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 | 146.12 | ||
Root | \(-3.16536 - 1.82752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.c.146.6 |
$q$-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 | \(-0.731474\pi\) | ||||
−0.664777 | + | 0.747042i | \(0.731474\pi\) | |||||||
\(6\) | −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 | \(0.160652\pi\) | ||||
−0.875318 | + | 0.483548i | \(0.839348\pi\) | |||||||
\(14\) | 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 | \(-0.673797\pi\) | ||||
−0.519274 | + | 0.854608i | \(0.673797\pi\) | |||||||
\(18\) | −100.409 | + | 882.482i | −0.0730453 | + | 0.641985i | ||||
\(19\) | 2767.79i | 1.75893i | 0.475964 | + | 0.879465i | \(0.342099\pi\) | ||||
−0.475964 | + | 0.879465i | \(0.657901\pi\) | |||||||
\(20\) | −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 | \(-0.914291\pi\) | ||
0.963968 | − | 0.266019i | \(-0.0857085\pi\) | |||||||
\(32\) | 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 | \(-0.691116\pi\) | ||||
−0.564980 | + | 0.825105i | \(0.691116\pi\) | |||||||
\(42\) | 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 | \(-0.571603\pi\) | ||||
−0.223056 | + | 0.974806i | \(0.571603\pi\) | |||||||
\(48\) | −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 | \(-0.546274\pi\) | ||||
−0.144862 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(60\) | −21562.4 | − | 1222.75i | −0.773250 | − | 0.0438489i | ||||
\(61\) | 5617.58i | 0.193297i | 0.995319 | + | 0.0966484i | \(0.0308122\pi\) | ||||
−0.995319 | + | 0.0966484i | \(0.969188\pi\) | |||||||
\(62\) | 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 | \(-0.808065\pi\) | ||
0.823648 | − | 0.567101i | \(-0.191935\pi\) | |||||||
\(74\) | 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 | \(-0.477890\pi\) | ||||
0.0694058 | + | 0.997589i | \(0.477890\pi\) | |||||||
\(84\) | 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 | \(-0.461329\pi\) | ||||
0.121189 | + | 0.992629i | \(0.461329\pi\) | |||||||
\(90\) | 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 | \(-0.967930\pi\) | ||
0.994929 | − | 0.100580i | \(-0.0320698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1082.14 | − | 9510.75i | 0.0110967 | − | 0.0975274i | ||||
\(100\) | 44721.0 | 0.447210 | ||||||||
\(101\) | 170598. | 1.66407 | 0.832034 | − | 0.554725i | \(-0.187176\pi\) | ||||
0.832034 | + | 0.554725i | \(0.187176\pi\) | |||||||
\(102\) | 3991.96 | − | 70395.9i | 0.0379914 | − | 0.669957i | ||||
\(103\) | − | 58887.8i | − | 0.546931i | −0.961882 | − | 0.273465i | \(-0.911830\pi\) | ||
0.961882 | − | 0.273465i | \(-0.0881699\pi\) | |||||||
\(104\) | −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 | \(-0.243871\pi\) | ||||
0.720590 | + | 0.693361i | \(0.243871\pi\) | |||||||
\(132\) | 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 | \(0.294328\pi\) | ||||
−0.602108 | + | 0.798415i | \(0.705672\pi\) | |||||||
\(140\) | 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 | \(-0.789741\pi\) | ||
0.789656 | − | 0.613550i | \(-0.210259\pi\) | |||||||
\(158\) | 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 | \(-0.422528\pi\) | ||||
0.240990 | + | 0.970527i | \(0.422528\pi\) | |||||||
\(168\) | 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 | \(-0.285905\pi\) | ||||
0.623021 | + | 0.782205i | \(0.285905\pi\) | |||||||
\(174\) | −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 | \(0.0169577\pi\) | ||||
−0.998581 | + | 0.0532489i | \(0.983042\pi\) | |||||||
\(182\) | 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 | \(0.0605346\pi\) | ||||
−0.981971 | + | 0.189031i | \(0.939465\pi\) | |||||||
\(200\) | 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 | \(-0.995986\pi\) | ||
0.999920 | − | 0.0126102i | \(-0.00401406\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 579247. | + | 65906.9i | 0.762794 | + | 0.0867910i | ||||
\(226\) | 69790.8 | 0.0908923 | ||||||||
\(227\) | −447047. | −0.575822 | −0.287911 | − | 0.957657i | \(-0.592961\pi\) | ||||
−0.287911 | + | 0.957657i | \(0.592961\pi\) | |||||||
\(228\) | −45534.2 | + | 802970.i | −0.0580097 | + | 1.02297i | ||||
\(229\) | − | 22000.4i | − | 0.0277231i | −0.999904 | − | 0.0138616i | \(-0.995588\pi\) | ||
0.999904 | − | 0.0138616i | \(-0.00441241\pi\) | |||||||
\(230\) | −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 | \(0.0472716\pi\) | ||||
−0.988993 | + | 0.147963i | \(0.952728\pi\) | |||||||
\(242\) | 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 | \(-0.657436\pi\) | ||||
−0.474681 | + | 0.880158i | \(0.657436\pi\) | |||||||
\(252\) | 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 | \(-0.420052\pi\) | ||||
0.248533 | + | 0.968623i | \(0.420052\pi\) | |||||||
\(258\) | −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 | \(-0.496080\pi\) | ||||
0.0123141 | + | 0.999924i | \(0.496080\pi\) | |||||||
\(270\) | 174035. | − | 1.01422e6i | 0.145287 | − | 0.846686i | ||||
\(271\) | 423724.i | 0.350477i | 0.984526 | + | 0.175239i | \(0.0560697\pi\) | ||||
−0.984526 | + | 0.175239i | \(0.943930\pi\) | |||||||
\(272\) | 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 | \(-0.827100\pi\) | ||
0.856068 | − | 0.516863i | \(-0.172900\pi\) | |||||||
\(284\) | − | 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 | \(-0.558499\pi\) | ||||
−0.182748 | + | 0.983160i | \(0.558499\pi\) | |||||||
\(294\) | 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 | \(-0.950514\pi\) | ||
0.987940 | − | 0.154840i | \(-0.0494861\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51972.1 | − | 916497.i | 0.0309652 | − | 0.546053i | ||||
\(310\) | −773342. | −0.457054 | ||||||||
\(311\) | 2.41299e6 | 1.41467 | 0.707335 | − | 0.706878i | \(-0.249897\pi\) | ||||
0.707335 | + | 0.706878i | \(0.249897\pi\) | |||||||
\(312\) | −1.69756e6 | − | 96264.1i | −0.987278 | − | 0.0559858i | ||||
\(313\) | 2.72163e6i | 1.57025i | 0.619339 | + | 0.785124i | \(0.287401\pi\) | ||||
−0.619339 | + | 0.785124i | \(0.712599\pi\) | |||||||
\(314\) | 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 | \(0.332176\pi\) | ||||
−0.503147 | + | 0.864201i | \(0.667824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −377520. | + | 2.20007e6i | −0.163558 | + | 0.953165i | ||||
\(352\) | 221793. | 0.0954096 | ||||||||
\(353\) | −1.93598e6 | −0.826922 | −0.413461 | − | 0.910522i | \(-0.635680\pi\) | ||||
−0.413461 | + | 0.910522i | \(0.635680\pi\) | |||||||
\(354\) | 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 | \(0.0611465\pi\) | ||||
−0.981606 | + | 0.190918i | \(0.938854\pi\) | |||||||
\(368\) | 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 | \(-0.681893\pi\) | ||||
−0.540837 | + | 0.841127i | \(0.681893\pi\) | |||||||
\(384\) | −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 | \(-0.812173\pi\) | ||
0.830898 | − | 0.556425i | \(-0.187827\pi\) | |||||||
\(398\) | −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 | \(0.135310\pi\) | ||||
−0.911002 | + | 0.412402i | \(0.864690\pi\) | |||||||
\(410\) | 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 | \(-0.342784\pi\) | ||||
0.474072 | + | 0.880486i | \(0.342784\pi\) | |||||||
\(420\) | 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 | \(-0.938059\pi\) | ||
0.981126 | − | 0.193367i | \(-0.0619408\pi\) | |||||||
\(434\) | 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 | \(-0.921495\pi\) | ||
0.969741 | − | 0.244138i | \(-0.0785049\pi\) | |||||||
\(440\) | −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 | \(-0.532466\pi\) | ||||
−0.101817 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(462\) | 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 | \(-0.395786\pi\) | ||||
0.321580 | + | 0.946883i | \(0.395786\pi\) | |||||||
\(468\) | −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 | \(-0.497404\pi\) | ||||
0.00815535 | + | 0.999967i | \(0.497404\pi\) | |||||||
\(480\) | 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 | \(-0.424015\pi\) | ||||
0.236452 | + | 0.971643i | \(0.424015\pi\) | |||||||
\(504\) | 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 | \(-0.277831\pi\) | ||||
0.642661 | + | 0.766151i | \(0.277831\pi\) | |||||||
\(510\) | −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 | \(-0.223509\pi\) | ||||
0.763440 | + | 0.645878i | \(0.223509\pi\) | |||||||
\(522\) | −4.67237e6 | − | 531624.i | −0.750517 | − | 0.0853942i | ||||
\(523\) | − | 1.32587e6i | − | 0.211957i | −0.994368 | − | 0.105979i | \(-0.966202\pi\) | ||
0.994368 | − | 0.105979i | \(-0.0337975\pi\) | |||||||
\(524\) | 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 | \(-0.348865\pi\) | ||||
0.457164 | + | 0.889382i | \(0.348865\pi\) | |||||||
\(564\) | −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 | \(0.0581214\pi\) | ||||
−0.983376 | + | 0.181581i | \(0.941879\pi\) | |||||||
\(578\) | 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 | \(-0.446186\pi\) | ||||
0.168258 | + | 0.985743i | \(0.446186\pi\) | |||||||
\(588\) | 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 | \(-0.491241\pi\) | ||||
0.0275144 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(594\) | 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 | \(-0.937976\pi\) | ||
0.981076 | − | 0.193622i | \(-0.0620235\pi\) | |||||||
\(602\) | 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 | \(-0.818198\pi\) | ||
0.841282 | − | 0.540597i | \(-0.181802\pi\) | |||||||
\(608\) | −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 | \(-0.928548\pi\) | ||
0.974912 | − | 0.222591i | \(-0.0714516\pi\) | |||||||
\(620\) | 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 | \(0.0738109\pi\) | ||||
−0.973235 | + | 0.229811i | \(0.926189\pi\) | |||||||
\(644\) | 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 | \(-0.385374\pi\) | ||||
0.352376 | + | 0.935859i | \(0.385374\pi\) | |||||||
\(648\) | −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 | \(-0.695237\pi\) | ||
0.575615 | − | 0.817721i | \(-0.304763\pi\) | |||||||
\(662\) | − | 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 | \(-0.694868\pi\) | ||||
−0.574666 | + | 0.818388i | \(0.694868\pi\) | |||||||
\(678\) | 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 | \(0.0537850\pi\) | ||||
−0.985758 | + | 0.168168i | \(0.946215\pi\) | |||||||
\(692\) | 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 | \(-0.198739\pi\) | ||||
0.811339 | + | 0.584575i | \(0.198739\pi\) | |||||||
\(720\) | 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 | \(-0.712491\pi\) | ||
0.619073 | − | 0.785334i | \(-0.287509\pi\) | |||||||
\(728\) | 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 | \(0.140613\pi\) | ||||
−0.904006 | + | 0.427520i | \(0.859387\pi\) | |||||||
\(734\) | −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 | \(-0.374842\pi\) | ||||
0.383143 | + | 0.923689i | \(0.374842\pi\) | |||||||
\(762\) | 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 | \(-0.971830\pi\) | ||
0.996087 | − | 0.0883834i | \(-0.0281701\pi\) | |||||||
\(770\) | 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 | \(-0.533592\pi\) | ||||
−0.105336 | + | 0.994437i | \(0.533592\pi\) | |||||||
\(774\) | −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 | \(-0.746231\pi\) | ||
0.698685 | − | 0.715429i | \(-0.253769\pi\) | |||||||
\(788\) | 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 | \(-0.459820\pi\) | ||||
0.125894 | + | 0.992044i | \(0.459820\pi\) | |||||||
\(798\) | 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 | \(0.145080\pi\) | ||||
−0.897917 | + | 0.440164i | \(0.854920\pi\) | |||||||
\(812\) | 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 | \(-0.998264\pi\) | ||
0.999985 | − | 0.00545399i | \(-0.00173607\pi\) | |||||||
\(830\) | − | 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 | \(-0.279871\pi\) | ||||
0.637735 | + | 0.770256i | \(0.279871\pi\) | |||||||
\(840\) | 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 | \(0.230326\pi\) | ||||
−0.749433 | + | 0.662080i | \(0.769674\pi\) | |||||||
\(854\) | 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 | \(-0.512775\pi\) | ||||
−0.0401220 | + | 0.999195i | \(0.512775\pi\) | |||||||
\(858\) | −74880.2 | + | 1.32047e6i | −0.00347255 | + | 0.0612364i | ||||
\(859\) | 3.93753e7i | 1.82071i | 0.413829 | + | 0.910354i | \(0.364191\pi\) | ||||
−0.413829 | + | 0.910354i | \(0.635809\pi\) | |||||||
\(860\) | −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 | \(-0.724442\pi\) | ||||
−0.648114 | + | 0.761544i | \(0.724442\pi\) | |||||||
\(882\) | 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 | \(-0.278770\pi\) | ||||
0.640398 | + | 0.768044i | \(0.278770\pi\) | |||||||
\(888\) | −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 | \(-0.442299\pi\) | ||||
0.180281 | + | 0.983615i | \(0.442299\pi\) | |||||||
\(930\) | −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 | \(0.100952\pi\) | ||||
−0.950128 | + | 0.311861i | \(0.899048\pi\) | |||||||
\(938\) | 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 | \(-0.226343\pi\) | ||||
0.757660 | + | 0.652650i | \(0.226343\pi\) | |||||||
\(942\) | 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 | \(-0.723266\pi\) | ||||
−0.645296 | + | 0.763932i | \(0.723266\pi\) | |||||||
\(972\) | 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 | \(-0.695592\pi\) | ||||
−0.576526 | + | 0.817079i | \(0.695592\pi\) | |||||||
\(984\) | 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 | \(0.0459483\pi\) | ||||
−0.989600 | + | 0.143850i | \(0.954052\pi\) | |||||||
\(998\) | 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.146.12 | 16 | ||
3.2 | odd | 2 | inner | 147.6.c.c.146.5 | 16 | ||
7.2 | even | 3 | 21.6.g.c.17.6 | yes | 16 | ||
7.3 | odd | 6 | 21.6.g.c.5.3 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 147.6.c.c.146.11 | 16 | ||
21.2 | odd | 6 | 21.6.g.c.17.3 | yes | 16 | ||
21.17 | even | 6 | 21.6.g.c.5.6 | yes | 16 | ||
21.20 | even | 2 | inner | 147.6.c.c.146.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.g.c.5.3 | ✓ | 16 | 7.3 | odd | 6 | ||
21.6.g.c.5.6 | yes | 16 | 21.17 | even | 6 | ||
21.6.g.c.17.3 | yes | 16 | 21.2 | odd | 6 | ||
21.6.g.c.17.6 | yes | 16 | 7.2 | even | 3 | ||
147.6.c.c.146.5 | 16 | 3.2 | odd | 2 | inner | ||
147.6.c.c.146.6 | 16 | 21.20 | even | 2 | inner | ||
147.6.c.c.146.11 | 16 | 7.6 | odd | 2 | inner | ||
147.6.c.c.146.12 | 16 | 1.1 | even | 1 | trivial |