Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 19^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.9 | ||
Root | \(-42.7313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.7.h.a.65.9 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 35.5064 | − | 20.4996i | 1.31505 | − | 0.759245i | 0.332123 | − | 0.943236i | \(-0.392235\pi\) |
0.982928 | + | 0.183991i | \(0.0589019\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.1615 | + | 34.9207i | 0.161292 | + | 0.279366i | 0.935332 | − | 0.353770i | \(-0.115101\pi\) |
−0.774040 | + | 0.633136i | \(0.781767\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 53.8286 | 0.156935 | 0.0784673 | − | 0.996917i | \(-0.474997\pi\) | ||||
0.0784673 | + | 0.996917i | \(0.474997\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 475.968 | − | 824.401i | 0.652905 | − | 1.13087i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1995.81 | 1.49948 | 0.749742 | − | 0.661731i | \(-0.230178\pi\) | ||||
0.749742 | + | 0.661731i | \(0.230178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1394.74 | + | 805.253i | 0.634838 | + | 0.366524i | 0.782623 | − | 0.622496i | \(-0.213881\pi\) |
−0.147785 | + | 0.989019i | \(0.547214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1431.72 | + | 826.606i | 0.424214 | + | 0.244920i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1591.10 | − | 2755.87i | −0.323856 | − | 0.560935i | 0.657424 | − | 0.753521i | \(-0.271646\pi\) |
−0.981280 | + | 0.192586i | \(0.938313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2912.77 | − | 6209.80i | −0.424665 | − | 0.905351i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1911.26 | − | 1103.46i | 0.206377 | − | 0.119152i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3377.10 | + | 5849.31i | −0.277562 | + | 0.480752i | −0.970778 | − | 0.239978i | \(-0.922860\pi\) |
0.693216 | + | 0.720730i | \(0.256193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6999.53 | − | 12123.5i | 0.447970 | − | 0.775906i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9140.20i | − | 0.464370i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 454.264 | + | 262.269i | 0.0186258 | + | 0.0107536i | 0.509284 | − | 0.860599i | \(-0.329910\pi\) |
−0.490658 | + | 0.871352i | \(0.663244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10098.7i | 0.338986i | 0.985531 | + | 0.169493i | \(0.0542130\pi\) | ||||
−0.985531 | + | 0.169493i | \(0.945787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 70864.0 | − | 40913.4i | 1.97190 | − | 1.13847i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1085.26 | + | 1879.73i | 0.0253123 | + | 0.0438422i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 45019.8i | − | 0.888788i | −0.895831 | − | 0.444394i | \(-0.853419\pi\) | ||
0.895831 | − | 0.444394i | \(-0.146581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 66029.5 | 1.11313 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66707.8 | − | 38513.8i | 0.967888 | − | 0.558811i | 0.0692965 | − | 0.997596i | \(-0.477925\pi\) |
0.898592 | + | 0.438785i | \(0.144591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24733.2 | + | 42839.2i | 0.311082 | + | 0.538810i | 0.978597 | − | 0.205786i | \(-0.0659752\pi\) |
−0.667515 | + | 0.744597i | \(0.732642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 38384.9 | 0.421233 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4692.75 | + | 8128.08i | −0.0451995 | + | 0.0782879i | −0.887740 | − | 0.460345i | \(-0.847726\pi\) |
0.842541 | + | 0.538633i | \(0.181059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −114751. | −0.975372 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −112989. | − | 65234.1i | −0.851774 | − | 0.491772i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54739.9 | + | 31604.1i | 0.367685 | + | 0.212283i | 0.672447 | − | 0.740145i | \(-0.265243\pi\) |
−0.304761 | + | 0.952429i | \(0.598577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40238.6 | + | 69695.2i | 0.241855 | + | 0.418904i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −230721. | − | 160777.i | −1.24584 | − | 0.868158i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −241556. | + | 139462.i | −1.17615 | + | 0.679049i | −0.955120 | − | 0.296219i | \(-0.904274\pi\) |
−0.221027 | + | 0.975268i | \(0.570941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −211690. | + | 366657.i | −0.932631 | + | 1.61536i | −0.153827 | + | 0.988098i | \(0.549160\pi\) |
−0.778804 | + | 0.627267i | \(0.784174\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25620.7 | − | 44376.3i | 0.102463 | − | 0.177472i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 64940.4i | 0.236469i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2972.38 | − | 1716.11i | −0.00988281 | − | 0.00570584i | 0.495050 | − | 0.868864i | \(-0.335150\pi\) |
−0.504933 | + | 0.863158i | \(0.668483\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 276917.i | 0.842951i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −173856. | + | 100376.i | −0.485752 | + | 0.280449i | −0.722810 | − | 0.691046i | \(-0.757150\pi\) |
0.237058 | + | 0.971495i | \(0.423817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 120923. | + | 209445.i | 0.310843 | + | 0.538396i | 0.978545 | − | 0.206032i | \(-0.0660553\pi\) |
−0.667702 | + | 0.744429i | \(0.732722\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 573950.i | − | 1.36047i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 107432. | 0.235321 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58299.2 | − | 33659.0i | 0.118245 | − | 0.0682685i | −0.439711 | − | 0.898139i | \(-0.644919\pi\) |
0.557956 | + | 0.829871i | \(0.311586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 159610. | + | 276453.i | 0.300335 | + | 0.520195i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −336237. | −0.588045 | −0.294023 | − | 0.955798i | \(-0.594994\pi\) | ||||
−0.294023 | + | 0.955798i | \(0.594994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 64158.1 | − | 111125.i | 0.104471 | − | 0.180949i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21505.7 | 0.0326584 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 345795. | + | 199645.i | 0.490511 | + | 0.283197i | 0.724786 | − | 0.688974i | \(-0.241938\pi\) |
−0.234275 | + | 0.972170i | \(0.575272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 75076.8 | + | 43345.6i | 0.0996281 | + | 0.0575203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 207020. | + | 358569.i | 0.257373 | + | 0.445783i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158125. | − | 226915.i | 0.184429 | − | 0.264663i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.20292e6 | + | 694509.i | −1.31802 | + | 0.760961i | −0.983410 | − | 0.181394i | \(-0.941939\pi\) |
−0.334613 | + | 0.942356i | \(0.608606\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 949943. | − | 1.64535e6i | 0.979021 | − | 1.69571i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −667775. | + | 1.15662e6i | −0.648136 | + | 1.12260i | 0.335432 | + | 0.942065i | \(0.391118\pi\) |
−0.983568 | + | 0.180540i | \(0.942215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 777460.i | − | 0.711486i | −0.934584 | − | 0.355743i | \(-0.884228\pi\) | ||
0.934584 | − | 0.355743i | \(-0.115772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 77067.6 | + | 44495.0i | 0.0665739 | + | 0.0384365i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 612619.i | − | 0.500080i | −0.968236 | − | 0.250040i | \(-0.919556\pi\) | ||
0.968236 | − | 0.250040i | \(-0.0804437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −565177. | + | 326305.i | −0.436420 | + | 0.251967i | −0.702078 | − | 0.712100i | \(-0.747744\pi\) |
0.265658 | + | 0.964067i | \(0.414411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −922888. | − | 1.59849e6i | −0.674808 | − | 1.16880i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.19449e6i | 0.827844i | 0.910312 | + | 0.413922i | \(0.135841\pi\) | ||||
−0.910312 | + | 0.413922i | \(0.864159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −272349. | −0.179074 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.32770e6 | − | 766549.i | 0.828978 | − | 0.478611i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −85646.9 | − | 148345.i | −0.0508242 | − | 0.0880302i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.21171e6 | 1.24845 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.57904e6 | − | 2.73497e6i | 0.848548 | − | 1.46973i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.19453e6 | 0.611600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.62269e6 | + | 1.51421e6i | 1.28037 | + | 0.739221i | 0.976916 | − | 0.213625i | \(-0.0685272\pi\) |
0.303453 | + | 0.952846i | \(0.401861\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.75637e6 | + | 1.01404e6i | 0.818178 | + | 0.472375i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.66590e6 | − | 2.88542e6i | −0.741027 | − | 1.28350i | −0.952028 | − | 0.306011i | \(-0.901005\pi\) |
0.211000 | − | 0.977486i | \(-0.432328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −156790. | − | 334265.i | −0.0666446 | − | 0.142081i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 319182. | − | 184280.i | 0.129729 | − | 0.0748992i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 947050. | − | 1.64034e6i | 0.368308 | − | 0.637928i | −0.620993 | − | 0.783816i | \(-0.713271\pi\) |
0.989301 | + | 0.145888i | \(0.0466038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −524600. | + | 908633.i | −0.195337 | + | 0.338333i | −0.947011 | − | 0.321202i | \(-0.895913\pi\) |
0.751674 | + | 0.659535i | \(0.229247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 384798.i | 0.137270i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.78364e6 | + | 1.60713e6i | 0.951929 | + | 0.549597i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21151.0i | 0.00693787i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.07441e6 | + | 2.35236e6i | −1.28266 | + | 0.740546i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.64323e6 | − | 4.57822e6i | −0.799055 | − | 1.38400i | −0.920232 | − | 0.391373i | \(-0.872000\pi\) |
0.121177 | − | 0.992631i | \(-0.461333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91871e6i | 1.42863i | 0.699823 | + | 0.714316i | \(0.253262\pi\) | ||||
−0.699823 | + | 0.714316i | \(0.746738\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.02926e6 | −0.845789 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −352655. | + | 203605.i | −0.0947011 | + | 0.0546757i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.54314e6 | + | 2.67279e6i | 0.398755 | + | 0.690664i | 0.993573 | − | 0.113197i | \(-0.0361091\pi\) |
−0.594818 | + | 0.803861i | \(0.702776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.59149e6 | 0.644700 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −181784. | + | 314860.i | −0.0435591 | + | 0.0754466i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.84972e6 | −1.35074 | −0.675371 | − | 0.737478i | \(-0.736016\pi\) | ||||
−0.675371 | + | 0.737478i | \(0.736016\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.85745e6 | + | 1.64975e6i | 0.636102 | + | 0.367254i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.57416e6 | − | 2.64089e6i | −0.982115 | − | 0.567024i | −0.0792070 | − | 0.996858i | \(-0.525239\pi\) |
−0.902908 | + | 0.429834i | \(0.858572\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.11654e6 | − | 1.93390e6i | −0.231320 | − | 0.400659i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.50575e6 | − | 554374.i | −1.30110 | − | 0.110870i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.75647e6 | + | 4.47820e6i | −1.49805 | + | 0.864898i | −0.999997 | − | 0.00224984i | \(-0.999284\pi\) |
−0.498050 | + | 0.867148i | \(0.665951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 376775. | − | 652593.i | 0.0703020 | − | 0.121767i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.71785e6 | + | 9.90360e6i | −1.03113 | + | 1.78597i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.92917e6i | − | 1.73123i | −0.500713 | − | 0.865613i | \(-0.666929\pi\) | ||
0.500713 | − | 0.865613i | \(-0.333071\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.52820e6 | + | 1.45966e6i | 0.426359 | + | 0.246158i | 0.697794 | − | 0.716298i | \(-0.254165\pi\) |
−0.271435 | + | 0.962457i | \(0.587498\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.73582e7i | 2.83238i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.57212e6 | − | 907667.i | 0.248297 | − | 0.143354i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.17555e6 | − | 5.50021e6i | −0.485617 | − | 0.841113i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 492004.i | − | 0.0728757i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.15338e6 | 1.17014 | 0.585070 | − | 0.810983i | \(-0.301067\pi\) | ||||
0.585070 | + | 0.810983i | \(0.301067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.47955e6 | − | 854219.i | 0.205806 | − | 0.118822i | −0.393555 | − | 0.919301i | \(-0.628755\pi\) |
0.599361 | + | 0.800479i | \(0.295422\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.33125e6 | + | 2.30580e6i | 0.179538 | + | 0.310969i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.30695e7 | 1.70947 | 0.854734 | − | 0.519066i | \(-0.173720\pi\) | ||||
0.854734 | + | 0.519066i | \(0.173720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.93470e6 | − | 1.20113e7i | 0.879972 | − | 1.52416i | 0.0286014 | − | 0.999591i | \(-0.490895\pi\) |
0.851370 | − | 0.524565i | \(-0.175772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −140718. | −0.0173285 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24452.4 | + | 14117.6i | 0.00292303 | + | 0.00168761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68986e6 | + | 1.55299e6i | 0.312225 | + | 0.180263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.21478e6 | + | 5.56817e6i | 0.362444 | + | 0.627771i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.81335e6 | − | 1.23936e7i | −0.636777 | − | 1.35756i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.62038e6 | + | 2.66758e6i | −0.491848 | + | 0.283968i | −0.725341 | − | 0.688390i | \(-0.758318\pi\) |
0.233493 | + | 0.972359i | \(0.424984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.11533e6 | + | 7.12796e6i | −0.425859 | + | 0.737609i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −997317. | + | 1.72740e6i | −0.100350 | + | 0.173811i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 543600.i | 0.0531986i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.58709e6 | + | 4.95776e6i | 0.817549 | + | 0.472012i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.12497e6i | − | 0.474804i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.07806e6 | + | 5.24122e6i | −0.818612 | + | 0.472626i | −0.849938 | − | 0.526883i | \(-0.823361\pi\) |
0.0313254 | + | 0.999509i | \(0.490027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.66310e6 | − | 1.15408e7i | −0.584964 | − | 1.01319i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.93360e7i | − | 1.65306i | −0.562889 | − | 0.826532i | \(-0.690310\pi\) | ||
0.562889 | − | 0.826532i | \(-0.309690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.87818e6 | 0.572753 | 0.286376 | − | 0.958117i | \(-0.407549\pi\) | ||||
0.286376 | + | 0.958117i | \(0.407549\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81451e6 | − | 2.20231e6i | 0.309459 | − | 0.178666i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.94154e6 | − | 5.09490e6i | −0.232545 | − | 0.402780i | 0.726011 | − | 0.687683i | \(-0.241372\pi\) |
−0.958556 | + | 0.284903i | \(0.908039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −378452. | −0.0291613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.37999e6 | − | 2.39022e6i | 0.103665 | − | 0.179553i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.89895e6 | −0.139098 | −0.0695488 | − | 0.997579i | \(-0.522156\pi\) | ||||
−0.0695488 | + | 0.997579i | \(0.522156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.47225e7 | + | 8.50001e6i | 1.05179 | + | 0.607251i | 0.923150 | − | 0.384440i | \(-0.125605\pi\) |
0.128640 | + | 0.991691i | \(0.458939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.71049e7 | + | 9.87549e6i | 1.19207 | + | 0.688240i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.31356e6 | − | 4.00721e6i | −0.157320 | − | 0.272486i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 937901. | − | 1.10066e7i | 0.0622395 | − | 0.730401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.19385e7 | + | 6.89272e6i | −0.773309 | + | 0.446470i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −789.615 | + | 1367.65i | −4.99338e−5 | + | 8.64878e-5i | −0.866050 | − | 0.499957i | \(-0.833349\pi\) |
0.866000 | + | 0.500043i | \(0.166683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.74006e6 | + | 1.16741e7i | −0.416200 | + | 0.720879i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 5.26086e6i | − | 0.317276i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.12130e7 | − | 6.47380e6i | −0.660573 | − | 0.381382i | 0.131922 | − | 0.991260i | \(-0.457885\pi\) |
−0.792495 | + | 0.609878i | \(0.791218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.42335e6i | − | 0.139482i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 432430. | − | 249664.i | 0.0243217 | − | 0.0140422i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.92640e6 | − | 1.19969e7i | −0.380751 | − | 0.659479i | 0.610419 | − | 0.792079i | \(-0.291001\pi\) |
−0.991170 | + | 0.132599i | \(0.957668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.54874e6i | 0.136958i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.63706e7 | 0.860062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.05526e7 | − | 1.76396e7i | 1.56961 | − | 0.906214i | 0.573396 | − | 0.819279i | \(-0.305626\pi\) |
0.996214 | − | 0.0869358i | \(-0.0277075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.49147e6 | + | 1.64397e7i | 0.476898 | + | 0.826012i | 0.999650 | − | 0.0264734i | \(-0.00842772\pi\) |
−0.522751 | + | 0.852485i | \(0.675094\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.55427e6 | 0.174688 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.39697e7 | − | 2.41963e7i | 0.671723 | − | 1.16346i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.84807e6 | −0.181052 | −0.0905261 | − | 0.995894i | \(-0.528855\pi\) | ||||
−0.0905261 | + | 0.995894i | \(0.528855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.32540e6 | + | 4.80667e6i | 0.383347 | + | 0.221326i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26128e7 | − | 7.28203e6i | −0.568453 | − | 0.328196i | 0.188079 | − | 0.982154i | \(-0.439774\pi\) |
−0.756531 | + | 0.653958i | \(0.773107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.88520e7 | + | 3.26526e7i | 0.831759 | + | 1.44065i | 0.896642 | + | 0.442756i | \(0.145999\pi\) |
−0.0648828 | + | 0.997893i | \(0.520667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 962771. | − | 1.12984e7i | 0.0415900 | − | 0.488072i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.59079e6 | − | 2.07314e6i | 0.151895 | − | 0.0876967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00555e6 | − | 1.21340e7i | 0.290234 | − | 0.502701i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.84743e7 | + | 4.93190e7i | −1.15551 | + | 2.00141i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.05616e6i | − | 0.240766i | −0.992728 | − | 0.120383i | \(-0.961588\pi\) | ||
0.992728 | − | 0.120383i | \(-0.0384122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.74025e6 | − | 5.62354e6i | −0.379406 | − | 0.219050i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.82421e7i | − | 0.696315i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.42035e6 | + | 5.43884e6i | −0.352414 | + | 0.203466i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.33135e6 | + | 2.30597e6i | 0.0488196 | + | 0.0845580i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.47565e7i | 1.96838i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.70719e7 | −0.601704 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.43057e7 | + | 1.98064e7i | −1.18564 | + | 0.684527i | −0.957311 | − | 0.289059i | \(-0.906658\pi\) |
−0.228324 | + | 0.973585i | \(0.573324\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.59376e7 | − | 2.76048e7i | −0.540192 | − | 0.935640i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.54908e7 | −1.84476 | −0.922380 | − | 0.386284i | \(-0.873759\pi\) | ||||
−0.922380 | + | 0.386284i | \(0.873759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.43988e6 | + | 1.46183e7i | −0.275235 | + | 0.476720i | −0.970194 | − | 0.242328i | \(-0.922089\pi\) |
0.694960 | + | 0.719049i | \(0.255422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.06620e6 | 0.0661061 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.61606e6 | + | 3.24243e6i | 0.176301 | + | 0.101787i | 0.585553 | − | 0.810634i | \(-0.300877\pi\) |
−0.409253 | + | 0.912421i | \(0.634211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 906625. | + | 523440.i | 0.0279290 | + | 0.0161248i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.25585e7 | − | 2.17519e7i | −0.379683 | − | 0.657630i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.24789e7 | + | 1.79077e7i | −0.370313 | + | 0.531413i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.95250e7 | − | 1.12728e7i | 0.568777 | − | 0.328383i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.33782e7 | + | 2.31718e7i | −0.382610 | + | 0.662699i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −252604. | + | 437523.i | −0.00709337 | + | 0.0122861i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50727e7i | 0.691380i | 0.938349 | + | 0.345690i | \(0.112355\pi\) | ||||
−0.938349 | + | 0.345690i | \(0.887645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.71144e7 | − | 2.14280e7i | −1.00510 | − | 0.580295i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 138397.i | − | 0.00368123i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.49392e7 | + | 2.01722e7i | −0.912901 | + | 0.527064i | −0.881363 | − | 0.472439i | \(-0.843374\pi\) |
−0.0315376 | + | 0.999503i | \(0.510040\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.44866e7 | + | 4.24121e7i | 0.628536 | + | 1.08866i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.01552e7i | 0.508304i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.25098e7 | −0.310004 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.67014e6 | + | 5.58306e6i | −0.235492 | + | 0.135961i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.13812e7 | − | 3.70333e7i | −0.511733 | − | 0.886348i | −0.999907 | − | 0.0136015i | \(-0.995670\pi\) |
0.488174 | − | 0.872746i | \(-0.337663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.87855e7 | 1.38291 | 0.691455 | − | 0.722420i | \(-0.256970\pi\) | ||||
0.691455 | + | 0.722420i | \(0.256970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.36017e6 | − | 1.27482e7i | 0.170203 | − | 0.294800i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.57708e7 | 1.49523 | 0.747617 | − | 0.664130i | \(-0.231198\pi\) | ||||
0.747617 | + | 0.664130i | \(0.231198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.01039e6 | − | 4.04745e6i | −0.156696 | − | 0.0904684i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.08202e6 | − | 3.51146e6i | −0.133673 | − | 0.0771761i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.59674e7 | − | 2.76564e7i | −0.345105 | − | 0.597739i | 0.640268 | − | 0.768152i | \(-0.278823\pi\) |
−0.985373 | + | 0.170413i | \(0.945490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00774e7 | + | 3.61755e7i | −0.639320 | + | 0.768941i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.85296e7 | − | 4.53391e7i | 1.64178 | − | 0.947879i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.87599e6 | + | 8.44546e6i | −0.100273 | + | 0.173678i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.77505e7 | − | 4.80653e7i | 0.561401 | − | 0.972375i | −0.435974 | − | 0.899959i | \(-0.643596\pi\) |
0.997375 | − | 0.0724154i | \(-0.0230707\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.33253e7i | − | 1.45940i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94657e6 | + | 1.70120e6i | 0.0577026 | + | 0.0333146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.32072e6i | − | 0.121798i | −0.998144 | − | 0.0608989i | \(-0.980603\pi\) | ||
0.998144 | − | 0.0608989i | \(-0.0193967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.24134e7 | − | 2.44874e7i | 0.804284 | − | 0.464354i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 422386. | + | 731595.i | 0.00788290 | + | 0.0136536i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.86114e7i | 0.892937i | 0.894799 | + | 0.446469i | \(0.147319\pi\) | ||||
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24163e8 | 2.24500 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.61488e7 | − | 9.32351e6i | 0.287438 | − | 0.165952i | −0.349348 | − | 0.936993i | \(-0.613597\pi\) |
0.636786 | + | 0.771041i | \(0.280264\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.16598e6 | + | 3.75160e6i | 0.0379554 | + | 0.0657406i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.70889e7 | 0.812429 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.32556e7 | + | 5.76003e7i | −0.564957 | + | 0.978534i | 0.432097 | + | 0.901827i | \(0.357774\pi\) |
−0.997054 | + | 0.0767070i | \(0.975559\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14933e7 | 0.359561 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.18300e8 | − | 6.83005e7i | −1.94898 | − | 1.12524i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35080e6 | + | 1.35723e6i | 0.0381438 | + | 0.0220223i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.11861e7 | + | 1.05977e8i | 0.977871 | + | 1.69372i | 0.670117 | + | 0.742255i | \(0.266244\pi\) |
0.307753 | + | 0.951466i | \(0.400423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.24194e7 | − | 8.65438e6i | −0.195515 | − | 0.136244i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.08056e7 | − | 4.66531e7i | 1.25317 | − | 0.723515i | 0.281428 | − | 0.959582i | \(-0.409192\pi\) |
0.971737 | + | 0.236067i | \(0.0758584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.13203e6 | + | 1.40851e7i | −0.124246 | + | 0.215201i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.43596e6 | + | 1.11474e7i | −0.0968832 | + | 0.167807i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.98511e7i | − | 1.33272i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.56148e7 | − | 5.52032e7i | −1.39751 | − | 0.806853i | −0.403379 | − | 0.915033i | \(-0.632164\pi\) |
−0.994131 | + | 0.108180i | \(0.965498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.76566e7i | − | 1.11854i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.30026e7 | + | 7.50706e6i | −0.184578 | + | 0.106566i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.77903e6 | − | 1.17416e7i | −0.0948470 | − | 0.164280i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.30163e7i | 0.593233i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.44215e7 | 0.196051 | 0.0980256 | − | 0.995184i | \(-0.468747\pi\) | ||||
0.0980256 | + | 0.995184i | \(0.468747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.16727e7 | + | 4.13802e7i | −0.960522 | + | 0.554557i | −0.896334 | − | 0.443380i | \(-0.853779\pi\) |
−0.0641881 | + | 0.997938i | \(0.520446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.46720e6 | + | 7.73741e6i | 0.0590220 | + | 0.102229i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.45479e7 | −0.580311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.13949e7 | + | 1.97366e7i | −0.146362 | + | 0.253507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.31782e8 | 1.66911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.24661e8 | − | 7.19731e7i | −1.55704 | − | 0.898956i | −0.997538 | − | 0.0701243i | \(-0.977660\pi\) |
−0.559499 | − | 0.828831i | \(-0.689006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.25908e6 | − | 3.03633e6i | −0.0647808 | − | 0.0374012i | 0.467260 | − | 0.884120i | \(-0.345241\pi\) |
−0.532041 | + | 0.846719i | \(0.678575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 433587. | + | 750994.i | 0.00526754 | + | 0.00912365i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.61598e7 | + | 3.93340e6i | 0.553120 | + | 0.0471329i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.32621e7 | − | 4.80714e7i | 0.984133 | − | 0.568190i | 0.0806179 | − | 0.996745i | \(-0.474311\pi\) |
0.903516 | + | 0.428555i | \(0.140977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.46180e7 | + | 9.46012e7i | −0.636825 | + | 1.10301i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.76533e6 | + | 3.05764e6i | −0.0203056 | + | 0.0351703i | −0.876000 | − | 0.482312i | \(-0.839797\pi\) |
0.855694 | + | 0.517482i | \(0.173131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.61006e7i | 0.182709i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.87703e8 | − | 1.08371e8i | −2.10160 | − | 1.21336i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.46471e7i | 0.382761i | 0.981516 | + | 0.191380i | \(0.0612964\pi\) | ||||
−0.981516 | + | 0.191380i | \(0.938704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.33136e8 | − | 7.68663e7i | 1.45133 | − | 0.837927i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.00832e8 | + | 1.74646e8i | 1.08468 | + | 1.87872i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.49565e6i | 0.0371102i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.35067e7 | 0.351062 | 0.175531 | − | 0.984474i | \(-0.443836\pi\) | ||||
0.175531 | + | 0.984474i | \(0.443836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.51892e7 | + | 1.45430e7i | −0.260481 | + | 0.150389i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.58650e6 | − | 1.66043e7i | −0.0978492 | − | 0.169480i | 0.812945 | − | 0.582341i | \(-0.197863\pi\) |
−0.910794 | + | 0.412861i | \(0.864530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.43784e7 | −0.850136 | −0.425068 | − | 0.905161i | \(-0.639750\pi\) | ||||
−0.425068 | + | 0.905161i | \(0.639750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.34766e6 | + | 1.44586e7i | −0.0830245 | + | 0.143803i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.18908e8 | 1.16751 | 0.583753 | − | 0.811931i | \(-0.301584\pi\) | ||||
0.583753 | + | 0.811931i | \(0.301584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −159999. | − | 92375.5i | −0.00155095 | − | 0.000895444i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.09582e8 | + | 6.32675e7i | 1.04877 | + | 0.605505i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.93628e7 | + | 8.54990e7i | 0.466463 | + | 0.807937i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.56728e7 | − | 8.15255e6i | −0.892704 | − | 0.0760699i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.21089e7 | − | 3.00851e7i | 0.480127 | − | 0.277202i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.54649e7 | + | 1.30709e8i | −0.686654 | + | 1.18932i | 0.286259 | + | 0.958152i | \(0.407588\pi\) |
−0.972914 | + | 0.231168i | \(0.925745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.62523e7 | − | 6.27909e7i | 0.325762 | − | 0.564237i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.49060e7i | 0.132288i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.85055e7 | − | 2.80047e7i | −0.425173 | − | 0.245474i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.09348e8i | − | 1.81252i | −0.422721 | − | 0.906260i | \(-0.638925\pi\) | ||
0.422721 | − | 0.906260i | \(-0.361075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.07702e8 | + | 1.19917e8i | −1.77629 | + | 1.02554i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.88325e7 | + | 3.26189e7i | 0.159098 | + | 0.275565i | 0.934544 | − | 0.355849i | \(-0.115808\pi\) |
−0.775446 | + | 0.631414i | \(0.782475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.66919e6i | − | 0.0139305i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.66091e7 | 0.631633 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.35842e6 | + | 5.40309e6i | −0.0762313 | + | 0.0440122i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.49677e7 | + | 6.05659e7i | 0.281427 | + | 0.487446i | 0.971736 | − | 0.236068i | \(-0.0758590\pi\) |
−0.690310 | + | 0.723514i | \(0.742526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.16549e8 | −1.72204 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.48199e7 | + | 2.56689e7i | −0.116451 | + | 0.201699i | −0.918359 | − | 0.395749i | \(-0.870485\pi\) |
0.801908 | + | 0.597448i | \(0.203818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.38534e7 | −0.418157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.92885e7 | − | 4.57772e7i | −0.608396 | − | 0.351258i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.65604e8 | + | 9.56113e7i | 1.25579 | + | 0.725030i | 0.972253 | − | 0.233932i | \(-0.0751593\pi\) |
0.283535 | + | 0.958962i | \(0.408493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.50913e6 | + | 1.12741e7i | 0.0487821 | + | 0.0844930i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.67588e7 | + | 2.66233e7i | −0.420418 | + | 0.197201i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.71495e7 | − | 1.56748e7i | 0.198765 | − | 0.114757i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.36585e6 | + | 1.62221e7i | −0.0677760 | + | 0.117391i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.83603e8 | + | 3.18009e8i | −1.31334 | + | 2.27477i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.73062e7i | − | 0.617350i | −0.951168 | − | 0.308675i | \(-0.900114\pi\) | ||
0.951168 | − | 0.308675i | \(-0.0998856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.23643e8 | − | 1.29120e8i | −1.56333 | − | 0.902588i | −0.996917 | − | 0.0784647i | \(-0.974998\pi\) |
−0.566411 | − | 0.824123i | \(-0.691668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.08949e7i | − | 0.213506i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.78308e7 | − | 1.60681e7i | 0.190149 | − | 0.109783i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.12083e7 | + | 8.86955e7i | 0.345918 | + | 0.599148i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.65518e8i | 1.77342i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24053e8 | 0.819270 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.13931e7 | − | 1.23513e7i | 0.139705 | − | 0.0806588i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.03544e8 | − | 3.52549e8i | −1.31442 | − | 2.27665i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.29022e8 | −1.46255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.18637e8 | − | 2.05485e8i | 0.749251 | − | 1.29774i | −0.198932 | − | 0.980013i | \(-0.563747\pi\) |
0.948182 | − | 0.317727i | \(-0.102919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.19689e8 | 0.747578 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.27896e7 | − | 1.31576e7i | −0.140782 | − | 0.0812806i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.47631e8 | − | 8.52346e7i | −0.902017 | − | 0.520780i | −0.0241628 | − | 0.999708i | \(-0.507692\pi\) |
−0.877854 | + | 0.478928i | \(0.841025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.01515e8 | + | 3.49034e8i | 1.21784 | + | 2.10936i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 305473. | − | 3.58482e6i | 0.00182607 | − | 0.0214295i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.13816e6 | − | 1.81182e6i | 0.0185567 | − | 0.0107137i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.72136e7 | − | 6.44559e7i | 0.217682 | − | 0.377037i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.18734e6 | + | 3.78859e6i | −0.0126576 | + | 0.0219236i | −0.872285 | − | 0.488998i | \(-0.837362\pi\) |
0.859627 | + | 0.510922i | \(0.170696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.96660e7i | 0.456076i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.25504e8 | − | 1.30195e8i | −1.27722 | − | 0.737404i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.04600e8i | − | 1.14652i | −0.819374 | − | 0.573259i | \(-0.805679\pi\) | ||
0.819374 | − | 0.573259i | \(-0.194321\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.17126e7 | + | 2.40828e7i | −0.231271 | + | 0.133525i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.59159e6 | + | 1.48811e7i | 0.0471329 | + | 0.0816366i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.15237e8i | 1.16837i | 0.811621 | + | 0.584184i | \(0.198585\pi\) | ||||
−0.811621 | + | 0.584184i | \(0.801415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.06574e8 | 1.10960 | 0.554800 | − | 0.831983i | \(-0.312795\pi\) | ||||
0.554800 | + | 0.831983i | \(0.312795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.89497e8 | − | 1.67141e8i | 1.53879 | − | 0.888422i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.72762e7 | + | 8.18848e7i | 0.248679 | + | 0.430725i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.13530e8 | 1.63212 | 0.816058 | − | 0.577970i | \(-0.196155\pi\) | ||||
0.816058 | + | 0.577970i | \(0.196155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.50223e7 | − | 6.06604e7i | 0.180430 | − | 0.312514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.80991e7 | −0.0922847 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.09251e8 | + | 6.30758e7i | 0.551338 | + | 0.318315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.35369e7 | + | 3.09096e7i | 0.267415 | + | 0.154392i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.12730e7 | − | 3.68458e7i | −0.105175 | − | 0.182169i | 0.808635 | − | 0.588311i | \(-0.200207\pi\) |
−0.913810 | + | 0.406142i | \(0.866874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.27111e7 | − | 2.94153e7i | 0.306901 | − | 0.143955i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.64051e8 | − | 2.67920e8i | 2.24804 | − | 1.29790i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.54553e6 | − | 1.48013e7i | 0.0409803 | − | 0.0709799i | −0.844808 | − | 0.535070i | \(-0.820285\pi\) |
0.885788 | + | 0.464090i | \(0.153619\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.45354e6 | − | 5.98171e6i | 0.0163951 | − | 0.0283971i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 5.68635e8i | − | 2.67246i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.39104e8 | + | 8.03116e7i | 0.647230 | + | 0.373678i | 0.787394 | − | 0.616450i | \(-0.211430\pi\) |
−0.140164 | + | 0.990128i | \(0.544763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.53421e6i | 0.00706740i | 0.999994 | + | 0.00353370i | \(0.00112481\pi\) | ||||
−0.999994 | + | 0.00353370i | \(0.998875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82952e6 | + | 1.63362e6i | −0.0129051 | + | 0.00745075i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.45913e7 | + | 7.72344e7i | 0.201365 | + | 0.348774i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.35483e7i | 0.284143i | 0.989856 | + | 0.142072i | \(0.0453764\pi\) | ||||
−0.989856 | + | 0.142072i | \(0.954624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.15762e6 | 0.00512524 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.30903e7 | + | 7.55771e6i | −0.0573888 | + | 0.0331334i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.29057e7 | − | 9.16354e7i | −0.229679 | − | 0.397815i | 0.728034 | − | 0.685541i | \(-0.240434\pi\) |
−0.957713 | + | 0.287726i | \(0.907101\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.27343e8 | 0.547456 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.32480e6 | − | 1.61510e7i | 0.0396994 | − | 0.0687614i | −0.845493 | − | 0.533987i | \(-0.820693\pi\) |
0.885192 | + | 0.465225i | \(0.154027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.32518e8 | 0.980356 | 0.490178 | − | 0.871622i | \(-0.336932\pi\) | ||||
0.490178 | + | 0.871622i | \(0.336932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.34638e7 | + | 3.08673e7i | 0.223247 | + | 0.128892i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.86137e7 | + | 1.07466e7i | 0.0769782 | + | 0.0444434i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.52841e7 | − | 1.47716e8i | −0.349324 | − | 0.605046i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.60475e8 | − | 3.20880e8i | −1.86811 | − | 1.30179i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.24069e8 | + | 7.16312e7i | −0.498553 | + | 0.287840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.44686e7 | + | 9.43425e7i | −0.216800 | + | 0.375508i | −0.953828 | − | 0.300354i | \(-0.902895\pi\) |
0.737028 | + | 0.675862i | \(0.236228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.09369e8 | + | 1.89432e8i | −0.431203 | + | 0.746866i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.22115e8i | 0.476922i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.60048e8 | − | 9.24040e7i | −0.619203 | − | 0.357497i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.91103e8i | 0.732427i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85786e8 | + | 1.64999e8i | −1.08509 | + | 0.626478i | −0.932266 | − | 0.361775i | \(-0.882171\pi\) |
−0.152827 | + | 0.988253i | \(0.548838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.05064e8 | − | 3.55181e8i | −0.771358 | − | 1.33603i | −0.936819 | − | 0.349815i | \(-0.886244\pi\) |
0.165461 | − | 0.986216i | \(-0.447089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.17784e7i | 0.304761i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.57074e8 | 0.579949 | 0.289975 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289975 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.82100e8 | + | 2.78341e8i | −1.76361 | + | 1.01822i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.11436e7 | + | 1.93013e7i | 0.0403908 | + | 0.0699589i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.03130e8 | 1.80693 | 0.903463 | − | 0.428665i | \(-0.141016\pi\) | ||||
0.903463 | + | 0.428665i | \(0.141016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.71740e7 | − | 1.16349e8i | 0.239044 | − | 0.414036i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.30222e8 | 0.811805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.96394e8 | + | 1.13388e8i | 0.686232 | + | 0.396197i | 0.802199 | − | 0.597057i | \(-0.203663\pi\) |
−0.115967 | + | 0.993253i | \(0.536997\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.36340e7 | + | 3.09656e7i | 0.185710 | + | 0.107220i | 0.589973 | − | 0.807423i | \(-0.299138\pi\) |
−0.404263 | + | 0.914643i | \(0.632472\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.05060e8 | − | 1.81969e8i | −0.360492 | − | 0.624391i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.51164e6 | − | 1.22145e7i | 0.0289433 | − | 0.0415347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.06819e6 | + | 1.77142e6i | −0.0103396 | + | 0.00596958i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.14886e8 | + | 3.72193e8i | −0.717678 | + | 1.24305i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.22493e8 | + | 7.31779e8i | −1.39846 | + | 2.42221i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.12478e8i | − | 1.68124i | −0.541624 | − | 0.840621i | \(-0.682190\pi\) | ||
0.541624 | − | 0.840621i | \(-0.317810\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.10812e8 | − | 6.39771e7i | −0.360308 | − | 0.208024i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.61035e8i | 0.841264i | 0.907231 | + | 0.420632i | \(0.138192\pi\) | ||||
−0.907231 | + | 0.420632i | \(0.861808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.47517e7 | + | 3.73844e7i | −0.206844 | + | 0.119421i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.96381e8 | − | 6.86552e8i | −1.25508 | − | 2.17386i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.68538e8i | 1.15670i | 0.815789 | + | 0.578350i | \(0.196303\pi\) | ||||
−0.815789 | + | 0.578350i | \(0.803697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.63758e7 | 0.237621 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.44219e8 | − | 1.41000e8i | 0.753199 | − | 0.434860i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.08986e7 | + | 8.81589e7i | 0.155614 | + | 0.269531i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.17534e7 | 0.278092 | 0.139046 | − | 0.990286i | \(-0.455596\pi\) | ||||
0.139046 | + | 0.990286i | \(0.455596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.11341e7 | − | 8.85668e7i | 0.153642 | − | 0.266116i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.23068e7 | −0.126025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.12278e8 | − | 1.22559e8i | −0.626913 | − | 0.361948i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.08887e8 | − | 1.20601e8i | −0.611617 | − | 0.353117i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.88928e8 | + | 3.27233e8i | 0.548457 | + | 0.949955i | 0.998381 | + | 0.0568880i | \(0.0181178\pi\) |
−0.449924 | + | 0.893067i | \(0.648549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.79564e8 | + | 1.31133e8i | −0.804665 | + | 0.377437i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.34374e7 | + | 7.75811e6i | −0.0383486 | + | 0.0221406i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.59454e7 | + | 6.22592e7i | −0.101715 | + | 0.176176i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.51715e8 | + | 4.35983e8i | −0.706269 | + | 1.22329i | 0.259963 | + | 0.965619i | \(0.416290\pi\) |
−0.966232 | + | 0.257675i | \(0.917044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.40825e7i | − | 0.178291i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.90706e7 | − | 3.41044e7i | −0.162968 | − | 0.0940896i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.29609e8i | 0.354582i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.74248e7 | + | 3.89277e7i | −0.182920 | + | 0.105609i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.59711e6 | − | 4.49833e6i | −0.00698722 | − | 0.0121022i | 0.862511 | − | 0.506039i | \(-0.168891\pi\) |
−0.869498 | + | 0.493937i | \(0.835557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.18496e7i | − | 0.111657i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.96988e8 | 1.84421 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.35926e6 | − | 3.67152e6i | 0.0166876 | − | 0.00963457i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.98308e7 | + | 1.20951e8i | 0.181737 | + | 0.314778i | 0.942472 | − | 0.334284i | \(-0.108495\pi\) |
−0.760735 | + | 0.649063i | \(0.775161\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.77063e8 | 1.48950 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.87063e7 | − | 1.36323e8i | 0.201492 | − | 0.348994i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.40120e8 | 0.355785 | 0.177893 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177893 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.64292e8 | − | 9.48542e7i | −0.413766 | − | 0.238888i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.93232e6 | − | 3.42503e6i | −0.0148191 | − | 0.00855581i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.14793e8 | + | 1.98828e8i | 0.284435 | + | 0.492656i | 0.972472 | − | 0.233020i | \(-0.0748607\pi\) |
−0.688037 | + | 0.725676i | \(0.741527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.92329e8 | − | 4.10030e8i | −0.472705 | − | 1.00777i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.24945e8 | + | 1.29872e8i | −0.548415 | + | 0.316627i | −0.748482 | − | 0.663155i | \(-0.769217\pi\) |
0.200068 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.06583e8 | − | 1.84607e8i | 0.257762 | − | 0.446458i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.60038e8 | + | 2.77194e8i | −0.383938 | + | 0.665000i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.29764e7i | − | 0.0784798i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.17994e8 | + | 2.99064e8i | 1.22294 | + | 0.706064i | 0.965543 | − | 0.260242i | \(-0.0838023\pi\) |
0.257396 | + | 0.966306i | \(0.417136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 64747.2i | 0.000151648i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.71765e8 | + | 9.91686e7i | −0.399111 | + | 0.230427i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.04726e8 | − | 5.27801e8i | −0.702460 | − | 1.21670i | −0.967600 | − | 0.252486i | \(-0.918752\pi\) |
0.265141 | − | 0.964210i | \(-0.414582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.52674e8i | 1.26399i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.84676e7 | 0.0872853 | 0.0436427 | − | 0.999047i | \(-0.486104\pi\) | ||||
0.0436427 | + | 0.999047i | \(0.486104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.04226e7 | + | 1.75645e7i | −0.0684894 | + | 0.0395424i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.10744e7 | − | 1.05784e8i | −0.136419 | − | 0.236285i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.49210e8 | −0.995550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.50076e7 | − | 7.79555e7i | 0.0989708 | − | 0.171423i | −0.812288 | − | 0.583256i | \(-0.801778\pi\) |
0.911259 | + | 0.411834i | \(0.135112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.30842e8 | −1.15825 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.41164e8 | + | 8.15009e7i | 0.305622 | + | 0.176451i | 0.644966 | − | 0.764211i | \(-0.276872\pi\) |
−0.339344 | + | 0.940662i | \(0.610205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.22432e8 | + | 7.06863e7i | 0.263021 | + | 0.151855i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.96778e7 | − | 8.60444e7i | −0.105901 | − | 0.183425i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.33468e8 | − | 3.02060e8i | −0.916947 | − | 0.638971i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.46984e8 | + | 2.00331e8i | −0.728377 | + | 0.420529i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.39719e6 | − | 4.15206e6i | 0.00499365 | − | 0.00864925i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.22240e7 | + | 1.07775e8i | −0.128632 | + | 0.222797i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.78169e8i | 0.570670i | 0.958428 | + | 0.285335i | \(0.0921049\pi\) | ||||
−0.958428 | + | 0.285335i | \(0.907895\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.91863e8 | − | 2.83977e8i | −1.00141 | − | 0.578166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.42979e7i | 0.129917i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.90503e8 | + | 3.40927e8i | −1.18414 | + | 0.683663i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.22482e7 | + | 9.04966e7i | 0.103985 | + | 0.180107i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.74509e8i | − | 1.33233i | −0.745803 | − | 0.666167i | \(-0.767934\pi\) | ||
0.745803 | − | 0.666167i | \(-0.232066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.98666e7 | 0.0585526 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.29175e8 | − | 1.90049e8i | 0.640514 | − | 0.369801i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.41340e8 | + | 4.18014e8i | 0.466104 | + | 0.807316i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.46602e7 | −0.0281029 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.23208e8 | − | 1.25263e9i | 1.37608 | − | 2.38344i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.15571e8 | 0.596008 | 0.298004 | − | 0.954565i | \(-0.403679\pi\) | ||||
0.298004 | + | 0.954565i | \(0.403679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.08837e8 | + | 4.09247e8i | 1.32887 | + | 0.767226i | 0.985126 | − | 0.171836i | \(-0.0549699\pi\) |
0.343749 | + | 0.939062i | \(0.388303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.74015e8 | + | 3.89143e8i | 1.25429 | + | 0.724165i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.17939e8 | − | 2.04277e8i | −0.217864 | − | 0.377351i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.93981e8 | − | 2.78369e8i | 0.355707 | − | 0.510452i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.14683e7 | − | 4.12623e7i | 0.130095 | − | 0.0751106i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.16362e8 | − | 2.01544e8i | 0.210272 | − | 0.364201i | −0.741528 | − | 0.670922i | \(-0.765899\pi\) |
0.951799 | + | 0.306721i | \(0.0992319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.52096e8 | + | 4.36643e8i | −0.452237 | + | 0.783297i | −0.998525 | − | 0.0543002i | \(-0.982707\pi\) |
0.546288 | + | 0.837598i | \(0.316041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.14550e9i | − | 2.04001i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.95537e7 | + | 5.17038e7i | 0.158331 | + | 0.0914126i | 0.577072 | − | 0.816693i | \(-0.304195\pi\) |
−0.418741 | + | 0.908106i | \(0.637528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.55442e8i | − | 0.448362i | −0.974547 | − | 0.224181i | \(-0.928029\pi\) | ||
0.974547 | − | 0.224181i | \(-0.0719708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.36631e8 | + | 7.88839e7i | −0.238093 | + | 0.137463i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.82582e8 | + | 3.16241e8i | 0.315880 | + | 0.547120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.12978e8i | − | 0.365826i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.23043e7 | 0.157415 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.35755e8 | − | 3.67053e8i | 1.07647 | − | 0.621503i | 0.146531 | − | 0.989206i | \(-0.453189\pi\) |
0.929943 | + | 0.367703i | \(0.119856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.97274e8 | − | 5.14894e8i | −0.499769 | − | 0.865625i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.97115e8 | −0.996725 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.50222e7 | − | 7.79808e7i | 0.0746202 | − | 0.129246i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.19053e8 | 0.195925 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.33873e9 | + | 7.72916e8i | 2.18761 | + | 1.26302i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.63335e8 | + | 1.52036e8i | 0.427287 | + | 0.246694i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.27815e8 | + | 3.94587e8i | 0.367058 | + | 0.635764i | 0.989104 | − | 0.147217i | \(-0.0470316\pi\) |
−0.622046 | + | 0.782981i | \(0.713698\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.11807e8 | − | 2.38363e8i | −0.178883 | − | 0.381364i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.13199e8 | + | 6.53558e7i | −0.179847 | + | 0.103834i | −0.587221 | − | 0.809427i | \(-0.699778\pi\) |
0.407374 | + | 0.913261i | \(0.366445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.48931e8 | − | 2.57956e8i | 0.234966 | − | 0.406974i | −0.724297 | − | 0.689489i | \(-0.757835\pi\) |
0.959263 | + | 0.282515i | \(0.0911687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.49972e7 | − | 1.47219e8i | 0.133167 | − | 0.230651i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.27524e7i | 0.0820748i | 0.999158 | + | 0.0410374i | \(0.0130663\pi\) | ||||
−0.999158 | + | 0.0410374i | \(0.986934\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.12764e8 | − | 1.80574e8i | −0.483246 | − | 0.279002i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.74445e8i | − | 0.881436i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.16354e8 | − | 6.71771e7i | 0.177306 | − | 0.102368i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.76380e6 | − | 4.78704e6i | −0.00418265 | − | 0.00724457i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.32226e9i | 1.98734i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.42999e7 | 0.0959812 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.37532e8 | − | 4.83549e8i | 1.24166 | − | 0.716873i | 0.272228 | − | 0.962233i | \(-0.412240\pi\) |
0.969432 | + | 0.245360i | \(0.0789062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.24149e8 | − | 2.15032e8i | −0.182800 | − | 0.316619i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00050e8 | 1.31625 | 0.658126 | − | 0.752908i | \(-0.271350\pi\) | ||||
0.658126 | + | 0.752908i | \(0.271350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.37516e8 | − | 5.84595e8i | 0.490244 | − | 0.849127i | −0.509693 | − | 0.860356i | \(-0.670241\pi\) |
0.999937 | + | 0.0112289i | \(0.00357435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.61121e8 | −0.665251 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.06508e9 | − | 6.14925e8i | −1.52620 | − | 0.881152i | −0.999517 | − | 0.0310913i | \(-0.990102\pi\) |
−0.526684 | − | 0.850061i | \(-0.676565\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41175e8 | + | 8.15077e7i | 0.200934 | + | 0.116009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.18552e8 | + | 5.51748e8i | 0.450347 | + | 0.780024i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.41427e7 | + | 5.46578e6i | 0.0900726 | + | 0.00767535i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.46734e8 | − | 2.00187e8i | 0.483646 | − | 0.279233i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.22988e8 | + | 3.86227e8i | −0.308962 | + | 0.535137i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.64859e6 | + | 4.58749e6i | −0.00364531 | + | 0.00631387i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.01142e8i | − | 0.274997i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.45430e7 | + | 5.45845e7i | 0.128400 | + | 0.0741320i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17715e8i | 0.158813i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.20201e8 | − | 4.15808e8i | 0.965232 | − | 0.557277i | 0.0674529 | − | 0.997722i | \(-0.478513\pi\) |
0.897779 | + | 0.440445i | \(0.145179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.35679e8 | + | 1.10103e9i | 0.846343 | + | 1.46591i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.31322e8i | − | 0.835017i | −0.908673 | − | 0.417509i | \(-0.862903\pi\) | ||
0.908673 | − | 0.417509i | \(-0.137097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.71065e8 | −0.881764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.06162e8 | + | 3.49968e8i | −0.791271 | + | 0.456840i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.96729e7 | − | 1.55318e8i | −0.116293 | − | 0.201425i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.18008e9 | −1.52042 | −0.760210 | − | 0.649677i | \(-0.774904\pi\) | ||||
−0.760210 | + | 0.649677i | \(0.774904\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.12047e8 | + | 1.40651e9i | −1.03945 | + | 1.80037i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.23312e8 | −0.411165 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.45799e8 | − | 3.15117e8i | −0.689617 | − | 0.398150i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.40939e8 | − | 3.70046e8i | −0.804595 | − | 0.464533i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.14268e8 | + | 1.97918e8i | 0.142521 | + | 0.246853i | 0.928445 | − | 0.371469i | \(-0.121146\pi\) |
−0.785925 | + | 0.618322i | \(0.787813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.34245e8 | + | 7.12584e8i | 0.414206 | + | 0.883053i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.97028e9 | + | 1.13754e9i | −2.42595 | + | 1.40062i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.28048e8 | − | 2.21785e8i | 0.156652 | − | 0.271330i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.36761e7 | + | 1.62252e8i | −0.113870 | + | 0.197229i | −0.917328 | − | 0.398133i | \(-0.869658\pi\) |
0.803457 | + | 0.595362i | \(0.202991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.92057e8i | 0.835882i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.27110e9 | − | 7.33870e8i | −1.52550 | − | 0.880745i | −0.999543 | − | 0.0302318i | \(-0.990375\pi\) |
−0.525953 | − | 0.850514i | \(-0.676291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.20260e8i | 0.620419i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.71811e7 | − | 9.91953e6i | 0.0203590 | − | 0.0117543i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.11295e8 | − | 1.40520e9i | −0.955276 | − | 1.65459i | −0.733736 | − | 0.679435i | \(-0.762225\pi\) |
−0.221540 | − | 0.975151i | \(-0.571108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.89495e8i | 0.455726i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.65874e8 | 0.309126 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.24323e8 | + | 4.18188e8i | −0.836861 | + | 0.483162i | −0.856196 | − | 0.516651i | \(-0.827178\pi\) |
0.0193350 | + | 0.999813i | \(0.493845\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.64384e8 | + | 2.84722e8i | 0.188734 | + | 0.326897i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.29213e7 | 0.0489708 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.09784e7 | − | 8.82971e7i | 0.0578003 | − | 0.100113i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.85519e8 | 0.885089 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.05044e8 | − | 2.91587e8i | −0.565523 | − | 0.326505i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.96599e7 | + | 3.44447e7i | 0.0663897 | + | 0.0383301i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.70384e8 | − | 1.33434e9i | −0.851977 | − | 1.47567i | −0.879421 | − | 0.476045i | \(-0.842070\pi\) |
0.0274439 | − | 0.999623i | \(-0.491263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.59800e7 | + | 8.91649e8i | −0.0835080 | + | 0.979993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.88684e8 | − | 5.70817e8i | 1.07994 | − | 0.623504i | 0.149060 | − | 0.988828i | \(-0.452375\pi\) |
0.930880 | + | 0.365324i | \(0.119042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.82384e7 | + | 4.89104e7i | −0.0306551 | + | 0.0530961i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.62175e8 | − | 8.00511e8i | 0.498647 | − | 0.863681i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.74801e8i | 0.509129i | 0.967056 | + | 0.254565i | \(0.0819322\pi\) | ||||
−0.967056 | + | 0.254565i | \(0.918068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.90142e8 | + | 3.98454e8i | 0.735513 | + | 0.424649i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.21243e8i | 0.658043i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.92307e8 | + | 2.26498e8i | −0.413014 | + | 0.238454i | −0.692084 | − | 0.721817i | \(-0.743307\pi\) |
0.279070 | + | 0.960271i | \(0.409974\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.63501e8 | + | 4.56397e8i | 0.275723 | + | 0.477567i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.07131e7i | 0.0215424i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.34106e8 | −0.345379 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.41754e8 | + | 1.97312e8i | −0.351150 | + | 0.202737i | −0.665192 | − | 0.746673i | \(-0.731650\pi\) |
0.314041 | + | 0.949409i | \(0.398317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.13980e8 | + | 8.90240e8i | 0.524927 | + | 0.909200i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.59256e8 | 0.567730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.07065e8 | + | 1.57108e9i | −0.915278 | + | 1.58531i | −0.108783 | + | 0.994066i | \(0.534695\pi\) |
−0.806494 | + | 0.591242i | \(0.798638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.11490e8 | −0.412727 |
(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 | 76.7.h.a.69.9 | yes | 20 | |
3.2 | odd | 2 | 684.7.y.c.145.4 | 20 | |||
19.8 | odd | 6 | inner | 76.7.h.a.65.9 | ✓ | 20 | |
57.8 | even | 6 | 684.7.y.c.217.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.h.a.65.9 | ✓ | 20 | 19.8 | odd | 6 | inner | |
76.7.h.a.69.9 | yes | 20 | 1.1 | even | 1 | trivial | |
684.7.y.c.145.4 | 20 | 3.2 | odd | 2 | |||
684.7.y.c.217.4 | 20 | 57.8 | even | 6 |