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: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 152x^{5} + 358x^{4} + 5771x^{3} - 13444x^{2} - 51316x + 92576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.60892\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60892 | −0.461197 | −0.230598 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230598 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −25.1935 | −0.787297 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −23.4803 | −0.266272 | ||||||||
\(7\) | 174.969 | 1.34963 | 0.674817 | − | 0.737985i | \(-0.264223\pi\) | ||||
0.674817 | + | 0.737985i | \(0.264223\pi\) | |||||||
\(8\) | 149.214 | 0.824296 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −226.742 | −0.454546 | ||||||||
\(13\) | −815.527 | −1.33838 | −0.669191 | − | 0.743091i | \(-0.733359\pi\) | ||||
−0.669191 | + | 0.743091i | \(0.733359\pi\) | |||||||
\(14\) | −456.481 | −0.622447 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 416.906 | 0.407135 | ||||||||
\(17\) | 462.991 | 0.388553 | 0.194276 | − | 0.980947i | \(-0.437764\pi\) | ||||
0.194276 | + | 0.980947i | \(0.437764\pi\) | |||||||
\(18\) | −211.323 | −0.153732 | ||||||||
\(19\) | −1996.09 | −1.26851 | −0.634257 | − | 0.773122i | \(-0.718694\pi\) | ||||
−0.634257 | + | 0.773122i | \(0.718694\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1574.72 | 0.779211 | ||||||||
\(22\) | −315.680 | −0.139056 | ||||||||
\(23\) | 1342.70 | 0.529250 | 0.264625 | − | 0.964351i | \(-0.414752\pi\) | ||||
0.264625 | + | 0.964351i | \(0.414752\pi\) | |||||||
\(24\) | 1342.92 | 0.475908 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2127.65 | 0.617257 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −4408.08 | −1.06256 | ||||||||
\(29\) | 6586.33 | 1.45428 | 0.727141 | − | 0.686488i | \(-0.240849\pi\) | ||||
0.727141 | + | 0.686488i | \(0.240849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4492.74 | −0.839667 | −0.419833 | − | 0.907601i | \(-0.637911\pi\) | ||||
−0.419833 | + | 0.907601i | \(0.637911\pi\) | |||||||
\(32\) | −5862.51 | −1.01207 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −1207.91 | −0.179199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2040.67 | −0.262432 | ||||||||
\(37\) | −9089.95 | −1.09158 | −0.545792 | − | 0.837921i | \(-0.683771\pi\) | ||||
−0.545792 | + | 0.837921i | \(0.683771\pi\) | |||||||
\(38\) | 5207.64 | 0.585035 | ||||||||
\(39\) | −7339.74 | −0.772715 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1108.16 | −0.102954 | −0.0514769 | − | 0.998674i | \(-0.516393\pi\) | ||||
−0.0514769 | + | 0.998674i | \(0.516393\pi\) | |||||||
\(42\) | −4108.32 | −0.359370 | ||||||||
\(43\) | −20231.4 | −1.66861 | −0.834304 | − | 0.551304i | \(-0.814130\pi\) | ||||
−0.834304 | + | 0.551304i | \(0.814130\pi\) | |||||||
\(44\) | −3048.42 | −0.237379 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3503.01 | −0.244088 | ||||||||
\(47\) | −9098.00 | −0.600761 | −0.300380 | − | 0.953820i | \(-0.597114\pi\) | ||||
−0.300380 | + | 0.953820i | \(0.597114\pi\) | |||||||
\(48\) | 3752.15 | 0.235059 | ||||||||
\(49\) | 13807.1 | 0.821510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4166.92 | 0.224331 | ||||||||
\(52\) | 20546.0 | 1.05370 | ||||||||
\(53\) | −38340.2 | −1.87484 | −0.937422 | − | 0.348196i | \(-0.886794\pi\) | ||||
−0.937422 | + | 0.348196i | \(0.886794\pi\) | |||||||
\(54\) | −1901.91 | −0.0887574 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 26107.7 | 1.11250 | ||||||||
\(57\) | −17964.8 | −0.732377 | ||||||||
\(58\) | −17183.2 | −0.670711 | ||||||||
\(59\) | 29309.0 | 1.09615 | 0.548076 | − | 0.836429i | \(-0.315361\pi\) | ||||
0.548076 | + | 0.836429i | \(0.315361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32390.1 | 1.11452 | 0.557260 | − | 0.830338i | \(-0.311853\pi\) | ||||
0.557260 | + | 0.830338i | \(0.311853\pi\) | |||||||
\(62\) | 11721.2 | 0.387252 | ||||||||
\(63\) | 14172.5 | 0.449878 | ||||||||
\(64\) | 1953.85 | 0.0596267 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2841.12 | −0.0802841 | ||||||||
\(67\) | 64412.9 | 1.75302 | 0.876508 | − | 0.481387i | \(-0.159867\pi\) | ||||
0.876508 | + | 0.481387i | \(0.159867\pi\) | |||||||
\(68\) | −11664.4 | −0.305907 | ||||||||
\(69\) | 12084.3 | 0.305562 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63314.4 | −1.49058 | −0.745292 | − | 0.666738i | \(-0.767690\pi\) | ||||
−0.745292 | + | 0.666738i | \(0.767690\pi\) | |||||||
\(72\) | 12086.3 | 0.274765 | ||||||||
\(73\) | −4121.83 | −0.0905279 | −0.0452640 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452640 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(74\) | 23715.0 | 0.503435 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 50288.4 | 0.998698 | ||||||||
\(77\) | 21171.2 | 0.406930 | ||||||||
\(78\) | 19148.8 | 0.356374 | ||||||||
\(79\) | −53233.3 | −0.959656 | −0.479828 | − | 0.877363i | \(-0.659301\pi\) | ||||
−0.479828 | + | 0.877363i | \(0.659301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 2891.10 | 0.0474820 | ||||||||
\(83\) | 119847. | 1.90956 | 0.954780 | − | 0.297315i | \(-0.0960910\pi\) | ||||
0.954780 | + | 0.297315i | \(0.0960910\pi\) | |||||||
\(84\) | −39672.7 | −0.613471 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 52782.1 | 0.769557 | ||||||||
\(87\) | 59277.0 | 0.839630 | ||||||||
\(88\) | 18054.8 | 0.248535 | ||||||||
\(89\) | 66306.8 | 0.887326 | 0.443663 | − | 0.896194i | \(-0.353679\pi\) | ||||
0.443663 | + | 0.896194i | \(0.353679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −142692. | −1.80632 | ||||||||
\(92\) | −33827.4 | −0.416677 | ||||||||
\(93\) | −40434.6 | −0.484782 | ||||||||
\(94\) | 23736.0 | 0.277069 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −52762.6 | −0.584316 | ||||||||
\(97\) | 180567. | 1.94854 | 0.974268 | − | 0.225394i | \(-0.0723670\pi\) | ||||
0.974268 | + | 0.225394i | \(0.0723670\pi\) | |||||||
\(98\) | −36021.7 | −0.378878 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −113813. | −1.11017 | −0.555084 | − | 0.831794i | \(-0.687314\pi\) | ||||
−0.555084 | + | 0.831794i | \(0.687314\pi\) | |||||||
\(102\) | −10871.2 | −0.103461 | ||||||||
\(103\) | −192758. | −1.79027 | −0.895135 | − | 0.445795i | \(-0.852921\pi\) | ||||
−0.895135 | + | 0.445795i | \(0.852921\pi\) | |||||||
\(104\) | −121688. | −1.10322 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 100027. | 0.864672 | ||||||||
\(107\) | 139114. | 1.17465 | 0.587327 | − | 0.809350i | \(-0.300180\pi\) | ||||
0.587327 | + | 0.809350i | \(0.300180\pi\) | |||||||
\(108\) | −18366.1 | −0.151515 | ||||||||
\(109\) | 97360.0 | 0.784900 | 0.392450 | − | 0.919773i | \(-0.371628\pi\) | ||||
0.392450 | + | 0.919773i | \(0.371628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −81809.6 | −0.630227 | ||||||||
\(112\) | 72945.6 | 0.549483 | ||||||||
\(113\) | 20952.6 | 0.154362 | 0.0771811 | − | 0.997017i | \(-0.475408\pi\) | ||||
0.0771811 | + | 0.997017i | \(0.475408\pi\) | |||||||
\(114\) | 46868.7 | 0.337770 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −165933. | −1.14495 | ||||||||
\(117\) | −66057.7 | −0.446127 | ||||||||
\(118\) | −76464.9 | −0.505542 | ||||||||
\(119\) | 81009.0 | 0.524404 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −84503.4 | −0.514013 | ||||||||
\(123\) | −9973.43 | −0.0594404 | ||||||||
\(124\) | 113188. | 0.661067 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −36974.9 | −0.207482 | ||||||||
\(127\) | −347758. | −1.91323 | −0.956616 | − | 0.291351i | \(-0.905895\pi\) | ||||
−0.956616 | + | 0.291351i | \(0.905895\pi\) | |||||||
\(128\) | 182503. | 0.984566 | ||||||||
\(129\) | −182083. | −0.963372 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −160486. | −0.817070 | −0.408535 | − | 0.912743i | \(-0.633960\pi\) | ||||
−0.408535 | + | 0.912743i | \(0.633960\pi\) | |||||||
\(132\) | −27435.7 | −0.137051 | ||||||||
\(133\) | −349253. | −1.71203 | ||||||||
\(134\) | −168048. | −0.808486 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 69084.5 | 0.320282 | ||||||||
\(137\) | 142596. | 0.649090 | 0.324545 | − | 0.945870i | \(-0.394789\pi\) | ||||
0.324545 | + | 0.945870i | \(0.394789\pi\) | |||||||
\(138\) | −31527.1 | −0.140924 | ||||||||
\(139\) | −124192. | −0.545201 | −0.272600 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272600 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −81882.0 | −0.346849 | ||||||||
\(142\) | 165182. | 0.687453 | ||||||||
\(143\) | −98678.7 | −0.403537 | ||||||||
\(144\) | 33769.4 | 0.135712 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10753.5 | 0.0417512 | ||||||||
\(147\) | 124264. | 0.474299 | ||||||||
\(148\) | 229008. | 0.859402 | ||||||||
\(149\) | −332027. | −1.22520 | −0.612601 | − | 0.790393i | \(-0.709877\pi\) | ||||
−0.612601 | + | 0.790393i | \(0.709877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −221114. | −0.789177 | −0.394589 | − | 0.918858i | \(-0.629113\pi\) | ||||
−0.394589 | + | 0.918858i | \(0.629113\pi\) | |||||||
\(152\) | −297843. | −1.04563 | ||||||||
\(153\) | 37502.2 | 0.129518 | ||||||||
\(154\) | −55234.1 | −0.187675 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 184914. | 0.608356 | ||||||||
\(157\) | −178933. | −0.579350 | −0.289675 | − | 0.957125i | \(-0.593547\pi\) | ||||
−0.289675 | + | 0.957125i | \(0.593547\pi\) | |||||||
\(158\) | 138882. | 0.442590 | ||||||||
\(159\) | −345062. | −1.08244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 234931. | 0.714293 | ||||||||
\(162\) | −17117.1 | −0.0512441 | ||||||||
\(163\) | −222185. | −0.655007 | −0.327504 | − | 0.944850i | \(-0.606207\pi\) | ||||
−0.327504 | + | 0.944850i | \(0.606207\pi\) | |||||||
\(164\) | 27918.4 | 0.0810553 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −312673. | −0.880683 | ||||||||
\(167\) | −286150. | −0.793968 | −0.396984 | − | 0.917826i | \(-0.629943\pi\) | ||||
−0.396984 | + | 0.917826i | \(0.629943\pi\) | |||||||
\(168\) | 234970. | 0.642301 | ||||||||
\(169\) | 293791. | 0.791265 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −161683. | −0.422838 | ||||||||
\(172\) | 509700. | 1.31369 | ||||||||
\(173\) | −585626. | −1.48767 | −0.743833 | − | 0.668366i | \(-0.766994\pi\) | ||||
−0.743833 | + | 0.668366i | \(0.766994\pi\) | |||||||
\(174\) | −154649. | −0.387235 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 50445.6 | 0.122756 | ||||||||
\(177\) | 263781. | 0.632863 | ||||||||
\(178\) | −172989. | −0.409232 | ||||||||
\(179\) | −511386. | −1.19293 | −0.596467 | − | 0.802638i | \(-0.703429\pi\) | ||||
−0.596467 | + | 0.802638i | \(0.703429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16277.3 | −0.0369306 | −0.0184653 | − | 0.999830i | \(-0.505878\pi\) | ||||
−0.0184653 | + | 0.999830i | \(0.505878\pi\) | |||||||
\(182\) | 372272. | 0.833071 | ||||||||
\(183\) | 291511. | 0.643469 | ||||||||
\(184\) | 200350. | 0.436258 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 105491. | 0.223580 | ||||||||
\(187\) | 56021.9 | 0.117153 | ||||||||
\(188\) | 229211. | 0.472977 | ||||||||
\(189\) | 127552. | 0.259737 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −219087. | −0.434543 | −0.217271 | − | 0.976111i | \(-0.569716\pi\) | ||||
−0.217271 | + | 0.976111i | \(0.569716\pi\) | |||||||
\(192\) | 17584.6 | 0.0344255 | ||||||||
\(193\) | 704505. | 1.36142 | 0.680708 | − | 0.732555i | \(-0.261672\pi\) | ||||
0.680708 | + | 0.732555i | \(0.261672\pi\) | |||||||
\(194\) | −471085. | −0.898658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −347850. | −0.646773 | ||||||||
\(197\) | 670027. | 1.23006 | 0.615031 | − | 0.788503i | \(-0.289144\pi\) | ||||
0.615031 | + | 0.788503i | \(0.289144\pi\) | |||||||
\(198\) | −25570.1 | −0.0463520 | ||||||||
\(199\) | −591128. | −1.05815 | −0.529077 | − | 0.848574i | \(-0.677462\pi\) | ||||
−0.529077 | + | 0.848574i | \(0.677462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 579716. | 1.01210 | ||||||||
\(202\) | 296930. | 0.512006 | ||||||||
\(203\) | 1.15240e6 | 1.96275 | ||||||||
\(204\) | −104979. | −0.176615 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 502890. | 0.825667 | ||||||||
\(207\) | 108759. | 0.176417 | ||||||||
\(208\) | −339998. | −0.544901 | ||||||||
\(209\) | −241526. | −0.382471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1070.59 | −0.00165545 | −0.000827723 | − | 1.00000i | \(-0.500263\pi\) | ||||
−0.000827723 | 1.00000i | \(0.500263\pi\) | ||||||||
\(212\) | 965925. | 1.47606 | ||||||||
\(213\) | −569829. | −0.860589 | ||||||||
\(214\) | −362937. | −0.541747 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 108777. | 0.158636 | ||||||||
\(217\) | −786090. | −1.13324 | ||||||||
\(218\) | −254005. | −0.361993 | ||||||||
\(219\) | −37096.4 | −0.0522663 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −377581. | −0.520032 | ||||||||
\(222\) | 213435. | 0.290659 | ||||||||
\(223\) | −515555. | −0.694246 | −0.347123 | − | 0.937820i | \(-0.612841\pi\) | ||||
−0.347123 | + | 0.937820i | \(0.612841\pi\) | |||||||
\(224\) | −1.02576e6 | −1.36592 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −54663.6 | −0.0711914 | ||||||||
\(227\) | −69874.2 | −0.0900020 | −0.0450010 | − | 0.998987i | \(-0.514329\pi\) | ||||
−0.0450010 | + | 0.998987i | \(0.514329\pi\) | |||||||
\(228\) | 452596. | 0.576599 | ||||||||
\(229\) | 502115. | 0.632725 | 0.316362 | − | 0.948638i | \(-0.397538\pi\) | ||||
0.316362 | + | 0.948638i | \(0.397538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 190541. | 0.234941 | ||||||||
\(232\) | 982770. | 1.19876 | ||||||||
\(233\) | −1.52257e6 | −1.83733 | −0.918664 | − | 0.395041i | \(-0.870730\pi\) | ||||
−0.918664 | + | 0.395041i | \(0.870730\pi\) | |||||||
\(234\) | 172339. | 0.205752 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −738396. | −0.862997 | ||||||||
\(237\) | −479099. | −0.554058 | ||||||||
\(238\) | −211346. | −0.241853 | ||||||||
\(239\) | −601975. | −0.681685 | −0.340843 | − | 0.940120i | \(-0.610712\pi\) | ||||
−0.340843 | + | 0.940120i | \(0.610712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −960570. | −1.06534 | −0.532668 | − | 0.846324i | \(-0.678811\pi\) | ||||
−0.532668 | + | 0.846324i | \(0.678811\pi\) | |||||||
\(242\) | −38197.3 | −0.0419270 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −816021. | −0.877459 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26019.9 | 0.0274137 | ||||||||
\(247\) | 1.62786e6 | 1.69776 | ||||||||
\(248\) | −670377. | −0.692134 | ||||||||
\(249\) | 1.07863e6 | 1.10248 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −999437. | −1.00132 | −0.500658 | − | 0.865645i | \(-0.666909\pi\) | ||||
−0.500658 | + | 0.865645i | \(0.666909\pi\) | |||||||
\(252\) | −357055. | −0.354188 | ||||||||
\(253\) | 162467. | 0.159575 | ||||||||
\(254\) | 907274. | 0.882377 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −538659. | −0.513705 | ||||||||
\(257\) | −222038. | −0.209698 | −0.104849 | − | 0.994488i | \(-0.533436\pi\) | ||||
−0.104849 | + | 0.994488i | \(0.533436\pi\) | |||||||
\(258\) | 475039. | 0.444304 | ||||||||
\(259\) | −1.59046e6 | −1.47324 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 533493. | 0.484761 | ||||||||
\(262\) | 418696. | 0.376830 | ||||||||
\(263\) | 501628. | 0.447190 | 0.223595 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223595 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(264\) | 162494. | 0.143492 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 911175. | 0.789583 | ||||||||
\(267\) | 596761. | 0.512298 | ||||||||
\(268\) | −1.62279e6 | −1.38015 | ||||||||
\(269\) | −1.50544e6 | −1.26848 | −0.634238 | − | 0.773138i | \(-0.718686\pi\) | ||||
−0.634238 | + | 0.773138i | \(0.718686\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 935698. | 0.773949 | 0.386975 | − | 0.922090i | \(-0.373520\pi\) | ||||
0.386975 | + | 0.922090i | \(0.373520\pi\) | |||||||
\(272\) | 193024. | 0.158193 | ||||||||
\(273\) | −1.28423e6 | −1.04288 | ||||||||
\(274\) | −372021. | −0.299358 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −304447. | −0.240569 | ||||||||
\(277\) | −1.06811e6 | −0.836404 | −0.418202 | − | 0.908354i | \(-0.637340\pi\) | ||||
−0.418202 | + | 0.908354i | \(0.637340\pi\) | |||||||
\(278\) | 324007. | 0.251445 | ||||||||
\(279\) | −363912. | −0.279889 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 683491. | 0.516377 | 0.258189 | − | 0.966095i | \(-0.416874\pi\) | ||||
0.258189 | + | 0.966095i | \(0.416874\pi\) | |||||||
\(282\) | 213624. | 0.159966 | ||||||||
\(283\) | −272388. | −0.202172 | −0.101086 | − | 0.994878i | \(-0.532232\pi\) | ||||
−0.101086 | + | 0.994878i | \(0.532232\pi\) | |||||||
\(284\) | 1.59511e6 | 1.17353 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 257445. | 0.186110 | ||||||||
\(287\) | −193893. | −0.138950 | ||||||||
\(288\) | −474863. | −0.337355 | ||||||||
\(289\) | −1.20550e6 | −0.849027 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.62510e6 | 1.12499 | ||||||||
\(292\) | 103843. | 0.0712724 | ||||||||
\(293\) | −1.53914e6 | −1.04739 | −0.523697 | − | 0.851905i | \(-0.675447\pi\) | ||||
−0.523697 | + | 0.851905i | \(0.675447\pi\) | |||||||
\(294\) | −324196. | −0.218745 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.35634e6 | −0.899789 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 866233. | 0.565059 | ||||||||
\(299\) | −1.09501e6 | −0.708338 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.53986e6 | −2.25201 | ||||||||
\(302\) | 576870. | 0.363966 | ||||||||
\(303\) | −1.02432e6 | −0.640956 | ||||||||
\(304\) | −832180. | −0.516456 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −97840.5 | −0.0597331 | ||||||||
\(307\) | 800678. | 0.484855 | 0.242428 | − | 0.970170i | \(-0.422056\pi\) | ||||
0.242428 | + | 0.970170i | \(0.422056\pi\) | |||||||
\(308\) | −533378. | −0.320375 | ||||||||
\(309\) | −1.73482e6 | −1.03361 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.17233e6 | 1.85985 | 0.929925 | − | 0.367750i | \(-0.119872\pi\) | ||||
0.929925 | + | 0.367750i | \(0.119872\pi\) | |||||||
\(312\) | −1.09519e6 | −0.636946 | ||||||||
\(313\) | −996401. | −0.574875 | −0.287437 | − | 0.957799i | \(-0.592803\pi\) | ||||
−0.287437 | + | 0.957799i | \(0.592803\pi\) | |||||||
\(314\) | 466822. | 0.267194 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.34113e6 | 0.755535 | ||||||||
\(317\) | 1.73853e6 | 0.971702 | 0.485851 | − | 0.874042i | \(-0.338510\pi\) | ||||
0.485851 | + | 0.874042i | \(0.338510\pi\) | |||||||
\(318\) | 900241. | 0.499219 | ||||||||
\(319\) | 796946. | 0.438483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.25202e6 | 0.678187 | ||||||||
\(322\) | −612918. | −0.329430 | ||||||||
\(323\) | −924170. | −0.492885 | ||||||||
\(324\) | −165295. | −0.0874775 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 579664. | 0.302087 | ||||||||
\(327\) | 876240. | 0.453162 | ||||||||
\(328\) | −165352. | −0.0848644 | ||||||||
\(329\) | −1.59187e6 | −0.810807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −530501. | −0.266144 | −0.133072 | − | 0.991106i | \(-0.542484\pi\) | ||||
−0.133072 | + | 0.991106i | \(0.542484\pi\) | |||||||
\(332\) | −3.01938e6 | −1.50339 | ||||||||
\(333\) | −736286. | −0.363861 | ||||||||
\(334\) | 746544. | 0.366176 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 656510. | 0.317244 | ||||||||
\(337\) | 1110.26 | 0.000532538 0 | 0.000266269 | − | 1.00000i | \(-0.499915\pi\) | ||||
0.000266269 | 1.00000i | \(0.499915\pi\) | ||||||||
\(338\) | −766478. | −0.364929 | ||||||||
\(339\) | 188573. | 0.0891211 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −543621. | −0.253169 | ||||||||
\(342\) | 421819. | 0.195012 | ||||||||
\(343\) | −524885. | −0.240896 | ||||||||
\(344\) | −3.01880e6 | −1.37543 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.52785e6 | 0.686107 | ||||||||
\(347\) | −1.08849e6 | −0.485289 | −0.242644 | − | 0.970115i | \(-0.578015\pi\) | ||||
−0.242644 | + | 0.970115i | \(0.578015\pi\) | |||||||
\(348\) | −1.49340e6 | −0.661039 | ||||||||
\(349\) | −591038. | −0.259748 | −0.129874 | − | 0.991531i | \(-0.541457\pi\) | ||||
−0.129874 | + | 0.991531i | \(0.541457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −594519. | −0.257572 | ||||||||
\(352\) | −709363. | −0.305149 | ||||||||
\(353\) | −980027. | −0.418602 | −0.209301 | − | 0.977851i | \(-0.567119\pi\) | ||||
−0.209301 | + | 0.977851i | \(0.567119\pi\) | |||||||
\(354\) | −688184. | −0.291875 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.67050e6 | −0.698589 | ||||||||
\(357\) | 729081. | 0.302765 | ||||||||
\(358\) | 1.33417e6 | 0.550177 | ||||||||
\(359\) | −2.87712e6 | −1.17821 | −0.589104 | − | 0.808057i | \(-0.700519\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50826e6 | 0.609129 | ||||||||
\(362\) | 42466.3 | 0.0170323 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 3.59491e6 | 1.42211 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −760530. | −0.296766 | ||||||||
\(367\) | −3.28496e6 | −1.27311 | −0.636554 | − | 0.771232i | \(-0.719641\pi\) | ||||
−0.636554 | + | 0.771232i | \(0.719641\pi\) | |||||||
\(368\) | 559781. | 0.215476 | ||||||||
\(369\) | −89760.9 | −0.0343179 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.70835e6 | −2.53035 | ||||||||
\(372\) | 1.01869e6 | 0.381667 | ||||||||
\(373\) | −1.03382e6 | −0.384744 | −0.192372 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192372 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(374\) | −146157. | −0.0540306 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.35755e6 | −0.495205 | ||||||||
\(377\) | −5.37133e6 | −1.94638 | ||||||||
\(378\) | −332774. | −0.119790 | ||||||||
\(379\) | 3.41421e6 | 1.22094 | 0.610468 | − | 0.792041i | \(-0.290982\pi\) | ||||
0.610468 | + | 0.792041i | \(0.290982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.12982e6 | −1.10461 | ||||||||
\(382\) | 571580. | 0.200410 | ||||||||
\(383\) | 1.82511e6 | 0.635758 | 0.317879 | − | 0.948131i | \(-0.397029\pi\) | ||||
0.317879 | + | 0.948131i | \(0.397029\pi\) | |||||||
\(384\) | 1.64253e6 | 0.568439 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.83800e6 | −0.627881 | ||||||||
\(387\) | −1.63874e6 | −0.556203 | ||||||||
\(388\) | −4.54911e6 | −1.53408 | ||||||||
\(389\) | −1.31381e6 | −0.440210 | −0.220105 | − | 0.975476i | \(-0.570640\pi\) | ||||
−0.220105 | + | 0.975476i | \(0.570640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 621659. | 0.205641 | ||||||||
\(392\) | 2.06021e6 | 0.677168 | ||||||||
\(393\) | −1.44438e6 | −0.471736 | ||||||||
\(394\) | −1.74805e6 | −0.567301 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −246922. | −0.0791264 | ||||||||
\(397\) | 4.07499e6 | 1.29763 | 0.648814 | − | 0.760947i | \(-0.275265\pi\) | ||||
0.648814 | + | 0.760947i | \(0.275265\pi\) | |||||||
\(398\) | 1.54221e6 | 0.488017 | ||||||||
\(399\) | −3.14328e6 | −0.988441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.88854e6 | 0.586495 | 0.293247 | − | 0.956037i | \(-0.405264\pi\) | ||||
0.293247 | + | 0.956037i | \(0.405264\pi\) | |||||||
\(402\) | −1.51244e6 | −0.466779 | ||||||||
\(403\) | 3.66395e6 | 1.12379 | ||||||||
\(404\) | 2.86735e6 | 0.874033 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00653e6 | −0.905213 | ||||||||
\(407\) | −1.09988e6 | −0.329125 | ||||||||
\(408\) | 621760. | 0.184915 | ||||||||
\(409\) | −2.77474e6 | −0.820188 | −0.410094 | − | 0.912043i | \(-0.634504\pi\) | ||||
−0.410094 | + | 0.912043i | \(0.634504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.28336e6 | 0.374752 | ||||||||
\(412\) | 4.85624e6 | 1.40948 | ||||||||
\(413\) | 5.12816e6 | 1.47940 | ||||||||
\(414\) | −283744. | −0.0813628 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.78103e6 | 1.35453 | ||||||||
\(417\) | −1.11773e6 | −0.314772 | ||||||||
\(418\) | 630124. | 0.176395 | ||||||||
\(419\) | 1.74694e6 | 0.486119 | 0.243060 | − | 0.970011i | \(-0.421849\pi\) | ||||
0.243060 | + | 0.970011i | \(0.421849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 321171. | 0.0883143 | 0.0441572 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441572 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(422\) | 2793.08 | 0.000763487 0 | ||||||||
\(423\) | −736938. | −0.200254 | ||||||||
\(424\) | −5.72088e6 | −1.54543 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.48664e6 | 0.396901 | ||||||||
\(427\) | 5.66726e6 | 1.50419 | ||||||||
\(428\) | −3.50476e6 | −0.924802 | ||||||||
\(429\) | −888109. | −0.232982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.16098e6 | 0.301046 | 0.150523 | − | 0.988607i | \(-0.451904\pi\) | ||||
0.150523 | + | 0.988607i | \(0.451904\pi\) | |||||||
\(432\) | 303924. | 0.0783531 | ||||||||
\(433\) | 1.65899e6 | 0.425229 | 0.212615 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(434\) | 2.05085e6 | 0.522648 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.45284e6 | −0.617950 | ||||||||
\(437\) | −2.68015e6 | −0.671361 | ||||||||
\(438\) | 96781.8 | 0.0241051 | ||||||||
\(439\) | 7.30846e6 | 1.80994 | 0.904971 | − | 0.425473i | \(-0.139892\pi\) | ||||
0.904971 | + | 0.425473i | \(0.139892\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.11838e6 | 0.273837 | ||||||||
\(442\) | 985081. | 0.239837 | ||||||||
\(443\) | 3.34639e6 | 0.810153 | 0.405077 | − | 0.914283i | \(-0.367245\pi\) | ||||
0.405077 | + | 0.914283i | \(0.367245\pi\) | |||||||
\(444\) | 2.06107e6 | 0.496176 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.34504e6 | 0.320184 | ||||||||
\(447\) | −2.98824e6 | −0.707370 | ||||||||
\(448\) | 341863. | 0.0804742 | ||||||||
\(449\) | −2.28621e6 | −0.535180 | −0.267590 | − | 0.963533i | \(-0.586227\pi\) | ||||
−0.267590 | + | 0.963533i | \(0.586227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −134087. | −0.0310417 | ||||||||
\(452\) | −527869. | −0.121529 | ||||||||
\(453\) | −1.99003e6 | −0.455632 | ||||||||
\(454\) | 182297. | 0.0415087 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.68059e6 | −0.603696 | ||||||||
\(457\) | 3.57185e6 | 0.800024 | 0.400012 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400012 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(458\) | −1.30998e6 | −0.291811 | ||||||||
\(459\) | 337520. | 0.0747770 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.95525e6 | −1.74342 | −0.871709 | − | 0.490024i | \(-0.836988\pi\) | ||||
−0.871709 | + | 0.490024i | \(0.836988\pi\) | |||||||
\(462\) | −497107. | −0.108354 | ||||||||
\(463\) | 5.70155e6 | 1.23606 | 0.618032 | − | 0.786153i | \(-0.287930\pi\) | ||||
0.618032 | + | 0.786153i | \(0.287930\pi\) | |||||||
\(464\) | 2.74588e6 | 0.592089 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.97226e6 | 0.847370 | ||||||||
\(467\) | 513186. | 0.108889 | 0.0544444 | − | 0.998517i | \(-0.482661\pi\) | ||||
0.0544444 | + | 0.998517i | \(0.482661\pi\) | |||||||
\(468\) | 1.66423e6 | 0.351235 | ||||||||
\(469\) | 1.12703e7 | 2.36593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.61040e6 | −0.334488 | ||||||||
\(472\) | 4.37329e6 | 0.903553 | ||||||||
\(473\) | −2.44800e6 | −0.503105 | ||||||||
\(474\) | 1.24993e6 | 0.255530 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.04090e6 | −0.412862 | ||||||||
\(477\) | −3.10556e6 | −0.624948 | ||||||||
\(478\) | 1.57051e6 | 0.314391 | ||||||||
\(479\) | 5.59628e6 | 1.11445 | 0.557225 | − | 0.830361i | \(-0.311866\pi\) | ||||
0.557225 | + | 0.830361i | \(0.311866\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.41310e6 | 1.46096 | ||||||||
\(482\) | 2.50605e6 | 0.491330 | ||||||||
\(483\) | 2.11438e6 | 0.412397 | ||||||||
\(484\) | −368858. | −0.0715725 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −154054. | −0.0295858 | ||||||||
\(487\) | 425345. | 0.0812678 | 0.0406339 | − | 0.999174i | \(-0.487062\pi\) | ||||
0.0406339 | + | 0.999174i | \(0.487062\pi\) | |||||||
\(488\) | 4.83304e6 | 0.918695 | ||||||||
\(489\) | −1.99967e6 | −0.378169 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.56781e6 | −1.04227 | −0.521136 | − | 0.853474i | \(-0.674492\pi\) | ||||
−0.521136 | + | 0.853474i | \(0.674492\pi\) | |||||||
\(492\) | 251266. | 0.0467973 | ||||||||
\(493\) | 3.04941e6 | 0.565065 | ||||||||
\(494\) | −4.24697e6 | −0.783000 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.87305e6 | −0.341857 | ||||||||
\(497\) | −1.10780e7 | −2.01174 | ||||||||
\(498\) | −2.81405e6 | −0.508462 | ||||||||
\(499\) | −5.31330e6 | −0.955241 | −0.477621 | − | 0.878566i | \(-0.658501\pi\) | ||||
−0.477621 | + | 0.878566i | \(0.658501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.57535e6 | −0.458398 | ||||||||
\(502\) | 2.60745e6 | 0.461804 | ||||||||
\(503\) | −1.03261e7 | −1.81976 | −0.909882 | − | 0.414867i | \(-0.863828\pi\) | ||||
−0.909882 | + | 0.414867i | \(0.863828\pi\) | |||||||
\(504\) | 2.11473e6 | 0.370832 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −423864. | −0.0735954 | ||||||||
\(507\) | 2.64412e6 | 0.456837 | ||||||||
\(508\) | 8.76125e6 | 1.50628 | ||||||||
\(509\) | 1.37144e6 | 0.234629 | 0.117314 | − | 0.993095i | \(-0.462571\pi\) | ||||
0.117314 | + | 0.993095i | \(0.462571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −721191. | −0.122179 | ||||||||
\(512\) | −4.43477e6 | −0.747646 | ||||||||
\(513\) | −1.45515e6 | −0.244126 | ||||||||
\(514\) | 579280. | 0.0967121 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.58730e6 | 0.758460 | ||||||||
\(517\) | −1.10086e6 | −0.181136 | ||||||||
\(518\) | 4.14939e6 | 0.679453 | ||||||||
\(519\) | −5.27064e6 | −0.858904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 524277. | 0.0846187 | 0.0423094 | − | 0.999105i | \(-0.486528\pi\) | ||||
0.0423094 | + | 0.999105i | \(0.486528\pi\) | |||||||
\(522\) | −1.39184e6 | −0.223570 | ||||||||
\(523\) | 1.42764e6 | 0.228225 | 0.114113 | − | 0.993468i | \(-0.463598\pi\) | ||||
0.114113 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(524\) | 4.04321e6 | 0.643277 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.30871e6 | −0.206243 | ||||||||
\(527\) | −2.08010e6 | −0.326255 | ||||||||
\(528\) | 454010. | 0.0708730 | ||||||||
\(529\) | −4.63349e6 | −0.719895 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.37403e6 | 0.365384 | ||||||||
\(532\) | 8.79892e6 | 1.34788 | ||||||||
\(533\) | 903733. | 0.137791 | ||||||||
\(534\) | −1.55690e6 | −0.236270 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.61128e6 | 1.44500 | ||||||||
\(537\) | −4.60248e6 | −0.688741 | ||||||||
\(538\) | 3.92757e6 | 0.585017 | ||||||||
\(539\) | 1.67066e6 | 0.247695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.39626e6 | 0.792683 | 0.396341 | − | 0.918103i | \(-0.370280\pi\) | ||||
0.396341 | + | 0.918103i | \(0.370280\pi\) | |||||||
\(542\) | −2.44116e6 | −0.356943 | ||||||||
\(543\) | −146496. | −0.0213219 | ||||||||
\(544\) | −2.71429e6 | −0.393241 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.35045e6 | 0.480974 | ||||||||
\(547\) | 7.34437e6 | 1.04951 | 0.524754 | − | 0.851254i | \(-0.324157\pi\) | ||||
0.524754 | + | 0.851254i | \(0.324157\pi\) | |||||||
\(548\) | −3.59249e6 | −0.511027 | ||||||||
\(549\) | 2.62360e6 | 0.371507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.31469e7 | −1.84478 | ||||||||
\(552\) | 1.80315e6 | 0.251874 | ||||||||
\(553\) | −9.31417e6 | −1.29518 | ||||||||
\(554\) | 2.78662e6 | 0.385747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.12883e6 | 0.429235 | ||||||||
\(557\) | −7.05449e6 | −0.963447 | −0.481723 | − | 0.876323i | \(-0.659989\pi\) | ||||
−0.481723 | + | 0.876323i | \(0.659989\pi\) | |||||||
\(558\) | 949418. | 0.129084 | ||||||||
\(559\) | 1.64992e7 | 2.23324 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 504197. | 0.0676383 | ||||||||
\(562\) | −1.78318e6 | −0.238152 | ||||||||
\(563\) | −126964. | −0.0168814 | −0.00844072 | − | 0.999964i | \(-0.502687\pi\) | ||||
−0.00844072 | + | 0.999964i | \(0.502687\pi\) | |||||||
\(564\) | 2.06290e6 | 0.273074 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 710638. | 0.0932411 | ||||||||
\(567\) | 1.14797e6 | 0.149959 | ||||||||
\(568\) | −9.44736e6 | −1.22868 | ||||||||
\(569\) | −1.36950e7 | −1.77330 | −0.886648 | − | 0.462445i | \(-0.846972\pi\) | ||||
−0.886648 | + | 0.462445i | \(0.846972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −484553. | −0.0621944 | −0.0310972 | − | 0.999516i | \(-0.509900\pi\) | ||||
−0.0310972 | + | 0.999516i | \(0.509900\pi\) | |||||||
\(572\) | 2.48606e6 | 0.317704 | ||||||||
\(573\) | −1.97178e6 | −0.250883 | ||||||||
\(574\) | 505853. | 0.0640833 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 158262. | 0.0198756 | ||||||||
\(577\) | 4.31027e6 | 0.538970 | 0.269485 | − | 0.963005i | \(-0.413147\pi\) | ||||
0.269485 | + | 0.963005i | \(0.413147\pi\) | |||||||
\(578\) | 3.14505e6 | 0.391569 | ||||||||
\(579\) | 6.34054e6 | 0.786014 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.09696e7 | 2.57720 | ||||||||
\(582\) | −4.23976e6 | −0.518841 | ||||||||
\(583\) | −4.63917e6 | −0.565287 | ||||||||
\(584\) | −615032. | −0.0746218 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.01551e6 | 0.483055 | ||||||||
\(587\) | 4.35136e6 | 0.521230 | 0.260615 | − | 0.965443i | \(-0.416075\pi\) | ||||
0.260615 | + | 0.965443i | \(0.416075\pi\) | |||||||
\(588\) | −3.13065e6 | −0.373415 | ||||||||
\(589\) | 8.96790e6 | 1.06513 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.03024e6 | 0.710176 | ||||||||
\(592\) | −3.78965e6 | −0.444422 | ||||||||
\(593\) | 2.85779e6 | 0.333729 | 0.166865 | − | 0.985980i | \(-0.446636\pi\) | ||||
0.166865 | + | 0.985980i | \(0.446636\pi\) | |||||||
\(594\) | −230131. | −0.0267614 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.36492e6 | 0.964598 | ||||||||
\(597\) | −5.32015e6 | −0.610926 | ||||||||
\(598\) | 2.85680e6 | 0.326683 | ||||||||
\(599\) | 1.62076e7 | 1.84566 | 0.922831 | − | 0.385206i | \(-0.125870\pi\) | ||||
0.922831 | + | 0.385206i | \(0.125870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.74322e6 | −0.761520 | −0.380760 | − | 0.924674i | \(-0.624338\pi\) | ||||
−0.380760 | + | 0.924674i | \(0.624338\pi\) | |||||||
\(602\) | 9.23524e6 | 1.03862 | ||||||||
\(603\) | 5.21745e6 | 0.584339 | ||||||||
\(604\) | 5.57065e6 | 0.621317 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.67237e6 | 0.295607 | ||||||||
\(607\) | 1.76156e6 | 0.194055 | 0.0970276 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970276 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(608\) | 1.17021e7 | 1.28382 | ||||||||
\(609\) | 1.03716e7 | 1.13319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.41967e6 | 0.804047 | ||||||||
\(612\) | −944813. | −0.101969 | ||||||||
\(613\) | 1.71643e7 | 1.84491 | 0.922456 | − | 0.386102i | \(-0.126179\pi\) | ||||
0.922456 | + | 0.386102i | \(0.126179\pi\) | |||||||
\(614\) | −2.08891e6 | −0.223614 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.15904e6 | 0.335431 | ||||||||
\(617\) | −5.60639e6 | −0.592885 | −0.296443 | − | 0.955051i | \(-0.595800\pi\) | ||||
−0.296443 | + | 0.955051i | \(0.595800\pi\) | |||||||
\(618\) | 4.52601e6 | 0.476699 | ||||||||
\(619\) | 679689. | 0.0712990 | 0.0356495 | − | 0.999364i | \(-0.488650\pi\) | ||||
0.0356495 | + | 0.999364i | \(0.488650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 978831. | 0.101854 | ||||||||
\(622\) | −8.27637e6 | −0.857757 | ||||||||
\(623\) | 1.16016e7 | 1.19756 | ||||||||
\(624\) | −3.05998e6 | −0.314599 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.59953e6 | 0.265131 | ||||||||
\(627\) | −2.17374e6 | −0.220820 | ||||||||
\(628\) | 4.50795e6 | 0.456121 | ||||||||
\(629\) | −4.20856e6 | −0.424138 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.79404e6 | −0.179374 | −0.0896868 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896868 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(632\) | −7.94312e6 | −0.791040 | ||||||||
\(633\) | −9635.27 | −0.000955773 0 | ||||||||
\(634\) | −4.53568e6 | −0.448146 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.69333e6 | 0.852203 | ||||||||
\(637\) | −1.12601e7 | −1.09949 | ||||||||
\(638\) | −2.07917e6 | −0.202227 | ||||||||
\(639\) | −5.12846e6 | −0.496861 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.87077e6 | −0.179836 | −0.0899179 | − | 0.995949i | \(-0.528660\pi\) | ||||
−0.0899179 | + | 0.995949i | \(0.528660\pi\) | |||||||
\(642\) | −3.26643e6 | −0.312778 | ||||||||
\(643\) | 1.17131e7 | 1.11724 | 0.558618 | − | 0.829425i | \(-0.311332\pi\) | ||||
0.558618 | + | 0.829425i | \(0.311332\pi\) | |||||||
\(644\) | −5.91875e6 | −0.562361 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.41109e6 | 0.227317 | ||||||||
\(647\) | 8.80680e6 | 0.827099 | 0.413550 | − | 0.910482i | \(-0.364289\pi\) | ||||
0.413550 | + | 0.910482i | \(0.364289\pi\) | |||||||
\(648\) | 978990. | 0.0915884 | ||||||||
\(649\) | 3.54638e6 | 0.330502 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.07481e6 | −0.654278 | ||||||||
\(652\) | 5.59763e6 | 0.515686 | ||||||||
\(653\) | −6.56212e6 | −0.602229 | −0.301114 | − | 0.953588i | \(-0.597359\pi\) | ||||
−0.301114 | + | 0.953588i | \(0.597359\pi\) | |||||||
\(654\) | −2.28604e6 | −0.208997 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −461998. | −0.0419161 | ||||||||
\(657\) | −333868. | −0.0301760 | ||||||||
\(658\) | 4.15306e6 | 0.373941 | ||||||||
\(659\) | −1.31437e7 | −1.17897 | −0.589486 | − | 0.807778i | \(-0.700670\pi\) | ||||
−0.589486 | + | 0.807778i | \(0.700670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.73548e7 | −1.54496 | −0.772478 | − | 0.635041i | \(-0.780983\pi\) | ||||
−0.772478 | + | 0.635041i | \(0.780983\pi\) | |||||||
\(662\) | 1.38404e6 | 0.122745 | ||||||||
\(663\) | −3.39823e6 | −0.300240 | ||||||||
\(664\) | 1.78828e7 | 1.57404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.92091e6 | 0.167812 | ||||||||
\(667\) | 8.84350e6 | 0.769678 | ||||||||
\(668\) | 7.20913e6 | 0.625089 | ||||||||
\(669\) | −4.64000e6 | −0.400823 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.91920e6 | 0.336041 | ||||||||
\(672\) | −9.23181e6 | −0.788613 | ||||||||
\(673\) | 1.02596e7 | 0.873159 | 0.436580 | − | 0.899666i | \(-0.356190\pi\) | ||||
0.436580 | + | 0.899666i | \(0.356190\pi\) | |||||||
\(674\) | −2896.59 | −0.000245605 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.40163e6 | −0.622961 | ||||||||
\(677\) | −1.22085e6 | −0.102375 | −0.0511873 | − | 0.998689i | \(-0.516301\pi\) | ||||
−0.0511873 | + | 0.998689i | \(0.516301\pi\) | |||||||
\(678\) | −491973. | −0.0411024 | ||||||||
\(679\) | 3.15936e7 | 2.62981 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −628868. | −0.0519627 | ||||||||
\(682\) | 1.41827e6 | 0.116761 | ||||||||
\(683\) | −8.61333e6 | −0.706511 | −0.353256 | − | 0.935527i | \(-0.614925\pi\) | ||||
−0.353256 | + | 0.935527i | \(0.614925\pi\) | |||||||
\(684\) | 4.07336e6 | 0.332899 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.36939e6 | 0.111100 | ||||||||
\(687\) | 4.51904e6 | 0.365304 | ||||||||
\(688\) | −8.43458e6 | −0.679348 | ||||||||
\(689\) | 3.12675e7 | 2.50926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.53208e7 | −1.22064 | −0.610319 | − | 0.792156i | \(-0.708959\pi\) | ||||
−0.610319 | + | 0.792156i | \(0.708959\pi\) | |||||||
\(692\) | 1.47540e7 | 1.17124 | ||||||||
\(693\) | 1.71487e6 | 0.135643 | ||||||||
\(694\) | 2.83978e6 | 0.223814 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.84493e6 | 0.692104 | ||||||||
\(697\) | −513067. | −0.0400030 | ||||||||
\(698\) | 1.54197e6 | 0.119795 | ||||||||
\(699\) | −1.37031e7 | −1.06078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 233349. | 0.0179354 | 0.00896768 | − | 0.999960i | \(-0.497145\pi\) | ||||
0.00896768 | + | 0.999960i | \(0.497145\pi\) | |||||||
\(702\) | 1.55105e6 | 0.118791 | ||||||||
\(703\) | 1.81443e7 | 1.38469 | ||||||||
\(704\) | 236416. | 0.0179781 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.55682e6 | 0.193058 | ||||||||
\(707\) | −1.99138e7 | −1.49832 | ||||||||
\(708\) | −6.64556e6 | −0.498252 | ||||||||
\(709\) | −3.15108e6 | −0.235420 | −0.117710 | − | 0.993048i | \(-0.537555\pi\) | ||||
−0.117710 | + | 0.993048i | \(0.537555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.31190e6 | −0.319885 | ||||||||
\(712\) | 9.89387e6 | 0.731419 | ||||||||
\(713\) | −6.03242e6 | −0.444393 | ||||||||
\(714\) | −1.90212e6 | −0.139634 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.28836e7 | 0.939194 | ||||||||
\(717\) | −5.41778e6 | −0.393571 | ||||||||
\(718\) | 7.50619e6 | 0.543386 | ||||||||
\(719\) | −2.38682e7 | −1.72186 | −0.860930 | − | 0.508723i | \(-0.830118\pi\) | ||||
−0.860930 | + | 0.508723i | \(0.830118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.37266e7 | −2.41621 | ||||||||
\(722\) | −3.93494e6 | −0.280928 | ||||||||
\(723\) | −8.64513e6 | −0.615072 | ||||||||
\(724\) | 410083. | 0.0290754 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −343775. | −0.0242066 | ||||||||
\(727\) | −2.60780e7 | −1.82995 | −0.914974 | − | 0.403513i | \(-0.867789\pi\) | ||||
−0.914974 | + | 0.403513i | \(0.867789\pi\) | |||||||
\(728\) | −2.12916e7 | −1.48895 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.36694e6 | −0.648343 | ||||||||
\(732\) | −7.34419e6 | −0.506601 | ||||||||
\(733\) | 822931. | 0.0565723 | 0.0282861 | − | 0.999600i | \(-0.490995\pi\) | ||||
0.0282861 | + | 0.999600i | \(0.490995\pi\) | |||||||
\(734\) | 8.57021e6 | 0.587153 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.87161e6 | −0.535635 | ||||||||
\(737\) | 7.79396e6 | 0.528554 | ||||||||
\(738\) | 234179. | 0.0158273 | ||||||||
\(739\) | 1.58916e7 | 1.07043 | 0.535215 | − | 0.844716i | \(-0.320231\pi\) | ||||
0.535215 | + | 0.844716i | \(0.320231\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.46508e7 | 0.980200 | ||||||||
\(742\) | 1.75016e7 | 1.16699 | ||||||||
\(743\) | 8.78449e6 | 0.583774 | 0.291887 | − | 0.956453i | \(-0.405717\pi\) | ||||
0.291887 | + | 0.956453i | \(0.405717\pi\) | |||||||
\(744\) | −6.03340e6 | −0.399604 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.69715e6 | 0.177443 | ||||||||
\(747\) | 9.70763e6 | 0.636520 | ||||||||
\(748\) | −1.41139e6 | −0.0922343 | ||||||||
\(749\) | 2.43406e7 | 1.58535 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.46203e7 | −0.945926 | −0.472963 | − | 0.881082i | \(-0.656816\pi\) | ||||
−0.472963 | + | 0.881082i | \(0.656816\pi\) | |||||||
\(752\) | −3.79301e6 | −0.244590 | ||||||||
\(753\) | −8.99493e6 | −0.578110 | ||||||||
\(754\) | 1.40134e7 | 0.897666 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.21349e6 | −0.204490 | ||||||||
\(757\) | −7.20669e6 | −0.457084 | −0.228542 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228542 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(758\) | −8.90742e6 | −0.563092 | ||||||||
\(759\) | 1.46220e6 | 0.0921305 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.92986e7 | −1.83394 | −0.916969 | − | 0.398958i | \(-0.869372\pi\) | ||||
−0.916969 | + | 0.398958i | \(0.869372\pi\) | |||||||
\(762\) | 8.16547e6 | 0.509441 | ||||||||
\(763\) | 1.70350e7 | 1.05933 | ||||||||
\(764\) | 5.51956e6 | 0.342114 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.76157e6 | −0.293209 | ||||||||
\(767\) | −2.39022e7 | −1.46707 | ||||||||
\(768\) | −4.84793e6 | −0.296588 | ||||||||
\(769\) | −9.38411e6 | −0.572239 | −0.286119 | − | 0.958194i | \(-0.592365\pi\) | ||||
−0.286119 | + | 0.958194i | \(0.592365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.99834e6 | −0.121069 | ||||||||
\(772\) | −1.77490e7 | −1.07184 | ||||||||
\(773\) | −3.43323e6 | −0.206659 | −0.103329 | − | 0.994647i | \(-0.532950\pi\) | ||||
−0.103329 | + | 0.994647i | \(0.532950\pi\) | |||||||
\(774\) | 4.27535e6 | 0.256519 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.69430e7 | 1.60617 | ||||||||
\(777\) | −1.43141e7 | −0.850575 | ||||||||
\(778\) | 3.42764e6 | 0.203024 | ||||||||
\(779\) | 2.21198e6 | 0.130598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.66104e6 | −0.449428 | ||||||||
\(782\) | −1.62186e6 | −0.0948412 | ||||||||
\(783\) | 4.80144e6 | 0.279877 | ||||||||
\(784\) | 5.75627e6 | 0.334465 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.76827e6 | 0.217563 | ||||||||
\(787\) | 9.21027e6 | 0.530073 | 0.265036 | − | 0.964238i | \(-0.414616\pi\) | ||||
0.265036 | + | 0.964238i | \(0.414616\pi\) | |||||||
\(788\) | −1.68803e7 | −0.968424 | ||||||||
\(789\) | 4.51465e6 | 0.258185 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.66605e6 | 0.208332 | ||||||||
\(792\) | 1.46244e6 | 0.0828449 | ||||||||
\(793\) | −2.64150e7 | −1.49165 | ||||||||
\(794\) | −1.06313e7 | −0.598462 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.48926e7 | 0.833082 | ||||||||
\(797\) | −1.76659e7 | −0.985120 | −0.492560 | − | 0.870279i | \(-0.663939\pi\) | ||||
−0.492560 | + | 0.870279i | \(0.663939\pi\) | |||||||
\(798\) | 8.20057e6 | 0.455866 | ||||||||
\(799\) | −4.21229e6 | −0.233427 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.37085e6 | 0.295775 | ||||||||
\(802\) | −4.92705e6 | −0.270490 | ||||||||
\(803\) | −498741. | −0.0272952 | ||||||||
\(804\) | −1.46051e7 | −0.796827 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.55896e6 | −0.518290 | ||||||||
\(807\) | −1.35489e7 | −0.732355 | ||||||||
\(808\) | −1.69825e7 | −0.915108 | ||||||||
\(809\) | 5.29802e6 | 0.284605 | 0.142302 | − | 0.989823i | \(-0.454549\pi\) | ||||
0.142302 | + | 0.989823i | \(0.454549\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.81272e7 | 0.967786 | 0.483893 | − | 0.875127i | \(-0.339222\pi\) | ||||
0.483893 | + | 0.875127i | \(0.339222\pi\) | |||||||
\(812\) | −2.90331e7 | −1.54527 | ||||||||
\(813\) | 8.42128e6 | 0.446840 | ||||||||
\(814\) | 2.86951e6 | 0.151791 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.73721e6 | 0.0913329 | ||||||||
\(817\) | 4.03836e7 | 2.11665 | ||||||||
\(818\) | 7.23908e6 | 0.378268 | ||||||||
\(819\) | −1.15580e7 | −0.602108 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.68262e7 | 1.90677 | 0.953387 | − | 0.301751i | \(-0.0975710\pi\) | ||||
0.953387 | + | 0.301751i | \(0.0975710\pi\) | |||||||
\(822\) | −3.34819e6 | −0.172835 | ||||||||
\(823\) | −3.25146e7 | −1.67332 | −0.836660 | − | 0.547723i | \(-0.815495\pi\) | ||||
−0.836660 | + | 0.547723i | \(0.815495\pi\) | |||||||
\(824\) | −2.87621e7 | −1.47571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.33790e7 | −0.682296 | ||||||||
\(827\) | 4.14035e6 | 0.210510 | 0.105255 | − | 0.994445i | \(-0.466434\pi\) | ||||
0.105255 | + | 0.994445i | \(0.466434\pi\) | |||||||
\(828\) | −2.74002e6 | −0.138892 | ||||||||
\(829\) | −2.81888e7 | −1.42459 | −0.712296 | − | 0.701879i | \(-0.752345\pi\) | ||||
−0.712296 | + | 0.701879i | \(0.752345\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.61298e6 | −0.482898 | ||||||||
\(832\) | −1.59342e6 | −0.0798033 | ||||||||
\(833\) | 6.39257e6 | 0.319200 | ||||||||
\(834\) | 2.91606e6 | 0.145172 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.08490e6 | 0.301119 | ||||||||
\(837\) | −3.27521e6 | −0.161594 | ||||||||
\(838\) | −4.55763e6 | −0.224197 | ||||||||
\(839\) | −470091. | −0.0230556 | −0.0115278 | − | 0.999934i | \(-0.503669\pi\) | ||||
−0.0115278 | + | 0.999934i | \(0.503669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.28686e7 | 1.11494 | ||||||||
\(842\) | −837911. | −0.0407303 | ||||||||
\(843\) | 6.15142e6 | 0.298130 | ||||||||
\(844\) | 26971.8 | 0.00130333 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.92262e6 | 0.0923563 | ||||||||
\(847\) | 2.56172e6 | 0.122694 | ||||||||
\(848\) | −1.59843e7 | −0.763314 | ||||||||
\(849\) | −2.45149e6 | −0.116724 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.22051e7 | −0.577721 | ||||||||
\(852\) | 1.43560e7 | 0.677540 | ||||||||
\(853\) | 3.80179e7 | 1.78902 | 0.894510 | − | 0.447047i | \(-0.147524\pi\) | ||||
0.894510 | + | 0.447047i | \(0.147524\pi\) | |||||||
\(854\) | −1.47855e7 | −0.693730 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.07576e7 | 0.968263 | ||||||||
\(857\) | −2.72661e7 | −1.26815 | −0.634076 | − | 0.773271i | \(-0.718619\pi\) | ||||
−0.634076 | + | 0.773271i | \(0.718619\pi\) | |||||||
\(858\) | 2.31701e6 | 0.107451 | ||||||||
\(859\) | 3.07007e7 | 1.41960 | 0.709799 | − | 0.704404i | \(-0.248786\pi\) | ||||
0.709799 | + | 0.704404i | \(0.248786\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.74504e6 | −0.0802228 | ||||||||
\(862\) | −3.02892e6 | −0.138841 | ||||||||
\(863\) | 2.20422e7 | 1.00746 | 0.503731 | − | 0.863861i | \(-0.331960\pi\) | ||||
0.503731 | + | 0.863861i | \(0.331960\pi\) | |||||||
\(864\) | −4.27377e6 | −0.194772 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.32817e6 | −0.196114 | ||||||||
\(867\) | −1.08495e7 | −0.490186 | ||||||||
\(868\) | 1.98044e7 | 0.892199 | ||||||||
\(869\) | −6.44123e6 | −0.289347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.25305e7 | −2.34620 | ||||||||
\(872\) | 1.45274e7 | 0.646990 | ||||||||
\(873\) | 1.46259e7 | 0.649512 | ||||||||
\(874\) | 6.99231e6 | 0.309630 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 934590. | 0.0411491 | ||||||||
\(877\) | −6.53105e6 | −0.286737 | −0.143369 | − | 0.989669i | \(-0.545793\pi\) | ||||
−0.143369 | + | 0.989669i | \(0.545793\pi\) | |||||||
\(878\) | −1.90672e7 | −0.834740 | ||||||||
\(879\) | −1.38523e7 | −0.604713 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.27023e7 | 0.985439 | 0.492719 | − | 0.870188i | \(-0.336003\pi\) | ||||
0.492719 | + | 0.870188i | \(0.336003\pi\) | |||||||
\(882\) | −2.91776e6 | −0.126293 | ||||||||
\(883\) | −2.91594e7 | −1.25857 | −0.629285 | − | 0.777174i | \(-0.716652\pi\) | ||||
−0.629285 | + | 0.777174i | \(0.716652\pi\) | |||||||
\(884\) | 9.51260e6 | 0.409420 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.73048e6 | −0.373640 | ||||||||
\(887\) | 1.47884e7 | 0.631120 | 0.315560 | − | 0.948906i | \(-0.397808\pi\) | ||||
0.315560 | + | 0.948906i | \(0.397808\pi\) | |||||||
\(888\) | −1.22071e7 | −0.519493 | ||||||||
\(889\) | −6.08468e7 | −2.58216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.29887e7 | 0.546578 | ||||||||
\(893\) | 1.81604e7 | 0.762073 | ||||||||
\(894\) | 7.79609e6 | 0.326237 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.19323e7 | 1.32880 | ||||||||
\(897\) | −9.85510e6 | −0.408959 | ||||||||
\(898\) | 5.96454e6 | 0.246823 | ||||||||
\(899\) | −2.95907e7 | −1.22111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77512e7 | −0.728475 | ||||||||
\(902\) | 349823. | 0.0143164 | ||||||||
\(903\) | −3.18588e7 | −1.30020 | ||||||||
\(904\) | 3.12641e6 | 0.127240 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.19183e6 | 0.210136 | ||||||||
\(907\) | 6.96226e6 | 0.281017 | 0.140508 | − | 0.990080i | \(-0.455126\pi\) | ||||
0.140508 | + | 0.990080i | \(0.455126\pi\) | |||||||
\(908\) | 1.76038e6 | 0.0708584 | ||||||||
\(909\) | −9.21887e6 | −0.370056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.40287e7 | 1.35847 | 0.679234 | − | 0.733922i | \(-0.262312\pi\) | ||||
0.679234 | + | 0.733922i | \(0.262312\pi\) | |||||||
\(912\) | −7.48962e6 | −0.298176 | ||||||||
\(913\) | 1.45015e7 | 0.575754 | ||||||||
\(914\) | −9.31869e6 | −0.368968 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.26501e7 | −0.498143 | ||||||||
\(917\) | −2.80801e7 | −1.10275 | ||||||||
\(918\) | −880564. | −0.0344869 | ||||||||
\(919\) | −2.25426e7 | −0.880470 | −0.440235 | − | 0.897883i | \(-0.645105\pi\) | ||||
−0.440235 | + | 0.897883i | \(0.645105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.20610e6 | 0.279931 | ||||||||
\(922\) | 2.07546e7 | 0.804059 | ||||||||
\(923\) | 5.16346e7 | 1.99497 | ||||||||
\(924\) | −4.80040e6 | −0.184968 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.48749e7 | −0.570069 | ||||||||
\(927\) | −1.56134e7 | −0.596757 | ||||||||
\(928\) | −3.86124e7 | −1.47183 | ||||||||
\(929\) | 3.13230e6 | 0.119076 | 0.0595381 | − | 0.998226i | \(-0.481037\pi\) | ||||
0.0595381 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.75602e7 | −1.04210 | ||||||||
\(932\) | 3.83588e7 | 1.44652 | ||||||||
\(933\) | 2.85510e7 | 1.07378 | ||||||||
\(934\) | −1.33886e6 | −0.0502191 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.85670e6 | −0.367741 | ||||||||
\(937\) | 1.11644e7 | 0.415417 | 0.207709 | − | 0.978191i | \(-0.433399\pi\) | ||||
0.207709 | + | 0.978191i | \(0.433399\pi\) | |||||||
\(938\) | −2.94032e7 | −1.09116 | ||||||||
\(939\) | −8.96761e6 | −0.331904 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.20914e7 | 0.813296 | 0.406648 | − | 0.913585i | \(-0.366698\pi\) | ||||
0.406648 | + | 0.913585i | \(0.366698\pi\) | |||||||
\(942\) | 4.20140e6 | 0.154265 | ||||||||
\(943\) | −1.48793e6 | −0.0544883 | ||||||||
\(944\) | 1.22191e7 | 0.446281 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.38664e6 | 0.232030 | ||||||||
\(947\) | −3.88629e7 | −1.40819 | −0.704093 | − | 0.710107i | \(-0.748646\pi\) | ||||
−0.704093 | + | 0.710107i | \(0.748646\pi\) | |||||||
\(948\) | 1.20702e7 | 0.436208 | ||||||||
\(949\) | 3.36146e6 | 0.121161 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.56467e7 | 0.561012 | ||||||||
\(952\) | 1.20876e7 | 0.432264 | ||||||||
\(953\) | 1.65779e6 | 0.0591287 | 0.0295643 | − | 0.999563i | \(-0.490588\pi\) | ||||
0.0295643 | + | 0.999563i | \(0.490588\pi\) | |||||||
\(954\) | 8.10216e6 | 0.288224 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.51659e7 | 0.536689 | ||||||||
\(957\) | 7.17252e6 | 0.253158 | ||||||||
\(958\) | −1.46003e7 | −0.513981 | ||||||||
\(959\) | 2.49498e7 | 0.876033 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.44445e6 | −0.294960 | ||||||||
\(962\) | −1.93402e7 | −0.673789 | ||||||||
\(963\) | 1.12682e7 | 0.391551 | ||||||||
\(964\) | 2.42001e7 | 0.838736 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.51626e6 | −0.190196 | ||||||||
\(967\) | 4.00243e7 | 1.37644 | 0.688221 | − | 0.725501i | \(-0.258392\pi\) | ||||
0.688221 | + | 0.725501i | \(0.258392\pi\) | |||||||
\(968\) | 2.18464e6 | 0.0749360 | ||||||||
\(969\) | −8.31753e6 | −0.284567 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.50158e7 | −1.19183 | −0.595917 | − | 0.803046i | \(-0.703211\pi\) | ||||
−0.595917 | + | 0.803046i | \(0.703211\pi\) | |||||||
\(972\) | −1.48765e6 | −0.0505052 | ||||||||
\(973\) | −2.17297e7 | −0.735821 | ||||||||
\(974\) | −1.10969e6 | −0.0374805 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.35036e7 | 0.453760 | ||||||||
\(977\) | 3.66007e7 | 1.22674 | 0.613370 | − | 0.789795i | \(-0.289813\pi\) | ||||
0.613370 | + | 0.789795i | \(0.289813\pi\) | |||||||
\(978\) | 5.21698e6 | 0.174410 | ||||||||
\(979\) | 8.02313e6 | 0.267539 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.88616e6 | 0.261633 | ||||||||
\(982\) | 1.45260e7 | 0.480692 | ||||||||
\(983\) | −4.10117e7 | −1.35371 | −0.676853 | − | 0.736119i | \(-0.736657\pi\) | ||||
−0.676853 | + | 0.736119i | \(0.736657\pi\) | |||||||
\(984\) | −1.48817e6 | −0.0489965 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.95568e6 | −0.260606 | ||||||||
\(987\) | −1.43268e7 | −0.468119 | ||||||||
\(988\) | −4.10116e7 | −1.33664 | ||||||||
\(989\) | −2.71648e7 | −0.883111 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.49847e7 | 1.13160 | 0.565802 | − | 0.824541i | \(-0.308567\pi\) | ||||
0.565802 | + | 0.824541i | \(0.308567\pi\) | |||||||
\(992\) | 2.63387e7 | 0.849797 | ||||||||
\(993\) | −4.77451e6 | −0.153658 | ||||||||
\(994\) | 2.89018e7 | 0.927809 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.71744e7 | −0.867983 | ||||||||
\(997\) | 5.02983e7 | 1.60256 | 0.801282 | − | 0.598287i | \(-0.204152\pi\) | ||||
0.801282 | + | 0.598287i | \(0.204152\pi\) | |||||||
\(998\) | 1.38620e7 | 0.440554 | ||||||||
\(999\) | −6.62658e6 | −0.210076 |
(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.m.1.4 | ✓ | 7 | |
5.4 | even | 2 | 825.6.a.o.1.4 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.m.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
825.6.a.o.1.4 | yes | 7 | 5.4 | even | 2 |