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: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + 42852537 x^{5} + 63733360 x^{4} - 448113518 x^{3} + \cdots + 522579400 \) |
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 | 1.11 | ||
Root | \(-7.57523\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.57523 | 1.51590 | 0.757950 | − | 0.652312i | \(-0.226201\pi\) | ||||
0.757950 | + | 0.652312i | \(0.226201\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 41.5346 | 1.29796 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 77.1771 | 0.875206 | ||||||||
\(7\) | 178.462 | 1.37658 | 0.688290 | − | 0.725435i | \(-0.258362\pi\) | ||||
0.688290 | + | 0.725435i | \(0.258362\pi\) | |||||||
\(8\) | 81.7612 | 0.451671 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 373.811 | 0.749375 | ||||||||
\(13\) | −361.980 | −0.594054 | −0.297027 | − | 0.954869i | \(-0.595995\pi\) | ||||
−0.297027 | + | 0.954869i | \(0.595995\pi\) | |||||||
\(14\) | 1530.36 | 2.08676 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −627.985 | −0.613267 | ||||||||
\(17\) | 934.004 | 0.783838 | 0.391919 | − | 0.920000i | \(-0.371811\pi\) | ||||
0.391919 | + | 0.920000i | \(0.371811\pi\) | |||||||
\(18\) | 694.594 | 0.505300 | ||||||||
\(19\) | 753.929 | 0.479122 | 0.239561 | − | 0.970881i | \(-0.422996\pi\) | ||||
0.239561 | + | 0.970881i | \(0.422996\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1606.16 | 0.794769 | ||||||||
\(22\) | 1037.60 | 0.457061 | ||||||||
\(23\) | 3231.01 | 1.27356 | 0.636780 | − | 0.771046i | \(-0.280266\pi\) | ||||
0.636780 | + | 0.771046i | \(0.280266\pi\) | |||||||
\(24\) | 735.851 | 0.260773 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3104.06 | −0.900527 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 7412.36 | 1.78674 | ||||||||
\(29\) | 2606.34 | 0.575488 | 0.287744 | − | 0.957707i | \(-0.407095\pi\) | ||||
0.287744 | + | 0.957707i | \(0.407095\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 662.215 | 0.123764 | 0.0618821 | − | 0.998083i | \(-0.480290\pi\) | ||||
0.0618821 | + | 0.998083i | \(0.480290\pi\) | |||||||
\(32\) | −8001.48 | −1.38132 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 8009.30 | 1.18822 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3364.30 | 0.432652 | ||||||||
\(37\) | −12924.2 | −1.55203 | −0.776013 | − | 0.630717i | \(-0.782761\pi\) | ||||
−0.776013 | + | 0.630717i | \(0.782761\pi\) | |||||||
\(38\) | 6465.11 | 0.726302 | ||||||||
\(39\) | −3257.82 | −0.342977 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2538.56 | −0.235846 | −0.117923 | − | 0.993023i | \(-0.537624\pi\) | ||||
−0.117923 | + | 0.993023i | \(0.537624\pi\) | |||||||
\(42\) | 13773.2 | 1.20479 | ||||||||
\(43\) | 22022.8 | 1.81636 | 0.908178 | − | 0.418583i | \(-0.137473\pi\) | ||||
0.908178 | + | 0.418583i | \(0.137473\pi\) | |||||||
\(44\) | 5025.68 | 0.391348 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27706.7 | 1.93059 | ||||||||
\(47\) | 20835.4 | 1.37581 | 0.687903 | − | 0.725802i | \(-0.258531\pi\) | ||||
0.687903 | + | 0.725802i | \(0.258531\pi\) | |||||||
\(48\) | −5651.87 | −0.354070 | ||||||||
\(49\) | 15041.8 | 0.894974 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8406.03 | 0.452549 | ||||||||
\(52\) | −15034.7 | −0.771056 | ||||||||
\(53\) | −27450.5 | −1.34233 | −0.671166 | − | 0.741307i | \(-0.734206\pi\) | ||||
−0.671166 | + | 0.741307i | \(0.734206\pi\) | |||||||
\(54\) | 6251.34 | 0.291735 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14591.3 | 0.621762 | ||||||||
\(57\) | 6785.36 | 0.276621 | ||||||||
\(58\) | 22350.0 | 0.872383 | ||||||||
\(59\) | 7759.71 | 0.290212 | 0.145106 | − | 0.989416i | \(-0.453648\pi\) | ||||
0.145106 | + | 0.989416i | \(0.453648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38469.2 | 1.32370 | 0.661849 | − | 0.749638i | \(-0.269772\pi\) | ||||
0.661849 | + | 0.749638i | \(0.269772\pi\) | |||||||
\(62\) | 5678.65 | 0.187614 | ||||||||
\(63\) | 14455.5 | 0.458860 | ||||||||
\(64\) | −48519.0 | −1.48068 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9338.43 | 0.263884 | ||||||||
\(67\) | 35521.3 | 0.966723 | 0.483362 | − | 0.875421i | \(-0.339416\pi\) | ||||
0.483362 | + | 0.875421i | \(0.339416\pi\) | |||||||
\(68\) | 38793.4 | 1.01739 | ||||||||
\(69\) | 29079.1 | 0.735290 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −62677.1 | −1.47558 | −0.737790 | − | 0.675030i | \(-0.764131\pi\) | ||||
−0.737790 | + | 0.675030i | \(0.764131\pi\) | |||||||
\(72\) | 6622.66 | 0.150557 | ||||||||
\(73\) | 68950.2 | 1.51436 | 0.757179 | − | 0.653208i | \(-0.226577\pi\) | ||||
0.757179 | + | 0.653208i | \(0.226577\pi\) | |||||||
\(74\) | −110828. | −2.35272 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 31314.1 | 0.621879 | ||||||||
\(77\) | 21594.0 | 0.415055 | ||||||||
\(78\) | −27936.5 | −0.519919 | ||||||||
\(79\) | −17313.8 | −0.312123 | −0.156061 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156061 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −21768.7 | −0.357518 | ||||||||
\(83\) | −89017.9 | −1.41835 | −0.709173 | − | 0.705035i | \(-0.750931\pi\) | ||||
−0.709173 | + | 0.705035i | \(0.750931\pi\) | |||||||
\(84\) | 66711.2 | 1.03158 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 188850. | 2.75342 | ||||||||
\(87\) | 23457.1 | 0.332258 | ||||||||
\(88\) | 9893.11 | 0.136184 | ||||||||
\(89\) | 129627. | 1.73468 | 0.867341 | − | 0.497714i | \(-0.165827\pi\) | ||||
0.867341 | + | 0.497714i | \(0.165827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −64599.8 | −0.817763 | ||||||||
\(92\) | 134199. | 1.65302 | ||||||||
\(93\) | 5959.94 | 0.0714553 | ||||||||
\(94\) | 178668. | 2.08559 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −72013.3 | −0.797507 | ||||||||
\(97\) | −136732. | −1.47551 | −0.737755 | − | 0.675069i | \(-0.764114\pi\) | ||||
−0.737755 | + | 0.675069i | \(0.764114\pi\) | |||||||
\(98\) | 128987. | 1.35669 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 51376.9 | 0.501146 | 0.250573 | − | 0.968098i | \(-0.419381\pi\) | ||||
0.250573 | + | 0.968098i | \(0.419381\pi\) | |||||||
\(102\) | 72083.7 | 0.686019 | ||||||||
\(103\) | −94899.7 | −0.881398 | −0.440699 | − | 0.897655i | \(-0.645269\pi\) | ||||
−0.440699 | + | 0.897655i | \(0.645269\pi\) | |||||||
\(104\) | −29595.9 | −0.268317 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −235394. | −2.03484 | ||||||||
\(107\) | −52232.6 | −0.441045 | −0.220522 | − | 0.975382i | \(-0.570776\pi\) | ||||
−0.220522 | + | 0.975382i | \(0.570776\pi\) | |||||||
\(108\) | 30278.7 | 0.249792 | ||||||||
\(109\) | 138553. | 1.11699 | 0.558496 | − | 0.829507i | \(-0.311378\pi\) | ||||
0.558496 | + | 0.829507i | \(0.311378\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −116318. | −0.896063 | ||||||||
\(112\) | −112072. | −0.844211 | ||||||||
\(113\) | −136642. | −1.00667 | −0.503336 | − | 0.864091i | \(-0.667894\pi\) | ||||
−0.503336 | + | 0.864091i | \(0.667894\pi\) | |||||||
\(114\) | 58186.0 | 0.419330 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 108253. | 0.746958 | ||||||||
\(117\) | −29320.4 | −0.198018 | ||||||||
\(118\) | 66541.3 | 0.439933 | ||||||||
\(119\) | 166685. | 1.07902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 329882. | 2.00659 | ||||||||
\(123\) | −22847.0 | −0.136165 | ||||||||
\(124\) | 27504.8 | 0.160640 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 123959. | 0.695587 | ||||||||
\(127\) | 23888.8 | 0.131427 | 0.0657136 | − | 0.997839i | \(-0.479068\pi\) | ||||
0.0657136 | + | 0.997839i | \(0.479068\pi\) | |||||||
\(128\) | −160014. | −0.863244 | ||||||||
\(129\) | 198205. | 1.04867 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 67597.5 | 0.344154 | 0.172077 | − | 0.985084i | \(-0.444952\pi\) | ||||
0.172077 | + | 0.985084i | \(0.444952\pi\) | |||||||
\(132\) | 45231.2 | 0.225945 | ||||||||
\(133\) | 134548. | 0.659550 | ||||||||
\(134\) | 304604. | 1.46546 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 76365.3 | 0.354037 | ||||||||
\(137\) | −205843. | −0.936991 | −0.468496 | − | 0.883466i | \(-0.655204\pi\) | ||||
−0.468496 | + | 0.883466i | \(0.655204\pi\) | |||||||
\(138\) | 249360. | 1.11463 | ||||||||
\(139\) | 43495.6 | 0.190945 | 0.0954724 | − | 0.995432i | \(-0.469564\pi\) | ||||
0.0954724 | + | 0.995432i | \(0.469564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 187519. | 0.794323 | ||||||||
\(142\) | −537470. | −2.23683 | ||||||||
\(143\) | −43799.6 | −0.179114 | ||||||||
\(144\) | −50866.8 | −0.204422 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 591264. | 2.29562 | ||||||||
\(147\) | 135376. | 0.516713 | ||||||||
\(148\) | −536801. | −2.01446 | ||||||||
\(149\) | 219355. | 0.809436 | 0.404718 | − | 0.914442i | \(-0.367370\pi\) | ||||
0.404718 | + | 0.914442i | \(0.367370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −32928.1 | −0.117523 | −0.0587616 | − | 0.998272i | \(-0.518715\pi\) | ||||
−0.0587616 | + | 0.998272i | \(0.518715\pi\) | |||||||
\(152\) | 61642.1 | 0.216406 | ||||||||
\(153\) | 75654.3 | 0.261279 | ||||||||
\(154\) | 185173. | 0.629182 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −135312. | −0.445169 | ||||||||
\(157\) | 457292. | 1.48062 | 0.740311 | − | 0.672265i | \(-0.234678\pi\) | ||||
0.740311 | + | 0.672265i | \(0.234678\pi\) | |||||||
\(158\) | −148470. | −0.473147 | ||||||||
\(159\) | −247054. | −0.774996 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 576614. | 1.75316 | ||||||||
\(162\) | 56262.1 | 0.168433 | ||||||||
\(163\) | −52822.0 | −0.155721 | −0.0778603 | − | 0.996964i | \(-0.524809\pi\) | ||||
−0.0778603 | + | 0.996964i | \(0.524809\pi\) | |||||||
\(164\) | −105438. | −0.306117 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −763349. | −2.15007 | ||||||||
\(167\) | −327606. | −0.908993 | −0.454497 | − | 0.890748i | \(-0.650181\pi\) | ||||
−0.454497 | + | 0.890748i | \(0.650181\pi\) | |||||||
\(168\) | 131322. | 0.358974 | ||||||||
\(169\) | −240264. | −0.647100 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 61068.2 | 0.159707 | ||||||||
\(172\) | 914707. | 2.35755 | ||||||||
\(173\) | 246387. | 0.625897 | 0.312949 | − | 0.949770i | \(-0.398683\pi\) | ||||
0.312949 | + | 0.949770i | \(0.398683\pi\) | |||||||
\(174\) | 201150. | 0.503670 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −75986.2 | −0.184907 | ||||||||
\(177\) | 69837.4 | 0.167554 | ||||||||
\(178\) | 1.11158e6 | 2.62961 | ||||||||
\(179\) | 302341. | 0.705285 | 0.352643 | − | 0.935758i | \(-0.385283\pi\) | ||||
0.352643 | + | 0.935758i | \(0.385283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −465374. | −1.05586 | −0.527929 | − | 0.849288i | \(-0.677031\pi\) | ||||
−0.527929 | + | 0.849288i | \(0.677031\pi\) | |||||||
\(182\) | −553958. | −1.23965 | ||||||||
\(183\) | 346223. | 0.764237 | ||||||||
\(184\) | 264172. | 0.575230 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 51107.8 | 0.108319 | ||||||||
\(187\) | 113014. | 0.236336 | ||||||||
\(188\) | 865390. | 1.78574 | ||||||||
\(189\) | 130099. | 0.264923 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 294182. | 0.583489 | 0.291745 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291745 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(192\) | −436671. | −0.854872 | ||||||||
\(193\) | −280529. | −0.542106 | −0.271053 | − | 0.962564i | \(-0.587372\pi\) | ||||
−0.271053 | + | 0.962564i | \(0.587372\pi\) | |||||||
\(194\) | −1.17251e6 | −2.23673 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 624756. | 1.16164 | ||||||||
\(197\) | −241625. | −0.443585 | −0.221792 | − | 0.975094i | \(-0.571191\pi\) | ||||
−0.221792 | + | 0.975094i | \(0.571191\pi\) | |||||||
\(198\) | 84045.8 | 0.152354 | ||||||||
\(199\) | 621763. | 1.11299 | 0.556496 | − | 0.830850i | \(-0.312145\pi\) | ||||
0.556496 | + | 0.830850i | \(0.312145\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 319692. | 0.558138 | ||||||||
\(202\) | 440569. | 0.759688 | ||||||||
\(203\) | 465134. | 0.792205 | ||||||||
\(204\) | 349141. | 0.587389 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −813787. | −1.33611 | ||||||||
\(207\) | 261712. | 0.424520 | ||||||||
\(208\) | 227318. | 0.364314 | ||||||||
\(209\) | 91225.4 | 0.144461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −446582. | −0.690550 | −0.345275 | − | 0.938502i | \(-0.612214\pi\) | ||||
−0.345275 | + | 0.938502i | \(0.612214\pi\) | |||||||
\(212\) | −1.14014e6 | −1.74229 | ||||||||
\(213\) | −564094. | −0.851927 | ||||||||
\(214\) | −447907. | −0.668580 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 59603.9 | 0.0869242 | ||||||||
\(217\) | 118181. | 0.170371 | ||||||||
\(218\) | 1.18813e6 | 1.69325 | ||||||||
\(219\) | 620552. | 0.874314 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −338090. | −0.465642 | ||||||||
\(222\) | −997451. | −1.35834 | ||||||||
\(223\) | 29867.7 | 0.0402198 | 0.0201099 | − | 0.999798i | \(-0.493598\pi\) | ||||
0.0201099 | + | 0.999798i | \(0.493598\pi\) | |||||||
\(224\) | −1.42796e6 | −1.90150 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.17174e6 | −1.52602 | ||||||||
\(227\) | 425464. | 0.548022 | 0.274011 | − | 0.961726i | \(-0.411649\pi\) | ||||
0.274011 | + | 0.961726i | \(0.411649\pi\) | |||||||
\(228\) | 281827. | 0.359042 | ||||||||
\(229\) | −1.31835e6 | −1.66127 | −0.830637 | − | 0.556814i | \(-0.812023\pi\) | ||||
−0.830637 | + | 0.556814i | \(0.812023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 194346. | 0.239632 | ||||||||
\(232\) | 213098. | 0.259931 | ||||||||
\(233\) | −320062. | −0.386228 | −0.193114 | − | 0.981176i | \(-0.561859\pi\) | ||||
−0.193114 | + | 0.981176i | \(0.561859\pi\) | |||||||
\(234\) | −251429. | −0.300176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 322296. | 0.376683 | ||||||||
\(237\) | −155825. | −0.180204 | ||||||||
\(238\) | 1.42936e6 | 1.63568 | ||||||||
\(239\) | 1.25534e6 | 1.42156 | 0.710781 | − | 0.703414i | \(-0.248342\pi\) | ||||
0.710781 | + | 0.703414i | \(0.248342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.07813e6 | −1.19572 | −0.597859 | − | 0.801601i | \(-0.703982\pi\) | ||||
−0.597859 | + | 0.801601i | \(0.703982\pi\) | |||||||
\(242\) | 125550. | 0.137809 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 1.59780e6 | 1.71810 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −195919. | −0.206413 | ||||||||
\(247\) | −272907. | −0.284624 | ||||||||
\(248\) | 54143.5 | 0.0559007 | ||||||||
\(249\) | −801161. | −0.818882 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −918775. | −0.920502 | −0.460251 | − | 0.887789i | \(-0.652241\pi\) | ||||
−0.460251 | + | 0.887789i | \(0.652241\pi\) | |||||||
\(252\) | 600401. | 0.595580 | ||||||||
\(253\) | 390953. | 0.383993 | ||||||||
\(254\) | 204852. | 0.199231 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 180449. | 0.172089 | ||||||||
\(257\) | 797355. | 0.753041 | 0.376521 | − | 0.926408i | \(-0.377120\pi\) | ||||
0.376521 | + | 0.926408i | \(0.377120\pi\) | |||||||
\(258\) | 1.69965e6 | 1.58969 | ||||||||
\(259\) | −2.30648e6 | −2.13649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 211114. | 0.191829 | ||||||||
\(262\) | 579664. | 0.521703 | ||||||||
\(263\) | −980563. | −0.874150 | −0.437075 | − | 0.899425i | \(-0.643986\pi\) | ||||
−0.437075 | + | 0.899425i | \(0.643986\pi\) | |||||||
\(264\) | 89038.0 | 0.0786259 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.15378e6 | 0.999813 | ||||||||
\(267\) | 1.16664e6 | 1.00152 | ||||||||
\(268\) | 1.47536e6 | 1.25476 | ||||||||
\(269\) | −1.32137e6 | −1.11338 | −0.556691 | − | 0.830719i | \(-0.687929\pi\) | ||||
−0.556691 | + | 0.830719i | \(0.687929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −62864.5 | −0.0519975 | −0.0259987 | − | 0.999662i | \(-0.508277\pi\) | ||||
−0.0259987 | + | 0.999662i | \(0.508277\pi\) | |||||||
\(272\) | −586540. | −0.480702 | ||||||||
\(273\) | −581398. | −0.472136 | ||||||||
\(274\) | −1.76515e6 | −1.42039 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.20779e6 | 0.954374 | ||||||||
\(277\) | 1.44313e6 | 1.13007 | 0.565037 | − | 0.825066i | \(-0.308862\pi\) | ||||
0.565037 | + | 0.825066i | \(0.308862\pi\) | |||||||
\(278\) | 372984. | 0.289453 | ||||||||
\(279\) | 53639.4 | 0.0412547 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −143939. | −0.108746 | −0.0543731 | − | 0.998521i | \(-0.517316\pi\) | ||||
−0.0543731 | + | 0.998521i | \(0.517316\pi\) | |||||||
\(282\) | 1.60802e6 | 1.20411 | ||||||||
\(283\) | −9060.12 | −0.00672462 | −0.00336231 | − | 0.999994i | \(-0.501070\pi\) | ||||
−0.00336231 | + | 0.999994i | \(0.501070\pi\) | |||||||
\(284\) | −2.60327e6 | −1.91524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −375591. | −0.271519 | ||||||||
\(287\) | −453037. | −0.324660 | ||||||||
\(288\) | −648120. | −0.460441 | ||||||||
\(289\) | −547494. | −0.385598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.23059e6 | −0.851886 | ||||||||
\(292\) | 2.86382e6 | 1.96557 | ||||||||
\(293\) | −1.85674e6 | −1.26352 | −0.631759 | − | 0.775165i | \(-0.717667\pi\) | ||||
−0.631759 | + | 0.775165i | \(0.717667\pi\) | |||||||
\(294\) | 1.16088e6 | 0.783286 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.05670e6 | −0.701006 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 1.88102e6 | 1.22703 | ||||||||
\(299\) | −1.16956e6 | −0.756563 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.93024e6 | 2.50036 | ||||||||
\(302\) | −282366. | −0.178154 | ||||||||
\(303\) | 462392. | 0.289337 | ||||||||
\(304\) | −473456. | −0.293830 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 648753. | 0.396074 | ||||||||
\(307\) | −504688. | −0.305617 | −0.152808 | − | 0.988256i | \(-0.548832\pi\) | ||||
−0.152808 | + | 0.988256i | \(0.548832\pi\) | |||||||
\(308\) | 896896. | 0.538723 | ||||||||
\(309\) | −854097. | −0.508875 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −448511. | −0.262950 | −0.131475 | − | 0.991320i | \(-0.541971\pi\) | ||||
−0.131475 | + | 0.991320i | \(0.541971\pi\) | |||||||
\(312\) | −266363. | −0.154913 | ||||||||
\(313\) | 825146. | 0.476069 | 0.238035 | − | 0.971257i | \(-0.423497\pi\) | ||||
0.238035 | + | 0.971257i | \(0.423497\pi\) | |||||||
\(314\) | 3.92138e6 | 2.24448 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −719123. | −0.405122 | ||||||||
\(317\) | 3.26266e6 | 1.82358 | 0.911789 | − | 0.410659i | \(-0.134701\pi\) | ||||
0.911789 | + | 0.410659i | \(0.134701\pi\) | |||||||
\(318\) | −2.11855e6 | −1.17482 | ||||||||
\(319\) | 315367. | 0.173516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −470094. | −0.254637 | ||||||||
\(322\) | 4.94460e6 | 2.65761 | ||||||||
\(323\) | 704172. | 0.375554 | ||||||||
\(324\) | 272508. | 0.144217 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −452961. | −0.236057 | ||||||||
\(327\) | 1.24698e6 | 0.644896 | ||||||||
\(328\) | −207556. | −0.106525 | ||||||||
\(329\) | 3.71834e6 | 1.89391 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.48175e6 | −1.74674 | −0.873369 | − | 0.487059i | \(-0.838070\pi\) | ||||
−0.873369 | + | 0.487059i | \(0.838070\pi\) | |||||||
\(332\) | −3.69732e6 | −1.84095 | ||||||||
\(333\) | −1.04686e6 | −0.517342 | ||||||||
\(334\) | −2.80930e6 | −1.37794 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00865e6 | −0.487406 | ||||||||
\(337\) | −1.52759e6 | −0.732710 | −0.366355 | − | 0.930475i | \(-0.619394\pi\) | ||||
−0.366355 | + | 0.930475i | \(0.619394\pi\) | |||||||
\(338\) | −2.06032e6 | −0.980939 | ||||||||
\(339\) | −1.22978e6 | −0.581203 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 80128.0 | 0.0373163 | ||||||||
\(342\) | 523674. | 0.242101 | ||||||||
\(343\) | −315017. | −0.144577 | ||||||||
\(344\) | 1.80061e6 | 0.820396 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.11283e6 | 0.948798 | ||||||||
\(347\) | −4.01479e6 | −1.78994 | −0.894972 | − | 0.446122i | \(-0.852805\pi\) | ||||
−0.894972 | + | 0.446122i | \(0.852805\pi\) | |||||||
\(348\) | 974279. | 0.431256 | ||||||||
\(349\) | −511478. | −0.224783 | −0.112391 | − | 0.993664i | \(-0.535851\pi\) | ||||
−0.112391 | + | 0.993664i | \(0.535851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −263883. | −0.114326 | ||||||||
\(352\) | −968179. | −0.416485 | ||||||||
\(353\) | −722636. | −0.308662 | −0.154331 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154331 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(354\) | 598872. | 0.253995 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.38400e6 | 2.25154 | ||||||||
\(357\) | 1.50016e6 | 0.622970 | ||||||||
\(358\) | 2.59264e6 | 1.06914 | ||||||||
\(359\) | 393345. | 0.161078 | 0.0805392 | − | 0.996751i | \(-0.474336\pi\) | ||||
0.0805392 | + | 0.996751i | \(0.474336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.90769e6 | −0.770442 | ||||||||
\(362\) | −3.99069e6 | −1.60058 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −2.68312e6 | −1.06142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.96894e6 | 1.15851 | ||||||||
\(367\) | −2.87578e6 | −1.11453 | −0.557264 | − | 0.830336i | \(-0.688149\pi\) | ||||
−0.557264 | + | 0.830336i | \(0.688149\pi\) | |||||||
\(368\) | −2.02903e6 | −0.781032 | ||||||||
\(369\) | −205623. | −0.0786152 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89888e6 | −1.84783 | ||||||||
\(372\) | 247543. | 0.0927458 | ||||||||
\(373\) | 3.86030e6 | 1.43665 | 0.718323 | − | 0.695710i | \(-0.244910\pi\) | ||||
0.718323 | + | 0.695710i | \(0.244910\pi\) | |||||||
\(374\) | 969125. | 0.358262 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.70353e6 | 0.621412 | ||||||||
\(377\) | −943443. | −0.341871 | ||||||||
\(378\) | 1.11563e6 | 0.401597 | ||||||||
\(379\) | −1.63355e6 | −0.584162 | −0.292081 | − | 0.956394i | \(-0.594348\pi\) | ||||
−0.292081 | + | 0.956394i | \(0.594348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 214999. | 0.0758795 | ||||||||
\(382\) | 2.52268e6 | 0.884512 | ||||||||
\(383\) | 3.86858e6 | 1.34758 | 0.673790 | − | 0.738923i | \(-0.264665\pi\) | ||||
0.673790 | + | 0.738923i | \(0.264665\pi\) | |||||||
\(384\) | −1.44013e6 | −0.498394 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.40560e6 | −0.821779 | ||||||||
\(387\) | 1.78385e6 | 0.605452 | ||||||||
\(388\) | −5.67912e6 | −1.91515 | ||||||||
\(389\) | −10040.7 | −0.00336428 | −0.00168214 | − | 0.999999i | \(-0.500535\pi\) | ||||
−0.00168214 | + | 0.999999i | \(0.500535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.01778e6 | 0.998264 | ||||||||
\(392\) | 1.22984e6 | 0.404234 | ||||||||
\(393\) | 608378. | 0.198697 | ||||||||
\(394\) | −2.07199e6 | −0.672431 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 407080. | 0.130449 | ||||||||
\(397\) | −3.77944e6 | −1.20352 | −0.601758 | − | 0.798679i | \(-0.705533\pi\) | ||||
−0.601758 | + | 0.798679i | \(0.705533\pi\) | |||||||
\(398\) | 5.33176e6 | 1.68719 | ||||||||
\(399\) | 1.21093e6 | 0.380791 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.77840e6 | −1.79451 | −0.897256 | − | 0.441510i | \(-0.854443\pi\) | ||||
−0.897256 | + | 0.441510i | \(0.854443\pi\) | |||||||
\(402\) | 2.74143e6 | 0.846082 | ||||||||
\(403\) | −239708. | −0.0735226 | ||||||||
\(404\) | 2.13392e6 | 0.650465 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.98863e6 | 1.20090 | ||||||||
\(407\) | −1.56383e6 | −0.467954 | ||||||||
\(408\) | 687287. | 0.204403 | ||||||||
\(409\) | 4.93158e6 | 1.45773 | 0.728866 | − | 0.684656i | \(-0.240048\pi\) | ||||
0.728866 | + | 0.684656i | \(0.240048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.85259e6 | −0.540972 | ||||||||
\(412\) | −3.94162e6 | −1.14401 | ||||||||
\(413\) | 1.38482e6 | 0.399501 | ||||||||
\(414\) | 2.24424e6 | 0.643530 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.89637e6 | 0.820580 | ||||||||
\(417\) | 391460. | 0.110242 | ||||||||
\(418\) | 782278. | 0.218988 | ||||||||
\(419\) | −4.38879e6 | −1.22126 | −0.610632 | − | 0.791914i | \(-0.709085\pi\) | ||||
−0.610632 | + | 0.791914i | \(0.709085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.32905e6 | −1.74034 | −0.870169 | − | 0.492754i | \(-0.835990\pi\) | ||||
−0.870169 | + | 0.492754i | \(0.835990\pi\) | |||||||
\(422\) | −3.82954e6 | −1.04681 | ||||||||
\(423\) | 1.68767e6 | 0.458602 | ||||||||
\(424\) | −2.24438e6 | −0.606293 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.83723e6 | −1.29144 | ||||||||
\(427\) | 6.86531e6 | 1.82218 | ||||||||
\(428\) | −2.16946e6 | −0.572456 | ||||||||
\(429\) | −394196. | −0.103412 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.39779e6 | −1.14036 | −0.570179 | − | 0.821520i | \(-0.693126\pi\) | ||||
−0.570179 | + | 0.821520i | \(0.693126\pi\) | |||||||
\(432\) | −457801. | −0.118023 | ||||||||
\(433\) | −1.57360e6 | −0.403344 | −0.201672 | − | 0.979453i | \(-0.564638\pi\) | ||||
−0.201672 | + | 0.979453i | \(0.564638\pi\) | |||||||
\(434\) | 1.01343e6 | 0.258266 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.75475e6 | 1.44981 | ||||||||
\(437\) | 2.43595e6 | 0.610190 | ||||||||
\(438\) | 5.32137e6 | 1.32537 | ||||||||
\(439\) | −7.89299e6 | −1.95470 | −0.977351 | − | 0.211626i | \(-0.932124\pi\) | ||||
−0.977351 | + | 0.211626i | \(0.932124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.21839e6 | 0.298325 | ||||||||
\(442\) | −2.89920e6 | −0.705867 | ||||||||
\(443\) | −557226. | −0.134903 | −0.0674516 | − | 0.997723i | \(-0.521487\pi\) | ||||
−0.0674516 | + | 0.997723i | \(0.521487\pi\) | |||||||
\(444\) | −4.83121e6 | −1.16305 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 256123. | 0.0609693 | ||||||||
\(447\) | 1.97420e6 | 0.467328 | ||||||||
\(448\) | −8.65881e6 | −2.03828 | ||||||||
\(449\) | 2.27558e6 | 0.532691 | 0.266346 | − | 0.963878i | \(-0.414184\pi\) | ||||
0.266346 | + | 0.963878i | \(0.414184\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −307166. | −0.0711101 | ||||||||
\(452\) | −5.67537e6 | −1.30662 | ||||||||
\(453\) | −296352. | −0.0678521 | ||||||||
\(454\) | 3.64845e6 | 0.830748 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 554779. | 0.124942 | ||||||||
\(457\) | 7.50427e6 | 1.68081 | 0.840404 | − | 0.541961i | \(-0.182318\pi\) | ||||
0.840404 | + | 0.541961i | \(0.182318\pi\) | |||||||
\(458\) | −1.13051e7 | −2.51833 | ||||||||
\(459\) | 680889. | 0.150850 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 436978. | 0.0957652 | 0.0478826 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478826 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(462\) | 1.66656e6 | 0.363258 | ||||||||
\(463\) | −3.11651e6 | −0.675642 | −0.337821 | − | 0.941210i | \(-0.609690\pi\) | ||||
−0.337821 | + | 0.941210i | \(0.609690\pi\) | |||||||
\(464\) | −1.63674e6 | −0.352928 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.74460e6 | −0.585484 | ||||||||
\(467\) | −1.89749e6 | −0.402613 | −0.201307 | − | 0.979528i | \(-0.564519\pi\) | ||||
−0.201307 | + | 0.979528i | \(0.564519\pi\) | |||||||
\(468\) | −1.21781e6 | −0.257019 | ||||||||
\(469\) | 6.33922e6 | 1.33077 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.11562e6 | 0.854837 | ||||||||
\(472\) | 634444. | 0.131081 | ||||||||
\(473\) | 2.66476e6 | 0.547652 | ||||||||
\(474\) | −1.33623e6 | −0.273172 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.92317e6 | 1.40051 | ||||||||
\(477\) | −2.22349e6 | −0.447444 | ||||||||
\(478\) | 1.07648e7 | 2.15495 | ||||||||
\(479\) | −6.10287e6 | −1.21533 | −0.607666 | − | 0.794193i | \(-0.707894\pi\) | ||||
−0.607666 | + | 0.794193i | \(0.707894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.67830e6 | 0.921987 | ||||||||
\(482\) | −9.24522e6 | −1.81259 | ||||||||
\(483\) | 5.18953e6 | 1.01219 | ||||||||
\(484\) | 608108. | 0.117996 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 506359. | 0.0972451 | ||||||||
\(487\) | −7.30170e6 | −1.39509 | −0.697544 | − | 0.716542i | \(-0.745724\pi\) | ||||
−0.697544 | + | 0.716542i | \(0.745724\pi\) | |||||||
\(488\) | 3.14529e6 | 0.597876 | ||||||||
\(489\) | −475398. | −0.0899053 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.40884e6 | 0.825317 | 0.412658 | − | 0.910886i | \(-0.364600\pi\) | ||||
0.412658 | + | 0.910886i | \(0.364600\pi\) | |||||||
\(492\) | −948942. | −0.176737 | ||||||||
\(493\) | 2.43433e6 | 0.451089 | ||||||||
\(494\) | −2.34024e6 | −0.431462 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −415861. | −0.0759004 | ||||||||
\(497\) | −1.11855e7 | −2.03125 | ||||||||
\(498\) | −6.87014e6 | −1.24134 | ||||||||
\(499\) | 3.45620e6 | 0.621367 | 0.310683 | − | 0.950513i | \(-0.399442\pi\) | ||||
0.310683 | + | 0.950513i | \(0.399442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.94845e6 | −0.524808 | ||||||||
\(502\) | −7.87871e6 | −1.39539 | ||||||||
\(503\) | 5.07651e6 | 0.894634 | 0.447317 | − | 0.894375i | \(-0.352380\pi\) | ||||
0.447317 | + | 0.894375i | \(0.352380\pi\) | |||||||
\(504\) | 1.18190e6 | 0.207254 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.35251e6 | 0.582095 | ||||||||
\(507\) | −2.16237e6 | −0.373603 | ||||||||
\(508\) | 992212. | 0.170587 | ||||||||
\(509\) | 7.63894e6 | 1.30689 | 0.653445 | − | 0.756974i | \(-0.273323\pi\) | ||||
0.653445 | + | 0.756974i | \(0.273323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23050e7 | 2.08463 | ||||||||
\(512\) | 6.66784e6 | 1.12411 | ||||||||
\(513\) | 549614. | 0.0922071 | ||||||||
\(514\) | 6.83750e6 | 1.14154 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.23237e6 | 1.36113 | ||||||||
\(517\) | 2.52109e6 | 0.414821 | ||||||||
\(518\) | −1.97786e7 | −3.23871 | ||||||||
\(519\) | 2.21748e6 | 0.361362 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.46786e6 | −1.52812 | −0.764060 | − | 0.645145i | \(-0.776797\pi\) | ||||
−0.764060 | + | 0.645145i | \(0.776797\pi\) | |||||||
\(522\) | 1.81035e6 | 0.290794 | ||||||||
\(523\) | −1.12533e6 | −0.179898 | −0.0899490 | − | 0.995946i | \(-0.528670\pi\) | ||||
−0.0899490 | + | 0.995946i | \(0.528670\pi\) | |||||||
\(524\) | 2.80764e6 | 0.446696 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.40855e6 | −1.32512 | ||||||||
\(527\) | 618511. | 0.0970110 | ||||||||
\(528\) | −683876. | −0.106756 | ||||||||
\(529\) | 4.00311e6 | 0.621953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 628537. | 0.0967374 | ||||||||
\(532\) | 5.58839e6 | 0.856067 | ||||||||
\(533\) | 918907. | 0.140105 | ||||||||
\(534\) | 1.00042e7 | 1.51820 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.90427e6 | 0.436641 | ||||||||
\(537\) | 2.72107e6 | 0.407196 | ||||||||
\(538\) | −1.13311e7 | −1.68778 | ||||||||
\(539\) | 1.82006e6 | 0.269845 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.05433e7 | 1.54876 | 0.774379 | − | 0.632722i | \(-0.218062\pi\) | ||||
0.774379 | + | 0.632722i | \(0.218062\pi\) | |||||||
\(542\) | −539078. | −0.0788230 | ||||||||
\(543\) | −4.18837e6 | −0.609600 | ||||||||
\(544\) | −7.47341e6 | −1.08273 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.98562e6 | −0.715711 | ||||||||
\(547\) | 9.65329e6 | 1.37945 | 0.689727 | − | 0.724070i | \(-0.257731\pi\) | ||||
0.689727 | + | 0.724070i | \(0.257731\pi\) | |||||||
\(548\) | −8.54962e6 | −1.21617 | ||||||||
\(549\) | 3.11601e6 | 0.441232 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.96499e6 | 0.275729 | ||||||||
\(552\) | 2.37754e6 | 0.332109 | ||||||||
\(553\) | −3.08987e6 | −0.429662 | ||||||||
\(554\) | 1.23752e7 | 1.71308 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.80657e6 | 0.247838 | ||||||||
\(557\) | 4.21289e6 | 0.575363 | 0.287682 | − | 0.957726i | \(-0.407115\pi\) | ||||
0.287682 | + | 0.957726i | \(0.407115\pi\) | |||||||
\(558\) | 459970. | 0.0625381 | ||||||||
\(559\) | −7.97180e6 | −1.07901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.01713e6 | 0.136449 | ||||||||
\(562\) | −1.23431e6 | −0.164848 | ||||||||
\(563\) | 9.59902e6 | 1.27631 | 0.638155 | − | 0.769908i | \(-0.279698\pi\) | ||||
0.638155 | + | 0.769908i | \(0.279698\pi\) | |||||||
\(564\) | 7.78851e6 | 1.03100 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −77692.6 | −0.0101939 | ||||||||
\(567\) | 1.17089e6 | 0.152953 | ||||||||
\(568\) | −5.12455e6 | −0.666477 | ||||||||
\(569\) | 4.20682e6 | 0.544720 | 0.272360 | − | 0.962195i | \(-0.412196\pi\) | ||||
0.272360 | + | 0.962195i | \(0.412196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.22447e7 | −1.57165 | −0.785826 | − | 0.618447i | \(-0.787762\pi\) | ||||
−0.785826 | + | 0.618447i | \(0.787762\pi\) | |||||||
\(572\) | −1.81920e6 | −0.232482 | ||||||||
\(573\) | 2.64764e6 | 0.336878 | ||||||||
\(574\) | −3.88490e6 | −0.492153 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.93004e6 | −0.493561 | ||||||||
\(577\) | 5.32012e6 | 0.665245 | 0.332623 | − | 0.943060i | \(-0.392066\pi\) | ||||
0.332623 | + | 0.943060i | \(0.392066\pi\) | |||||||
\(578\) | −4.69489e6 | −0.584529 | ||||||||
\(579\) | −2.52476e6 | −0.312985 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.58863e7 | −1.95247 | ||||||||
\(582\) | −1.05526e7 | −1.29137 | ||||||||
\(583\) | −3.32151e6 | −0.404728 | ||||||||
\(584\) | 5.63745e6 | 0.683992 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.59220e7 | −1.91537 | ||||||||
\(587\) | −5.70534e6 | −0.683418 | −0.341709 | − | 0.939806i | \(-0.611006\pi\) | ||||
−0.341709 | + | 0.939806i | \(0.611006\pi\) | |||||||
\(588\) | 5.62280e6 | 0.670671 | ||||||||
\(589\) | 499263. | 0.0592981 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.17463e6 | −0.256104 | ||||||||
\(592\) | 8.11620e6 | 0.951806 | ||||||||
\(593\) | 2.15575e6 | 0.251746 | 0.125873 | − | 0.992046i | \(-0.459827\pi\) | ||||
0.125873 | + | 0.992046i | \(0.459827\pi\) | |||||||
\(594\) | 756413. | 0.0879615 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.11083e6 | 1.05061 | ||||||||
\(597\) | 5.59587e6 | 0.642587 | ||||||||
\(598\) | −1.00293e7 | −1.14687 | ||||||||
\(599\) | 5.13968e6 | 0.585287 | 0.292643 | − | 0.956222i | \(-0.405465\pi\) | ||||
0.292643 | + | 0.956222i | \(0.405465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.48666e6 | −0.845478 | −0.422739 | − | 0.906252i | \(-0.638931\pi\) | ||||
−0.422739 | + | 0.906252i | \(0.638931\pi\) | |||||||
\(602\) | 3.37027e7 | 3.79030 | ||||||||
\(603\) | 2.87723e6 | 0.322241 | ||||||||
\(604\) | −1.36765e6 | −0.152540 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.96512e6 | 0.438606 | ||||||||
\(607\) | −8.62794e6 | −0.950464 | −0.475232 | − | 0.879861i | \(-0.657636\pi\) | ||||
−0.475232 | + | 0.879861i | \(0.657636\pi\) | |||||||
\(608\) | −6.03254e6 | −0.661822 | ||||||||
\(609\) | 4.18620e6 | 0.457380 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54200e6 | −0.817304 | ||||||||
\(612\) | 3.14227e6 | 0.339129 | ||||||||
\(613\) | −1.44646e7 | −1.55473 | −0.777367 | − | 0.629047i | \(-0.783445\pi\) | ||||
−0.777367 | + | 0.629047i | \(0.783445\pi\) | |||||||
\(614\) | −4.32782e6 | −0.463285 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.76555e6 | 0.187468 | ||||||||
\(617\) | 5.82746e6 | 0.616264 | 0.308132 | − | 0.951344i | \(-0.400296\pi\) | ||||
0.308132 | + | 0.951344i | \(0.400296\pi\) | |||||||
\(618\) | −7.32408e6 | −0.771404 | ||||||||
\(619\) | −2.32647e6 | −0.244045 | −0.122023 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122023 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.35541e6 | 0.245097 | ||||||||
\(622\) | −3.84609e6 | −0.398605 | ||||||||
\(623\) | 2.31335e7 | 2.38793 | ||||||||
\(624\) | 2.04586e6 | 0.210337 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.07582e6 | 0.721674 | ||||||||
\(627\) | 821028. | 0.0834044 | ||||||||
\(628\) | 1.89934e7 | 1.92178 | ||||||||
\(629\) | −1.20712e7 | −1.21654 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −398154. | −0.0398087 | −0.0199043 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199043 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | −1.41560e6 | −0.140977 | ||||||||
\(633\) | −4.01924e6 | −0.398689 | ||||||||
\(634\) | 2.79781e7 | 2.76436 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.02613e7 | −1.00591 | ||||||||
\(637\) | −5.44484e6 | −0.531663 | ||||||||
\(638\) | 2.70435e6 | 0.263033 | ||||||||
\(639\) | −5.07684e6 | −0.491860 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.81586e7 | 1.74557 | 0.872784 | − | 0.488107i | \(-0.162312\pi\) | ||||
0.872784 | + | 0.488107i | \(0.162312\pi\) | |||||||
\(642\) | −4.03116e6 | −0.386005 | ||||||||
\(643\) | −4.48264e6 | −0.427569 | −0.213784 | − | 0.976881i | \(-0.568579\pi\) | ||||
−0.213784 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(644\) | 2.39494e7 | 2.27552 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.03844e6 | 0.569303 | ||||||||
\(647\) | 1.75122e7 | 1.64467 | 0.822336 | − | 0.569003i | \(-0.192671\pi\) | ||||
0.822336 | + | 0.569003i | \(0.192671\pi\) | |||||||
\(648\) | 536435. | 0.0501857 | ||||||||
\(649\) | 938925. | 0.0875023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.06362e6 | 0.0983639 | ||||||||
\(652\) | −2.19394e6 | −0.202118 | ||||||||
\(653\) | −1.89639e7 | −1.74039 | −0.870193 | − | 0.492711i | \(-0.836006\pi\) | ||||
−0.870193 | + | 0.492711i | \(0.836006\pi\) | |||||||
\(654\) | 1.06931e7 | 0.977599 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.59418e6 | 0.144636 | ||||||||
\(657\) | 5.58496e6 | 0.504786 | ||||||||
\(658\) | 3.18856e7 | 2.87098 | ||||||||
\(659\) | 23732.7 | 0.00212879 | 0.00106440 | − | 0.999999i | \(-0.499661\pi\) | ||||
0.00106440 | + | 0.999999i | \(0.499661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.09938e7 | 0.978686 | 0.489343 | − | 0.872091i | \(-0.337237\pi\) | ||||
0.489343 | + | 0.872091i | \(0.337237\pi\) | |||||||
\(662\) | −2.98568e7 | −2.64788 | ||||||||
\(663\) | −3.04281e6 | −0.268839 | ||||||||
\(664\) | −7.27821e6 | −0.640626 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.97706e6 | −0.784239 | ||||||||
\(667\) | 8.42112e6 | 0.732918 | ||||||||
\(668\) | −1.36070e7 | −1.17983 | ||||||||
\(669\) | 268810. | 0.0232209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.65477e6 | 0.399110 | ||||||||
\(672\) | −1.28517e7 | −1.09783 | ||||||||
\(673\) | 1.19040e6 | 0.101310 | 0.0506552 | − | 0.998716i | \(-0.483869\pi\) | ||||
0.0506552 | + | 0.998716i | \(0.483869\pi\) | |||||||
\(674\) | −1.30994e7 | −1.11072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.97925e6 | −0.839907 | ||||||||
\(677\) | −2.03890e7 | −1.70972 | −0.854860 | − | 0.518859i | \(-0.826357\pi\) | ||||
−0.854860 | + | 0.518859i | \(0.826357\pi\) | |||||||
\(678\) | −1.05456e7 | −0.881046 | ||||||||
\(679\) | −2.44016e7 | −2.03116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.82918e6 | 0.316401 | ||||||||
\(682\) | 687116. | 0.0565678 | ||||||||
\(683\) | −2.37020e7 | −1.94416 | −0.972082 | − | 0.234640i | \(-0.924609\pi\) | ||||
−0.972082 | + | 0.234640i | \(0.924609\pi\) | |||||||
\(684\) | 2.53644e6 | 0.207293 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.70134e6 | −0.219164 | ||||||||
\(687\) | −1.18651e7 | −0.959137 | ||||||||
\(688\) | −1.38300e7 | −1.11391 | ||||||||
\(689\) | 9.93651e6 | 0.797418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.32012e7 | −1.05176 | −0.525881 | − | 0.850558i | \(-0.676264\pi\) | ||||
−0.525881 | + | 0.850558i | \(0.676264\pi\) | |||||||
\(692\) | 1.02336e7 | 0.812387 | ||||||||
\(693\) | 1.74911e6 | 0.138352 | ||||||||
\(694\) | −3.44278e7 | −2.71338 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.91788e6 | 0.150071 | ||||||||
\(697\) | −2.37102e6 | −0.184865 | ||||||||
\(698\) | −4.38604e6 | −0.340749 | ||||||||
\(699\) | −2.88056e6 | −0.222989 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.76550e6 | 0.750584 | 0.375292 | − | 0.926907i | \(-0.377542\pi\) | ||||
0.375292 | + | 0.926907i | \(0.377542\pi\) | |||||||
\(702\) | −2.26286e6 | −0.173306 | ||||||||
\(703\) | −9.74392e6 | −0.743610 | ||||||||
\(704\) | −5.87080e6 | −0.446442 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.19677e6 | −0.467900 | ||||||||
\(707\) | 9.16884e6 | 0.689868 | ||||||||
\(708\) | 2.90067e6 | 0.217478 | ||||||||
\(709\) | −6.77780e6 | −0.506376 | −0.253188 | − | 0.967417i | \(-0.581479\pi\) | ||||
−0.253188 | + | 0.967417i | \(0.581479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.40242e6 | −0.104041 | ||||||||
\(712\) | 1.05985e7 | 0.783506 | ||||||||
\(713\) | 2.13963e6 | 0.157621 | ||||||||
\(714\) | 1.28642e7 | 0.944361 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.25576e7 | 0.915429 | ||||||||
\(717\) | 1.12980e7 | 0.820739 | ||||||||
\(718\) | 3.37302e6 | 0.244179 | ||||||||
\(719\) | −9.77686e6 | −0.705305 | −0.352653 | − | 0.935754i | \(-0.614720\pi\) | ||||
−0.352653 | + | 0.935754i | \(0.614720\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.69360e7 | −1.21331 | ||||||||
\(722\) | −1.63589e7 | −1.16791 | ||||||||
\(723\) | −9.70317e6 | −0.690348 | ||||||||
\(724\) | −1.93291e7 | −1.37046 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.12995e6 | 0.0795642 | ||||||||
\(727\) | −1.13969e7 | −0.799745 | −0.399873 | − | 0.916571i | \(-0.630946\pi\) | ||||
−0.399873 | + | 0.916571i | \(0.630946\pi\) | |||||||
\(728\) | −5.28176e6 | −0.369360 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.05694e7 | 1.42373 | ||||||||
\(732\) | 1.43802e7 | 0.991946 | ||||||||
\(733\) | −6.58492e6 | −0.452679 | −0.226340 | − | 0.974048i | \(-0.572676\pi\) | ||||
−0.226340 | + | 0.974048i | \(0.572676\pi\) | |||||||
\(734\) | −2.46605e7 | −1.68951 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.58529e7 | −1.75920 | ||||||||
\(737\) | 4.29808e6 | 0.291478 | ||||||||
\(738\) | −1.76327e6 | −0.119173 | ||||||||
\(739\) | −1.51924e7 | −1.02333 | −0.511664 | − | 0.859186i | \(-0.670971\pi\) | ||||
−0.511664 | + | 0.859186i | \(0.670971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.45616e6 | −0.164328 | ||||||||
\(742\) | −4.20090e7 | −2.80112 | ||||||||
\(743\) | −6.92543e6 | −0.460230 | −0.230115 | − | 0.973163i | \(-0.573910\pi\) | ||||
−0.230115 | + | 0.973163i | \(0.573910\pi\) | |||||||
\(744\) | 487292. | 0.0322743 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.31030e7 | 2.17781 | ||||||||
\(747\) | −7.21045e6 | −0.472782 | ||||||||
\(748\) | 4.69401e6 | 0.306754 | ||||||||
\(749\) | −9.32156e6 | −0.607133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.53073e7 | −0.990370 | −0.495185 | − | 0.868788i | \(-0.664900\pi\) | ||||
−0.495185 | + | 0.868788i | \(0.664900\pi\) | |||||||
\(752\) | −1.30843e7 | −0.843737 | ||||||||
\(753\) | −8.26898e6 | −0.531452 | ||||||||
\(754\) | −8.09024e6 | −0.518242 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.40361e6 | 0.343858 | ||||||||
\(757\) | 9.00842e6 | 0.571359 | 0.285679 | − | 0.958325i | \(-0.407781\pi\) | ||||
0.285679 | + | 0.958325i | \(0.407781\pi\) | |||||||
\(758\) | −1.40080e7 | −0.885531 | ||||||||
\(759\) | 3.51857e6 | 0.221698 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.62103e7 | 1.01468 | 0.507339 | − | 0.861746i | \(-0.330629\pi\) | ||||
0.507339 | + | 0.861746i | \(0.330629\pi\) | |||||||
\(762\) | 1.84367e6 | 0.115026 | ||||||||
\(763\) | 2.47265e7 | 1.53763 | ||||||||
\(764\) | 1.22187e7 | 0.757343 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.31740e7 | 2.04280 | ||||||||
\(767\) | −2.80886e6 | −0.172402 | ||||||||
\(768\) | 1.62404e6 | 0.0993558 | ||||||||
\(769\) | 1.67909e7 | 1.02390 | 0.511950 | − | 0.859015i | \(-0.328923\pi\) | ||||
0.511950 | + | 0.859015i | \(0.328923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.17619e6 | 0.434768 | ||||||||
\(772\) | −1.16516e7 | −0.703629 | ||||||||
\(773\) | 1.62605e7 | 0.978780 | 0.489390 | − | 0.872065i | \(-0.337219\pi\) | ||||
0.489390 | + | 0.872065i | \(0.337219\pi\) | |||||||
\(774\) | 1.52969e7 | 0.917806 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.11794e7 | −0.666445 | ||||||||
\(777\) | −2.07583e7 | −1.23350 | ||||||||
\(778\) | −86101.7 | −0.00509991 | ||||||||
\(779\) | −1.91389e6 | −0.112999 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.58393e6 | −0.444904 | ||||||||
\(782\) | 2.58781e7 | 1.51327 | ||||||||
\(783\) | 1.90002e6 | 0.110753 | ||||||||
\(784\) | −9.44604e6 | −0.548858 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.21698e6 | 0.301205 | ||||||||
\(787\) | −5.01128e6 | −0.288411 | −0.144206 | − | 0.989548i | \(-0.546063\pi\) | ||||
−0.144206 | + | 0.989548i | \(0.546063\pi\) | |||||||
\(788\) | −1.00358e7 | −0.575753 | ||||||||
\(789\) | −8.82506e6 | −0.504691 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.43855e7 | −1.38577 | ||||||||
\(792\) | 801342. | 0.0453947 | ||||||||
\(793\) | −1.39251e7 | −0.786348 | ||||||||
\(794\) | −3.24096e7 | −1.82441 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.58247e7 | 1.44461 | ||||||||
\(797\) | 3.07160e7 | 1.71285 | 0.856424 | − | 0.516273i | \(-0.172681\pi\) | ||||
0.856424 | + | 0.516273i | \(0.172681\pi\) | |||||||
\(798\) | 1.03840e7 | 0.577242 | ||||||||
\(799\) | 1.94604e7 | 1.07841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.04998e7 | 0.578227 | ||||||||
\(802\) | −4.95511e7 | −2.72030 | ||||||||
\(803\) | 8.34297e6 | 0.456596 | ||||||||
\(804\) | 1.32783e7 | 0.724438 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.05556e6 | −0.111453 | ||||||||
\(807\) | −1.18924e7 | −0.642812 | ||||||||
\(808\) | 4.20064e6 | 0.226353 | ||||||||
\(809\) | 6.14509e6 | 0.330108 | 0.165054 | − | 0.986284i | \(-0.447220\pi\) | ||||
0.165054 | + | 0.986284i | \(0.447220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.46687e7 | −0.783138 | −0.391569 | − | 0.920149i | \(-0.628068\pi\) | ||||
−0.391569 | + | 0.920149i | \(0.628068\pi\) | |||||||
\(812\) | 1.93191e7 | 1.02825 | ||||||||
\(813\) | −565780. | −0.0300208 | ||||||||
\(814\) | −1.34102e7 | −0.709371 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.27886e6 | −0.277533 | ||||||||
\(817\) | 1.66036e7 | 0.870257 | ||||||||
\(818\) | 4.22894e7 | 2.20978 | ||||||||
\(819\) | −5.23258e6 | −0.272588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.54951e7 | −0.802300 | −0.401150 | − | 0.916012i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916012i | \(0.631389\pi\) | |||||||
\(822\) | −1.58864e7 | −0.820060 | ||||||||
\(823\) | 2.53285e7 | 1.30349 | 0.651747 | − | 0.758436i | \(-0.274036\pi\) | ||||
0.651747 | + | 0.758436i | \(0.274036\pi\) | |||||||
\(824\) | −7.75912e6 | −0.398102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.18751e7 | 0.605603 | ||||||||
\(827\) | −6.01962e6 | −0.306059 | −0.153030 | − | 0.988222i | \(-0.548903\pi\) | ||||
−0.153030 | + | 0.988222i | \(0.548903\pi\) | |||||||
\(828\) | 1.08701e7 | 0.551008 | ||||||||
\(829\) | −2.70703e7 | −1.36807 | −0.684033 | − | 0.729451i | \(-0.739775\pi\) | ||||
−0.684033 | + | 0.729451i | \(0.739775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.29882e7 | 0.652449 | ||||||||
\(832\) | 1.75629e7 | 0.879605 | ||||||||
\(833\) | 1.40491e7 | 0.701514 | ||||||||
\(834\) | 3.35686e6 | 0.167116 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.78901e6 | 0.187504 | ||||||||
\(837\) | 482755. | 0.0238184 | ||||||||
\(838\) | −3.76349e7 | −1.85132 | ||||||||
\(839\) | 2.29868e7 | 1.12739 | 0.563694 | − | 0.825984i | \(-0.309380\pi\) | ||||
0.563694 | + | 0.825984i | \(0.309380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37181e7 | −0.668814 | ||||||||
\(842\) | −5.42731e7 | −2.63818 | ||||||||
\(843\) | −1.29546e6 | −0.0627847 | ||||||||
\(844\) | −1.85486e7 | −0.896303 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.44721e7 | 0.695196 | ||||||||
\(847\) | 2.61287e6 | 0.125144 | ||||||||
\(848\) | 1.72385e7 | 0.823208 | ||||||||
\(849\) | −81541.1 | −0.00388246 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.17582e7 | −1.97660 | ||||||||
\(852\) | −2.34294e7 | −1.10576 | ||||||||
\(853\) | −3.27587e7 | −1.54154 | −0.770768 | − | 0.637116i | \(-0.780127\pi\) | ||||
−0.770768 | + | 0.637116i | \(0.780127\pi\) | |||||||
\(854\) | 5.88716e7 | 2.76224 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.27060e6 | −0.199207 | ||||||||
\(857\) | −5.91710e6 | −0.275205 | −0.137603 | − | 0.990488i | \(-0.543940\pi\) | ||||
−0.137603 | + | 0.990488i | \(0.543940\pi\) | |||||||
\(858\) | −3.38032e6 | −0.156762 | ||||||||
\(859\) | −3.88859e7 | −1.79808 | −0.899041 | − | 0.437865i | \(-0.855735\pi\) | ||||
−0.899041 | + | 0.437865i | \(0.855735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.07734e6 | −0.187443 | ||||||||
\(862\) | −3.77121e7 | −1.72867 | ||||||||
\(863\) | 7.21944e6 | 0.329972 | 0.164986 | − | 0.986296i | \(-0.447242\pi\) | ||||
0.164986 | + | 0.986296i | \(0.447242\pi\) | |||||||
\(864\) | −5.83308e6 | −0.265836 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.34940e7 | −0.611430 | ||||||||
\(867\) | −4.92745e6 | −0.222625 | ||||||||
\(868\) | 4.90858e6 | 0.221134 | ||||||||
\(869\) | −2.09497e6 | −0.0941086 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.28580e7 | −0.574286 | ||||||||
\(872\) | 1.13283e7 | 0.504514 | ||||||||
\(873\) | −1.10753e7 | −0.491837 | ||||||||
\(874\) | 2.08889e7 | 0.924988 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.57744e7 | 1.13482 | ||||||||
\(877\) | 2.38159e7 | 1.04561 | 0.522803 | − | 0.852453i | \(-0.324886\pi\) | ||||
0.522803 | + | 0.852453i | \(0.324886\pi\) | |||||||
\(878\) | −6.76842e7 | −2.96313 | ||||||||
\(879\) | −1.67106e7 | −0.729493 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.82240e6 | −0.426361 | −0.213181 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213181 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(882\) | 1.04480e7 | 0.452231 | ||||||||
\(883\) | −175255. | −0.00756430 | −0.00378215 | − | 0.999993i | \(-0.501204\pi\) | ||||
−0.00378215 | + | 0.999993i | \(0.501204\pi\) | |||||||
\(884\) | −1.40424e7 | −0.604383 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.77834e6 | −0.204500 | ||||||||
\(887\) | 4.60415e7 | 1.96490 | 0.982450 | − | 0.186524i | \(-0.0597221\pi\) | ||||
0.982450 | + | 0.186524i | \(0.0597221\pi\) | |||||||
\(888\) | −9.51028e6 | −0.404726 | ||||||||
\(889\) | 4.26325e6 | 0.180920 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.24054e6 | 0.0522035 | ||||||||
\(893\) | 1.57084e7 | 0.659179 | ||||||||
\(894\) | 1.69292e7 | 0.708423 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.85565e7 | −1.18833 | ||||||||
\(897\) | −1.05261e7 | −0.436802 | ||||||||
\(898\) | 1.95136e7 | 0.807507 | ||||||||
\(899\) | 1.72596e6 | 0.0712248 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.56388e7 | −1.05217 | ||||||||
\(902\) | −2.63402e6 | −0.107796 | ||||||||
\(903\) | 3.53722e7 | 1.44358 | ||||||||
\(904\) | −1.11720e7 | −0.454685 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.54129e6 | −0.102857 | ||||||||
\(907\) | 3.68866e7 | 1.48885 | 0.744425 | − | 0.667706i | \(-0.232724\pi\) | ||||
0.744425 | + | 0.667706i | \(0.232724\pi\) | |||||||
\(908\) | 1.76715e7 | 0.711309 | ||||||||
\(909\) | 4.16153e6 | 0.167049 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.44197e7 | −1.37408 | −0.687038 | − | 0.726622i | \(-0.741089\pi\) | ||||
−0.687038 | + | 0.726622i | \(0.741089\pi\) | |||||||
\(912\) | −4.26110e6 | −0.169643 | ||||||||
\(913\) | −1.07712e7 | −0.427647 | ||||||||
\(914\) | 6.43509e7 | 2.54794 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.47570e7 | −2.15626 | ||||||||
\(917\) | 1.20636e7 | 0.473755 | ||||||||
\(918\) | 5.83878e6 | 0.228673 | ||||||||
\(919\) | −1.33270e7 | −0.520527 | −0.260263 | − | 0.965538i | \(-0.583809\pi\) | ||||
−0.260263 | + | 0.965538i | \(0.583809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.54220e6 | −0.176448 | ||||||||
\(922\) | 3.74719e6 | 0.145171 | ||||||||
\(923\) | 2.26878e7 | 0.876574 | ||||||||
\(924\) | 8.07206e6 | 0.311032 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.67248e7 | −1.02421 | ||||||||
\(927\) | −7.68688e6 | −0.293799 | ||||||||
\(928\) | −2.08546e7 | −0.794935 | ||||||||
\(929\) | 2.43196e7 | 0.924521 | 0.462260 | − | 0.886744i | \(-0.347039\pi\) | ||||
0.462260 | + | 0.886744i | \(0.347039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.13405e7 | 0.428802 | ||||||||
\(932\) | −1.32936e7 | −0.501307 | ||||||||
\(933\) | −4.03660e6 | −0.151814 | ||||||||
\(934\) | −1.62714e7 | −0.610322 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.39727e6 | −0.0894390 | ||||||||
\(937\) | 3.18520e7 | 1.18519 | 0.592595 | − | 0.805501i | \(-0.298104\pi\) | ||||
0.592595 | + | 0.805501i | \(0.298104\pi\) | |||||||
\(938\) | 5.43603e7 | 2.01732 | ||||||||
\(939\) | 7.42631e6 | 0.274859 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.35961e7 | 1.97315 | 0.986573 | − | 0.163318i | \(-0.0522197\pi\) | ||||
0.986573 | + | 0.163318i | \(0.0522197\pi\) | |||||||
\(942\) | 3.52924e7 | 1.29585 | ||||||||
\(943\) | −8.20212e6 | −0.300363 | ||||||||
\(944\) | −4.87299e6 | −0.177978 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.28509e7 | 0.830186 | ||||||||
\(947\) | 1.82063e7 | 0.659700 | 0.329850 | − | 0.944033i | \(-0.393002\pi\) | ||||
0.329850 | + | 0.944033i | \(0.393002\pi\) | |||||||
\(948\) | −6.47211e6 | −0.233897 | ||||||||
\(949\) | −2.49586e7 | −0.899610 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.93640e7 | 1.05284 | ||||||||
\(952\) | 1.36283e7 | 0.487360 | ||||||||
\(953\) | −1.33257e6 | −0.0475289 | −0.0237645 | − | 0.999718i | \(-0.507565\pi\) | ||||
−0.0237645 | + | 0.999718i | \(0.507565\pi\) | |||||||
\(954\) | −1.90669e7 | −0.678281 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.21399e7 | 1.84512 | ||||||||
\(957\) | 2.83830e6 | 0.100180 | ||||||||
\(958\) | −5.23335e7 | −1.84232 | ||||||||
\(959\) | −3.67353e7 | −1.28984 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.81906e7 | −0.984682 | ||||||||
\(962\) | 4.01175e7 | 1.39764 | ||||||||
\(963\) | −4.23084e6 | −0.147015 | ||||||||
\(964\) | −4.47797e7 | −1.55199 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.45014e7 | 1.53437 | ||||||||
\(967\) | −5.74029e7 | −1.97409 | −0.987047 | − | 0.160429i | \(-0.948712\pi\) | ||||
−0.987047 | + | 0.160429i | \(0.948712\pi\) | |||||||
\(968\) | 1.19707e6 | 0.0410610 | ||||||||
\(969\) | 6.33755e6 | 0.216826 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.56758e7 | 1.21430 | 0.607149 | − | 0.794588i | \(-0.292313\pi\) | ||||
0.607149 | + | 0.794588i | \(0.292313\pi\) | |||||||
\(972\) | 2.45258e6 | 0.0832639 | ||||||||
\(973\) | 7.76232e6 | 0.262851 | ||||||||
\(974\) | −6.26137e7 | −2.11481 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.41581e7 | −0.811780 | ||||||||
\(977\) | 5.30033e7 | 1.77651 | 0.888253 | − | 0.459354i | \(-0.151919\pi\) | ||||
0.888253 | + | 0.459354i | \(0.151919\pi\) | |||||||
\(978\) | −4.07665e6 | −0.136288 | ||||||||
\(979\) | 1.56848e7 | 0.523026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12228e7 | 0.372331 | ||||||||
\(982\) | 3.78068e7 | 1.25110 | ||||||||
\(983\) | 2.40146e7 | 0.792667 | 0.396333 | − | 0.918107i | \(-0.370282\pi\) | ||||
0.396333 | + | 0.918107i | \(0.370282\pi\) | |||||||
\(984\) | −1.86800e6 | −0.0615020 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.08750e7 | 0.683806 | ||||||||
\(987\) | 3.34650e7 | 1.09345 | ||||||||
\(988\) | −1.13351e7 | −0.369430 | ||||||||
\(989\) | 7.11559e7 | 2.31324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.40921e7 | 1.74964 | 0.874822 | − | 0.484444i | \(-0.160978\pi\) | ||||
0.874822 | + | 0.484444i | \(0.160978\pi\) | |||||||
\(992\) | −5.29870e6 | −0.170958 | ||||||||
\(993\) | −3.13358e7 | −1.00848 | ||||||||
\(994\) | −9.59182e7 | −3.07918 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.32759e7 | −1.06287 | ||||||||
\(997\) | 4.73500e7 | 1.50863 | 0.754314 | − | 0.656513i | \(-0.227969\pi\) | ||||
0.754314 | + | 0.656513i | \(0.227969\pi\) | |||||||
\(998\) | 2.96378e7 | 0.941931 | ||||||||
\(999\) | −9.42174e6 | −0.298688 |
(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.1.11 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.23 | yes | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.4 | ✓ | 26 | ||
5.4 | even | 2 | 825.6.a.v.1.3 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.4 | ✓ | 26 | 5.3 | odd | 4 | ||
165.6.c.b.34.23 | yes | 26 | 5.2 | odd | 4 | ||
825.6.a.v.1.3 | 13 | 5.4 | even | 2 | |||
825.6.a.y.1.11 | 13 | 1.1 | even | 1 | trivial |