Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, 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("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} + \cdots + 41943040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{50}\cdot 3^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Root | \(-1.31722 + 0.760496i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.c.107.5 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.10571 | + | 3.89142i | −0.725793 | + | 0.687913i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.71366 | − | 31.9541i | 0.0535519 | − | 0.998565i | ||||
\(5\) | 98.6190i | 1.76415i | 0.471108 | + | 0.882076i | \(0.343854\pi\) | ||||
−0.471108 | + | 0.882076i | \(0.656146\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 67.7266i | 0.522413i | 0.965283 | + | 0.261207i | \(0.0841204\pi\) | ||||
−0.965283 | + | 0.261207i | \(0.915880\pi\) | |||||||
\(8\) | 117.311 | + | 137.863i | 0.648058 | + | 0.761591i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −383.768 | − | 404.901i | −1.21358 | − | 1.28041i | ||||
\(11\) | 403.224 | 1.00476 | 0.502382 | − | 0.864646i | \(-0.332457\pi\) | ||||
0.502382 | + | 0.864646i | \(0.332457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 525.857 | 0.862998 | 0.431499 | − | 0.902114i | \(-0.357985\pi\) | ||||
0.431499 | + | 0.902114i | \(0.357985\pi\) | |||||||
\(14\) | −263.553 | − | 278.066i | −0.359375 | − | 0.379164i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1018.13 | − | 109.517i | −0.994264 | − | 0.106950i | ||||
\(17\) | 462.383i | 0.388043i | 0.980997 | + | 0.194021i | \(0.0621531\pi\) | ||||
−0.980997 | + | 0.194021i | \(0.937847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1958.86i | 1.24486i | 0.782676 | + | 0.622430i | \(0.213854\pi\) | ||||
−0.782676 | + | 0.622430i | \(0.786146\pi\) | |||||||
\(20\) | 3151.28 | + | 169.000i | 1.76162 | + | 0.0944737i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1655.52 | + | 1569.11i | −0.729252 | + | 0.691191i | ||||
\(23\) | −696.614 | −0.274582 | −0.137291 | − | 0.990531i | \(-0.543840\pi\) | ||||
−0.137291 | + | 0.990531i | \(0.543840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6600.72 | −2.11223 | ||||||||
\(26\) | −2159.02 | + | 2046.33i | −0.626358 | + | 0.593667i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2164.14 | + | 116.060i | 0.521664 | + | 0.0279762i | ||||
\(29\) | 4664.43i | 1.02992i | 0.857214 | + | 0.514960i | \(0.172193\pi\) | ||||
−0.857214 | + | 0.514960i | \(0.827807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8849.55i | − | 1.65393i | −0.562254 | − | 0.826965i | \(-0.690066\pi\) | ||
0.562254 | − | 0.826965i | \(-0.309934\pi\) | |||||||
\(32\) | 4606.31 | − | 3512.32i | 0.795203 | − | 0.606343i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1799.33 | − | 1898.41i | −0.266939 | − | 0.281639i | ||||
\(35\) | −6679.13 | −0.921616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14878.3 | −1.78669 | −0.893343 | − | 0.449375i | \(-0.851647\pi\) | ||||
−0.893343 | + | 0.449375i | \(0.851647\pi\) | |||||||
\(38\) | −7622.77 | − | 8042.52i | −0.856355 | − | 0.903511i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13595.9 | + | 11569.1i | −1.34356 | + | 1.14327i | ||||
\(41\) | − | 5373.92i | − | 0.499265i | −0.968341 | − | 0.249633i | \(-0.919690\pi\) | ||
0.968341 | − | 0.249633i | \(-0.0803098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1880.14i | 0.155067i | 0.996990 | + | 0.0775335i | \(0.0247045\pi\) | ||||
−0.996990 | + | 0.0775335i | \(0.975296\pi\) | |||||||
\(44\) | 690.989 | − | 12884.6i | 0.0538071 | − | 1.00332i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2860.09 | − | 2710.82i | 0.199290 | − | 0.188889i | ||||
\(47\) | −25776.3 | −1.70207 | −0.851034 | − | 0.525111i | \(-0.824024\pi\) | ||||
−0.851034 | + | 0.525111i | \(0.824024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12220.1 | 0.727084 | ||||||||
\(50\) | 27100.6 | − | 25686.2i | 1.53304 | − | 1.45303i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 901.142 | − | 16803.3i | 0.0462152 | − | 0.861759i | ||||
\(53\) | 31909.4i | 1.56037i | 0.625547 | + | 0.780186i | \(0.284876\pi\) | ||||
−0.625547 | + | 0.780186i | \(0.715124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39765.5i | 1.77256i | ||||||||
\(56\) | −9336.97 | + | 7945.08i | −0.397865 | + | 0.338554i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18151.3 | − | 19150.8i | −0.708495 | − | 0.747509i | ||||
\(59\) | 5011.77 | 0.187439 | 0.0937197 | − | 0.995599i | \(-0.470124\pi\) | ||||
0.0937197 | + | 0.995599i | \(0.470124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21451.5 | 0.738132 | 0.369066 | − | 0.929403i | \(-0.379678\pi\) | ||||
0.369066 | + | 0.929403i | \(0.379678\pi\) | |||||||
\(62\) | 34437.3 | + | 36333.7i | 1.13776 | + | 1.20041i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5244.24 | + | 32345.6i | −0.160042 | + | 0.987110i | ||||
\(65\) | 51859.6i | 1.52246i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 18429.1i | − | 0.501553i | −0.968045 | − | 0.250776i | \(-0.919314\pi\) | ||
0.968045 | − | 0.250776i | \(-0.0806859\pi\) | |||||||
\(68\) | 14775.0 | + | 792.368i | 0.387486 | + | 0.0207804i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 27422.6 | − | 25991.3i | 0.668903 | − | 0.633991i | ||||
\(71\) | −67791.2 | −1.59598 | −0.797990 | − | 0.602671i | \(-0.794103\pi\) | ||||
−0.797990 | + | 0.602671i | \(0.794103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52806.9 | 1.15980 | 0.579901 | − | 0.814687i | \(-0.303091\pi\) | ||||
0.579901 | + | 0.814687i | \(0.303091\pi\) | |||||||
\(74\) | 61085.9 | − | 57897.7i | 1.29677 | − | 1.22908i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62593.7 | + | 3356.83i | 1.24307 | + | 0.0666646i | ||||
\(77\) | 27309.0i | 0.524902i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 94935.6i | − | 1.71144i | −0.517440 | − | 0.855720i | \(-0.673115\pi\) | ||
0.517440 | − | 0.855720i | \(-0.326885\pi\) | |||||||
\(80\) | 10800.5 | − | 100407.i | 0.188676 | − | 1.75403i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20912.2 | + | 22063.7i | 0.343451 | + | 0.362363i | ||||
\(83\) | 82255.2 | 1.31059 | 0.655297 | − | 0.755371i | \(-0.272543\pi\) | ||||
0.655297 | + | 0.755371i | \(0.272543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −45599.8 | −0.684566 | ||||||||
\(86\) | −7316.42 | − | 7719.31i | −0.106673 | − | 0.112547i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 47302.6 | + | 55589.5i | 0.651146 | + | 0.765220i | ||||
\(89\) | 20696.7i | 0.276966i | 0.990365 | + | 0.138483i | \(0.0442226\pi\) | ||||
−0.990365 | + | 0.138483i | \(0.955777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35614.5i | 0.450841i | ||||||||
\(92\) | −1193.76 | + | 22259.7i | −0.0147044 | + | 0.274188i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 105830. | − | 100307.i | 1.23535 | − | 1.17087i | ||||
\(95\) | −193181. | −2.19612 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19858.5 | 0.214298 | 0.107149 | − | 0.994243i | \(-0.465828\pi\) | ||||
0.107149 | + | 0.994243i | \(0.465828\pi\) | |||||||
\(98\) | −50172.2 | + | 47553.6i | −0.527713 | + | 0.500171i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11311.4 | + | 210920.i | −0.113114 | + | 2.10920i | ||||
\(101\) | 42840.9i | 0.417884i | 0.977928 | + | 0.208942i | \(0.0670020\pi\) | ||||
−0.977928 | + | 0.208942i | \(0.932998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 92957.3i | 0.863357i | 0.902027 | + | 0.431679i | \(0.142079\pi\) | ||||
−0.902027 | + | 0.431679i | \(0.857921\pi\) | |||||||
\(104\) | 61688.9 | + | 72496.1i | 0.559273 | + | 0.657251i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −124173. | − | 131010.i | −1.07340 | − | 1.13251i | ||||
\(107\) | 48825.7 | 0.412277 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 104798. | 0.844863 | 0.422432 | − | 0.906395i | \(-0.361177\pi\) | ||||
0.422432 | + | 0.906395i | \(0.361177\pi\) | |||||||
\(110\) | −154745. | − | 163266.i | −1.21936 | − | 1.28651i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7417.21 | − | 68954.3i | 0.0558722 | − | 0.519417i | ||||
\(113\) | − | 57875.8i | − | 0.426384i | −0.977010 | − | 0.213192i | \(-0.931614\pi\) | ||
0.977010 | − | 0.213192i | \(-0.0683860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 68699.4i | − | 0.484405i | ||||||
\(116\) | 149048. | + | 7993.26i | 1.02844 | + | 0.0551542i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20576.8 | + | 19502.9i | −0.136042 | + | 0.128942i | ||||
\(119\) | −31315.6 | −0.202719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1538.38 | 0.00955215 | ||||||||
\(122\) | −88073.8 | + | 83477.0i | −0.535731 | + | 0.507770i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −282779. | − | 15165.1i | −1.65156 | − | 0.0885711i | ||||
\(125\) | − | 342772.i | − | 1.96214i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 204929.i | 1.12744i | 0.825965 | + | 0.563721i | \(0.190631\pi\) | ||||
−0.825965 | + | 0.563721i | \(0.809369\pi\) | |||||||
\(128\) | −104339. | − | 153209.i | −0.562889 | − | 0.826533i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −201807. | − | 212920.i | −1.04732 | − | 1.10499i | ||||
\(131\) | 106839. | 0.543938 | 0.271969 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271969 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −132667. | −0.650331 | ||||||||
\(134\) | 71715.3 | + | 75664.4i | 0.345025 | + | 0.364024i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −63745.3 | + | 54242.6i | −0.295530 | + | 0.251474i | ||||
\(137\) | 141277.i | 0.643089i | 0.946895 | + | 0.321544i | \(0.104202\pi\) | ||||
−0.946895 | + | 0.321544i | \(0.895798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 202692.i | − | 0.889816i | −0.895576 | − | 0.444908i | \(-0.853236\pi\) | ||
0.895576 | − | 0.444908i | \(-0.146764\pi\) | |||||||
\(140\) | −11445.8 | + | 213426.i | −0.0493543 | + | 0.920293i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 278331. | − | 263804.i | 1.15835 | − | 1.09789i | ||||
\(143\) | 212038. | 0.867110 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −460002. | −1.81693 | ||||||||
\(146\) | −216810. | + | 205494.i | −0.841776 | + | 0.797843i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25496.3 | + | 475422.i | −0.0956805 | + | 1.78412i | ||||
\(149\) | − | 27975.3i | − | 0.103231i | −0.998667 | − | 0.0516153i | \(-0.983563\pi\) | ||
0.998667 | − | 0.0516153i | \(-0.0164370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26904.4i | − | 0.0960242i | −0.998847 | − | 0.0480121i | \(-0.984711\pi\) | ||
0.998847 | − | 0.0480121i | \(-0.0152886\pi\) | |||||||
\(152\) | −270054. | + | 229796.i | −0.948074 | + | 0.806741i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −106271. | − | 112123.i | −0.361087 | − | 0.380971i | ||||
\(155\) | 872734. | 2.91778 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −169696. | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588585\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588585\pi\) | |||||||
\(158\) | 369435. | + | 389778.i | 1.17732 | + | 1.24215i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 346381. | + | 454270.i | 1.06968 | + | 1.40286i | ||||
\(161\) | − | 47179.3i | − | 0.143445i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 120390.i | 0.354912i | 0.984129 | + | 0.177456i | \(0.0567868\pi\) | ||||
−0.984129 | + | 0.177456i | \(0.943213\pi\) | |||||||
\(164\) | −171719. | − | 9209.08i | −0.498549 | − | 0.0267366i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −337716. | + | 320090.i | −0.951220 | + | 0.901574i | ||||
\(167\) | −252246. | −0.699896 | −0.349948 | − | 0.936769i | \(-0.613801\pi\) | ||||
−0.349948 | + | 0.936769i | \(0.613801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −94767.0 | −0.255235 | ||||||||
\(170\) | 187219. | − | 177448.i | 0.496853 | − | 0.470922i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60078.2 | + | 3221.93i | 0.154844 | + | 0.00830414i | ||||
\(173\) | 71644.3i | 0.181998i | 0.995851 | + | 0.0909989i | \(0.0290060\pi\) | ||||
−0.995851 | + | 0.0909989i | \(0.970994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 447044.i | − | 1.10346i | ||||||
\(176\) | −410533. | − | 44159.9i | −0.999002 | − | 0.107460i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −80539.7 | − | 84974.7i | −0.190528 | − | 0.201020i | ||||
\(179\) | −472794. | −1.10291 | −0.551455 | − | 0.834205i | \(-0.685927\pi\) | ||||
−0.551455 | + | 0.834205i | \(0.685927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 142613. | 0.323566 | 0.161783 | − | 0.986826i | \(-0.448275\pi\) | ||||
0.161783 | + | 0.986826i | \(0.448275\pi\) | |||||||
\(182\) | −138591. | − | 146223.i | −0.310139 | − | 0.327218i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −81720.5 | − | 96037.1i | −0.177945 | − | 0.209119i | ||||
\(185\) | − | 1.46728e6i | − | 3.15199i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 186444.i | 0.389892i | ||||||||
\(188\) | −44171.9 | + | 823659.i | −0.0911490 | + | 1.69962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 793146. | − | 751750.i | 1.59393 | − | 1.51074i | ||||
\(191\) | 762070. | 1.51151 | 0.755755 | − | 0.654854i | \(-0.227270\pi\) | ||||
0.755755 | + | 0.654854i | \(0.227270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 766564. | 1.48134 | 0.740670 | − | 0.671869i | \(-0.234508\pi\) | ||||
0.740670 | + | 0.671869i | \(0.234508\pi\) | |||||||
\(194\) | −81533.3 | + | 77277.9i | −0.155536 | + | 0.147418i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20941.1 | − | 390482.i | 0.0389368 | − | 0.726041i | ||||
\(197\) | − | 279378.i | − | 0.512893i | −0.966558 | − | 0.256446i | \(-0.917448\pi\) | ||
0.966558 | − | 0.256446i | \(-0.0825517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 50473.8i | − | 0.0903510i | −0.998979 | − | 0.0451755i | \(-0.985615\pi\) | ||
0.998979 | − | 0.0451755i | \(-0.0143847\pi\) | |||||||
\(200\) | −774337. | − | 909993.i | −1.36885 | − | 1.60865i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −166712. | − | 175892.i | −0.287468 | − | 0.303297i | ||||
\(203\) | −315906. | −0.538044 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 529970. | 0.880779 | ||||||||
\(206\) | −361736. | − | 381656.i | −0.593915 | − | 0.626619i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −535389. | − | 57590.3i | −0.858048 | − | 0.0922978i | ||||
\(209\) | 789861.i | 1.25079i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 762679.i | 1.17933i | 0.807647 | + | 0.589666i | \(0.200740\pi\) | ||||
−0.807647 | + | 0.589666i | \(0.799260\pi\) | |||||||
\(212\) | 1.01963e6 | + | 54681.8i | 1.55813 | + | 0.0835610i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −200464. | + | 190001.i | −0.299228 | + | 0.283611i | ||||
\(215\) | −185418. | −0.273562 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 599350. | 0.864034 | ||||||||
\(218\) | −430269. | + | 407813.i | −0.613196 | + | 0.581192i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.27067e6 | + | 68144.7i | 1.77001 | + | 0.0949239i | ||||
\(221\) | 243147.i | 0.334880i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12395e6i | 1.51351i | 0.653697 | + | 0.756756i | \(0.273217\pi\) | ||||
−0.653697 | + | 0.756756i | \(0.726783\pi\) | |||||||
\(224\) | 237877. | + | 311969.i | 0.316762 | + | 0.415424i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 225219. | + | 237621.i | 0.293315 | + | 0.309467i | ||||
\(227\) | −630849. | −0.812570 | −0.406285 | − | 0.913746i | \(-0.633176\pi\) | ||||
−0.406285 | + | 0.913746i | \(0.633176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 551782. | 0.695311 | 0.347655 | − | 0.937622i | \(-0.386978\pi\) | ||||
0.347655 | + | 0.937622i | \(0.386978\pi\) | |||||||
\(230\) | 267338. | + | 282060.i | 0.333228 | + | 0.351578i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −643051. | + | 547189.i | −0.784378 | + | 0.667448i | ||||
\(233\) | 506640.i | 0.611377i | 0.952132 | + | 0.305689i | \(0.0988867\pi\) | ||||
−0.952132 | + | 0.305689i | \(0.901113\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.54204e6i | − | 3.00270i | ||||||
\(236\) | 8588.47 | − | 160146.i | 0.0100377 | − | 0.187170i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 128573. | − | 121862.i | 0.147132 | − | 0.139453i | ||||
\(239\) | 843448. | 0.955132 | 0.477566 | − | 0.878596i | \(-0.341519\pi\) | ||||
0.477566 | + | 0.878596i | \(0.341519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −160398. | −0.177892 | −0.0889460 | − | 0.996036i | \(-0.528350\pi\) | ||||
−0.0889460 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(242\) | −6316.15 | + | 5986.50i | −0.00693289 | + | 0.00657105i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 36760.7 | − | 685464.i | 0.0395284 | − | 0.737073i | ||||
\(245\) | 1.20514e6i | 1.28269i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03008e6i | 1.07431i | ||||||||
\(248\) | 1.22002e6 | − | 1.03815e6i | 1.25962 | − | 1.07184i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.33387e6 | + | 1.40732e6i | 1.34978 | + | 1.42411i | ||||
\(251\) | −793734. | −0.795227 | −0.397613 | − | 0.917553i | \(-0.630161\pi\) | ||||
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −280891. | −0.275891 | ||||||||
\(254\) | −797465. | − | 841379.i | −0.775582 | − | 0.818290i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.02459e6 | + | 223004.i | 0.977123 | + | 0.212674i | ||||
\(257\) | − | 410870.i | − | 0.388036i | −0.980998 | − | 0.194018i | \(-0.937848\pi\) | ||
0.980998 | − | 0.194018i | \(-0.0621520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.00766e6i | − | 0.933389i | ||||||
\(260\) | 1.65712e6 | + | 88869.7i | 1.52027 | + | 0.0815306i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −438648. | + | 415754.i | −0.394787 | + | 0.374182i | ||||
\(263\) | 808668. | 0.720910 | 0.360455 | − | 0.932777i | \(-0.382621\pi\) | ||||
0.360455 | + | 0.932777i | \(0.382621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.14687e6 | −2.75273 | ||||||||
\(266\) | 544693. | − | 516264.i | 0.472006 | − | 0.447371i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −588884. | − | 31581.2i | −0.500833 | − | 0.0268591i | ||||
\(269\) | − | 693759.i | − | 0.584558i | −0.956333 | − | 0.292279i | \(-0.905586\pi\) | ||
0.956333 | − | 0.292279i | \(-0.0944136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 34964.4i | − | 0.0289203i | −0.999895 | − | 0.0144602i | \(-0.995397\pi\) | ||
0.999895 | − | 0.0144602i | \(-0.00460297\pi\) | |||||||
\(272\) | 50638.8 | − | 470764.i | 0.0415012 | − | 0.385817i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −549769. | − | 580043.i | −0.442389 | − | 0.466749i | ||||
\(275\) | −2.66157e6 | −2.12229 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −348977. | −0.273274 | −0.136637 | − | 0.990621i | \(-0.543629\pi\) | ||||
−0.136637 | + | 0.990621i | \(0.543629\pi\) | |||||||
\(278\) | 788761. | + | 832195.i | 0.612116 | + | 0.645822i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −783536. | − | 920803.i | −0.597261 | − | 0.701894i | ||||
\(281\) | 1.85655e6i | 1.40263i | 0.712854 | + | 0.701313i | \(0.247402\pi\) | ||||
−0.712854 | + | 0.701313i | \(0.752598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 70998.4i | − | 0.0526966i | −0.999653 | − | 0.0263483i | \(-0.991612\pi\) | ||
0.999653 | − | 0.0263483i | \(-0.00838789\pi\) | |||||||
\(284\) | −116171. | + | 2.16620e6i | −0.0854678 | + | 1.59369i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −870567. | + | 825130.i | −0.629342 | + | 0.596496i | ||||
\(287\) | 363957. | 0.260823 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.20606e6 | 0.849423 | ||||||||
\(290\) | 1.88863e6 | − | 1.79006e6i | 1.31872 | − | 1.24989i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 90493.2 | − | 1.68740e6i | 0.0621096 | − | 1.15814i | ||||
\(293\) | 2.36601e6i | 1.61008i | 0.593221 | + | 0.805039i | \(0.297856\pi\) | ||||
−0.593221 | + | 0.805039i | \(0.702144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 494256.i | 0.330671i | ||||||||
\(296\) | −1.74539e6 | − | 2.05116e6i | −1.15788 | − | 1.36072i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 108864. | + | 114858.i | 0.0710137 | + | 0.0749241i | ||||
\(299\) | −366320. | −0.236964 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −127336. | −0.0810090 | ||||||||
\(302\) | 104696. | + | 110461.i | 0.0660562 | + | 0.0696937i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 214529. | − | 1.99437e6i | 0.133138 | − | 1.23772i | ||||
\(305\) | 2.11553e6i | 1.30218i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19907.0i | 0.0120548i | 0.999982 | + | 0.00602741i | \(0.00191860\pi\) | ||||
−0.999982 | + | 0.00602741i | \(0.998081\pi\) | |||||||
\(308\) | 872633. | + | 46798.3i | 0.524149 | + | 0.0281095i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.58319e6 | + | 3.39618e6i | −2.11771 | + | 2.00718i | ||||
\(311\) | −2.54109e6 | −1.48977 | −0.744885 | − | 0.667193i | \(-0.767495\pi\) | ||||
−0.744885 | + | 0.667193i | \(0.767495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 964745. | 0.556611 | 0.278306 | − | 0.960493i | \(-0.410227\pi\) | ||||
0.278306 | + | 0.960493i | \(0.410227\pi\) | |||||||
\(314\) | 696721. | − | 660358.i | 0.398781 | − | 0.377968i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.03358e6 | − | 162688.i | −1.70898 | − | 0.0916509i | ||||
\(317\) | − | 1.96724e6i | − | 1.09954i | −0.835317 | − | 0.549769i | \(-0.814716\pi\) | ||
0.835317 | − | 0.549769i | \(-0.185284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.88081e6i | 1.03483i | ||||||||
\(320\) | −3.18990e6 | − | 517182.i | −1.74141 | − | 0.282337i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 183595. | + | 193704.i | 0.0986779 | + | 0.104112i | ||||
\(323\) | −905745. | −0.483059 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.47104e6 | −1.82285 | ||||||||
\(326\) | −468488. | − | 494286.i | −0.244149 | − | 0.257593i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 740863. | − | 630420.i | 0.380236 | − | 0.323553i | ||||
\(329\) | − | 1.74574e6i | − | 0.889182i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.34318e6i | 1.17554i | 0.809029 | + | 0.587769i | \(0.199993\pi\) | ||||
−0.809029 | + | 0.587769i | \(0.800007\pi\) | |||||||
\(332\) | 140958. | − | 2.62839e6i | 0.0701849 | − | 1.30871i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.03565e6 | − | 981597.i | 0.507980 | − | 0.481467i | ||||
\(335\) | 1.81746e6 | 0.884815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.39138e6 | 1.62668 | 0.813338 | − | 0.581791i | \(-0.197648\pi\) | ||||
0.813338 | + | 0.581791i | \(0.197648\pi\) | |||||||
\(338\) | 389086. | − | 368779.i | 0.185248 | − | 0.175580i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −78142.6 | + | 1.45710e6i | −0.0366598 | + | 0.683584i | ||||
\(341\) | − | 3.56835e6i | − | 1.66181i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.96591e6i | 0.902252i | ||||||||
\(344\) | −259201. | + | 220561.i | −0.118098 | + | 0.100492i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −278798. | − | 294150.i | −0.125199 | − | 0.132093i | ||||
\(347\) | 952624. | 0.424715 | 0.212358 | − | 0.977192i | \(-0.431886\pi\) | ||||
0.212358 | + | 0.977192i | \(0.431886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.24091e6 | −0.545350 | −0.272675 | − | 0.962106i | \(-0.587908\pi\) | ||||
−0.272675 | + | 0.962106i | \(0.587908\pi\) | |||||||
\(350\) | 1.73964e6 | + | 1.83543e6i | 0.759082 | + | 0.800881i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.85737e6 | − | 1.41625e6i | 0.798992 | − | 0.609233i | ||||
\(353\) | − | 322727.i | − | 0.137847i | −0.997622 | − | 0.0689236i | \(-0.978044\pi\) | ||
0.997622 | − | 0.0689236i | \(-0.0219565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.68550e6i | − | 2.81555i | ||||||
\(356\) | 661345. | + | 35467.2i | 0.276569 | + | 0.0148321i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.94116e6 | − | 1.83984e6i | 0.800484 | − | 0.758705i | ||||
\(359\) | −2.01638e6 | −0.825725 | −0.412862 | − | 0.910793i | \(-0.635471\pi\) | ||||
−0.412862 | + | 0.910793i | \(0.635471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36105e6 | −0.549675 | ||||||||
\(362\) | −585528. | + | 554968.i | −0.234842 | + | 0.222585i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.13803e6 | + | 61031.3i | 0.450194 | + | 0.0241434i | ||||
\(365\) | 5.20777e6i | 2.04607i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.80423e6i | − | 1.08680i | −0.839475 | − | 0.543398i | \(-0.817138\pi\) | ||
0.839475 | − | 0.543398i | \(-0.182862\pi\) | |||||||
\(368\) | 709241. | + | 76291.1i | 0.273007 | + | 0.0293666i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.70981e6 | + | 6.02423e6i | 2.16829 | + | 2.28769i | ||||
\(371\) | −2.16111e6 | −0.815159 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 793282. | 0.295227 | 0.147613 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147613 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(374\) | −725531. | − | 765483.i | −0.268211 | − | 0.282981i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.02385e6 | − | 3.55360e6i | −1.10304 | − | 1.29628i | ||||
\(377\) | 2.45282e6i | 0.888819i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 875935.i | 0.313237i | 0.987659 | + | 0.156619i | \(0.0500594\pi\) | ||||
−0.987659 | + | 0.156619i | \(0.949941\pi\) | |||||||
\(380\) | −331048. | + | 6.17293e6i | −0.117607 | + | 2.19297i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.12883e6 | + | 2.96554e6i | −1.09704 | + | 1.03979i | ||||
\(383\) | 5.68554e6 | 1.98050 | 0.990250 | − | 0.139305i | \(-0.0444867\pi\) | ||||
0.990250 | + | 0.139305i | \(0.0444867\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.69318e6 | −0.926007 | ||||||||
\(386\) | −3.14729e6 | + | 2.98302e6i | −1.07515 | + | 1.01903i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 34030.8 | − | 634561.i | 0.0114761 | − | 0.213990i | ||||
\(389\) | − | 2.56686e6i | − | 0.860059i | −0.902815 | − | 0.430029i | \(-0.858503\pi\) | ||
0.902815 | − | 0.430029i | \(-0.141497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 322102.i | − | 0.106550i | ||||||
\(392\) | 1.43355e6 | + | 1.68470e6i | 0.471193 | + | 0.553741i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.08718e6 | + | 1.14704e6i | 0.352825 | + | 0.372254i | ||||
\(395\) | 9.36246e6 | 3.01924 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.13240e6 | 1.95278 | 0.976392 | − | 0.216004i | \(-0.0693025\pi\) | ||||
0.976392 | + | 0.216004i | \(0.0693025\pi\) | |||||||
\(398\) | 196415. | + | 207231.i | 0.0621536 | + | 0.0655762i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.72037e6 | + | 722891.i | 2.10011 | + | 0.225903i | ||||
\(401\) | − | 5.63051e6i | − | 1.74858i | −0.485401 | − | 0.874292i | \(-0.661326\pi\) | ||
0.485401 | − | 0.874292i | \(-0.338674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.65360e6i | − | 1.42734i | ||||||
\(404\) | 1.36894e6 | + | 73414.9i | 0.417284 | + | 0.0223785i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.29702e6 | − | 1.22932e6i | 0.390509 | − | 0.370127i | ||||
\(407\) | −5.99928e6 | −1.79520 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.86885e6 | 0.848008 | 0.424004 | − | 0.905660i | \(-0.360624\pi\) | ||||
0.424004 | + | 0.905660i | \(0.360624\pi\) | |||||||
\(410\) | −2.17590e6 | + | 2.06234e6i | −0.639264 | + | 0.605899i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.97037e6 | + | 159297.i | 0.862118 | + | 0.0462345i | ||||
\(413\) | 339430.i | 0.0979208i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.11193e6i | 2.31209i | ||||||||
\(416\) | 2.42226e6 | − | 1.84698e6i | 0.686258 | − | 0.523273i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.07368e6 | − | 3.24294e6i | −0.860435 | − | 0.907816i | ||||
\(419\) | 5.25000e6 | 1.46091 | 0.730456 | − | 0.682960i | \(-0.239308\pi\) | ||||
0.730456 | + | 0.682960i | \(0.239308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.82887e6 | 1.05285 | 0.526423 | − | 0.850223i | \(-0.323533\pi\) | ||||
0.526423 | + | 0.850223i | \(0.323533\pi\) | |||||||
\(422\) | −2.96791e6 | − | 3.13134e6i | −0.811277 | − | 0.855951i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.39911e6 | + | 3.74332e6i | −1.18837 | + | 1.01121i | ||||
\(425\) | − | 3.05206e6i | − | 0.819635i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.45284e6i | 0.385610i | ||||||||
\(428\) | 83670.8 | − | 1.56018e6i | 0.0220782 | − | 0.411685i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 761271. | − | 721539.i | 0.198549 | − | 0.188186i | ||||
\(431\) | −763450. | −0.197965 | −0.0989823 | − | 0.995089i | \(-0.531559\pi\) | ||||
−0.0989823 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −126626. | −0.0324566 | −0.0162283 | − | 0.999868i | \(-0.505166\pi\) | ||||
−0.0162283 | + | 0.999868i | \(0.505166\pi\) | |||||||
\(434\) | −2.46075e6 | + | 2.33232e6i | −0.627110 | + | 0.594380i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 179588. | − | 3.34872e6i | 0.0452441 | − | 0.843651i | ||||
\(437\) | − | 1.36457e6i | − | 0.341816i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.36482e6i | 1.57625i | 0.615516 | + | 0.788124i | \(0.288948\pi\) | ||||
−0.615516 | + | 0.788124i | \(0.711052\pi\) | |||||||
\(440\) | −5.48218e6 | + | 4.66494e6i | −1.34996 | + | 1.14872i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −946189. | − | 998292.i | −0.230368 | − | 0.243054i | ||||
\(443\) | 5.00344e6 | 1.21132 | 0.605661 | − | 0.795723i | \(-0.292909\pi\) | ||||
0.605661 | + | 0.795723i | \(0.292909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.04109e6 | −0.488610 | ||||||||
\(446\) | −4.37378e6 | − | 4.61462e6i | −1.04116 | − | 1.09850i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.19066e6 | − | 355175.i | −0.515679 | − | 0.0836078i | ||||
\(449\) | − | 2.33255e6i | − | 0.546028i | −0.962010 | − | 0.273014i | \(-0.911979\pi\) | ||
0.962010 | − | 0.273014i | \(-0.0880205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.16689e6i | − | 0.501644i | ||||||
\(452\) | −1.84937e6 | − | 99179.6i | −0.425772 | − | 0.0228337i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.59008e6 | − | 2.45490e6i | 0.589758 | − | 0.558978i | ||||
\(455\) | −3.51227e6 | −0.795352 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.50222e6 | 0.784429 | 0.392214 | − | 0.919874i | \(-0.371709\pi\) | ||||
0.392214 | + | 0.919874i | \(0.371709\pi\) | |||||||
\(458\) | −2.26546e6 | + | 2.14722e6i | −0.504652 | + | 0.478313i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.19523e6 | − | 117728.i | −0.483710 | − | 0.0259408i | ||||
\(461\) | − | 4.55640e6i | − | 0.998550i | −0.866444 | − | 0.499275i | \(-0.833600\pi\) | ||
0.866444 | − | 0.499275i | \(-0.166400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.28727e6i | 0.712660i | 0.934360 | + | 0.356330i | \(0.115972\pi\) | ||||
−0.934360 | + | 0.356330i | \(0.884028\pi\) | |||||||
\(464\) | 510834. | − | 4.74898e6i | 0.110150 | − | 1.02401i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.97155e6 | − | 2.08011e6i | −0.420574 | − | 0.443734i | ||||
\(467\) | −4.27154e6 | −0.906343 | −0.453171 | − | 0.891423i | \(-0.649707\pi\) | ||||
−0.453171 | + | 0.891423i | \(0.649707\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.24814e6 | 0.262018 | ||||||||
\(470\) | 9.89215e6 | + | 1.04369e7i | 2.06560 | + | 2.17934i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 587935. | + | 690935.i | 0.121472 | + | 0.142752i | ||||
\(473\) | 758117.i | 0.155806i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.29299e7i | − | 2.62943i | ||||||
\(476\) | −53664.4 | + | 1.00066e6i | −0.0108560 | + | 0.202428i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.46295e6 | + | 3.28221e6i | −0.693228 | + | 0.657048i | ||||
\(479\) | −2.08964e6 | −0.416134 | −0.208067 | − | 0.978115i | \(-0.566717\pi\) | ||||
−0.208067 | + | 0.978115i | \(0.566717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.82385e6 | −1.54191 | ||||||||
\(482\) | 658547. | − | 624176.i | 0.129113 | − | 0.122374i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2636.27 | − | 49157.6i | 0.000511536 | − | 0.00953845i | ||||
\(485\) | 1.95843e6i | 0.378054i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.02802e6i | − | 0.387480i | −0.981053 | − | 0.193740i | \(-0.937938\pi\) | ||
0.981053 | − | 0.193740i | \(-0.0620618\pi\) | |||||||
\(488\) | 2.51650e6 | + | 2.95737e6i | 0.478352 | + | 0.562155i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.68969e6 | − | 4.94793e6i | −0.882377 | − | 0.930966i | ||||
\(491\) | 7.39231e6 | 1.38381 | 0.691905 | − | 0.721988i | \(-0.256772\pi\) | ||||
0.691905 | + | 0.721988i | \(0.256772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.15675e6 | −0.399653 | ||||||||
\(494\) | −4.00849e6 | − | 4.22922e6i | −0.739032 | − | 0.779728i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −969176. | + | 9.00996e6i | −0.176888 | + | 1.64444i | ||||
\(497\) | − | 4.59127e6i | − | 0.833761i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 579614.i | 0.104205i | 0.998642 | + | 0.0521024i | \(0.0165922\pi\) | ||||
−0.998642 | + | 0.0521024i | \(0.983408\pi\) | |||||||
\(500\) | −1.09530e7 | − | 587395.i | −1.95933 | − | 0.105076i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.25884e6 | − | 3.08876e6i | 0.577170 | − | 0.547047i | ||||
\(503\) | 1.39449e6 | 0.245750 | 0.122875 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122875 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.22493e6 | −0.737210 | ||||||||
\(506\) | 1.15326e6 | − | 1.09307e6i | 0.200240 | − | 0.189789i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.54832e6 | + | 351179.i | 1.12582 | + | 0.0603767i | ||||
\(509\) | 2.31186e6i | 0.395519i | 0.980251 | + | 0.197759i | \(0.0633665\pi\) | ||||
−0.980251 | + | 0.197759i | \(0.936634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.57643e6i | 0.605896i | ||||||||
\(512\) | −5.07446e6 | + | 3.07151e6i | −0.855490 | + | 0.517819i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.59887e6 | + | 1.68691e6i | 0.266935 | + | 0.281634i | ||||
\(515\) | −9.16736e6 | −1.52309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.03936e7 | −1.71018 | ||||||||
\(518\) | 3.92121e6 | + | 4.13714e6i | 0.642090 | + | 0.677447i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.14950e6 | + | 6.08370e6i | −1.15949 | + | 0.986641i | ||||
\(521\) | 2.65886e6i | 0.429143i | 0.976708 | + | 0.214571i | \(0.0688355\pi\) | ||||
−0.976708 | + | 0.214571i | \(0.931165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.85731e6i | − | 0.616638i | −0.951283 | − | 0.308319i | \(-0.900234\pi\) | ||
0.951283 | − | 0.308319i | \(-0.0997664\pi\) | |||||||
\(524\) | 183085. | − | 3.41393e6i | 0.0291290 | − | 0.543158i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.32016e6 | + | 3.14687e6i | −0.523232 | + | 0.495923i | ||||
\(527\) | 4.09188e6 | 0.641795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.95107e6 | −0.924605 | ||||||||
\(530\) | 1.29201e7 | − | 1.22458e7i | 1.99792 | − | 1.89364i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −227347. | + | 4.23926e6i | −0.0348265 | + | 0.649398i | ||||
\(533\) | − | 2.82591e6i | − | 0.430865i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.81515e6i | 0.727319i | ||||||||
\(536\) | 2.54068e6 | − | 2.16193e6i | 0.381978 | − | 0.325035i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.69971e6 | + | 2.84837e6i | 0.402125 | + | 0.424268i | ||||
\(539\) | 4.92744e6 | 0.730549 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.07371e6 | −1.03909 | −0.519546 | − | 0.854442i | \(-0.673899\pi\) | ||||
−0.519546 | + | 0.854442i | \(0.673899\pi\) | |||||||
\(542\) | 136061. | + | 143554.i | 0.0198947 | + | 0.0209902i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.62403e6 | + | 2.12988e6i | 0.235287 | + | 0.308573i | ||||
\(545\) | 1.03351e7i | 1.49047i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47235e6i | 0.353298i | 0.984274 | + | 0.176649i | \(0.0565258\pi\) | ||||
−0.984274 | + | 0.176649i | \(0.943474\pi\) | |||||||
\(548\) | 4.51438e6 | + | 242101.i | 0.642166 | + | 0.0344386i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.09276e7 | − | 1.03573e7i | 1.54035 | − | 1.45995i | ||||
\(551\) | −9.13699e6 | −1.28211 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.42967e6 | 0.894079 | ||||||||
\(554\) | 1.43280e6 | − | 1.35802e6i | 0.198340 | − | 0.187988i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.47684e6 | − | 347346.i | −0.888539 | − | 0.0476514i | ||||
\(557\) | 5.84907e6i | 0.798820i | 0.916772 | + | 0.399410i | \(0.130785\pi\) | ||||
−0.916772 | + | 0.399410i | \(0.869215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 988686.i | 0.133822i | ||||||||
\(560\) | 6.80020e6 | + | 731478.i | 0.916330 | + | 0.0985670i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.22464e6 | − | 7.62247e6i | −0.964884 | − | 1.01802i | ||||
\(563\) | 310076. | 0.0412284 | 0.0206142 | − | 0.999788i | \(-0.493438\pi\) | ||||
0.0206142 | + | 0.999788i | \(0.493438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.70766e6 | 0.752206 | ||||||||
\(566\) | 276285. | + | 291498.i | 0.0362506 | + | 0.0382468i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.95265e6 | − | 9.34587e6i | −1.03429 | − | 1.21548i | ||||
\(569\) | 4.87432e6i | 0.631151i | 0.948900 | + | 0.315575i | \(0.102198\pi\) | ||||
−0.948900 | + | 0.315575i | \(0.897802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.04563e7i | − | 1.34211i | −0.741409 | − | 0.671054i | \(-0.765842\pi\) | ||
0.741409 | − | 0.671054i | \(-0.234158\pi\) | |||||||
\(572\) | 363362. | − | 6.77549e6i | 0.0464354 | − | 0.865865i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.49430e6 | + | 1.41631e6i | −0.189303 | + | 0.179423i | ||||
\(575\) | 4.59815e6 | 0.579981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.62808e6 | 1.20393 | 0.601963 | − | 0.798524i | \(-0.294385\pi\) | ||||
0.601963 | + | 0.798524i | \(0.294385\pi\) | |||||||
\(578\) | −4.95173e6 | + | 4.69329e6i | −0.616506 | + | 0.584329i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −788287. | + | 1.46989e7i | −0.0973004 | + | 1.81433i | ||||
\(581\) | 5.57086e6i | 0.684672i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.28666e7i | 1.56781i | ||||||||
\(584\) | 6.19484e6 | + | 7.28011e6i | 0.751619 | + | 0.883295i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.20714e6 | − | 9.71414e6i | −1.10759 | − | 1.16858i | ||||
\(587\) | −584872. | −0.0700593 | −0.0350296 | − | 0.999386i | \(-0.511153\pi\) | ||||
−0.0350296 | + | 0.999386i | \(0.511153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.73351e7 | 2.05891 | ||||||||
\(590\) | −1.92336e6 | − | 2.02927e6i | −0.227473 | − | 0.239999i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.51480e7 | + | 1.62942e6i | 1.77644 | + | 0.191086i | ||||
\(593\) | 6.31733e6i | 0.737728i | 0.929483 | + | 0.368864i | \(0.120253\pi\) | ||||
−0.929483 | + | 0.368864i | \(0.879747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.08832e6i | − | 0.357626i | ||||||
\(596\) | −893924. | − | 47940.2i | −0.103083 | − | 0.00552820i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.50400e6 | − | 1.42550e6i | 0.171987 | − | 0.163010i | ||||
\(599\) | −9.48535e6 | −1.08016 | −0.540078 | − | 0.841615i | \(-0.681605\pi\) | ||||
−0.540078 | + | 0.841615i | \(0.681605\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.10737e7 | −1.25057 | −0.625284 | − | 0.780397i | \(-0.715017\pi\) | ||||
−0.625284 | + | 0.780397i | \(0.715017\pi\) | |||||||
\(602\) | 522802. | − | 495516.i | 0.0587958 | − | 0.0557271i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −859705. | − | 46105.0i | −0.0958864 | − | 0.00514228i | ||||
\(605\) | 151714.i | 0.0168514i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.47030e6i | 0.822936i | 0.911424 | + | 0.411468i | \(0.134984\pi\) | ||||
−0.911424 | + | 0.411468i | \(0.865016\pi\) | |||||||
\(608\) | 6.88015e6 | + | 9.02313e6i | 0.754812 | + | 0.989916i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.23242e6 | − | 8.68575e6i | −0.895784 | − | 0.945111i | ||||
\(611\) | −1.35547e7 | −1.46888 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 527227. | 0.0566692 | 0.0283346 | − | 0.999598i | \(-0.490980\pi\) | ||||
0.0283346 | + | 0.999598i | \(0.490980\pi\) | |||||||
\(614\) | −77466.7 | − | 81732.5i | −0.00829266 | − | 0.00874931i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.76489e6 | + | 3.20364e6i | −0.399761 | + | 0.340167i | ||||
\(617\) | 9.29470e6i | 0.982929i | 0.870897 | + | 0.491465i | \(0.163538\pi\) | ||||
−0.870897 | + | 0.491465i | \(0.836462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.38720e6i | − | 0.355316i | −0.984092 | − | 0.177658i | \(-0.943148\pi\) | ||
0.984092 | − | 0.177658i | \(-0.0568520\pi\) | |||||||
\(620\) | 1.49557e6 | − | 2.78874e7i | 0.156253 | − | 2.91359i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.04330e7 | − | 9.88845e6i | 1.08126 | − | 1.02483i | ||||
\(623\) | −1.40172e6 | −0.144691 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.31766e7 | 1.34928 | ||||||||
\(626\) | −3.96096e6 | + | 3.75423e6i | −0.403985 | + | 0.382900i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −290801. | + | 5.42247e6i | −0.0294237 | + | 0.548653i | ||||
\(629\) | − | 6.87946e6i | − | 0.693311i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.26464e6i | 0.126443i | 0.998000 | + | 0.0632216i | \(0.0201375\pi\) | ||||
−0.998000 | + | 0.0632216i | \(0.979863\pi\) | |||||||
\(632\) | 1.30881e7 | − | 1.11370e7i | 1.30342 | − | 1.10911i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.65538e6 | + | 8.07693e6i | 0.756386 | + | 0.798037i | ||||
\(635\) | −2.02099e7 | −1.98898 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.42603e6 | 0.627472 | ||||||||
\(638\) | −7.31902e6 | − | 7.72205e6i | −0.711871 | − | 0.751071i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.51093e7 | − | 1.02898e7i | 1.45813 | − | 0.993021i | ||||
\(641\) | − | 1.06313e7i | − | 1.02197i | −0.859588 | − | 0.510987i | \(-0.829280\pi\) | ||
0.859588 | − | 0.510987i | \(-0.170720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.49352e7i | − | 1.42457i | −0.701893 | − | 0.712283i | \(-0.747661\pi\) | ||
0.701893 | − | 0.712283i | \(-0.252339\pi\) | |||||||
\(644\) | −1.50757e6 | − | 80849.3i | −0.143240 | − | 0.00768178i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.71873e6 | − | 3.52464e6i | 0.350601 | − | 0.332302i | ||||
\(647\) | 4.38900e6 | 0.412197 | 0.206099 | − | 0.978531i | \(-0.433923\pi\) | ||||
0.206099 | + | 0.978531i | \(0.433923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.02086e6 | 0.188332 | ||||||||
\(650\) | 1.42511e7 | − | 1.35073e7i | 1.32301 | − | 1.25396i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.84695e6 | + | 206308.i | 0.354403 | + | 0.0190062i | ||||
\(653\) | − | 7.73540e6i | − | 0.709905i | −0.934884 | − | 0.354952i | \(-0.884497\pi\) | ||
0.934884 | − | 0.354952i | \(-0.115503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.05363e7i | 0.959589i | ||||||||
\(656\) | −588535. | + | 5.47133e6i | −0.0533965 | + | 0.496402i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.79343e6 | + | 7.16751e6i | 0.611680 | + | 0.645363i | ||||
\(659\) | −1.45433e6 | −0.130452 | −0.0652258 | − | 0.997871i | \(-0.520777\pi\) | ||||
−0.0652258 | + | 0.997871i | \(0.520777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.13463e7 | −1.01007 | −0.505034 | − | 0.863100i | \(-0.668520\pi\) | ||||
−0.505034 | + | 0.863100i | \(0.668520\pi\) | |||||||
\(662\) | −9.11832e6 | − | 9.62043e6i | −0.808667 | − | 0.853197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.64944e6 | + | 1.13399e7i | 0.849341 | + | 0.998137i | ||||
\(665\) | − | 1.30835e7i | − | 1.14728i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.24931e6i | − | 0.282798i | ||||||
\(668\) | −432265. | + | 8.06030e6i | −0.0374808 | + | 0.698892i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.46195e6 | + | 7.07250e6i | −0.642193 | + | 0.608675i | ||||
\(671\) | 8.64977e6 | 0.741649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.63098e6 | 0.223913 | 0.111957 | − | 0.993713i | \(-0.464288\pi\) | ||||
0.111957 | + | 0.993713i | \(0.464288\pi\) | |||||||
\(674\) | −1.39240e7 | + | 1.31973e7i | −1.18063 | + | 1.11901i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −162399. | + | 3.02819e6i | −0.0136683 | + | 0.254869i | ||||
\(677\) | 2.00948e7i | 1.68504i | 0.538661 | + | 0.842522i | \(0.318930\pi\) | ||||
−0.538661 | + | 0.842522i | \(0.681070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.34495e6i | 0.111952i | ||||||||
\(680\) | −5.34935e6 | − | 6.28651e6i | −0.443638 | − | 0.521359i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.38859e7 | + | 1.46506e7i | 1.14318 | + | 1.20613i | ||||
\(683\) | −9.59174e6 | −0.786766 | −0.393383 | − | 0.919375i | \(-0.628695\pi\) | ||||
−0.393383 | + | 0.919375i | \(0.628695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39326e7 | −1.13451 | ||||||||
\(686\) | −7.65018e6 | − | 8.07144e6i | −0.620670 | − | 0.654848i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 205907. | − | 1.91422e6i | 0.0165844 | − | 0.154178i | ||||
\(689\) | 1.67798e7i | 1.34660i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 537489.i | 0.0428227i | 0.999771 | + | 0.0214114i | \(0.00681597\pi\) | ||||
−0.999771 | + | 0.0214114i | \(0.993184\pi\) | |||||||
\(692\) | 2.28933e6 | + | 122774.i | 0.181737 | + | 0.00974634i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.91120e6 | + | 3.70706e6i | −0.308256 | + | 0.292167i | ||||
\(695\) | 1.99893e7 | 1.56977 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.48481e6 | 0.193736 | ||||||||
\(698\) | 5.09480e6 | − | 4.82889e6i | 0.395811 | − | 0.375153i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.42849e7 | − | 766082.i | −1.10187 | − | 0.0590922i | ||||
\(701\) | 1.34046e7i | 1.03029i | 0.857104 | + | 0.515143i | \(0.172261\pi\) | ||||
−0.857104 | + | 0.515143i | \(0.827739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.91445e7i | − | 2.22417i | ||||||
\(704\) | −2.11460e6 | + | 1.30425e7i | −0.160804 | + | 0.991814i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.25587e6 | + | 1.32502e6i | 0.0948269 | + | 0.100049i | ||||
\(707\) | −2.90147e6 | −0.218308 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75400e7 | 1.31043 | 0.655217 | − | 0.755441i | \(-0.272577\pi\) | ||||
0.655217 | + | 0.755441i | \(0.272577\pi\) | |||||||
\(710\) | 2.60161e7 | + | 2.74487e7i | 1.93685 | + | 2.04351i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.85331e6 | + | 2.42795e6i | −0.210935 | + | 0.179490i | ||||
\(713\) | 6.16472e6i | 0.454140i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.09110e7i | 1.52971i | ||||||||
\(716\) | −810210. | + | 1.51077e7i | −0.0590629 | + | 1.10133i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.27865e6 | − | 7.84657e6i | 0.599305 | − | 0.568026i | ||||
\(719\) | 9.18586e6 | 0.662670 | 0.331335 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.29568e6 | −0.451029 | ||||||||
\(722\) | 5.58808e6 | − | 5.29642e6i | 0.398951 | − | 0.378129i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 244391. | − | 4.55707e6i | 0.0173276 | − | 0.323102i | ||||
\(725\) | − | 3.07886e7i | − | 2.17543i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.08483e6i | − | 0.286641i | −0.989676 | − | 0.143321i | \(-0.954222\pi\) | ||
0.989676 | − | 0.143321i | \(-0.0457780\pi\) | |||||||
\(728\) | −4.90991e6 | + | 4.17798e6i | −0.343357 | + | 0.292171i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.02656e7 | − | 2.13816e7i | −1.40751 | − | 1.48502i | ||||
\(731\) | −869345. | −0.0601726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.95584e7 | −1.34454 | −0.672269 | − | 0.740307i | \(-0.734680\pi\) | ||||
−0.672269 | + | 0.740307i | \(0.734680\pi\) | |||||||
\(734\) | 1.09124e7 | + | 1.15133e7i | 0.747621 | + | 0.788789i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.20882e6 | + | 2.44673e6i | −0.218349 | + | 0.166491i | ||||
\(737\) | − | 7.43104e6i | − | 0.503942i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.93503e7i | − | 1.30340i | −0.758477 | − | 0.651699i | \(-0.774056\pi\) | ||
0.758477 | − | 0.651699i | \(-0.225944\pi\) | |||||||
\(740\) | −4.68856e7 | − | 2.51443e6i | −3.14746 | − | 0.168795i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.87289e6 | − | 8.40980e6i | 0.591637 | − | 0.560758i | ||||
\(743\) | 1.80071e7 | 1.19666 | 0.598330 | − | 0.801249i | \(-0.295831\pi\) | ||||
0.598330 | + | 0.801249i | \(0.295831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.75890e6 | 0.182115 | ||||||||
\(746\) | −3.25699e6 | + | 3.08700e6i | −0.214274 | + | 0.203090i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.95764e6 | + | 319502.i | 0.389332 | + | 0.0208794i | ||||
\(749\) | 3.30680e6i | 0.215379i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64226e7i | 1.06253i | 0.847205 | + | 0.531267i | \(0.178284\pi\) | ||||
−0.847205 | + | 0.531267i | \(0.821716\pi\) | |||||||
\(752\) | 2.62436e7 | + | 2.82295e6i | 1.69230 | + | 0.182036i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.54498e6 | − | 1.00706e7i | −0.611430 | − | 0.645099i | ||||
\(755\) | 2.65328e6 | 0.169401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.25867e7 | 1.43256 | 0.716279 | − | 0.697814i | \(-0.245844\pi\) | ||||
0.716279 | + | 0.697814i | \(0.245844\pi\) | |||||||
\(758\) | −3.40863e6 | − | 3.59633e6i | −0.215480 | − | 0.227346i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.26623e7 | − | 2.66325e7i | −1.42321 | − | 1.67255i | ||||
\(761\) | − | 2.24952e7i | − | 1.40808i | −0.710159 | − | 0.704041i | \(-0.751377\pi\) | ||
0.710159 | − | 0.704041i | \(-0.248623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.09760e6i | 0.441368i | ||||||||
\(764\) | 1.30593e6 | − | 2.43512e7i | 0.0809443 | − | 1.50934i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.33432e7 | + | 2.21248e7i | −1.43743 | + | 1.36241i | ||||
\(767\) | 2.63547e6 | 0.161760 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.86118e7 | −1.13494 | −0.567468 | − | 0.823395i | \(-0.692077\pi\) | ||||
−0.567468 | + | 0.823395i | \(0.692077\pi\) | |||||||
\(770\) | 1.10574e7 | − | 1.04803e7i | 0.672090 | − | 0.637012i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.31363e6 | − | 2.44948e7i | 0.0793287 | − | 1.47921i | ||||
\(773\) | 1.63770e7i | 0.985793i | 0.870088 | + | 0.492896i | \(0.164062\pi\) | ||||
−0.870088 | + | 0.492896i | \(0.835938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.84134e7i | 3.49348i | ||||||||
\(776\) | 2.32962e6 | + | 2.73775e6i | 0.138877 | + | 0.163207i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.98873e6 | + | 1.05388e7i | 0.591645 | + | 0.624225i | ||||
\(779\) | 1.05268e7 | 0.621515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.73350e7 | −1.60358 | ||||||||
\(782\) | 1.25344e6 | + | 1.32246e6i | 0.0732969 | + | 0.0773330i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.24416e7 | − | 1.33831e6i | −0.722914 | − | 0.0777618i | ||||
\(785\) | − | 1.67352e7i | − | 0.969298i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.08535e7i | − | 0.624643i | −0.949976 | − | 0.312322i | \(-0.898893\pi\) | ||
0.949976 | − | 0.312322i | \(-0.101107\pi\) | |||||||
\(788\) | −8.92726e6 | − | 478759.i | −0.512157 | − | 0.0274664i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.84395e7 | + | 3.64333e7i | −2.19134 | + | 2.07697i | ||||
\(791\) | 3.91973e6 | 0.222749 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.12805e7 | 0.637006 | ||||||||
\(794\) | −2.51779e7 | + | 2.38638e7i | −1.41732 | + | 1.34335i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.61284e6 | − | 86495.0i | −0.0902214 | − | 0.00483847i | ||||
\(797\) | − | 2.34260e7i | − | 1.30633i | −0.757215 | − | 0.653165i | \(-0.773441\pi\) | ||
0.757215 | − | 0.653165i | \(-0.226559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.19185e7i | − | 0.660475i | ||||||
\(800\) | −3.04049e7 | + | 2.31838e7i | −1.67965 | + | 1.28074i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.19107e7 | + | 2.31172e7i | 1.20287 | + | 1.26911i | ||||
\(803\) | 2.12930e7 | 1.16533 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.65278e6 | 0.253059 | ||||||||
\(806\) | 1.81091e7 | + | 1.91063e7i | 0.981883 | + | 1.03595i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.90617e6 | + | 5.02572e6i | −0.318257 | + | 0.270813i | ||||
\(809\) | − | 3.41203e7i | − | 1.83291i | −0.400133 | − | 0.916457i | \(-0.631036\pi\) | ||
0.400133 | − | 0.916457i | \(-0.368964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.96027e7i | − | 1.04656i | −0.852160 | − | 0.523281i | \(-0.824708\pi\) | ||
0.852160 | − | 0.523281i | \(-0.175292\pi\) | |||||||
\(812\) | −541356. | + | 1.00945e7i | −0.0288133 | + | 0.537272i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.46313e7 | − | 2.33457e7i | 1.30294 | − | 1.23494i | ||||
\(815\) | −1.18727e7 | −0.626119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.68294e6 | −0.193037 | ||||||||
\(818\) | −1.17787e7 | + | 1.11639e7i | −0.615478 | + | 0.583355i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 908190. | − | 1.69347e7i | 0.0471674 | − | 0.879515i | ||||
\(821\) | 2.53758e7i | 1.31390i | 0.753934 | + | 0.656950i | \(0.228154\pi\) | ||||
−0.753934 | + | 0.656950i | \(0.771846\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.26091e7i | 0.648908i | 0.945901 | + | 0.324454i | \(0.105181\pi\) | ||||
−0.945901 | + | 0.324454i | \(0.894819\pi\) | |||||||
\(824\) | −1.28153e7 | + | 1.09049e7i | −0.657525 | + | 0.559506i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.32086e6 | − | 1.39360e6i | −0.0673609 | − | 0.0710702i | ||||
\(827\) | −1.62032e7 | −0.823831 | −0.411916 | − | 0.911222i | \(-0.635140\pi\) | ||||
−0.411916 | + | 0.911222i | \(0.635140\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.31970e7 | −0.666942 | −0.333471 | − | 0.942760i | \(-0.608220\pi\) | ||||
−0.333471 | + | 0.942760i | \(0.608220\pi\) | |||||||
\(830\) | −3.15669e7 | − | 3.33052e7i | −1.59051 | − | 1.67810i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.75772e6 | + | 1.70092e7i | −0.138115 | + | 0.851874i | ||||
\(833\) | 5.65037e6i | 0.282140i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.48763e7i | − | 1.23472i | ||||||
\(836\) | 2.52393e7 | + | 1.35355e6i | 1.24900 | + | 0.0669823i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.15550e7 | + | 2.04300e7i | −1.06032 | + | 1.00498i | ||||
\(839\) | 2.51468e7 | 1.23333 | 0.616663 | − | 0.787227i | \(-0.288484\pi\) | ||||
0.616663 | + | 0.787227i | \(0.288484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.24576e6 | −0.0607356 | ||||||||
\(842\) | −1.57202e7 | + | 1.48997e7i | −0.764149 | + | 0.724267i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.43707e7 | + | 1.30697e6i | 1.17764 | + | 0.0631555i | ||||
\(845\) | − | 9.34583e6i | − | 0.450273i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 104189.i | 0.00499017i | ||||||||
\(848\) | 3.49462e6 | − | 3.24878e7i | 0.166882 | − | 1.55142i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.18768e7 | + | 1.25309e7i | 0.563837 | + | 0.594886i | ||||
\(851\) | 1.03644e7 | 0.490593 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.63408e7 | −0.768956 | −0.384478 | − | 0.923134i | \(-0.625618\pi\) | ||||
−0.384478 | + | 0.923134i | \(0.625618\pi\) | |||||||
\(854\) | −5.65361e6 | − | 5.96493e6i | −0.265266 | − | 0.279873i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.72780e6 | + | 6.73124e6i | 0.267179 | + | 0.313986i | ||||
\(857\) | 3.65159e7i | 1.69836i | 0.528101 | + | 0.849181i | \(0.322904\pi\) | ||||
−0.528101 | + | 0.849181i | \(0.677096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.09455e7i | − | 0.968516i | −0.874925 | − | 0.484258i | \(-0.839090\pi\) | ||
0.874925 | − | 0.484258i | \(-0.160910\pi\) | |||||||
\(860\) | −317743. | + | 5.92485e6i | −0.0146497 | + | 0.273169i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.13450e6 | − | 2.97091e6i | 0.143681 | − | 0.136182i | ||||
\(863\) | −2.99156e7 | −1.36732 | −0.683661 | − | 0.729799i | \(-0.739613\pi\) | ||||
−0.683661 | + | 0.729799i | \(0.739613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.06549e6 | −0.321072 | ||||||||
\(866\) | 519888. | − | 492754.i | 0.0235568 | − | 0.0223273i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.02708e6 | − | 1.91517e7i | 0.0462707 | − | 0.862794i | ||||
\(869\) | − | 3.82803e7i | − | 1.71959i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.69107e6i | − | 0.432839i | ||||||
\(872\) | 1.22939e7 | + | 1.44477e7i | 0.547520 | + | 0.643440i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.31013e6 | + | 5.60253e6i | 0.235140 | + | 0.248088i | ||||
\(875\) | 2.32148e7 | 1.02505 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.01027e6 | 0.263873 | 0.131937 | − | 0.991258i | \(-0.457880\pi\) | ||||
0.131937 | + | 0.991258i | \(0.457880\pi\) | |||||||
\(878\) | −2.47682e7 | − | 2.61321e7i | −1.08432 | − | 1.14403i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.35500e6 | − | 4.04864e7i | 0.189575 | − | 1.76239i | ||||
\(881\) | − | 3.80007e6i | − | 0.164950i | −0.996593 | − | 0.0824750i | \(-0.973718\pi\) | ||
0.996593 | − | 0.0824750i | \(-0.0262825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.26490e7i | 1.40918i | 0.709613 | + | 0.704592i | \(0.248870\pi\) | ||||
−0.709613 | + | 0.704592i | \(0.751130\pi\) | |||||||
\(884\) | 7.76955e6 | + | 416673.i | 0.334399 | + | 0.0179335i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.05427e7 | + | 1.94705e7i | −0.879169 | + | 0.833283i | ||||
\(887\) | −3.86440e7 | −1.64920 | −0.824600 | − | 0.565716i | \(-0.808600\pi\) | ||||
−0.824600 | + | 0.565716i | \(0.808600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38791e7 | −0.588991 | ||||||||
\(890\) | 8.38012e6 | − | 7.94275e6i | 0.354630 | − | 0.336121i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.59149e7 | + | 1.92608e6i | 1.51134 | + | 0.0810515i | ||||
\(893\) | − | 5.04924e7i | − | 2.11883i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.66265e7i | − | 1.94570i | ||||||
\(896\) | 1.03763e7 | − | 7.06654e6i | 0.431792 | − | 0.294060i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.07693e6 | + | 9.57676e6i | 0.375620 | + | 0.396304i | ||||
\(899\) | 4.12781e7 | 1.70341 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.47543e7 | −0.605491 | ||||||||
\(902\) | 8.43229e6 | + | 8.89662e6i | 0.345087 | + | 0.364090i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.97892e6 | − | 6.78947e6i | 0.324730 | − | 0.276322i | ||||
\(905\) | 1.40644e7i | 0.570820i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21928e7i | 0.492138i | 0.969252 | + | 0.246069i | \(0.0791389\pi\) | ||||
−0.969252 | + | 0.246069i | \(0.920861\pi\) | |||||||
\(908\) | −1.08106e6 | + | 2.01582e7i | −0.0435147 | + | 0.811404i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.44204e7 | − | 1.36677e7i | 0.577261 | − | 0.547133i | ||||
\(911\) | 8.17620e6 | 0.326404 | 0.163202 | − | 0.986593i | \(-0.447818\pi\) | ||||
0.163202 | + | 0.986593i | \(0.447818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.31673e7 | 1.31684 | ||||||||
\(914\) | −1.43791e7 | + | 1.36286e7i | −0.569333 | + | 0.539619i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 945568. | − | 1.76317e7i | 0.0372352 | − | 0.694313i | ||||
\(917\) | 7.23581e6i | 0.284161i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.31066e6i | − | 0.0511920i | −0.999672 | − | 0.0255960i | \(-0.991852\pi\) | ||
0.999672 | − | 0.0255960i | \(-0.00814835\pi\) | |||||||
\(920\) | 9.47108e6 | − | 8.05920e6i | 0.368918 | − | 0.313922i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.77309e7 | + | 1.87073e7i | 0.686915 | + | 0.724741i | ||||
\(923\) | −3.56485e7 | −1.37733 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.82073e7 | 3.77389 | ||||||||
\(926\) | −1.27921e7 | − | 1.34966e7i | −0.490248 | − | 0.517244i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.63830e7 | + | 2.14858e7i | 0.624485 | + | 0.818995i | ||||
\(929\) | 7.54802e6i | 0.286942i | 0.989655 | + | 0.143471i | \(0.0458263\pi\) | ||||
−0.989655 | + | 0.143471i | \(0.954174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.39375e7i | 0.905118i | ||||||||
\(932\) | 1.61892e7 | + | 868209.i | 0.610500 | + | 0.0327404i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.75377e7 | − | 1.66224e7i | 0.657818 | − | 0.623485i | ||||
\(935\) | −1.83869e7 | −0.687828 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.52871e7 | 0.568822 | 0.284411 | − | 0.958702i | \(-0.408202\pi\) | ||||
0.284411 | + | 0.958702i | \(0.408202\pi\) | |||||||
\(938\) | −5.12449e6 | + | 4.85703e6i | −0.190171 | + | 0.180245i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.12285e7 | − | 4.35620e6i | −2.99839 | − | 0.160801i | ||||
\(941\) | 3.53718e7i | 1.30221i | 0.758986 | + | 0.651107i | \(0.225695\pi\) | ||||
−0.758986 | + | 0.651107i | \(0.774305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.74354e6i | 0.137089i | ||||||||
\(944\) | −5.10261e6 | − | 548873.i | −0.186364 | − | 0.0200467i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.95015e6 | − | 3.11261e6i | −0.107181 | − | 0.113083i | ||||
\(947\) | 1.28282e7 | 0.464826 | 0.232413 | − | 0.972617i | \(-0.425338\pi\) | ||||
0.232413 | + | 0.972617i | \(0.425338\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.77689e7 | 1.00091 | ||||||||
\(950\) | 5.03157e7 | + | 5.30864e7i | 1.80882 | + | 1.90842i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.67367e6 | − | 4.31725e6i | −0.131373 | − | 0.154389i | ||||
\(953\) | − | 1.90229e7i | − | 0.678490i | −0.940698 | − | 0.339245i | \(-0.889828\pi\) | ||
0.940698 | − | 0.339245i | \(-0.110172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.51546e7i | 2.66653i | ||||||||
\(956\) | 1.44538e6 | − | 2.69516e7i | 0.0511492 | − | 0.953761i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.57947e6 | − | 8.13169e6i | 0.302027 | − | 0.286264i | ||||
\(959\) | −9.56823e6 | −0.335958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.96854e7 | −1.73548 | ||||||||
\(962\) | 3.21224e7 | − | 3.04459e7i | 1.11911 | − | 1.06070i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −274868. | + | 5.12537e6i | −0.00952646 | + | 0.177637i | ||||
\(965\) | 7.55978e7i | 2.61331i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.63296e7i | − | 1.24938i | −0.780873 | − | 0.624690i | \(-0.785226\pi\) | ||
0.780873 | − | 0.624690i | \(-0.214774\pi\) | |||||||
\(968\) | 180469. | + | 212086.i | 0.00619035 | + | 0.00727483i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.62107e6 | − | 8.04073e6i | −0.260068 | − | 0.274389i | ||||
\(971\) | 4.25414e7 | 1.44798 | 0.723991 | − | 0.689809i | \(-0.242306\pi\) | ||||
0.723991 | + | 0.689809i | \(0.242306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.37277e7 | 0.464851 | ||||||||
\(974\) | 7.89186e6 | + | 8.32644e6i | 0.266552 | + | 0.281230i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.18404e7 | − | 2.34931e6i | −0.733898 | − | 0.0789433i | ||||
\(977\) | 5.19393e7i | 1.74084i | 0.492308 | + | 0.870421i | \(0.336153\pi\) | ||||
−0.492308 | + | 0.870421i | \(0.663847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.34541e6i | 0.278286i | ||||||||
\(980\) | 3.85090e7 | + | 2.06520e6i | 1.28085 | + | 0.0686904i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.03507e7 | + | 2.87666e7i | −1.00436 | + | 0.951941i | ||||
\(983\) | 7.20689e6 | 0.237884 | 0.118942 | − | 0.992901i | \(-0.462050\pi\) | ||||
0.118942 | + | 0.992901i | \(0.462050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.75520e7 | 0.904820 | ||||||||
\(986\) | 8.85499e6 | − | 8.39283e6i | 0.290065 | − | 0.274926i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.29154e7 | + | 1.76521e6i | 1.07277 | + | 0.0575314i | ||||
\(989\) | − | 1.30973e6i | − | 0.0425786i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.43917e7i | 0.465510i | 0.972535 | + | 0.232755i | \(0.0747740\pi\) | ||||
−0.972535 | + | 0.232755i | \(0.925226\pi\) | |||||||
\(992\) | −3.10824e7 | − | 4.07637e7i | −1.00285 | − | 1.31521i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.78666e7 | + | 1.88504e7i | 0.573555 | + | 0.605138i | ||||
\(995\) | 4.97768e6 | 0.159393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.43826e7 | 1.09547 | 0.547736 | − | 0.836652i | \(-0.315490\pi\) | ||||
0.547736 | + | 0.836652i | \(0.315490\pi\) | |||||||
\(998\) | −2.25552e6 | − | 2.37973e6i | −0.0716838 | − | 0.0756311i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.6.b.c.107.6 | yes | 20 | |
3.2 | odd | 2 | inner | 108.6.b.c.107.15 | yes | 20 | |
4.3 | odd | 2 | inner | 108.6.b.c.107.16 | yes | 20 | |
12.11 | even | 2 | inner | 108.6.b.c.107.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.c.107.5 | ✓ | 20 | 12.11 | even | 2 | inner | |
108.6.b.c.107.6 | yes | 20 | 1.1 | even | 1 | trivial | |
108.6.b.c.107.15 | yes | 20 | 3.2 | odd | 2 | inner | |
108.6.b.c.107.16 | yes | 20 | 4.3 | odd | 2 | inner |