Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{70}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 70 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.36660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-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 | ||||||||
\(3\) | −12.7332 | −0.816835 | −0.408418 | − | 0.912795i | \(-0.633919\pi\) | ||||
−0.408418 | + | 0.912795i | \(0.633919\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −68.7332 | −0.530178 | −0.265089 | − | 0.964224i | \(-0.585401\pi\) | ||||
−0.265089 | + | 0.964224i | \(0.585401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −80.8656 | −0.332780 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 327.332 | 0.815655 | 0.407828 | − | 0.913059i | \(-0.366286\pi\) | ||||
0.407828 | + | 0.913059i | \(0.366286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 719.328 | 1.18051 | 0.590254 | − | 0.807218i | \(-0.299028\pi\) | ||||
0.590254 | + | 0.807218i | \(0.299028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 318.330 | 0.365300 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −379.328 | −0.318341 | −0.159171 | − | 0.987251i | \(-0.550882\pi\) | ||||
−0.159171 | + | 0.987251i | \(0.550882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1029.33 | 0.654139 | 0.327069 | − | 0.945000i | \(-0.393939\pi\) | ||||
0.327069 | + | 0.945000i | \(0.393939\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 875.194 | 0.433068 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 779.120 | 0.307104 | 0.153552 | − | 0.988141i | \(-0.450929\pi\) | ||||
0.153552 | + | 0.988141i | \(0.450929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4123.85 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1392.66 | −0.307503 | −0.153751 | − | 0.988110i | \(-0.549135\pi\) | ||||
−0.153751 | + | 0.988110i | \(0.549135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2744.68 | −0.512965 | −0.256483 | − | 0.966549i | \(-0.582564\pi\) | ||||
−0.256483 | + | 0.966549i | \(0.582564\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4167.98 | −0.666256 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1718.33 | 0.237103 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12640.6 | −1.51797 | −0.758985 | − | 0.651108i | \(-0.774304\pi\) | ||||
−0.758985 | + | 0.651108i | \(0.774304\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9159.35 | −0.964280 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8210.43 | 0.762792 | 0.381396 | − | 0.924412i | \(-0.375443\pi\) | ||||
0.381396 | + | 0.924412i | \(0.375443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22524.5 | 1.85774 | 0.928869 | − | 0.370408i | \(-0.120782\pi\) | ||||
0.928869 | + | 0.370408i | \(0.120782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2021.64 | 0.148824 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7739.18 | −0.511035 | −0.255517 | − | 0.966804i | \(-0.582246\pi\) | ||||
−0.255517 | + | 0.966804i | \(0.582246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12082.7 | −0.718912 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4830.06 | 0.260032 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2401.86 | 0.117451 | 0.0587256 | − | 0.998274i | \(-0.481296\pi\) | ||||
0.0587256 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8183.30 | −0.364772 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13106.6 | −0.534323 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15734.7 | 0.588474 | 0.294237 | − | 0.955732i | \(-0.404934\pi\) | ||||
0.294237 | + | 0.955732i | \(0.404934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32082.1 | −1.10392 | −0.551961 | − | 0.833870i | \(-0.686120\pi\) | ||||
−0.551961 | + | 0.833870i | \(0.686120\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5558.15 | 0.176433 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17983.2 | −0.527939 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9009.07 | 0.245184 | 0.122592 | − | 0.992457i | \(-0.460879\pi\) | ||||
0.122592 | + | 0.992457i | \(0.460879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9920.70 | −0.250853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −43832.3 | −1.03192 | −0.515962 | − | 0.856611i | \(-0.672566\pi\) | ||||
−0.515962 | + | 0.856611i | \(0.672566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65837.5 | −1.44599 | −0.722997 | − | 0.690852i | \(-0.757236\pi\) | ||||
−0.722997 | + | 0.690852i | \(0.757236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7958.25 | −0.163367 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22498.6 | −0.432442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39601.3 | −0.713907 | −0.356954 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356954 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −32859.4 | −0.556477 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63101.4 | −1.00541 | −0.502706 | − | 0.864458i | \(-0.667662\pi\) | ||||
−0.502706 | + | 0.864458i | \(0.667662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9483.20 | 0.142366 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17733.0 | 0.251179 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34510.9 | 0.461829 | 0.230915 | − | 0.972974i | \(-0.425828\pi\) | ||||
0.230915 | + | 0.972974i | \(0.425828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49441.7 | −0.625879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34948.6 | 0.419008 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25733.2 | −0.292540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14081.3 | −0.151955 | −0.0759773 | − | 0.997110i | \(-0.524208\pi\) | ||||
−0.0759773 | + | 0.997110i | \(0.524208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26469.9 | −0.271434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −184018. | −1.79497 | −0.897485 | − | 0.441044i | \(-0.854608\pi\) | ||||
−0.897485 | + | 0.441044i | \(0.854608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70168.0 | 0.651697 | 0.325849 | − | 0.945422i | \(-0.394350\pi\) | ||||
0.325849 | + | 0.945422i | \(0.394350\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −21879.8 | −0.193674 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7952.89 | 0.0671530 | 0.0335765 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335765 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −168681. | −1.35988 | −0.679939 | − | 0.733269i | \(-0.737994\pi\) | ||||
−0.679939 | + | 0.733269i | \(0.737994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 160955. | 1.23993 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −61891.3 | −0.455967 | −0.227984 | − | 0.973665i | \(-0.573213\pi\) | ||||
−0.227984 | + | 0.973665i | \(0.573213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19478.0 | −0.137341 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −58168.9 | −0.392849 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26072.4 | 0.168777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53904.8 | −0.334706 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −104545. | −0.623075 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 358695. | 1.97340 | 0.986702 | − | 0.162538i | \(-0.0519681\pi\) | ||||
0.986702 | + | 0.162538i | \(0.0519681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −286809. | −1.51747 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −312592. | −1.59148 | −0.795738 | − | 0.605641i | \(-0.792917\pi\) | ||||
−0.795738 | + | 0.605641i | \(0.792917\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −70749.0 | −0.346810 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −103096. | −0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −33573.9 | −0.152827 | −0.0764135 | − | 0.997076i | \(-0.524347\pi\) | ||||
−0.0764135 | + | 0.997076i | \(0.524347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 342175. | 1.50214 | 0.751072 | − | 0.660220i | \(-0.229537\pi\) | ||||
0.751072 | + | 0.660220i | \(0.229537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98544.6 | 0.417431 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 235459. | 0.962887 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34816.4 | 0.137519 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 153852. | 0.587232 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 239318. | 0.883099 | 0.441549 | − | 0.897237i | \(-0.354429\pi\) | ||||
0.441549 | + | 0.897237i | \(0.354429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −169513. | −0.605007 | −0.302503 | − | 0.953148i | \(-0.597822\pi\) | ||||
−0.302503 | + | 0.953148i | \(0.597822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 30674.6 | 0.105938 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 68617.1 | 0.229405 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −186382. | −0.603469 | −0.301735 | − | 0.953392i | \(-0.597566\pi\) | ||||
−0.301735 | + | 0.953392i | \(0.597566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30583.3 | −0.0959383 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −53551.4 | −0.162820 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −403058. | −1.18822 | −0.594112 | − | 0.804382i | \(-0.702496\pi\) | ||||
−0.594112 | + | 0.804382i | \(0.702496\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 104200. | 0.297959 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −167631. | −0.465119 | −0.232560 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232560 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 146140. | 0.393597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −83237.2 | −0.217684 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −84080.4 | −0.213589 | −0.106795 | − | 0.994281i | \(-0.534059\pi\) | ||||
−0.106795 | + | 0.994281i | \(0.534059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −42958.3 | −0.106036 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −200353. | −0.480686 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 741698. | 1.73019 | 0.865096 | − | 0.501607i | \(-0.167257\pi\) | ||||
0.865096 | + | 0.501607i | \(0.167257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 343670. | 0.779732 | 0.389866 | − | 0.920872i | \(-0.372521\pi\) | ||||
0.389866 | + | 0.920872i | \(0.372521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 408508. | 0.901722 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 316015. | 0.678857 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −124166. | −0.259657 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −283445. | −0.577184 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −631035. | −1.25161 | −0.625806 | − | 0.779978i | \(-0.715230\pi\) | ||||
−0.625806 | + | 0.779978i | \(0.715230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 847791. | 1.63831 | 0.819154 | − | 0.573574i | \(-0.194444\pi\) | ||||
0.819154 | + | 0.573574i | \(0.194444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 228984. | 0.431239 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 397282. | 0.729346 | 0.364673 | − | 0.931136i | \(-0.381181\pi\) | ||||
0.364673 | + | 0.931136i | \(0.381181\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −896038. | −1.60396 | −0.801980 | − | 0.597350i | \(-0.796220\pi\) | ||||
−0.801980 | + | 0.597350i | \(0.796220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −114714. | −0.200275 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 95721.7 | 0.163031 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −205261. | −0.341131 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −63004.0 | −0.102198 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 336932. | 0.533552 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −876761. | −1.35574 | −0.677868 | − | 0.735184i | \(-0.737096\pi\) | ||||
−0.677868 | + | 0.735184i | \(0.737096\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 558125. | 0.842913 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −563113. | −0.830806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 188651. | 0.271963 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 838322. | 1.18114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −272861. | −0.375804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −54891.1 | −0.0739162 | −0.0369581 | − | 0.999317i | \(-0.511767\pi\) | ||||
−0.0369581 | + | 0.999317i | \(0.511767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50541.0 | −0.0665561 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 803329. | 1.03473 | 0.517367 | − | 0.855764i | \(-0.326912\pi\) | ||||
0.517367 | + | 0.855764i | \(0.326912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 589546. | 0.742898 | 0.371449 | − | 0.928453i | \(-0.378861\pi\) | ||||
0.371449 | + | 0.928453i | \(0.378861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 286479. | 0.353234 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.02048e6 | 1.23144 | 0.615720 | − | 0.787965i | \(-0.288865\pi\) | ||||
0.615720 | + | 0.787965i | \(0.288865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 193480. | 0.228542 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 504251. | 0.583145 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.65512e6 | −1.87428 | −0.937139 | − | 0.348956i | \(-0.886536\pi\) | ||||
−0.937139 | + | 0.348956i | \(0.886536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.19028e6 | −1.32010 | −0.660049 | − | 0.751223i | \(-0.729464\pi\) | ||||
−0.660049 | + | 0.751223i | \(0.729464\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −583689. | −0.634112 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 302069. | 0.321507 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 740424. | 0.772215 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 803483. | 0.821256 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23776.0 | −0.0238207 | −0.0119104 | − | 0.999929i | \(-0.503791\pi\) | ||||
−0.0119104 | + | 0.999929i | \(0.503791\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 255031. | 0.250491 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −120751. | −0.116290 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −341681. | −0.322692 | −0.161346 | − | 0.986898i | \(-0.551584\pi\) | ||||
−0.161346 | + | 0.986898i | \(0.551584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 868828. | 0.804794 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 112618. | 0.102331 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.09120e6 | 0.972782 | 0.486391 | − | 0.873741i | \(-0.338313\pi\) | ||||
0.486391 | + | 0.873741i | \(0.338313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −60046.4 | −0.0525258 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −439434. | −0.377238 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 922907. | 0.777638 | 0.388819 | − | 0.921314i | \(-0.372883\pi\) | ||||
0.388819 | + | 0.921314i | \(0.372883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.34302e6 | 1.11086 | 0.555430 | − | 0.831564i | \(-0.312554\pi\) | ||||
0.555430 | + | 0.831564i | \(0.312554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 629551. | 0.511240 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 204583. | 0.163131 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 247543. | 0.193843 | 0.0969217 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969217 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 221951. | 0.170705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.03588e6 | 0.782604 | 0.391302 | − | 0.920262i | \(-0.372025\pi\) | ||||
0.391302 | + | 0.920262i | \(0.372025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.39427e6 | −1.77708 | −0.888542 | − | 0.458795i | \(-0.848281\pi\) | ||||
−0.888542 | + | 0.458795i | \(0.848281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 327666. | 0.238957 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −564329. | −0.404415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.27597e6 | −0.898659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 179300. | 0.124122 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.44817e6 | 1.66599 | 0.832995 | − | 0.553280i | \(-0.186624\pi\) | ||||
0.832995 | + | 0.553280i | \(0.186624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −393367. | −0.263174 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.34987e6 | 0.887973 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 560443. | 0.362538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.54818e6 | −0.984931 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34314e6 | 1.46620 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 802053. | 0.493689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −939476. | −0.568905 | −0.284453 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284453 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −893463. | −0.532329 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.13941e6 | 0.668004 | 0.334002 | − | 0.942572i | \(-0.391601\pi\) | ||||
0.334002 | + | 0.942572i | \(0.391601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.51692e6 | 0.875191 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −138954. | −0.0789031 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.73484e6 | −1.52857 | −0.764284 | − | 0.644880i | \(-0.776907\pi\) | ||||
−0.764284 | + | 0.644880i | \(0.776907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −455861. | −0.250816 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −101266. | −0.0548530 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −390453. | −0.208239 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 449580. | 0.236101 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.14785e6 | 1.11080 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 531939. | 0.270939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 122807. | 0.0616104 | 0.0308052 | − | 0.999525i | \(-0.490193\pi\) | ||||
0.0308052 | + | 0.999525i | \(0.490193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.02219e6 | 0.505150 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −225227. | −0.109650 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.65582e6 | −0.794217 | −0.397108 | − | 0.917772i | \(-0.629986\pi\) | ||||
−0.397108 | + | 0.917772i | \(0.629986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 788075. | 0.372450 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −898423. | −0.418403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.98568e6 | 0.911329 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 248017. | 0.112185 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.63896e6 | −0.730711 | −0.365355 | − | 0.930868i | \(-0.619052\pi\) | ||||
−0.365355 | + | 0.930868i | \(0.619052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.07756e6 | −0.913040 | −0.456520 | − | 0.889713i | \(-0.650904\pi\) | ||||
−0.456520 | + | 0.889713i | \(0.650904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96640e6 | 1.28517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.87344e6 | −1.65447 | −0.827236 | − | 0.561854i | \(-0.810088\pi\) | ||||
−0.827236 | + | 0.561854i | \(0.810088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.09581e6 | 0.461491 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −331985. | −0.137863 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.16016e6 | −1.29411 | −0.647057 | − | 0.762441i | \(-0.724001\pi\) | ||||
−0.647057 | + | 0.762441i | \(0.724001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.41658e6 | −0.572103 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 686380. | 0.273400 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.64594e6 | 0.646668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.76875e6 | −0.685491 | −0.342745 | − | 0.939428i | \(-0.611357\pi\) | ||||
−0.342745 | + | 0.939428i | \(0.611357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −663941. | −0.253842 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −165087. | −0.0622700 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.86744e6 | 1.43930 | 0.719651 | − | 0.694336i | \(-0.244302\pi\) | ||||
0.719651 | + | 0.694336i | \(0.244302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 198956. | 0.0730600 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00178e6 | −0.363009 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.06193e6 | −1.81016 | −0.905082 | − | 0.425236i | \(-0.860191\pi\) | ||||
−0.905082 | + | 0.425236i | \(0.860191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.56734e6 | −1.61195 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.23524e6 | −1.47530 | −0.737652 | − | 0.675181i | \(-0.764065\pi\) | ||||
−0.737652 | + | 0.675181i | \(0.764065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 562464. | 0.193394 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.82146e6 | −0.618219 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 390940. | 0.130989 | 0.0654947 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654947 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −295542. | −0.0977637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.98030e6 | 1.29997 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 990033. | 0.319269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.36908e6 | −1.07284 | −0.536421 | − | 0.843951i | \(-0.680224\pi\) | ||||
−0.536421 | + | 0.843951i | \(0.680224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 900861. | 0.283286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.51542e6 | −1.71284 | −0.856422 | − | 0.516277i | \(-0.827318\pi\) | ||||
−0.856422 | + | 0.516277i | \(0.827318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.97433e6 | −0.605559 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 821485. | 0.248864 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.13767e6 | −1.23814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.29662e6 | −0.974453 | −0.487227 | − | 0.873276i | \(-0.661991\pi\) | ||||
−0.487227 | + | 0.873276i | \(0.661991\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 427503. | 0.124834 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.08149e6 | −0.311996 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.57754e6 | 0.449634 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.35699e6 | −1.22700 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.88088e6 | 1.91474 | 0.957368 | − | 0.288870i | \(-0.0932795\pi\) | ||||
0.957368 | + | 0.288870i | \(0.0932795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.04971e6 | −0.838596 | −0.419298 | − | 0.907849i | \(-0.637724\pi\) | ||||
−0.419298 | + | 0.907849i | \(0.637724\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 625834. | 0.170062 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −237080. | −0.0636682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.20511e6 | 0.585275 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.99815e6 | −0.786520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.20632e6 | −1.60931 | −0.804657 | − | 0.593740i | \(-0.797651\pi\) | ||||
−0.804657 | + | 0.593740i | \(0.797651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.87723e6 | 0.481169 | 0.240585 | − | 0.970628i | \(-0.422661\pi\) | ||||
0.240585 | + | 0.970628i | \(0.422661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −443324. | −0.112331 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 801971. | 0.200888 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.85883e6 | −0.460341 | −0.230170 | − | 0.973150i | \(-0.573928\pi\) | ||||
−0.230170 | + | 0.973150i | \(0.573928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 977079. | 0.239240 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.39604e6 | 1.06427 | 0.532136 | − | 0.846659i | \(-0.321390\pi\) | ||||
0.532136 | + | 0.846659i | \(0.321390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −862772. | −0.206536 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.04728e6 | −0.721346 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −984885. | −0.230552 | −0.115276 | − | 0.993333i | \(-0.536775\pi\) | ||||
−0.115276 | + | 0.993333i | \(0.536775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.68754e6 | 0.622175 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.15844e6 | 0.494191 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.23604e6 | 0.279901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −696014. | −0.155893 | −0.0779466 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779466 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.56429e6 | −0.346566 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.03623e6 | −1.32286 | −0.661430 | − | 0.750007i | \(-0.730050\pi\) | ||||
−0.661430 | + | 0.750007i | \(0.730050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.07793e6 | −0.450483 | −0.225241 | − | 0.974303i | \(-0.572317\pi\) | ||||
−0.225241 | + | 0.974303i | \(0.572317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −873715. | −0.187386 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.81361e6 | 0.384816 | 0.192408 | − | 0.981315i | \(-0.438370\pi\) | ||||
0.192408 | + | 0.981315i | \(0.438370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −619222. | −0.129991 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.37324e6 | 0.492935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.37300e6 | 1.51527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 643330. | 0.130828 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −194228. | −0.0390854 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.10687e6 | 1.21613 | 0.608065 | − | 0.793887i | \(-0.291946\pi\) | ||||
0.608065 | + | 0.793887i | \(0.291946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.09273e6 | −1.79197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 681881. | 0.132997 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 352033. | 0.0679561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.32848e6 | 0.253823 | 0.126912 | − | 0.991914i | \(-0.459494\pi\) | ||||
0.126912 | + | 0.991914i | \(0.459494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.13222e6 | 0.970583 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.72480e6 | 1.63325 | 0.816623 | − | 0.577171i | \(-0.195843\pi\) | ||||
0.816623 | + | 0.577171i | \(0.195843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 528273. | 0.0978907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 661748. | 0.121389 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01273e6 | 0.547104 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.20143e6 | −0.935129 | −0.467564 | − | 0.883959i | \(-0.654868\pi\) | ||||
−0.467564 | + | 0.883959i | \(0.654868\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.13448e6 | 0.379926 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.44189e6 | −1.13525 | −0.567627 | − | 0.823286i | \(-0.692139\pi\) | ||||
−0.567627 | + | 0.823286i | \(0.692139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.60045e6 | 0.802735 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.86083e6 | −0.321504 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.31511e6 | 0.396075 | 0.198038 | − | 0.980194i | \(-0.436543\pi\) | ||||
0.198038 | + | 0.980194i | \(0.436543\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.52522e6 | 0.766633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.24479e6 | 0.712136 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.75420e6 | −0.291448 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.53328e6 | −0.416828 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.07061e6 | 0.174467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.65617e6 | −1.55851 | −0.779257 | − | 0.626705i | \(-0.784403\pi\) | ||||
−0.779257 | + | 0.626705i | \(0.784403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.40583e6 | 1.02405 | 0.512025 | − | 0.858970i | \(-0.328895\pi\) | ||||
0.512025 | + | 0.858970i | \(0.328895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 546996. | 0.0866136 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.04114e6 | 0.163298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.82931e6 | −0.905687 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.27239e6 | −0.195833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.90599e6 | 0.900481 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −198822. | −0.0300317 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.44418e6 | −1.41328 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.95507e6 | −0.586384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32300e6 | −0.194342 | −0.0971709 | − | 0.995268i | \(-0.530979\pi\) | ||||
−0.0971709 | + | 0.995268i | \(0.530979\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.37602e6 | −0.636912 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.21702e6 | 0.608156 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68044e6 | −0.668834 | −0.334417 | − | 0.942425i | \(-0.608539\pi\) | ||||
−0.334417 | + | 0.942425i | \(0.608539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.59434e6 | 0.367363 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.43350e6 | −0.201149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.72192e6 | 0.378498 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.02388e6 | −0.554514 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.58860e6 | −1.03639 | −0.518195 | − | 0.855262i | \(-0.673396\pi\) | ||||
−0.518195 | + | 0.855262i | \(0.673396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.62025e7 | 2.19307 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.58103e6 | 0.212097 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 399946. | 0.0531777 | 0.0265889 | − | 0.999646i | \(-0.491536\pi\) | ||||
0.0265889 | + | 0.999646i | \(0.491536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54728e6 | 0.203915 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.25853e6 | 0.295032 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.57419e6 | 0.203834 | 0.101917 | − | 0.994793i | \(-0.467502\pi\) | ||||
0.101917 | + | 0.994793i | \(0.467502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.11290e6 | −0.399554 | −0.199777 | − | 0.979841i | \(-0.564022\pi\) | ||||
−0.199777 | + | 0.979841i | \(0.564022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.03509e6 | 1.02236 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 486950. | 0.0614207 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.57621e6 | −0.697267 | −0.348634 | − | 0.937259i | \(-0.613354\pi\) | ||||
−0.348634 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.07951e7 | −1.33823 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.33716e6 | 0.533047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 786205. | 0.0957997 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.45422e6 | 0.175688 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.11890e7 | 1.34028 | 0.670138 | − | 0.742236i | \(-0.266235\pi\) | ||||
0.670138 | + | 0.742236i | \(0.266235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.82518e6 | −0.335551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.05868e6 | −0.595756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.44707e7 | 1.68987 | 0.844934 | − | 0.534871i | \(-0.179640\pi\) | ||||
0.844934 | + | 0.534871i | \(0.179640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −651811. | −0.0754795 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.14094e7 | 1.31017 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.32734e6 | 0.265028 | 0.132514 | − | 0.991181i | \(-0.457695\pi\) | ||||
0.132514 | + | 0.991181i | \(0.457695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.28568e6 | 0.483987 | 0.241993 | − | 0.970278i | \(-0.422199\pi\) | ||||
0.241993 | + | 0.970278i | \(0.422199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −728524. | −0.0815925 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.34762e6 | 0.149685 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.04310e7 | 1.14909 | 0.574547 | − | 0.818471i | \(-0.305178\pi\) | ||||
0.574547 | + | 0.818471i | \(0.305178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.21884e6 | −0.133170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.56701e6 | −0.603280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.52495e6 | −0.378880 | −0.189440 | − | 0.981892i | \(-0.560667\pi\) | ||||
−0.189440 | + | 0.981892i | \(0.560667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.61363e6 | 0.278648 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.16178e7 | 1.22861 | 0.614303 | − | 0.789070i | \(-0.289437\pi\) | ||||
0.614303 | + | 0.789070i | \(0.289437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.04132e7 | −1.09234 | −0.546171 | − | 0.837673i | \(-0.683915\pi\) | ||||
−0.546171 | + | 0.837673i | \(0.683915\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.21297e6 | 0.334332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.37204e6 | −0.244851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.29022e6 | −0.435824 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.79493e6 | 0.483232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.57325e6 | −0.657214 | −0.328607 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328607 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.11640e7 | 1.10741 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.96738e6 | −0.882533 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.69146e6 | −0.848680 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.54452e6 | 0.343404 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.21768e6 | 0.693829 | 0.346914 | − | 0.937897i | \(-0.387229\pi\) | ||||
0.346914 | + | 0.937897i | \(0.387229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −989729. | −0.0944036 | −0.0472018 | − | 0.998885i | \(-0.515030\pi\) | ||||
−0.0472018 | + | 0.998885i | \(0.515030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.17023e6 | 0.678631 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.31383e6 | −0.405138 | −0.202569 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202569 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.15046e6 | 0.479992 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40213e6 | −0.222149 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.49637e7 | 1.37327 | 0.686633 | − | 0.727004i | \(-0.259088\pi\) | ||||
0.686633 | + | 0.727004i | \(0.259088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.81481e6 | 0.711730 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.32399e6 | 0.481198 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.42210e6 | −0.396657 | −0.198328 | − | 0.980136i | \(-0.563551\pi\) | ||||
−0.198328 | + | 0.980136i | \(0.563551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.57925e7 | −1.40587 | −0.702937 | − | 0.711252i | \(-0.748128\pi\) | ||||
−0.702937 | + | 0.711252i | \(0.748128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.47440e6 | 0.306970 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.76873e6 | 0.155098 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.08505e6 | −0.0944352 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 698939. | 0.0603773 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05015e7 | −0.900420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.60799e6 | −0.477276 | −0.238638 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238638 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.57740e6 | 0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.01232e6 | 0.588017 | 0.294009 | − | 0.955803i | \(-0.405011\pi\) | ||||
0.294009 | + | 0.955803i | \(0.405011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 967853. | 0.0805629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.02289e7 | −0.845207 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.16662e7 | 1.77718 | 0.888590 | − | 0.458703i | \(-0.151686\pi\) | ||||
0.888590 | + | 0.458703i | \(0.151686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 839347. | 0.0683463 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.50681e6 | −0.606825 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.72772e6 | 0.138652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.20276e6 | 0.334842 | 0.167421 | − | 0.985885i | \(-0.446456\pi\) | ||||
0.167421 | + | 0.985885i | \(0.446456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.81936e6 | 0.143908 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.55439e6 | −0.671780 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.11444e6 | −0.242828 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.29939e7 | −1.00588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50989e6 | 0.116051 | 0.0580256 | − | 0.998315i | \(-0.481519\pi\) | ||||
0.0580256 | + | 0.998315i | \(0.481519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.30113e7 | −0.992963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.46361e6 | −0.186681 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.26482e7 | 0.951653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.08359e6 | −0.155667 | −0.0778336 | − | 0.996966i | \(-0.524800\pi\) | ||||
−0.0778336 | + | 0.996966i | \(0.524800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.20238e6 | 0.237574 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.13844e6 | −0.157534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.88648e6 | −0.430616 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.10749e7 | 1.53098 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.03357e7 | 0.745618 | 0.372809 | − | 0.927908i | \(-0.378395\pi\) | ||||
0.372809 | + | 0.927908i | \(0.378395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82287e6 | −0.345515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.51561e7 | 1.07830 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −870410. | −0.0615005 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.39227e6 | 0.238042 | 0.119021 | − | 0.992892i | \(-0.462024\pi\) | ||||
0.119021 | + | 0.992892i | \(0.462024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.54171e7 | 1.07444 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.54418e6 | −0.591394 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.99922e7 | 1.37436 | 0.687180 | − | 0.726487i | \(-0.258848\pi\) | ||||
0.687180 | + | 0.726487i | \(0.258848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.84630e6 | −0.262618 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.94896e6 | 0.199986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.37515e7 | 1.59986 | 0.799928 | − | 0.600096i | \(-0.204871\pi\) | ||||
0.799928 | + | 0.600096i | \(0.204871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.42797e6 | −0.630773 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 768079. | 0.0510427 | 0.0255214 | − | 0.999674i | \(-0.491875\pi\) | ||||
0.0255214 | + | 0.999674i | \(0.491875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.98294e6 | −0.394934 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.10273e6 | 0.334581 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −546628. | −0.0356030 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.34656e7 | −1.51821 | −0.759105 | − | 0.650968i | \(-0.774363\pi\) | ||||
−0.759105 | + | 0.650968i | \(0.774363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 302745. | 0.0194576 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.23782e6 | 0.270567 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.58118e7 | −1.63711 | −0.818557 | − | 0.574425i | \(-0.805226\pi\) | ||||
−0.818557 | + | 0.574425i | \(0.805226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.24736e6 | −0.204610 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.19501e7 | 0.748013 | 0.374006 | − | 0.927426i | \(-0.377984\pi\) | ||||
0.374006 | + | 0.927426i | \(0.377984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15940e7 | 0.720977 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −766865. | −0.0473767 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.13184e7 | 0.694698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.61907e7 | −0.987302 | −0.493651 | − | 0.869660i | \(-0.664338\pi\) | ||||
−0.493651 | + | 0.869660i | \(0.664338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.35070e6 | 0.263586 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.40818e7 | 0.847637 | 0.423818 | − | 0.905747i | \(-0.360689\pi\) | ||||
0.423818 | + | 0.905747i | \(0.360689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.71543e6 | −0.102593 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.10630e7 | −0.657384 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.45122e6 | 0.498972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.43477e7 | −0.841695 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.74310e6 | −0.334766 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.65955e6 | 0.269880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.41819e6 | 0.254277 | 0.127139 | − | 0.991885i | \(-0.459421\pi\) | ||||
0.127139 | + | 0.991885i | \(0.459421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.38945e7 | −0.794602 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.25399e6 | 0.241744 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.30776e7 | −1.30319 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 764583. | 0.0429049 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.04472e6 | −0.337078 | −0.168539 | − | 0.985695i | \(-0.553905\pi\) | ||||
−0.168539 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.93569e6 | 0.162683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.79074e6 | −0.153688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.15507e7 | −1.17943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.33879e6 | 0.0728151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.17516e7 | −0.635202 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.71556e7 | −0.921583 | −0.460791 | − | 0.887509i | \(-0.652434\pi\) | ||||
−0.460791 | + | 0.887509i | \(0.652434\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.83020e7 | 0.977114 | 0.488557 | − | 0.872532i | \(-0.337523\pi\) | ||||
0.488557 | + | 0.872532i | \(0.337523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71009e7 | −0.907389 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00764e7 | 0.531390 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.31851e7 | 1.21522 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.99813e6 | 0.208280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 77887.9 | 0.00403285 | 0.00201643 | − | 0.999998i | \(-0.499358\pi\) | ||||
0.00201643 | + | 0.999998i | \(0.499358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 423648. | 0.0218025 | 0.0109012 | − | 0.999941i | \(-0.496530\pi\) | ||||
0.0109012 | + | 0.999941i | \(0.496530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.60499e6 | −0.133251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.18956e6 | 0.263856 | 0.131928 | − | 0.991259i | \(-0.457883\pi\) | ||||
0.131928 | + | 0.991259i | \(0.457883\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.08613e7 | 1.05428 | 0.527139 | − | 0.849779i | \(-0.323265\pi\) | ||||
0.527139 | + | 0.849779i | \(0.323265\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.15201e6 | −0.158338 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.58332e6 | 0.228859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.19079e6 | 0.208008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.13187e7 | −0.558446 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.18798e6 | 0.401580 | 0.200790 | − | 0.979634i | \(-0.435649\pi\) | ||||
0.200790 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.85717e7 | −0.905442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.31900e7 | −0.639258 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.65350e6 | −0.176022 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.70505e6 | 0.177454 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.04868e7 | 1.45158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.84854e6 | −0.466174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.11924e7 | −1.46783 | −0.733915 | − | 0.679241i | \(-0.762309\pi\) | ||||
−0.733915 | + | 0.679241i | \(0.762309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.08093e6 | 0.0973514 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.88654e7 | −0.877433 | −0.438716 | − | 0.898626i | \(-0.644567\pi\) | ||||
−0.438716 | + | 0.898626i | \(0.644567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.30703e7 | 0.604369 | 0.302184 | − | 0.953249i | \(-0.402284\pi\) | ||||
0.302184 | + | 0.953249i | \(0.402284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.18571e6 | 0.330341 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.58115e6 | −0.255092 | −0.127546 | − | 0.991833i | \(-0.540710\pi\) | ||||
−0.127546 | + | 0.991833i | \(0.540710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.10201e6 | 0.0955201 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.62471e7 | 0.734056 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.29628e7 | −0.582302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.48047e6 | 0.289442 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.13869e6 | 0.0505675 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.07396e6 | 0.0474205 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.17437e7 | −0.954629 | −0.477315 | − | 0.878732i | \(-0.658390\pi\) | ||||
−0.477315 | + | 0.878732i | \(0.658390\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.11730e7 | −1.36084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26789e7 | 0.984425 | 0.492212 | − | 0.870475i | \(-0.336188\pi\) | ||||
0.492212 | + | 0.870475i | \(0.336188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.34145e7 | −1.01061 | −0.505304 | − | 0.862942i | \(-0.668619\pi\) | ||||
−0.505304 | + | 0.862942i | \(0.668619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.00882e6 | 0.214970 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.56731e7 | 0.668875 | 0.334437 | − | 0.942418i | \(-0.391454\pi\) | ||||
0.334437 | + | 0.942418i | \(0.391454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.46543e7 | −1.04626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.07559e7 | −0.453894 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.96616e6 | −0.334288 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.85424e7 | −0.773765 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.13624e6 | −0.296134 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.82240e6 | 0.157738 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −911092. | −0.0373895 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.97133e7 | 0.804527 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.59175e6 | −0.348707 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.67553e7 | −1.48355 | −0.741775 | − | 0.670649i | \(-0.766016\pi\) | ||||
−0.741775 | + | 0.670649i | \(0.766016\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.48807e7 | 0.597331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.11183e7 | 0.843067 | 0.421534 | − | 0.906813i | \(-0.361492\pi\) | ||||
0.421534 | + | 0.906813i | \(0.361492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.06551e7 | −0.820070 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.02127e7 | −0.403262 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.14855e7 | 0.843765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.27922e6 | −0.284312 | −0.142156 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142156 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19625e7 | 0.464702 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.15298e7 | −1.21819 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.90037e6 | −0.303594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.67418e6 | −0.216872 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.41165e7 | −1.29696 | −0.648478 | − | 0.761234i | \(-0.724594\pi\) | ||||
−0.648478 | + | 0.761234i | \(0.724594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24371e7 | −0.470268 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.45083e7 | −0.545649 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.10416e6 | 0.116122 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.73880e7 | −1.76327 | −0.881637 | − | 0.471929i | \(-0.843558\pi\) | ||||
−0.881637 | + | 0.471929i | \(0.843558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.93153e7 | −0.714887 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.97476e7 | 1.46331 | 0.731656 | − | 0.681674i | \(-0.238748\pi\) | ||||
0.731656 | + | 0.681674i | \(0.238748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.39691e6 | 0.234256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.08613e6 | 0.258125 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.76410e7 | −1.00156 | −0.500782 | − | 0.865573i | \(-0.666954\pi\) | ||||
−0.500782 | + | 0.865573i | \(0.666954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.73588e7 | −1.70701 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.48233e7 | 1.24859 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.22977e6 | −0.186531 | −0.0932654 | − | 0.995641i | \(-0.529731\pi\) | ||||
−0.0932654 | + | 0.995641i | \(0.529731\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.57759e7 | 0.559738 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.80457e6 | 0.204876 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.30764e6 | 0.0810255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.10959e7 | −0.736866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −643115. | −0.0223472 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.11948e7 | −0.732673 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.76477e7 | −0.606905 | −0.303453 | − | 0.952847i | \(-0.598139\pi\) | ||||
−0.303453 | + | 0.952847i | \(0.598139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.97172e6 | 0.170097 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.66934e7 | −1.24893 | −0.624467 | − | 0.781051i | \(-0.714684\pi\) | ||||
−0.624467 | + | 0.781051i | \(0.714684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.35188e7 | −0.796404 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.72459e6 | −0.192856 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.16023e7 | 1.05921 | 0.529605 | − | 0.848244i | \(-0.322340\pi\) | ||||
0.529605 | + | 0.848244i | \(0.322340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12965e7 | 0.376693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.36405e7 | 0.452540 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.73829e7 | 1.23393 | 0.616963 | − | 0.786992i | \(-0.288363\pi\) | ||||
0.616963 | + | 0.786992i | \(0.288363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.93206e6 | −0.326174 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.77328e6 | −0.221313 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.75493e7 | 0.570518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84243e7 | 0.919401 | 0.459701 | − | 0.888074i | \(-0.347957\pi\) | ||||
0.459701 | + | 0.888074i | \(0.347957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.56373e6 | −0.0503256 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.24010e7 | 0.717313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.70600e7 | 0.543553 | 0.271776 | − | 0.962360i | \(-0.412389\pi\) | ||||
0.271776 | + | 0.962360i | \(0.412389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.21279e7 | −1.65256 |
(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 | 320.6.a.v.1.1 | 2 | ||
4.3 | odd | 2 | 320.6.a.r.1.2 | 2 | |||
8.3 | odd | 2 | 160.6.a.e.1.1 | yes | 2 | ||
8.5 | even | 2 | 160.6.a.a.1.2 | ✓ | 2 | ||
40.3 | even | 4 | 800.6.c.g.449.2 | 4 | |||
40.13 | odd | 4 | 800.6.c.f.449.3 | 4 | |||
40.19 | odd | 2 | 800.6.a.g.1.2 | 2 | |||
40.27 | even | 4 | 800.6.c.g.449.3 | 4 | |||
40.29 | even | 2 | 800.6.a.l.1.1 | 2 | |||
40.37 | odd | 4 | 800.6.c.f.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.a.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
160.6.a.e.1.1 | yes | 2 | 8.3 | odd | 2 | ||
320.6.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
320.6.a.v.1.1 | 2 | 1.1 | even | 1 | trivial | ||
800.6.a.g.1.2 | 2 | 40.19 | odd | 2 | |||
800.6.a.l.1.1 | 2 | 40.29 | even | 2 | |||
800.6.c.f.449.2 | 4 | 40.37 | odd | 4 | |||
800.6.c.f.449.3 | 4 | 40.13 | odd | 4 | |||
800.6.c.g.449.2 | 4 | 40.3 | even | 4 | |||
800.6.c.g.449.3 | 4 | 40.27 | even | 4 |