Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.34253.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 52x + 48 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.921799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.92180 | 0.516506 | 0.258253 | − | 0.966077i | \(-0.416853\pi\) | ||||
0.258253 | + | 0.966077i | \(0.416853\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −23.4631 | −0.733222 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −26.2962 | −0.298205 | ||||||||
\(7\) | 85.0105 | 0.655734 | 0.327867 | − | 0.944724i | \(-0.393670\pi\) | ||||
0.327867 | + | 0.944724i | \(0.393670\pi\) | |||||||
\(8\) | −162.052 | −0.895219 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 211.168 | 0.423326 | ||||||||
\(13\) | −724.085 | −1.18831 | −0.594157 | − | 0.804349i | \(-0.702514\pi\) | ||||
−0.594157 | + | 0.804349i | \(0.702514\pi\) | |||||||
\(14\) | 248.384 | 0.338690 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 277.335 | 0.270835 | ||||||||
\(17\) | 2098.75 | 1.76132 | 0.880662 | − | 0.473745i | \(-0.157098\pi\) | ||||
0.880662 | + | 0.473745i | \(0.157098\pi\) | |||||||
\(18\) | 236.666 | 0.172169 | ||||||||
\(19\) | −6.40223 | −0.00406862 | −0.00203431 | − | 0.999998i | \(-0.500648\pi\) | ||||
−0.00203431 | + | 0.999998i | \(0.500648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −765.094 | −0.378588 | ||||||||
\(22\) | −353.538 | −0.155732 | ||||||||
\(23\) | −1569.80 | −0.618764 | −0.309382 | − | 0.950938i | \(-0.600122\pi\) | ||||
−0.309382 | + | 0.950938i | \(0.600122\pi\) | |||||||
\(24\) | 1458.47 | 0.516855 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2115.63 | −0.613771 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −1994.61 | −0.480798 | ||||||||
\(29\) | −5145.94 | −1.13624 | −0.568119 | − | 0.822946i | \(-0.692329\pi\) | ||||
−0.568119 | + | 0.822946i | \(0.692329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1031.88 | −0.192852 | −0.0964259 | − | 0.995340i | \(-0.530741\pi\) | ||||
−0.0964259 | + | 0.995340i | \(0.530741\pi\) | |||||||
\(32\) | 5995.98 | 1.03511 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 6132.14 | 0.909735 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1900.51 | −0.244407 | ||||||||
\(37\) | 12641.6 | 1.51809 | 0.759045 | − | 0.651039i | \(-0.225666\pi\) | ||||
0.759045 | + | 0.651039i | \(0.225666\pi\) | |||||||
\(38\) | −18.7060 | −0.00210147 | ||||||||
\(39\) | 6516.76 | 0.686073 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13808.7 | 1.28290 | 0.641450 | − | 0.767165i | \(-0.278333\pi\) | ||||
0.641450 | + | 0.767165i | \(0.278333\pi\) | |||||||
\(42\) | −2235.45 | −0.195543 | ||||||||
\(43\) | 17012.0 | 1.40308 | 0.701542 | − | 0.712628i | \(-0.252495\pi\) | ||||
0.701542 | + | 0.712628i | \(0.252495\pi\) | |||||||
\(44\) | 2839.03 | 0.221075 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4586.64 | −0.319595 | ||||||||
\(47\) | −8078.06 | −0.533412 | −0.266706 | − | 0.963778i | \(-0.585935\pi\) | ||||
−0.266706 | + | 0.963778i | \(0.585935\pi\) | |||||||
\(48\) | −2496.02 | −0.156367 | ||||||||
\(49\) | −9580.22 | −0.570013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18888.8 | −1.01690 | ||||||||
\(52\) | 16989.3 | 0.871297 | ||||||||
\(53\) | 22110.8 | 1.08122 | 0.540612 | − | 0.841272i | \(-0.318193\pi\) | ||||
0.540612 | + | 0.841272i | \(0.318193\pi\) | |||||||
\(54\) | −2129.99 | −0.0994016 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13776.1 | −0.587025 | ||||||||
\(57\) | 57.6201 | 0.00234902 | ||||||||
\(58\) | −15035.4 | −0.586874 | ||||||||
\(59\) | −16890.6 | −0.631706 | −0.315853 | − | 0.948808i | \(-0.602291\pi\) | ||||
−0.315853 | + | 0.948808i | \(0.602291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34398.6 | −1.18363 | −0.591816 | − | 0.806073i | \(-0.701589\pi\) | ||||
−0.591816 | + | 0.806073i | \(0.701589\pi\) | |||||||
\(62\) | −3014.94 | −0.0996091 | ||||||||
\(63\) | 6885.85 | 0.218578 | ||||||||
\(64\) | 8644.32 | 0.263804 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3181.84 | 0.0899122 | ||||||||
\(67\) | 37306.5 | 1.01531 | 0.507654 | − | 0.861561i | \(-0.330513\pi\) | ||||
0.507654 | + | 0.861561i | \(0.330513\pi\) | |||||||
\(68\) | −49243.3 | −1.29144 | ||||||||
\(69\) | 14128.2 | 0.357244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56607.5 | −1.33269 | −0.666344 | − | 0.745645i | \(-0.732142\pi\) | ||||
−0.666344 | + | 0.745645i | \(0.732142\pi\) | |||||||
\(72\) | −13126.2 | −0.298406 | ||||||||
\(73\) | 27777.9 | 0.610088 | 0.305044 | − | 0.952338i | \(-0.401329\pi\) | ||||
0.305044 | + | 0.952338i | \(0.401329\pi\) | |||||||
\(74\) | 36936.2 | 0.784102 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 150.216 | 0.00298320 | ||||||||
\(77\) | −10286.3 | −0.197711 | ||||||||
\(78\) | 19040.7 | 0.354361 | ||||||||
\(79\) | −12759.9 | −0.230028 | −0.115014 | − | 0.993364i | \(-0.536691\pi\) | ||||
−0.115014 | + | 0.993364i | \(0.536691\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 40346.2 | 0.662625 | ||||||||
\(83\) | 69258.6 | 1.10352 | 0.551758 | − | 0.834004i | \(-0.313957\pi\) | ||||
0.551758 | + | 0.834004i | \(0.313957\pi\) | |||||||
\(84\) | 17951.5 | 0.277589 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 49705.6 | 0.724702 | ||||||||
\(87\) | 46313.5 | 0.656008 | ||||||||
\(88\) | 19608.3 | 0.269919 | ||||||||
\(89\) | 59029.2 | 0.789936 | 0.394968 | − | 0.918695i | \(-0.370756\pi\) | ||||
0.394968 | + | 0.918695i | \(0.370756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61554.8 | −0.779217 | ||||||||
\(92\) | 36832.4 | 0.453691 | ||||||||
\(93\) | 9286.89 | 0.111343 | ||||||||
\(94\) | −23602.5 | −0.275510 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −53963.8 | −0.597620 | ||||||||
\(97\) | −104905. | −1.13205 | −0.566027 | − | 0.824387i | \(-0.691520\pi\) | ||||
−0.566027 | + | 0.824387i | \(0.691520\pi\) | |||||||
\(98\) | −27991.5 | −0.294415 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 135417. | 1.32090 | 0.660451 | − | 0.750869i | \(-0.270365\pi\) | ||||
0.660451 | + | 0.750869i | \(0.270365\pi\) | |||||||
\(102\) | −55189.3 | −0.525236 | ||||||||
\(103\) | −167505. | −1.55573 | −0.777867 | − | 0.628428i | \(-0.783698\pi\) | ||||
−0.777867 | + | 0.628428i | \(0.783698\pi\) | |||||||
\(104\) | 117339. | 1.06380 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 64603.4 | 0.558458 | ||||||||
\(107\) | −57989.6 | −0.489656 | −0.244828 | − | 0.969567i | \(-0.578731\pi\) | ||||
−0.244828 | + | 0.969567i | \(0.578731\pi\) | |||||||
\(108\) | 17104.6 | 0.141109 | ||||||||
\(109\) | −14956.1 | −0.120574 | −0.0602869 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602869 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −113774. | −0.876469 | ||||||||
\(112\) | 23576.4 | 0.177596 | ||||||||
\(113\) | −198323. | −1.46109 | −0.730544 | − | 0.682866i | \(-0.760733\pi\) | ||||
−0.730544 | + | 0.682866i | \(0.760733\pi\) | |||||||
\(114\) | 168.354 | 0.00121328 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 120740. | 0.833115 | ||||||||
\(117\) | −58650.9 | −0.396105 | ||||||||
\(118\) | −49351.0 | −0.326280 | ||||||||
\(119\) | 178416. | 1.15496 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −100506. | −0.611353 | ||||||||
\(123\) | −124278. | −0.740682 | ||||||||
\(124\) | 24211.0 | 0.141403 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20119.1 | 0.112897 | ||||||||
\(127\) | 40986.5 | 0.225492 | 0.112746 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(128\) | −166614. | −0.898851 | ||||||||
\(129\) | −153108. | −0.810071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −238406. | −1.21378 | −0.606889 | − | 0.794787i | \(-0.707583\pi\) | ||||
−0.606889 | + | 0.794787i | \(0.707583\pi\) | |||||||
\(132\) | −25551.3 | −0.127637 | ||||||||
\(133\) | −544.257 | −0.00266793 | ||||||||
\(134\) | 109002. | 0.524413 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −340107. | −1.57677 | ||||||||
\(137\) | −149534. | −0.680673 | −0.340337 | − | 0.940304i | \(-0.610541\pi\) | ||||
−0.340337 | + | 0.940304i | \(0.610541\pi\) | |||||||
\(138\) | 41279.8 | 0.184518 | ||||||||
\(139\) | 167700. | 0.736202 | 0.368101 | − | 0.929786i | \(-0.380008\pi\) | ||||
0.368101 | + | 0.929786i | \(0.380008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 72702.5 | 0.307965 | ||||||||
\(142\) | −165396. | −0.688341 | ||||||||
\(143\) | 87614.3 | 0.358290 | ||||||||
\(144\) | 22464.2 | 0.0902785 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 81161.5 | 0.315114 | ||||||||
\(147\) | 86221.9 | 0.329097 | ||||||||
\(148\) | −296611. | −1.11310 | ||||||||
\(149\) | −272698. | −1.00627 | −0.503136 | − | 0.864207i | \(-0.667821\pi\) | ||||
−0.503136 | + | 0.864207i | \(0.667821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −448320. | −1.60009 | −0.800047 | − | 0.599937i | \(-0.795192\pi\) | ||||
−0.800047 | + | 0.599937i | \(0.795192\pi\) | |||||||
\(152\) | 1037.49 | 0.00364231 | ||||||||
\(153\) | 169999. | 0.587108 | ||||||||
\(154\) | −30054.4 | −0.102119 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −152903. | −0.503044 | ||||||||
\(157\) | 366634. | 1.18709 | 0.593545 | − | 0.804801i | \(-0.297728\pi\) | ||||
0.593545 | + | 0.804801i | \(0.297728\pi\) | |||||||
\(158\) | −37281.9 | −0.118811 | ||||||||
\(159\) | −198998. | −0.624245 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133450. | −0.405744 | ||||||||
\(162\) | 19169.9 | 0.0573896 | ||||||||
\(163\) | −501806. | −1.47934 | −0.739668 | − | 0.672972i | \(-0.765018\pi\) | ||||
−0.739668 | + | 0.672972i | \(0.765018\pi\) | |||||||
\(164\) | −323994. | −0.940650 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 202360. | 0.569973 | ||||||||
\(167\) | 195231. | 0.541700 | 0.270850 | − | 0.962622i | \(-0.412695\pi\) | ||||
0.270850 | + | 0.962622i | \(0.412695\pi\) | |||||||
\(168\) | 123985. | 0.338919 | ||||||||
\(169\) | 153006. | 0.412089 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −518.581 | −0.00135621 | ||||||||
\(172\) | −399154. | −1.02877 | ||||||||
\(173\) | −618180. | −1.57036 | −0.785181 | − | 0.619266i | \(-0.787430\pi\) | ||||
−0.785181 | + | 0.619266i | \(0.787430\pi\) | |||||||
\(174\) | 135319. | 0.338832 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −33557.6 | −0.0816600 | ||||||||
\(177\) | 152015. | 0.364716 | ||||||||
\(178\) | 172471. | 0.408007 | ||||||||
\(179\) | −88898.6 | −0.207378 | −0.103689 | − | 0.994610i | \(-0.533065\pi\) | ||||
−0.103689 | + | 0.994610i | \(0.533065\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −378128. | −0.857911 | −0.428956 | − | 0.903326i | \(-0.641118\pi\) | ||||
−0.428956 | + | 0.903326i | \(0.641118\pi\) | |||||||
\(182\) | −179851. | −0.402470 | ||||||||
\(183\) | 309588. | 0.683370 | ||||||||
\(184\) | 254389. | 0.553930 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 27134.4 | 0.0575093 | ||||||||
\(187\) | −253949. | −0.531059 | ||||||||
\(188\) | 189536. | 0.391109 | ||||||||
\(189\) | −61972.7 | −0.126196 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 125442. | 0.248806 | 0.124403 | − | 0.992232i | \(-0.460299\pi\) | ||||
0.124403 | + | 0.992232i | \(0.460299\pi\) | |||||||
\(192\) | −77798.9 | −0.152307 | ||||||||
\(193\) | 928398. | 1.79408 | 0.897038 | − | 0.441953i | \(-0.145714\pi\) | ||||
0.897038 | + | 0.441953i | \(0.145714\pi\) | |||||||
\(194\) | −306512. | −0.584713 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 224781. | 0.417946 | ||||||||
\(197\) | −1.03233e6 | −1.89519 | −0.947595 | − | 0.319473i | \(-0.896494\pi\) | ||||
−0.947595 | + | 0.319473i | \(0.896494\pi\) | |||||||
\(198\) | −28636.6 | −0.0519108 | ||||||||
\(199\) | −155017. | −0.277489 | −0.138744 | − | 0.990328i | \(-0.544307\pi\) | ||||
−0.138744 | + | 0.990328i | \(0.544307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −335759. | −0.586188 | ||||||||
\(202\) | 395662. | 0.682254 | ||||||||
\(203\) | −437459. | −0.745070 | ||||||||
\(204\) | 443189. | 0.745614 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −489417. | −0.803546 | ||||||||
\(207\) | −127154. | −0.206255 | ||||||||
\(208\) | −200814. | −0.321837 | ||||||||
\(209\) | 774.670 | 0.00122674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −364263. | −0.563259 | −0.281630 | − | 0.959523i | \(-0.590875\pi\) | ||||
−0.281630 | + | 0.959523i | \(0.590875\pi\) | |||||||
\(212\) | −518789. | −0.792777 | ||||||||
\(213\) | 509468. | 0.769428 | ||||||||
\(214\) | −169434. | −0.252910 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 118136. | 0.172285 | ||||||||
\(217\) | −87720.4 | −0.126459 | ||||||||
\(218\) | −43698.8 | −0.0622771 | ||||||||
\(219\) | −250001. | −0.352234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.51968e6 | −2.09301 | ||||||||
\(222\) | −332426. | −0.452702 | ||||||||
\(223\) | 74806.0 | 0.100734 | 0.0503668 | − | 0.998731i | \(-0.483961\pi\) | ||||
0.0503668 | + | 0.998731i | \(0.483961\pi\) | |||||||
\(224\) | 509721. | 0.678755 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −579459. | −0.754661 | ||||||||
\(227\) | −1.22677e6 | −1.58015 | −0.790075 | − | 0.613010i | \(-0.789958\pi\) | ||||
−0.790075 | + | 0.613010i | \(0.789958\pi\) | |||||||
\(228\) | −1351.94 | −0.00172235 | ||||||||
\(229\) | −440852. | −0.555526 | −0.277763 | − | 0.960650i | \(-0.589593\pi\) | ||||
−0.277763 | + | 0.960650i | \(0.589593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 92576.4 | 0.114149 | ||||||||
\(232\) | 833910. | 1.01718 | ||||||||
\(233\) | 514549. | 0.620922 | 0.310461 | − | 0.950586i | \(-0.399517\pi\) | ||||
0.310461 | + | 0.950586i | \(0.399517\pi\) | |||||||
\(234\) | −171366. | −0.204590 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 396306. | 0.463181 | ||||||||
\(237\) | 114839. | 0.132807 | ||||||||
\(238\) | 521296. | 0.596544 | ||||||||
\(239\) | −984315. | −1.11465 | −0.557326 | − | 0.830294i | \(-0.688173\pi\) | ||||
−0.557326 | + | 0.830294i | \(0.688173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 284794. | 0.315855 | 0.157927 | − | 0.987451i | \(-0.449519\pi\) | ||||
0.157927 | + | 0.987451i | \(0.449519\pi\) | |||||||
\(242\) | 42778.1 | 0.0469551 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 807098. | 0.867865 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −363116. | −0.382567 | ||||||||
\(247\) | 4635.76 | 0.00483480 | ||||||||
\(248\) | 167218. | 0.172645 | ||||||||
\(249\) | −623328. | −0.637115 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 134529. | 0.134782 | 0.0673911 | − | 0.997727i | \(-0.478532\pi\) | ||||
0.0673911 | + | 0.997727i | \(0.478532\pi\) | |||||||
\(252\) | −161563. | −0.160266 | ||||||||
\(253\) | 189946. | 0.186564 | ||||||||
\(254\) | 119754. | 0.116468 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −763432. | −0.728066 | ||||||||
\(257\) | −2.06732e6 | −1.95242 | −0.976212 | − | 0.216817i | \(-0.930433\pi\) | ||||
−0.976212 | + | 0.216817i | \(0.930433\pi\) | |||||||
\(258\) | −447350. | −0.418407 | ||||||||
\(259\) | 1.07467e6 | 0.995462 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −416821. | −0.378746 | ||||||||
\(262\) | −696575. | −0.626924 | ||||||||
\(263\) | 661739. | 0.589926 | 0.294963 | − | 0.955509i | \(-0.404693\pi\) | ||||
0.294963 | + | 0.955509i | \(0.404693\pi\) | |||||||
\(264\) | −176475. | −0.155838 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1590.21 | −0.00137800 | ||||||||
\(267\) | −531263. | −0.456070 | ||||||||
\(268\) | −875327. | −0.744446 | ||||||||
\(269\) | 703008. | 0.592351 | 0.296176 | − | 0.955133i | \(-0.404289\pi\) | ||||
0.296176 | + | 0.955133i | \(0.404289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.33847e6 | −1.10710 | −0.553549 | − | 0.832817i | \(-0.686727\pi\) | ||||
−0.553549 | + | 0.832817i | \(0.686727\pi\) | |||||||
\(272\) | 582059. | 0.477029 | ||||||||
\(273\) | 553993. | 0.449881 | ||||||||
\(274\) | −436908. | −0.351572 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −331492. | −0.261939 | ||||||||
\(277\) | 33171.1 | 0.0259753 | 0.0129877 | − | 0.999916i | \(-0.495866\pi\) | ||||
0.0129877 | + | 0.999916i | \(0.495866\pi\) | |||||||
\(278\) | 489987. | 0.380253 | ||||||||
\(279\) | −83582.0 | −0.0642839 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −321114. | −0.242601 | −0.121301 | − | 0.992616i | \(-0.538707\pi\) | ||||
−0.121301 | + | 0.992616i | \(0.538707\pi\) | |||||||
\(282\) | 212422. | 0.159066 | ||||||||
\(283\) | 1.90591e6 | 1.41461 | 0.707305 | − | 0.706908i | \(-0.249911\pi\) | ||||
0.707305 | + | 0.706908i | \(0.249911\pi\) | |||||||
\(284\) | 1.32819e6 | 0.977155 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 255991. | 0.185059 | ||||||||
\(287\) | 1.17388e6 | 0.841240 | ||||||||
\(288\) | 485675. | 0.345036 | ||||||||
\(289\) | 2.98491e6 | 2.10226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 944146. | 0.653592 | ||||||||
\(292\) | −651756. | −0.447330 | ||||||||
\(293\) | −272957. | −0.185748 | −0.0928742 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928742 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(294\) | 251923. | 0.169981 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.04859e6 | −1.35902 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −796768. | −0.519746 | ||||||||
\(299\) | 1.13667e6 | 0.735286 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.44620e6 | 0.920050 | ||||||||
\(302\) | −1.30990e6 | −0.826459 | ||||||||
\(303\) | −1.21876e6 | −0.762624 | ||||||||
\(304\) | −1775.57 | −0.00110193 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 496703. | 0.303245 | ||||||||
\(307\) | 843806. | 0.510971 | 0.255486 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255486 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(308\) | 241348. | 0.144966 | ||||||||
\(309\) | 1.50755e6 | 0.898204 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.06909e6 | 1.21305 | 0.606523 | − | 0.795066i | \(-0.292564\pi\) | ||||
0.606523 | + | 0.795066i | \(0.292564\pi\) | |||||||
\(312\) | −1.05605e6 | −0.614186 | ||||||||
\(313\) | −603113. | −0.347967 | −0.173983 | − | 0.984749i | \(-0.555664\pi\) | ||||
−0.173983 | + | 0.984749i | \(0.555664\pi\) | |||||||
\(314\) | 1.07123e6 | 0.613139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 299387. | 0.168661 | ||||||||
\(317\) | 1.67334e6 | 0.935268 | 0.467634 | − | 0.883922i | \(-0.345107\pi\) | ||||
0.467634 | + | 0.883922i | \(0.345107\pi\) | |||||||
\(318\) | −581431. | −0.322426 | ||||||||
\(319\) | 622659. | 0.342589 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 521907. | 0.282703 | ||||||||
\(322\) | −389913. | −0.209569 | ||||||||
\(323\) | −13436.7 | −0.00716616 | ||||||||
\(324\) | −153941. | −0.0814691 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.46618e6 | −0.764086 | ||||||||
\(327\) | 134605. | 0.0696133 | ||||||||
\(328\) | −2.23772e6 | −1.14848 | ||||||||
\(329\) | −686720. | −0.349776 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.20421e6 | −1.10582 | −0.552909 | − | 0.833242i | \(-0.686482\pi\) | ||||
−0.552909 | + | 0.833242i | \(0.686482\pi\) | |||||||
\(332\) | −1.62502e6 | −0.809122 | ||||||||
\(333\) | 1.02397e6 | 0.506030 | ||||||||
\(334\) | 570427. | 0.279791 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −212188. | −0.102535 | ||||||||
\(337\) | −1.07377e6 | −0.515036 | −0.257518 | − | 0.966273i | \(-0.582905\pi\) | ||||
−0.257518 | + | 0.966273i | \(0.582905\pi\) | |||||||
\(338\) | 447052. | 0.212847 | ||||||||
\(339\) | 1.78490e6 | 0.843559 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 124857. | 0.0581470 | ||||||||
\(342\) | −1515.19 | −0.000700489 0 | ||||||||
\(343\) | −2.24319e6 | −1.02951 | ||||||||
\(344\) | −2.75683e6 | −1.25607 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.80620e6 | −0.811101 | ||||||||
\(347\) | 1.39783e6 | 0.623203 | 0.311601 | − | 0.950213i | \(-0.399135\pi\) | ||||
0.311601 | + | 0.950213i | \(0.399135\pi\) | |||||||
\(348\) | −1.08666e6 | −0.480999 | ||||||||
\(349\) | −2.66674e6 | −1.17197 | −0.585985 | − | 0.810322i | \(-0.699292\pi\) | ||||
−0.585985 | + | 0.810322i | \(0.699292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 527858. | 0.228691 | ||||||||
\(352\) | −725514. | −0.312097 | ||||||||
\(353\) | 594048. | 0.253738 | 0.126869 | − | 0.991920i | \(-0.459507\pi\) | ||||
0.126869 | + | 0.991920i | \(0.459507\pi\) | |||||||
\(354\) | 444159. | 0.188378 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.38501e6 | −0.579198 | ||||||||
\(357\) | −1.60575e6 | −0.666816 | ||||||||
\(358\) | −259744. | −0.107112 | ||||||||
\(359\) | −3.35774e6 | −1.37503 | −0.687513 | − | 0.726172i | \(-0.741298\pi\) | ||||
−0.687513 | + | 0.726172i | \(0.741298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47606e6 | −0.999983 | ||||||||
\(362\) | −1.10481e6 | −0.443116 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 1.44427e6 | 0.571339 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 904553. | 0.352965 | ||||||||
\(367\) | −2.58775e6 | −1.00290 | −0.501450 | − | 0.865187i | \(-0.667200\pi\) | ||||
−0.501450 | + | 0.865187i | \(0.667200\pi\) | |||||||
\(368\) | −435362. | −0.167583 | ||||||||
\(369\) | 1.11850e6 | 0.427633 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.87965e6 | 0.708995 | ||||||||
\(372\) | −217899. | −0.0816391 | ||||||||
\(373\) | 1.07376e6 | 0.399608 | 0.199804 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199804 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(374\) | −741989. | −0.274295 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.30907e6 | 0.477520 | ||||||||
\(377\) | 3.72610e6 | 1.35021 | ||||||||
\(378\) | −181072. | −0.0651810 | ||||||||
\(379\) | 5.16745e6 | 1.84790 | 0.923949 | − | 0.382516i | \(-0.124942\pi\) | ||||
0.923949 | + | 0.382516i | \(0.124942\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −368878. | −0.130188 | ||||||||
\(382\) | 366517. | 0.128510 | ||||||||
\(383\) | −2.42092e6 | −0.843302 | −0.421651 | − | 0.906758i | \(-0.638549\pi\) | ||||
−0.421651 | + | 0.906758i | \(0.638549\pi\) | |||||||
\(384\) | 1.49953e6 | 0.518952 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.71259e6 | 0.926651 | ||||||||
\(387\) | 1.37797e6 | 0.467695 | ||||||||
\(388\) | 2.46140e6 | 0.830047 | ||||||||
\(389\) | 1.92154e6 | 0.643835 | 0.321918 | − | 0.946768i | \(-0.395673\pi\) | ||||
0.321918 | + | 0.946768i | \(0.395673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.29463e6 | −1.08984 | ||||||||
\(392\) | 1.55249e6 | 0.510287 | ||||||||
\(393\) | 2.14566e6 | 0.700775 | ||||||||
\(394\) | −3.01626e6 | −0.978877 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 229962. | 0.0736915 | ||||||||
\(397\) | −4.09572e6 | −1.30423 | −0.652114 | − | 0.758121i | \(-0.726118\pi\) | ||||
−0.652114 | + | 0.758121i | \(0.726118\pi\) | |||||||
\(398\) | −452928. | −0.143325 | ||||||||
\(399\) | 4898.31 | 0.00154033 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.97525e6 | 1.85565 | 0.927823 | − | 0.373022i | \(-0.121678\pi\) | ||||
0.927823 | + | 0.373022i | \(0.121678\pi\) | |||||||
\(402\) | −981020. | −0.302770 | ||||||||
\(403\) | 747167. | 0.229168 | ||||||||
\(404\) | −3.17731e6 | −0.968514 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.27817e6 | −0.384833 | ||||||||
\(407\) | −1.52963e6 | −0.457721 | ||||||||
\(408\) | 3.06097e6 | 0.910350 | ||||||||
\(409\) | −1.92665e6 | −0.569500 | −0.284750 | − | 0.958602i | \(-0.591911\pi\) | ||||
−0.284750 | + | 0.958602i | \(0.591911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.34581e6 | 0.392987 | ||||||||
\(412\) | 3.93019e6 | 1.14070 | ||||||||
\(413\) | −1.43588e6 | −0.414231 | ||||||||
\(414\) | −371518. | −0.106532 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.34160e6 | −1.23003 | ||||||||
\(417\) | −1.50930e6 | −0.425047 | ||||||||
\(418\) | 2263.43 | 0.000633616 0 | ||||||||
\(419\) | −1.47857e6 | −0.411441 | −0.205720 | − | 0.978611i | \(-0.565954\pi\) | ||||
−0.205720 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.82644e6 | 1.32715 | 0.663577 | − | 0.748108i | \(-0.269037\pi\) | ||||
0.663577 | + | 0.748108i | \(0.269037\pi\) | |||||||
\(422\) | −1.06430e6 | −0.290927 | ||||||||
\(423\) | −654323. | −0.177804 | ||||||||
\(424\) | −3.58311e6 | −0.967932 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.48856e6 | 0.397414 | ||||||||
\(427\) | −2.92425e6 | −0.776147 | ||||||||
\(428\) | 1.36062e6 | 0.359026 | ||||||||
\(429\) | −788528. | −0.206859 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.89229e6 | 0.749978 | 0.374989 | − | 0.927029i | \(-0.377647\pi\) | ||||
0.374989 | + | 0.927029i | \(0.377647\pi\) | |||||||
\(432\) | −202178. | −0.0521223 | ||||||||
\(433\) | −2.36700e6 | −0.606706 | −0.303353 | − | 0.952878i | \(-0.598106\pi\) | ||||
−0.303353 | + | 0.952878i | \(0.598106\pi\) | |||||||
\(434\) | −256301. | −0.0653170 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 350917. | 0.0884073 | ||||||||
\(437\) | 10050.2 | 0.00251752 | ||||||||
\(438\) | −730453. | −0.181931 | ||||||||
\(439\) | 3.22037e6 | 0.797525 | 0.398762 | − | 0.917054i | \(-0.369440\pi\) | ||||
0.398762 | + | 0.917054i | \(0.369440\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −775997. | −0.190004 | ||||||||
\(442\) | −4.44019e6 | −1.08105 | ||||||||
\(443\) | 3.80335e6 | 0.920782 | 0.460391 | − | 0.887716i | \(-0.347709\pi\) | ||||
0.460391 | + | 0.887716i | \(0.347709\pi\) | |||||||
\(444\) | 2.66950e6 | 0.642646 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 218568. | 0.0520295 | ||||||||
\(447\) | 2.45428e6 | 0.580972 | ||||||||
\(448\) | 734858. | 0.172985 | ||||||||
\(449\) | −6.55303e6 | −1.53400 | −0.767001 | − | 0.641646i | \(-0.778252\pi\) | ||||
−0.767001 | + | 0.641646i | \(0.778252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67085e6 | −0.386809 | ||||||||
\(452\) | 4.65326e6 | 1.07130 | ||||||||
\(453\) | 4.03488e6 | 0.923815 | ||||||||
\(454\) | −3.58437e6 | −0.816157 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9337.45 | −0.00210289 | ||||||||
\(457\) | 7.41470e6 | 1.66074 | 0.830372 | − | 0.557209i | \(-0.188128\pi\) | ||||
0.830372 | + | 0.557209i | \(0.188128\pi\) | |||||||
\(458\) | −1.28808e6 | −0.286932 | ||||||||
\(459\) | −1.52999e6 | −0.338967 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 409525. | 0.0897487 | 0.0448743 | − | 0.998993i | \(-0.485711\pi\) | ||||
0.0448743 | + | 0.998993i | \(0.485711\pi\) | |||||||
\(462\) | 270490. | 0.0589584 | ||||||||
\(463\) | −7.07192e6 | −1.53315 | −0.766575 | − | 0.642154i | \(-0.778041\pi\) | ||||
−0.766575 | + | 0.642154i | \(0.778041\pi\) | |||||||
\(464\) | −1.42715e6 | −0.307734 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50341e6 | 0.320710 | ||||||||
\(467\) | 6.35423e6 | 1.34825 | 0.674125 | − | 0.738617i | \(-0.264521\pi\) | ||||
0.674125 | + | 0.738617i | \(0.264521\pi\) | |||||||
\(468\) | 1.37613e6 | 0.290432 | ||||||||
\(469\) | 3.17145e6 | 0.665772 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.29970e6 | −0.685366 | ||||||||
\(472\) | 2.73716e6 | 0.565516 | ||||||||
\(473\) | −2.05845e6 | −0.423046 | ||||||||
\(474\) | 335537. | 0.0685954 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.18619e6 | −0.846841 | ||||||||
\(477\) | 1.79098e6 | 0.360408 | ||||||||
\(478\) | −2.87597e6 | −0.575725 | ||||||||
\(479\) | 6.36751e6 | 1.26803 | 0.634017 | − | 0.773319i | \(-0.281405\pi\) | ||||
0.634017 | + | 0.773319i | \(0.281405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.15358e6 | −1.80397 | ||||||||
\(482\) | 832109. | 0.163141 | ||||||||
\(483\) | 1.20105e6 | 0.234257 | ||||||||
\(484\) | −343523. | −0.0666565 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −172529. | −0.0331339 | ||||||||
\(487\) | 2.94280e6 | 0.562261 | 0.281130 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281130 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(488\) | 5.57437e6 | 1.05961 | ||||||||
\(489\) | 4.51626e6 | 0.854095 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −501628. | −0.0939027 | −0.0469513 | − | 0.998897i | \(-0.514951\pi\) | ||||
−0.0469513 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(492\) | 2.91595e6 | 0.543084 | ||||||||
\(493\) | −1.08001e7 | −2.00129 | ||||||||
\(494\) | 13544.8 | 0.00249720 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −286176. | −0.0522311 | ||||||||
\(497\) | −4.81224e6 | −0.873888 | ||||||||
\(498\) | −1.82124e6 | −0.329074 | ||||||||
\(499\) | −9.19784e6 | −1.65362 | −0.826808 | − | 0.562484i | \(-0.809846\pi\) | ||||
−0.826808 | + | 0.562484i | \(0.809846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.75708e6 | −0.312750 | ||||||||
\(502\) | 393068. | 0.0696158 | ||||||||
\(503\) | 6.53811e6 | 1.15221 | 0.576106 | − | 0.817375i | \(-0.304572\pi\) | ||||
0.576106 | + | 0.817375i | \(0.304572\pi\) | |||||||
\(504\) | −1.11587e6 | −0.195675 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 554984. | 0.0963616 | ||||||||
\(507\) | −1.37705e6 | −0.237920 | ||||||||
\(508\) | −961669. | −0.165336 | ||||||||
\(509\) | −1.49017e6 | −0.254942 | −0.127471 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127471 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.36141e6 | 0.400055 | ||||||||
\(512\) | 3.10107e6 | 0.522801 | ||||||||
\(513\) | 4667.23 | 0.000783007 0 | ||||||||
\(514\) | −6.04029e6 | −1.00844 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.59238e6 | 0.593962 | ||||||||
\(517\) | 977445. | 0.160830 | ||||||||
\(518\) | 3.13996e6 | 0.514162 | ||||||||
\(519\) | 5.56362e6 | 0.906649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.82163e6 | 0.616814 | 0.308407 | − | 0.951255i | \(-0.400204\pi\) | ||||
0.308407 | + | 0.951255i | \(0.400204\pi\) | |||||||
\(522\) | −1.21787e6 | −0.195625 | ||||||||
\(523\) | 4.18273e6 | 0.668660 | 0.334330 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334330 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(524\) | 5.59375e6 | 0.889968 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.93347e6 | 0.304700 | ||||||||
\(527\) | −2.16566e6 | −0.339675 | ||||||||
\(528\) | 302018. | 0.0471464 | ||||||||
\(529\) | −3.97207e6 | −0.617131 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.36814e6 | −0.210569 | ||||||||
\(532\) | 12769.9 | 0.00195619 | ||||||||
\(533\) | −9.99866e6 | −1.52449 | ||||||||
\(534\) | −1.55224e6 | −0.235563 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.04560e6 | −0.908923 | ||||||||
\(537\) | 800088. | 0.119730 | ||||||||
\(538\) | 2.05405e6 | 0.305953 | ||||||||
\(539\) | 1.15921e6 | 0.171866 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.80424e6 | 0.411928 | 0.205964 | − | 0.978560i | \(-0.433967\pi\) | ||||
0.205964 | + | 0.978560i | \(0.433967\pi\) | |||||||
\(542\) | −3.91075e6 | −0.571823 | ||||||||
\(543\) | 3.40315e6 | 0.495315 | ||||||||
\(544\) | 1.25841e7 | 1.82316 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.61866e6 | 0.232366 | ||||||||
\(547\) | 8.42403e6 | 1.20379 | 0.601896 | − | 0.798574i | \(-0.294412\pi\) | ||||
0.601896 | + | 0.798574i | \(0.294412\pi\) | |||||||
\(548\) | 3.50853e6 | 0.499084 | ||||||||
\(549\) | −2.78629e6 | −0.394544 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32945.5 | 0.00462293 | ||||||||
\(552\) | −2.28951e6 | −0.319811 | ||||||||
\(553\) | −1.08473e6 | −0.150837 | ||||||||
\(554\) | 96919.4 | 0.0134164 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.93477e6 | −0.539799 | ||||||||
\(557\) | 3.56702e6 | 0.487155 | 0.243577 | − | 0.969881i | \(-0.421679\pi\) | ||||
0.243577 | + | 0.969881i | \(0.421679\pi\) | |||||||
\(558\) | −244210. | −0.0332030 | ||||||||
\(559\) | −1.23181e7 | −1.66730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.28554e6 | 0.306607 | ||||||||
\(562\) | −938231. | −0.125305 | ||||||||
\(563\) | −4.70552e6 | −0.625658 | −0.312829 | − | 0.949810i | \(-0.601277\pi\) | ||||
−0.312829 | + | 0.949810i | \(0.601277\pi\) | |||||||
\(564\) | −1.70583e6 | −0.225807 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.56869e6 | 0.730655 | ||||||||
\(567\) | 557754. | 0.0728593 | ||||||||
\(568\) | 9.17337e6 | 1.19305 | ||||||||
\(569\) | 2.60879e6 | 0.337799 | 0.168900 | − | 0.985633i | \(-0.445979\pi\) | ||||
0.168900 | + | 0.985633i | \(0.445979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.13036e6 | 0.145086 | 0.0725431 | − | 0.997365i | \(-0.476889\pi\) | ||||
0.0725431 | + | 0.997365i | \(0.476889\pi\) | |||||||
\(572\) | −2.05570e6 | −0.262706 | ||||||||
\(573\) | −1.12898e6 | −0.143648 | ||||||||
\(574\) | 3.42985e6 | 0.434506 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 700190. | 0.0879346 | ||||||||
\(577\) | −1.12075e7 | −1.40142 | −0.700710 | − | 0.713446i | \(-0.747133\pi\) | ||||
−0.700710 | + | 0.713446i | \(0.747133\pi\) | |||||||
\(578\) | 8.72132e6 | 1.08583 | ||||||||
\(579\) | −8.35558e6 | −1.03581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.88771e6 | 0.723613 | ||||||||
\(582\) | 2.75861e6 | 0.337584 | ||||||||
\(583\) | −2.67541e6 | −0.326001 | ||||||||
\(584\) | −4.50147e6 | −0.546162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −797526. | −0.0959402 | ||||||||
\(587\) | −9.05798e6 | −1.08502 | −0.542508 | − | 0.840051i | \(-0.682525\pi\) | ||||
−0.542508 | + | 0.840051i | \(0.682525\pi\) | |||||||
\(588\) | −2.02303e6 | −0.241301 | ||||||||
\(589\) | 6606.31 | 0.000784641 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.29097e6 | 1.09419 | ||||||||
\(592\) | 3.50596e6 | 0.411152 | ||||||||
\(593\) | −1.00907e7 | −1.17837 | −0.589186 | − | 0.807997i | \(-0.700552\pi\) | ||||
−0.589186 | + | 0.807997i | \(0.700552\pi\) | |||||||
\(594\) | 257729. | 0.0299707 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.39833e6 | 0.737821 | ||||||||
\(597\) | 1.39515e6 | 0.160208 | ||||||||
\(598\) | 3.32112e6 | 0.379780 | ||||||||
\(599\) | −1.29126e7 | −1.47044 | −0.735222 | − | 0.677827i | \(-0.762922\pi\) | ||||
−0.735222 | + | 0.677827i | \(0.762922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.82591e6 | 0.206202 | 0.103101 | − | 0.994671i | \(-0.467124\pi\) | ||||
0.103101 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(602\) | 4.22550e6 | 0.475211 | ||||||||
\(603\) | 3.02183e6 | 0.338436 | ||||||||
\(604\) | 1.05190e7 | 1.17322 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.56096e6 | −0.393900 | ||||||||
\(607\) | 1.26409e6 | 0.139253 | 0.0696267 | − | 0.997573i | \(-0.477819\pi\) | ||||
0.0696267 | + | 0.997573i | \(0.477819\pi\) | |||||||
\(608\) | −38387.7 | −0.00421146 | ||||||||
\(609\) | 3.93713e6 | 0.430166 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.84920e6 | 0.633860 | ||||||||
\(612\) | −3.98870e6 | −0.430480 | ||||||||
\(613\) | −1.59125e7 | −1.71036 | −0.855180 | − | 0.518332i | \(-0.826553\pi\) | ||||
−0.855180 | + | 0.518332i | \(0.826553\pi\) | |||||||
\(614\) | 2.46543e6 | 0.263920 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.66691e6 | 0.176995 | ||||||||
\(617\) | −85225.6 | −0.00901274 | −0.00450637 | − | 0.999990i | \(-0.501434\pi\) | ||||
−0.00450637 | + | 0.999990i | \(0.501434\pi\) | |||||||
\(618\) | 4.40475e6 | 0.463928 | ||||||||
\(619\) | −1.20387e7 | −1.26285 | −0.631425 | − | 0.775437i | \(-0.717530\pi\) | ||||
−0.631425 | + | 0.775437i | \(0.717530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.14439e6 | 0.119081 | ||||||||
\(622\) | 6.04545e6 | 0.626546 | ||||||||
\(623\) | 5.01810e6 | 0.517987 | ||||||||
\(624\) | 1.80733e6 | 0.185813 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.76218e6 | −0.179727 | ||||||||
\(627\) | −6972.03 | −0.000708256 0 | ||||||||
\(628\) | −8.60236e6 | −0.870400 | ||||||||
\(629\) | 2.65316e7 | 2.67385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 121417. | 0.0121396 | 0.00606981 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00606981 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(632\) | 2.06777e6 | 0.205925 | ||||||||
\(633\) | 3.27836e6 | 0.325198 | ||||||||
\(634\) | 4.88916e6 | 0.483071 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.66910e6 | 0.457710 | ||||||||
\(637\) | 6.93689e6 | 0.677355 | ||||||||
\(638\) | 1.81928e6 | 0.176949 | ||||||||
\(639\) | −4.58521e6 | −0.444229 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.25328e7 | 1.20477 | 0.602385 | − | 0.798206i | \(-0.294217\pi\) | ||||
0.602385 | + | 0.798206i | \(0.294217\pi\) | |||||||
\(642\) | 1.52491e6 | 0.146018 | ||||||||
\(643\) | 3.45380e6 | 0.329435 | 0.164717 | − | 0.986341i | \(-0.447329\pi\) | ||||
0.164717 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(644\) | 3.13114e6 | 0.297501 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39259.4 | −0.00370137 | ||||||||
\(647\) | −1.71115e7 | −1.60704 | −0.803521 | − | 0.595276i | \(-0.797043\pi\) | ||||
−0.803521 | + | 0.595276i | \(0.797043\pi\) | |||||||
\(648\) | −1.06322e6 | −0.0994688 | ||||||||
\(649\) | 2.04376e6 | 0.190467 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 789483. | 0.0730114 | ||||||||
\(652\) | 1.17739e7 | 1.08468 | ||||||||
\(653\) | −1.61622e7 | −1.48326 | −0.741630 | − | 0.670809i | \(-0.765947\pi\) | ||||
−0.741630 | + | 0.670809i | \(0.765947\pi\) | |||||||
\(654\) | 393289. | 0.0359557 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.82964e6 | 0.347455 | ||||||||
\(657\) | 2.25001e6 | 0.203363 | ||||||||
\(658\) | −2.00646e6 | −0.180661 | ||||||||
\(659\) | 9.54805e6 | 0.856449 | 0.428224 | − | 0.903672i | \(-0.359139\pi\) | ||||
0.428224 | + | 0.903672i | \(0.359139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.24374e7 | −1.10720 | −0.553599 | − | 0.832784i | \(-0.686746\pi\) | ||||
−0.553599 | + | 0.832784i | \(0.686746\pi\) | |||||||
\(662\) | −6.44027e6 | −0.571162 | ||||||||
\(663\) | 1.36771e7 | 1.20840 | ||||||||
\(664\) | −1.12235e7 | −0.987889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.99183e6 | 0.261367 | ||||||||
\(667\) | 8.07810e6 | 0.703064 | ||||||||
\(668\) | −4.58073e6 | −0.397186 | ||||||||
\(669\) | −673254. | −0.0581586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.16224e6 | 0.356878 | ||||||||
\(672\) | −4.58749e6 | −0.391879 | ||||||||
\(673\) | −1.37772e7 | −1.17253 | −0.586266 | − | 0.810119i | \(-0.699403\pi\) | ||||
−0.586266 | + | 0.810119i | \(0.699403\pi\) | |||||||
\(674\) | −3.13735e6 | −0.266019 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.58999e6 | −0.302153 | ||||||||
\(677\) | 1.06456e6 | 0.0892683 | 0.0446341 | − | 0.999003i | \(-0.485788\pi\) | ||||
0.0446341 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(678\) | 5.21513e6 | 0.435703 | ||||||||
\(679\) | −8.91804e6 | −0.742326 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.10409e7 | 0.912300 | ||||||||
\(682\) | 364807. | 0.0300333 | ||||||||
\(683\) | 1.48070e7 | 1.21455 | 0.607275 | − | 0.794492i | \(-0.292263\pi\) | ||||
0.607275 | + | 0.794492i | \(0.292263\pi\) | |||||||
\(684\) | 12167.5 | 0.000994400 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.55415e6 | −0.531748 | ||||||||
\(687\) | 3.96767e6 | 0.320733 | ||||||||
\(688\) | 4.71803e6 | 0.380005 | ||||||||
\(689\) | −1.60101e7 | −1.28483 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.56554e7 | 1.24729 | 0.623646 | − | 0.781707i | \(-0.285651\pi\) | ||||
0.623646 | + | 0.781707i | \(0.285651\pi\) | |||||||
\(692\) | 1.45044e7 | 1.15142 | ||||||||
\(693\) | −833188. | −0.0659037 | ||||||||
\(694\) | 4.08417e6 | 0.321888 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.50519e6 | −0.587271 | ||||||||
\(697\) | 2.89810e7 | 2.25960 | ||||||||
\(698\) | −7.79167e6 | −0.605330 | ||||||||
\(699\) | −4.63094e6 | −0.358490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.56474e7 | 1.20267 | 0.601334 | − | 0.798998i | \(-0.294636\pi\) | ||||
0.601334 | + | 0.798998i | \(0.294636\pi\) | |||||||
\(702\) | 1.54229e6 | 0.118120 | ||||||||
\(703\) | −80934.4 | −0.00617653 | ||||||||
\(704\) | −1.04596e6 | −0.0795398 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.73569e6 | 0.131057 | ||||||||
\(707\) | 1.15119e7 | 0.866160 | ||||||||
\(708\) | −3.56675e6 | −0.267417 | ||||||||
\(709\) | −635875. | −0.0475068 | −0.0237534 | − | 0.999718i | \(-0.507562\pi\) | ||||
−0.0237534 | + | 0.999718i | \(0.507562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.03355e6 | −0.0766759 | ||||||||
\(712\) | −9.56580e6 | −0.707166 | ||||||||
\(713\) | 1.61984e6 | 0.119330 | ||||||||
\(714\) | −4.69167e6 | −0.344415 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08584e6 | 0.152054 | ||||||||
\(717\) | 8.85884e6 | 0.643545 | ||||||||
\(718\) | −9.81064e6 | −0.710209 | ||||||||
\(719\) | −2.50359e6 | −0.180610 | −0.0903048 | − | 0.995914i | \(-0.528784\pi\) | ||||
−0.0903048 | + | 0.995914i | \(0.528784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.42397e7 | −1.02015 | ||||||||
\(722\) | −7.23454e6 | −0.516497 | ||||||||
\(723\) | −2.56314e6 | −0.182359 | ||||||||
\(724\) | 8.87205e6 | 0.629039 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −385003. | −0.0271095 | ||||||||
\(727\) | −8.82888e6 | −0.619540 | −0.309770 | − | 0.950811i | \(-0.600252\pi\) | ||||
−0.309770 | + | 0.950811i | \(0.600252\pi\) | |||||||
\(728\) | 9.97508e6 | 0.697570 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.57040e7 | 2.47129 | ||||||||
\(732\) | −7.26389e6 | −0.501062 | ||||||||
\(733\) | 2.93960e6 | 0.202082 | 0.101041 | − | 0.994882i | \(-0.467783\pi\) | ||||
0.101041 | + | 0.994882i | \(0.467783\pi\) | |||||||
\(734\) | −7.56089e6 | −0.518004 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.41250e6 | −0.640487 | ||||||||
\(737\) | −4.51409e6 | −0.306127 | ||||||||
\(738\) | 3.26804e6 | 0.220875 | ||||||||
\(739\) | −1.51762e6 | −0.102224 | −0.0511120 | − | 0.998693i | \(-0.516277\pi\) | ||||
−0.0511120 | + | 0.998693i | \(0.516277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41721.8 | −0.00279137 | ||||||||
\(742\) | 5.49197e6 | 0.366200 | ||||||||
\(743\) | 1.07165e7 | 0.712168 | 0.356084 | − | 0.934454i | \(-0.384112\pi\) | ||||
0.356084 | + | 0.934454i | \(0.384112\pi\) | |||||||
\(744\) | −1.50496e6 | −0.0996764 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.13731e6 | 0.206400 | ||||||||
\(747\) | 5.60995e6 | 0.367839 | ||||||||
\(748\) | 5.95844e6 | 0.389384 | ||||||||
\(749\) | −4.92973e6 | −0.321084 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.69694e7 | −1.74490 | −0.872452 | − | 0.488700i | \(-0.837471\pi\) | ||||
−0.872452 | + | 0.488700i | \(0.837471\pi\) | |||||||
\(752\) | −2.24033e6 | −0.144467 | ||||||||
\(753\) | −1.21076e6 | −0.0778165 | ||||||||
\(754\) | 1.08869e7 | 0.697391 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.45407e6 | 0.0925296 | ||||||||
\(757\) | 2.81995e7 | 1.78855 | 0.894275 | − | 0.447518i | \(-0.147692\pi\) | ||||
0.894275 | + | 0.447518i | \(0.147692\pi\) | |||||||
\(758\) | 1.50982e7 | 0.954450 | ||||||||
\(759\) | −1.70951e6 | −0.107713 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.29643e6 | 0.331529 | 0.165764 | − | 0.986165i | \(-0.446991\pi\) | ||||
0.165764 | + | 0.986165i | \(0.446991\pi\) | |||||||
\(762\) | −1.07779e6 | −0.0672428 | ||||||||
\(763\) | −1.27143e6 | −0.0790643 | ||||||||
\(764\) | −2.94326e6 | −0.182430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.07344e6 | −0.435571 | ||||||||
\(767\) | 1.22302e7 | 0.750665 | ||||||||
\(768\) | 6.87089e6 | 0.420349 | ||||||||
\(769\) | 6.09571e6 | 0.371714 | 0.185857 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185857 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.86059e7 | 1.12723 | ||||||||
\(772\) | −2.17831e7 | −1.31546 | ||||||||
\(773\) | −1.02486e7 | −0.616901 | −0.308451 | − | 0.951240i | \(-0.599810\pi\) | ||||
−0.308451 | + | 0.951240i | \(0.599810\pi\) | |||||||
\(774\) | 4.02615e6 | 0.241567 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.70001e7 | 1.01344 | ||||||||
\(777\) | −9.67201e6 | −0.574730 | ||||||||
\(778\) | 5.61434e6 | 0.332545 | ||||||||
\(779\) | −88406.4 | −0.00521963 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.84951e6 | 0.401820 | ||||||||
\(782\) | −9.62624e6 | −0.562911 | ||||||||
\(783\) | 3.75139e6 | 0.218669 | ||||||||
\(784\) | −2.65693e6 | −0.154380 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.26917e6 | 0.361954 | ||||||||
\(787\) | 1.62333e7 | 0.934267 | 0.467133 | − | 0.884187i | \(-0.345287\pi\) | ||||
0.467133 | + | 0.884187i | \(0.345287\pi\) | |||||||
\(788\) | 2.42217e7 | 1.38959 | ||||||||
\(789\) | −5.95565e6 | −0.340594 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.68595e7 | −0.958084 | ||||||||
\(792\) | 1.58827e6 | 0.0899729 | ||||||||
\(793\) | 2.49075e7 | 1.40653 | ||||||||
\(794\) | −1.19669e7 | −0.673642 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.63717e6 | 0.203461 | ||||||||
\(797\) | −1.29153e7 | −0.720211 | −0.360105 | − | 0.932912i | \(-0.617259\pi\) | ||||
−0.360105 | + | 0.932912i | \(0.617259\pi\) | |||||||
\(798\) | 14311.9 | 0.000795590 0 | ||||||||
\(799\) | −1.69539e7 | −0.939511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.78136e6 | 0.263312 | ||||||||
\(802\) | 1.74585e7 | 0.958452 | ||||||||
\(803\) | −3.36113e6 | −0.183948 | ||||||||
\(804\) | 7.87794e6 | 0.429806 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.18307e6 | 0.118367 | ||||||||
\(807\) | −6.32707e6 | −0.341994 | ||||||||
\(808\) | −2.19447e7 | −1.18250 | ||||||||
\(809\) | 1.40361e6 | 0.0754007 | 0.0377004 | − | 0.999289i | \(-0.487997\pi\) | ||||
0.0377004 | + | 0.999289i | \(0.487997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.27909e7 | −0.682887 | −0.341444 | − | 0.939902i | \(-0.610916\pi\) | ||||
−0.341444 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(812\) | 1.02641e7 | 0.546301 | ||||||||
\(813\) | 1.20462e7 | 0.639183 | ||||||||
\(814\) | −4.46928e6 | −0.236416 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.23853e6 | −0.275413 | ||||||||
\(817\) | −108915. | −0.00570862 | ||||||||
\(818\) | −5.62928e6 | −0.294150 | ||||||||
\(819\) | −4.98594e6 | −0.259739 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.20603e6 | −0.269556 | −0.134778 | − | 0.990876i | \(-0.543032\pi\) | ||||
−0.134778 | + | 0.990876i | \(0.543032\pi\) | |||||||
\(822\) | 3.93217e6 | 0.202980 | ||||||||
\(823\) | −3.77702e7 | −1.94379 | −0.971896 | − | 0.235409i | \(-0.924357\pi\) | ||||
−0.971896 | + | 0.235409i | \(0.924357\pi\) | |||||||
\(824\) | 2.71446e7 | 1.39272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.19535e6 | −0.213953 | ||||||||
\(827\) | 2.54890e7 | 1.29595 | 0.647976 | − | 0.761661i | \(-0.275616\pi\) | ||||
0.647976 | + | 0.761661i | \(0.275616\pi\) | |||||||
\(828\) | 2.98342e6 | 0.151230 | ||||||||
\(829\) | 1.71410e7 | 0.866262 | 0.433131 | − | 0.901331i | \(-0.357409\pi\) | ||||
0.433131 | + | 0.901331i | \(0.357409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −298540. | −0.0149969 | ||||||||
\(832\) | −6.25922e6 | −0.313482 | ||||||||
\(833\) | −2.01065e7 | −1.00398 | ||||||||
\(834\) | −4.40988e6 | −0.219539 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18176.1 | −0.000899469 0 | ||||||||
\(837\) | 752238. | 0.0371143 | ||||||||
\(838\) | −4.32009e6 | −0.212512 | ||||||||
\(839\) | −1.01094e7 | −0.495818 | −0.247909 | − | 0.968783i | \(-0.579743\pi\) | ||||
−0.247909 | + | 0.968783i | \(0.579743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.96954e6 | 0.291039 | ||||||||
\(842\) | 1.41019e7 | 0.685483 | ||||||||
\(843\) | 2.89003e6 | 0.140066 | ||||||||
\(844\) | 8.54672e6 | 0.412994 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.91180e6 | −0.0918368 | ||||||||
\(847\) | 1.24464e6 | 0.0596121 | ||||||||
\(848\) | 6.13212e6 | 0.292834 | ||||||||
\(849\) | −1.71532e7 | −0.816726 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.98448e7 | −0.939339 | ||||||||
\(852\) | −1.19537e7 | −0.564161 | ||||||||
\(853\) | −3.29141e7 | −1.54885 | −0.774425 | − | 0.632666i | \(-0.781961\pi\) | ||||
−0.774425 | + | 0.632666i | \(0.781961\pi\) | |||||||
\(854\) | −8.54406e6 | −0.400885 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.39734e6 | 0.438349 | ||||||||
\(857\) | −6.94241e6 | −0.322893 | −0.161446 | − | 0.986881i | \(-0.551616\pi\) | ||||
−0.161446 | + | 0.986881i | \(0.551616\pi\) | |||||||
\(858\) | −2.30392e6 | −0.106844 | ||||||||
\(859\) | −1.84275e7 | −0.852085 | −0.426042 | − | 0.904703i | \(-0.640093\pi\) | ||||
−0.426042 | + | 0.904703i | \(0.640093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.05649e7 | −0.485690 | ||||||||
\(862\) | 8.45068e6 | 0.387368 | ||||||||
\(863\) | 2.60648e7 | 1.19131 | 0.595657 | − | 0.803239i | \(-0.296892\pi\) | ||||
0.595657 | + | 0.803239i | \(0.296892\pi\) | |||||||
\(864\) | −4.37107e6 | −0.199207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.91589e6 | −0.313367 | ||||||||
\(867\) | −2.68642e7 | −1.21374 | ||||||||
\(868\) | 2.05819e6 | 0.0927228 | ||||||||
\(869\) | 1.54395e6 | 0.0693559 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.70131e7 | −1.20650 | ||||||||
\(872\) | 2.42367e6 | 0.107940 | ||||||||
\(873\) | −8.49731e6 | −0.377352 | ||||||||
\(874\) | 29364.8 | 0.00130031 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.86580e6 | 0.258266 | ||||||||
\(877\) | −1.86288e6 | −0.0817875 | −0.0408937 | − | 0.999164i | \(-0.513021\pi\) | ||||
−0.0408937 | + | 0.999164i | \(0.513021\pi\) | |||||||
\(878\) | 9.40927e6 | 0.411926 | ||||||||
\(879\) | 2.45661e6 | 0.107242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.01838e7 | 0.442051 | 0.221025 | − | 0.975268i | \(-0.429060\pi\) | ||||
0.221025 | + | 0.975268i | \(0.429060\pi\) | |||||||
\(882\) | −2.26731e6 | −0.0981384 | ||||||||
\(883\) | −6.25954e6 | −0.270172 | −0.135086 | − | 0.990834i | \(-0.543131\pi\) | ||||
−0.135086 | + | 0.990834i | \(0.543131\pi\) | |||||||
\(884\) | 3.56563e7 | 1.53464 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.11126e7 | 0.475589 | ||||||||
\(887\) | −1.80319e7 | −0.769540 | −0.384770 | − | 0.923012i | \(-0.625719\pi\) | ||||
−0.384770 | + | 0.923012i | \(0.625719\pi\) | |||||||
\(888\) | 1.84374e7 | 0.784632 | ||||||||
\(889\) | 3.48428e6 | 0.147863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −1.75518e6 | −0.0738600 | ||||||||
\(893\) | 51717.6 | 0.00217025 | ||||||||
\(894\) | 7.17091e6 | 0.300075 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.41640e7 | −0.589407 | ||||||||
\(897\) | −1.02300e7 | −0.424518 | ||||||||
\(898\) | −1.91466e7 | −0.792321 | ||||||||
\(899\) | 5.30998e6 | 0.219126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.64052e7 | 1.90439 | ||||||||
\(902\) | −4.88189e6 | −0.199789 | ||||||||
\(903\) | −1.30158e7 | −0.531191 | ||||||||
\(904\) | 3.21386e7 | 1.30799 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.17891e7 | 0.477156 | ||||||||
\(907\) | −2.69733e7 | −1.08872 | −0.544360 | − | 0.838852i | \(-0.683228\pi\) | ||||
−0.544360 | + | 0.838852i | \(0.683228\pi\) | |||||||
\(908\) | 2.87838e7 | 1.15860 | ||||||||
\(909\) | 1.09688e7 | 0.440301 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.31660e7 | −1.72324 | −0.861621 | − | 0.507553i | \(-0.830550\pi\) | ||||
−0.861621 | + | 0.507553i | \(0.830550\pi\) | |||||||
\(912\) | 15980.1 | 0.000636198 0 | ||||||||
\(913\) | −8.38029e6 | −0.332723 | ||||||||
\(914\) | 2.16643e7 | 0.857784 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.03438e7 | 0.407323 | ||||||||
\(917\) | −2.02670e7 | −0.795915 | ||||||||
\(918\) | −4.47033e6 | −0.175079 | ||||||||
\(919\) | −3.69944e7 | −1.44493 | −0.722465 | − | 0.691407i | \(-0.756991\pi\) | ||||
−0.722465 | + | 0.691407i | \(0.756991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.59425e6 | −0.295010 | ||||||||
\(922\) | 1.19655e6 | 0.0463557 | ||||||||
\(923\) | 4.09887e7 | 1.58365 | ||||||||
\(924\) | −2.17213e6 | −0.0836962 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.06627e7 | −0.791882 | ||||||||
\(927\) | −1.35679e7 | −0.518578 | ||||||||
\(928\) | −3.08550e7 | −1.17613 | ||||||||
\(929\) | 1.63853e6 | 0.0622895 | 0.0311447 | − | 0.999515i | \(-0.490085\pi\) | ||||
0.0311447 | + | 0.999515i | \(0.490085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 61334.7 | 0.00231917 | ||||||||
\(932\) | −1.20729e7 | −0.455273 | ||||||||
\(933\) | −1.86218e7 | −0.700353 | ||||||||
\(934\) | 1.85658e7 | 0.696380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.50449e6 | 0.354600 | ||||||||
\(937\) | 2.02831e7 | 0.754719 | 0.377360 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377360 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(938\) | 9.26633e6 | 0.343875 | ||||||||
\(939\) | 5.42802e6 | 0.200899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.83342e7 | −0.674975 | −0.337487 | − | 0.941330i | \(-0.609577\pi\) | ||||
−0.337487 | + | 0.941330i | \(0.609577\pi\) | |||||||
\(942\) | −9.64107e6 | −0.353996 | ||||||||
\(943\) | −2.16769e7 | −0.793812 | ||||||||
\(944\) | −4.68436e6 | −0.171088 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.01438e6 | −0.218506 | ||||||||
\(947\) | 6.09095e6 | 0.220704 | 0.110352 | − | 0.993893i | \(-0.464802\pi\) | ||||
0.110352 | + | 0.993893i | \(0.464802\pi\) | |||||||
\(948\) | −2.69448e6 | −0.0973766 | ||||||||
\(949\) | −2.01136e7 | −0.724976 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.50601e7 | −0.539977 | ||||||||
\(952\) | −2.89127e7 | −1.03394 | ||||||||
\(953\) | 5.31211e7 | 1.89467 | 0.947337 | − | 0.320238i | \(-0.103763\pi\) | ||||
0.947337 | + | 0.320238i | \(0.103763\pi\) | |||||||
\(954\) | 5.23288e6 | 0.186153 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.30951e7 | 0.817287 | ||||||||
\(957\) | −5.60393e6 | −0.197794 | ||||||||
\(958\) | 1.86046e7 | 0.654947 | ||||||||
\(959\) | −1.27120e7 | −0.446340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.75644e7 | −0.962808 | ||||||||
\(962\) | −2.67449e7 | −0.931759 | ||||||||
\(963\) | −4.69716e6 | −0.163219 | ||||||||
\(964\) | −6.68214e6 | −0.231592 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.50922e6 | 0.120995 | ||||||||
\(967\) | 2.17670e6 | 0.0748570 | 0.0374285 | − | 0.999299i | \(-0.488083\pi\) | ||||
0.0374285 | + | 0.999299i | \(0.488083\pi\) | |||||||
\(968\) | −2.37260e6 | −0.0813836 | ||||||||
\(969\) | 120930. | 0.00413739 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.83305e7 | 1.64503 | 0.822514 | − | 0.568745i | \(-0.192571\pi\) | ||||
0.822514 | + | 0.568745i | \(0.192571\pi\) | |||||||
\(972\) | 1.38547e6 | 0.0470362 | ||||||||
\(973\) | 1.42563e7 | 0.482753 | ||||||||
\(974\) | 8.59826e6 | 0.290411 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.53996e6 | −0.320569 | ||||||||
\(977\) | 3.84816e7 | 1.28978 | 0.644892 | − | 0.764274i | \(-0.276902\pi\) | ||||
0.644892 | + | 0.764274i | \(0.276902\pi\) | |||||||
\(978\) | 1.31956e7 | 0.441145 | ||||||||
\(979\) | −7.14253e6 | −0.238175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.21145e6 | −0.0401913 | ||||||||
\(982\) | −1.46566e6 | −0.0485013 | ||||||||
\(983\) | 1.53385e7 | 0.506288 | 0.253144 | − | 0.967429i | \(-0.418535\pi\) | ||||
0.253144 | + | 0.967429i | \(0.418535\pi\) | |||||||
\(984\) | 2.01395e7 | 0.663073 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.15556e7 | −1.03368 | ||||||||
\(987\) | 6.18048e6 | 0.201943 | ||||||||
\(988\) | −108769. | −0.00354498 | ||||||||
\(989\) | −2.67054e7 | −0.868178 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.29143e7 | −1.38809 | −0.694046 | − | 0.719931i | \(-0.744174\pi\) | ||||
−0.694046 | + | 0.719931i | \(0.744174\pi\) | |||||||
\(992\) | −6.18712e6 | −0.199622 | ||||||||
\(993\) | 1.98379e7 | 0.638444 | ||||||||
\(994\) | −1.40604e7 | −0.451368 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.46252e7 | 0.467147 | ||||||||
\(997\) | −6.10887e7 | −1.94636 | −0.973180 | − | 0.230044i | \(-0.926113\pi\) | ||||
−0.973180 | + | 0.230044i | \(0.926113\pi\) | |||||||
\(998\) | −2.68742e7 | −0.854102 | ||||||||
\(999\) | −9.21572e6 | −0.292156 |
(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 | 825.6.a.j.1.2 | 3 | ||
5.4 | even | 2 | 165.6.a.a.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 495.6.a.e.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.a.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
495.6.a.e.1.2 | 3 | 15.14 | odd | 2 | |||
825.6.a.j.1.2 | 3 | 1.1 | even | 1 | trivial |