Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), 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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.11 | ||
Root | \(3.16536 - 1.82752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.c.146.5 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.65505i | 0.646127i | 0.946377 | + | 0.323064i | \(0.104713\pi\) | ||||
−0.946377 | + | 0.323064i | \(0.895287\pi\) | |||||||
\(3\) | −15.5635 | − | 0.882561i | −0.998396 | − | 0.0566163i | ||||
\(4\) | 18.6406 | 0.582520 | ||||||||
\(5\) | 74.3244 | 1.32955 | 0.664777 | − | 0.747042i | \(-0.268526\pi\) | ||||
0.664777 | + | 0.747042i | \(0.268526\pi\) | |||||||
\(6\) | 3.22580 | − | 56.8851i | 0.0365813 | − | 0.645091i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 185.094i | 1.02251i | ||||||||
\(9\) | 241.442 | + | 27.4714i | 0.993589 | + | 0.113051i | ||||
\(10\) | 271.659i | 0.859061i | ||||||||
\(11\) | − | 39.3914i | − | 0.0981567i | −0.998795 | − | 0.0490783i | \(-0.984372\pi\) | ||
0.998795 | − | 0.0490783i | \(-0.0156284\pi\) | |||||||
\(12\) | −290.113 | − | 16.4515i | −0.581586 | − | 0.0329801i | ||||
\(13\) | − | 589.288i | − | 0.967096i | −0.875318 | − | 0.483548i | \(-0.839348\pi\) | ||
0.875318 | − | 0.483548i | \(-0.160652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1156.74 | − | 65.5958i | −1.32742 | − | 0.0752745i | ||||
\(16\) | −80.0263 | −0.0781507 | ||||||||
\(17\) | 1237.51 | 1.03855 | 0.519274 | − | 0.854608i | \(-0.326203\pi\) | ||||
0.519274 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(18\) | −100.409 | + | 882.482i | −0.0730453 | + | 0.641985i | ||||
\(19\) | − | 2767.79i | − | 1.75893i | −0.475964 | − | 0.879465i | \(-0.657901\pi\) | ||
0.475964 | − | 0.879465i | \(-0.342099\pi\) | |||||||
\(20\) | 1385.45 | 0.774492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 143.977 | 0.0634217 | ||||||||
\(23\) | − | 463.253i | − | 0.182599i | −0.995823 | − | 0.0912997i | \(-0.970898\pi\) | ||
0.995823 | − | 0.0912997i | \(-0.0291021\pi\) | |||||||
\(24\) | 163.357 | − | 2880.70i | 0.0578907 | − | 1.02087i | ||||
\(25\) | 2399.11 | 0.767716 | ||||||||
\(26\) | 2153.88 | 0.624867 | ||||||||
\(27\) | −3733.43 | − | 640.637i | −0.985595 | − | 0.169123i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5294.57i | 1.16906i | 0.811373 | + | 0.584529i | \(0.198721\pi\) | ||||
−0.811373 | + | 0.584529i | \(0.801279\pi\) | |||||||
\(30\) | 239.756 | − | 4227.95i | 0.0486369 | − | 0.857683i | ||||
\(31\) | 2846.74i | 0.532039i | 0.963968 | + | 0.266019i | \(0.0857085\pi\) | ||||
−0.963968 | + | 0.266019i | \(0.914291\pi\) | |||||||
\(32\) | 5630.50i | 0.972014i | ||||||||
\(33\) | −34.7653 | + | 613.066i | −0.00555727 | + | 0.0979992i | ||||
\(34\) | 4523.16i | 0.671034i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4500.64 | + | 512.084i | 0.578785 | + | 0.0658545i | ||||
\(37\) | 7847.11 | 0.942336 | 0.471168 | − | 0.882044i | \(-0.343833\pi\) | ||||
0.471168 | + | 0.882044i | \(0.343833\pi\) | |||||||
\(38\) | 10116.4 | 1.13649 | ||||||||
\(39\) | −520.083 | + | 9171.36i | −0.0547534 | + | 0.965544i | ||||
\(40\) | 13757.0i | 1.35948i | ||||||||
\(41\) | 12162.5 | 1.12996 | 0.564980 | − | 0.825105i | \(-0.308884\pi\) | ||||
0.564980 | + | 0.825105i | \(0.308884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5350.18 | 0.441262 | 0.220631 | − | 0.975357i | \(-0.429188\pi\) | ||||
0.220631 | + | 0.975357i | \(0.429188\pi\) | |||||||
\(44\) | − | 734.281i | − | 0.0571782i | ||||||
\(45\) | 17945.0 | + | 2041.79i | 1.32103 | + | 0.150307i | ||||
\(46\) | 1693.21 | 0.117982 | ||||||||
\(47\) | 6755.99 | 0.446112 | 0.223056 | − | 0.974806i | \(-0.428397\pi\) | ||||
0.223056 | + | 0.974806i | \(0.428397\pi\) | |||||||
\(48\) | 1245.49 | + | 70.6281i | 0.0780253 | + | 0.00442460i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8768.86i | 0.496042i | ||||||||
\(51\) | −19259.9 | − | 1092.18i | −1.03688 | − | 0.0587987i | ||||
\(52\) | − | 10984.7i | − | 0.563352i | ||||||
\(53\) | 16011.8i | 0.782977i | 0.920183 | + | 0.391489i | \(0.128040\pi\) | ||||
−0.920183 | + | 0.391489i | \(0.871960\pi\) | |||||||
\(54\) | 2341.56 | − | 13645.9i | 0.109275 | − | 0.636820i | ||||
\(55\) | − | 2927.74i | − | 0.130505i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2442.74 | + | 43076.3i | −0.0995841 | + | 1.75611i | ||||
\(58\) | −19351.9 | −0.755360 | ||||||||
\(59\) | 7746.64 | 0.289723 | 0.144862 | − | 0.989452i | \(-0.453726\pi\) | ||||
0.144862 | + | 0.989452i | \(0.453726\pi\) | |||||||
\(60\) | −21562.4 | − | 1222.75i | −0.773250 | − | 0.0438489i | ||||
\(61\) | − | 5617.58i | − | 0.193297i | −0.995319 | − | 0.0966484i | \(-0.969188\pi\) | ||
0.995319 | − | 0.0966484i | \(-0.0308122\pi\) | |||||||
\(62\) | −10405.0 | −0.343765 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23140.6 | −0.706195 | ||||||||
\(65\) | − | 43798.5i | − | 1.28581i | ||||||
\(66\) | −2240.79 | − | 127.069i | −0.0633199 | − | 0.00359070i | ||||
\(67\) | −12887.4 | −0.350734 | −0.175367 | − | 0.984503i | \(-0.556111\pi\) | ||||
−0.175367 | + | 0.984503i | \(0.556111\pi\) | |||||||
\(68\) | 23068.0 | 0.604975 | ||||||||
\(69\) | −408.849 | + | 7209.82i | −0.0103381 | + | 0.182306i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 60637.7i | − | 1.42757i | −0.700366 | − | 0.713784i | \(-0.746980\pi\) | ||
0.700366 | − | 0.713784i | \(-0.253020\pi\) | |||||||
\(72\) | −5084.79 | + | 44689.5i | −0.115596 | + | 1.01595i | ||||
\(73\) | 51641.4i | 1.13420i | 0.823648 | + | 0.567101i | \(0.191935\pi\) | ||||
−0.823648 | + | 0.567101i | \(0.808065\pi\) | |||||||
\(74\) | 28681.6i | 0.608869i | ||||||||
\(75\) | −37338.5 | − | 2117.36i | −0.766484 | − | 0.0434652i | ||||
\(76\) | − | 51593.3i | − | 1.02461i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −33521.7 | − | 1900.93i | −0.623864 | − | 0.0353776i | ||||
\(79\) | 67372.2 | 1.21454 | 0.607272 | − | 0.794494i | \(-0.292264\pi\) | ||||
0.607272 | + | 0.794494i | \(0.292264\pi\) | |||||||
\(80\) | −5947.90 | −0.103906 | ||||||||
\(81\) | 57539.6 | + | 13265.5i | 0.974439 | + | 0.224652i | ||||
\(82\) | 44454.5i | 0.730097i | ||||||||
\(83\) | −8712.06 | −0.138812 | −0.0694058 | − | 0.997589i | \(-0.522110\pi\) | ||||
−0.0694058 | + | 0.997589i | \(0.522110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 91977.1 | 1.38081 | ||||||||
\(86\) | 19555.1i | 0.285112i | ||||||||
\(87\) | 4672.78 | − | 82401.9i | 0.0661877 | − | 1.16718i | ||||
\(88\) | 7291.11 | 0.100366 | ||||||||
\(89\) | −18112.0 | −0.242378 | −0.121189 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121189 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(90\) | −7462.85 | + | 65589.9i | −0.0971177 | + | 0.853554i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 8635.34i | − | 0.106368i | ||||||
\(93\) | 2512.42 | − | 44305.1i | 0.0301221 | − | 0.531185i | ||||
\(94\) | 24693.4i | 0.288245i | ||||||||
\(95\) | − | 205714.i | − | 2.33859i | ||||||
\(96\) | 4969.26 | − | 87630.1i | 0.0550318 | − | 0.970454i | ||||
\(97\) | 18641.1i | 0.201160i | 0.994929 | + | 0.100580i | \(0.0320698\pi\) | ||||
−0.994929 | + | 0.100580i | \(0.967930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1082.14 | − | 9510.75i | 0.0110967 | − | 0.0975274i | ||||
\(100\) | 44721.0 | 0.447210 | ||||||||
\(101\) | −170598. | −1.66407 | −0.832034 | − | 0.554725i | \(-0.812824\pi\) | ||||
−0.832034 | + | 0.554725i | \(0.812824\pi\) | |||||||
\(102\) | 3991.96 | − | 70395.9i | 0.0379914 | − | 0.669957i | ||||
\(103\) | 58887.8i | 0.546931i | 0.961882 | + | 0.273465i | \(0.0881699\pi\) | ||||
−0.961882 | + | 0.273465i | \(0.911830\pi\) | |||||||
\(104\) | 109074. | 0.988864 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −58523.7 | −0.505903 | ||||||||
\(107\) | 147582.i | 1.24616i | 0.782157 | + | 0.623082i | \(0.214120\pi\) | ||||
−0.782157 | + | 0.623082i | \(0.785880\pi\) | |||||||
\(108\) | −69593.5 | − | 11941.9i | −0.574129 | − | 0.0985175i | ||||
\(109\) | 26156.0 | 0.210865 | 0.105433 | − | 0.994426i | \(-0.466377\pi\) | ||||
0.105433 | + | 0.994426i | \(0.466377\pi\) | |||||||
\(110\) | 10701.0 | 0.0843226 | ||||||||
\(111\) | −122128. | − | 6925.56i | −0.940824 | − | 0.0533516i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19094.4i | − | 0.140672i | −0.997523 | − | 0.0703362i | \(-0.977593\pi\) | ||
0.997523 | − | 0.0703362i | \(-0.0224072\pi\) | |||||||
\(114\) | −157446. | − | 8928.33i | −1.13467 | − | 0.0643440i | ||||
\(115\) | − | 34431.0i | − | 0.242776i | ||||||
\(116\) | 98694.2i | 0.681000i | ||||||||
\(117\) | 16188.6 | − | 142279.i | 0.109331 | − | 0.960896i | ||||
\(118\) | 28314.3i | 0.187198i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12141.4 | − | 214106.i | 0.0769688 | − | 1.35730i | ||||
\(121\) | 159499. | 0.990365 | ||||||||
\(122\) | 20532.5 | 0.124894 | ||||||||
\(123\) | −189290. | − | 10734.1i | −1.12815 | − | 0.0639741i | ||||
\(124\) | 53065.0i | 0.309923i | ||||||||
\(125\) | −53951.2 | −0.308835 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −42178.1 | −0.232048 | −0.116024 | − | 0.993246i | \(-0.537015\pi\) | ||||
−0.116024 | + | 0.993246i | \(0.537015\pi\) | |||||||
\(128\) | 95596.2i | 0.515722i | ||||||||
\(129\) | −83267.2 | − | 4721.86i | −0.440555 | − | 0.0249827i | ||||
\(130\) | 160085. | 0.830794 | ||||||||
\(131\) | −283072. | −1.44118 | −0.720590 | − | 0.693361i | \(-0.756129\pi\) | ||||
−0.720590 | + | 0.693361i | \(0.756129\pi\) | |||||||
\(132\) | −648.048 | + | 11427.9i | −0.00323722 | + | 0.0570865i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 47104.0i | − | 0.226619i | ||||||
\(135\) | −277485. | − | 47615.0i | −1.31040 | − | 0.224858i | ||||
\(136\) | 229055.i | 1.06192i | ||||||||
\(137\) | − | 263686.i | − | 1.20029i | −0.799891 | − | 0.600145i | \(-0.795110\pi\) | ||
0.799891 | − | 0.600145i | \(-0.204890\pi\) | |||||||
\(138\) | −26352.2 | − | 1494.36i | −0.117793 | − | 0.00667972i | ||||
\(139\) | − | 363744.i | − | 1.59683i | −0.602108 | − | 0.798415i | \(-0.705672\pi\) | ||
0.602108 | − | 0.798415i | \(-0.294328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −105147. | − | 5962.57i | −0.445397 | − | 0.0252572i | ||||
\(142\) | 221634. | 0.922390 | ||||||||
\(143\) | −23212.9 | −0.0949269 | ||||||||
\(144\) | −19321.7 | − | 2198.43i | −0.0776497 | − | 0.00883501i | ||||
\(145\) | 393516.i | 1.55433i | ||||||||
\(146\) | −188752. | −0.732839 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 146275. | 0.548929 | ||||||||
\(149\) | − | 385877.i | − | 1.42391i | −0.702224 | − | 0.711957i | \(-0.747809\pi\) | ||
0.702224 | − | 0.711957i | \(-0.252191\pi\) | |||||||
\(150\) | 7739.06 | − | 136474.i | 0.0280841 | − | 0.495246i | ||||
\(151\) | −276533. | −0.986970 | −0.493485 | − | 0.869754i | \(-0.664277\pi\) | ||||
−0.493485 | + | 0.869754i | \(0.664277\pi\) | |||||||
\(152\) | 512300. | 1.79852 | ||||||||
\(153\) | 298787. | + | 33996.1i | 1.03189 | + | 0.117409i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 211582.i | 0.707375i | ||||||||
\(156\) | −9694.67 | + | 170960.i | −0.0318949 | + | 0.562449i | ||||
\(157\) | 378991.i | 1.22710i | 0.789656 | + | 0.613550i | \(0.210259\pi\) | ||||
−0.789656 | + | 0.613550i | \(0.789741\pi\) | |||||||
\(158\) | 246248.i | 0.784749i | ||||||||
\(159\) | 14131.3 | − | 249198.i | 0.0443293 | − | 0.781722i | ||||
\(160\) | 418484.i | 1.29235i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −48486.0 | + | 210310.i | −0.145154 | + | 0.629611i | ||||
\(163\) | −231513. | −0.682505 | −0.341252 | − | 0.939972i | \(-0.610851\pi\) | ||||
−0.341252 | + | 0.939972i | \(0.610851\pi\) | |||||||
\(164\) | 226717. | 0.658224 | ||||||||
\(165\) | −2583.91 | + | 45565.8i | −0.00738869 | + | 0.130295i | ||||
\(166\) | − | 31843.0i | − | 0.0896899i | ||||||
\(167\) | −173708. | −0.481981 | −0.240990 | − | 0.970527i | \(-0.577472\pi\) | ||||
−0.240990 | + | 0.970527i | \(0.577472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24032.3 | 0.0647260 | ||||||||
\(170\) | 336181.i | 0.892176i | ||||||||
\(171\) | 76034.9 | − | 668260.i | 0.198849 | − | 1.74765i | ||||
\(172\) | 99730.7 | 0.257044 | ||||||||
\(173\) | −490510. | −1.24604 | −0.623021 | − | 0.782205i | \(-0.714095\pi\) | ||||
−0.623021 | + | 0.782205i | \(0.714095\pi\) | |||||||
\(174\) | 301183. | + | 17079.2i | 0.754148 | + | 0.0427657i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3152.35i | 0.00767101i | ||||||||
\(177\) | −120564. | − | 6836.88i | −0.289259 | − | 0.0164031i | ||||
\(178\) | − | 66200.4i | − | 0.156607i | ||||||
\(179\) | 641321.i | 1.49604i | 0.663677 | + | 0.748019i | \(0.268995\pi\) | ||||
−0.663677 | + | 0.748019i | \(0.731005\pi\) | |||||||
\(180\) | 334507. | + | 38060.3i | 0.769527 | + | 0.0875571i | ||||
\(181\) | − | 46939.3i | − | 0.106498i | −0.998581 | − | 0.0532489i | \(-0.983042\pi\) | ||
0.998581 | − | 0.0532489i | \(-0.0169577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4957.85 | + | 87428.9i | −0.0109437 | + | 0.192987i | ||||
\(184\) | 85745.4 | 0.186709 | ||||||||
\(185\) | 583232. | 1.25289 | ||||||||
\(186\) | 161937. | + | 9183.01i | 0.343213 | + | 0.0194627i | ||||
\(187\) | − | 48747.3i | − | 0.101940i | ||||||
\(188\) | 125936. | 0.259869 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 751894. | 1.51103 | ||||||||
\(191\) | − | 761400.i | − | 1.51018i | −0.655620 | − | 0.755091i | \(-0.727593\pi\) | ||
0.655620 | − | 0.755091i | \(-0.272407\pi\) | |||||||
\(192\) | 360148. | + | 20423.0i | 0.705062 | + | 0.0399821i | ||||
\(193\) | 556313. | 1.07504 | 0.537522 | − | 0.843250i | \(-0.319361\pi\) | ||||
0.537522 | + | 0.843250i | \(0.319361\pi\) | |||||||
\(194\) | −68133.9 | −0.129975 | ||||||||
\(195\) | −38654.8 | + | 681656.i | −0.0727976 | + | 1.28374i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 545896.i | 1.00218i | 0.865396 | + | 0.501088i | \(0.167067\pi\) | ||||
−0.865396 | + | 0.501088i | \(0.832933\pi\) | |||||||
\(198\) | 34762.2 | + | 3955.26i | 0.0630151 | + | 0.00716988i | ||||
\(199\) | − | 211201.i | − | 0.378062i | −0.981971 | − | 0.189031i | \(-0.939465\pi\) | ||
0.981971 | − | 0.189031i | \(-0.0605346\pi\) | |||||||
\(200\) | 444061.i | 0.784996i | ||||||||
\(201\) | 200572. | + | 11373.9i | 0.350171 | + | 0.0198573i | ||||
\(202\) | − | 623544.i | − | 1.07520i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −359017. | − | 20358.9i | −0.604004 | − | 0.0342514i | ||||
\(205\) | 903969. | 1.50234 | ||||||||
\(206\) | −215238. | −0.353387 | ||||||||
\(207\) | 12726.2 | − | 111849.i | 0.0206430 | − | 0.181429i | ||||
\(208\) | 47158.6i | 0.0755792i | ||||||||
\(209\) | −109027. | −0.172651 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −670640. | −1.03701 | −0.518506 | − | 0.855074i | \(-0.673512\pi\) | ||||
−0.518506 | + | 0.855074i | \(0.673512\pi\) | |||||||
\(212\) | 298469.i | 0.456100i | ||||||||
\(213\) | −53516.5 | + | 943732.i | −0.0808236 | + | 1.42528i | ||||
\(214\) | −539420. | −0.805180 | ||||||||
\(215\) | 397649. | 0.586683 | ||||||||
\(216\) | 118578. | − | 691035.i | 0.172930 | − | 1.00778i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 95601.5i | 0.136246i | ||||||||
\(219\) | 45576.7 | − | 803718.i | 0.0642144 | − | 1.13238i | ||||
\(220\) | − | 54575.0i | − | 0.0760216i | ||||||
\(221\) | − | 729250.i | − | 1.00437i | ||||||
\(222\) | 25313.2 | − | 446384.i | 0.0344719 | − | 0.607892i | ||||
\(223\) | 18729.0i | 0.0252204i | 0.999920 | + | 0.0126102i | \(0.00401406\pi\) | ||||
−0.999920 | + | 0.0126102i | \(0.995986\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 579247. | + | 65906.9i | 0.762794 | + | 0.0867910i | ||||
\(226\) | 69790.8 | 0.0908923 | ||||||||
\(227\) | 447047. | 0.575822 | 0.287911 | − | 0.957657i | \(-0.407039\pi\) | ||||
0.287911 | + | 0.957657i | \(0.407039\pi\) | |||||||
\(228\) | −45534.2 | + | 802970.i | −0.0580097 | + | 1.02297i | ||||
\(229\) | 22000.4i | 0.0277231i | 0.999904 | + | 0.0138616i | \(0.00441241\pi\) | ||||
−0.999904 | + | 0.0138616i | \(0.995588\pi\) | |||||||
\(230\) | 125847. | 0.156864 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −979993. | −1.19537 | ||||||||
\(233\) | 533090.i | 0.643296i | 0.946859 | + | 0.321648i | \(0.104237\pi\) | ||||
−0.946859 | + | 0.321648i | \(0.895763\pi\) | |||||||
\(234\) | 520036. | + | 59170.0i | 0.620861 | + | 0.0706418i | ||||
\(235\) | 502135. | 0.593131 | ||||||||
\(236\) | 144402. | 0.168770 | ||||||||
\(237\) | −1.04854e6 | − | 59460.1i | −1.21259 | − | 0.0687629i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 269068.i | 0.304697i | 0.988327 | + | 0.152348i | \(0.0486836\pi\) | ||||
−0.988327 | + | 0.152348i | \(0.951316\pi\) | |||||||
\(240\) | 92569.9 | + | 5249.39i | 0.103739 | + | 0.00588275i | ||||
\(241\) | − | 266824.i | − | 0.295926i | −0.988993 | − | 0.147963i | \(-0.952728\pi\) | ||
0.988993 | − | 0.147963i | \(-0.0472716\pi\) | |||||||
\(242\) | 582977.i | 0.639902i | ||||||||
\(243\) | −883808. | − | 257239.i | −0.960157 | − | 0.279461i | ||||
\(244\) | − | 104715.i | − | 0.112599i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 39233.8 | − | 691865.i | 0.0413354 | − | 0.728926i | ||||
\(247\) | −1.63102e6 | −1.70105 | ||||||||
\(248\) | −526914. | −0.544014 | ||||||||
\(249\) | 135590. | + | 7688.92i | 0.138589 | + | 0.00785899i | ||||
\(250\) | − | 197194.i | − | 0.199546i | ||||||
\(251\) | 947580. | 0.949361 | 0.474681 | − | 0.880158i | \(-0.342564\pi\) | ||||
0.474681 | + | 0.880158i | \(0.342564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18248.2 | −0.0179233 | ||||||||
\(254\) | − | 154163.i | − | 0.149932i | ||||||
\(255\) | −1.43148e6 | − | 81175.4i | −1.37859 | − | 0.0781761i | ||||
\(256\) | −1.08991e6 | −1.03942 | ||||||||
\(257\) | −526317. | −0.497066 | −0.248533 | − | 0.968623i | \(-0.579948\pi\) | ||||
−0.248533 | + | 0.968623i | \(0.579948\pi\) | |||||||
\(258\) | 17258.6 | − | 304346.i | 0.0161420 | − | 0.284654i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 816432.i | − | 0.749008i | ||||||
\(261\) | −145449. | + | 1.27833e6i | −0.132163 | + | 1.16156i | ||||
\(262\) | − | 1.03464e6i | − | 0.931186i | ||||||
\(263\) | − | 1.36537e6i | − | 1.21720i | −0.793477 | − | 0.608601i | \(-0.791731\pi\) | ||
0.793477 | − | 0.608601i | \(-0.208269\pi\) | |||||||
\(264\) | −113475. | − | 6434.85i | −0.100205 | − | 0.00568236i | ||||
\(265\) | 1.19006e6i | 1.04101i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 281886. | + | 15985.0i | 0.241989 | + | 0.0137225i | ||||
\(268\) | −240229. | −0.204310 | ||||||||
\(269\) | −29229.0 | −0.0246283 | −0.0123141 | − | 0.999924i | \(-0.503920\pi\) | ||||
−0.0123141 | + | 0.999924i | \(0.503920\pi\) | |||||||
\(270\) | 174035. | − | 1.01422e6i | 0.145287 | − | 0.846686i | ||||
\(271\) | − | 423724.i | − | 0.350477i | −0.984526 | − | 0.175239i | \(-0.943930\pi\) | ||
0.984526 | − | 0.175239i | \(-0.0560697\pi\) | |||||||
\(272\) | −99033.3 | −0.0811632 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 963785. | 0.775540 | ||||||||
\(275\) | − | 94504.4i | − | 0.0753564i | ||||||
\(276\) | −7621.21 | + | 134396.i | −0.00602215 | + | 0.106197i | ||||
\(277\) | −746981. | −0.584938 | −0.292469 | − | 0.956275i | \(-0.594477\pi\) | ||||
−0.292469 | + | 0.956275i | \(0.594477\pi\) | |||||||
\(278\) | 1.32950e6 | 1.03175 | ||||||||
\(279\) | −78203.9 | + | 687323.i | −0.0601475 | + | 0.528628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 841921.i | − | 0.636071i | −0.948079 | − | 0.318035i | \(-0.896977\pi\) | ||
0.948079 | − | 0.318035i | \(-0.103023\pi\) | |||||||
\(282\) | 21793.5 | − | 384315.i | 0.0163194 | − | 0.287783i | ||||
\(283\) | 1.39274e6i | 1.03373i | 0.856068 | + | 0.516863i | \(0.172900\pi\) | ||||
−0.856068 | + | 0.516863i | \(0.827100\pi\) | |||||||
\(284\) | − | 1.13033e6i | − | 0.831587i | ||||||
\(285\) | −181555. | + | 3.20162e6i | −0.132403 | + | 2.33484i | ||||
\(286\) | − | 84844.2i | − | 0.0613348i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −154678. | + | 1.35944e6i | −0.109887 | + | 0.965782i | ||||
\(289\) | 111574. | 0.0785809 | ||||||||
\(290\) | −1.43832e6 | −1.00429 | ||||||||
\(291\) | 16451.9 | − | 290119.i | 0.0113889 | − | 0.200837i | ||||
\(292\) | 962628.i | 0.660696i | ||||||||
\(293\) | 537097. | 0.365497 | 0.182748 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182748 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 575764. | 0.385203 | ||||||||
\(296\) | 1.45245e6i | 0.963547i | ||||||||
\(297\) | −25235.6 | + | 147065.i | −0.0166006 | + | 0.0967427i | ||||
\(298\) | 1.41040e6 | 0.920029 | ||||||||
\(299\) | −272990. | −0.176591 | ||||||||
\(300\) | −696013. | − | 39469.0i | −0.446492 | − | 0.0253194i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1.01074e6i | − | 0.637708i | ||||||
\(303\) | 2.65510e6 | + | 150563.i | 1.66140 | + | 0.0942134i | ||||
\(304\) | 221496.i | 0.137462i | ||||||||
\(305\) | − | 417523.i | − | 0.256999i | ||||||
\(306\) | −124257. | + | 1.09208e6i | −0.0758610 | + | 0.666732i | ||||
\(307\) | 511397.i | 0.309679i | 0.987940 | + | 0.154840i | \(0.0494861\pi\) | ||||
−0.987940 | + | 0.154840i | \(0.950514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51972.1 | − | 916497.i | 0.0309652 | − | 0.546053i | ||||
\(310\) | −773342. | −0.457054 | ||||||||
\(311\) | −2.41299e6 | −1.41467 | −0.707335 | − | 0.706878i | \(-0.750103\pi\) | ||||
−0.707335 | + | 0.706878i | \(0.750103\pi\) | |||||||
\(312\) | −1.69756e6 | − | 96264.1i | −0.987278 | − | 0.0559858i | ||||
\(313\) | − | 2.72163e6i | − | 1.57025i | −0.619339 | − | 0.785124i | \(-0.712599\pi\) | ||
0.619339 | − | 0.785124i | \(-0.287401\pi\) | |||||||
\(314\) | −1.38523e6 | −0.792862 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.25586e6 | 0.707495 | ||||||||
\(317\) | − | 1.65080e6i | − | 0.922672i | −0.887226 | − | 0.461336i | \(-0.847370\pi\) | ||
0.887226 | − | 0.461336i | \(-0.152630\pi\) | |||||||
\(318\) | 910831. | + | 51650.7i | 0.505091 | + | 0.0286424i | ||||
\(319\) | 208561. | 0.114751 | ||||||||
\(320\) | −1.71991e6 | −0.938925 | ||||||||
\(321\) | 130250. | − | 2.29689e6i | 0.0705532 | − | 1.24416i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.42516e6i | − | 1.82673i | ||||||
\(324\) | 1.07258e6 | + | 247277.i | 0.567630 | + | 0.130865i | ||||
\(325\) | − | 1.41377e6i | − | 0.742455i | ||||||
\(326\) | − | 846190.i | − | 0.440985i | ||||||
\(327\) | −407078. | − | 23084.3i | −0.210527 | − | 0.0119384i | ||||
\(328\) | 2.25120e6i | 1.15539i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −166545. | − | 9444.31i | −0.0841873 | − | 0.00477403i | ||||
\(331\) | −2.62569e6 | −1.31727 | −0.658633 | − | 0.752464i | \(-0.728865\pi\) | ||||
−0.658633 | + | 0.752464i | \(0.728865\pi\) | |||||||
\(332\) | −162398. | −0.0808605 | ||||||||
\(333\) | 1.89462e6 | + | 215571.i | 0.936295 | + | 0.106532i | ||||
\(334\) | − | 634912.i | − | 0.311421i | ||||||
\(335\) | −957847. | −0.466320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.01254e6 | −1.44497 | −0.722483 | − | 0.691388i | \(-0.756999\pi\) | ||||
−0.722483 | + | 0.691388i | \(0.756999\pi\) | |||||||
\(338\) | 87839.2i | 0.0418212i | ||||||||
\(339\) | −16851.9 | + | 297174.i | −0.00796436 | + | 0.140447i | ||||
\(340\) | 1.71451e6 | 0.804347 | ||||||||
\(341\) | 112137. | 0.0522232 | ||||||||
\(342\) | 2.44252e6 | + | 277911.i | 1.12921 | + | 0.128482i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 990285.i | 0.451195i | ||||||||
\(345\) | −30387.5 | + | 535866.i | −0.0137451 | + | 0.242386i | ||||
\(346\) | − | 1.79284e6i | − | 0.805101i | ||||||
\(347\) | 2.90956e6i | 1.29719i | 0.761134 | + | 0.648595i | \(0.224643\pi\) | ||||
−0.761134 | + | 0.648595i | \(0.775357\pi\) | |||||||
\(348\) | 87103.7 | − | 1.53602e6i | 0.0385557 | − | 0.679907i | ||||
\(349\) | − | 3.93286e6i | − | 1.72840i | −0.503147 | − | 0.864201i | \(-0.667824\pi\) | ||
0.503147 | − | 0.864201i | \(-0.332176\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −377520. | + | 2.20007e6i | −0.163558 | + | 0.953165i | ||||
\(352\) | 221793. | 0.0954096 | ||||||||
\(353\) | 1.93598e6 | 0.826922 | 0.413461 | − | 0.910522i | \(-0.364320\pi\) | ||||
0.413461 | + | 0.910522i | \(0.364320\pi\) | |||||||
\(354\) | 24989.1 | − | 440669.i | 0.0105985 | − | 0.186898i | ||||
\(355\) | − | 4.50686e6i | − | 1.89803i | ||||||
\(356\) | −337620. | −0.141190 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.34406e6 | −0.966631 | ||||||||
\(359\) | 1.39251e6i | 0.570247i | 0.958491 | + | 0.285123i | \(0.0920346\pi\) | ||||
−0.958491 | + | 0.285123i | \(0.907965\pi\) | |||||||
\(360\) | −377924. | + | 3.32152e6i | −0.153691 | + | 1.35077i | ||||
\(361\) | −5.18454e6 | −2.09383 | ||||||||
\(362\) | 171565. | 0.0688111 | ||||||||
\(363\) | −2.48236e6 | − | 140768.i | −0.988777 | − | 0.0560708i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.83821e6i | 1.50798i | ||||||||
\(366\) | −319557. | − | 18121.2i | −0.124694 | − | 0.00707105i | ||||
\(367\) | − | 985240.i | − | 0.381836i | −0.981606 | − | 0.190918i | \(-0.938854\pi\) | ||
0.981606 | − | 0.190918i | \(-0.0611465\pi\) | |||||||
\(368\) | 37072.5i | 0.0142703i | ||||||||
\(369\) | 2.93654e6 | + | 334120.i | 1.12272 | + | 0.127743i | ||||
\(370\) | 2.13174e6i | 0.809524i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 46833.1 | − | 825875.i | 0.0175467 | − | 0.309426i | ||||
\(373\) | 2.51585e6 | 0.936296 | 0.468148 | − | 0.883650i | \(-0.344921\pi\) | ||||
0.468148 | + | 0.883650i | \(0.344921\pi\) | |||||||
\(374\) | 178173. | 0.0658664 | ||||||||
\(375\) | 839667. | + | 47615.2i | 0.308339 | + | 0.0174851i | ||||
\(376\) | 1.25049e6i | 0.456154i | ||||||||
\(377\) | 3.12003e6 | 1.13059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −627888. | −0.224535 | −0.112268 | − | 0.993678i | \(-0.535811\pi\) | ||||
−0.112268 | + | 0.993678i | \(0.535811\pi\) | |||||||
\(380\) | − | 3.83464e6i | − | 1.36228i | ||||||
\(381\) | 656437. | + | 37224.8i | 0.231676 | + | 0.0131377i | ||||
\(382\) | 2.78295e6 | 0.975770 | ||||||||
\(383\) | 3.10523e6 | 1.08167 | 0.540837 | − | 0.841127i | \(-0.318107\pi\) | ||||
0.540837 | + | 0.841127i | \(0.318107\pi\) | |||||||
\(384\) | 84369.5 | − | 1.48781e6i | 0.0291983 | − | 0.514895i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.03335e6i | 0.694615i | ||||||||
\(387\) | 1.29176e6 | + | 146977.i | 0.438434 | + | 0.0498852i | ||||
\(388\) | 347481.i | 0.117180i | ||||||||
\(389\) | − | 669791.i | − | 0.224422i | −0.993684 | − | 0.112211i | \(-0.964207\pi\) | ||
0.993684 | − | 0.112211i | \(-0.0357932\pi\) | |||||||
\(390\) | −2.49148e6 | − | 141285.i | −0.829462 | − | 0.0470365i | ||||
\(391\) | − | 573281.i | − | 0.189638i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.40558e6 | + | 249828.i | 1.43887 | + | 0.0815943i | ||||
\(394\) | −1.99527e6 | −0.647533 | ||||||||
\(395\) | 5.00740e6 | 1.61480 | ||||||||
\(396\) | 20171.7 | − | 177286.i | 0.00646405 | − | 0.0568117i | ||||
\(397\) | 3.49472e6i | 1.11285i | 0.830898 | + | 0.556425i | \(0.187827\pi\) | ||||
−0.830898 | + | 0.556425i | \(0.812173\pi\) | |||||||
\(398\) | 771949. | 0.244276 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −191992. | −0.0599975 | ||||||||
\(401\) | 2.81146e6i | 0.873115i | 0.899676 | + | 0.436558i | \(0.143802\pi\) | ||||
−0.899676 | + | 0.436558i | \(0.856198\pi\) | |||||||
\(402\) | −41572.1 | + | 733101.i | −0.0128303 | + | 0.226255i | ||||
\(403\) | 1.67755e6 | 0.514532 | ||||||||
\(404\) | −3.18006e6 | −0.969353 | ||||||||
\(405\) | 4.27660e6 | + | 985950.i | 1.29557 | + | 0.298688i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 309109.i | − | 0.0924965i | ||||||
\(408\) | 202155. | − | 3.56489e6i | 0.0601222 | − | 1.06022i | ||||
\(409\) | − | 2.79035e6i | − | 0.824803i | −0.911002 | − | 0.412402i | \(-0.864690\pi\) | ||
0.911002 | − | 0.412402i | \(-0.135310\pi\) | |||||||
\(410\) | 3.30405e6i | 0.970704i | ||||||||
\(411\) | −232719. | + | 4.10387e6i | −0.0679560 | + | 1.19836i | ||||
\(412\) | 1.09771e6i | 0.318598i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 408813. | + | 46514.9i | 0.117226 | + | 0.0133380i | ||||
\(415\) | −647518. | −0.184557 | ||||||||
\(416\) | 3.31799e6 | 0.940030 | ||||||||
\(417\) | −321026. | + | 5.66111e6i | −0.0904066 | + | 1.59427i | ||||
\(418\) | − | 398499.i | − | 0.111554i | ||||||
\(419\) | −3.40729e6 | −0.948144 | −0.474072 | − | 0.880486i | \(-0.657216\pi\) | ||||
−0.474072 | + | 0.880486i | \(0.657216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.77099e6 | 1.03693 | 0.518465 | − | 0.855099i | \(-0.326504\pi\) | ||||
0.518465 | + | 0.855099i | \(0.326504\pi\) | |||||||
\(422\) | − | 2.45122e6i | − | 0.670041i | ||||||
\(423\) | 1.63118e6 | + | 185596.i | 0.443252 | + | 0.0504334i | ||||
\(424\) | −2.96368e6 | −0.800601 | ||||||||
\(425\) | 2.96892e6 | 0.797309 | ||||||||
\(426\) | −3.44938e6 | − | 195605.i | −0.920911 | − | 0.0522223i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.75103e6i | 0.725915i | ||||||||
\(429\) | 361273. | + | 20486.8i | 0.0947746 | + | 0.00537441i | ||||
\(430\) | 1.45342e6i | 0.379071i | ||||||||
\(431\) | 3.00701e6i | 0.779726i | 0.920873 | + | 0.389863i | \(0.127478\pi\) | ||||
−0.920873 | + | 0.389863i | \(0.872522\pi\) | |||||||
\(432\) | 298773. | + | 51267.8i | 0.0770249 | + | 0.0132171i | ||||
\(433\) | 1.50880e6i | 0.386734i | 0.981126 | + | 0.193367i | \(0.0619408\pi\) | ||||
−0.981126 | + | 0.193367i | \(0.938059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 347302. | − | 6.12447e6i | 0.0880002 | − | 1.55183i | ||||
\(436\) | 487565. | 0.122833 | ||||||||
\(437\) | −1.28219e6 | −0.321179 | ||||||||
\(438\) | 2.93763e6 | + | 166585.i | 0.731664 | + | 0.0414906i | ||||
\(439\) | 1.97163e6i | 0.488275i | 0.969741 | + | 0.244138i | \(0.0785049\pi\) | ||||
−0.969741 | + | 0.244138i | \(0.921495\pi\) | |||||||
\(440\) | 541907. | 0.133442 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.66544e6 | 0.648954 | ||||||||
\(443\) | 2.13681e6i | 0.517316i | 0.965969 | + | 0.258658i | \(0.0832803\pi\) | ||||
−0.965969 | + | 0.258658i | \(0.916720\pi\) | |||||||
\(444\) | −2.27655e6 | − | 129097.i | −0.548049 | − | 0.0310784i | ||||
\(445\) | −1.34617e6 | −0.322254 | ||||||||
\(446\) | −68455.3 | −0.0162956 | ||||||||
\(447\) | −340560. | + | 6.00558e6i | −0.0806167 | + | 1.42163i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.91347e6i | 1.38429i | 0.721759 | + | 0.692144i | \(0.243334\pi\) | ||||
−0.721759 | + | 0.692144i | \(0.756666\pi\) | |||||||
\(450\) | −240893. | + | 2.11717e6i | −0.0560780 | + | 0.492862i | ||||
\(451\) | − | 479098.i | − | 0.110913i | ||||||
\(452\) | − | 355931.i | − | 0.0819445i | ||||||
\(453\) | 4.30380e6 | + | 244057.i | 0.985387 | + | 0.0558786i | ||||
\(454\) | 1.63398e6i | 0.372054i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.97316e6 | − | 452136.i | −1.79564 | − | 0.101826i | ||||
\(457\) | −7.51891e6 | −1.68409 | −0.842044 | − | 0.539410i | \(-0.818647\pi\) | ||||
−0.842044 | + | 0.539410i | \(0.818647\pi\) | |||||||
\(458\) | −80412.5 | −0.0179126 | ||||||||
\(459\) | −4.62016e6 | − | 792795.i | −1.02359 | − | 0.175642i | ||||
\(460\) | − | 641816.i | − | 0.141422i | ||||||
\(461\) | 929187. | 0.203634 | 0.101817 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101817 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.21496e6 | 0.263396 | 0.131698 | − | 0.991290i | \(-0.457957\pi\) | ||||
0.131698 | + | 0.991290i | \(0.457957\pi\) | |||||||
\(464\) | − | 423705.i | − | 0.0913627i | ||||||
\(465\) | 186734. | − | 3.29295e6i | 0.0400489 | − | 0.706240i | ||||
\(466\) | −1.94847e6 | −0.415651 | ||||||||
\(467\) | −3.03117e6 | −0.643159 | −0.321580 | − | 0.946883i | \(-0.604214\pi\) | ||||
−0.321580 | + | 0.946883i | \(0.604214\pi\) | |||||||
\(468\) | 301765. | − | 2.65217e6i | 0.0636876 | − | 0.559741i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.83532e6i | 0.383238i | ||||||||
\(471\) | 334483. | − | 5.89841e6i | 0.0694739 | − | 1.22513i | ||||
\(472\) | 1.43386e6i | 0.296245i | ||||||||
\(473\) | − | 210751.i | − | 0.0433129i | ||||||
\(474\) | 217329. | − | 3.83248e6i | 0.0444296 | − | 0.783490i | ||||
\(475\) | − | 6.64023e6i | − | 1.35036i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −439865. | + | 3.86591e6i | −0.0885164 | + | 0.777958i | ||||
\(478\) | −983457. | −0.196873 | ||||||||
\(479\) | −81905.2 | −0.0163107 | −0.00815535 | − | 0.999967i | \(-0.502596\pi\) | ||||
−0.00815535 | + | 0.999967i | \(0.502596\pi\) | |||||||
\(480\) | 369337. | − | 6.51305e6i | 0.0731678 | − | 1.29027i | ||||
\(481\) | − | 4.62421e6i | − | 0.911329i | ||||||
\(482\) | 975255. | 0.191206 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.97317e6 | 0.576907 | ||||||||
\(485\) | 1.38549e6i | 0.267453i | ||||||||
\(486\) | 940222. | − | 3.23036e6i | 0.180567 | − | 0.620383i | ||||
\(487\) | 4.41516e6 | 0.843575 | 0.421787 | − | 0.906695i | \(-0.361403\pi\) | ||||
0.421787 | + | 0.906695i | \(0.361403\pi\) | |||||||
\(488\) | 1.03978e6 | 0.197648 | ||||||||
\(489\) | 3.60314e6 | + | 204324.i | 0.681410 | + | 0.0386409i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.60786e6i | − | 1.79855i | −0.437381 | − | 0.899276i | \(-0.644094\pi\) | ||
0.437381 | − | 0.899276i | \(-0.355906\pi\) | |||||||
\(492\) | −3.52849e6 | − | 200091.i | −0.657168 | − | 0.0372662i | ||||
\(493\) | 6.55209e6i | 1.21412i | ||||||||
\(494\) | − | 5.96147e6i | − | 1.09910i | ||||||
\(495\) | 80429.1 | − | 706880.i | 0.0147537 | − | 0.129668i | ||||
\(496\) | − | 227814.i | − | 0.0415792i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −28103.4 | + | 495587.i | −0.00507791 | + | 0.0895460i | ||||
\(499\) | 1.00695e7 | 1.81032 | 0.905160 | − | 0.425071i | \(-0.139751\pi\) | ||||
0.905160 | + | 0.425071i | \(0.139751\pi\) | |||||||
\(500\) | −1.00568e6 | −0.179902 | ||||||||
\(501\) | 2.70350e6 | + | 153308.i | 0.481208 | + | 0.0272880i | ||||
\(502\) | 3.46345e6i | 0.613408i | ||||||||
\(503\) | −2.68345e6 | −0.472904 | −0.236452 | − | 0.971643i | \(-0.575985\pi\) | ||||
−0.236452 | + | 0.971643i | \(0.575985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.26796e7 | −2.21247 | ||||||||
\(506\) | − | 66698.0i | − | 0.0115808i | ||||||
\(507\) | −374026. | − | 21210.0i | −0.0646222 | − | 0.00366455i | ||||
\(508\) | −786227. | −0.135173 | ||||||||
\(509\) | −7.51287e6 | −1.28532 | −0.642661 | − | 0.766151i | \(-0.722169\pi\) | ||||
−0.642661 | + | 0.766151i | \(0.722169\pi\) | |||||||
\(510\) | 296700. | − | 5.23213e6i | 0.0505117 | − | 0.890745i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 924585.i | − | 0.155873i | ||||||
\(513\) | −1.77315e6 | + | 1.03333e7i | −0.297475 | + | 1.73359i | ||||
\(514\) | − | 1.92371e6i | − | 0.321168i | ||||||
\(515\) | 4.37680e6i | 0.727174i | ||||||||
\(516\) | −1.55215e6 | − | 88018.4i | −0.256632 | − | 0.0145529i | ||||
\(517\) | − | 266128.i | − | 0.0437889i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.63403e6 | + | 432905.i | 1.24404 | + | 0.0705463i | ||||
\(520\) | 8.10683e6 | 1.31475 | ||||||||
\(521\) | −9.46018e6 | −1.52688 | −0.763440 | − | 0.645878i | \(-0.776491\pi\) | ||||
−0.763440 | + | 0.645878i | \(0.776491\pi\) | |||||||
\(522\) | −4.67237e6 | − | 531624.i | −0.750517 | − | 0.0853942i | ||||
\(523\) | 1.32587e6i | 0.211957i | 0.994368 | + | 0.105979i | \(0.0337975\pi\) | ||||
−0.994368 | + | 0.105979i | \(0.966202\pi\) | |||||||
\(524\) | −5.27664e6 | −0.839517 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.99051e6 | 0.786466 | ||||||||
\(527\) | 3.52287e6i | 0.552548i | ||||||||
\(528\) | 2782.14 | − | 49061.4i | 0.000434304 | − | 0.00765871i | ||||
\(529\) | 6.22174e6 | 0.966657 | ||||||||
\(530\) | −4.34974e6 | −0.672626 | ||||||||
\(531\) | 1.87037e6 | + | 212811.i | 0.287866 | + | 0.0327535i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 7.16721e6i | − | 1.09278i | ||||||
\(534\) | −58425.9 | + | 1.03031e6i | −0.00886650 | + | 0.156356i | ||||
\(535\) | 1.09690e7i | 1.65684i | ||||||||
\(536\) | − | 2.38538e6i | − | 0.358629i | ||||||
\(537\) | 566005. | − | 9.98116e6i | 0.0847002 | − | 1.49364i | ||||
\(538\) | − | 106833.i | − | 0.0159130i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.17249e6 | − | 887573.i | −0.763335 | − | 0.130984i | ||||
\(541\) | 6.92295e6 | 1.01695 | 0.508473 | − | 0.861078i | \(-0.330210\pi\) | ||||
0.508473 | + | 0.861078i | \(0.330210\pi\) | |||||||
\(542\) | 1.54873e6 | 0.226453 | ||||||||
\(543\) | −41426.8 | + | 730538.i | −0.00602951 | + | 0.106327i | ||||
\(544\) | 6.96780e6i | 1.00948i | ||||||||
\(545\) | 1.94403e6 | 0.280357 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.97756e6 | −1.42579 | −0.712896 | − | 0.701270i | \(-0.752617\pi\) | ||||
−0.712896 | + | 0.701270i | \(0.752617\pi\) | |||||||
\(548\) | − | 4.91528e6i | − | 0.699193i | ||||||
\(549\) | 154323. | − | 1.35632e6i | 0.0218524 | − | 0.192058i | ||||
\(550\) | 345418. | 0.0486898 | ||||||||
\(551\) | 1.46542e7 | 2.05629 | ||||||||
\(552\) | −1.33449e6 | − | 75675.5i | −0.186410 | − | 0.0105708i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 2.73025e6i | − | 0.377944i | ||||||
\(555\) | −9.07710e6 | − | 514738.i | −1.25088 | − | 0.0709338i | ||||
\(556\) | − | 6.78041e6i | − | 0.930185i | ||||||
\(557\) | − | 1.25386e7i | − | 1.71242i | −0.516628 | − | 0.856210i | \(-0.672813\pi\) | ||
0.516628 | − | 0.856210i | \(-0.327187\pi\) | |||||||
\(558\) | −2.51220e6 | − | 285839.i | −0.341561 | − | 0.0388629i | ||||
\(559\) | − | 3.15280e6i | − | 0.426743i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43022.4 | + | 758676.i | −0.00577149 | + | 0.101777i | ||||
\(562\) | 3.07726e6 | 0.410982 | ||||||||
\(563\) | −6.87659e6 | −0.914329 | −0.457164 | − | 0.889382i | \(-0.651135\pi\) | ||||
−0.457164 | + | 0.889382i | \(0.651135\pi\) | |||||||
\(564\) | −1.96000e6 | − | 111146.i | −0.259452 | − | 0.0147128i | ||||
\(565\) | − | 1.41918e6i | − | 0.187032i | ||||||
\(566\) | −5.09055e6 | −0.667918 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.12237e7 | 1.45970 | ||||||||
\(569\) | − | 2.64936e6i | − | 0.343053i | −0.985180 | − | 0.171526i | \(-0.945130\pi\) | ||
0.985180 | − | 0.171526i | \(-0.0548699\pi\) | |||||||
\(570\) | −1.17021e7 | − | 663592.i | −1.50860 | − | 0.0855488i | ||||
\(571\) | 1.09557e6 | 0.140621 | 0.0703105 | − | 0.997525i | \(-0.477601\pi\) | ||||
0.0703105 | + | 0.997525i | \(0.477601\pi\) | |||||||
\(572\) | −432703. | −0.0552968 | ||||||||
\(573\) | −671982. | + | 1.18500e7i | −0.0855009 | + | 1.50776i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.11140e6i | − | 0.140184i | ||||||
\(576\) | −5.58712e6 | − | 635704.i | −0.701668 | − | 0.0798360i | ||||
\(577\) | − | 2.90428e6i | − | 0.363161i | −0.983376 | − | 0.181581i | \(-0.941879\pi\) | ||
0.983376 | − | 0.181581i | \(-0.0581214\pi\) | |||||||
\(578\) | 407807.i | 0.0507733i | ||||||||
\(579\) | −8.65816e6 | − | 490980.i | −1.07332 | − | 0.0608650i | ||||
\(580\) | 7.33539e6i | 0.905426i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.06040e6 | + | 60132.3i | 0.129766 | + | 0.00735869i | ||||
\(583\) | 630726. | 0.0768545 | ||||||||
\(584\) | −9.55850e6 | −1.15973 | ||||||||
\(585\) | 1.20321e6 | − | 1.05748e7i | 0.145362 | − | 1.27756i | ||||
\(586\) | 1.96311e6i | 0.236157i | ||||||||
\(587\) | −2.80932e6 | −0.336516 | −0.168258 | − | 0.985743i | \(-0.553814\pi\) | ||||
−0.168258 | + | 0.985743i | \(0.553814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.87916e6 | 0.935819 | ||||||||
\(590\) | 2.10444e6i | 0.248890i | ||||||||
\(591\) | 481786. | − | 8.49602e6i | 0.0567395 | − | 1.00057i | ||||
\(592\) | −627976. | −0.0736442 | ||||||||
\(593\) | −471223. | −0.0550288 | −0.0275144 | − | 0.999621i | \(-0.508759\pi\) | ||||
−0.0275144 | + | 0.999621i | \(0.508759\pi\) | |||||||
\(594\) | −537529. | − | 92237.3i | −0.0625081 | − | 0.0107261i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.19300e6i | − | 0.829458i | ||||||
\(597\) | −186398. | + | 3.28701e6i | −0.0214045 | + | 0.377455i | ||||
\(598\) | − | 997791.i | − | 0.114100i | ||||||
\(599\) | − | 1.73472e6i | − | 0.197544i | −0.995110 | − | 0.0987719i | \(-0.968509\pi\) | ||
0.995110 | − | 0.0987719i | \(-0.0314914\pi\) | |||||||
\(600\) | 391911. | − | 6.91112e6i | 0.0444436 | − | 0.783737i | ||||
\(601\) | 3.42903e6i | 0.387244i | 0.981076 | + | 0.193622i | \(0.0620235\pi\) | ||||
−0.981076 | + | 0.193622i | \(0.937976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.11156e6 | − | 354034.i | −0.348486 | − | 0.0396508i | ||||
\(604\) | −5.15475e6 | −0.574930 | ||||||||
\(605\) | 1.18547e7 | 1.31674 | ||||||||
\(606\) | −550316. | + | 9.70451e6i | −0.0608738 | + | 1.07347i | ||||
\(607\) | 9.81466e6i | 1.08119i | 0.841282 | + | 0.540597i | \(0.181802\pi\) | ||||
−0.841282 | + | 0.540597i | \(0.818198\pi\) | |||||||
\(608\) | 1.55840e7 | 1.70970 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.52607e6 | 0.166054 | ||||||||
\(611\) | − | 3.98122e6i | − | 0.431433i | ||||||
\(612\) | 5.56958e6 | + | 633709.i | 0.601096 | + | 0.0683930i | ||||
\(613\) | −2.75780e6 | −0.296422 | −0.148211 | − | 0.988956i | \(-0.547352\pi\) | ||||
−0.148211 | + | 0.988956i | \(0.547352\pi\) | |||||||
\(614\) | −1.86918e6 | −0.200092 | ||||||||
\(615\) | −1.40689e7 | − | 797808.i | −1.49993 | − | 0.0850571i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.46419e6i | 0.577847i | 0.957352 | + | 0.288923i | \(0.0932973\pi\) | ||||
−0.957352 | + | 0.288923i | \(0.906703\pi\) | |||||||
\(618\) | 3.34984e6 | + | 189960.i | 0.352820 | + | 0.0200074i | ||||
\(619\) | 4.24390e6i | 0.445183i | 0.974912 | + | 0.222591i | \(0.0714516\pi\) | ||||
−0.974912 | + | 0.222591i | \(0.928548\pi\) | |||||||
\(620\) | 3.94402e6i | 0.412060i | ||||||||
\(621\) | −296777. | + | 1.72952e6i | −0.0308817 | + | 0.179969i | ||||
\(622\) | − | 8.81960e6i | − | 0.914057i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 41620.3 | − | 733950.i | 0.00427901 | − | 0.0754580i | ||||
\(625\) | −1.15071e7 | −1.17833 | ||||||||
\(626\) | 9.94768e6 | 1.01458 | ||||||||
\(627\) | 1.69684e6 | + | 96222.9i | 0.172374 | + | 0.00977484i | ||||
\(628\) | 7.06464e6i | 0.714810i | ||||||||
\(629\) | 9.71088e6 | 0.978660 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.97794e6 | 0.197761 | 0.0988804 | − | 0.995099i | \(-0.468474\pi\) | ||||
0.0988804 | + | 0.995099i | \(0.468474\pi\) | |||||||
\(632\) | 1.24702e7i | 1.24188i | ||||||||
\(633\) | 1.04375e7 | + | 591881.i | 1.03535 | + | 0.0587118i | ||||
\(634\) | 6.03376e6 | 0.596163 | ||||||||
\(635\) | −3.13486e6 | −0.308521 | ||||||||
\(636\) | 263417. | − | 4.64521e6i | 0.0258227 | − | 0.455368i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 762299.i | 0.0741436i | ||||||||
\(639\) | 1.66580e6 | − | 1.46405e7i | 0.161388 | − | 1.41842i | ||||
\(640\) | 7.10513e6i | 0.685681i | ||||||||
\(641\) | 6.87312e6i | 0.660707i | 0.943857 | + | 0.330353i | \(0.107168\pi\) | ||||
−0.943857 | + | 0.330353i | \(0.892832\pi\) | |||||||
\(642\) | 8.39524e6 | + | 476071.i | 0.803888 | + | 0.0455863i | ||||
\(643\) | − | 4.81869e6i | − | 0.459623i | −0.973235 | − | 0.229811i | \(-0.926189\pi\) | ||
0.973235 | − | 0.229811i | \(-0.0738109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.18878e6 | − | 350949.i | −0.585742 | − | 0.0332158i | ||||
\(646\) | 1.25191e7 | 1.18030 | ||||||||
\(647\) | −7.50407e6 | −0.704752 | −0.352376 | − | 0.935859i | \(-0.614626\pi\) | ||||
−0.352376 | + | 0.935859i | \(0.614626\pi\) | |||||||
\(648\) | −2.45536e6 | + | 1.06502e7i | −0.229709 | + | 0.996372i | ||||
\(649\) | − | 305151.i | − | 0.0284383i | ||||||
\(650\) | 5.16739e6 | 0.479720 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.31554e6 | −0.397573 | ||||||||
\(653\) | 1.40288e7i | 1.28747i | 0.765248 | + | 0.643735i | \(0.222616\pi\) | ||||
−0.765248 | + | 0.643735i | \(0.777384\pi\) | |||||||
\(654\) | 84374.1 | − | 1.48789e6i | 0.00771374 | − | 0.136027i | ||||
\(655\) | −2.10391e7 | −1.91613 | ||||||||
\(656\) | −973319. | −0.0883071 | ||||||||
\(657\) | −1.41866e6 | + | 1.24684e7i | −0.128223 | + | 1.12693i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.93455e6i | 0.442623i | 0.975203 | + | 0.221311i | \(0.0710337\pi\) | ||||
−0.975203 | + | 0.221311i | \(0.928966\pi\) | |||||||
\(660\) | −48165.7 | + | 849375.i | −0.00430406 | + | 0.0758996i | ||||
\(661\) | 1.83713e7i | 1.63544i | 0.575615 | + | 0.817721i | \(0.304763\pi\) | ||||
−0.575615 | + | 0.817721i | \(0.695237\pi\) | |||||||
\(662\) | − | 9.59702e6i | − | 0.851121i | ||||||
\(663\) | −643608. | + | 1.13496e7i | −0.0568640 | + | 1.00276i | ||||
\(664\) | − | 1.61255e6i | − | 0.141936i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −787923. | + | 6.92494e6i | −0.0688332 | + | 0.604965i | ||||
\(667\) | 2.45273e6 | 0.213469 | ||||||||
\(668\) | −3.23804e6 | −0.280763 | ||||||||
\(669\) | 16529.5 | − | 291488.i | 0.00142789 | − | 0.0251800i | ||||
\(670\) | − | 3.50097e6i | − | 0.301302i | ||||||
\(671\) | −221284. | −0.0189734 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.27763e6 | 0.449160 | 0.224580 | − | 0.974456i | \(-0.427899\pi\) | ||||
0.224580 | + | 0.974456i | \(0.427899\pi\) | |||||||
\(674\) | − | 1.10110e7i | − | 0.933632i | ||||||
\(675\) | −8.95691e6 | − | 1.53696e6i | −0.756657 | − | 0.129838i | ||||
\(676\) | 447978. | 0.0377042 | ||||||||
\(677\) | 1.37062e7 | 1.14933 | 0.574666 | − | 0.818388i | \(-0.305132\pi\) | ||||
0.574666 | + | 0.818388i | \(0.305132\pi\) | |||||||
\(678\) | −1.08619e6 | − | 61594.6i | −0.0907465 | − | 0.00514599i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.70244e7i | 1.41189i | ||||||||
\(681\) | −6.95759e6 | − | 394546.i | −0.574899 | − | 0.0326009i | ||||
\(682\) | 409866.i | 0.0337428i | ||||||||
\(683\) | 1.56582e7i | 1.28437i | 0.766549 | + | 0.642186i | \(0.221972\pi\) | ||||
−0.766549 | + | 0.642186i | \(0.778028\pi\) | |||||||
\(684\) | 1.41734e6 | − | 1.24568e7i | 0.115833 | − | 1.01804i | ||||
\(685\) | − | 1.95983e7i | − | 1.59585i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19416.7 | − | 342402.i | 0.00156958 | − | 0.0276786i | ||||
\(688\) | −428155. | −0.0344850 | ||||||||
\(689\) | 9.43554e6 | 0.757214 | ||||||||
\(690\) | −1.95861e6 | − | 111068.i | −0.156612 | − | 0.00888106i | ||||
\(691\) | − | 4.22151e6i | − | 0.336336i | −0.985758 | − | 0.168168i | \(-0.946215\pi\) | ||
0.985758 | − | 0.168168i | \(-0.0537850\pi\) | |||||||
\(692\) | −9.14342e6 | −0.725844 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.06346e7 | −0.838150 | ||||||||
\(695\) | − | 2.70350e7i | − | 2.12307i | ||||||
\(696\) | 1.52521e7 | + | 864904.i | 1.19345 | + | 0.0676776i | ||||
\(697\) | 1.50512e7 | 1.17352 | ||||||||
\(698\) | 1.43748e7 | 1.11677 | ||||||||
\(699\) | 470485. | − | 8.29673e6i | 0.0364211 | − | 0.642264i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.08992e7i | 1.60633i | 0.595758 | + | 0.803164i | \(0.296852\pi\) | ||||
−0.595758 | + | 0.803164i | \(0.703148\pi\) | |||||||
\(702\) | −8.04134e6 | − | 1.37985e6i | −0.615865 | − | 0.105679i | ||||
\(703\) | − | 2.17191e7i | − | 1.65750i | ||||||
\(704\) | 911541.i | 0.0693177i | ||||||||
\(705\) | −7.81495e6 | − | 443164.i | −0.592179 | − | 0.0335809i | ||||
\(706\) | 7.07610e6i | 0.534297i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.24740e6 | − | 127444.i | −0.168499 | − | 0.00955511i | ||||
\(709\) | 2.06100e6 | 0.153979 | 0.0769895 | − | 0.997032i | \(-0.475469\pi\) | ||||
0.0769895 | + | 0.997032i | \(0.475469\pi\) | |||||||
\(710\) | 1.64728e7 | 1.22637 | ||||||||
\(711\) | 1.62665e7 | + | 1.85081e6i | 1.20676 | + | 0.137305i | ||||
\(712\) | − | 3.35243e6i | − | 0.247833i | ||||||
\(713\) | 1.31876e6 | 0.0971499 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.72528e6 | −0.126210 | ||||||||
\(716\) | 1.19546e7i | 0.871472i | ||||||||
\(717\) | 237469. | − | 4.18763e6i | 0.0172508 | − | 0.304208i | ||||
\(718\) | −5.08970e6 | −0.368452 | ||||||||
\(719\) | −2.24934e7 | −1.62268 | −0.811339 | − | 0.584575i | \(-0.801261\pi\) | ||||
−0.811339 | + | 0.584575i | \(0.801261\pi\) | |||||||
\(720\) | −1.43607e6 | − | 163397.i | −0.103239 | − | 0.0117466i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.89497e7i | − | 1.35288i | ||||||
\(723\) | −235489. | + | 4.15271e6i | −0.0167542 | + | 0.295451i | ||||
\(724\) | − | 874979.i | − | 0.0620370i | ||||||
\(725\) | 1.27023e7i | 0.897504i | ||||||||
\(726\) | 514513. | − | 9.07314e6i | 0.0362289 | − | 0.638875i | ||||
\(727\) | 2.23831e7i | 1.57067i | 0.619073 | + | 0.785334i | \(0.287509\pi\) | ||||
−0.619073 | + | 0.785334i | \(0.712491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.35281e7 | + | 4.78355e6i | 0.942795 | + | 0.333374i | ||||
\(730\) | −1.40288e7 | −0.974350 | ||||||||
\(731\) | 6.62090e6 | 0.458272 | ||||||||
\(732\) | −92417.6 | + | 1.62973e6i | −0.00637495 | + | 0.112419i | ||||
\(733\) | − | 1.24379e7i | − | 0.855040i | −0.904006 | − | 0.427520i | \(-0.859387\pi\) | ||
0.904006 | − | 0.427520i | \(-0.140613\pi\) | |||||||
\(734\) | 3.60110e6 | 0.246715 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.60835e6 | 0.177489 | ||||||||
\(737\) | 507652.i | 0.0344269i | ||||||||
\(738\) | −1.22123e6 | + | 1.07332e7i | −0.0825382 | + | 0.725417i | ||||
\(739\) | −1.34548e7 | −0.906291 | −0.453145 | − | 0.891437i | \(-0.649698\pi\) | ||||
−0.453145 | + | 0.891437i | \(0.649698\pi\) | |||||||
\(740\) | 1.08718e7 | 0.729832 | ||||||||
\(741\) | 2.53844e7 | + | 1.43948e6i | 1.69832 | + | 0.0963073i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.80287e7i | − | 1.19810i | −0.800713 | − | 0.599049i | \(-0.795546\pi\) | ||
0.800713 | − | 0.599049i | \(-0.204454\pi\) | |||||||
\(744\) | 8.20060e6 | + | 465034.i | 0.543142 | + | 0.0308001i | ||||
\(745\) | − | 2.86801e7i | − | 1.89317i | ||||||
\(746\) | 9.19556e6i | 0.604966i | ||||||||
\(747\) | −2.10346e6 | − | 239332.i | −0.137922 | − | 0.0156928i | ||||
\(748\) | − | 908680.i | − | 0.0593823i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −174036. | + | 3.06902e6i | −0.0112976 | + | 0.199226i | ||||
\(751\) | 8.24075e6 | 0.533171 | 0.266586 | − | 0.963811i | \(-0.414105\pi\) | ||||
0.266586 | + | 0.963811i | \(0.414105\pi\) | |||||||
\(752\) | −540657. | −0.0348640 | ||||||||
\(753\) | −1.47476e7 | − | 836297.i | −0.947838 | − | 0.0537493i | ||||
\(754\) | 1.14039e7i | 0.730505i | ||||||||
\(755\) | −2.05531e7 | −1.31223 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.17983e7 | −0.748308 | −0.374154 | − | 0.927367i | \(-0.622067\pi\) | ||||
−0.374154 | + | 0.927367i | \(0.622067\pi\) | |||||||
\(758\) | − | 2.29496e6i | − | 0.145078i | ||||||
\(759\) | 284005. | + | 16105.2i | 0.0178946 | + | 0.00101475i | ||||
\(760\) | 3.80764e7 | 2.39123 | ||||||||
\(761\) | −1.22420e7 | −0.766286 | −0.383143 | − | 0.923689i | \(-0.625158\pi\) | ||||
−0.383143 | + | 0.923689i | \(0.625158\pi\) | |||||||
\(762\) | −136058. | + | 2.39931e6i | −0.00848862 | + | 0.149692i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.41930e7i | − | 0.879711i | ||||||
\(765\) | 2.22072e7 | + | 2.52674e6i | 1.37195 | + | 0.156101i | ||||
\(766\) | 1.13498e7i | 0.698899i | ||||||||
\(767\) | − | 4.56500e6i | − | 0.280190i | ||||||
\(768\) | 1.69627e7 | + | 961910.i | 1.03775 | + | 0.0588479i | ||||
\(769\) | 2.89879e6i | 0.176767i | 0.996087 | + | 0.0883834i | \(0.0281701\pi\) | ||||
−0.996087 | + | 0.0883834i | \(0.971830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.19131e6 | + | 464507.i | 0.496269 | + | 0.0281421i | ||||
\(772\) | 1.03700e7 | 0.626234 | ||||||||
\(773\) | 3.49988e6 | 0.210671 | 0.105336 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105336 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(774\) | −537207. | + | 4.72144e6i | −0.0322322 | + | 0.283284i | ||||
\(775\) | 6.82964e6i | 0.408455i | ||||||||
\(776\) | −3.45035e6 | −0.205688 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.44812e6 | 0.145005 | ||||||||
\(779\) | − | 3.36632e7i | − | 1.98752i | ||||||
\(780\) | −720551. | + | 1.27065e7i | −0.0424061 | + | 0.747807i | ||||
\(781\) | −2.38860e6 | −0.140125 | ||||||||
\(782\) | 2.09537e6 | 0.122530 | ||||||||
\(783\) | 3.39190e6 | − | 1.97669e7i | 0.197715 | − | 1.15222i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.81683e7i | 1.63150i | ||||||||
\(786\) | −913134. | + | 1.61026e7i | −0.0527203 | + | 0.929692i | ||||
\(787\) | 2.48618e7i | 1.43086i | 0.698685 | + | 0.715429i | \(0.253769\pi\) | ||||
−0.698685 | + | 0.715429i | \(0.746231\pi\) | |||||||
\(788\) | 1.01758e7i | 0.583788i | ||||||||
\(789\) | −1.20503e6 | + | 2.12499e7i | −0.0689134 | + | 1.21525i | ||||
\(790\) | 1.83023e7i | 1.04337i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.76038e6 | + | 200297.i | 0.0997226 | + | 0.0113465i | ||||
\(793\) | −3.31037e6 | −0.186936 | ||||||||
\(794\) | −1.27734e7 | −0.719043 | ||||||||
\(795\) | 1.05030e6 | − | 1.85215e7i | 0.0589382 | − | 1.03934i | ||||
\(796\) | − | 3.93692e6i | − | 0.220229i | ||||||
\(797\) | −4.51523e6 | −0.251787 | −0.125894 | − | 0.992044i | \(-0.540180\pi\) | ||||
−0.125894 | + | 0.992044i | \(0.540180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.36060e6 | 0.463309 | ||||||||
\(800\) | 1.35082e7i | 0.746230i | ||||||||
\(801\) | −4.37301e6 | − | 497563.i | −0.240824 | − | 0.0274010i | ||||
\(802\) | −1.02760e7 | −0.564143 | ||||||||
\(803\) | 2.03423e6 | 0.111330 | ||||||||
\(804\) | 3.73879e6 | + | 212017.i | 0.203982 | + | 0.0115673i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.13152e6i | 0.332453i | ||||||||
\(807\) | 454905. | + | 25796.4i | 0.0245888 | + | 0.00139436i | ||||
\(808\) | − | 3.15767e7i | − | 1.70152i | ||||||
\(809\) | − | 3.23092e7i | − | 1.73562i | −0.496894 | − | 0.867811i | \(-0.665526\pi\) | ||
0.496894 | − | 0.867811i | \(-0.334474\pi\) | |||||||
\(810\) | −3.60369e6 | + | 1.56312e7i | −0.192990 | + | 0.837103i | ||||
\(811\) | − | 1.64891e7i | − | 0.880329i | −0.897917 | − | 0.440164i | \(-0.854920\pi\) | ||
0.897917 | − | 0.440164i | \(-0.145080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −373962. | + | 6.59461e6i | −0.0198427 | + | 0.349915i | ||||
\(814\) | 1.12981e6 | 0.0597645 | ||||||||
\(815\) | −1.72070e7 | −0.907428 | ||||||||
\(816\) | 1.54130e6 | + | 87403.0i | 0.0810330 | + | 0.00459516i | ||||
\(817\) | − | 1.48081e7i | − | 0.776150i | ||||||
\(818\) | 1.01989e7 | 0.532928 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.68506e7 | 0.875145 | ||||||||
\(821\) | 1.74100e7i | 0.901449i | 0.892663 | + | 0.450724i | \(0.148834\pi\) | ||||
−0.892663 | + | 0.450724i | \(0.851166\pi\) | |||||||
\(822\) | −1.49998e7 | − | 850599.i | −0.774296 | − | 0.0439082i | ||||
\(823\) | 1.58051e7 | 0.813387 | 0.406693 | − | 0.913565i | \(-0.366682\pi\) | ||||
0.406693 | + | 0.913565i | \(0.366682\pi\) | |||||||
\(824\) | −1.08998e7 | −0.559241 | ||||||||
\(825\) | −83405.9 | + | 1.47081e6i | −0.00426640 | + | 0.0752355i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.08010e6i | − | 0.359978i | −0.983669 | − | 0.179989i | \(-0.942394\pi\) | ||
0.983669 | − | 0.179989i | \(-0.0576061\pi\) | |||||||
\(828\) | 237225. | − | 2.08494e6i | 0.0120250 | − | 0.105686i | ||||
\(829\) | 215839.i | 0.0109080i | 0.999985 | + | 0.00545399i | \(0.00173607\pi\) | ||||
−0.999985 | + | 0.00545399i | \(0.998264\pi\) | |||||||
\(830\) | − | 2.36671e6i | − | 0.119248i | ||||||
\(831\) | 1.16256e7 | + | 659256.i | 0.584000 | + | 0.0331170i | ||||
\(832\) | 1.36365e7i | 0.682958i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.06916e7 | − | 1.17336e6i | −1.03010 | − | 0.0584141i | ||||
\(835\) | −1.29108e7 | −0.640820 | ||||||||
\(836\) | −2.03233e6 | −0.100572 | ||||||||
\(837\) | 1.82373e6 | − | 1.06281e7i | 0.0899800 | − | 0.524375i | ||||
\(838\) | − | 1.24538e7i | − | 0.612621i | ||||||
\(839\) | −2.60061e7 | −1.27547 | −0.637735 | − | 0.770256i | \(-0.720129\pi\) | ||||
−0.637735 | + | 0.770256i | \(0.720129\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.52137e6 | −0.366697 | ||||||||
\(842\) | 1.37831e7i | 0.669989i | ||||||||
\(843\) | −743046. | + | 1.31032e7i | −0.0360120 | + | 0.635050i | ||||
\(844\) | −1.25012e7 | −0.604080 | ||||||||
\(845\) | 1.78619e6 | 0.0860568 | ||||||||
\(846\) | −678363. | + | 5.96204e6i | −0.0325864 | + | 0.286397i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1.28136e6i | − | 0.0611902i | ||||||
\(849\) | 1.22918e6 | − | 2.16759e7i | 0.0585257 | − | 1.03207i | ||||
\(850\) | 1.08516e7i | 0.515163i | ||||||||
\(851\) | − | 3.63520e6i | − | 0.172070i | ||||||
\(852\) | −997581. | + | 1.75918e7i | −0.0470814 | + | 0.830253i | ||||
\(853\) | − | 2.81393e7i | − | 1.32416i | −0.749433 | − | 0.662080i | \(-0.769674\pi\) | ||
0.749433 | − | 0.662080i | \(-0.230326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.65125e6 | − | 4.96680e7i | 0.264380 | − | 2.32360i | ||||
\(856\) | −2.73166e7 | −1.27421 | ||||||||
\(857\) | 1.72530e6 | 0.0802440 | 0.0401220 | − | 0.999195i | \(-0.487225\pi\) | ||||
0.0401220 | + | 0.999195i | \(0.487225\pi\) | |||||||
\(858\) | −74880.2 | + | 1.32047e6i | −0.00347255 | + | 0.0612364i | ||||
\(859\) | − | 3.93753e7i | − | 1.82071i | −0.413829 | − | 0.910354i | \(-0.635809\pi\) | ||
0.413829 | − | 0.910354i | \(-0.364191\pi\) | |||||||
\(860\) | 7.41242e6 | 0.341754 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.09908e7 | −0.503802 | ||||||||
\(863\) | 3.69584e7i | 1.68922i | 0.535382 | + | 0.844610i | \(0.320168\pi\) | ||||
−0.535382 | + | 0.844610i | \(0.679832\pi\) | |||||||
\(864\) | 3.60711e6 | − | 2.10211e7i | 0.164390 | − | 0.958012i | ||||
\(865\) | −3.64569e7 | −1.65668 | ||||||||
\(866\) | −5.51474e6 | −0.249879 | ||||||||
\(867\) | −1.73647e6 | − | 98470.6i | −0.0784549 | − | 0.00444896i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.65389e6i | − | 0.119215i | ||||||
\(870\) | 2.23852e7 | + | 1.26940e6i | 1.00268 | + | 0.0568593i | ||||
\(871\) | 7.59439e6i | 0.339193i | ||||||||
\(872\) | 4.84132e6i | 0.215612i | ||||||||
\(873\) | −512096. | + | 4.50074e6i | −0.0227413 | + | 0.199870i | ||||
\(874\) | − | 4.68645e6i | − | 0.207523i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 849578. | − | 1.49818e7i | 0.0374062 | − | 0.659636i | ||||
\(877\) | −3.48022e7 | −1.52795 | −0.763973 | − | 0.645248i | \(-0.776754\pi\) | ||||
−0.763973 | + | 0.645248i | \(0.776754\pi\) | |||||||
\(878\) | −7.20641e6 | −0.315488 | ||||||||
\(879\) | −8.35909e6 | − | 474021.i | −0.364911 | − | 0.0206931i | ||||
\(880\) | 234296.i | 0.0101990i | ||||||||
\(881\) | 2.98621e7 | 1.29623 | 0.648114 | − | 0.761544i | \(-0.275558\pi\) | ||||
0.648114 | + | 0.761544i | \(0.275558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.38129e7 | −1.45942 | −0.729710 | − | 0.683757i | \(-0.760345\pi\) | ||||
−0.729710 | + | 0.683757i | \(0.760345\pi\) | |||||||
\(884\) | − | 1.35937e7i | − | 0.585068i | ||||||
\(885\) | −8.96088e6 | − | 508147.i | −0.384585 | − | 0.0218088i | ||||
\(886\) | −7.81013e6 | −0.334252 | ||||||||
\(887\) | −3.00116e7 | −1.28080 | −0.640398 | − | 0.768044i | \(-0.721230\pi\) | ||||
−0.640398 | + | 0.768044i | \(0.721230\pi\) | |||||||
\(888\) | 1.28188e6 | − | 2.26052e7i | 0.0545525 | − | 0.962001i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 4.92030e6i | − | 0.208217i | ||||||
\(891\) | 522547. | − | 2.26657e6i | 0.0220511 | − | 0.0956477i | ||||
\(892\) | 349120.i | 0.0146914i | ||||||||
\(893\) | − | 1.86991e7i | − | 0.784680i | ||||||
\(894\) | −2.19507e7 | − | 1.24476e6i | −0.918553 | − | 0.0520886i | ||||
\(895\) | 4.76658e7i | 1.98906i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.24866e6 | + | 240930.i | 0.176308 | + | 0.00999793i | ||||
\(898\) | −2.16140e7 | −0.894426 | ||||||||
\(899\) | −1.50723e7 | −0.621984 | ||||||||
\(900\) | 1.07975e7 | + | 1.22855e6i | 0.444343 | + | 0.0505575i | ||||
\(901\) | 1.98147e7i | 0.813159i | ||||||||
\(902\) | 1.75112e6 | 0.0716639 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.53425e6 | 0.143839 | ||||||||
\(905\) | − | 3.48874e6i | − | 0.141595i | ||||||
\(906\) | −892039. | + | 1.57306e7i | −0.0361047 | + | 0.636685i | ||||
\(907\) | 1.06507e7 | 0.429892 | 0.214946 | − | 0.976626i | \(-0.431042\pi\) | ||||
0.214946 | + | 0.976626i | \(0.431042\pi\) | |||||||
\(908\) | 8.33324e6 | 0.335428 | ||||||||
\(909\) | −4.11896e7 | − | 4.68657e6i | −1.65340 | − | 0.188125i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.33185e7i | − | 0.531690i | −0.964016 | − | 0.265845i | \(-0.914349\pi\) | ||
0.964016 | − | 0.265845i | \(-0.0856509\pi\) | |||||||
\(912\) | 195483. | − | 3.44724e6i | 0.00778257 | − | 0.137241i | ||||
\(913\) | 343180.i | 0.0136253i | ||||||||
\(914\) | − | 2.74820e7i | − | 1.08813i | ||||||
\(915\) | −368489. | + | 6.49810e6i | −0.0145503 | + | 0.256586i | ||||
\(916\) | 410101.i | 0.0161493i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.89770e6 | − | 1.68869e7i | 0.113487 | − | 0.661367i | ||||
\(919\) | 1.18307e6 | 0.0462086 | 0.0231043 | − | 0.999733i | \(-0.492645\pi\) | ||||
0.0231043 | + | 0.999733i | \(0.492645\pi\) | |||||||
\(920\) | 6.37297e6 | 0.248240 | ||||||||
\(921\) | 451339. | − | 7.95910e6i | 0.0175329 | − | 0.309182i | ||||
\(922\) | 3.39622e6i | 0.131574i | ||||||||
\(923\) | −3.57331e7 | −1.38059 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.88261e7 | 0.723446 | ||||||||
\(926\) | 4.44073e6i | 0.170187i | ||||||||
\(927\) | −1.61773e6 | + | 1.42180e7i | −0.0618310 | + | 0.543424i | ||||
\(928\) | −2.98111e7 | −1.13634 | ||||||||
\(929\) | −9.48459e6 | −0.360561 | −0.180281 | − | 0.983615i | \(-0.557701\pi\) | ||||
−0.180281 | + | 0.983615i | \(0.557701\pi\) | |||||||
\(930\) | 1.20359e7 | + | 682522.i | 0.456321 | + | 0.0258767i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.93714e6i | 0.374733i | ||||||||
\(933\) | 3.75545e7 | + | 2.12961e6i | 1.41240 | + | 0.0800934i | ||||
\(934\) | − | 1.10791e7i | − | 0.415563i | ||||||
\(935\) | − | 3.62311e6i | − | 0.135535i | ||||||
\(936\) | 2.63350e7 | + | 2.99640e6i | 0.982524 | + | 0.111792i | ||||
\(937\) | − | 1.67626e7i | − | 0.623723i | −0.950128 | − | 0.311861i | \(-0.899048\pi\) | ||
0.950128 | − | 0.311861i | \(-0.100952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.40200e6 | + | 4.23580e7i | −0.0889016 | + | 1.56773i | ||||
\(940\) | 9.36011e6 | 0.345510 | ||||||||
\(941\) | −4.11603e7 | −1.51532 | −0.757660 | − | 0.652650i | \(-0.773657\pi\) | ||||
−0.757660 | + | 0.652650i | \(0.773657\pi\) | |||||||
\(942\) | 2.15590e7 | + | 1.22255e6i | 0.791591 | + | 0.0448889i | ||||
\(943\) | − | 5.63432e6i | − | 0.206330i | ||||||
\(944\) | −619935. | −0.0226421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 770305. | 0.0279856 | ||||||||
\(947\) | − | 2.24751e7i | − | 0.814381i | −0.913343 | − | 0.407190i | \(-0.866509\pi\) | ||
0.913343 | − | 0.407190i | \(-0.133491\pi\) | |||||||
\(948\) | −1.95455e7 | − | 1.10837e6i | −0.706361 | − | 0.0400558i | ||||
\(949\) | 3.04317e7 | 1.09688 | ||||||||
\(950\) | 2.42703e7 | 0.872503 | ||||||||
\(951\) | −1.45693e6 | + | 2.56922e7i | −0.0522383 | + | 0.921192i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.77762e6i | − | 0.134737i | −0.997728 | − | 0.0673683i | \(-0.978540\pi\) | ||
0.997728 | − | 0.0673683i | \(-0.0214603\pi\) | |||||||
\(954\) | −1.41301e7 | − | 1.60773e6i | −0.502660 | − | 0.0571928i | ||||
\(955\) | − | 5.65906e7i | − | 2.00787i | ||||||
\(956\) | 5.01561e6i | 0.177492i | ||||||||
\(957\) | −3.24593e6 | − | 184068.i | −0.114567 | − | 0.00649677i | ||||
\(958\) | − | 299367.i | − | 0.0105388i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.67677e7 | + | 1.51793e6i | 0.937419 | + | 0.0531585i | ||||
\(961\) | 2.05252e7 | 0.716935 | ||||||||
\(962\) | 1.69017e7 | 0.588834 | ||||||||
\(963\) | −4.05429e6 | + | 3.56326e7i | −0.140880 | + | 1.23817i | ||||
\(964\) | − | 4.97378e6i | − | 0.172383i | ||||||
\(965\) | 4.13476e7 | 1.42933 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.72823e7 | 1.28214 | 0.641072 | − | 0.767481i | \(-0.278490\pi\) | ||||
0.641072 | + | 0.767481i | \(0.278490\pi\) | |||||||
\(968\) | 2.95223e7i | 1.01266i | ||||||||
\(969\) | −3.02291e6 | + | 5.33073e7i | −0.103423 | + | 1.82380i | ||||
\(970\) | −5.06401e6 | −0.172809 | ||||||||
\(971\) | 3.79173e7 | 1.29059 | 0.645296 | − | 0.763932i | \(-0.276734\pi\) | ||||
0.645296 | + | 0.763932i | \(0.276734\pi\) | |||||||
\(972\) | −1.64747e7 | − | 4.79510e6i | −0.559311 | − | 0.162792i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.61376e7i | 0.545056i | ||||||||
\(975\) | −1.24774e6 | + | 2.20031e7i | −0.0420350 | + | 0.741264i | ||||
\(976\) | 449554.i | 0.0151063i | ||||||||
\(977\) | 2.56335e7i | 0.859154i | 0.903030 | + | 0.429577i | \(0.141337\pi\) | ||||
−0.903030 | + | 0.429577i | \(0.858663\pi\) | |||||||
\(978\) | −746814. | + | 1.31696e7i | −0.0249669 | + | 0.440278i | ||||
\(979\) | 713459.i | 0.0237910i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.31517e6 | + | 718542.i | 0.209514 | + | 0.0238385i | ||||
\(982\) | 3.51172e7 | 1.16209 | ||||||||
\(983\) | 3.49327e7 | 1.15305 | 0.576526 | − | 0.817079i | \(-0.304408\pi\) | ||||
0.576526 | + | 0.817079i | \(0.304408\pi\) | |||||||
\(984\) | 1.98682e6 | − | 3.50365e7i | 0.0654141 | − | 1.15354i | ||||
\(985\) | 4.05733e7i | 1.33245i | ||||||||
\(986\) | −2.39482e7 | −0.784477 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.04033e7 | −0.990897 | ||||||||
\(989\) | − | 2.47849e6i | − | 0.0805742i | ||||||
\(990\) | 2.58368e6 | + | 293972.i | 0.0837820 | + | 0.00953275i | ||||
\(991\) | 4.96071e7 | 1.60457 | 0.802286 | − | 0.596940i | \(-0.203617\pi\) | ||||
0.802286 | + | 0.596940i | \(0.203617\pi\) | |||||||
\(992\) | −1.60286e7 | −0.517149 | ||||||||
\(993\) | 4.08648e7 | + | 2.31733e6i | 1.31515 | + | 0.0745787i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.56974e7i | − | 0.502654i | ||||||
\(996\) | 2.52748e6 | + | 143326.i | 0.0807308 | + | 0.00457802i | ||||
\(997\) | − | 9.02979e6i | − | 0.287700i | −0.989600 | − | 0.143850i | \(-0.954052\pi\) | ||
0.989600 | − | 0.143850i | \(-0.0459483\pi\) | |||||||
\(998\) | 3.68044e7i | 1.16970i | ||||||||
\(999\) | −2.92966e7 | − | 5.02715e6i | −0.928761 | − | 0.159371i |
(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 | 147.6.c.c.146.11 | 16 | ||
3.2 | odd | 2 | inner | 147.6.c.c.146.6 | 16 | ||
7.4 | even | 3 | 21.6.g.c.5.3 | ✓ | 16 | ||
7.5 | odd | 6 | 21.6.g.c.17.6 | yes | 16 | ||
7.6 | odd | 2 | inner | 147.6.c.c.146.12 | 16 | ||
21.5 | even | 6 | 21.6.g.c.17.3 | yes | 16 | ||
21.11 | odd | 6 | 21.6.g.c.5.6 | yes | 16 | ||
21.20 | even | 2 | inner | 147.6.c.c.146.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.g.c.5.3 | ✓ | 16 | 7.4 | even | 3 | ||
21.6.g.c.5.6 | yes | 16 | 21.11 | odd | 6 | ||
21.6.g.c.17.3 | yes | 16 | 21.5 | even | 6 | ||
21.6.g.c.17.6 | yes | 16 | 7.5 | odd | 6 | ||
147.6.c.c.146.5 | 16 | 21.20 | even | 2 | inner | ||
147.6.c.c.146.6 | 16 | 3.2 | odd | 2 | inner | ||
147.6.c.c.146.11 | 16 | 1.1 | even | 1 | trivial | ||
147.6.c.c.146.12 | 16 | 7.6 | odd | 2 | inner |