Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,6,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(94.3056860500\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7081}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1770 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(42.5743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.5743 | −0.332268 | −0.166134 | − | 0.986103i | \(-0.553128\pi\) | ||||
−0.166134 | + | 0.986103i | \(0.553128\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −161.426 | −0.402245 | −0.201123 | − | 0.979566i | \(-0.564459\pi\) | ||||
−0.201123 | + | 0.979566i | \(0.564459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.1283 | 0.0231863 | 0.0115932 | − | 0.999933i | \(-0.496310\pi\) | ||||
0.0115932 | + | 0.999933i | \(0.496310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −167.169 | −0.191835 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −765.703 | −0.642596 | −0.321298 | − | 0.946978i | \(-0.604119\pi\) | ||||
−0.321298 | + | 0.946978i | \(0.604119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1414.29 | 0.898783 | 0.449392 | − | 0.893335i | \(-0.351641\pi\) | ||||
0.449392 | + | 0.893335i | \(0.351641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4185.43 | 1.64976 | 0.824880 | − | 0.565308i | \(-0.191242\pi\) | ||||
0.824880 | + | 0.565308i | \(0.191242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2779.99 | −0.889598 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4202.60 | −0.927947 | −0.463974 | − | 0.885849i | \(-0.653577\pi\) | ||||
−0.463974 | + | 0.885849i | \(0.653577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2387.35 | −0.446182 | −0.223091 | − | 0.974798i | \(-0.571615\pi\) | ||||
−0.223091 | + | 0.974798i | \(0.571615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1452.83 | −0.232236 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −672.939 | −0.0808112 | −0.0404056 | − | 0.999183i | \(-0.512865\pi\) | ||||
−0.0404056 | + | 0.999183i | \(0.512865\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 127.155 | 0.0133866 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4173.45 | −0.387735 | −0.193868 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193868 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5430.94 | −0.447923 | −0.223962 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223962 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1504.52 | −0.110756 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6302.68 | 0.416179 | 0.208090 | − | 0.978110i | \(-0.433275\pi\) | ||||
0.208090 | + | 0.978110i | \(0.433275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6891.32 | −0.371003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16416.7 | 0.802778 | 0.401389 | − | 0.915908i | \(-0.368528\pi\) | ||||
0.401389 | + | 0.915908i | \(0.368528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2998.37 | 0.133653 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12728.6 | 0.518913 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3966.49 | 0.148346 | 0.0741731 | − | 0.997245i | \(-0.476368\pi\) | ||||
0.0741731 | + | 0.997245i | \(0.476368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50338.7 | −1.73212 | −0.866059 | − | 0.499942i | \(-0.833355\pi\) | ||||
−0.866059 | + | 0.499942i | \(0.833355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −262.424 | −0.00770407 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13645.3 | 0.371360 | 0.185680 | − | 0.982610i | \(-0.440551\pi\) | ||||
0.185680 | + | 0.982610i | \(0.440551\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37668.9 | 0.952490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −83957.2 | −1.97657 | −0.988284 | − | 0.152624i | \(-0.951228\pi\) | ||||
−0.988284 | + | 0.152624i | \(0.951228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28578.3 | −0.627668 | −0.313834 | − | 0.949478i | \(-0.601613\pi\) | ||||
−0.313834 | + | 0.949478i | \(0.601613\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25019.9 | −0.513610 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −59955.5 | −1.08084 | −0.540420 | − | 0.841396i | \(-0.681734\pi\) | ||||
−0.540420 | + | 0.841396i | \(0.681734\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −61583.0 | −0.981219 | −0.490610 | − | 0.871380i | \(-0.663226\pi\) | ||||
−0.490610 | + | 0.871380i | \(0.663226\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14222.4 | 0.213514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −37823.4 | −0.535751 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 42298.3 | 0.566042 | 0.283021 | − | 0.959114i | \(-0.408663\pi\) | ||||
0.283021 | + | 0.959114i | \(0.408663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21486.2 | −0.257603 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26269.5 | −0.298637 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 44638.1 | 0.481700 | 0.240850 | − | 0.970562i | \(-0.422574\pi\) | ||||
0.240850 | + | 0.970562i | \(0.422574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13075.5 | −0.134082 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −111924. | −1.09175 | −0.545873 | − | 0.837868i | \(-0.683802\pi\) | ||||
−0.545873 | + | 0.837868i | \(0.683802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 166949. | 1.55057 | 0.775285 | − | 0.631612i | \(-0.217606\pi\) | ||||
0.775285 | + | 0.631612i | \(0.217606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 102986. | 0.869595 | 0.434798 | − | 0.900528i | \(-0.356820\pi\) | ||||
0.434798 | + | 0.900528i | \(0.356820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −137821. | −1.11109 | −0.555546 | − | 0.831486i | \(-0.687491\pi\) | ||||
−0.555546 | + | 0.831486i | \(0.687491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6056.45 | −0.0466563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −129967. | −0.957495 | −0.478748 | − | 0.877953i | \(-0.658909\pi\) | ||||
−0.478748 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −77741.7 | −0.548162 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1144.39 | 0.00772877 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −134993. | −0.838199 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −37561.0 | −0.223859 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 109681. | 0.627853 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −243265. | −1.33835 | −0.669177 | − | 0.743103i | \(-0.733353\pi\) | ||||
−0.669177 | + | 0.743103i | \(0.733353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −48878.4 | −0.258609 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 194336. | 0.989405 | 0.494703 | − | 0.869062i | \(-0.335277\pi\) | ||||
0.494703 | + | 0.869062i | \(0.335277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13540.7 | −0.0639450 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3093.70 | −0.0140824 | −0.00704121 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00704121 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22600.4 | 0.0992155 | 0.0496078 | − | 0.998769i | \(-0.484203\pi\) | ||||
0.0496078 | + | 0.998769i | \(0.484203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56724.1 | 0.240281 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2280.67 | −0.00932658 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 78060.6 | 0.308327 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −352794. | −1.30183 | −0.650917 | − | 0.759149i | \(-0.725616\pi\) | ||||
−0.650917 | + | 0.759149i | \(0.725616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 145096. | 0.517863 | 0.258931 | − | 0.965896i | \(-0.416630\pi\) | ||||
0.258931 | + | 0.965896i | \(0.416630\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −62021.9 | −0.214199 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 44343.5 | 0.148252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −217895. | −0.705503 | −0.352751 | − | 0.935717i | \(-0.614754\pi\) | ||||
−0.352751 | + | 0.935717i | \(0.614754\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 147750. | 0.463484 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −322111. | −0.949591 | −0.474795 | − | 0.880096i | \(-0.657478\pi\) | ||||
−0.474795 | + | 0.880096i | \(0.657478\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26985.4 | 0.0771647 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 707392. | 1.96277 | 0.981384 | − | 0.192056i | \(-0.0615155\pi\) | ||||
0.981384 | + | 0.192056i | \(0.0615155\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −371093. | −0.999462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 114558. | 0.299594 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −170507. | −0.433140 | −0.216570 | − | 0.976267i | \(-0.569487\pi\) | ||||
−0.216570 | + | 0.976267i | \(0.569487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35698.4 | 0.0856477 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −415406. | −0.969037 | −0.484519 | − | 0.874781i | \(-0.661005\pi\) | ||||
−0.484519 | + | 0.874781i | \(0.661005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1162.38 | −0.00263726 | −0.00131863 | − | 0.999999i | \(-0.500420\pi\) | ||||
−0.00131863 | + | 0.999999i | \(0.500420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −453048. | −1.00004 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12499.4 | 0.0268510 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 123604. | 0.258481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −745614. | −1.47887 | −0.739436 | − | 0.673227i | \(-0.764908\pi\) | ||||
−0.739436 | + | 0.673227i | \(0.764908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −198373. | −0.383344 | −0.191672 | − | 0.981459i | \(-0.561391\pi\) | ||||
−0.191672 | + | 0.981459i | \(0.561391\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2361.82 | −0.00444795 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −469368. | −0.861684 | −0.430842 | − | 0.902427i | \(-0.641783\pi\) | ||||
−0.430842 | + | 0.902427i | \(0.641783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −193593. | −0.346544 | −0.173272 | − | 0.984874i | \(-0.555434\pi\) | ||||
−0.173272 | + | 0.984874i | \(0.555434\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 122807. | 0.214405 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 77519.0 | 0.128832 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 339020. | 0.549920 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −228303. | −0.361531 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −298066. | −0.460900 | −0.230450 | − | 0.973084i | \(-0.574020\pi\) | ||||
−0.230450 | + | 0.973084i | \(0.574020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −755615. | −1.14117 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 100876. | 0.148831 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −257205. | −0.362384 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10818.1 | −0.0148994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −187215. | −0.252103 | −0.126051 | − | 0.992024i | \(-0.540230\pi\) | ||||
−0.126051 | + | 0.992024i | \(0.540230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −225180. | −0.296533 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.33896e6 | −1.72466 | −0.862332 | − | 0.506344i | \(-0.830997\pi\) | ||||
−0.862332 | + | 0.506344i | \(0.830997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 951656. | 1.19920 | 0.599600 | − | 0.800300i | \(-0.295326\pi\) | ||||
0.599600 | + | 0.800300i | \(0.295326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 743419. | 0.897106 | 0.448553 | − | 0.893756i | \(-0.351940\pi\) | ||||
0.448553 | + | 0.893756i | \(0.351940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −117068. | −0.138283 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −539599. | −0.624023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −625847. | −0.708718 | −0.354359 | − | 0.935110i | \(-0.615301\pi\) | ||||
−0.354359 | + | 0.935110i | \(0.615301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.33282e6 | −1.47819 | −0.739094 | − | 0.673602i | \(-0.764746\pi\) | ||||
−0.739094 | + | 0.673602i | \(0.764746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19981.5 | 0.0208395 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −554247. | −0.566507 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.78809e6 | 1.79145 | 0.895726 | − | 0.444606i | \(-0.146656\pi\) | ||||
0.895726 | + | 0.444606i | \(0.146656\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −675636. | −0.663608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 128002. | 0.123272 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 508924. | 0.480640 | 0.240320 | − | 0.970694i | \(-0.422748\pi\) | ||||
0.240320 | + | 0.970694i | \(0.422748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −340411. | −0.309316 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −336493. | −0.299976 | −0.149988 | − | 0.988688i | \(-0.547924\pi\) | ||||
−0.149988 | + | 0.988688i | \(0.547924\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −304929. | −0.266737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 380685. | 0.326804 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.49553e6 | 1.26013 | 0.630064 | − | 0.776544i | \(-0.283029\pi\) | ||||
0.630064 | + | 0.776544i | \(0.283029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.77697e6 | −1.46979 | −0.734897 | − | 0.678179i | \(-0.762770\pi\) | ||||
−0.734897 | + | 0.678179i | \(0.762770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 448762. | 0.357837 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 881265. | 0.690092 | 0.345046 | − | 0.938586i | \(-0.387863\pi\) | ||||
0.345046 | + | 0.938586i | \(0.387863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −193375. | −0.148727 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.13932e6 | −0.860756 | −0.430378 | − | 0.902649i | \(-0.641620\pi\) | ||||
−0.430378 | + | 0.902649i | \(0.641620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −897466. | −0.666119 | −0.333059 | − | 0.942906i | \(-0.608081\pi\) | ||||
−0.333059 | + | 0.942906i | \(0.608081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −236426. | −0.172418 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −833556. | −0.587071 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 401743. | 0.278110 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.84614e6 | −1.25631 | −0.628153 | − | 0.778090i | \(-0.716189\pi\) | ||||
−0.628153 | + | 0.778090i | \(0.716189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73674.9 | −0.0492907 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −117679. | −0.0774121 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 59133.1 | 0.0382519 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.00732e6 | −0.630320 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 935008. | 0.575527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.38565e6 | 0.839089 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50254e6 | 0.895221 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.31248e6 | 1.35574 | 0.677871 | − | 0.735181i | \(-0.262903\pi\) | ||||
0.677871 | + | 0.735181i | \(0.262903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.16880e6 | −0.674341 | −0.337171 | − | 0.941444i | \(-0.609470\pi\) | ||||
−0.337171 | + | 0.941444i | \(0.609470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.43433e6 | 0.801681 | 0.400840 | − | 0.916148i | \(-0.368718\pi\) | ||||
0.400840 | + | 0.916148i | \(0.368718\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 678408. | 0.373262 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 926871. | 0.502061 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08293e6 | −0.577554 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39276.6 | −0.0206265 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.24039e6 | −0.641489 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.23418e6 | −1.12085 | −0.560426 | − | 0.828205i | \(-0.689362\pi\) | ||||
−0.560426 | + | 0.828205i | \(0.689362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −54508.0 | −0.0269371 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −253452. | −0.123391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.08787e6 | 1.48110 | 0.740549 | − | 0.672002i | \(-0.234565\pi\) | ||||
0.740549 | + | 0.672002i | \(0.234565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.16970e6 | −0.552810 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 385380. | 0.179475 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −699675. | −0.316482 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.11754e6 | −1.38992 | −0.694959 | − | 0.719050i | \(-0.744577\pi\) | ||||
−0.694959 | + | 0.719050i | \(0.744577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 613026. | 0.269411 | 0.134706 | − | 0.990886i | \(-0.456991\pi\) | ||||
0.134706 | + | 0.990886i | \(0.456991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10299.5 | 0.00446221 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.78370e6 | 1.61614 | 0.808071 | − | 0.589085i | \(-0.200512\pi\) | ||||
0.808071 | + | 0.589085i | \(0.200512\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.55945e6 | 0.656750 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.72213e6 | 1.52425 | 0.762125 | − | 0.647430i | \(-0.224156\pi\) | ||||
0.762125 | + | 0.647430i | \(0.224156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −475879. | −0.192189 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.21493e6 | −0.483934 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 530824. | 0.208554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.13795e6 | 1.60369 | 0.801845 | − | 0.597532i | \(-0.203852\pi\) | ||||
0.801845 | + | 0.597532i | \(0.203852\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −338049. | −0.129245 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.94418e6 | 1.09570 | 0.547851 | − | 0.836576i | \(-0.315446\pi\) | ||||
0.547851 | + | 0.836576i | \(0.315446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 987132. | 0.362491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −59375.7 | −0.0215157 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.97504e6 | 1.06388 | 0.531942 | − | 0.846781i | \(-0.321462\pi\) | ||||
0.531942 | + | 0.846781i | \(0.321462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.18939e6 | −0.772699 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.06104e6 | 0.717942 | 0.358971 | − | 0.933349i | \(-0.383128\pi\) | ||||
0.358971 | + | 0.933349i | \(0.383128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −439906. | −0.149308 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.09084e6 | 0.700562 | 0.350281 | − | 0.936645i | \(-0.386086\pi\) | ||||
0.350281 | + | 0.936645i | \(0.386086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.20480e6 | −1.06013 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.74902e6 | 0.571233 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.11363e6 | 0.359128 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.17129e6 | 0.372984 | 0.186492 | − | 0.982457i | \(-0.440288\pi\) | ||||
0.186492 | + | 0.982457i | \(0.440288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.09149e6 | 0.960078 | 0.480039 | − | 0.877247i | \(-0.340623\pi\) | ||||
0.480039 | + | 0.877247i | \(0.340623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33729.2 | −0.0103453 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −121866. | −0.0369187 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 108630. | 0.0325059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.34853e6 | −1.28539 | −0.642693 | − | 0.766124i | \(-0.722183\pi\) | ||||
−0.642693 | + | 0.766124i | \(0.722183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27843.3 | −0.00813048 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.14386e6 | 0.326028 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 203404. | 0.0572821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.13660e6 | 0.872818 | 0.436409 | − | 0.899748i | \(-0.356250\pi\) | ||||
0.436409 | + | 0.899748i | \(0.356250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.02560e6 | 1.65690 | 0.828448 | − | 0.560066i | \(-0.189224\pi\) | ||||
0.828448 | + | 0.560066i | \(0.189224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 510517. | 0.138726 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.12865e6 | 0.571652 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20526.0 | −0.00538471 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.29863e6 | −0.596040 | −0.298020 | − | 0.954560i | \(-0.596326\pi\) | ||||
−0.298020 | + | 0.954560i | \(0.596326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.62982e6 | −1.44303 | −0.721515 | − | 0.692399i | \(-0.756554\pi\) | ||||
−0.721515 | + | 0.692399i | \(0.756554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 702545. | 0.178013 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.91942e6 | 1.48278 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.44963e6 | −1.34960 | −0.674801 | − | 0.737999i | \(-0.735771\pi\) | ||||
−0.674801 | + | 0.737999i | \(0.735771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.70933e6 | 1.38222 | 0.691108 | − | 0.722751i | \(-0.257123\pi\) | ||||
0.691108 | + | 0.722751i | \(0.257123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −785664. | −0.188077 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.17515e6 | −0.751615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.38234e6 | 1.25996 | 0.629978 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629978 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 673701. | 0.155965 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.30587e6 | 0.298988 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.39051e6 | −1.43135 | −0.715673 | − | 0.698435i | \(-0.753880\pi\) | ||||
−0.715673 | + | 0.698435i | \(0.753880\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −558197. | −0.123668 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.34511e6 | 1.60970 | 0.804851 | − | 0.593476i | \(-0.202245\pi\) | ||||
0.804851 | + | 0.593476i | \(0.202245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.63416e6 | −1.00466 | −0.502329 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502329 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 399091. | 0.0855933 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.63195e6 | −1.61936 | −0.809680 | − | 0.586872i | \(-0.800359\pi\) | ||||
−0.809680 | + | 0.586872i | \(0.800359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.96106e6 | −0.407322 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 876693. | 0.180175 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.93172e6 | −0.799556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.32975e6 | 0.267593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.61262e6 | 1.91427 | 0.957135 | − | 0.289644i | \(-0.0935368\pi\) | ||||
0.957135 | + | 0.289644i | \(0.0935368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9507.49 | −0.00187371 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −829124. | −0.160053 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.80223e6 | 0.535404 | 0.267702 | − | 0.963502i | \(-0.413736\pi\) | ||||
0.267702 | + | 0.963502i | \(0.413736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.89900e6 | −0.548246 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.82008e6 | 0.902299 | 0.451149 | − | 0.892448i | \(-0.351014\pi\) | ||||
0.451149 | + | 0.892448i | \(0.351014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.21794e6 | 0.596295 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 242868. | 0.0445511 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.59658e6 | 0.826387 | 0.413194 | − | 0.910643i | \(-0.364413\pi\) | ||||
0.413194 | + | 0.910643i | \(0.364413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.36653e6 | 1.13320 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.80055e6 | 0.317311 | 0.158656 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158656 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.07892e6 | 0.362752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.33984e6 | −0.577040 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.83205e6 | −0.826678 | −0.413339 | − | 0.910577i | \(-0.635638\pi\) | ||||
−0.413339 | + | 0.910577i | \(0.635638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.03102e6 | 0.172971 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.10097e6 | −0.515204 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.01741e6 | −0.167406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.53457e6 | −0.250073 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.81125e6 | 0.453738 | 0.226869 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226869 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.45429e6 | −0.392349 | −0.196174 | − | 0.980569i | \(-0.562852\pi\) | ||||
−0.196174 | + | 0.980569i | \(0.562852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.82800e6 | 0.286715 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.10815e7 | 1.72171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 321286. | 0.0494487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58963.7 | −0.00899015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.91289e6 | −0.288939 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.73866e6 | −0.559474 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.15846e6 | −0.170172 | −0.0850862 | − | 0.996374i | \(-0.527117\pi\) | ||||
−0.0850862 | + | 0.996374i | \(0.527117\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10461.4 | −0.00152262 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.55994e6 | 0.369180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.63638e6 | 0.662538 | 0.331269 | − | 0.943536i | \(-0.392523\pi\) | ||||
0.331269 | + | 0.943536i | \(0.392523\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.07744e6 | −0.577373 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.94370e6 | −0.834023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 112495. | 0.0155024 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 271832. | 0.0371247 | 0.0185624 | − | 0.999828i | \(-0.494091\pi\) | ||||
0.0185624 | + | 0.999828i | \(0.494091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −76730.0 | −0.0103857 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.11244e6 | 0.149234 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.38244e6 | 0.449738 | 0.224869 | − | 0.974389i | \(-0.427805\pi\) | ||||
0.224869 | + | 0.974389i | \(0.427805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.41405e6 | 0.318145 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.31226e7 | 1.69918 | 0.849590 | − | 0.527443i | \(-0.176849\pi\) | ||||
0.849590 | + | 0.527443i | \(0.176849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.47162e7 | −1.88889 | −0.944443 | − | 0.328674i | \(-0.893398\pi\) | ||||
−0.944443 | + | 0.328674i | \(0.893398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.71053e6 | −0.853828 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.16355e7 | −1.46762 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.88295e6 | −0.485537 | −0.242769 | − | 0.970084i | \(-0.578056\pi\) | ||||
−0.242769 | + | 0.970084i | \(0.578056\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.78536e6 | −0.221324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.65007e6 | −0.322914 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21256.3 | −0.00256802 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.97913e6 | 0.596428 | 0.298214 | − | 0.954499i | \(-0.403609\pi\) | ||||
0.298214 | + | 0.954499i | \(0.403609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.37641e6 | −0.401021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.22431e6 | −0.497493 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.53269e7 | 1.78985 | 0.894926 | − | 0.446215i | \(-0.147228\pi\) | ||||
0.894926 | + | 0.446215i | \(0.147228\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.74234e6 | −0.200077 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.62961e6 | −0.754955 | −0.377477 | − | 0.926019i | \(-0.623208\pi\) | ||||
−0.377477 | + | 0.926019i | \(0.623208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45010e6 | −0.163762 | −0.0818808 | − | 0.996642i | \(-0.526093\pi\) | ||||
−0.0818808 | + | 0.996642i | \(0.526093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.10527e6 | 0.123787 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50740e6 | 0.278507 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.91110e6 | 0.430851 | 0.215425 | − | 0.976520i | \(-0.430886\pi\) | ||||
0.215425 | + | 0.976520i | \(0.430886\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 89046.1 | 0.00964966 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17753e7 | 1.26567 | 0.632835 | − | 0.774287i | \(-0.281891\pi\) | ||||
0.632835 | + | 0.774287i | \(0.281891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 697671. | 0.0743812 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.61462e6 | −0.488004 | −0.244002 | − | 0.969775i | \(-0.578460\pi\) | ||||
−0.244002 | + | 0.969775i | \(0.578460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.67466e6 | −0.595269 | −0.297634 | − | 0.954680i | \(-0.596198\pi\) | ||||
−0.297634 | + | 0.954680i | \(0.596198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.05118e6 | 0.317497 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.65022e6 | 0.680983 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.05473e6 | −0.208730 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 515271. | 0.0519289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.67894e6 | 0.567798 | 0.283899 | − | 0.958854i | \(-0.408372\pi\) | ||||
0.283899 | + | 0.958854i | \(0.408372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.68260e6 | −0.266101 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.51849e6 | 0.444692 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.80053e6 | −0.658856 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.10737e6 | −0.202580 | −0.101290 | − | 0.994857i | \(-0.532297\pi\) | ||||
−0.101290 | + | 0.994857i | \(0.532297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.30987e6 | −0.220323 | −0.110162 | − | 0.993914i | \(-0.535137\pi\) | ||||
−0.110162 | + | 0.993914i | \(0.535137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 907885. | 0.0859274 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.86066e6 | 0.926073 | 0.463036 | − | 0.886339i | \(-0.346760\pi\) | ||||
0.463036 | + | 0.886339i | \(0.346760\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −640293. | −0.0596715 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.00309e7 | 0.920570 | 0.460285 | − | 0.887771i | \(-0.347747\pi\) | ||||
0.460285 | + | 0.887771i | \(0.347747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.60966e6 | −0.328748 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.31484e6 | −0.209223 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.42828e7 | −1.28115 | −0.640575 | − | 0.767895i | \(-0.721304\pi\) | ||||
−0.640575 | + | 0.767895i | \(0.721304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.96419e7 | −1.74856 | −0.874280 | − | 0.485421i | \(-0.838666\pi\) | ||||
−0.874280 | + | 0.485421i | \(0.838666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −97362.7 | −0.00860219 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.75897e7 | −1.53089 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.68493e6 | −0.145552 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.12596e6 | 0.696736 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.00150e6 | −0.766086 | −0.383043 | − | 0.923731i | \(-0.625124\pi\) | ||||
−0.383043 | + | 0.923731i | \(0.625124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.02662e6 | −0.171203 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.34236e7 | 1.12564 | 0.562818 | − | 0.826581i | \(-0.309717\pi\) | ||||
0.562818 | + | 0.826581i | \(0.309717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.20507e7 | −0.995735 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.01681e6 | −0.657582 | −0.328791 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328791 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57463.5 | 0.00467913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.56491e6 | 0.692358 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 231940. | 0.0186135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.41973e7 | −1.92785 | −0.963923 | − | 0.266181i | \(-0.914238\pi\) | ||||
−0.963923 | + | 0.266181i | \(0.914238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −419788. | −0.0329661 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.19562e6 | 0.249157 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.69077e6 | 0.517944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.56268e6 | −0.120109 | −0.0600543 | − | 0.998195i | \(-0.519127\pi\) | ||||
−0.0600543 | + | 0.998195i | \(0.519127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −951732. | −0.0726317 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.05361e6 | −0.0798377 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.95390e7 | −1.45978 | −0.729889 | − | 0.683566i | \(-0.760428\pi\) | ||||
−0.729889 | + | 0.683566i | \(0.760428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.85639e6 | −0.360280 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.99210e6 | −0.736093 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42362.0 | 0.00309892 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.63262e6 | −0.409178 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.10190e6 | −0.584473 | −0.292237 | − | 0.956346i | \(-0.594399\pi\) | ||||
−0.292237 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.19954e7 | −0.853432 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.16832e7 | 0.825500 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.52759e7 | 1.77366 | 0.886829 | − | 0.462098i | \(-0.152903\pi\) | ||||
0.886829 | + | 0.462098i | \(0.152903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.15848e6 | 0.287834 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.74414e7 | 1.88646 | 0.943228 | − | 0.332145i | \(-0.107772\pi\) | ||||
0.943228 | + | 0.332145i | \(0.107772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.20270e6 | −0.149378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.53569e6 | −0.440231 | −0.220115 | − | 0.975474i | \(-0.570643\pi\) | ||||
−0.220115 | + | 0.975474i | \(0.570643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 179834. | 0.0120317 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.46784e7 | −1.64000 | −0.820001 | − | 0.572362i | \(-0.806027\pi\) | ||||
−0.820001 | + | 0.572362i | \(0.806027\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.55292e6 | 0.432558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.98823e6 | −0.327073 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.27822e6 | −0.212099 | −0.106049 | − | 0.994361i | \(-0.533820\pi\) | ||||
−0.106049 | + | 0.994361i | \(0.533820\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.60928e7 | 1.03430 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.69507e6 | −0.172069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.68090e6 | 0.233461 | 0.116731 | − | 0.993164i | \(-0.462759\pi\) | ||||
0.116731 | + | 0.993164i | \(0.462759\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.08073e6 | −0.383134 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.10198e7 | 1.31573 | 0.657866 | − | 0.753135i | \(-0.271459\pi\) | ||||
0.657866 | + | 0.753135i | \(0.271459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.15202e6 | 0.0711713 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56039.8 | 0.00343960 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.15418e6 | −0.253320 | −0.126660 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126660 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.58032e6 | 0.277498 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.46348e6 | 0.0880924 | 0.0440462 | − | 0.999029i | \(-0.485975\pi\) | ||||
0.0440462 | + | 0.999029i | \(0.485975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.63682e6 | 0.396923 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.90247e6 | −0.348490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.35528e7 | 0.795065 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.06370e6 | −0.178584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.04726e6 | 0.234416 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.01711e7 | −1.16089 | −0.580446 | − | 0.814299i | \(-0.697122\pi\) | ||||
−0.580446 | + | 0.814299i | \(0.697122\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.02844e6 | −0.173191 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −711201. | −0.0401614 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.74436e6 | −0.154001 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.19496e7 | 1.22400 | 0.612000 | − | 0.790858i | \(-0.290365\pi\) | ||||
0.612000 | + | 0.790858i | \(0.290365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.82598e6 | −0.267435 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.42617e6 | 0.188681 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.61328e6 | 0.252476 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.34598e7 | 0.727535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.36276e7 | −1.26926 | −0.634628 | − | 0.772818i | \(-0.718847\pi\) | ||||
−0.634628 | + | 0.772818i | \(0.718847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.85032e6 | −0.152174 | −0.0760872 | − | 0.997101i | \(-0.524243\pi\) | ||||
−0.0760872 | + | 0.997101i | \(0.524243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.59927e7 | −0.848586 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.98300e6 | 0.315518 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.68093e6 | −0.402586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.41313e7 | −0.731685 | −0.365843 | − | 0.930677i | \(-0.619219\pi\) | ||||
−0.365843 | + | 0.930677i | \(0.619219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.23188e7 | −1.66324 | −0.831620 | − | 0.555345i | \(-0.812586\pi\) | ||||
−0.831620 | + | 0.555345i | \(0.812586\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.03886e6 | 0.206597 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.35291e7 | −1.70474 | −0.852369 | − | 0.522941i | \(-0.824835\pi\) | ||||
−0.852369 | + | 0.522941i | \(0.824835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.99517e7 | −1.00831 | −0.504154 | − | 0.863614i | \(-0.668195\pi\) | ||||
−0.504154 | + | 0.863614i | \(0.668195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.93138e6 | 0.398425 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.31393e7 | −0.652165 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.74038e6 | −0.0858677 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.34067e6 | −0.114798 | −0.0573990 | − | 0.998351i | \(-0.518281\pi\) | ||||
−0.0573990 | + | 0.998351i | \(0.518281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.84928e6 | −0.138914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.02539e7 | −0.496958 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.89281e6 | 0.332089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.07719e6 | −0.384584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.81654e6 | −0.133319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.79465e7 | −0.844514 | −0.422257 | − | 0.906476i | \(-0.638762\pi\) | ||||
−0.422257 | + | 0.906476i | \(0.638762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.12783e6 | −0.0995456 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.68442e7 | −1.71363 | −0.856815 | − | 0.515624i | \(-0.827560\pi\) | ||||
−0.856815 | + | 0.515624i | \(0.827560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.40612e7 | 1.11259 | 0.556293 | − | 0.830986i | \(-0.312223\pi\) | ||||
0.556293 | + | 0.830986i | \(0.312223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.64770e7 | 0.753098 | 0.376549 | − | 0.926397i | \(-0.377111\pi\) | ||||
0.376549 | + | 0.926397i | \(0.377111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.16706e6 | 0.143918 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.50201e6 | −0.338945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.67835e6 | 0.434762 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 192784. | 0.00861046 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.61569e6 | 0.160567 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.04983e7 | 1.33899 | 0.669494 | − | 0.742817i | \(-0.266511\pi\) | ||||
0.669494 | + | 0.742817i | \(0.266511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.66153e7 | −0.725329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.35008e7 | 1.02010 | 0.510051 | − | 0.860144i | \(-0.329627\pi\) | ||||
0.510051 | + | 0.860144i | \(0.329627\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.42812e7 | −1.91125 | −0.955625 | − | 0.294587i | \(-0.904818\pi\) | ||||
−0.955625 | + | 0.294587i | \(0.904818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −663074. | −0.0284580 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.52662e7 | −0.651510 | −0.325755 | − | 0.945454i | \(-0.605618\pi\) | ||||
−0.325755 | + | 0.945454i | \(0.605618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.05911e6 | −0.0446939 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.91382e6 | 0.374055 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.71590e6 | 0.321980 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 532198. | 0.0220847 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.00331e7 | 0.414033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.25703e7 | −0.515862 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21590.5 | 0.000876275 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.67694e7 | 1.08049 | 0.540245 | − | 0.841508i | \(-0.318332\pi\) | ||||
0.540245 | + | 0.841508i | \(0.318332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.06588e6 | −0.363915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.60537e7 | 0.640883 | 0.320442 | − | 0.947268i | \(-0.396169\pi\) | ||||
0.320442 | + | 0.947268i | \(0.396169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.94108e6 | 0.394691 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.41507e6 | 0.332281 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08072e7 | 0.422107 | 0.211053 | − | 0.977475i | \(-0.432311\pi\) | ||||
0.211053 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.24709e7 | 0.484448 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.18617e6 | −0.0458293 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.87077e6 | 0.0718894 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.35229e7 | 0.516856 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.16937e6 | −0.0824695 | −0.0412348 | − | 0.999149i | \(-0.513129\pi\) | ||||
−0.0412348 | + | 0.999149i | \(0.513129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.08123e7 | 0.782738 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.29586e6 | −0.0858849 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.51305e6 | −0.130718 | −0.0653589 | − | 0.997862i | \(-0.520819\pi\) | ||||
−0.0653589 | + | 0.997862i | \(0.520819\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.05192e7 | −0.389331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.29297e7 | −0.476008 | −0.238004 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238004 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.74677e7 | −0.639670 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.48662e7 | −0.901019 | −0.450510 | − | 0.892772i | \(-0.648758\pi\) | ||||
−0.450510 | + | 0.892772i | \(0.648758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −403763. | −0.0145533 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.29090e7 | 0.462850 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.33465e7 | 1.18937 | 0.594686 | − | 0.803958i | \(-0.297276\pi\) | ||||
0.594686 | + | 0.803958i | \(0.297276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.38493e7 | 0.491382 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.10567e6 | 0.215503 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.29297e7 | −0.800922 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.34184e6 | 0.289865 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.68465e6 | 0.127373 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.48706e7 | −0.855305 | −0.427652 | − | 0.903943i | \(-0.640659\pi\) | ||||
−0.427652 | + | 0.903943i | \(0.640659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.74634e6 | −0.333451 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.79491e7 | −1.63205 | −0.816024 | − | 0.578018i | \(-0.803826\pi\) | ||||
−0.816024 | + | 0.578018i | \(0.803826\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −353489. | −0.0119087 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.85191e6 | −0.263171 | −0.131586 | − | 0.991305i | \(-0.542007\pi\) | ||||
−0.131586 | + | 0.991305i | \(0.542007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.82804e6 | −0.227687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.11635e7 | −0.370364 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.84868e7 | −0.940284 | −0.470142 | − | 0.882591i | \(-0.655797\pi\) | ||||
−0.470142 | + | 0.882591i | \(0.655797\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.71820e6 | 0.286310 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.27308e7 | −0.738966 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.03795e7 | −0.335733 | −0.167867 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167867 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.01076e7 | −0.647124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.59587e6 | 0.115145 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.68161e7 | 0.535781 | 0.267890 | − | 0.963449i | \(-0.413674\pi\) | ||||
0.267890 | + | 0.963449i | \(0.413674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −490572. | −0.0155521 |
(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 | 588.6.a.l.1.1 | 2 | ||
7.2 | even | 3 | 84.6.i.b.25.2 | ✓ | 4 | ||
7.3 | odd | 6 | 588.6.i.m.373.1 | 4 | |||
7.4 | even | 3 | 84.6.i.b.37.2 | yes | 4 | ||
7.5 | odd | 6 | 588.6.i.m.361.1 | 4 | |||
7.6 | odd | 2 | 588.6.a.h.1.2 | 2 | |||
21.2 | odd | 6 | 252.6.k.e.109.1 | 4 | |||
21.11 | odd | 6 | 252.6.k.e.37.1 | 4 | |||
28.11 | odd | 6 | 336.6.q.g.289.2 | 4 | |||
28.23 | odd | 6 | 336.6.q.g.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.i.b.25.2 | ✓ | 4 | 7.2 | even | 3 | ||
84.6.i.b.37.2 | yes | 4 | 7.4 | even | 3 | ||
252.6.k.e.37.1 | 4 | 21.11 | odd | 6 | |||
252.6.k.e.109.1 | 4 | 21.2 | odd | 6 | |||
336.6.q.g.193.2 | 4 | 28.23 | odd | 6 | |||
336.6.q.g.289.2 | 4 | 28.11 | odd | 6 | |||
588.6.a.h.1.2 | 2 | 7.6 | odd | 2 | |||
588.6.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
588.6.i.m.361.1 | 4 | 7.5 | odd | 6 | |||
588.6.i.m.373.1 | 4 | 7.3 | odd | 6 |