2.72562e7 | −1.11236 | ||||||||
\(904\) | 1.21628e7 | 0.495007 | ||||||||
\(905\) | −1.01000e7 | −0.409920 | ||||||||
\(906\) | −3.33517e7 | −1.34989 | ||||||||
\(907\) | 1.84383e7 | 0.744224 | 0.372112 | − | 0.928188i | \(-0.378634\pi\) | ||||
0.372112 | + | 0.928188i | \(0.378634\pi\) | |||||||
\(908\) | 3.05176e7 | 1.22839 | ||||||||
\(909\) | −4.88263e6 | −0.195995 | ||||||||
\(910\) | −2.99481e7 | −1.19885 | ||||||||
\(911\) | 3.20540e7 | 1.27964 | 0.639819 | − | 0.768526i | \(-0.279009\pi\) | ||||
0.639819 | + | 0.768526i | \(0.279009\pi\) | |||||||
\(912\) | −155876. | −0.00620573 | ||||||||
\(913\) | 9.35595e6 | 0.371459 | ||||||||
\(914\) | 4.04468e7 | 1.60147 | ||||||||
\(915\) | 9.89659e6 | 0.390781 | ||||||||
\(916\) | 1.84441e7 | 0.726303 | ||||||||
\(917\) | 3.10691e7 | 1.22013 | ||||||||
\(918\) | 5.36832e6 | 0.210248 | ||||||||
\(919\) | 2.41323e7 | 0.942563 | 0.471282 | − | 0.881983i | \(-0.343792\pi\) | ||||
0.471282 | + | 0.881983i | \(0.343792\pi\) | |||||||
\(920\) | 4.53787e6 | 0.176759 | ||||||||
\(921\) | −1.69423e7 | −0.658147 | ||||||||
\(922\) | −2.06264e7 | −0.799089 | ||||||||
\(923\) | 3.28019e7 | 1.26735 | ||||||||
\(924\) | −3.23393e6 | −0.124609 | ||||||||
\(925\) | −1.95095e6 | −0.0749708 | ||||||||
\(926\) | −1.75160e7 | −0.671287 | ||||||||
\(927\) | 6.76638e6 | 0.258617 | ||||||||
\(928\) | 1.98950e7 | 0.758359 | ||||||||
\(929\) | −2.12500e7 | −0.807828 | −0.403914 | − | 0.914797i | \(-0.632350\pi\) | ||||
−0.403914 | + | 0.914797i | \(0.632350\pi\) | |||||||
\(930\) | 1.56416e7 | 0.593025 | ||||||||
\(931\) | −68151.4 | −0.00257692 | ||||||||
\(932\) | −1.30993e7 | −0.493977 | ||||||||
\(933\) | 1.38147e7 | 0.519562 | ||||||||
\(934\) | −1.20945e6 | −0.0453652 | ||||||||
\(935\) | −3.08546e6 | −0.115422 | ||||||||
\(936\) | −7.80913e6 | −0.291349 | ||||||||
\(937\) | −2.96484e7 | −1.10320 | −0.551598 | − | 0.834110i | \(-0.685982\pi\) | ||||
−0.551598 | + | 0.834110i | \(0.685982\pi\) | |||||||
\(938\) | 3.35478e7 | 1.24496 | ||||||||
\(939\) | 2.00611e7 | 0.742490 | ||||||||
\(940\) | −1.24356e7 | −0.459038 | ||||||||
\(941\) | −4.32235e7 | −1.59128 | −0.795638 | − | 0.605772i | \(-0.792864\pi\) | ||||
−0.795638 | + | 0.605772i | \(0.792864\pi\) | |||||||
\(942\) | 1.00591e7 | 0.369344 | ||||||||
\(943\) | 1.24569e7 | 0.456175 | ||||||||
\(944\) | 1.83558e7 | 0.670415 | ||||||||
\(945\) | 2.68946e6 | 0.0979682 | ||||||||
\(946\) | −1.79279e7 | −0.651330 | ||||||||
\(947\) | 1.03051e7 | 0.373402 | 0.186701 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186701 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(948\) | 1.54082e7 | 0.556841 | ||||||||
\(949\) | −5.57504e7 | −2.00947 | ||||||||
\(950\) | 61877.4 | 0.00222445 | ||||||||
\(951\) | −9.05929e6 | −0.324820 | ||||||||
\(952\) | 1.29061e7 | 0.461531 | ||||||||
\(953\) | 2.76302e7 | 0.985488 | 0.492744 | − | 0.870174i | \(-0.335994\pi\) | ||||
0.492744 | + | 0.870174i | \(0.335994\pi\) | |||||||
\(954\) | −1.33105e7 | −0.473505 | ||||||||
\(955\) | −4.53205e6 | −0.160800 | ||||||||
\(956\) | −2.14263e7 | −0.758231 | ||||||||
\(957\) | −3.39875e6 | −0.119961 | ||||||||
\(958\) | −3.89164e7 | −1.37000 | ||||||||
\(959\) | 3.52087e6 | 0.123624 | ||||||||
\(960\) | −1.26150e6 | −0.0441785 | ||||||||
\(961\) | 6.40882e7 | 2.23856 | ||||||||
\(962\) | −2.53395e7 | −0.882797 | ||||||||
\(963\) | 1.29023e7 | 0.448335 | ||||||||
\(964\) | −2.45423e7 | −0.850596 | ||||||||
\(965\) | −1.70940e7 | −0.590917 | ||||||||
\(966\) | −2.02986e7 | −0.699879 | ||||||||
\(967\) | −1.92779e7 | −0.662968 | −0.331484 | − | 0.943461i | \(-0.607549\pi\) | ||||
−0.331484 | + | 0.943461i | \(0.607549\pi\) | |||||||
\(968\) | 1.25537e6 | 0.0430611 | ||||||||
\(969\) | 125884. | 0.00430688 | ||||||||
\(970\) | −3.80476e6 | −0.129837 | ||||||||
\(971\) | −2.79869e7 | −0.952592 | −0.476296 | − | 0.879285i | \(-0.658021\pi\) | ||||
−0.476296 | + | 0.879285i | \(0.658021\pi\) | |||||||
\(972\) | −1.18828e6 | −0.0403415 | ||||||||
\(973\) | 4.31539e7 | 1.46129 | ||||||||
\(974\) | −1.00046e7 | −0.337910 | ||||||||
\(975\) | 6.32467e6 | 0.213072 | ||||||||
\(976\) | −5.55527e7 | −1.86673 | ||||||||
\(977\) | 3.40783e7 | 1.14220 | 0.571099 | − | 0.820881i | \(-0.306517\pi\) | ||||
0.571099 | + | 0.820881i | \(0.306517\pi\) | |||||||
\(978\) | 1.19656e7 | 0.400026 | ||||||||
\(979\) | 8.49634e6 | 0.283319 | ||||||||
\(980\) | −2.50026e6 | −0.0831610 | ||||||||
\(981\) | −2.52447e6 | −0.0837526 | ||||||||
\(982\) | 2.45174e7 | 0.811328 | ||||||||
\(983\) | −5.50760e7 | −1.81794 | −0.908968 | − | 0.416866i | \(-0.863128\pi\) | ||||
−0.908968 | + | 0.416866i | \(0.863128\pi\) | |||||||
\(984\) | 4.54094e6 | 0.149506 | ||||||||
\(985\) | 1.10524e7 | 0.362967 | ||||||||
\(986\) | −2.29828e7 | −0.752853 | ||||||||
\(987\) | −3.28293e7 | −1.07268 | ||||||||
\(988\) | 310281. | 0.0101126 | ||||||||
\(989\) | −4.34446e7 | −1.41236 | ||||||||
\(990\) | 1.76900e6 | 0.0573640 | ||||||||
\(991\) | −6.15387e6 | −0.199051 | −0.0995255 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995255 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(992\) | −6.13810e7 | −1.98041 | ||||||||
\(993\) | 2.67267e7 | 0.860146 | ||||||||
\(994\) | 3.10812e7 | 0.997774 | ||||||||
\(995\) | −2.31404e7 | −0.740990 | ||||||||
\(996\) | −1.40039e7 | −0.447303 | ||||||||
\(997\) | 1.41497e7 | 0.450828 | 0.225414 | − | 0.974263i | \(-0.427627\pi\) | ||||
0.225414 | + | 0.974263i | \(0.427627\pi\) | |||||||
\(998\) | −2.04528e7 | −0.650021 | ||||||||
\(999\) | 2.27559e6 | 0.0721406 |
(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 | 165.6.a.e.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.a.1.3 | 3 | |||
5.4 | even | 2 | 825.6.a.f.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.e.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.a.1.3 | 3 | 3.2 | odd | 2 | |||
825.6.a.f.1.3 | 3 | 5.4 | even | 2 |