Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.13 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.253656 | + | 5.65116i | −0.0448405 | + | 0.998994i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.8713 | − | 2.86690i | −0.995979 | − | 0.0895907i | ||||
\(5\) | −84.3255 | + | 48.6853i | −1.50846 | + | 0.870910i | −0.508508 | + | 0.861057i | \(0.669803\pi\) |
−0.999951 | + | 0.00985262i | \(0.996864\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −87.9661 | − | 50.7872i | −0.678532 | − | 0.391750i | 0.120770 | − | 0.992681i | \(-0.461464\pi\) |
−0.799302 | + | 0.600930i | \(0.794797\pi\) | |||||||
\(8\) | 24.2857 | − | 179.383i | 0.134161 | − | 0.990960i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −253.739 | − | 488.886i | −0.802394 | − | 1.54599i | ||||
\(11\) | 73.2291 | − | 126.837i | 0.182474 | − | 0.316055i | −0.760248 | − | 0.649633i | \(-0.774923\pi\) |
0.942723 | + | 0.333578i | \(0.108256\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 402.832 | + | 697.726i | 0.661098 | + | 1.14506i | 0.980327 | + | 0.197378i | \(0.0632427\pi\) |
−0.319229 | + | 0.947678i | \(0.603424\pi\) | |||||||
\(14\) | 309.320 | − | 484.228i | 0.421782 | − | 0.660283i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1007.56 | + | 182.744i | 0.983947 | + | 0.178461i | ||||
\(17\) | 1238.37i | 1.03927i | 0.854389 | + | 0.519633i | \(0.173931\pi\) | ||||
−0.854389 | + | 0.519633i | \(0.826069\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2616.12i | − | 1.66254i | −0.555866 | − | 0.831272i | \(-0.687613\pi\) | ||
0.555866 | − | 0.831272i | \(-0.312387\pi\) | |||||||
\(20\) | 2827.14 | − | 1309.91i | 1.58042 | − | 0.732263i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 698.199 | + | 446.002i | 0.307555 | + | 0.196463i | ||||
\(23\) | −84.5912 | − | 146.516i | −0.0333431 | − | 0.0577519i | 0.848872 | − | 0.528598i | \(-0.177282\pi\) |
−0.882215 | + | 0.470846i | \(0.843949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3178.02 | − | 5504.50i | 1.01697 | − | 1.76144i | ||||
\(26\) | −4045.15 | + | 2099.49i | −1.17355 | + | 0.609088i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2657.99 | + | 1870.85i | 0.640706 | + | 0.450965i | ||||
\(29\) | −1952.82 | − | 1127.46i | −0.431189 | − | 0.248947i | 0.268664 | − | 0.963234i | \(-0.413418\pi\) |
−0.699853 | + | 0.714287i | \(0.746751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1787.03 | − | 1031.74i | 0.333985 | − | 0.192826i | −0.323624 | − | 0.946186i | \(-0.604901\pi\) |
0.657609 | + | 0.753359i | \(0.271568\pi\) | |||||||
\(32\) | −1288.29 | + | 5647.54i | −0.222402 | + | 0.974955i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6998.21 | − | 314.119i | −1.03822 | − | 0.0466012i | ||||
\(35\) | 9890.37 | 1.36472 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 445.632 | 0.0535146 | 0.0267573 | − | 0.999642i | \(-0.491482\pi\) | ||||
0.0267573 | + | 0.999642i | \(0.491482\pi\) | |||||||
\(38\) | 14784.1 | + | 663.594i | 1.66087 | + | 0.0745492i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6685.41 | + | 16308.9i | 0.660660 | + | 1.61166i | ||||
\(41\) | 1720.61 | − | 993.393i | 0.159853 | − | 0.0922914i | −0.417939 | − | 0.908475i | \(-0.637248\pi\) |
0.577793 | + | 0.816184i | \(0.303914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3464.26 | + | 2000.09i | 0.285719 | + | 0.164960i | 0.636010 | − | 0.771681i | \(-0.280584\pi\) |
−0.350291 | + | 0.936641i | \(0.613917\pi\) | |||||||
\(44\) | −2697.54 | + | 3832.51i | −0.210056 | + | 0.298436i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 849.444 | − | 440.874i | 0.0591889 | − | 0.0307199i | ||||
\(47\) | 3539.24 | − | 6130.14i | 0.233703 | − | 0.404786i | −0.725192 | − | 0.688547i | \(-0.758249\pi\) |
0.958895 | + | 0.283761i | \(0.0915822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3244.81 | − | 5620.18i | −0.193063 | − | 0.334395i | ||||
\(50\) | 30300.7 | + | 19355.8i | 1.71407 | + | 1.09493i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10838.5 | − | 23392.3i | −0.555853 | − | 1.19968i | ||||
\(53\) | 6234.98i | 0.304891i | 0.988312 | + | 0.152446i | \(0.0487149\pi\) | ||||
−0.988312 | + | 0.152446i | \(0.951285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14260.7i | 0.635675i | ||||||||
\(56\) | −11246.7 | + | 14546.2i | −0.479241 | + | 0.619840i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6866.81 | − | 10749.7i | 0.268031 | − | 0.419592i | ||||
\(59\) | −16724.9 | − | 28968.4i | −0.625509 | − | 1.08341i | −0.988442 | − | 0.151598i | \(-0.951558\pi\) |
0.362933 | − | 0.931815i | \(-0.381775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14717.5 | − | 25491.5i | 0.506420 | − | 0.877145i | −0.493553 | − | 0.869716i | \(-0.664302\pi\) |
0.999972 | − | 0.00742891i | \(-0.00236472\pi\) | |||||||
\(62\) | 5377.25 | + | 10360.5i | 0.177656 | + | 0.342296i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −31588.4 | − | 8712.87i | −0.964002 | − | 0.265896i | ||||
\(65\) | −67938.0 | − | 39224.1i | −1.99448 | − | 1.15151i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23308.8 | − | 13457.4i | 0.634357 | − | 0.366246i | −0.148081 | − | 0.988975i | \(-0.547310\pi\) |
0.782437 | + | 0.622729i | \(0.213976\pi\) | |||||||
\(68\) | 3550.28 | − | 39468.4i | 0.0931086 | − | 1.03509i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2508.75 | + | 55892.1i | −0.0611945 | + | 1.36334i | ||||
\(71\) | −36309.5 | −0.854819 | −0.427409 | − | 0.904058i | \(-0.640574\pi\) | ||||
−0.427409 | + | 0.904058i | \(0.640574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38203.0 | −0.839056 | −0.419528 | − | 0.907742i | \(-0.637804\pi\) | ||||
−0.419528 | + | 0.907742i | \(0.637804\pi\) | |||||||
\(74\) | −113.037 | + | 2518.34i | −0.00239962 | + | 0.0534608i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7500.15 | + | 83379.1i | −0.148948 | + | 1.65586i | ||||
\(77\) | −12883.4 | + | 7438.21i | −0.247629 | + | 0.142969i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 54553.0 | + | 31496.2i | 0.983448 | + | 0.567794i | 0.903309 | − | 0.428990i | \(-0.141130\pi\) |
0.0801384 | + | 0.996784i | \(0.474464\pi\) | |||||||
\(80\) | −93860.1 | + | 33643.5i | −1.63967 | + | 0.587728i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5177.38 | + | 9975.41i | 0.0850307 | + | 0.163831i | ||||
\(83\) | 39957.8 | − | 69208.9i | 0.636658 | − | 1.10272i | −0.349503 | − | 0.936935i | \(-0.613650\pi\) |
0.986161 | − | 0.165789i | \(-0.0530170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60290.3 | − | 104426.i | −0.905107 | − | 1.56769i | ||||
\(86\) | −12181.6 | + | 19069.8i | −0.177606 | + | 0.278035i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20973.9 | − | 16216.4i | −0.288717 | − | 0.223227i | ||||
\(89\) | − | 96604.3i | − | 1.29277i | −0.763011 | − | 0.646385i | \(-0.776280\pi\) | ||
0.763011 | − | 0.646385i | \(-0.223720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 81835.0i | − | 1.03594i | ||||||
\(92\) | 2275.98 | + | 4912.18i | 0.0280349 | + | 0.0605069i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 33744.7 | + | 21555.8i | 0.393900 | + | 0.251619i | ||||
\(95\) | 127367. | + | 220605.i | 1.44793 | + | 2.50788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8318.60 | + | 14408.2i | −0.0897678 | + | 0.155482i | −0.907413 | − | 0.420240i | \(-0.861946\pi\) |
0.817645 | + | 0.575723i | \(0.195279\pi\) | |||||||
\(98\) | 32583.6 | − | 16911.4i | 0.342716 | − | 0.177875i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −117069. | + | 166324.i | −1.17069 | + | 1.66324i | ||||
\(101\) | −25178.9 | − | 14537.1i | −0.245603 | − | 0.141799i | 0.372146 | − | 0.928174i | \(-0.378622\pi\) |
−0.617749 | + | 0.786375i | \(0.711955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −132194. | + | 76322.2i | −1.22777 | + | 0.708855i | −0.966564 | − | 0.256427i | \(-0.917455\pi\) |
−0.261210 | + | 0.965282i | \(0.584121\pi\) | |||||||
\(104\) | 134943. | − | 55316.5i | 1.22340 | − | 0.501500i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −35234.9 | − | 1581.54i | −0.304585 | − | 0.0136715i | ||||
\(107\) | −160032. | −1.35129 | −0.675645 | − | 0.737227i | \(-0.736135\pi\) | ||||
−0.675645 | + | 0.737227i | \(0.736135\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 136775. | 1.10265 | 0.551327 | − | 0.834289i | \(-0.314122\pi\) | ||||
0.551327 | + | 0.834289i | \(0.314122\pi\) | |||||||
\(110\) | −80589.7 | − | 3617.32i | −0.635035 | − | 0.0285039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −79350.2 | − | 67246.5i | −0.597727 | − | 0.506553i | ||||
\(113\) | −29144.4 | + | 16826.5i | −0.214713 | + | 0.123965i | −0.603500 | − | 0.797363i | \(-0.706228\pi\) |
0.388787 | + | 0.921328i | \(0.372894\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14266.4 | + | 8236.70i | 0.100593 | + | 0.0580776i | ||||
\(116\) | 59006.6 | + | 41532.2i | 0.407151 | + | 0.286576i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 167947. | − | 87167.2i | 1.11037 | − | 0.576299i | ||||
\(119\) | 62893.2 | − | 108934.i | 0.407133 | − | 0.705175i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69800.5 | + | 120898.i | 0.433406 | + | 0.750682i | ||||
\(122\) | 140324. | + | 89637.3i | 0.853555 | + | 0.545242i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −59912.8 | + | 27759.7i | −0.349917 | + | 0.162129i | ||||
\(125\) | 314609.i | 1.80093i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7342.22i | − | 0.0403941i | −0.999796 | − | 0.0201971i | \(-0.993571\pi\) | ||
0.999796 | − | 0.0201971i | \(-0.00642936\pi\) | |||||||
\(128\) | 57250.4 | − | 176301.i | 0.308855 | − | 0.951109i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 238894. | − | 373980.i | 1.23979 | − | 1.94084i | ||||
\(131\) | −104864. | − | 181630.i | −0.533886 | − | 0.924718i | −0.999216 | − | 0.0395811i | \(-0.987398\pi\) |
0.465330 | − | 0.885137i | \(-0.345936\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −132865. | + | 230130.i | −0.651302 | + | 1.12809i | ||||
\(134\) | 70137.3 | + | 135136.i | 0.337433 | + | 0.650141i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 222142. | + | 30074.6i | 1.02987 | + | 0.139429i | ||||
\(137\) | 221740. | + | 128022.i | 1.00935 | + | 0.582749i | 0.911002 | − | 0.412403i | \(-0.135310\pi\) |
0.0983495 | + | 0.995152i | \(0.468644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 31429.4 | − | 18145.7i | 0.137974 | − | 0.0796595i | −0.429424 | − | 0.903103i | \(-0.641283\pi\) |
0.567398 | + | 0.823444i | \(0.307950\pi\) | |||||||
\(140\) | −315219. | − | 28354.7i | −1.35923 | − | 0.122266i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9210.11 | − | 205191.i | 0.0383305 | − | 0.853959i | ||||
\(143\) | 117996. | 0.482534 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 219563. | 0.867241 | ||||||||
\(146\) | 9690.43 | − | 215892.i | 0.0376236 | − | 0.838212i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14202.9 | − | 1277.58i | −0.0532994 | − | 0.00479441i | ||||
\(149\) | 411222. | − | 237419.i | 1.51744 | − | 0.876092i | 0.517646 | − | 0.855595i | \(-0.326808\pi\) |
0.999790 | − | 0.0204977i | \(-0.00652507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 103973. | + | 60029.0i | 0.371090 | + | 0.214249i | 0.673935 | − | 0.738791i | \(-0.264603\pi\) |
−0.302844 | + | 0.953040i | \(0.597936\pi\) | |||||||
\(152\) | −469287. | − | 63534.2i | −1.64751 | − | 0.223048i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −38766.6 | − | 74692.7i | −0.131721 | − | 0.253791i | ||||
\(155\) | −100461. | + | 174004.i | −0.335869 | + | 0.581742i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −111283. | − | 192748.i | −0.360312 | − | 0.624079i | 0.627700 | − | 0.778456i | \(-0.283997\pi\) |
−0.988012 | + | 0.154376i | \(0.950663\pi\) | |||||||
\(158\) | −191828. | + | 300299.i | −0.611321 | + | 0.956998i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −166317. | − | 538953.i | −0.513613 | − | 1.66437i | ||||
\(161\) | 17184.6i | 0.0522486i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 489772.i | − | 1.44386i | −0.691967 | − | 0.721929i | \(-0.743255\pi\) | ||
0.691967 | − | 0.721929i | \(-0.256745\pi\) | |||||||
\(164\) | −57686.0 | + | 26727.9i | −0.167479 | + | 0.0775989i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 380975. | + | 243363.i | 1.07307 | + | 0.685464i | ||||
\(167\) | −43035.4 | − | 74539.6i | −0.119408 | − | 0.206822i | 0.800125 | − | 0.599833i | \(-0.204766\pi\) |
−0.919533 | + | 0.393012i | \(0.871433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −138901. | + | 240584.i | −0.374102 | + | 0.647963i | ||||
\(170\) | 605421. | − | 314222.i | 1.60670 | − | 0.833901i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −104676. | − | 73677.2i | −0.269791 | − | 0.189894i | ||||
\(173\) | 170126. | + | 98222.4i | 0.432171 | + | 0.249514i | 0.700271 | − | 0.713877i | \(-0.253062\pi\) |
−0.268100 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −559116. | + | 322806.i | −1.38009 | + | 0.796795i | ||||
\(176\) | 96961.4 | − | 114413.i | 0.235949 | − | 0.278417i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 545927. | + | 24504.2i | 1.29147 | + | 0.0579684i | ||||
\(179\) | 348859. | 0.813799 | 0.406900 | − | 0.913473i | \(-0.366610\pi\) | ||||
0.406900 | + | 0.913473i | \(0.366610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −35362.9 | −0.0802326 | −0.0401163 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401163 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(182\) | 462463. | + | 20757.9i | 1.03490 | + | 0.0464521i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −28336.8 | + | 11616.0i | −0.0617031 | + | 0.0252936i | ||||
\(185\) | −37578.1 | + | 21695.7i | −0.0807246 | + | 0.0466064i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 157070. | + | 90684.5i | 0.328465 | + | 0.189640i | ||||
\(188\) | −130375. | + | 185229.i | −0.269029 | + | 0.382221i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.27898e6 | + | 663811.i | −2.57028 | + | 1.33401i | ||||
\(191\) | −434850. | + | 753182.i | −0.862494 | + | 1.49388i | 0.00701997 | + | 0.999975i | \(0.497765\pi\) |
−0.869514 | + | 0.493908i | \(0.835568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 426577. | + | 738854.i | 0.824336 | + | 1.42779i | 0.902425 | + | 0.430846i | \(0.141785\pi\) |
−0.0780890 | + | 0.996946i | \(0.524882\pi\) | |||||||
\(194\) | −79313.2 | − | 50664.5i | −0.151301 | − | 0.0966495i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 87303.9 | + | 188425.i | 0.162328 | + | 0.350347i | ||||
\(197\) | 259841.i | 0.477026i | 0.971139 | + | 0.238513i | \(0.0766600\pi\) | ||||
−0.971139 | + | 0.238513i | \(0.923340\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 264379.i | − | 0.473255i | −0.971600 | − | 0.236627i | \(-0.923958\pi\) | ||
0.971600 | − | 0.236627i | \(-0.0760420\pi\) | |||||||
\(200\) | −910232. | − | 703763.i | −1.60908 | − | 1.24409i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 88538.2 | − | 138603.i | 0.152669 | − | 0.238998i | ||||
\(203\) | 114521. | + | 198357.i | 0.195050 | + | 0.337837i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −96727.3 | + | 167537.i | −0.160755 | + | 0.278436i | ||||
\(206\) | −397777. | − | 766409.i | −0.653089 | − | 1.25832i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 278373. | + | 776617.i | 0.446138 | + | 1.24465i | ||||
\(209\) | −331819. | − | 191576.i | −0.525455 | − | 0.303372i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −889657. | + | 513644.i | −1.37568 | + | 0.794247i | −0.991636 | − | 0.129069i | \(-0.958801\pi\) |
−0.384041 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(212\) | 17875.1 | − | 198717.i | 0.0273154 | − | 0.303665i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 40593.2 | − | 904369.i | 0.0605924 | − | 1.34993i | ||||
\(215\) | −389500. | −0.574661 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −209597. | −0.302159 | ||||||||
\(218\) | −34693.7 | + | 772936.i | −0.0494435 | + | 1.10155i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 40884.1 | − | 454508.i | 0.0569506 | − | 0.633119i | ||||
\(221\) | −864041. | + | 498854.i | −1.19002 | + | 0.687057i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 524934. | + | 303071.i | 0.706875 | + | 0.408115i | 0.809903 | − | 0.586564i | \(-0.199520\pi\) |
−0.103028 | + | 0.994678i | \(0.532853\pi\) | |||||||
\(224\) | 400149. | − | 431364.i | 0.532846 | − | 0.574412i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −87696.8 | − | 168968.i | −0.114212 | − | 0.220056i | ||||
\(227\) | 85552.8 | − | 148182.i | 0.110197 | − | 0.190867i | −0.805653 | − | 0.592388i | \(-0.798185\pi\) |
0.915850 | + | 0.401522i | \(0.131519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −689040. | − | 1.19345e6i | −0.868271 | − | 1.50389i | −0.863762 | − | 0.503900i | \(-0.831898\pi\) |
−0.00450932 | − | 0.999990i | \(-0.501435\pi\) | |||||||
\(230\) | −50165.7 | + | 78532.4i | −0.0625298 | + | 0.0978879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −249673. | + | 322921.i | −0.304545 | + | 0.393892i | ||||
\(233\) | − | 1.36894e6i | − | 1.65194i | −0.563711 | − | 0.825972i | \(-0.690627\pi\) | ||
0.563711 | − | 0.825972i | \(-0.309373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 689236.i | 0.814138i | ||||||||
\(236\) | 449995. | + | 971209.i | 0.525930 | + | 1.13510i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 599652. | + | 383052.i | 0.686210 | + | 0.438344i | ||||
\(239\) | −155455. | − | 269255.i | −0.176039 | − | 0.304908i | 0.764481 | − | 0.644646i | \(-0.222995\pi\) |
−0.940520 | + | 0.339737i | \(0.889662\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 196168. | − | 339774.i | 0.217564 | − | 0.376832i | −0.736499 | − | 0.676439i | \(-0.763522\pi\) |
0.954063 | + | 0.299607i | \(0.0968557\pi\) | |||||||
\(242\) | −700920. | + | 363788.i | −0.769361 | + | 0.399309i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −542149. | + | 770255.i | −0.582967 | + | 0.828247i | ||||
\(245\) | 547241. | + | 315950.i | 0.582456 | + | 0.336281i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.82533e6 | − | 1.05386e6i | 1.90371 | − | 1.09910i | ||||
\(248\) | −141677. | − | 345619.i | −0.146275 | − | 0.356835i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.77791e6 | − | 79802.4i | −1.79912 | − | 0.0807544i | ||||
\(251\) | 241581. | 0.242035 | 0.121017 | − | 0.992650i | \(-0.461384\pi\) | ||||
0.121017 | + | 0.992650i | \(0.461384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24778.1 | −0.0243370 | ||||||||
\(254\) | 41492.1 | + | 1862.40i | 0.0403535 | + | 0.00181129i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 981785. | + | 368252.i | 0.936303 | + | 0.351192i | ||||
\(257\) | 231851. | − | 133859.i | 0.218966 | − | 0.126420i | −0.386506 | − | 0.922287i | \(-0.626318\pi\) |
0.605471 | + | 0.795867i | \(0.292985\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39200.5 | − | 22632.4i | −0.0363113 | − | 0.0209644i | ||||
\(260\) | 2.05282e6 | + | 1.44489e6i | 1.88329 | + | 1.32557i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.05302e6 | − | 546533.i | 0.947728 | − | 0.491885i | ||||
\(263\) | 829311. | − | 1.43641e6i | 0.739313 | − | 1.28053i | −0.213493 | − | 0.976945i | \(-0.568484\pi\) |
0.952805 | − | 0.303582i | \(-0.0981827\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −303552. | − | 525767.i | −0.265533 | − | 0.459916i | ||||
\(266\) | −1.26680e6 | − | 809218.i | −1.09775 | − | 0.701231i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −781464. | + | 362080.i | −0.664618 | + | 0.307941i | ||||
\(269\) | − | 1.42634e6i | − | 1.20183i | −0.799312 | − | 0.600916i | \(-0.794803\pi\) | ||
0.799312 | − | 0.600916i | \(-0.205197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.91215e6i | − | 1.58161i | −0.612068 | − | 0.790805i | \(-0.709662\pi\) | ||
0.612068 | − | 0.790805i | \(-0.290338\pi\) | |||||||
\(272\) | −226304. | + | 1.24773e6i | −0.185468 | + | 1.02258i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −779716. | + | 1.22061e6i | −0.627423 | + | 0.982205i | ||||
\(275\) | −465447. | − | 806179.i | −0.371141 | − | 0.642835i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 169154. | − | 292983.i | 0.132459 | − | 0.229426i | −0.792165 | − | 0.610307i | \(-0.791046\pi\) |
0.924624 | + | 0.380881i | \(0.124379\pi\) | |||||||
\(278\) | 94572.4 | + | 182215.i | 0.0733926 | + | 0.141408i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 240195. | − | 1.77416e6i | 0.183091 | − | 1.35238i | ||||
\(281\) | −817291. | − | 471863.i | −0.617463 | − | 0.356492i | 0.158418 | − | 0.987372i | \(-0.449361\pi\) |
−0.775881 | + | 0.630880i | \(0.782694\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.92014e6 | + | 1.10859e6i | −1.42517 | + | 0.822821i | −0.996734 | − | 0.0807515i | \(-0.974268\pi\) |
−0.428434 | + | 0.903573i | \(0.640935\pi\) | |||||||
\(284\) | 1.15723e6 | + | 104096.i | 0.851381 | + | 0.0765838i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29930.4 | + | 666816.i | −0.0216370 | + | 0.482049i | ||||
\(287\) | −201807. | −0.144621 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −113695. | −0.0800752 | ||||||||
\(290\) | −55693.5 | + | 1.24079e6i | −0.0388875 | + | 0.866369i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.21758e6 | + | 109524.i | 0.835682 | + | 0.0751716i | ||||
\(293\) | −1.18621e6 | + | 684857.i | −0.807219 | + | 0.466048i | −0.845989 | − | 0.533200i | \(-0.820989\pi\) |
0.0387699 | + | 0.999248i | \(0.487656\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.82067e6 | + | 1.62851e6i | 1.88711 | + | 1.08952i | ||||
\(296\) | 10822.5 | − | 79938.8i | 0.00717956 | − | 0.0530308i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.23739e6 | + | 2.38410e6i | 0.807169 | + | 1.55519i | ||||
\(299\) | 68152.1 | − | 118043.i | 0.0440861 | − | 0.0763593i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −203158. | − | 351880.i | −0.129246 | − | 0.223861i | ||||
\(302\) | −365607. | + | 572343.i | −0.230673 | + | 0.361110i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 478079. | − | 2.63590e6i | 0.296699 | − | 1.63586i | ||||
\(305\) | 2.86611e6i | 1.76418i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 809224.i | − | 0.490030i | −0.969519 | − | 0.245015i | \(-0.921207\pi\) | ||
0.969519 | − | 0.245015i | \(-0.0787929\pi\) | |||||||
\(308\) | 431934. | − | 200130.i | 0.259442 | − | 0.120209i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −957843. | − | 611860.i | −0.566096 | − | 0.361616i | ||||
\(311\) | 35523.7 | + | 61528.8i | 0.0208265 | + | 0.0360726i | 0.876251 | − | 0.481855i | \(-0.160037\pi\) |
−0.855424 | + | 0.517928i | \(0.826704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 893740. | − | 1.54800e6i | 0.515644 | − | 0.893122i | −0.484191 | − | 0.874963i | \(-0.660886\pi\) |
0.999835 | − | 0.0181599i | \(-0.00578080\pi\) | |||||||
\(314\) | 1.11748e6 | − | 579986.i | 0.639608 | − | 0.331966i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.64838e6 | − | 1.16022e6i | −0.928624 | − | 0.653618i | ||||
\(317\) | 287153. | + | 165788.i | 0.160496 | + | 0.0926627i | 0.578097 | − | 0.815968i | \(-0.303796\pi\) |
−0.417601 | + | 0.908631i | \(0.637129\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −286007. | + | 165126.i | −0.157362 | + | 0.0908529i | ||||
\(320\) | 3.08790e6 | − | 803175.i | 1.68573 | − | 0.438466i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −97113.0 | − | 4358.98i | −0.0521961 | − | 0.00234285i | ||||
\(323\) | 3.23971e6 | 1.72783 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.12084e6 | 2.68926 | ||||||||
\(326\) | 2.76778e6 | + | 124234.i | 1.44241 | + | 0.0647433i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −136412. | − | 332773.i | −0.0700110 | − | 0.170790i | ||||
\(329\) | −622666. | + | 359496.i | −0.317150 | + | 0.183107i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.05838e6 | − | 1.18840e6i | −1.03265 | − | 0.596203i | −0.114910 | − | 0.993376i | \(-0.536658\pi\) |
−0.917744 | + | 0.397173i | \(0.869991\pi\) | |||||||
\(332\) | −1.47192e6 | + | 2.09122e6i | −0.732891 | + | 1.04125i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 432152. | − | 224293.i | 0.211968 | − | 0.110014i | ||||
\(335\) | −1.31035e6 | + | 2.26960e6i | −0.637934 | + | 1.10493i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −62983.9 | − | 109091.i | −0.0302103 | − | 0.0523257i | 0.850525 | − | 0.525935i | \(-0.176284\pi\) |
−0.880735 | + | 0.473609i | \(0.842951\pi\) | |||||||
\(338\) | −1.32435e6 | − | 845980.i | −0.630536 | − | 0.402780i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.62215e6 | + | 3.50104e6i | 0.761017 | + | 1.64248i | ||||
\(341\) | − | 302214.i | − | 0.140743i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.36634e6i | 1.08603i | ||||||||
\(344\) | 442914. | − | 572855.i | 0.201801 | − | 0.261005i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −598224. | + | 936496.i | −0.268642 | + | 0.420548i | ||||
\(347\) | −577346. | − | 999992.i | −0.257402 | − | 0.445834i | 0.708143 | − | 0.706069i | \(-0.249533\pi\) |
−0.965545 | + | 0.260235i | \(0.916200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.82275e6 | + | 3.15709e6i | −0.801056 | + | 1.38747i | 0.117865 | + | 0.993030i | \(0.462395\pi\) |
−0.918922 | + | 0.394440i | \(0.870938\pi\) | |||||||
\(350\) | −1.68241e6 | − | 3.24154e6i | −0.734110 | − | 1.41443i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 621974. | + | 576967.i | 0.267557 | + | 0.248196i | ||||
\(353\) | −990369. | − | 571790.i | −0.423020 | − | 0.244230i | 0.273349 | − | 0.961915i | \(-0.411869\pi\) |
−0.696368 | + | 0.717685i | \(0.745202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.06181e6 | − | 1.76774e6i | 1.28946 | − | 0.744470i | ||||
\(356\) | −276955. | + | 3.07891e6i | −0.115820 | + | 1.28757i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −88490.1 | + | 1.97146e6i | −0.0364911 | + | 0.812981i | ||||
\(359\) | −111222. | −0.0455466 | −0.0227733 | − | 0.999741i | \(-0.507250\pi\) | ||||
−0.0227733 | + | 0.999741i | \(0.507250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.36797e6 | −1.76405 | ||||||||
\(362\) | 8970.00 | − | 199841.i | 0.00359767 | − | 0.0801519i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −234613. | + | 2.60819e6i | −0.0928108 | + | 1.03178i | ||||
\(365\) | 3.22149e6 | − | 1.85993e6i | 1.26568 | − | 0.730742i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.77385e6 | − | 2.17883e6i | −1.46258 | − | 0.844421i | −0.463450 | − | 0.886123i | \(-0.653388\pi\) |
−0.999130 | + | 0.0417025i | \(0.986722\pi\) | |||||||
\(368\) | −58455.9 | − | 163083.i | −0.0225014 | − | 0.0627752i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −113074. | − | 217863.i | −0.0429398 | − | 0.0827333i | ||||
\(371\) | 316657. | − | 548466.i | 0.119441 | − | 0.206878i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.34963e6 | − | 2.33763e6i | −0.502277 | − | 0.869970i | −0.999997 | − | 0.00263144i | \(-0.999162\pi\) |
0.497719 | − | 0.867338i | \(-0.334171\pi\) | |||||||
\(374\) | −552315. | + | 864626.i | −0.204177 | + | 0.319631i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.01369e6 | − | 783753.i | −0.369773 | − | 0.285897i | ||||
\(377\) | − | 1.81671e6i | − | 0.658313i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.05325e6i | − | 0.734249i | −0.930172 | − | 0.367125i | \(-0.880342\pi\) | ||
0.930172 | − | 0.367125i | \(-0.119658\pi\) | |||||||
\(380\) | −3.42689e6 | − | 7.39613e6i | −1.21742 | − | 2.62752i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.14606e6 | − | 2.64846e6i | −1.45371 | − | 0.928613i | ||||
\(383\) | 2.72270e6 | + | 4.71586e6i | 0.948426 | + | 1.64272i | 0.748741 | + | 0.662862i | \(0.230658\pi\) |
0.199685 | + | 0.979860i | \(0.436008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 724263. | − | 1.25446e6i | 0.249026 | − | 0.431326i | ||||
\(386\) | −4.28359e6 | + | 2.22324e6i | −1.46332 | + | 0.759484i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 306432. | − | 435361.i | 0.103337 | − | 0.146815i | ||||
\(389\) | −2.51571e6 | − | 1.45244e6i | −0.842919 | − | 0.486660i | 0.0153362 | − | 0.999882i | \(-0.495118\pi\) |
−0.858255 | + | 0.513223i | \(0.828451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 181441. | − | 104755.i | 0.0600196 | − | 0.0346523i | ||||
\(392\) | −1.08697e6 | + | 445574.i | −0.357274 | + | 0.146455i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.46841e6 | − | 65910.3i | −0.476547 | − | 0.0213901i | ||||
\(395\) | −6.13361e6 | −1.97799 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.59810e6 | −0.508896 | −0.254448 | − | 0.967086i | \(-0.581894\pi\) | ||||
−0.254448 | + | 0.967086i | \(0.581894\pi\) | |||||||
\(398\) | 1.49405e6 | + | 67061.4i | 0.472779 | + | 0.0212210i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.20797e6 | − | 4.96536e6i | 1.31499 | − | 1.55167i | ||||
\(401\) | 1.48732e6 | − | 858705.i | 0.461895 | − | 0.266675i | −0.250945 | − | 0.968001i | \(-0.580741\pi\) |
0.712841 | + | 0.701326i | \(0.247408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.43974e6 | + | 831237.i | 0.441594 | + | 0.254954i | ||||
\(404\) | 760810. | + | 535501.i | 0.231912 | + | 0.163233i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.15000e6 | + | 596864.i | −0.346243 | + | 0.179705i | ||||
\(407\) | 32633.2 | − | 56522.4i | 0.00976504 | − | 0.0169135i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.74998e6 | + | 4.76310e6i | 0.812870 | + | 1.40793i | 0.910847 | + | 0.412744i | \(0.135430\pi\) |
−0.0979768 | + | 0.995189i | \(0.531237\pi\) | |||||||
\(410\) | −922242. | − | 589119.i | −0.270947 | − | 0.173079i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.43200e6 | − | 2.05350e6i | 1.28634 | − | 0.596008i | ||||
\(413\) | 3.39765e6i | 0.980174i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.78143e6i | 2.21789i | ||||||||
\(416\) | −4.45940e6 | + | 1.37614e6i | −1.26341 | + | 0.389878i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.16679e6 | − | 1.82657e6i | 0.326628 | − | 0.511323i | ||||
\(419\) | −3.22137e6 | − | 5.57958e6i | −0.896408 | − | 1.55262i | −0.832052 | − | 0.554698i | \(-0.812834\pi\) |
−0.0643564 | − | 0.997927i | \(-0.520499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.68713e6 | + | 2.92220e6i | −0.463921 | + | 0.803535i | −0.999152 | − | 0.0411706i | \(-0.986891\pi\) |
0.535231 | + | 0.844706i | \(0.320225\pi\) | |||||||
\(422\) | −2.67702e6 | − | 5.15789e6i | −0.731762 | − | 1.40991i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.11845e6 | + | 151421.i | 0.302135 | + | 0.0409044i | ||||
\(425\) | 6.81659e6 | + | 3.93556e6i | 1.83060 | + | 1.05690i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.58929e6 | + | 1.49493e6i | −0.687244 | + | 0.396780i | ||||
\(428\) | 5.10044e6 | + | 458797.i | 1.34586 | + | 0.121063i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 98799.1 | − | 2.20113e6i | 0.0257681 | − | 0.574083i | ||||
\(431\) | −1.69209e6 | −0.438763 | −0.219382 | − | 0.975639i | \(-0.570404\pi\) | ||||
−0.219382 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.34335e6 | −0.856964 | −0.428482 | − | 0.903550i | \(-0.640951\pi\) | ||||
−0.428482 | + | 0.903550i | \(0.640951\pi\) | |||||||
\(434\) | 53165.5 | − | 1.18447e6i | 0.0135490 | − | 0.301855i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.35919e6 | − | 392120.i | −1.09822 | − | 0.0987876i | ||||
\(437\) | −383304. | + | 221300.i | −0.0960150 | + | 0.0554343i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.12524e6 | + | 2.38171e6i | 1.02162 | + | 0.589831i | 0.914572 | − | 0.404424i | \(-0.132528\pi\) |
0.107045 | + | 0.994254i | \(0.465861\pi\) | |||||||
\(440\) | 2.55813e6 | + | 346332.i | 0.629928 | + | 0.0852826i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.59994e6 | − | 5.00937e6i | −0.633005 | − | 1.21963i | ||||
\(443\) | 2.19145e6 | − | 3.79571e6i | 0.530546 | − | 0.918932i | −0.468819 | − | 0.883294i | \(-0.655320\pi\) |
0.999365 | − | 0.0356380i | \(-0.0113463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.70321e6 | + | 8.14620e6i | 1.12589 | + | 1.95009i | ||||
\(446\) | −1.84586e6 | + | 2.88961e6i | −0.439401 | + | 0.687864i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.33621e6 | + | 2.37073e6i | 0.549941 | + | 0.558067i | ||||
\(449\) | 2.64215e6i | 0.618502i | 0.950981 | + | 0.309251i | \(0.100078\pi\) | ||||
−0.950981 | + | 0.309251i | \(0.899922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 290981.i | − | 0.0673633i | ||||||
\(452\) | 977110. | − | 452729.i | 0.224956 | − | 0.104230i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 815699. | + | 521060.i | 0.185733 | + | 0.118645i | ||||
\(455\) | 3.98416e6 | + | 6.90077e6i | 0.902212 | + | 1.56268i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.74172e6 | − | 3.01674e6i | 0.390110 | − | 0.675690i | −0.602354 | − | 0.798229i | \(-0.705770\pi\) |
0.992464 | + | 0.122539i | \(0.0391037\pi\) | |||||||
\(458\) | 6.91917e6 | − | 3.59115e6i | 1.54131 | − | 0.799963i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −431075. | − | 303415.i | −0.0949856 | − | 0.0668563i | ||||
\(461\) | −2.93883e6 | − | 1.69673e6i | −0.644054 | − | 0.371845i | 0.142121 | − | 0.989849i | \(-0.454608\pi\) |
−0.786174 | + | 0.618005i | \(0.787941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −167674. | + | 96806.8i | −0.0363508 | + | 0.0209871i | −0.518065 | − | 0.855341i | \(-0.673348\pi\) |
0.481714 | + | 0.876328i | \(0.340014\pi\) | |||||||
\(464\) | −1.76155e6 | − | 1.49285e6i | −0.379840 | − | 0.321901i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.73612e6 | + | 347240.i | 1.65028 | + | 0.0740739i | ||||
\(467\) | −3.24407e6 | −0.688332 | −0.344166 | − | 0.938909i | \(-0.611838\pi\) | ||||
−0.344166 | + | 0.938909i | \(0.611838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.73385e6 | −0.573908 | ||||||||
\(470\) | −3.89498e6 | − | 174829.i | −0.813319 | − | 0.0365063i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.60261e6 | + | 2.29664e6i | −1.15754 | + | 0.474503i | ||||
\(473\) | 507369. | − | 292930.i | 0.104273 | − | 0.0602020i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.44004e7 | − | 8.31408e6i | −2.92847 | − | 1.69075i | ||||
\(476\) | −2.31679e6 | + | 3.29157e6i | −0.468673 | + | 0.665864i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.56104e6 | − | 810201.i | 0.312495 | − | 0.162190i | ||||
\(479\) | −4.10699e6 | + | 7.11352e6i | −0.817871 | + | 1.41659i | 0.0893767 | + | 0.995998i | \(0.471513\pi\) |
−0.907248 | + | 0.420596i | \(0.861821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 179515. | + | 310929.i | 0.0353784 | + | 0.0612772i | ||||
\(482\) | 1.87036e6 | + | 1.19477e6i | 0.366697 | + | 0.234242i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.87803e6 | − | 4.05329e6i | −0.364409 | − | 0.786492i | ||||
\(485\) | − | 1.61997e6i | − | 0.312719i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.63906e6i | 0.313165i | 0.987665 | + | 0.156583i | \(0.0500477\pi\) | ||||
−0.987665 | + | 0.156583i | \(0.949952\pi\) | |||||||
\(488\) | −4.21532e6 | − | 3.25915e6i | −0.801273 | − | 0.619520i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.92429e6 | + | 3.01240e6i | −0.362060 | + | 0.566791i | ||||
\(491\) | 2.03219e6 | + | 3.51985e6i | 0.380417 | + | 0.658902i | 0.991122 | − | 0.132957i | \(-0.0424471\pi\) |
−0.610705 | + | 0.791858i | \(0.709114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.39621e6 | − | 2.41831e6i | 0.258722 | − | 0.448120i | ||||
\(494\) | 5.49251e6 | + | 1.05826e7i | 1.01264 | + | 1.95107i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.98908e6 | − | 712974.i | 0.363036 | − | 0.130128i | ||||
\(497\) | 3.19400e6 | + | 1.84406e6i | 0.580022 | + | 0.334876i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.92199e6 | − | 1.68701e6i | 0.525325 | − | 0.303296i | −0.213786 | − | 0.976881i | \(-0.568579\pi\) |
0.739111 | + | 0.673584i | \(0.235246\pi\) | |||||||
\(500\) | 901954. | − | 1.00270e7i | 0.161346 | − | 1.79369i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −61278.3 | + | 1.36521e6i | −0.0108529 | + | 0.241791i | ||||
\(503\) | 7.37612e6 | 1.29989 | 0.649947 | − | 0.759979i | \(-0.274791\pi\) | ||||
0.649947 | + | 0.759979i | \(0.274791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.83097e6 | 0.493977 | ||||||||
\(506\) | 6285.12 | − | 140025.i | 0.00109128 | − | 0.0243125i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21049.4 | + | 234006.i | −0.00361894 | + | 0.0402317i | ||||
\(509\) | 5.72270e6 | − | 3.30400e6i | 0.979054 | − | 0.565257i | 0.0770693 | − | 0.997026i | \(-0.475444\pi\) |
0.901984 | + | 0.431769i | \(0.142110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.36057e6 | + | 1.94023e6i | 0.569326 | + | 0.328700i | ||||
\(512\) | −2.33009e6 | + | 5.45482e6i | −0.392823 | + | 0.919614i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 697650. | + | 1.34418e6i | 0.116474 | + | 0.224414i | ||||
\(515\) | 7.43154e6 | − | 1.28718e7i | 1.23470 | − | 2.13856i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −518350. | − | 897809.i | −0.0852898 | − | 0.147726i | ||||
\(518\) | 137843. | − | 215788.i | 0.0225715 | − | 0.0353348i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.68604e6 | + | 1.12343e7i | −1.40868 | + | 1.82196i | ||||
\(521\) | 1.91733e6i | 0.309459i | 0.987957 | + | 0.154730i | \(0.0494506\pi\) | ||||
−0.987957 | + | 0.154730i | \(0.950549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.16891e6i | − | 0.826313i | −0.910660 | − | 0.413157i | \(-0.864426\pi\) | ||
0.910660 | − | 0.413157i | \(-0.135574\pi\) | |||||||
\(524\) | 2.82144e6 | + | 6.08943e6i | 0.448893 | + | 0.968831i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.90702e6 | + | 5.05093e6i | 1.24609 | + | 0.795988i | ||||
\(527\) | 1.27767e6 | + | 2.21300e6i | 0.200398 | + | 0.347100i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20386e6 | − | 5.54925e6i | 0.497776 | − | 0.862174i | ||||
\(530\) | 3.04819e6 | − | 1.58206e6i | 0.471360 | − | 0.244643i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.89435e6 | − | 6.95362e6i | 0.749750 | − | 1.06520i | ||||
\(533\) | 1.38623e6 | + | 800342.i | 0.211358 | + | 0.122027i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.34948e7 | − | 7.79123e6i | 2.03837 | − | 1.17685i | ||||
\(536\) | −1.84795e6 | − | 4.50803e6i | −0.277829 | − | 0.677758i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.06051e6 | + | 361801.i | 1.20062 | + | 0.0538907i | ||||
\(539\) | −950459. | −0.140916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.10786e6 | 0.456528 | 0.228264 | − | 0.973599i | \(-0.426695\pi\) | ||||
0.228264 | + | 0.973599i | \(0.426695\pi\) | |||||||
\(542\) | 1.08059e7 | + | 485029.i | 1.58002 | + | 0.0709201i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.99373e6 | − | 1.59538e6i | −1.01324 | − | 0.231135i | ||||
\(545\) | −1.15336e7 | + | 6.65892e6i | −1.66331 | + | 0.960313i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.78249e6 | − | 2.18382e6i | −0.540517 | − | 0.312068i | 0.204772 | − | 0.978810i | \(-0.434355\pi\) |
−0.745288 | + | 0.666742i | \(0.767688\pi\) | |||||||
\(548\) | −6.70011e6 | − | 4.71592e6i | −0.953083 | − | 0.670834i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.67391e6 | − | 2.42583e6i | 0.658831 | − | 0.341943i | ||||
\(551\) | −2.94957e6 | + | 5.10881e6i | −0.413885 | + | 0.716870i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.19921e6 | − | 5.54120e6i | −0.444867 | − | 0.770532i | ||||
\(554\) | 1.61279e6 | + | 1.03023e6i | 0.223256 | + | 0.142614i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.05372e6 | + | 488224.i | −0.144556 | + | 0.0669780i | ||||
\(557\) | − | 4.46009e6i | − | 0.609124i | −0.952493 | − | 0.304562i | \(-0.901490\pi\) | ||
0.952493 | − | 0.304562i | \(-0.0985100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.22281e6i | 0.436219i | ||||||||
\(560\) | 9.96516e6 | + | 1.80741e6i | 1.34281 | + | 0.243549i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.87389e6 | − | 4.49896e6i | 0.383821 | − | 0.600857i | ||||
\(563\) | −5.22200e6 | − | 9.04476e6i | −0.694330 | − | 1.20261i | −0.970406 | − | 0.241478i | \(-0.922368\pi\) |
0.276077 | − | 0.961136i | \(-0.410966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.63841e6 | − | 2.83781e6i | 0.215924 | − | 0.373992i | ||||
\(566\) | −5.77778e6 | − | 1.11322e7i | −0.758089 | − | 1.46063i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −881801. | + | 6.51330e6i | −0.114683 | + | 0.847091i | ||||
\(569\) | −2.55116e6 | − | 1.47291e6i | −0.330337 | − | 0.190720i | 0.325654 | − | 0.945489i | \(-0.394416\pi\) |
−0.655991 | + | 0.754769i | \(0.727749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −199833. | + | 115373.i | −0.0256493 | + | 0.0148086i | −0.512770 | − | 0.858526i | \(-0.671381\pi\) |
0.487121 | + | 0.873335i | \(0.338047\pi\) | |||||||
\(572\) | −3.76069e6 | − | 338284.i | −0.480594 | − | 0.0432306i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 51189.5 | − | 1.14044e6i | 0.00648487 | − | 0.144475i | ||||
\(575\) | −1.07533e6 | −0.135635 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.42964e6 | 0.553897 | 0.276949 | − | 0.960885i | \(-0.410677\pi\) | ||||
0.276949 | + | 0.960885i | \(0.410677\pi\) | |||||||
\(578\) | 28839.5 | − | 642511.i | 0.00359061 | − | 0.0799947i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.99777e6 | − | 629467.i | −0.863754 | − | 0.0776967i | ||||
\(581\) | −7.02986e6 | + | 4.05869e6i | −0.863985 | + | 0.498822i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 790822. | + | 456582.i | 0.0963624 | + | 0.0556349i | ||||
\(584\) | −927787. | + | 6.85297e6i | −0.112568 | + | 0.831470i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.56935e6 | − | 6.87717e6i | −0.429383 | − | 0.827305i | ||||
\(587\) | 509131. | − | 881841.i | 0.0609866 | − | 0.105632i | −0.833920 | − | 0.551885i | \(-0.813909\pi\) |
0.894907 | + | 0.446253i | \(0.147242\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.69915e6 | − | 4.67507e6i | −0.320582 | − | 0.555265i | ||||
\(590\) | −9.91848e6 | + | 1.55270e7i | −1.17305 | + | 1.83636i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 449002. | + | 81436.6i | 0.0526555 | + | 0.00955026i | ||||
\(593\) | − | 1.12943e6i | − | 0.131893i | −0.997823 | − | 0.0659466i | \(-0.978993\pi\) | ||
0.997823 | − | 0.0659466i | \(-0.0210067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.22479e7i | 1.41831i | ||||||||
\(596\) | −1.37868e7 | + | 6.38792e6i | −1.58982 | + | 0.736621i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 649793. | + | 415081.i | 0.0743057 | + | 0.0474657i | ||||
\(599\) | −6.98600e6 | − | 1.21001e7i | −0.795539 | − | 1.37791i | −0.922496 | − | 0.386006i | \(-0.873855\pi\) |
0.126958 | − | 0.991908i | \(-0.459479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.90974e6 | + | 1.37001e7i | −0.893256 | + | 1.54717i | −0.0573087 | + | 0.998357i | \(0.518252\pi\) |
−0.835948 | + | 0.548809i | \(0.815081\pi\) | |||||||
\(602\) | 2.04007e6 | − | 1.05882e6i | 0.229432 | − | 0.119078i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.14167e6 | − | 2.21128e6i | −0.350403 | − | 0.246634i | ||||
\(605\) | −1.17719e7 | − | 6.79652e6i | −1.30755 | − | 0.754915i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.40500e6 | + | 2.54323e6i | −0.485259 | + | 0.280165i | −0.722606 | − | 0.691261i | \(-0.757056\pi\) |
0.237346 | + | 0.971425i | \(0.423722\pi\) | |||||||
\(608\) | 1.47746e7 | + | 3.37032e6i | 1.62091 | + | 0.369753i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.61969e7 | − | 727007.i | −1.76241 | − | 0.0791068i | ||||
\(611\) | 5.70288e6 | 0.618004 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.62634e6 | −0.282293 | −0.141147 | − | 0.989989i | \(-0.545079\pi\) | ||||
−0.141147 | + | 0.989989i | \(0.545079\pi\) | |||||||
\(614\) | 4.57306e6 | + | 205264.i | 0.489537 | + | 0.0219732i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.02141e6 | + | 2.49169e6i | 0.108454 | + | 0.264571i | ||||
\(617\) | 8.21879e6 | − | 4.74512e6i | 0.869150 | − | 0.501804i | 0.00208438 | − | 0.999998i | \(-0.499337\pi\) |
0.867066 | + | 0.498194i | \(0.166003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.66128e6 | + | 1.53649e6i | 0.279167 | + | 0.161177i | 0.633046 | − | 0.774114i | \(-0.281804\pi\) |
−0.353879 | + | 0.935291i | \(0.615138\pi\) | |||||||
\(620\) | 3.70069e6 | − | 5.25773e6i | 0.386637 | − | 0.549312i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −356720. | + | 185143.i | −0.0369702 | + | 0.0191881i | ||||
\(623\) | −4.90627e6 | + | 8.49790e6i | −0.506443 | + | 0.877186i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.38553e6 | − | 9.32800e6i | −0.551478 | − | 0.955188i | ||||
\(626\) | 8.52132e6 | + | 5.44333e6i | 0.869102 | + | 0.555174i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.99414e6 | + | 6.46216e6i | 0.302952 | + | 0.653850i | ||||
\(629\) | 551856.i | 0.0556159i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.80779e6i | − | 0.280731i | −0.990100 | − | 0.140366i | \(-0.955172\pi\) | ||
0.990100 | − | 0.140366i | \(-0.0448278\pi\) | |||||||
\(632\) | 6.97474e6 | − | 9.02097e6i | 0.694601 | − | 0.898381i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00973e6 | + | 1.58070e6i | −0.0997662 | + | 0.156180i | ||||
\(635\) | 357459. | + | 619137.i | 0.0351796 | + | 0.0609329i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.61423e6 | − | 4.52798e6i | 0.255267 | − | 0.442136i | ||||
\(638\) | −860607. | − | 1.65816e6i | −0.0837053 | − | 0.161277i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.75561e6 | + | 1.76539e7i | 0.362436 | + | 1.70369i | ||||
\(641\) | −8.96448e6 | − | 5.17564e6i | −0.861747 | − | 0.497530i | 0.00284982 | − | 0.999996i | \(-0.499093\pi\) |
−0.864597 | + | 0.502466i | \(0.832426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.22376e6 | + | 2.43859e6i | −0.402876 | + | 0.232601i | −0.687724 | − | 0.725972i | \(-0.741390\pi\) |
0.284848 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(644\) | 49266.6 | − | 547696.i | 0.00468099 | − | 0.0520385i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −821772. | + | 1.83081e7i | −0.0774765 | + | 1.72609i | ||||
\(647\) | 9.58644e6 | 0.900319 | 0.450160 | − | 0.892948i | \(-0.351367\pi\) | ||||
0.450160 | + | 0.892948i | \(0.351367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.89900e6 | −0.456557 | ||||||||
\(650\) | −1.29893e6 | + | 2.89387e7i | −0.120588 | + | 2.68656i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.40413e6 | + | 1.56097e7i | −0.129356 | + | 1.43805i | ||||
\(653\) | 3.50930e6 | − | 2.02609e6i | 0.322060 | − | 0.185942i | −0.330250 | − | 0.943893i | \(-0.607133\pi\) |
0.652311 | + | 0.757952i | \(0.273800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.76854e7 | + | 1.02107e7i | 1.61069 | + | 0.929934i | ||||
\(656\) | 1.91515e6 | − | 686474.i | 0.173758 | − | 0.0622823i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.87363e6 | − | 3.60997e6i | −0.168702 | − | 0.325042i | ||||
\(659\) | −3.07530e6 | + | 5.32657e6i | −0.275850 | + | 0.477787i | −0.970349 | − | 0.241707i | \(-0.922293\pi\) |
0.694499 | + | 0.719494i | \(0.255626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.19391e6 | + | 2.06791e6i | 0.106284 | + | 0.184089i | 0.914262 | − | 0.405124i | \(-0.132771\pi\) |
−0.807978 | + | 0.589212i | \(0.799438\pi\) | |||||||
\(662\) | 7.23798e6 | − | 1.13308e7i | 0.641908 | − | 1.00488i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.14445e7 | − | 8.84853e6i | −1.00734 | − | 0.778844i | ||||
\(665\) | − | 2.58744e7i | − | 2.26890i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 381493.i | 0.0332026i | ||||||||
\(668\) | 1.15790e6 | + | 2.49905e6i | 0.100399 | + | 0.216688i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.24935e7 | − | 7.98071e6i | −1.07522 | − | 0.686838i | ||||
\(671\) | −2.15550e6 | − | 3.73344e6i | −0.184817 | − | 0.320113i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.33582e6 | − | 9.24191e6i | 0.454113 | − | 0.786546i | −0.544524 | − | 0.838745i | \(-0.683290\pi\) |
0.998637 | + | 0.0521992i | \(0.0166231\pi\) | |||||||
\(674\) | 632469. | − | 328261.i | 0.0536278 | − | 0.0278336i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.11670e6 | − | 7.26951e6i | 0.430649 | − | 0.611841i | ||||
\(677\) | 1.20806e7 | + | 6.97471e6i | 1.01301 | + | 0.584864i | 0.912073 | − | 0.410029i | \(-0.134481\pi\) |
0.100941 | + | 0.994892i | \(0.467815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.46351e6 | − | 844957.i | 0.121821 | − | 0.0703332i | ||||
\(680\) | −2.01964e7 | + | 8.27899e6i | −1.67495 | + | 0.686602i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.70786e6 | + | 76658.3i | 0.140602 | + | 0.00631100i | ||||
\(683\) | 1.34097e7 | 1.09994 | 0.549968 | − | 0.835186i | \(-0.314640\pi\) | ||||
0.549968 | + | 0.835186i | \(0.314640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.49311e7 | −2.03009 | ||||||||
\(686\) | −1.33726e7 | − | 600237.i | −1.08494 | − | 0.0486981i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.12495e6 | + | 2.64829e6i | 0.251694 | + | 0.213302i | ||||
\(689\) | −4.35030e6 | + | 2.51165e6i | −0.349118 | + | 0.201563i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.05848e6 | − | 611111.i | −0.0843307 | − | 0.0486883i | 0.457242 | − | 0.889342i | \(-0.348837\pi\) |
−0.541572 | + | 0.840654i | \(0.682171\pi\) | |||||||
\(692\) | −5.14055e6 | − | 3.61821e6i | −0.408079 | − | 0.287229i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.79757e6 | − | 3.00902e6i | 0.456927 | − | 0.237152i | ||||
\(695\) | −1.76686e6 | + | 3.06030e6i | −0.138753 | + | 0.240326i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.23018e6 | + | 2.13074e6i | 0.0959154 | + | 0.166130i | ||||
\(698\) | −1.73789e7 | − | 1.11015e7i | −1.35015 | − | 0.862465i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.87452e7 | − | 8.68532e6i | 1.44592 | − | 0.669948i | ||||
\(701\) | 1.38380e7i | 1.06360i | 0.846870 | + | 0.531801i | \(0.178484\pi\) | ||||
−0.846870 | + | 0.531801i | \(0.821516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.16583e6i | − | 0.0889704i | ||||||
\(704\) | −3.41830e6 | + | 3.36853e6i | −0.259943 | + | 0.256158i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.48249e6 | − | 5.45170e6i | 0.262953 | − | 0.411643i | ||||
\(707\) | 1.47660e6 | + | 2.55754e6i | 0.111100 | + | 0.192430i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.12116e7 | − | 1.94191e7i | 0.837632 | − | 1.45082i | −0.0542381 | − | 0.998528i | \(-0.517273\pi\) |
0.891870 | − | 0.452292i | \(-0.149394\pi\) | |||||||
\(710\) | 9.21314e6 | + | 1.77512e7i | 0.685901 | + | 1.32155i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.73292e7 | − | 2.34610e6i | −1.28108 | − | 0.173439i | ||||
\(713\) | −302333. | − | 174552.i | −0.0222722 | − | 0.0128588i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.95008e6 | + | 5.74468e6i | −0.727883 | + | 0.420243i | ||||
\(716\) | −1.11186e7 | − | 1.00014e6i | −0.810527 | − | 0.0729088i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28212.2 | − | 628536.i | 0.00204233 | − | 0.0455008i | ||||
\(719\) | −1.71887e7 | −1.24000 | −0.619999 | − | 0.784603i | \(-0.712867\pi\) | ||||
−0.619999 | + | 0.784603i | \(0.712867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.55048e7 | 1.11078 | ||||||||
\(722\) | 1.10796e6 | − | 2.46841e7i | 0.0791009 | − | 1.76228i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.12706e6 | + | 101382.i | 0.0799100 | + | 0.00718810i | ||||
\(725\) | −1.24122e7 | + | 7.16620e6i | −0.877010 | + | 0.506342i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12449e7 | − | 6.49227e6i | −0.789081 | − | 0.455576i | 0.0505582 | − | 0.998721i | \(-0.483900\pi\) |
−0.839639 | + | 0.543145i | \(0.817233\pi\) | |||||||
\(728\) | −1.46798e7 | − | 1.98742e6i | −1.02658 | − | 0.138983i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.69361e6 | + | 1.86769e7i | 0.673253 | + | 1.29718i | ||||
\(731\) | −2.47685e6 | + | 4.29002e6i | −0.171437 | + | 0.296938i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.50187e6 | + | 6.06542e6i | 0.240736 | + | 0.416967i | 0.960924 | − | 0.276812i | \(-0.0892780\pi\) |
−0.720188 | + | 0.693779i | \(0.755945\pi\) | |||||||
\(734\) | 1.32702e7 | − | 2.07740e7i | 0.909154 | − | 1.42324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 936434. | − | 288977.i | 0.0637210 | − | 0.0196639i | ||||
\(737\) | − | 3.94188e6i | − | 0.267322i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.74291e7i | − | 1.84757i | −0.382917 | − | 0.923783i | \(-0.625080\pi\) | ||
0.382917 | − | 0.923783i | \(-0.374920\pi\) | |||||||
\(740\) | 1.25986e6 | − | 583739.i | 0.0845755 | − | 0.0391868i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.01915e6 | + | 1.92860e6i | 0.201315 | + | 0.128598i | ||||
\(743\) | 3.05209e6 | + | 5.28638e6i | 0.202827 | + | 0.351306i | 0.949438 | − | 0.313954i | \(-0.101654\pi\) |
−0.746611 | + | 0.665260i | \(0.768320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.31176e7 | + | 4.00409e7i | −1.52599 | + | 2.64310i | ||||
\(746\) | 1.35527e7 | − | 7.03404e6i | 0.891617 | − | 0.462762i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.74605e6 | − | 3.34054e6i | −0.310155 | − | 0.218304i | ||||
\(749\) | 1.40774e7 | + | 8.12760e6i | 0.916893 | + | 0.529368i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.95951e7 | − | 1.13132e7i | 1.26779 | − | 0.731958i | 0.293219 | − | 0.956045i | \(-0.405274\pi\) |
0.974569 | + | 0.224088i | \(0.0719402\pi\) | |||||||
\(752\) | 4.68625e6 | − | 5.52972e6i | 0.302190 | − | 0.356581i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.02665e7 | + | 460820.i | 0.657651 | + | 0.0295191i | ||||
\(755\) | −1.16901e7 | −0.746366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.79038e7 | 1.76980 | 0.884900 | − | 0.465781i | \(-0.154226\pi\) | ||||
0.884900 | + | 0.465781i | \(0.154226\pi\) | |||||||
\(758\) | 1.16032e7 | + | 520819.i | 0.733511 | + | 0.0329241i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.26660e7 | − | 1.74898e7i | 2.67946 | − | 1.09838i | ||||
\(761\) | −8.70509e6 | + | 5.02588e6i | −0.544893 | + | 0.314594i | −0.747060 | − | 0.664757i | \(-0.768535\pi\) |
0.202166 | + | 0.979351i | \(0.435202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20315e7 | − | 6.94641e6i | −0.748186 | − | 0.431966i | ||||
\(764\) | 1.60185e7 | − | 2.27582e7i | 0.992864 | − | 1.41060i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.73407e7 | + | 1.41902e7i | −1.68360 | + | 0.873812i | ||||
\(767\) | 1.34747e7 | − | 2.33388e7i | 0.827046 | − | 1.43249i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.07441e7 | + | 1.86093e7i | 0.655169 | + | 1.13479i | 0.981851 | + | 0.189652i | \(0.0607361\pi\) |
−0.326682 | + | 0.945134i | \(0.605931\pi\) | |||||||
\(770\) | 6.90545e6 | + | 4.41113e6i | 0.419725 | + | 0.268116i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14774e7 | − | 2.47712e7i | −0.693105 | − | 1.49590i | ||||
\(773\) | 3.11372e7i | 1.87426i | 0.348977 | + | 0.937131i | \(0.386529\pi\) | ||||
−0.348977 | + | 0.937131i | \(0.613471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.31156e7i | − | 0.784392i | ||||||
\(776\) | 2.38257e6 | + | 1.84213e6i | 0.142034 | + | 0.109816i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.84612e6 | − | 1.38482e7i | 0.523967 | − | 0.820249i | ||||
\(779\) | −2.59883e6 | − | 4.50131e6i | −0.153439 | − | 0.265763i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.65891e6 | + | 4.60537e6i | −0.155983 | + | 0.270170i | ||||
\(782\) | 545964. | + | 1.05192e6i | 0.0319262 | + | 0.0615131i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.24229e6 | − | 6.25565e6i | −0.130287 | − | 0.363481i | ||||
\(785\) | 1.87680e7 | + | 1.08357e7i | 1.08703 | + | 0.627599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.67812e7 | + | 1.54621e7i | −1.54132 | + | 0.889883i | −0.542567 | + | 0.840012i | \(0.682548\pi\) |
−0.998756 | + | 0.0498707i | \(0.984119\pi\) | |||||||
\(788\) | 744939. | − | 8.28148e6i | 0.0427371 | − | 0.475108i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55583e6 | − | 3.46621e7i | 0.0886939 | − | 1.97600i | ||||
\(791\) | 3.41829e6 | 0.194253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.37148e7 | 1.33917 | ||||||||
\(794\) | 405369. | − | 9.03115e6i | 0.0228191 | − | 0.508384i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −757950. | + | 8.42612e6i | −0.0423992 | + | 0.471352i | ||||
\(797\) | 3.04761e7 | − | 1.75954e7i | 1.69947 | − | 0.981190i | 0.753213 | − | 0.657777i | \(-0.228503\pi\) |
0.946258 | − | 0.323413i | \(-0.104830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.59136e6 | + | 4.38287e6i | 0.420681 | + | 0.242880i | ||||
\(800\) | 2.69927e7 | + | 2.50394e7i | 1.49115 | + | 1.38324i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.47542e6 | + | 8.62291e6i | 0.245696 | + | 0.473389i | ||||
\(803\) | −2.79757e6 | + | 4.84554e6i | −0.153106 | + | 0.265188i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −836638. | − | 1.44910e6i | −0.0455038 | − | 0.0788150i | ||||
\(806\) | −5.06266e6 | + | 7.92539e6i | −0.274499 | + | 0.429717i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.21919e6 | + | 4.16363e6i | −0.173468 | + | 0.224359i | ||||
\(809\) | 1.11312e7i | 0.597960i | 0.954259 | + | 0.298980i | \(0.0966463\pi\) | ||||
−0.954259 | + | 0.298980i | \(0.903354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.50552e7i | 1.33766i | 0.743416 | + | 0.668829i | \(0.233204\pi\) | ||||
−0.743416 | + | 0.668829i | \(0.766796\pi\) | |||||||
\(812\) | −3.08128e6 | − | 6.65021e6i | −0.163999 | − | 0.353953i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 311140. | + | 198753.i | 0.0164587 | + | 0.0105136i | ||||
\(815\) | 2.38447e7 | + | 4.13002e7i | 1.25747 | + | 2.17800i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.23247e6 | − | 9.06291e6i | 0.274253 | − | 0.475021i | ||||
\(818\) | −2.76146e7 | + | 1.43324e7i | −1.44297 | + | 0.748920i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.56314e6 | − | 5.06231e6i | 0.185054 | − | 0.262914i | ||||
\(821\) | 5.80988e6 | + | 3.35434e6i | 0.300822 | + | 0.173680i | 0.642812 | − | 0.766024i | \(-0.277768\pi\) |
−0.341990 | + | 0.939704i | \(0.611101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.35383e7 | + | 1.35898e7i | −1.21136 | + | 0.699382i | −0.963057 | − | 0.269299i | \(-0.913208\pi\) |
−0.248308 | + | 0.968681i | \(0.579875\pi\) | |||||||
\(824\) | 1.04805e7 | + | 2.55669e7i | 0.537728 | + | 1.31177i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.92007e7 | − | 861833.i | −0.979188 | − | 0.0439514i | ||||
\(827\) | −8.21918e6 | −0.417893 | −0.208946 | − | 0.977927i | \(-0.567003\pi\) | ||||
−0.208946 | + | 0.977927i | \(0.567003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.64615e7 | −1.33730 | −0.668649 | − | 0.743578i | \(-0.733127\pi\) | ||||
−0.668649 | + | 0.743578i | \(0.733127\pi\) | |||||||
\(830\) | −4.39741e7 | − | 1.97381e6i | −2.21566 | − | 0.0994510i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.64564e6 | − | 2.55499e7i | −0.332834 | − | 1.27962i | ||||
\(833\) | 6.95984e6 | − | 4.01827e6i | 0.347526 | − | 0.200644i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.25797e6 | + | 4.19039e6i | 0.360246 | + | 0.207988i | ||||
\(836\) | 1.00263e7 | + | 7.05707e6i | 0.496163 | + | 0.349228i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.23482e7 | − | 1.67892e7i | 1.59126 | − | 0.825886i | ||||
\(839\) | −1.49153e6 | + | 2.58341e6i | −0.0731522 | + | 0.126703i | −0.900281 | − | 0.435309i | \(-0.856639\pi\) |
0.827129 | + | 0.562012i | \(0.189973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.71324e6 | − | 1.33597e7i | −0.376051 | − | 0.651339i | ||||
\(842\) | −1.60859e7 | − | 1.02755e7i | −0.781925 | − | 0.499486i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.98271e7 | − | 1.38199e7i | 1.44130 | − | 0.667805i | ||||
\(845\) | − | 2.70498e7i | − | 1.30323i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.41799e7i | − | 0.679148i | ||||||
\(848\) | −1.13940e6 | + | 6.28212e6i | −0.0544112 | + | 0.299997i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.39696e7 | + | 3.75234e7i | −1.13792 | + | 1.78137i | ||||
\(851\) | −37696.5 | − | 65292.3i | −0.00178434 | − | 0.00309057i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.05595e7 | + | 1.82895e7i | −0.496900 | + | 0.860656i | −0.999994 | − | 0.00357565i | \(-0.998862\pi\) |
0.503093 | + | 0.864232i | \(0.332195\pi\) | |||||||
\(854\) | −7.79129e6 | − | 1.50117e7i | −0.365565 | − | 0.704344i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.88650e6 | + | 2.87071e7i | −0.181290 | + | 1.33907i | ||||
\(857\) | 449133. | + | 259307.i | 0.0208893 | + | 0.0120604i | 0.510408 | − | 0.859932i | \(-0.329494\pi\) |
−0.489519 | + | 0.871993i | \(0.662828\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.14050e7 | − | 1.23582e7i | 0.989767 | − | 0.571442i | 0.0845625 | − | 0.996418i | \(-0.473051\pi\) |
0.905205 | + | 0.424976i | \(0.139717\pi\) | |||||||
\(860\) | 1.24139e7 | + | 1.11666e6i | 0.572350 | + | 0.0514843i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 429209. | − | 9.56228e6i | 0.0196743 | − | 0.438322i | ||||
\(863\) | −1.06376e7 | −0.486202 | −0.243101 | − | 0.970001i | \(-0.578165\pi\) | ||||
−0.243101 | + | 0.970001i | \(0.578165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.91280e7 | −0.869217 | ||||||||
\(866\) | 848061. | − | 1.88938e7i | 0.0384266 | − | 0.856102i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.68014e6 | + | 600894.i | 0.300944 | + | 0.0270707i | ||||
\(869\) | 7.98974e6 | − | 4.61288e6i | 0.358908 | − | 0.207216i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.87791e7 | + | 1.08421e7i | 0.838744 | + | 0.484249i | ||||
\(872\) | 3.32167e6 | − | 2.45350e7i | 0.147933 | − | 1.09269i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.15338e6 | − | 2.22225e6i | −0.0510732 | − | 0.0984042i | ||||
\(875\) | 1.59781e7 | − | 2.76749e7i | 0.705514 | − | 1.22199i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.42674e6 | + | 1.45955e7i | 0.369965 | + | 0.640798i | 0.989560 | − | 0.144124i | \(-0.0460364\pi\) |
−0.619595 | + | 0.784922i | \(0.712703\pi\) | |||||||
\(878\) | −1.45058e7 | + | 2.27083e7i | −0.635047 | + | 0.994141i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.60606e6 | + | 1.43686e7i | −0.113443 | + | 0.625470i | ||||
\(881\) | − | 1.43365e6i | − | 0.0622305i | −0.999516 | − | 0.0311153i | \(-0.990094\pi\) | ||
0.999516 | − | 0.0311153i | \(-0.00990589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9.05105e6i | − | 0.390658i | −0.980738 | − | 0.195329i | \(-0.937422\pi\) | ||
0.980738 | − | 0.195329i | \(-0.0625775\pi\) | |||||||
\(884\) | 2.89683e7 | − | 1.34220e7i | 1.24679 | − | 0.577680i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.08943e7 | + | 1.33471e7i | 0.894218 | + | 0.571217i | ||||
\(887\) | −5.07142e6 | − | 8.78395e6i | −0.216431 | − | 0.374870i | 0.737283 | − | 0.675584i | \(-0.236108\pi\) |
−0.953714 | + | 0.300714i | \(0.902775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −372891. | + | 645867.i | −0.0158244 | + | 0.0274087i | ||||
\(890\) | −4.72285e7 | + | 2.45123e7i | −1.99862 | + | 1.03731i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.58615e7 | − | 1.11642e7i | −0.667470 | − | 0.469803i | ||||
\(893\) | −1.60372e7 | − | 9.25906e6i | −0.672975 | − | 0.388542i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.94177e7 | + | 1.69843e7i | −1.22758 | + | 0.708746i | ||||
\(896\) | −1.39900e7 | + | 1.26009e7i | −0.582165 | + | 0.524364i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.49312e7 | − | 670196.i | −0.617880 | − | 0.0277339i | ||||
\(899\) | −4.65299e6 | −0.192014 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.72119e6 | −0.316863 | ||||||||
\(902\) | 1.64438e6 | + | 73809.1i | 0.0672955 | + | 0.00302060i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.31060e6 | + | 5.63665e6i | 0.0940380 | + | 0.229403i | ||||
\(905\) | 2.98199e6 | − | 1.72165e6i | 0.121028 | − | 0.0698754i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.75879e7 | + | 1.59279e7i | 1.11353 | + | 0.642894i | 0.939740 | − | 0.341890i | \(-0.111067\pi\) |
0.173785 | + | 0.984784i | \(0.444400\pi\) | |||||||
\(908\) | −3.15150e6 | + | 4.47748e6i | −0.126854 | + | 0.180227i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00080e7 | + | 2.07647e7i | −1.60156 | + | 0.831233i | ||||
\(911\) | −1.33238e7 | + | 2.30775e7i | −0.531903 | + | 0.921283i | 0.467404 | + | 0.884044i | \(0.345189\pi\) |
−0.999306 | + | 0.0372385i | \(0.988144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.85214e6 | − | 1.01362e7i | −0.232348 | − | 0.402438i | ||||
\(914\) | 1.66063e7 | + | 1.06079e7i | 0.657517 | + | 0.420016i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.85391e7 | + | 4.00123e7i | 0.730045 | + | 1.57563i | ||||
\(917\) | 2.13030e7i | 0.836601i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.74009e7i | 1.07023i | 0.844780 | + | 0.535114i | \(0.179731\pi\) | ||||
−0.844780 | + | 0.535114i | \(0.820269\pi\) | |||||||
\(920\) | 1.82399e6 | − | 2.35911e6i | 0.0710482 | − | 0.0918922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.03340e7 | − | 1.61774e7i | 0.400350 | − | 0.626732i | ||||
\(923\) | −1.46266e7 | − | 2.53341e7i | −0.565119 | − | 0.978815i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.41623e6 | − | 2.45298e6i | 0.0544226 | − | 0.0942627i | ||||
\(926\) | −504540. | − | 972111.i | −0.0193361 | − | 0.0372553i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.88319e6 | − | 9.57614e6i | 0.338609 | − | 0.365023i | ||||
\(929\) | −6.04164e6 | − | 3.48814e6i | −0.229676 | − | 0.132604i | 0.380747 | − | 0.924679i | \(-0.375667\pi\) |
−0.610423 | + | 0.792076i | \(0.709000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47030e7 | + | 8.48881e6i | −0.555947 | + | 0.320976i | ||||
\(932\) | −3.92462e6 | + | 4.36300e7i | −0.147999 | + | 1.64530i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 822877. | − | 1.83328e7i | 0.0308651 | − | 0.687640i | ||||
\(935\) | −1.76600e7 | −0.660636 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.72933e7 | 1.75975 | 0.879874 | − | 0.475207i | \(-0.157627\pi\) | ||||
0.879874 | + | 0.475207i | \(0.157627\pi\) | |||||||
\(938\) | 693457. | − | 1.54494e7i | 0.0257343 | − | 0.573331i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.97597e6 | − | 2.19669e7i | 0.0729392 | − | 0.810864i | ||||
\(941\) | −1.33836e7 | + | 7.72703e6i | −0.492719 | + | 0.284471i | −0.725702 | − | 0.688009i | \(-0.758485\pi\) |
0.232983 | + | 0.972481i | \(0.425151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −291096. | − | 168065.i | −0.0106600 | − | 0.00615456i | ||||
\(944\) | −1.15576e7 | − | 3.22438e7i | −0.422121 | − | 1.17765i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.52670e6 | + | 2.94153e6i | 0.0554658 | + | 0.106867i | ||||
\(947\) | −1.20235e7 | + | 2.08253e7i | −0.435668 | + | 0.754600i | −0.997350 | − | 0.0727539i | \(-0.976821\pi\) |
0.561682 | + | 0.827353i | \(0.310155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.53894e7 | − | 2.66553e7i | −0.554698 | − | 0.960765i | ||||
\(950\) | 5.06370e7 | − | 7.92702e7i | 1.82037 | − | 2.84971i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.80135e7 | − | 1.39275e7i | −0.644179 | − | 0.498059i | ||||
\(953\) | 5.61504e6i | 0.200272i | 0.994974 | + | 0.100136i | \(0.0319278\pi\) | ||||
−0.994974 | + | 0.100136i | \(0.968072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.46833e7i | − | 3.00462i | ||||||
\(956\) | 4.18261e6 | + | 9.02719e6i | 0.148014 | + | 0.319454i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.91579e7 | − | 2.50137e7i | −1.37850 | − | 0.880569i | ||||
\(959\) | −1.30037e7 | − | 2.25231e7i | −0.456584 | − | 0.790827i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.21856e7 | + | 2.11061e7i | −0.425636 | + | 0.737223i | ||||
\(962\) | −1.80265e6 | + | 935600.i | −0.0628019 | + | 0.0325951i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.22625e6 | + | 1.02666e7i | −0.250449 | + | 0.355824i | ||||
\(965\) | −7.19427e7 | − | 4.15361e7i | −2.48696 | − | 1.43585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −183562. | + | 105980.i | −0.00631272 | + | 0.00364465i | −0.503153 | − | 0.864197i | \(-0.667827\pi\) |
0.496840 | + | 0.867842i | \(0.334493\pi\) | |||||||
\(968\) | 2.33822e7 | − | 9.58492e6i | 0.802041 | − | 0.328776i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.15474e6 | + | 410916.i | 0.312404 | + | 0.0140225i | ||||
\(971\) | 4.76645e7 | 1.62236 | 0.811180 | − | 0.584797i | \(-0.198826\pi\) | ||||
0.811180 | + | 0.584797i | \(0.198826\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.68629e6 | −0.124827 | ||||||||
\(974\) | −9.26262e6 | − | 415758.i | −0.312850 | − | 0.0140425i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.94873e7 | − | 2.29947e7i | 0.654826 | − | 0.772688i | ||||
\(977\) | 3.11073e6 | − | 1.79598e6i | 0.104262 | − | 0.0601956i | −0.446962 | − | 0.894553i | \(-0.647494\pi\) |
0.551224 | + | 0.834357i | \(0.314161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22530e7 | − | 7.07424e6i | −0.408586 | − | 0.235897i | ||||
\(980\) | −1.65355e7 | − | 1.16386e7i | −0.549986 | − | 0.387111i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.04067e7 | + | 1.05914e7i | −0.675297 | + | 0.350489i | ||||
\(983\) | −1.09466e7 | + | 1.89600e7i | −0.361322 | + | 0.625827i | −0.988179 | − | 0.153307i | \(-0.951008\pi\) |
0.626857 | + | 0.779134i | \(0.284341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.26505e7 | − | 2.19112e7i | −0.415447 | − | 0.719575i | ||||
\(986\) | 1.33121e7 | + | 8.50364e6i | 0.436068 | + | 0.278556i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.11971e7 | + | 2.83547e7i | −1.99452 | + | 0.924131i | ||||
\(989\) | − | 676760.i | − | 0.0220011i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.07362e7i | 0.670725i | 0.942089 | + | 0.335362i | \(0.108859\pi\) | ||||
−0.942089 | + | 0.335362i | \(0.891141\pi\) | |||||||
\(992\) | 3.52459e6 | + | 1.14215e7i | 0.113718 | + | 0.368505i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.12313e7 | + | 1.75821e7i | −0.360547 | + | 0.564422i | ||||
\(995\) | 1.28714e7 | + | 2.22939e7i | 0.412162 | + | 0.713886i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.72454e6 | − | 1.68434e7i | 0.309836 | − | 0.536651i | −0.668491 | − | 0.743721i | \(-0.733059\pi\) |
0.978326 | + | 0.207070i | \(0.0663927\pi\) | |||||||
\(998\) | 8.79241e6 | + | 1.69406e7i | 0.279436 | + | 0.538397i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.h.a.35.13 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.16 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.23 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.6 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.23 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.6 | ✓ | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.13 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.16 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.6 | ✓ | 56 | 12.11 | even | 2 | ||
36.6.h.a.11.16 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.6 | yes | 56 | 9.4 | even | 3 | ||
36.6.h.a.23.16 | yes | 56 | 36.31 | odd | 6 | ||
108.6.h.a.35.13 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.35.23 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.13 | 56 | 36.23 | even | 6 | inner | ||
108.6.h.a.71.23 | 56 | 9.5 | odd | 6 | inner |