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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 30x^{14} + 619x^{12} + 5604x^{10} + 40971x^{8} - 4866x^{6} + 568069x^{4} - 7909632x^{2} + 20340100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{32}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.12 | ||
Root | \(1.73205 + 3.22829i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.b.107.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.82945 | + | 4.16357i | 0.676958 | + | 0.736022i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.67058 | + | 31.8884i | −0.0834557 | + | 0.996511i | ||||
\(5\) | − | 46.0468i | − | 0.823709i | −0.911250 | − | 0.411855i | \(-0.864881\pi\) | ||
0.911250 | − | 0.411855i | \(-0.135119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 134.772i | − | 1.03957i | −0.854297 | − | 0.519785i | \(-0.826012\pi\) | ||
0.854297 | − | 0.519785i | \(-0.173988\pi\) | |||||||
\(8\) | −142.996 | + | 110.996i | −0.789950 | + | 0.613171i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 191.719 | − | 176.334i | 0.606268 | − | 0.557617i | ||||
\(11\) | −471.524 | −1.17496 | −0.587479 | − | 0.809239i | \(-0.699880\pi\) | ||||
−0.587479 | + | 0.809239i | \(0.699880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −987.091 | −1.61994 | −0.809970 | − | 0.586471i | \(-0.800517\pi\) | ||||
−0.809970 | + | 0.586471i | \(0.800517\pi\) | |||||||
\(14\) | 561.131 | − | 516.102i | 0.765146 | − | 0.703745i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1009.74 | − | 170.321i | −0.986070 | − | 0.166329i | ||||
\(17\) | − | 1467.20i | − | 1.23131i | −0.788016 | − | 0.615654i | \(-0.788892\pi\) | ||
0.788016 | − | 0.615654i | \(-0.211108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 308.416i | − | 0.195999i | −0.995186 | − | 0.0979994i | \(-0.968756\pi\) | ||
0.995186 | − | 0.0979994i | \(-0.0312443\pi\) | |||||||
\(20\) | 1468.36 | + | 122.972i | 0.820836 | + | 0.0687432i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1805.68 | − | 1963.22i | −0.795397 | − | 0.864795i | ||||
\(23\) | 2118.55 | 0.835062 | 0.417531 | − | 0.908663i | \(-0.362896\pi\) | ||||
0.417531 | + | 0.908663i | \(0.362896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1004.70 | 0.321503 | ||||||||
\(26\) | −3780.02 | − | 4109.82i | −1.09663 | − | 1.19231i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4297.65 | + | 359.919i | 1.03594 | + | 0.0867580i | ||||
\(29\) | − | 5196.05i | − | 1.14730i | −0.819100 | − | 0.573651i | \(-0.805526\pi\) | ||
0.819100 | − | 0.573651i | \(-0.194474\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6363.26i | 1.18926i | 0.804001 | + | 0.594628i | \(0.202701\pi\) | ||||
−0.804001 | + | 0.594628i | \(0.797299\pi\) | |||||||
\(32\) | −3157.59 | − | 4856.34i | −0.545106 | − | 0.838367i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6108.79 | − | 5618.57i | 0.906270 | − | 0.833544i | ||||
\(35\) | −6205.80 | −0.856304 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8747.55 | −1.05047 | −0.525233 | − | 0.850958i | \(-0.676022\pi\) | ||||
−0.525233 | + | 0.850958i | \(0.676022\pi\) | |||||||
\(38\) | 1284.11 | − | 1181.07i | 0.144259 | − | 0.132683i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5111.00 | + | 6584.51i | 0.505075 | + | 0.650689i | ||||
\(41\) | − | 1393.48i | − | 0.129462i | −0.997903 | − | 0.0647308i | \(-0.979381\pi\) | ||
0.997903 | − | 0.0647308i | \(-0.0206189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9414.92i | 0.776508i | 0.921552 | + | 0.388254i | \(0.126922\pi\) | ||||
−0.921552 | + | 0.388254i | \(0.873078\pi\) | |||||||
\(44\) | 1259.24 | − | 15036.1i | 0.0980569 | − | 1.17086i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8112.88 | + | 8820.71i | 0.565302 | + | 0.614623i | ||||
\(47\) | 11122.7 | 0.734454 | 0.367227 | − | 0.930131i | \(-0.380307\pi\) | ||||
0.367227 | + | 0.930131i | \(0.380307\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1356.43 | −0.0807064 | ||||||||
\(50\) | 3847.44 | + | 4183.12i | 0.217644 | + | 0.236633i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2636.11 | − | 31476.7i | 0.135193 | − | 1.61429i | ||||
\(53\) | − | 28464.4i | − | 1.39191i | −0.718084 | − | 0.695957i | \(-0.754981\pi\) | ||
0.718084 | − | 0.695957i | \(-0.245019\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21712.2i | 0.967824i | ||||||||
\(56\) | 14959.1 | + | 19271.9i | 0.637435 | + | 0.821209i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 21634.1 | − | 19898.0i | 0.844439 | − | 0.776676i | ||||
\(59\) | −15062.9 | −0.563351 | −0.281676 | − | 0.959510i | \(-0.590890\pi\) | ||||
−0.281676 | + | 0.959510i | \(0.590890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37841.4 | −1.30209 | −0.651047 | − | 0.759037i | \(-0.725670\pi\) | ||||
−0.651047 | + | 0.759037i | \(0.725670\pi\) | |||||||
\(62\) | −26493.9 | + | 24367.8i | −0.875319 | + | 0.805077i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8127.84 | − | 31744.0i | 0.248042 | − | 0.968749i | ||||
\(65\) | 45452.3i | 1.33436i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65223.3i | 1.77507i | 0.460740 | + | 0.887535i | \(0.347584\pi\) | ||||
−0.460740 | + | 0.887535i | \(0.652416\pi\) | |||||||
\(68\) | 46786.6 | + | 3918.28i | 1.22701 | + | 0.102760i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −23764.8 | − | 25838.3i | −0.579682 | − | 0.630258i | ||||
\(71\) | −9860.03 | −0.232131 | −0.116065 | − | 0.993242i | \(-0.537028\pi\) | ||||
−0.116065 | + | 0.993242i | \(0.537028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −54858.1 | −1.20485 | −0.602426 | − | 0.798175i | \(-0.705799\pi\) | ||||
−0.602426 | + | 0.798175i | \(0.705799\pi\) | |||||||
\(74\) | −33498.3 | − | 36421.0i | −0.711122 | − | 0.773166i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9834.89 | + | 823.651i | 0.195315 | + | 0.0163572i | ||||
\(77\) | 63548.2i | 1.22145i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 91648.1i | − | 1.65217i | −0.563543 | − | 0.826087i | \(-0.690562\pi\) | ||
0.563543 | − | 0.826087i | \(-0.309438\pi\) | |||||||
\(80\) | −7842.73 | + | 46495.1i | −0.137007 | + | 0.812235i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5801.85 | − | 5336.27i | 0.0952866 | − | 0.0876401i | ||||
\(83\) | 45138.1 | 0.719197 | 0.359598 | − | 0.933107i | \(-0.382914\pi\) | ||||
0.359598 | + | 0.933107i | \(0.382914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −67559.8 | −1.01424 | ||||||||
\(86\) | −39199.7 | + | 36054.0i | −0.571526 | + | 0.525663i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 67426.2 | − | 52337.3i | 0.928158 | − | 0.720451i | ||||
\(89\) | 73149.6i | 0.978896i | 0.872032 | + | 0.489448i | \(0.162802\pi\) | ||||
−0.872032 | + | 0.489448i | \(0.837198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133032.i | 1.68404i | ||||||||
\(92\) | −5657.75 | + | 67557.0i | −0.0696906 | + | 0.832148i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 42593.8 | + | 46310.0i | 0.497194 | + | 0.540574i | ||||
\(95\) | −14201.6 | −0.161446 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11422.1 | −0.123259 | −0.0616293 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616293 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(98\) | −5194.40 | − | 5647.60i | −0.0546349 | − | 0.0594017i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2683.12 | + | 32038.1i | −0.0268312 | + | 0.320381i | ||||
\(101\) | − | 78611.4i | − | 0.766800i | −0.923582 | − | 0.383400i | \(-0.874753\pi\) | ||
0.923582 | − | 0.383400i | \(-0.125247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 101937.i | 0.946758i | 0.880859 | + | 0.473379i | \(0.156966\pi\) | ||||
−0.880859 | + | 0.473379i | \(0.843034\pi\) | |||||||
\(104\) | 141150. | − | 109563.i | 1.27967 | − | 0.993301i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 118513. | − | 109003.i | 1.02448 | − | 0.942267i | ||||
\(107\) | 135660. | 1.14550 | 0.572748 | − | 0.819731i | \(-0.305877\pi\) | ||||
0.572748 | + | 0.819731i | \(0.305877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 225285. | 1.81621 | 0.908106 | − | 0.418741i | \(-0.137529\pi\) | ||||
0.908106 | + | 0.418741i | \(0.137529\pi\) | |||||||
\(110\) | −90400.1 | + | 83145.7i | −0.712340 | + | 0.655176i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −22954.5 | + | 136084.i | −0.172911 | + | 1.02509i | ||||
\(113\) | 59823.0i | 0.440730i | 0.975418 | + | 0.220365i | \(0.0707248\pi\) | ||||
−0.975418 | + | 0.220365i | \(0.929275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 97552.2i | − | 0.687848i | ||||||
\(116\) | 165693. | + | 13876.5i | 1.14330 | + | 0.0957489i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −57682.8 | − | 62715.5i | −0.381365 | − | 0.414639i | ||||
\(119\) | −197737. | −1.28003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 61284.2 | 0.380527 | ||||||||
\(122\) | −144912. | − | 157555.i | −0.881463 | − | 0.958369i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −202914. | − | 16993.6i | −1.18511 | − | 0.0992502i | ||||
\(125\) | − | 190159.i | − | 1.08853i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 75992.2i | − | 0.418080i | −0.977907 | − | 0.209040i | \(-0.932966\pi\) | ||
0.977907 | − | 0.209040i | \(-0.0670339\pi\) | |||||||
\(128\) | 163293. | − | 87721.3i | 0.880934 | − | 0.473238i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −189244. | + | 174058.i | −0.982118 | + | 0.903306i | ||||
\(131\) | −371533. | −1.89156 | −0.945778 | − | 0.324815i | \(-0.894698\pi\) | ||||
−0.945778 | + | 0.324815i | \(0.894698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −41565.8 | −0.203754 | ||||||||
\(134\) | −271561. | + | 249769.i | −1.30649 | + | 1.20165i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 162853. | + | 209804.i | 0.755003 | + | 0.972672i | ||||
\(137\) | − | 389370.i | − | 1.77240i | −0.463304 | − | 0.886199i | \(-0.653336\pi\) | ||
0.463304 | − | 0.886199i | \(-0.346664\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 104310.i | − | 0.457918i | −0.973436 | − | 0.228959i | \(-0.926468\pi\) | ||
0.973436 | − | 0.228959i | \(-0.0735322\pi\) | |||||||
\(140\) | 16573.1 | − | 197893.i | 0.0714634 | − | 0.853317i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −37758.5 | − | 41052.9i | −0.157143 | − | 0.170853i | ||||
\(143\) | 465438. | 1.90336 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −239261. | −0.945044 | ||||||||
\(146\) | −210077. | − | 228405.i | −0.815634 | − | 0.886797i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23361.1 | − | 278945.i | 0.0876674 | − | 1.04680i | ||||
\(149\) | 227251.i | 0.838570i | 0.907855 | + | 0.419285i | \(0.137719\pi\) | ||||
−0.907855 | + | 0.419285i | \(0.862281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 488350.i | − | 1.74296i | −0.490427 | − | 0.871482i | \(-0.663159\pi\) | ||
0.490427 | − | 0.871482i | \(-0.336841\pi\) | |||||||
\(152\) | 34232.9 | + | 44102.4i | 0.120181 | + | 0.154829i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −264587. | + | 243355.i | −0.899015 | + | 0.826872i | ||||
\(155\) | 293008. | 0.979602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 307615. | 0.995998 | 0.497999 | − | 0.867178i | \(-0.334068\pi\) | ||||
0.497999 | + | 0.867178i | \(0.334068\pi\) | |||||||
\(158\) | 381583. | − | 350962.i | 1.21604 | − | 1.11845i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −223619. | + | 145397.i | −0.690571 | + | 0.449009i | ||||
\(161\) | − | 285520.i | − | 0.868105i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 409730.i | − | 1.20789i | −0.797024 | − | 0.603947i | \(-0.793594\pi\) | ||
0.797024 | − | 0.603947i | \(-0.206406\pi\) | |||||||
\(164\) | 44435.8 | + | 3721.40i | 0.129010 | + | 0.0108043i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 172854. | + | 187935.i | 0.486866 | + | 0.529344i | ||||
\(167\) | −107694. | −0.298814 | −0.149407 | − | 0.988776i | \(-0.547736\pi\) | ||||
−0.149407 | + | 0.988776i | \(0.547736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 603056. | 1.62421 | ||||||||
\(170\) | −258717. | − | 281290.i | −0.686598 | − | 0.746503i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −300227. | − | 25143.3i | −0.773799 | − | 0.0648040i | ||||
\(173\) | 299962.i | 0.761994i | 0.924576 | + | 0.380997i | \(0.124419\pi\) | ||||
−0.924576 | + | 0.380997i | \(0.875581\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 135405.i | − | 0.334225i | ||||||
\(176\) | 476115. | + | 80310.5i | 1.15859 | + | 0.195430i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −304563. | + | 280123.i | −0.720489 | + | 0.662672i | ||||
\(179\) | −539891. | −1.25943 | −0.629714 | − | 0.776827i | \(-0.716828\pi\) | ||||
−0.629714 | + | 0.776827i | \(0.716828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25867.6 | 0.0586894 | 0.0293447 | − | 0.999569i | \(-0.490658\pi\) | ||||
0.0293447 | + | 0.999569i | \(0.490658\pi\) | |||||||
\(182\) | −553888. | + | 509440.i | −1.23949 | + | 1.14003i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −302944. | + | 235150.i | −0.659657 | + | 0.512036i | ||||
\(185\) | 402796.i | 0.865279i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 691821.i | 1.44674i | ||||||||
\(188\) | −29704.0 | + | 354684.i | −0.0612943 | + | 0.731892i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −54384.2 | − | 59129.2i | −0.109292 | − | 0.118828i | ||||
\(191\) | 519499. | 1.03039 | 0.515194 | − | 0.857073i | \(-0.327720\pi\) | ||||
0.515194 | + | 0.857073i | \(0.327720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 259328. | 0.501137 | 0.250569 | − | 0.968099i | \(-0.419382\pi\) | ||||
0.250569 | + | 0.968099i | \(0.419382\pi\) | |||||||
\(194\) | −43740.5 | − | 47556.8i | −0.0834410 | − | 0.0907211i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3622.46 | − | 43254.4i | 0.00673541 | − | 0.0804249i | ||||
\(197\) | − | 372151.i | − | 0.683209i | −0.939844 | − | 0.341604i | \(-0.889030\pi\) | ||
0.939844 | − | 0.341604i | \(-0.110970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2717.29i | − | 0.00486412i | −0.999997 | − | 0.00243206i | \(-0.999226\pi\) | ||
0.999997 | − | 0.00243206i | \(-0.000774149\pi\) | |||||||
\(200\) | −143668. | + | 111517.i | −0.253971 | + | 0.197136i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 327304. | − | 301039.i | 0.564382 | − | 0.519092i | ||||
\(203\) | −700280. | −1.19270 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −64165.2 | −0.106639 | ||||||||
\(206\) | −424422. | + | 390363.i | −0.696835 | + | 0.640916i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 996702. | + | 168122.i | 1.59737 | + | 0.269443i | ||||
\(209\) | 145426.i | 0.230290i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 693979.i | − | 1.07310i | −0.843868 | − | 0.536550i | \(-0.819727\pi\) | ||
0.843868 | − | 0.536550i | \(-0.180273\pi\) | |||||||
\(212\) | 907683. | + | 76016.5i | 1.38706 | + | 0.116163i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 519505. | + | 564832.i | 0.775453 | + | 0.843110i | ||||
\(215\) | 433527. | 0.639617 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 857588. | 1.23632 | ||||||||
\(218\) | 862719. | + | 937990.i | 1.22950 | + | 1.33677i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −692366. | − | 57984.1i | −0.964448 | − | 0.0807704i | ||||
\(221\) | 1.44826e6i | 1.99465i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 609819.i | 0.821180i | 0.911820 | + | 0.410590i | \(0.134677\pi\) | ||||
−0.911820 | + | 0.410590i | \(0.865323\pi\) | |||||||
\(224\) | −654498. | + | 425555.i | −0.871541 | + | 0.566676i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −249077. | + | 229089.i | −0.324387 | + | 0.298356i | ||||
\(227\) | 165538. | 0.213223 | 0.106611 | − | 0.994301i | \(-0.466000\pi\) | ||||
0.106611 | + | 0.994301i | \(0.466000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −793320. | −0.999677 | −0.499839 | − | 0.866119i | \(-0.666607\pi\) | ||||
−0.499839 | + | 0.866119i | \(0.666607\pi\) | |||||||
\(230\) | 406165. | − | 373572.i | 0.506271 | − | 0.465644i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 576740. | + | 743015.i | 0.703493 | + | 0.906312i | ||||
\(233\) | − | 523254.i | − | 0.631426i | −0.948855 | − | 0.315713i | \(-0.897756\pi\) | ||
0.948855 | − | 0.315713i | \(-0.102244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 512163.i | − | 0.604977i | ||||||
\(236\) | 40226.8 | − | 480332.i | 0.0470149 | − | 0.561386i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −757225. | − | 823292.i | −0.866528 | − | 0.942131i | ||||
\(239\) | −521703. | −0.590784 | −0.295392 | − | 0.955376i | \(-0.595450\pi\) | ||||
−0.295392 | + | 0.955376i | \(0.595450\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.08959e6 | −1.20842 | −0.604212 | − | 0.796824i | \(-0.706512\pi\) | ||||
−0.604212 | + | 0.796824i | \(0.706512\pi\) | |||||||
\(242\) | 234685. | + | 255161.i | 0.257601 | + | 0.280076i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 101058. | − | 1.20670e6i | 0.108667 | − | 1.29755i | ||||
\(245\) | 62459.3i | 0.0664786i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 304435.i | 0.317506i | ||||||||
\(248\) | −706296. | − | 909923.i | −0.729218 | − | 0.939453i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 791740. | − | 728205.i | 0.801185 | − | 0.736892i | ||||
\(251\) | 1.15105e6 | 1.15321 | 0.576606 | − | 0.817022i | \(-0.304377\pi\) | ||||
0.576606 | + | 0.817022i | \(0.304377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −998947. | −0.981162 | ||||||||
\(254\) | 316399. | − | 291008.i | 0.307716 | − | 0.283023i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 990558. | + | 343958.i | 0.944669 | + | 0.328024i | ||||
\(257\) | 1.26233e6i | 1.19218i | 0.802918 | + | 0.596090i | \(0.203280\pi\) | ||||
−0.802918 | + | 0.596090i | \(0.796720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.17892e6i | 1.09203i | ||||||||
\(260\) | −1.44940e6 | − | 121384.i | −1.32970 | − | 0.111360i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.42277e6 | − | 1.54690e6i | −1.28050 | − | 1.39223i | ||||
\(263\) | 243029. | 0.216655 | 0.108328 | − | 0.994115i | \(-0.465450\pi\) | ||||
0.108328 | + | 0.994115i | \(0.465450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.31069e6 | −1.14653 | ||||||||
\(266\) | −159174. | − | 173062.i | −0.137933 | − | 0.149968i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.07986e6 | − | 174184.i | −1.76888 | − | 0.148140i | ||||
\(269\) | − | 813756.i | − | 0.685667i | −0.939396 | − | 0.342834i | \(-0.888613\pi\) | ||
0.939396 | − | 0.342834i | \(-0.111387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.85687e6i | 1.53589i | 0.640518 | + | 0.767943i | \(0.278720\pi\) | ||||
−0.640518 | + | 0.767943i | \(0.721280\pi\) | |||||||
\(272\) | −249895. | + | 1.48148e6i | −0.204802 | + | 1.21416i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.62117e6 | − | 1.49108e6i | 1.30452 | − | 1.19984i | ||||
\(275\) | −473739. | −0.377752 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 634180. | 0.496607 | 0.248304 | − | 0.968682i | \(-0.420127\pi\) | ||||
0.248304 | + | 0.968682i | \(0.420127\pi\) | |||||||
\(278\) | 434301. | − | 399449.i | 0.337038 | − | 0.309991i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 887406. | − | 688818.i | 0.676437 | − | 0.525061i | ||||
\(281\) | − | 2.12892e6i | − | 1.60840i | −0.594361 | − | 0.804198i | \(-0.702595\pi\) | ||
0.594361 | − | 0.804198i | \(-0.297405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.03774e6i | − | 0.770234i | −0.922868 | − | 0.385117i | \(-0.874161\pi\) | ||
0.922868 | − | 0.385117i | \(-0.125839\pi\) | |||||||
\(284\) | 26332.0 | − | 314420.i | 0.0193726 | − | 0.231321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.78237e6 | + | 1.93788e6i | 1.28850 | + | 1.40092i | ||||
\(287\) | −187802. | −0.134584 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −732819. | −0.516121 | ||||||||
\(290\) | −916239. | − | 996179.i | −0.639755 | − | 0.695573i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 146503. | − | 1.74934e6i | 0.100552 | − | 1.20065i | ||||
\(293\) | − | 2.07720e6i | − | 1.41354i | −0.707442 | − | 0.706771i | \(-0.750151\pi\) | ||
0.707442 | − | 0.706771i | \(-0.249849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 693599.i | 0.464038i | ||||||||
\(296\) | 1.25087e6 | − | 970942.i | 0.829816 | − | 0.644116i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −946173. | + | 870246.i | −0.617206 | + | 0.567677i | ||||
\(299\) | −2.09120e6 | −1.35275 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26887e6 | 0.807234 | ||||||||
\(302\) | 2.03328e6 | − | 1.87011e6i | 1.28286 | − | 1.17991i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −52529.8 | + | 311419.i | −0.0326003 | + | 0.193269i | ||||
\(305\) | 1.74247e6i | 1.07255i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 277720.i | 0.168175i | 0.996458 | + | 0.0840876i | \(0.0267976\pi\) | ||||
−0.996458 | + | 0.0840876i | \(0.973202\pi\) | |||||||
\(308\) | −2.02645e6 | − | 169711.i | −1.21719 | − | 0.101937i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.12206e6 | + | 1.21996e6i | 0.663149 | + | 0.721008i | ||||
\(311\) | 752701. | 0.441287 | 0.220644 | − | 0.975354i | \(-0.429184\pi\) | ||||
0.220644 | + | 0.975354i | \(0.429184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.71292e6 | −0.988274 | −0.494137 | − | 0.869384i | \(-0.664516\pi\) | ||||
−0.494137 | + | 0.869384i | \(0.664516\pi\) | |||||||
\(314\) | 1.17800e6 | + | 1.28078e6i | 0.674249 | + | 0.733076i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.92251e6 | + | 244754.i | 1.64641 | + | 0.137883i | ||||
\(317\) | − | 738922.i | − | 0.413000i | −0.978447 | − | 0.206500i | \(-0.933793\pi\) | ||
0.978447 | − | 0.206500i | \(-0.0662074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.45006e6i | 1.34803i | ||||||||
\(320\) | −1.46171e6 | − | 374261.i | −0.797968 | − | 0.204315i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.18878e6 | − | 1.09339e6i | 0.638944 | − | 0.587671i | ||||
\(323\) | −452508. | −0.241335 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −991727. | −0.520815 | ||||||||
\(326\) | 1.70594e6 | − | 1.56904e6i | 0.889036 | − | 0.817694i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 154671. | + | 199262.i | 0.0793822 | + | 0.102268i | ||||
\(329\) | − | 1.49902e6i | − | 0.763517i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.07446e6i | 0.539038i | 0.962995 | + | 0.269519i | \(0.0868647\pi\) | ||||
−0.962995 | + | 0.269519i | \(0.913135\pi\) | |||||||
\(332\) | −120545. | + | 1.43938e6i | −0.0600210 | + | 0.716688i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −412410. | − | 448392.i | −0.202285 | − | 0.219934i | ||||
\(335\) | 3.00332e6 | 1.46214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 125481. | 0.0601871 | 0.0300935 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300935 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(338\) | 2.30938e6 | + | 2.51086e6i | 1.09952 | + | 1.19545i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 180424. | − | 2.15437e6i | 0.0846441 | − | 1.01070i | ||||
\(341\) | − | 3.00043e6i | − | 1.39733i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.08230e6i | − | 0.955670i | ||||||
\(344\) | −1.04502e6 | − | 1.34630e6i | −0.476132 | − | 0.613402i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.24891e6 | + | 1.14869e6i | −0.560844 | + | 0.515838i | ||||
\(347\) | −2.54277e6 | −1.13366 | −0.566830 | − | 0.823835i | \(-0.691830\pi\) | ||||
−0.566830 | + | 0.823835i | \(0.691830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 554946. | 0.243886 | 0.121943 | − | 0.992537i | \(-0.461087\pi\) | ||||
0.121943 | + | 0.992537i | \(0.461087\pi\) | |||||||
\(350\) | 563767. | − | 518526.i | 0.245997 | − | 0.226256i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.48888e6 | + | 2.28988e6i | 0.640477 | + | 0.985046i | ||||
\(353\) | 2.07681e6i | 0.887075i | 0.896256 | + | 0.443538i | \(0.146277\pi\) | ||||
−0.896256 | + | 0.443538i | \(0.853723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 454022.i | 0.191208i | ||||||||
\(356\) | −2.33262e6 | − | 195352.i | −0.975482 | − | 0.0816945i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.06749e6 | − | 2.24787e6i | −0.852579 | − | 0.926966i | ||||
\(359\) | 3.54117e6 | 1.45014 | 0.725071 | − | 0.688674i | \(-0.241807\pi\) | ||||
0.725071 | + | 0.688674i | \(0.241807\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.38098e6 | 0.961585 | ||||||||
\(362\) | 99058.7 | + | 107701.i | 0.0397302 | + | 0.0431966i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.24217e6 | − | 355273.i | −1.67817 | − | 0.140543i | ||||
\(365\) | 2.52604e6i | 0.992448i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.66740e6i | − | 0.646211i | −0.946363 | − | 0.323105i | \(-0.895273\pi\) | ||
0.946363 | − | 0.323105i | \(-0.104727\pi\) | |||||||
\(368\) | −2.13917e6 | − | 360833.i | −0.823429 | − | 0.138895i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.67707e6 | + | 1.54249e6i | −0.636864 | + | 0.585758i | ||||
\(371\) | −3.83620e6 | −1.44699 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 304727. | 0.113407 | 0.0567034 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567034 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(374\) | −2.88044e6 | + | 2.64929e6i | −1.06483 | + | 0.979380i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.59050e6 | + | 1.23457e6i | −0.580182 | + | 0.450346i | ||||
\(377\) | 5.12897e6i | 1.85856i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 805622.i | 0.288093i | 0.989571 | + | 0.144047i | \(0.0460115\pi\) | ||||
−0.989571 | + | 0.144047i | \(0.953988\pi\) | |||||||
\(380\) | 37926.4 | − | 452865.i | 0.0134736 | − | 0.160883i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.98940e6 | + | 2.16297e6i | 0.697530 | + | 0.758389i | ||||
\(383\) | 1.84820e6 | 0.643800 | 0.321900 | − | 0.946774i | \(-0.395679\pi\) | ||||
0.321900 | + | 0.946774i | \(0.395679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.92619e6 | 1.00612 | ||||||||
\(386\) | 993086. | + | 1.07973e6i | 0.339249 | + | 0.368848i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30503.7 | − | 364233.i | 0.0102866 | − | 0.122829i | ||||
\(389\) | 3.65126e6i | 1.22340i | 0.791090 | + | 0.611700i | \(0.209514\pi\) | ||||
−0.791090 | + | 0.611700i | \(0.790486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.10833e6i | − | 1.02822i | ||||||
\(392\) | 193965. | − | 150558.i | 0.0637540 | − | 0.0494869i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.54947e6 | − | 1.42513e6i | 0.502856 | − | 0.462504i | ||||
\(395\) | −4.22010e6 | −1.36091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.73747e6 | −0.553274 | −0.276637 | − | 0.960974i | \(-0.589220\pi\) | ||||
−0.276637 | + | 0.960974i | \(0.589220\pi\) | |||||||
\(398\) | 11313.6 | − | 10405.8i | 0.00358010 | − | 0.00329280i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.01448e6 | − | 171121.i | −0.317024 | − | 0.0534753i | ||||
\(401\) | − | 2.93873e6i | − | 0.912640i | −0.889816 | − | 0.456320i | \(-0.849167\pi\) | ||
0.889816 | − | 0.456320i | \(-0.150833\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.28112e6i | − | 1.92652i | ||||||
\(404\) | 2.50679e6 | + | 209938.i | 0.764125 | + | 0.0639938i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.68169e6 | − | 2.91566e6i | −0.807409 | − | 0.877854i | ||||
\(407\) | 4.12469e6 | 1.23425 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.82104e6 | −0.538285 | −0.269142 | − | 0.963100i | \(-0.586740\pi\) | ||||
−0.269142 | + | 0.963100i | \(0.586740\pi\) | |||||||
\(410\) | −245718. | − | 267156.i | −0.0721900 | − | 0.0784884i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.25061e6 | − | 272231.i | −0.943456 | − | 0.0790124i | ||||
\(413\) | 2.03006e6i | 0.585643i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.07846e6i | − | 0.592409i | ||||||
\(416\) | 3.11683e6 | + | 4.79365e6i | 0.883040 | + | 1.35810i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −605490. | + | 556901.i | −0.169499 | + | 0.155897i | ||||
\(419\) | 5.56903e6 | 1.54969 | 0.774845 | − | 0.632151i | \(-0.217828\pi\) | ||||
0.774845 | + | 0.632151i | \(0.217828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 220888. | 0.0607390 | 0.0303695 | − | 0.999539i | \(-0.490332\pi\) | ||||
0.0303695 | + | 0.999539i | \(0.490332\pi\) | |||||||
\(422\) | 2.88943e6 | − | 2.65756e6i | 0.789825 | − | 0.726444i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.15943e6 | + | 4.07030e6i | 0.853481 | + | 1.09954i | ||||
\(425\) | − | 1.47409e6i | − | 0.395869i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.09995e6i | 1.35362i | ||||||||
\(428\) | −362292. | + | 4.32599e6i | −0.0955982 | + | 1.14150i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.66017e6 | + | 1.80502e6i | 0.432994 | + | 0.470772i | ||||
\(431\) | −2.90126e6 | −0.752304 | −0.376152 | − | 0.926558i | \(-0.622753\pi\) | ||||
−0.376152 | + | 0.926558i | \(0.622753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.33580e6 | 0.342392 | 0.171196 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171196 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(434\) | 3.28409e6 | + | 3.57063e6i | 0.836934 | + | 0.909955i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −601642. | + | 7.18398e6i | −0.151573 | + | 1.80988i | ||||
\(437\) | − | 653394.i | − | 0.163671i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.00279e6i | − | 1.98189i | −0.134262 | − | 0.990946i | \(-0.542866\pi\) | ||
0.134262 | − | 0.990946i | \(-0.457134\pi\) | |||||||
\(440\) | −2.40996e6 | − | 3.10476e6i | −0.593442 | − | 0.764533i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.02993e6 | + | 5.54604e6i | −1.46810 | + | 1.35029i | ||||
\(443\) | −4.46062e6 | −1.07991 | −0.539953 | − | 0.841695i | \(-0.681558\pi\) | ||||
−0.539953 | + | 0.841695i | \(0.681558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.36830e6 | 0.806326 | ||||||||
\(446\) | −2.53902e6 | + | 2.33527e6i | −0.604407 | + | 0.555905i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.27819e6 | − | 1.09540e6i | −1.00708 | − | 0.257857i | ||||
\(449\) | − | 394596.i | − | 0.0923712i | −0.998933 | − | 0.0461856i | \(-0.985293\pi\) | ||
0.998933 | − | 0.0461856i | \(-0.0147066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 657060.i | 0.152112i | ||||||||
\(452\) | −1.90766e6 | − | 159762.i | −0.439192 | − | 0.0367814i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 633920. | + | 689229.i | 0.144343 | + | 0.156936i | ||||
\(455\) | 6.12569e6 | 1.38716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.29879e6 | 0.738863 | 0.369431 | − | 0.929258i | \(-0.379552\pi\) | ||||
0.369431 | + | 0.929258i | \(0.379552\pi\) | |||||||
\(458\) | −3.03798e6 | − | 3.30304e6i | −0.676739 | − | 0.735784i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.11078e6 | + | 260521.i | 0.685448 | + | 0.0574048i | ||||
\(461\) | 574515.i | 0.125907i | 0.998016 | + | 0.0629534i | \(0.0200519\pi\) | ||||
−0.998016 | + | 0.0629534i | \(0.979948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 362906.i | 0.0786760i | 0.999226 | + | 0.0393380i | \(0.0125249\pi\) | ||||
−0.999226 | + | 0.0393380i | \(0.987475\pi\) | |||||||
\(464\) | −884995. | + | 5.24663e6i | −0.190830 | + | 1.13132i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.17860e6 | − | 2.00378e6i | 0.464743 | − | 0.427449i | ||||
\(467\) | −9.20629e6 | −1.95340 | −0.976702 | − | 0.214598i | \(-0.931156\pi\) | ||||
−0.976702 | + | 0.214598i | \(0.931156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.79026e6 | 1.84531 | ||||||||
\(470\) | 2.13243e6 | − | 1.96130e6i | 0.445276 | − | 0.409544i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.15394e6 | − | 1.67192e6i | 0.445019 | − | 0.345431i | ||||
\(473\) | − | 4.43937e6i | − | 0.912364i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 309865.i | − | 0.0630141i | ||||||
\(476\) | 528073. | − | 6.30551e6i | 0.106826 | − | 1.27557i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.99784e6 | − | 2.17215e6i | −0.399936 | − | 0.434830i | ||||
\(479\) | −2.27095e6 | −0.452240 | −0.226120 | − | 0.974099i | \(-0.572604\pi\) | ||||
−0.226120 | + | 0.974099i | \(0.572604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.63463e6 | 1.70169 | ||||||||
\(482\) | −4.17252e6 | − | 4.53657e6i | −0.818052 | − | 0.889426i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −163665. | + | 1.95425e6i | −0.0317571 | + | 0.379199i | ||||
\(485\) | 525952.i | 0.101529i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.09989e6i | 1.16547i | 0.812664 | + | 0.582733i | \(0.198016\pi\) | ||||
−0.812664 | + | 0.582733i | \(0.801984\pi\) | |||||||
\(488\) | 5.41117e6 | − | 4.20024e6i | 1.02859 | − | 0.798407i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −260054. | + | 239185.i | −0.0489297 | + | 0.0450033i | ||||
\(491\) | −536585. | −0.100446 | −0.0502232 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502232 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.62364e6 | −1.41268 | ||||||||
\(494\) | −1.26754e6 | + | 1.16582e6i | −0.233691 | + | 0.214938i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.08380e6 | − | 6.42522e6i | 0.197808 | − | 1.17269i | ||||
\(497\) | 1.32885e6i | 0.241316i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.52841e6i | − | 0.634348i | −0.948367 | − | 0.317174i | \(-0.897266\pi\) | ||
0.948367 | − | 0.317174i | \(-0.102734\pi\) | |||||||
\(500\) | 6.06386e6 | + | 507835.i | 1.08474 | + | 0.0908444i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.40789e6 | + | 4.79247e6i | 0.780676 | + | 0.848789i | ||||
\(503\) | 3.34461e6 | 0.589422 | 0.294711 | − | 0.955586i | \(-0.404777\pi\) | ||||
0.294711 | + | 0.955586i | \(0.404777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.61980e6 | −0.631621 | ||||||||
\(506\) | −3.82542e6 | − | 4.15918e6i | −0.664206 | − | 0.722157i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.42327e6 | + | 202943.i | 0.416622 | + | 0.0348912i | ||||
\(509\) | − | 5.31062e6i | − | 0.908553i | −0.890861 | − | 0.454277i | \(-0.849898\pi\) | ||
0.890861 | − | 0.454277i | \(-0.150102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.39332e6i | 1.25253i | ||||||||
\(512\) | 2.36120e6 | + | 5.44143e6i | 0.398068 | + | 0.917356i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.25581e6 | + | 4.83405e6i | −0.877470 | + | 0.807055i | ||||
\(515\) | 4.69387e6 | 0.779854 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.24461e6 | −0.862953 | ||||||||
\(518\) | −4.90853e6 | + | 4.51463e6i | −0.803761 | + | 0.739261i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.04502e6 | − | 6.49951e6i | −0.818191 | − | 1.05408i | ||||
\(521\) | − | 4.42521e6i | − | 0.714232i | −0.934060 | − | 0.357116i | \(-0.883760\pi\) | ||
0.934060 | − | 0.357116i | \(-0.116240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 88509.2i | − | 0.0141493i | −0.999975 | − | 0.00707463i | \(-0.997748\pi\) | ||
0.999975 | − | 0.00707463i | \(-0.00225194\pi\) | |||||||
\(524\) | 992209. | − | 1.18476e7i | 0.157861 | − | 1.88496i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 930669. | + | 1.01187e6i | 0.146667 | + | 0.159463i | ||||
\(527\) | 9.33618e6 | 1.46434 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.94810e6 | −0.302672 | ||||||||
\(530\) | −5.01924e6 | − | 5.45716e6i | −0.776154 | − | 0.843872i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 111005. | − | 1.32547e6i | 0.0170045 | − | 0.203044i | ||||
\(533\) | 1.37549e6i | 0.209720i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.24672e6i | − | 0.943557i | ||||||
\(536\) | −7.23951e6 | − | 9.32668e6i | −1.08842 | − | 1.40222i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.38813e6 | − | 3.11624e6i | 0.504666 | − | 0.464168i | ||||
\(539\) | 639591. | 0.0948267 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.49057e6 | −0.512747 | −0.256373 | − | 0.966578i | \(-0.582528\pi\) | ||||
−0.256373 | + | 0.966578i | \(0.582528\pi\) | |||||||
\(542\) | −7.73122e6 | + | 7.11081e6i | −1.13045 | + | 1.03973i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.12522e6 | + | 4.63282e6i | −1.03229 | + | 0.671194i | ||||
\(545\) | − | 1.03737e7i | − | 1.49603i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.73741e6i | − | 0.676975i | −0.940971 | − | 0.338487i | \(-0.890085\pi\) | ||
0.940971 | − | 0.338487i | \(-0.109915\pi\) | |||||||
\(548\) | 1.24164e7 | + | 1.03984e6i | 1.76622 | + | 0.147917i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.81416e6 | − | 1.97244e6i | −0.255723 | − | 0.278034i | ||||
\(551\) | −1.60254e6 | −0.224870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23516e7 | −1.71755 | ||||||||
\(554\) | 2.42856e6 | + | 2.64045e6i | 0.336182 | + | 0.365514i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.32627e6 | + | 278568.i | 0.456321 | + | 0.0382159i | ||||
\(557\) | 6.51222e6i | 0.889388i | 0.895683 | + | 0.444694i | \(0.146688\pi\) | ||||
−0.895683 | + | 0.444694i | \(0.853312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.29339e6i | − | 1.25790i | ||||||
\(560\) | 6.26622e6 | + | 1.05698e6i | 0.844376 | + | 0.142428i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.86389e6 | − | 8.15259e6i | 1.18381 | − | 1.08882i | ||||
\(563\) | −1.30164e7 | −1.73069 | −0.865343 | − | 0.501180i | \(-0.832900\pi\) | ||||
−0.865343 | + | 0.501180i | \(0.832900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.75466e6 | 0.363033 | ||||||||
\(566\) | 4.32070e6 | − | 3.97398e6i | 0.566909 | − | 0.521416i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.40995e6 | − | 1.09442e6i | 0.183372 | − | 0.142336i | ||||
\(569\) | 2.32444e6i | 0.300980i | 0.988612 | + | 0.150490i | \(0.0480851\pi\) | ||||
−0.988612 | + | 0.150490i | \(0.951915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.30746e7i | 1.67818i | 0.543992 | + | 0.839091i | \(0.316912\pi\) | ||||
−0.543992 | + | 0.839091i | \(0.683088\pi\) | |||||||
\(572\) | −1.24299e6 | + | 1.48420e7i | −0.158846 | + | 1.89672i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −719178. | − | 781925.i | −0.0911081 | − | 0.0990571i | ||||
\(575\) | 2.12850e6 | 0.268475 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.92814e6 | −1.24145 | −0.620724 | − | 0.784029i | \(-0.713161\pi\) | ||||
−0.620724 | + | 0.784029i | \(0.713161\pi\) | |||||||
\(578\) | −2.80629e6 | − | 3.05114e6i | −0.349393 | − | 0.379877i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 638966. | − | 7.62964e6i | 0.0788693 | − | 0.941747i | ||||
\(581\) | − | 6.08334e6i | − | 0.747656i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.34217e7i | 1.63544i | ||||||||
\(584\) | 7.84450e6 | − | 6.08902e6i | 0.951773 | − | 0.738780i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.64855e6 | − | 7.95453e6i | 1.04040 | − | 0.956909i | ||||
\(587\) | −8.76459e6 | −1.04987 | −0.524936 | − | 0.851142i | \(-0.675911\pi\) | ||||
−0.524936 | + | 0.851142i | \(0.675911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.96253e6 | 0.233093 | ||||||||
\(590\) | −2.88785e6 | + | 2.65610e6i | −0.341542 | + | 0.314134i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.83272e6 | + | 1.48989e6i | 1.03583 | + | 0.174723i | ||||
\(593\) | 6.94712e6i | 0.811275i | 0.914034 | + | 0.405637i | \(0.132950\pi\) | ||||
−0.914034 | + | 0.405637i | \(0.867050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.10515e6i | 1.05437i | ||||||||
\(596\) | −7.24665e6 | − | 606891.i | −0.835645 | − | 0.0699834i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.00815e6 | − | 8.70685e6i | −0.915755 | − | 0.995653i | ||||
\(599\) | 7.15594e6 | 0.814892 | 0.407446 | − | 0.913229i | \(-0.366420\pi\) | ||||
0.407446 | + | 0.913229i | \(0.366420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.05362e6 | 0.231918 | 0.115959 | − | 0.993254i | \(-0.463006\pi\) | ||||
0.115959 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(602\) | 4.85906e6 | + | 5.28301e6i | 0.546464 | + | 0.594142i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.55727e7 | + | 1.30418e6i | 1.73688 | + | 0.145460i | ||||
\(605\) | − | 2.82194e6i | − | 0.313444i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.85546e6i | 0.204399i | 0.994764 | + | 0.102200i | \(0.0325881\pi\) | ||||
−0.994764 | + | 0.102200i | \(0.967412\pi\) | |||||||
\(608\) | −1.49777e6 | + | 973853.i | −0.164319 | + | 0.106840i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.25490e6 | + | 6.67272e6i | −0.789418 | + | 0.726069i | ||||
\(611\) | −1.09791e7 | −1.18977 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 527592. | 0.0567083 | 0.0283542 | − | 0.999598i | \(-0.490973\pi\) | ||||
0.0283542 | + | 0.999598i | \(0.490973\pi\) | |||||||
\(614\) | −1.15631e6 | + | 1.06352e6i | −0.123781 | + | 0.113848i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.05358e6 | − | 9.08715e6i | −0.748959 | − | 0.964886i | ||||
\(617\) | 1.33503e7i | 1.41182i | 0.708301 | + | 0.705910i | \(0.249462\pi\) | ||||
−0.708301 | + | 0.705910i | \(0.750538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.22140e7i | 1.28124i | 0.767856 | + | 0.640622i | \(0.221324\pi\) | ||||
−0.767856 | + | 0.640622i | \(0.778676\pi\) | |||||||
\(620\) | −782501. | + | 9.34353e6i | −0.0817533 | + | 0.976185i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.88243e6 | + | 3.13392e6i | 0.298733 | + | 0.324797i | ||||
\(623\) | 9.85850e6 | 1.01763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.61653e6 | −0.575133 | ||||||||
\(626\) | −6.55956e6 | − | 7.13187e6i | −0.669020 | − | 0.727391i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −821511. | + | 9.80934e6i | −0.0831217 | + | 0.992524i | ||||
\(629\) | 1.28344e7i | 1.29345i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 842912.i | 0.0842770i | 0.999112 | + | 0.0421385i | \(0.0134171\pi\) | ||||
−0.999112 | + | 0.0421385i | \(0.986583\pi\) | |||||||
\(632\) | 1.01726e7 | + | 1.31053e7i | 1.01307 | + | 1.30513i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.07655e6 | − | 2.82967e6i | 0.303977 | − | 0.279584i | ||||
\(635\) | −3.49919e6 | −0.344377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.33892e6 | 0.130740 | ||||||||
\(638\) | −1.02010e7 | + | 9.38240e6i | −0.992181 | + | 0.912561i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.03928e6 | − | 7.51913e6i | −0.389811 | − | 0.725634i | ||||
\(641\) | − | 4.62200e6i | − | 0.444309i | −0.975011 | − | 0.222155i | \(-0.928691\pi\) | ||
0.975011 | − | 0.222155i | \(-0.0713090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.28181e6i | − | 0.885330i | −0.896687 | − | 0.442665i | \(-0.854033\pi\) | ||
0.896687 | − | 0.442665i | \(-0.145967\pi\) | |||||||
\(644\) | 9.10478e6 | + | 762505.i | 0.865077 | + | 0.0724483i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.73286e6 | − | 1.88405e6i | −0.163374 | − | 0.177628i | ||||
\(647\) | 1.74226e7 | 1.63626 | 0.818129 | − | 0.575034i | \(-0.195011\pi\) | ||||
0.818129 | + | 0.575034i | \(0.195011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.10254e6 | 0.661914 | ||||||||
\(650\) | −3.79777e6 | − | 4.12912e6i | −0.352570 | − | 0.383331i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.30656e7 | + | 1.09422e6i | 1.20368 | + | 0.100806i | ||||
\(653\) | − | 3.94341e6i | − | 0.361901i | −0.983492 | − | 0.180950i | \(-0.942083\pi\) | ||
0.983492 | − | 0.180950i | \(-0.0579173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.71079e7i | 1.55809i | ||||||||
\(656\) | −237339. | + | 1.40705e6i | −0.0215332 | + | 0.127658i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.24128e6 | − | 5.74044e6i | 0.561965 | − | 0.516869i | ||||
\(659\) | −1.46127e7 | −1.31074 | −0.655371 | − | 0.755307i | \(-0.727488\pi\) | ||||
−0.655371 | + | 0.755307i | \(0.727488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.83511e6 | 0.430430 | 0.215215 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215215 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(662\) | −4.47358e6 | + | 4.11459e6i | −0.396744 | + | 0.364906i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.45457e6 | + | 5.01014e6i | −0.568129 | + | 0.440991i | ||||
\(665\) | 1.91397e6i | 0.167834i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.10081e7i | − | 0.958068i | ||||||
\(668\) | 287606. | − | 3.43419e6i | 0.0249377 | − | 0.297772i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.15011e7 | + | 1.25045e7i | 0.989809 | + | 1.07617i | ||||
\(671\) | 1.78431e7 | 1.52991 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.36686e6 | −0.371648 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(674\) | 480524. | + | 522448.i | 0.0407441 | + | 0.0442990i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.61051e6 | + | 1.92305e7i | −0.135549 | + | 1.61854i | ||||
\(677\) | 3.80499e6i | 0.319067i | 0.987193 | + | 0.159534i | \(0.0509990\pi\) | ||||
−0.987193 | + | 0.159534i | \(0.949001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.53938e6i | 0.128136i | ||||||||
\(680\) | 9.66080e6 | − | 7.49886e6i | 0.801199 | − | 0.621903i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.24925e7 | − | 1.14900e7i | 1.02846 | − | 0.945932i | ||||
\(683\) | 8.23750e6 | 0.675684 | 0.337842 | − | 0.941203i | \(-0.390303\pi\) | ||||
0.337842 | + | 0.941203i | \(0.390303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.79292e7 | −1.45994 | ||||||||
\(686\) | 8.66980e6 | − | 7.97407e6i | 0.703394 | − | 0.646949i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.60356e6 | − | 9.50659e6i | 0.129156 | − | 0.765691i | ||||
\(689\) | 2.80969e7i | 2.25482i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.65718e6i | 0.211703i | 0.994382 | + | 0.105851i | \(0.0337568\pi\) | ||||
−0.994382 | + | 0.105851i | \(0.966243\pi\) | |||||||
\(692\) | −9.56531e6 | − | 801074.i | −0.759336 | − | 0.0635927i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.73741e6 | − | 1.05870e7i | −0.767440 | − | 0.834398i | ||||
\(695\) | −4.80313e6 | −0.377191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.04451e6 | −0.159407 | ||||||||
\(698\) | 2.12514e6 | + | 2.31055e6i | 0.165101 | + | 0.179505i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.31784e6 | + | 361609.i | 0.333059 | + | 0.0278930i | ||||
\(701\) | − | 1.26405e7i | − | 0.971561i | −0.874081 | − | 0.485780i | \(-0.838535\pi\) | ||
0.874081 | − | 0.485780i | \(-0.161465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.69789e6i | 0.205890i | ||||||||
\(704\) | −3.83247e6 | + | 1.49681e7i | −0.291439 | + | 1.13824i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.64695e6 | + | 7.95305e6i | −0.652907 | + | 0.600513i | ||||
\(707\) | −1.05946e7 | −0.797143 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00735e7 | −0.752599 | −0.376300 | − | 0.926498i | \(-0.622804\pi\) | ||||
−0.376300 | + | 0.926498i | \(0.622804\pi\) | |||||||
\(710\) | −1.89035e6 | + | 1.73866e6i | −0.140733 | + | 0.129440i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.11930e6 | − | 1.04601e7i | −0.600231 | − | 0.773279i | ||||
\(713\) | 1.34809e7i | 0.993103i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.14319e7i | − | 1.56782i | ||||||
\(716\) | 1.44182e6 | − | 1.72162e7i | 0.105106 | − | 1.25503i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.35607e7 | + | 1.47439e7i | 0.981686 | + | 1.06734i | ||||
\(719\) | −3.82437e6 | −0.275891 | −0.137946 | − | 0.990440i | \(-0.544050\pi\) | ||||
−0.137946 | + | 0.990440i | \(0.544050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.37382e7 | 0.984222 | ||||||||
\(722\) | 9.11784e6 | + | 9.91336e6i | 0.650952 | + | 0.707747i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −69081.5 | + | 824875.i | −0.00489796 | + | 0.0584846i | ||||
\(725\) | − | 5.22045e6i | − | 0.368861i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.74022e6i | − | 0.122115i | −0.998134 | − | 0.0610575i | \(-0.980553\pi\) | ||
0.998134 | − | 0.0610575i | \(-0.0194473\pi\) | |||||||
\(728\) | −1.47660e7 | − | 1.90231e7i | −1.03261 | − | 1.33031i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.05173e7 | + | 9.67334e6i | −0.730463 | + | 0.671845i | ||||
\(731\) | 1.38136e7 | 0.956121 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.39703e7 | 1.64783 | 0.823917 | − | 0.566711i | \(-0.191784\pi\) | ||||
0.823917 | + | 0.566711i | \(0.191784\pi\) | |||||||
\(734\) | 6.94233e6 | − | 6.38523e6i | 0.475625 | − | 0.437458i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.68951e6 | − | 1.02884e7i | −0.455197 | − | 0.700088i | ||||
\(737\) | − | 3.07544e7i | − | 2.08563i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.52306e6i | − | 0.439380i | −0.975570 | − | 0.219690i | \(-0.929495\pi\) | ||
0.975570 | − | 0.219690i | \(-0.0705046\pi\) | |||||||
\(740\) | −1.28445e7 | − | 1.07570e6i | −0.862261 | − | 0.0722125i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.46905e7 | − | 1.59723e7i | −0.979553 | − | 1.06502i | ||||
\(743\) | −2.51966e7 | −1.67444 | −0.837219 | − | 0.546868i | \(-0.815820\pi\) | ||||
−0.837219 | + | 0.546868i | \(0.815820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.04642e7 | 0.690738 | ||||||||
\(746\) | 1.16694e6 | + | 1.26875e6i | 0.0767716 | + | 0.0834698i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.20610e7 | − | 1.84756e6i | −1.44169 | − | 0.120738i | ||||
\(749\) | − | 1.82832e7i | − | 1.19082i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.46901e6i | − | 0.418541i | −0.977858 | − | 0.209270i | \(-0.932891\pi\) | ||
0.977858 | − | 0.209270i | \(-0.0671089\pi\) | |||||||
\(752\) | −1.12310e7 | − | 1.89442e6i | −0.724223 | − | 0.122161i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.13548e7 | + | 1.96412e7i | −1.36794 | + | 1.25817i | ||||
\(755\) | −2.24869e7 | −1.43570 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.26991e7 | −0.805440 | −0.402720 | − | 0.915323i | \(-0.631935\pi\) | ||||
−0.402720 | + | 0.915323i | \(0.631935\pi\) | |||||||
\(758\) | −3.35426e6 | + | 3.08509e6i | −0.212043 | + | 0.195027i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.03077e6 | − | 1.57632e6i | 0.127534 | − | 0.0989940i | ||||
\(761\) | − | 1.71063e7i | − | 1.07076i | −0.844610 | − | 0.535382i | \(-0.820167\pi\) | ||
0.844610 | − | 0.535382i | \(-0.179833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.03621e7i | − | 1.88808i | ||||||
\(764\) | −1.38736e6 | + | 1.65660e7i | −0.0859918 | + | 1.02679i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.07758e6 | + | 7.69509e6i | 0.435826 | + | 0.473851i | ||||
\(767\) | 1.48685e7 | 0.912596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.68095e6 | −0.468381 | −0.234190 | − | 0.972191i | \(-0.575244\pi\) | ||||
−0.234190 | + | 0.972191i | \(0.575244\pi\) | |||||||
\(770\) | 1.12057e7 | + | 1.21834e7i | 0.681102 | + | 0.740527i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −692558. | + | 8.26956e6i | −0.0418228 | + | 0.499389i | ||||
\(773\) | − | 2.27192e6i | − | 0.136755i | −0.997660 | − | 0.0683776i | \(-0.978218\pi\) | ||
0.997660 | − | 0.0683776i | \(-0.0217823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.39315e6i | 0.382349i | ||||||||
\(776\) | 1.63332e6 | − | 1.26781e6i | 0.0973682 | − | 0.0755787i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.52022e7 | + | 1.39823e7i | −0.900448 | + | 0.828190i | ||||
\(779\) | −429772. | −0.0253743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.64924e6 | 0.272744 | ||||||||
\(782\) | 1.29417e7 | − | 1.19032e7i | 0.756791 | − | 0.696061i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.36964e6 | + | 231029.i | 0.0795822 | + | 0.0134238i | ||||
\(785\) | − | 1.41647e7i | − | 0.820413i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.56436e7i | 0.900324i | 0.892947 | + | 0.450162i | \(0.148634\pi\) | ||||
−0.892947 | + | 0.450162i | \(0.851366\pi\) | |||||||
\(788\) | 1.18673e7 | + | 993859.i | 0.680825 | + | 0.0570176i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.61607e7 | − | 1.75707e7i | −0.921280 | − | 1.00166i | ||||
\(791\) | 8.06246e6 | 0.458170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.73529e7 | 2.10931 | ||||||||
\(794\) | −6.65355e6 | − | 7.23406e6i | −0.374543 | − | 0.407222i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 86650.1 | + | 7256.76i | 0.00484715 | + | 0.000405938i | ||||
\(797\) | 2.26016e7i | 1.26036i | 0.776451 | + | 0.630178i | \(0.217018\pi\) | ||||
−0.776451 | + | 0.630178i | \(0.782982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.63192e7i | − | 0.904340i | ||||||
\(800\) | −3.17242e6 | − | 4.87915e6i | −0.175253 | − | 0.269537i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.22356e7 | − | 1.12537e7i | 0.671723 | − | 0.617819i | ||||
\(803\) | 2.58669e7 | 1.41565 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.31473e7 | −0.715066 | ||||||||
\(806\) | 2.61519e7 | − | 2.40533e7i | 1.41796 | − | 1.30418i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.72554e6 | + | 1.12411e7i | 0.470180 | + | 0.605734i | ||||
\(809\) | − | 2.72883e6i | − | 0.146590i | −0.997310 | − | 0.0732952i | \(-0.976648\pi\) | ||
0.997310 | − | 0.0732952i | \(-0.0233515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.69137e6i | − | 0.143688i | −0.997416 | − | 0.0718442i | \(-0.977112\pi\) | ||
0.997416 | − | 0.0718442i | \(-0.0228884\pi\) | |||||||
\(812\) | 1.87016e6 | − | 2.23308e7i | 0.0995377 | − | 1.18854i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.57953e7 | + | 1.71734e7i | 0.835539 | + | 0.908438i | ||||
\(815\) | −1.88667e7 | −0.994954 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.90372e6 | 0.152194 | ||||||||
\(818\) | −6.97360e6 | − | 7.58204e6i | −0.364396 | − | 0.396189i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 171359. | − | 2.04612e6i | 0.00889961 | − | 0.106267i | ||||
\(821\) | − | 1.32663e7i | − | 0.686895i | −0.939172 | − | 0.343448i | \(-0.888405\pi\) | ||
0.939172 | − | 0.343448i | \(-0.111595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.55966e6i | − | 0.131729i | −0.997829 | − | 0.0658646i | \(-0.979019\pi\) | ||
0.997829 | − | 0.0658646i | \(-0.0209805\pi\) | |||||||
\(824\) | −1.13146e7 | − | 1.45766e7i | −0.580525 | − | 0.747892i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.45228e6 | + | 7.77401e6i | −0.431046 | + | 0.396456i | ||||
\(827\) | 1.61642e7 | 0.821846 | 0.410923 | − | 0.911670i | \(-0.365206\pi\) | ||||
0.410923 | + | 0.911670i | \(0.365206\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06742e7 | 1.04482 | 0.522411 | − | 0.852694i | \(-0.325033\pi\) | ||||
0.522411 | + | 0.852694i | \(0.325033\pi\) | |||||||
\(830\) | 8.65381e6 | − | 7.95937e6i | 0.436026 | − | 0.401036i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.02292e6 | + | 3.13342e7i | −0.401813 | + | 1.56932i | ||||
\(833\) | 1.99016e6i | 0.0993745i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.95897e6i | 0.246136i | ||||||||
\(836\) | −4.63739e6 | − | 388371.i | −0.229487 | − | 0.0192190i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.13264e7 | + | 2.31870e7i | 1.04907 | + | 1.14061i | ||||
\(839\) | 6.10993e6 | 0.299662 | 0.149831 | − | 0.988712i | \(-0.452127\pi\) | ||||
0.149831 | + | 0.988712i | \(0.452127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.48774e6 | −0.316303 | ||||||||
\(842\) | 845882. | + | 919684.i | 0.0411178 | + | 0.0447052i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.21299e7 | + | 1.85333e6i | 1.06936 | + | 0.0895563i | ||||
\(845\) | − | 2.77688e7i | − | 1.33787i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.25939e6i | − | 0.395584i | ||||||
\(848\) | −4.84808e6 | + | 2.87415e7i | −0.231516 | + | 1.37252i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.13747e6 | − | 5.64496e6i | 0.291368 | − | 0.267987i | ||||
\(851\) | −1.85321e7 | −0.877204 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52983e7 | 1.19047 | 0.595236 | − | 0.803551i | \(-0.297058\pi\) | ||||
0.595236 | + | 0.803551i | \(0.297058\pi\) | |||||||
\(854\) | −2.12340e7 | + | 1.95300e7i | −0.996292 | + | 0.916343i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.93989e7 | + | 1.50578e7i | −0.904885 | + | 0.702386i | ||||
\(857\) | 4.03581e7i | 1.87706i | 0.345197 | + | 0.938530i | \(0.387812\pi\) | ||||
−0.345197 | + | 0.938530i | \(0.612188\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 358772.i | − | 0.0165896i | −0.999966 | − | 0.00829479i | \(-0.997360\pi\) | ||
0.999966 | − | 0.00829479i | \(-0.00264034\pi\) | |||||||
\(860\) | −1.15777e6 | + | 1.38245e7i | −0.0533796 | + | 0.637385i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.11102e7 | − | 1.20796e7i | −0.509278 | − | 0.553712i | ||||
\(863\) | −6.43324e6 | −0.294038 | −0.147019 | − | 0.989134i | \(-0.546968\pi\) | ||||
−0.147019 | + | 0.989134i | \(0.546968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.38123e7 | 0.627662 | ||||||||
\(866\) | 5.11540e6 | + | 5.56171e6i | 0.231785 | + | 0.252008i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.29026e6 | + | 2.73471e7i | −0.103178 | + | 1.23200i | ||||
\(869\) | 4.32143e7i | 1.94123i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.43813e7i | − | 2.87551i | ||||||
\(872\) | −3.22149e7 | + | 2.50057e7i | −1.43472 | + | 1.11365i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.72045e6 | − | 2.50214e6i | 0.120465 | − | 0.110798i | ||||
\(875\) | −2.56281e7 | −1.13161 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.17951e7 | 1.39592 | 0.697962 | − | 0.716135i | \(-0.254090\pi\) | ||||
0.697962 | + | 0.716135i | \(0.254090\pi\) | |||||||
\(878\) | 3.33201e7 | − | 3.06463e7i | 1.45872 | − | 1.34166i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.69804e6 | − | 2.19236e7i | 0.160977 | − | 0.954343i | ||||
\(881\) | − | 2.35865e7i | − | 1.02382i | −0.859039 | − | 0.511910i | \(-0.828938\pi\) | ||
0.859039 | − | 0.511910i | \(-0.171062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.09627e7i | 0.473167i | 0.971611 | + | 0.236583i | \(0.0760277\pi\) | ||||
−0.971611 | + | 0.236583i | \(0.923972\pi\) | |||||||
\(884\) | −4.61827e7 | − | 3.86770e6i | −1.98769 | − | 0.166465i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.70817e7 | − | 1.85721e7i | −0.731051 | − | 0.794834i | ||||
\(887\) | 1.34104e7 | 0.572311 | 0.286156 | − | 0.958183i | \(-0.407623\pi\) | ||||
0.286156 | + | 0.958183i | \(0.407623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.02416e7 | −0.434624 | ||||||||
\(890\) | 1.28987e7 | + | 1.40241e7i | 0.545849 | + | 0.593474i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.94461e7 | − | 1.62857e6i | −0.818316 | − | 0.0685322i | ||||
\(893\) | − | 3.43041e6i | − | 0.143952i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.48602e7i | 1.03740i | ||||||||
\(896\) | −1.18223e7 | − | 2.20073e7i | −0.491965 | − | 0.915793i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.64293e6 | − | 1.51109e6i | 0.0679872 | − | 0.0625314i | ||||
\(899\) | 3.30638e7 | 1.36444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.17629e7 | −1.71388 | ||||||||
\(902\) | −2.73571e6 | + | 2.51618e6i | −0.111958 | + | 0.102973i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.64011e6 | − | 8.55447e6i | −0.270243 | − | 0.348154i | ||||
\(905\) | − | 1.19112e6i | − | 0.0483430i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.79385e7i | 1.93493i | 0.252996 | + | 0.967467i | \(0.418584\pi\) | ||||
−0.252996 | + | 0.967467i | \(0.581416\pi\) | |||||||
\(908\) | −442083. | + | 5.27874e6i | −0.0177946 | + | 0.212479i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.34581e7 | + | 2.55047e7i | 0.939050 | + | 1.02098i | ||||
\(911\) | −4.06580e6 | −0.162312 | −0.0811560 | − | 0.996701i | \(-0.525861\pi\) | ||||
−0.0811560 | + | 0.996701i | \(0.525861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12837e7 | −0.845026 | ||||||||
\(914\) | 1.26326e7 | + | 1.37347e7i | 0.500179 | + | 0.543819i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.11863e6 | − | 2.52977e7i | 0.0834287 | − | 0.996190i | ||||
\(917\) | 5.00721e7i | 1.96640i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.78821e7i | 0.698441i | 0.937041 | + | 0.349220i | \(0.113554\pi\) | ||||
−0.937041 | + | 0.349220i | \(0.886446\pi\) | |||||||
\(920\) | 1.08279e7 | + | 1.39496e7i | 0.421769 | + | 0.543366i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.39203e6 | + | 2.20008e6i | −0.0926701 | + | 0.0852336i | ||||
\(923\) | 9.73275e6 | 0.376038 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.78864e6 | −0.337728 | ||||||||
\(926\) | −1.51098e6 | + | 1.38973e6i | −0.0579072 | + | 0.0532603i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.52338e7 | + | 1.64070e7i | −0.961860 | + | 0.625402i | ||||
\(929\) | − | 2.23070e7i | − | 0.848012i | −0.905659 | − | 0.424006i | \(-0.860624\pi\) | ||
0.905659 | − | 0.424006i | \(-0.139376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 418346.i | 0.0158184i | ||||||||
\(932\) | 1.66857e7 | + | 1.39739e6i | 0.629223 | + | 0.0526961i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.52550e7 | − | 3.83310e7i | −1.32237 | − | 1.43775i | ||||
\(935\) | 3.18561e7 | 1.19169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.03539e7 | −1.50154 | −0.750770 | − | 0.660563i | \(-0.770317\pi\) | ||||
−0.750770 | + | 0.660563i | \(0.770317\pi\) | |||||||
\(938\) | 3.36619e7 | + | 3.65988e7i | 1.24920 | + | 1.35819i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.63320e7 | + | 1.36777e6i | 0.602866 | + | 0.0504887i | ||||
\(941\) | 1.30625e7i | 0.480898i | 0.970662 | + | 0.240449i | \(0.0772946\pi\) | ||||
−0.970662 | + | 0.240449i | \(0.922705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.95215e6i | − | 0.108108i | ||||||
\(944\) | 1.52096e7 | + | 2.56553e6i | 0.555504 | + | 0.0937017i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.84836e7 | − | 1.70003e7i | 0.671520 | − | 0.617632i | ||||
\(947\) | −3.87893e7 | −1.40552 | −0.702760 | − | 0.711427i | \(-0.748049\pi\) | ||||
−0.702760 | + | 0.711427i | \(0.748049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.41500e7 | 1.95179 | ||||||||
\(950\) | 1.29014e6 | − | 1.18661e6i | 0.0463798 | − | 0.0426579i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.82757e7 | − | 2.19480e7i | 1.01116 | − | 0.784879i | ||||
\(953\) | 1.45546e7i | 0.519120i | 0.965727 | + | 0.259560i | \(0.0835775\pi\) | ||||
−0.965727 | + | 0.259560i | \(0.916423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.39212e7i | − | 0.848741i | ||||||
\(956\) | 1.39325e6 | − | 1.66363e7i | 0.0493043 | − | 0.588723i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.69649e6 | − | 9.45525e6i | −0.306147 | − | 0.332858i | ||||
\(959\) | −5.24761e7 | −1.84253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.18620e7 | −0.414332 | ||||||||
\(962\) | 3.30659e7 | + | 3.59509e7i | 1.15197 | + | 1.25248i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.90983e6 | − | 3.47451e7i | 0.100850 | − | 1.20421i | ||||
\(965\) | − | 1.19412e7i | − | 0.412792i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.33422e7i | 0.802741i | 0.915916 | + | 0.401370i | \(0.131466\pi\) | ||||
−0.915916 | + | 0.401370i | \(0.868534\pi\) | |||||||
\(968\) | −8.76341e6 | + | 6.80230e6i | −0.300597 | + | 0.233328i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.18984e6 | + | 2.01411e6i | −0.0747278 | + | 0.0687311i | ||||
\(971\) | −5.87811e6 | −0.200074 | −0.100037 | − | 0.994984i | \(-0.531896\pi\) | ||||
−0.100037 | + | 0.994984i | \(0.531896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.40580e7 | −0.476038 | ||||||||
\(974\) | −2.53973e7 | + | 2.33592e7i | −0.857808 | + | 0.788971i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.82098e7 | + | 6.44518e6i | 1.28396 | + | 0.216576i | ||||
\(977\) | 4.06645e7i | 1.36295i | 0.731843 | + | 0.681473i | \(0.238660\pi\) | ||||
−0.731843 | + | 0.681473i | \(0.761340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.44918e7i | − | 1.15016i | ||||||
\(980\) | −1.99173e6 | − | 166803.i | −0.0662467 | − | 0.00554802i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.05483e6 | − | 2.23411e6i | −0.0679980 | − | 0.0739308i | ||||
\(983\) | 3.43471e7 | 1.13372 | 0.566861 | − | 0.823814i | \(-0.308158\pi\) | ||||
0.566861 | + | 0.823814i | \(0.308158\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.71363e7 | −0.562765 | ||||||||
\(986\) | −2.91944e7 | − | 3.17415e7i | −0.956328 | − | 1.03977i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.70793e6 | − | 813018.i | −0.316399 | − | 0.0264977i | ||||
\(989\) | 1.99460e7i | 0.648432i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.27854e7i | − | 1.06046i | −0.847853 | − | 0.530232i | \(-0.822105\pi\) | ||
0.847853 | − | 0.530232i | \(-0.177895\pi\) | |||||||
\(992\) | 3.09022e7 | − | 2.00926e7i | 0.997034 | − | 0.648272i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.53277e6 | + | 5.08878e6i | −0.177614 | + | 0.163361i | ||||
\(995\) | −125123. | −0.00400662 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.68704e7 | −1.49335 | −0.746673 | − | 0.665191i | \(-0.768350\pi\) | ||||
−0.746673 | + | 0.665191i | \(0.768350\pi\) | |||||||
\(998\) | 1.46908e7 | − | 1.35119e7i | 0.466894 | − | 0.429427i | ||||
\(999\) | 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.b.107.12 | yes | 16 | |
3.2 | odd | 2 | inner | 108.6.b.b.107.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 108.6.b.b.107.6 | yes | 16 | |
12.11 | even | 2 | inner | 108.6.b.b.107.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.b.107.5 | ✓ | 16 | 3.2 | odd | 2 | inner | |
108.6.b.b.107.6 | yes | 16 | 4.3 | odd | 2 | inner | |
108.6.b.b.107.11 | yes | 16 | 12.11 | even | 2 | inner | |
108.6.b.b.107.12 | yes | 16 | 1.1 | even | 1 | trivial |