Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,6,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(157.657294876\) |
Analytic rank: | \(0\) |
Dimension: | \(218\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.0108 | −1.94646 | −0.973230 | − | 0.229832i | \(-0.926182\pi\) | ||||
−0.973230 | + | 0.229832i | \(0.926182\pi\) | |||||||
\(3\) | −2.28470 | −0.146563 | −0.0732817 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732817 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(4\) | 89.2387 | 2.78871 | ||||||||
\(5\) | 53.2861 | 0.953210 | 0.476605 | − | 0.879118i | \(-0.341867\pi\) | ||||
0.476605 | + | 0.879118i | \(0.341867\pi\) | |||||||
\(6\) | 25.1565 | 0.285280 | ||||||||
\(7\) | −155.822 | −1.20195 | −0.600973 | − | 0.799270i | \(-0.705220\pi\) | ||||
−0.600973 | + | 0.799270i | \(0.705220\pi\) | |||||||
\(8\) | −630.246 | −3.48165 | ||||||||
\(9\) | −237.780 | −0.978519 | ||||||||
\(10\) | −586.724 | −1.85539 | ||||||||
\(11\) | 217.525 | 0.542035 | 0.271018 | − | 0.962574i | \(-0.412640\pi\) | ||||
0.271018 | + | 0.962574i | \(0.412640\pi\) | |||||||
\(12\) | −203.883 | −0.408723 | ||||||||
\(13\) | 243.228 | 0.399168 | 0.199584 | − | 0.979881i | \(-0.436041\pi\) | ||||
0.199584 | + | 0.979881i | \(0.436041\pi\) | |||||||
\(14\) | 1715.74 | 2.33954 | ||||||||
\(15\) | −121.743 | −0.139706 | ||||||||
\(16\) | 4083.90 | 3.98819 | ||||||||
\(17\) | 2084.02 | 1.74896 | 0.874479 | − | 0.485063i | \(-0.161203\pi\) | ||||
0.874479 | + | 0.485063i | \(0.161203\pi\) | |||||||
\(18\) | 2618.16 | 1.90465 | ||||||||
\(19\) | 1306.56 | 0.830321 | 0.415160 | − | 0.909748i | \(-0.363726\pi\) | ||||
0.415160 | + | 0.909748i | \(0.363726\pi\) | |||||||
\(20\) | 4755.18 | 2.65823 | ||||||||
\(21\) | 356.007 | 0.176161 | ||||||||
\(22\) | −2395.13 | −1.05505 | ||||||||
\(23\) | 3740.51 | 1.47439 | 0.737194 | − | 0.675681i | \(-0.236151\pi\) | ||||
0.737194 | + | 0.675681i | \(0.236151\pi\) | |||||||
\(24\) | 1439.92 | 0.510283 | ||||||||
\(25\) | −285.596 | −0.0913906 | ||||||||
\(26\) | −2678.15 | −0.776965 | ||||||||
\(27\) | 1098.44 | 0.289979 | ||||||||
\(28\) | −13905.4 | −3.35187 | ||||||||
\(29\) | 7864.58 | 1.73652 | 0.868261 | − | 0.496107i | \(-0.165238\pi\) | ||||
0.868261 | + | 0.496107i | \(0.165238\pi\) | |||||||
\(30\) | 1340.49 | 0.271932 | ||||||||
\(31\) | 983.718 | 0.183851 | 0.0919256 | − | 0.995766i | \(-0.470698\pi\) | ||||
0.0919256 | + | 0.995766i | \(0.470698\pi\) | |||||||
\(32\) | −24799.4 | −4.28120 | ||||||||
\(33\) | −496.979 | −0.0794426 | ||||||||
\(34\) | −22946.8 | −3.40428 | ||||||||
\(35\) | −8303.16 | −1.14571 | ||||||||
\(36\) | −21219.2 | −2.72880 | ||||||||
\(37\) | 14182.4 | 1.70312 | 0.851561 | − | 0.524256i | \(-0.175656\pi\) | ||||
0.851561 | + | 0.524256i | \(0.175656\pi\) | |||||||
\(38\) | −14386.3 | −1.61619 | ||||||||
\(39\) | −555.703 | −0.0585034 | ||||||||
\(40\) | −33583.3 | −3.31874 | ||||||||
\(41\) | −167.212 | −0.0155349 | −0.00776745 | − | 0.999970i | \(-0.502472\pi\) | ||||
−0.00776745 | + | 0.999970i | \(0.502472\pi\) | |||||||
\(42\) | −3919.94 | −0.342891 | ||||||||
\(43\) | −5446.52 | −0.449209 | −0.224604 | − | 0.974450i | \(-0.572109\pi\) | ||||
−0.224604 | + | 0.974450i | \(0.572109\pi\) | |||||||
\(44\) | 19411.6 | 1.51158 | ||||||||
\(45\) | −12670.4 | −0.932734 | ||||||||
\(46\) | −41186.2 | −2.86984 | ||||||||
\(47\) | 6004.24 | 0.396473 | 0.198236 | − | 0.980154i | \(-0.436479\pi\) | ||||
0.198236 | + | 0.980154i | \(0.436479\pi\) | |||||||
\(48\) | −9330.49 | −0.584523 | ||||||||
\(49\) | 7473.61 | 0.444672 | ||||||||
\(50\) | 3144.65 | 0.177888 | ||||||||
\(51\) | −4761.36 | −0.256333 | ||||||||
\(52\) | 21705.4 | 1.11316 | ||||||||
\(53\) | −8231.84 | −0.402538 | −0.201269 | − | 0.979536i | \(-0.564507\pi\) | ||||
−0.201269 | + | 0.979536i | \(0.564507\pi\) | |||||||
\(54\) | −12094.7 | −0.564432 | ||||||||
\(55\) | 11591.1 | 0.516674 | ||||||||
\(56\) | 98206.4 | 4.18475 | ||||||||
\(57\) | −2985.10 | −0.121695 | ||||||||
\(58\) | −86595.6 | −3.38007 | ||||||||
\(59\) | 42969.0 | 1.60704 | 0.803518 | − | 0.595281i | \(-0.202959\pi\) | ||||
0.803518 | + | 0.595281i | \(0.202959\pi\) | |||||||
\(60\) | −10864.1 | −0.389599 | ||||||||
\(61\) | −16381.0 | −0.563658 | −0.281829 | − | 0.959465i | \(-0.590941\pi\) | ||||
−0.281829 | + | 0.959465i | \(0.590941\pi\) | |||||||
\(62\) | −10831.6 | −0.357859 | ||||||||
\(63\) | 37051.5 | 1.17613 | ||||||||
\(64\) | 142377. | 4.34500 | ||||||||
\(65\) | 12960.7 | 0.380491 | ||||||||
\(66\) | 5472.16 | 0.154632 | ||||||||
\(67\) | −48469.1 | −1.31910 | −0.659550 | − | 0.751661i | \(-0.729253\pi\) | ||||
−0.659550 | + | 0.751661i | \(0.729253\pi\) | |||||||
\(68\) | 185975. | 4.87733 | ||||||||
\(69\) | −8545.94 | −0.216091 | ||||||||
\(70\) | 91424.8 | 2.23007 | ||||||||
\(71\) | −57809.5 | −1.36099 | −0.680493 | − | 0.732755i | \(-0.738234\pi\) | ||||
−0.680493 | + | 0.732755i | \(0.738234\pi\) | |||||||
\(72\) | 149860. | 3.40686 | ||||||||
\(73\) | 67650.1 | 1.48580 | 0.742902 | − | 0.669400i | \(-0.233449\pi\) | ||||
0.742902 | + | 0.669400i | \(0.233449\pi\) | |||||||
\(74\) | −156160. | −3.31506 | ||||||||
\(75\) | 652.500 | 0.0133945 | ||||||||
\(76\) | 116596. | 2.31552 | ||||||||
\(77\) | −33895.3 | −0.651497 | ||||||||
\(78\) | 6118.76 | 0.113875 | ||||||||
\(79\) | −71461.7 | −1.28827 | −0.644133 | − | 0.764913i | \(-0.722782\pi\) | ||||
−0.644133 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(80\) | 217615. | 3.80158 | ||||||||
\(81\) | 55271.0 | 0.936019 | ||||||||
\(82\) | 1841.15 | 0.0302381 | ||||||||
\(83\) | −53097.9 | −0.846024 | −0.423012 | − | 0.906124i | \(-0.639027\pi\) | ||||
−0.423012 | + | 0.906124i | \(0.639027\pi\) | |||||||
\(84\) | 31769.6 | 0.491262 | ||||||||
\(85\) | 111049. | 1.66712 | ||||||||
\(86\) | 59970.8 | 0.874367 | ||||||||
\(87\) | −17968.2 | −0.254511 | ||||||||
\(88\) | −137094. | −1.88718 | ||||||||
\(89\) | −36484.4 | −0.488239 | −0.244119 | − | 0.969745i | \(-0.578499\pi\) | ||||
−0.244119 | + | 0.969745i | \(0.578499\pi\) | |||||||
\(90\) | 139511. | 1.81553 | ||||||||
\(91\) | −37900.4 | −0.479778 | ||||||||
\(92\) | 333798. | 4.11164 | ||||||||
\(93\) | −2247.50 | −0.0269459 | ||||||||
\(94\) | −66111.8 | −0.771719 | ||||||||
\(95\) | 69621.5 | 0.791470 | ||||||||
\(96\) | 56659.0 | 0.627467 | ||||||||
\(97\) | 76922.5 | 0.830088 | 0.415044 | − | 0.909801i | \(-0.363766\pi\) | ||||
0.415044 | + | 0.909801i | \(0.363766\pi\) | |||||||
\(98\) | −82290.7 | −0.865537 | ||||||||
\(99\) | −51723.1 | −0.530392 | ||||||||
\(100\) | −25486.2 | −0.254862 | ||||||||
\(101\) | −71112.7 | −0.693655 | −0.346828 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(102\) | 52426.5 | 0.498943 | ||||||||
\(103\) | −14390.0 | −0.133650 | −0.0668249 | − | 0.997765i | \(-0.521287\pi\) | ||||
−0.0668249 | + | 0.997765i | \(0.521287\pi\) | |||||||
\(104\) | −153294. | −1.38976 | ||||||||
\(105\) | 18970.2 | 0.167919 | ||||||||
\(106\) | 90639.5 | 0.783525 | ||||||||
\(107\) | 189423. | 1.59946 | 0.799729 | − | 0.600362i | \(-0.204977\pi\) | ||||
0.799729 | + | 0.600362i | \(0.204977\pi\) | |||||||
\(108\) | 98023.1 | 0.808666 | ||||||||
\(109\) | −10822.1 | −0.0872457 | −0.0436228 | − | 0.999048i | \(-0.513890\pi\) | ||||
−0.0436228 | + | 0.999048i | \(0.513890\pi\) | |||||||
\(110\) | −127627. | −1.00568 | ||||||||
\(111\) | −32402.5 | −0.249615 | ||||||||
\(112\) | −636364. | −4.79358 | ||||||||
\(113\) | −37219.4 | −0.274204 | −0.137102 | − | 0.990557i | \(-0.543779\pi\) | ||||
−0.137102 | + | 0.990557i | \(0.543779\pi\) | |||||||
\(114\) | 32868.5 | 0.236874 | ||||||||
\(115\) | 199317. | 1.40540 | ||||||||
\(116\) | 701825. | 4.84266 | ||||||||
\(117\) | −57834.8 | −0.390593 | ||||||||
\(118\) | −473125. | −3.12803 | ||||||||
\(119\) | −324737. | −2.10215 | ||||||||
\(120\) | 76727.8 | 0.486407 | ||||||||
\(121\) | −113734. | −0.706198 | ||||||||
\(122\) | 180369. | 1.09714 | ||||||||
\(123\) | 382.029 | 0.00227685 | ||||||||
\(124\) | 87785.7 | 0.512707 | ||||||||
\(125\) | −181737. | −1.04032 | ||||||||
\(126\) | −407968. | −2.28928 | ||||||||
\(127\) | −113235. | −0.622973 | −0.311487 | − | 0.950251i | \(-0.600827\pi\) | ||||
−0.311487 | + | 0.950251i | \(0.600827\pi\) | |||||||
\(128\) | −774110. | −4.17617 | ||||||||
\(129\) | 12443.7 | 0.0658376 | ||||||||
\(130\) | −142708. | −0.740610 | ||||||||
\(131\) | −256211. | −1.30443 | −0.652213 | − | 0.758036i | \(-0.726159\pi\) | ||||
−0.652213 | + | 0.758036i | \(0.726159\pi\) | |||||||
\(132\) | −44349.8 | −0.221542 | ||||||||
\(133\) | −203591. | −0.998000 | ||||||||
\(134\) | 533685. | 2.56758 | ||||||||
\(135\) | 58531.4 | 0.276411 | ||||||||
\(136\) | −1.31345e6 | −6.08926 | ||||||||
\(137\) | 272936. | 1.24240 | 0.621198 | − | 0.783653i | \(-0.286646\pi\) | ||||
0.621198 | + | 0.783653i | \(0.286646\pi\) | |||||||
\(138\) | 94098.1 | 0.420613 | ||||||||
\(139\) | 182273. | 0.800174 | 0.400087 | − | 0.916477i | \(-0.368980\pi\) | ||||
0.400087 | + | 0.916477i | \(0.368980\pi\) | |||||||
\(140\) | −740963. | −3.19504 | ||||||||
\(141\) | −13717.9 | −0.0581085 | ||||||||
\(142\) | 636532. | 2.64911 | ||||||||
\(143\) | 52908.2 | 0.216363 | ||||||||
\(144\) | −971071. | −3.90252 | ||||||||
\(145\) | 419072. | 1.65527 | ||||||||
\(146\) | −744885. | −2.89206 | ||||||||
\(147\) | −17074.9 | −0.0651727 | ||||||||
\(148\) | 1.26562e6 | 4.74951 | ||||||||
\(149\) | −98402.4 | −0.363112 | −0.181556 | − | 0.983381i | \(-0.558113\pi\) | ||||
−0.181556 | + | 0.983381i | \(0.558113\pi\) | |||||||
\(150\) | −7184.58 | −0.0260719 | ||||||||
\(151\) | 345272. | 1.23231 | 0.616153 | − | 0.787627i | \(-0.288690\pi\) | ||||
0.616153 | + | 0.787627i | \(0.288690\pi\) | |||||||
\(152\) | −823455. | −2.89089 | ||||||||
\(153\) | −495538. | −1.71139 | ||||||||
\(154\) | 373215. | 1.26811 | ||||||||
\(155\) | 52418.5 | 0.175249 | ||||||||
\(156\) | −49590.2 | −0.163149 | ||||||||
\(157\) | 81303.7 | 0.263246 | 0.131623 | − | 0.991300i | \(-0.457981\pi\) | ||||
0.131623 | + | 0.991300i | \(0.457981\pi\) | |||||||
\(158\) | 786854. | 2.50756 | ||||||||
\(159\) | 18807.3 | 0.0589974 | ||||||||
\(160\) | −1.32146e6 | −4.08088 | ||||||||
\(161\) | −582856. | −1.77213 | ||||||||
\(162\) | −608580. | −1.82192 | ||||||||
\(163\) | −164978. | −0.486360 | −0.243180 | − | 0.969981i | \(-0.578191\pi\) | ||||
−0.243180 | + | 0.969981i | \(0.578191\pi\) | |||||||
\(164\) | −14921.8 | −0.0433223 | ||||||||
\(165\) | −26482.1 | −0.0757255 | ||||||||
\(166\) | 584653. | 1.64675 | ||||||||
\(167\) | −74335.4 | −0.206255 | −0.103128 | − | 0.994668i | \(-0.532885\pi\) | ||||
−0.103128 | + | 0.994668i | \(0.532885\pi\) | |||||||
\(168\) | −224372. | −0.613332 | ||||||||
\(169\) | −312133. | −0.840665 | ||||||||
\(170\) | −1.22275e6 | −3.24499 | ||||||||
\(171\) | −310674. | −0.812485 | ||||||||
\(172\) | −486041. | −1.25271 | ||||||||
\(173\) | 618915. | 1.57223 | 0.786115 | − | 0.618080i | \(-0.212089\pi\) | ||||
0.786115 | + | 0.618080i | \(0.212089\pi\) | |||||||
\(174\) | 197845. | 0.495395 | ||||||||
\(175\) | 44502.2 | 0.109847 | ||||||||
\(176\) | 888352. | 2.16174 | ||||||||
\(177\) | −98171.3 | −0.235533 | ||||||||
\(178\) | 401724. | 0.950337 | ||||||||
\(179\) | 752051. | 1.75434 | 0.877172 | − | 0.480176i | \(-0.159427\pi\) | ||||
0.877172 | + | 0.480176i | \(0.159427\pi\) | |||||||
\(180\) | −1.13069e6 | −2.60112 | ||||||||
\(181\) | 416131. | 0.944134 | 0.472067 | − | 0.881563i | \(-0.343508\pi\) | ||||
0.472067 | + | 0.881563i | \(0.343508\pi\) | |||||||
\(182\) | 417315. | 0.933869 | ||||||||
\(183\) | 37425.6 | 0.0826117 | ||||||||
\(184\) | −2.35744e6 | −5.13330 | ||||||||
\(185\) | 755725. | 1.62343 | ||||||||
\(186\) | 24746.9 | 0.0524491 | ||||||||
\(187\) | 453326. | 0.947997 | ||||||||
\(188\) | 535811. | 1.10565 | ||||||||
\(189\) | −171161. | −0.348538 | ||||||||
\(190\) | −766591. | −1.54056 | ||||||||
\(191\) | −301813. | −0.598625 | −0.299312 | − | 0.954155i | \(-0.596757\pi\) | ||||
−0.299312 | + | 0.954155i | \(0.596757\pi\) | |||||||
\(192\) | −325288. | −0.636818 | ||||||||
\(193\) | 870837. | 1.68284 | 0.841421 | − | 0.540379i | \(-0.181719\pi\) | ||||
0.841421 | + | 0.540379i | \(0.181719\pi\) | |||||||
\(194\) | −846982. | −1.61573 | ||||||||
\(195\) | −29611.2 | −0.0557661 | ||||||||
\(196\) | 666935. | 1.24006 | ||||||||
\(197\) | −646022. | −1.18599 | −0.592996 | − | 0.805205i | \(-0.702055\pi\) | ||||
−0.592996 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(198\) | 569515. | 1.03239 | ||||||||
\(199\) | −130234. | −0.233126 | −0.116563 | − | 0.993183i | \(-0.537188\pi\) | ||||
−0.116563 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(200\) | 179996. | 0.318190 | ||||||||
\(201\) | 110737. | 0.193332 | ||||||||
\(202\) | 783011. | 1.35017 | ||||||||
\(203\) | −1.22548e6 | −2.08721 | ||||||||
\(204\) | −424897. | −0.714839 | ||||||||
\(205\) | −8910.08 | −0.0148080 | ||||||||
\(206\) | 158446. | 0.260144 | ||||||||
\(207\) | −889420. | −1.44272 | ||||||||
\(208\) | 993321. | 1.59196 | ||||||||
\(209\) | 284210. | 0.450063 | ||||||||
\(210\) | −208878. | −0.326847 | ||||||||
\(211\) | 422732. | 0.653670 | 0.326835 | − | 0.945081i | \(-0.394018\pi\) | ||||
0.326835 | + | 0.945081i | \(0.394018\pi\) | |||||||
\(212\) | −734598. | −1.12256 | ||||||||
\(213\) | 132077. | 0.199471 | ||||||||
\(214\) | −2.08570e6 | −3.11328 | ||||||||
\(215\) | −290224. | −0.428190 | ||||||||
\(216\) | −692286. | −1.00960 | ||||||||
\(217\) | −153285. | −0.220979 | ||||||||
\(218\) | 119160. | 0.169820 | ||||||||
\(219\) | −154560. | −0.217765 | ||||||||
\(220\) | 1.03437e6 | 1.44085 | ||||||||
\(221\) | 506892. | 0.698128 | ||||||||
\(222\) | 356779. | 0.485867 | ||||||||
\(223\) | −443348. | −0.597011 | −0.298506 | − | 0.954408i | \(-0.596488\pi\) | ||||
−0.298506 | + | 0.954408i | \(0.596488\pi\) | |||||||
\(224\) | 3.86429e6 | 5.14577 | ||||||||
\(225\) | 67909.0 | 0.0894275 | ||||||||
\(226\) | 409817. | 0.533727 | ||||||||
\(227\) | 839246. | 1.08100 | 0.540498 | − | 0.841345i | \(-0.318236\pi\) | ||||
0.540498 | + | 0.841345i | \(0.318236\pi\) | |||||||
\(228\) | −266386. | −0.339371 | ||||||||
\(229\) | −546725. | −0.688938 | −0.344469 | − | 0.938798i | \(-0.611941\pi\) | ||||
−0.344469 | + | 0.938798i | \(0.611941\pi\) | |||||||
\(230\) | −2.19465e6 | −2.73556 | ||||||||
\(231\) | 77440.5 | 0.0954856 | ||||||||
\(232\) | −4.95662e6 | −6.04597 | ||||||||
\(233\) | −357259. | −0.431116 | −0.215558 | − | 0.976491i | \(-0.569157\pi\) | ||||
−0.215558 | + | 0.976491i | \(0.569157\pi\) | |||||||
\(234\) | 636810. | 0.760275 | ||||||||
\(235\) | 319942. | 0.377922 | ||||||||
\(236\) | 3.83450e6 | 4.48155 | ||||||||
\(237\) | 163268. | 0.188813 | ||||||||
\(238\) | 3.57563e6 | 4.09176 | ||||||||
\(239\) | −677830. | −0.767585 | −0.383792 | − | 0.923419i | \(-0.625382\pi\) | ||||
−0.383792 | + | 0.923419i | \(0.625382\pi\) | |||||||
\(240\) | −497185. | −0.557173 | ||||||||
\(241\) | 958280. | 1.06280 | 0.531398 | − | 0.847122i | \(-0.321667\pi\) | ||||
0.531398 | + | 0.847122i | \(0.321667\pi\) | |||||||
\(242\) | 1.25231e6 | 1.37459 | ||||||||
\(243\) | −393198. | −0.427165 | ||||||||
\(244\) | −1.46182e6 | −1.57188 | ||||||||
\(245\) | 398239. | 0.423866 | ||||||||
\(246\) | −4206.47 | −0.00443179 | ||||||||
\(247\) | 317793. | 0.331437 | ||||||||
\(248\) | −619985. | −0.640106 | ||||||||
\(249\) | 121313. | 0.123996 | ||||||||
\(250\) | 2.00108e6 | 2.02495 | ||||||||
\(251\) | −1.33663e6 | −1.33914 | −0.669570 | − | 0.742749i | \(-0.733522\pi\) | ||||
−0.669570 | + | 0.742749i | \(0.733522\pi\) | |||||||
\(252\) | 3.30642e6 | 3.27987 | ||||||||
\(253\) | 813655. | 0.799170 | ||||||||
\(254\) | 1.24681e6 | 1.21259 | ||||||||
\(255\) | −253714. | −0.244340 | ||||||||
\(256\) | 3.96755e6 | 3.78375 | ||||||||
\(257\) | 910408. | 0.859812 | 0.429906 | − | 0.902874i | \(-0.358547\pi\) | ||||
0.429906 | + | 0.902874i | \(0.358547\pi\) | |||||||
\(258\) | −137015. | −0.128150 | ||||||||
\(259\) | −2.20994e6 | −2.04706 | ||||||||
\(260\) | 1.15659e6 | 1.06108 | ||||||||
\(261\) | −1.87004e6 | −1.69922 | ||||||||
\(262\) | 2.82110e6 | 2.53901 | ||||||||
\(263\) | 1.77275e6 | 1.58037 | 0.790183 | − | 0.612871i | \(-0.209985\pi\) | ||||
0.790183 | + | 0.612871i | \(0.209985\pi\) | |||||||
\(264\) | 313219. | 0.276591 | ||||||||
\(265\) | −438642. | −0.383703 | ||||||||
\(266\) | 2.24171e6 | 1.94257 | ||||||||
\(267\) | 83355.8 | 0.0715579 | ||||||||
\(268\) | −4.32531e6 | −3.67858 | ||||||||
\(269\) | −353105. | −0.297525 | −0.148762 | − | 0.988873i | \(-0.547529\pi\) | ||||
−0.148762 | + | 0.988873i | \(0.547529\pi\) | |||||||
\(270\) | −644480. | −0.538022 | ||||||||
\(271\) | 1.26264e6 | 1.04437 | 0.522187 | − | 0.852831i | \(-0.325116\pi\) | ||||
0.522187 | + | 0.852831i | \(0.325116\pi\) | |||||||
\(272\) | 8.51093e6 | 6.97517 | ||||||||
\(273\) | 86591.0 | 0.0703179 | ||||||||
\(274\) | −3.00526e6 | −2.41828 | ||||||||
\(275\) | −62124.2 | −0.0495369 | ||||||||
\(276\) | −762629. | −0.602616 | ||||||||
\(277\) | −691468. | −0.541468 | −0.270734 | − | 0.962654i | \(-0.587266\pi\) | ||||
−0.270734 | + | 0.962654i | \(0.587266\pi\) | |||||||
\(278\) | −2.00698e6 | −1.55751 | ||||||||
\(279\) | −233909. | −0.179902 | ||||||||
\(280\) | 5.23303e6 | 3.98895 | ||||||||
\(281\) | −1.47133e6 | −1.11159 | −0.555793 | − | 0.831321i | \(-0.687585\pi\) | ||||
−0.555793 | + | 0.831321i | \(0.687585\pi\) | |||||||
\(282\) | 151045. | 0.113106 | ||||||||
\(283\) | 70113.3 | 0.0520396 | 0.0260198 | − | 0.999661i | \(-0.491717\pi\) | ||||
0.0260198 | + | 0.999661i | \(0.491717\pi\) | |||||||
\(284\) | −5.15885e6 | −3.79539 | ||||||||
\(285\) | −159064. | −0.116001 | ||||||||
\(286\) | −582564. | −0.421142 | ||||||||
\(287\) | 26055.4 | 0.0186721 | ||||||||
\(288\) | 5.89679e6 | 4.18924 | ||||||||
\(289\) | 2.92328e6 | 2.05885 | ||||||||
\(290\) | −4.61434e6 | −3.22192 | ||||||||
\(291\) | −175745. | −0.121661 | ||||||||
\(292\) | 6.03701e6 | 4.14347 | ||||||||
\(293\) | 862952. | 0.587242 | 0.293621 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293621 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(294\) | 188009. | 0.126856 | ||||||||
\(295\) | 2.28965e6 | 1.53184 | ||||||||
\(296\) | −8.93841e6 | −5.92968 | ||||||||
\(297\) | 238938. | 0.157179 | ||||||||
\(298\) | 1.08349e6 | 0.706782 | ||||||||
\(299\) | 909798. | 0.588528 | ||||||||
\(300\) | 58228.2 | 0.0373534 | ||||||||
\(301\) | 848690. | 0.539924 | ||||||||
\(302\) | −3.80173e6 | −2.39863 | ||||||||
\(303\) | 162471. | 0.101665 | ||||||||
\(304\) | 5.33587e6 | 3.31147 | ||||||||
\(305\) | −872879. | −0.537285 | ||||||||
\(306\) | 5.45630e6 | 3.33115 | ||||||||
\(307\) | −2.91488e6 | −1.76512 | −0.882562 | − | 0.470196i | \(-0.844183\pi\) | ||||
−0.882562 | + | 0.470196i | \(0.844183\pi\) | |||||||
\(308\) | −3.02477e6 | −1.81683 | ||||||||
\(309\) | 32876.9 | 0.0195882 | ||||||||
\(310\) | −577172. | −0.341115 | ||||||||
\(311\) | −678022. | −0.397505 | −0.198752 | − | 0.980050i | \(-0.563689\pi\) | ||||
−0.198752 | + | 0.980050i | \(0.563689\pi\) | |||||||
\(312\) | 350230. | 0.203689 | ||||||||
\(313\) | 1.89750e6 | 1.09476 | 0.547382 | − | 0.836883i | \(-0.315625\pi\) | ||||
0.547382 | + | 0.836883i | \(0.315625\pi\) | |||||||
\(314\) | −895223. | −0.512397 | ||||||||
\(315\) | 1.97433e6 | 1.12110 | ||||||||
\(316\) | −6.37715e6 | −3.59260 | ||||||||
\(317\) | −1.86471e6 | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(318\) | −207084. | −0.114836 | ||||||||
\(319\) | 1.71074e6 | 0.941257 | ||||||||
\(320\) | 7.58670e6 | 4.14170 | ||||||||
\(321\) | −432774. | −0.234422 | ||||||||
\(322\) | 6.41773e6 | 3.44939 | ||||||||
\(323\) | 2.72290e6 | 1.45220 | ||||||||
\(324\) | 4.93231e6 | 2.61028 | ||||||||
\(325\) | −69464.9 | −0.0364802 | ||||||||
\(326\) | 1.81655e6 | 0.946681 | ||||||||
\(327\) | 24725.2 | 0.0127870 | ||||||||
\(328\) | 105385. | 0.0540871 | ||||||||
\(329\) | −935595. | −0.476539 | ||||||||
\(330\) | 291590. | 0.147397 | ||||||||
\(331\) | −1.43989e6 | −0.722371 | −0.361185 | − | 0.932494i | \(-0.617628\pi\) | ||||
−0.361185 | + | 0.932494i | \(0.617628\pi\) | |||||||
\(332\) | −4.73839e6 | −2.35931 | ||||||||
\(333\) | −3.37230e6 | −1.66654 | ||||||||
\(334\) | 818496. | 0.401467 | ||||||||
\(335\) | −2.58273e6 | −1.25738 | ||||||||
\(336\) | 1.45390e6 | 0.702564 | ||||||||
\(337\) | 1.61221e6 | 0.773298 | 0.386649 | − | 0.922227i | \(-0.373632\pi\) | ||||
0.386649 | + | 0.922227i | \(0.373632\pi\) | |||||||
\(338\) | 3.43685e6 | 1.63632 | ||||||||
\(339\) | 85035.1 | 0.0401883 | ||||||||
\(340\) | 9.90988e6 | 4.64912 | ||||||||
\(341\) | 213983. | 0.0996538 | ||||||||
\(342\) | 3.42079e6 | 1.58147 | ||||||||
\(343\) | 1.45435e6 | 0.667474 | ||||||||
\(344\) | 3.43265e6 | 1.56399 | ||||||||
\(345\) | −455380. | −0.205980 | ||||||||
\(346\) | −6.81478e6 | −3.06028 | ||||||||
\(347\) | 163830. | 0.0730414 | 0.0365207 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365207 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(348\) | −1.60346e6 | −0.709756 | ||||||||
\(349\) | 2.27839e6 | 1.00130 | 0.500651 | − | 0.865649i | \(-0.333094\pi\) | ||||
0.500651 | + | 0.865649i | \(0.333094\pi\) | |||||||
\(350\) | −490007. | −0.213812 | ||||||||
\(351\) | 267171. | 0.115750 | ||||||||
\(352\) | −5.39448e6 | −2.32056 | ||||||||
\(353\) | −2.44490e6 | −1.04430 | −0.522148 | − | 0.852855i | \(-0.674869\pi\) | ||||
−0.522148 | + | 0.852855i | \(0.674869\pi\) | |||||||
\(354\) | 1.08095e6 | 0.458455 | ||||||||
\(355\) | −3.08044e6 | −1.29731 | ||||||||
\(356\) | −3.25582e6 | −1.36156 | ||||||||
\(357\) | 741926. | 0.308099 | ||||||||
\(358\) | −8.28072e6 | −3.41476 | ||||||||
\(359\) | 630896. | 0.258358 | 0.129179 | − | 0.991621i | \(-0.458766\pi\) | ||||
0.129179 | + | 0.991621i | \(0.458766\pi\) | |||||||
\(360\) | 7.98545e6 | 3.24746 | ||||||||
\(361\) | −768997. | −0.310568 | ||||||||
\(362\) | −4.58195e6 | −1.83772 | ||||||||
\(363\) | 259848. | 0.103503 | ||||||||
\(364\) | −3.38218e6 | −1.33796 | ||||||||
\(365\) | 3.60481e6 | 1.41628 | ||||||||
\(366\) | −412088. | −0.160800 | ||||||||
\(367\) | 4.50319e6 | 1.74524 | 0.872619 | − | 0.488401i | \(-0.162420\pi\) | ||||
0.872619 | + | 0.488401i | \(0.162420\pi\) | |||||||
\(368\) | 1.52759e7 | 5.88013 | ||||||||
\(369\) | 39759.7 | 0.0152012 | ||||||||
\(370\) | −8.32117e6 | −3.15995 | ||||||||
\(371\) | 1.28270e6 | 0.483829 | ||||||||
\(372\) | −200564. | −0.0751442 | ||||||||
\(373\) | −2.91475e6 | −1.08475 | −0.542374 | − | 0.840137i | \(-0.682474\pi\) | ||||
−0.542374 | + | 0.840137i | \(0.682474\pi\) | |||||||
\(374\) | −4.99151e6 | −1.84524 | ||||||||
\(375\) | 415215. | 0.152474 | ||||||||
\(376\) | −3.78415e6 | −1.38038 | ||||||||
\(377\) | 1.91289e6 | 0.693164 | ||||||||
\(378\) | 1.88463e6 | 0.678416 | ||||||||
\(379\) | 3.35371e6 | 1.19930 | 0.599650 | − | 0.800263i | \(-0.295307\pi\) | ||||
0.599650 | + | 0.800263i | \(0.295307\pi\) | |||||||
\(380\) | 6.21293e6 | 2.20718 | ||||||||
\(381\) | 258707. | 0.0913052 | ||||||||
\(382\) | 3.32322e6 | 1.16520 | ||||||||
\(383\) | −4.08288e6 | −1.42223 | −0.711115 | − | 0.703076i | \(-0.751810\pi\) | ||||
−0.711115 | + | 0.703076i | \(0.751810\pi\) | |||||||
\(384\) | 1.76861e6 | 0.612074 | ||||||||
\(385\) | −1.80615e6 | −0.621013 | ||||||||
\(386\) | −9.58865e6 | −3.27559 | ||||||||
\(387\) | 1.29508e6 | 0.439559 | ||||||||
\(388\) | 6.86446e6 | 2.31487 | ||||||||
\(389\) | −3.04530e6 | −1.02037 | −0.510183 | − | 0.860066i | \(-0.670422\pi\) | ||||
−0.510183 | + | 0.860066i | \(0.670422\pi\) | |||||||
\(390\) | 326045. | 0.108546 | ||||||||
\(391\) | 7.79530e6 | 2.57864 | ||||||||
\(392\) | −4.71021e6 | −1.54819 | ||||||||
\(393\) | 585364. | 0.191181 | ||||||||
\(394\) | 7.11325e6 | 2.30849 | ||||||||
\(395\) | −3.80791e6 | −1.22799 | ||||||||
\(396\) | −4.61571e6 | −1.47911 | ||||||||
\(397\) | 555960. | 0.177038 | 0.0885192 | − | 0.996074i | \(-0.471787\pi\) | ||||
0.0885192 | + | 0.996074i | \(0.471787\pi\) | |||||||
\(398\) | 1.43398e6 | 0.453770 | ||||||||
\(399\) | 465145. | 0.146270 | ||||||||
\(400\) | −1.16635e6 | −0.364483 | ||||||||
\(401\) | −1.46495e6 | −0.454947 | −0.227474 | − | 0.973784i | \(-0.573047\pi\) | ||||
−0.227474 | + | 0.973784i | \(0.573047\pi\) | |||||||
\(402\) | −1.21931e6 | −0.376313 | ||||||||
\(403\) | 239268. | 0.0733875 | ||||||||
\(404\) | −6.34600e6 | −1.93440 | ||||||||
\(405\) | 2.94517e6 | 0.892223 | ||||||||
\(406\) | 1.34935e7 | 4.06266 | ||||||||
\(407\) | 3.08503e6 | 0.923152 | ||||||||
\(408\) | 3.00083e6 | 0.892463 | ||||||||
\(409\) | 732963. | 0.216658 | 0.108329 | − | 0.994115i | \(-0.465450\pi\) | ||||
0.108329 | + | 0.994115i | \(0.465450\pi\) | |||||||
\(410\) | 98107.5 | 0.0288232 | ||||||||
\(411\) | −623578. | −0.182090 | ||||||||
\(412\) | −1.28415e6 | −0.372710 | ||||||||
\(413\) | −6.69553e6 | −1.93157 | ||||||||
\(414\) | 9.79326e6 | 2.80819 | ||||||||
\(415\) | −2.82938e6 | −0.806438 | ||||||||
\(416\) | −6.03190e6 | −1.70892 | ||||||||
\(417\) | −416438. | −0.117276 | ||||||||
\(418\) | −3.12939e6 | −0.876030 | ||||||||
\(419\) | 3.71422e6 | 1.03355 | 0.516776 | − | 0.856121i | \(-0.327132\pi\) | ||||
0.516776 | + | 0.856121i | \(0.327132\pi\) | |||||||
\(420\) | 1.69288e6 | 0.468276 | ||||||||
\(421\) | 3.39542e6 | 0.933659 | 0.466829 | − | 0.884347i | \(-0.345396\pi\) | ||||
0.466829 | + | 0.884347i | \(0.345396\pi\) | |||||||
\(422\) | −4.65463e6 | −1.27234 | ||||||||
\(423\) | −1.42769e6 | −0.387956 | ||||||||
\(424\) | 5.18808e6 | 1.40150 | ||||||||
\(425\) | −595187. | −0.159838 | ||||||||
\(426\) | −1.45428e6 | −0.388262 | ||||||||
\(427\) | 2.55253e6 | 0.677486 | ||||||||
\(428\) | 1.69038e7 | 4.46042 | ||||||||
\(429\) | −120879. | −0.0317109 | ||||||||
\(430\) | 3.19561e6 | 0.833456 | ||||||||
\(431\) | 313706. | 0.0813448 | 0.0406724 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406724 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(432\) | 4.48591e6 | 1.15649 | ||||||||
\(433\) | −5.15537e6 | −1.32142 | −0.660709 | − | 0.750642i | \(-0.729744\pi\) | ||||
−0.660709 | + | 0.750642i | \(0.729744\pi\) | |||||||
\(434\) | 1.68780e6 | 0.430127 | ||||||||
\(435\) | −957454. | −0.242602 | ||||||||
\(436\) | −965747. | −0.243303 | ||||||||
\(437\) | 4.88721e6 | 1.22421 | ||||||||
\(438\) | 1.70184e6 | 0.423870 | ||||||||
\(439\) | −2.05460e6 | −0.508821 | −0.254411 | − | 0.967096i | \(-0.581882\pi\) | ||||
−0.254411 | + | 0.967096i | \(0.581882\pi\) | |||||||
\(440\) | −7.30522e6 | −1.79888 | ||||||||
\(441\) | −1.77707e6 | −0.435120 | ||||||||
\(442\) | −5.58131e6 | −1.35888 | ||||||||
\(443\) | 399939. | 0.0968244 | 0.0484122 | − | 0.998827i | \(-0.484584\pi\) | ||||
0.0484122 | + | 0.998827i | \(0.484584\pi\) | |||||||
\(444\) | −2.89156e6 | −0.696105 | ||||||||
\(445\) | −1.94411e6 | −0.465394 | ||||||||
\(446\) | 4.88164e6 | 1.16206 | ||||||||
\(447\) | 224820. | 0.0532189 | ||||||||
\(448\) | −2.21855e7 | −5.22245 | ||||||||
\(449\) | −5.93650e6 | −1.38968 | −0.694840 | − | 0.719165i | \(-0.744525\pi\) | ||||
−0.694840 | + | 0.719165i | \(0.744525\pi\) | |||||||
\(450\) | −747735. | −0.174067 | ||||||||
\(451\) | −36372.8 | −0.00842046 | ||||||||
\(452\) | −3.32141e6 | −0.764674 | ||||||||
\(453\) | −788841. | −0.180611 | ||||||||
\(454\) | −9.24080e6 | −2.10412 | ||||||||
\(455\) | −2.01956e6 | −0.457329 | ||||||||
\(456\) | 1.88135e6 | 0.423698 | ||||||||
\(457\) | 7.70943e6 | 1.72676 | 0.863380 | − | 0.504555i | \(-0.168343\pi\) | ||||
0.863380 | + | 0.504555i | \(0.168343\pi\) | |||||||
\(458\) | 6.01990e6 | 1.34099 | ||||||||
\(459\) | 2.28917e6 | 0.507160 | ||||||||
\(460\) | 1.77868e7 | 3.91925 | ||||||||
\(461\) | 7.30818e6 | 1.60161 | 0.800805 | − | 0.598925i | \(-0.204405\pi\) | ||||
0.800805 | + | 0.598925i | \(0.204405\pi\) | |||||||
\(462\) | −852685. | −0.185859 | ||||||||
\(463\) | 1.87526e6 | 0.406545 | 0.203273 | − | 0.979122i | \(-0.434842\pi\) | ||||
0.203273 | + | 0.979122i | \(0.434842\pi\) | |||||||
\(464\) | 3.21182e7 | 6.92558 | ||||||||
\(465\) | −119760. | −0.0256851 | ||||||||
\(466\) | 3.93373e6 | 0.839150 | ||||||||
\(467\) | 4.74025e6 | 1.00579 | 0.502897 | − | 0.864346i | \(-0.332268\pi\) | ||||
0.502897 | + | 0.864346i | \(0.332268\pi\) | |||||||
\(468\) | −5.16110e6 | −1.08925 | ||||||||
\(469\) | 7.55256e6 | 1.58549 | ||||||||
\(470\) | −3.52284e6 | −0.735610 | ||||||||
\(471\) | −185755. | −0.0385822 | ||||||||
\(472\) | −2.70811e7 | −5.59514 | ||||||||
\(473\) | −1.18476e6 | −0.243487 | ||||||||
\(474\) | −1.79772e6 | −0.367517 | ||||||||
\(475\) | −373148. | −0.0758835 | ||||||||
\(476\) | −2.89791e7 | −5.86229 | ||||||||
\(477\) | 1.95737e6 | 0.393891 | ||||||||
\(478\) | 7.46348e6 | 1.49407 | ||||||||
\(479\) | 5.85191e6 | 1.16536 | 0.582679 | − | 0.812703i | \(-0.302005\pi\) | ||||
0.582679 | + | 0.812703i | \(0.302005\pi\) | |||||||
\(480\) | 3.01914e6 | 0.598108 | ||||||||
\(481\) | 3.44956e6 | 0.679832 | ||||||||
\(482\) | −1.05515e7 | −2.06869 | ||||||||
\(483\) | 1.33165e6 | 0.259730 | ||||||||
\(484\) | −1.01495e7 | −1.96938 | ||||||||
\(485\) | 4.09890e6 | 0.791248 | ||||||||
\(486\) | 4.32944e6 | 0.831459 | ||||||||
\(487\) | 8.68893e6 | 1.66014 | 0.830068 | − | 0.557662i | \(-0.188301\pi\) | ||||
0.830068 | + | 0.557662i | \(0.188301\pi\) | |||||||
\(488\) | 1.03241e7 | 1.96246 | ||||||||
\(489\) | 376926. | 0.0712827 | ||||||||
\(490\) | −4.38495e6 | −0.825038 | ||||||||
\(491\) | −82009.0 | −0.0153517 | −0.00767587 | − | 0.999971i | \(-0.502443\pi\) | ||||
−0.00767587 | + | 0.999971i | \(0.502443\pi\) | |||||||
\(492\) | 34091.8 | 0.00634947 | ||||||||
\(493\) | 1.63899e7 | 3.03711 | ||||||||
\(494\) | −3.49916e6 | −0.645130 | ||||||||
\(495\) | −2.75612e6 | −0.505575 | ||||||||
\(496\) | 4.01741e6 | 0.733233 | ||||||||
\(497\) | 9.00802e6 | 1.63583 | ||||||||
\(498\) | −1.33576e6 | −0.241354 | ||||||||
\(499\) | 497257. | 0.0893983 | 0.0446992 | − | 0.999000i | \(-0.485767\pi\) | ||||
0.0446992 | + | 0.999000i | \(0.485767\pi\) | |||||||
\(500\) | −1.62180e7 | −2.90116 | ||||||||
\(501\) | 169834. | 0.0302295 | ||||||||
\(502\) | 1.47174e7 | 2.60658 | ||||||||
\(503\) | 1.37133e6 | 0.241669 | 0.120835 | − | 0.992673i | \(-0.461443\pi\) | ||||
0.120835 | + | 0.992673i | \(0.461443\pi\) | |||||||
\(504\) | −2.33515e7 | −4.09486 | ||||||||
\(505\) | −3.78931e6 | −0.661199 | ||||||||
\(506\) | −8.95903e6 | −1.55555 | ||||||||
\(507\) | 713130. | 0.123211 | ||||||||
\(508\) | −1.01049e7 | −1.73729 | ||||||||
\(509\) | −3.31526e6 | −0.567182 | −0.283591 | − | 0.958945i | \(-0.591526\pi\) | ||||
−0.283591 | + | 0.958945i | \(0.591526\pi\) | |||||||
\(510\) | 2.79360e6 | 0.475597 | ||||||||
\(511\) | −1.05414e7 | −1.78585 | ||||||||
\(512\) | −1.89145e7 | −3.18875 | ||||||||
\(513\) | 1.43518e6 | 0.240775 | ||||||||
\(514\) | −1.00244e7 | −1.67359 | ||||||||
\(515\) | −766788. | −0.127396 | ||||||||
\(516\) | 1.11046e6 | 0.183602 | ||||||||
\(517\) | 1.30607e6 | 0.214902 | ||||||||
\(518\) | 2.43333e7 | 3.98452 | ||||||||
\(519\) | −1.41403e6 | −0.230431 | ||||||||
\(520\) | −8.16841e6 | −1.32474 | ||||||||
\(521\) | −1.47501e6 | −0.238069 | −0.119034 | − | 0.992890i | \(-0.537980\pi\) | ||||
−0.119034 | + | 0.992890i | \(0.537980\pi\) | |||||||
\(522\) | 2.05907e7 | 3.30747 | ||||||||
\(523\) | −9.15225e6 | −1.46310 | −0.731549 | − | 0.681788i | \(-0.761203\pi\) | ||||
−0.731549 | + | 0.681788i | \(0.761203\pi\) | |||||||
\(524\) | −2.28639e7 | −3.63766 | ||||||||
\(525\) | −101674. | −0.0160995 | ||||||||
\(526\) | −1.95195e7 | −3.07612 | ||||||||
\(527\) | 2.05009e6 | 0.321548 | ||||||||
\(528\) | −2.02962e6 | −0.316832 | ||||||||
\(529\) | 7.55510e6 | 1.17382 | ||||||||
\(530\) | 4.82982e6 | 0.746864 | ||||||||
\(531\) | −1.02172e7 | −1.57251 | ||||||||
\(532\) | −1.81682e7 | −2.78313 | ||||||||
\(533\) | −40670.7 | −0.00620103 | ||||||||
\(534\) | −917818. | −0.139285 | ||||||||
\(535\) | 1.00936e7 | 1.52462 | ||||||||
\(536\) | 3.05474e7 | 4.59264 | ||||||||
\(537\) | −1.71821e6 | −0.257123 | ||||||||
\(538\) | 3.88798e6 | 0.579120 | ||||||||
\(539\) | 1.62570e6 | 0.241028 | ||||||||
\(540\) | 5.22327e6 | 0.770829 | ||||||||
\(541\) | −7.71693e6 | −1.13358 | −0.566789 | − | 0.823863i | \(-0.691815\pi\) | ||||
−0.566789 | + | 0.823863i | \(0.691815\pi\) | |||||||
\(542\) | −1.39027e7 | −2.03283 | ||||||||
\(543\) | −950734. | −0.138376 | ||||||||
\(544\) | −5.16823e7 | −7.48764 | ||||||||
\(545\) | −576665. | −0.0831635 | ||||||||
\(546\) | −953440. | −0.136871 | ||||||||
\(547\) | −8.83614e6 | −1.26268 | −0.631341 | − | 0.775505i | \(-0.717495\pi\) | ||||
−0.631341 | + | 0.775505i | \(0.717495\pi\) | |||||||
\(548\) | 2.43565e7 | 3.46468 | ||||||||
\(549\) | 3.89508e6 | 0.551550 | ||||||||
\(550\) | 684040. | 0.0964217 | ||||||||
\(551\) | 1.02756e7 | 1.44187 | ||||||||
\(552\) | 5.38605e6 | 0.752355 | ||||||||
\(553\) | 1.11353e7 | 1.54843 | ||||||||
\(554\) | 7.61365e6 | 1.05395 | ||||||||
\(555\) | −1.72660e6 | −0.237936 | ||||||||
\(556\) | 1.62658e7 | 2.23145 | ||||||||
\(557\) | 8.19942e6 | 1.11981 | 0.559906 | − | 0.828556i | \(-0.310837\pi\) | ||||
0.559906 | + | 0.828556i | \(0.310837\pi\) | |||||||
\(558\) | 2.57553e6 | 0.350172 | ||||||||
\(559\) | −1.32475e6 | −0.179310 | ||||||||
\(560\) | −3.39093e7 | −4.56929 | ||||||||
\(561\) | −1.03571e6 | −0.138942 | ||||||||
\(562\) | 1.62005e7 | 2.16366 | ||||||||
\(563\) | −1.07596e7 | −1.43062 | −0.715312 | − | 0.698806i | \(-0.753715\pi\) | ||||
−0.715312 | + | 0.698806i | \(0.753715\pi\) | |||||||
\(564\) | −1.22417e6 | −0.162048 | ||||||||
\(565\) | −1.98328e6 | −0.261374 | ||||||||
\(566\) | −772006. | −0.101293 | ||||||||
\(567\) | −8.61245e6 | −1.12504 | ||||||||
\(568\) | 3.64342e7 | 4.73848 | ||||||||
\(569\) | 6.88906e6 | 0.892029 | 0.446015 | − | 0.895026i | \(-0.352843\pi\) | ||||
0.446015 | + | 0.895026i | \(0.352843\pi\) | |||||||
\(570\) | 1.75143e6 | 0.225791 | ||||||||
\(571\) | −1.07655e7 | −1.38179 | −0.690895 | − | 0.722955i | \(-0.742783\pi\) | ||||
−0.690895 | + | 0.722955i | \(0.742783\pi\) | |||||||
\(572\) | 4.72146e6 | 0.603374 | ||||||||
\(573\) | 689552. | 0.0877365 | ||||||||
\(574\) | −286892. | −0.0363445 | ||||||||
\(575\) | −1.06827e6 | −0.134745 | ||||||||
\(576\) | −3.38544e7 | −4.25166 | ||||||||
\(577\) | 1.25111e7 | 1.56443 | 0.782217 | − | 0.623006i | \(-0.214089\pi\) | ||||
0.782217 | + | 0.623006i | \(0.214089\pi\) | |||||||
\(578\) | −3.21878e7 | −4.00748 | ||||||||
\(579\) | −1.98960e6 | −0.246643 | ||||||||
\(580\) | 3.73975e7 | 4.61607 | ||||||||
\(581\) | 8.27385e6 | 1.01687 | ||||||||
\(582\) | 1.93510e6 | 0.236807 | ||||||||
\(583\) | −1.79063e6 | −0.218190 | ||||||||
\(584\) | −4.26362e7 | −5.17305 | ||||||||
\(585\) | −3.08179e6 | −0.372318 | ||||||||
\(586\) | −9.50183e6 | −1.14304 | ||||||||
\(587\) | 1.05563e7 | 1.26449 | 0.632247 | − | 0.774767i | \(-0.282133\pi\) | ||||
0.632247 | + | 0.774767i | \(0.282133\pi\) | |||||||
\(588\) | −1.52374e6 | −0.181748 | ||||||||
\(589\) | 1.28529e6 | 0.152655 | ||||||||
\(590\) | −2.52110e7 | −2.98167 | ||||||||
\(591\) | 1.47597e6 | 0.173823 | ||||||||
\(592\) | 5.79196e7 | 6.79237 | ||||||||
\(593\) | 2.54089e6 | 0.296721 | 0.148361 | − | 0.988933i | \(-0.452600\pi\) | ||||
0.148361 | + | 0.988933i | \(0.452600\pi\) | |||||||
\(594\) | −2.63091e6 | −0.305942 | ||||||||
\(595\) | −1.73039e7 | −2.00379 | ||||||||
\(596\) | −8.78130e6 | −1.01261 | ||||||||
\(597\) | 297544. | 0.0341677 | ||||||||
\(598\) | −1.00176e7 | −1.14555 | ||||||||
\(599\) | −1.48177e7 | −1.68739 | −0.843694 | − | 0.536824i | \(-0.819624\pi\) | ||||
−0.843694 | + | 0.536824i | \(0.819624\pi\) | |||||||
\(600\) | −411236. | −0.0466351 | ||||||||
\(601\) | −2.79389e6 | −0.315517 | −0.157759 | − | 0.987478i | \(-0.550427\pi\) | ||||
−0.157759 | + | 0.987478i | \(0.550427\pi\) | |||||||
\(602\) | −9.34479e6 | −1.05094 | ||||||||
\(603\) | 1.15250e7 | 1.29076 | ||||||||
\(604\) | 3.08116e7 | 3.43654 | ||||||||
\(605\) | −6.06043e6 | −0.673155 | ||||||||
\(606\) | −1.78894e6 | −0.197886 | ||||||||
\(607\) | 2.70648e6 | 0.298149 | 0.149074 | − | 0.988826i | \(-0.452371\pi\) | ||||
0.149074 | + | 0.988826i | \(0.452371\pi\) | |||||||
\(608\) | −3.24019e7 | −3.55477 | ||||||||
\(609\) | 2.79985e6 | 0.305908 | ||||||||
\(610\) | 9.61113e6 | 1.04580 | ||||||||
\(611\) | 1.46040e6 | 0.158259 | ||||||||
\(612\) | −4.42212e7 | −4.77257 | ||||||||
\(613\) | 1.48550e7 | 1.59670 | 0.798348 | − | 0.602197i | \(-0.205708\pi\) | ||||
0.798348 | + | 0.602197i | \(0.205708\pi\) | |||||||
\(614\) | 3.20953e7 | 3.43574 | ||||||||
\(615\) | 20356.8 | 0.00217031 | ||||||||
\(616\) | 2.13624e7 | 2.26828 | ||||||||
\(617\) | −7.75787e6 | −0.820407 | −0.410204 | − | 0.911994i | \(-0.634542\pi\) | ||||
−0.410204 | + | 0.911994i | \(0.634542\pi\) | |||||||
\(618\) | −362002. | −0.0381276 | ||||||||
\(619\) | −1.34491e7 | −1.41080 | −0.705400 | − | 0.708810i | \(-0.749232\pi\) | ||||
−0.705400 | + | 0.708810i | \(0.749232\pi\) | |||||||
\(620\) | 4.67775e6 | 0.488718 | ||||||||
\(621\) | 4.10872e6 | 0.427541 | ||||||||
\(622\) | 7.46559e6 | 0.773728 | ||||||||
\(623\) | 5.68508e6 | 0.586836 | ||||||||
\(624\) | −2.26944e6 | −0.233323 | ||||||||
\(625\) | −8.79157e6 | −0.900257 | ||||||||
\(626\) | −2.08930e7 | −2.13091 | ||||||||
\(627\) | −649334. | −0.0659628 | ||||||||
\(628\) | 7.25544e6 | 0.734116 | ||||||||
\(629\) | 2.95564e7 | 2.97869 | ||||||||
\(630\) | −2.17390e7 | −2.18217 | ||||||||
\(631\) | −1.19256e7 | −1.19236 | −0.596179 | − | 0.802852i | \(-0.703315\pi\) | ||||
−0.596179 | + | 0.802852i | \(0.703315\pi\) | |||||||
\(632\) | 4.50385e7 | 4.48529 | ||||||||
\(633\) | −965815. | −0.0958042 | ||||||||
\(634\) | 2.05320e7 | 2.02866 | ||||||||
\(635\) | −6.03382e6 | −0.593825 | ||||||||
\(636\) | 1.67834e6 | 0.164527 | ||||||||
\(637\) | 1.81779e6 | 0.177499 | ||||||||
\(638\) | −1.88367e7 | −1.83212 | ||||||||
\(639\) | 1.37460e7 | 1.33175 | ||||||||
\(640\) | −4.12493e7 | −3.98076 | ||||||||
\(641\) | 5.46967e6 | 0.525795 | 0.262897 | − | 0.964824i | \(-0.415322\pi\) | ||||
0.262897 | + | 0.964824i | \(0.415322\pi\) | |||||||
\(642\) | 4.76520e6 | 0.456293 | ||||||||
\(643\) | 1.92397e6 | 0.183515 | 0.0917575 | − | 0.995781i | \(-0.470752\pi\) | ||||
0.0917575 | + | 0.995781i | \(0.470752\pi\) | |||||||
\(644\) | −5.20133e7 | −4.94196 | ||||||||
\(645\) | 663074. | 0.0627571 | ||||||||
\(646\) | −2.99814e7 | −2.82664 | ||||||||
\(647\) | 1.29937e7 | 1.22031 | 0.610156 | − | 0.792282i | \(-0.291107\pi\) | ||||
0.610156 | + | 0.792282i | \(0.291107\pi\) | |||||||
\(648\) | −3.48343e7 | −3.25889 | ||||||||
\(649\) | 9.34684e6 | 0.871070 | ||||||||
\(650\) | 764868. | 0.0710073 | ||||||||
\(651\) | 350211. | 0.0323875 | ||||||||
\(652\) | −1.47225e7 | −1.35632 | ||||||||
\(653\) | −1.87036e7 | −1.71650 | −0.858249 | − | 0.513234i | \(-0.828447\pi\) | ||||
−0.858249 | + | 0.513234i | \(0.828447\pi\) | |||||||
\(654\) | −272245. | −0.0248895 | ||||||||
\(655\) | −1.36525e7 | −1.24339 | ||||||||
\(656\) | −682879. | −0.0619561 | ||||||||
\(657\) | −1.60859e7 | −1.45389 | ||||||||
\(658\) | 1.03017e7 | 0.927564 | ||||||||
\(659\) | 740764. | 0.0664456 | 0.0332228 | − | 0.999448i | \(-0.489423\pi\) | ||||
0.0332228 | + | 0.999448i | \(0.489423\pi\) | |||||||
\(660\) | −2.36322e6 | −0.211176 | ||||||||
\(661\) | −1.69004e7 | −1.50450 | −0.752252 | − | 0.658876i | \(-0.771032\pi\) | ||||
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | 1.58544e7 | 1.40607 | ||||||||
\(663\) | −1.15810e6 | −0.102320 | ||||||||
\(664\) | 3.34648e7 | 2.94556 | ||||||||
\(665\) | −1.08486e7 | −0.951303 | ||||||||
\(666\) | 3.71318e7 | 3.24385 | ||||||||
\(667\) | 2.94176e7 | 2.56031 | ||||||||
\(668\) | −6.63359e6 | −0.575185 | ||||||||
\(669\) | 1.01292e6 | 0.0875001 | ||||||||
\(670\) | 2.84380e7 | 2.44744 | ||||||||
\(671\) | −3.56328e6 | −0.305523 | ||||||||
\(672\) | −8.82875e6 | −0.754181 | ||||||||
\(673\) | 4.63004e6 | 0.394046 | 0.197023 | − | 0.980399i | \(-0.436873\pi\) | ||||
0.197023 | + | 0.980399i | \(0.436873\pi\) | |||||||
\(674\) | −1.77518e7 | −1.50519 | ||||||||
\(675\) | −313709. | −0.0265013 | ||||||||
\(676\) | −2.78543e7 | −2.34437 | ||||||||
\(677\) | 4.66171e6 | 0.390907 | 0.195454 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195454 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(678\) | −936309. | −0.0782248 | ||||||||
\(679\) | −1.19862e7 | −0.997720 | ||||||||
\(680\) | −6.99883e7 | −5.80435 | ||||||||
\(681\) | −1.91742e6 | −0.158435 | ||||||||
\(682\) | −2.35614e6 | −0.193972 | ||||||||
\(683\) | 6.47801e6 | 0.531362 | 0.265681 | − | 0.964061i | \(-0.414403\pi\) | ||||
0.265681 | + | 0.964061i | \(0.414403\pi\) | |||||||
\(684\) | −2.77242e7 | −2.26578 | ||||||||
\(685\) | 1.45437e7 | 1.18426 | ||||||||
\(686\) | −1.60136e7 | −1.29921 | ||||||||
\(687\) | 1.24910e6 | 0.100973 | ||||||||
\(688\) | −2.22431e7 | −1.79153 | ||||||||
\(689\) | −2.00221e6 | −0.160680 | ||||||||
\(690\) | 5.01411e6 | 0.400933 | ||||||||
\(691\) | 8.03340e6 | 0.640036 | 0.320018 | − | 0.947411i | \(-0.396311\pi\) | ||||
0.320018 | + | 0.947411i | \(0.396311\pi\) | |||||||
\(692\) | 5.52312e7 | 4.38449 | ||||||||
\(693\) | 8.05962e6 | 0.637502 | ||||||||
\(694\) | −1.80390e6 | −0.142172 | ||||||||
\(695\) | 9.71259e6 | 0.762734 | ||||||||
\(696\) | 1.13244e7 | 0.886118 | ||||||||
\(697\) | −348473. | −0.0271699 | ||||||||
\(698\) | −2.50870e7 | −1.94899 | ||||||||
\(699\) | 816230. | 0.0631858 | ||||||||
\(700\) | 3.97132e6 | 0.306330 | ||||||||
\(701\) | −1.97958e6 | −0.152152 | −0.0760759 | − | 0.997102i | \(-0.524239\pi\) | ||||
−0.0760759 | + | 0.997102i | \(0.524239\pi\) | |||||||
\(702\) | −2.94178e6 | −0.225303 | ||||||||
\(703\) | 1.85302e7 | 1.41414 | ||||||||
\(704\) | 3.09705e7 | 2.35514 | ||||||||
\(705\) | −730972. | −0.0553896 | ||||||||
\(706\) | 2.69204e7 | 2.03268 | ||||||||
\(707\) | 1.10809e7 | 0.833735 | ||||||||
\(708\) | −8.76067e6 | −0.656832 | ||||||||
\(709\) | 5.10052e6 | 0.381065 | 0.190532 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190532 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(710\) | 3.39183e7 | 2.52515 | ||||||||
\(711\) | 1.69922e7 | 1.26059 | ||||||||
\(712\) | 2.29941e7 | 1.69988 | ||||||||
\(713\) | 3.67961e6 | 0.271068 | ||||||||
\(714\) | −8.16923e6 | −0.599702 | ||||||||
\(715\) | 2.81927e6 | 0.206239 | ||||||||
\(716\) | 6.71120e7 | 4.89235 | ||||||||
\(717\) | 1.54864e6 | 0.112500 | ||||||||
\(718\) | −6.94670e6 | −0.502883 | ||||||||
\(719\) | 1.89165e6 | 0.136464 | 0.0682319 | − | 0.997669i | \(-0.478264\pi\) | ||||
0.0682319 | + | 0.997669i | \(0.478264\pi\) | |||||||
\(720\) | −5.17446e7 | −3.71992 | ||||||||
\(721\) | 2.24229e6 | 0.160640 | ||||||||
\(722\) | 8.46730e6 | 0.604508 | ||||||||
\(723\) | −2.18938e6 | −0.155767 | ||||||||
\(724\) | 3.71350e7 | 2.63291 | ||||||||
\(725\) | −2.24609e6 | −0.158702 | ||||||||
\(726\) | −2.86114e6 | −0.201464 | ||||||||
\(727\) | −1.36241e7 | −0.956030 | −0.478015 | − | 0.878352i | \(-0.658644\pi\) | ||||
−0.478015 | + | 0.878352i | \(0.658644\pi\) | |||||||
\(728\) | 2.38866e7 | 1.67042 | ||||||||
\(729\) | −1.25325e7 | −0.873412 | ||||||||
\(730\) | −3.96920e7 | −2.75674 | ||||||||
\(731\) | −1.13507e7 | −0.785647 | ||||||||
\(732\) | 3.33981e6 | 0.230380 | ||||||||
\(733\) | 2.84192e7 | 1.95367 | 0.976835 | − | 0.213993i | \(-0.0686471\pi\) | ||||
0.976835 | + | 0.213993i | \(0.0686471\pi\) | |||||||
\(734\) | −4.95839e7 | −3.39704 | ||||||||
\(735\) | −909856. | −0.0621233 | ||||||||
\(736\) | −9.27623e7 | −6.31215 | ||||||||
\(737\) | −1.05432e7 | −0.714999 | ||||||||
\(738\) | −437788. | −0.0295885 | ||||||||
\(739\) | 1.55531e7 | 1.04762 | 0.523811 | − | 0.851834i | \(-0.324510\pi\) | ||||
0.523811 | + | 0.851834i | \(0.324510\pi\) | |||||||
\(740\) | 6.74399e7 | 4.52728 | ||||||||
\(741\) | −726060. | −0.0485766 | ||||||||
\(742\) | −1.41237e7 | −0.941754 | ||||||||
\(743\) | −1.26836e7 | −0.842892 | −0.421446 | − | 0.906853i | \(-0.638477\pi\) | ||||
−0.421446 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(744\) | 1.41648e6 | 0.0938161 | ||||||||
\(745\) | −5.24348e6 | −0.346122 | ||||||||
\(746\) | 3.20938e7 | 2.11142 | ||||||||
\(747\) | 1.26256e7 | 0.827850 | ||||||||
\(748\) | 4.04542e7 | 2.64369 | ||||||||
\(749\) | −2.95163e7 | −1.92246 | ||||||||
\(750\) | −4.57186e6 | −0.296784 | ||||||||
\(751\) | 2.60057e6 | 0.168255 | 0.0841277 | − | 0.996455i | \(-0.473190\pi\) | ||||
0.0841277 | + | 0.996455i | \(0.473190\pi\) | |||||||
\(752\) | 2.45208e7 | 1.58121 | ||||||||
\(753\) | 3.05379e6 | 0.196269 | ||||||||
\(754\) | −2.10625e7 | −1.34922 | ||||||||
\(755\) | 1.83982e7 | 1.17465 | ||||||||
\(756\) | −1.52742e7 | −0.971972 | ||||||||
\(757\) | 8.94406e6 | 0.567277 | 0.283639 | − | 0.958931i | \(-0.408458\pi\) | ||||
0.283639 | + | 0.958931i | \(0.408458\pi\) | |||||||
\(758\) | −3.69272e7 | −2.33439 | ||||||||
\(759\) | −1.85896e6 | −0.117129 | ||||||||
\(760\) | −4.38787e7 | −2.75562 | ||||||||
\(761\) | −1.86914e6 | −0.116998 | −0.0584991 | − | 0.998287i | \(-0.518631\pi\) | ||||
−0.0584991 | + | 0.998287i | \(0.518631\pi\) | |||||||
\(762\) | −2.84858e6 | −0.177722 | ||||||||
\(763\) | 1.68632e6 | 0.104865 | ||||||||
\(764\) | −2.69334e7 | −1.66939 | ||||||||
\(765\) | −2.64053e7 | −1.63131 | ||||||||
\(766\) | 4.49560e7 | 2.76832 | ||||||||
\(767\) | 1.04513e7 | 0.641477 | ||||||||
\(768\) | −9.06465e6 | −0.554559 | ||||||||
\(769\) | −1.40225e6 | −0.0855087 | −0.0427544 | − | 0.999086i | \(-0.513613\pi\) | ||||
−0.0427544 | + | 0.999086i | \(0.513613\pi\) | |||||||
\(770\) | 1.98872e7 | 1.20878 | ||||||||
\(771\) | −2.08001e6 | −0.126017 | ||||||||
\(772\) | 7.77123e7 | 4.69296 | ||||||||
\(773\) | 4.11509e6 | 0.247702 | 0.123851 | − | 0.992301i | \(-0.460475\pi\) | ||||
0.123851 | + | 0.992301i | \(0.460475\pi\) | |||||||
\(774\) | −1.42599e7 | −0.855585 | ||||||||
\(775\) | −280946. | −0.0168023 | ||||||||
\(776\) | −4.84801e7 | −2.89008 | ||||||||
\(777\) | 5.04904e6 | 0.300024 | ||||||||
\(778\) | 3.35313e7 | 1.98610 | ||||||||
\(779\) | −218473. | −0.0128989 | ||||||||
\(780\) | −2.64247e6 | −0.155515 | ||||||||
\(781\) | −1.25750e7 | −0.737702 | ||||||||
\(782\) | −8.58328e7 | −5.01922 | ||||||||
\(783\) | 8.63875e6 | 0.503554 | ||||||||
\(784\) | 3.05215e7 | 1.77344 | ||||||||
\(785\) | 4.33236e6 | 0.250928 | ||||||||
\(786\) | −6.44536e6 | −0.372127 | ||||||||
\(787\) | −3.13109e7 | −1.80202 | −0.901008 | − | 0.433802i | \(-0.857172\pi\) | ||||
−0.901008 | + | 0.433802i | \(0.857172\pi\) | |||||||
\(788\) | −5.76502e7 | −3.30739 | ||||||||
\(789\) | −4.05019e6 | −0.231624 | ||||||||
\(790\) | 4.19283e7 | 2.39023 | ||||||||
\(791\) | 5.79962e6 | 0.329578 | ||||||||
\(792\) | 3.25983e7 | 1.84664 | ||||||||
\(793\) | −3.98432e6 | −0.224994 | ||||||||
\(794\) | −6.12159e6 | −0.344598 | ||||||||
\(795\) | 1.00216e6 | 0.0562369 | ||||||||
\(796\) | −1.16219e7 | −0.650120 | ||||||||
\(797\) | −3.69257e6 | −0.205913 | −0.102956 | − | 0.994686i | \(-0.532830\pi\) | ||||
−0.102956 | + | 0.994686i | \(0.532830\pi\) | |||||||
\(798\) | −5.12164e6 | −0.284709 | ||||||||
\(799\) | 1.25130e7 | 0.693415 | ||||||||
\(800\) | 7.08259e6 | 0.391261 | ||||||||
\(801\) | 8.67526e6 | 0.477751 | ||||||||
\(802\) | 1.61303e7 | 0.885537 | ||||||||
\(803\) | 1.47156e7 | 0.805358 | ||||||||
\(804\) | 9.88204e6 | 0.539146 | ||||||||
\(805\) | −3.10581e7 | −1.68921 | ||||||||
\(806\) | −2.63454e6 | −0.142846 | ||||||||
\(807\) | 806738. | 0.0436063 | ||||||||
\(808\) | 4.48185e7 | 2.41507 | ||||||||
\(809\) | −2.83800e7 | −1.52455 | −0.762275 | − | 0.647253i | \(-0.775918\pi\) | ||||
−0.762275 | + | 0.647253i | \(0.775918\pi\) | |||||||
\(810\) | −3.24288e7 | −1.73668 | ||||||||
\(811\) | −1.03767e7 | −0.553995 | −0.276997 | − | 0.960871i | \(-0.589339\pi\) | ||||
−0.276997 | + | 0.960871i | \(0.589339\pi\) | |||||||
\(812\) | −1.09360e8 | −5.82061 | ||||||||
\(813\) | −2.88475e6 | −0.153067 | ||||||||
\(814\) | −3.39688e7 | −1.79688 | ||||||||
\(815\) | −8.79105e6 | −0.463604 | ||||||||
\(816\) | −1.94449e7 | −1.02231 | ||||||||
\(817\) | −7.11622e6 | −0.372987 | ||||||||
\(818\) | −8.07054e6 | −0.421715 | ||||||||
\(819\) | 9.01196e6 | 0.469472 | ||||||||
\(820\) | −795124. | −0.0412952 | ||||||||
\(821\) | 3.15619e7 | 1.63420 | 0.817100 | − | 0.576497i | \(-0.195581\pi\) | ||||
0.817100 | + | 0.576497i | \(0.195581\pi\) | |||||||
\(822\) | 6.86612e6 | 0.354431 | ||||||||
\(823\) | 5.81986e6 | 0.299511 | 0.149756 | − | 0.988723i | \(-0.452151\pi\) | ||||
0.149756 | + | 0.988723i | \(0.452151\pi\) | |||||||
\(824\) | 9.06926e6 | 0.465322 | ||||||||
\(825\) | 141935. | 0.00726031 | ||||||||
\(826\) | 7.37235e7 | 3.75972 | ||||||||
\(827\) | −1.84354e7 | −0.937322 | −0.468661 | − | 0.883378i | \(-0.655263\pi\) | ||||
−0.468661 | + | 0.883378i | \(0.655263\pi\) | |||||||
\(828\) | −7.93706e7 | −4.02332 | ||||||||
\(829\) | 1.93633e7 | 0.978571 | 0.489285 | − | 0.872124i | \(-0.337258\pi\) | ||||
0.489285 | + | 0.872124i | \(0.337258\pi\) | |||||||
\(830\) | 3.11539e7 | 1.56970 | ||||||||
\(831\) | 1.57980e6 | 0.0793594 | ||||||||
\(832\) | 3.46301e7 | 1.73438 | ||||||||
\(833\) | 1.55751e7 | 0.777713 | ||||||||
\(834\) | 4.58533e6 | 0.228274 | ||||||||
\(835\) | −3.96104e6 | −0.196604 | ||||||||
\(836\) | 2.53625e7 | 1.25509 | ||||||||
\(837\) | 1.08055e6 | 0.0533129 | ||||||||
\(838\) | −4.08967e7 | −2.01177 | ||||||||
\(839\) | −2.79155e7 | −1.36911 | −0.684557 | − | 0.728959i | \(-0.740005\pi\) | ||||
−0.684557 | + | 0.728959i | \(0.740005\pi\) | |||||||
\(840\) | −1.19559e7 | −0.584634 | ||||||||
\(841\) | 4.13404e7 | 2.01551 | ||||||||
\(842\) | −3.73864e7 | −1.81733 | ||||||||
\(843\) | 3.36154e6 | 0.162918 | ||||||||
\(844\) | 3.77240e7 | 1.82290 | ||||||||
\(845\) | −1.66323e7 | −0.801330 | ||||||||
\(846\) | 1.57201e7 | 0.755142 | ||||||||
\(847\) | 1.77223e7 | 0.848811 | ||||||||
\(848\) | −3.36180e7 | −1.60540 | ||||||||
\(849\) | −160188. | −0.00762711 | ||||||||
\(850\) | 6.55351e6 | 0.311119 | ||||||||
\(851\) | 5.30495e7 | 2.51106 | ||||||||
\(852\) | 1.17864e7 | 0.556266 | ||||||||
\(853\) | 3.67026e7 | 1.72713 | 0.863563 | − | 0.504242i | \(-0.168228\pi\) | ||||
0.863563 | + | 0.504242i | \(0.168228\pi\) | |||||||
\(854\) | −2.81055e7 | −1.31870 | ||||||||
\(855\) | −1.65546e7 | −0.774468 | ||||||||
\(856\) | −1.19383e8 | −5.56875 | ||||||||
\(857\) | 467751. | 0.0217552 | 0.0108776 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108776 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(858\) | 1.33098e6 | 0.0617241 | ||||||||
\(859\) | −1.66567e7 | −0.770206 | −0.385103 | − | 0.922873i | \(-0.625834\pi\) | ||||
−0.385103 | + | 0.922873i | \(0.625834\pi\) | |||||||
\(860\) | −2.58992e7 | −1.19410 | ||||||||
\(861\) | −59528.7 | −0.00273665 | ||||||||
\(862\) | −3.45417e6 | −0.158334 | ||||||||
\(863\) | −2.83692e7 | −1.29664 | −0.648321 | − | 0.761367i | \(-0.724529\pi\) | ||||
−0.648321 | + | 0.761367i | \(0.724529\pi\) | |||||||
\(864\) | −2.72405e7 | −1.24146 | ||||||||
\(865\) | 3.29796e7 | 1.49867 | ||||||||
\(866\) | 5.67650e7 | 2.57209 | ||||||||
\(867\) | −6.67881e6 | −0.301753 | ||||||||
\(868\) | −1.36790e7 | −0.616246 | ||||||||
\(869\) | −1.55447e7 | −0.698286 | ||||||||
\(870\) | 1.05424e7 | 0.472216 | ||||||||
\(871\) | −1.17890e7 | −0.526542 | ||||||||
\(872\) | 6.82057e6 | 0.303759 | ||||||||
\(873\) | −1.82906e7 | −0.812257 | ||||||||
\(874\) | −5.38123e7 | −2.38288 | ||||||||
\(875\) | 2.83187e7 | 1.25041 | ||||||||
\(876\) | −1.37927e7 | −0.607282 | ||||||||
\(877\) | 1.84690e7 | 0.810856 | 0.405428 | − | 0.914127i | \(-0.367122\pi\) | ||||
0.405428 | + | 0.914127i | \(0.367122\pi\) | |||||||
\(878\) | 2.26229e7 | 0.990401 | ||||||||
\(879\) | −1.97158e6 | −0.0860683 | ||||||||
\(880\) | 4.73368e7 | 2.06059 | ||||||||
\(881\) | −2.04875e7 | −0.889303 | −0.444651 | − | 0.895704i | \(-0.646672\pi\) | ||||
−0.444651 | + | 0.895704i | \(0.646672\pi\) | |||||||
\(882\) | 1.95671e7 | 0.846944 | ||||||||
\(883\) | −3.82446e6 | −0.165070 | −0.0825350 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825350 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(884\) | 4.52344e7 | 1.94688 | ||||||||
\(885\) | −5.23116e6 | −0.224512 | ||||||||
\(886\) | −4.40367e6 | −0.188465 | ||||||||
\(887\) | −4.25938e7 | −1.81776 | −0.908881 | − | 0.417055i | \(-0.863062\pi\) | ||||
−0.908881 | + | 0.417055i | \(0.863062\pi\) | |||||||
\(888\) | 2.04216e7 | 0.869074 | ||||||||
\(889\) | 1.76445e7 | 0.748780 | ||||||||
\(890\) | 2.14063e7 | 0.905871 | ||||||||
\(891\) | 1.20228e7 | 0.507355 | ||||||||
\(892\) | −3.95638e7 | −1.66489 | ||||||||
\(893\) | 7.84491e6 | 0.329200 | ||||||||
\(894\) | −2.47546e6 | −0.103588 | ||||||||
\(895\) | 4.00738e7 | 1.67226 | ||||||||
\(896\) | 1.20624e8 | 5.01952 | ||||||||
\(897\) | −2.07861e6 | −0.0862567 | ||||||||
\(898\) | 6.53659e7 | 2.70496 | ||||||||
\(899\) | 7.73653e6 | 0.319262 | ||||||||
\(900\) | 6.06011e6 | 0.249387 | ||||||||
\(901\) | −1.71553e7 | −0.704022 | ||||||||
\(902\) | 400496. | 0.0163901 | ||||||||
\(903\) | −1.93900e6 | −0.0791332 | ||||||||
\(904\) | 2.34574e7 | 0.954682 | ||||||||
\(905\) | 2.21740e7 | 0.899958 | ||||||||
\(906\) | 8.68581e6 | 0.351552 | ||||||||
\(907\) | 4.91611e7 | 1.98428 | 0.992140 | − | 0.125131i | \(-0.0399352\pi\) | ||||
0.992140 | + | 0.125131i | \(0.0399352\pi\) | |||||||
\(908\) | 7.48932e7 | 3.01459 | ||||||||
\(909\) | 1.69092e7 | 0.678755 | ||||||||
\(910\) | 2.22371e7 | 0.890173 | ||||||||
\(911\) | 6.96714e6 | 0.278137 | 0.139068 | − | 0.990283i | \(-0.455589\pi\) | ||||
0.139068 | + | 0.990283i | \(0.455589\pi\) | |||||||
\(912\) | −1.21909e7 | −0.485341 | ||||||||
\(913\) | −1.15501e7 | −0.458575 | ||||||||
\(914\) | −8.48874e7 | −3.36107 | ||||||||
\(915\) | 1.99427e6 | 0.0787463 | ||||||||
\(916\) | −4.87890e7 | −1.92125 | ||||||||
\(917\) | 3.99234e7 | 1.56785 | ||||||||
\(918\) | −2.52056e7 | −0.987168 | ||||||||
\(919\) | 1.03025e7 | 0.402398 | 0.201199 | − | 0.979550i | \(-0.435516\pi\) | ||||
0.201199 | + | 0.979550i | \(0.435516\pi\) | |||||||
\(920\) | −1.25619e8 | −4.89312 | ||||||||
\(921\) | 6.65963e6 | 0.258703 | ||||||||
\(922\) | −8.04692e7 | −3.11747 | ||||||||
\(923\) | −1.40609e7 | −0.543262 | ||||||||
\(924\) | 6.91068e6 | 0.266282 | ||||||||
\(925\) | −4.05044e6 | −0.155649 | ||||||||
\(926\) | −2.06482e7 | −0.791324 | ||||||||
\(927\) | 3.42166e6 | 0.130779 | ||||||||
\(928\) | −1.95036e8 | −7.43440 | ||||||||
\(929\) | 9.04403e6 | 0.343813 | 0.171907 | − | 0.985113i | \(-0.445007\pi\) | ||||
0.171907 | + | 0.985113i | \(0.445007\pi\) | |||||||
\(930\) | 1.31866e6 | 0.0499950 | ||||||||
\(931\) | 9.76472e6 | 0.369220 | ||||||||
\(932\) | −3.18814e7 | −1.20226 | ||||||||
\(933\) | 1.54907e6 | 0.0582597 | ||||||||
\(934\) | −5.21941e7 | −1.95774 | ||||||||
\(935\) | 2.41560e7 | 0.903640 | ||||||||
\(936\) | 3.64502e7 | 1.35991 | ||||||||
\(937\) | −7.60906e6 | −0.283128 | −0.141564 | − | 0.989929i | \(-0.545213\pi\) | ||||
−0.141564 | + | 0.989929i | \(0.545213\pi\) | |||||||
\(938\) | −8.31601e7 | −3.08608 | ||||||||
\(939\) | −4.33521e6 | −0.160452 | ||||||||
\(940\) | 2.85512e7 | 1.05391 | ||||||||
\(941\) | 3.49843e7 | 1.28795 | 0.643976 | − | 0.765046i | \(-0.277284\pi\) | ||||
0.643976 | + | 0.765046i | \(0.277284\pi\) | |||||||
\(942\) | 2.04531e6 | 0.0750988 | ||||||||
\(943\) | −625459. | −0.0229044 | ||||||||
\(944\) | 1.75481e8 | 6.40916 | ||||||||
\(945\) | −9.12050e6 | −0.332230 | ||||||||
\(946\) | 1.30452e7 | 0.473938 | ||||||||
\(947\) | −1.56286e7 | −0.566298 | −0.283149 | − | 0.959076i | \(-0.591379\pi\) | ||||
−0.283149 | + | 0.959076i | \(0.591379\pi\) | |||||||
\(948\) | 1.45699e7 | 0.526544 | ||||||||
\(949\) | 1.64544e7 | 0.593085 | ||||||||
\(950\) | 4.10868e6 | 0.147704 | ||||||||
\(951\) | 4.26030e6 | 0.152753 | ||||||||
\(952\) | 2.04664e8 | 7.31896 | ||||||||
\(953\) | −2.51790e7 | −0.898062 | −0.449031 | − | 0.893516i | \(-0.648231\pi\) | ||||
−0.449031 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(954\) | −2.15523e7 | −0.766694 | ||||||||
\(955\) | −1.60824e7 | −0.570615 | ||||||||
\(956\) | −6.04887e7 | −2.14057 | ||||||||
\(957\) | −3.90853e6 | −0.137954 | ||||||||
\(958\) | −6.44345e7 | −2.26832 | ||||||||
\(959\) | −4.25296e7 | −1.49329 | ||||||||
\(960\) | −1.73333e7 | −0.607021 | ||||||||
\(961\) | −2.76614e7 | −0.966199 | ||||||||
\(962\) | −3.79826e7 | −1.32327 | ||||||||
\(963\) | −4.50410e7 | −1.56510 | ||||||||
\(964\) | 8.55157e7 | 2.96383 | ||||||||
\(965\) | 4.64035e7 | 1.60410 | ||||||||
\(966\) | −1.46626e7 | −0.505554 | ||||||||
\(967\) | 2.41861e7 | 0.831765 | 0.415882 | − | 0.909418i | \(-0.363473\pi\) | ||||
0.415882 | + | 0.909418i | \(0.363473\pi\) | |||||||
\(968\) | 7.16803e7 | 2.45873 | ||||||||
\(969\) | −6.22100e6 | −0.212839 | ||||||||
\(970\) | −4.51323e7 | −1.54013 | ||||||||
\(971\) | −2.98587e7 | −1.01630 | −0.508152 | − | 0.861267i | \(-0.669671\pi\) | ||||
−0.508152 | + | 0.861267i | \(0.669671\pi\) | |||||||
\(972\) | −3.50885e7 | −1.19124 | ||||||||
\(973\) | −2.84021e7 | −0.961765 | ||||||||
\(974\) | −9.56725e7 | −3.23139 | ||||||||
\(975\) | 158706. | 0.00534666 | ||||||||
\(976\) | −6.68984e7 | −2.24797 | ||||||||
\(977\) | 8.08644e6 | 0.271032 | 0.135516 | − | 0.990775i | \(-0.456731\pi\) | ||||
0.135516 | + | 0.990775i | \(0.456731\pi\) | |||||||
\(978\) | −4.15027e6 | −0.138749 | ||||||||
\(979\) | −7.93627e6 | −0.264643 | ||||||||
\(980\) | 3.55383e7 | 1.18204 | ||||||||
\(981\) | 2.57327e6 | 0.0853716 | ||||||||
\(982\) | 902988. | 0.0298816 | ||||||||
\(983\) | 966289. | 0.0318950 | ||||||||
\(984\) | −240773. | −0.00792719 | ||||||||
\(985\) | −3.44240e7 | −1.13050 | ||||||||
\(986\) | −1.80467e8 | −5.91161 | ||||||||
\(987\) | 2.13755e6 | 0.0698432 | ||||||||
\(988\) | 2.83594e7 | 0.924282 | ||||||||
\(989\) | −2.03728e7 | −0.662308 | ||||||||
\(990\) | 3.03472e7 | 0.984082 | ||||||||
\(991\) | −3.46275e7 | −1.12005 | −0.560025 | − | 0.828476i | \(-0.689208\pi\) | ||||
−0.560025 | + | 0.828476i | \(0.689208\pi\) | |||||||
\(992\) | −2.43956e7 | −0.787104 | ||||||||
\(993\) | 3.28972e6 | 0.105873 | ||||||||
\(994\) | −9.91859e7 | −3.18408 | ||||||||
\(995\) | −6.93963e6 | −0.222218 | ||||||||
\(996\) | 1.08258e7 | 0.345789 | ||||||||
\(997\) | 5.61449e7 | 1.78884 | 0.894422 | − | 0.447225i | \(-0.147588\pi\) | ||||
0.894422 | + | 0.447225i | \(0.147588\pi\) | |||||||
\(998\) | −5.47522e6 | −0.174010 | ||||||||
\(999\) | 1.55785e7 | 0.493869 |
(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 | 983.6.a.b.1.4 | ✓ | 218 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.6.a.b.1.4 | ✓ | 218 | 1.1 | even | 1 | trivial |