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: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + \cdots + 522579400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{7} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.33747\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.33747 | −0.589987 | −0.294994 | − | 0.955499i | \(-0.595318\pi\) | ||||
−0.294994 | + | 0.955499i | \(0.595318\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −20.8613 | −0.651915 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −30.0373 | −0.340629 | ||||||||
\(7\) | 103.473 | 0.798146 | 0.399073 | − | 0.916919i | \(-0.369332\pi\) | ||||
0.399073 | + | 0.916919i | \(0.369332\pi\) | |||||||
\(8\) | 176.423 | 0.974609 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −187.751 | −0.376383 | ||||||||
\(13\) | −357.925 | −0.587400 | −0.293700 | − | 0.955898i | \(-0.594887\pi\) | ||||
−0.293700 | + | 0.955898i | \(0.594887\pi\) | |||||||
\(14\) | −345.339 | −0.470896 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 78.7535 | 0.0769078 | ||||||||
\(17\) | 2067.63 | 1.73521 | 0.867603 | − | 0.497258i | \(-0.165660\pi\) | ||||
0.867603 | + | 0.497258i | \(0.165660\pi\) | |||||||
\(18\) | −270.335 | −0.196662 | ||||||||
\(19\) | 1320.17 | 0.838967 | 0.419484 | − | 0.907763i | \(-0.362211\pi\) | ||||
0.419484 | + | 0.907763i | \(0.362211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 931.258 | 0.460810 | ||||||||
\(22\) | −403.834 | −0.177888 | ||||||||
\(23\) | −2498.44 | −0.984802 | −0.492401 | − | 0.870369i | \(-0.663881\pi\) | ||||
−0.492401 | + | 0.870369i | \(0.663881\pi\) | |||||||
\(24\) | 1587.81 | 0.562691 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1194.57 | 0.346559 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −2158.58 | −0.520323 | ||||||||
\(29\) | 1657.60 | 0.366003 | 0.183002 | − | 0.983113i | \(-0.441419\pi\) | ||||
0.183002 | + | 0.983113i | \(0.441419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4690.57 | 0.876640 | 0.438320 | − | 0.898819i | \(-0.355574\pi\) | ||||
0.438320 | + | 0.898819i | \(0.355574\pi\) | |||||||
\(32\) | −5908.38 | −1.01998 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −6900.67 | −1.02375 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1689.76 | −0.217305 | ||||||||
\(37\) | 5214.75 | 0.626223 | 0.313112 | − | 0.949716i | \(-0.398629\pi\) | ||||
0.313112 | + | 0.949716i | \(0.398629\pi\) | |||||||
\(38\) | −4406.02 | −0.494980 | ||||||||
\(39\) | −3221.33 | −0.339136 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13577.0 | 1.26138 | 0.630688 | − | 0.776037i | \(-0.282773\pi\) | ||||
0.630688 | + | 0.776037i | \(0.282773\pi\) | |||||||
\(42\) | −3108.05 | −0.271872 | ||||||||
\(43\) | 10764.0 | 0.887774 | 0.443887 | − | 0.896083i | \(-0.353599\pi\) | ||||
0.443887 | + | 0.896083i | \(0.353599\pi\) | |||||||
\(44\) | −2524.21 | −0.196560 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8338.46 | 0.581021 | ||||||||
\(47\) | −2926.95 | −0.193273 | −0.0966363 | − | 0.995320i | \(-0.530808\pi\) | ||||
−0.0966363 | + | 0.995320i | \(0.530808\pi\) | |||||||
\(48\) | 708.782 | 0.0444027 | ||||||||
\(49\) | −6100.32 | −0.362963 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18608.7 | 1.00182 | ||||||||
\(52\) | 7466.78 | 0.382935 | ||||||||
\(53\) | −21529.9 | −1.05282 | −0.526408 | − | 0.850232i | \(-0.676462\pi\) | ||||
−0.526408 | + | 0.850232i | \(0.676462\pi\) | |||||||
\(54\) | −2433.02 | −0.113543 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 18255.0 | 0.777880 | ||||||||
\(57\) | 11881.5 | 0.484378 | ||||||||
\(58\) | −5532.19 | −0.215937 | ||||||||
\(59\) | −4541.09 | −0.169836 | −0.0849181 | − | 0.996388i | \(-0.527063\pi\) | ||||
−0.0849181 | + | 0.996388i | \(0.527063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3649.55 | 0.125578 | 0.0627892 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627892 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(62\) | −15654.6 | −0.517207 | ||||||||
\(63\) | 8381.32 | 0.266049 | ||||||||
\(64\) | 17198.9 | 0.524870 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3634.51 | −0.102704 | ||||||||
\(67\) | −55473.7 | −1.50973 | −0.754867 | − | 0.655878i | \(-0.772299\pi\) | ||||
−0.754867 | + | 0.655878i | \(0.772299\pi\) | |||||||
\(68\) | −43133.4 | −1.13121 | ||||||||
\(69\) | −22485.9 | −0.568575 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4491.83 | 0.105749 | 0.0528746 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528746 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(72\) | 14290.3 | 0.324870 | ||||||||
\(73\) | 33559.8 | 0.737076 | 0.368538 | − | 0.929613i | \(-0.379859\pi\) | ||||
0.368538 | + | 0.929613i | \(0.379859\pi\) | |||||||
\(74\) | −17404.1 | −0.369464 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27540.4 | −0.546935 | ||||||||
\(77\) | 12520.2 | 0.240650 | ||||||||
\(78\) | 10751.1 | 0.200086 | ||||||||
\(79\) | −7912.05 | −0.142634 | −0.0713168 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713168 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −45312.9 | −0.744196 | ||||||||
\(83\) | −20569.6 | −0.327741 | −0.163870 | − | 0.986482i | \(-0.552398\pi\) | ||||
−0.163870 | + | 0.986482i | \(0.552398\pi\) | |||||||
\(84\) | −19427.2 | −0.300409 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −35924.5 | −0.523775 | ||||||||
\(87\) | 14918.4 | 0.211312 | ||||||||
\(88\) | 21347.2 | 0.293856 | ||||||||
\(89\) | −111119. | −1.48701 | −0.743504 | − | 0.668732i | \(-0.766837\pi\) | ||||
−0.743504 | + | 0.668732i | \(0.766837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −37035.6 | −0.468831 | ||||||||
\(92\) | 52120.6 | 0.642007 | ||||||||
\(93\) | 42215.1 | 0.506128 | ||||||||
\(94\) | 9768.61 | 0.114028 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −53175.4 | −0.588888 | ||||||||
\(97\) | −58271.1 | −0.628816 | −0.314408 | − | 0.949288i | \(-0.601806\pi\) | ||||
−0.314408 | + | 0.949288i | \(0.601806\pi\) | |||||||
\(98\) | 20359.7 | 0.214144 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56503.6 | −0.551153 | −0.275577 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275577 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(102\) | −62106.0 | −0.591062 | ||||||||
\(103\) | 95588.6 | 0.887796 | 0.443898 | − | 0.896077i | \(-0.353595\pi\) | ||||
0.443898 | + | 0.896077i | \(0.353595\pi\) | |||||||
\(104\) | −63146.3 | −0.572486 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 71855.5 | 0.621148 | ||||||||
\(107\) | 211645. | 1.78710 | 0.893550 | − | 0.448964i | \(-0.148207\pi\) | ||||
0.893550 | + | 0.448964i | \(0.148207\pi\) | |||||||
\(108\) | −15207.9 | −0.125461 | ||||||||
\(109\) | 370.739 | 0.00298884 | 0.00149442 | − | 0.999999i | \(-0.499524\pi\) | ||||
0.00149442 | + | 0.999999i | \(0.499524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 46932.8 | 0.361550 | ||||||||
\(112\) | 8148.87 | 0.0613836 | ||||||||
\(113\) | −14124.9 | −0.104061 | −0.0520307 | − | 0.998645i | \(-0.516569\pi\) | ||||
−0.0520307 | + | 0.998645i | \(0.516569\pi\) | |||||||
\(114\) | −39654.2 | −0.285777 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −34579.6 | −0.238603 | ||||||||
\(117\) | −28992.0 | −0.195800 | ||||||||
\(118\) | 15155.8 | 0.100201 | ||||||||
\(119\) | 213944. | 1.38495 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −12180.3 | −0.0740897 | ||||||||
\(123\) | 122193. | 0.728255 | ||||||||
\(124\) | −97851.3 | −0.571495 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −27972.4 | −0.156965 | ||||||||
\(127\) | 39049.1 | 0.214834 | 0.107417 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107417 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(128\) | 131667. | 0.710317 | ||||||||
\(129\) | 96876.0 | 0.512556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −152838. | −0.778131 | −0.389066 | − | 0.921210i | \(-0.627202\pi\) | ||||
−0.389066 | + | 0.921210i | \(0.627202\pi\) | |||||||
\(132\) | −22717.9 | −0.113484 | ||||||||
\(133\) | 136602. | 0.669618 | ||||||||
\(134\) | 185142. | 0.890724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 364778. | 1.69115 | ||||||||
\(137\) | 323866. | 1.47422 | 0.737112 | − | 0.675771i | \(-0.236189\pi\) | ||||
0.737112 | + | 0.675771i | \(0.236189\pi\) | |||||||
\(138\) | 75046.2 | 0.335452 | ||||||||
\(139\) | 195925. | 0.860108 | 0.430054 | − | 0.902803i | \(-0.358494\pi\) | ||||
0.430054 | + | 0.902803i | \(0.358494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −26342.5 | −0.111586 | ||||||||
\(142\) | −14991.4 | −0.0623907 | ||||||||
\(143\) | −43309.0 | −0.177108 | ||||||||
\(144\) | 6379.04 | 0.0256359 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −112005. | −0.434865 | ||||||||
\(147\) | −54902.9 | −0.209557 | ||||||||
\(148\) | −108786. | −0.408244 | ||||||||
\(149\) | 435048. | 1.60536 | 0.802679 | − | 0.596411i | \(-0.203407\pi\) | ||||
0.802679 | + | 0.596411i | \(0.203407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −94062.6 | −0.335718 | −0.167859 | − | 0.985811i | \(-0.553685\pi\) | ||||
−0.167859 | + | 0.985811i | \(0.553685\pi\) | |||||||
\(152\) | 232908. | 0.817665 | ||||||||
\(153\) | 167478. | 0.578402 | ||||||||
\(154\) | −41786.0 | −0.141981 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 67201.0 | 0.221088 | ||||||||
\(157\) | −194996. | −0.631360 | −0.315680 | − | 0.948866i | \(-0.602233\pi\) | ||||
−0.315680 | + | 0.948866i | \(0.602233\pi\) | |||||||
\(158\) | 26406.3 | 0.0841520 | ||||||||
\(159\) | −193769. | −0.607844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −258521. | −0.786015 | ||||||||
\(162\) | −21897.2 | −0.0655542 | ||||||||
\(163\) | 154239. | 0.454701 | 0.227350 | − | 0.973813i | \(-0.426994\pi\) | ||||
0.227350 | + | 0.973813i | \(0.426994\pi\) | |||||||
\(164\) | −283234. | −0.822309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 68650.4 | 0.193363 | ||||||||
\(167\) | −297517. | −0.825506 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(168\) | 164295. | 0.449109 | ||||||||
\(169\) | −243182. | −0.654961 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 106934. | 0.279656 | ||||||||
\(172\) | −224551. | −0.578753 | ||||||||
\(173\) | −49837.8 | −0.126603 | −0.0633014 | − | 0.997994i | \(-0.520163\pi\) | ||||
−0.0633014 | + | 0.997994i | \(0.520163\pi\) | |||||||
\(174\) | −49789.8 | −0.124671 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9529.18 | 0.0231886 | ||||||||
\(177\) | −40869.8 | −0.0980550 | ||||||||
\(178\) | 370856. | 0.877316 | ||||||||
\(179\) | −825399. | −1.92545 | −0.962724 | − | 0.270487i | \(-0.912815\pi\) | ||||
−0.962724 | + | 0.270487i | \(0.912815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −631320. | −1.43236 | −0.716182 | − | 0.697914i | \(-0.754112\pi\) | ||||
−0.716182 | + | 0.697914i | \(0.754112\pi\) | |||||||
\(182\) | 123605. | 0.276604 | ||||||||
\(183\) | 32846.0 | 0.0725027 | ||||||||
\(184\) | −440782. | −0.959797 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −140892. | −0.298609 | ||||||||
\(187\) | 250184. | 0.523184 | ||||||||
\(188\) | 61059.9 | 0.125997 | ||||||||
\(189\) | 75431.9 | 0.153603 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 367056. | 0.728030 | 0.364015 | − | 0.931393i | \(-0.381406\pi\) | ||||
0.364015 | + | 0.931393i | \(0.381406\pi\) | |||||||
\(192\) | 154790. | 0.303034 | ||||||||
\(193\) | 239853. | 0.463501 | 0.231751 | − | 0.972775i | \(-0.425555\pi\) | ||||
0.231751 | + | 0.972775i | \(0.425555\pi\) | |||||||
\(194\) | 194478. | 0.370994 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 127260. | 0.236621 | ||||||||
\(197\) | 889966. | 1.63383 | 0.816917 | − | 0.576755i | \(-0.195681\pi\) | ||||
0.816917 | + | 0.576755i | \(0.195681\pi\) | |||||||
\(198\) | −32710.6 | −0.0592960 | ||||||||
\(199\) | 2447.34 | 0.00438089 | 0.00219045 | − | 0.999998i | \(-0.499303\pi\) | ||||
0.00219045 | + | 0.999998i | \(0.499303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −499264. | −0.871645 | ||||||||
\(202\) | 188579. | 0.325174 | ||||||||
\(203\) | 171517. | 0.292124 | ||||||||
\(204\) | −388201. | −0.653102 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −319024. | −0.523788 | ||||||||
\(207\) | −202373. | −0.328267 | ||||||||
\(208\) | −28187.9 | −0.0451756 | ||||||||
\(209\) | 159740. | 0.252958 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 779165. | 1.20482 | 0.602411 | − | 0.798186i | \(-0.294207\pi\) | ||||
0.602411 | + | 0.798186i | \(0.294207\pi\) | |||||||
\(212\) | 449141. | 0.686347 | ||||||||
\(213\) | 40426.4 | 0.0610543 | ||||||||
\(214\) | −706360. | −1.05437 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 128612. | 0.187564 | ||||||||
\(217\) | 485348. | 0.699687 | ||||||||
\(218\) | −1237.33 | −0.00176338 | ||||||||
\(219\) | 302038. | 0.425551 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −740058. | −1.01926 | ||||||||
\(222\) | −156637. | −0.213310 | ||||||||
\(223\) | 1.27044e6 | 1.71077 | 0.855387 | − | 0.517990i | \(-0.173320\pi\) | ||||
0.855387 | + | 0.517990i | \(0.173320\pi\) | |||||||
\(224\) | −611358. | −0.814096 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 47141.5 | 0.0613949 | ||||||||
\(227\) | 1755.97 | 0.00226179 | 0.00113089 | − | 0.999999i | \(-0.499640\pi\) | ||||
0.00113089 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(228\) | −247863. | −0.315773 | ||||||||
\(229\) | −185101. | −0.233249 | −0.116624 | − | 0.993176i | \(-0.537207\pi\) | ||||
−0.116624 | + | 0.993176i | \(0.537207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 112682. | 0.138939 | ||||||||
\(232\) | 292439. | 0.356710 | ||||||||
\(233\) | 172318. | 0.207941 | 0.103971 | − | 0.994580i | \(-0.466845\pi\) | ||||
0.103971 | + | 0.994580i | \(0.466845\pi\) | |||||||
\(234\) | 96759.9 | 0.115520 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 94733.0 | 0.110719 | ||||||||
\(237\) | −71208.5 | −0.0823495 | ||||||||
\(238\) | −714033. | −0.817102 | ||||||||
\(239\) | 1.58068e6 | 1.78999 | 0.894994 | − | 0.446078i | \(-0.147180\pi\) | ||||
0.894994 | + | 0.446078i | \(0.147180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.44227e6 | 1.59957 | 0.799785 | − | 0.600287i | \(-0.204947\pi\) | ||||
0.799785 | + | 0.600287i | \(0.204947\pi\) | |||||||
\(242\) | −48863.9 | −0.0536352 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −76134.3 | −0.0818664 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −407816. | −0.429662 | ||||||||
\(247\) | −472521. | −0.492810 | ||||||||
\(248\) | 827525. | 0.854381 | ||||||||
\(249\) | −185126. | −0.189221 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.18482e6 | 1.18705 | 0.593524 | − | 0.804816i | \(-0.297736\pi\) | ||||
0.593524 | + | 0.804816i | \(0.297736\pi\) | |||||||
\(252\) | −174845. | −0.173441 | ||||||||
\(253\) | −302311. | −0.296929 | ||||||||
\(254\) | −130325. | −0.126749 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −989801. | −0.943948 | ||||||||
\(257\) | −307999. | −0.290882 | −0.145441 | − | 0.989367i | \(-0.546460\pi\) | ||||
−0.145441 | + | 0.989367i | \(0.546460\pi\) | |||||||
\(258\) | −323321. | −0.302402 | ||||||||
\(259\) | 539586. | 0.499818 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 134266. | 0.122001 | ||||||||
\(262\) | 510093. | 0.459088 | ||||||||
\(263\) | 1.92302e6 | 1.71433 | 0.857163 | − | 0.515045i | \(-0.172225\pi\) | ||||
0.857163 | + | 0.515045i | \(0.172225\pi\) | |||||||
\(264\) | 192125. | 0.169658 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −455905. | −0.395066 | ||||||||
\(267\) | −1.00007e6 | −0.858524 | ||||||||
\(268\) | 1.15725e6 | 0.984218 | ||||||||
\(269\) | −1.14532e6 | −0.965040 | −0.482520 | − | 0.875885i | \(-0.660278\pi\) | ||||
−0.482520 | + | 0.875885i | \(0.660278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −737503. | −0.610015 | −0.305008 | − | 0.952350i | \(-0.598659\pi\) | ||||
−0.305008 | + | 0.952350i | \(0.598659\pi\) | |||||||
\(272\) | 162833. | 0.133451 | ||||||||
\(273\) | −333321. | −0.270680 | ||||||||
\(274\) | −1.08089e6 | −0.869774 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 469085. | 0.370663 | ||||||||
\(277\) | 1.91454e6 | 1.49922 | 0.749611 | − | 0.661878i | \(-0.230240\pi\) | ||||
0.749611 | + | 0.661878i | \(0.230240\pi\) | |||||||
\(278\) | −653895. | −0.507453 | ||||||||
\(279\) | 379936. | 0.292213 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09912e6 | −0.830387 | −0.415193 | − | 0.909733i | \(-0.636286\pi\) | ||||
−0.415193 | + | 0.909733i | \(0.636286\pi\) | |||||||
\(282\) | 87917.5 | 0.0658343 | ||||||||
\(283\) | 371541. | 0.275766 | 0.137883 | − | 0.990449i | \(-0.455970\pi\) | ||||
0.137883 | + | 0.990449i | \(0.455970\pi\) | |||||||
\(284\) | −93705.2 | −0.0689395 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 144543. | 0.104491 | ||||||||
\(287\) | 1.40485e6 | 1.00676 | ||||||||
\(288\) | −478578. | −0.339995 | ||||||||
\(289\) | 2.85525e6 | 2.01094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −524440. | −0.363047 | ||||||||
\(292\) | −700100. | −0.480511 | ||||||||
\(293\) | 2.86231e6 | 1.94781 | 0.973907 | − | 0.226948i | \(-0.0728748\pi\) | ||||
0.973907 | + | 0.226948i | \(0.0728748\pi\) | |||||||
\(294\) | 183237. | 0.123636 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 920003. | 0.610323 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −1.45196e6 | −0.947141 | ||||||||
\(299\) | 894254. | 0.578473 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11378e6 | 0.708573 | ||||||||
\(302\) | 313931. | 0.198069 | ||||||||
\(303\) | −508532. | −0.318209 | ||||||||
\(304\) | 103968. | 0.0645231 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −558954. | −0.341250 | ||||||||
\(307\) | −2.67276e6 | −1.61851 | −0.809253 | − | 0.587460i | \(-0.800128\pi\) | ||||
−0.809253 | + | 0.587460i | \(0.800128\pi\) | |||||||
\(308\) | −261188. | −0.156883 | ||||||||
\(309\) | 860298. | 0.512569 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.84386e6 | 1.08100 | 0.540500 | − | 0.841344i | \(-0.318235\pi\) | ||||
0.540500 | + | 0.841344i | \(0.318235\pi\) | |||||||
\(312\) | −568317. | −0.330525 | ||||||||
\(313\) | 1.87741e6 | 1.08318 | 0.541588 | − | 0.840644i | \(-0.317823\pi\) | ||||
0.541588 | + | 0.840644i | \(0.317823\pi\) | |||||||
\(314\) | 650794. | 0.372494 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 165056. | 0.0929849 | ||||||||
\(317\) | −2.04246e6 | −1.14158 | −0.570789 | − | 0.821097i | \(-0.693362\pi\) | ||||
−0.570789 | + | 0.821097i | \(0.693362\pi\) | |||||||
\(318\) | 646699. | 0.358620 | ||||||||
\(319\) | 200570. | 0.110354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.90481e6 | 1.03178 | ||||||||
\(322\) | 862807. | 0.463739 | ||||||||
\(323\) | 2.72962e6 | 1.45578 | ||||||||
\(324\) | −136871. | −0.0724350 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −514769. | −0.268268 | ||||||||
\(327\) | 3336.65 | 0.00172561 | ||||||||
\(328\) | 2.39530e6 | 1.22935 | ||||||||
\(329\) | −302860. | −0.154260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.48973e6 | −1.24906 | −0.624528 | − | 0.781002i | \(-0.714709\pi\) | ||||
−0.624528 | + | 0.781002i | \(0.714709\pi\) | |||||||
\(332\) | 429108. | 0.213659 | ||||||||
\(333\) | 422395. | 0.208741 | ||||||||
\(334\) | 992954. | 0.487038 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 73339.8 | 0.0354398 | ||||||||
\(337\) | −2.26543e6 | −1.08662 | −0.543308 | − | 0.839534i | \(-0.682828\pi\) | ||||
−0.543308 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(338\) | 811615. | 0.386419 | ||||||||
\(339\) | −127124. | −0.0600799 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 567559. | 0.264317 | ||||||||
\(342\) | −356888. | −0.164993 | ||||||||
\(343\) | −2.37029e6 | −1.08784 | ||||||||
\(344\) | 1.89902e6 | 0.865232 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 166332. | 0.0746941 | ||||||||
\(347\) | 887458. | 0.395662 | 0.197831 | − | 0.980236i | \(-0.436610\pi\) | ||||
0.197831 | + | 0.980236i | \(0.436610\pi\) | |||||||
\(348\) | −311217. | −0.137757 | ||||||||
\(349\) | 3.37834e6 | 1.48470 | 0.742351 | − | 0.670011i | \(-0.233711\pi\) | ||||
0.742351 | + | 0.670011i | \(0.233711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −260928. | −0.113045 | ||||||||
\(352\) | −714914. | −0.307537 | ||||||||
\(353\) | 1.23199e6 | 0.526222 | 0.263111 | − | 0.964766i | \(-0.415251\pi\) | ||||
0.263111 | + | 0.964766i | \(0.415251\pi\) | |||||||
\(354\) | 136402. | 0.0578512 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.31808e6 | 0.969402 | ||||||||
\(357\) | 1.92550e6 | 0.799600 | ||||||||
\(358\) | 2.75475e6 | 1.13599 | ||||||||
\(359\) | 1.03637e6 | 0.424405 | 0.212202 | − | 0.977226i | \(-0.431936\pi\) | ||||
0.212202 | + | 0.977226i | \(0.431936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −733257. | −0.296134 | ||||||||
\(362\) | 2.10701e6 | 0.845076 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 772611. | 0.305638 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −109623. | −0.0427757 | ||||||||
\(367\) | 4.31603e6 | 1.67270 | 0.836352 | − | 0.548192i | \(-0.184684\pi\) | ||||
0.836352 | + | 0.548192i | \(0.184684\pi\) | |||||||
\(368\) | −196761. | −0.0757389 | ||||||||
\(369\) | 1.09974e6 | 0.420458 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.22777e6 | −0.840301 | ||||||||
\(372\) | −880661. | −0.329953 | ||||||||
\(373\) | −2.03599e6 | −0.757712 | −0.378856 | − | 0.925456i | \(-0.623682\pi\) | ||||
−0.378856 | + | 0.925456i | \(0.623682\pi\) | |||||||
\(374\) | −834981. | −0.308672 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −516381. | −0.188365 | ||||||||
\(377\) | −593297. | −0.214990 | ||||||||
\(378\) | −251752. | −0.0906240 | ||||||||
\(379\) | −3.67933e6 | −1.31574 | −0.657872 | − | 0.753130i | \(-0.728543\pi\) | ||||
−0.657872 | + | 0.753130i | \(0.728543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 351442. | 0.124034 | ||||||||
\(382\) | −1.22504e6 | −0.429528 | ||||||||
\(383\) | −3.35614e6 | −1.16908 | −0.584539 | − | 0.811366i | \(-0.698725\pi\) | ||||
−0.584539 | + | 0.811366i | \(0.698725\pi\) | |||||||
\(384\) | 1.18500e6 | 0.410102 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −800501. | −0.273460 | ||||||||
\(387\) | 871884. | 0.295925 | ||||||||
\(388\) | 1.21561e6 | 0.409935 | ||||||||
\(389\) | 5.94481e6 | 1.99188 | 0.995942 | − | 0.0900021i | \(-0.0286874\pi\) | ||||
0.995942 | + | 0.0900021i | \(0.0286874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.16585e6 | −1.70883 | ||||||||
\(392\) | −1.07624e6 | −0.353747 | ||||||||
\(393\) | −1.37554e6 | −0.449254 | ||||||||
\(394\) | −2.97024e6 | −0.963941 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −204461. | −0.0655199 | ||||||||
\(397\) | 4.07424e6 | 1.29739 | 0.648695 | − | 0.761048i | \(-0.275315\pi\) | ||||
0.648695 | + | 0.761048i | \(0.275315\pi\) | |||||||
\(398\) | −8167.95 | −0.00258467 | ||||||||
\(399\) | 1.22942e6 | 0.386604 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.76526e6 | 0.548209 | 0.274105 | − | 0.961700i | \(-0.411619\pi\) | ||||
0.274105 | + | 0.961700i | \(0.411619\pi\) | |||||||
\(402\) | 1.66628e6 | 0.514260 | ||||||||
\(403\) | −1.67887e6 | −0.514939 | ||||||||
\(404\) | 1.17874e6 | 0.359305 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −572433. | −0.172349 | ||||||||
\(407\) | 630985. | 0.188813 | ||||||||
\(408\) | 3.28300e6 | 0.976384 | ||||||||
\(409\) | −3.05109e6 | −0.901877 | −0.450938 | − | 0.892555i | \(-0.648911\pi\) | ||||
−0.450938 | + | 0.892555i | \(0.648911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.91479e6 | 0.851144 | ||||||||
\(412\) | −1.99410e6 | −0.578767 | ||||||||
\(413\) | −469881. | −0.135554 | ||||||||
\(414\) | 675416. | 0.193674 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.11476e6 | 0.599139 | ||||||||
\(417\) | 1.76333e6 | 0.496584 | ||||||||
\(418\) | −533129. | −0.149242 | ||||||||
\(419\) | −6.61264e6 | −1.84009 | −0.920046 | − | 0.391810i | \(-0.871849\pi\) | ||||
−0.920046 | + | 0.391810i | \(0.871849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.29303e6 | 0.630527 | 0.315263 | − | 0.949004i | \(-0.397907\pi\) | ||||
0.315263 | + | 0.949004i | \(0.397907\pi\) | |||||||
\(422\) | −2.60044e6 | −0.710830 | ||||||||
\(423\) | −237083. | −0.0644242 | ||||||||
\(424\) | −3.79837e6 | −1.02608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −134922. | −0.0360213 | ||||||||
\(427\) | 377630. | 0.100230 | ||||||||
\(428\) | −4.41519e6 | −1.16504 | ||||||||
\(429\) | −389781. | −0.102253 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.53759e6 | 1.43591 | 0.717956 | − | 0.696089i | \(-0.245078\pi\) | ||||
0.717956 | + | 0.696089i | \(0.245078\pi\) | |||||||
\(432\) | 57411.3 | 0.0148009 | ||||||||
\(433\) | −2.55617e6 | −0.655195 | −0.327598 | − | 0.944817i | \(-0.606239\pi\) | ||||
−0.327598 | + | 0.944817i | \(0.606239\pi\) | |||||||
\(434\) | −1.61983e6 | −0.412806 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7734.09 | −0.00194847 | ||||||||
\(437\) | −3.29835e6 | −0.826216 | ||||||||
\(438\) | −1.00804e6 | −0.251070 | ||||||||
\(439\) | −696199. | −0.172414 | −0.0862070 | − | 0.996277i | \(-0.527475\pi\) | ||||
−0.0862070 | + | 0.996277i | \(0.527475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −494126. | −0.120988 | ||||||||
\(442\) | 2.46992e6 | 0.601351 | ||||||||
\(443\) | 6.82989e6 | 1.65350 | 0.826750 | − | 0.562570i | \(-0.190187\pi\) | ||||
0.826750 | + | 0.562570i | \(0.190187\pi\) | |||||||
\(444\) | −979077. | −0.235700 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.24006e6 | −1.00933 | ||||||||
\(447\) | 3.91544e6 | 0.926854 | ||||||||
\(448\) | 1.77963e6 | 0.418923 | ||||||||
\(449\) | −6.68298e6 | −1.56442 | −0.782212 | − | 0.623013i | \(-0.785909\pi\) | ||||
−0.782212 | + | 0.623013i | \(0.785909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64282e6 | 0.380319 | ||||||||
\(452\) | 294664. | 0.0678392 | ||||||||
\(453\) | −846564. | −0.193827 | ||||||||
\(454\) | −5860.49 | −0.00133443 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.09617e6 | 0.472079 | ||||||||
\(457\) | 616838. | 0.138159 | 0.0690797 | − | 0.997611i | \(-0.477994\pi\) | ||||
0.0690797 | + | 0.997611i | \(0.477994\pi\) | |||||||
\(458\) | 617769. | 0.137614 | ||||||||
\(459\) | 1.50730e6 | 0.333941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.55459e6 | 0.779001 | 0.389500 | − | 0.921026i | \(-0.372648\pi\) | ||||
0.389500 | + | 0.921026i | \(0.372648\pi\) | |||||||
\(462\) | −376074. | −0.0819725 | ||||||||
\(463\) | −3.23948e6 | −0.702299 | −0.351150 | − | 0.936319i | \(-0.614209\pi\) | ||||
−0.351150 | + | 0.936319i | \(0.614209\pi\) | |||||||
\(464\) | 130542. | 0.0281485 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −575106. | −0.122683 | ||||||||
\(467\) | 7.20656e6 | 1.52910 | 0.764550 | − | 0.644564i | \(-0.222961\pi\) | ||||
0.764550 | + | 0.644564i | \(0.222961\pi\) | |||||||
\(468\) | 604809. | 0.127645 | ||||||||
\(469\) | −5.74004e6 | −1.20499 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.75497e6 | −0.364516 | ||||||||
\(472\) | −801154. | −0.165524 | ||||||||
\(473\) | 1.30244e6 | 0.267674 | ||||||||
\(474\) | 237656. | 0.0485852 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.46315e6 | −0.902868 | ||||||||
\(477\) | −1.74392e6 | −0.350939 | ||||||||
\(478\) | −5.27549e6 | −1.05607 | ||||||||
\(479\) | 772579. | 0.153852 | 0.0769261 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769261 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.86649e6 | −0.367844 | ||||||||
\(482\) | −4.81353e6 | −0.943726 | ||||||||
\(483\) | −2.32669e6 | −0.453806 | ||||||||
\(484\) | −305430. | −0.0592650 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −197074. | −0.0378477 | ||||||||
\(487\) | −3.08873e6 | −0.590143 | −0.295072 | − | 0.955475i | \(-0.595344\pi\) | ||||
−0.295072 | + | 0.955475i | \(0.595344\pi\) | |||||||
\(488\) | 643865. | 0.122390 | ||||||||
\(489\) | 1.38815e6 | 0.262522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.82049e6 | 0.902375 | 0.451187 | − | 0.892429i | \(-0.351001\pi\) | ||||
0.451187 | + | 0.892429i | \(0.351001\pi\) | |||||||
\(492\) | −2.54910e6 | −0.474761 | ||||||||
\(493\) | 3.42731e6 | 0.635091 | ||||||||
\(494\) | 1.57703e6 | 0.290751 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 369399. | 0.0674204 | ||||||||
\(497\) | 464783. | 0.0844033 | ||||||||
\(498\) | 617854. | 0.111638 | ||||||||
\(499\) | −9.37761e6 | −1.68594 | −0.842968 | − | 0.537964i | \(-0.819194\pi\) | ||||
−0.842968 | + | 0.537964i | \(0.819194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.67765e6 | −0.476606 | ||||||||
\(502\) | −3.95430e6 | −0.700343 | ||||||||
\(503\) | 4.35545e6 | 0.767562 | 0.383781 | − | 0.923424i | \(-0.374622\pi\) | ||||
0.383781 | + | 0.923424i | \(0.374622\pi\) | |||||||
\(504\) | 1.47866e6 | 0.259293 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.00895e6 | 0.175184 | ||||||||
\(507\) | −2.18864e6 | −0.378142 | ||||||||
\(508\) | −814615. | −0.140053 | ||||||||
\(509\) | 1.05979e7 | 1.81311 | 0.906556 | − | 0.422086i | \(-0.138702\pi\) | ||||
0.906556 | + | 0.422086i | \(0.138702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.47253e6 | 0.588294 | ||||||||
\(512\) | −909912. | −0.153400 | ||||||||
\(513\) | 962402. | 0.161459 | ||||||||
\(514\) | 1.02794e6 | 0.171617 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.02096e6 | −0.334143 | ||||||||
\(517\) | −354161. | −0.0582739 | ||||||||
\(518\) | −1.80086e6 | −0.294886 | ||||||||
\(519\) | −448540. | −0.0730942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.52699e6 | 1.05346 | 0.526731 | − | 0.850032i | \(-0.323418\pi\) | ||||
0.526731 | + | 0.850032i | \(0.323418\pi\) | |||||||
\(522\) | −448108. | −0.0719791 | ||||||||
\(523\) | −9.35815e6 | −1.49601 | −0.748007 | − | 0.663690i | \(-0.768989\pi\) | ||||
−0.748007 | + | 0.663690i | \(0.768989\pi\) | |||||||
\(524\) | 3.18839e6 | 0.507275 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.41801e6 | −1.01143 | ||||||||
\(527\) | 9.69837e6 | 1.52115 | ||||||||
\(528\) | 85762.6 | 0.0133879 | ||||||||
\(529\) | −194157. | −0.0301657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −367829. | −0.0566121 | ||||||||
\(532\) | −2.84969e6 | −0.436534 | ||||||||
\(533\) | −4.85955e6 | −0.740932 | ||||||||
\(534\) | 3.33771e6 | 0.506518 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.78685e6 | −1.47140 | ||||||||
\(537\) | −7.42860e6 | −1.11166 | ||||||||
\(538\) | 3.82247e6 | 0.569361 | ||||||||
\(539\) | −738139. | −0.109438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.93079e6 | 1.45878 | 0.729392 | − | 0.684096i | \(-0.239803\pi\) | ||||
0.729392 | + | 0.684096i | \(0.239803\pi\) | |||||||
\(542\) | 2.46140e6 | 0.359901 | ||||||||
\(543\) | −5.68188e6 | −0.826975 | ||||||||
\(544\) | −1.22163e7 | −1.76988 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.11245e6 | 0.159698 | ||||||||
\(547\) | −8.79495e6 | −1.25680 | −0.628399 | − | 0.777891i | \(-0.716289\pi\) | ||||
−0.628399 | + | 0.777891i | \(0.716289\pi\) | |||||||
\(548\) | −6.75625e6 | −0.961068 | ||||||||
\(549\) | 295614. | 0.0418595 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.18831e6 | 0.307065 | ||||||||
\(552\) | −3.96704e6 | −0.554139 | ||||||||
\(553\) | −818685. | −0.113842 | ||||||||
\(554\) | −6.38974e6 | −0.884522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.08725e6 | −0.560717 | ||||||||
\(557\) | 2.78134e6 | 0.379853 | 0.189927 | − | 0.981798i | \(-0.439175\pi\) | ||||
0.189927 | + | 0.981798i | \(0.439175\pi\) | |||||||
\(558\) | −1.26803e6 | −0.172402 | ||||||||
\(559\) | −3.85271e6 | −0.521479 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.25165e6 | 0.302061 | ||||||||
\(562\) | 3.66829e6 | 0.489918 | ||||||||
\(563\) | −460410. | −0.0612172 | −0.0306086 | − | 0.999531i | \(-0.509745\pi\) | ||||
−0.0306086 | + | 0.999531i | \(0.509745\pi\) | |||||||
\(564\) | 549539. | 0.0727446 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.24001e6 | −0.162698 | ||||||||
\(567\) | 678887. | 0.0886829 | ||||||||
\(568\) | 792462. | 0.103064 | ||||||||
\(569\) | 8.74980e6 | 1.13297 | 0.566484 | − | 0.824073i | \(-0.308303\pi\) | ||||
0.566484 | + | 0.824073i | \(0.308303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.95646e6 | −1.14960 | −0.574799 | − | 0.818295i | \(-0.694920\pi\) | ||||
−0.574799 | + | 0.818295i | \(0.694920\pi\) | |||||||
\(572\) | 903480. | 0.115459 | ||||||||
\(573\) | 3.30351e6 | 0.420328 | ||||||||
\(574\) | −4.68866e6 | −0.593977 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.39311e6 | 0.174957 | ||||||||
\(577\) | −1.14055e7 | −1.42618 | −0.713091 | − | 0.701071i | \(-0.752706\pi\) | ||||
−0.713091 | + | 0.701071i | \(0.752706\pi\) | |||||||
\(578\) | −9.52931e6 | −1.18643 | ||||||||
\(579\) | 2.15867e6 | 0.267603 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.12840e6 | −0.261585 | ||||||||
\(582\) | 1.75030e6 | 0.214193 | ||||||||
\(583\) | −2.60512e6 | −0.317436 | ||||||||
\(584\) | 5.92072e6 | 0.718361 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.55288e6 | −1.14919 | ||||||||
\(587\) | 1.05278e7 | 1.26108 | 0.630539 | − | 0.776157i | \(-0.282834\pi\) | ||||
0.630539 | + | 0.776157i | \(0.282834\pi\) | |||||||
\(588\) | 1.14534e6 | 0.136613 | ||||||||
\(589\) | 6.19234e6 | 0.735472 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.00969e6 | 0.943294 | ||||||||
\(592\) | 410680. | 0.0481614 | ||||||||
\(593\) | 7.64531e6 | 0.892809 | 0.446404 | − | 0.894831i | \(-0.352704\pi\) | ||||
0.446404 | + | 0.894831i | \(0.352704\pi\) | |||||||
\(594\) | −294395. | −0.0342345 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.07566e6 | −1.04656 | ||||||||
\(597\) | 22026.1 | 0.00252931 | ||||||||
\(598\) | −2.98455e6 | −0.341292 | ||||||||
\(599\) | −1.28357e7 | −1.46168 | −0.730838 | − | 0.682550i | \(-0.760871\pi\) | ||||
−0.730838 | + | 0.682550i | \(0.760871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.49774e7 | −1.69142 | −0.845710 | − | 0.533643i | \(-0.820823\pi\) | ||||
−0.845710 | + | 0.533643i | \(0.820823\pi\) | |||||||
\(602\) | −3.71722e6 | −0.418049 | ||||||||
\(603\) | −4.49337e6 | −0.503245 | ||||||||
\(604\) | 1.96227e6 | 0.218860 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.69721e6 | 0.187739 | ||||||||
\(607\) | −273921. | −0.0301754 | −0.0150877 | − | 0.999886i | \(-0.504803\pi\) | ||||
−0.0150877 | + | 0.999886i | \(0.504803\pi\) | |||||||
\(608\) | −7.80005e6 | −0.855733 | ||||||||
\(609\) | 1.54365e6 | 0.168658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.04763e6 | 0.113528 | ||||||||
\(612\) | −3.49381e6 | −0.377069 | ||||||||
\(613\) | −3.61183e6 | −0.388219 | −0.194109 | − | 0.980980i | \(-0.562182\pi\) | ||||
−0.194109 | + | 0.980980i | \(0.562182\pi\) | |||||||
\(614\) | 8.92027e6 | 0.954898 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.20886e6 | 0.234540 | ||||||||
\(617\) | −1.11537e7 | −1.17952 | −0.589759 | − | 0.807579i | \(-0.700777\pi\) | ||||
−0.589759 | + | 0.807579i | \(0.700777\pi\) | |||||||
\(618\) | −2.87122e6 | −0.302409 | ||||||||
\(619\) | −8.08693e6 | −0.848314 | −0.424157 | − | 0.905589i | \(-0.639430\pi\) | ||||
−0.424157 | + | 0.905589i | \(0.639430\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.82136e6 | −0.189525 | ||||||||
\(622\) | −6.15382e6 | −0.637777 | ||||||||
\(623\) | −1.14978e7 | −1.18685 | ||||||||
\(624\) | −253691. | −0.0260822 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.26582e6 | −0.639060 | ||||||||
\(627\) | 1.43766e6 | 0.146045 | ||||||||
\(628\) | 4.06787e6 | 0.411593 | ||||||||
\(629\) | 1.07822e7 | 1.08663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.09030e7 | −1.09012 | −0.545060 | − | 0.838397i | \(-0.683493\pi\) | ||||
−0.545060 | + | 0.838397i | \(0.683493\pi\) | |||||||
\(632\) | −1.39587e6 | −0.139012 | ||||||||
\(633\) | 7.01248e6 | 0.695605 | ||||||||
\(634\) | 6.81665e6 | 0.673516 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.04227e6 | 0.396262 | ||||||||
\(637\) | 2.18346e6 | 0.213205 | ||||||||
\(638\) | −669396. | −0.0651075 | ||||||||
\(639\) | 363838. | 0.0352497 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.28118e7 | −1.23159 | −0.615794 | − | 0.787907i | \(-0.711165\pi\) | ||||
−0.615794 | + | 0.787907i | \(0.711165\pi\) | |||||||
\(642\) | −6.35724e6 | −0.608739 | ||||||||
\(643\) | −4.42120e6 | −0.421709 | −0.210854 | − | 0.977517i | \(-0.567625\pi\) | ||||
−0.210854 | + | 0.977517i | \(0.567625\pi\) | |||||||
\(644\) | 5.39308e6 | 0.512415 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.11003e6 | −0.858892 | ||||||||
\(647\) | −2.82953e6 | −0.265738 | −0.132869 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132869 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(648\) | 1.15751e6 | 0.108290 | ||||||||
\(649\) | −549472. | −0.0512076 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.36813e6 | 0.403964 | ||||||||
\(652\) | −3.21763e6 | −0.296426 | ||||||||
\(653\) | −1.51923e7 | −1.39425 | −0.697127 | − | 0.716948i | \(-0.745539\pi\) | ||||
−0.697127 | + | 0.716948i | \(0.745539\pi\) | |||||||
\(654\) | −11136.0 | −0.00101809 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.06924e6 | 0.0970096 | ||||||||
\(657\) | 2.71834e6 | 0.245692 | ||||||||
\(658\) | 1.01079e6 | 0.0910113 | ||||||||
\(659\) | −1.45583e7 | −1.30587 | −0.652933 | − | 0.757416i | \(-0.726462\pi\) | ||||
−0.652933 | + | 0.757416i | \(0.726462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.60047e6 | 0.498564 | 0.249282 | − | 0.968431i | \(-0.419805\pi\) | ||||
0.249282 | + | 0.968431i | \(0.419805\pi\) | |||||||
\(662\) | 8.30941e6 | 0.736928 | ||||||||
\(663\) | −6.66052e6 | −0.588470 | ||||||||
\(664\) | −3.62895e6 | −0.319419 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.40973e6 | −0.123155 | ||||||||
\(667\) | −4.14141e6 | −0.360440 | ||||||||
\(668\) | 6.20658e6 | 0.538159 | ||||||||
\(669\) | 1.14340e7 | 0.987715 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 441596. | 0.0378633 | ||||||||
\(672\) | −5.50222e6 | −0.470018 | ||||||||
\(673\) | −2.22862e6 | −0.189670 | −0.0948351 | − | 0.995493i | \(-0.530232\pi\) | ||||
−0.0948351 | + | 0.995493i | \(0.530232\pi\) | |||||||
\(674\) | 7.56081e6 | 0.641089 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.07310e6 | 0.426979 | ||||||||
\(677\) | −1.47850e7 | −1.23980 | −0.619898 | − | 0.784683i | \(-0.712826\pi\) | ||||
−0.619898 | + | 0.784683i | \(0.712826\pi\) | |||||||
\(678\) | 424274. | 0.0354464 | ||||||||
\(679\) | −6.02949e6 | −0.501887 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15803.7 | 0.00130584 | ||||||||
\(682\) | −1.89421e6 | −0.155944 | ||||||||
\(683\) | 415268. | 0.0340625 | 0.0170313 | − | 0.999855i | \(-0.494579\pi\) | ||||
0.0170313 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(684\) | −2.23077e6 | −0.182312 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.91078e6 | 0.641814 | ||||||||
\(687\) | −1.66591e6 | −0.134666 | ||||||||
\(688\) | 847703. | 0.0682767 | ||||||||
\(689\) | 7.70610e6 | 0.618424 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.64233e6 | 0.688550 | 0.344275 | − | 0.938869i | \(-0.388125\pi\) | ||||
0.344275 | + | 0.938869i | \(0.388125\pi\) | |||||||
\(692\) | 1.03968e6 | 0.0825342 | ||||||||
\(693\) | 1.01414e6 | 0.0802167 | ||||||||
\(694\) | −2.96187e6 | −0.233436 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.63195e6 | 0.205947 | ||||||||
\(697\) | 2.80723e7 | 2.18875 | ||||||||
\(698\) | −1.12751e7 | −0.875956 | ||||||||
\(699\) | 1.55086e6 | 0.120055 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.30512e7 | −1.00313 | −0.501564 | − | 0.865121i | \(-0.667242\pi\) | ||||
−0.501564 | + | 0.865121i | \(0.667242\pi\) | |||||||
\(702\) | 870839. | 0.0666953 | ||||||||
\(703\) | 6.88434e6 | 0.525381 | ||||||||
\(704\) | 2.08107e6 | 0.158254 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.11172e6 | −0.310464 | ||||||||
\(707\) | −5.84660e6 | −0.439901 | ||||||||
\(708\) | 852597. | 0.0639235 | ||||||||
\(709\) | −1.56007e7 | −1.16555 | −0.582773 | − | 0.812635i | \(-0.698032\pi\) | ||||
−0.582773 | + | 0.812635i | \(0.698032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −640876. | −0.0475445 | ||||||||
\(712\) | −1.96039e7 | −1.44925 | ||||||||
\(713\) | −1.17191e7 | −0.863317 | ||||||||
\(714\) | −6.42630e6 | −0.471754 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.72189e7 | 1.25523 | ||||||||
\(717\) | 1.42262e7 | 1.03345 | ||||||||
\(718\) | −3.45887e6 | −0.250394 | ||||||||
\(719\) | −6.44874e6 | −0.465214 | −0.232607 | − | 0.972571i | \(-0.574726\pi\) | ||||
−0.232607 | + | 0.972571i | \(0.574726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.89085e6 | 0.708591 | ||||||||
\(722\) | 2.44723e6 | 0.174715 | ||||||||
\(723\) | 1.29804e7 | 0.923512 | ||||||||
\(724\) | 1.31701e7 | 0.933779 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −439775. | −0.0309663 | ||||||||
\(727\) | 8.36468e6 | 0.586967 | 0.293483 | − | 0.955964i | \(-0.405185\pi\) | ||||
0.293483 | + | 0.955964i | \(0.405185\pi\) | |||||||
\(728\) | −6.53394e6 | −0.456927 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.22560e7 | 1.54047 | ||||||||
\(732\) | −685209. | −0.0472656 | ||||||||
\(733\) | 3.08435e6 | 0.212033 | 0.106017 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106017 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(734\) | −1.44046e7 | −0.986875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.47617e7 | 1.00448 | ||||||||
\(737\) | −6.71232e6 | −0.455202 | ||||||||
\(738\) | −3.67034e6 | −0.248065 | ||||||||
\(739\) | −2.28100e7 | −1.53644 | −0.768218 | − | 0.640189i | \(-0.778856\pi\) | ||||
−0.768218 | + | 0.640189i | \(0.778856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.25269e6 | −0.284524 | ||||||||
\(742\) | 7.43511e6 | 0.495767 | ||||||||
\(743\) | 1.21470e7 | 0.807232 | 0.403616 | − | 0.914929i | \(-0.367753\pi\) | ||||
0.403616 | + | 0.914929i | \(0.367753\pi\) | |||||||
\(744\) | 7.44772e6 | 0.493277 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.79507e6 | 0.447040 | ||||||||
\(747\) | −1.66614e6 | −0.109247 | ||||||||
\(748\) | −5.21915e6 | −0.341072 | ||||||||
\(749\) | 2.18996e7 | 1.42637 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.29619e7 | 1.48562 | 0.742809 | − | 0.669503i | \(-0.233493\pi\) | ||||
0.742809 | + | 0.669503i | \(0.233493\pi\) | |||||||
\(752\) | −230508. | −0.0148642 | ||||||||
\(753\) | 1.06634e7 | 0.685342 | ||||||||
\(754\) | 1.98011e6 | 0.126842 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.57361e6 | −0.100136 | ||||||||
\(757\) | 8.97752e6 | 0.569399 | 0.284699 | − | 0.958617i | \(-0.408106\pi\) | ||||
0.284699 | + | 0.958617i | \(0.408106\pi\) | |||||||
\(758\) | 1.22797e7 | 0.776272 | ||||||||
\(759\) | −2.72080e6 | −0.171432 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.81766e7 | 1.13776 | 0.568880 | − | 0.822421i | \(-0.307377\pi\) | ||||
0.568880 | + | 0.822421i | \(0.307377\pi\) | |||||||
\(762\) | −1.17293e6 | −0.0731786 | ||||||||
\(763\) | 38361.5 | 0.00238553 | ||||||||
\(764\) | −7.65726e6 | −0.474613 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.12010e7 | 0.689741 | ||||||||
\(767\) | 1.62537e6 | 0.0997618 | ||||||||
\(768\) | −8.90821e6 | −0.544989 | ||||||||
\(769\) | −1.53679e7 | −0.937127 | −0.468564 | − | 0.883430i | \(-0.655228\pi\) | ||||
−0.468564 | + | 0.883430i | \(0.655228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.77199e6 | −0.167941 | ||||||||
\(772\) | −5.00363e6 | −0.302163 | ||||||||
\(773\) | 732946. | 0.0441188 | 0.0220594 | − | 0.999757i | \(-0.492978\pi\) | ||||
0.0220594 | + | 0.999757i | \(0.492978\pi\) | |||||||
\(774\) | −2.90989e6 | −0.174592 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.02804e7 | −0.612850 | ||||||||
\(777\) | 4.85628e6 | 0.288570 | ||||||||
\(778\) | −1.98406e7 | −1.17519 | ||||||||
\(779\) | 1.79239e7 | 1.05825 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 543511. | 0.0318846 | ||||||||
\(782\) | 1.72409e7 | 1.00819 | ||||||||
\(783\) | 1.20839e6 | 0.0704373 | ||||||||
\(784\) | −480422. | −0.0279147 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.59083e6 | 0.265054 | ||||||||
\(787\) | 2.25077e7 | 1.29537 | 0.647685 | − | 0.761908i | \(-0.275737\pi\) | ||||
0.647685 | + | 0.761908i | \(0.275737\pi\) | |||||||
\(788\) | −1.85658e7 | −1.06512 | ||||||||
\(789\) | 1.73071e7 | 0.989767 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.46155e6 | −0.0830562 | ||||||||
\(792\) | 1.72912e6 | 0.0979519 | ||||||||
\(793\) | −1.30627e6 | −0.0737648 | ||||||||
\(794\) | −1.35977e7 | −0.765444 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −51054.7 | −0.00285597 | ||||||||
\(797\) | −5.07705e6 | −0.283117 | −0.141558 | − | 0.989930i | \(-0.545211\pi\) | ||||
−0.141558 | + | 0.989930i | \(0.545211\pi\) | |||||||
\(798\) | −4.10314e6 | −0.228092 | ||||||||
\(799\) | −6.05185e6 | −0.335368 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00063e6 | −0.495669 | ||||||||
\(802\) | −5.89149e6 | −0.323437 | ||||||||
\(803\) | 4.06073e6 | 0.222237 | ||||||||
\(804\) | 1.04153e7 | 0.568238 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.60320e6 | 0.303807 | ||||||||
\(807\) | −1.03079e7 | −0.557166 | ||||||||
\(808\) | −9.96853e6 | −0.537159 | ||||||||
\(809\) | 1.15468e7 | 0.620282 | 0.310141 | − | 0.950691i | \(-0.399624\pi\) | ||||
0.310141 | + | 0.950691i | \(0.399624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.62543e7 | −1.40168 | −0.700838 | − | 0.713320i | \(-0.747190\pi\) | ||||
−0.700838 | + | 0.713320i | \(0.747190\pi\) | |||||||
\(812\) | −3.57806e6 | −0.190440 | ||||||||
\(813\) | −6.63753e6 | −0.352192 | ||||||||
\(814\) | −2.10590e6 | −0.111398 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.46550e6 | 0.0770479 | ||||||||
\(817\) | 1.42103e7 | 0.744813 | ||||||||
\(818\) | 1.01829e7 | 0.532096 | ||||||||
\(819\) | −2.99989e6 | −0.156277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.96273e6 | −0.205180 | −0.102590 | − | 0.994724i | \(-0.532713\pi\) | ||||
−0.102590 | + | 0.994724i | \(0.532713\pi\) | |||||||
\(822\) | −9.72803e6 | −0.502164 | ||||||||
\(823\) | −9.86765e6 | −0.507825 | −0.253913 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253913 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(824\) | 1.68640e7 | 0.865254 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.56821e6 | 0.0799752 | ||||||||
\(827\) | 5.90399e6 | 0.300180 | 0.150090 | − | 0.988672i | \(-0.452044\pi\) | ||||
0.150090 | + | 0.988672i | \(0.452044\pi\) | |||||||
\(828\) | 4.22177e6 | 0.214002 | ||||||||
\(829\) | 2.38090e7 | 1.20325 | 0.601624 | − | 0.798779i | \(-0.294520\pi\) | ||||
0.601624 | + | 0.798779i | \(0.294520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.72309e7 | 0.865576 | ||||||||
\(832\) | −6.15593e6 | −0.308309 | ||||||||
\(833\) | −1.26132e7 | −0.629816 | ||||||||
\(834\) | −5.88505e6 | −0.292978 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.33239e6 | −0.164907 | ||||||||
\(837\) | 3.41943e6 | 0.168709 | ||||||||
\(838\) | 2.20695e7 | 1.08563 | ||||||||
\(839\) | 1.88904e7 | 0.926479 | 0.463240 | − | 0.886233i | \(-0.346687\pi\) | ||||
0.463240 | + | 0.886233i | \(0.346687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.77635e7 | −0.866042 | ||||||||
\(842\) | −7.65291e6 | −0.372003 | ||||||||
\(843\) | −9.89210e6 | −0.479424 | ||||||||
\(844\) | −1.62544e7 | −0.785442 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 791257. | 0.0380095 | ||||||||
\(847\) | 1.51495e6 | 0.0725587 | ||||||||
\(848\) | −1.69556e6 | −0.0809697 | ||||||||
\(849\) | 3.34387e6 | 0.159214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.30287e7 | −0.616706 | ||||||||
\(852\) | −843347. | −0.0398022 | ||||||||
\(853\) | 2.79626e7 | 1.31585 | 0.657924 | − | 0.753085i | \(-0.271435\pi\) | ||||
0.657924 | + | 0.753085i | \(0.271435\pi\) | |||||||
\(854\) | −1.26033e6 | −0.0591344 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.73391e7 | 1.74172 | ||||||||
\(857\) | 2.82523e6 | 0.131402 | 0.0657009 | − | 0.997839i | \(-0.479072\pi\) | ||||
0.0657009 | + | 0.997839i | \(0.479072\pi\) | |||||||
\(858\) | 1.30088e6 | 0.0603281 | ||||||||
\(859\) | 5.68353e6 | 0.262806 | 0.131403 | − | 0.991329i | \(-0.458052\pi\) | ||||
0.131403 | + | 0.991329i | \(0.458052\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.26437e7 | 0.581254 | ||||||||
\(862\) | −1.84816e7 | −0.847170 | ||||||||
\(863\) | −2.23836e6 | −0.102306 | −0.0511532 | − | 0.998691i | \(-0.516290\pi\) | ||||
−0.0511532 | + | 0.998691i | \(0.516290\pi\) | |||||||
\(864\) | −4.30721e6 | −0.196296 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.53116e6 | 0.386557 | ||||||||
\(867\) | 2.56972e7 | 1.16102 | ||||||||
\(868\) | −1.01250e7 | −0.456136 | ||||||||
\(869\) | −957359. | −0.0430056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.98555e7 | 0.886818 | ||||||||
\(872\) | 65406.9 | 0.00291295 | ||||||||
\(873\) | −4.71996e6 | −0.209605 | ||||||||
\(874\) | 1.10082e7 | 0.487457 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.30090e6 | −0.277423 | ||||||||
\(877\) | 6.04256e6 | 0.265291 | 0.132645 | − | 0.991164i | \(-0.457653\pi\) | ||||
0.132645 | + | 0.991164i | \(0.457653\pi\) | |||||||
\(878\) | 2.32355e6 | 0.101722 | ||||||||
\(879\) | 2.57608e7 | 1.12457 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.77877e7 | 1.64025 | 0.820126 | − | 0.572183i | \(-0.193903\pi\) | ||||
0.820126 | + | 0.572183i | \(0.193903\pi\) | |||||||
\(882\) | 1.64913e6 | 0.0713812 | ||||||||
\(883\) | 4.27448e7 | 1.84494 | 0.922469 | − | 0.386070i | \(-0.126168\pi\) | ||||
0.922469 | + | 0.386070i | \(0.126168\pi\) | |||||||
\(884\) | 1.54386e7 | 0.664471 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.27946e7 | −0.975544 | ||||||||
\(887\) | −971018. | −0.0414398 | −0.0207199 | − | 0.999785i | \(-0.506596\pi\) | ||||
−0.0207199 | + | 0.999785i | \(0.506596\pi\) | |||||||
\(888\) | 8.28002e6 | 0.352370 | ||||||||
\(889\) | 4.04053e6 | 0.171468 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −2.65030e7 | −1.11528 | ||||||||
\(893\) | −3.86406e6 | −0.162149 | ||||||||
\(894\) | −1.30677e7 | −0.546832 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.36240e7 | 0.566937 | ||||||||
\(897\) | 8.04828e6 | 0.333981 | ||||||||
\(898\) | 2.23043e7 | 0.922990 | ||||||||
\(899\) | 7.77509e6 | 0.320853 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.45159e7 | −1.82685 | ||||||||
\(902\) | −5.48286e6 | −0.224383 | ||||||||
\(903\) | 1.00241e7 | 0.409095 | ||||||||
\(904\) | −2.49196e6 | −0.101419 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.82538e6 | 0.114355 | ||||||||
\(907\) | 1.74008e7 | 0.702348 | 0.351174 | − | 0.936310i | \(-0.385783\pi\) | ||||
0.351174 | + | 0.936310i | \(0.385783\pi\) | |||||||
\(908\) | −36631.7 | −0.00147449 | ||||||||
\(909\) | −4.57679e6 | −0.183718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.56534e7 | −0.624903 | −0.312451 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312451 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(912\) | 935711. | 0.0372524 | ||||||||
\(913\) | −2.48892e6 | −0.0988175 | ||||||||
\(914\) | −2.05868e6 | −0.0815123 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.86144e6 | 0.152058 | ||||||||
\(917\) | −1.58146e7 | −0.621062 | ||||||||
\(918\) | −5.03059e6 | −0.197021 | ||||||||
\(919\) | −3.32140e7 | −1.29728 | −0.648639 | − | 0.761097i | \(-0.724661\pi\) | ||||
−0.648639 | + | 0.761097i | \(0.724661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.40549e7 | −0.934445 | ||||||||
\(922\) | −1.18634e7 | −0.459601 | ||||||||
\(923\) | −1.60774e6 | −0.0621171 | ||||||||
\(924\) | −2.35069e6 | −0.0905766 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.08117e7 | 0.414348 | ||||||||
\(927\) | 7.74268e6 | 0.295932 | ||||||||
\(928\) | −9.79372e6 | −0.373317 | ||||||||
\(929\) | −7.05863e6 | −0.268338 | −0.134169 | − | 0.990958i | \(-0.542836\pi\) | ||||
−0.134169 | + | 0.990958i | \(0.542836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.05345e6 | −0.304514 | ||||||||
\(932\) | −3.59477e6 | −0.135560 | ||||||||
\(933\) | 1.65947e7 | 0.624116 | ||||||||
\(934\) | −2.40517e7 | −0.902150 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.11485e6 | −0.190829 | ||||||||
\(937\) | −4.85427e6 | −0.180624 | −0.0903120 | − | 0.995914i | \(-0.528786\pi\) | ||||
−0.0903120 | + | 0.995914i | \(0.528786\pi\) | |||||||
\(938\) | 1.91572e7 | 0.710928 | ||||||||
\(939\) | 1.68967e7 | 0.625372 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.79442e7 | −1.39692 | −0.698460 | − | 0.715649i | \(-0.746131\pi\) | ||||
−0.698460 | + | 0.715649i | \(0.746131\pi\) | |||||||
\(942\) | 5.85715e6 | 0.215060 | ||||||||
\(943\) | −3.39213e7 | −1.24220 | ||||||||
\(944\) | −357627. | −0.0130617 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.34687e6 | −0.157924 | ||||||||
\(947\) | −1.42196e7 | −0.515244 | −0.257622 | − | 0.966246i | \(-0.582939\pi\) | ||||
−0.257622 | + | 0.966246i | \(0.582939\pi\) | |||||||
\(948\) | 1.48550e6 | 0.0536849 | ||||||||
\(949\) | −1.20119e7 | −0.432958 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.83821e7 | −0.659090 | ||||||||
\(952\) | 3.77447e7 | 1.34978 | ||||||||
\(953\) | −1.27436e7 | −0.454529 | −0.227264 | − | 0.973833i | \(-0.572978\pi\) | ||||
−0.227264 | + | 0.973833i | \(0.572978\pi\) | |||||||
\(954\) | 5.82030e6 | 0.207049 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.29751e7 | −1.16692 | ||||||||
\(957\) | 1.80513e6 | 0.0637130 | ||||||||
\(958\) | −2.57846e6 | −0.0907709 | ||||||||
\(959\) | 3.35114e7 | 1.17665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.62771e6 | −0.231502 | ||||||||
\(962\) | 6.22937e6 | 0.217023 | ||||||||
\(963\) | 1.71433e7 | 0.595700 | ||||||||
\(964\) | −3.00875e7 | −1.04278 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.76526e6 | 0.267740 | ||||||||
\(967\) | 4.44841e7 | 1.52981 | 0.764906 | − | 0.644142i | \(-0.222785\pi\) | ||||
0.764906 | + | 0.644142i | \(0.222785\pi\) | |||||||
\(968\) | 2.58301e6 | 0.0886008 | ||||||||
\(969\) | 2.45666e7 | 0.840495 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.58495e7 | −0.539469 | −0.269734 | − | 0.962935i | \(-0.586936\pi\) | ||||
−0.269734 | + | 0.962935i | \(0.586936\pi\) | |||||||
\(972\) | −1.23184e6 | −0.0418204 | ||||||||
\(973\) | 2.02730e7 | 0.686492 | ||||||||
\(974\) | 1.03086e7 | 0.348177 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 287415. | 0.00965795 | ||||||||
\(977\) | −3.72698e7 | −1.24917 | −0.624584 | − | 0.780958i | \(-0.714731\pi\) | ||||
−0.624584 | + | 0.780958i | \(0.714731\pi\) | |||||||
\(978\) | −4.63292e6 | −0.154885 | ||||||||
\(979\) | −1.34454e7 | −0.448350 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30029.9 | 0.000996279 0 | ||||||||
\(982\) | −1.60882e7 | −0.532390 | ||||||||
\(983\) | 1.71461e7 | 0.565955 | 0.282978 | − | 0.959127i | \(-0.408678\pi\) | ||||
0.282978 | + | 0.959127i | \(0.408678\pi\) | |||||||
\(984\) | 2.15577e7 | 0.709764 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.14385e7 | −0.374695 | ||||||||
\(987\) | −2.72574e6 | −0.0890619 | ||||||||
\(988\) | 9.85740e6 | 0.321270 | ||||||||
\(989\) | −2.68932e7 | −0.874281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.65029e7 | 1.18071 | 0.590354 | − | 0.807144i | \(-0.298988\pi\) | ||||
0.590354 | + | 0.807144i | \(0.298988\pi\) | |||||||
\(992\) | −2.77137e7 | −0.894159 | ||||||||
\(993\) | −2.24076e7 | −0.721143 | ||||||||
\(994\) | −1.55120e6 | −0.0497969 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.86197e6 | 0.123356 | ||||||||
\(997\) | 5.88370e6 | 0.187462 | 0.0937309 | − | 0.995598i | \(-0.470121\pi\) | ||||
0.0937309 | + | 0.995598i | \(0.470121\pi\) | |||||||
\(998\) | 3.12975e7 | 0.994681 | ||||||||
\(999\) | 3.80155e6 | 0.120517 |
(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.y.1.5 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.11 | ✓ | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.16 | yes | 26 | ||
5.4 | even | 2 | 825.6.a.v.1.9 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.11 | ✓ | 26 | 5.2 | odd | 4 | ||
165.6.c.b.34.16 | yes | 26 | 5.3 | odd | 4 | ||
825.6.a.v.1.9 | 13 | 5.4 | even | 2 | |||
825.6.a.y.1.5 | 13 | 1.1 | even | 1 | trivial |