Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,6,Mod(7,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.7");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.c (of order \(3\), 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: | \(6.09458515289\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 386x^{6} + 3436x^{5} + 128708x^{4} + 568528x^{3} + 7340704x^{2} - 19430784x + 211527936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(2.36148 - 4.09020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.7 |
Dual form | 38.6.c.b.11.2 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | − | 3.46410i | −0.353553 | − | 0.612372i | ||||
\(3\) | −3.86148 | − | 6.68827i | −0.247714 | − | 0.429053i | 0.715177 | − | 0.698943i | \(-0.246346\pi\) |
−0.962891 | + | 0.269890i | \(0.913013\pi\) | |||||||
\(4\) | −8.00000 | + | 13.8564i | −0.250000 | + | 0.433013i | ||||
\(5\) | 46.3693 | + | 80.3140i | 0.829480 | + | 1.43670i | 0.898447 | + | 0.439082i | \(0.144696\pi\) |
−0.0689670 | + | 0.997619i | \(0.521970\pi\) | |||||||
\(6\) | −15.4459 | + | 26.7531i | −0.175160 | + | 0.303386i | ||||
\(7\) | 13.5472 | 0.104497 | 0.0522485 | − | 0.998634i | \(-0.483361\pi\) | ||||
0.0522485 | + | 0.998634i | \(0.483361\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 91.6780 | − | 158.791i | 0.377276 | − | 0.653461i | ||||
\(10\) | 185.477 | − | 321.256i | 0.586531 | − | 1.01590i | ||||
\(11\) | 407.324 | 1.01498 | 0.507490 | − | 0.861657i | \(-0.330573\pi\) | ||||
0.507490 | + | 0.861657i | \(0.330573\pi\) | |||||||
\(12\) | 123.567 | 0.247714 | ||||||||
\(13\) | −86.6070 | + | 150.008i | −0.142133 | + | 0.246181i | −0.928300 | − | 0.371833i | \(-0.878729\pi\) |
0.786167 | + | 0.618014i | \(0.212063\pi\) | |||||||
\(14\) | −27.0944 | − | 46.9288i | −0.0369453 | − | 0.0639911i | ||||
\(15\) | 358.108 | − | 620.262i | 0.410947 | − | 0.711782i | ||||
\(16\) | −128.000 | − | 221.703i | −0.125000 | − | 0.216506i | ||||
\(17\) | 822.219 | + | 1424.13i | 0.690026 | + | 1.19516i | 0.971829 | + | 0.235687i | \(0.0757342\pi\) |
−0.281803 | + | 0.959472i | \(0.590932\pi\) | |||||||
\(18\) | −733.424 | −0.533548 | ||||||||
\(19\) | 1573.31 | − | 27.9814i | 0.999842 | − | 0.0177822i | ||||
\(20\) | −1483.82 | −0.829480 | ||||||||
\(21\) | −52.3121 | − | 90.6073i | −0.0258854 | − | 0.0448348i | ||||
\(22\) | −814.647 | − | 1411.01i | −0.358850 | − | 0.621546i | ||||
\(23\) | 778.168 | − | 1347.83i | 0.306728 | − | 0.531269i | −0.670916 | − | 0.741533i | \(-0.734099\pi\) |
0.977645 | + | 0.210264i | \(0.0674324\pi\) | |||||||
\(24\) | −247.135 | − | 428.050i | −0.0875801 | − | 0.151693i | ||||
\(25\) | −2737.73 | + | 4741.89i | −0.876074 | + | 1.51740i | ||||
\(26\) | 692.856 | 0.201006 | ||||||||
\(27\) | −3292.73 | −0.869253 | ||||||||
\(28\) | −108.377 | + | 187.715i | −0.0261243 | + | 0.0452486i | ||||
\(29\) | −2204.59 | + | 3818.47i | −0.486781 | + | 0.843129i | −0.999885 | − | 0.0151973i | \(-0.995162\pi\) |
0.513103 | + | 0.858327i | \(0.328496\pi\) | |||||||
\(30\) | −2864.87 | −0.581167 | ||||||||
\(31\) | −1489.86 | −0.278445 | −0.139223 | − | 0.990261i | \(-0.544460\pi\) | ||||
−0.139223 | + | 0.990261i | \(0.544460\pi\) | |||||||
\(32\) | −512.000 | + | 886.810i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1572.87 | − | 2724.29i | −0.251425 | − | 0.435480i | ||||
\(34\) | 3288.88 | − | 5696.50i | 0.487922 | − | 0.845106i | ||||
\(35\) | 628.174 | + | 1088.03i | 0.0866782 | + | 0.150131i | ||||
\(36\) | 1466.85 | + | 2540.66i | 0.188638 | + | 0.326730i | ||||
\(37\) | 7117.66 | 0.854737 | 0.427369 | − | 0.904077i | \(-0.359441\pi\) | ||||
0.427369 | + | 0.904077i | \(0.359441\pi\) | |||||||
\(38\) | −3243.56 | − | 5394.16i | −0.364387 | − | 0.605989i | ||||
\(39\) | 1337.72 | 0.140833 | ||||||||
\(40\) | 2967.64 | + | 5140.10i | 0.293265 | + | 0.507951i | ||||
\(41\) | −9665.80 | − | 16741.7i | −0.898004 | − | 1.55539i | −0.830042 | − | 0.557701i | \(-0.811684\pi\) |
−0.0679617 | − | 0.997688i | \(-0.521650\pi\) | |||||||
\(42\) | −209.249 | + | 362.429i | −0.0183037 | + | 0.0317030i | ||||
\(43\) | 7845.40 | + | 13588.6i | 0.647059 | + | 1.12074i | 0.983822 | + | 0.179150i | \(0.0573347\pi\) |
−0.336763 | + | 0.941590i | \(0.609332\pi\) | |||||||
\(44\) | −3258.59 | + | 5644.04i | −0.253745 | + | 0.439500i | ||||
\(45\) | 17004.2 | 1.25177 | ||||||||
\(46\) | −6225.34 | −0.433779 | ||||||||
\(47\) | 6510.80 | − | 11277.0i | 0.429922 | − | 0.744647i | −0.566944 | − | 0.823756i | \(-0.691874\pi\) |
0.996866 | + | 0.0791097i | \(0.0252077\pi\) | |||||||
\(48\) | −988.538 | + | 1712.20i | −0.0619285 | + | 0.107263i | ||||
\(49\) | −16623.5 | −0.989080 | ||||||||
\(50\) | 21901.8 | 1.23896 | ||||||||
\(51\) | 6349.96 | − | 10998.5i | 0.341858 | − | 0.592115i | ||||
\(52\) | −1385.71 | − | 2400.12i | −0.0710664 | − | 0.123091i | ||||
\(53\) | 820.131 | − | 1420.51i | 0.0401045 | − | 0.0694631i | −0.845276 | − | 0.534329i | \(-0.820564\pi\) |
0.885381 | + | 0.464866i | \(0.153898\pi\) | |||||||
\(54\) | 6585.45 | + | 11406.3i | 0.307327 | + | 0.532307i | ||||
\(55\) | 18887.3 | + | 32713.8i | 0.841906 | + | 1.45822i | ||||
\(56\) | 867.020 | 0.0369453 | ||||||||
\(57\) | −6262.46 | − | 10414.7i | −0.255304 | − | 0.424580i | ||||
\(58\) | 17636.8 | 0.688412 | ||||||||
\(59\) | −23457.7 | − | 40629.9i | −0.877313 | − | 1.51955i | −0.854278 | − | 0.519817i | \(-0.826000\pi\) |
−0.0230358 | − | 0.999735i | \(-0.507333\pi\) | |||||||
\(60\) | 5729.73 | + | 9924.19i | 0.205474 | + | 0.355891i | ||||
\(61\) | −13828.9 | + | 23952.4i | −0.475843 | + | 0.824184i | −0.999617 | − | 0.0276730i | \(-0.991190\pi\) |
0.523774 | + | 0.851857i | \(0.324524\pi\) | |||||||
\(62\) | 2979.71 | + | 5161.01i | 0.0984453 | + | 0.170512i | ||||
\(63\) | 1241.98 | − | 2151.17i | 0.0394242 | − | 0.0682847i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −16063.6 | −0.471585 | ||||||||
\(66\) | −6291.48 | + | 10897.2i | −0.177784 | + | 0.307931i | ||||
\(67\) | −6090.69 | + | 10549.4i | −0.165760 | + | 0.287105i | −0.936925 | − | 0.349531i | \(-0.886341\pi\) |
0.771165 | + | 0.636635i | \(0.219674\pi\) | |||||||
\(68\) | −26311.0 | −0.690026 | ||||||||
\(69\) | −12019.5 | −0.303923 | ||||||||
\(70\) | 2512.70 | − | 4352.12i | 0.0612907 | − | 0.106159i | ||||
\(71\) | −6079.27 | − | 10529.6i | −0.143122 | − | 0.247894i | 0.785549 | − | 0.618800i | \(-0.212381\pi\) |
−0.928671 | + | 0.370906i | \(0.879047\pi\) | |||||||
\(72\) | 5867.39 | − | 10162.6i | 0.133387 | − | 0.231033i | ||||
\(73\) | −23003.1 | − | 39842.6i | −0.505219 | − | 0.875065i | −0.999982 | − | 0.00603695i | \(-0.998078\pi\) |
0.494763 | − | 0.869028i | \(-0.335255\pi\) | |||||||
\(74\) | −14235.3 | − | 24656.3i | −0.302195 | − | 0.523418i | ||||
\(75\) | 42286.7 | 0.868062 | ||||||||
\(76\) | −12198.8 | + | 22024.3i | −0.242261 | + | 0.437390i | ||||
\(77\) | 5518.09 | 0.106062 | ||||||||
\(78\) | −2675.45 | − | 4634.01i | −0.0497920 | − | 0.0862423i | ||||
\(79\) | −22669.4 | − | 39264.5i | −0.408669 | − | 0.707835i | 0.586072 | − | 0.810259i | \(-0.300674\pi\) |
−0.994741 | + | 0.102424i | \(0.967340\pi\) | |||||||
\(80\) | 11870.5 | − | 20560.4i | 0.207370 | − | 0.359175i | ||||
\(81\) | −9562.96 | − | 16563.5i | −0.161950 | − | 0.280505i | ||||
\(82\) | −38663.2 | + | 66966.6i | −0.634985 | + | 1.09983i | ||||
\(83\) | 23692.9 | 0.377505 | 0.188753 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188753 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(84\) | 1673.99 | 0.0258854 | ||||||||
\(85\) | −76251.5 | + | 132072.i | −1.14473 | + | 1.98272i | ||||
\(86\) | 31381.6 | − | 54354.5i | 0.457540 | − | 0.792483i | ||||
\(87\) | 34052.0 | 0.482330 | ||||||||
\(88\) | 26068.7 | 0.358850 | ||||||||
\(89\) | −57570.6 | + | 99715.3i | −0.770417 | + | 1.33440i | 0.166917 | + | 0.985971i | \(0.446619\pi\) |
−0.937334 | + | 0.348431i | \(0.886715\pi\) | |||||||
\(90\) | −34008.4 | − | 58904.2i | −0.442568 | − | 0.766550i | ||||
\(91\) | −1173.28 | + | 2032.18i | −0.0148525 | + | 0.0257252i | ||||
\(92\) | 12450.7 | + | 21565.2i | 0.153364 | + | 0.265634i | ||||
\(93\) | 5753.04 | + | 9964.56i | 0.0689748 | + | 0.119468i | ||||
\(94\) | −52086.4 | −0.608001 | ||||||||
\(95\) | 75200.8 | + | 125062.i | 0.854896 | + | 1.42172i | ||||
\(96\) | 7908.30 | 0.0875801 | ||||||||
\(97\) | −19513.7 | − | 33798.7i | −0.210577 | − | 0.364729i | 0.741319 | − | 0.671153i | \(-0.234201\pi\) |
−0.951895 | + | 0.306424i | \(0.900867\pi\) | |||||||
\(98\) | 33246.9 | + | 57585.4i | 0.349693 | + | 0.605686i | ||||
\(99\) | 37342.6 | − | 64679.3i | 0.382928 | − | 0.663250i | ||||
\(100\) | −43803.7 | − | 75870.2i | −0.438037 | − | 0.758702i | ||||
\(101\) | 99163.8 | − | 171757.i | 0.967274 | − | 1.67537i | 0.263898 | − | 0.964551i | \(-0.414992\pi\) |
0.703376 | − | 0.710818i | \(-0.251675\pi\) | |||||||
\(102\) | −50799.7 | −0.483460 | ||||||||
\(103\) | 182403. | 1.69410 | 0.847052 | − | 0.531511i | \(-0.178375\pi\) | ||||
0.847052 | + | 0.531511i | \(0.178375\pi\) | |||||||
\(104\) | −5542.85 | + | 9600.49i | −0.0502516 | + | 0.0870383i | ||||
\(105\) | 4851.36 | − | 8402.80i | 0.0429428 | − | 0.0743791i | ||||
\(106\) | −6561.04 | −0.0567164 | ||||||||
\(107\) | 26608.0 | 0.224674 | 0.112337 | − | 0.993670i | \(-0.464166\pi\) | ||||
0.112337 | + | 0.993670i | \(0.464166\pi\) | |||||||
\(108\) | 26341.8 | − | 45625.4i | 0.217313 | − | 0.376398i | ||||
\(109\) | 22504.5 | + | 38979.0i | 0.181428 | + | 0.314242i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648823i | \(0.775261\pi\) | |||||||
\(110\) | 75549.3 | − | 130855.i | 0.595318 | − | 1.03112i | ||||
\(111\) | −27484.7 | − | 47604.8i | −0.211730 | − | 0.366728i | ||||
\(112\) | −1734.04 | − | 3003.45i | −0.0130621 | − | 0.0226243i | ||||
\(113\) | 12010.0 | 0.0884805 | 0.0442403 | − | 0.999021i | \(-0.485913\pi\) | ||||
0.0442403 | + | 0.999021i | \(0.485913\pi\) | |||||||
\(114\) | −23552.7 | + | 42523.2i | −0.169738 | + | 0.306453i | ||||
\(115\) | 144332. | 1.01770 | ||||||||
\(116\) | −35273.5 | − | 61095.5i | −0.243391 | − | 0.421565i | ||||
\(117\) | 15879.9 | + | 27504.8i | 0.107247 | + | 0.185757i | ||||
\(118\) | −93830.7 | + | 162519.i | −0.620354 | + | 1.07449i | ||||
\(119\) | 11138.8 | + | 19292.9i | 0.0721057 | + | 0.124891i | ||||
\(120\) | 22918.9 | − | 39696.7i | 0.145292 | − | 0.251653i | ||||
\(121\) | 4861.47 | 0.0301859 | ||||||||
\(122\) | 110631. | 0.672944 | ||||||||
\(123\) | −74648.5 | + | 129295.i | −0.444896 | + | 0.770582i | ||||
\(124\) | 11918.8 | − | 20644.0i | 0.0696113 | − | 0.120570i | ||||
\(125\) | −217979. | −1.24778 | ||||||||
\(126\) | −9935.83 | −0.0557542 | ||||||||
\(127\) | −122810. | + | 212713.i | −0.675654 | + | 1.17027i | 0.300623 | + | 0.953743i | \(0.402805\pi\) |
−0.976277 | + | 0.216525i | \(0.930528\pi\) | |||||||
\(128\) | −8192.00 | − | 14189.0i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 60589.7 | − | 104944.i | 0.320571 | − | 0.555245i | ||||
\(130\) | 32127.3 | + | 55646.1i | 0.166731 | + | 0.288786i | ||||
\(131\) | −142223. | − | 246338.i | −0.724090 | − | 1.25416i | −0.959347 | − | 0.282228i | \(-0.908927\pi\) |
0.235257 | − | 0.971933i | \(-0.424407\pi\) | |||||||
\(132\) | 50331.9 | 0.251425 | ||||||||
\(133\) | 21314.0 | − | 379.070i | 0.104481 | − | 0.00185819i | ||||
\(134\) | 48725.5 | 0.234420 | ||||||||
\(135\) | −152682. | − | 264452.i | −0.721028 | − | 1.24886i | ||||
\(136\) | 52622.0 | + | 91144.0i | 0.243961 | + | 0.422553i | ||||
\(137\) | −124079. | + | 214911.i | −0.564802 | + | 0.978266i | 0.432266 | + | 0.901746i | \(0.357714\pi\) |
−0.997068 | + | 0.0765196i | \(0.975619\pi\) | |||||||
\(138\) | 24039.0 | + | 41636.8i | 0.107453 | + | 0.186114i | ||||
\(139\) | −22825.8 | + | 39535.4i | −0.100205 | + | 0.173560i | −0.911769 | − | 0.410704i | \(-0.865283\pi\) |
0.811564 | + | 0.584263i | \(0.198616\pi\) | |||||||
\(140\) | −20101.6 | −0.0866782 | ||||||||
\(141\) | −100565. | −0.425991 | ||||||||
\(142\) | −24317.1 | + | 42118.4i | −0.101202 | + | 0.175288i | ||||
\(143\) | −35277.1 | + | 61101.7i | −0.144262 | + | 0.249869i | ||||
\(144\) | −46939.1 | −0.188638 | ||||||||
\(145\) | −408902. | −1.61510 | ||||||||
\(146\) | −92012.5 | + | 159370.i | −0.357244 | + | 0.618764i | ||||
\(147\) | 64191.2 | + | 111182.i | 0.245009 | + | 0.424368i | ||||
\(148\) | −56941.2 | + | 98625.1i | −0.213684 | + | 0.370112i | ||||
\(149\) | 50801.3 | + | 87990.4i | 0.187460 | + | 0.324691i | 0.944403 | − | 0.328791i | \(-0.106641\pi\) |
−0.756943 | + | 0.653481i | \(0.773308\pi\) | |||||||
\(150\) | −84573.5 | − | 146486.i | −0.306906 | − | 0.531577i | ||||
\(151\) | 381041. | 1.35997 | 0.679986 | − | 0.733225i | \(-0.261986\pi\) | ||||
0.679986 | + | 0.733225i | \(0.261986\pi\) | |||||||
\(152\) | 100692. | − | 1790.81i | 0.353497 | − | 0.00628696i | ||||
\(153\) | 301518. | 1.04132 | ||||||||
\(154\) | −11036.2 | − | 19115.2i | −0.0374988 | − | 0.0649497i | ||||
\(155\) | −69083.6 | − | 119656.i | −0.230965 | − | 0.400043i | ||||
\(156\) | −10701.8 | + | 18536.0i | −0.0352083 | + | 0.0609825i | ||||
\(157\) | −178383. | − | 308969.i | −0.577570 | − | 1.00038i | −0.995757 | − | 0.0920203i | \(-0.970668\pi\) |
0.418187 | − | 0.908361i | \(-0.362666\pi\) | |||||||
\(158\) | −90677.4 | + | 157058.i | −0.288972 | + | 0.500515i | ||||
\(159\) | −12667.7 | −0.0397378 | ||||||||
\(160\) | −94964.4 | −0.293265 | ||||||||
\(161\) | 10542.0 | − | 18259.3i | 0.0320522 | − | 0.0555160i | ||||
\(162\) | −38251.9 | + | 66254.2i | −0.114516 | + | 0.198347i | ||||
\(163\) | −354161. | −1.04407 | −0.522037 | − | 0.852923i | \(-0.674828\pi\) | ||||
−0.522037 | + | 0.852923i | \(0.674828\pi\) | |||||||
\(164\) | 309306. | 0.898004 | ||||||||
\(165\) | 145866. | − | 252647.i | 0.417104 | − | 0.722445i | ||||
\(166\) | −47385.8 | − | 82074.6i | −0.133468 | − | 0.231174i | ||||
\(167\) | 306334. | − | 530586.i | 0.849971 | − | 1.47219i | −0.0312618 | − | 0.999511i | \(-0.509953\pi\) |
0.881233 | − | 0.472682i | \(-0.156714\pi\) | |||||||
\(168\) | −3347.98 | − | 5798.87i | −0.00915186 | − | 0.0158515i | ||||
\(169\) | 170645. | + | 295566.i | 0.459596 | + | 0.796044i | ||||
\(170\) | 610012. | 1.61889 | ||||||||
\(171\) | 139795. | − | 252393.i | 0.365596 | − | 0.660066i | ||||
\(172\) | −251053. | −0.647059 | ||||||||
\(173\) | −79786.5 | − | 138194.i | −0.202682 | − | 0.351055i | 0.746710 | − | 0.665150i | \(-0.231632\pi\) |
−0.949392 | + | 0.314095i | \(0.898299\pi\) | |||||||
\(174\) | −68103.9 | − | 117959.i | −0.170529 | − | 0.295365i | ||||
\(175\) | −37088.5 | + | 64239.2i | −0.0915471 | + | 0.158564i | ||||
\(176\) | −52137.4 | − | 90304.6i | −0.126873 | − | 0.219750i | ||||
\(177\) | −181162. | + | 313783.i | −0.434645 | + | 0.752828i | ||||
\(178\) | 460565. | 1.08953 | ||||||||
\(179\) | −221072. | −0.515706 | −0.257853 | − | 0.966184i | \(-0.583015\pi\) | ||||
−0.257853 | + | 0.966184i | \(0.583015\pi\) | |||||||
\(180\) | −136034. | + | 235617.i | −0.312943 | + | 0.542032i | ||||
\(181\) | 63950.3 | − | 110765.i | 0.145093 | − | 0.251308i | −0.784315 | − | 0.620363i | \(-0.786985\pi\) |
0.929408 | + | 0.369055i | \(0.120319\pi\) | |||||||
\(182\) | 9386.25 | 0.0210046 | ||||||||
\(183\) | 213600. | 0.471492 | ||||||||
\(184\) | 49802.7 | − | 86260.9i | 0.108445 | − | 0.187832i | ||||
\(185\) | 330041. | + | 571648.i | 0.708987 | + | 1.22800i | ||||
\(186\) | 23012.2 | − | 39858.3i | 0.0487725 | − | 0.0844765i | ||||
\(187\) | 334909. | + | 580080.i | 0.700363 | + | 1.21306i | ||||
\(188\) | 104173. | + | 180433.i | 0.214961 | + | 0.372323i | ||||
\(189\) | −44607.2 | −0.0908344 | ||||||||
\(190\) | 282825. | − | 510627.i | 0.568373 | − | 1.02617i | ||||
\(191\) | −478653. | −0.949375 | −0.474687 | − | 0.880154i | \(-0.657439\pi\) | ||||
−0.474687 | + | 0.880154i | \(0.657439\pi\) | |||||||
\(192\) | −15816.6 | − | 27395.2i | −0.0309642 | − | 0.0536316i | ||||
\(193\) | 111799. | + | 193642.i | 0.216046 | + | 0.374203i | 0.953596 | − | 0.301090i | \(-0.0973505\pi\) |
−0.737550 | + | 0.675293i | \(0.764017\pi\) | |||||||
\(194\) | −78054.8 | + | 135195.i | −0.148900 | + | 0.257903i | ||||
\(195\) | 62029.4 | + | 107438.i | 0.116818 | + | 0.202335i | ||||
\(196\) | 132988. | − | 230342.i | 0.247270 | − | 0.428284i | ||||
\(197\) | 343584. | 0.630765 | 0.315383 | − | 0.948965i | \(-0.397867\pi\) | ||||
0.315383 | + | 0.948965i | \(0.397867\pi\) | |||||||
\(198\) | −298741. | −0.541541 | ||||||||
\(199\) | −241246. | + | 417850.i | −0.431844 | + | 0.747977i | −0.997032 | − | 0.0769857i | \(-0.975470\pi\) |
0.565188 | + | 0.824962i | \(0.308804\pi\) | |||||||
\(200\) | −175215. | + | 303481.i | −0.309739 | + | 0.536483i | ||||
\(201\) | 94076.3 | 0.164244 | ||||||||
\(202\) | −793310. | −1.36793 | ||||||||
\(203\) | −29866.0 | + | 51729.5i | −0.0508672 | + | 0.0881045i | ||||
\(204\) | 101599. | + | 175975.i | 0.170929 | + | 0.296058i | ||||
\(205\) | 896394. | − | 1.55260e6i | 1.48975 | − | 2.58033i | ||||
\(206\) | −364807. | − | 631864.i | −0.598956 | − | 1.03742i | ||||
\(207\) | −142682. | − | 247132.i | −0.231442 | − | 0.400870i | ||||
\(208\) | 44342.8 | 0.0710664 | ||||||||
\(209\) | 640848. | − | 11397.5i | 1.01482 | − | 0.0180486i | ||||
\(210\) | −38810.9 | −0.0607303 | ||||||||
\(211\) | −414026. | − | 717115.i | −0.640209 | − | 1.10887i | −0.985386 | − | 0.170337i | \(-0.945514\pi\) |
0.345177 | − | 0.938538i | \(-0.387819\pi\) | |||||||
\(212\) | 13122.1 | + | 22728.1i | 0.0200523 | + | 0.0347315i | ||||
\(213\) | −46949.9 | + | 81319.6i | −0.0709065 | + | 0.122814i | ||||
\(214\) | −53216.0 | − | 92172.8i | −0.0794342 | − | 0.137584i | ||||
\(215\) | −727572. | + | 1.26019e6i | −1.07345 | + | 1.85926i | ||||
\(216\) | −210735. | −0.307327 | ||||||||
\(217\) | −20183.4 | −0.0290967 | ||||||||
\(218\) | 90018.1 | − | 155916.i | 0.128289 | − | 0.222203i | ||||
\(219\) | −177652. | + | 307702.i | −0.250299 | + | 0.433531i | ||||
\(220\) | −604394. | −0.841906 | ||||||||
\(221\) | −284840. | −0.392301 | ||||||||
\(222\) | −109939. | + | 190419.i | −0.149716 | + | 0.259316i | ||||
\(223\) | 377744. | + | 654272.i | 0.508669 | + | 0.881041i | 0.999950 | + | 0.0100395i | \(0.00319572\pi\) |
−0.491280 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(224\) | −6936.16 | + | 12013.8i | −0.00923632 | + | 0.0159978i | ||||
\(225\) | 501979. | + | 869454.i | 0.661043 | + | 1.14496i | ||||
\(226\) | −24020.0 | − | 41603.9i | −0.0312826 | − | 0.0541830i | ||||
\(227\) | −1.00051e6 | −1.28872 | −0.644358 | − | 0.764724i | \(-0.722875\pi\) | ||||
−0.644358 | + | 0.764724i | \(0.722875\pi\) | |||||||
\(228\) | 194410. | − | 3457.59i | 0.247675 | − | 0.00440490i | ||||
\(229\) | −210261. | −0.264954 | −0.132477 | − | 0.991186i | \(-0.542293\pi\) | ||||
−0.132477 | + | 0.991186i | \(0.542293\pi\) | |||||||
\(230\) | −288665. | − | 499982.i | −0.359811 | − | 0.623211i | ||||
\(231\) | −21308.0 | − | 36906.5i | −0.0262731 | − | 0.0455064i | ||||
\(232\) | −141094. | + | 244382.i | −0.172103 | + | 0.298091i | ||||
\(233\) | −202554. | − | 350834.i | −0.244428 | − | 0.423362i | 0.717542 | − | 0.696515i | \(-0.245267\pi\) |
−0.961971 | + | 0.273152i | \(0.911934\pi\) | |||||||
\(234\) | 63519.6 | − | 110019.i | 0.0758348 | − | 0.131350i | ||||
\(235\) | 1.20761e6 | 1.42645 | ||||||||
\(236\) | 750645. | 0.877313 | ||||||||
\(237\) | −175074. | + | 303238.i | −0.202466 | + | 0.350681i | ||||
\(238\) | 44555.0 | − | 77171.6i | 0.0509864 | − | 0.0883110i | ||||
\(239\) | −1.57147e6 | −1.77956 | −0.889780 | − | 0.456390i | \(-0.849142\pi\) | ||||
−0.889780 | + | 0.456390i | \(0.849142\pi\) | |||||||
\(240\) | −183351. | −0.205474 | ||||||||
\(241\) | 477803. | − | 827578.i | 0.529915 | − | 0.917839i | −0.469476 | − | 0.882945i | \(-0.655557\pi\) |
0.999391 | − | 0.0348939i | \(-0.0111093\pi\) | |||||||
\(242\) | −9722.93 | − | 16840.6i | −0.0106723 | − | 0.0184850i | ||||
\(243\) | −473921. | + | 820855.i | −0.514861 | + | 0.891765i | ||||
\(244\) | −221263. | − | 383238.i | −0.237922 | − | 0.412092i | ||||
\(245\) | −770819. | − | 1.33510e6i | −0.820422 | − | 1.42101i | ||||
\(246\) | 597188. | 0.629178 | ||||||||
\(247\) | −132063. | + | 238433.i | −0.137733 | + | 0.248670i | ||||
\(248\) | −95350.8 | −0.0984453 | ||||||||
\(249\) | −91489.6 | − | 158465.i | −0.0935133 | − | 0.161970i | ||||
\(250\) | 435957. | + | 755100.i | 0.441158 | + | 0.764108i | ||||
\(251\) | 714398. | − | 1.23737e6i | 0.715741 | − | 1.23970i | −0.246932 | − | 0.969033i | \(-0.579422\pi\) |
0.962673 | − | 0.270667i | \(-0.0872443\pi\) | |||||||
\(252\) | 19871.7 | + | 34418.7i | 0.0197121 | + | 0.0341424i | ||||
\(253\) | 316966. | − | 549001.i | 0.311323 | − | 0.539228i | ||||
\(254\) | 982480. | 0.955520 | ||||||||
\(255\) | 1.17777e6 | 1.13426 | ||||||||
\(256\) | −32768.0 | + | 56755.8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −822272. | + | 1.42422e6i | −0.776574 | + | 1.34506i | 0.157332 | + | 0.987546i | \(0.449711\pi\) |
−0.933906 | + | 0.357519i | \(0.883623\pi\) | |||||||
\(258\) | −484717. | −0.453356 | ||||||||
\(259\) | 96424.2 | 0.0893175 | ||||||||
\(260\) | 128509. | − | 222584.i | 0.117896 | − | 0.204203i | ||||
\(261\) | 404226. | + | 700139.i | 0.367301 | + | 0.636185i | ||||
\(262\) | −568893. | + | 985352.i | −0.512009 | + | 0.886826i | ||||
\(263\) | −446870. | − | 774001.i | −0.398375 | − | 0.690005i | 0.595151 | − | 0.803614i | \(-0.297092\pi\) |
−0.993526 | + | 0.113609i | \(0.963759\pi\) | |||||||
\(264\) | −100664. | − | 174355.i | −0.0888921 | − | 0.153966i | ||||
\(265\) | 152116. | 0.133064 | ||||||||
\(266\) | −43941.1 | − | 73075.6i | −0.0380773 | − | 0.0633240i | ||||
\(267\) | 889231. | 0.763372 | ||||||||
\(268\) | −97451.1 | − | 168790.i | −0.0828800 | − | 0.143552i | ||||
\(269\) | 799499. | + | 1.38477e6i | 0.673655 | + | 1.16680i | 0.976860 | + | 0.213879i | \(0.0686098\pi\) |
−0.303206 | + | 0.952925i | \(0.598057\pi\) | |||||||
\(270\) | −610726. | + | 1.05781e6i | −0.509844 | + | 0.883076i | ||||
\(271\) | −753944. | − | 1.30587e6i | −0.623614 | − | 1.08013i | −0.988807 | − | 0.149200i | \(-0.952330\pi\) |
0.365193 | − | 0.930932i | \(-0.381003\pi\) | |||||||
\(272\) | 210488. | − | 364576.i | 0.172506 | − | 0.298790i | ||||
\(273\) | 18122.4 | 0.0147166 | ||||||||
\(274\) | 992630. | 0.798751 | ||||||||
\(275\) | −1.11514e6 | + | 1.93148e6i | −0.889198 | + | 1.54014i | ||||
\(276\) | 96156.0 | − | 166547.i | 0.0759808 | − | 0.131603i | ||||
\(277\) | 1.68831e6 | 1.32207 | 0.661034 | − | 0.750356i | \(-0.270118\pi\) | ||||
0.661034 | + | 0.750356i | \(0.270118\pi\) | |||||||
\(278\) | 182606. | 0.141711 | ||||||||
\(279\) | −136587. | + | 236576.i | −0.105051 | + | 0.181953i | ||||
\(280\) | 40203.1 | + | 69633.9i | 0.0306454 | + | 0.0530793i | ||||
\(281\) | 680516. | − | 1.17869e6i | 0.514129 | − | 0.890498i | −0.485736 | − | 0.874105i | \(-0.661448\pi\) |
0.999866 | − | 0.0163928i | \(-0.00521822\pi\) | |||||||
\(282\) | 201130. | + | 348368.i | 0.150610 | + | 0.260865i | ||||
\(283\) | −880309. | − | 1.52474e6i | −0.653385 | − | 1.13170i | −0.982296 | − | 0.187335i | \(-0.940015\pi\) |
0.328911 | − | 0.944361i | \(-0.393318\pi\) | |||||||
\(284\) | 194537. | 0.143122 | ||||||||
\(285\) | 546061. | − | 985886.i | 0.398225 | − | 0.718977i | ||||
\(286\) | 282217. | 0.204017 | ||||||||
\(287\) | −130944. | − | 226802.i | −0.0938388 | − | 0.162534i | ||||
\(288\) | 93878.3 | + | 162602.i | 0.0666936 | + | 0.115517i | ||||
\(289\) | −642160. | + | 1.11225e6i | −0.452271 | + | 0.783357i | ||||
\(290\) | 817804. | + | 1.41648e6i | 0.571024 | + | 0.989043i | ||||
\(291\) | −150703. | + | 261026.i | −0.104325 | + | 0.180697i | ||||
\(292\) | 736100. | 0.505219 | ||||||||
\(293\) | 1.57450e6 | 1.07145 | 0.535727 | − | 0.844391i | \(-0.320038\pi\) | ||||
0.535727 | + | 0.844391i | \(0.320038\pi\) | |||||||
\(294\) | 256765. | − | 444729.i | 0.173247 | − | 0.300073i | ||||
\(295\) | 2.17543e6 | − | 3.76796e6i | 1.45543 | − | 2.52087i | ||||
\(296\) | 455530. | 0.302195 | ||||||||
\(297\) | −1.34121e6 | −0.882275 | ||||||||
\(298\) | 203205. | − | 351962.i | 0.132554 | − | 0.229591i | ||||
\(299\) | 134790. | + | 233462.i | 0.0871923 | + | 0.151022i | ||||
\(300\) | −338294. | + | 585942.i | −0.217016 | + | 0.375882i | ||||
\(301\) | 106283. | + | 184088.i | 0.0676158 | + | 0.117114i | ||||
\(302\) | −762083. | − | 1.31997e6i | −0.480823 | − | 0.832809i | ||||
\(303\) | −1.53167e6 | −0.958429 | ||||||||
\(304\) | −207588. | − | 345226.i | −0.128830 | − | 0.214249i | ||||
\(305\) | −2.56495e6 | −1.57881 | ||||||||
\(306\) | −603035. | − | 1.04449e6i | −0.368162 | − | 0.637676i | ||||
\(307\) | −664137. | − | 1.15032e6i | −0.402172 | − | 0.696582i | 0.591816 | − | 0.806073i | \(-0.298411\pi\) |
−0.993988 | + | 0.109491i | \(0.965078\pi\) | |||||||
\(308\) | −44144.7 | + | 76460.9i | −0.0265156 | + | 0.0459264i | ||||
\(309\) | −704346. | − | 1.21996e6i | −0.419653 | − | 0.726860i | ||||
\(310\) | −276335. | + | 478625.i | −0.163317 | + | 0.282873i | ||||
\(311\) | 2.54829e6 | 1.49399 | 0.746995 | − | 0.664830i | \(-0.231496\pi\) | ||||
0.746995 | + | 0.664830i | \(0.231496\pi\) | |||||||
\(312\) | 85614.3 | 0.0497920 | ||||||||
\(313\) | −1.21398e6 | + | 2.10268e6i | −0.700408 | + | 1.21314i | 0.267915 | + | 0.963442i | \(0.413665\pi\) |
−0.968323 | + | 0.249700i | \(0.919668\pi\) | |||||||
\(314\) | −713533. | + | 1.23588e6i | −0.408404 | + | 0.707376i | ||||
\(315\) | 230359. | 0.130806 | ||||||||
\(316\) | 725419. | 0.408669 | ||||||||
\(317\) | −1.03419e6 | + | 1.79128e6i | −0.578035 | + | 1.00119i | 0.417670 | + | 0.908599i | \(0.362847\pi\) |
−0.995705 | + | 0.0925870i | \(0.970486\pi\) | |||||||
\(318\) | 25335.3 | + | 43882.1i | 0.0140494 | + | 0.0243343i | ||||
\(319\) | −897983. | + | 1.55535e6i | −0.494073 | + | 0.855760i | ||||
\(320\) | 189929. | + | 328966.i | 0.103685 | + | 0.179588i | ||||
\(321\) | −102746. | − | 177962.i | −0.0556548 | − | 0.0963970i | ||||
\(322\) | −84335.9 | −0.0453286 | ||||||||
\(323\) | 1.33346e6 | + | 2.21759e6i | 0.711169 | + | 1.18270i | ||||
\(324\) | 306015. | 0.161950 | ||||||||
\(325\) | −474213. | − | 821361.i | −0.249038 | − | 0.431346i | ||||
\(326\) | 708322. | + | 1.22685e6i | 0.369136 | + | 0.639362i | ||||
\(327\) | 173801. | − | 301033.i | 0.0898843 | − | 0.155684i | ||||
\(328\) | −618611. | − | 1.07147e6i | −0.317492 | − | 0.549913i | ||||
\(329\) | 88203.0 | − | 152772.i | 0.0449256 | − | 0.0778134i | ||||
\(330\) | −1.16693e6 | −0.589874 | ||||||||
\(331\) | −1.75837e6 | −0.882146 | −0.441073 | − | 0.897471i | \(-0.645402\pi\) | ||||
−0.441073 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(332\) | −189543. | + | 328299.i | −0.0943763 | + | 0.163465i | ||||
\(333\) | 652532. | − | 1.13022e6i | 0.322472 | − | 0.558537i | ||||
\(334\) | −2.45067e6 | −1.20204 | ||||||||
\(335\) | −1.12969e6 | −0.549978 | ||||||||
\(336\) | −13391.9 | + | 23195.5i | −0.00647134 | + | 0.0112087i | ||||
\(337\) | 1.02655e6 | + | 1.77805e6i | 0.492388 | + | 0.852841i | 0.999962 | − | 0.00876740i | \(-0.00279079\pi\) |
−0.507574 | + | 0.861608i | \(0.669457\pi\) | |||||||
\(338\) | 682580. | − | 1.18226e6i | 0.324984 | − | 0.562888i | ||||
\(339\) | −46376.4 | − | 80326.3i | −0.0219178 | − | 0.0379628i | ||||
\(340\) | −1.22002e6 | − | 2.11314e6i | −0.572363 | − | 0.991361i | ||||
\(341\) | −606853. | −0.282617 | ||||||||
\(342\) | −1.15391e6 | + | 20522.2i | −0.533464 | + | 0.00948767i | ||||
\(343\) | −452889. | −0.207853 | ||||||||
\(344\) | 502106. | + | 869673.i | 0.228770 | + | 0.396241i | ||||
\(345\) | −557336. | − | 965335.i | −0.252098 | − | 0.436647i | ||||
\(346\) | −319146. | + | 552777.i | −0.143318 | + | 0.248233i | ||||
\(347\) | 1.97893e6 | + | 3.42761e6i | 0.882282 | + | 1.52816i | 0.848797 | + | 0.528718i | \(0.177327\pi\) |
0.0334848 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(348\) | −272416. | + | 471838.i | −0.120582 | + | 0.208855i | ||||
\(349\) | −1.77975e6 | −0.782161 | −0.391081 | − | 0.920356i | \(-0.627899\pi\) | ||||
−0.391081 | + | 0.920356i | \(0.627899\pi\) | |||||||
\(350\) | 296708. | 0.129467 | ||||||||
\(351\) | 285173. | − | 493935.i | 0.123549 | − | 0.213994i | ||||
\(352\) | −208550. | + | 361219.i | −0.0897125 | + | 0.155387i | ||||
\(353\) | 517037. | 0.220844 | 0.110422 | − | 0.993885i | \(-0.464780\pi\) | ||||
0.110422 | + | 0.993885i | \(0.464780\pi\) | |||||||
\(354\) | 1.44930e6 | 0.614681 | ||||||||
\(355\) | 563783. | − | 976501.i | 0.237433 | − | 0.411246i | ||||
\(356\) | −921130. | − | 1.59544e6i | −0.385209 | − | 0.667201i | ||||
\(357\) | 86024.1 | − | 148998.i | 0.0357231 | − | 0.0618743i | ||||
\(358\) | 442145. | + | 765817.i | 0.182329 | + | 0.315804i | ||||
\(359\) | 1.79989e6 | + | 3.11751e6i | 0.737073 | + | 1.27665i | 0.953808 | + | 0.300418i | \(0.0971261\pi\) |
−0.216735 | + | 0.976231i | \(0.569541\pi\) | |||||||
\(360\) | 1.08827e6 | 0.442568 | ||||||||
\(361\) | 2.47453e6 | − | 88047.1i | 0.999368 | − | 0.0355588i | ||||
\(362\) | −511602. | −0.205192 | ||||||||
\(363\) | −18772.4 | − | 32514.8i | −0.00747746 | − | 0.0129513i | ||||
\(364\) | −18772.5 | − | 32514.9i | −0.00742623 | − | 0.0128626i | ||||
\(365\) | 2.13328e6 | − | 3.69495e6i | 0.838138 | − | 1.45170i | ||||
\(366\) | −427200. | − | 739933.i | −0.166697 | − | 0.288728i | ||||
\(367\) | −1.59551e6 | + | 2.76351e6i | −0.618352 | + | 1.07102i | 0.371435 | + | 0.928459i | \(0.378866\pi\) |
−0.989787 | + | 0.142557i | \(0.954467\pi\) | |||||||
\(368\) | −398422. | −0.153364 | ||||||||
\(369\) | −3.54457e6 | −1.35518 | ||||||||
\(370\) | 1.32016e6 | − | 2.28659e6i | 0.501330 | − | 0.868329i | ||||
\(371\) | 11110.5 | − | 19243.9i | 0.00419080 | − | 0.00725869i | ||||
\(372\) | −184097. | −0.0689748 | ||||||||
\(373\) | −1.28141e6 | −0.476888 | −0.238444 | − | 0.971156i | \(-0.576637\pi\) | ||||
−0.238444 | + | 0.971156i | \(0.576637\pi\) | |||||||
\(374\) | 1.33964e6 | − | 2.32032e6i | 0.495231 | − | 0.857766i | ||||
\(375\) | 841719. | + | 1.45790e6i | 0.309093 | + | 0.535365i | ||||
\(376\) | 416691. | − | 721730.i | 0.152000 | − | 0.263272i | ||||
\(377\) | −381867. | − | 661412.i | −0.138375 | − | 0.239673i | ||||
\(378\) | 89214.4 | + | 154524.i | 0.0321148 | + | 0.0556245i | ||||
\(379\) | 2.65807e6 | 0.950534 | 0.475267 | − | 0.879842i | \(-0.342351\pi\) | ||||
0.475267 | + | 0.879842i | \(0.342351\pi\) | |||||||
\(380\) | −2.33451e6 | + | 41519.4i | −0.829349 | + | 0.0147500i | ||||
\(381\) | 1.89691e6 | 0.669476 | ||||||||
\(382\) | 957307. | + | 1.65810e6i | 0.335655 | + | 0.581371i | ||||
\(383\) | −2.45014e6 | − | 4.24376e6i | −0.853480 | − | 1.47827i | −0.878048 | − | 0.478573i | \(-0.841154\pi\) |
0.0245671 | − | 0.999698i | \(-0.492179\pi\) | |||||||
\(384\) | −63266.4 | + | 109581.i | −0.0218950 | + | 0.0379233i | ||||
\(385\) | 255870. | + | 443180.i | 0.0879767 | + | 0.152380i | ||||
\(386\) | 447198. | − | 774569.i | 0.152768 | − | 0.264601i | ||||
\(387\) | 2.87700e6 | 0.976479 | ||||||||
\(388\) | 624438. | 0.210577 | ||||||||
\(389\) | 2.03475e6 | − | 3.52430e6i | 0.681770 | − | 1.18086i | −0.292671 | − | 0.956213i | \(-0.594544\pi\) |
0.974440 | − | 0.224647i | \(-0.0721228\pi\) | |||||||
\(390\) | 248117. | − | 429752.i | 0.0826030 | − | 0.143073i | ||||
\(391\) | 2.55930e6 | 0.846601 | ||||||||
\(392\) | −1.06390e6 | −0.349693 | ||||||||
\(393\) | −1.09838e6 | + | 1.90246e6i | −0.358734 | + | 0.621346i | ||||
\(394\) | −687169. | − | 1.19021e6i | −0.223009 | − | 0.386263i | ||||
\(395\) | 2.10233e6 | − | 3.64133e6i | 0.677965 | − | 1.17427i | ||||
\(396\) | 597482. | + | 1.03487e6i | 0.191464 | + | 0.331625i | ||||
\(397\) | 1.84561e6 | + | 3.19669e6i | 0.587711 | + | 1.01795i | 0.994531 | + | 0.104437i | \(0.0333041\pi\) |
−0.406820 | + | 0.913508i | \(0.633363\pi\) | |||||||
\(398\) | 1.92997e6 | 0.610720 | ||||||||
\(399\) | −84838.7 | − | 141090.i | −0.0266785 | − | 0.0443674i | ||||
\(400\) | 1.40172e6 | 0.438037 | ||||||||
\(401\) | 756153. | + | 1.30970e6i | 0.234827 | + | 0.406733i | 0.959223 | − | 0.282652i | \(-0.0912142\pi\) |
−0.724395 | + | 0.689385i | \(0.757881\pi\) | |||||||
\(402\) | −188153. | − | 325890.i | −0.0580691 | − | 0.100579i | ||||
\(403\) | 129032. | − | 223490.i | 0.0395762 | − | 0.0685481i | ||||
\(404\) | 1.58662e6 | + | 2.74811e6i | 0.483637 | + | 0.837684i | ||||
\(405\) | 886856. | − | 1.53608e6i | 0.268668 | − | 0.465346i | ||||
\(406\) | 238928. | 0.0719371 | ||||||||
\(407\) | 2.89919e6 | 0.867542 | ||||||||
\(408\) | 406397. | − | 703901.i | 0.120865 | − | 0.209344i | ||||
\(409\) | −2.42366e6 | + | 4.19791e6i | −0.716414 | + | 1.24087i | 0.245997 | + | 0.969271i | \(0.420885\pi\) |
−0.962412 | + | 0.271595i | \(0.912449\pi\) | |||||||
\(410\) | −7.17115e6 | −2.10683 | ||||||||
\(411\) | 1.91651e6 | 0.559637 | ||||||||
\(412\) | −1.45923e6 | + | 2.52746e6i | −0.423526 | + | 0.733568i | ||||
\(413\) | −317785. | − | 550420.i | −0.0916767 | − | 0.158789i | ||||
\(414\) | −570727. | + | 988528.i | −0.163654 | + | 0.283458i | ||||
\(415\) | 1.09862e6 | + | 1.90287e6i | 0.313133 | + | 0.542362i | ||||
\(416\) | −88685.6 | − | 153608.i | −0.0251258 | − | 0.0435191i | ||||
\(417\) | 352565. | 0.0992884 | ||||||||
\(418\) | −1.32118e6 | − | 2.19717e6i | −0.369846 | − | 0.615067i | ||||
\(419\) | −4.81922e6 | −1.34104 | −0.670520 | − | 0.741891i | \(-0.733929\pi\) | ||||
−0.670520 | + | 0.741891i | \(0.733929\pi\) | |||||||
\(420\) | 77621.7 | + | 134445.i | 0.0214714 | + | 0.0371895i | ||||
\(421\) | 135639. | + | 234934.i | 0.0372976 | + | 0.0646013i | 0.884072 | − | 0.467351i | \(-0.154792\pi\) |
−0.846774 | + | 0.531953i | \(0.821458\pi\) | |||||||
\(422\) | −1.65611e6 | + | 2.86846e6i | −0.452696 | + | 0.784093i | ||||
\(423\) | −1.19379e6 | − | 2.06771e6i | −0.324398 | − | 0.561874i | ||||
\(424\) | 52488.4 | − | 90912.5i | 0.0141791 | − | 0.0245589i | ||||
\(425\) | −9.00406e6 | −2.41805 | ||||||||
\(426\) | 375599. | 0.100277 | ||||||||
\(427\) | −187343. | + | 324488.i | −0.0497242 | + | 0.0861248i | ||||
\(428\) | −212864. | + | 368691.i | −0.0561685 | + | 0.0972867i | ||||
\(429\) | 544886. | 0.142943 | ||||||||
\(430\) | 5.82058e6 | 1.51808 | ||||||||
\(431\) | −270464. | + | 468458.i | −0.0701320 | + | 0.121472i | −0.898959 | − | 0.438033i | \(-0.855675\pi\) |
0.828827 | + | 0.559505i | \(0.189009\pi\) | |||||||
\(432\) | 421469. | + | 730006.i | 0.108657 | + | 0.188199i | ||||
\(433\) | −1.41642e6 | + | 2.45330e6i | −0.363054 | + | 0.628828i | −0.988462 | − | 0.151470i | \(-0.951599\pi\) |
0.625408 | + | 0.780298i | \(0.284933\pi\) | |||||||
\(434\) | 40366.7 | + | 69917.2i | 0.0102872 | + | 0.0178180i | ||||
\(435\) | 1.57897e6 | + | 2.73485e6i | 0.400083 | + | 0.692964i | ||||
\(436\) | −720145. | −0.181428 | ||||||||
\(437\) | 1.18659e6 | − | 2.14233e6i | 0.297233 | − | 0.536639i | ||||
\(438\) | 1.42122e6 | 0.353977 | ||||||||
\(439\) | −511961. | − | 886743.i | −0.126787 | − | 0.219602i | 0.795643 | − | 0.605766i | \(-0.207133\pi\) |
−0.922430 | + | 0.386164i | \(0.873800\pi\) | |||||||
\(440\) | 1.20879e6 | + | 2.09368e6i | 0.297659 | + | 0.515560i | ||||
\(441\) | −1.52401e6 | + | 2.63966e6i | −0.373156 | + | 0.646325i | ||||
\(442\) | 569680. | + | 986714.i | 0.138700 | + | 0.240235i | ||||
\(443\) | 1.76654e6 | − | 3.05973e6i | 0.427674 | − | 0.740754i | −0.568992 | − | 0.822343i | \(-0.692666\pi\) |
0.996666 | + | 0.0815897i | \(0.0259997\pi\) | |||||||
\(444\) | 879509. | 0.211730 | ||||||||
\(445\) | −1.06780e7 | −2.55618 | ||||||||
\(446\) | 1.51098e6 | − | 2.61709e6i | 0.359683 | − | 0.622990i | ||||
\(447\) | 392336. | − | 679546.i | 0.0928730 | − | 0.160861i | ||||
\(448\) | 55489.3 | 0.0130621 | ||||||||
\(449\) | 529252. | 0.123893 | 0.0619465 | − | 0.998079i | \(-0.480269\pi\) | ||||
0.0619465 | + | 0.998079i | \(0.480269\pi\) | |||||||
\(450\) | 2.00792e6 | − | 3.47781e6i | 0.467428 | − | 0.809609i | ||||
\(451\) | −3.93711e6 | − | 6.81927e6i | −0.911457 | − | 1.57869i | ||||
\(452\) | −96080.2 | + | 166416.i | −0.0221201 | + | 0.0383132i | ||||
\(453\) | −1.47138e6 | − | 2.54851e6i | −0.336884 | − | 0.583500i | ||||
\(454\) | 2.00102e6 | + | 3.46587e6i | 0.455630 | + | 0.789174i | ||||
\(455\) | −217617. | −0.0492793 | ||||||||
\(456\) | −400798. | − | 666541.i | −0.0902637 | − | 0.150112i | ||||
\(457\) | 2.85284e6 | 0.638979 | 0.319489 | − | 0.947590i | \(-0.396489\pi\) | ||||
0.319489 | + | 0.947590i | \(0.396489\pi\) | |||||||
\(458\) | 420523. | + | 728367.i | 0.0936754 | + | 0.162251i | ||||
\(459\) | −2.70734e6 | − | 4.68926e6i | −0.599807 | − | 1.03890i | ||||
\(460\) | −1.15466e6 | + | 1.99993e6i | −0.254425 | + | 0.440677i | ||||
\(461\) | −1.78342e6 | − | 3.08898e6i | −0.390843 | − | 0.676960i | 0.601718 | − | 0.798709i | \(-0.294483\pi\) |
−0.992561 | + | 0.121749i | \(0.961150\pi\) | |||||||
\(462\) | −85231.9 | + | 147626.i | −0.0185779 | + | 0.0321779i | ||||
\(463\) | 197336. | 0.0427813 | 0.0213907 | − | 0.999771i | \(-0.493191\pi\) | ||||
0.0213907 | + | 0.999771i | \(0.493191\pi\) | |||||||
\(464\) | 1.12875e6 | 0.243391 | ||||||||
\(465\) | −533530. | + | 924100.i | −0.114426 | + | 0.198192i | ||||
\(466\) | −810217. | + | 1.40334e6i | −0.172837 | + | 0.299362i | ||||
\(467\) | 2.41563e6 | 0.512552 | 0.256276 | − | 0.966604i | \(-0.417504\pi\) | ||||
0.256276 | + | 0.966604i | \(0.417504\pi\) | |||||||
\(468\) | −508157. | −0.107247 | ||||||||
\(469\) | −82511.8 | + | 142915.i | −0.0173214 | + | 0.0300016i | ||||
\(470\) | −2.41521e6 | − | 4.18327e6i | −0.504325 | − | 0.873517i | ||||
\(471\) | −1.37765e6 | + | 2.38615e6i | −0.286144 | + | 0.495617i | ||||
\(472\) | −1.50129e6 | − | 2.60031e6i | −0.310177 | − | 0.537243i | ||||
\(473\) | 3.19562e6 | + | 5.53497e6i | 0.656753 | + | 1.13753i | ||||
\(474\) | 1.40059e6 | 0.286330 | ||||||||
\(475\) | −4.17462e6 | + | 7.53708e6i | −0.848952 | + | 1.53274i | ||||
\(476\) | −356440. | −0.0721057 | ||||||||
\(477\) | −150376. | − | 260459.i | −0.0302609 | − | 0.0524135i | ||||
\(478\) | 3.14295e6 | + | 5.44375e6i | 0.629169 | + | 1.08975i | ||||
\(479\) | 3.37480e6 | − | 5.84533e6i | 0.672063 | − | 1.16405i | −0.305255 | − | 0.952271i | \(-0.598742\pi\) |
0.977318 | − | 0.211776i | \(-0.0679249\pi\) | |||||||
\(480\) | 366703. | + | 635148.i | 0.0726459 | + | 0.125826i | ||||
\(481\) | −616439. | + | 1.06770e6i | −0.121486 | + | 0.210420i | ||||
\(482\) | −3.82242e6 | −0.749412 | ||||||||
\(483\) | −162830. | −0.0317591 | ||||||||
\(484\) | −38891.7 | + | 67362.5i | −0.00754647 | + | 0.0130709i | ||||
\(485\) | 1.80967e6 | − | 3.13445e6i | 0.349338 | − | 0.605071i | ||||
\(486\) | 3.79137e6 | 0.728123 | ||||||||
\(487\) | −10531.5 | −0.00201219 | −0.00100610 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100610 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(488\) | −885051. | + | 1.53295e6i | −0.168236 | + | 0.291393i | ||||
\(489\) | 1.36758e6 | + | 2.36872e6i | 0.258632 | + | 0.447963i | ||||
\(490\) | −3.08328e6 | + | 5.34039e6i | −0.580126 | + | 1.00481i | ||||
\(491\) | −211476. | − | 366287.i | −0.0395874 | − | 0.0685674i | 0.845553 | − | 0.533892i | \(-0.179271\pi\) |
−0.885140 | + | 0.465324i | \(0.845938\pi\) | |||||||
\(492\) | −1.19438e6 | − | 2.06872e6i | −0.222448 | − | 0.385291i | ||||
\(493\) | −7.25064e6 | −1.34357 | ||||||||
\(494\) | 1.09008e6 | − | 19387.1i | 0.200974 | − | 0.00357434i | ||||
\(495\) | 6.92621e6 | 1.27052 | ||||||||
\(496\) | 190702. | + | 330305.i | 0.0348057 | + | 0.0602852i | ||||
\(497\) | −82357.0 | − | 142647.i | −0.0149558 | − | 0.0259042i | ||||
\(498\) | −365958. | + | 633859.i | −0.0661239 | + | 0.114530i | ||||
\(499\) | −1.44908e6 | − | 2.50988e6i | −0.260520 | − | 0.451233i | 0.705860 | − | 0.708351i | \(-0.250561\pi\) |
−0.966380 | + | 0.257118i | \(0.917227\pi\) | |||||||
\(500\) | 1.74383e6 | − | 3.02040e6i | 0.311946 | − | 0.540306i | ||||
\(501\) | −4.73161e6 | −0.842199 | ||||||||
\(502\) | −5.71518e6 | −1.01221 | ||||||||
\(503\) | −1.62618e6 | + | 2.81662e6i | −0.286581 | + | 0.496373i | −0.972991 | − | 0.230841i | \(-0.925852\pi\) |
0.686410 | + | 0.727215i | \(0.259185\pi\) | |||||||
\(504\) | 79486.7 | − | 137675.i | 0.0139386 | − | 0.0241423i | ||||
\(505\) | 1.83926e7 | 3.20934 | ||||||||
\(506\) | −2.53573e6 | −0.440277 | ||||||||
\(507\) | 1.31788e6 | − | 2.28264e6i | 0.227697 | − | 0.394382i | ||||
\(508\) | −1.96496e6 | − | 3.40341e6i | −0.337827 | − | 0.585134i | ||||
\(509\) | 4.05317e6 | − | 7.02030e6i | 0.693427 | − | 1.20105i | −0.277281 | − | 0.960789i | \(-0.589433\pi\) |
0.970708 | − | 0.240262i | \(-0.0772333\pi\) | |||||||
\(510\) | −2.35555e6 | − | 4.07993e6i | −0.401020 | − | 0.694588i | ||||
\(511\) | −311628. | − | 539755.i | −0.0527939 | − | 0.0914417i | ||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −5.18049e6 | + | 92135.2i | −0.869116 | + | 0.0154572i | ||||
\(514\) | 6.57817e6 | 1.09824 | ||||||||
\(515\) | 8.45792e6 | + | 1.46496e7i | 1.40522 | + | 2.43392i | ||||
\(516\) | 969435. | + | 1.67911e6i | 0.160286 | + | 0.277623i | ||||
\(517\) | 2.65200e6 | − | 4.59340e6i | 0.436363 | − | 0.755802i | ||||
\(518\) | −192848. | − | 334023.i | −0.0315785 | − | 0.0546956i | ||||
\(519\) | −616188. | + | 1.06727e6i | −0.100414 | + | 0.173922i | ||||
\(520\) | −1.02807e6 | −0.166731 | ||||||||
\(521\) | 8.35290e6 | 1.34816 | 0.674082 | − | 0.738656i | \(-0.264539\pi\) | ||||
0.674082 | + | 0.738656i | \(0.264539\pi\) | |||||||
\(522\) | 1.61690e6 | − | 2.80056e6i | 0.259721 | − | 0.449850i | ||||
\(523\) | 377576. | − | 653980.i | 0.0603601 | − | 0.104547i | −0.834266 | − | 0.551362i | \(-0.814108\pi\) |
0.894626 | + | 0.446815i | \(0.147442\pi\) | |||||||
\(524\) | 4.55115e6 | 0.724090 | ||||||||
\(525\) | 572866. | 0.0907100 | ||||||||
\(526\) | −1.78748e6 | + | 3.09600e6i | −0.281693 | + | 0.487907i | ||||
\(527\) | −1.22499e6 | − | 2.12174e6i | −0.192135 | − | 0.332787i | ||||
\(528\) | −402655. | + | 697419.i | −0.0628562 | + | 0.108870i | ||||
\(529\) | 2.00708e6 | + | 3.47637e6i | 0.311836 | + | 0.540115i | ||||
\(530\) | −304231. | − | 526944.i | −0.0470451 | − | 0.0814845i | ||||
\(531\) | −8.60221e6 | −1.32396 | ||||||||
\(532\) | −165259. | + | 298368.i | −0.0253155 | + | 0.0457059i | ||||
\(533\) | 3.34850e6 | 0.510544 | ||||||||
\(534\) | −1.77846e6 | − | 3.08039e6i | −0.269893 | − | 0.467468i | ||||
\(535\) | 1.23379e6 | + | 2.13700e6i | 0.186363 | + | 0.322789i | ||||
\(536\) | −389804. | + | 675161.i | −0.0586050 | + | 0.101507i | ||||
\(537\) | 853666. | + | 1.47859e6i | 0.127747 | + | 0.221265i | ||||
\(538\) | 3.19800e6 | − | 5.53909e6i | 0.476346 | − | 0.825055i | ||||
\(539\) | −6.77113e6 | −1.00390 | ||||||||
\(540\) | 4.88581e6 | 0.721028 | ||||||||
\(541\) | −660689. | + | 1.14435e6i | −0.0970518 | + | 0.168099i | −0.910463 | − | 0.413590i | \(-0.864275\pi\) |
0.813411 | + | 0.581689i | \(0.197608\pi\) | |||||||
\(542\) | −3.01578e6 | + | 5.22348e6i | −0.440962 | + | 0.763769i | ||||
\(543\) | −987770. | −0.143766 | ||||||||
\(544\) | −1.68391e6 | −0.243961 | ||||||||
\(545\) | −2.08704e6 | + | 3.61486e6i | −0.300981 | + | 0.521315i | ||||
\(546\) | −36244.8 | − | 62777.8i | −0.00520312 | − | 0.00901207i | ||||
\(547\) | −462911. | + | 801785.i | −0.0661499 | + | 0.114575i | −0.897203 | − | 0.441617i | \(-0.854405\pi\) |
0.831054 | + | 0.556192i | \(0.187738\pi\) | |||||||
\(548\) | −1.98526e6 | − | 3.43857e6i | −0.282401 | − | 0.489133i | ||||
\(549\) | 2.53562e6 | + | 4.39181e6i | 0.359048 | + | 0.621889i | ||||
\(550\) | 8.92114e6 | 1.25752 | ||||||||
\(551\) | −3.36167e6 | + | 6.06934e6i | −0.471711 | + | 0.851652i | ||||
\(552\) | −769248. | −0.107453 | ||||||||
\(553\) | −307106. | − | 531923.i | −0.0427047 | − | 0.0739667i | ||||
\(554\) | −3.37663e6 | − | 5.84849e6i | −0.467422 | − | 0.809598i | ||||
\(555\) | 2.54889e6 | − | 4.41481e6i | 0.351252 | − | 0.608386i | ||||
\(556\) | −365212. | − | 632566.i | −0.0501024 | − | 0.0867799i | ||||
\(557\) | 6.32640e6 | − | 1.09576e7i | 0.864009 | − | 1.49651i | −0.00401820 | − | 0.999992i | \(-0.501279\pi\) |
0.868028 | − | 0.496516i | \(-0.165388\pi\) | |||||||
\(558\) | 1.09270e6 | 0.148564 | ||||||||
\(559\) | −2.71787e6 | −0.367874 | ||||||||
\(560\) | 160813. | − | 278536.i | 0.0216696 | − | 0.0375328i | ||||
\(561\) | 2.58649e6 | − | 4.47993e6i | 0.346979 | − | 0.600986i | ||||
\(562\) | −5.44413e6 | −0.727089 | ||||||||
\(563\) | 3.01142e6 | 0.400406 | 0.200203 | − | 0.979754i | \(-0.435840\pi\) | ||||
0.200203 | + | 0.979754i | \(0.435840\pi\) | |||||||
\(564\) | 804522. | − | 1.39347e6i | 0.106498 | − | 0.184459i | ||||
\(565\) | 556897. | + | 964573.i | 0.0733928 | + | 0.127120i | ||||
\(566\) | −3.52124e6 | + | 6.09896e6i | −0.462013 | + | 0.800230i | ||||
\(567\) | −129551. | − | 224389.i | −0.0169233 | − | 0.0293119i | ||||
\(568\) | −389073. | − | 673895.i | −0.0506012 | − | 0.0876438i | ||||
\(569\) | −1.15340e7 | −1.49348 | −0.746742 | − | 0.665114i | \(-0.768383\pi\) | ||||
−0.746742 | + | 0.665114i | \(0.768383\pi\) | |||||||
\(570\) | −4.50733e6 | + | 80163.0i | −0.581075 | + | 0.0103344i | ||||
\(571\) | −2.07265e6 | −0.266034 | −0.133017 | − | 0.991114i | \(-0.542466\pi\) | ||||
−0.133017 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(572\) | −564433. | − | 977627.i | −0.0721311 | − | 0.124935i | ||||
\(573\) | 1.84831e6 | + | 3.20136e6i | 0.235173 | + | 0.407332i | ||||
\(574\) | −523778. | + | 907210.i | −0.0663540 | + | 0.114929i | ||||
\(575\) | 4.26083e6 | + | 7.37997e6i | 0.537433 | + | 0.930861i | ||||
\(576\) | 375513. | − | 650408.i | 0.0471595 | − | 0.0816826i | ||||
\(577\) | −1.99741e6 | −0.249762 | −0.124881 | − | 0.992172i | \(-0.539855\pi\) | ||||
−0.124881 | + | 0.992172i | \(0.539855\pi\) | |||||||
\(578\) | 5.13728e6 | 0.639608 | ||||||||
\(579\) | 863422. | − | 1.49549e6i | 0.107035 | − | 0.185390i | ||||
\(580\) | 3.27122e6 | − | 5.66592e6i | 0.403775 | − | 0.699359i | ||||
\(581\) | 320972. | 0.0394482 | ||||||||
\(582\) | 1.20563e6 | 0.147539 | ||||||||
\(583\) | 334058. | − | 578606.i | 0.0407053 | − | 0.0705037i | ||||
\(584\) | −1.47220e6 | − | 2.54993e6i | −0.178622 | − | 0.309382i | ||||
\(585\) | −1.47268e6 | + | 2.55076e6i | −0.177918 | + | 0.308163i | ||||
\(586\) | −3.14900e6 | − | 5.45422e6i | −0.378816 | − | 0.656129i | ||||
\(587\) | −2.96558e6 | − | 5.13654e6i | −0.355234 | − | 0.615284i | 0.631924 | − | 0.775030i | \(-0.282266\pi\) |
−0.987158 | + | 0.159747i | \(0.948932\pi\) | |||||||
\(588\) | −2.05412e6 | −0.245009 | ||||||||
\(589\) | −2.34401e6 | + | 41688.3i | −0.278401 | + | 0.00495137i | ||||
\(590\) | −1.74035e7 | −2.05829 | ||||||||
\(591\) | −1.32674e6 | − | 2.29799e6i | −0.156249 | − | 0.270632i | ||||
\(592\) | −911060. | − | 1.57800e6i | −0.106842 | − | 0.185056i | ||||
\(593\) | 926869. | − | 1.60538e6i | 0.108238 | − | 0.187474i | −0.806818 | − | 0.590800i | \(-0.798812\pi\) |
0.915057 | + | 0.403325i | \(0.132146\pi\) | |||||||
\(594\) | 2.68241e6 | + | 4.64607e6i | 0.311931 | + | 0.540281i | ||||
\(595\) | −1.03299e6 | + | 1.78920e6i | −0.119620 | + | 0.207189i | ||||
\(596\) | −1.62564e6 | −0.187460 | ||||||||
\(597\) | 3.72626e6 | 0.427895 | ||||||||
\(598\) | 539158. | − | 933849.i | 0.0616543 | − | 0.106788i | ||||
\(599\) | −3.08767e6 | + | 5.34800e6i | −0.351612 | + | 0.609010i | −0.986532 | − | 0.163568i | \(-0.947700\pi\) |
0.634920 | + | 0.772578i | \(0.281033\pi\) | |||||||
\(600\) | 2.70635e6 | 0.306906 | ||||||||
\(601\) | 1.98620e6 | 0.224303 | 0.112152 | − | 0.993691i | \(-0.464226\pi\) | ||||
0.112152 | + | 0.993691i | \(0.464226\pi\) | |||||||
\(602\) | 425133. | − | 736351.i | 0.0478116 | − | 0.0828121i | ||||
\(603\) | 1.11677e6 | + | 1.93429e6i | 0.125074 | + | 0.216635i | ||||
\(604\) | −3.04833e6 | + | 5.27986e6i | −0.339993 | + | 0.588885i | ||||
\(605\) | 225423. | + | 390444.i | 0.0250386 | + | 0.0433681i | ||||
\(606\) | 3.06335e6 | + | 5.30588e6i | 0.338856 | + | 0.586916i | ||||
\(607\) | −9.42545e6 | −1.03832 | −0.519159 | − | 0.854678i | \(-0.673755\pi\) | ||||
−0.519159 | + | 0.854678i | \(0.673755\pi\) | |||||||
\(608\) | −780722. | + | 1.40956e6i | −0.0856520 | + | 0.154641i | ||||
\(609\) | 461308. | 0.0504020 | ||||||||
\(610\) | 5.12990e6 | + | 8.88525e6i | 0.558193 | + | 0.966819i | ||||
\(611\) | 1.12776e6 | + | 1.95334e6i | 0.122212 | + | 0.211678i | ||||
\(612\) | −2.41214e6 | + | 4.17795e6i | −0.260330 | + | 0.450905i | ||||
\(613\) | 2.82659e6 | + | 4.89581e6i | 0.303817 | + | 0.526227i | 0.976997 | − | 0.213252i | \(-0.0684055\pi\) |
−0.673180 | + | 0.739479i | \(0.735072\pi\) | |||||||
\(614\) | −2.65655e6 | + | 4.60127e6i | −0.284378 | + | 0.492558i | ||||
\(615\) | −1.38456e7 | −1.47613 | ||||||||
\(616\) | 353158. | 0.0374988 | ||||||||
\(617\) | 5.05780e6 | − | 8.76036e6i | 0.534871 | − | 0.926423i | −0.464299 | − | 0.885678i | \(-0.653694\pi\) |
0.999170 | − | 0.0407444i | \(-0.0129729\pi\) | |||||||
\(618\) | −2.81739e6 | + | 4.87986e6i | −0.296739 | + | 0.513968i | ||||
\(619\) | 1.82708e6 | 0.191659 | 0.0958297 | − | 0.995398i | \(-0.469450\pi\) | ||||
0.0958297 | + | 0.995398i | \(0.469450\pi\) | |||||||
\(620\) | 2.21068e6 | 0.230965 | ||||||||
\(621\) | −2.56229e6 | + | 4.43802e6i | −0.266624 | + | 0.461807i | ||||
\(622\) | −5.09658e6 | − | 8.82753e6i | −0.528205 | − | 0.914878i | ||||
\(623\) | −779920. | + | 1.35086e6i | −0.0805063 | + | 0.139441i | ||||
\(624\) | −171229. | − | 296577.i | −0.0176041 | − | 0.0304913i | ||||
\(625\) | −1.55212e6 | − | 2.68834e6i | −0.158937 | − | 0.275286i | ||||
\(626\) | 9.71185e6 | 0.990527 | ||||||||
\(627\) | −2.55085e6 | − | 4.24215e6i | −0.259129 | − | 0.430941i | ||||
\(628\) | 5.70826e6 | 0.577570 | ||||||||
\(629\) | 5.85227e6 | + | 1.01364e7i | 0.589791 | + | 1.02155i | ||||
\(630\) | −460718. | − | 797987.i | −0.0462470 | − | 0.0801022i | ||||
\(631\) | 2.21793e6 | − | 3.84157e6i | 0.221756 | − | 0.384092i | −0.733585 | − | 0.679597i | \(-0.762155\pi\) |
0.955341 | + | 0.295505i | \(0.0954879\pi\) | |||||||
\(632\) | −1.45084e6 | − | 2.51293e6i | −0.144486 | − | 0.250257i | ||||
\(633\) | −3.19751e6 | + | 5.53824e6i | −0.317177 | + | 0.549367i | ||||
\(634\) | 8.27356e6 | 0.817465 | ||||||||
\(635\) | −2.27785e7 | −2.24177 | ||||||||
\(636\) | 101341. | − | 175528.i | 0.00993444 | − | 0.0172070i | ||||
\(637\) | 1.43971e6 | − | 2.49365e6i | 0.140581 | − | 0.243493i | ||||
\(638\) | 7.18386e6 | 0.698725 | ||||||||
\(639\) | −2.22934e6 | −0.215985 | ||||||||
\(640\) | 759715. | − | 1.31587e6i | 0.0733164 | − | 0.126988i | ||||
\(641\) | −3.19408e6 | − | 5.53230e6i | −0.307044 | − | 0.531815i | 0.670671 | − | 0.741755i | \(-0.266006\pi\) |
−0.977714 | + | 0.209940i | \(0.932673\pi\) | |||||||
\(642\) | −410985. | + | 711846.i | −0.0393539 | + | 0.0681630i | ||||
\(643\) | 829278. | + | 1.43635e6i | 0.0790993 | + | 0.137004i | 0.902862 | − | 0.429931i | \(-0.141462\pi\) |
−0.823762 | + | 0.566935i | \(0.808129\pi\) | |||||||
\(644\) | 168672. | + | 292148.i | 0.0160261 | + | 0.0277580i | ||||
\(645\) | 1.12380e7 | 1.06363 | ||||||||
\(646\) | 5.01504e6 | − | 9.05441e6i | 0.472817 | − | 0.853648i | ||||
\(647\) | 8.62286e6 | 0.809824 | 0.404912 | − | 0.914356i | \(-0.367302\pi\) | ||||
0.404912 | + | 0.914356i | \(0.367302\pi\) | |||||||
\(648\) | −612030. | − | 1.06007e6i | −0.0572578 | − | 0.0991735i | ||||
\(649\) | −9.55486e6 | − | 1.65495e7i | −0.890456 | − | 1.54232i | ||||
\(650\) | −1.89685e6 | + | 3.28545e6i | −0.176096 | + | 0.305008i | ||||
\(651\) | 77937.6 | + | 134992.i | 0.00720766 | + | 0.0124840i | ||||
\(652\) | 2.83329e6 | − | 4.90740e6i | 0.261019 | − | 0.452097i | ||||
\(653\) | 1.73010e7 | 1.58777 | 0.793887 | − | 0.608065i | \(-0.208054\pi\) | ||||
0.793887 | + | 0.608065i | \(0.208054\pi\) | |||||||
\(654\) | −1.39041e6 | −0.127116 | ||||||||
\(655\) | 1.31896e7 | − | 2.28451e7i | 1.20124 | − | 2.08060i | ||||
\(656\) | −2.47445e6 | + | 4.28586e6i | −0.224501 | + | 0.388847i | ||||
\(657\) | −8.43552e6 | −0.762427 | ||||||||
\(658\) | −705624. | −0.0635344 | ||||||||
\(659\) | 1.99931e6 | − | 3.46291e6i | 0.179336 | − | 0.310618i | −0.762318 | − | 0.647203i | \(-0.775939\pi\) |
0.941653 | + | 0.336585i | \(0.109272\pi\) | |||||||
\(660\) | 2.33385e6 | + | 4.04235e6i | 0.208552 | + | 0.361222i | ||||
\(661\) | −6.01867e6 | + | 1.04246e7i | −0.535793 | + | 0.928021i | 0.463332 | + | 0.886185i | \(0.346654\pi\) |
−0.999125 | + | 0.0418356i | \(0.986679\pi\) | |||||||
\(662\) | 3.51674e6 | + | 6.09118e6i | 0.311886 | + | 0.540202i | ||||
\(663\) | 1.09990e6 | + | 1.90509e6i | 0.0971785 | + | 0.168318i | ||||
\(664\) | 1.51635e6 | 0.133468 | ||||||||
\(665\) | 1.01876e6 | + | 1.69423e6i | 0.0893342 | + | 0.148566i | ||||
\(666\) | −5.22026e6 | −0.456044 | ||||||||
\(667\) | 3.43109e6 | + | 5.94282e6i | 0.298619 | + | 0.517223i | ||||
\(668\) | 4.90135e6 | + | 8.48938e6i | 0.424986 | + | 0.736097i | ||||
\(669\) | 2.91730e6 | − | 5.05291e6i | 0.252009 | − | 0.436492i | ||||
\(670\) | 2.25937e6 | + | 3.91335e6i | 0.194447 | + | 0.336792i | ||||
\(671\) | −5.63284e6 | + | 9.75637e6i | −0.482971 | + | 0.836531i | ||||
\(672\) | 107135. | 0.00915186 | ||||||||
\(673\) | 5.14140e6 | 0.437566 | 0.218783 | − | 0.975774i | \(-0.429791\pi\) | ||||
0.218783 | + | 0.975774i | \(0.429791\pi\) | |||||||
\(674\) | 4.10622e6 | − | 7.11218e6i | 0.348171 | − | 0.603050i | ||||
\(675\) | 9.01460e6 | − | 1.56137e7i | 0.761530 | − | 1.31901i | ||||
\(676\) | −5.46064e6 | −0.459596 | ||||||||
\(677\) | 9.45731e6 | 0.793042 | 0.396521 | − | 0.918026i | \(-0.370217\pi\) | ||||
0.396521 | + | 0.918026i | \(0.370217\pi\) | |||||||
\(678\) | −185506. | + | 321305.i | −0.0154983 | + | 0.0268438i | ||||
\(679\) | −264356. | − | 457877.i | −0.0220046 | − | 0.0381131i | ||||
\(680\) | −4.88010e6 | + | 8.45258e6i | −0.404721 | + | 0.700998i | ||||
\(681\) | 3.86345e6 | + | 6.69169e6i | 0.319233 | + | 0.552927i | ||||
\(682\) | 1.21371e6 | + | 2.10220e6i | 0.0999201 | + | 0.173067i | ||||
\(683\) | 1.30968e6 | 0.107427 | 0.0537136 | − | 0.998556i | \(-0.482894\pi\) | ||||
0.0537136 | + | 0.998556i | \(0.482894\pi\) | |||||||
\(684\) | 2.37890e6 | + | 3.95620e6i | 0.194418 | + | 0.323324i | ||||
\(685\) | −2.30138e7 | −1.87397 | ||||||||
\(686\) | 905778. | + | 1.56885e6i | 0.0734871 | + | 0.127283i | ||||
\(687\) | 811919. | + | 1.40629e6i | 0.0656328 | + | 0.113679i | ||||
\(688\) | 2.00842e6 | − | 3.47869e6i | 0.161765 | − | 0.280185i | ||||
\(689\) | 142058. | + | 246052.i | 0.0114003 | + | 0.0197460i | ||||
\(690\) | −2.22935e6 | + | 3.86134e6i | −0.178260 | + | 0.308756i | ||||
\(691\) | 5.70771e6 | 0.454744 | 0.227372 | − | 0.973808i | \(-0.426987\pi\) | ||||
0.227372 | + | 0.973808i | \(0.426987\pi\) | |||||||
\(692\) | 2.55317e6 | 0.202682 | ||||||||
\(693\) | 505887. | − | 876222.i | 0.0400148 | − | 0.0693077i | ||||
\(694\) | 7.91573e6 | − | 1.37105e7i | 0.623868 | − | 1.08057i | ||||
\(695\) | −4.23366e6 | −0.332471 | ||||||||
\(696\) | 2.17933e6 | 0.170529 | ||||||||
\(697\) | 1.58948e7 | − | 2.75306e7i | 1.23929 | − | 2.14652i | ||||
\(698\) | 3.55951e6 | + | 6.16525e6i | 0.276536 | + | 0.478974i | ||||
\(699\) | −1.56432e6 | + | 2.70948e6i | −0.121097 | + | 0.209745i | ||||
\(700\) | −593417. | − | 1.02783e6i | −0.0457736 | − | 0.0792821i | ||||
\(701\) | 5.28777e6 | + | 9.15869e6i | 0.406423 | + | 0.703945i | 0.994486 | − | 0.104870i | \(-0.0334427\pi\) |
−0.588063 | + | 0.808815i | \(0.700109\pi\) | |||||||
\(702\) | −2.28139e6 | −0.174725 | ||||||||
\(703\) | 1.11983e7 | − | 199162.i | 0.854602 | − | 0.0151991i | ||||
\(704\) | 1.66840e6 | 0.126873 | ||||||||
\(705\) | −4.66314e6 | − | 8.07680e6i | −0.353351 | − | 0.612021i | ||||
\(706\) | −1.03407e6 | − | 1.79107e6i | −0.0780800 | − | 0.135239i | ||||
\(707\) | 1.34339e6 | − | 2.32682e6i | 0.101077 | − | 0.175071i | ||||
\(708\) | −2.89860e6 | − | 5.02052e6i | −0.217323 | − | 0.376414i | ||||
\(709\) | −4.57650e6 | + | 7.92674e6i | −0.341915 | + | 0.592214i | −0.984788 | − | 0.173758i | \(-0.944409\pi\) |
0.642873 | + | 0.765973i | \(0.277742\pi\) | |||||||
\(710\) | −4.51027e6 | −0.335781 | ||||||||
\(711\) | −8.31312e6 | −0.616723 | ||||||||
\(712\) | −3.68452e6 | + | 6.38178e6i | −0.272384 | + | 0.471782i | ||||
\(713\) | −1.15936e6 | + | 2.00807e6i | −0.0854070 | + | 0.147929i | ||||
\(714\) | −688193. | −0.0505201 | ||||||||
\(715\) | −6.54310e6 | −0.478650 | ||||||||
\(716\) | 1.76858e6 | − | 3.06327e6i | 0.128926 | − | 0.223307i | ||||
\(717\) | 6.06821e6 | + | 1.05105e7i | 0.440822 | + | 0.763525i | ||||
\(718\) | 7.19957e6 | − | 1.24700e7i | 0.521189 | − | 0.902727i | ||||
\(719\) | 3.66367e6 | + | 6.34567e6i | 0.264298 | + | 0.457778i | 0.967380 | − | 0.253331i | \(-0.0815263\pi\) |
−0.703081 | + | 0.711110i | \(0.748193\pi\) | |||||||
\(720\) | −2.17654e6 | − | 3.76987e6i | −0.156471 | − | 0.271016i | ||||
\(721\) | 2.47105e6 | 0.177029 | ||||||||
\(722\) | −5.25407e6 | − | 8.39594e6i | −0.375105 | − | 0.599413i | ||||
\(723\) | −7.38009e6 | −0.525069 | ||||||||
\(724\) | 1.02320e6 | + | 1.77224e6i | 0.0725464 | + | 0.125654i | ||||
\(725\) | −1.20712e7 | − | 2.09079e7i | −0.852912 | − | 1.47729i | ||||
\(726\) | −75089.8 | + | 130059.i | −0.00528736 | + | 0.00915798i | ||||
\(727\) | −6.53539e6 | − | 1.13196e7i | −0.458602 | − | 0.794321i | 0.540286 | − | 0.841482i | \(-0.318316\pi\) |
−0.998887 | + | 0.0471604i | \(0.984983\pi\) | |||||||
\(728\) | −75090.0 | + | 130060.i | −0.00525114 | + | 0.00909524i | ||||
\(729\) | 2.67253e6 | 0.186254 | ||||||||
\(730\) | −1.70662e7 | −1.18531 | ||||||||
\(731\) | −1.29013e7 | + | 2.23457e7i | −0.892975 | + | 1.54668i | ||||
\(732\) | −1.70880e6 | + | 2.95973e6i | −0.117873 | + | 0.204162i | ||||
\(733\) | −2.64582e6 | −0.181886 | −0.0909431 | − | 0.995856i | \(-0.528988\pi\) | ||||
−0.0909431 | + | 0.995856i | \(0.528988\pi\) | |||||||
\(734\) | 1.27641e7 | 0.874481 | ||||||||
\(735\) | −5.95300e6 | + | 1.03109e7i | −0.406460 | + | 0.704009i | ||||
\(736\) | 796844. | + | 1.38017e6i | 0.0542224 | + | 0.0939159i | ||||
\(737\) | −2.48088e6 | + | 4.29701e6i | −0.168243 | + | 0.291406i | ||||
\(738\) | 7.08913e6 | + | 1.22787e7i | 0.479129 | + | 0.829875i | ||||
\(739\) | 966766. | + | 1.67449e6i | 0.0651194 | + | 0.112790i | 0.896747 | − | 0.442544i | \(-0.145924\pi\) |
−0.831628 | + | 0.555334i | \(0.812591\pi\) | |||||||
\(740\) | −1.05613e7 | −0.708987 | ||||||||
\(741\) | 2.10466e6 | − | 37431.4i | 0.140811 | − | 0.00250432i | ||||
\(742\) | −88883.7 | −0.00592669 | ||||||||
\(743\) | −256361. | − | 444030.i | −0.0170365 | − | 0.0295080i | 0.857381 | − | 0.514681i | \(-0.172090\pi\) |
−0.874418 | + | 0.485173i | \(0.838756\pi\) | |||||||
\(744\) | 368195. | + | 637732.i | 0.0243863 | + | 0.0422383i | ||||
\(745\) | −4.71124e6 | + | 8.16011e6i | −0.310989 | + | 0.538649i | ||||
\(746\) | 2.56282e6 | + | 4.43894e6i | 0.168605 | + | 0.292033i | ||||
\(747\) | 2.17212e6 | − | 3.76222e6i | 0.142424 | − | 0.246685i | ||||
\(748\) | −1.07171e7 | −0.700363 | ||||||||
\(749\) | 360463. | 0.0234778 | ||||||||
\(750\) | 3.36688e6 | − | 5.83160e6i | 0.218562 | − | 0.378560i | ||||
\(751\) | −9.12644e6 | + | 1.58075e7i | −0.590475 | + | 1.02273i | 0.403693 | + | 0.914894i | \(0.367726\pi\) |
−0.994168 | + | 0.107839i | \(0.965607\pi\) | |||||||
\(752\) | −3.33353e6 | −0.214961 | ||||||||
\(753\) | −1.10345e7 | −0.709196 | ||||||||
\(754\) | −1.52747e6 | + | 2.64565e6i | −0.0978460 | + | 0.169474i | ||||
\(755\) | 1.76686e7 | + | 3.06030e7i | 1.12807 | + | 1.95387i | ||||
\(756\) | 356858. | − | 618095.i | 0.0227086 | − | 0.0393325i | ||||
\(757\) | −4.03976e6 | − | 6.99707e6i | −0.256222 | − | 0.443789i | 0.709005 | − | 0.705203i | \(-0.249144\pi\) |
−0.965227 | + | 0.261415i | \(0.915811\pi\) | |||||||
\(758\) | −5.31613e6 | − | 9.20781e6i | −0.336065 | − | 0.582081i | ||||
\(759\) | −4.89583e6 | −0.308476 | ||||||||
\(760\) | 4.81285e6 | + | 8.00395e6i | 0.302252 | + | 0.502655i | ||||
\(761\) | −2.07126e7 | −1.29650 | −0.648251 | − | 0.761427i | \(-0.724499\pi\) | ||||
−0.648251 | + | 0.761427i | \(0.724499\pi\) | |||||||
\(762\) | −3.79382e6 | − | 6.57110e6i | −0.236695 | − | 0.409968i | ||||
\(763\) | 304873. | + | 528056.i | 0.0189587 | + | 0.0328374i | ||||
\(764\) | 3.82923e6 | − | 6.63242e6i | 0.237344 | − | 0.411091i | ||||
\(765\) | 1.39812e7 | + | 2.42161e7i | 0.863754 | + | 1.49607i | ||||
\(766\) | −9.80055e6 | + | 1.69751e7i | −0.603502 | + | 1.04530i | ||||
\(767\) | 8.12639e6 | 0.498780 | ||||||||
\(768\) | 506131. | 0.0309642 | ||||||||
\(769\) | −801219. | + | 1.38775e6i | −0.0488579 | + | 0.0846244i | −0.889420 | − | 0.457091i | \(-0.848891\pi\) |
0.840562 | + | 0.541715i | \(0.182225\pi\) | |||||||
\(770\) | 1.02348e6 | − | 1.77272e6i | 0.0622089 | − | 0.107749i | ||||
\(771\) | 1.27007e7 | 0.769472 | ||||||||
\(772\) | −3.57758e6 | −0.216046 | ||||||||
\(773\) | −7.14089e6 | + | 1.23684e7i | −0.429837 | + | 0.744499i | −0.996858 | − | 0.0792040i | \(-0.974762\pi\) |
0.567022 | + | 0.823703i | \(0.308095\pi\) | |||||||
\(774\) | −5.75401e6 | − | 9.96623e6i | −0.345237 | − | 0.597969i | ||||
\(775\) | 4.07882e6 | − | 7.06473e6i | 0.243939 | − | 0.422514i | ||||
\(776\) | −1.24888e6 | − | 2.16312e6i | −0.0744501 | − | 0.128951i | ||||
\(777\) | −372340. | − | 644912.i | −0.0221252 | − | 0.0383220i | ||||
\(778\) | −1.62780e7 | −0.964168 | ||||||||
\(779\) | −1.56758e7 | − | 2.60694e7i | −0.925520 | − | 1.53917i | ||||
\(780\) | −1.98494e6 | −0.116818 | ||||||||
\(781\) | −2.47623e6 | − | 4.28896e6i | −0.145266 | − | 0.251608i | ||||
\(782\) | −5.11860e6 | − | 8.86567e6i | −0.299319 | − | 0.518435i | ||||
\(783\) | 7.25913e6 | − | 1.25732e7i | 0.423136 | − | 0.732893i | ||||
\(784\) | 2.12780e6 | + | 3.68547e6i | 0.123635 | + | 0.214142i | ||||
\(785\) | 1.65430e7 | − | 2.86534e7i | 0.958166 | − | 1.65959i | ||||
\(786\) | 8.78707e6 | 0.507327 | ||||||||
\(787\) | 3.41257e7 | 1.96401 | 0.982007 | − | 0.188847i | \(-0.0604750\pi\) | ||||
0.982007 | + | 0.188847i | \(0.0604750\pi\) | |||||||
\(788\) | −2.74868e6 | + | 4.76085e6i | −0.157691 | + | 0.273129i | ||||
\(789\) | −3.45115e6 | + | 5.97757e6i | −0.197366 | + | 0.341848i | ||||
\(790\) | −1.68186e7 | −0.958787 | ||||||||
\(791\) | 162702. | 0.00924595 | ||||||||
\(792\) | 2.38993e6 | − | 4.13947e6i | 0.135385 | − | 0.234494i | ||||
\(793\) | −2.39536e6 | − | 4.14889e6i | −0.135266 | − | 0.234287i | ||||
\(794\) | 7.38244e6 | − | 1.27868e7i | 0.415574 | − | 0.719796i | ||||
\(795\) | −587391. | − | 1.01739e6i | −0.0329617 | − | 0.0570913i | ||||
\(796\) | −3.85994e6 | − | 6.68560e6i | −0.215922 | − | 0.373988i | ||||
\(797\) | −8.99775e6 | −0.501751 | −0.250875 | − | 0.968019i | \(-0.580718\pi\) | ||||
−0.250875 | + | 0.968019i | \(0.580718\pi\) | |||||||
\(798\) | −319072. | + | 576070.i | −0.0177371 | + | 0.0320234i | ||||
\(799\) | 2.14132e7 | 1.18663 | ||||||||
\(800\) | −2.80344e6 | − | 4.85569e6i | −0.154869 | − | 0.268242i | ||||
\(801\) | 1.05559e7 | + | 1.82834e7i | 0.581319 | + | 1.00687i | ||||
\(802\) | 3.02461e6 | − | 5.23878e6i | 0.166048 | − | 0.287604i | ||||
\(803\) | −9.36971e6 | − | 1.62288e7i | −0.512788 | − | 0.888174i | ||||
\(804\) | −752610. | + | 1.30356e6i | −0.0410610 | + | 0.0711198i | ||||
\(805\) | 1.95530e6 | 0.106347 | ||||||||
\(806\) | −1.03226e6 | −0.0559693 | ||||||||
\(807\) | 6.17449e6 | − | 1.06945e7i | 0.333747 | − | 0.578067i | ||||
\(808\) | 6.34648e6 | − | 1.09924e7i | 0.341983 | − | 0.592332i | ||||
\(809\) | 7.88214e6 | 0.423421 | 0.211711 | − | 0.977332i | \(-0.432097\pi\) | ||||
0.211711 | + | 0.977332i | \(0.432097\pi\) | |||||||
\(810\) | −7.09485e6 | −0.379954 | ||||||||
\(811\) | 4.74871e6 | − | 8.22500e6i | 0.253526 | − | 0.439121i | −0.710968 | − | 0.703225i | \(-0.751743\pi\) |
0.964494 | + | 0.264104i | \(0.0850762\pi\) | |||||||
\(812\) | −477857. | − | 827672.i | −0.0254336 | − | 0.0440523i | ||||
\(813\) | −5.82268e6 | + | 1.00852e7i | −0.308956 | + | 0.535127i | ||||
\(814\) | −5.79838e6 | − | 1.00431e7i | −0.306722 | − | 0.531259i | ||||
\(815\) | −1.64222e7 | − | 2.84441e7i | −0.866039 | − | 1.50002i | ||||
\(816\) | −3.25118e6 | −0.170929 | ||||||||
\(817\) | 1.27235e7 | + | 2.11597e7i | 0.666886 | + | 1.10906i | ||||
\(818\) | 1.93893e7 | 1.01316 | ||||||||
\(819\) | 215128. | + | 372613.i | 0.0112070 | + | 0.0194110i | ||||
\(820\) | 1.43423e7 | + | 2.48416e7i | 0.744876 | + | 1.29016i | ||||
\(821\) | −1.28242e7 | + | 2.22122e7i | −0.664008 | + | 1.15010i | 0.315545 | + | 0.948911i | \(0.397813\pi\) |
−0.979553 | + | 0.201185i | \(0.935521\pi\) | |||||||
\(822\) | −3.83302e6 | − | 6.63898e6i | −0.197862 | − | 0.342706i | ||||
\(823\) | −2.31688e6 | + | 4.01296e6i | −0.119235 | + | 0.206521i | −0.919465 | − | 0.393172i | \(-0.871378\pi\) |
0.800230 | + | 0.599694i | \(0.204711\pi\) | |||||||
\(824\) | 1.16738e7 | 0.598956 | ||||||||
\(825\) | 1.72244e7 | 0.881067 | ||||||||
\(826\) | −1.27114e6 | + | 2.20168e6i | −0.0648252 | + | 0.112281i | ||||
\(827\) | −1.17966e7 | + | 2.04323e7i | −0.599780 | + | 1.03885i | 0.393073 | + | 0.919507i | \(0.371412\pi\) |
−0.992853 | + | 0.119342i | \(0.961921\pi\) | |||||||
\(828\) | 4.56581e6 | 0.231442 | ||||||||
\(829\) | −2.79814e7 | −1.41411 | −0.707054 | − | 0.707160i | \(-0.749976\pi\) | ||||
−0.707054 | + | 0.707160i | \(0.749976\pi\) | |||||||
\(830\) | 4.39450e6 | − | 7.61149e6i | 0.221419 | − | 0.383508i | ||||
\(831\) | −6.51939e6 | − | 1.12919e7i | −0.327495 | − | 0.567237i | ||||
\(832\) | −354742. | + | 614432.i | −0.0177666 | + | 0.0307727i | ||||
\(833\) | −1.36681e7 | − | 2.36739e7i | −0.682491 | − | 1.18211i | ||||
\(834\) | −705129. | − | 1.22132e6i | −0.0351038 | − | 0.0608015i | ||||
\(835\) | 5.68180e7 | 2.82014 | ||||||||
\(836\) | −4.96885e6 | + | 8.97103e6i | −0.245890 | + | 0.443942i | ||||
\(837\) | 4.90569e6 | 0.242040 | ||||||||
\(838\) | 9.63845e6 | + | 1.66943e7i | 0.474130 | + | 0.821216i | ||||
\(839\) | 1.78055e7 | + | 3.08400e7i | 0.873271 | + | 1.51255i | 0.858594 | + | 0.512657i | \(0.171339\pi\) |
0.0146769 | + | 0.999892i | \(0.495328\pi\) | |||||||
\(840\) | 310487. | − | 537779.i | 0.0151826 | − | 0.0262970i | ||||
\(841\) | 535104. | + | 926828.i | 0.0260885 | + | 0.0451865i | ||||
\(842\) | 542557. | − | 939737.i | 0.0263734 | − | 0.0456800i | ||||
\(843\) | −1.05112e7 | −0.509428 | ||||||||
\(844\) | 1.32488e7 | 0.640209 | ||||||||
\(845\) | −1.58254e7 | + | 2.74104e7i | −0.762452 | + | 1.32061i | ||||
\(846\) | −4.77518e6 | + | 8.27085e6i | −0.229384 | + | 0.397305i | ||||
\(847\) | 65859.2 | 0.00315434 | ||||||||
\(848\) | −419907. | −0.0200523 | ||||||||
\(849\) | −6.79858e6 | + | 1.17755e7i | −0.323705 | + | 0.560673i | ||||
\(850\) | 1.80081e7 | + | 3.11910e7i | 0.854911 | + | 1.48075i | ||||
\(851\) | 5.53873e6 | − | 9.59336e6i | 0.262172 | − | 0.454095i | ||||
\(852\) | −751199. | − | 1.30111e6i | −0.0354532 | − | 0.0614068i | ||||
\(853\) | −3.82673e6 | − | 6.62809e6i | −0.180076 | − | 0.311900i | 0.761830 | − | 0.647776i | \(-0.224301\pi\) |
−0.941906 | + | 0.335876i | \(0.890968\pi\) | |||||||
\(854\) | 1.49874e6 | 0.0703206 | ||||||||
\(855\) | 2.67529e7 | − | 475801.i | 1.25157 | − | 0.0222592i | ||||
\(856\) | 1.70291e6 | 0.0794342 | ||||||||
\(857\) | −1.66066e7 | − | 2.87634e7i | −0.772374 | − | 1.33779i | −0.936259 | − | 0.351311i | \(-0.885736\pi\) |
0.163885 | − | 0.986479i | \(-0.447597\pi\) | |||||||
\(858\) | −1.08977e6 | − | 1.88754e6i | −0.0505380 | − | 0.0875343i | ||||
\(859\) | −8.41483e6 | + | 1.45749e7i | −0.389101 | + | 0.673943i | −0.992329 | − | 0.123626i | \(-0.960548\pi\) |
0.603228 | + | 0.797569i | \(0.293881\pi\) | |||||||
\(860\) | −1.16412e7 | − | 2.01631e7i | −0.536723 | − | 0.929631i | ||||
\(861\) | −1.01128e6 | + | 1.75158e6i | −0.0464903 | + | 0.0805236i | ||||
\(862\) | 2.16371e6 | 0.0991817 | ||||||||
\(863\) | −3.06089e6 | −0.139901 | −0.0699505 | − | 0.997550i | \(-0.522284\pi\) | ||||
−0.0699505 | + | 0.997550i | \(0.522284\pi\) | |||||||
\(864\) | 1.68588e6 | − | 2.92002e6i | 0.0768319 | − | 0.133077i | ||||
\(865\) | 7.39930e6 | − | 1.28160e7i | 0.336241 | − | 0.582386i | ||||
\(866\) | 1.13313e7 | 0.513436 | ||||||||
\(867\) | 9.91875e6 | 0.448135 | ||||||||
\(868\) | 161467. | − | 279669.i | 0.00727418 | − | 0.0125993i | ||||
\(869\) | −9.23376e6 | − | 1.59933e7i | −0.414791 | − | 0.718439i | ||||
\(870\) | 6.31587e6 | − | 1.09394e7i | 0.282901 | − | 0.489999i | ||||
\(871\) | −1.05499e6 | − | 1.82730e6i | −0.0471199 | − | 0.0816141i | ||||
\(872\) | 1.44029e6 | + | 2.49465e6i | 0.0641444 | + | 0.111101i | ||||
\(873\) | −7.15591e6 | −0.317782 | ||||||||
\(874\) | −9.79442e6 | + | 174194.i | −0.433711 | + | 0.00771355i | ||||
\(875\) | −2.95300e6 | −0.130390 | ||||||||
\(876\) | −2.84243e6 | − | 4.92324e6i | −0.125150 | − | 0.216766i | ||||
\(877\) | 7.48891e6 | + | 1.29712e7i | 0.328791 | + | 0.569482i | 0.982272 | − | 0.187460i | \(-0.0600256\pi\) |
−0.653481 | + | 0.756943i | \(0.726692\pi\) | |||||||
\(878\) | −2.04785e6 | + | 3.54697e6i | −0.0896522 | + | 0.155282i | ||||
\(879\) | −6.07989e6 | − | 1.05307e7i | −0.265414 | − | 0.459710i | ||||
\(880\) | 4.83515e6 | − | 8.37473e6i | 0.210477 | − | 0.364556i | ||||
\(881\) | 4.06522e7 | 1.76459 | 0.882295 | − | 0.470697i | \(-0.155997\pi\) | ||||
0.882295 | + | 0.470697i | \(0.155997\pi\) | |||||||
\(882\) | 1.21921e7 | 0.527722 | ||||||||
\(883\) | −1.16198e7 | + | 2.01261e7i | −0.501529 | + | 0.868674i | 0.498469 | + | 0.866907i | \(0.333896\pi\) |
−0.999998 | + | 0.00176685i | \(0.999438\pi\) | |||||||
\(884\) | 2.27872e6 | − | 3.94686e6i | 0.0980754 | − | 0.169872i | ||||
\(885\) | −3.36015e7 | −1.44212 | ||||||||
\(886\) | −1.41323e7 | −0.604823 | ||||||||
\(887\) | 4.16037e6 | − | 7.20597e6i | 0.177551 | − | 0.307527i | −0.763490 | − | 0.645819i | \(-0.776516\pi\) |
0.941041 | + | 0.338292i | \(0.109849\pi\) | |||||||
\(888\) | −1.75902e6 | − | 3.04671e6i | −0.0748580 | − | 0.129658i | ||||
\(889\) | −1.66373e6 | + | 2.88167e6i | −0.0706039 | + | 0.122290i | ||||
\(890\) | 2.13561e7 | + | 3.69898e7i | 0.903747 | + | 1.56534i | ||||
\(891\) | −3.89522e6 | − | 6.74672e6i | −0.164376 | − | 0.284707i | ||||
\(892\) | −1.20878e7 | −0.508669 | ||||||||
\(893\) | 9.92798e6 | − | 1.79245e7i | 0.416613 | − | 0.752174i | ||||
\(894\) | −3.13869e6 | −0.131342 | ||||||||
\(895\) | −1.02510e7 | − | 1.77552e7i | −0.427767 | − | 0.740915i | ||||
\(896\) | −110979. | − | 192221.i | −0.00461816 | − | 0.00799889i | ||||
\(897\) | 1.04097e6 | − | 1.80302e6i | 0.0431975 | − | 0.0748202i | ||||
\(898\) | −1.05850e6 | − | 1.83338e6i | −0.0438028 | − | 0.0758686i | ||||
\(899\) | 3.28453e6 | − | 5.68897e6i | 0.135542 | − | 0.234766i | ||||
\(900\) | −1.60633e7 | −0.661043 | ||||||||
\(901\) | 2.69731e6 | 0.110693 | ||||||||
\(902\) | −1.57484e7 | + | 2.72771e7i | −0.644497 | + | 1.11630i | ||||
\(903\) | 820820. | − | 1.42170e6i | 0.0334987 | − | 0.0580215i | ||||
\(904\) | 768641. | 0.0312826 | ||||||||
\(905\) | 1.18613e7 | 0.481406 | ||||||||
\(906\) | −5.88553e6 | + | 1.01940e7i | −0.238213 | + | 0.412597i | ||||
\(907\) | −9.07944e6 | − | 1.57260e7i | −0.366472 | − | 0.634748i | 0.622539 | − | 0.782589i | \(-0.286101\pi\) |
−0.989011 | + | 0.147840i | \(0.952768\pi\) | |||||||
\(908\) | 8.00408e6 | − | 1.38635e7i | 0.322179 | − | 0.558030i | ||||
\(909\) | −1.81823e7 | − | 3.14926e7i | −0.729858 | − | 1.26415i | ||||
\(910\) | 435234. | + | 753848.i | 0.0174229 | + | 0.0301773i | ||||
\(911\) | −7.89177e6 | −0.315049 | −0.157525 | − | 0.987515i | \(-0.550351\pi\) | ||||
−0.157525 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(912\) | −1.50737e6 | + | 2.72149e6i | −0.0600113 | + | 0.108348i | ||||
\(913\) | 9.65068e6 | 0.383161 | ||||||||
\(914\) | −5.70567e6 | − | 9.88251e6i | −0.225913 | − | 0.391293i | ||||
\(915\) | 9.90450e6 | + | 1.71551e7i | 0.391093 | + | 0.677393i | ||||
\(916\) | 1.68209e6 | − | 2.91347e6i | 0.0662385 | − | 0.114729i | ||||
\(917\) | −1.92673e6 | − | 3.33719e6i | −0.0756653 | − | 0.131056i | ||||
\(918\) | −1.08294e7 | + | 1.87570e7i | −0.424128 | + | 0.734611i | ||||
\(919\) | −1.79687e6 | −0.0701824 | −0.0350912 | − | 0.999384i | \(-0.511172\pi\) | ||||
−0.0350912 | + | 0.999384i | \(0.511172\pi\) | |||||||
\(920\) | 9.23728e6 | 0.359811 | ||||||||
\(921\) | −5.12910e6 | + | 8.88386e6i | −0.199247 | + | 0.345106i | ||||
\(922\) | −7.13370e6 | + | 1.23559e7i | −0.276368 | + | 0.478683i | ||||
\(923\) | 2.10603e6 | 0.0813692 | ||||||||
\(924\) | 681855. | 0.0262731 | ||||||||
\(925\) | −1.94862e7 | + | 3.37511e7i | −0.748813 | + | 1.29698i | ||||
\(926\) | −394673. | − | 683593.i | −0.0151255 | − | 0.0261981i | ||||
\(927\) | 1.67224e7 | − | 2.89640e7i | 0.639144 | − | 1.10703i | ||||
\(928\) | −2.25750e6 | − | 3.91011e6i | −0.0860515 | − | 0.149046i | ||||
\(929\) | −1.07464e7 | − | 1.86132e7i | −0.408528 | − | 0.707591i | 0.586197 | − | 0.810169i | \(-0.300624\pi\) |
−0.994725 | + | 0.102577i | \(0.967291\pi\) | |||||||
\(930\) | 4.26824e6 | 0.161823 | ||||||||
\(931\) | −2.61539e7 | + | 465148.i | −0.988924 | + | 0.0175880i | ||||
\(932\) | 6.48174e6 | 0.244428 | ||||||||
\(933\) | −9.84016e6 | − | 1.70437e7i | −0.370082 | − | 0.641001i | ||||
\(934\) | −4.83125e6 | − | 8.36798e6i | −0.181214 | − | 0.313873i | ||||
\(935\) | −3.10590e7 | + | 5.37958e7i | −1.16187 | + | 2.01242i | ||||
\(936\) | 1.01631e6 | + | 1.76031e6i | 0.0379174 | + | 0.0656748i | ||||
\(937\) | −1.00820e7 | + | 1.74626e7i | −0.375145 | + | 0.649769i | −0.990349 | − | 0.138598i | \(-0.955740\pi\) |
0.615204 | + | 0.788368i | \(0.289074\pi\) | |||||||
\(938\) | 660094. | 0.0244962 | ||||||||
\(939\) | 1.87510e7 | 0.694003 | ||||||||
\(940\) | −9.66085e6 | + | 1.67331e7i | −0.356612 | + | 0.617669i | ||||
\(941\) | 1.19732e7 | − | 2.07382e7i | 0.440794 | − | 0.763477i | −0.556955 | − | 0.830543i | \(-0.688030\pi\) |
0.997749 | + | 0.0670657i | \(0.0213637\pi\) | |||||||
\(942\) | 1.10212e7 | 0.404669 | ||||||||
\(943\) | −3.00865e7 | −1.10177 | ||||||||
\(944\) | −6.00516e6 | + | 1.04012e7i | −0.219328 | + | 0.379888i | ||||
\(945\) | −2.06841e6 | − | 3.58258e6i | −0.0753453 | − | 0.130502i | ||||
\(946\) | 1.27825e7 | − | 2.21399e7i | 0.464394 | − | 0.804354i | ||||
\(947\) | 1.42076e7 | + | 2.46082e7i | 0.514807 | + | 0.891672i | 0.999852 | + | 0.0171827i | \(0.00546970\pi\) |
−0.485046 | + | 0.874489i | \(0.661197\pi\) | |||||||
\(948\) | −2.80119e6 | − | 4.85180e6i | −0.101233 | − | 0.175341i | ||||
\(949\) | 7.96893e6 | 0.287233 | ||||||||
\(950\) | 3.44585e7 | − | 612845.i | 1.23876 | − | 0.0220314i | ||||
\(951\) | 1.59741e7 | 0.572749 | ||||||||
\(952\) | 712881. | + | 1.23475e6i | 0.0254932 | + | 0.0441555i | ||||
\(953\) | −1.78515e7 | − | 3.09197e7i | −0.636712 | − | 1.10282i | −0.986150 | − | 0.165857i | \(-0.946961\pi\) |
0.349438 | − | 0.936959i | \(-0.386372\pi\) | |||||||
\(954\) | −601503. | + | 1.04183e6i | −0.0213977 | + | 0.0370619i | ||||
\(955\) | −2.21948e7 | − | 3.84426e7i | −0.787487 | − | 1.36397i | ||||
\(956\) | 1.25718e7 | − | 2.17750e7i | 0.444890 | − | 0.770572i | ||||
\(957\) | 1.38702e7 | 0.489555 | ||||||||
\(958\) | −2.69984e7 | −0.950440 | ||||||||
\(959\) | −1.68092e6 | + | 2.91144e6i | −0.0590201 | + | 0.102226i | ||||
\(960\) | 1.46681e6 | − | 2.54059e6i | 0.0513684 | − | 0.0889727i | ||||
\(961\) | −2.64095e7 | −0.922468 | ||||||||
\(962\) | 4.93151e6 | 0.171808 | ||||||||
\(963\) | 2.43937e6 | − | 4.22511e6i | 0.0847640 | − | 0.146816i | ||||
\(964\) | 7.64484e6 | + | 1.32413e7i | 0.264957 | + | 0.458919i | ||||
\(965\) | −1.03681e7 | + | 1.79581e7i | −0.358412 | + | 0.620787i | ||||
\(966\) | 325661. | + | 564061.i | 0.0112285 | + | 0.0194484i | ||||
\(967\) | 1.15441e7 | + | 1.99950e7i | 0.397004 | + | 0.687631i | 0.993355 | − | 0.115093i | \(-0.0367165\pi\) |
−0.596351 | + | 0.802724i | \(0.703383\pi\) | |||||||
\(968\) | 311134. | 0.0106723 | ||||||||
\(969\) | 9.68273e6 | − | 1.74817e7i | 0.331275 | − | 0.598101i | ||||
\(970\) | −1.44774e7 | −0.494039 | ||||||||
\(971\) | −1.79907e6 | − | 3.11608e6i | −0.0612350 | − | 0.106062i | 0.833783 | − | 0.552093i | \(-0.186171\pi\) |
−0.895018 | + | 0.446031i | \(0.852837\pi\) | |||||||
\(972\) | −7.58273e6 | − | 1.31337e7i | −0.257430 | − | 0.445883i | ||||
\(973\) | −309225. | + | 535593.i | −0.0104711 | + | 0.0181365i | ||||
\(974\) | 21063.1 | + | 36482.3i | 0.000711417 | + | 0.00123221i | ||||
\(975\) | −3.66233e6 | + | 6.34334e6i | −0.123380 | + | 0.213701i | ||||
\(976\) | 7.08041e6 | 0.237922 | ||||||||
\(977\) | −4.22278e7 | −1.41535 | −0.707673 | − | 0.706540i | \(-0.750255\pi\) | ||||
−0.707673 | + | 0.706540i | \(0.750255\pi\) | |||||||
\(978\) | 5.47033e6 | − | 9.47490e6i | 0.182880 | − | 0.316758i | ||||
\(979\) | −2.34499e7 | + | 4.06164e7i | −0.781959 | + | 1.35439i | ||||
\(980\) | 2.46662e7 | 0.820422 | ||||||||
\(981\) | 8.25268e6 | 0.273793 | ||||||||
\(982\) | −845903. | + | 1.46515e6i | −0.0279925 | + | 0.0484845i | ||||
\(983\) | 1.53664e7 | + | 2.66153e7i | 0.507209 | + | 0.878512i | 0.999965 | + | 0.00834479i | \(0.00265626\pi\) |
−0.492756 | + | 0.870168i | \(0.664010\pi\) | |||||||
\(984\) | −4.77751e6 | + | 8.27488e6i | −0.157294 | + | 0.272442i | ||||
\(985\) | 1.59318e7 | + | 2.75947e7i | 0.523207 | + | 0.906222i | ||||
\(986\) | 1.45013e7 | + | 2.51169e7i | 0.475022 | + | 0.822763i | ||||
\(987\) | −1.36238e6 | −0.0445148 | ||||||||
\(988\) | −2.24732e6 | − | 3.73737e6i | −0.0732440 | − | 0.121808i | ||||
\(989\) | 2.44202e7 | 0.793885 | ||||||||
\(990\) | −1.38524e7 | − | 2.39931e7i | −0.449198 | − | 0.778033i | ||||
\(991\) | 2.27497e7 | + | 3.94036e7i | 0.735854 | + | 1.27454i | 0.954348 | + | 0.298698i | \(0.0965523\pi\) |
−0.218494 | + | 0.975838i | \(0.570114\pi\) | |||||||
\(992\) | 762806. | − | 1.32122e6i | 0.0246113 | − | 0.0426281i | ||||
\(993\) | 6.78991e6 | + | 1.17605e7i | 0.218520 | + | 0.378487i | ||||
\(994\) | −329428. | + | 570586.i | −0.0105753 | + | 0.0183170i | ||||
\(995\) | −4.47457e7 | −1.43283 | ||||||||
\(996\) | 2.92767e6 | 0.0935133 | ||||||||
\(997\) | 434529. | − | 752626.i | 0.0138446 | − | 0.0239796i | −0.859020 | − | 0.511942i | \(-0.828926\pi\) |
0.872865 | + | 0.487962i | \(0.162260\pi\) | |||||||
\(998\) | −5.79631e6 | + | 1.00395e7i | −0.184215 | + | 0.319070i | ||||
\(999\) | −2.34365e7 | −0.742983 |
(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 | 38.6.c.b.7.2 | ✓ | 8 | |
3.2 | odd | 2 | 342.6.g.d.235.1 | 8 | |||
4.3 | odd | 2 | 304.6.i.b.273.3 | 8 | |||
19.7 | even | 3 | 722.6.a.j.1.3 | 4 | |||
19.11 | even | 3 | inner | 38.6.c.b.11.2 | yes | 8 | |
19.12 | odd | 6 | 722.6.a.g.1.2 | 4 | |||
57.11 | odd | 6 | 342.6.g.d.163.1 | 8 | |||
76.11 | odd | 6 | 304.6.i.b.49.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.6.c.b.7.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
38.6.c.b.11.2 | yes | 8 | 19.11 | even | 3 | inner | |
304.6.i.b.49.3 | 8 | 76.11 | odd | 6 | |||
304.6.i.b.273.3 | 8 | 4.3 | odd | 2 | |||
342.6.g.d.163.1 | 8 | 57.11 | odd | 6 | |||
342.6.g.d.235.1 | 8 | 3.2 | odd | 2 | |||
722.6.a.g.1.2 | 4 | 19.12 | odd | 6 | |||
722.6.a.j.1.3 | 4 | 19.7 | even | 3 |