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: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + \cdots - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(6.73090\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.73090 | 1.18987 | 0.594933 | − | 0.803775i | \(-0.297179\pi\) | ||||
0.594933 | + | 0.803775i | \(0.297179\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 13.3050 | 0.415781 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −60.5781 | −0.686969 | ||||||||
\(7\) | −2.41142 | −0.0186006 | −0.00930031 | − | 0.999957i | \(-0.502960\pi\) | ||||
−0.00930031 | + | 0.999957i | \(0.502960\pi\) | |||||||
\(8\) | −125.834 | −0.695142 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −119.745 | −0.240051 | ||||||||
\(13\) | −334.983 | −0.549748 | −0.274874 | − | 0.961480i | \(-0.588636\pi\) | ||||
−0.274874 | + | 0.961480i | \(0.588636\pi\) | |||||||
\(14\) | −16.2310 | −0.0221322 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1272.74 | −1.24291 | ||||||||
\(17\) | 1211.39 | 1.01663 | 0.508313 | − | 0.861173i | \(-0.330269\pi\) | ||||
0.508313 | + | 0.861173i | \(0.330269\pi\) | |||||||
\(18\) | 545.203 | 0.396622 | ||||||||
\(19\) | −746.587 | −0.474456 | −0.237228 | − | 0.971454i | \(-0.576239\pi\) | ||||
−0.237228 | + | 0.971454i | \(0.576239\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.7028 | 0.0107391 | ||||||||
\(22\) | 814.439 | 0.358758 | ||||||||
\(23\) | −3387.32 | −1.33517 | −0.667584 | − | 0.744534i | \(-0.732672\pi\) | ||||
−0.667584 | + | 0.744534i | \(0.732672\pi\) | |||||||
\(24\) | 1132.51 | 0.401341 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2254.73 | −0.654127 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −32.0839 | −0.00773379 | ||||||||
\(29\) | −2012.09 | −0.444275 | −0.222137 | − | 0.975015i | \(-0.571303\pi\) | ||||
−0.222137 | + | 0.975015i | \(0.571303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8689.78 | 1.62407 | 0.812035 | − | 0.583609i | \(-0.198360\pi\) | ||||
0.812035 | + | 0.583609i | \(0.198360\pi\) | |||||||
\(32\) | −4539.97 | −0.783751 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 8153.73 | 1.20965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1077.70 | 0.138594 | ||||||||
\(37\) | −1392.25 | −0.167192 | −0.0835958 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835958 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(38\) | −5025.20 | −0.564540 | ||||||||
\(39\) | 3014.84 | 0.317397 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2339.11 | 0.217316 | 0.108658 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108658 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(42\) | 146.079 | 0.0127781 | ||||||||
\(43\) | −10534.9 | −0.868877 | −0.434439 | − | 0.900701i | \(-0.643053\pi\) | ||||
−0.434439 | + | 0.900701i | \(0.643053\pi\) | |||||||
\(44\) | 1609.90 | 0.125363 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22799.7 | −1.58867 | ||||||||
\(47\) | 22537.9 | 1.48823 | 0.744113 | − | 0.668054i | \(-0.232873\pi\) | ||||
0.744113 | + | 0.668054i | \(0.232873\pi\) | |||||||
\(48\) | 11454.6 | 0.717593 | ||||||||
\(49\) | −16801.2 | −0.999654 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10902.5 | −0.586949 | ||||||||
\(52\) | −4456.94 | −0.228575 | ||||||||
\(53\) | −5835.91 | −0.285377 | −0.142688 | − | 0.989768i | \(-0.545575\pi\) | ||||
−0.142688 | + | 0.989768i | \(0.545575\pi\) | |||||||
\(54\) | −4906.83 | −0.228990 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 303.439 | 0.0129301 | ||||||||
\(57\) | 6719.28 | 0.273928 | ||||||||
\(58\) | −13543.2 | −0.528628 | ||||||||
\(59\) | 27573.2 | 1.03123 | 0.515617 | − | 0.856819i | \(-0.327563\pi\) | ||||
0.515617 | + | 0.856819i | \(0.327563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13969.9 | 0.480693 | 0.240347 | − | 0.970687i | \(-0.422739\pi\) | ||||
0.240347 | + | 0.970687i | \(0.422739\pi\) | |||||||
\(62\) | 58490.0 | 1.93242 | ||||||||
\(63\) | −195.325 | −0.00620021 | ||||||||
\(64\) | 10169.5 | 0.310349 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7329.95 | −0.207129 | ||||||||
\(67\) | −18128.3 | −0.493366 | −0.246683 | − | 0.969096i | \(-0.579341\pi\) | ||||
−0.246683 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(68\) | 16117.5 | 0.422694 | ||||||||
\(69\) | 30485.8 | 0.770860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 986.398 | 0.0232224 | 0.0116112 | − | 0.999933i | \(-0.496304\pi\) | ||||
0.0116112 | + | 0.999933i | \(0.496304\pi\) | |||||||
\(72\) | −10192.6 | −0.231714 | ||||||||
\(73\) | 11598.8 | 0.254745 | 0.127372 | − | 0.991855i | \(-0.459346\pi\) | ||||
0.127372 | + | 0.991855i | \(0.459346\pi\) | |||||||
\(74\) | −9371.12 | −0.198936 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9933.34 | −0.197270 | ||||||||
\(77\) | −291.782 | −0.00560830 | ||||||||
\(78\) | 20292.6 | 0.377660 | ||||||||
\(79\) | −48553.4 | −0.875289 | −0.437645 | − | 0.899148i | \(-0.644187\pi\) | ||||
−0.437645 | + | 0.899148i | \(0.644187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 15744.3 | 0.258577 | ||||||||
\(83\) | 34168.5 | 0.544416 | 0.272208 | − | 0.962239i | \(-0.412246\pi\) | ||||
0.272208 | + | 0.962239i | \(0.412246\pi\) | |||||||
\(84\) | 288.755 | 0.00446510 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −70909.2 | −1.03385 | ||||||||
\(87\) | 18108.8 | 0.256502 | ||||||||
\(88\) | −15225.9 | −0.209593 | ||||||||
\(89\) | 124210. | 1.66219 | 0.831097 | − | 0.556128i | \(-0.187713\pi\) | ||||
0.831097 | + | 0.556128i | \(0.187713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 807.783 | 0.0102257 | ||||||||
\(92\) | −45068.2 | −0.555138 | ||||||||
\(93\) | −78208.0 | −0.937657 | ||||||||
\(94\) | 151700. | 1.77079 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 40859.7 | 0.452499 | ||||||||
\(97\) | 138028. | 1.48949 | 0.744744 | − | 0.667351i | \(-0.232572\pi\) | ||||
0.744744 | + | 0.667351i | \(0.232572\pi\) | |||||||
\(98\) | −113087. | −1.18945 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5951.66 | −0.0580543 | −0.0290272 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290272 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(102\) | −73383.6 | −0.698390 | ||||||||
\(103\) | 191198. | 1.77578 | 0.887892 | − | 0.460052i | \(-0.152169\pi\) | ||||
0.887892 | + | 0.460052i | \(0.152169\pi\) | |||||||
\(104\) | 42152.3 | 0.382153 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −39280.9 | −0.339560 | ||||||||
\(107\) | −88404.1 | −0.746471 | −0.373236 | − | 0.927737i | \(-0.621752\pi\) | ||||
−0.373236 | + | 0.927737i | \(0.621752\pi\) | |||||||
\(108\) | −9699.34 | −0.0800171 | ||||||||
\(109\) | 223100. | 1.79859 | 0.899296 | − | 0.437341i | \(-0.144080\pi\) | ||||
0.899296 | + | 0.437341i | \(0.144080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12530.3 | 0.0965281 | ||||||||
\(112\) | 3069.10 | 0.0231188 | ||||||||
\(113\) | −12365.3 | −0.0910978 | −0.0455489 | − | 0.998962i | \(-0.514504\pi\) | ||||
−0.0455489 | + | 0.998962i | \(0.514504\pi\) | |||||||
\(114\) | 45226.8 | 0.325937 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −26770.8 | −0.184721 | ||||||||
\(117\) | −27133.6 | −0.183249 | ||||||||
\(118\) | 185592. | 1.22703 | ||||||||
\(119\) | −2921.16 | −0.0189099 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 94029.9 | 0.571961 | ||||||||
\(123\) | −21052.0 | −0.125467 | ||||||||
\(124\) | 115618. | 0.675257 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1314.71 | −0.00737741 | ||||||||
\(127\) | 207000. | 1.13883 | 0.569417 | − | 0.822049i | \(-0.307169\pi\) | ||||
0.569417 | + | 0.822049i | \(0.307169\pi\) | |||||||
\(128\) | 213729. | 1.15302 | ||||||||
\(129\) | 94813.9 | 0.501647 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −104541. | −0.532239 | −0.266119 | − | 0.963940i | \(-0.585742\pi\) | ||||
−0.266119 | + | 0.963940i | \(0.585742\pi\) | |||||||
\(132\) | −14489.1 | −0.0723782 | ||||||||
\(133\) | 1800.33 | 0.00882518 | ||||||||
\(134\) | −122020. | −0.587040 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −152434. | −0.706699 | ||||||||
\(137\) | 159251. | 0.724907 | 0.362453 | − | 0.932002i | \(-0.381939\pi\) | ||||
0.362453 | + | 0.932002i | \(0.381939\pi\) | |||||||
\(138\) | 205197. | 0.917220 | ||||||||
\(139\) | 184879. | 0.811614 | 0.405807 | − | 0.913959i | \(-0.366990\pi\) | ||||
0.405807 | + | 0.913959i | \(0.366990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −202841. | −0.859227 | ||||||||
\(142\) | 6639.35 | 0.0276315 | ||||||||
\(143\) | −40532.9 | −0.165755 | ||||||||
\(144\) | −103092. | −0.414302 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 78070.3 | 0.303112 | ||||||||
\(147\) | 151211. | 0.577151 | ||||||||
\(148\) | −18523.9 | −0.0695151 | ||||||||
\(149\) | 270575. | 0.998442 | 0.499221 | − | 0.866475i | \(-0.333620\pi\) | ||||
0.499221 | + | 0.866475i | \(0.333620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −287926. | −1.02764 | −0.513818 | − | 0.857899i | \(-0.671769\pi\) | ||||
−0.513818 | + | 0.857899i | \(0.671769\pi\) | |||||||
\(152\) | 93946.1 | 0.329815 | ||||||||
\(153\) | 98122.4 | 0.338875 | ||||||||
\(154\) | −1963.95 | −0.00667312 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 40112.5 | 0.131968 | ||||||||
\(157\) | −400095. | −1.29543 | −0.647715 | − | 0.761883i | \(-0.724275\pi\) | ||||
−0.647715 | + | 0.761883i | \(0.724275\pi\) | |||||||
\(158\) | −326808. | −1.04148 | ||||||||
\(159\) | 52523.1 | 0.164762 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8168.23 | 0.0248350 | ||||||||
\(162\) | 44161.4 | 0.132207 | ||||||||
\(163\) | −230209. | −0.678661 | −0.339331 | − | 0.940667i | \(-0.610201\pi\) | ||||
−0.339331 | + | 0.940667i | \(0.610201\pi\) | |||||||
\(164\) | 31121.9 | 0.0903559 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 229985. | 0.647782 | ||||||||
\(167\) | 505911. | 1.40373 | 0.701864 | − | 0.712311i | \(-0.252351\pi\) | ||||
0.701864 | + | 0.712311i | \(0.252351\pi\) | |||||||
\(168\) | −2730.95 | −0.00746518 | ||||||||
\(169\) | −259080. | −0.697777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −60473.5 | −0.158152 | ||||||||
\(172\) | −140167. | −0.361263 | ||||||||
\(173\) | 182355. | 0.463237 | 0.231619 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231619 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(174\) | 121888. | 0.305203 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −154001. | −0.374751 | ||||||||
\(177\) | −248159. | −0.595383 | ||||||||
\(178\) | 836045. | 1.97779 | ||||||||
\(179\) | 293039. | 0.683586 | 0.341793 | − | 0.939775i | \(-0.388966\pi\) | ||||
0.341793 | + | 0.939775i | \(0.388966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 234051. | 0.531024 | 0.265512 | − | 0.964108i | \(-0.414459\pi\) | ||||
0.265512 | + | 0.964108i | \(0.414459\pi\) | |||||||
\(182\) | 5437.11 | 0.0121672 | ||||||||
\(183\) | −125729. | −0.277528 | ||||||||
\(184\) | 426240. | 0.928132 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −526410. | −1.11569 | ||||||||
\(187\) | 146578. | 0.306524 | ||||||||
\(188\) | 299867. | 0.618776 | ||||||||
\(189\) | 1757.92 | 0.00357969 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 560936. | 1.11258 | 0.556288 | − | 0.830990i | \(-0.312225\pi\) | ||||
0.556288 | + | 0.830990i | \(0.312225\pi\) | |||||||
\(192\) | −91525.5 | −0.179180 | ||||||||
\(193\) | 490651. | 0.948155 | 0.474078 | − | 0.880483i | \(-0.342782\pi\) | ||||
0.474078 | + | 0.880483i | \(0.342782\pi\) | |||||||
\(194\) | 929050. | 1.77229 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −223540. | −0.415637 | ||||||||
\(197\) | −1.01719e6 | −1.86740 | −0.933698 | − | 0.358061i | \(-0.883438\pi\) | ||||
−0.933698 | + | 0.358061i | \(0.883438\pi\) | |||||||
\(198\) | 65969.5 | 0.119586 | ||||||||
\(199\) | −104543. | −0.187138 | −0.0935689 | − | 0.995613i | \(-0.529828\pi\) | ||||
−0.0935689 | + | 0.995613i | \(0.529828\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 163154. | 0.284845 | ||||||||
\(202\) | −40060.0 | −0.0690769 | ||||||||
\(203\) | 4851.98 | 0.00826379 | ||||||||
\(204\) | −145058. | −0.244042 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.28693e6 | 2.11295 | ||||||||
\(207\) | −274373. | −0.445056 | ||||||||
\(208\) | 426345. | 0.683286 | ||||||||
\(209\) | −90337.0 | −0.143054 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29310.5 | 0.0453228 | 0.0226614 | − | 0.999743i | \(-0.492786\pi\) | ||||
0.0226614 | + | 0.999743i | \(0.492786\pi\) | |||||||
\(212\) | −77646.7 | −0.118654 | ||||||||
\(213\) | −8877.59 | −0.0134074 | ||||||||
\(214\) | −595039. | −0.888201 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 91733.1 | 0.133780 | ||||||||
\(217\) | −20954.7 | −0.0302087 | ||||||||
\(218\) | 1.50166e6 | 2.14008 | ||||||||
\(219\) | −104389. | −0.147077 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −405794. | −0.558888 | ||||||||
\(222\) | 84340.1 | 0.114855 | ||||||||
\(223\) | 794924. | 1.07044 | 0.535221 | − | 0.844712i | \(-0.320228\pi\) | ||||
0.535221 | + | 0.844712i | \(0.320228\pi\) | |||||||
\(224\) | 10947.8 | 0.0145782 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −83229.4 | −0.108394 | ||||||||
\(227\) | 379790. | 0.489191 | 0.244596 | − | 0.969625i | \(-0.421345\pi\) | ||||
0.244596 | + | 0.969625i | \(0.421345\pi\) | |||||||
\(228\) | 89400.0 | 0.113894 | ||||||||
\(229\) | 162001. | 0.204140 | 0.102070 | − | 0.994777i | \(-0.467453\pi\) | ||||
0.102070 | + | 0.994777i | \(0.467453\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2626.03 | 0.00323795 | ||||||||
\(232\) | 253189. | 0.308834 | ||||||||
\(233\) | −463134. | −0.558878 | −0.279439 | − | 0.960163i | \(-0.590148\pi\) | ||||
−0.279439 | + | 0.960163i | \(0.590148\pi\) | |||||||
\(234\) | −182634. | −0.218042 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 366861. | 0.428767 | ||||||||
\(237\) | 436980. | 0.505348 | ||||||||
\(238\) | −19662.0 | −0.0225002 | ||||||||
\(239\) | 932706. | 1.05621 | 0.528105 | − | 0.849179i | \(-0.322903\pi\) | ||||
0.528105 | + | 0.849179i | \(0.322903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 414220. | 0.459397 | 0.229699 | − | 0.973262i | \(-0.426226\pi\) | ||||
0.229699 | + | 0.973262i | \(0.426226\pi\) | |||||||
\(242\) | 98547.1 | 0.108170 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 185869. | 0.199863 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −141699. | −0.149289 | ||||||||
\(247\) | 250094. | 0.260832 | ||||||||
\(248\) | −1.09347e6 | −1.12896 | ||||||||
\(249\) | −307516. | −0.314318 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.90536e6 | 1.90894 | 0.954472 | − | 0.298300i | \(-0.0964195\pi\) | ||||
0.954472 | + | 0.298300i | \(0.0964195\pi\) | |||||||
\(252\) | −2598.80 | −0.00257793 | ||||||||
\(253\) | −409865. | −0.402568 | ||||||||
\(254\) | 1.39329e6 | 1.35506 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.11316e6 | 1.06160 | ||||||||
\(257\) | −631671. | −0.596565 | −0.298283 | − | 0.954478i | \(-0.596414\pi\) | ||||
−0.298283 | + | 0.954478i | \(0.596414\pi\) | |||||||
\(258\) | 638183. | 0.596892 | ||||||||
\(259\) | 3357.31 | 0.00310987 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −162979. | −0.148092 | ||||||||
\(262\) | −703652. | −0.633293 | ||||||||
\(263\) | −961547. | −0.857198 | −0.428599 | − | 0.903495i | \(-0.640993\pi\) | ||||
−0.428599 | + | 0.903495i | \(0.640993\pi\) | |||||||
\(264\) | 137033. | 0.121009 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12117.9 | 0.0105008 | ||||||||
\(267\) | −1.11789e6 | −0.959668 | ||||||||
\(268\) | −241197. | −0.205132 | ||||||||
\(269\) | 720581. | 0.607158 | 0.303579 | − | 0.952806i | \(-0.401818\pi\) | ||||
0.303579 | + | 0.952806i | \(0.401818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −632223. | −0.522934 | −0.261467 | − | 0.965212i | \(-0.584206\pi\) | ||||
−0.261467 | + | 0.965212i | \(0.584206\pi\) | |||||||
\(272\) | −1.54178e6 | −1.26357 | ||||||||
\(273\) | −7270.05 | −0.00590379 | ||||||||
\(274\) | 1.07191e6 | 0.862542 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 405614. | 0.320509 | ||||||||
\(277\) | −2.37840e6 | −1.86246 | −0.931228 | − | 0.364437i | \(-0.881262\pi\) | ||||
−0.931228 | + | 0.364437i | \(0.881262\pi\) | |||||||
\(278\) | 1.24440e6 | 0.965712 | ||||||||
\(279\) | 703872. | 0.541356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.11538e6 | 1.59817 | 0.799085 | − | 0.601218i | \(-0.205317\pi\) | ||||
0.799085 | + | 0.601218i | \(0.205317\pi\) | |||||||
\(282\) | −1.36530e6 | −1.02237 | ||||||||
\(283\) | 40867.3 | 0.0303326 | 0.0151663 | − | 0.999885i | \(-0.495172\pi\) | ||||
0.0151663 | + | 0.999885i | \(0.495172\pi\) | |||||||
\(284\) | 13124.0 | 0.00965542 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −272823. | −0.197227 | ||||||||
\(287\) | −5640.58 | −0.00404221 | ||||||||
\(288\) | −367738. | −0.261250 | ||||||||
\(289\) | 47603.2 | 0.0335267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.24225e6 | −0.859956 | ||||||||
\(292\) | 154322. | 0.105918 | ||||||||
\(293\) | −837587. | −0.569982 | −0.284991 | − | 0.958530i | \(-0.591991\pi\) | ||||
−0.284991 | + | 0.958530i | \(0.591991\pi\) | |||||||
\(294\) | 1.01778e6 | 0.686732 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 175193. | 0.116222 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 1.82122e6 | 1.18801 | ||||||||
\(299\) | 1.13469e6 | 0.734007 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25404.0 | 0.0161617 | ||||||||
\(302\) | −1.93800e6 | −1.22275 | ||||||||
\(303\) | 53564.9 | 0.0335177 | ||||||||
\(304\) | 950209. | 0.589705 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 660452. | 0.403216 | ||||||||
\(307\) | −632213. | −0.382840 | −0.191420 | − | 0.981508i | \(-0.561309\pi\) | ||||
−0.191420 | + | 0.981508i | \(0.561309\pi\) | |||||||
\(308\) | −3882.15 | −0.00233182 | ||||||||
\(309\) | −1.72078e6 | −1.02525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.99159e6 | 1.16761 | 0.583806 | − | 0.811893i | \(-0.301563\pi\) | ||||
0.583806 | + | 0.811893i | \(0.301563\pi\) | |||||||
\(312\) | −379370. | −0.220636 | ||||||||
\(313\) | −305651. | −0.176346 | −0.0881728 | − | 0.996105i | \(-0.528103\pi\) | ||||
−0.0881728 | + | 0.996105i | \(0.528103\pi\) | |||||||
\(314\) | −2.69300e6 | −1.54139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −646002. | −0.363929 | ||||||||
\(317\) | 770054. | 0.430401 | 0.215200 | − | 0.976570i | \(-0.430960\pi\) | ||||
0.215200 | + | 0.976570i | \(0.430960\pi\) | |||||||
\(318\) | 353528. | 0.196045 | ||||||||
\(319\) | −243463. | −0.133954 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 795637. | 0.430975 | ||||||||
\(322\) | 54979.5 | 0.0295503 | ||||||||
\(323\) | −904406. | −0.482344 | ||||||||
\(324\) | 87294.1 | 0.0461979 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.54951e6 | −0.807516 | ||||||||
\(327\) | −2.00790e6 | −1.03842 | ||||||||
\(328\) | −294340. | −0.151065 | ||||||||
\(329\) | −54348.3 | −0.0276819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 965864. | 0.484558 | 0.242279 | − | 0.970207i | \(-0.422105\pi\) | ||||
0.242279 | + | 0.970207i | \(0.422105\pi\) | |||||||
\(332\) | 454612. | 0.226358 | ||||||||
\(333\) | −112773. | −0.0557305 | ||||||||
\(334\) | 3.40524e6 | 1.67025 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −27621.9 | −0.0133477 | ||||||||
\(337\) | −1.11434e6 | −0.534494 | −0.267247 | − | 0.963628i | \(-0.586114\pi\) | ||||
−0.267247 | + | 0.963628i | \(0.586114\pi\) | |||||||
\(338\) | −1.74384e6 | −0.830261 | ||||||||
\(339\) | 111288. | 0.0525953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.05146e6 | 0.489675 | ||||||||
\(342\) | −407041. | −0.188180 | ||||||||
\(343\) | 81043.4 | 0.0371948 | ||||||||
\(344\) | 1.32565e6 | 0.603993 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.22742e6 | 0.551190 | ||||||||
\(347\) | −2.70207e6 | −1.20468 | −0.602342 | − | 0.798238i | \(-0.705766\pi\) | ||||
−0.602342 | + | 0.798238i | \(0.705766\pi\) | |||||||
\(348\) | 240937. | 0.106649 | ||||||||
\(349\) | −760601. | −0.334267 | −0.167133 | − | 0.985934i | \(-0.553451\pi\) | ||||
−0.167133 | + | 0.985934i | \(0.553451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 244202. | 0.105799 | ||||||||
\(352\) | −549336. | −0.236310 | ||||||||
\(353\) | −2.61113e6 | −1.11530 | −0.557650 | − | 0.830076i | \(-0.688297\pi\) | ||||
−0.557650 | + | 0.830076i | \(0.688297\pi\) | |||||||
\(354\) | −1.67033e6 | −0.708426 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.65261e6 | 0.691109 | ||||||||
\(357\) | 26290.5 | 0.0109176 | ||||||||
\(358\) | 1.97242e6 | 0.813376 | ||||||||
\(359\) | −1.34676e6 | −0.551512 | −0.275756 | − | 0.961228i | \(-0.588928\pi\) | ||||
−0.275756 | + | 0.961228i | \(0.588928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91871e6 | −0.774891 | ||||||||
\(362\) | 1.57537e6 | 0.631847 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 10747.6 | 0.00425164 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −846269. | −0.330222 | ||||||||
\(367\) | −1.80461e6 | −0.699388 | −0.349694 | − | 0.936864i | \(-0.613714\pi\) | ||||
−0.349694 | + | 0.936864i | \(0.613714\pi\) | |||||||
\(368\) | 4.31116e6 | 1.65949 | ||||||||
\(369\) | 189468. | 0.0724386 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14072.8 | 0.00530818 | ||||||||
\(372\) | −1.04056e6 | −0.389860 | ||||||||
\(373\) | 715758. | 0.266376 | 0.133188 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133188 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(374\) | 986601. | 0.364723 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.83604e6 | −1.03453 | ||||||||
\(377\) | 674014. | 0.244239 | ||||||||
\(378\) | 11832.4 | 0.00425935 | ||||||||
\(379\) | 4.22778e6 | 1.51187 | 0.755934 | − | 0.654648i | \(-0.227183\pi\) | ||||
0.755934 | + | 0.654648i | \(0.227183\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.86300e6 | −0.657506 | ||||||||
\(382\) | 3.77560e6 | 1.32382 | ||||||||
\(383\) | −4.99412e6 | −1.73965 | −0.869825 | − | 0.493361i | \(-0.835768\pi\) | ||||
−0.869825 | + | 0.493361i | \(0.835768\pi\) | |||||||
\(384\) | −1.92356e6 | −0.665699 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.30252e6 | 1.12818 | ||||||||
\(387\) | −853325. | −0.289626 | ||||||||
\(388\) | 1.83646e6 | 0.619301 | ||||||||
\(389\) | 1.96218e6 | 0.657455 | 0.328727 | − | 0.944425i | \(-0.393380\pi\) | ||||
0.328727 | + | 0.944425i | \(0.393380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.10335e6 | −1.35737 | ||||||||
\(392\) | 2.11416e6 | 0.694902 | ||||||||
\(393\) | 940865. | 0.307288 | ||||||||
\(394\) | −6.84660e6 | −2.22195 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 130402. | 0.0417876 | ||||||||
\(397\) | −4.49019e6 | −1.42984 | −0.714921 | − | 0.699205i | \(-0.753537\pi\) | ||||
−0.714921 | + | 0.699205i | \(0.753537\pi\) | |||||||
\(398\) | −703667. | −0.222669 | ||||||||
\(399\) | −16203.0 | −0.00509522 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.74027e6 | 1.47212 | 0.736059 | − | 0.676918i | \(-0.236685\pi\) | ||||
0.736059 | + | 0.676918i | \(0.236685\pi\) | |||||||
\(402\) | 1.09818e6 | 0.338928 | ||||||||
\(403\) | −2.91093e6 | −0.892830 | ||||||||
\(404\) | −79186.8 | −0.0241379 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 32658.2 | 0.00983280 | ||||||||
\(407\) | −168463. | −0.0504101 | ||||||||
\(408\) | 1.37191e6 | 0.408013 | ||||||||
\(409\) | −1.77250e6 | −0.523935 | −0.261967 | − | 0.965077i | \(-0.584371\pi\) | ||||
−0.261967 | + | 0.965077i | \(0.584371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.43326e6 | −0.418525 | ||||||||
\(412\) | 2.54389e6 | 0.738338 | ||||||||
\(413\) | −66490.5 | −0.0191816 | ||||||||
\(414\) | −1.84677e6 | −0.529557 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.52081e6 | 0.430866 | ||||||||
\(417\) | −1.66391e6 | −0.468586 | ||||||||
\(418\) | −608049. | −0.170215 | ||||||||
\(419\) | −2.99507e6 | −0.833435 | −0.416718 | − | 0.909036i | \(-0.636820\pi\) | ||||
−0.416718 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.49888e6 | −1.51206 | −0.756030 | − | 0.654537i | \(-0.772864\pi\) | ||||
−0.756030 | + | 0.654537i | \(0.772864\pi\) | |||||||
\(422\) | 197286. | 0.0539281 | ||||||||
\(423\) | 1.82557e6 | 0.496075 | ||||||||
\(424\) | 734356. | 0.198377 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −59754.1 | −0.0159531 | ||||||||
\(427\) | −33687.2 | −0.00894119 | ||||||||
\(428\) | −1.17622e6 | −0.310369 | ||||||||
\(429\) | 364796. | 0.0956989 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −597155. | −0.154844 | −0.0774219 | − | 0.996998i | \(-0.524669\pi\) | ||||
−0.0774219 | + | 0.996998i | \(0.524669\pi\) | |||||||
\(432\) | 927825. | 0.239198 | ||||||||
\(433\) | 1.07785e6 | 0.276274 | 0.138137 | − | 0.990413i | \(-0.455889\pi\) | ||||
0.138137 | + | 0.990413i | \(0.455889\pi\) | |||||||
\(434\) | −141044. | −0.0359443 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.96834e6 | 0.747820 | ||||||||
\(437\) | 2.52893e6 | 0.633479 | ||||||||
\(438\) | −702633. | −0.175002 | ||||||||
\(439\) | 4.45787e6 | 1.10399 | 0.551996 | − | 0.833847i | \(-0.313866\pi\) | ||||
0.551996 | + | 0.833847i | \(0.313866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36090e6 | −0.333218 | ||||||||
\(442\) | −2.73136e6 | −0.665002 | ||||||||
\(443\) | −2.35378e6 | −0.569845 | −0.284923 | − | 0.958551i | \(-0.591968\pi\) | ||||
−0.284923 | + | 0.958551i | \(0.591968\pi\) | |||||||
\(444\) | 166715. | 0.0401346 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.35055e6 | 1.27368 | ||||||||
\(447\) | −2.43518e6 | −0.576451 | ||||||||
\(448\) | −24522.9 | −0.00577268 | ||||||||
\(449\) | 1.43645e6 | 0.336260 | 0.168130 | − | 0.985765i | \(-0.446227\pi\) | ||||
0.168130 | + | 0.985765i | \(0.446227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 283033. | 0.0655232 | ||||||||
\(452\) | −164520. | −0.0378767 | ||||||||
\(453\) | 2.59134e6 | 0.593305 | ||||||||
\(454\) | 2.55633e6 | 0.582072 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −845515. | −0.190419 | ||||||||
\(457\) | 4.60085e6 | 1.03050 | 0.515250 | − | 0.857040i | \(-0.327699\pi\) | ||||
0.515250 | + | 0.857040i | \(0.327699\pi\) | |||||||
\(458\) | 1.09041e6 | 0.242899 | ||||||||
\(459\) | −883102. | −0.195650 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.67111e6 | −1.02369 | −0.511844 | − | 0.859078i | \(-0.671038\pi\) | ||||
−0.511844 | + | 0.859078i | \(0.671038\pi\) | |||||||
\(462\) | 17675.6 | 0.00385273 | ||||||||
\(463\) | 326607. | 0.0708065 | 0.0354032 | − | 0.999373i | \(-0.488728\pi\) | ||||
0.0354032 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(464\) | 2.56086e6 | 0.552192 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.11731e6 | −0.664990 | ||||||||
\(467\) | 1.63074e6 | 0.346014 | 0.173007 | − | 0.984921i | \(-0.444652\pi\) | ||||
0.173007 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(468\) | −361012. | −0.0761917 | ||||||||
\(469\) | 43714.8 | 0.00917692 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.60085e6 | 0.747916 | ||||||||
\(472\) | −3.46965e6 | −0.716854 | ||||||||
\(473\) | −1.27472e6 | −0.261976 | ||||||||
\(474\) | 2.94127e6 | 0.601297 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −38866.0 | −0.00786236 | ||||||||
\(477\) | −472708. | −0.0951256 | ||||||||
\(478\) | 6.27795e6 | 1.25675 | ||||||||
\(479\) | −7.31820e6 | −1.45736 | −0.728678 | − | 0.684856i | \(-0.759865\pi\) | ||||
−0.728678 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 466381. | 0.0919133 | ||||||||
\(482\) | 2.78807e6 | 0.546621 | ||||||||
\(483\) | −73514.1 | −0.0143385 | ||||||||
\(484\) | 194798. | 0.0377983 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −397453. | −0.0763299 | ||||||||
\(487\) | 2.80682e6 | 0.536281 | 0.268141 | − | 0.963380i | \(-0.413591\pi\) | ||||
0.268141 | + | 0.963380i | \(0.413591\pi\) | |||||||
\(488\) | −1.75789e6 | −0.334150 | ||||||||
\(489\) | 2.07188e6 | 0.391825 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.39394e6 | −0.448136 | −0.224068 | − | 0.974574i | \(-0.571934\pi\) | ||||
−0.224068 | + | 0.974574i | \(0.571934\pi\) | |||||||
\(492\) | −280097. | −0.0521670 | ||||||||
\(493\) | −2.43742e6 | −0.451661 | ||||||||
\(494\) | 1.68336e6 | 0.310355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.10598e7 | −2.01857 | ||||||||
\(497\) | −2378.62 | −0.000431950 0 | ||||||||
\(498\) | −2.06986e6 | −0.373997 | ||||||||
\(499\) | 5.55266e6 | 0.998274 | 0.499137 | − | 0.866523i | \(-0.333650\pi\) | ||||
0.499137 | + | 0.866523i | \(0.333650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.55320e6 | −0.810443 | ||||||||
\(502\) | 1.28248e7 | 2.27139 | ||||||||
\(503\) | −3.38576e6 | −0.596673 | −0.298336 | − | 0.954461i | \(-0.596432\pi\) | ||||
−0.298336 | + | 0.954461i | \(0.596432\pi\) | |||||||
\(504\) | 24578.5 | 0.00431002 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.75876e6 | −0.479002 | ||||||||
\(507\) | 2.33172e6 | 0.402862 | ||||||||
\(508\) | 2.75413e6 | 0.473506 | ||||||||
\(509\) | 4.81925e6 | 0.824489 | 0.412244 | − | 0.911073i | \(-0.364745\pi\) | ||||
0.412244 | + | 0.911073i | \(0.364745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27969.5 | −0.00473841 | ||||||||
\(512\) | 653266. | 0.110132 | ||||||||
\(513\) | 544262. | 0.0913092 | ||||||||
\(514\) | −4.25171e6 | −0.709833 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.26150e6 | 0.208575 | ||||||||
\(517\) | 2.72708e6 | 0.448717 | ||||||||
\(518\) | 22597.7 | 0.00370032 | ||||||||
\(519\) | −1.64120e6 | −0.267450 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.32781e6 | 1.02131 | 0.510657 | − | 0.859785i | \(-0.329402\pi\) | ||||
0.510657 | + | 0.859785i | \(0.329402\pi\) | |||||||
\(522\) | −1.09700e6 | −0.176209 | ||||||||
\(523\) | −3.74833e6 | −0.599216 | −0.299608 | − | 0.954062i | \(-0.596856\pi\) | ||||
−0.299608 | + | 0.954062i | \(0.596856\pi\) | |||||||
\(524\) | −1.39091e6 | −0.221295 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.47208e6 | −1.01995 | ||||||||
\(527\) | 1.05267e7 | 1.65107 | ||||||||
\(528\) | 1.38601e6 | 0.216362 | ||||||||
\(529\) | 5.03756e6 | 0.782674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.23343e6 | 0.343744 | ||||||||
\(532\) | 23953.4 | 0.00366934 | ||||||||
\(533\) | −783562. | −0.119469 | ||||||||
\(534\) | −7.52441e6 | −1.14188 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.28116e6 | 0.342960 | ||||||||
\(537\) | −2.63735e6 | −0.394669 | ||||||||
\(538\) | 4.85016e6 | 0.722437 | ||||||||
\(539\) | −2.03294e6 | −0.301407 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.24091e6 | 0.622968 | 0.311484 | − | 0.950251i | \(-0.399174\pi\) | ||||
0.311484 | + | 0.950251i | \(0.399174\pi\) | |||||||
\(542\) | −4.25543e6 | −0.622221 | ||||||||
\(543\) | −2.10646e6 | −0.306587 | ||||||||
\(544\) | −5.49966e6 | −0.796781 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −48934.0 | −0.00702472 | ||||||||
\(547\) | 6.27240e6 | 0.896325 | 0.448162 | − | 0.893952i | \(-0.352079\pi\) | ||||
0.448162 | + | 0.893952i | \(0.352079\pi\) | |||||||
\(548\) | 2.11884e6 | 0.301402 | ||||||||
\(549\) | 1.13156e6 | 0.160231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.50220e6 | 0.210789 | ||||||||
\(552\) | −3.83616e6 | −0.535857 | ||||||||
\(553\) | 117082. | 0.0162809 | ||||||||
\(554\) | −1.60088e7 | −2.21607 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.45981e6 | 0.337454 | ||||||||
\(557\) | 7.08639e6 | 0.967803 | 0.483902 | − | 0.875122i | \(-0.339219\pi\) | ||||
0.483902 | + | 0.875122i | \(0.339219\pi\) | |||||||
\(558\) | 4.73769e6 | 0.644142 | ||||||||
\(559\) | 3.52900e6 | 0.477664 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31920e6 | −0.176972 | ||||||||
\(562\) | 1.42384e7 | 1.90161 | ||||||||
\(563\) | 3.35539e6 | 0.446140 | 0.223070 | − | 0.974802i | \(-0.428392\pi\) | ||||
0.223070 | + | 0.974802i | \(0.428392\pi\) | |||||||
\(564\) | −2.69880e6 | −0.357250 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 275074. | 0.0360918 | ||||||||
\(567\) | −15821.3 | −0.00206674 | ||||||||
\(568\) | −124123. | −0.0161428 | ||||||||
\(569\) | 7.59058e6 | 0.982865 | 0.491433 | − | 0.870916i | \(-0.336473\pi\) | ||||
0.491433 | + | 0.870916i | \(0.336473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00981e7 | −1.29613 | −0.648067 | − | 0.761584i | \(-0.724422\pi\) | ||||
−0.648067 | + | 0.761584i | \(0.724422\pi\) | |||||||
\(572\) | −539290. | −0.0689180 | ||||||||
\(573\) | −5.04842e6 | −0.642346 | ||||||||
\(574\) | −37966.2 | −0.00480969 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 823730. | 0.103450 | ||||||||
\(577\) | 1.34784e7 | 1.68538 | 0.842692 | − | 0.538396i | \(-0.180970\pi\) | ||||
0.842692 | + | 0.538396i | \(0.180970\pi\) | |||||||
\(578\) | 320412. | 0.0398923 | ||||||||
\(579\) | −4.41586e6 | −0.547418 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −82394.5 | −0.0101265 | ||||||||
\(582\) | −8.36145e6 | −1.02323 | ||||||||
\(583\) | −706145. | −0.0860443 | ||||||||
\(584\) | −1.45952e6 | −0.177084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.63771e6 | −0.678202 | ||||||||
\(587\) | −3.66148e6 | −0.438593 | −0.219296 | − | 0.975658i | \(-0.570376\pi\) | ||||
−0.219296 | + | 0.975658i | \(0.570376\pi\) | |||||||
\(588\) | 2.01186e6 | 0.239968 | ||||||||
\(589\) | −6.48768e6 | −0.770550 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.15471e6 | 1.07814 | ||||||||
\(592\) | 1.77197e6 | 0.207804 | ||||||||
\(593\) | 4.20157e6 | 0.490653 | 0.245327 | − | 0.969440i | \(-0.421105\pi\) | ||||
0.245327 | + | 0.969440i | \(0.421105\pi\) | |||||||
\(594\) | −593726. | −0.0690430 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.60001e6 | 0.415133 | ||||||||
\(597\) | 940886. | 0.108044 | ||||||||
\(598\) | 7.63750e6 | 0.873370 | ||||||||
\(599\) | 5.56521e6 | 0.633745 | 0.316873 | − | 0.948468i | \(-0.397367\pi\) | ||||
0.316873 | + | 0.948468i | \(0.397367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −455310. | −0.0514187 | −0.0257093 | − | 0.999669i | \(-0.508184\pi\) | ||||
−0.0257093 | + | 0.999669i | \(0.508184\pi\) | |||||||
\(602\) | 170992. | 0.0192302 | ||||||||
\(603\) | −1.46839e6 | −0.164455 | ||||||||
\(604\) | −3.83086e6 | −0.427271 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 360540. | 0.0398816 | ||||||||
\(607\) | 8.22381e6 | 0.905944 | 0.452972 | − | 0.891525i | \(-0.350364\pi\) | ||||
0.452972 | + | 0.891525i | \(0.350364\pi\) | |||||||
\(608\) | 3.38948e6 | 0.371856 | ||||||||
\(609\) | −43667.8 | −0.00477110 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54980e6 | −0.818149 | ||||||||
\(612\) | 1.30552e6 | 0.140898 | ||||||||
\(613\) | −2.86125e6 | −0.307543 | −0.153771 | − | 0.988106i | \(-0.549142\pi\) | ||||
−0.153771 | + | 0.988106i | \(0.549142\pi\) | |||||||
\(614\) | −4.25536e6 | −0.455528 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36716.1 | 0.00389856 | ||||||||
\(617\) | −1.59938e7 | −1.69137 | −0.845685 | − | 0.533683i | \(-0.820808\pi\) | ||||
−0.845685 | + | 0.533683i | \(0.820808\pi\) | |||||||
\(618\) | −1.15824e7 | −1.21991 | ||||||||
\(619\) | 6.22085e6 | 0.652564 | 0.326282 | − | 0.945273i | \(-0.394204\pi\) | ||||
0.326282 | + | 0.945273i | \(0.394204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.46935e6 | 0.256953 | ||||||||
\(622\) | 1.34052e7 | 1.38930 | ||||||||
\(623\) | −299522. | −0.0309178 | ||||||||
\(624\) | −3.83710e6 | −0.394496 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.05730e6 | −0.209828 | ||||||||
\(627\) | 813033. | 0.0825923 | ||||||||
\(628\) | −5.32326e6 | −0.538615 | ||||||||
\(629\) | −1.68656e6 | −0.169971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.11719e6 | −0.911565 | −0.455783 | − | 0.890091i | \(-0.650641\pi\) | ||||
−0.455783 | + | 0.890091i | \(0.650641\pi\) | |||||||
\(632\) | 6.10967e6 | 0.608450 | ||||||||
\(633\) | −263795. | −0.0261672 | ||||||||
\(634\) | 5.18316e6 | 0.512119 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 698820. | 0.0685051 | ||||||||
\(637\) | 5.62811e6 | 0.549558 | ||||||||
\(638\) | −1.63872e6 | −0.159387 | ||||||||
\(639\) | 79898.3 | 0.00774079 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.50107e6 | 0.913330 | 0.456665 | − | 0.889639i | \(-0.349044\pi\) | ||||
0.456665 | + | 0.889639i | \(0.349044\pi\) | |||||||
\(642\) | 5.35535e6 | 0.512803 | ||||||||
\(643\) | −5.32410e6 | −0.507830 | −0.253915 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253915 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(644\) | 108678. | 0.0103259 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.08747e6 | −0.573925 | ||||||||
\(647\) | 2.02469e6 | 0.190150 | 0.0950752 | − | 0.995470i | \(-0.469691\pi\) | ||||
0.0950752 | + | 0.995470i | \(0.469691\pi\) | |||||||
\(648\) | −825598. | −0.0772380 | ||||||||
\(649\) | 3.33636e6 | 0.310929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 188592. | 0.0174410 | ||||||||
\(652\) | −3.06293e6 | −0.282175 | ||||||||
\(653\) | −1.14621e7 | −1.05192 | −0.525959 | − | 0.850510i | \(-0.676293\pi\) | ||||
−0.525959 | + | 0.850510i | \(0.676293\pi\) | |||||||
\(654\) | −1.35149e7 | −1.23558 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.97708e6 | −0.270103 | ||||||||
\(657\) | 939502. | 0.0849150 | ||||||||
\(658\) | −365813. | −0.0329378 | ||||||||
\(659\) | −8.95330e6 | −0.803100 | −0.401550 | − | 0.915837i | \(-0.631528\pi\) | ||||
−0.401550 | + | 0.915837i | \(0.631528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.38575e7 | −1.23362 | −0.616812 | − | 0.787111i | \(-0.711576\pi\) | ||||
−0.616812 | + | 0.787111i | \(0.711576\pi\) | |||||||
\(662\) | 6.50113e6 | 0.576559 | ||||||||
\(663\) | 3.65215e6 | 0.322674 | ||||||||
\(664\) | −4.29956e6 | −0.378446 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −759061. | −0.0663118 | ||||||||
\(667\) | 6.81557e6 | 0.593182 | ||||||||
\(668\) | 6.73115e6 | 0.583644 | ||||||||
\(669\) | −7.15431e6 | −0.618020 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.69036e6 | 0.144935 | ||||||||
\(672\) | −98529.9 | −0.00841676 | ||||||||
\(673\) | −9.94769e6 | −0.846612 | −0.423306 | − | 0.905987i | \(-0.639130\pi\) | ||||
−0.423306 | + | 0.905987i | \(0.639130\pi\) | |||||||
\(674\) | −7.50051e6 | −0.635976 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.44705e6 | −0.290122 | ||||||||
\(677\) | 1.32600e7 | 1.11192 | 0.555960 | − | 0.831209i | \(-0.312351\pi\) | ||||
0.555960 | + | 0.831209i | \(0.312351\pi\) | |||||||
\(678\) | 749065. | 0.0625814 | ||||||||
\(679\) | −332842. | −0.0277054 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.41811e6 | −0.282435 | ||||||||
\(682\) | 7.07729e6 | 0.582648 | ||||||||
\(683\) | −2.05349e7 | −1.68438 | −0.842192 | − | 0.539178i | \(-0.818735\pi\) | ||||
−0.842192 | + | 0.539178i | \(0.818735\pi\) | |||||||
\(684\) | −804600. | −0.0657567 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 545495. | 0.0442568 | ||||||||
\(687\) | −1.45801e6 | −0.117860 | ||||||||
\(688\) | 1.34081e7 | 1.07993 | ||||||||
\(689\) | 1.95493e6 | 0.156885 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.74373e7 | 1.38926 | 0.694630 | − | 0.719367i | \(-0.255568\pi\) | ||||
0.694630 | + | 0.719367i | \(0.255568\pi\) | |||||||
\(692\) | 2.42624e6 | 0.192605 | ||||||||
\(693\) | −23634.3 | −0.00186943 | ||||||||
\(694\) | −1.81874e7 | −1.43341 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.27870e6 | −0.178305 | ||||||||
\(697\) | 2.83357e6 | 0.220929 | ||||||||
\(698\) | −5.11953e6 | −0.397733 | ||||||||
\(699\) | 4.16821e6 | 0.322668 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.83721e6 | 0.141209 | 0.0706046 | − | 0.997504i | \(-0.477507\pi\) | ||||
0.0706046 | + | 0.997504i | \(0.477507\pi\) | |||||||
\(702\) | 1.64370e6 | 0.125887 | ||||||||
\(703\) | 1.03944e6 | 0.0793251 | ||||||||
\(704\) | 1.23051e6 | 0.0935736 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.75752e7 | −1.32706 | ||||||||
\(707\) | 14351.9 | 0.00107985 | ||||||||
\(708\) | −3.30175e6 | −0.247549 | ||||||||
\(709\) | 4.37773e6 | 0.327065 | 0.163532 | − | 0.986538i | \(-0.447711\pi\) | ||||
0.163532 | + | 0.986538i | \(0.447711\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.93282e6 | −0.291763 | ||||||||
\(712\) | −1.56299e7 | −1.15546 | ||||||||
\(713\) | −2.94350e7 | −2.16841 | ||||||||
\(714\) | 176958. | 0.0129905 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.89889e6 | 0.284222 | ||||||||
\(717\) | −8.39436e6 | −0.609803 | ||||||||
\(718\) | −9.06492e6 | −0.656225 | ||||||||
\(719\) | −1.65258e7 | −1.19217 | −0.596087 | − | 0.802920i | \(-0.703279\pi\) | ||||
−0.596087 | + | 0.802920i | \(0.703279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −461058. | −0.0330307 | ||||||||
\(722\) | −1.29146e7 | −0.922017 | ||||||||
\(723\) | −3.72798e6 | −0.265233 | ||||||||
\(724\) | 3.11405e6 | 0.220790 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −886924. | −0.0624518 | ||||||||
\(727\) | −1.37064e7 | −0.961803 | −0.480902 | − | 0.876774i | \(-0.659691\pi\) | ||||
−0.480902 | + | 0.876774i | \(0.659691\pi\) | |||||||
\(728\) | −101647. | −0.00710829 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.27618e7 | −0.883323 | ||||||||
\(732\) | −1.67282e6 | −0.115391 | ||||||||
\(733\) | −2.48655e6 | −0.170938 | −0.0854688 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854688 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(734\) | −1.21466e7 | −0.832178 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.53783e7 | 1.04644 | ||||||||
\(737\) | −2.19352e6 | −0.148756 | ||||||||
\(738\) | 1.27529e6 | 0.0861923 | ||||||||
\(739\) | −2.27900e7 | −1.53509 | −0.767544 | − | 0.640996i | \(-0.778521\pi\) | ||||
−0.767544 | + | 0.640996i | \(0.778521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.25084e6 | −0.150591 | ||||||||
\(742\) | 94722.6 | 0.00631603 | ||||||||
\(743\) | 1.24390e7 | 0.826634 | 0.413317 | − | 0.910587i | \(-0.364370\pi\) | ||||
0.413317 | + | 0.910587i | \(0.364370\pi\) | |||||||
\(744\) | 9.84124e6 | 0.651805 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.81770e6 | 0.316951 | ||||||||
\(747\) | 2.76765e6 | 0.181472 | ||||||||
\(748\) | 1.95022e6 | 0.127447 | ||||||||
\(749\) | 213179. | 0.0138848 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.85180e7 | 1.84510 | 0.922549 | − | 0.385880i | \(-0.126102\pi\) | ||||
0.922549 | + | 0.385880i | \(0.126102\pi\) | |||||||
\(752\) | −2.86848e7 | −1.84973 | ||||||||
\(753\) | −1.71483e7 | −1.10213 | ||||||||
\(754\) | 4.53672e6 | 0.290612 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 23389.2 | 0.00148837 | ||||||||
\(757\) | 1.53660e6 | 0.0974586 | 0.0487293 | − | 0.998812i | \(-0.484483\pi\) | ||||
0.0487293 | + | 0.998812i | \(0.484483\pi\) | |||||||
\(758\) | 2.84567e7 | 1.79892 | ||||||||
\(759\) | 3.68879e6 | 0.232423 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.69462e6 | −0.231264 | −0.115632 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115632 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(762\) | −1.25396e7 | −0.782344 | ||||||||
\(763\) | −537986. | −0.0334549 | ||||||||
\(764\) | 7.46325e6 | 0.462588 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.36149e7 | −2.06995 | ||||||||
\(767\) | −9.23654e6 | −0.566919 | ||||||||
\(768\) | −1.00185e7 | −0.612913 | ||||||||
\(769\) | −1.49715e6 | −0.0912956 | −0.0456478 | − | 0.998958i | \(-0.514535\pi\) | ||||
−0.0456478 | + | 0.998958i | \(0.514535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.68504e6 | 0.344427 | ||||||||
\(772\) | 6.52811e6 | 0.394225 | ||||||||
\(773\) | −5.52587e6 | −0.332623 | −0.166311 | − | 0.986073i | \(-0.553186\pi\) | ||||
−0.166311 | + | 0.986073i | \(0.553186\pi\) | |||||||
\(774\) | −5.74365e6 | −0.344616 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.73686e7 | −1.03541 | ||||||||
\(777\) | −30215.8 | −0.00179548 | ||||||||
\(778\) | 1.32073e7 | 0.782283 | ||||||||
\(779\) | −1.74635e6 | −0.103107 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 119354. | 0.00700181 | ||||||||
\(782\) | −2.76192e7 | −1.61508 | ||||||||
\(783\) | 1.46681e6 | 0.0855007 | ||||||||
\(784\) | 2.13835e7 | 1.24248 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.33286e6 | 0.365632 | ||||||||
\(787\) | −6.04216e6 | −0.347741 | −0.173870 | − | 0.984769i | \(-0.555627\pi\) | ||||
−0.173870 | + | 0.984769i | \(0.555627\pi\) | |||||||
\(788\) | −1.35337e7 | −0.776428 | ||||||||
\(789\) | 8.65393e6 | 0.494904 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29817.9 | 0.00169448 | ||||||||
\(792\) | −1.23330e6 | −0.0698644 | ||||||||
\(793\) | −4.67967e6 | −0.264260 | ||||||||
\(794\) | −3.02230e7 | −1.70132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.39094e6 | −0.0778084 | ||||||||
\(797\) | 3.45685e6 | 0.192768 | 0.0963840 | − | 0.995344i | \(-0.469272\pi\) | ||||
0.0963840 | + | 0.995344i | \(0.469272\pi\) | |||||||
\(798\) | −109061. | −0.00606263 | ||||||||
\(799\) | 2.73021e7 | 1.51297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00610e7 | 0.554065 | ||||||||
\(802\) | 3.19063e7 | 1.75162 | ||||||||
\(803\) | 1.40345e6 | 0.0768085 | ||||||||
\(804\) | 2.17077e6 | 0.118433 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.95931e7 | −1.06235 | ||||||||
\(807\) | −6.48523e6 | −0.350543 | ||||||||
\(808\) | 748922. | 0.0403560 | ||||||||
\(809\) | 7.36347e6 | 0.395559 | 0.197779 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197779 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.37010e7 | 1.79925 | 0.899623 | − | 0.436667i | \(-0.143841\pi\) | ||||
0.899623 | + | 0.436667i | \(0.143841\pi\) | |||||||
\(812\) | 64555.6 | 0.00343593 | ||||||||
\(813\) | 5.69000e6 | 0.301916 | ||||||||
\(814\) | −1.13391e6 | −0.0599813 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.38760e7 | 0.729523 | ||||||||
\(817\) | 7.86520e6 | 0.412244 | ||||||||
\(818\) | −1.19305e7 | −0.623412 | ||||||||
\(819\) | 65430.4 | 0.00340855 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.10298e7 | −1.08888 | −0.544438 | − | 0.838801i | \(-0.683257\pi\) | ||||
−0.544438 | + | 0.838801i | \(0.683257\pi\) | |||||||
\(822\) | −9.64715e6 | −0.497989 | ||||||||
\(823\) | 1.99288e7 | 1.02561 | 0.512803 | − | 0.858506i | \(-0.328607\pi\) | ||||
0.512803 | + | 0.858506i | \(0.328607\pi\) | |||||||
\(824\) | −2.40592e7 | −1.23442 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −447541. | −0.0228235 | ||||||||
\(827\) | −1.87978e7 | −0.955748 | −0.477874 | − | 0.878428i | \(-0.658593\pi\) | ||||
−0.477874 | + | 0.878428i | \(0.658593\pi\) | |||||||
\(828\) | −3.65053e6 | −0.185046 | ||||||||
\(829\) | 7.27718e6 | 0.367771 | 0.183885 | − | 0.982948i | \(-0.441133\pi\) | ||||
0.183885 | + | 0.982948i | \(0.441133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.14056e7 | 1.07529 | ||||||||
\(832\) | −3.40661e6 | −0.170614 | ||||||||
\(833\) | −2.03527e7 | −1.01627 | ||||||||
\(834\) | −1.11996e7 | −0.557554 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.20193e6 | −0.0594792 | ||||||||
\(837\) | −6.33485e6 | −0.312552 | ||||||||
\(838\) | −2.01595e7 | −0.991677 | ||||||||
\(839\) | 3.52339e6 | 0.172805 | 0.0864025 | − | 0.996260i | \(-0.472463\pi\) | ||||
0.0864025 | + | 0.996260i | \(0.472463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.64627e7 | −0.802620 | ||||||||
\(842\) | −3.70124e7 | −1.79915 | ||||||||
\(843\) | −1.90384e7 | −0.922704 | ||||||||
\(844\) | 389976. | 0.0188444 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.22877e7 | 0.590263 | ||||||||
\(847\) | −35305.6 | −0.00169097 | ||||||||
\(848\) | 7.42757e6 | 0.354697 | ||||||||
\(849\) | −367806. | −0.0175125 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.71600e6 | 0.223229 | ||||||||
\(852\) | −118116. | −0.00557456 | ||||||||
\(853\) | 4.55380e6 | 0.214290 | 0.107145 | − | 0.994243i | \(-0.465829\pi\) | ||||
0.107145 | + | 0.994243i | \(0.465829\pi\) | |||||||
\(854\) | −226745. | −0.0106388 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.11243e7 | 0.518904 | ||||||||
\(857\) | −2.88776e7 | −1.34310 | −0.671552 | − | 0.740958i | \(-0.734372\pi\) | ||||
−0.671552 | + | 0.740958i | \(0.734372\pi\) | |||||||
\(858\) | 2.45541e6 | 0.113869 | ||||||||
\(859\) | 1.25501e7 | 0.580316 | 0.290158 | − | 0.956979i | \(-0.406292\pi\) | ||||
0.290158 | + | 0.956979i | \(0.406292\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50765.2 | 0.00233377 | ||||||||
\(862\) | −4.01939e6 | −0.184243 | ||||||||
\(863\) | 2.86046e7 | 1.30740 | 0.653701 | − | 0.756753i | \(-0.273215\pi\) | ||||
0.653701 | + | 0.756753i | \(0.273215\pi\) | |||||||
\(864\) | 3.30964e6 | 0.150833 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.25492e6 | 0.328729 | ||||||||
\(867\) | −428428. | −0.0193567 | ||||||||
\(868\) | −278802. | −0.0125602 | ||||||||
\(869\) | −5.87496e6 | −0.263910 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.07266e6 | 0.271227 | ||||||||
\(872\) | −2.80736e7 | −1.25028 | ||||||||
\(873\) | 1.11802e7 | 0.496496 | ||||||||
\(874\) | 1.70219e7 | 0.753755 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.38890e6 | −0.0611519 | ||||||||
\(877\) | 3.42227e7 | 1.50250 | 0.751251 | − | 0.660017i | \(-0.229451\pi\) | ||||
0.751251 | + | 0.660017i | \(0.229451\pi\) | |||||||
\(878\) | 3.00055e7 | 1.31360 | ||||||||
\(879\) | 7.53828e6 | 0.329079 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.25799e6 | −0.228234 | −0.114117 | − | 0.993467i | \(-0.536404\pi\) | ||||
−0.114117 | + | 0.993467i | \(0.536404\pi\) | |||||||
\(882\) | −9.16005e6 | −0.396485 | ||||||||
\(883\) | 8.94488e6 | 0.386076 | 0.193038 | − | 0.981191i | \(-0.438166\pi\) | ||||
0.193038 | + | 0.981191i | \(0.438166\pi\) | |||||||
\(884\) | −5.39909e6 | −0.232375 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.58431e7 | −0.678040 | ||||||||
\(887\) | 4.14864e7 | 1.77050 | 0.885252 | − | 0.465112i | \(-0.153986\pi\) | ||||
0.885252 | + | 0.465112i | \(0.153986\pi\) | |||||||
\(888\) | −1.57674e6 | −0.0671007 | ||||||||
\(889\) | −499163. | −0.0211830 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.05765e7 | 0.445070 | ||||||||
\(893\) | −1.68265e7 | −0.706098 | ||||||||
\(894\) | −1.63909e7 | −0.685899 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −515390. | −0.0214470 | ||||||||
\(897\) | −1.02122e7 | −0.423779 | ||||||||
\(898\) | 9.66861e6 | 0.400104 | ||||||||
\(899\) | −1.74846e7 | −0.721533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.06954e6 | −0.290121 | ||||||||
\(902\) | 1.90506e6 | 0.0779638 | ||||||||
\(903\) | −228636. | −0.00933094 | ||||||||
\(904\) | 1.55597e6 | 0.0633259 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.74420e7 | 0.705954 | ||||||||
\(907\) | 3.66068e7 | 1.47755 | 0.738777 | − | 0.673950i | \(-0.235404\pi\) | ||||
0.738777 | + | 0.673950i | \(0.235404\pi\) | |||||||
\(908\) | 5.05310e6 | 0.203396 | ||||||||
\(909\) | −482084. | −0.0193514 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.81370e7 | 1.12326 | 0.561631 | − | 0.827388i | \(-0.310174\pi\) | ||||
0.561631 | + | 0.827388i | \(0.310174\pi\) | |||||||
\(912\) | −8.55188e6 | −0.340467 | ||||||||
\(913\) | 4.13439e6 | 0.164147 | ||||||||
\(914\) | 3.09679e7 | 1.22616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.15542e6 | 0.0848776 | ||||||||
\(917\) | 252091. | 0.00989997 | ||||||||
\(918\) | −5.94407e6 | −0.232797 | ||||||||
\(919\) | −9.39900e6 | −0.367107 | −0.183554 | − | 0.983010i | \(-0.558760\pi\) | ||||
−0.183554 | + | 0.983010i | \(0.558760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.68991e6 | 0.221033 | ||||||||
\(922\) | −3.14408e7 | −1.21805 | ||||||||
\(923\) | −330426. | −0.0127665 | ||||||||
\(924\) | 34939.4 | 0.00134628 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.19836e6 | 0.0842502 | ||||||||
\(927\) | 1.54870e7 | 0.591928 | ||||||||
\(928\) | 9.13481e6 | 0.348201 | ||||||||
\(929\) | −3.51723e7 | −1.33709 | −0.668546 | − | 0.743671i | \(-0.733083\pi\) | ||||
−0.668546 | + | 0.743671i | \(0.733083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25435e7 | 0.474292 | ||||||||
\(932\) | −6.16200e6 | −0.232371 | ||||||||
\(933\) | −1.79243e7 | −0.674121 | ||||||||
\(934\) | 1.09764e7 | 0.411710 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.41433e6 | 0.127384 | ||||||||
\(937\) | −1.09773e7 | −0.408457 | −0.204229 | − | 0.978923i | \(-0.565469\pi\) | ||||
−0.204229 | + | 0.978923i | \(0.565469\pi\) | |||||||
\(938\) | 294240. | 0.0109193 | ||||||||
\(939\) | 2.75086e6 | 0.101813 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.86362e7 | 1.05424 | 0.527122 | − | 0.849790i | \(-0.323271\pi\) | ||||
0.527122 | + | 0.849790i | \(0.323271\pi\) | |||||||
\(942\) | 2.42370e7 | 0.889920 | ||||||||
\(943\) | −7.92331e6 | −0.290153 | ||||||||
\(944\) | −3.50934e7 | −1.28173 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.58001e6 | −0.311717 | ||||||||
\(947\) | −1.64152e7 | −0.594800 | −0.297400 | − | 0.954753i | \(-0.596119\pi\) | ||||
−0.297400 | + | 0.954753i | \(0.596119\pi\) | |||||||
\(948\) | 5.81402e6 | 0.210114 | ||||||||
\(949\) | −3.88539e6 | −0.140046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.93049e6 | −0.248492 | ||||||||
\(952\) | 367582. | 0.0131450 | ||||||||
\(953\) | −2.15286e7 | −0.767862 | −0.383931 | − | 0.923362i | \(-0.625430\pi\) | ||||
−0.383931 | + | 0.923362i | \(0.625430\pi\) | |||||||
\(954\) | −3.18175e6 | −0.113187 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.24097e7 | 0.439152 | ||||||||
\(957\) | 2.19116e6 | 0.0773383 | ||||||||
\(958\) | −4.92581e7 | −1.73406 | ||||||||
\(959\) | −384022. | −0.0134837 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.68831e7 | 1.63760 | ||||||||
\(962\) | 3.13916e6 | 0.109365 | ||||||||
\(963\) | −7.16073e6 | −0.248824 | ||||||||
\(964\) | 5.51119e6 | 0.191009 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −494816. | −0.0170609 | ||||||||
\(967\) | 1.52551e7 | 0.524624 | 0.262312 | − | 0.964983i | \(-0.415515\pi\) | ||||
0.262312 | + | 0.964983i | \(0.415515\pi\) | |||||||
\(968\) | −1.84234e6 | −0.0631947 | ||||||||
\(969\) | 8.13966e6 | 0.278482 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.95235e7 | −0.664521 | −0.332261 | − | 0.943188i | \(-0.607811\pi\) | ||||
−0.332261 | + | 0.943188i | \(0.607811\pi\) | |||||||
\(972\) | −785647. | −0.0266724 | ||||||||
\(973\) | −445820. | −0.0150965 | ||||||||
\(974\) | 1.88924e7 | 0.638103 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.77800e7 | −0.597457 | ||||||||
\(977\) | −5.23977e7 | −1.75621 | −0.878104 | − | 0.478469i | \(-0.841192\pi\) | ||||
−0.878104 | + | 0.478469i | \(0.841192\pi\) | |||||||
\(978\) | 1.39456e7 | 0.466219 | ||||||||
\(979\) | 1.50294e7 | 0.501170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.80711e7 | 0.599531 | ||||||||
\(982\) | −1.61134e7 | −0.533222 | ||||||||
\(983\) | 3.04687e7 | 1.00570 | 0.502851 | − | 0.864373i | \(-0.332284\pi\) | ||||
0.502851 | + | 0.864373i | \(0.332284\pi\) | |||||||
\(984\) | 2.64906e6 | 0.0872177 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.64060e7 | −0.537416 | ||||||||
\(987\) | 489134. | 0.0159822 | ||||||||
\(988\) | 3.32750e6 | 0.108449 | ||||||||
\(989\) | 3.56850e7 | 1.16010 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.04432e6 | 0.0661250 | 0.0330625 | − | 0.999453i | \(-0.489474\pi\) | ||||
0.0330625 | + | 0.999453i | \(0.489474\pi\) | |||||||
\(992\) | −3.94513e7 | −1.27287 | ||||||||
\(993\) | −8.69277e6 | −0.279760 | ||||||||
\(994\) | −16010.2 | −0.000513963 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.09150e6 | −0.130688 | ||||||||
\(997\) | 4.98989e7 | 1.58984 | 0.794919 | − | 0.606715i | \(-0.207513\pi\) | ||||
0.794919 | + | 0.606715i | \(0.207513\pi\) | |||||||
\(998\) | 3.73744e7 | 1.18781 | ||||||||
\(999\) | 1.01495e6 | 0.0321760 |
(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.u.1.8 | yes | 10 | |
5.4 | even | 2 | 825.6.a.t.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.3 | ✓ | 10 | 5.4 | even | 2 | ||
825.6.a.u.1.8 | yes | 10 | 1.1 | even | 1 | trivial |