Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), 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: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 11^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.7 | ||
Root | \(-17.1892i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.7.d.b.43.4 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | − | 4.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 20.1892i | 0.747749i | 0.927479 | + | 0.373875i | \(0.121971\pi\) | ||||
−0.927479 | + | 0.373875i | \(0.878029\pi\) | |||||||
\(4\) | 32.0000i | 0.500000i | ||||||||
\(5\) | 9.27541 | − | 9.27541i | 0.0742032 | − | 0.0742032i | −0.669031 | − | 0.743234i | \(-0.733291\pi\) |
0.743234 | + | 0.669031i | \(0.233291\pi\) | |||||||
\(6\) | 80.7569 | − | 80.7569i | 0.373875 | − | 0.373875i | ||||
\(7\) | 8.30790 | 0.0242213 | 0.0121106 | − | 0.999927i | \(-0.496145\pi\) | ||||
0.0121106 | + | 0.999927i | \(0.496145\pi\) | |||||||
\(8\) | 128.000 | − | 128.000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 321.395 | 0.440871 | ||||||||
\(10\) | −74.2032 | −0.0742032 | ||||||||
\(11\) | 243.820i | 0.183186i | 0.995797 | + | 0.0915929i | \(0.0291958\pi\) | ||||
−0.995797 | + | 0.0915929i | \(0.970804\pi\) | |||||||
\(12\) | −646.055 | −0.373875 | ||||||||
\(13\) | 1658.09 | − | 1658.09i | 0.754704 | − | 0.754704i | −0.220649 | − | 0.975353i | \(-0.570817\pi\) |
0.975353 | + | 0.220649i | \(0.0708175\pi\) | |||||||
\(14\) | −33.2316 | − | 33.2316i | −0.0121106 | − | 0.0121106i | ||||
\(15\) | 187.263 | + | 187.263i | 0.0554854 | + | 0.0554854i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | −6733.96 | + | 6733.96i | −1.37064 | + | 1.37064i | −0.511150 | + | 0.859492i | \(0.670780\pi\) |
−0.859492 | + | 0.511150i | \(0.829220\pi\) | |||||||
\(18\) | −1285.58 | − | 1285.58i | −0.220436 | − | 0.220436i | ||||
\(19\) | −2804.19 | + | 2804.19i | −0.408834 | + | 0.408834i | −0.881332 | − | 0.472498i | \(-0.843352\pi\) |
0.472498 | + | 0.881332i | \(0.343352\pi\) | |||||||
\(20\) | 296.813 | + | 296.813i | 0.0371016 | + | 0.0371016i | ||||
\(21\) | 167.730i | 0.0181114i | ||||||||
\(22\) | 975.281 | − | 975.281i | 0.0915929 | − | 0.0915929i | ||||
\(23\) | 4070.88 | − | 4070.88i | 0.334584 | − | 0.334584i | −0.519740 | − | 0.854324i | \(-0.673971\pi\) |
0.854324 | + | 0.519740i | \(0.173971\pi\) | |||||||
\(24\) | 2584.22 | + | 2584.22i | 0.186937 | + | 0.186937i | ||||
\(25\) | 15452.9i | 0.988988i | ||||||||
\(26\) | −13264.7 | −0.754704 | ||||||||
\(27\) | 21206.7i | 1.07741i | ||||||||
\(28\) | 265.853i | 0.0121106i | ||||||||
\(29\) | 29954.3 | + | 29954.3i | 1.22819 | + | 1.22819i | 0.964648 | + | 0.263542i | \(0.0848908\pi\) |
0.263542 | + | 0.964648i | \(0.415109\pi\) | |||||||
\(30\) | − | 1498.11i | − | 0.0554854i | ||||||
\(31\) | −4347.19 | − | 4347.19i | −0.145923 | − | 0.145923i | 0.630371 | − | 0.776294i | \(-0.282903\pi\) |
−0.776294 | + | 0.630371i | \(0.782903\pi\) | |||||||
\(32\) | 4096.00 | + | 4096.00i | 0.125000 | + | 0.125000i | ||||
\(33\) | −4922.54 | −0.136977 | ||||||||
\(34\) | 53871.7 | 1.37064 | ||||||||
\(35\) | 77.0591 | − | 77.0591i | 0.00179730 | − | 0.00179730i | ||||
\(36\) | 10284.6i | 0.220436i | ||||||||
\(37\) | −10586.5 | + | 49534.4i | −0.209001 | + | 0.977915i | ||||
\(38\) | 22433.5 | 0.408834 | ||||||||
\(39\) | 33475.5 | + | 33475.5i | 0.564330 | + | 0.564330i | ||||
\(40\) | − | 2374.50i | − | 0.0371016i | ||||||
\(41\) | − | 10298.7i | − | 0.149428i | −0.997205 | − | 0.0747139i | \(-0.976196\pi\) | ||
0.997205 | − | 0.0747139i | \(-0.0238044\pi\) | |||||||
\(42\) | 670.920 | − | 670.920i | 0.00905572 | − | 0.00905572i | ||||
\(43\) | −76826.5 | + | 76826.5i | −0.966286 | + | 0.966286i | −0.999450 | − | 0.0331642i | \(-0.989442\pi\) |
0.0331642 | + | 0.999450i | \(0.489442\pi\) | |||||||
\(44\) | −7802.25 | −0.0915929 | ||||||||
\(45\) | 2981.07 | − | 2981.07i | 0.0327141 | − | 0.0327141i | ||||
\(46\) | −32567.0 | −0.334584 | ||||||||
\(47\) | 124505. | 1.19920 | 0.599602 | − | 0.800299i | \(-0.295326\pi\) | ||||
0.599602 | + | 0.800299i | \(0.295326\pi\) | |||||||
\(48\) | − | 20673.8i | − | 0.186937i | ||||||
\(49\) | −117580. | −0.999413 | ||||||||
\(50\) | 61811.7 | − | 61811.7i | 0.494494 | − | 0.494494i | ||||
\(51\) | −135953. | − | 135953.i | −1.02490 | − | 1.02490i | ||||
\(52\) | 53058.7 | + | 53058.7i | 0.377352 | + | 0.377352i | ||||
\(53\) | −82881.1 | −0.556708 | −0.278354 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278354 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(54\) | 84826.7 | − | 84826.7i | 0.538705 | − | 0.538705i | ||||
\(55\) | 2261.53 | + | 2261.53i | 0.0135930 | + | 0.0135930i | ||||
\(56\) | 1063.41 | − | 1063.41i | 0.00605532 | − | 0.00605532i | ||||
\(57\) | −56614.4 | − | 56614.4i | −0.305705 | − | 0.305705i | ||||
\(58\) | − | 239635.i | − | 1.22819i | ||||||
\(59\) | −144216. | + | 144216.i | −0.702192 | + | 0.702192i | −0.964881 | − | 0.262688i | \(-0.915391\pi\) |
0.262688 | + | 0.964881i | \(0.415391\pi\) | |||||||
\(60\) | −5992.43 | + | 5992.43i | −0.0277427 | + | 0.0277427i | ||||
\(61\) | −70415.2 | − | 70415.2i | −0.310225 | − | 0.310225i | 0.534772 | − | 0.844997i | \(-0.320398\pi\) |
−0.844997 | + | 0.534772i | \(0.820398\pi\) | |||||||
\(62\) | 34777.6i | 0.145923i | ||||||||
\(63\) | 2670.12 | 0.0106785 | ||||||||
\(64\) | − | 32768.0i | − | 0.125000i | ||||||
\(65\) | − | 30758.8i | − | 0.112003i | ||||||
\(66\) | 19690.2 | + | 19690.2i | 0.0684885 | + | 0.0684885i | ||||
\(67\) | − | 483835.i | − | 1.60869i | −0.594161 | − | 0.804346i | \(-0.702516\pi\) | ||
0.594161 | − | 0.804346i | \(-0.297484\pi\) | |||||||
\(68\) | −215487. | − | 215487.i | −0.685321 | − | 0.685321i | ||||
\(69\) | 82187.9 | + | 82187.9i | 0.250185 | + | 0.250185i | ||||
\(70\) | −616.473 | −0.00179730 | ||||||||
\(71\) | 172911. | 0.483112 | 0.241556 | − | 0.970387i | \(-0.422342\pi\) | ||||
0.241556 | + | 0.970387i | \(0.422342\pi\) | |||||||
\(72\) | 41138.6 | − | 41138.6i | 0.110218 | − | 0.110218i | ||||
\(73\) | 526876.i | 1.35438i | 0.735810 | + | 0.677189i | \(0.236802\pi\) | ||||
−0.735810 | + | 0.677189i | \(0.763198\pi\) | |||||||
\(74\) | 240483. | − | 155791.i | 0.593458 | − | 0.384457i | ||||
\(75\) | −311983. | −0.739515 | ||||||||
\(76\) | −89734.1 | − | 89734.1i | −0.204417 | − | 0.204417i | ||||
\(77\) | 2025.63i | 0.00443699i | ||||||||
\(78\) | − | 267804.i | − | 0.564330i | ||||||
\(79\) | 616752. | − | 616752.i | 1.25092 | − | 1.25092i | 0.295612 | − | 0.955308i | \(-0.404477\pi\) |
0.955308 | − | 0.295612i | \(-0.0955234\pi\) | |||||||
\(80\) | −9498.02 | + | 9498.02i | −0.0185508 | + | 0.0185508i | ||||
\(81\) | −193849. | −0.364762 | ||||||||
\(82\) | −41194.9 | + | 41194.9i | −0.0747139 | + | 0.0747139i | ||||
\(83\) | 359323. | 0.628422 | 0.314211 | − | 0.949353i | \(-0.398260\pi\) | ||||
0.314211 | + | 0.949353i | \(0.398260\pi\) | |||||||
\(84\) | −5367.36 | −0.00905572 | ||||||||
\(85\) | 124920.i | 0.203412i | ||||||||
\(86\) | 614612. | 0.966286 | ||||||||
\(87\) | −604755. | + | 604755.i | −0.918378 | + | 0.918378i | ||||
\(88\) | 31209.0 | + | 31209.0i | 0.0457964 | + | 0.0457964i | ||||
\(89\) | 312844. | + | 312844.i | 0.443770 | + | 0.443770i | 0.893277 | − | 0.449507i | \(-0.148400\pi\) |
−0.449507 | + | 0.893277i | \(0.648400\pi\) | |||||||
\(90\) | −23848.6 | −0.0327141 | ||||||||
\(91\) | 13775.2 | − | 13775.2i | 0.0182799 | − | 0.0182799i | ||||
\(92\) | 130268. | + | 130268.i | 0.167292 | + | 0.167292i | ||||
\(93\) | 87766.5 | − | 87766.5i | 0.109114 | − | 0.109114i | ||||
\(94\) | −498020. | − | 498020.i | −0.599602 | − | 0.599602i | ||||
\(95\) | 52020.0i | 0.0606736i | ||||||||
\(96\) | −82695.1 | + | 82695.1i | −0.0934687 | + | 0.0934687i | ||||
\(97\) | 34447.0 | − | 34447.0i | 0.0377430 | − | 0.0377430i | −0.687983 | − | 0.725726i | \(-0.741504\pi\) |
0.725726 | + | 0.687983i | \(0.241504\pi\) | |||||||
\(98\) | 470320. | + | 470320.i | 0.499707 | + | 0.499707i | ||||
\(99\) | 78362.6i | 0.0807613i | ||||||||
\(100\) | −494494. | −0.494494 | ||||||||
\(101\) | 434158.i | 0.421389i | 0.977552 | + | 0.210695i | \(0.0675726\pi\) | ||||
−0.977552 | + | 0.210695i | \(0.932427\pi\) | |||||||
\(102\) | 1.08763e6i | 1.02490i | ||||||||
\(103\) | −111529. | − | 111529.i | −0.102065 | − | 0.102065i | 0.654230 | − | 0.756295i | \(-0.272993\pi\) |
−0.756295 | + | 0.654230i | \(0.772993\pi\) | |||||||
\(104\) | − | 424470.i | − | 0.377352i | ||||||
\(105\) | 1555.76 | + | 1555.76i | 0.00134393 | + | 0.00134393i | ||||
\(106\) | 331524. | + | 331524.i | 0.278354 | + | 0.278354i | ||||
\(107\) | 219793. | 0.179416 | 0.0897081 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897081 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(108\) | −678613. | −0.538705 | ||||||||
\(109\) | −806861. | + | 806861.i | −0.623044 | + | 0.623044i | −0.946309 | − | 0.323264i | \(-0.895220\pi\) |
0.323264 | + | 0.946309i | \(0.395220\pi\) | |||||||
\(110\) | − | 18092.3i | − | 0.0135930i | ||||||
\(111\) | −1.00006e6 | − | 213734.i | −0.731236 | − | 0.156280i | ||||
\(112\) | −8507.29 | −0.00605532 | ||||||||
\(113\) | −298812. | − | 298812.i | −0.207092 | − | 0.207092i | 0.595938 | − | 0.803030i | \(-0.296780\pi\) |
−0.803030 | + | 0.595938i | \(0.796780\pi\) | |||||||
\(114\) | 452916.i | 0.305705i | ||||||||
\(115\) | − | 75518.1i | − | 0.0496544i | ||||||
\(116\) | −958538. | + | 958538.i | −0.614095 | + | 0.614095i | ||||
\(117\) | 532901. | − | 532901.i | 0.332727 | − | 0.332727i | ||||
\(118\) | 1.15372e6 | 0.702192 | ||||||||
\(119\) | −55945.1 | + | 55945.1i | −0.0331987 | + | 0.0331987i | ||||
\(120\) | 47939.4 | 0.0277427 | ||||||||
\(121\) | 1.71211e6 | 0.966443 | ||||||||
\(122\) | 563321.i | 0.310225i | ||||||||
\(123\) | 207923. | 0.111735 | ||||||||
\(124\) | 139110. | − | 139110.i | 0.0729615 | − | 0.0729615i | ||||
\(125\) | 288260. | + | 288260.i | 0.147589 | + | 0.147589i | ||||
\(126\) | −10680.5 | − | 10680.5i | −0.00533923 | − | 0.00533923i | ||||
\(127\) | −1.72567e6 | −0.842456 | −0.421228 | − | 0.906955i | \(-0.638401\pi\) | ||||
−0.421228 | + | 0.906955i | \(0.638401\pi\) | |||||||
\(128\) | −131072. | + | 131072.i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −1.55107e6 | − | 1.55107e6i | −0.722539 | − | 0.722539i | ||||
\(130\) | −123035. | + | 123035.i | −0.0560015 | + | 0.0560015i | ||||
\(131\) | 2.54435e6 | + | 2.54435e6i | 1.13178 | + | 1.13178i | 0.989881 | + | 0.141900i | \(0.0453211\pi\) |
0.141900 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(132\) | − | 157521.i | − | 0.0684885i | ||||||
\(133\) | −23296.9 | + | 23296.9i | −0.00990247 | + | 0.00990247i | ||||
\(134\) | −1.93534e6 | + | 1.93534e6i | −0.804346 | + | 0.804346i | ||||
\(135\) | 196700. | + | 196700.i | 0.0799473 | + | 0.0799473i | ||||
\(136\) | 1.72389e6i | 0.685321i | ||||||||
\(137\) | 2.65306e6 | 1.03178 | 0.515889 | − | 0.856656i | \(-0.327462\pi\) | ||||
0.515889 | + | 0.856656i | \(0.327462\pi\) | |||||||
\(138\) | − | 657503.i | − | 0.250185i | ||||||
\(139\) | − | 3.85559e6i | − | 1.43564i | −0.696227 | − | 0.717822i | \(-0.745139\pi\) | ||
0.696227 | − | 0.717822i | \(-0.254861\pi\) | |||||||
\(140\) | 2465.89 | + | 2465.89i | 0.000898649 | + | 0.000898649i | ||||
\(141\) | 2.51366e6i | 0.896703i | ||||||||
\(142\) | −691644. | − | 691644.i | −0.241556 | − | 0.241556i | ||||
\(143\) | 404275. | + | 404275.i | 0.138251 | + | 0.138251i | ||||
\(144\) | −329109. | −0.110218 | ||||||||
\(145\) | 555677. | 0.182271 | ||||||||
\(146\) | 2.10750e6 | − | 2.10750e6i | 0.677189 | − | 0.677189i | ||||
\(147\) | − | 2.37385e6i | − | 0.747311i | ||||||
\(148\) | −1.58510e6 | − | 338768.i | −0.488958 | − | 0.104500i | ||||
\(149\) | 3.78950e6 | 1.14557 | 0.572787 | − | 0.819704i | \(-0.305862\pi\) | ||||
0.572787 | + | 0.819704i | \(0.305862\pi\) | |||||||
\(150\) | 1.24793e6 | + | 1.24793e6i | 0.369757 | + | 0.369757i | ||||
\(151\) | − | 3.87072e6i | − | 1.12425i | −0.827054 | − | 0.562123i | \(-0.809985\pi\) | ||
0.827054 | − | 0.562123i | \(-0.190015\pi\) | |||||||
\(152\) | 717873.i | 0.204417i | ||||||||
\(153\) | −2.16426e6 | + | 2.16426e6i | −0.604276 | + | 0.604276i | ||||
\(154\) | 8102.53 | − | 8102.53i | 0.00221850 | − | 0.00221850i | ||||
\(155\) | −80644.0 | −0.0216559 | ||||||||
\(156\) | −1.07122e6 | + | 1.07122e6i | −0.282165 | + | 0.282165i | ||||
\(157\) | 5.05290e6 | 1.30570 | 0.652848 | − | 0.757489i | \(-0.273574\pi\) | ||||
0.652848 | + | 0.757489i | \(0.273574\pi\) | |||||||
\(158\) | −4.93402e6 | −1.25092 | ||||||||
\(159\) | − | 1.67331e6i | − | 0.416278i | ||||||
\(160\) | 75984.1 | 0.0185508 | ||||||||
\(161\) | 33820.5 | − | 33820.5i | 0.00810405 | − | 0.00810405i | ||||
\(162\) | 775397. | + | 775397.i | 0.182381 | + | 0.182381i | ||||
\(163\) | −3.01651e6 | − | 3.01651e6i | −0.696535 | − | 0.696535i | 0.267127 | − | 0.963661i | \(-0.413926\pi\) |
−0.963661 | + | 0.267127i | \(0.913926\pi\) | |||||||
\(164\) | 329559. | 0.0747139 | ||||||||
\(165\) | −45658.6 | + | 45658.6i | −0.0101641 | + | 0.0101641i | ||||
\(166\) | −1.43729e6 | − | 1.43729e6i | −0.314211 | − | 0.314211i | ||||
\(167\) | −3.98933e6 | + | 3.98933e6i | −0.856545 | + | 0.856545i | −0.990929 | − | 0.134384i | \(-0.957094\pi\) |
0.134384 | + | 0.990929i | \(0.457094\pi\) | |||||||
\(168\) | 21469.4 | + | 21469.4i | 0.00452786 | + | 0.00452786i | ||||
\(169\) | − | 671687.i | − | 0.139158i | ||||||
\(170\) | 499682. | − | 499682.i | 0.101706 | − | 0.101706i | ||||
\(171\) | −901253. | + | 901253.i | −0.180243 | + | 0.180243i | ||||
\(172\) | −2.45845e6 | − | 2.45845e6i | −0.483143 | − | 0.483143i | ||||
\(173\) | − | 8.15262e6i | − | 1.57456i | −0.616597 | − | 0.787279i | \(-0.711489\pi\) | ||
0.616597 | − | 0.787279i | \(-0.288511\pi\) | |||||||
\(174\) | 4.83804e6 | 0.918378 | ||||||||
\(175\) | 128381.i | 0.0239545i | ||||||||
\(176\) | − | 249672.i | − | 0.0457964i | ||||||
\(177\) | −2.91160e6 | − | 2.91160e6i | −0.525064 | − | 0.525064i | ||||
\(178\) | − | 2.50275e6i | − | 0.443770i | ||||||
\(179\) | −254389. | − | 254389.i | −0.0443546 | − | 0.0443546i | 0.684582 | − | 0.728936i | \(-0.259985\pi\) |
−0.728936 | + | 0.684582i | \(0.759985\pi\) | |||||||
\(180\) | 95394.2 | + | 95394.2i | 0.0163570 | + | 0.0163570i | ||||
\(181\) | 827492. | 0.139549 | 0.0697747 | − | 0.997563i | \(-0.477772\pi\) | ||||
0.0697747 | + | 0.997563i | \(0.477772\pi\) | |||||||
\(182\) | −110202. | −0.0182799 | ||||||||
\(183\) | 1.42163e6 | − | 1.42163e6i | 0.231971 | − | 0.231971i | ||||
\(184\) | − | 1.04215e6i | − | 0.167292i | ||||||
\(185\) | 361257. | + | 557645.i | 0.0570560 | + | 0.0880730i | ||||
\(186\) | −702132. | −0.109114 | ||||||||
\(187\) | −1.64188e6 | − | 1.64188e6i | −0.251082 | − | 0.251082i | ||||
\(188\) | 3.98416e6i | 0.599602i | ||||||||
\(189\) | 176183.i | 0.0260963i | ||||||||
\(190\) | 208080. | − | 208080.i | 0.0303368 | − | 0.0303368i | ||||
\(191\) | −5.09562e6 | + | 5.09562e6i | −0.731302 | + | 0.731302i | −0.970878 | − | 0.239576i | \(-0.922992\pi\) |
0.239576 | + | 0.970878i | \(0.422992\pi\) | |||||||
\(192\) | 661561. | 0.0934687 | ||||||||
\(193\) | 1.99638e6 | − | 1.99638e6i | 0.277696 | − | 0.277696i | −0.554492 | − | 0.832189i | \(-0.687088\pi\) |
0.832189 | + | 0.554492i | \(0.187088\pi\) | |||||||
\(194\) | −275576. | −0.0377430 | ||||||||
\(195\) | 620997. | 0.0837502 | ||||||||
\(196\) | − | 3.76256e6i | − | 0.499707i | ||||||
\(197\) | 1.62058e6 | 0.211969 | 0.105984 | − | 0.994368i | \(-0.466201\pi\) | ||||
0.105984 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(198\) | 313450. | − | 313450.i | 0.0403806 | − | 0.0403806i | ||||
\(199\) | −3.85892e6 | − | 3.85892e6i | −0.489673 | − | 0.489673i | 0.418530 | − | 0.908203i | \(-0.362546\pi\) |
−0.908203 | + | 0.418530i | \(0.862546\pi\) | |||||||
\(200\) | 1.97798e6 | + | 1.97798e6i | 0.247247 | + | 0.247247i | ||||
\(201\) | 9.76825e6 | 1.20290 | ||||||||
\(202\) | 1.73663e6 | − | 1.73663e6i | 0.210695 | − | 0.210695i | ||||
\(203\) | 248857. | + | 248857.i | 0.0297483 | + | 0.0297483i | ||||
\(204\) | 4.35051e6 | − | 4.35051e6i | 0.512448 | − | 0.512448i | ||||
\(205\) | −95524.8 | − | 95524.8i | −0.0110880 | − | 0.0110880i | ||||
\(206\) | 892232.i | 0.102065i | ||||||||
\(207\) | 1.30836e6 | − | 1.30836e6i | 0.147508 | − | 0.147508i | ||||
\(208\) | −1.69788e6 | + | 1.69788e6i | −0.188676 | + | 0.188676i | ||||
\(209\) | −683718. | − | 683718.i | −0.0748925 | − | 0.0748925i | ||||
\(210\) | − | 12446.1i | − | 0.00134393i | ||||||
\(211\) | −5.98273e6 | −0.636872 | −0.318436 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318436 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(212\) | − | 2.65219e6i | − | 0.278354i | ||||||
\(213\) | 3.49094e6i | 0.361247i | ||||||||
\(214\) | −879170. | − | 879170.i | −0.0897081 | − | 0.0897081i | ||||
\(215\) | 1.42519e6i | 0.143403i | ||||||||
\(216\) | 2.71445e6 | + | 2.71445e6i | 0.269353 | + | 0.269353i | ||||
\(217\) | −36116.0 | − | 36116.0i | −0.00353444 | − | 0.00353444i | ||||
\(218\) | 6.45488e6 | 0.623044 | ||||||||
\(219\) | −1.06372e7 | −1.01273 | ||||||||
\(220\) | −72369.0 | + | 72369.0i | −0.00679649 | + | 0.00679649i | ||||
\(221\) | 2.23310e7i | 2.06886i | ||||||||
\(222\) | 3.14531e6 | + | 4.85518e6i | 0.287478 | + | 0.443758i | ||||
\(223\) | −1.19672e7 | −1.07914 | −0.539570 | − | 0.841941i | \(-0.681413\pi\) | ||||
−0.539570 | + | 0.841941i | \(0.681413\pi\) | |||||||
\(224\) | 34029.1 | + | 34029.1i | 0.00302766 | + | 0.00302766i | ||||
\(225\) | 4.96650e6i | 0.436016i | ||||||||
\(226\) | 2.39050e6i | 0.207092i | ||||||||
\(227\) | −9.17918e6 | + | 9.17918e6i | −0.784741 | + | 0.784741i | −0.980627 | − | 0.195886i | \(-0.937242\pi\) |
0.195886 | + | 0.980627i | \(0.437242\pi\) | |||||||
\(228\) | 1.81166e6 | − | 1.81166e6i | 0.152853 | − | 0.152853i | ||||
\(229\) | 430968. | 0.0358871 | 0.0179436 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179436 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(230\) | −302073. | + | 302073.i | −0.0248272 | + | 0.0248272i | ||||
\(231\) | −40896.0 | −0.00331776 | ||||||||
\(232\) | 7.66831e6 | 0.614095 | ||||||||
\(233\) | 1.94580e7i | 1.53826i | 0.639093 | + | 0.769130i | \(0.279310\pi\) | ||||
−0.639093 | + | 0.769130i | \(0.720690\pi\) | |||||||
\(234\) | −4.26320e6 | −0.332727 | ||||||||
\(235\) | 1.15483e6 | − | 1.15483e6i | 0.0889848 | − | 0.0889848i | ||||
\(236\) | −4.61490e6 | − | 4.61490e6i | −0.351096 | − | 0.351096i | ||||
\(237\) | 1.24518e7 | + | 1.24518e7i | 0.935374 | + | 0.935374i | ||||
\(238\) | 447560. | 0.0331987 | ||||||||
\(239\) | 1.68305e7 | − | 1.68305e7i | 1.23283 | − | 1.23283i | 0.269957 | − | 0.962872i | \(-0.412990\pi\) |
0.962872 | − | 0.269957i | \(-0.0870095\pi\) | |||||||
\(240\) | −191758. | − | 191758.i | −0.0138714 | − | 0.0138714i | ||||
\(241\) | −4.80533e6 | + | 4.80533e6i | −0.343299 | + | 0.343299i | −0.857606 | − | 0.514307i | \(-0.828049\pi\) |
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(242\) | −6.84845e6 | − | 6.84845e6i | −0.483221 | − | 0.483221i | ||||
\(243\) | 1.15460e7i | 0.804660i | ||||||||
\(244\) | 2.25329e6 | − | 2.25329e6i | 0.155113 | − | 0.155113i | ||||
\(245\) | −1.09060e6 | + | 1.09060e6i | −0.0741597 | + | 0.0741597i | ||||
\(246\) | −831692. | − | 831692.i | −0.0558673 | − | 0.0558673i | ||||
\(247\) | 9.29918e6i | 0.617097i | ||||||||
\(248\) | −1.11288e6 | −0.0729615 | ||||||||
\(249\) | 7.25446e6i | 0.469902i | ||||||||
\(250\) | − | 2.30608e6i | − | 0.147589i | ||||||
\(251\) | −6.57840e6 | − | 6.57840e6i | −0.416005 | − | 0.416005i | 0.467819 | − | 0.883824i | \(-0.345040\pi\) |
−0.883824 | + | 0.467819i | \(0.845040\pi\) | |||||||
\(252\) | 85443.7i | 0.00533923i | ||||||||
\(253\) | 992563. | + | 992563.i | 0.0612910 | + | 0.0612910i | ||||
\(254\) | 6.90269e6 | + | 6.90269e6i | 0.421228 | + | 0.421228i | ||||
\(255\) | −2.52205e6 | −0.152101 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 8.58905e6 | − | 8.58905e6i | 0.505994 | − | 0.505994i | −0.407300 | − | 0.913294i | \(-0.633530\pi\) |
0.913294 | + | 0.407300i | \(0.133530\pi\) | |||||||
\(258\) | 1.24085e7i | 0.722539i | ||||||||
\(259\) | −87951.7 | + | 411526.i | −0.00506226 | + | 0.0236864i | ||||
\(260\) | 984283. | 0.0560015 | ||||||||
\(261\) | 9.62717e6 | + | 9.62717e6i | 0.541474 | + | 0.541474i | ||||
\(262\) | − | 2.03548e7i | − | 1.13178i | ||||||
\(263\) | − | 7.85817e6i | − | 0.431970i | −0.976397 | − | 0.215985i | \(-0.930704\pi\) | ||
0.976397 | − | 0.215985i | \(-0.0692963\pi\) | |||||||
\(264\) | −630085. | + | 630085.i | −0.0342442 | + | 0.0342442i | ||||
\(265\) | −768756. | + | 768756.i | −0.0413096 | + | 0.0413096i | ||||
\(266\) | 186375. | 0.00990247 | ||||||||
\(267\) | −6.31608e6 | + | 6.31608e6i | −0.331829 | + | 0.331829i | ||||
\(268\) | 1.54827e7 | 0.804346 | ||||||||
\(269\) | 1.61362e7 | 0.828983 | 0.414491 | − | 0.910053i | \(-0.363960\pi\) | ||||
0.414491 | + | 0.910053i | \(0.363960\pi\) | |||||||
\(270\) | − | 1.57360e6i | − | 0.0799473i | ||||||
\(271\) | 1.77920e7 | 0.893955 | 0.446978 | − | 0.894545i | \(-0.352500\pi\) | ||||
0.446978 | + | 0.894545i | \(0.352500\pi\) | |||||||
\(272\) | 6.89558e6 | − | 6.89558e6i | 0.342660 | − | 0.342660i | ||||
\(273\) | 278111. | + | 278111.i | 0.0136688 | + | 0.0136688i | ||||
\(274\) | −1.06123e7 | − | 1.06123e7i | −0.515889 | − | 0.515889i | ||||
\(275\) | −3.76774e6 | −0.181168 | ||||||||
\(276\) | −2.63001e6 | + | 2.63001e6i | −0.125092 | + | 0.125092i | ||||
\(277\) | −1.30922e7 | − | 1.30922e7i | −0.615990 | − | 0.615990i | 0.328511 | − | 0.944500i | \(-0.393453\pi\) |
−0.944500 | + | 0.328511i | \(0.893453\pi\) | |||||||
\(278\) | −1.54224e7 | + | 1.54224e7i | −0.717822 | + | 0.717822i | ||||
\(279\) | −1.39717e6 | − | 1.39717e6i | −0.0643333 | − | 0.0643333i | ||||
\(280\) | − | 19727.1i | − | 0.000898649i | ||||||
\(281\) | −1.08811e7 | + | 1.08811e7i | −0.490404 | + | 0.490404i | −0.908434 | − | 0.418029i | \(-0.862721\pi\) |
0.418029 | + | 0.908434i | \(0.362721\pi\) | |||||||
\(282\) | 1.00546e7 | − | 1.00546e7i | 0.448352 | − | 0.448352i | ||||
\(283\) | −6.68314e6 | − | 6.68314e6i | −0.294864 | − | 0.294864i | 0.544134 | − | 0.838998i | \(-0.316858\pi\) |
−0.838998 | + | 0.544134i | \(0.816858\pi\) | |||||||
\(284\) | 5.53315e6i | 0.241556i | ||||||||
\(285\) | −1.05024e6 | −0.0453686 | ||||||||
\(286\) | − | 3.23420e6i | − | 0.138251i | ||||||
\(287\) | − | 85560.7i | − | 0.00361933i | ||||||
\(288\) | 1.31643e6 | + | 1.31643e6i | 0.0551089 | + | 0.0551089i | ||||
\(289\) | − | 6.65549e7i | − | 2.75732i | ||||||
\(290\) | −2.22271e6 | − | 2.22271e6i | −0.0911357 | − | 0.0911357i | ||||
\(291\) | 695458. | + | 695458.i | 0.0282223 | + | 0.0282223i | ||||
\(292\) | −1.68600e7 | −0.677189 | ||||||||
\(293\) | 9.50505e6 | 0.377878 | 0.188939 | − | 0.981989i | \(-0.439495\pi\) | ||||
0.188939 | + | 0.981989i | \(0.439495\pi\) | |||||||
\(294\) | −9.49540e6 | + | 9.49540e6i | −0.373655 | + | 0.373655i | ||||
\(295\) | 2.67532e6i | 0.104210i | ||||||||
\(296\) | 4.98532e6 | + | 7.69547e6i | 0.192229 | + | 0.296729i | ||||
\(297\) | −5.17061e6 | −0.197366 | ||||||||
\(298\) | −1.51580e7 | − | 1.51580e7i | −0.572787 | − | 0.572787i | ||||
\(299\) | − | 1.34997e7i | − | 0.505024i | ||||||
\(300\) | − | 9.98345e6i | − | 0.369757i | ||||||
\(301\) | −638267. | + | 638267.i | −0.0234047 | + | 0.0234047i | ||||
\(302\) | −1.54829e7 | + | 1.54829e7i | −0.562123 | + | 0.562123i | ||||
\(303\) | −8.76531e6 | −0.315093 | ||||||||
\(304\) | 2.87149e6 | − | 2.87149e6i | 0.102208 | − | 0.102208i | ||||
\(305\) | −1.30626e6 | −0.0460394 | ||||||||
\(306\) | 1.73141e7 | 0.604276 | ||||||||
\(307\) | − | 3.80384e7i | − | 1.31464i | −0.753611 | − | 0.657321i | \(-0.771690\pi\) | ||
0.753611 | − | 0.657321i | \(-0.228310\pi\) | |||||||
\(308\) | −64820.3 | −0.00221850 | ||||||||
\(309\) | 2.25168e6 | − | 2.25168e6i | 0.0763189 | − | 0.0763189i | ||||
\(310\) | 322576. | + | 322576.i | 0.0108280 | + | 0.0108280i | ||||
\(311\) | −3.91219e7 | − | 3.91219e7i | −1.30058 | − | 1.30058i | −0.927997 | − | 0.372588i | \(-0.878470\pi\) |
−0.372588 | − | 0.927997i | \(-0.621530\pi\) | |||||||
\(312\) | 8.56972e6 | 0.282165 | ||||||||
\(313\) | −2.13307e7 | + | 2.13307e7i | −0.695619 | + | 0.695619i | −0.963462 | − | 0.267844i | \(-0.913689\pi\) |
0.267844 | + | 0.963462i | \(0.413689\pi\) | |||||||
\(314\) | −2.02116e7 | − | 2.02116e7i | −0.652848 | − | 0.652848i | ||||
\(315\) | 24766.4 | − | 24766.4i | 0.000792376 | − | 0.000792376i | ||||
\(316\) | 1.97361e7 | + | 1.97361e7i | 0.625460 | + | 0.625460i | ||||
\(317\) | 1.11986e7i | 0.351548i | 0.984431 | + | 0.175774i | \(0.0562427\pi\) | ||||
−0.984431 | + | 0.175774i | \(0.943757\pi\) | |||||||
\(318\) | −6.69322e6 | + | 6.69322e6i | −0.208139 | + | 0.208139i | ||||
\(319\) | −7.30347e6 | + | 7.30347e6i | −0.224987 | + | 0.224987i | ||||
\(320\) | −303937. | − | 303937.i | −0.00927541 | − | 0.00927541i | ||||
\(321\) | 4.43744e6i | 0.134158i | ||||||||
\(322\) | −270564. | −0.00810405 | ||||||||
\(323\) | − | 3.77666e7i | − | 1.12073i | ||||||
\(324\) | − | 6.20318e6i | − | 0.182381i | ||||||
\(325\) | 2.56223e7 | + | 2.56223e7i | 0.746393 | + | 0.746393i | ||||
\(326\) | 2.41321e7i | 0.696535i | ||||||||
\(327\) | −1.62899e7 | − | 1.62899e7i | −0.465881 | − | 0.465881i | ||||
\(328\) | −1.31824e6 | − | 1.31824e6i | −0.0373570 | − | 0.0373570i | ||||
\(329\) | 1.03437e6 | 0.0290462 | ||||||||
\(330\) | 365269. | 0.0101641 | ||||||||
\(331\) | 4.88035e7 | − | 4.88035e7i | 1.34576 | − | 1.34576i | 0.455545 | − | 0.890213i | \(-0.349444\pi\) |
0.890213 | − | 0.455545i | \(-0.150556\pi\) | |||||||
\(332\) | 1.14983e7i | 0.314211i | ||||||||
\(333\) | −3.40245e6 | + | 1.59201e7i | −0.0921424 | + | 0.431135i | ||||
\(334\) | 3.19146e7 | 0.856545 | ||||||||
\(335\) | −4.48777e6 | − | 4.48777e6i | −0.119370 | − | 0.119370i | ||||
\(336\) | − | 171756.i | − | 0.00452786i | ||||||
\(337\) | − | 1.93250e7i | − | 0.504928i | −0.967606 | − | 0.252464i | \(-0.918759\pi\) | ||
0.967606 | − | 0.252464i | \(-0.0812409\pi\) | |||||||
\(338\) | −2.68675e6 | + | 2.68675e6i | −0.0695788 | + | 0.0695788i | ||||
\(339\) | 6.03279e6 | − | 6.03279e6i | 0.154853 | − | 0.154853i | ||||
\(340\) | −3.99745e6 | −0.101706 | ||||||||
\(341\) | 1.05993e6 | − | 1.05993e6i | 0.0267310 | − | 0.0267310i | ||||
\(342\) | 7.21002e6 | 0.180243 | ||||||||
\(343\) | −1.95426e6 | −0.0484283 | ||||||||
\(344\) | 1.96676e7i | 0.483143i | ||||||||
\(345\) | 1.52465e6 | 0.0371290 | ||||||||
\(346\) | −3.26105e7 | + | 3.26105e7i | −0.787279 | + | 0.787279i | ||||
\(347\) | 1.17866e7 | + | 1.17866e7i | 0.282099 | + | 0.282099i | 0.833946 | − | 0.551847i | \(-0.186077\pi\) |
−0.551847 | + | 0.833946i | \(0.686077\pi\) | |||||||
\(348\) | −1.93522e7 | − | 1.93522e7i | −0.459189 | − | 0.459189i | ||||
\(349\) | 6.10844e7 | 1.43699 | 0.718496 | − | 0.695531i | \(-0.244831\pi\) | ||||
0.718496 | + | 0.695531i | \(0.244831\pi\) | |||||||
\(350\) | 513526. | − | 513526.i | 0.0119773 | − | 0.0119773i | ||||
\(351\) | 3.51625e7 | + | 3.51625e7i | 0.813126 | + | 0.813126i | ||||
\(352\) | −998688. | + | 998688.i | −0.0228982 | + | 0.0228982i | ||||
\(353\) | 7.87288e6 | + | 7.87288e6i | 0.178982 | + | 0.178982i | 0.790912 | − | 0.611930i | \(-0.209607\pi\) |
−0.611930 | + | 0.790912i | \(0.709607\pi\) | |||||||
\(354\) | 2.32928e7i | 0.525064i | ||||||||
\(355\) | 1.60382e6 | − | 1.60382e6i | 0.0358485 | − | 0.0358485i | ||||
\(356\) | −1.00110e7 | + | 1.00110e7i | −0.221885 | + | 0.221885i | ||||
\(357\) | −1.12949e6 | − | 1.12949e6i | −0.0248243 | − | 0.0248243i | ||||
\(358\) | 2.03511e6i | 0.0443546i | ||||||||
\(359\) | 6.52112e7 | 1.40942 | 0.704708 | − | 0.709498i | \(-0.251078\pi\) | ||||
0.704708 | + | 0.709498i | \(0.251078\pi\) | |||||||
\(360\) | − | 763154.i | − | 0.0163570i | ||||||
\(361\) | 3.13189e7i | 0.665710i | ||||||||
\(362\) | −3.30997e6 | − | 3.30997e6i | −0.0697747 | − | 0.0697747i | ||||
\(363\) | 3.45662e7i | 0.722657i | ||||||||
\(364\) | 440807. | + | 440807.i | 0.00913995 | + | 0.00913995i | ||||
\(365\) | 4.88699e6 | + | 4.88699e6i | 0.100499 | + | 0.100499i | ||||
\(366\) | −1.13730e7 | −0.231971 | ||||||||
\(367\) | −9.42630e7 | −1.90697 | −0.953483 | − | 0.301447i | \(-0.902530\pi\) | ||||
−0.953483 | + | 0.301447i | \(0.902530\pi\) | |||||||
\(368\) | −4.16858e6 | + | 4.16858e6i | −0.0836459 | + | 0.0836459i | ||||
\(369\) | − | 3.30996e6i | − | 0.0658784i | ||||||
\(370\) | 785554. | − | 3.67561e6i | 0.0155085 | − | 0.0725645i | ||||
\(371\) | −688568. | −0.0134842 | ||||||||
\(372\) | 2.80853e6 | + | 2.80853e6i | 0.0545569 | + | 0.0545569i | ||||
\(373\) | − | 3.92074e7i | − | 0.755512i | −0.925905 | − | 0.377756i | \(-0.876696\pi\) | ||
0.925905 | − | 0.377756i | \(-0.123304\pi\) | |||||||
\(374\) | 1.31350e7i | 0.251082i | ||||||||
\(375\) | −5.81976e6 | + | 5.81976e6i | −0.110360 | + | 0.110360i | ||||
\(376\) | 1.59366e7 | − | 1.59366e7i | 0.299801 | − | 0.299801i | ||||
\(377\) | 9.93337e7 | 1.85384 | ||||||||
\(378\) | 704731. | − | 704731.i | 0.0130481 | − | 0.0130481i | ||||
\(379\) | 3.68081e7 | 0.676122 | 0.338061 | − | 0.941124i | \(-0.390229\pi\) | ||||
0.338061 | + | 0.941124i | \(0.390229\pi\) | |||||||
\(380\) | −1.66464e6 | −0.0303368 | ||||||||
\(381\) | − | 3.48400e7i | − | 0.629946i | ||||||
\(382\) | 4.07649e7 | 0.731302 | ||||||||
\(383\) | −2.45374e7 | + | 2.45374e7i | −0.436749 | + | 0.436749i | −0.890916 | − | 0.454168i | \(-0.849937\pi\) |
0.454168 | + | 0.890916i | \(0.349937\pi\) | |||||||
\(384\) | −2.64624e6 | − | 2.64624e6i | −0.0467343 | − | 0.0467343i | ||||
\(385\) | 18788.6 | + | 18788.6i | 0.000329239 | + | 0.000329239i | ||||
\(386\) | −1.59710e7 | −0.277696 | ||||||||
\(387\) | −2.46917e7 | + | 2.46917e7i | −0.426007 | + | 0.426007i | ||||
\(388\) | 1.10230e6 | + | 1.10230e6i | 0.0188715 | + | 0.0188715i | ||||
\(389\) | −6.32206e7 | + | 6.32206e7i | −1.07401 | + | 1.07401i | −0.0769809 | + | 0.997033i | \(0.524528\pi\) |
−0.997033 | + | 0.0769809i | \(0.975472\pi\) | |||||||
\(390\) | −2.48399e6 | − | 2.48399e6i | −0.0418751 | − | 0.0418751i | ||||
\(391\) | 5.48263e7i | 0.917189i | ||||||||
\(392\) | −1.50502e7 | + | 1.50502e7i | −0.249853 | + | 0.249853i | ||||
\(393\) | −5.13684e7 | + | 5.13684e7i | −0.846288 | + | 0.846288i | ||||
\(394\) | −6.48232e6 | − | 6.48232e6i | −0.105984 | − | 0.105984i | ||||
\(395\) | − | 1.14413e7i | − | 0.185645i | ||||||
\(396\) | −2.50760e6 | −0.0403806 | ||||||||
\(397\) | 1.08622e7i | 0.173599i | 0.996226 | + | 0.0867994i | \(0.0276639\pi\) | ||||
−0.996226 | + | 0.0867994i | \(0.972336\pi\) | |||||||
\(398\) | 3.08714e7i | 0.489673i | ||||||||
\(399\) | −470347. | − | 470347.i | −0.00740457 | − | 0.00740457i | ||||
\(400\) | − | 1.58238e7i | − | 0.247247i | ||||||
\(401\) | −4.52618e7 | − | 4.52618e7i | −0.701937 | − | 0.701937i | 0.262889 | − | 0.964826i | \(-0.415325\pi\) |
−0.964826 | + | 0.262889i | \(0.915325\pi\) | |||||||
\(402\) | −3.90730e7 | − | 3.90730e7i | −0.601449 | − | 0.601449i | ||||
\(403\) | −1.44160e7 | −0.220258 | ||||||||
\(404\) | −1.38930e7 | −0.210695 | ||||||||
\(405\) | −1.79803e6 | + | 1.79803e6i | −0.0270665 | + | 0.0270665i | ||||
\(406\) | − | 1.99086e6i | − | 0.0297483i | ||||||
\(407\) | −1.20775e7 | − | 2.58121e6i | −0.179140 | − | 0.0382859i | ||||
\(408\) | −3.48041e7 | −0.512448 | ||||||||
\(409\) | −1.64004e7 | − | 1.64004e7i | −0.239709 | − | 0.239709i | 0.577020 | − | 0.816730i | \(-0.304215\pi\) |
−0.816730 | + | 0.577020i | \(0.804215\pi\) | |||||||
\(410\) | 764198.i | 0.0110880i | ||||||||
\(411\) | 5.35633e7i | 0.771511i | ||||||||
\(412\) | 3.56893e6 | − | 3.56893e6i | 0.0510324 | − | 0.0510324i | ||||
\(413\) | −1.19813e6 | + | 1.19813e6i | −0.0170080 | + | 0.0170080i | ||||
\(414\) | −1.04669e7 | −0.147508 | ||||||||
\(415\) | 3.33287e6 | − | 3.33287e6i | 0.0466309 | − | 0.0466309i | ||||
\(416\) | 1.35830e7 | 0.188676 | ||||||||
\(417\) | 7.78415e7 | 1.07350 | ||||||||
\(418\) | 5.46975e6i | 0.0748925i | ||||||||
\(419\) | 8.17876e7 | 1.11185 | 0.555924 | − | 0.831233i | \(-0.312365\pi\) | ||||
0.555924 | + | 0.831233i | \(0.312365\pi\) | |||||||
\(420\) | −49784.5 | + | 49784.5i | −0.000671964 | + | 0.000671964i | ||||
\(421\) | 4.36761e7 | + | 4.36761e7i | 0.585326 | + | 0.585326i | 0.936362 | − | 0.351036i | \(-0.114171\pi\) |
−0.351036 | + | 0.936362i | \(0.614171\pi\) | |||||||
\(422\) | 2.39309e7 | + | 2.39309e7i | 0.318436 | + | 0.318436i | ||||
\(423\) | 4.00153e7 | 0.528694 | ||||||||
\(424\) | −1.06088e7 | + | 1.06088e7i | −0.139177 | + | 0.139177i | ||||
\(425\) | −1.04059e8 | − | 1.04059e8i | −1.35555 | − | 1.35555i | ||||
\(426\) | 1.39638e7 | − | 1.39638e7i | 0.180623 | − | 0.180623i | ||||
\(427\) | −585002. | − | 585002.i | −0.00751405 | − | 0.00751405i | ||||
\(428\) | 7.03336e6i | 0.0897081i | ||||||||
\(429\) | −8.16200e6 | + | 8.16200e6i | −0.103377 | + | 0.103377i | ||||
\(430\) | 5.70077e6 | − | 5.70077e6i | 0.0717015 | − | 0.0717015i | ||||
\(431\) | −4.06283e7 | − | 4.06283e7i | −0.507454 | − | 0.507454i | 0.406290 | − | 0.913744i | \(-0.366822\pi\) |
−0.913744 | + | 0.406290i | \(0.866822\pi\) | |||||||
\(432\) | − | 2.17156e7i | − | 0.269353i | ||||||
\(433\) | −1.37685e8 | −1.69599 | −0.847995 | − | 0.530004i | \(-0.822191\pi\) | ||||
−0.847995 | + | 0.530004i | \(0.822191\pi\) | |||||||
\(434\) | 288928.i | 0.00353444i | ||||||||
\(435\) | 1.12187e7i | 0.136293i | ||||||||
\(436\) | −2.58195e7 | − | 2.58195e7i | −0.311522 | − | 0.311522i | ||||
\(437\) | 2.28310e7i | 0.273578i | ||||||||
\(438\) | 4.25489e7 | + | 4.25489e7i | 0.506367 | + | 0.506367i | ||||
\(439\) | 8.19502e6 | + | 8.19502e6i | 0.0968626 | + | 0.0968626i | 0.753878 | − | 0.657015i | \(-0.228181\pi\) |
−0.657015 | + | 0.753878i | \(0.728181\pi\) | |||||||
\(440\) | 578952. | 0.00679649 | ||||||||
\(441\) | −3.77896e7 | −0.440612 | ||||||||
\(442\) | 8.93239e7 | − | 8.93239e7i | 1.03443 | − | 1.03443i | ||||
\(443\) | 1.24481e8i | 1.43183i | 0.698187 | + | 0.715915i | \(0.253990\pi\) | ||||
−0.698187 | + | 0.715915i | \(0.746010\pi\) | |||||||
\(444\) | 6.83947e6 | − | 3.20019e7i | 0.0781401 | − | 0.365618i | ||||
\(445\) | 5.80351e6 | 0.0658583 | ||||||||
\(446\) | 4.78688e7 | + | 4.78688e7i | 0.539570 | + | 0.539570i | ||||
\(447\) | 7.65071e7i | 0.856602i | ||||||||
\(448\) | − | 272233.i | − | 0.00302766i | ||||||
\(449\) | −1.48915e7 | + | 1.48915e7i | −0.164513 | + | 0.164513i | −0.784563 | − | 0.620050i | \(-0.787112\pi\) |
0.620050 | + | 0.784563i | \(0.287112\pi\) | |||||||
\(450\) | 1.98660e7 | − | 1.98660e7i | 0.218008 | − | 0.218008i | ||||
\(451\) | 2.51103e6 | 0.0273730 | ||||||||
\(452\) | 9.56199e6 | − | 9.56199e6i | 0.103546 | − | 0.103546i | ||||
\(453\) | 7.81469e7 | 0.840653 | ||||||||
\(454\) | 7.34334e7 | 0.784741 | ||||||||
\(455\) | − | 255541.i | − | 0.00271286i | ||||||
\(456\) | −1.44933e7 | −0.152853 | ||||||||
\(457\) | 6.38802e7 | − | 6.38802e7i | 0.669295 | − | 0.669295i | −0.288258 | − | 0.957553i | \(-0.593076\pi\) |
0.957553 | + | 0.288258i | \(0.0930760\pi\) | |||||||
\(458\) | −1.72387e6 | − | 1.72387e6i | −0.0179436 | − | 0.0179436i | ||||
\(459\) | −1.42805e8 | − | 1.42805e8i | −1.47674 | − | 1.47674i | ||||
\(460\) | 2.41658e6 | 0.0248272 | ||||||||
\(461\) | 1.26741e8 | − | 1.26741e8i | 1.29365 | − | 1.29365i | 0.361131 | − | 0.932515i | \(-0.382391\pi\) |
0.932515 | − | 0.361131i | \(-0.117609\pi\) | |||||||
\(462\) | 163584. | + | 163584.i | 0.00165888 | + | 0.00165888i | ||||
\(463\) | 1.91810e7 | − | 1.91810e7i | 0.193254 | − | 0.193254i | −0.603847 | − | 0.797100i | \(-0.706366\pi\) |
0.797100 | + | 0.603847i | \(0.206366\pi\) | |||||||
\(464\) | −3.06732e7 | − | 3.06732e7i | −0.307048 | − | 0.307048i | ||||
\(465\) | − | 1.62814e6i | − | 0.0161932i | ||||||
\(466\) | 7.78319e7 | − | 7.78319e7i | 0.769130 | − | 0.769130i | ||||
\(467\) | 5.31830e7 | − | 5.31830e7i | 0.522182 | − | 0.522182i | −0.396048 | − | 0.918230i | \(-0.629618\pi\) |
0.918230 | + | 0.396048i | \(0.129618\pi\) | |||||||
\(468\) | 1.70528e7 | + | 1.70528e7i | 0.166364 | + | 0.166364i | ||||
\(469\) | − | 4.01965e6i | − | 0.0389646i | ||||||
\(470\) | −9.23867e6 | −0.0889848 | ||||||||
\(471\) | 1.02014e8i | 0.976333i | ||||||||
\(472\) | 3.69192e7i | 0.351096i | ||||||||
\(473\) | −1.87318e7 | − | 1.87318e7i | −0.177010 | − | 0.177010i | ||||
\(474\) | − | 9.96140e7i | − | 0.935374i | ||||||
\(475\) | −4.33330e7 | − | 4.33330e7i | −0.404332 | − | 0.404332i | ||||
\(476\) | −1.79024e6 | − | 1.79024e6i | −0.0165993 | − | 0.0165993i | ||||
\(477\) | −2.66376e7 | −0.245437 | ||||||||
\(478\) | −1.34644e8 | −1.23283 | ||||||||
\(479\) | 3.57644e7 | − | 3.57644e7i | 0.325420 | − | 0.325420i | −0.525422 | − | 0.850842i | \(-0.676092\pi\) |
0.850842 | + | 0.525422i | \(0.176092\pi\) | |||||||
\(480\) | 1.53406e6i | 0.0138714i | ||||||||
\(481\) | 6.45789e7 | + | 9.96855e7i | 0.580303 | + | 0.895771i | ||||
\(482\) | 3.84426e7 | 0.343299 | ||||||||
\(483\) | 682809. | + | 682809.i | 0.00605979 | + | 0.00605979i | ||||
\(484\) | 5.47876e7i | 0.483221i | ||||||||
\(485\) | − | 639020.i | − | 0.00560130i | ||||||
\(486\) | 4.61840e7 | − | 4.61840e7i | 0.402330 | − | 0.402330i | ||||
\(487\) | −1.06035e8 | + | 1.06035e8i | −0.918044 | + | 0.918044i | −0.996887 | − | 0.0788427i | \(-0.974878\pi\) |
0.0788427 | + | 0.996887i | \(0.474878\pi\) | |||||||
\(488\) | −1.80263e7 | −0.155113 | ||||||||
\(489\) | 6.09011e7 | − | 6.09011e7i | 0.520833 | − | 0.520833i | ||||
\(490\) | 8.72482e6 | 0.0741597 | ||||||||
\(491\) | 1.16072e8 | 0.980579 | 0.490290 | − | 0.871560i | \(-0.336891\pi\) | ||||
0.490290 | + | 0.871560i | \(0.336891\pi\) | |||||||
\(492\) | 6.65354e6i | 0.0558673i | ||||||||
\(493\) | −4.03423e8 | −3.36682 | ||||||||
\(494\) | 3.71967e7 | − | 3.71967e7i | 0.308549 | − | 0.308549i | ||||
\(495\) | 726845. | + | 726845.i | 0.00599275 | + | 0.00599275i | ||||
\(496\) | 4.45153e6 | + | 4.45153e6i | 0.0364808 | + | 0.0364808i | ||||
\(497\) | 1.43653e6 | 0.0117016 | ||||||||
\(498\) | 2.90178e7 | − | 2.90178e7i | 0.234951 | − | 0.234951i | ||||
\(499\) | 5.94999e7 | + | 5.94999e7i | 0.478867 | + | 0.478867i | 0.904769 | − | 0.425902i | \(-0.140043\pi\) |
−0.425902 | + | 0.904769i | \(0.640043\pi\) | |||||||
\(500\) | −9.22433e6 | + | 9.22433e6i | −0.0737947 | + | 0.0737947i | ||||
\(501\) | −8.05414e7 | − | 8.05414e7i | −0.640481 | − | 0.640481i | ||||
\(502\) | 5.26272e7i | 0.416005i | ||||||||
\(503\) | −6.36091e7 | + | 6.36091e7i | −0.499822 | + | 0.499822i | −0.911382 | − | 0.411561i | \(-0.864984\pi\) |
0.411561 | + | 0.911382i | \(0.364984\pi\) | |||||||
\(504\) | 341775. | − | 341775.i | 0.00266962 | − | 0.00266962i | ||||
\(505\) | 4.02699e6 | + | 4.02699e6i | 0.0312684 | + | 0.0312684i | ||||
\(506\) | − | 7.94050e6i | − | 0.0612910i | ||||||
\(507\) | 1.35609e7 | 0.104055 | ||||||||
\(508\) | − | 5.52215e7i | − | 0.421228i | ||||||
\(509\) | − | 8.59204e7i | − | 0.651543i | −0.945449 | − | 0.325771i | \(-0.894376\pi\) | ||
0.945449 | − | 0.325771i | \(-0.105624\pi\) | |||||||
\(510\) | 1.00882e7 | + | 1.00882e7i | 0.0760506 | + | 0.0760506i | ||||
\(511\) | 4.37723e6i | 0.0328047i | ||||||||
\(512\) | −4.19430e6 | − | 4.19430e6i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.94675e7 | − | 5.94675e7i | −0.440482 | − | 0.440482i | ||||
\(514\) | −6.87124e7 | −0.505994 | ||||||||
\(515\) | −2.06895e6 | −0.0151471 | ||||||||
\(516\) | 4.96342e7 | − | 4.96342e7i | 0.361270 | − | 0.361270i | ||||
\(517\) | 3.03568e7i | 0.219677i | ||||||||
\(518\) | 1.99791e6 | − | 1.29430e6i | 0.0143743 | − | 0.00931205i | ||||
\(519\) | 1.64595e8 | 1.17737 | ||||||||
\(520\) | −3.93713e6 | − | 3.93713e6i | −0.0280008 | − | 0.0280008i | ||||
\(521\) | − | 1.09155e8i | − | 0.771845i | −0.922531 | − | 0.385922i | \(-0.873883\pi\) | ||
0.922531 | − | 0.385922i | \(-0.126117\pi\) | |||||||
\(522\) | − | 7.70174e7i | − | 0.541474i | ||||||
\(523\) | 4.80117e7 | − | 4.80117e7i | 0.335616 | − | 0.335616i | −0.519099 | − | 0.854714i | \(-0.673732\pi\) |
0.854714 | + | 0.519099i | \(0.173732\pi\) | |||||||
\(524\) | −8.14191e7 | + | 8.14191e7i | −0.565890 | + | 0.565890i | ||||
\(525\) | −2.59192e6 | −0.0179120 | ||||||||
\(526\) | −3.14327e7 | + | 3.14327e7i | −0.215985 | + | 0.215985i | ||||
\(527\) | 5.85477e7 | 0.400016 | ||||||||
\(528\) | 5.04068e6 | 0.0342442 | ||||||||
\(529\) | 1.14892e8i | 0.776107i | ||||||||
\(530\) | 6.15005e6 | 0.0413096 | ||||||||
\(531\) | −4.63502e7 | + | 4.63502e7i | −0.309576 | + | 0.309576i | ||||
\(532\) | −745502. | − | 745502.i | −0.00495124 | − | 0.00495124i | ||||
\(533\) | −1.70762e7 | − | 1.70762e7i | −0.112774 | − | 0.112774i | ||||
\(534\) | 5.05286e7 | 0.331829 | ||||||||
\(535\) | 2.03866e6 | − | 2.03866e6i | 0.0133133 | − | 0.0133133i | ||||
\(536\) | −6.19309e7 | − | 6.19309e7i | −0.402173 | − | 0.402173i | ||||
\(537\) | 5.13591e6 | − | 5.13591e6i | 0.0331661 | − | 0.0331661i | ||||
\(538\) | −6.45449e7 | − | 6.45449e7i | −0.414491 | − | 0.414491i | ||||
\(539\) | − | 2.86684e7i | − | 0.183078i | ||||||
\(540\) | −6.29441e6 | + | 6.29441e6i | −0.0399737 | + | 0.0399737i | ||||
\(541\) | 4.71584e7 | − | 4.71584e7i | 0.297829 | − | 0.297829i | −0.542334 | − | 0.840163i | \(-0.682459\pi\) |
0.840163 | + | 0.542334i | \(0.182459\pi\) | |||||||
\(542\) | −7.11678e7 | − | 7.11678e7i | −0.446978 | − | 0.446978i | ||||
\(543\) | 1.67064e7i | 0.104348i | ||||||||
\(544\) | −5.51646e7 | −0.342660 | ||||||||
\(545\) | 1.49679e7i | 0.0924638i | ||||||||
\(546\) | − | 2.22489e6i | − | 0.0136688i | ||||||
\(547\) | −2.83095e7 | − | 2.83095e7i | −0.172970 | − | 0.172970i | 0.615313 | − | 0.788283i | \(-0.289030\pi\) |
−0.788283 | + | 0.615313i | \(0.789030\pi\) | |||||||
\(548\) | 8.48980e7i | 0.515889i | ||||||||
\(549\) | −2.26311e7 | − | 2.26311e7i | −0.136769 | − | 0.136769i | ||||
\(550\) | 1.50709e7 | + | 1.50709e7i | 0.0905842 | + | 0.0905842i | ||||
\(551\) | −1.67995e8 | −1.00425 | ||||||||
\(552\) | 2.10401e7 | 0.125092 | ||||||||
\(553\) | 5.12391e6 | − | 5.12391e6i | 0.0302989 | − | 0.0302989i | ||||
\(554\) | 1.04738e8i | 0.615990i | ||||||||
\(555\) | −1.12584e7 | + | 7.29350e6i | −0.0658565 | + | 0.0426636i | ||||
\(556\) | 1.23379e8 | 0.717822 | ||||||||
\(557\) | 1.45283e8 | + | 1.45283e8i | 0.840716 | + | 0.840716i | 0.988952 | − | 0.148236i | \(-0.0473595\pi\) |
−0.148236 | + | 0.988952i | \(0.547359\pi\) | |||||||
\(558\) | 1.11773e7i | 0.0643333i | ||||||||
\(559\) | 2.54770e8i | 1.45852i | ||||||||
\(560\) | −78908.5 | + | 78908.5i | −0.000449324 | + | 0.000449324i | ||||
\(561\) | 3.31482e7 | − | 3.31482e7i | 0.187746 | − | 0.187746i | ||||
\(562\) | 8.70489e7 | 0.490404 | ||||||||
\(563\) | 5.63680e7 | − | 5.63680e7i | 0.315869 | − | 0.315869i | −0.531309 | − | 0.847178i | \(-0.678300\pi\) |
0.847178 | + | 0.531309i | \(0.178300\pi\) | |||||||
\(564\) | −8.04371e7 | −0.448352 | ||||||||
\(565\) | −5.54321e6 | −0.0307338 | ||||||||
\(566\) | 5.34651e7i | 0.294864i | ||||||||
\(567\) | −1.61048e6 | −0.00883499 | ||||||||
\(568\) | 2.21326e7 | − | 2.21326e7i | 0.120778 | − | 0.120778i | ||||
\(569\) | 3.84710e7 | + | 3.84710e7i | 0.208832 | + | 0.208832i | 0.803771 | − | 0.594939i | \(-0.202824\pi\) |
−0.594939 | + | 0.803771i | \(0.702824\pi\) | |||||||
\(570\) | 4.20098e6 | + | 4.20098e6i | 0.0226843 | + | 0.0226843i | ||||
\(571\) | 2.43126e8 | 1.30594 | 0.652970 | − | 0.757384i | \(-0.273523\pi\) | ||||
0.652970 | + | 0.757384i | \(0.273523\pi\) | |||||||
\(572\) | −1.29368e7 | + | 1.29368e7i | −0.0691255 | + | 0.0691255i | ||||
\(573\) | −1.02877e8 | − | 1.02877e8i | −0.546830 | − | 0.546830i | ||||
\(574\) | −342243. | + | 342243.i | −0.00180967 | + | 0.00180967i | ||||
\(575\) | 6.29070e7 | + | 6.29070e7i | 0.330899 | + | 0.330899i | ||||
\(576\) | − | 1.05315e7i | − | 0.0551089i | ||||||
\(577\) | −2.09577e8 | + | 2.09577e8i | −1.09098 | + | 1.09098i | −0.0955517 | + | 0.995424i | \(0.530462\pi\) |
−0.995424 | + | 0.0955517i | \(0.969538\pi\) | |||||||
\(578\) | −2.66220e8 | + | 2.66220e8i | −1.37866 | + | 1.37866i | ||||
\(579\) | 4.03053e7 | + | 4.03053e7i | 0.207647 | + | 0.207647i | ||||
\(580\) | 1.77817e7i | 0.0911357i | ||||||||
\(581\) | 2.98522e6 | 0.0152212 | ||||||||
\(582\) | − | 5.56367e6i | − | 0.0282223i | ||||||
\(583\) | − | 2.02081e7i | − | 0.101981i | ||||||
\(584\) | 6.74401e7 | + | 6.74401e7i | 0.338594 | + | 0.338594i | ||||
\(585\) | − | 9.88574e6i | − | 0.0493789i | ||||||
\(586\) | −3.80202e7 | − | 3.80202e7i | −0.188939 | − | 0.188939i | ||||
\(587\) | 1.24110e8 | + | 1.24110e8i | 0.613610 | + | 0.613610i | 0.943885 | − | 0.330275i | \(-0.107142\pi\) |
−0.330275 | + | 0.943885i | \(0.607142\pi\) | |||||||
\(588\) | 7.59632e7 | 0.373655 | ||||||||
\(589\) | 2.43807e7 | 0.119317 | ||||||||
\(590\) | 1.07013e7 | − | 1.07013e7i | 0.0521050 | − | 0.0521050i | ||||
\(591\) | 3.27182e7i | 0.158499i | ||||||||
\(592\) | 1.08406e7 | − | 5.07232e7i | 0.0522502 | − | 0.244479i | ||||
\(593\) | −2.45373e8 | −1.17669 | −0.588345 | − | 0.808610i | \(-0.700220\pi\) | ||||
−0.588345 | + | 0.808610i | \(0.700220\pi\) | |||||||
\(594\) | 2.06825e7 | + | 2.06825e7i | 0.0986831 | + | 0.0986831i | ||||
\(595\) | 1.03783e6i | 0.00492690i | ||||||||
\(596\) | 1.21264e8i | 0.572787i | ||||||||
\(597\) | 7.79086e7 | − | 7.79086e7i | 0.366153 | − | 0.366153i | ||||
\(598\) | −5.39989e7 | + | 5.39989e7i | −0.252512 | + | 0.252512i | ||||
\(599\) | 3.44657e8 | 1.60364 | 0.801819 | − | 0.597567i | \(-0.203866\pi\) | ||||
0.801819 | + | 0.597567i | \(0.203866\pi\) | |||||||
\(600\) | −3.99338e7 | + | 3.99338e7i | −0.184879 | + | 0.184879i | ||||
\(601\) | 1.91557e8 | 0.882421 | 0.441210 | − | 0.897404i | \(-0.354549\pi\) | ||||
0.441210 | + | 0.897404i | \(0.354549\pi\) | |||||||
\(602\) | 5.10613e6 | 0.0234047 | ||||||||
\(603\) | − | 1.55502e8i | − | 0.709226i | ||||||
\(604\) | 1.23863e8 | 0.562123 | ||||||||
\(605\) | 1.58805e7 | − | 1.58805e7i | 0.0717132 | − | 0.0717132i | ||||
\(606\) | 3.50612e7 | + | 3.50612e7i | 0.157547 | + | 0.157547i | ||||
\(607\) | −3.62425e7 | − | 3.62425e7i | −0.162051 | − | 0.162051i | 0.621424 | − | 0.783475i | \(-0.286555\pi\) |
−0.783475 | + | 0.621424i | \(0.786555\pi\) | |||||||
\(608\) | −2.29719e7 | −0.102208 | ||||||||
\(609\) | −5.02424e6 | + | 5.02424e6i | −0.0222443 | + | 0.0222443i | ||||
\(610\) | 5.22504e6 | + | 5.22504e6i | 0.0230197 | + | 0.0230197i | ||||
\(611\) | 2.06440e8 | − | 2.06440e8i | 0.905044 | − | 0.905044i | ||||
\(612\) | −6.92564e7 | − | 6.92564e7i | −0.302138 | − | 0.302138i | ||||
\(613\) | 4.08087e8i | 1.77162i | 0.464047 | + | 0.885811i | \(0.346397\pi\) | ||||
−0.464047 | + | 0.885811i | \(0.653603\pi\) | |||||||
\(614\) | −1.52154e8 | + | 1.52154e8i | −0.657321 | + | 0.657321i | ||||
\(615\) | 1.92857e6 | − | 1.92857e6i | 0.00829107 | − | 0.00829107i | ||||
\(616\) | 259281. | + | 259281.i | 0.00110925 | + | 0.00110925i | ||||
\(617\) | − | 2.02329e8i | − | 0.861396i | −0.902496 | − | 0.430698i | \(-0.858267\pi\) | ||
0.902496 | − | 0.430698i | \(-0.141733\pi\) | |||||||
\(618\) | −1.80135e7 | −0.0763189 | ||||||||
\(619\) | 1.53352e8i | 0.646574i | 0.946301 | + | 0.323287i | \(0.104788\pi\) | ||||
−0.946301 | + | 0.323287i | \(0.895212\pi\) | |||||||
\(620\) | − | 2.58061e6i | − | 0.0108280i | ||||||
\(621\) | 8.63298e7 | + | 8.63298e7i | 0.360484 | + | 0.360484i | ||||
\(622\) | 3.12975e8i | 1.30058i | ||||||||
\(623\) | 2.59908e6 | + | 2.59908e6i | 0.0107487 | + | 0.0107487i | ||||
\(624\) | −3.42789e7 | − | 3.42789e7i | −0.141082 | − | 0.141082i | ||||
\(625\) | −2.36105e8 | −0.967085 | ||||||||
\(626\) | 1.70645e8 | 0.695619 | ||||||||
\(627\) | 1.38037e7 | − | 1.38037e7i | 0.0560008 | − | 0.0560008i | ||||
\(628\) | 1.61693e8i | 0.652848i | ||||||||
\(629\) | −2.62273e8 | − | 4.04852e8i | −1.05391 | − | 1.62684i | ||||
\(630\) | −198131. | −0.000792376 | ||||||||
\(631\) | −1.36434e8 | − | 1.36434e8i | −0.543042 | − | 0.543042i | 0.381378 | − | 0.924419i | \(-0.375450\pi\) |
−0.924419 | + | 0.381378i | \(0.875450\pi\) | |||||||
\(632\) | − | 1.57889e8i | − | 0.625460i | ||||||
\(633\) | − | 1.20787e8i | − | 0.476221i | ||||||
\(634\) | 4.47942e7 | − | 4.47942e7i | 0.175774 | − | 0.175774i | ||||
\(635\) | −1.60063e7 | + | 1.60063e7i | −0.0625130 | + | 0.0625130i | ||||
\(636\) | 5.35458e7 | 0.208139 | ||||||||
\(637\) | −1.94958e8 | + | 1.94958e8i | −0.754262 | + | 0.754262i | ||||
\(638\) | 5.84278e7 | 0.224987 | ||||||||
\(639\) | 5.55728e7 | 0.212990 | ||||||||
\(640\) | 2.43149e6i | 0.00927541i | ||||||||
\(641\) | 3.98764e8 | 1.51406 | 0.757028 | − | 0.653382i | \(-0.226650\pi\) | ||||
0.757028 | + | 0.653382i | \(0.226650\pi\) | |||||||
\(642\) | 1.77498e7 | − | 1.77498e7i | 0.0670791 | − | 0.0670791i | ||||
\(643\) | 2.88666e8 | + | 2.88666e8i | 1.08583 | + | 1.08583i | 0.995953 | + | 0.0898795i | \(0.0286482\pi\) |
0.0898795 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(644\) | 1.08225e6 | + | 1.08225e6i | 0.00405202 | + | 0.00405202i | ||||
\(645\) | −2.87736e7 | −0.107230 | ||||||||
\(646\) | −1.51066e8 | + | 1.51066e8i | −0.560364 | + | 0.560364i | ||||
\(647\) | 8.75493e6 | + | 8.75493e6i | 0.0323251 | + | 0.0323251i | 0.723085 | − | 0.690759i | \(-0.242724\pi\) |
−0.690759 | + | 0.723085i | \(0.742724\pi\) | |||||||
\(648\) | −2.48127e7 | + | 2.48127e7i | −0.0911904 | + | 0.0911904i | ||||
\(649\) | −3.51627e7 | − | 3.51627e7i | −0.128632 | − | 0.128632i | ||||
\(650\) | − | 2.04978e8i | − | 0.746393i | ||||||
\(651\) | 729155. | − | 729155.i | 0.00264288 | − | 0.00264288i | ||||
\(652\) | 9.65285e7 | − | 9.65285e7i | 0.348267 | − | 0.348267i | ||||
\(653\) | −1.85611e8 | − | 1.85611e8i | −0.666599 | − | 0.666599i | 0.290328 | − | 0.956927i | \(-0.406236\pi\) |
−0.956927 | + | 0.290328i | \(0.906236\pi\) | |||||||
\(654\) | 1.30319e8i | 0.465881i | ||||||||
\(655\) | 4.71997e7 | 0.167964 | ||||||||
\(656\) | 1.05459e7i | 0.0373570i | ||||||||
\(657\) | 1.69335e8i | 0.597106i | ||||||||
\(658\) | −4.13750e6 | − | 4.13750e6i | −0.0145231 | − | 0.0145231i | ||||
\(659\) | − | 3.74110e8i | − | 1.30720i | −0.756839 | − | 0.653601i | \(-0.773257\pi\) | ||
0.756839 | − | 0.653601i | \(-0.226743\pi\) | |||||||
\(660\) | −1.46107e6 | − | 1.46107e6i | −0.00508207 | − | 0.00508207i | ||||
\(661\) | −2.47910e8 | − | 2.47910e8i | −0.858400 | − | 0.858400i | 0.132749 | − | 0.991150i | \(-0.457619\pi\) |
−0.991150 | + | 0.132749i | \(0.957619\pi\) | |||||||
\(662\) | −3.90428e8 | −1.34576 | ||||||||
\(663\) | −4.50845e8 | −1.54699 | ||||||||
\(664\) | 4.59934e7 | − | 4.59934e7i | 0.157105 | − | 0.157105i | ||||
\(665\) | 432177.i | 0.00146959i | ||||||||
\(666\) | 7.72902e7 | − | 5.00706e7i | 0.261639 | − | 0.169496i | ||||
\(667\) | 2.43881e8 | 0.821865 | ||||||||
\(668\) | −1.27658e8 | − | 1.27658e8i | −0.428272 | − | 0.428272i | ||||
\(669\) | − | 2.41608e8i | − | 0.806926i | ||||||
\(670\) | 3.59021e7i | 0.119370i | ||||||||
\(671\) | 1.71686e7 | − | 1.71686e7i | 0.0568288 | − | 0.0568288i | ||||
\(672\) | −687022. | + | 687022.i | −0.00226393 | + | 0.00226393i | ||||
\(673\) | 3.46494e8 | 1.13671 | 0.568356 | − | 0.822782i | \(-0.307579\pi\) | ||||
0.568356 | + | 0.822782i | \(0.307579\pi\) | |||||||
\(674\) | −7.72999e7 | + | 7.72999e7i | −0.252464 | + | 0.252464i | ||||
\(675\) | −3.27705e8 | −1.06555 | ||||||||
\(676\) | 2.14940e7 | 0.0695788 | ||||||||
\(677\) | − | 3.89453e7i | − | 0.125513i | −0.998029 | − | 0.0627565i | \(-0.980011\pi\) | ||
0.998029 | − | 0.0627565i | \(-0.0199892\pi\) | |||||||
\(678\) | −4.82623e7 | −0.154853 | ||||||||
\(679\) | 286182. | − | 286182.i | 0.000914183 | − | 0.000914183i | ||||
\(680\) | 1.59898e7 | + | 1.59898e7i | 0.0508530 | + | 0.0508530i | ||||
\(681\) | −1.85320e8 | − | 1.85320e8i | −0.586789 | − | 0.586789i | ||||
\(682\) | −8.47947e6 | −0.0267310 | ||||||||
\(683\) | 2.57774e8 | − | 2.57774e8i | 0.809054 | − | 0.809054i | −0.175437 | − | 0.984491i | \(-0.556134\pi\) |
0.984491 | + | 0.175437i | \(0.0561338\pi\) | |||||||
\(684\) | −2.88401e7 | − | 2.88401e7i | −0.0901215 | − | 0.0901215i | ||||
\(685\) | 2.46082e7 | − | 2.46082e7i | 0.0765612 | − | 0.0765612i | ||||
\(686\) | 7.81703e6 | + | 7.81703e6i | 0.0242142 | + | 0.0242142i | ||||
\(687\) | 8.70091e6i | 0.0268346i | ||||||||
\(688\) | 7.86703e7 | − | 7.86703e7i | 0.241571 | − | 0.241571i | ||||
\(689\) | −1.37424e8 | + | 1.37424e8i | −0.420150 | + | 0.420150i | ||||
\(690\) | −6.09861e6 | − | 6.09861e6i | −0.0185645 | − | 0.0185645i | ||||
\(691\) | 3.05557e7i | 0.0926100i | 0.998927 | + | 0.0463050i | \(0.0147446\pi\) | ||||
−0.998927 | + | 0.0463050i | \(0.985255\pi\) | |||||||
\(692\) | 2.60884e8 | 0.787279 | ||||||||
\(693\) | 651029.i | 0.00195614i | ||||||||
\(694\) | − | 9.42932e7i | − | 0.282099i | ||||||
\(695\) | −3.57622e7 | − | 3.57622e7i | −0.106529 | − | 0.106529i | ||||
\(696\) | 1.54817e8i | 0.459189i | ||||||||
\(697\) | 6.93512e7 | + | 6.93512e7i | 0.204812 | + | 0.204812i | ||||
\(698\) | −2.44338e8 | − | 2.44338e8i | −0.718496 | − | 0.718496i | ||||
\(699\) | −3.92841e8 | −1.15023 | ||||||||
\(700\) | −4.10820e6 | −0.0119773 | ||||||||
\(701\) | 1.93439e8 | − | 1.93439e8i | 0.561551 | − | 0.561551i | −0.368197 | − | 0.929748i | \(-0.620025\pi\) |
0.929748 | + | 0.368197i | \(0.120025\pi\) | |||||||
\(702\) | − | 2.81300e8i | − | 0.813126i | ||||||
\(703\) | −1.09217e8 | − | 1.68590e8i | −0.314358 | − | 0.485251i | ||||
\(704\) | 7.98950e6 | 0.0228982 | ||||||||
\(705\) | 2.33152e7 | + | 2.33152e7i | 0.0665383 | + | 0.0665383i | ||||
\(706\) | − | 6.29830e7i | − | 0.178982i | ||||||
\(707\) | 3.60694e6i | 0.0102066i | ||||||||
\(708\) | 9.31712e7 | − | 9.31712e7i | 0.262532 | − | 0.262532i | ||||
\(709\) | 3.90628e8 | − | 3.90628e8i | 1.09604 | − | 1.09604i | 0.101166 | − | 0.994870i | \(-0.467743\pi\) |
0.994870 | − | 0.101166i | \(-0.0322573\pi\) | |||||||
\(710\) | −1.28306e7 | −0.0358485 | ||||||||
\(711\) | 1.98221e8 | − | 1.98221e8i | 0.551494 | − | 0.551494i | ||||
\(712\) | 8.00881e7 | 0.221885 | ||||||||
\(713\) | −3.53938e7 | −0.0976470 | ||||||||
\(714\) | 9.03590e6i | 0.0248243i | ||||||||
\(715\) | 7.49963e6 | 0.0205174 | ||||||||
\(716\) | 8.14043e6 | − | 8.14043e6i | 0.0221773 | − | 0.0221773i | ||||
\(717\) | 3.39795e8 | + | 3.39795e8i | 0.921847 | + | 0.921847i | ||||
\(718\) | −2.60845e8 | − | 2.60845e8i | −0.704708 | − | 0.704708i | ||||
\(719\) | −2.40488e8 | −0.647003 | −0.323501 | − | 0.946228i | \(-0.604860\pi\) | ||||
−0.323501 | + | 0.946228i | \(0.604860\pi\) | |||||||
\(720\) | −3.05262e6 | + | 3.05262e6i | −0.00817852 | + | 0.00817852i | ||||
\(721\) | −926571. | − | 926571.i | −0.00247214 | − | 0.00247214i | ||||
\(722\) | 1.25276e8 | − | 1.25276e8i | 0.332855 | − | 0.332855i | ||||
\(723\) | −9.70159e7 | − | 9.70159e7i | −0.256701 | − | 0.256701i | ||||
\(724\) | 2.64797e7i | 0.0697747i | ||||||||
\(725\) | −4.62882e8 | + | 4.62882e8i | −1.21466 | + | 1.21466i | ||||
\(726\) | 1.38265e8 | − | 1.38265e8i | 0.361328 | − | 0.361328i | ||||
\(727\) | 4.28916e8 | + | 4.28916e8i | 1.11627 | + | 1.11627i | 0.992284 | + | 0.123986i | \(0.0395677\pi\) |
0.123986 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(728\) | − | 3.52645e6i | − | 0.00913995i | ||||||
\(729\) | −3.74421e8 | −0.966445 | ||||||||
\(730\) | − | 3.90959e7i | − | 0.100499i | ||||||
\(731\) | − | 1.03469e9i | − | 2.64886i | ||||||
\(732\) | 4.54921e7 | + | 4.54921e7i | 0.115985 | + | 0.115985i | ||||
\(733\) | 3.86581e8i | 0.981586i | 0.871276 | + | 0.490793i | \(0.163293\pi\) | ||||
−0.871276 | + | 0.490793i | \(0.836707\pi\) | |||||||
\(734\) | 3.77052e8 | + | 3.77052e8i | 0.953483 | + | 0.953483i | ||||
\(735\) | −2.20184e7 | − | 2.20184e7i | −0.0554529 | − | 0.0554529i | ||||
\(736\) | 3.33487e7 | 0.0836459 | ||||||||
\(737\) | 1.17969e8 | 0.294689 | ||||||||
\(738\) | −1.32398e7 | + | 1.32398e7i | −0.0329392 | + | 0.0329392i | ||||
\(739\) | 2.15335e8i | 0.533556i | 0.963758 | + | 0.266778i | \(0.0859591\pi\) | ||||
−0.963758 | + | 0.266778i | \(0.914041\pi\) | |||||||
\(740\) | −1.78447e7 | + | 1.15602e7i | −0.0440365 | + | 0.0285280i | ||||
\(741\) | −1.87743e8 | −0.461434 | ||||||||
\(742\) | 2.75427e6 | + | 2.75427e6i | 0.00674209 | + | 0.00674209i | ||||
\(743\) | 5.62436e8i | 1.37122i | 0.727970 | + | 0.685609i | \(0.240464\pi\) | ||||
−0.727970 | + | 0.685609i | \(0.759536\pi\) | |||||||
\(744\) | − | 2.24682e7i | − | 0.0545569i | ||||||
\(745\) | 3.51492e7 | − | 3.51492e7i | 0.0850053 | − | 0.0850053i | ||||
\(746\) | −1.56830e8 | + | 1.56830e8i | −0.377756 | + | 0.377756i | ||||
\(747\) | 1.15485e8 | 0.277053 | ||||||||
\(748\) | 5.25400e7 | − | 5.25400e7i | 0.125541 | − | 0.125541i | ||||
\(749\) | 1.82601e6 | 0.00434569 | ||||||||
\(750\) | 4.65580e7 | 0.110360 | ||||||||
\(751\) | 1.10982e8i | 0.262020i | 0.991381 | + | 0.131010i | \(0.0418219\pi\) | ||||
−0.991381 | + | 0.131010i | \(0.958178\pi\) | |||||||
\(752\) | −1.27493e8 | −0.299801 | ||||||||
\(753\) | 1.32813e8 | − | 1.32813e8i | 0.311068 | − | 0.311068i | ||||
\(754\) | −3.97335e8 | − | 3.97335e8i | −0.926921 | − | 0.926921i | ||||
\(755\) | −3.59025e7 | − | 3.59025e7i | −0.0834226 | − | 0.0834226i | ||||
\(756\) | −5.63785e6 | −0.0130481 | ||||||||
\(757\) | 2.08014e8 | − | 2.08014e8i | 0.479518 | − | 0.479518i | −0.425459 | − | 0.904978i | \(-0.639887\pi\) |
0.904978 | + | 0.425459i | \(0.139887\pi\) | |||||||
\(758\) | −1.47232e8 | − | 1.47232e8i | −0.338061 | − | 0.338061i | ||||
\(759\) | −2.00391e7 | + | 2.00391e7i | −0.0458303 | + | 0.0458303i | ||||
\(760\) | 6.65856e6 | + | 6.65856e6i | 0.0151684 | + | 0.0151684i | ||||
\(761\) | 2.96475e8i | 0.672719i | 0.941734 | + | 0.336359i | \(0.109196\pi\) | ||||
−0.941734 | + | 0.336359i | \(0.890804\pi\) | |||||||
\(762\) | −1.39360e8 | + | 1.39360e8i | −0.314973 | + | 0.314973i | ||||
\(763\) | −6.70331e6 | + | 6.70331e6i | −0.0150909 | + | 0.0150909i | ||||
\(764\) | −1.63060e8 | − | 1.63060e8i | −0.365651 | − | 0.365651i | ||||
\(765\) | 4.01488e7i | 0.0896785i | ||||||||
\(766\) | 1.96299e8 | 0.436749 | ||||||||
\(767\) | 4.78244e8i | 1.05990i | ||||||||
\(768\) | 2.11699e7i | 0.0467343i | ||||||||
\(769\) | 4.29336e8 | + | 4.29336e8i | 0.944101 | + | 0.944101i | 0.998518 | − | 0.0544175i | \(-0.0173302\pi\) |
−0.0544175 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(770\) | − | 150309.i | − | 0.000329239i | ||||||
\(771\) | 1.73406e8 | + | 1.73406e8i | 0.378357 | + | 0.378357i | ||||
\(772\) | 6.38840e7 | + | 6.38840e7i | 0.138848 | + | 0.138848i | ||||
\(773\) | −3.70319e8 | −0.801746 | −0.400873 | − | 0.916134i | \(-0.631293\pi\) | ||||
−0.400873 | + | 0.916134i | \(0.631293\pi\) | |||||||
\(774\) | 1.97533e8 | 0.426007 | ||||||||
\(775\) | 6.71769e7 | − | 6.71769e7i | 0.144316 | − | 0.144316i | ||||
\(776\) | − | 8.81843e6i | − | 0.0188715i | ||||||
\(777\) | −8.30840e6 | − | 1.77568e6i | −0.0177115 | − | 0.00378530i | ||||
\(778\) | 5.05765e8 | 1.07401 | ||||||||
\(779\) | 2.88796e7 | + | 2.88796e7i | 0.0610911 | + | 0.0610911i | ||||
\(780\) | 1.98719e7i | 0.0418751i | ||||||||
\(781\) | 4.21592e7i | 0.0884992i | ||||||||
\(782\) | 2.19305e8 | − | 2.19305e8i | 0.458594 | − | 0.458594i | ||||
\(783\) | −6.35231e8 | + | 6.35231e8i | −1.32326 | + | 1.32326i | ||||
\(784\) | 1.20402e8 | 0.249853 | ||||||||
\(785\) | 4.68677e7 | − | 4.68677e7i | 0.0968869 | − | 0.0968869i | ||||
\(786\) | 4.10947e8 | 0.846288 | ||||||||
\(787\) | −3.63995e8 | −0.746744 | −0.373372 | − | 0.927682i | \(-0.621798\pi\) | ||||
−0.373372 | + | 0.927682i | \(0.621798\pi\) | |||||||
\(788\) | 5.18585e7i | 0.105984i | ||||||||
\(789\) | 1.58650e8 | 0.323006 | ||||||||
\(790\) | −4.57650e7 | + | 4.57650e7i | −0.0928223 | + | 0.0928223i | ||||
\(791\) | −2.48250e6 | − | 2.48250e6i | −0.00501603 | − | 0.00501603i | ||||
\(792\) | 1.00304e7 | + | 1.00304e7i | 0.0201903 | + | 0.0201903i | ||||
\(793\) | −2.33509e8 | −0.468256 | ||||||||
\(794\) | 4.34488e7 | − | 4.34488e7i | 0.0867994 | − | 0.0867994i | ||||
\(795\) | −1.55206e7 | − | 1.55206e7i | −0.0308892 | − | 0.0308892i | ||||
\(796\) | 1.23485e8 | − | 1.23485e8i | 0.244837 | − | 0.244837i | ||||
\(797\) | −4.55860e8 | − | 4.55860e8i | −0.900444 | − | 0.900444i | 0.0950306 | − | 0.995474i | \(-0.469705\pi\) |
−0.995474 | + | 0.0950306i | \(0.969705\pi\) | |||||||
\(798\) | 3.76278e6i | 0.00740457i | ||||||||
\(799\) | −8.38411e8 | + | 8.38411e8i | −1.64368 | + | 1.64368i | ||||
\(800\) | −6.32952e7 | + | 6.32952e7i | −0.123623 | + | 0.123623i | ||||
\(801\) | 1.00547e8 | + | 1.00547e8i | 0.195645 | + | 0.195645i | ||||
\(802\) | 3.62094e8i | 0.701937i | ||||||||
\(803\) | −1.28463e8 | −0.248103 | ||||||||
\(804\) | 3.12584e8i | 0.601449i | ||||||||
\(805\) | − | 627397.i | − | 0.00120269i | ||||||
\(806\) | 5.76642e7 | + | 5.76642e7i | 0.110129 | + | 0.110129i | ||||
\(807\) | 3.25778e8i | 0.619871i | ||||||||
\(808\) | 5.55722e7 | + | 5.55722e7i | 0.105347 | + | 0.105347i | ||||
\(809\) | 4.76133e8 | + | 4.76133e8i | 0.899255 | + | 0.899255i | 0.995370 | − | 0.0961157i | \(-0.0306419\pi\) |
−0.0961157 | + | 0.995370i | \(0.530642\pi\) | |||||||
\(810\) | 1.43842e7 | 0.0270665 | ||||||||
\(811\) | 2.09397e8 | 0.392561 | 0.196281 | − | 0.980548i | \(-0.437114\pi\) | ||||
0.196281 | + | 0.980548i | \(0.437114\pi\) | |||||||
\(812\) | −7.96344e6 | + | 7.96344e6i | −0.0148742 | + | 0.0148742i | ||||
\(813\) | 3.59206e8i | 0.668454i | ||||||||
\(814\) | 3.79851e7 | + | 5.86347e7i | 0.0704271 | + | 0.108713i | ||||
\(815\) | −5.59588e7 | −0.103370 | ||||||||
\(816\) | 1.39216e8 | + | 1.39216e8i | 0.256224 | + | 0.256224i | ||||
\(817\) | − | 4.30872e8i | − | 0.790100i | ||||||
\(818\) | 1.31203e8i | 0.239709i | ||||||||
\(819\) | 4.42728e6 | − | 4.42728e6i | 0.00805908 | − | 0.00805908i | ||||
\(820\) | 3.05679e6 | − | 3.05679e6i | 0.00554402 | − | 0.00554402i | ||||
\(821\) | 1.68790e8 | 0.305013 | 0.152506 | − | 0.988302i | \(-0.451266\pi\) | ||||
0.152506 | + | 0.988302i | \(0.451266\pi\) | |||||||
\(822\) | 2.14253e8 | − | 2.14253e8i | 0.385755 | − | 0.385755i | ||||
\(823\) | −4.01876e8 | −0.720928 | −0.360464 | − | 0.932773i | \(-0.617382\pi\) | ||||
−0.360464 | + | 0.932773i | \(0.617382\pi\) | |||||||
\(824\) | −2.85514e7 | −0.0510324 | ||||||||
\(825\) | − | 7.60677e7i | − | 0.135469i | ||||||
\(826\) | 9.58503e6 | 0.0170080 | ||||||||
\(827\) | 2.23264e8 | − | 2.23264e8i | 0.394731 | − | 0.394731i | −0.481639 | − | 0.876370i | \(-0.659958\pi\) |
0.876370 | + | 0.481639i | \(0.159958\pi\) | |||||||
\(828\) | 4.18675e7 | + | 4.18675e7i | 0.0737542 | + | 0.0737542i | ||||
\(829\) | 4.07300e8 | + | 4.07300e8i | 0.714909 | + | 0.714909i | 0.967558 | − | 0.252649i | \(-0.0813018\pi\) |
−0.252649 | + | 0.967558i | \(0.581302\pi\) | |||||||
\(830\) | −2.66630e7 | −0.0466309 | ||||||||
\(831\) | 2.64322e8 | − | 2.64322e8i | 0.460606 | − | 0.460606i | ||||
\(832\) | −5.43322e7 | − | 5.43322e7i | −0.0943381 | − | 0.0943381i | ||||
\(833\) | 7.91779e8 | − | 7.91779e8i | 1.36984 | − | 1.36984i | ||||
\(834\) | −3.11366e8 | − | 3.11366e8i | −0.536751 | − | 0.536751i | ||||
\(835\) | 7.40052e7i | 0.127117i | ||||||||
\(836\) | 2.18790e7 | − | 2.18790e7i | 0.0374463 | − | 0.0374463i | ||||
\(837\) | 9.21895e7 | − | 9.21895e7i | 0.157219 | − | 0.157219i | ||||
\(838\) | −3.27150e8 | − | 3.27150e8i | −0.555924 | − | 0.555924i | ||||
\(839\) | − | 2.92272e7i | − | 0.0494881i | −0.999694 | − | 0.0247441i | \(-0.992123\pi\) | ||
0.999694 | − | 0.0247441i | \(-0.00787708\pi\) | |||||||
\(840\) | 398276. | 0.000671964 | ||||||||
\(841\) | 1.19970e9i | 2.01690i | ||||||||
\(842\) | − | 3.49409e8i | − | 0.585326i | ||||||
\(843\) | −2.19681e8 | − | 2.19681e8i | −0.366699 | − | 0.366699i | ||||
\(844\) | − | 1.91447e8i | − | 0.318436i | ||||||
\(845\) | −6.23017e6 | − | 6.23017e6i | −0.0103260 | − | 0.0103260i | ||||
\(846\) | −1.60061e8 | − | 1.60061e8i | −0.264347 | − | 0.264347i | ||||
\(847\) | 1.42241e7 | 0.0234085 | ||||||||
\(848\) | 8.48702e7 | 0.139177 | ||||||||
\(849\) | 1.34927e8 | − | 1.34927e8i | 0.220484 | − | 0.220484i | ||||
\(850\) | 8.32476e8i | 1.35555i | ||||||||
\(851\) | 1.58552e8 | + | 2.44745e8i | 0.257266 | + | 0.397123i | ||||
\(852\) | −1.11710e8 | −0.180623 | ||||||||
\(853\) | −4.61668e8 | − | 4.61668e8i | −0.743845 | − | 0.743845i | 0.229471 | − | 0.973316i | \(-0.426300\pi\) |
−0.973316 | + | 0.229471i | \(0.926300\pi\) | |||||||
\(854\) | 4.68002e6i | 0.00751405i | ||||||||
\(855\) | 1.67190e7i | 0.0267492i | ||||||||
\(856\) | 2.81334e7 | − | 2.81334e7i | 0.0448540 | − | 0.0448540i | ||||
\(857\) | −2.21175e8 | + | 2.21175e8i | −0.351393 | + | 0.351393i | −0.860628 | − | 0.509235i | \(-0.829929\pi\) |
0.509235 | + | 0.860628i | \(0.329929\pi\) | |||||||
\(858\) | 6.52960e7 | 0.103377 | ||||||||
\(859\) | 1.54957e8 | − | 1.54957e8i | 0.244474 | − | 0.244474i | −0.574224 | − | 0.818698i | \(-0.694696\pi\) |
0.818698 | + | 0.574224i | \(0.194696\pi\) | |||||||
\(860\) | −4.56062e7 | −0.0717015 | ||||||||
\(861\) | 1.72740e6 | 0.00270635 | ||||||||
\(862\) | 3.25027e8i | 0.507454i | ||||||||
\(863\) | −1.02709e9 | −1.59800 | −0.798999 | − | 0.601332i | \(-0.794637\pi\) | ||||
−0.798999 | + | 0.601332i | \(0.794637\pi\) | |||||||
\(864\) | −8.68625e7 | + | 8.68625e7i | −0.134676 | + | 0.134676i | ||||
\(865\) | −7.56188e7 | − | 7.56188e7i | −0.116837 | − | 0.116837i | ||||
\(866\) | 5.50741e8 | + | 5.50741e8i | 0.847995 | + | 0.847995i | ||||
\(867\) | 1.34369e9 | 2.06178 | ||||||||
\(868\) | 1.15571e6 | − | 1.15571e6i | 0.00176722 | − | 0.00176722i | ||||
\(869\) | 1.50377e8 | + | 1.50377e8i | 0.229151 | + | 0.229151i | ||||
\(870\) | 4.48748e7 | − | 4.48748e7i | 0.0681466 | − | 0.0681466i | ||||
\(871\) | −8.02240e8 | − | 8.02240e8i | −1.21409 | − | 1.21409i | ||||
\(872\) | 2.06556e8i | 0.311522i | ||||||||
\(873\) | 1.10711e7 | − | 1.10711e7i | 0.0166398 | − | 0.0166398i | ||||
\(874\) | 9.13242e7 | − | 9.13242e7i | 0.136789 | − | 0.136789i | ||||
\(875\) | 2.39484e6 | + | 2.39484e6i | 0.00357480 | + | 0.00357480i | ||||
\(876\) | − | 3.40391e8i | − | 0.506367i | ||||||
\(877\) | −1.81172e8 | −0.268591 | −0.134296 | − | 0.990941i | \(-0.542877\pi\) | ||||
−0.134296 | + | 0.990941i | \(0.542877\pi\) | |||||||
\(878\) | − | 6.55601e7i | − | 0.0968626i | ||||||
\(879\) | 1.91900e8i | 0.282558i | ||||||||
\(880\) | −2.31581e6 | − | 2.31581e6i | −0.00339824 | − | 0.00339824i | ||||
\(881\) | 8.94016e8i | 1.30743i | 0.756742 | + | 0.653714i | \(0.226790\pi\) | ||||
−0.756742 | + | 0.653714i | \(0.773210\pi\) | |||||||
\(882\) | 1.51158e8 | + | 1.51158e8i | 0.220306 | + | 0.220306i | ||||
\(883\) | −9.00390e8 | − | 9.00390e8i | −1.30782 | − | 1.30782i | −0.922984 | − | 0.384838i | \(-0.874257\pi\) |
−0.384838 | − | 0.922984i | \(-0.625743\pi\) | |||||||
\(884\) | −7.14591e8 | −1.03443 | ||||||||
\(885\) | −5.40126e7 | −0.0779229 | ||||||||
\(886\) | 4.97924e8 | − | 4.97924e8i | 0.715915 | − | 0.715915i | ||||
\(887\) | − | 2.33052e8i | − | 0.333950i | −0.985961 | − | 0.166975i | \(-0.946600\pi\) | ||
0.985961 | − | 0.166975i | \(-0.0534000\pi\) | |||||||
\(888\) | −1.55366e8 | + | 1.00650e8i | −0.221879 | + | 0.143739i | ||||
\(889\) | −1.43367e7 | −0.0204054 | ||||||||
\(890\) | −2.32140e7 | − | 2.32140e7i | −0.0329292 | − | 0.0329292i | ||||
\(891\) | − | 4.72644e7i | − | 0.0668191i | ||||||
\(892\) | − | 3.82950e8i | − | 0.539570i | ||||||
\(893\) | −3.49135e8 | + | 3.49135e8i | −0.490275 | + | 0.490275i | ||||
\(894\) | 3.06028e8 | − | 3.06028e8i | 0.428301 | − | 0.428301i | ||||
\(895\) | −4.71911e6 | −0.00658251 | ||||||||
\(896\) | −1.08893e6 | + | 1.08893e6i | −0.00151383 | + | 0.00151383i | ||||
\(897\) | 2.72549e8 | 0.377631 | ||||||||
\(898\) | 1.19132e8 | 0.164513 | ||||||||
\(899\) | − | 2.60435e8i | − | 0.358442i | ||||||
\(900\) | −1.58928e8 | −0.218008 | ||||||||
\(901\) | 5.58118e8 | − | 5.58118e8i | 0.763048 | − | 0.763048i | ||||
\(902\) | −1.00441e7 | − | 1.00441e7i | −0.0136865 | − | 0.0136865i | ||||
\(903\) | −1.28861e7 | − | 1.28861e7i | −0.0175008 | − | 0.0175008i | ||||
\(904\) | −7.64959e7 | −0.103546 | ||||||||
\(905\) | 7.67532e6 | − | 7.67532e6i | 0.0103550 | − | 0.0103550i | ||||
\(906\) | −3.12587e8 | − | 3.12587e8i | −0.420327 | − | 0.420327i | ||||
\(907\) | 8.26420e8 | − | 8.26420e8i | 1.10759 | − | 1.10759i | 0.114124 | − | 0.993467i | \(-0.463594\pi\) |
0.993467 | − | 0.114124i | \(-0.0364061\pi\) | |||||||
\(908\) | −2.93734e8 | − | 2.93734e8i | −0.392370 | − | 0.392370i | ||||
\(909\) | 1.39536e8i | 0.185778i | ||||||||
\(910\) | −1.02217e6 | + | 1.02217e6i | −0.00135643 | + | 0.00135643i | ||||
\(911\) | −4.57595e8 | + | 4.57595e8i | −0.605237 | + | 0.605237i | −0.941698 | − | 0.336460i | \(-0.890770\pi\) |
0.336460 | + | 0.941698i | \(0.390770\pi\) | |||||||
\(912\) | 5.79732e7 | + | 5.79732e7i | 0.0764263 | + | 0.0764263i | ||||
\(913\) | 8.76103e7i | 0.115118i | ||||||||
\(914\) | −5.11042e8 | −0.669295 | ||||||||
\(915\) | − | 2.63724e7i | − | 0.0344259i | ||||||
\(916\) | 1.37910e7i | 0.0179436i | ||||||||
\(917\) | 2.11382e7 | + | 2.11382e7i | 0.0274132 | + | 0.0274132i | ||||
\(918\) | 1.14244e9i | 1.47674i | ||||||||
\(919\) | −5.96266e8 | − | 5.96266e8i | −0.768233 | − | 0.768233i | 0.209562 | − | 0.977795i | \(-0.432796\pi\) |
−0.977795 | + | 0.209562i | \(0.932796\pi\) | |||||||
\(920\) | −9.66632e6 | − | 9.66632e6i | −0.0124136 | − | 0.0124136i | ||||
\(921\) | 7.67967e8 | 0.983022 | ||||||||
\(922\) | −1.01393e9 | −1.29365 | ||||||||
\(923\) | 2.86701e8 | − | 2.86701e8i | 0.364607 | − | 0.364607i | ||||
\(924\) | − | 1.30867e6i | − | 0.00165888i | ||||||
\(925\) | −7.65451e8 | − | 1.63593e8i | −0.967146 | − | 0.206699i | ||||
\(926\) | −1.53448e8 | −0.193254 | ||||||||
\(927\) | −3.58449e7 | − | 3.58449e7i | −0.0449974 | − | 0.0449974i | ||||
\(928\) | 2.45386e8i | 0.307048i | ||||||||
\(929\) | 1.45466e7i | 0.0181432i | 0.999959 | + | 0.00907159i | \(0.00288762\pi\) | ||||
−0.999959 | + | 0.00907159i | \(0.997112\pi\) | |||||||
\(930\) | −6.51256e6 | + | 6.51256e6i | −0.00809660 | + | 0.00809660i | ||||
\(931\) | 3.29717e8 | − | 3.29717e8i | 0.408594 | − | 0.408594i | ||||
\(932\) | −6.22655e8 | −0.769130 | ||||||||
\(933\) | 7.89841e8 | − | 7.89841e8i | 0.972511 | − | 0.972511i | ||||
\(934\) | −4.25464e8 | −0.522182 | ||||||||
\(935\) | −3.04581e7 | −0.0372622 | ||||||||
\(936\) | − | 1.36423e8i | − | 0.166364i | ||||||
\(937\) | −3.48928e7 | −0.0424147 | −0.0212074 | − | 0.999775i | \(-0.506751\pi\) | ||||
−0.0212074 | + | 0.999775i | \(0.506751\pi\) | |||||||
\(938\) | −1.60786e7 | + | 1.60786e7i | −0.0194823 | + | 0.0194823i | ||||
\(939\) | −4.30650e8 | − | 4.30650e8i | −0.520148 | − | 0.520148i | ||||
\(940\) | 3.69547e7 | + | 3.69547e7i | 0.0444924 | + | 0.0444924i | ||||
\(941\) | 1.25247e9 | 1.50313 | 0.751567 | − | 0.659657i | \(-0.229298\pi\) | ||||
0.751567 | + | 0.659657i | \(0.229298\pi\) | |||||||
\(942\) | 4.08057e8 | − | 4.08057e8i | 0.488167 | − | 0.488167i | ||||
\(943\) | −4.19248e7 | − | 4.19248e7i | −0.0499961 | − | 0.0499961i | ||||
\(944\) | 1.47677e8 | − | 1.47677e8i | 0.175548 | − | 0.175548i | ||||
\(945\) | 1.63417e6 | + | 1.63417e6i | 0.00193643 | + | 0.00193643i | ||||
\(946\) | 1.49855e8i | 0.177010i | ||||||||
\(947\) | −5.62450e8 | + | 5.62450e8i | −0.662269 | + | 0.662269i | −0.955914 | − | 0.293646i | \(-0.905131\pi\) |
0.293646 | + | 0.955914i | \(0.405131\pi\) | |||||||
\(948\) | −3.98456e8 | + | 3.98456e8i | −0.467687 | + | 0.467687i | ||||
\(949\) | 8.73605e8 | + | 8.73605e8i | 1.02215 | + | 1.02215i | ||||
\(950\) | 3.46664e8i | 0.404332i | ||||||||
\(951\) | −2.26090e8 | −0.262870 | ||||||||
\(952\) | 1.43219e7i | 0.0165993i | ||||||||
\(953\) | − | 8.73569e8i | − | 1.00930i | −0.863325 | − | 0.504648i | \(-0.831622\pi\) | ||
0.863325 | − | 0.504648i | \(-0.168378\pi\) | |||||||
\(954\) | 1.06550e8 | + | 1.06550e8i | 0.122718 | + | 0.122718i | ||||
\(955\) | 9.45278e7i | 0.108530i | ||||||||
\(956\) | 5.38576e8 | + | 5.38576e8i | 0.616415 | + | 0.616415i | ||||
\(957\) | −1.47451e8 | − | 1.47451e8i | −0.168234 | − | 0.168234i | ||||
\(958\) | −2.86115e8 | −0.325420 | ||||||||
\(959\) | 2.20414e7 | 0.0249910 | ||||||||
\(960\) | 6.13624e6 | − | 6.13624e6i | 0.00693568 | − | 0.00693568i | ||||
\(961\) | − | 8.49707e8i | − | 0.957413i | ||||||
\(962\) | 1.40427e8 | − | 6.57058e8i | 0.157734 | − | 0.738037i | ||||
\(963\) | 7.06402e7 | 0.0790994 | ||||||||
\(964\) | −1.53771e8 | − | 1.53771e8i | −0.171649 | − | 0.171649i | ||||
\(965\) | − | 3.70344e7i | − | 0.0412119i | ||||||
\(966\) | − | 5.46247e6i | − | 0.00605979i | ||||||
\(967\) | 9.51226e8 | − | 9.51226e8i | 1.05197 | − | 1.05197i | 0.0533996 | − | 0.998573i | \(-0.482994\pi\) |
0.998573 | − | 0.0533996i | \(-0.0170057\pi\) | |||||||
\(968\) | 2.19150e8 | − | 2.19150e8i | 0.241611 | − | 0.241611i | ||||
\(969\) | 7.62479e8 | 0.838024 | ||||||||
\(970\) | −2.55608e6 | + | 2.55608e6i | −0.00280065 | + | 0.00280065i | ||||
\(971\) | 7.81268e8 | 0.853380 | 0.426690 | − | 0.904398i | \(-0.359680\pi\) | ||||
0.426690 | + | 0.904398i | \(0.359680\pi\) | |||||||
\(972\) | −3.69472e8 | −0.402330 | ||||||||
\(973\) | − | 3.20319e7i | − | 0.0347731i | ||||||
\(974\) | 8.48283e8 | 0.918044 | ||||||||
\(975\) | −5.17294e8 | + | 5.17294e8i | −0.558115 | + | 0.558115i | ||||
\(976\) | 7.21051e7 | + | 7.21051e7i | 0.0775563 | + | 0.0775563i | ||||
\(977\) | −1.11773e9 | − | 1.11773e9i | −1.19854 | − | 1.19854i | −0.974603 | − | 0.223939i | \(-0.928109\pi\) |
−0.223939 | − | 0.974603i | \(-0.571891\pi\) | |||||||
\(978\) | −4.87209e8 | −0.520833 | ||||||||
\(979\) | −7.62777e7 | + | 7.62777e7i | −0.0812923 | + | 0.0812923i | ||||
\(980\) | −3.48993e7 | − | 3.48993e7i | −0.0370799 | − | 0.0370799i | ||||
\(981\) | −2.59321e8 | + | 2.59321e8i | −0.274682 | + | 0.274682i | ||||
\(982\) | −4.64288e8 | − | 4.64288e8i | −0.490290 | − | 0.490290i | ||||
\(983\) | 5.46258e8i | 0.575091i | 0.957767 | + | 0.287546i | \(0.0928393\pi\) | ||||
−0.957767 | + | 0.287546i | \(0.907161\pi\) | |||||||
\(984\) | 2.66142e7 | − | 2.66142e7i | 0.0279336 | − | 0.0279336i | ||||
\(985\) | 1.50315e7 | − | 1.50315e7i | 0.0157288 | − | 0.0157288i | ||||
\(986\) | 1.61369e9 | + | 1.61369e9i | 1.68341 | + | 1.68341i | ||||
\(987\) | 2.08832e7i | 0.0217193i | ||||||||
\(988\) | −2.97574e8 | −0.308549 | ||||||||
\(989\) | 6.25503e8i | 0.646607i | ||||||||
\(990\) | − | 5.81476e6i | − | 0.00599275i | ||||||
\(991\) | 7.28375e8 | + | 7.28375e8i | 0.748400 | + | 0.748400i | 0.974179 | − | 0.225778i | \(-0.0724925\pi\) |
−0.225778 | + | 0.974179i | \(0.572492\pi\) | |||||||
\(992\) | − | 3.56122e7i | − | 0.0364808i | ||||||
\(993\) | 9.85305e8 | + | 9.85305e8i | 1.00629 | + | 1.00629i | ||||
\(994\) | −5.74611e6 | − | 5.74611e6i | −0.00585079 | − | 0.00585079i | ||||
\(995\) | −7.15861e7 | −0.0726707 | ||||||||
\(996\) | −2.32143e8 | −0.234951 | ||||||||
\(997\) | 4.98472e8 | − | 4.98472e8i | 0.502985 | − | 0.502985i | −0.409379 | − | 0.912364i | \(-0.634255\pi\) |
0.912364 | + | 0.409379i | \(0.134255\pi\) | |||||||
\(998\) | − | 4.75999e8i | − | 0.478867i | ||||||
\(999\) | −1.05046e9 | − | 2.24505e8i | −1.05362 | − | 0.225179i |
(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 | 74.7.d.b.31.7 | ✓ | 20 | |
37.6 | odd | 4 | inner | 74.7.d.b.43.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.b.31.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
74.7.d.b.43.4 | yes | 20 | 37.6 | odd | 4 | inner |