Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59417 | −0.458590 | −0.229295 | − | 0.973357i | \(-0.573642\pi\) | ||||
−0.229295 | + | 0.973357i | \(0.573642\pi\) | |||||||
\(3\) | 30.0518 | 1.92782 | 0.963912 | − | 0.266220i | \(-0.0857748\pi\) | ||||
0.963912 | + | 0.266220i | \(0.0857748\pi\) | |||||||
\(4\) | −25.2703 | −0.789696 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −77.9597 | −0.884080 | ||||||||
\(7\) | −144.749 | −1.11653 | −0.558266 | − | 0.829662i | \(-0.688533\pi\) | ||||
−0.558266 | + | 0.829662i | \(0.688533\pi\) | |||||||
\(8\) | 148.569 | 0.820736 | ||||||||
\(9\) | 660.111 | 2.71651 | ||||||||
\(10\) | −64.8544 | −0.205088 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −759.417 | −1.52239 | ||||||||
\(13\) | −665.516 | −1.09220 | −0.546098 | − | 0.837722i | \(-0.683887\pi\) | ||||
−0.546098 | + | 0.837722i | \(0.683887\pi\) | |||||||
\(14\) | 375.505 | 0.512030 | ||||||||
\(15\) | 751.295 | 0.862149 | ||||||||
\(16\) | 423.234 | 0.413315 | ||||||||
\(17\) | −777.887 | −0.652821 | −0.326411 | − | 0.945228i | \(-0.605839\pi\) | ||||
−0.326411 | + | 0.945228i | \(0.605839\pi\) | |||||||
\(18\) | −1712.44 | −1.24576 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −631.756 | −0.353163 | ||||||||
\(21\) | −4349.98 | −2.15248 | ||||||||
\(22\) | −313.895 | −0.138270 | ||||||||
\(23\) | 2896.34 | 1.14164 | 0.570820 | − | 0.821075i | \(-0.306625\pi\) | ||||
0.570820 | + | 0.821075i | \(0.306625\pi\) | |||||||
\(24\) | 4464.77 | 1.58223 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1726.47 | 0.500869 | ||||||||
\(27\) | 12535.0 | 3.30913 | ||||||||
\(28\) | 3657.85 | 0.881720 | ||||||||
\(29\) | −6731.31 | −1.48629 | −0.743147 | − | 0.669128i | \(-0.766668\pi\) | ||||
−0.743147 | + | 0.669128i | \(0.766668\pi\) | |||||||
\(30\) | −1948.99 | −0.395373 | ||||||||
\(31\) | 3887.42 | 0.726536 | 0.363268 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363268 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(32\) | −5852.15 | −1.01028 | ||||||||
\(33\) | 3636.27 | 0.581261 | ||||||||
\(34\) | 2017.98 | 0.299377 | ||||||||
\(35\) | −3618.73 | −0.499328 | ||||||||
\(36\) | −16681.2 | −2.14521 | ||||||||
\(37\) | −7108.78 | −0.853672 | −0.426836 | − | 0.904329i | \(-0.640372\pi\) | ||||
−0.426836 | + | 0.904329i | \(0.640372\pi\) | |||||||
\(38\) | 936.497 | 0.105208 | ||||||||
\(39\) | −20000.0 | −2.10556 | ||||||||
\(40\) | 3714.23 | 0.367044 | ||||||||
\(41\) | −2590.18 | −0.240642 | −0.120321 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120321 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(42\) | 11284.6 | 0.987104 | ||||||||
\(43\) | 4330.35 | 0.357151 | 0.178576 | − | 0.983926i | \(-0.442851\pi\) | ||||
0.178576 | + | 0.983926i | \(0.442851\pi\) | |||||||
\(44\) | −3057.70 | −0.238102 | ||||||||
\(45\) | 16502.8 | 1.21486 | ||||||||
\(46\) | −7513.60 | −0.523544 | ||||||||
\(47\) | −13303.1 | −0.878432 | −0.439216 | − | 0.898381i | \(-0.644744\pi\) | ||||
−0.439216 | + | 0.898381i | \(0.644744\pi\) | |||||||
\(48\) | 12719.0 | 0.796798 | ||||||||
\(49\) | 4145.35 | 0.246644 | ||||||||
\(50\) | −1621.36 | −0.0917179 | ||||||||
\(51\) | −23376.9 | −1.25853 | ||||||||
\(52\) | 16817.8 | 0.862502 | ||||||||
\(53\) | 16504.1 | 0.807051 | 0.403525 | − | 0.914968i | \(-0.367785\pi\) | ||||
0.403525 | + | 0.914968i | \(0.367785\pi\) | |||||||
\(54\) | −32517.9 | −1.51753 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −21505.3 | −0.916378 | ||||||||
\(57\) | −10848.7 | −0.442273 | ||||||||
\(58\) | 17462.2 | 0.681599 | ||||||||
\(59\) | −10810.7 | −0.404318 | −0.202159 | − | 0.979353i | \(-0.564796\pi\) | ||||
−0.202159 | + | 0.979353i | \(0.564796\pi\) | |||||||
\(60\) | −18985.4 | −0.680835 | ||||||||
\(61\) | −28655.1 | −0.985999 | −0.493000 | − | 0.870029i | \(-0.664100\pi\) | ||||
−0.493000 | + | 0.870029i | \(0.664100\pi\) | |||||||
\(62\) | −10084.6 | −0.333182 | ||||||||
\(63\) | −95550.6 | −3.03307 | ||||||||
\(64\) | 1638.02 | 0.0499884 | ||||||||
\(65\) | −16637.9 | −0.488444 | ||||||||
\(66\) | −9433.12 | −0.266560 | ||||||||
\(67\) | −39787.3 | −1.08282 | −0.541412 | − | 0.840757i | \(-0.682110\pi\) | ||||
−0.541412 | + | 0.840757i | \(0.682110\pi\) | |||||||
\(68\) | 19657.4 | 0.515530 | ||||||||
\(69\) | 87040.1 | 2.20088 | ||||||||
\(70\) | 9387.62 | 0.228987 | ||||||||
\(71\) | 51462.1 | 1.21155 | 0.605775 | − | 0.795636i | \(-0.292863\pi\) | ||||
0.605775 | + | 0.795636i | \(0.292863\pi\) | |||||||
\(72\) | 98072.1 | 2.22954 | ||||||||
\(73\) | 7933.28 | 0.174239 | 0.0871195 | − | 0.996198i | \(-0.472234\pi\) | ||||
0.0871195 | + | 0.996198i | \(0.472234\pi\) | |||||||
\(74\) | 18441.4 | 0.391485 | ||||||||
\(75\) | 18782.4 | 0.385565 | ||||||||
\(76\) | 9122.56 | 0.181169 | ||||||||
\(77\) | −17514.7 | −0.336647 | ||||||||
\(78\) | 51883.4 | 0.965588 | ||||||||
\(79\) | 69304.9 | 1.24938 | 0.624692 | − | 0.780871i | \(-0.285224\pi\) | ||||
0.624692 | + | 0.780871i | \(0.285224\pi\) | |||||||
\(80\) | 10580.9 | 0.184840 | ||||||||
\(81\) | 216291. | 3.66291 | ||||||||
\(82\) | 6719.39 | 0.110356 | ||||||||
\(83\) | −61145.2 | −0.974243 | −0.487121 | − | 0.873334i | \(-0.661953\pi\) | ||||
−0.487121 | + | 0.873334i | \(0.661953\pi\) | |||||||
\(84\) | 109925. | 1.69980 | ||||||||
\(85\) | −19447.2 | −0.291951 | ||||||||
\(86\) | −11233.7 | −0.163786 | ||||||||
\(87\) | −202288. | −2.86531 | ||||||||
\(88\) | 17976.9 | 0.247461 | ||||||||
\(89\) | 34860.5 | 0.466508 | 0.233254 | − | 0.972416i | \(-0.425063\pi\) | ||||
0.233254 | + | 0.972416i | \(0.425063\pi\) | |||||||
\(90\) | −42811.1 | −0.557122 | ||||||||
\(91\) | 96333.0 | 1.21947 | ||||||||
\(92\) | −73191.1 | −0.901548 | ||||||||
\(93\) | 116824. | 1.40063 | ||||||||
\(94\) | 34510.6 | 0.402840 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −175868. | −1.94764 | ||||||||
\(97\) | −152355. | −1.64410 | −0.822050 | − | 0.569415i | \(-0.807170\pi\) | ||||
−0.822050 | + | 0.569415i | \(0.807170\pi\) | |||||||
\(98\) | −10753.8 | −0.113108 | ||||||||
\(99\) | 79873.5 | 0.819058 | ||||||||
\(100\) | −15793.9 | −0.157939 | ||||||||
\(101\) | −12408.5 | −0.121036 | −0.0605181 | − | 0.998167i | \(-0.519275\pi\) | ||||
−0.0605181 | + | 0.998167i | \(0.519275\pi\) | |||||||
\(102\) | 60643.8 | 0.577147 | ||||||||
\(103\) | 8677.70 | 0.0805956 | 0.0402978 | − | 0.999188i | \(-0.487169\pi\) | ||||
0.0402978 | + | 0.999188i | \(0.487169\pi\) | |||||||
\(104\) | −98875.1 | −0.896404 | ||||||||
\(105\) | −108749. | −0.962618 | ||||||||
\(106\) | −42814.4 | −0.370105 | ||||||||
\(107\) | −163744. | −1.38263 | −0.691314 | − | 0.722555i | \(-0.742968\pi\) | ||||
−0.691314 | + | 0.722555i | \(0.742968\pi\) | |||||||
\(108\) | −316761. | −2.61320 | ||||||||
\(109\) | −138019. | −1.11268 | −0.556342 | − | 0.830953i | \(-0.687796\pi\) | ||||
−0.556342 | + | 0.830953i | \(0.687796\pi\) | |||||||
\(110\) | −7847.38 | −0.0618362 | ||||||||
\(111\) | −213632. | −1.64573 | ||||||||
\(112\) | −61262.8 | −0.461479 | ||||||||
\(113\) | −74196.5 | −0.546623 | −0.273311 | − | 0.961926i | \(-0.588119\pi\) | ||||
−0.273311 | + | 0.961926i | \(0.588119\pi\) | |||||||
\(114\) | 28143.4 | 0.202822 | ||||||||
\(115\) | 72408.4 | 0.510557 | ||||||||
\(116\) | 170102. | 1.17372 | ||||||||
\(117\) | −439315. | −2.96696 | ||||||||
\(118\) | 28044.8 | 0.185416 | ||||||||
\(119\) | 112599. | 0.728896 | ||||||||
\(120\) | 111619. | 0.707597 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 74336.2 | 0.452169 | ||||||||
\(123\) | −77839.7 | −0.463915 | ||||||||
\(124\) | −98236.1 | −0.573742 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 247875. | 1.39093 | ||||||||
\(127\) | 220133. | 1.21109 | 0.605545 | − | 0.795811i | \(-0.292955\pi\) | ||||
0.605545 | + | 0.795811i | \(0.292955\pi\) | |||||||
\(128\) | 183020. | 0.987353 | ||||||||
\(129\) | 130135. | 0.688525 | ||||||||
\(130\) | 43161.6 | 0.223996 | ||||||||
\(131\) | −352552. | −1.79492 | −0.897460 | − | 0.441095i | \(-0.854590\pi\) | ||||
−0.897460 | + | 0.441095i | \(0.854590\pi\) | |||||||
\(132\) | −91889.5 | −0.459019 | ||||||||
\(133\) | 52254.5 | 0.256150 | ||||||||
\(134\) | 103215. | 0.496572 | ||||||||
\(135\) | 313374. | 1.47989 | ||||||||
\(136\) | −115570. | −0.535794 | ||||||||
\(137\) | −183588. | −0.835685 | −0.417842 | − | 0.908519i | \(-0.637214\pi\) | ||||
−0.417842 | + | 0.908519i | \(0.637214\pi\) | |||||||
\(138\) | −225797. | −1.00930 | ||||||||
\(139\) | −122620. | −0.538299 | −0.269150 | − | 0.963098i | \(-0.586743\pi\) | ||||
−0.269150 | + | 0.963098i | \(0.586743\pi\) | |||||||
\(140\) | 91446.3 | 0.394317 | ||||||||
\(141\) | −399782. | −1.69346 | ||||||||
\(142\) | −133502. | −0.555604 | ||||||||
\(143\) | −80527.5 | −0.329309 | ||||||||
\(144\) | 279382. | 1.12277 | ||||||||
\(145\) | −168283. | −0.664691 | ||||||||
\(146\) | −20580.3 | −0.0799042 | ||||||||
\(147\) | 124575. | 0.475487 | ||||||||
\(148\) | 179641. | 0.674141 | ||||||||
\(149\) | 272693. | 1.00626 | 0.503128 | − | 0.864212i | \(-0.332183\pi\) | ||||
0.503128 | + | 0.864212i | \(0.332183\pi\) | |||||||
\(150\) | −48724.8 | −0.176816 | ||||||||
\(151\) | −523658. | −1.86898 | −0.934492 | − | 0.355985i | \(-0.884145\pi\) | ||||
−0.934492 | + | 0.355985i | \(0.884145\pi\) | |||||||
\(152\) | −53633.4 | −0.188290 | ||||||||
\(153\) | −513492. | −1.77339 | ||||||||
\(154\) | 45436.1 | 0.154383 | ||||||||
\(155\) | 97185.5 | 0.324917 | ||||||||
\(156\) | 505404. | 1.66275 | ||||||||
\(157\) | −271502. | −0.879072 | −0.439536 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439536 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(158\) | −179789. | −0.572955 | ||||||||
\(159\) | 495977. | 1.55585 | ||||||||
\(160\) | −146304. | −0.451810 | ||||||||
\(161\) | −419242. | −1.27468 | ||||||||
\(162\) | −561096. | −1.67977 | ||||||||
\(163\) | 280699. | 0.827507 | 0.413753 | − | 0.910389i | \(-0.364218\pi\) | ||||
0.413753 | + | 0.910389i | \(0.364218\pi\) | |||||||
\(164\) | 65454.6 | 0.190034 | ||||||||
\(165\) | 90906.7 | 0.259948 | ||||||||
\(166\) | 158621. | 0.446778 | ||||||||
\(167\) | 526263. | 1.46020 | 0.730099 | − | 0.683342i | \(-0.239474\pi\) | ||||
0.730099 | + | 0.683342i | \(0.239474\pi\) | |||||||
\(168\) | −646272. | −1.76662 | ||||||||
\(169\) | 71618.7 | 0.192890 | ||||||||
\(170\) | 50449.4 | 0.133886 | ||||||||
\(171\) | −238300. | −0.623210 | ||||||||
\(172\) | −109429. | −0.282041 | ||||||||
\(173\) | −190186. | −0.483130 | −0.241565 | − | 0.970385i | \(-0.577661\pi\) | ||||
−0.241565 | + | 0.970385i | \(0.577661\pi\) | |||||||
\(174\) | 524771. | 1.31400 | ||||||||
\(175\) | −90468.3 | −0.223306 | ||||||||
\(176\) | 51211.3 | 0.124619 | ||||||||
\(177\) | −324881. | −0.779455 | ||||||||
\(178\) | −90434.3 | −0.213936 | ||||||||
\(179\) | 457020. | 1.06611 | 0.533056 | − | 0.846080i | \(-0.321044\pi\) | ||||
0.533056 | + | 0.846080i | \(0.321044\pi\) | |||||||
\(180\) | −417030. | −0.959369 | ||||||||
\(181\) | −474720. | −1.07706 | −0.538531 | − | 0.842605i | \(-0.681021\pi\) | ||||
−0.538531 | + | 0.842605i | \(0.681021\pi\) | |||||||
\(182\) | −249905. | −0.559237 | ||||||||
\(183\) | −861136. | −1.90083 | ||||||||
\(184\) | 430306. | 0.936985 | ||||||||
\(185\) | −177720. | −0.381774 | ||||||||
\(186\) | −303062. | −0.642316 | ||||||||
\(187\) | −94124.4 | −0.196833 | ||||||||
\(188\) | 336173. | 0.693694 | ||||||||
\(189\) | −1.81442e6 | −3.69475 | ||||||||
\(190\) | 23412.4 | 0.0470503 | ||||||||
\(191\) | 385660. | 0.764929 | 0.382465 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382465 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(192\) | 49225.4 | 0.0963688 | ||||||||
\(193\) | −637298. | −1.23154 | −0.615771 | − | 0.787925i | \(-0.711155\pi\) | ||||
−0.615771 | + | 0.787925i | \(0.711155\pi\) | |||||||
\(194\) | 395236. | 0.753967 | ||||||||
\(195\) | −499999. | −0.941635 | ||||||||
\(196\) | −104754. | −0.194774 | ||||||||
\(197\) | −221197. | −0.406082 | −0.203041 | − | 0.979170i | \(-0.565082\pi\) | ||||
−0.203041 | + | 0.979170i | \(0.565082\pi\) | |||||||
\(198\) | −207206. | −0.375611 | ||||||||
\(199\) | −77746.7 | −0.139171 | −0.0695856 | − | 0.997576i | \(-0.522168\pi\) | ||||
−0.0695856 | + | 0.997576i | \(0.522168\pi\) | |||||||
\(200\) | 92855.7 | 0.164147 | ||||||||
\(201\) | −1.19568e6 | −2.08749 | ||||||||
\(202\) | 32189.8 | 0.0555060 | ||||||||
\(203\) | 974352. | 1.65949 | ||||||||
\(204\) | 590741. | 0.993852 | ||||||||
\(205\) | −64754.6 | −0.107618 | ||||||||
\(206\) | −22511.5 | −0.0369603 | ||||||||
\(207\) | 1.91190e6 | 3.10127 | ||||||||
\(208\) | −281669. | −0.451420 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | 282115. | 0.441446 | ||||||||
\(211\) | 2153.47 | 0.00332991 | 0.00166495 | − | 0.999999i | \(-0.499470\pi\) | ||||
0.00166495 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(212\) | −417062. | −0.637324 | ||||||||
\(213\) | 1.54653e6 | 2.33566 | ||||||||
\(214\) | 424780. | 0.634059 | ||||||||
\(215\) | 108259. | 0.159723 | ||||||||
\(216\) | 1.86231e6 | 2.71592 | ||||||||
\(217\) | −562701. | −0.811201 | ||||||||
\(218\) | 358045. | 0.510266 | ||||||||
\(219\) | 238409. | 0.335902 | ||||||||
\(220\) | −76442.5 | −0.106483 | ||||||||
\(221\) | 517697. | 0.713008 | ||||||||
\(222\) | 554198. | 0.754715 | ||||||||
\(223\) | −1.34187e6 | −1.80697 | −0.903483 | − | 0.428624i | \(-0.858998\pi\) | ||||
−0.903483 | + | 0.428624i | \(0.858998\pi\) | |||||||
\(224\) | 847095. | 1.12801 | ||||||||
\(225\) | 412570. | 0.543302 | ||||||||
\(226\) | 192479. | 0.250675 | ||||||||
\(227\) | −272518. | −0.351019 | −0.175509 | − | 0.984478i | \(-0.556157\pi\) | ||||
−0.175509 | + | 0.984478i | \(0.556157\pi\) | |||||||
\(228\) | 274150. | 0.349261 | ||||||||
\(229\) | −459425. | −0.578930 | −0.289465 | − | 0.957189i | \(-0.593477\pi\) | ||||
−0.289465 | + | 0.957189i | \(0.593477\pi\) | |||||||
\(230\) | −187840. | −0.234136 | ||||||||
\(231\) | −526347. | −0.648997 | ||||||||
\(232\) | −1.00006e6 | −1.21985 | ||||||||
\(233\) | −189474. | −0.228644 | −0.114322 | − | 0.993444i | \(-0.536470\pi\) | ||||
−0.114322 | + | 0.993444i | \(0.536470\pi\) | |||||||
\(234\) | 1.13966e6 | 1.36062 | ||||||||
\(235\) | −332578. | −0.392847 | ||||||||
\(236\) | 273189. | 0.319288 | ||||||||
\(237\) | 2.08274e6 | 2.40859 | ||||||||
\(238\) | −292101. | −0.334264 | ||||||||
\(239\) | 1.32750e6 | 1.50328 | 0.751642 | − | 0.659572i | \(-0.229262\pi\) | ||||
0.751642 | + | 0.659572i | \(0.229262\pi\) | |||||||
\(240\) | 317974. | 0.356339 | ||||||||
\(241\) | 175730. | 0.194897 | 0.0974483 | − | 0.995241i | \(-0.468932\pi\) | ||||
0.0974483 | + | 0.995241i | \(0.468932\pi\) | |||||||
\(242\) | −37981.3 | −0.0416900 | ||||||||
\(243\) | 3.45394e6 | 3.75231 | ||||||||
\(244\) | 724121. | 0.778639 | ||||||||
\(245\) | 103634. | 0.110303 | ||||||||
\(246\) | 201930. | 0.212747 | ||||||||
\(247\) | 240251. | 0.250567 | ||||||||
\(248\) | 577550. | 0.596294 | ||||||||
\(249\) | −1.83752e6 | −1.87817 | ||||||||
\(250\) | −40534.0 | −0.0410175 | ||||||||
\(251\) | −131282. | −0.131529 | −0.0657644 | − | 0.997835i | \(-0.520949\pi\) | ||||
−0.0657644 | + | 0.997835i | \(0.520949\pi\) | |||||||
\(252\) | 2.41459e6 | 2.39520 | ||||||||
\(253\) | 350457. | 0.344217 | ||||||||
\(254\) | −571064. | −0.555393 | ||||||||
\(255\) | −584423. | −0.562830 | ||||||||
\(256\) | −527201. | −0.502778 | ||||||||
\(257\) | −755502. | −0.713514 | −0.356757 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356757 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(258\) | −337593. | −0.315751 | ||||||||
\(259\) | 1.02899e6 | 0.953152 | ||||||||
\(260\) | 420444. | 0.385722 | ||||||||
\(261\) | −4.44341e6 | −4.03753 | ||||||||
\(262\) | 914582. | 0.823132 | ||||||||
\(263\) | 1.56982e6 | 1.39946 | 0.699732 | − | 0.714406i | \(-0.253303\pi\) | ||||
0.699732 | + | 0.714406i | \(0.253303\pi\) | |||||||
\(264\) | 540237. | 0.477062 | ||||||||
\(265\) | 412601. | 0.360924 | ||||||||
\(266\) | −135557. | −0.117468 | ||||||||
\(267\) | 1.04762e6 | 0.899346 | ||||||||
\(268\) | 1.00544e6 | 0.855101 | ||||||||
\(269\) | −1.19913e6 | −1.01038 | −0.505192 | − | 0.863007i | \(-0.668578\pi\) | ||||
−0.505192 | + | 0.863007i | \(0.668578\pi\) | |||||||
\(270\) | −812946. | −0.678660 | ||||||||
\(271\) | 436478. | 0.361027 | 0.180513 | − | 0.983573i | \(-0.442224\pi\) | ||||
0.180513 | + | 0.983573i | \(0.442224\pi\) | |||||||
\(272\) | −329228. | −0.269821 | ||||||||
\(273\) | 2.89498e6 | 2.35093 | ||||||||
\(274\) | 476259. | 0.383236 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −2.19953e6 | −1.73803 | ||||||||
\(277\) | −538959. | −0.422042 | −0.211021 | − | 0.977481i | \(-0.567679\pi\) | ||||
−0.211021 | + | 0.977481i | \(0.567679\pi\) | |||||||
\(278\) | 318097. | 0.246859 | ||||||||
\(279\) | 2.56613e6 | 1.97364 | ||||||||
\(280\) | −537632. | −0.409817 | ||||||||
\(281\) | 397007. | 0.299938 | 0.149969 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149969 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(282\) | 1.03711e6 | 0.776605 | ||||||||
\(283\) | −1.76214e6 | −1.30790 | −0.653950 | − | 0.756537i | \(-0.726890\pi\) | ||||
−0.653950 | + | 0.756537i | \(0.726890\pi\) | |||||||
\(284\) | −1.30046e6 | −0.956755 | ||||||||
\(285\) | −271218. | −0.197791 | ||||||||
\(286\) | 208902. | 0.151018 | ||||||||
\(287\) | 374927. | 0.268684 | ||||||||
\(288\) | −3.86307e6 | −2.74443 | ||||||||
\(289\) | −814748. | −0.573824 | ||||||||
\(290\) | 436555. | 0.304820 | ||||||||
\(291\) | −4.57855e6 | −3.16954 | ||||||||
\(292\) | −200476. | −0.137596 | ||||||||
\(293\) | 2.52332e6 | 1.71713 | 0.858565 | − | 0.512705i | \(-0.171357\pi\) | ||||
0.858565 | + | 0.512705i | \(0.171357\pi\) | |||||||
\(294\) | −323170. | −0.218053 | ||||||||
\(295\) | −270267. | −0.180817 | ||||||||
\(296\) | −1.05615e6 | −0.700639 | ||||||||
\(297\) | 1.51673e6 | 0.997739 | ||||||||
\(298\) | −707413. | −0.461458 | ||||||||
\(299\) | −1.92756e6 | −1.24689 | ||||||||
\(300\) | −474636. | −0.304479 | ||||||||
\(301\) | −626816. | −0.398771 | ||||||||
\(302\) | 1.35846e6 | 0.857096 | ||||||||
\(303\) | −372897. | −0.233337 | ||||||||
\(304\) | −152788. | −0.0948209 | ||||||||
\(305\) | −716376. | −0.440952 | ||||||||
\(306\) | 1.33209e6 | 0.813260 | ||||||||
\(307\) | 552768. | 0.334732 | 0.167366 | − | 0.985895i | \(-0.446474\pi\) | ||||
0.167366 | + | 0.985895i | \(0.446474\pi\) | |||||||
\(308\) | 442600. | 0.265849 | ||||||||
\(309\) | 260781. | 0.155374 | ||||||||
\(310\) | −252116. | −0.149003 | ||||||||
\(311\) | 3.00558e6 | 1.76209 | 0.881045 | − | 0.473033i | \(-0.156841\pi\) | ||||
0.881045 | + | 0.473033i | \(0.156841\pi\) | |||||||
\(312\) | −2.97138e6 | −1.72811 | ||||||||
\(313\) | −2.59535e6 | −1.49739 | −0.748694 | − | 0.662915i | \(-0.769319\pi\) | ||||
−0.748694 | + | 0.662915i | \(0.769319\pi\) | |||||||
\(314\) | 704324. | 0.403133 | ||||||||
\(315\) | −2.38877e6 | −1.35643 | ||||||||
\(316\) | −1.75135e6 | −0.986634 | ||||||||
\(317\) | −1.88311e6 | −1.05251 | −0.526255 | − | 0.850327i | \(-0.676404\pi\) | ||||
−0.526255 | + | 0.850327i | \(0.676404\pi\) | |||||||
\(318\) | −1.28665e6 | −0.713498 | ||||||||
\(319\) | −814488. | −0.448134 | ||||||||
\(320\) | 40950.5 | 0.0223555 | ||||||||
\(321\) | −4.92080e6 | −2.66546 | ||||||||
\(322\) | 1.08759e6 | 0.584554 | ||||||||
\(323\) | 280817. | 0.149768 | ||||||||
\(324\) | −5.46573e6 | −2.89258 | ||||||||
\(325\) | −415948. | −0.218439 | ||||||||
\(326\) | −728182. | −0.379486 | ||||||||
\(327\) | −4.14771e6 | −2.14506 | ||||||||
\(328\) | −384821. | −0.197503 | ||||||||
\(329\) | 1.92561e6 | 0.980798 | ||||||||
\(330\) | −235828. | −0.119209 | ||||||||
\(331\) | 1.45682e6 | 0.730861 | 0.365430 | − | 0.930839i | \(-0.380922\pi\) | ||||
0.365430 | + | 0.930839i | \(0.380922\pi\) | |||||||
\(332\) | 1.54516e6 | 0.769355 | ||||||||
\(333\) | −4.69259e6 | −2.31901 | ||||||||
\(334\) | −1.36522e6 | −0.669631 | ||||||||
\(335\) | −994683. | −0.484254 | ||||||||
\(336\) | −1.84106e6 | −0.889651 | ||||||||
\(337\) | −1.53753e6 | −0.737476 | −0.368738 | − | 0.929533i | \(-0.620210\pi\) | ||||
−0.368738 | + | 0.929533i | \(0.620210\pi\) | |||||||
\(338\) | −185792. | −0.0884574 | ||||||||
\(339\) | −2.22974e6 | −1.05379 | ||||||||
\(340\) | 491435. | 0.230552 | ||||||||
\(341\) | 470378. | 0.219059 | ||||||||
\(342\) | 618192. | 0.285797 | ||||||||
\(343\) | 1.83276e6 | 0.841146 | ||||||||
\(344\) | 643357. | 0.293127 | ||||||||
\(345\) | 2.17600e6 | 0.984264 | ||||||||
\(346\) | 493376. | 0.221558 | ||||||||
\(347\) | −684400. | −0.305131 | −0.152565 | − | 0.988293i | \(-0.548754\pi\) | ||||
−0.152565 | + | 0.988293i | \(0.548754\pi\) | |||||||
\(348\) | 5.11187e6 | 2.26272 | ||||||||
\(349\) | −226242. | −0.0994281 | −0.0497140 | − | 0.998763i | \(-0.515831\pi\) | ||||
−0.0497140 | + | 0.998763i | \(0.515831\pi\) | |||||||
\(350\) | 234691. | 0.102406 | ||||||||
\(351\) | −8.34221e6 | −3.61421 | ||||||||
\(352\) | −708111. | −0.304610 | ||||||||
\(353\) | −3.71916e6 | −1.58858 | −0.794289 | − | 0.607540i | \(-0.792156\pi\) | ||||
−0.794289 | + | 0.607540i | \(0.792156\pi\) | |||||||
\(354\) | 842798. | 0.357450 | ||||||||
\(355\) | 1.28655e6 | 0.541822 | ||||||||
\(356\) | −880935. | −0.368399 | ||||||||
\(357\) | 3.38379e6 | 1.40518 | ||||||||
\(358\) | −1.18559e6 | −0.488908 | ||||||||
\(359\) | −463313. | −0.189731 | −0.0948655 | − | 0.995490i | \(-0.530242\pi\) | ||||
−0.0948655 | + | 0.995490i | \(0.530242\pi\) | |||||||
\(360\) | 2.45180e6 | 0.997078 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 1.23151e6 | 0.493930 | ||||||||
\(363\) | 439989. | 0.175257 | ||||||||
\(364\) | −2.43436e6 | −0.963011 | ||||||||
\(365\) | 198332. | 0.0779221 | ||||||||
\(366\) | 2.23394e6 | 0.871703 | ||||||||
\(367\) | 2.33654e6 | 0.905539 | 0.452770 | − | 0.891628i | \(-0.350436\pi\) | ||||
0.452770 | + | 0.891628i | \(0.350436\pi\) | |||||||
\(368\) | 1.22583e6 | 0.471856 | ||||||||
\(369\) | −1.70981e6 | −0.653705 | ||||||||
\(370\) | 461036. | 0.175077 | ||||||||
\(371\) | −2.38895e6 | −0.901098 | ||||||||
\(372\) | −2.95217e6 | −1.10607 | ||||||||
\(373\) | 4.95822e6 | 1.84525 | 0.922623 | − | 0.385704i | \(-0.126041\pi\) | ||||
0.922623 | + | 0.385704i | \(0.126041\pi\) | |||||||
\(374\) | 244175. | 0.0902656 | ||||||||
\(375\) | 469560. | 0.172430 | ||||||||
\(376\) | −1.97643e6 | −0.720961 | ||||||||
\(377\) | 4.47980e6 | 1.62332 | ||||||||
\(378\) | 4.70694e6 | 1.69437 | ||||||||
\(379\) | −5.33490e6 | −1.90778 | −0.953891 | − | 0.300154i | \(-0.902962\pi\) | ||||
−0.953891 | + | 0.300154i | \(0.902962\pi\) | |||||||
\(380\) | 228064. | 0.0810211 | ||||||||
\(381\) | 6.61541e6 | 2.33477 | ||||||||
\(382\) | −1.00047e6 | −0.350789 | ||||||||
\(383\) | −175997. | −0.0613069 | −0.0306534 | − | 0.999530i | \(-0.509759\pi\) | ||||
−0.0306534 | + | 0.999530i | \(0.509759\pi\) | |||||||
\(384\) | 5.50007e6 | 1.90344 | ||||||||
\(385\) | −437867. | −0.150553 | ||||||||
\(386\) | 1.65326e6 | 0.564772 | ||||||||
\(387\) | 2.85852e6 | 0.970204 | ||||||||
\(388\) | 3.85006e6 | 1.29834 | ||||||||
\(389\) | −969606. | −0.324879 | −0.162439 | − | 0.986719i | \(-0.551936\pi\) | ||||
−0.162439 | + | 0.986719i | \(0.551936\pi\) | |||||||
\(390\) | 1.29709e6 | 0.431824 | ||||||||
\(391\) | −2.25302e6 | −0.745287 | ||||||||
\(392\) | 615871. | 0.202430 | ||||||||
\(393\) | −1.05948e7 | −3.46029 | ||||||||
\(394\) | 573823. | 0.186225 | ||||||||
\(395\) | 1.73262e6 | 0.558742 | ||||||||
\(396\) | −2.01842e6 | −0.646806 | ||||||||
\(397\) | −1.72016e6 | −0.547764 | −0.273882 | − | 0.961763i | \(-0.588308\pi\) | ||||
−0.273882 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(398\) | 201689. | 0.0638225 | ||||||||
\(399\) | 1.57034e6 | 0.493812 | ||||||||
\(400\) | 264521. | 0.0826629 | ||||||||
\(401\) | −2.55022e6 | −0.791985 | −0.395993 | − | 0.918254i | \(-0.629599\pi\) | ||||
−0.395993 | + | 0.918254i | \(0.629599\pi\) | |||||||
\(402\) | 3.10181e6 | 0.957303 | ||||||||
\(403\) | −2.58714e6 | −0.793519 | ||||||||
\(404\) | 313566. | 0.0955818 | ||||||||
\(405\) | 5.40727e6 | 1.63810 | ||||||||
\(406\) | −2.52764e6 | −0.761027 | ||||||||
\(407\) | −860163. | −0.257392 | ||||||||
\(408\) | −3.47309e6 | −1.03292 | ||||||||
\(409\) | 254985. | 0.0753714 | 0.0376857 | − | 0.999290i | \(-0.488001\pi\) | ||||
0.0376857 | + | 0.999290i | \(0.488001\pi\) | |||||||
\(410\) | 167985. | 0.0493526 | ||||||||
\(411\) | −5.51715e6 | −1.61105 | ||||||||
\(412\) | −219288. | −0.0636460 | ||||||||
\(413\) | 1.56484e6 | 0.451434 | ||||||||
\(414\) | −4.95981e6 | −1.42221 | ||||||||
\(415\) | −1.52863e6 | −0.435695 | ||||||||
\(416\) | 3.89470e6 | 1.10342 | ||||||||
\(417\) | −3.68495e6 | −1.03775 | ||||||||
\(418\) | 113316. | 0.0317213 | ||||||||
\(419\) | 3.25431e6 | 0.905573 | 0.452787 | − | 0.891619i | \(-0.350430\pi\) | ||||
0.452787 | + | 0.891619i | \(0.350430\pi\) | |||||||
\(420\) | 2.74813e6 | 0.760175 | ||||||||
\(421\) | −2.08852e6 | −0.574292 | −0.287146 | − | 0.957887i | \(-0.592707\pi\) | ||||
−0.287146 | + | 0.957887i | \(0.592707\pi\) | |||||||
\(422\) | −5586.47 | −0.00152706 | ||||||||
\(423\) | −8.78153e6 | −2.38627 | ||||||||
\(424\) | 2.45199e6 | 0.662376 | ||||||||
\(425\) | −486180. | −0.130564 | ||||||||
\(426\) | −4.01196e6 | −1.07111 | ||||||||
\(427\) | 4.14780e6 | 1.10090 | ||||||||
\(428\) | 4.13785e6 | 1.09185 | ||||||||
\(429\) | −2.42000e6 | −0.634850 | ||||||||
\(430\) | −280842. | −0.0732473 | ||||||||
\(431\) | −362649. | −0.0940358 | −0.0470179 | − | 0.998894i | \(-0.514972\pi\) | ||||
−0.0470179 | + | 0.998894i | \(0.514972\pi\) | |||||||
\(432\) | 5.30522e6 | 1.36771 | ||||||||
\(433\) | −4.47651e6 | −1.14741 | −0.573706 | − | 0.819061i | \(-0.694495\pi\) | ||||
−0.573706 | + | 0.819061i | \(0.694495\pi\) | |||||||
\(434\) | 1.45974e6 | 0.372008 | ||||||||
\(435\) | −5.05720e6 | −1.28141 | ||||||||
\(436\) | 3.48777e6 | 0.878682 | ||||||||
\(437\) | −1.04558e6 | −0.261910 | ||||||||
\(438\) | −618476. | −0.154041 | ||||||||
\(439\) | 1.41522e6 | 0.350480 | 0.175240 | − | 0.984526i | \(-0.443930\pi\) | ||||
0.175240 | + | 0.984526i | \(0.443930\pi\) | |||||||
\(440\) | 449421. | 0.110668 | ||||||||
\(441\) | 2.73639e6 | 0.670011 | ||||||||
\(442\) | −1.34300e6 | −0.326978 | ||||||||
\(443\) | −740508. | −0.179275 | −0.0896377 | − | 0.995974i | \(-0.528571\pi\) | ||||
−0.0896377 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(444\) | 5.39853e6 | 1.29963 | ||||||||
\(445\) | 871514. | 0.208629 | ||||||||
\(446\) | 3.48106e6 | 0.828656 | ||||||||
\(447\) | 8.19491e6 | 1.93988 | ||||||||
\(448\) | −237102. | −0.0558136 | ||||||||
\(449\) | −4.15714e6 | −0.973147 | −0.486574 | − | 0.873640i | \(-0.661753\pi\) | ||||
−0.486574 | + | 0.873640i | \(0.661753\pi\) | |||||||
\(450\) | −1.07028e6 | −0.249152 | ||||||||
\(451\) | −313412. | −0.0725562 | ||||||||
\(452\) | 1.87497e6 | 0.431665 | ||||||||
\(453\) | −1.57369e7 | −3.60307 | ||||||||
\(454\) | 706959. | 0.160974 | ||||||||
\(455\) | 2.40832e6 | 0.545364 | ||||||||
\(456\) | −1.61178e6 | −0.362990 | ||||||||
\(457\) | 8.65673e6 | 1.93893 | 0.969467 | − | 0.245220i | \(-0.0788602\pi\) | ||||
0.969467 | + | 0.245220i | \(0.0788602\pi\) | |||||||
\(458\) | 1.19183e6 | 0.265492 | ||||||||
\(459\) | −9.75078e6 | −2.16027 | ||||||||
\(460\) | −1.82978e6 | −0.403185 | ||||||||
\(461\) | 2.80291e6 | 0.614266 | 0.307133 | − | 0.951667i | \(-0.400630\pi\) | ||||
0.307133 | + | 0.951667i | \(0.400630\pi\) | |||||||
\(462\) | 1.36544e6 | 0.297623 | ||||||||
\(463\) | −5.90007e6 | −1.27910 | −0.639550 | − | 0.768749i | \(-0.720879\pi\) | ||||
−0.639550 | + | 0.768749i | \(0.720879\pi\) | |||||||
\(464\) | −2.84892e6 | −0.614307 | ||||||||
\(465\) | 2.92060e6 | 0.626383 | ||||||||
\(466\) | 491529. | 0.104854 | ||||||||
\(467\) | 5.86542e6 | 1.24453 | 0.622267 | − | 0.782805i | \(-0.286212\pi\) | ||||
0.622267 | + | 0.782805i | \(0.286212\pi\) | |||||||
\(468\) | 1.11016e7 | 2.34299 | ||||||||
\(469\) | 5.75919e6 | 1.20901 | ||||||||
\(470\) | 862764. | 0.180156 | ||||||||
\(471\) | −8.15914e6 | −1.69470 | ||||||||
\(472\) | −1.60613e6 | −0.331839 | ||||||||
\(473\) | 523973. | 0.107685 | ||||||||
\(474\) | −5.40299e6 | −1.10456 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −2.84540e6 | −0.575606 | ||||||||
\(477\) | 1.08945e7 | 2.19236 | ||||||||
\(478\) | −3.44378e6 | −0.689390 | ||||||||
\(479\) | −5.37524e6 | −1.07043 | −0.535216 | − | 0.844715i | \(-0.679770\pi\) | ||||
−0.535216 | + | 0.844715i | \(0.679770\pi\) | |||||||
\(480\) | −4.39670e6 | −0.871010 | ||||||||
\(481\) | 4.73101e6 | 0.932376 | ||||||||
\(482\) | −455875. | −0.0893776 | ||||||||
\(483\) | −1.25990e7 | −2.45736 | ||||||||
\(484\) | −369982. | −0.0717905 | ||||||||
\(485\) | −3.80888e6 | −0.735264 | ||||||||
\(486\) | −8.96013e6 | −1.72077 | ||||||||
\(487\) | −8.03326e6 | −1.53486 | −0.767431 | − | 0.641132i | \(-0.778465\pi\) | ||||
−0.767431 | + | 0.641132i | \(0.778465\pi\) | |||||||
\(488\) | −4.25725e6 | −0.809245 | ||||||||
\(489\) | 8.43551e6 | 1.59529 | ||||||||
\(490\) | −268844. | −0.0505836 | ||||||||
\(491\) | 3.32940e6 | 0.623251 | 0.311625 | − | 0.950205i | \(-0.399127\pi\) | ||||
0.311625 | + | 0.950205i | \(0.399127\pi\) | |||||||
\(492\) | 1.96703e6 | 0.366352 | ||||||||
\(493\) | 5.23620e6 | 0.970284 | ||||||||
\(494\) | −623254. | −0.114907 | ||||||||
\(495\) | 1.99684e6 | 0.366294 | ||||||||
\(496\) | 1.64529e6 | 0.300288 | ||||||||
\(497\) | −7.44909e6 | −1.35273 | ||||||||
\(498\) | 4.76686e6 | 0.861309 | ||||||||
\(499\) | −4.80316e6 | −0.863527 | −0.431763 | − | 0.901987i | \(-0.642108\pi\) | ||||
−0.431763 | + | 0.901987i | \(0.642108\pi\) | |||||||
\(500\) | −394848. | −0.0706325 | ||||||||
\(501\) | 1.58152e7 | 2.81500 | ||||||||
\(502\) | 340569. | 0.0603178 | ||||||||
\(503\) | 1.24139e6 | 0.218770 | 0.109385 | − | 0.993999i | \(-0.465112\pi\) | ||||
0.109385 | + | 0.993999i | \(0.465112\pi\) | |||||||
\(504\) | −1.41959e7 | −2.48935 | ||||||||
\(505\) | −310212. | −0.0541290 | ||||||||
\(506\) | −909146. | −0.157855 | ||||||||
\(507\) | 2.15227e6 | 0.371858 | ||||||||
\(508\) | −5.56283e6 | −0.956393 | ||||||||
\(509\) | −9.62858e6 | −1.64728 | −0.823640 | − | 0.567113i | \(-0.808060\pi\) | ||||
−0.823640 | + | 0.567113i | \(0.808060\pi\) | |||||||
\(510\) | 1.51610e6 | 0.258108 | ||||||||
\(511\) | −1.14834e6 | −0.194544 | ||||||||
\(512\) | −4.48897e6 | −0.756784 | ||||||||
\(513\) | −4.52512e6 | −0.759165 | ||||||||
\(514\) | 1.95990e6 | 0.327210 | ||||||||
\(515\) | 216943. | 0.0360435 | ||||||||
\(516\) | −3.28854e6 | −0.543725 | ||||||||
\(517\) | −1.60968e6 | −0.264857 | ||||||||
\(518\) | −2.66938e6 | −0.437106 | ||||||||
\(519\) | −5.71544e6 | −0.931389 | ||||||||
\(520\) | −2.47188e6 | −0.400884 | ||||||||
\(521\) | 569169. | 0.0918644 | 0.0459322 | − | 0.998945i | \(-0.485374\pi\) | ||||
0.0459322 | + | 0.998945i | \(0.485374\pi\) | |||||||
\(522\) | 1.15270e7 | 1.85157 | ||||||||
\(523\) | 2.23753e6 | 0.357697 | 0.178848 | − | 0.983877i | \(-0.442763\pi\) | ||||
0.178848 | + | 0.983877i | \(0.442763\pi\) | |||||||
\(524\) | 8.90909e6 | 1.41744 | ||||||||
\(525\) | −2.71874e6 | −0.430496 | ||||||||
\(526\) | −4.07240e6 | −0.641780 | ||||||||
\(527\) | −3.02397e6 | −0.474298 | ||||||||
\(528\) | 1.53899e6 | 0.240244 | ||||||||
\(529\) | 1.95242e6 | 0.303342 | ||||||||
\(530\) | −1.07036e6 | −0.165516 | ||||||||
\(531\) | −7.13626e6 | −1.09833 | ||||||||
\(532\) | −1.32048e6 | −0.202281 | ||||||||
\(533\) | 1.72381e6 | 0.262828 | ||||||||
\(534\) | −2.71772e6 | −0.412431 | ||||||||
\(535\) | −4.09359e6 | −0.618330 | ||||||||
\(536\) | −5.91117e6 | −0.888712 | ||||||||
\(537\) | 1.37343e7 | 2.05528 | ||||||||
\(538\) | 3.11076e6 | 0.463352 | ||||||||
\(539\) | 501587. | 0.0743660 | ||||||||
\(540\) | −7.91904e6 | −1.16866 | ||||||||
\(541\) | −1.39018e6 | −0.204210 | −0.102105 | − | 0.994774i | \(-0.532558\pi\) | ||||
−0.102105 | + | 0.994774i | \(0.532558\pi\) | |||||||
\(542\) | −1.13230e6 | −0.165563 | ||||||||
\(543\) | −1.42662e7 | −2.07639 | ||||||||
\(544\) | 4.55232e6 | 0.659531 | ||||||||
\(545\) | −3.45047e6 | −0.497608 | ||||||||
\(546\) | −7.51009e6 | −1.07811 | ||||||||
\(547\) | −8.62746e6 | −1.23286 | −0.616431 | − | 0.787409i | \(-0.711422\pi\) | ||||
−0.616431 | + | 0.787409i | \(0.711422\pi\) | |||||||
\(548\) | 4.63931e6 | 0.659937 | ||||||||
\(549\) | −1.89155e7 | −2.67847 | ||||||||
\(550\) | −196184. | −0.0276540 | ||||||||
\(551\) | 2.43000e6 | 0.340979 | ||||||||
\(552\) | 1.29315e7 | 1.80634 | ||||||||
\(553\) | −1.00318e7 | −1.39498 | ||||||||
\(554\) | 1.39815e6 | 0.193544 | ||||||||
\(555\) | −5.34080e6 | −0.735993 | ||||||||
\(556\) | 3.09864e6 | 0.425093 | ||||||||
\(557\) | 9.32183e6 | 1.27310 | 0.636551 | − | 0.771234i | \(-0.280360\pi\) | ||||
0.636551 | + | 0.771234i | \(0.280360\pi\) | |||||||
\(558\) | −6.65699e6 | −0.905091 | ||||||||
\(559\) | −2.88192e6 | −0.390079 | ||||||||
\(560\) | −1.53157e6 | −0.206380 | ||||||||
\(561\) | −2.82861e6 | −0.379460 | ||||||||
\(562\) | −1.02990e6 | −0.137549 | ||||||||
\(563\) | 3.35530e6 | 0.446128 | 0.223064 | − | 0.974804i | \(-0.428394\pi\) | ||||
0.223064 | + | 0.974804i | \(0.428394\pi\) | |||||||
\(564\) | 1.01026e7 | 1.33732 | ||||||||
\(565\) | −1.85491e6 | −0.244457 | ||||||||
\(566\) | 4.57130e6 | 0.599790 | ||||||||
\(567\) | −3.13080e7 | −4.08975 | ||||||||
\(568\) | 7.64567e6 | 0.994362 | ||||||||
\(569\) | 1.10414e6 | 0.142970 | 0.0714849 | − | 0.997442i | \(-0.477226\pi\) | ||||
0.0714849 | + | 0.997442i | \(0.477226\pi\) | |||||||
\(570\) | 703586. | 0.0907047 | ||||||||
\(571\) | −1.15796e7 | −1.48629 | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||||
−0.743146 | + | 0.669129i | \(0.766667\pi\) | |||||||
\(572\) | 2.03495e6 | 0.260054 | ||||||||
\(573\) | 1.15898e7 | 1.47465 | ||||||||
\(574\) | −972627. | −0.123216 | ||||||||
\(575\) | 1.81021e6 | 0.228328 | ||||||||
\(576\) | 1.08127e6 | 0.135794 | ||||||||
\(577\) | 9.06103e6 | 1.13302 | 0.566510 | − | 0.824055i | \(-0.308293\pi\) | ||||
0.566510 | + | 0.824055i | \(0.308293\pi\) | |||||||
\(578\) | 2.11360e6 | 0.263150 | ||||||||
\(579\) | −1.91520e7 | −2.37420 | ||||||||
\(580\) | 4.25255e6 | 0.524903 | ||||||||
\(581\) | 8.85072e6 | 1.08777 | ||||||||
\(582\) | 1.18776e7 | 1.45352 | ||||||||
\(583\) | 1.99699e6 | 0.243335 | ||||||||
\(584\) | 1.17864e6 | 0.143004 | ||||||||
\(585\) | −1.09829e7 | −1.32686 | ||||||||
\(586\) | −6.54593e6 | −0.787458 | ||||||||
\(587\) | −8.08821e6 | −0.968852 | −0.484426 | − | 0.874832i | \(-0.660972\pi\) | ||||
−0.484426 | + | 0.874832i | \(0.660972\pi\) | |||||||
\(588\) | −3.14805e6 | −0.375490 | ||||||||
\(589\) | −1.40336e6 | −0.166679 | ||||||||
\(590\) | 701121. | 0.0829207 | ||||||||
\(591\) | −6.64737e6 | −0.782854 | ||||||||
\(592\) | −3.00868e6 | −0.352835 | ||||||||
\(593\) | −2.61518e6 | −0.305397 | −0.152698 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152698 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(594\) | −3.93466e6 | −0.457553 | ||||||||
\(595\) | 2.81497e6 | 0.325972 | ||||||||
\(596\) | −6.89102e6 | −0.794635 | ||||||||
\(597\) | −2.33643e6 | −0.268298 | ||||||||
\(598\) | 5.00042e6 | 0.571813 | ||||||||
\(599\) | 1.58662e7 | 1.80678 | 0.903391 | − | 0.428817i | \(-0.141069\pi\) | ||||
0.903391 | + | 0.428817i | \(0.141069\pi\) | |||||||
\(600\) | 2.79048e6 | 0.316447 | ||||||||
\(601\) | 3.38022e6 | 0.381732 | 0.190866 | − | 0.981616i | \(-0.438870\pi\) | ||||
0.190866 | + | 0.981616i | \(0.438870\pi\) | |||||||
\(602\) | 1.62607e6 | 0.182872 | ||||||||
\(603\) | −2.62641e7 | −2.94150 | ||||||||
\(604\) | 1.32330e7 | 1.47593 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 967361. | 0.107006 | ||||||||
\(607\) | 6.05529e6 | 0.667057 | 0.333529 | − | 0.942740i | \(-0.391761\pi\) | ||||
0.333529 | + | 0.942740i | \(0.391761\pi\) | |||||||
\(608\) | 2.11263e6 | 0.231774 | ||||||||
\(609\) | 2.92810e7 | 3.19921 | ||||||||
\(610\) | 1.85841e6 | 0.202216 | ||||||||
\(611\) | 8.85343e6 | 0.959420 | ||||||||
\(612\) | 1.29761e7 | 1.40044 | ||||||||
\(613\) | 2.34791e6 | 0.252365 | 0.126183 | − | 0.992007i | \(-0.459727\pi\) | ||||
0.126183 | + | 0.992007i | \(0.459727\pi\) | |||||||
\(614\) | −1.43398e6 | −0.153505 | ||||||||
\(615\) | −1.94599e6 | −0.207469 | ||||||||
\(616\) | −2.60214e6 | −0.276298 | ||||||||
\(617\) | −2786.40 | −0.000294666 0 | −0.000147333 | − | 1.00000i | \(-0.500047\pi\) | ||||
−0.000147333 | 1.00000i | \(0.500047\pi\) | ||||||||
\(618\) | −676511. | −0.0712530 | ||||||||
\(619\) | 7.38249e6 | 0.774420 | 0.387210 | − | 0.921992i | \(-0.373439\pi\) | ||||
0.387210 | + | 0.921992i | \(0.373439\pi\) | |||||||
\(620\) | −2.45590e6 | −0.256585 | ||||||||
\(621\) | 3.63054e7 | 3.77783 | ||||||||
\(622\) | −7.79701e6 | −0.808076 | ||||||||
\(623\) | −5.04604e6 | −0.520871 | ||||||||
\(624\) | −8.46467e6 | −0.870259 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 6.73278e6 | 0.686687 | ||||||||
\(627\) | −1.31269e6 | −0.133350 | ||||||||
\(628\) | 6.86093e6 | 0.694199 | ||||||||
\(629\) | 5.52983e6 | 0.557295 | ||||||||
\(630\) | 6.19688e6 | 0.622044 | ||||||||
\(631\) | 1.43702e7 | 1.43678 | 0.718389 | − | 0.695642i | \(-0.244880\pi\) | ||||
0.718389 | + | 0.695642i | \(0.244880\pi\) | |||||||
\(632\) | 1.02966e7 | 1.02541 | ||||||||
\(633\) | 64715.6 | 0.00641948 | ||||||||
\(634\) | 4.88510e6 | 0.482670 | ||||||||
\(635\) | 5.50333e6 | 0.541616 | ||||||||
\(636\) | −1.25335e7 | −1.22865 | ||||||||
\(637\) | −2.75880e6 | −0.269384 | ||||||||
\(638\) | 2.11293e6 | 0.205510 | ||||||||
\(639\) | 3.39707e7 | 3.29118 | ||||||||
\(640\) | 4.57549e6 | 0.441558 | ||||||||
\(641\) | 814356. | 0.0782833 | 0.0391417 | − | 0.999234i | \(-0.487538\pi\) | ||||
0.0391417 | + | 0.999234i | \(0.487538\pi\) | |||||||
\(642\) | 1.27654e7 | 1.22235 | ||||||||
\(643\) | −1.58604e7 | −1.51282 | −0.756408 | − | 0.654100i | \(-0.773048\pi\) | ||||
−0.756408 | + | 0.654100i | \(0.773048\pi\) | |||||||
\(644\) | 1.05944e7 | 1.00661 | ||||||||
\(645\) | 3.25338e6 | 0.307918 | ||||||||
\(646\) | −728489. | −0.0686818 | ||||||||
\(647\) | 1.48375e7 | 1.39348 | 0.696738 | − | 0.717326i | \(-0.254634\pi\) | ||||
0.696738 | + | 0.717326i | \(0.254634\pi\) | |||||||
\(648\) | 3.21341e7 | 3.00628 | ||||||||
\(649\) | −1.30809e6 | −0.121907 | ||||||||
\(650\) | 1.07904e6 | 0.100174 | ||||||||
\(651\) | −1.69102e7 | −1.56385 | ||||||||
\(652\) | −7.09333e6 | −0.653478 | ||||||||
\(653\) | 9.80135e6 | 0.899504 | 0.449752 | − | 0.893153i | \(-0.351512\pi\) | ||||
0.449752 | + | 0.893153i | \(0.351512\pi\) | |||||||
\(654\) | 1.07599e7 | 0.983702 | ||||||||
\(655\) | −8.81381e6 | −0.802713 | ||||||||
\(656\) | −1.09625e6 | −0.0994607 | ||||||||
\(657\) | 5.23685e6 | 0.473322 | ||||||||
\(658\) | −4.99538e6 | −0.449784 | ||||||||
\(659\) | 5.03359e6 | 0.451507 | 0.225753 | − | 0.974185i | \(-0.427516\pi\) | ||||
0.225753 | + | 0.974185i | \(0.427516\pi\) | |||||||
\(660\) | −2.29724e6 | −0.205280 | ||||||||
\(661\) | −1.47344e7 | −1.31168 | −0.655840 | − | 0.754900i | \(-0.727685\pi\) | ||||
−0.655840 | + | 0.754900i | \(0.727685\pi\) | |||||||
\(662\) | −3.77923e6 | −0.335165 | ||||||||
\(663\) | 1.55577e7 | 1.37456 | ||||||||
\(664\) | −9.08429e6 | −0.799596 | ||||||||
\(665\) | 1.30636e6 | 0.114554 | ||||||||
\(666\) | 1.21734e7 | 1.06347 | ||||||||
\(667\) | −1.94961e7 | −1.69681 | ||||||||
\(668\) | −1.32988e7 | −1.15311 | ||||||||
\(669\) | −4.03258e7 | −3.48351 | ||||||||
\(670\) | 2.58038e6 | 0.222074 | ||||||||
\(671\) | −3.46726e6 | −0.297290 | ||||||||
\(672\) | 2.54567e7 | 2.17460 | ||||||||
\(673\) | 1.09990e7 | 0.936088 | 0.468044 | − | 0.883705i | \(-0.344959\pi\) | ||||
0.468044 | + | 0.883705i | \(0.344959\pi\) | |||||||
\(674\) | 3.98861e6 | 0.338199 | ||||||||
\(675\) | 7.83434e6 | 0.661825 | ||||||||
\(676\) | −1.80982e6 | −0.152324 | ||||||||
\(677\) | −1.29517e7 | −1.08606 | −0.543031 | − | 0.839713i | \(-0.682723\pi\) | ||||
−0.543031 | + | 0.839713i | \(0.682723\pi\) | |||||||
\(678\) | 5.78434e6 | 0.483258 | ||||||||
\(679\) | 2.20533e7 | 1.83569 | ||||||||
\(680\) | −2.88925e6 | −0.239614 | ||||||||
\(681\) | −8.18966e6 | −0.676703 | ||||||||
\(682\) | −1.22024e6 | −0.100458 | ||||||||
\(683\) | 2.26814e7 | 1.86045 | 0.930226 | − | 0.366987i | \(-0.119610\pi\) | ||||
0.930226 | + | 0.366987i | \(0.119610\pi\) | |||||||
\(684\) | 6.02191e6 | 0.492146 | ||||||||
\(685\) | −4.58970e6 | −0.373730 | ||||||||
\(686\) | −4.75451e6 | −0.385741 | ||||||||
\(687\) | −1.38066e7 | −1.11608 | ||||||||
\(688\) | 1.83275e6 | 0.147616 | ||||||||
\(689\) | −1.09837e7 | −0.881457 | ||||||||
\(690\) | −5.64493e6 | −0.451373 | ||||||||
\(691\) | −5.78332e6 | −0.460768 | −0.230384 | − | 0.973100i | \(-0.573998\pi\) | ||||
−0.230384 | + | 0.973100i | \(0.573998\pi\) | |||||||
\(692\) | 4.80605e6 | 0.381525 | ||||||||
\(693\) | −1.15616e7 | −0.914504 | ||||||||
\(694\) | 1.77545e6 | 0.139930 | ||||||||
\(695\) | −3.06550e6 | −0.240735 | ||||||||
\(696\) | −3.00537e7 | −2.35167 | ||||||||
\(697\) | 2.01487e6 | 0.157096 | ||||||||
\(698\) | 586911. | 0.0455967 | ||||||||
\(699\) | −5.69404e6 | −0.440786 | ||||||||
\(700\) | 2.28616e6 | 0.176344 | ||||||||
\(701\) | −2.58390e6 | −0.198601 | −0.0993004 | − | 0.995057i | \(-0.531660\pi\) | ||||
−0.0993004 | + | 0.995057i | \(0.531660\pi\) | |||||||
\(702\) | 2.16412e7 | 1.65744 | ||||||||
\(703\) | 2.56627e6 | 0.195846 | ||||||||
\(704\) | 198200. | 0.0150721 | ||||||||
\(705\) | −9.99456e6 | −0.757340 | ||||||||
\(706\) | 9.64816e6 | 0.728506 | ||||||||
\(707\) | 1.79612e6 | 0.135141 | ||||||||
\(708\) | 8.20982e6 | 0.615532 | ||||||||
\(709\) | 2.55024e7 | 1.90531 | 0.952655 | − | 0.304053i | \(-0.0983401\pi\) | ||||
0.952655 | + | 0.304053i | \(0.0983401\pi\) | |||||||
\(710\) | −3.33754e6 | −0.248474 | ||||||||
\(711\) | 4.57490e7 | 3.39396 | ||||||||
\(712\) | 5.17920e6 | 0.382880 | ||||||||
\(713\) | 1.12593e7 | 0.829443 | ||||||||
\(714\) | −8.77815e6 | −0.644403 | ||||||||
\(715\) | −2.01319e6 | −0.147272 | ||||||||
\(716\) | −1.15490e7 | −0.841904 | ||||||||
\(717\) | 3.98939e7 | 2.89807 | ||||||||
\(718\) | 1.20192e6 | 0.0870087 | ||||||||
\(719\) | 2.36466e7 | 1.70587 | 0.852935 | − | 0.522017i | \(-0.174820\pi\) | ||||
0.852935 | + | 0.522017i | \(0.174820\pi\) | |||||||
\(720\) | 6.98454e6 | 0.502119 | ||||||||
\(721\) | −1.25609e6 | −0.0899876 | ||||||||
\(722\) | −338075. | −0.0241363 | ||||||||
\(723\) | 5.28102e6 | 0.375727 | ||||||||
\(724\) | 1.19963e7 | 0.850552 | ||||||||
\(725\) | −4.20707e6 | −0.297259 | ||||||||
\(726\) | −1.14141e6 | −0.0803709 | ||||||||
\(727\) | 8.37216e6 | 0.587491 | 0.293746 | − | 0.955884i | \(-0.405098\pi\) | ||||
0.293746 | + | 0.955884i | \(0.405098\pi\) | |||||||
\(728\) | 1.43121e7 | 1.00086 | ||||||||
\(729\) | 5.12385e7 | 3.57090 | ||||||||
\(730\) | −514508. | −0.0357343 | ||||||||
\(731\) | −3.36853e6 | −0.233156 | ||||||||
\(732\) | 2.17611e7 | 1.50108 | ||||||||
\(733\) | −1.26328e7 | −0.868439 | −0.434219 | − | 0.900807i | \(-0.642976\pi\) | ||||
−0.434219 | + | 0.900807i | \(0.642976\pi\) | |||||||
\(734\) | −6.06138e6 | −0.415271 | ||||||||
\(735\) | 3.11438e6 | 0.212644 | ||||||||
\(736\) | −1.69498e7 | −1.15337 | ||||||||
\(737\) | −4.81427e6 | −0.326484 | ||||||||
\(738\) | 4.43555e6 | 0.299782 | ||||||||
\(739\) | 1.86296e7 | 1.25485 | 0.627427 | − | 0.778675i | \(-0.284108\pi\) | ||||
0.627427 | + | 0.778675i | \(0.284108\pi\) | |||||||
\(740\) | 4.49102e6 | 0.301485 | ||||||||
\(741\) | 7.21999e6 | 0.483049 | ||||||||
\(742\) | 6.19735e6 | 0.413234 | ||||||||
\(743\) | 1.94042e7 | 1.28950 | 0.644752 | − | 0.764392i | \(-0.276961\pi\) | ||||
0.644752 | + | 0.764392i | \(0.276961\pi\) | |||||||
\(744\) | 1.73564e7 | 1.14955 | ||||||||
\(745\) | 6.81732e6 | 0.450011 | ||||||||
\(746\) | −1.28625e7 | −0.846210 | ||||||||
\(747\) | −4.03626e7 | −2.64654 | ||||||||
\(748\) | 2.37855e6 | 0.155438 | ||||||||
\(749\) | 2.37018e7 | 1.54375 | ||||||||
\(750\) | −1.21812e6 | −0.0790746 | ||||||||
\(751\) | −3.36122e6 | −0.217469 | −0.108734 | − | 0.994071i | \(-0.534680\pi\) | ||||
−0.108734 | + | 0.994071i | \(0.534680\pi\) | |||||||
\(752\) | −5.63033e6 | −0.363069 | ||||||||
\(753\) | −3.94526e6 | −0.253564 | ||||||||
\(754\) | −1.16214e7 | −0.744439 | ||||||||
\(755\) | −1.30915e7 | −0.835835 | ||||||||
\(756\) | 4.58510e7 | 2.91772 | ||||||||
\(757\) | −2.29717e6 | −0.145698 | −0.0728489 | − | 0.997343i | \(-0.523209\pi\) | ||||
−0.0728489 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(758\) | 1.38397e7 | 0.874889 | ||||||||
\(759\) | 1.05319e7 | 0.663591 | ||||||||
\(760\) | −1.34084e6 | −0.0842057 | ||||||||
\(761\) | −2.81089e7 | −1.75947 | −0.879736 | − | 0.475462i | \(-0.842281\pi\) | ||||
−0.879736 | + | 0.475462i | \(0.842281\pi\) | |||||||
\(762\) | −1.71615e7 | −1.07070 | ||||||||
\(763\) | 1.99781e7 | 1.24235 | ||||||||
\(764\) | −9.74573e6 | −0.604061 | ||||||||
\(765\) | −1.28373e7 | −0.793086 | ||||||||
\(766\) | 456568. | 0.0281147 | ||||||||
\(767\) | 7.19469e6 | 0.441595 | ||||||||
\(768\) | −1.58434e7 | −0.969269 | ||||||||
\(769\) | 1.39588e7 | 0.851202 | 0.425601 | − | 0.904911i | \(-0.360063\pi\) | ||||
0.425601 | + | 0.904911i | \(0.360063\pi\) | |||||||
\(770\) | 1.13590e6 | 0.0690421 | ||||||||
\(771\) | −2.27042e7 | −1.37553 | ||||||||
\(772\) | 1.61047e7 | 0.972543 | ||||||||
\(773\) | −6.58993e6 | −0.396673 | −0.198336 | − | 0.980134i | \(-0.563554\pi\) | ||||
−0.198336 | + | 0.980134i | \(0.563554\pi\) | |||||||
\(774\) | −7.41549e6 | −0.444926 | ||||||||
\(775\) | 2.42964e6 | 0.145307 | ||||||||
\(776\) | −2.26353e7 | −1.34937 | ||||||||
\(777\) | 3.09230e7 | 1.83751 | ||||||||
\(778\) | 2.51533e6 | 0.148986 | ||||||||
\(779\) | 935056. | 0.0552070 | ||||||||
\(780\) | 1.26351e7 | 0.743605 | ||||||||
\(781\) | 6.22691e6 | 0.365296 | ||||||||
\(782\) | 5.84474e6 | 0.341781 | ||||||||
\(783\) | −8.43766e7 | −4.91833 | ||||||||
\(784\) | 1.75445e6 | 0.101942 | ||||||||
\(785\) | −6.78756e6 | −0.393133 | ||||||||
\(786\) | 2.74848e7 | 1.58685 | ||||||||
\(787\) | −8.37335e6 | −0.481906 | −0.240953 | − | 0.970537i | \(-0.577460\pi\) | ||||
−0.240953 | + | 0.970537i | \(0.577460\pi\) | |||||||
\(788\) | 5.58970e6 | 0.320681 | ||||||||
\(789\) | 4.71761e7 | 2.69792 | ||||||||
\(790\) | −4.49473e6 | −0.256233 | ||||||||
\(791\) | 1.07399e7 | 0.610322 | ||||||||
\(792\) | 1.18667e7 | 0.672230 | ||||||||
\(793\) | 1.90704e7 | 1.07690 | ||||||||
\(794\) | 4.46241e6 | 0.251199 | ||||||||
\(795\) | 1.23994e7 | 0.695798 | ||||||||
\(796\) | 1.96468e6 | 0.109903 | ||||||||
\(797\) | −2.51179e7 | −1.40067 | −0.700337 | − | 0.713812i | \(-0.746967\pi\) | ||||
−0.700337 | + | 0.713812i | \(0.746967\pi\) | |||||||
\(798\) | −4.07374e6 | −0.226457 | ||||||||
\(799\) | 1.03483e7 | 0.573460 | ||||||||
\(800\) | −3.65760e6 | −0.202056 | ||||||||
\(801\) | 2.30118e7 | 1.26727 | ||||||||
\(802\) | 6.61572e6 | 0.363196 | ||||||||
\(803\) | 959927. | 0.0525351 | ||||||||
\(804\) | 3.02152e7 | 1.64848 | ||||||||
\(805\) | −1.04811e7 | −0.570053 | ||||||||
\(806\) | 6.71149e6 | 0.363900 | ||||||||
\(807\) | −3.60361e7 | −1.94784 | ||||||||
\(808\) | −1.84352e6 | −0.0993388 | ||||||||
\(809\) | −3.35330e7 | −1.80136 | −0.900682 | − | 0.434478i | \(-0.856933\pi\) | ||||
−0.900682 | + | 0.434478i | \(0.856933\pi\) | |||||||
\(810\) | −1.40274e7 | −0.751216 | ||||||||
\(811\) | 3.03912e7 | 1.62254 | 0.811271 | − | 0.584670i | \(-0.198776\pi\) | ||||
0.811271 | + | 0.584670i | \(0.198776\pi\) | |||||||
\(812\) | −2.46221e7 | −1.31050 | ||||||||
\(813\) | 1.31170e7 | 0.695996 | ||||||||
\(814\) | 2.23141e6 | 0.118037 | ||||||||
\(815\) | 7.01747e6 | 0.370072 | ||||||||
\(816\) | −9.89391e6 | −0.520167 | ||||||||
\(817\) | −1.56326e6 | −0.0819361 | ||||||||
\(818\) | −661476. | −0.0345645 | ||||||||
\(819\) | 6.35905e7 | 3.31270 | ||||||||
\(820\) | 1.63637e6 | 0.0849857 | ||||||||
\(821\) | 1.12359e7 | 0.581768 | 0.290884 | − | 0.956758i | \(-0.406051\pi\) | ||||
0.290884 | + | 0.956758i | \(0.406051\pi\) | |||||||
\(822\) | 1.43124e7 | 0.738813 | ||||||||
\(823\) | 3.15343e7 | 1.62287 | 0.811434 | − | 0.584445i | \(-0.198688\pi\) | ||||
0.811434 | + | 0.584445i | \(0.198688\pi\) | |||||||
\(824\) | 1.28924e6 | 0.0661477 | ||||||||
\(825\) | 2.27267e6 | 0.116252 | ||||||||
\(826\) | −4.05947e6 | −0.207023 | ||||||||
\(827\) | −6.25717e6 | −0.318137 | −0.159068 | − | 0.987268i | \(-0.550849\pi\) | ||||
−0.159068 | + | 0.987268i | \(0.550849\pi\) | |||||||
\(828\) | −4.83143e7 | −2.44906 | ||||||||
\(829\) | −1.05136e7 | −0.531331 | −0.265665 | − | 0.964065i | \(-0.585592\pi\) | ||||
−0.265665 | + | 0.964065i | \(0.585592\pi\) | |||||||
\(830\) | 3.96553e6 | 0.199805 | ||||||||
\(831\) | −1.61967e7 | −0.813624 | ||||||||
\(832\) | −1.09013e6 | −0.0545970 | ||||||||
\(833\) | −3.22461e6 | −0.161015 | ||||||||
\(834\) | 9.55940e6 | 0.475900 | ||||||||
\(835\) | 1.31566e7 | 0.653020 | ||||||||
\(836\) | 1.10383e6 | 0.0546244 | ||||||||
\(837\) | 4.87286e7 | 2.40420 | ||||||||
\(838\) | −8.44224e6 | −0.415287 | ||||||||
\(839\) | 1.60935e7 | 0.789308 | 0.394654 | − | 0.918830i | \(-0.370864\pi\) | ||||
0.394654 | + | 0.918830i | \(0.370864\pi\) | |||||||
\(840\) | −1.61568e7 | −0.790055 | ||||||||
\(841\) | 2.47994e7 | 1.20907 | ||||||||
\(842\) | 5.41798e6 | 0.263365 | ||||||||
\(843\) | 1.19308e7 | 0.578228 | ||||||||
\(844\) | −54418.7 | −0.00262961 | ||||||||
\(845\) | 1.79047e6 | 0.0862631 | ||||||||
\(846\) | 2.27808e7 | 1.09432 | ||||||||
\(847\) | −2.11927e6 | −0.101503 | ||||||||
\(848\) | 6.98508e6 | 0.333566 | ||||||||
\(849\) | −5.29556e7 | −2.52140 | ||||||||
\(850\) | 1.26124e6 | 0.0598754 | ||||||||
\(851\) | −2.05894e7 | −0.974586 | ||||||||
\(852\) | −3.90812e7 | −1.84446 | ||||||||
\(853\) | 4.17886e6 | 0.196646 | 0.0983230 | − | 0.995155i | \(-0.468652\pi\) | ||||
0.0983230 | + | 0.995155i | \(0.468652\pi\) | |||||||
\(854\) | −1.07601e7 | −0.504861 | ||||||||
\(855\) | −5.95750e6 | −0.278708 | ||||||||
\(856\) | −2.43272e7 | −1.13477 | ||||||||
\(857\) | 2.18794e7 | 1.01762 | 0.508808 | − | 0.860880i | \(-0.330086\pi\) | ||||
0.508808 | + | 0.860880i | \(0.330086\pi\) | |||||||
\(858\) | 6.27789e6 | 0.291136 | ||||||||
\(859\) | 5.19684e6 | 0.240302 | 0.120151 | − | 0.992756i | \(-0.461662\pi\) | ||||
0.120151 | + | 0.992756i | \(0.461662\pi\) | |||||||
\(860\) | −2.73573e6 | −0.126133 | ||||||||
\(861\) | 1.12672e7 | 0.517976 | ||||||||
\(862\) | 940775. | 0.0431238 | ||||||||
\(863\) | −9.08022e6 | −0.415020 | −0.207510 | − | 0.978233i | \(-0.566536\pi\) | ||||
−0.207510 | + | 0.978233i | \(0.566536\pi\) | |||||||
\(864\) | −7.33565e7 | −3.34314 | ||||||||
\(865\) | −4.75465e6 | −0.216062 | ||||||||
\(866\) | 1.16128e7 | 0.526192 | ||||||||
\(867\) | −2.44847e7 | −1.10623 | ||||||||
\(868\) | 1.42196e7 | 0.640602 | ||||||||
\(869\) | 8.38589e6 | 0.376704 | ||||||||
\(870\) | 1.31193e7 | 0.587640 | ||||||||
\(871\) | 2.64791e7 | 1.18265 | ||||||||
\(872\) | −2.05053e7 | −0.913220 | ||||||||
\(873\) | −1.00571e8 | −4.46621 | ||||||||
\(874\) | 2.71241e6 | 0.120109 | ||||||||
\(875\) | −2.26171e6 | −0.0998657 | ||||||||
\(876\) | −6.02467e6 | −0.265261 | ||||||||
\(877\) | −2.78324e7 | −1.22195 | −0.610973 | − | 0.791651i | \(-0.709222\pi\) | ||||
−0.610973 | + | 0.791651i | \(0.709222\pi\) | |||||||
\(878\) | −3.67133e6 | −0.160726 | ||||||||
\(879\) | 7.58303e7 | 3.31032 | ||||||||
\(880\) | 1.28028e6 | 0.0557313 | ||||||||
\(881\) | 3.03635e7 | 1.31799 | 0.658994 | − | 0.752148i | \(-0.270982\pi\) | ||||
0.658994 | + | 0.752148i | \(0.270982\pi\) | |||||||
\(882\) | −7.09868e6 | −0.307260 | ||||||||
\(883\) | −2.09839e7 | −0.905700 | −0.452850 | − | 0.891587i | \(-0.649593\pi\) | ||||
−0.452850 | + | 0.891587i | \(0.649593\pi\) | |||||||
\(884\) | −1.30823e7 | −0.563060 | ||||||||
\(885\) | −8.12202e6 | −0.348583 | ||||||||
\(886\) | 1.92101e6 | 0.0822138 | ||||||||
\(887\) | 3.45134e7 | 1.47292 | 0.736458 | − | 0.676483i | \(-0.236497\pi\) | ||||
0.736458 | + | 0.676483i | \(0.236497\pi\) | |||||||
\(888\) | −3.17391e7 | −1.35071 | ||||||||
\(889\) | −3.18641e7 | −1.35222 | ||||||||
\(890\) | −2.26086e6 | −0.0956750 | ||||||||
\(891\) | 2.61712e7 | 1.10441 | ||||||||
\(892\) | 3.39095e7 | 1.42695 | ||||||||
\(893\) | 4.80242e6 | 0.201526 | ||||||||
\(894\) | −2.12590e7 | −0.889610 | ||||||||
\(895\) | 1.14255e7 | 0.476780 | ||||||||
\(896\) | −2.64920e7 | −1.10241 | ||||||||
\(897\) | −5.79266e7 | −2.40379 | ||||||||
\(898\) | 1.07843e7 | 0.446275 | ||||||||
\(899\) | −2.61674e7 | −1.07985 | ||||||||
\(900\) | −1.04257e7 | −0.429043 | ||||||||
\(901\) | −1.28383e7 | −0.526860 | ||||||||
\(902\) | 813046. | 0.0332735 | ||||||||
\(903\) | −1.88369e7 | −0.768761 | ||||||||
\(904\) | −1.10233e7 | −0.448633 | ||||||||
\(905\) | −1.18680e7 | −0.481677 | ||||||||
\(906\) | 4.08242e7 | 1.65233 | ||||||||
\(907\) | 4.21126e7 | 1.69978 | 0.849892 | − | 0.526957i | \(-0.176667\pi\) | ||||
0.849892 | + | 0.526957i | \(0.176667\pi\) | |||||||
\(908\) | 6.88660e6 | 0.277198 | ||||||||
\(909\) | −8.19098e6 | −0.328796 | ||||||||
\(910\) | −6.24761e6 | −0.250098 | ||||||||
\(911\) | 2.24069e7 | 0.894510 | 0.447255 | − | 0.894406i | \(-0.352402\pi\) | ||||
0.447255 | + | 0.894406i | \(0.352402\pi\) | |||||||
\(912\) | −4.59154e6 | −0.182798 | ||||||||
\(913\) | −7.39857e6 | −0.293745 | ||||||||
\(914\) | −2.24571e7 | −0.889175 | ||||||||
\(915\) | −2.15284e7 | −0.850079 | ||||||||
\(916\) | 1.16098e7 | 0.457179 | ||||||||
\(917\) | 5.10317e7 | 2.00409 | ||||||||
\(918\) | 2.52952e7 | 0.990677 | ||||||||
\(919\) | 7.90951e6 | 0.308930 | 0.154465 | − | 0.987998i | \(-0.450635\pi\) | ||||
0.154465 | + | 0.987998i | \(0.450635\pi\) | |||||||
\(920\) | 1.07576e7 | 0.419032 | ||||||||
\(921\) | 1.66117e7 | 0.645304 | ||||||||
\(922\) | −7.27123e6 | −0.281696 | ||||||||
\(923\) | −3.42488e7 | −1.32325 | ||||||||
\(924\) | 1.33009e7 | 0.512510 | ||||||||
\(925\) | −4.44299e6 | −0.170734 | ||||||||
\(926\) | 1.53058e7 | 0.586582 | ||||||||
\(927\) | 5.72825e6 | 0.218939 | ||||||||
\(928\) | 3.93927e7 | 1.50157 | ||||||||
\(929\) | 668234. | 0.0254032 | 0.0127016 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127016 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(930\) | −7.57655e6 | −0.287253 | ||||||||
\(931\) | −1.49647e6 | −0.0565841 | ||||||||
\(932\) | 4.78806e6 | 0.180559 | ||||||||
\(933\) | 9.03233e7 | 3.39700 | ||||||||
\(934\) | −1.52159e7 | −0.570730 | ||||||||
\(935\) | −2.35311e6 | −0.0880264 | ||||||||
\(936\) | −6.52686e7 | −2.43509 | ||||||||
\(937\) | 2.14457e7 | 0.797979 | 0.398989 | − | 0.916956i | \(-0.369361\pi\) | ||||
0.398989 | + | 0.916956i | \(0.369361\pi\) | |||||||
\(938\) | −1.49403e7 | −0.554438 | ||||||||
\(939\) | −7.79949e7 | −2.88670 | ||||||||
\(940\) | 8.40432e6 | 0.310229 | ||||||||
\(941\) | 3.60761e7 | 1.32815 | 0.664073 | − | 0.747667i | \(-0.268826\pi\) | ||||
0.664073 | + | 0.747667i | \(0.268826\pi\) | |||||||
\(942\) | 2.11662e7 | 0.777170 | ||||||||
\(943\) | −7.50204e6 | −0.274726 | ||||||||
\(944\) | −4.57545e6 | −0.167111 | ||||||||
\(945\) | −4.53606e7 | −1.65234 | ||||||||
\(946\) | −1.35928e6 | −0.0493833 | ||||||||
\(947\) | −9.57308e6 | −0.346878 | −0.173439 | − | 0.984845i | \(-0.555488\pi\) | ||||
−0.173439 | + | 0.984845i | \(0.555488\pi\) | |||||||
\(948\) | −5.26313e7 | −1.90206 | ||||||||
\(949\) | −5.27972e6 | −0.190303 | ||||||||
\(950\) | 585311. | 0.0210415 | ||||||||
\(951\) | −5.65907e7 | −2.02906 | ||||||||
\(952\) | 1.67287e7 | 0.598231 | ||||||||
\(953\) | −1.23929e6 | −0.0442018 | −0.0221009 | − | 0.999756i | \(-0.507036\pi\) | ||||
−0.0221009 | + | 0.999756i | \(0.507036\pi\) | |||||||
\(954\) | −2.82623e7 | −1.00539 | ||||||||
\(955\) | 9.64150e6 | 0.342087 | ||||||||
\(956\) | −3.35464e7 | −1.18714 | ||||||||
\(957\) | −2.44769e7 | −0.863924 | ||||||||
\(958\) | 1.39443e7 | 0.490889 | ||||||||
\(959\) | 2.65742e7 | 0.933069 | ||||||||
\(960\) | 1.23064e6 | 0.0430974 | ||||||||
\(961\) | −1.35171e7 | −0.472145 | ||||||||
\(962\) | −1.22731e7 | −0.427578 | ||||||||
\(963\) | −1.08089e8 | −3.75592 | ||||||||
\(964\) | −4.44075e6 | −0.153909 | ||||||||
\(965\) | −1.59324e7 | −0.550762 | ||||||||
\(966\) | 3.26840e7 | 1.12692 | ||||||||
\(967\) | 1.45327e7 | 0.499781 | 0.249890 | − | 0.968274i | \(-0.419605\pi\) | ||||
0.249890 | + | 0.968274i | \(0.419605\pi\) | |||||||
\(968\) | 2.17520e6 | 0.0746124 | ||||||||
\(969\) | 8.43907e6 | 0.288726 | ||||||||
\(970\) | 9.88091e6 | 0.337184 | ||||||||
\(971\) | −9.42194e6 | −0.320695 | −0.160348 | − | 0.987061i | \(-0.551262\pi\) | ||||
−0.160348 | + | 0.987061i | \(0.551262\pi\) | |||||||
\(972\) | −8.72820e7 | −2.96319 | ||||||||
\(973\) | 1.77491e7 | 0.601029 | ||||||||
\(974\) | 2.08397e7 | 0.703872 | ||||||||
\(975\) | −1.25000e7 | −0.421112 | ||||||||
\(976\) | −1.21278e7 | −0.407528 | ||||||||
\(977\) | 4.50753e7 | 1.51078 | 0.755392 | − | 0.655274i | \(-0.227447\pi\) | ||||
0.755392 | + | 0.655274i | \(0.227447\pi\) | |||||||
\(978\) | −2.18832e7 | −0.731582 | ||||||||
\(979\) | 4.21813e6 | 0.140657 | ||||||||
\(980\) | −2.61885e6 | −0.0871055 | ||||||||
\(981\) | −9.11078e7 | −3.02262 | ||||||||
\(982\) | −8.63705e6 | −0.285816 | ||||||||
\(983\) | 1.41997e6 | 0.0468702 | 0.0234351 | − | 0.999725i | \(-0.492540\pi\) | ||||
0.0234351 | + | 0.999725i | \(0.492540\pi\) | |||||||
\(984\) | −1.15646e7 | −0.380752 | ||||||||
\(985\) | −5.52992e6 | −0.181605 | ||||||||
\(986\) | −1.35836e7 | −0.444962 | ||||||||
\(987\) | 5.78682e7 | 1.89081 | ||||||||
\(988\) | −6.07121e6 | −0.197871 | ||||||||
\(989\) | 1.25422e7 | 0.407738 | ||||||||
\(990\) | −5.18014e6 | −0.167979 | ||||||||
\(991\) | 1.85275e7 | 0.599285 | 0.299643 | − | 0.954052i | \(-0.403133\pi\) | ||||
0.299643 | + | 0.954052i | \(0.403133\pi\) | |||||||
\(992\) | −2.27498e7 | −0.734003 | ||||||||
\(993\) | 4.37800e7 | 1.40897 | ||||||||
\(994\) | 1.93243e7 | 0.620350 | ||||||||
\(995\) | −1.94367e6 | −0.0622393 | ||||||||
\(996\) | 4.64347e7 | 1.48318 | ||||||||
\(997\) | −6.24362e7 | −1.98929 | −0.994646 | − | 0.103337i | \(-0.967048\pi\) | ||||
−0.994646 | + | 0.103337i | \(0.967048\pi\) | |||||||
\(998\) | 1.24602e7 | 0.396005 | ||||||||
\(999\) | −8.91082e7 | −2.82491 |
(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 | 1045.6.a.e.1.17 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.e.1.17 | ✓ | 38 | 1.1 | even | 1 | trivial |