Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(172.412606299\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-6.09504\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.09504 | 1.43101 | 0.715507 | − | 0.698605i | \(-0.246196\pi\) | ||||
0.715507 | + | 0.698605i | \(0.246196\pi\) | |||||||
\(3\) | −11.1803 | −0.717218 | −0.358609 | − | 0.933488i | \(-0.616749\pi\) | ||||
−0.358609 | + | 0.933488i | \(0.616749\pi\) | |||||||
\(4\) | 33.5297 | 1.04780 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −90.5052 | −1.02635 | ||||||||
\(7\) | −223.489 | −1.72389 | −0.861946 | − | 0.507000i | \(-0.830755\pi\) | ||||
−0.861946 | + | 0.507000i | \(0.830755\pi\) | |||||||
\(8\) | 12.3830 | 0.0684073 | ||||||||
\(9\) | −118.000 | −0.485598 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −631.897 | −1.57458 | −0.787289 | − | 0.616584i | \(-0.788516\pi\) | ||||
−0.787289 | + | 0.616584i | \(0.788516\pi\) | |||||||
\(12\) | −374.873 | −0.751504 | ||||||||
\(13\) | −28.5724 | −0.0468909 | −0.0234454 | − | 0.999725i | \(-0.507464\pi\) | ||||
−0.0234454 | + | 0.999725i | \(0.507464\pi\) | |||||||
\(14\) | −1809.15 | −2.46692 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −972.709 | −0.949911 | ||||||||
\(17\) | 1743.07 | 1.46283 | 0.731414 | − | 0.681933i | \(-0.238861\pi\) | ||||
0.731414 | + | 0.681933i | \(0.238861\pi\) | |||||||
\(18\) | −955.217 | −0.694897 | ||||||||
\(19\) | −2027.92 | −1.28874 | −0.644371 | − | 0.764713i | \(-0.722881\pi\) | ||||
−0.644371 | + | 0.764713i | \(0.722881\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2498.68 | 1.23641 | ||||||||
\(22\) | −5115.23 | −2.25324 | ||||||||
\(23\) | −2980.86 | −1.17496 | −0.587479 | − | 0.809239i | \(-0.699880\pi\) | ||||
−0.587479 | + | 0.809239i | \(0.699880\pi\) | |||||||
\(24\) | −138.447 | −0.0490630 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −231.295 | −0.0671015 | ||||||||
\(27\) | 4036.10 | 1.06550 | ||||||||
\(28\) | −7493.51 | −1.80630 | ||||||||
\(29\) | 766.139 | 0.169166 | 0.0845829 | − | 0.996416i | \(-0.473044\pi\) | ||||
0.0845829 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8355.33 | −1.56156 | −0.780781 | − | 0.624805i | \(-0.785178\pi\) | ||||
−0.780781 | + | 0.624805i | \(0.785178\pi\) | |||||||
\(32\) | −8270.38 | −1.42774 | ||||||||
\(33\) | 7064.81 | 1.12932 | ||||||||
\(34\) | 14110.3 | 2.09333 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3956.51 | −0.508811 | ||||||||
\(37\) | −14892.6 | −1.78841 | −0.894204 | − | 0.447661i | \(-0.852257\pi\) | ||||
−0.894204 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(38\) | −16416.1 | −1.84421 | ||||||||
\(39\) | 319.449 | 0.0336310 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5342.20 | −0.496319 | −0.248159 | − | 0.968719i | \(-0.579826\pi\) | ||||
−0.248159 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(42\) | 20226.9 | 1.76932 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | −21187.3 | −1.64985 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24130.2 | −1.68138 | ||||||||
\(47\) | 6282.09 | 0.414820 | 0.207410 | − | 0.978254i | \(-0.433497\pi\) | ||||
0.207410 | + | 0.978254i | \(0.433497\pi\) | |||||||
\(48\) | 10875.2 | 0.681294 | ||||||||
\(49\) | 33140.1 | 1.97181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19488.1 | −1.04917 | ||||||||
\(52\) | −958.024 | −0.0491324 | ||||||||
\(53\) | 915.172 | 0.0447521 | 0.0223760 | − | 0.999750i | \(-0.492877\pi\) | ||||
0.0223760 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(54\) | 32672.4 | 1.52474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2767.47 | −0.117927 | ||||||||
\(57\) | 22672.8 | 0.924310 | ||||||||
\(58\) | 6201.92 | 0.242079 | ||||||||
\(59\) | −14644.5 | −0.547704 | −0.273852 | − | 0.961772i | \(-0.588298\pi\) | ||||
−0.273852 | + | 0.961772i | \(0.588298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21324.9 | −0.733775 | −0.366887 | − | 0.930265i | \(-0.619577\pi\) | ||||
−0.366887 | + | 0.930265i | \(0.619577\pi\) | |||||||
\(62\) | −67636.7 | −2.23462 | ||||||||
\(63\) | 26371.7 | 0.837118 | ||||||||
\(64\) | −35822.4 | −1.09321 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 57189.9 | 1.61607 | ||||||||
\(67\) | 12868.9 | 0.350232 | 0.175116 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175116 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(68\) | 58444.8 | 1.53276 | ||||||||
\(69\) | 33327.0 | 0.842702 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56454.6 | 1.32909 | 0.664544 | − | 0.747249i | \(-0.268626\pi\) | ||||
0.664544 | + | 0.747249i | \(0.268626\pi\) | |||||||
\(72\) | −1461.20 | −0.0332184 | ||||||||
\(73\) | 25591.3 | 0.562064 | 0.281032 | − | 0.959698i | \(-0.409323\pi\) | ||||
0.281032 | + | 0.959698i | \(0.409323\pi\) | |||||||
\(74\) | −120556. | −2.55924 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −67995.4 | −1.35035 | ||||||||
\(77\) | 141222. | 2.71440 | ||||||||
\(78\) | 2585.95 | 0.0481265 | ||||||||
\(79\) | 5795.13 | 0.104471 | 0.0522355 | − | 0.998635i | \(-0.483365\pi\) | ||||
0.0522355 | + | 0.998635i | \(0.483365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16450.9 | −0.278597 | ||||||||
\(82\) | −43245.4 | −0.710240 | ||||||||
\(83\) | 7857.24 | 0.125192 | 0.0625958 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625958 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(84\) | 83779.9 | 1.29551 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14967.7 | 0.218228 | ||||||||
\(87\) | −8565.68 | −0.121329 | ||||||||
\(88\) | −7824.80 | −0.107713 | ||||||||
\(89\) | −7560.11 | −0.101170 | −0.0505852 | − | 0.998720i | \(-0.516109\pi\) | ||||
−0.0505852 | + | 0.998720i | \(0.516109\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6385.60 | 0.0808348 | ||||||||
\(92\) | −99947.5 | −1.23113 | ||||||||
\(93\) | 93415.3 | 1.11998 | ||||||||
\(94\) | 50853.8 | 0.593613 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 92465.6 | 1.02400 | ||||||||
\(97\) | −111712. | −1.20551 | −0.602754 | − | 0.797927i | \(-0.705930\pi\) | ||||
−0.602754 | + | 0.797927i | \(0.705930\pi\) | |||||||
\(98\) | 268271. | 2.82168 | ||||||||
\(99\) | 74563.9 | 0.764611 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10492.3 | 0.102345 | 0.0511724 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511724 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(102\) | −157757. | −1.50137 | ||||||||
\(103\) | 11286.6 | 0.104826 | 0.0524130 | − | 0.998625i | \(-0.483309\pi\) | ||||
0.0524130 | + | 0.998625i | \(0.483309\pi\) | |||||||
\(104\) | −353.813 | −0.00320768 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7408.36 | 0.0640409 | ||||||||
\(107\) | −39045.4 | −0.329693 | −0.164847 | − | 0.986319i | \(-0.552713\pi\) | ||||
−0.164847 | + | 0.986319i | \(0.552713\pi\) | |||||||
\(108\) | 135329. | 1.11643 | ||||||||
\(109\) | −14622.8 | −0.117887 | −0.0589433 | − | 0.998261i | \(-0.518773\pi\) | ||||
−0.0589433 | + | 0.998261i | \(0.518773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 166504. | 1.28268 | ||||||||
\(112\) | 217389. | 1.63755 | ||||||||
\(113\) | 859.121 | 0.00632934 | 0.00316467 | − | 0.999995i | \(-0.498993\pi\) | ||||
0.00316467 | + | 0.999995i | \(0.498993\pi\) | |||||||
\(114\) | 183537. | 1.32270 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 25688.4 | 0.177252 | ||||||||
\(117\) | 3371.55 | 0.0227701 | ||||||||
\(118\) | −118548. | −0.783772 | ||||||||
\(119\) | −389557. | −2.52176 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 238242. | 1.47930 | ||||||||
\(122\) | −172626. | −1.05004 | ||||||||
\(123\) | 59727.6 | 0.355969 | ||||||||
\(124\) | −280152. | −1.63621 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 213480. | 1.19793 | ||||||||
\(127\) | −193396. | −1.06399 | −0.531997 | − | 0.846746i | \(-0.678558\pi\) | ||||
−0.531997 | + | 0.846746i | \(0.678558\pi\) | |||||||
\(128\) | −25331.5 | −0.136658 | ||||||||
\(129\) | −20672.4 | −0.109375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −269599. | −1.37259 | −0.686293 | − | 0.727325i | \(-0.740763\pi\) | ||||
−0.686293 | + | 0.727325i | \(0.740763\pi\) | |||||||
\(132\) | 236881. | 1.18330 | ||||||||
\(133\) | 453216. | 2.22165 | ||||||||
\(134\) | 104175. | 0.501187 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21584.6 | 0.100068 | ||||||||
\(137\) | −148987. | −0.678183 | −0.339091 | − | 0.940753i | \(-0.610120\pi\) | ||||
−0.339091 | + | 0.940753i | \(0.610120\pi\) | |||||||
\(138\) | 269784. | 1.20592 | ||||||||
\(139\) | −16355.6 | −0.0718008 | −0.0359004 | − | 0.999355i | \(-0.511430\pi\) | ||||
−0.0359004 | + | 0.999355i | \(0.511430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70235.8 | −0.297516 | ||||||||
\(142\) | 457003. | 1.90194 | ||||||||
\(143\) | 18054.8 | 0.0738333 | ||||||||
\(144\) | 114780. | 0.461275 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 207163. | 0.804322 | ||||||||
\(147\) | −370518. | −1.41422 | ||||||||
\(148\) | −499345. | −1.87390 | ||||||||
\(149\) | −150536. | −0.555489 | −0.277744 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277744 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 428141. | 1.52807 | 0.764037 | − | 0.645172i | \(-0.223214\pi\) | ||||
0.764037 | + | 0.645172i | \(0.223214\pi\) | |||||||
\(152\) | −25111.8 | −0.0881594 | ||||||||
\(153\) | −205683. | −0.710346 | ||||||||
\(154\) | 1.14320e6 | 3.88435 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10711.0 | 0.0352387 | ||||||||
\(157\) | 434190. | 1.40582 | 0.702912 | − | 0.711277i | \(-0.251883\pi\) | ||||
0.702912 | + | 0.711277i | \(0.251883\pi\) | |||||||
\(158\) | 46911.8 | 0.149499 | ||||||||
\(159\) | −10231.9 | −0.0320970 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 666189. | 2.02550 | ||||||||
\(162\) | −133171. | −0.398677 | ||||||||
\(163\) | 571830. | 1.68577 | 0.842884 | − | 0.538095i | \(-0.180856\pi\) | ||||
0.842884 | + | 0.538095i | \(0.180856\pi\) | |||||||
\(164\) | −179122. | −0.520044 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 63604.7 | 0.179151 | ||||||||
\(167\) | −605744. | −1.68073 | −0.840365 | − | 0.542020i | \(-0.817660\pi\) | ||||
−0.840365 | + | 0.542020i | \(0.817660\pi\) | |||||||
\(168\) | 30941.2 | 0.0845793 | ||||||||
\(169\) | −370477. | −0.997801 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 239295. | 0.625810 | ||||||||
\(172\) | 61996.4 | 0.159789 | ||||||||
\(173\) | 85238.8 | 0.216532 | 0.108266 | − | 0.994122i | \(-0.465470\pi\) | ||||
0.108266 | + | 0.994122i | \(0.465470\pi\) | |||||||
\(174\) | −69339.6 | −0.173623 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 614652. | 1.49571 | ||||||||
\(177\) | 163731. | 0.392823 | ||||||||
\(178\) | −61199.4 | −0.144776 | ||||||||
\(179\) | 77941.8 | 0.181818 | 0.0909092 | − | 0.995859i | \(-0.471023\pi\) | ||||
0.0909092 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −347661. | −0.788787 | −0.394393 | − | 0.918942i | \(-0.629045\pi\) | ||||
−0.394393 | + | 0.918942i | \(0.629045\pi\) | |||||||
\(182\) | 51691.7 | 0.115676 | ||||||||
\(183\) | 238420. | 0.526277 | ||||||||
\(184\) | −36912.2 | −0.0803757 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 756201. | 1.60271 | ||||||||
\(187\) | −1.10144e6 | −2.30334 | ||||||||
\(188\) | 210637. | 0.434650 | ||||||||
\(189\) | −902023. | −1.83680 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −192163. | −0.381142 | −0.190571 | − | 0.981673i | \(-0.561034\pi\) | ||||
−0.190571 | + | 0.981673i | \(0.561034\pi\) | |||||||
\(192\) | 400506. | 0.784072 | ||||||||
\(193\) | 271724. | 0.525091 | 0.262546 | − | 0.964920i | \(-0.415438\pi\) | ||||
0.262546 | + | 0.964920i | \(0.415438\pi\) | |||||||
\(194\) | −904313. | −1.72510 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.11118e6 | 2.06606 | ||||||||
\(197\) | −76788.1 | −0.140971 | −0.0704853 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704853 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(198\) | 603598. | 1.09417 | ||||||||
\(199\) | −694776. | −1.24369 | −0.621845 | − | 0.783140i | \(-0.713617\pi\) | ||||
−0.621845 | + | 0.783140i | \(0.713617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −143879. | −0.251193 | ||||||||
\(202\) | 84935.3 | 0.146457 | ||||||||
\(203\) | −171223. | −0.291624 | ||||||||
\(204\) | −653432. | −1.09932 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 91365.3 | 0.150008 | ||||||||
\(207\) | 351743. | 0.570557 | ||||||||
\(208\) | 27792.6 | 0.0445422 | ||||||||
\(209\) | 1.28143e6 | 2.02923 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −433533. | −0.670372 | −0.335186 | − | 0.942152i | \(-0.608799\pi\) | ||||
−0.335186 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(212\) | 30685.5 | 0.0468914 | ||||||||
\(213\) | −631181. | −0.953246 | ||||||||
\(214\) | −316074. | −0.471796 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 49979.2 | 0.0728878 | ||||||||
\(217\) | 1.86732e6 | 2.69196 | ||||||||
\(218\) | −118372. | −0.168698 | ||||||||
\(219\) | −286119. | −0.403123 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −49803.8 | −0.0685933 | ||||||||
\(222\) | 1.34786e6 | 1.83553 | ||||||||
\(223\) | −1.04204e6 | −1.40320 | −0.701602 | − | 0.712569i | \(-0.747531\pi\) | ||||
−0.701602 | + | 0.712569i | \(0.747531\pi\) | |||||||
\(224\) | 1.84834e6 | 2.46128 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6954.62 | 0.00905737 | ||||||||
\(227\) | −924970. | −1.19141 | −0.595707 | − | 0.803202i | \(-0.703128\pi\) | ||||
−0.595707 | + | 0.803202i | \(0.703128\pi\) | |||||||
\(228\) | 760211. | 0.968495 | ||||||||
\(229\) | −137140. | −0.172812 | −0.0864062 | − | 0.996260i | \(-0.527538\pi\) | ||||
−0.0864062 | + | 0.996260i | \(0.527538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.57890e6 | −1.94682 | ||||||||
\(232\) | 9487.13 | 0.0115722 | ||||||||
\(233\) | −428602. | −0.517208 | −0.258604 | − | 0.965983i | \(-0.583262\pi\) | ||||
−0.258604 | + | 0.965983i | \(0.583262\pi\) | |||||||
\(234\) | 27292.8 | 0.0325843 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −491027. | −0.573886 | ||||||||
\(237\) | −64791.5 | −0.0749285 | ||||||||
\(238\) | −3.15348e6 | −3.60868 | ||||||||
\(239\) | −1.17134e6 | −1.32645 | −0.663223 | − | 0.748422i | \(-0.730812\pi\) | ||||
−0.663223 | + | 0.748422i | \(0.730812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 119252. | 0.132258 | 0.0661291 | − | 0.997811i | \(-0.478935\pi\) | ||||
0.0661291 | + | 0.997811i | \(0.478935\pi\) | |||||||
\(242\) | 1.92858e6 | 2.11690 | ||||||||
\(243\) | −796846. | −0.865683 | ||||||||
\(244\) | −715018. | −0.768852 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 483497. | 0.509397 | ||||||||
\(247\) | 57942.4 | 0.0604302 | ||||||||
\(248\) | −103464. | −0.106822 | ||||||||
\(249\) | −87846.6 | −0.0897897 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −141272. | −0.141538 | −0.0707690 | − | 0.997493i | \(-0.522545\pi\) | ||||
−0.0707690 | + | 0.997493i | \(0.522545\pi\) | |||||||
\(252\) | 884235. | 0.877135 | ||||||||
\(253\) | 1.88360e6 | 1.85006 | ||||||||
\(254\) | −1.56555e6 | −1.52259 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 941257. | 0.897652 | ||||||||
\(257\) | 196749. | 0.185815 | 0.0929074 | − | 0.995675i | \(-0.470384\pi\) | ||||
0.0929074 | + | 0.995675i | \(0.470384\pi\) | |||||||
\(258\) | −167344. | −0.156517 | ||||||||
\(259\) | 3.32833e6 | 3.08302 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90404.5 | −0.0821465 | ||||||||
\(262\) | −2.18241e6 | −1.96419 | ||||||||
\(263\) | 1.96879e6 | 1.75513 | 0.877565 | − | 0.479457i | \(-0.159166\pi\) | ||||
0.877565 | + | 0.479457i | \(0.159166\pi\) | |||||||
\(264\) | 87483.9 | 0.0772535 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.66880e6 | 3.17922 | ||||||||
\(267\) | 84524.6 | 0.0725612 | ||||||||
\(268\) | 431492. | 0.366974 | ||||||||
\(269\) | −531007. | −0.447424 | −0.223712 | − | 0.974655i | \(-0.571818\pi\) | ||||
−0.223712 | + | 0.974655i | \(0.571818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68769e6 | −1.39595 | −0.697975 | − | 0.716122i | \(-0.745916\pi\) | ||||
−0.697975 | + | 0.716122i | \(0.745916\pi\) | |||||||
\(272\) | −1.69550e6 | −1.38956 | ||||||||
\(273\) | −71393.2 | −0.0579762 | ||||||||
\(274\) | −1.20606e6 | −0.970489 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.11745e6 | 0.882986 | ||||||||
\(277\) | −13630.1 | −0.0106733 | −0.00533665 | − | 0.999986i | \(-0.501699\pi\) | ||||
−0.00533665 | + | 0.999986i | \(0.501699\pi\) | |||||||
\(278\) | −132399. | −0.102748 | ||||||||
\(279\) | 985930. | 0.758291 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.12070e6 | 0.846692 | 0.423346 | − | 0.905968i | \(-0.360855\pi\) | ||||
0.423346 | + | 0.905968i | \(0.360855\pi\) | |||||||
\(282\) | −568562. | −0.425750 | ||||||||
\(283\) | 1.52947e6 | 1.13521 | 0.567605 | − | 0.823301i | \(-0.307870\pi\) | ||||
0.567605 | + | 0.823301i | \(0.307870\pi\) | |||||||
\(284\) | 1.89291e6 | 1.39262 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 146154. | 0.105657 | ||||||||
\(287\) | 1.19392e6 | 0.855600 | ||||||||
\(288\) | 975907. | 0.693309 | ||||||||
\(289\) | 1.61845e6 | 1.13987 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.24898e6 | 0.864613 | ||||||||
\(292\) | 858070. | 0.588932 | ||||||||
\(293\) | 1.58484e6 | 1.07849 | 0.539246 | − | 0.842148i | \(-0.318709\pi\) | ||||
0.539246 | + | 0.842148i | \(0.318709\pi\) | |||||||
\(294\) | −2.99936e6 | −2.02376 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −184416. | −0.122340 | ||||||||
\(297\) | −2.55040e6 | −1.67771 | ||||||||
\(298\) | −1.21860e6 | −0.794912 | ||||||||
\(299\) | 85170.4 | 0.0550948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −413230. | −0.262891 | ||||||||
\(302\) | 3.46582e6 | 2.18670 | ||||||||
\(303\) | −117307. | −0.0734035 | ||||||||
\(304\) | 1.97257e6 | 1.22419 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.66501e6 | −1.01652 | ||||||||
\(307\) | −695751. | −0.421316 | −0.210658 | − | 0.977560i | \(-0.567561\pi\) | ||||
−0.210658 | + | 0.977560i | \(0.567561\pi\) | |||||||
\(308\) | 4.73512e6 | 2.84416 | ||||||||
\(309\) | −126188. | −0.0751831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −988763. | −0.579684 | −0.289842 | − | 0.957075i | \(-0.593603\pi\) | ||||
−0.289842 | + | 0.957075i | \(0.593603\pi\) | |||||||
\(312\) | 3955.75 | 0.00230061 | ||||||||
\(313\) | 3.07551e6 | 1.77442 | 0.887208 | − | 0.461369i | \(-0.152642\pi\) | ||||
0.887208 | + | 0.461369i | \(0.152642\pi\) | |||||||
\(314\) | 3.51479e6 | 2.01176 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 194309. | 0.109465 | ||||||||
\(317\) | −904527. | −0.505561 | −0.252780 | − | 0.967524i | \(-0.581345\pi\) | ||||
−0.252780 | + | 0.967524i | \(0.581345\pi\) | |||||||
\(318\) | −82827.9 | −0.0459313 | ||||||||
\(319\) | −484120. | −0.266365 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 436540. | 0.236462 | ||||||||
\(322\) | 5.39283e6 | 2.89852 | ||||||||
\(323\) | −3.53481e6 | −1.88521 | ||||||||
\(324\) | −551594. | −0.291915 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.62899e6 | 2.41236 | ||||||||
\(327\) | 163488. | 0.0845505 | ||||||||
\(328\) | −66152.7 | −0.0339518 | ||||||||
\(329\) | −1.40398e6 | −0.715105 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.09309e6 | −1.05007 | −0.525034 | − | 0.851081i | \(-0.675947\pi\) | ||||
−0.525034 | + | 0.851081i | \(0.675947\pi\) | |||||||
\(332\) | 263451. | 0.131176 | ||||||||
\(333\) | 1.75733e6 | 0.868446 | ||||||||
\(334\) | −4.90353e6 | −2.40515 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.43049e6 | −1.17448 | ||||||||
\(337\) | 647484. | 0.310566 | 0.155283 | − | 0.987870i | \(-0.450371\pi\) | ||||
0.155283 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(338\) | −2.99902e6 | −1.42787 | ||||||||
\(339\) | −9605.25 | −0.00453952 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.27970e6 | 2.45880 | ||||||||
\(342\) | 1.93710e6 | 0.895544 | ||||||||
\(343\) | −3.65027e6 | −1.67529 | ||||||||
\(344\) | 22896.2 | 0.0104320 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 690012. | 0.309860 | ||||||||
\(347\) | 462018. | 0.205985 | 0.102992 | − | 0.994682i | \(-0.467158\pi\) | ||||
0.102992 | + | 0.994682i | \(0.467158\pi\) | |||||||
\(348\) | −287205. | −0.127129 | ||||||||
\(349\) | 2.85075e6 | 1.25284 | 0.626420 | − | 0.779486i | \(-0.284520\pi\) | ||||
0.626420 | + | 0.779486i | \(0.284520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −115321. | −0.0499621 | ||||||||
\(352\) | 5.22602e6 | 2.24810 | ||||||||
\(353\) | 809444. | 0.345740 | 0.172870 | − | 0.984945i | \(-0.444696\pi\) | ||||
0.172870 | + | 0.984945i | \(0.444696\pi\) | |||||||
\(354\) | 1.32541e6 | 0.562136 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −253488. | −0.106007 | ||||||||
\(357\) | 4.35538e6 | 1.80865 | ||||||||
\(358\) | 630942. | 0.260185 | ||||||||
\(359\) | 3.46118e6 | 1.41739 | 0.708694 | − | 0.705516i | \(-0.249285\pi\) | ||||
0.708694 | + | 0.705516i | \(0.249285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.63635e6 | 0.660856 | ||||||||
\(362\) | −2.81433e6 | −1.12877 | ||||||||
\(363\) | −2.66363e6 | −1.06098 | ||||||||
\(364\) | 214107. | 0.0846990 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.93002e6 | 0.753110 | ||||||||
\(367\) | −2.13602e6 | −0.827827 | −0.413914 | − | 0.910316i | \(-0.635838\pi\) | ||||
−0.413914 | + | 0.910316i | \(0.635838\pi\) | |||||||
\(368\) | 2.89951e6 | 1.11611 | ||||||||
\(369\) | 630381. | 0.241011 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −204531. | −0.0771478 | ||||||||
\(372\) | 3.13219e6 | 1.17352 | ||||||||
\(373\) | −2.37193e6 | −0.882734 | −0.441367 | − | 0.897327i | \(-0.645506\pi\) | ||||
−0.441367 | + | 0.897327i | \(0.645506\pi\) | |||||||
\(374\) | −8.91622e6 | −3.29611 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 77791.4 | 0.0283767 | ||||||||
\(377\) | −21890.4 | −0.00793233 | ||||||||
\(378\) | −7.30191e6 | −2.62849 | ||||||||
\(379\) | −5.47562e6 | −1.95810 | −0.979051 | − | 0.203616i | \(-0.934731\pi\) | ||||
−0.979051 | + | 0.203616i | \(0.934731\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.16224e6 | 0.763116 | ||||||||
\(382\) | −1.55557e6 | −0.545419 | ||||||||
\(383\) | −3.16966e6 | −1.10412 | −0.552059 | − | 0.833805i | \(-0.686158\pi\) | ||||
−0.552059 | + | 0.833805i | \(0.686158\pi\) | |||||||
\(384\) | 283214. | 0.0980138 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.19962e6 | 0.751413 | ||||||||
\(387\) | −218182. | −0.0740529 | ||||||||
\(388\) | −3.74567e6 | −1.26314 | ||||||||
\(389\) | −311235. | −0.104283 | −0.0521416 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521416 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.19587e6 | −1.71876 | ||||||||
\(392\) | 410376. | 0.134886 | ||||||||
\(393\) | 3.01420e6 | 0.984444 | ||||||||
\(394\) | −621603. | −0.201731 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50011e6 | 0.801162 | ||||||||
\(397\) | 496314. | 0.158045 | 0.0790224 | − | 0.996873i | \(-0.474820\pi\) | ||||
0.0790224 | + | 0.996873i | \(0.474820\pi\) | |||||||
\(398\) | −5.62424e6 | −1.77974 | ||||||||
\(399\) | −5.06711e6 | −1.59341 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.63670e6 | −1.75051 | −0.875253 | − | 0.483665i | \(-0.839305\pi\) | ||||
−0.875253 | + | 0.483665i | \(0.839305\pi\) | |||||||
\(402\) | −1.16471e6 | −0.359461 | ||||||||
\(403\) | 238732. | 0.0732230 | ||||||||
\(404\) | 351802. | 0.107237 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.38606e6 | −0.417318 | ||||||||
\(407\) | 9.41059e6 | 2.81599 | ||||||||
\(408\) | −241323. | −0.0717707 | ||||||||
\(409\) | −720515. | −0.212978 | −0.106489 | − | 0.994314i | \(-0.533961\pi\) | ||||
−0.106489 | + | 0.994314i | \(0.533961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.66572e6 | 0.486405 | ||||||||
\(412\) | 378435. | 0.109837 | ||||||||
\(413\) | 3.27289e6 | 0.944182 | ||||||||
\(414\) | 2.84737e6 | 0.816476 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 236305. | 0.0669482 | ||||||||
\(417\) | 182861. | 0.0514969 | ||||||||
\(418\) | 1.03733e7 | 2.90385 | ||||||||
\(419\) | −3.94151e6 | −1.09680 | −0.548400 | − | 0.836216i | \(-0.684763\pi\) | ||||
−0.548400 | + | 0.836216i | \(0.684763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.39506e6 | 1.20854 | 0.604268 | − | 0.796781i | \(-0.293466\pi\) | ||||
0.604268 | + | 0.796781i | \(0.293466\pi\) | |||||||
\(422\) | −3.50947e6 | −0.959312 | ||||||||
\(423\) | −741288. | −0.201436 | ||||||||
\(424\) | 11332.6 | 0.00306137 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.10944e6 | −1.36411 | ||||||||
\(427\) | 4.76588e6 | 1.26495 | ||||||||
\(428\) | −1.30918e6 | −0.345454 | ||||||||
\(429\) | −201859. | −0.0529546 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.24913e6 | 0.323903 | 0.161951 | − | 0.986799i | \(-0.448221\pi\) | ||||
0.161951 | + | 0.986799i | \(0.448221\pi\) | |||||||
\(432\) | −3.92595e6 | −1.01213 | ||||||||
\(433\) | −971902. | −0.249117 | −0.124558 | − | 0.992212i | \(-0.539751\pi\) | ||||
−0.124558 | + | 0.992212i | \(0.539751\pi\) | |||||||
\(434\) | 1.51160e7 | 3.85224 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −490299. | −0.123522 | ||||||||
\(437\) | 6.04494e6 | 1.51422 | ||||||||
\(438\) | −2.31615e6 | −0.576874 | ||||||||
\(439\) | −1.32453e6 | −0.328021 | −0.164010 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164010 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.91054e6 | −0.957504 | ||||||||
\(442\) | −403164. | −0.0981581 | ||||||||
\(443\) | −4.76446e6 | −1.15346 | −0.576732 | − | 0.816933i | \(-0.695672\pi\) | ||||
−0.576732 | + | 0.816933i | \(0.695672\pi\) | |||||||
\(444\) | 5.58284e6 | 1.34399 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.43533e6 | −2.00801 | ||||||||
\(447\) | 1.68304e6 | 0.398407 | ||||||||
\(448\) | 8.00589e6 | 1.88458 | ||||||||
\(449\) | −5.40007e6 | −1.26411 | −0.632053 | − | 0.774926i | \(-0.717787\pi\) | ||||
−0.632053 | + | 0.774926i | \(0.717787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.37572e6 | 0.781493 | ||||||||
\(452\) | 28806.1 | 0.00663190 | ||||||||
\(453\) | −4.78676e6 | −1.09596 | ||||||||
\(454\) | −7.48767e6 | −1.70493 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 280758. | 0.0632295 | ||||||||
\(457\) | −2.12752e6 | −0.476523 | −0.238261 | − | 0.971201i | \(-0.576577\pi\) | ||||
−0.238261 | + | 0.971201i | \(0.576577\pi\) | |||||||
\(458\) | −1.11015e6 | −0.247297 | ||||||||
\(459\) | 7.03522e6 | 1.55864 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.80905e6 | 0.615612 | 0.307806 | − | 0.951449i | \(-0.400405\pi\) | ||||
0.307806 | + | 0.951449i | \(0.400405\pi\) | |||||||
\(462\) | −1.27813e7 | −2.78593 | ||||||||
\(463\) | 2.85342e6 | 0.618605 | 0.309302 | − | 0.950964i | \(-0.399904\pi\) | ||||
0.309302 | + | 0.950964i | \(0.399904\pi\) | |||||||
\(464\) | −745230. | −0.160692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.46955e6 | −0.740132 | ||||||||
\(467\) | 559463. | 0.118708 | 0.0593539 | − | 0.998237i | \(-0.481096\pi\) | ||||
0.0593539 | + | 0.998237i | \(0.481096\pi\) | |||||||
\(468\) | 113047. | 0.0238586 | ||||||||
\(469\) | −2.87606e6 | −0.603762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.85439e6 | −1.00828 | ||||||||
\(472\) | −181344. | −0.0374669 | ||||||||
\(473\) | −1.16838e6 | −0.240121 | ||||||||
\(474\) | −524490. | −0.107224 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.30617e7 | −2.64231 | ||||||||
\(477\) | −107991. | −0.0217315 | ||||||||
\(478\) | −9.48208e6 | −1.89816 | ||||||||
\(479\) | 5.46747e6 | 1.08880 | 0.544399 | − | 0.838826i | \(-0.316758\pi\) | ||||
0.544399 | + | 0.838826i | \(0.316758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 425517. | 0.0838600 | ||||||||
\(482\) | 965349. | 0.189263 | ||||||||
\(483\) | −7.44821e6 | −1.45273 | ||||||||
\(484\) | 7.98819e6 | 1.55001 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.45050e6 | −1.23881 | ||||||||
\(487\) | −9.34759e6 | −1.78598 | −0.892991 | − | 0.450074i | \(-0.851397\pi\) | ||||
−0.892991 | + | 0.450074i | \(0.851397\pi\) | |||||||
\(488\) | −264067. | −0.0501955 | ||||||||
\(489\) | −6.39325e6 | −1.20906 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04964e7 | −1.96488 | −0.982438 | − | 0.186589i | \(-0.940257\pi\) | ||||
−0.982438 | + | 0.186589i | \(0.940257\pi\) | |||||||
\(492\) | 2.00265e6 | 0.372986 | ||||||||
\(493\) | 1.33544e6 | 0.247460 | ||||||||
\(494\) | 469046. | 0.0864766 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.12730e6 | 1.48335 | ||||||||
\(497\) | −1.26170e7 | −2.29120 | ||||||||
\(498\) | −711122. | −0.128490 | ||||||||
\(499\) | 5.74842e6 | 1.03347 | 0.516734 | − | 0.856146i | \(-0.327148\pi\) | ||||
0.516734 | + | 0.856146i | \(0.327148\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.77242e6 | 1.20545 | ||||||||
\(502\) | −1.14361e6 | −0.202543 | ||||||||
\(503\) | −3.10341e6 | −0.546915 | −0.273457 | − | 0.961884i | \(-0.588167\pi\) | ||||
−0.273457 | + | 0.961884i | \(0.588167\pi\) | |||||||
\(504\) | 326562. | 0.0572650 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.52478e7 | 2.64747 | ||||||||
\(507\) | 4.14205e6 | 0.715642 | ||||||||
\(508\) | −6.48453e6 | −1.11486 | ||||||||
\(509\) | −7.92714e6 | −1.35620 | −0.678098 | − | 0.734972i | \(-0.737195\pi\) | ||||
−0.678098 | + | 0.734972i | \(0.737195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.71937e6 | −0.968938 | ||||||||
\(512\) | 8.43012e6 | 1.42121 | ||||||||
\(513\) | −8.18488e6 | −1.37315 | ||||||||
\(514\) | 1.59269e6 | 0.265904 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −693141. | −0.114603 | ||||||||
\(517\) | −3.96963e6 | −0.653166 | ||||||||
\(518\) | 2.69429e7 | 4.41185 | ||||||||
\(519\) | −952998. | −0.155301 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.37136e6 | −0.705541 | −0.352771 | − | 0.935710i | \(-0.614760\pi\) | ||||
−0.352771 | + | 0.935710i | \(0.614760\pi\) | |||||||
\(522\) | −731828. | −0.117553 | ||||||||
\(523\) | −1.11680e6 | −0.178534 | −0.0892671 | − | 0.996008i | \(-0.528452\pi\) | ||||
−0.0892671 | + | 0.996008i | \(0.528452\pi\) | |||||||
\(524\) | −9.03957e6 | −1.43820 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.59374e7 | 2.51162 | ||||||||
\(527\) | −1.45640e7 | −2.28430 | ||||||||
\(528\) | −6.87201e6 | −1.07275 | ||||||||
\(529\) | 2.44920e6 | 0.380527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.72806e6 | 0.265964 | ||||||||
\(532\) | 1.51962e7 | 2.32786 | ||||||||
\(533\) | 152640. | 0.0232728 | ||||||||
\(534\) | 684230. | 0.103836 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 159357. | 0.0239584 | ||||||||
\(537\) | −871415. | −0.130403 | ||||||||
\(538\) | −4.29852e6 | −0.640271 | ||||||||
\(539\) | −2.09411e7 | −3.10476 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6212.12 | −0.000912528 0 | −0.000456264 | − | 1.00000i | \(-0.500145\pi\) | ||||
−0.000456264 | 1.00000i | \(0.500145\pi\) | ||||||||
\(542\) | −1.36619e7 | −1.99763 | ||||||||
\(543\) | 3.88696e6 | 0.565732 | ||||||||
\(544\) | −1.44159e7 | −2.08855 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −577931. | −0.0829648 | ||||||||
\(547\) | 9.82839e6 | 1.40448 | 0.702238 | − | 0.711942i | \(-0.252184\pi\) | ||||
0.702238 | + | 0.711942i | \(0.252184\pi\) | |||||||
\(548\) | −4.99549e6 | −0.710602 | ||||||||
\(549\) | 2.51635e6 | 0.356319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.55367e6 | −0.218011 | ||||||||
\(552\) | 412690. | 0.0576470 | ||||||||
\(553\) | −1.29515e6 | −0.180097 | ||||||||
\(554\) | −110336. | −0.0152737 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −548398. | −0.0752332 | ||||||||
\(557\) | 6.27045e6 | 0.856369 | 0.428184 | − | 0.903691i | \(-0.359153\pi\) | ||||
0.428184 | + | 0.903691i | \(0.359153\pi\) | |||||||
\(558\) | 7.98115e6 | 1.08513 | ||||||||
\(559\) | −52830.4 | −0.00715079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.23145e7 | 1.65200 | ||||||||
\(562\) | 9.07215e6 | 1.21163 | ||||||||
\(563\) | 6.71129e6 | 0.892350 | 0.446175 | − | 0.894946i | \(-0.352786\pi\) | ||||
0.446175 | + | 0.894946i | \(0.352786\pi\) | |||||||
\(564\) | −2.35499e6 | −0.311739 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.23812e7 | 1.62450 | ||||||||
\(567\) | 3.67659e6 | 0.480272 | ||||||||
\(568\) | 699080. | 0.0909193 | ||||||||
\(569\) | −7.01697e6 | −0.908592 | −0.454296 | − | 0.890851i | \(-0.650109\pi\) | ||||
−0.454296 | + | 0.890851i | \(0.650109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61627e6 | 0.207455 | 0.103727 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103727 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(572\) | 605372. | 0.0773628 | ||||||||
\(573\) | 2.14845e6 | 0.273362 | ||||||||
\(574\) | 9.66484e6 | 1.22438 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.22705e6 | 0.530861 | ||||||||
\(577\) | −1.08712e7 | −1.35937 | −0.679686 | − | 0.733503i | \(-0.737884\pi\) | ||||
−0.679686 | + | 0.733503i | \(0.737884\pi\) | |||||||
\(578\) | 1.31014e7 | 1.63117 | ||||||||
\(579\) | −3.03796e6 | −0.376605 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.75600e6 | −0.215817 | ||||||||
\(582\) | 1.01105e7 | 1.23727 | ||||||||
\(583\) | −578294. | −0.0704656 | ||||||||
\(584\) | 316898. | 0.0384493 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.28294e7 | 1.54334 | ||||||||
\(587\) | −8.65320e6 | −1.03653 | −0.518264 | − | 0.855221i | \(-0.673422\pi\) | ||||
−0.518264 | + | 0.855221i | \(0.673422\pi\) | |||||||
\(588\) | −1.24233e7 | −1.48182 | ||||||||
\(589\) | 1.69439e7 | 2.01245 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 858517. | 0.101107 | ||||||||
\(592\) | 1.44862e7 | 1.69883 | ||||||||
\(593\) | −5.13574e6 | −0.599745 | −0.299872 | − | 0.953979i | \(-0.596944\pi\) | ||||
−0.299872 | + | 0.953979i | \(0.596944\pi\) | |||||||
\(594\) | −2.06456e7 | −2.40083 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.04743e6 | −0.582043 | ||||||||
\(597\) | 7.76782e6 | 0.891997 | ||||||||
\(598\) | 689458. | 0.0788415 | ||||||||
\(599\) | 7.56853e6 | 0.861875 | 0.430937 | − | 0.902382i | \(-0.358183\pi\) | ||||
0.430937 | + | 0.902382i | \(0.358183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.56891e6 | 0.290110 | 0.145055 | − | 0.989424i | \(-0.453664\pi\) | ||||
0.145055 | + | 0.989424i | \(0.453664\pi\) | |||||||
\(602\) | −3.34512e6 | −0.376201 | ||||||||
\(603\) | −1.51854e6 | −0.170072 | ||||||||
\(604\) | 1.43554e7 | 1.60112 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −949604. | −0.105042 | ||||||||
\(607\) | −2.62172e6 | −0.288812 | −0.144406 | − | 0.989519i | \(-0.546127\pi\) | ||||
−0.144406 | + | 0.989519i | \(0.546127\pi\) | |||||||
\(608\) | 1.67716e7 | 1.83999 | ||||||||
\(609\) | 1.91433e6 | 0.209158 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −179494. | −0.0194513 | ||||||||
\(612\) | −6.89650e6 | −0.744303 | ||||||||
\(613\) | −537167. | −0.0577376 | −0.0288688 | − | 0.999583i | \(-0.509190\pi\) | ||||
−0.0288688 | + | 0.999583i | \(0.509190\pi\) | |||||||
\(614\) | −5.63213e6 | −0.602909 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.74875e6 | 0.185685 | ||||||||
\(617\) | −1.15522e7 | −1.22166 | −0.610830 | − | 0.791762i | \(-0.709164\pi\) | ||||
−0.610830 | + | 0.791762i | \(0.709164\pi\) | |||||||
\(618\) | −1.02149e6 | −0.107588 | ||||||||
\(619\) | 2.20752e6 | 0.231568 | 0.115784 | − | 0.993274i | \(-0.463062\pi\) | ||||
0.115784 | + | 0.993274i | \(0.463062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20311e7 | −1.25192 | ||||||||
\(622\) | −8.00408e6 | −0.829536 | ||||||||
\(623\) | 1.68960e6 | 0.174407 | ||||||||
\(624\) | −310731. | −0.0319465 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.48963e7 | 2.53922 | ||||||||
\(627\) | −1.43268e7 | −1.45540 | ||||||||
\(628\) | 1.45583e7 | 1.47303 | ||||||||
\(629\) | −2.59589e7 | −2.61613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.43943e7 | −1.43919 | −0.719594 | − | 0.694395i | \(-0.755672\pi\) | ||||
−0.719594 | + | 0.694395i | \(0.755672\pi\) | |||||||
\(632\) | 71761.3 | 0.00714657 | ||||||||
\(633\) | 4.84704e6 | 0.480803 | ||||||||
\(634\) | −7.32219e6 | −0.723465 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −343074. | −0.0336314 | ||||||||
\(637\) | −946893. | −0.0924597 | ||||||||
\(638\) | −3.91897e6 | −0.381172 | ||||||||
\(639\) | −6.66166e6 | −0.645402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.90224e6 | 0.471248 | 0.235624 | − | 0.971844i | \(-0.424287\pi\) | ||||
0.235624 | + | 0.971844i | \(0.424287\pi\) | |||||||
\(642\) | 3.53381e6 | 0.338381 | ||||||||
\(643\) | 1.80253e7 | 1.71931 | 0.859656 | − | 0.510874i | \(-0.170678\pi\) | ||||
0.859656 | + | 0.510874i | \(0.170678\pi\) | |||||||
\(644\) | 2.23371e7 | 2.12233 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.86144e7 | −2.69776 | ||||||||
\(647\) | 1.24242e7 | 1.16683 | 0.583415 | − | 0.812174i | \(-0.301716\pi\) | ||||
0.583415 | + | 0.812174i | \(0.301716\pi\) | |||||||
\(648\) | −203712. | −0.0190581 | ||||||||
\(649\) | 9.25383e6 | 0.862402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.08772e7 | −1.93073 | ||||||||
\(652\) | 1.91733e7 | 1.76635 | ||||||||
\(653\) | 1.28553e7 | 1.17977 | 0.589887 | − | 0.807486i | \(-0.299172\pi\) | ||||
0.589887 | + | 0.807486i | \(0.299172\pi\) | |||||||
\(654\) | 1.32344e6 | 0.120993 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.19641e6 | 0.471459 | ||||||||
\(657\) | −3.01978e6 | −0.272937 | ||||||||
\(658\) | −1.13652e7 | −1.02333 | ||||||||
\(659\) | −5.18218e6 | −0.464835 | −0.232417 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232417 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.47130e6 | 0.576087 | 0.288043 | − | 0.957617i | \(-0.406995\pi\) | ||||
0.288043 | + | 0.957617i | \(0.406995\pi\) | |||||||
\(662\) | −1.69436e7 | −1.50266 | ||||||||
\(663\) | 556823. | 0.0491964 | ||||||||
\(664\) | 97296.6 | 0.00856402 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.42257e7 | 1.24276 | ||||||||
\(667\) | −2.28375e6 | −0.198763 | ||||||||
\(668\) | −2.03104e7 | −1.76108 | ||||||||
\(669\) | 1.16503e7 | 1.00640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.34751e7 | 1.15539 | ||||||||
\(672\) | −2.06650e7 | −1.76527 | ||||||||
\(673\) | −6.21171e6 | −0.528657 | −0.264328 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264328 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(674\) | 5.24141e6 | 0.444425 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.24220e7 | −1.04550 | ||||||||
\(677\) | −1.85078e7 | −1.55197 | −0.775984 | − | 0.630752i | \(-0.782747\pi\) | ||||
−0.775984 | + | 0.630752i | \(0.782747\pi\) | |||||||
\(678\) | −77754.9 | −0.00649611 | ||||||||
\(679\) | 2.49663e7 | 2.07817 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.03415e7 | 0.854504 | ||||||||
\(682\) | 4.27394e7 | 3.51858 | ||||||||
\(683\) | 4.91590e6 | 0.403228 | 0.201614 | − | 0.979465i | \(-0.435381\pi\) | ||||
0.201614 | + | 0.979465i | \(0.435381\pi\) | |||||||
\(684\) | 8.02348e6 | 0.655726 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.95491e7 | −2.39736 | ||||||||
\(687\) | 1.53327e6 | 0.123944 | ||||||||
\(688\) | −1.79854e6 | −0.144860 | ||||||||
\(689\) | −26148.7 | −0.00209846 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.07645e7 | −0.857630 | −0.428815 | − | 0.903392i | \(-0.641069\pi\) | ||||
−0.428815 | + | 0.903392i | \(0.641069\pi\) | |||||||
\(692\) | 2.85803e6 | 0.226883 | ||||||||
\(693\) | −1.66642e7 | −1.31811 | ||||||||
\(694\) | 3.74005e6 | 0.294767 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −106069. | −0.00829977 | ||||||||
\(697\) | −9.31185e6 | −0.726029 | ||||||||
\(698\) | 2.30769e7 | 1.79283 | ||||||||
\(699\) | 4.79192e6 | 0.370951 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.02819e6 | 0.693914 | 0.346957 | − | 0.937881i | \(-0.387215\pi\) | ||||
0.346957 | + | 0.937881i | \(0.387215\pi\) | |||||||
\(702\) | −933529. | −0.0714966 | ||||||||
\(703\) | 3.02010e7 | 2.30480 | ||||||||
\(704\) | 2.26360e7 | 1.72135 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.55248e6 | 0.494760 | ||||||||
\(707\) | −2.34490e6 | −0.176431 | ||||||||
\(708\) | 5.48984e6 | 0.411601 | ||||||||
\(709\) | 4.91059e6 | 0.366875 | 0.183438 | − | 0.983031i | \(-0.441277\pi\) | ||||
0.183438 | + | 0.983031i | \(0.441277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −683827. | −0.0507308 | ||||||||
\(712\) | −93617.2 | −0.00692079 | ||||||||
\(713\) | 2.49061e7 | 1.83477 | ||||||||
\(714\) | 3.52570e7 | 2.58821 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.61336e6 | 0.190510 | ||||||||
\(717\) | 1.30960e7 | 0.951352 | ||||||||
\(718\) | 2.80184e7 | 2.02830 | ||||||||
\(719\) | 1.44751e7 | 1.04424 | 0.522119 | − | 0.852873i | \(-0.325142\pi\) | ||||
0.522119 | + | 0.852873i | \(0.325142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.52242e6 | −0.180709 | ||||||||
\(722\) | 1.32463e7 | 0.945695 | ||||||||
\(723\) | −1.33328e6 | −0.0948580 | ||||||||
\(724\) | −1.16570e7 | −0.826493 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.15622e7 | −1.51828 | ||||||||
\(727\) | −1.55189e7 | −1.08899 | −0.544495 | − | 0.838764i | \(-0.683279\pi\) | ||||
−0.544495 | + | 0.838764i | \(0.683279\pi\) | |||||||
\(728\) | 79073.2 | 0.00552969 | ||||||||
\(729\) | 1.29066e7 | 0.899481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.22294e6 | 0.223079 | ||||||||
\(732\) | 7.99414e6 | 0.551435 | ||||||||
\(733\) | −1.03870e6 | −0.0714050 | −0.0357025 | − | 0.999362i | \(-0.511367\pi\) | ||||
−0.0357025 | + | 0.999362i | \(0.511367\pi\) | |||||||
\(734\) | −1.72912e7 | −1.18463 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.46529e7 | 1.67754 | ||||||||
\(737\) | −8.13184e6 | −0.551467 | ||||||||
\(738\) | 5.10296e6 | 0.344891 | ||||||||
\(739\) | 1.33918e6 | 0.0902046 | 0.0451023 | − | 0.998982i | \(-0.485639\pi\) | ||||
0.0451023 | + | 0.998982i | \(0.485639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −647816. | −0.0433417 | ||||||||
\(742\) | −1.65568e6 | −0.110400 | ||||||||
\(743\) | −1.56518e7 | −1.04014 | −0.520070 | − | 0.854124i | \(-0.674094\pi\) | ||||
−0.520070 | + | 0.854124i | \(0.674094\pi\) | |||||||
\(744\) | 1.15677e6 | 0.0766149 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.92009e7 | −1.26321 | ||||||||
\(747\) | −927157. | −0.0607927 | ||||||||
\(748\) | −3.69310e7 | −2.41345 | ||||||||
\(749\) | 8.72620e6 | 0.568356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.92274e7 | 1.24400 | 0.622002 | − | 0.783016i | \(-0.286320\pi\) | ||||
0.622002 | + | 0.783016i | \(0.286320\pi\) | |||||||
\(752\) | −6.11065e6 | −0.394042 | ||||||||
\(753\) | 1.57947e6 | 0.101514 | ||||||||
\(754\) | −177204. | −0.0113513 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.02446e7 | −1.92461 | ||||||||
\(757\) | 2.73627e7 | 1.73548 | 0.867739 | − | 0.497021i | \(-0.165573\pi\) | ||||
0.867739 | + | 0.497021i | \(0.165573\pi\) | |||||||
\(758\) | −4.43254e7 | −2.80207 | ||||||||
\(759\) | −2.10592e7 | −1.32690 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.86301e6 | 0.366994 | 0.183497 | − | 0.983020i | \(-0.441258\pi\) | ||||
0.183497 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(762\) | 1.75034e7 | 1.09203 | ||||||||
\(763\) | 3.26803e6 | 0.203224 | ||||||||
\(764\) | −6.44317e6 | −0.399361 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.56585e7 | −1.58001 | ||||||||
\(767\) | 418430. | 0.0256823 | ||||||||
\(768\) | −1.05236e7 | −0.643813 | ||||||||
\(769\) | −1.36162e7 | −0.830308 | −0.415154 | − | 0.909751i | \(-0.636272\pi\) | ||||
−0.415154 | + | 0.909751i | \(0.636272\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.19972e6 | −0.133270 | ||||||||
\(772\) | 9.11083e6 | 0.550192 | ||||||||
\(773\) | 9.44787e6 | 0.568703 | 0.284351 | − | 0.958720i | \(-0.408222\pi\) | ||||
0.284351 | + | 0.958720i | \(0.408222\pi\) | |||||||
\(774\) | −1.76620e6 | −0.105971 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.38333e6 | −0.0824655 | ||||||||
\(777\) | −3.72118e7 | −2.21120 | ||||||||
\(778\) | −2.51946e6 | −0.149231 | ||||||||
\(779\) | 1.08335e7 | 0.639627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.56735e7 | −2.09275 | ||||||||
\(782\) | −4.20608e7 | −2.45958 | ||||||||
\(783\) | 3.09221e6 | 0.180246 | ||||||||
\(784\) | −3.22357e7 | −1.87304 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.44001e7 | 1.40875 | ||||||||
\(787\) | −2.97678e7 | −1.71320 | −0.856602 | − | 0.515977i | \(-0.827429\pi\) | ||||
−0.856602 | + | 0.515977i | \(0.827429\pi\) | |||||||
\(788\) | −2.57468e6 | −0.147709 | ||||||||
\(789\) | −2.20117e7 | −1.25881 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −192004. | −0.0109111 | ||||||||
\(792\) | 923328. | 0.0523050 | ||||||||
\(793\) | 609304. | 0.0344073 | ||||||||
\(794\) | 4.01768e6 | 0.226164 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.32956e7 | −1.30314 | ||||||||
\(797\) | 1.80924e7 | 1.00891 | 0.504453 | − | 0.863439i | \(-0.331694\pi\) | ||||
0.504453 | + | 0.863439i | \(0.331694\pi\) | |||||||
\(798\) | −4.10184e7 | −2.28019 | ||||||||
\(799\) | 1.09501e7 | 0.606810 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 892095. | 0.0491281 | ||||||||
\(802\) | −4.56293e7 | −2.50500 | ||||||||
\(803\) | −1.61711e7 | −0.885013 | ||||||||
\(804\) | −4.82422e6 | −0.263201 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.93254e6 | 0.104783 | ||||||||
\(807\) | 5.93683e6 | 0.320901 | ||||||||
\(808\) | 129926. | 0.00700113 | ||||||||
\(809\) | −1.57182e7 | −0.844366 | −0.422183 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422183 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.57562e6 | −0.0841202 | −0.0420601 | − | 0.999115i | \(-0.513392\pi\) | ||||
−0.0420601 | + | 0.999115i | \(0.513392\pi\) | |||||||
\(812\) | −5.74106e6 | −0.305564 | ||||||||
\(813\) | 1.88690e7 | 1.00120 | ||||||||
\(814\) | 7.61791e7 | 4.02972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.89563e7 | 0.996617 | ||||||||
\(817\) | −3.74962e6 | −0.196531 | ||||||||
\(818\) | −5.83260e6 | −0.304775 | ||||||||
\(819\) | −753503. | −0.0392532 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.61911e7 | 1.35611 | 0.678056 | − | 0.735010i | \(-0.262823\pi\) | ||||
0.678056 | + | 0.735010i | \(0.262823\pi\) | |||||||
\(822\) | 1.34841e7 | 0.696053 | ||||||||
\(823\) | 3.66910e7 | 1.88825 | 0.944126 | − | 0.329585i | \(-0.106909\pi\) | ||||
0.944126 | + | 0.329585i | \(0.106909\pi\) | |||||||
\(824\) | 139762. | 0.00717086 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.64942e7 | 1.35114 | ||||||||
\(827\) | −1.38402e7 | −0.703685 | −0.351843 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351843 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(828\) | 1.17938e7 | 0.597832 | ||||||||
\(829\) | −2.83219e7 | −1.43132 | −0.715660 | − | 0.698449i | \(-0.753874\pi\) | ||||
−0.715660 | + | 0.698449i | \(0.753874\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 152389. | 0.00765509 | ||||||||
\(832\) | 1.02353e6 | 0.0512617 | ||||||||
\(833\) | 5.77657e7 | 2.88441 | ||||||||
\(834\) | 1.48027e6 | 0.0736928 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.29661e7 | 2.12623 | ||||||||
\(837\) | −3.37229e7 | −1.66384 | ||||||||
\(838\) | −3.19067e7 | −1.56954 | ||||||||
\(839\) | 2.80231e7 | 1.37439 | 0.687197 | − | 0.726471i | \(-0.258841\pi\) | ||||
0.687197 | + | 0.726471i | \(0.258841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99242e7 | −0.971383 | ||||||||
\(842\) | 3.55782e7 | 1.72943 | ||||||||
\(843\) | −1.25298e7 | −0.607263 | ||||||||
\(844\) | −1.45362e7 | −0.702418 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00076e6 | −0.288257 | ||||||||
\(847\) | −5.32444e7 | −2.55015 | ||||||||
\(848\) | −890197. | −0.0425105 | ||||||||
\(849\) | −1.71000e7 | −0.814193 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.43928e7 | 2.10130 | ||||||||
\(852\) | −2.11633e7 | −0.998815 | ||||||||
\(853\) | 2.38300e7 | 1.12138 | 0.560689 | − | 0.828027i | \(-0.310537\pi\) | ||||
0.560689 | + | 0.828027i | \(0.310537\pi\) | |||||||
\(854\) | 3.85800e7 | 1.81016 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −483501. | −0.0225534 | ||||||||
\(857\) | 3.83129e7 | 1.78194 | 0.890971 | − | 0.454061i | \(-0.150025\pi\) | ||||
0.890971 | + | 0.454061i | \(0.150025\pi\) | |||||||
\(858\) | −1.63405e6 | −0.0757789 | ||||||||
\(859\) | 2.68650e7 | 1.24224 | 0.621118 | − | 0.783717i | \(-0.286679\pi\) | ||||
0.621118 | + | 0.783717i | \(0.286679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.33484e7 | −0.613652 | ||||||||
\(862\) | 1.01118e7 | 0.463510 | ||||||||
\(863\) | 1.63558e7 | 0.747558 | 0.373779 | − | 0.927518i | \(-0.378062\pi\) | ||||
0.373779 | + | 0.927518i | \(0.378062\pi\) | |||||||
\(864\) | −3.33801e7 | −1.52126 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.86758e6 | −0.356489 | ||||||||
\(867\) | −1.80948e7 | −0.817535 | ||||||||
\(868\) | 6.26107e7 | 2.82065 | ||||||||
\(869\) | −3.66192e6 | −0.164498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −367696. | −0.0164227 | ||||||||
\(872\) | −181075. | −0.00806431 | ||||||||
\(873\) | 1.31820e7 | 0.585392 | ||||||||
\(874\) | 4.89341e7 | 2.16687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.59350e6 | −0.422393 | ||||||||
\(877\) | 2.30604e7 | 1.01243 | 0.506217 | − | 0.862406i | \(-0.331043\pi\) | ||||
0.506217 | + | 0.862406i | \(0.331043\pi\) | |||||||
\(878\) | −1.07221e7 | −0.469402 | ||||||||
\(879\) | −1.77191e7 | −0.773515 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.15095e7 | −1.36774 | −0.683868 | − | 0.729606i | \(-0.739704\pi\) | ||||
−0.683868 | + | 0.729606i | \(0.739704\pi\) | |||||||
\(882\) | −3.16560e7 | −1.37020 | ||||||||
\(883\) | −2.86348e7 | −1.23593 | −0.617963 | − | 0.786208i | \(-0.712042\pi\) | ||||
−0.617963 | + | 0.786208i | \(0.712042\pi\) | |||||||
\(884\) | −1.66991e6 | −0.0718723 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.85685e7 | −1.65063 | ||||||||
\(887\) | 2.45670e7 | 1.04844 | 0.524220 | − | 0.851583i | \(-0.324357\pi\) | ||||
0.524220 | + | 0.851583i | \(0.324357\pi\) | |||||||
\(888\) | 2.06183e6 | 0.0877446 | ||||||||
\(889\) | 4.32219e7 | 1.83421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.03953e7 | 0.438673 | ||||||||
\(892\) | −3.49392e7 | −1.47028 | ||||||||
\(893\) | −1.27396e7 | −0.534596 | ||||||||
\(894\) | 1.36243e7 | 0.570126 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.66130e6 | 0.235584 | ||||||||
\(897\) | −952233. | −0.0395150 | ||||||||
\(898\) | −4.37138e7 | −1.80895 | ||||||||
\(899\) | −6.40134e6 | −0.264163 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.59521e6 | 0.0654646 | ||||||||
\(902\) | 2.73266e7 | 1.11833 | ||||||||
\(903\) | 4.62005e6 | 0.188550 | ||||||||
\(904\) | 10638.5 | 0.000432973 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.87490e7 | −1.56834 | ||||||||
\(907\) | −1.90832e7 | −0.770254 | −0.385127 | − | 0.922864i | \(-0.625842\pi\) | ||||
−0.385127 | + | 0.922864i | \(0.625842\pi\) | |||||||
\(908\) | −3.10140e7 | −1.24837 | ||||||||
\(909\) | −1.23809e6 | −0.0496984 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.04616e7 | −1.21606 | −0.608032 | − | 0.793912i | \(-0.708041\pi\) | ||||
−0.608032 | + | 0.793912i | \(0.708041\pi\) | |||||||
\(912\) | −2.20540e7 | −0.878012 | ||||||||
\(913\) | −4.96497e6 | −0.197124 | ||||||||
\(914\) | −1.72224e7 | −0.681911 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.59826e6 | −0.181073 | ||||||||
\(917\) | 6.02522e7 | 2.36619 | ||||||||
\(918\) | 5.69504e7 | 2.23044 | ||||||||
\(919\) | 2.73866e7 | 1.06967 | 0.534834 | − | 0.844957i | \(-0.320374\pi\) | ||||
0.534834 | + | 0.844957i | \(0.320374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.77872e6 | 0.302175 | ||||||||
\(922\) | 2.27394e7 | 0.880950 | ||||||||
\(923\) | −1.61304e6 | −0.0623221 | ||||||||
\(924\) | −5.29402e7 | −2.03989 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.30986e7 | 0.885232 | ||||||||
\(927\) | −1.33182e6 | −0.0509033 | ||||||||
\(928\) | −6.33626e6 | −0.241525 | ||||||||
\(929\) | −2.65451e7 | −1.00913 | −0.504563 | − | 0.863375i | \(-0.668346\pi\) | ||||
−0.504563 | + | 0.863375i | \(0.668346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.72054e7 | −2.54115 | ||||||||
\(932\) | −1.43709e7 | −0.541932 | ||||||||
\(933\) | 1.10547e7 | 0.415760 | ||||||||
\(934\) | 4.52888e6 | 0.169873 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 41750.0 | 0.00155764 | ||||||||
\(937\) | 2.34660e7 | 0.873151 | 0.436576 | − | 0.899668i | \(-0.356191\pi\) | ||||
0.436576 | + | 0.899668i | \(0.356191\pi\) | |||||||
\(938\) | −2.32818e7 | −0.863993 | ||||||||
\(939\) | −3.43852e7 | −1.27264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.18303e7 | −0.803686 | −0.401843 | − | 0.915709i | \(-0.631630\pi\) | ||||
−0.401843 | + | 0.915709i | \(0.631630\pi\) | |||||||
\(942\) | −3.92965e7 | −1.44287 | ||||||||
\(943\) | 1.59244e7 | 0.583154 | ||||||||
\(944\) | 1.42449e7 | 0.520270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.45806e6 | −0.343617 | ||||||||
\(947\) | −1.87197e7 | −0.678305 | −0.339152 | − | 0.940731i | \(-0.610140\pi\) | ||||
−0.339152 | + | 0.940731i | \(0.610140\pi\) | |||||||
\(948\) | −2.17244e6 | −0.0785103 | ||||||||
\(949\) | −731206. | −0.0263557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.01129e7 | 0.362598 | ||||||||
\(952\) | −4.82390e6 | −0.172507 | ||||||||
\(953\) | −5.37413e7 | −1.91680 | −0.958399 | − | 0.285432i | \(-0.907863\pi\) | ||||
−0.958399 | + | 0.285432i | \(0.907863\pi\) | |||||||
\(954\) | −874188. | −0.0310981 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.92748e7 | −1.38986 | ||||||||
\(957\) | 5.41262e6 | 0.191042 | ||||||||
\(958\) | 4.42594e7 | 1.55809 | ||||||||
\(959\) | 3.32969e7 | 1.16911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.11823e7 | 1.43847 | ||||||||
\(962\) | 3.44458e6 | 0.120005 | ||||||||
\(963\) | 4.60736e6 | 0.160098 | ||||||||
\(964\) | 3.99848e6 | 0.138581 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.02936e7 | −2.07887 | ||||||||
\(967\) | −1.78136e7 | −0.612611 | −0.306306 | − | 0.951933i | \(-0.599093\pi\) | ||||
−0.306306 | + | 0.951933i | \(0.599093\pi\) | |||||||
\(968\) | 2.95016e6 | 0.101195 | ||||||||
\(969\) | 3.95203e7 | 1.35211 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.06231e7 | 1.04232 | 0.521160 | − | 0.853459i | \(-0.325500\pi\) | ||||
0.521160 | + | 0.853459i | \(0.325500\pi\) | |||||||
\(972\) | −2.67180e7 | −0.907065 | ||||||||
\(973\) | 3.65529e6 | 0.123777 | ||||||||
\(974\) | −7.56691e7 | −2.55577 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.07429e7 | 0.697021 | ||||||||
\(977\) | 1.93935e7 | 0.650011 | 0.325005 | − | 0.945712i | \(-0.394634\pi\) | ||||
0.325005 | + | 0.945712i | \(0.394634\pi\) | |||||||
\(978\) | −5.17536e7 | −1.73019 | ||||||||
\(979\) | 4.77721e6 | 0.159301 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.72550e6 | 0.0572455 | ||||||||
\(982\) | −8.49685e7 | −2.81177 | ||||||||
\(983\) | −3.41089e7 | −1.12586 | −0.562929 | − | 0.826505i | \(-0.690325\pi\) | ||||
−0.562929 | + | 0.826505i | \(0.690325\pi\) | |||||||
\(984\) | 739609. | 0.0243509 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.08104e7 | 0.354120 | ||||||||
\(987\) | 1.56969e7 | 0.512886 | ||||||||
\(988\) | 1.94279e6 | 0.0633190 | ||||||||
\(989\) | −5.51162e6 | −0.179179 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.15321e7 | −0.373013 | −0.186507 | − | 0.982454i | \(-0.559717\pi\) | ||||
−0.186507 | + | 0.982454i | \(0.559717\pi\) | |||||||
\(992\) | 6.91017e7 | 2.22951 | ||||||||
\(993\) | 2.34014e7 | 0.753128 | ||||||||
\(994\) | −1.02135e8 | −3.27875 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.94547e6 | −0.0940819 | ||||||||
\(997\) | −3.45745e7 | −1.10159 | −0.550793 | − | 0.834642i | \(-0.685675\pi\) | ||||
−0.550793 | + | 0.834642i | \(0.685675\pi\) | |||||||
\(998\) | 4.65337e7 | 1.47891 | ||||||||
\(999\) | −6.01081e7 | −1.90554 |
(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 | 1075.6.a.a.1.7 | 8 | ||
5.4 | even | 2 | 43.6.a.a.1.2 | ✓ | 8 | ||
15.14 | odd | 2 | 387.6.a.c.1.7 | 8 | |||
20.19 | odd | 2 | 688.6.a.e.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.2 | ✓ | 8 | 5.4 | even | 2 | ||
387.6.a.c.1.7 | 8 | 15.14 | odd | 2 | |||
688.6.a.e.1.2 | 8 | 20.19 | odd | 2 | |||
1075.6.a.a.1.7 | 8 | 1.1 | even | 1 | trivial |