Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,6,Mod(9,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.9");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.c (of order \(3\), 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: | \(2.24537347738\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{79})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 79x^{2} + 6241 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(4.44410 + 7.69740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.9 |
Dual form | 14.6.c.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 3.46410i | −0.353553 | + | 0.612372i | ||||
\(3\) | −12.3882 | − | 21.4570i | −0.794703 | − | 1.37647i | −0.923028 | − | 0.384734i | \(-0.874293\pi\) |
0.128325 | − | 0.991732i | \(-0.459040\pi\) | |||||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | 18.0528 | − | 31.2683i | 0.322938 | − | 0.559345i | −0.658155 | − | 0.752883i | \(-0.728663\pi\) |
0.981093 | + | 0.193538i | \(0.0619962\pi\) | |||||||
\(6\) | 99.1056 | 1.12388 | ||||||||
\(7\) | −124.435 | − | 36.3731i | −0.959835 | − | 0.280566i | ||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −185.435 | + | 321.182i | −0.763106 | + | 1.32174i | ||||
\(10\) | 72.2111 | + | 125.073i | 0.228352 | + | 0.395517i | ||||
\(11\) | −77.7174 | − | 134.610i | −0.193658 | − | 0.335426i | 0.752801 | − | 0.658248i | \(-0.228702\pi\) |
−0.946460 | + | 0.322821i | \(0.895369\pi\) | |||||||
\(12\) | −198.211 | + | 343.312i | −0.397352 | + | 0.688233i | ||||
\(13\) | 1158.87 | 1.90185 | 0.950925 | − | 0.309422i | \(-0.100136\pi\) | ||||
0.950925 | + | 0.309422i | \(0.100136\pi\) | |||||||
\(14\) | 374.869 | − | 358.308i | 0.511164 | − | 0.488581i | ||||
\(15\) | −894.565 | −1.02656 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | −619.040 | − | 1072.21i | −0.519513 | − | 0.899823i | −0.999743 | − | 0.0226804i | \(-0.992780\pi\) |
0.480230 | − | 0.877143i | \(-0.340553\pi\) | |||||||
\(18\) | −741.739 | − | 1284.73i | −0.539597 | − | 0.934610i | ||||
\(19\) | 140.140 | − | 242.729i | 0.0890588 | − | 0.154254i | −0.818055 | − | 0.575140i | \(-0.804947\pi\) |
0.907114 | + | 0.420886i | \(0.138281\pi\) | |||||||
\(20\) | −577.689 | −0.322938 | ||||||||
\(21\) | 761.065 | + | 3120.59i | 0.376594 | + | 1.54415i | ||||
\(22\) | 621.739 | 0.273874 | ||||||||
\(23\) | 1741.20 | − | 3015.84i | 0.686322 | − | 1.18874i | −0.286698 | − | 0.958021i | \(-0.592557\pi\) |
0.973019 | − | 0.230723i | \(-0.0741092\pi\) | |||||||
\(24\) | −792.844 | − | 1373.25i | −0.280970 | − | 0.486654i | ||||
\(25\) | 910.694 | + | 1577.37i | 0.291422 | + | 0.504758i | ||||
\(26\) | −2317.74 | + | 4014.44i | −0.672405 | + | 1.16464i | ||||
\(27\) | 3168.14 | 0.836364 | ||||||||
\(28\) | 491.478 | + | 2015.20i | 0.118470 | + | 0.485762i | ||||
\(29\) | −5656.78 | −1.24903 | −0.624517 | − | 0.781011i | \(-0.714704\pi\) | ||||
−0.624517 | + | 0.781011i | \(0.714704\pi\) | |||||||
\(30\) | 1789.13 | − | 3098.87i | 0.362943 | − | 0.628636i | ||||
\(31\) | 1157.35 | + | 2004.59i | 0.216302 | + | 0.374646i | 0.953675 | − | 0.300840i | \(-0.0972671\pi\) |
−0.737372 | + | 0.675486i | \(0.763934\pi\) | |||||||
\(32\) | −512.000 | − | 886.810i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1925.56 | + | 3335.16i | −0.307802 | + | 0.533128i | ||||
\(34\) | 4952.32 | 0.734703 | ||||||||
\(35\) | −3383.72 | + | 3234.23i | −0.466900 | + | 0.446273i | ||||
\(36\) | 5933.91 | 0.763106 | ||||||||
\(37\) | 1166.59 | − | 2020.59i | 0.140092 | − | 0.242646i | −0.787439 | − | 0.616392i | \(-0.788594\pi\) |
0.927531 | + | 0.373746i | \(0.121927\pi\) | |||||||
\(38\) | 560.558 | + | 970.916i | 0.0629741 | + | 0.109074i | ||||
\(39\) | −14356.3 | − | 24865.8i | −1.51141 | − | 2.61783i | ||||
\(40\) | 1155.38 | − | 2001.17i | 0.114176 | − | 0.197758i | ||||
\(41\) | 3812.61 | 0.354211 | 0.177106 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177106 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(42\) | −12332.2 | − | 3604.77i | −1.07874 | − | 0.315322i | ||||
\(43\) | 3925.73 | 0.323780 | 0.161890 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161890 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(44\) | −1243.48 | + | 2153.77i | −0.0968292 | + | 0.167713i | ||||
\(45\) | 6695.22 | + | 11596.5i | 0.492872 | + | 0.853679i | ||||
\(46\) | 6964.78 | + | 12063.4i | 0.485303 | + | 0.840569i | ||||
\(47\) | 5558.23 | − | 9627.13i | 0.367022 | − | 0.635700i | −0.622077 | − | 0.782956i | \(-0.713711\pi\) |
0.989098 | + | 0.147256i | \(0.0470442\pi\) | |||||||
\(48\) | 6342.76 | 0.397352 | ||||||||
\(49\) | 14161.0 | + | 9052.14i | 0.842566 | + | 0.538594i | ||||
\(50\) | −7285.56 | −0.412133 | ||||||||
\(51\) | −15337.6 | + | 26565.5i | −0.825717 | + | 1.43018i | ||||
\(52\) | −9270.96 | − | 16057.8i | −0.475462 | − | 0.823525i | ||||
\(53\) | 5593.10 | + | 9687.54i | 0.273504 | + | 0.473722i | 0.969757 | − | 0.244074i | \(-0.0784841\pi\) |
−0.696253 | + | 0.717797i | \(0.745151\pi\) | |||||||
\(54\) | −6336.29 | + | 10974.8i | −0.295699 | + | 0.512166i | ||||
\(55\) | −5612.06 | −0.250159 | ||||||||
\(56\) | −7963.82 | − | 2327.88i | −0.339353 | − | 0.0991950i | ||||
\(57\) | −6944.31 | −0.283101 | ||||||||
\(58\) | 11313.6 | − | 19595.7i | 0.441600 | − | 0.764874i | ||||
\(59\) | 3005.18 | + | 5205.12i | 0.112393 | + | 0.194671i | 0.916735 | − | 0.399497i | \(-0.130815\pi\) |
−0.804342 | + | 0.594167i | \(0.797482\pi\) | |||||||
\(60\) | 7156.52 | + | 12395.5i | 0.256640 | + | 0.444513i | ||||
\(61\) | 7419.36 | − | 12850.7i | 0.255295 | − | 0.442183i | −0.709681 | − | 0.704523i | \(-0.751161\pi\) |
0.964975 | + | 0.262340i | \(0.0844942\pi\) | |||||||
\(62\) | −9258.81 | −0.305897 | ||||||||
\(63\) | 34756.9 | − | 33221.4i | 1.10329 | − | 1.05455i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 20920.8 | − | 36235.9i | 0.614179 | − | 1.06379i | ||||
\(66\) | −7702.22 | − | 13340.6i | −0.217649 | − | 0.376979i | ||||
\(67\) | 21491.9 | + | 37225.1i | 0.584909 | + | 1.01309i | 0.994887 | + | 0.100997i | \(0.0322032\pi\) |
−0.409977 | + | 0.912096i | \(0.634463\pi\) | |||||||
\(68\) | −9904.64 | + | 17155.3i | −0.259757 | + | 0.449912i | ||||
\(69\) | −86281.1 | −2.18169 | ||||||||
\(70\) | −4436.27 | − | 18190.0i | −0.108211 | − | 0.443698i | ||||
\(71\) | −19962.4 | −0.469967 | −0.234984 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234984 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(72\) | −11867.8 | + | 20555.7i | −0.269799 | + | 0.467305i | ||||
\(73\) | −22775.3 | − | 39448.0i | −0.500215 | − | 0.866398i | −1.00000 | 0.000248463i | \(-0.999921\pi\) | |
0.499785 | − | 0.866150i | \(-0.333412\pi\) | |||||||
\(74\) | 4666.35 | + | 8082.36i | 0.0990599 | + | 0.171577i | ||||
\(75\) | 22563.7 | − | 39081.5i | 0.463188 | − | 0.802266i | ||||
\(76\) | −4484.47 | −0.0890588 | ||||||||
\(77\) | 4774.54 | + | 19577.0i | 0.0917709 | + | 0.376288i | ||||
\(78\) | 114850. | 2.13745 | ||||||||
\(79\) | −54496.0 | + | 94389.9i | −0.982419 | + | 1.70160i | −0.329534 | + | 0.944144i | \(0.606892\pi\) |
−0.652885 | + | 0.757457i | \(0.726442\pi\) | |||||||
\(80\) | 4621.51 | + | 8004.69i | 0.0807345 | + | 0.139836i | ||||
\(81\) | 5813.07 | + | 10068.5i | 0.0984448 | + | 0.170511i | ||||
\(82\) | −7625.22 | + | 13207.3i | −0.125233 | + | 0.216909i | ||||
\(83\) | 55829.0 | 0.889538 | 0.444769 | − | 0.895645i | \(-0.353286\pi\) | ||||
0.444769 | + | 0.895645i | \(0.353286\pi\) | |||||||
\(84\) | 37151.6 | − | 35510.4i | 0.574486 | − | 0.549107i | ||||
\(85\) | −44701.6 | −0.671082 | ||||||||
\(86\) | −7851.47 | + | 13599.1i | −0.114473 | + | 0.198274i | ||||
\(87\) | 70077.3 | + | 121377.i | 0.992611 | + | 1.71925i | ||||
\(88\) | −4973.91 | − | 8615.07i | −0.0684686 | − | 0.118591i | ||||
\(89\) | 47772.9 | − | 82745.1i | 0.639303 | − | 1.10731i | −0.346283 | − | 0.938130i | \(-0.612556\pi\) |
0.985586 | − | 0.169175i | \(-0.0541103\pi\) | |||||||
\(90\) | −53561.8 | −0.697026 | ||||||||
\(91\) | −144204. | − | 42151.6i | −1.82546 | − | 0.533594i | ||||
\(92\) | −55718.2 | −0.686322 | ||||||||
\(93\) | 28675.0 | − | 49666.5i | 0.343792 | − | 0.595465i | ||||
\(94\) | 22232.9 | + | 38508.5i | 0.259523 | + | 0.449508i | ||||
\(95\) | −5059.82 | − | 8763.86i | −0.0575209 | − | 0.0996292i | ||||
\(96\) | −12685.5 | + | 21971.9i | −0.140485 | + | 0.243327i | ||||
\(97\) | 15004.9 | 0.161922 | 0.0809609 | − | 0.996717i | \(-0.474201\pi\) | ||||
0.0809609 | + | 0.996717i | \(0.474201\pi\) | |||||||
\(98\) | −59679.5 | + | 30950.9i | −0.627712 | + | 0.325542i | ||||
\(99\) | 57646.0 | 0.591127 | ||||||||
\(100\) | 14571.1 | − | 25237.9i | 0.145711 | − | 0.252379i | ||||
\(101\) | −13438.1 | − | 23275.4i | −0.131079 | − | 0.227036i | 0.793014 | − | 0.609204i | \(-0.208511\pi\) |
−0.924093 | + | 0.382168i | \(0.875178\pi\) | |||||||
\(102\) | −61350.3 | − | 106262.i | −0.583870 | − | 1.01129i | ||||
\(103\) | 25957.6 | − | 44959.9i | 0.241086 | − | 0.417573i | −0.719938 | − | 0.694038i | \(-0.755830\pi\) |
0.961024 | + | 0.276466i | \(0.0891632\pi\) | |||||||
\(104\) | 74167.6 | 0.672405 | ||||||||
\(105\) | 111315. | + | 32538.1i | 0.985327 | + | 0.288017i | ||||
\(106\) | −44744.8 | −0.386793 | ||||||||
\(107\) | 12487.4 | − | 21628.8i | 0.105442 | − | 0.182630i | −0.808477 | − | 0.588528i | \(-0.799708\pi\) |
0.913919 | + | 0.405898i | \(0.133041\pi\) | |||||||
\(108\) | −25345.1 | − | 43899.1i | −0.209091 | − | 0.362156i | ||||
\(109\) | 1818.07 | + | 3148.99i | 0.0146570 | + | 0.0253867i | 0.873261 | − | 0.487253i | \(-0.162001\pi\) |
−0.858604 | + | 0.512640i | \(0.828668\pi\) | |||||||
\(110\) | 11224.1 | − | 19440.7i | 0.0884444 | − | 0.153190i | ||||
\(111\) | −57807.7 | −0.445326 | ||||||||
\(112\) | 23991.6 | − | 22931.7i | 0.180724 | − | 0.172740i | ||||
\(113\) | 62175.0 | 0.458057 | 0.229028 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229028 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(114\) | 13888.6 | − | 24055.8i | 0.100091 | − | 0.173363i | ||||
\(115\) | −62866.8 | − | 108889.i | −0.443279 | − | 0.767781i | ||||
\(116\) | 45254.2 | + | 78382.7i | 0.312259 | + | 0.540848i | ||||
\(117\) | −214895. | + | 372208.i | −1.45131 | + | 2.51375i | ||||
\(118\) | −24041.4 | −0.158948 | ||||||||
\(119\) | 38030.6 | + | 155936.i | 0.246187 | + | 1.00944i | ||||
\(120\) | −57252.2 | −0.362943 | ||||||||
\(121\) | 68445.5 | − | 118551.i | 0.424993 | − | 0.736109i | ||||
\(122\) | 29677.4 | + | 51402.8i | 0.180521 | + | 0.312671i | ||||
\(123\) | −47231.3 | − | 81807.1i | −0.281493 | − | 0.487560i | ||||
\(124\) | 18517.6 | − | 32073.4i | 0.108151 | − | 0.187323i | ||||
\(125\) | 178592. | 1.02232 | ||||||||
\(126\) | 45568.5 | + | 186844.i | 0.255705 | + | 1.04846i | ||||
\(127\) | 63550.3 | 0.349630 | 0.174815 | − | 0.984601i | \(-0.444067\pi\) | ||||
0.174815 | + | 0.984601i | \(0.444067\pi\) | |||||||
\(128\) | −8192.00 | + | 14189.0i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −48632.7 | − | 84234.4i | −0.257309 | − | 0.445672i | ||||
\(130\) | 83683.2 | + | 144944.i | 0.434290 | + | 0.752213i | ||||
\(131\) | −68148.5 | + | 118037.i | −0.346959 | + | 0.600950i | −0.985708 | − | 0.168465i | \(-0.946119\pi\) |
0.638749 | + | 0.769415i | \(0.279452\pi\) | |||||||
\(132\) | 61617.8 | 0.307802 | ||||||||
\(133\) | −26267.0 | + | 25106.6i | −0.128760 | + | 0.123072i | ||||
\(134\) | −171935. | −0.827187 | ||||||||
\(135\) | 57193.8 | − | 99062.5i | 0.270094 | − | 0.467816i | ||||
\(136\) | −39618.6 | − | 68621.4i | −0.183676 | − | 0.318136i | ||||
\(137\) | −167652. | − | 290381.i | −0.763144 | − | 1.32180i | −0.941222 | − | 0.337788i | \(-0.890321\pi\) |
0.178078 | − | 0.984016i | \(-0.443012\pi\) | |||||||
\(138\) | 172562. | − | 298886.i | 0.771343 | − | 1.33601i | ||||
\(139\) | 58195.2 | 0.255476 | 0.127738 | − | 0.991808i | \(-0.459228\pi\) | ||||
0.127738 | + | 0.991808i | \(0.459228\pi\) | |||||||
\(140\) | 71884.6 | + | 21012.3i | 0.309967 | + | 0.0906054i | ||||
\(141\) | −275426. | −1.16669 | ||||||||
\(142\) | 39924.9 | − | 69151.9i | 0.166158 | − | 0.287795i | ||||
\(143\) | −90064.3 | − | 155996.i | −0.368309 | − | 0.637930i | ||||
\(144\) | −47471.3 | − | 82222.7i | −0.190776 | − | 0.330435i | ||||
\(145\) | −102121. | + | 176878.i | −0.403360 | + | 0.698641i | ||||
\(146\) | 182202. | 0.707411 | ||||||||
\(147\) | 18802.5 | − | 415992.i | 0.0717665 | − | 1.58779i | ||||
\(148\) | −37330.8 | −0.140092 | ||||||||
\(149\) | −141529. | + | 245135.i | −0.522251 | + | 0.904566i | 0.477414 | + | 0.878679i | \(0.341574\pi\) |
−0.999665 | + | 0.0258870i | \(0.991759\pi\) | |||||||
\(150\) | 90254.9 | + | 156326.i | 0.327524 | + | 0.567287i | ||||
\(151\) | 120779. | + | 209195.i | 0.431071 | + | 0.746637i | 0.996966 | − | 0.0778407i | \(-0.0248026\pi\) |
−0.565895 | + | 0.824477i | \(0.691469\pi\) | |||||||
\(152\) | 8968.93 | − | 15534.6i | 0.0314870 | − | 0.0545372i | ||||
\(153\) | 459166. | 1.58577 | ||||||||
\(154\) | −77365.9 | − | 22614.6i | −0.262874 | − | 0.0768398i | ||||
\(155\) | 83573.6 | 0.279409 | ||||||||
\(156\) | −229701. | + | 397853.i | −0.755703 | + | 1.30892i | ||||
\(157\) | 107014. | + | 185354.i | 0.346492 | + | 0.600142i | 0.985624 | − | 0.168956i | \(-0.0540394\pi\) |
−0.639132 | + | 0.769097i | \(0.720706\pi\) | |||||||
\(158\) | −217984. | − | 377559.i | −0.694675 | − | 1.20321i | ||||
\(159\) | 138577. | − | 240022.i | 0.434708 | − | 0.752937i | ||||
\(160\) | −36972.1 | −0.114176 | ||||||||
\(161\) | −326360. | + | 311942.i | −0.992277 | + | 0.948440i | ||||
\(162\) | −46504.5 | −0.139222 | ||||||||
\(163\) | −32233.0 | + | 55829.2i | −0.0950237 | + | 0.164586i | −0.909619 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(164\) | −30500.9 | − | 52829.1i | −0.0885529 | − | 0.153378i | ||||
\(165\) | 69523.3 | + | 120418.i | 0.198802 | + | 0.344335i | ||||
\(166\) | −111658. | + | 193397.i | −0.314499 | + | 0.544729i | ||||
\(167\) | −442694. | −1.22832 | −0.614162 | − | 0.789180i | \(-0.710506\pi\) | ||||
−0.614162 | + | 0.789180i | \(0.710506\pi\) | |||||||
\(168\) | 48708.2 | + | 199718.i | 0.133146 | + | 0.545938i | ||||
\(169\) | 971685. | 2.61703 | ||||||||
\(170\) | 89403.2 | − | 154851.i | 0.237263 | − | 0.410952i | ||||
\(171\) | 51973.5 | + | 90020.7i | 0.135923 | + | 0.235425i | ||||
\(172\) | −31405.9 | − | 54396.6i | −0.0809449 | − | 0.140201i | ||||
\(173\) | 39299.5 | − | 68068.8i | 0.0998325 | − | 0.172915i | −0.811783 | − | 0.583960i | \(-0.801503\pi\) |
0.911615 | + | 0.411045i | \(0.134836\pi\) | |||||||
\(174\) | −560618. | −1.40376 | ||||||||
\(175\) | −55948.3 | − | 229404.i | −0.138099 | − | 0.566247i | ||||
\(176\) | 39791.3 | 0.0968292 | ||||||||
\(177\) | 74457.4 | − | 128964.i | 0.178638 | − | 0.309411i | ||||
\(178\) | 191092. | + | 330980.i | 0.452055 | + | 0.782983i | ||||
\(179\) | 255214. | + | 442043.i | 0.595348 | + | 1.03117i | 0.993498 | + | 0.113853i | \(0.0363193\pi\) |
−0.398149 | + | 0.917321i | \(0.630347\pi\) | |||||||
\(180\) | 107124. | − | 185543.i | 0.246436 | − | 0.426839i | ||||
\(181\) | −22051.8 | −0.0500319 | −0.0250160 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250160 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(182\) | 434425. | − | 415233.i | 0.972156 | − | 0.929208i | ||||
\(183\) | −367650. | −0.811534 | ||||||||
\(184\) | 111436. | − | 193014.i | 0.242651 | − | 0.420285i | ||||
\(185\) | −42120.3 | − | 72954.5i | −0.0904820 | − | 0.156719i | ||||
\(186\) | 114700. | + | 198666.i | 0.243098 | + | 0.421057i | ||||
\(187\) | −96220.4 | + | 166659.i | −0.201216 | + | 0.348517i | ||||
\(188\) | −177863. | −0.367022 | ||||||||
\(189\) | −394227. | − | 115235.i | −0.802771 | − | 0.234655i | ||||
\(190\) | 40478.5 | 0.0813469 | ||||||||
\(191\) | 279076. | − | 483374.i | 0.553528 | − | 0.958738i | −0.444489 | − | 0.895784i | \(-0.646615\pi\) |
0.998016 | − | 0.0629535i | \(-0.0200520\pi\) | |||||||
\(192\) | −50742.0 | − | 87887.8i | −0.0993379 | − | 0.172058i | ||||
\(193\) | 24658.1 | + | 42709.1i | 0.0476504 | + | 0.0825330i | 0.888867 | − | 0.458166i | \(-0.151493\pi\) |
−0.841216 | + | 0.540699i | \(0.818160\pi\) | |||||||
\(194\) | −30009.9 | + | 51978.7i | −0.0572480 | + | 0.0991564i | ||||
\(195\) | −1.03668e6 | −1.95236 | ||||||||
\(196\) | 12142.2 | − | 268638.i | 0.0225765 | − | 0.499490i | ||||
\(197\) | −941509. | −1.72846 | −0.864229 | − | 0.503099i | \(-0.832193\pi\) | ||||
−0.864229 | + | 0.503099i | \(0.832193\pi\) | |||||||
\(198\) | −115292. | + | 199692.i | −0.208995 | + | 0.361990i | ||||
\(199\) | −320006. | − | 554267.i | −0.572830 | − | 0.992170i | −0.996274 | − | 0.0862477i | \(-0.972512\pi\) |
0.423444 | − | 0.905922i | \(-0.360821\pi\) | |||||||
\(200\) | 58284.4 | + | 100952.i | 0.103033 | + | 0.178459i | ||||
\(201\) | 532493. | − | 922304.i | 0.929658 | − | 1.61022i | ||||
\(202\) | 107505. | 0.185374 | ||||||||
\(203\) | 703900. | + | 205754.i | 1.19887 | + | 0.350436i | ||||
\(204\) | 490803. | 0.825717 | ||||||||
\(205\) | 68828.2 | − | 119214.i | 0.114388 | − | 0.198126i | ||||
\(206\) | 103830. | + | 179840.i | 0.170473 | + | 0.295268i | ||||
\(207\) | 645756. | + | 1.11848e6i | 1.04747 | + | 1.81428i | ||||
\(208\) | −148335. | + | 256924.i | −0.237731 | + | 0.411762i | ||||
\(209\) | −43565.1 | −0.0689879 | ||||||||
\(210\) | −335345. | + | 320530.i | −0.524740 | + | 0.501558i | ||||
\(211\) | 921869. | 1.42549 | 0.712743 | − | 0.701425i | \(-0.247452\pi\) | ||||
0.712743 | + | 0.701425i | \(0.247452\pi\) | |||||||
\(212\) | 89489.7 | − | 155001.i | 0.136752 | − | 0.236861i | ||||
\(213\) | 247298. | + | 428333.i | 0.373484 | + | 0.646894i | ||||
\(214\) | 49949.5 | + | 86515.1i | 0.0745585 | + | 0.129139i | ||||
\(215\) | 70870.4 | − | 122751.i | 0.104561 | − | 0.181105i | ||||
\(216\) | 202761. | 0.295699 | ||||||||
\(217\) | −71101.5 | − | 291537.i | −0.102501 | − | 0.420285i | ||||
\(218\) | −14544.6 | −0.0207281 | ||||||||
\(219\) | −564290. | + | 977378.i | −0.795045 | + | 1.37706i | ||||
\(220\) | 44896.5 | + | 77762.9i | 0.0625396 | + | 0.108322i | ||||
\(221\) | −717387. | − | 1.24255e6i | −0.988036 | − | 1.71133i | ||||
\(222\) | 115615. | − | 200252.i | 0.157446 | − | 0.272705i | ||||
\(223\) | −837700. | −1.12805 | −0.564023 | − | 0.825759i | \(-0.690747\pi\) | ||||
−0.564023 | + | 0.825759i | \(0.690747\pi\) | |||||||
\(224\) | 31454.6 | + | 128973.i | 0.0418855 | + | 0.171743i | ||||
\(225\) | −675497. | −0.889544 | ||||||||
\(226\) | −124350. | + | 215380.i | −0.161948 | + | 0.280501i | ||||
\(227\) | 665344. | + | 1.15241e6i | 0.857002 | + | 1.48437i | 0.874775 | + | 0.484529i | \(0.161009\pi\) |
−0.0177731 | + | 0.999842i | \(0.505658\pi\) | |||||||
\(228\) | 55554.4 | + | 96223.1i | 0.0707753 | + | 0.122586i | ||||
\(229\) | −505317. | + | 875234.i | −0.636759 | + | 1.10290i | 0.349381 | + | 0.936981i | \(0.386392\pi\) |
−0.986140 | + | 0.165918i | \(0.946941\pi\) | |||||||
\(230\) | 502935. | 0.626891 | ||||||||
\(231\) | 360916. | − | 344971.i | 0.445017 | − | 0.425357i | ||||
\(232\) | −362034. | −0.441600 | ||||||||
\(233\) | −743050. | + | 1.28700e6i | −0.896661 | + | 1.55306i | −0.0649249 | + | 0.997890i | \(0.520681\pi\) |
−0.831736 | + | 0.555172i | \(0.812653\pi\) | |||||||
\(234\) | −859579. | − | 1.48883e6i | −1.02623 | − | 1.77749i | ||||
\(235\) | −200683. | − | 347593.i | −0.237050 | − | 0.410583i | ||||
\(236\) | 48082.8 | − | 83281.9i | 0.0561966 | − | 0.0973353i | ||||
\(237\) | 2.70043e6 | 3.12293 | ||||||||
\(238\) | −616241. | − | 180131.i | −0.705193 | − | 0.206132i | ||||
\(239\) | 875637. | 0.991584 | 0.495792 | − | 0.868441i | \(-0.334878\pi\) | ||||
0.495792 | + | 0.868441i | \(0.334878\pi\) | |||||||
\(240\) | 114504. | − | 198327.i | 0.128320 | − | 0.222257i | ||||
\(241\) | −726472. | − | 1.25829e6i | −0.805706 | − | 1.39552i | −0.915814 | − | 0.401604i | \(-0.868453\pi\) |
0.110108 | − | 0.993920i | \(-0.464880\pi\) | |||||||
\(242\) | 273782. | + | 474204.i | 0.300515 | + | 0.520508i | ||||
\(243\) | 528956. | − | 916179.i | 0.574651 | − | 0.995324i | ||||
\(244\) | −237419. | −0.255295 | ||||||||
\(245\) | 538691. | − | 279374.i | 0.573356 | − | 0.297352i | ||||
\(246\) | 377851. | 0.398091 | ||||||||
\(247\) | 162403. | − | 281291.i | 0.169376 | − | 0.293369i | ||||
\(248\) | 74070.4 | + | 128294.i | 0.0764743 | + | 0.132457i | ||||
\(249\) | −691621. | − | 1.19792e6i | −0.706919 | − | 1.22442i | ||||
\(250\) | −357184. | + | 618661.i | −0.361445 | + | 0.626041i | ||||
\(251\) | −198384. | −0.198757 | −0.0993786 | − | 0.995050i | \(-0.531685\pi\) | ||||
−0.0993786 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(252\) | −738385. | − | 215835.i | −0.732456 | − | 0.214101i | ||||
\(253\) | −541284. | −0.531648 | ||||||||
\(254\) | −127101. | + | 220145.i | −0.123613 | + | 0.214104i | ||||
\(255\) | 553772. | + | 959161.i | 0.533311 | + | 0.923722i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −239786. | + | 415321.i | −0.226460 | + | 0.392240i | −0.956756 | − | 0.290890i | \(-0.906048\pi\) |
0.730297 | + | 0.683130i | \(0.239382\pi\) | |||||||
\(258\) | 389062. | 0.363890 | ||||||||
\(259\) | −218659. | + | 208999.i | −0.202543 | + | 0.193595i | ||||
\(260\) | −669466. | −0.614179 | ||||||||
\(261\) | 1.04896e6 | − | 1.81686e6i | 0.953145 | − | 1.65090i | ||||
\(262\) | −272594. | − | 472147.i | −0.245337 | − | 0.424936i | ||||
\(263\) | −227471. | − | 393992.i | −0.202786 | − | 0.351235i | 0.746639 | − | 0.665229i | \(-0.231666\pi\) |
−0.949425 | + | 0.313994i | \(0.898333\pi\) | |||||||
\(264\) | −123236. | + | 213450.i | −0.108824 | + | 0.188489i | ||||
\(265\) | 403884. | 0.353299 | ||||||||
\(266\) | −34437.7 | − | 141205.i | −0.0298422 | − | 0.122362i | ||||
\(267\) | −2.36728e6 | −2.03222 | ||||||||
\(268\) | 343871. | − | 595602.i | 0.292455 | − | 0.506546i | ||||
\(269\) | 430068. | + | 744900.i | 0.362374 | + | 0.627650i | 0.988351 | − | 0.152192i | \(-0.0486331\pi\) |
−0.625977 | + | 0.779841i | \(0.715300\pi\) | |||||||
\(270\) | 228775. | + | 396250.i | 0.190985 | + | 0.330796i | ||||
\(271\) | −652790. | + | 1.13067e6i | −0.539946 | + | 0.935214i | 0.458960 | + | 0.888457i | \(0.348222\pi\) |
−0.998906 | + | 0.0467569i | \(0.985111\pi\) | |||||||
\(272\) | 316949. | 0.259757 | ||||||||
\(273\) | 881975. | + | 3.61636e6i | 0.716226 | + | 2.93673i | ||||
\(274\) | 1.34121e6 | 1.07925 | ||||||||
\(275\) | 141554. | − | 245178.i | 0.112873 | − | 0.195501i | ||||
\(276\) | 690248. | + | 1.19555e6i | 0.545422 | + | 0.944699i | ||||
\(277\) | 271554. | + | 470346.i | 0.212646 | + | 0.368314i | 0.952542 | − | 0.304408i | \(-0.0984586\pi\) |
−0.739896 | + | 0.672721i | \(0.765125\pi\) | |||||||
\(278\) | −116390. | + | 201594.i | −0.0903245 | + | 0.156447i | ||||
\(279\) | −858452. | −0.660246 | ||||||||
\(280\) | −216558. | + | 206991.i | −0.165074 | + | 0.157781i | ||||
\(281\) | 998089. | 0.754055 | 0.377028 | − | 0.926202i | \(-0.376946\pi\) | ||||
0.377028 | + | 0.926202i | \(0.376946\pi\) | |||||||
\(282\) | 550851. | − | 954102.i | 0.412488 | − | 0.714450i | ||||
\(283\) | −888660. | − | 1.53920e6i | −0.659583 | − | 1.14243i | −0.980724 | − | 0.195400i | \(-0.937399\pi\) |
0.321140 | − | 0.947032i | \(-0.395934\pi\) | |||||||
\(284\) | 159699. | + | 276608.i | 0.117492 | + | 0.203502i | ||||
\(285\) | −125364. | + | 217137.i | −0.0914241 | + | 0.158351i | ||||
\(286\) | 720514. | 0.520868 | ||||||||
\(287\) | −474421. | − | 138676.i | −0.339984 | − | 0.0993796i | ||||
\(288\) | 379770. | 0.269799 | ||||||||
\(289\) | −56493.2 | + | 97849.1i | −0.0397880 | + | 0.0689148i | ||||
\(290\) | −408482. | − | 707512.i | −0.285219 | − | 0.494014i | ||||
\(291\) | −185884. | − | 321961.i | −0.128680 | − | 0.222880i | ||||
\(292\) | −364405. | + | 631167.i | −0.250108 | + | 0.433199i | ||||
\(293\) | −1.63987e6 | −1.11594 | −0.557969 | − | 0.829862i | \(-0.688419\pi\) | ||||
−0.557969 | + | 0.829862i | \(0.688419\pi\) | |||||||
\(294\) | 1.40343e6 | + | 897118.i | 0.946942 | + | 0.605315i | ||||
\(295\) | 217007. | 0.145184 | ||||||||
\(296\) | 74661.6 | − | 129318.i | 0.0495300 | − | 0.0857884i | ||||
\(297\) | −246220. | − | 426465.i | −0.161969 | − | 0.280538i | ||||
\(298\) | −566116. | − | 980541.i | −0.369287 | − | 0.639625i | ||||
\(299\) | 2.01782e6 | − | 3.49496e6i | 1.30528 | − | 2.26081i | ||||
\(300\) | −722039. | −0.463188 | ||||||||
\(301\) | −488498. | − | 142791.i | −0.310775 | − | 0.0908415i | ||||
\(302\) | −966231. | −0.609626 | ||||||||
\(303\) | −332947. | + | 576681.i | −0.208338 | + | 0.360852i | ||||
\(304\) | 35875.7 | + | 62138.6i | 0.0222647 | + | 0.0385636i | ||||
\(305\) | −267880. | − | 463982.i | −0.164889 | − | 0.285595i | ||||
\(306\) | −918332. | + | 1.59060e6i | −0.560656 | + | 0.971084i | ||||
\(307\) | 2.38130e6 | 1.44201 | 0.721006 | − | 0.692928i | \(-0.243680\pi\) | ||||
0.721006 | + | 0.692928i | \(0.243680\pi\) | |||||||
\(308\) | 233071. | − | 222774.i | 0.139995 | − | 0.133810i | ||||
\(309\) | −1.28627e6 | −0.766366 | ||||||||
\(310\) | −167147. | + | 289507.i | −0.0987859 | + | 0.171102i | ||||
\(311\) | 622564. | + | 1.07831e6i | 0.364992 | + | 0.632184i | 0.988775 | − | 0.149413i | \(-0.0477385\pi\) |
−0.623783 | + | 0.781597i | \(0.714405\pi\) | |||||||
\(312\) | −918803. | − | 1.59141e6i | −0.534363 | − | 0.925543i | ||||
\(313\) | −831495. | + | 1.44019e6i | −0.479732 | + | 0.830921i | −0.999730 | − | 0.0232470i | \(-0.992600\pi\) |
0.519997 | + | 0.854168i | \(0.325933\pi\) | |||||||
\(314\) | −856115. | −0.490014 | ||||||||
\(315\) | −411319. | − | 1.68653e6i | −0.233562 | − | 0.957673i | ||||
\(316\) | 1.74387e6 | 0.982419 | ||||||||
\(317\) | 1.31243e6 | − | 2.27319e6i | 0.733547 | − | 1.27054i | −0.221812 | − | 0.975090i | \(-0.571197\pi\) |
0.955358 | − | 0.295450i | \(-0.0954697\pi\) | |||||||
\(318\) | 554308. | + | 960089.i | 0.307385 | + | 0.532407i | ||||
\(319\) | 439630. | + | 761462.i | 0.241886 | + | 0.418959i | ||||
\(320\) | 73944.2 | − | 128075.i | 0.0403672 | − | 0.0699181i | ||||
\(321\) | −618784. | −0.335179 | ||||||||
\(322\) | −427879. | − | 1.75443e6i | −0.229976 | − | 0.942967i | ||||
\(323\) | −347008. | −0.185069 | ||||||||
\(324\) | 93009.0 | − | 161096.i | 0.0492224 | − | 0.0852557i | ||||
\(325\) | 1.05538e6 | + | 1.82796e6i | 0.554241 | + | 0.959974i | ||||
\(326\) | −128932. | − | 223317.i | −0.0671919 | − | 0.116380i | ||||
\(327\) | 45045.3 | − | 78020.7i | 0.0232959 | − | 0.0403497i | ||||
\(328\) | 244007. | 0.125233 | ||||||||
\(329\) | −1.04180e6 | + | 995780.i | −0.530636 | + | 0.507193i | ||||
\(330\) | −556186. | −0.281148 | ||||||||
\(331\) | −869428. | + | 1.50589e6i | −0.436178 | + | 0.755482i | −0.997391 | − | 0.0721894i | \(-0.977001\pi\) |
0.561213 | + | 0.827671i | \(0.310335\pi\) | |||||||
\(332\) | −446632. | − | 773589.i | −0.222385 | − | 0.385181i | ||||
\(333\) | 432652. | + | 749375.i | 0.213810 | + | 0.370330i | ||||
\(334\) | 885389. | − | 1.53354e6i | 0.434278 | − | 0.752191i | ||||
\(335\) | 1.55196e6 | 0.755558 | ||||||||
\(336\) | −789259. | − | 230705.i | −0.381392 | − | 0.111483i | ||||
\(337\) | 853564. | 0.409413 | 0.204706 | − | 0.978823i | \(-0.434376\pi\) | ||||
0.204706 | + | 0.978823i | \(0.434376\pi\) | |||||||
\(338\) | −1.94337e6 | + | 3.36602e6i | −0.925260 | + | 1.60260i | ||||
\(339\) | −770236. | − | 1.33409e6i | −0.364019 | − | 0.630500i | ||||
\(340\) | 357613. | + | 619403.i | 0.167771 | + | 0.290587i | ||||
\(341\) | 179892. | − | 311583.i | 0.0837774 | − | 0.145107i | ||||
\(342\) | −415788. | −0.192224 | ||||||||
\(343\) | −1.43287e6 | − | 1.64148e6i | −0.657613 | − | 0.753356i | ||||
\(344\) | 251247. | 0.114473 | ||||||||
\(345\) | −1.55761e6 | + | 2.69786e6i | −0.704550 | + | 1.22032i | ||||
\(346\) | 157198. | + | 272275.i | 0.0705922 | + | 0.122269i | ||||
\(347\) | 1.49250e6 | + | 2.58508e6i | 0.665411 | + | 1.15253i | 0.979174 | + | 0.203024i | \(0.0650770\pi\) |
−0.313763 | + | 0.949501i | \(0.601590\pi\) | |||||||
\(348\) | 1.12124e6 | − | 1.94204e6i | 0.496306 | − | 0.859627i | ||||
\(349\) | 2.87467e6 | 1.26335 | 0.631676 | − | 0.775233i | \(-0.282367\pi\) | ||||
0.631676 | + | 0.775233i | \(0.282367\pi\) | |||||||
\(350\) | 906576. | + | 264998.i | 0.395580 | + | 0.115631i | ||||
\(351\) | 3.67146e6 | 1.59064 | ||||||||
\(352\) | −79582.6 | + | 137841.i | −0.0342343 | + | 0.0592955i | ||||
\(353\) | −735546. | − | 1.27400e6i | −0.314176 | − | 0.544169i | 0.665086 | − | 0.746767i | \(-0.268395\pi\) |
−0.979262 | + | 0.202598i | \(0.935062\pi\) | |||||||
\(354\) | 297830. | + | 515856.i | 0.126316 | + | 0.218786i | ||||
\(355\) | −360377. | + | 624192.i | −0.151770 | + | 0.262874i | ||||
\(356\) | −1.52873e6 | −0.639303 | ||||||||
\(357\) | 2.87480e6 | − | 2.74779e6i | 1.19381 | − | 1.14107i | ||||
\(358\) | −2.04171e6 | −0.841950 | ||||||||
\(359\) | −1.53900e6 | + | 2.66562e6i | −0.630233 | + | 1.09160i | 0.357270 | + | 0.934001i | \(0.383707\pi\) |
−0.987504 | + | 0.157595i | \(0.949626\pi\) | |||||||
\(360\) | 428494. | + | 742174.i | 0.174256 | + | 0.301821i | ||||
\(361\) | 1.19877e6 | + | 2.07633e6i | 0.484137 | + | 0.838550i | ||||
\(362\) | 44103.6 | − | 76389.6i | 0.0176890 | − | 0.0306382i | ||||
\(363\) | −3.39167e6 | −1.35097 | ||||||||
\(364\) | 569559. | + | 2.33536e6i | 0.225312 | + | 0.923846i | ||||
\(365\) | −1.64463e6 | −0.646154 | ||||||||
\(366\) | 735299. | − | 1.27358e6i | 0.286920 | − | 0.496961i | ||||
\(367\) | −808349. | − | 1.40010e6i | −0.313281 | − | 0.542618i | 0.665790 | − | 0.746139i | \(-0.268095\pi\) |
−0.979071 | + | 0.203521i | \(0.934761\pi\) | |||||||
\(368\) | 445746. | + | 772055.i | 0.171580 | + | 0.297186i | ||||
\(369\) | −706990. | + | 1.22454e6i | −0.270301 | + | 0.468175i | ||||
\(370\) | 336962. | 0.127961 | ||||||||
\(371\) | −343611. | − | 1.40890e6i | −0.129608 | − | 0.531431i | ||||
\(372\) | −917599. | −0.343792 | ||||||||
\(373\) | 2.38059e6 | − | 4.12331e6i | 0.885958 | − | 1.53452i | 0.0413462 | − | 0.999145i | \(-0.486835\pi\) |
0.844612 | − | 0.535379i | \(-0.179831\pi\) | |||||||
\(374\) | −384881. | − | 666634.i | −0.142281 | − | 0.246439i | ||||
\(375\) | −2.21243e6 | − | 3.83205e6i | −0.812442 | − | 1.40719i | ||||
\(376\) | 355727. | − | 616136.i | 0.129762 | − | 0.224754i | ||||
\(377\) | −6.55547e6 | −2.37548 | ||||||||
\(378\) | 1.18764e6 | − | 1.13517e6i | 0.427519 | − | 0.408632i | ||||
\(379\) | 1.00193e6 | 0.358294 | 0.179147 | − | 0.983822i | \(-0.442666\pi\) | ||||
0.179147 | + | 0.983822i | \(0.442666\pi\) | |||||||
\(380\) | −80957.1 | + | 140222.i | −0.0287605 | + | 0.0498146i | ||||
\(381\) | −787273. | − | 1.36360e6i | −0.277852 | − | 0.481253i | ||||
\(382\) | 1.11630e6 | + | 1.93350e6i | 0.391403 | + | 0.677930i | ||||
\(383\) | 1.41076e6 | − | 2.44351e6i | 0.491424 | − | 0.851172i | −0.508527 | − | 0.861046i | \(-0.669810\pi\) |
0.999951 | + | 0.00987425i | \(0.00314312\pi\) | |||||||
\(384\) | 405936. | 0.140485 | ||||||||
\(385\) | 698335. | + | 204128.i | 0.240111 | + | 0.0701859i | ||||
\(386\) | −197265. | −0.0673879 | ||||||||
\(387\) | −727967. | + | 1.26088e6i | −0.247078 | + | 0.427952i | ||||
\(388\) | −120040. | − | 207915.i | −0.0404804 | − | 0.0701142i | ||||
\(389\) | 621198. | + | 1.07595e6i | 0.208140 | + | 0.360510i | 0.951129 | − | 0.308795i | \(-0.0999256\pi\) |
−0.742988 | + | 0.669304i | \(0.766592\pi\) | |||||||
\(390\) | 2.07337e6 | − | 3.59118e6i | 0.690264 | − | 1.19557i | ||||
\(391\) | −4.31148e6 | −1.42621 | ||||||||
\(392\) | 906304. | + | 579337.i | 0.297892 | + | 0.190422i | ||||
\(393\) | 3.37695e6 | 1.10292 | ||||||||
\(394\) | 1.88302e6 | − | 3.26148e6i | 0.611102 | − | 1.05846i | ||||
\(395\) | 1.96761e6 | + | 3.40800e6i | 0.634521 | + | 1.09902i | ||||
\(396\) | −461168. | − | 798766.i | −0.147782 | − | 0.255966i | ||||
\(397\) | −1.37281e6 | + | 2.37778e6i | −0.437154 | + | 0.757173i | −0.997469 | − | 0.0711068i | \(-0.977347\pi\) |
0.560315 | + | 0.828280i | \(0.310680\pi\) | |||||||
\(398\) | 2.56005e6 | 0.810103 | ||||||||
\(399\) | 864113. | + | 252586.i | 0.271730 | + | 0.0794285i | ||||
\(400\) | −466276. | −0.145711 | ||||||||
\(401\) | 1.85668e6 | − | 3.21586e6i | 0.576601 | − | 0.998702i | −0.419265 | − | 0.907864i | \(-0.637712\pi\) |
0.995866 | − | 0.0908378i | \(-0.0289545\pi\) | |||||||
\(402\) | 2.12997e6 | + | 3.68922e6i | 0.657368 | + | 1.13859i | ||||
\(403\) | 1.34122e6 | + | 2.32306e6i | 0.411374 | + | 0.712521i | ||||
\(404\) | −215009. | + | 372407.i | −0.0655396 | + | 0.113518i | ||||
\(405\) | 419768. | 0.127166 | ||||||||
\(406\) | −2.12055e6 | + | 2.02687e6i | −0.638461 | + | 0.610255i | ||||
\(407\) | −362656. | −0.108520 | ||||||||
\(408\) | −981605. | + | 1.70019e6i | −0.291935 | + | 0.505647i | ||||
\(409\) | −1.87970e6 | − | 3.25574e6i | −0.555623 | − | 0.962367i | −0.997855 | − | 0.0654664i | \(-0.979146\pi\) |
0.442232 | − | 0.896901i | \(-0.354187\pi\) | |||||||
\(410\) | 275313. | + | 476856.i | 0.0808847 | + | 0.140096i | ||||
\(411\) | −4.15380e6 | + | 7.19460e6i | −1.21295 | + | 2.10088i | ||||
\(412\) | −830643. | −0.241086 | ||||||||
\(413\) | −184622. | − | 757005.i | −0.0532609 | − | 0.218385i | ||||
\(414\) | −5.16605e6 | −1.48135 | ||||||||
\(415\) | 1.00787e6 | − | 1.74568e6i | 0.287266 | − | 0.497559i | ||||
\(416\) | −593341. | − | 1.02770e6i | −0.168101 | − | 0.291160i | ||||
\(417\) | −720934. | − | 1.24869e6i | −0.203028 | − | 0.351654i | ||||
\(418\) | 87130.2 | − | 150914.i | 0.0243909 | − | 0.0422463i | ||||
\(419\) | 4.60027e6 | 1.28011 | 0.640056 | − | 0.768328i | \(-0.278911\pi\) | ||||
0.640056 | + | 0.768328i | \(0.278911\pi\) | |||||||
\(420\) | −439659. | − | 1.80273e6i | −0.121617 | − | 0.498663i | ||||
\(421\) | −404864. | −0.111328 | −0.0556639 | − | 0.998450i | \(-0.517728\pi\) | ||||
−0.0556639 | + | 0.998450i | \(0.517728\pi\) | |||||||
\(422\) | −1.84374e6 | + | 3.19345e6i | −0.503986 | + | 0.872929i | ||||
\(423\) | 2.06138e6 | + | 3.57041e6i | 0.560153 | + | 0.970213i | ||||
\(424\) | 357959. | + | 620003.i | 0.0966982 | + | 0.167486i | ||||
\(425\) | 1.12751e6 | − | 1.95291e6i | 0.302795 | − | 0.524457i | ||||
\(426\) | −1.97839e6 | −0.528187 | ||||||||
\(427\) | −1.39065e6 | + | 1.32921e6i | −0.369102 | + | 0.352796i | ||||
\(428\) | −399596. | −0.105442 | ||||||||
\(429\) | −2.23147e6 | + | 3.86502e6i | −0.585393 | + | 1.01393i | ||||
\(430\) | 283482. | + | 491004.i | 0.0739356 | + | 0.128060i | ||||
\(431\) | −47379.2 | − | 82063.2i | −0.0122856 | − | 0.0212792i | 0.859817 | − | 0.510602i | \(-0.170577\pi\) |
−0.872103 | + | 0.489323i | \(0.837244\pi\) | |||||||
\(432\) | −405522. | + | 702385.i | −0.104546 | + | 0.181078i | ||||
\(433\) | 4.31727e6 | 1.10660 | 0.553298 | − | 0.832983i | \(-0.313369\pi\) | ||||
0.553298 | + | 0.832983i | \(0.313369\pi\) | |||||||
\(434\) | 1.15212e6 | + | 336771.i | 0.293611 | + | 0.0858244i | ||||
\(435\) | 5.06036e6 | 1.28221 | ||||||||
\(436\) | 29089.2 | − | 50383.9i | 0.00732850 | − | 0.0126933i | ||||
\(437\) | −488021. | − | 845277.i | −0.122246 | − | 0.211736i | ||||
\(438\) | −2.25716e6 | − | 3.90951e6i | −0.562182 | − | 0.973727i | ||||
\(439\) | 1.11184e6 | − | 1.92576e6i | 0.275346 | − | 0.476914i | −0.694876 | − | 0.719130i | \(-0.744541\pi\) |
0.970222 | + | 0.242216i | \(0.0778741\pi\) | |||||||
\(440\) | −359172. | −0.0884444 | ||||||||
\(441\) | −5.53333e6 | + | 2.86968e6i | −1.35485 | + | 0.702647i | ||||
\(442\) | 5.73909e6 | 1.39729 | ||||||||
\(443\) | 2.34213e6 | − | 4.05668e6i | 0.567024 | − | 0.982114i | −0.429835 | − | 0.902908i | \(-0.641428\pi\) |
0.996858 | − | 0.0792062i | \(-0.0252386\pi\) | |||||||
\(444\) | 462461. | + | 801006.i | 0.111331 | + | 0.192832i | ||||
\(445\) | −1.72487e6 | − | 2.98756e6i | −0.412910 | − | 0.715182i | ||||
\(446\) | 1.67540e6 | − | 2.90188e6i | 0.398824 | − | 0.690784i | ||||
\(447\) | 7.01315e6 | 1.66014 | ||||||||
\(448\) | −509685. | − | 148984.i | −0.119979 | − | 0.0350707i | ||||
\(449\) | 897932. | 0.210198 | 0.105099 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105099 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(450\) | 1.35099e6 | − | 2.33999e6i | 0.314501 | − | 0.544732i | ||||
\(451\) | −296306. | − | 513217.i | −0.0685960 | − | 0.118812i | ||||
\(452\) | −497400. | − | 861522.i | −0.114514 | − | 0.198344i | ||||
\(453\) | 2.99246e6 | − | 5.18310e6i | 0.685147 | − | 1.18671i | ||||
\(454\) | −5.32276e6 | −1.21198 | ||||||||
\(455\) | −3.92129e6 | + | 3.74805e6i | −0.887974 | + | 0.848745i | ||||
\(456\) | −444436. | −0.100091 | ||||||||
\(457\) | −2.99091e6 | + | 5.18040e6i | −0.669903 | + | 1.16031i | 0.308027 | + | 0.951377i | \(0.400331\pi\) |
−0.977931 | + | 0.208929i | \(0.933002\pi\) | |||||||
\(458\) | −2.02127e6 | − | 3.50094e6i | −0.450256 | − | 0.779867i | ||||
\(459\) | −1.96121e6 | − | 3.39691e6i | −0.434502 | − | 0.752580i | ||||
\(460\) | −1.00587e6 | + | 1.74222e6i | −0.221639 | + | 0.383891i | ||||
\(461\) | 1.62507e6 | 0.356138 | 0.178069 | − | 0.984018i | \(-0.443015\pi\) | ||||
0.178069 | + | 0.984018i | \(0.443015\pi\) | |||||||
\(462\) | 473184. | + | 1.94019e6i | 0.103139 | + | 0.422902i | ||||
\(463\) | −8.46295e6 | −1.83472 | −0.917359 | − | 0.398060i | \(-0.869683\pi\) | ||||
−0.917359 | + | 0.398060i | \(0.869683\pi\) | |||||||
\(464\) | 724068. | − | 1.25412e6i | 0.156129 | − | 0.270424i | ||||
\(465\) | −1.03533e6 | − | 1.79324e6i | −0.222047 | − | 0.384596i | ||||
\(466\) | −2.97220e6 | − | 5.14800e6i | −0.634035 | − | 1.09818i | ||||
\(467\) | −3.83297e6 | + | 6.63890e6i | −0.813286 | + | 1.40865i | 0.0972658 | + | 0.995258i | \(0.468990\pi\) |
−0.910552 | + | 0.413395i | \(0.864343\pi\) | |||||||
\(468\) | 6.87663e6 | 1.45131 | ||||||||
\(469\) | −1.32035e6 | − | 5.41383e6i | −0.277177 | − | 1.13651i | ||||
\(470\) | 1.60546e6 | 0.335240 | ||||||||
\(471\) | 2.65143e6 | − | 4.59241e6i | 0.550717 | − | 0.953869i | ||||
\(472\) | 192331. | + | 333127.i | 0.0397370 | + | 0.0688265i | ||||
\(473\) | −305098. | − | 528445.i | −0.0627027 | − | 0.108604i | ||||
\(474\) | −5.40086e6 | + | 9.35456e6i | −1.10412 | + | 1.91239i | ||||
\(475\) | 510497. | 0.103815 | ||||||||
\(476\) | 1.85647e6 | − | 1.77446e6i | 0.375553 | − | 0.358962i | ||||
\(477\) | −4.14862e6 | −0.834849 | ||||||||
\(478\) | −1.75127e6 | + | 3.03330e6i | −0.350578 | + | 0.607219i | ||||
\(479\) | 1.20146e6 | + | 2.08099e6i | 0.239261 | + | 0.414412i | 0.960502 | − | 0.278272i | \(-0.0897616\pi\) |
−0.721242 | + | 0.692683i | \(0.756428\pi\) | |||||||
\(480\) | 458017. | + | 793309.i | 0.0907358 | + | 0.157159i | ||||
\(481\) | 1.35192e6 | − | 2.34160e6i | 0.266434 | − | 0.461477i | ||||
\(482\) | 5.81178e6 | 1.13944 | ||||||||
\(483\) | 1.07364e7 | + | 3.13831e6i | 2.09406 | + | 0.612107i | ||||
\(484\) | −2.19026e6 | −0.424993 | ||||||||
\(485\) | 270881. | − | 469180.i | 0.0522907 | − | 0.0905701i | ||||
\(486\) | 2.11582e6 | + | 3.66472e6i | 0.406339 | + | 0.703801i | ||||
\(487\) | 85150.8 | + | 147486.i | 0.0162692 | + | 0.0281791i | 0.874045 | − | 0.485844i | \(-0.161488\pi\) |
−0.857776 | + | 0.514023i | \(0.828154\pi\) | |||||||
\(488\) | 474839. | − | 822445.i | 0.0902603 | − | 0.156335i | ||||
\(489\) | 1.59724e6 | 0.302063 | ||||||||
\(490\) | −109600. | + | 2.42483e6i | −0.0206215 | + | 0.456237i | ||||
\(491\) | −5.77628e6 | −1.08130 | −0.540648 | − | 0.841249i | \(-0.681821\pi\) | ||||
−0.540648 | + | 0.841249i | \(0.681821\pi\) | |||||||
\(492\) | −755701. | + | 1.30891e6i | −0.140746 | + | 0.243780i | ||||
\(493\) | 3.50177e6 | + | 6.06525e6i | 0.648890 | + | 1.12391i | ||||
\(494\) | 649614. | + | 1.12516e6i | 0.119767 | + | 0.207443i | ||||
\(495\) | 1.04067e6 | − | 1.80249e6i | 0.190897 | − | 0.330644i | ||||
\(496\) | −592564. | −0.108151 | ||||||||
\(497\) | 2.48402e6 | + | 726095.i | 0.451091 | + | 0.131857i | ||||
\(498\) | 5.53296e6 | 0.999734 | ||||||||
\(499\) | −271801. | + | 470773.i | −0.0488652 | + | 0.0846369i | −0.889423 | − | 0.457084i | \(-0.848894\pi\) |
0.840558 | + | 0.541721i | \(0.182227\pi\) | |||||||
\(500\) | −1.42874e6 | − | 2.47464e6i | −0.255580 | − | 0.442678i | ||||
\(501\) | 5.48418e6 | + | 9.49888e6i | 0.976152 | + | 1.69075i | ||||
\(502\) | 396769. | − | 687223.i | 0.0702713 | − | 0.121713i | ||||
\(503\) | −5.40086e6 | −0.951794 | −0.475897 | − | 0.879501i | \(-0.657876\pi\) | ||||
−0.475897 | + | 0.879501i | \(0.657876\pi\) | |||||||
\(504\) | 2.22444e6 | − | 2.12617e6i | 0.390072 | − | 0.372839i | ||||
\(505\) | −970378. | −0.169322 | ||||||||
\(506\) | 1.08257e6 | − | 1.87506e6i | 0.187966 | − | 0.325567i | ||||
\(507\) | −1.20374e7 | − | 2.08494e7i | −2.07976 | − | 3.60225i | ||||
\(508\) | −508402. | − | 880579.i | −0.0874074 | − | 0.151394i | ||||
\(509\) | −4.17209e6 | + | 7.22628e6i | −0.713772 | + | 1.23629i | 0.249659 | + | 0.968334i | \(0.419681\pi\) |
−0.963431 | + | 0.267955i | \(0.913652\pi\) | |||||||
\(510\) | −4.43018e6 | −0.754216 | ||||||||
\(511\) | 1.39919e6 | + | 5.73710e6i | 0.237042 | + | 0.971942i | ||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 443982. | − | 769000.i | 0.0744856 | − | 0.129013i | ||||
\(514\) | −959144. | − | 1.66129e6i | −0.160131 | − | 0.277355i | ||||
\(515\) | −937213. | − | 1.62330e6i | −0.155711 | − | 0.269700i | ||||
\(516\) | −778124. | + | 1.34775e6i | −0.128654 | + | 0.222836i | ||||
\(517\) | −1.72788e6 | −0.284307 | ||||||||
\(518\) | −286676. | − | 1.17546e6i | −0.0469426 | − | 0.192478i | ||||
\(519\) | −1.94740e6 | −0.317349 | ||||||||
\(520\) | 1.33893e6 | − | 2.31910e6i | 0.217145 | − | 0.376106i | ||||
\(521\) | 5.73919e6 | + | 9.94057e6i | 0.926310 | + | 1.60442i | 0.789441 | + | 0.613827i | \(0.210371\pi\) |
0.136870 | + | 0.990589i | \(0.456296\pi\) | |||||||
\(522\) | 4.19585e6 | + | 7.26743e6i | 0.673976 | + | 1.16736i | ||||
\(523\) | 2.19367e6 | − | 3.79955e6i | 0.350685 | − | 0.607404i | −0.635685 | − | 0.771949i | \(-0.719282\pi\) |
0.986370 | + | 0.164545i | \(0.0526155\pi\) | |||||||
\(524\) | 2.18075e6 | 0.346959 | ||||||||
\(525\) | −4.22922e6 | + | 4.04238e6i | −0.669673 | + | 0.640088i | ||||
\(526\) | 1.81977e6 | 0.286782 | ||||||||
\(527\) | 1.43289e6 | − | 2.48184e6i | 0.224744 | − | 0.389267i | ||||
\(528\) | −492942. | − | 853801.i | −0.0769505 | − | 0.133282i | ||||
\(529\) | −2.84535e6 | − | 4.92829e6i | −0.442075 | − | 0.765697i | ||||
\(530\) | −807769. | + | 1.39910e6i | −0.124910 | + | 0.216350i | ||||
\(531\) | −2.22906e6 | −0.343071 | ||||||||
\(532\) | 558023. | + | 163114.i | 0.0854817 | + | 0.0249869i | ||||
\(533\) | 4.41832e6 | 0.673657 | ||||||||
\(534\) | 4.73456e6 | − | 8.20050e6i | 0.718500 | − | 1.24448i | ||||
\(535\) | −450864. | − | 780919.i | −0.0681022 | − | 0.117956i | ||||
\(536\) | 1.37548e6 | + | 2.38241e6i | 0.206797 | + | 0.358182i | ||||
\(537\) | 6.32327e6 | − | 1.09522e7i | 0.946250 | − | 1.63895i | ||||
\(538\) | −3.44055e6 | −0.512474 | ||||||||
\(539\) | 117957. | − | 2.60973e6i | 0.0174885 | − | 0.386922i | ||||
\(540\) | −1.83020e6 | −0.270094 | ||||||||
\(541\) | −3.61153e6 | + | 6.25535e6i | −0.530515 | + | 0.918879i | 0.468851 | + | 0.883277i | \(0.344668\pi\) |
−0.999366 | + | 0.0356020i | \(0.988665\pi\) | |||||||
\(542\) | −2.61116e6 | − | 4.52266e6i | −0.381799 | − | 0.661296i | ||||
\(543\) | 273182. | + | 473165.i | 0.0397605 | + | 0.0688673i | ||||
\(544\) | −633897. | + | 1.09794e6i | −0.0918378 | + | 0.159068i | ||||
\(545\) | 131285. | 0.0189332 | ||||||||
\(546\) | −1.42914e7 | − | 4.17746e6i | −2.05160 | − | 0.599696i | ||||
\(547\) | 3.54529e6 | 0.506622 | 0.253311 | − | 0.967385i | \(-0.418480\pi\) | ||||
0.253311 | + | 0.967385i | \(0.418480\pi\) | |||||||
\(548\) | −2.68243e6 | + | 4.64610e6i | −0.381572 | + | 0.660902i | ||||
\(549\) | 2.75161e6 | + | 4.76593e6i | 0.389634 | + | 0.674865i | ||||
\(550\) | 566214. | + | 980712.i | 0.0798131 | + | 0.138240i | ||||
\(551\) | −792739. | + | 1.37306e6i | −0.111237 | + | 0.192669i | ||||
\(552\) | −5.52199e6 | −0.771343 | ||||||||
\(553\) | 1.02144e7 | − | 9.76319e6i | 1.42037 | − | 1.35762i | ||||
\(554\) | −2.17243e6 | −0.300727 | ||||||||
\(555\) | −1.04359e6 | + | 1.80755e6i | −0.143813 | + | 0.249091i | ||||
\(556\) | −465562. | − | 806377.i | −0.0638691 | − | 0.110624i | ||||
\(557\) | −5.18314e6 | − | 8.97747e6i | −0.707873 | − | 1.22607i | −0.965645 | − | 0.259866i | \(-0.916322\pi\) |
0.257772 | − | 0.966206i | \(-0.417012\pi\) | |||||||
\(558\) | 1.71690e6 | − | 2.97377e6i | 0.233432 | − | 0.404316i | ||||
\(559\) | 4.54941e6 | 0.615780 | ||||||||
\(560\) | −283921. | − | 1.16416e6i | −0.0382585 | − | 0.156871i | ||||
\(561\) | 4.76799e6 | 0.639628 | ||||||||
\(562\) | −1.99618e6 | + | 3.45748e6i | −0.266599 | + | 0.461763i | ||||
\(563\) | 2.24141e6 | + | 3.88223e6i | 0.298023 | + | 0.516191i | 0.975684 | − | 0.219184i | \(-0.0703394\pi\) |
−0.677660 | + | 0.735375i | \(0.737006\pi\) | |||||||
\(564\) | 2.20340e6 | + | 3.81641e6i | 0.291673 | + | 0.505193i | ||||
\(565\) | 1.12243e6 | − | 1.94411e6i | 0.147924 | − | 0.256212i | ||||
\(566\) | 7.10928e6 | 0.932792 | ||||||||
\(567\) | −357124. | − | 1.46431e6i | −0.0466511 | − | 0.191283i | ||||
\(568\) | −1.27760e6 | −0.166158 | ||||||||
\(569\) | −3.24668e6 | + | 5.62341e6i | −0.420396 | + | 0.728147i | −0.995978 | − | 0.0895969i | \(-0.971442\pi\) |
0.575582 | + | 0.817744i | \(0.304775\pi\) | |||||||
\(570\) | −501456. | − | 868547.i | −0.0646466 | − | 0.111971i | ||||
\(571\) | 248754. | + | 430854.i | 0.0319286 | + | 0.0553019i | 0.881548 | − | 0.472094i | \(-0.156502\pi\) |
−0.849620 | + | 0.527396i | \(0.823168\pi\) | |||||||
\(572\) | −1.44103e6 | + | 2.49593e6i | −0.184155 | + | 0.318965i | ||||
\(573\) | −1.38290e7 | −1.75956 | ||||||||
\(574\) | 1.42923e6 | − | 1.36609e6i | 0.181060 | − | 0.173061i | ||||
\(575\) | 6.34279e6 | 0.800038 | ||||||||
\(576\) | −759541. | + | 1.31556e6i | −0.0953882 | + | 0.165217i | ||||
\(577\) | 3.27561e6 | + | 5.67353e6i | 0.409594 | + | 0.709437i | 0.994844 | − | 0.101416i | \(-0.0323372\pi\) |
−0.585250 | + | 0.810853i | \(0.699004\pi\) | |||||||
\(578\) | −225973. | − | 391397.i | −0.0281343 | − | 0.0487301i | ||||
\(579\) | 610939. | − | 1.05818e6i | 0.0757359 | − | 0.131178i | ||||
\(580\) | 3.26786e6 | 0.403360 | ||||||||
\(581\) | −6.94707e6 | − | 2.03067e6i | −0.853810 | − | 0.249574i | ||||
\(582\) | 1.48707e6 | 0.181981 | ||||||||
\(583\) | 869363. | − | 1.50578e6i | 0.105933 | − | 0.183481i | ||||
\(584\) | −1.45762e6 | − | 2.52467e6i | −0.176853 | − | 0.306318i | ||||
\(585\) | 7.75889e6 | + | 1.34388e7i | 0.937368 | + | 1.62357i | ||||
\(586\) | 3.27974e6 | − | 5.68067e6i | 0.394543 | − | 0.683369i | ||||
\(587\) | −30793.5 | −0.00368862 | −0.00184431 | − | 0.999998i | \(-0.500587\pi\) | ||||
−0.00184431 | + | 0.999998i | \(0.500587\pi\) | |||||||
\(588\) | −5.91457e6 | + | 3.06740e6i | −0.705473 | + | 0.365870i | ||||
\(589\) | 648763. | 0.0770544 | ||||||||
\(590\) | −434014. | + | 751735.i | −0.0513303 | + | 0.0889067i | ||||
\(591\) | 1.16636e7 | + | 2.02019e7i | 1.37361 | + | 2.37916i | ||||
\(592\) | 298646. | + | 517271.i | 0.0350230 | + | 0.0606616i | ||||
\(593\) | −285468. | + | 494446.i | −0.0333366 | + | 0.0577407i | −0.882212 | − | 0.470852i | \(-0.843947\pi\) |
0.848876 | + | 0.528592i | \(0.177280\pi\) | |||||||
\(594\) | 1.96976e6 | 0.229059 | ||||||||
\(595\) | 5.56243e6 | + | 1.62593e6i | 0.644128 | + | 0.188283i | ||||
\(596\) | 4.52893e6 | 0.522251 | ||||||||
\(597\) | −7.92859e6 | + | 1.37327e7i | −0.910459 | + | 1.57696i | ||||
\(598\) | 8.07127e6 | + | 1.39799e7i | 0.922973 | + | 1.59864i | ||||
\(599\) | −4.53555e6 | − | 7.85581e6i | −0.516492 | − | 0.894590i | −0.999817 | − | 0.0191488i | \(-0.993904\pi\) |
0.483325 | − | 0.875441i | \(-0.339429\pi\) | |||||||
\(600\) | 1.44408e6 | − | 2.50122e6i | 0.163762 | − | 0.283644i | ||||
\(601\) | −1.36309e7 | −1.53936 | −0.769679 | − | 0.638431i | \(-0.779584\pi\) | ||||
−0.769679 | + | 0.638431i | \(0.779584\pi\) | |||||||
\(602\) | 1.47164e6 | − | 1.40662e6i | 0.165504 | − | 0.158193i | ||||
\(603\) | −1.59414e7 | −1.78539 | ||||||||
\(604\) | 1.93246e6 | − | 3.34712e6i | 0.215535 | − | 0.373318i | ||||
\(605\) | −2.47126e6 | − | 4.28035e6i | −0.274493 | − | 0.475435i | ||||
\(606\) | −1.33179e6 | − | 2.30672e6i | −0.147317 | − | 0.255161i | ||||
\(607\) | 1.97825e6 | − | 3.42644e6i | 0.217927 | − | 0.377460i | −0.736247 | − | 0.676713i | \(-0.763404\pi\) |
0.954174 | + | 0.299253i | \(0.0967373\pi\) | |||||||
\(608\) | −287006. | −0.0314870 | ||||||||
\(609\) | −4.30518e6 | − | 1.76525e7i | −0.470379 | − | 1.92869i | ||||
\(610\) | 2.14304e6 | 0.233188 | ||||||||
\(611\) | 6.44126e6 | − | 1.11566e7i | 0.698020 | − | 1.20901i | ||||
\(612\) | −3.67333e6 | − | 6.36239e6i | −0.396444 | − | 0.686660i | ||||
\(613\) | −661552. | − | 1.14584e6i | −0.0711070 | − | 0.123161i | 0.828280 | − | 0.560315i | \(-0.189320\pi\) |
−0.899387 | + | 0.437154i | \(0.855987\pi\) | |||||||
\(614\) | −4.76261e6 | + | 8.24908e6i | −0.509828 | + | 0.883049i | ||||
\(615\) | −3.41063e6 | −0.363619 | ||||||||
\(616\) | 305571. | + | 1.25293e6i | 0.0324459 | + | 0.133038i | ||||
\(617\) | 9.26370e6 | 0.979651 | 0.489826 | − | 0.871820i | \(-0.337060\pi\) | ||||
0.489826 | + | 0.871820i | \(0.337060\pi\) | |||||||
\(618\) | 2.57254e6 | − | 4.45577e6i | 0.270951 | − | 0.469301i | ||||
\(619\) | −334693. | − | 579705.i | −0.0351091 | − | 0.0608107i | 0.847937 | − | 0.530097i | \(-0.177845\pi\) |
−0.883046 | + | 0.469286i | \(0.844511\pi\) | |||||||
\(620\) | −668589. | − | 1.15803e6i | −0.0698521 | − | 0.120987i | ||||
\(621\) | 5.51636e6 | − | 9.55461e6i | 0.574015 | − | 0.994223i | ||||
\(622\) | −4.98051e6 | −0.516176 | ||||||||
\(623\) | −8.95430e6 | + | 8.55872e6i | −0.924297 | + | 0.883463i | ||||
\(624\) | 7.35043e6 | 0.755703 | ||||||||
\(625\) | 378164. | − | 654999.i | 0.0387240 | − | 0.0670719i | ||||
\(626\) | −3.32598e6 | − | 5.76077e6i | −0.339222 | − | 0.587550i | ||||
\(627\) | 539693. | + | 934776.i | 0.0548249 | + | 0.0949595i | ||||
\(628\) | 1.71223e6 | − | 2.96567e6i | 0.173246 | − | 0.300071i | ||||
\(629\) | −2.88866e6 | −0.291118 | ||||||||
\(630\) | 6.66495e6 | + | 1.94821e6i | 0.669030 | + | 0.195562i | ||||
\(631\) | −666246. | −0.0666133 | −0.0333067 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333067 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(632\) | −3.48774e6 | + | 6.04095e6i | −0.347338 | + | 0.601607i | ||||
\(633\) | −1.14203e7 | − | 1.97805e7i | −1.13284 | − | 1.96213i | ||||
\(634\) | 5.24972e6 | + | 9.09277e6i | 0.518696 | + | 0.898407i | ||||
\(635\) | 1.14726e6 | − | 1.98711e6i | 0.112909 | − | 0.195564i | ||||
\(636\) | −4.43446e6 | −0.434708 | ||||||||
\(637\) | 1.64108e7 | + | 1.04903e7i | 1.60243 | + | 1.02432i | ||||
\(638\) | −3.51704e6 | −0.342078 | ||||||||
\(639\) | 3.70173e6 | − | 6.41158e6i | 0.358635 | − | 0.621173i | ||||
\(640\) | 295777. | + | 512300.i | 0.0285439 | + | 0.0494396i | ||||
\(641\) | 1.05439e6 | + | 1.82625e6i | 0.101357 | + | 0.175556i | 0.912244 | − | 0.409647i | \(-0.134348\pi\) |
−0.810887 | + | 0.585203i | \(0.801015\pi\) | |||||||
\(642\) | 1.23757e6 | − | 2.14353e6i | 0.118504 | − | 0.205254i | ||||
\(643\) | 1.25977e7 | 1.20161 | 0.600806 | − | 0.799395i | \(-0.294846\pi\) | ||||
0.600806 | + | 0.799395i | \(0.294846\pi\) | |||||||
\(644\) | 6.93328e6 | + | 2.02664e6i | 0.658756 | + | 0.192558i | ||||
\(645\) | −3.51182e6 | −0.332379 | ||||||||
\(646\) | 694016. | − | 1.20207e6i | 0.0654317 | − | 0.113331i | ||||
\(647\) | −8.56496e6 | − | 1.48349e7i | −0.804386 | − | 1.39324i | −0.916705 | − | 0.399565i | \(-0.869161\pi\) |
0.112319 | − | 0.993672i | \(-0.464172\pi\) | |||||||
\(648\) | 372036. | + | 644386.i | 0.0348055 | + | 0.0602849i | ||||
\(649\) | 467109. | − | 809056.i | 0.0435318 | − | 0.0753992i | ||||
\(650\) | −8.44301e6 | −0.783815 | ||||||||
\(651\) | −5.37469e6 | + | 5.13724e6i | −0.497051 | + | 0.475092i | ||||
\(652\) | 1.03146e6 | 0.0950237 | ||||||||
\(653\) | 4.12762e6 | − | 7.14925e6i | 0.378806 | − | 0.656112i | −0.612083 | − | 0.790794i | \(-0.709668\pi\) |
0.990889 | + | 0.134682i | \(0.0430013\pi\) | |||||||
\(654\) | 180181. | + | 312083.i | 0.0164727 | + | 0.0285316i | ||||
\(655\) | 2.46054e6 | + | 4.26178e6i | 0.224092 | + | 0.388139i | ||||
\(656\) | −488014. | + | 845265.i | −0.0442764 | + | 0.0766890i | ||||
\(657\) | 1.68933e7 | 1.52687 | ||||||||
\(658\) | −1.36587e6 | − | 5.60048e6i | −0.122983 | − | 0.504267i | ||||
\(659\) | −1.05417e7 | −0.945581 | −0.472790 | − | 0.881175i | \(-0.656753\pi\) | ||||
−0.472790 | + | 0.881175i | \(0.656753\pi\) | |||||||
\(660\) | 1.11237e6 | − | 1.92668e6i | 0.0994009 | − | 0.172167i | ||||
\(661\) | −2.23820e6 | − | 3.87668e6i | −0.199249 | − | 0.345109i | 0.749036 | − | 0.662529i | \(-0.230517\pi\) |
−0.948285 | + | 0.317420i | \(0.897184\pi\) | |||||||
\(662\) | −3.47771e6 | − | 6.02357e6i | −0.308424 | − | 0.534206i | ||||
\(663\) | −1.77743e7 | + | 3.07859e7i | −1.57039 | + | 2.72000i | ||||
\(664\) | 3.57306e6 | 0.314499 | ||||||||
\(665\) | 310848. | + | 1.27457e6i | 0.0272580 | + | 0.111766i | ||||
\(666\) | −3.46121e6 | −0.302373 | ||||||||
\(667\) | −9.84956e6 | + | 1.70599e7i | −0.857240 | + | 1.48478i | ||||
\(668\) | 3.54155e6 | + | 6.13415e6i | 0.307081 | + | 0.531880i | ||||
\(669\) | 1.03776e7 | + | 1.79745e7i | 0.896461 | + | 1.55272i | ||||
\(670\) | −3.10391e6 | + | 5.37614e6i | −0.267130 | + | 0.462683i | ||||
\(671\) | −2.30645e6 | −0.197760 | ||||||||
\(672\) | 2.37771e6 | − | 2.27266e6i | 0.203112 | − | 0.194139i | ||||
\(673\) | −1.87165e7 | −1.59289 | −0.796447 | − | 0.604708i | \(-0.793290\pi\) | ||||
−0.796447 | + | 0.604708i | \(0.793290\pi\) | |||||||
\(674\) | −1.70713e6 | + | 2.95683e6i | −0.144749 | + | 0.250713i | ||||
\(675\) | 2.88521e6 | + | 4.99733e6i | 0.243735 | + | 0.422162i | ||||
\(676\) | −7.77348e6 | − | 1.34641e7i | −0.654258 | − | 1.13321i | ||||
\(677\) | −2.08116e6 | + | 3.60467e6i | −0.174515 | + | 0.302270i | −0.939993 | − | 0.341192i | \(-0.889169\pi\) |
0.765478 | + | 0.643462i | \(0.222503\pi\) | |||||||
\(678\) | 6.16188e6 | 0.514801 | ||||||||
\(679\) | −1.86714e6 | − | 545776.i | −0.155418 | − | 0.0454297i | ||||
\(680\) | −2.86090e6 | −0.237263 | ||||||||
\(681\) | 1.64848e7 | − | 2.85526e7i | 1.36212 | − | 2.35927i | ||||
\(682\) | 719570. | + | 1.24633e6i | 0.0592396 | + | 0.102606i | ||||
\(683\) | 6.43455e6 | + | 1.11450e7i | 0.527796 | + | 0.914170i | 0.999475 | + | 0.0323992i | \(0.0103148\pi\) |
−0.471679 | + | 0.881770i | \(0.656352\pi\) | |||||||
\(684\) | 831576. | − | 1.44033e6i | 0.0679613 | − | 0.117712i | ||||
\(685\) | −1.21063e7 | −0.985793 | ||||||||
\(686\) | 8.55199e6 | − | 1.68063e6i | 0.693836 | − | 0.136352i | ||||
\(687\) | 2.50398e7 | 2.02414 | ||||||||
\(688\) | −502494. | + | 870345.i | −0.0404725 | + | 0.0701004i | ||||
\(689\) | 6.48168e6 | + | 1.12266e7i | 0.520163 | + | 0.900949i | ||||
\(690\) | −6.23045e6 | − | 1.07915e7i | −0.498192 | − | 0.862894i | ||||
\(691\) | 4.64518e6 | − | 8.04569e6i | 0.370090 | − | 0.641015i | −0.619489 | − | 0.785006i | \(-0.712660\pi\) |
0.989579 | + | 0.143990i | \(0.0459934\pi\) | |||||||
\(692\) | −1.25758e6 | −0.0998325 | ||||||||
\(693\) | −7.17316e6 | − | 2.09676e6i | −0.567385 | − | 0.165850i | ||||
\(694\) | −1.19400e7 | −0.941033 | ||||||||
\(695\) | 1.05059e6 | − | 1.81967e6i | 0.0825029 | − | 0.142899i | ||||
\(696\) | 4.48495e6 | + | 7.76816e6i | 0.350941 | + | 0.607848i | ||||
\(697\) | −2.36016e6 | − | 4.08791e6i | −0.184018 | − | 0.318728i | ||||
\(698\) | −5.74934e6 | + | 9.95815e6i | −0.446662 | + | 0.773642i | ||||
\(699\) | 3.68202e7 | 2.85032 | ||||||||
\(700\) | −2.73113e6 | + | 2.61048e6i | −0.210668 | + | 0.201361i | ||||
\(701\) | 2.50809e7 | 1.92774 | 0.963870 | − | 0.266375i | \(-0.0858258\pi\) | ||||
0.963870 | + | 0.266375i | \(0.0858258\pi\) | |||||||
\(702\) | −7.34293e6 | + | 1.27183e7i | −0.562376 | + | 0.974063i | ||||
\(703\) | −326970. | − | 566329.i | −0.0249528 | − | 0.0432196i | ||||
\(704\) | −318330. | − | 551364.i | −0.0242073 | − | 0.0419283i | ||||
\(705\) | −4.97220e6 | + | 8.61210e6i | −0.376769 | + | 0.652584i | ||||
\(706\) | 5.88437e6 | 0.444312 | ||||||||
\(707\) | 825564. | + | 3.38505e6i | 0.0621158 | + | 0.254693i | ||||
\(708\) | −2.38264e6 | −0.178638 | ||||||||
\(709\) | −4.96890e6 | + | 8.60639e6i | −0.371231 | + | 0.642991i | −0.989755 | − | 0.142774i | \(-0.954398\pi\) |
0.618524 | + | 0.785766i | \(0.287731\pi\) | |||||||
\(710\) | −1.44151e6 | − | 2.49677e6i | −0.107318 | − | 0.185880i | ||||
\(711\) | −2.02109e7 | − | 3.50063e7i | −1.49938 | − | 2.59700i | ||||
\(712\) | 3.05747e6 | − | 5.29569e6i | 0.226028 | − | 0.391491i | ||||
\(713\) | 8.06069e6 | 0.593811 | ||||||||
\(714\) | 3.76904e6 | + | 1.54542e7i | 0.276685 | + | 1.13449i | ||||
\(715\) | −6.50364e6 | −0.475764 | ||||||||
\(716\) | 4.08342e6 | − | 7.07269e6i | 0.297674 | − | 0.515587i | ||||
\(717\) | −1.08476e7 | − | 1.87885e7i | −0.788015 | − | 1.36488i | ||||
\(718\) | −6.15598e6 | − | 1.06625e7i | −0.445642 | − | 0.771875i | ||||
\(719\) | 7.00047e6 | − | 1.21252e7i | 0.505016 | − | 0.874713i | −0.494968 | − | 0.868911i | \(-0.664820\pi\) |
0.999983 | − | 0.00580117i | \(-0.00184658\pi\) | |||||||
\(720\) | −3.42795e6 | −0.246436 | ||||||||
\(721\) | −4.86536e6 | + | 4.65041e6i | −0.348559 | + | 0.333160i | ||||
\(722\) | −9.59017e6 | −0.684673 | ||||||||
\(723\) | −1.79994e7 | + | 3.11758e7i | −1.28059 | + | 2.21805i | ||||
\(724\) | 176414. | + | 305559.i | 0.0125080 | + | 0.0216645i | ||||
\(725\) | −5.15160e6 | − | 8.92283e6i | −0.363996 | − | 0.630460i | ||||
\(726\) | 6.78333e6 | − | 1.17491e7i | 0.477641 | − | 0.827298i | ||||
\(727\) | 8.27315e6 | 0.580544 | 0.290272 | − | 0.956944i | \(-0.406254\pi\) | ||||
0.290272 | + | 0.956944i | \(0.406254\pi\) | |||||||
\(728\) | −9.22903e6 | − | 2.69770e6i | −0.645398 | − | 0.188654i | ||||
\(729\) | −2.33861e7 | −1.62982 | ||||||||
\(730\) | 3.28926e6 | − | 5.69716e6i | 0.228450 | − | 0.395687i | ||||
\(731\) | −2.43019e6 | − | 4.20921e6i | −0.168208 | − | 0.291345i | ||||
\(732\) | 2.94120e6 | + | 5.09430e6i | 0.202883 | + | 0.351404i | ||||
\(733\) | 1.64295e6 | − | 2.84568e6i | 0.112945 | − | 0.195626i | −0.804012 | − | 0.594614i | \(-0.797305\pi\) |
0.916956 | + | 0.398988i | \(0.130638\pi\) | |||||||
\(734\) | 6.46679e6 | 0.443046 | ||||||||
\(735\) | −1.26679e7 | − | 8.09773e6i | −0.864943 | − | 0.552898i | ||||
\(736\) | −3.56597e6 | −0.242651 | ||||||||
\(737\) | 3.34059e6 | − | 5.78608e6i | 0.226545 | − | 0.392388i | ||||
\(738\) | −2.82796e6 | − | 4.89817e6i | −0.191132 | − | 0.331050i | ||||
\(739\) | −5.04564e6 | − | 8.73930e6i | −0.339864 | − | 0.588662i | 0.644543 | − | 0.764568i | \(-0.277048\pi\) |
−0.984407 | + | 0.175907i | \(0.943714\pi\) | |||||||
\(740\) | −673925. | + | 1.16727e6i | −0.0452410 | + | 0.0783597i | ||||
\(741\) | −8.04754e6 | −0.538416 | ||||||||
\(742\) | 5.56781e6 | + | 1.62751e6i | 0.371257 | + | 0.108521i | ||||
\(743\) | 1.73443e7 | 1.15261 | 0.576307 | − | 0.817233i | \(-0.304493\pi\) | ||||
0.576307 | + | 0.817233i | \(0.304493\pi\) | |||||||
\(744\) | 1.83520e6 | − | 3.17866e6i | 0.121549 | − | 0.210529i | ||||
\(745\) | 5.10998e6 | + | 8.85074e6i | 0.337309 | + | 0.584237i | ||||
\(746\) | 9.52237e6 | + | 1.64932e7i | 0.626467 | + | 1.08507i | ||||
\(747\) | −1.03526e7 | + | 1.79313e7i | −0.678812 | + | 1.17574i | ||||
\(748\) | 3.07905e6 | 0.201216 | ||||||||
\(749\) | −2.34057e6 | + | 2.23717e6i | −0.152446 | + | 0.145711i | ||||
\(750\) | 1.76995e7 | 1.14897 | ||||||||
\(751\) | 8.79857e6 | − | 1.52396e7i | 0.569262 | − | 0.985990i | −0.427377 | − | 0.904073i | \(-0.640562\pi\) |
0.996639 | − | 0.0819170i | \(-0.0261042\pi\) | |||||||
\(752\) | 1.42291e6 | + | 2.46455e6i | 0.0917554 | + | 0.158925i | ||||
\(753\) | 2.45762e6 | + | 4.25673e6i | 0.157953 | + | 0.273583i | ||||
\(754\) | 1.31109e7 | − | 2.27088e7i | 0.839857 | − | 1.45468i | ||||
\(755\) | 8.72158e6 | 0.556836 | ||||||||
\(756\) | 1.55707e6 | + | 6.38445e6i | 0.0990841 | + | 0.406274i | ||||
\(757\) | −4.66480e6 | −0.295865 | −0.147932 | − | 0.988997i | \(-0.547262\pi\) | ||||
−0.147932 | + | 0.988997i | \(0.547262\pi\) | |||||||
\(758\) | −2.00386e6 | + | 3.47079e6i | −0.126676 | + | 0.219409i | ||||
\(759\) | 6.70554e6 | + | 1.16143e7i | 0.422502 | + | 0.731795i | ||||
\(760\) | −323828. | − | 560887.i | −0.0203367 | − | 0.0352242i | ||||
\(761\) | −9.13585e6 | + | 1.58238e7i | −0.571857 | + | 0.990485i | 0.424518 | + | 0.905419i | \(0.360443\pi\) |
−0.996375 | + | 0.0850658i | \(0.972890\pi\) | |||||||
\(762\) | 6.29819e6 | 0.392942 | ||||||||
\(763\) | −111693. | − | 457973.i | −0.00694566 | − | 0.0284792i | ||||
\(764\) | −8.93044e6 | −0.553528 | ||||||||
\(765\) | 8.28923e6 | − | 1.43574e7i | 0.512107 | − | 0.886995i | ||||
\(766\) | 5.64305e6 | + | 9.77404e6i | 0.347489 | + | 0.601869i | ||||
\(767\) | 3.48261e6 | + | 6.03205e6i | 0.213755 | + | 0.370234i | ||||
\(768\) | −811873. | + | 1.40620e6i | −0.0496689 | + | 0.0860291i | ||||
\(769\) | −2.31895e7 | −1.41409 | −0.707043 | − | 0.707171i | \(-0.749971\pi\) | ||||
−0.707043 | + | 0.707171i | \(0.749971\pi\) | |||||||
\(770\) | −2.10379e6 | + | 2.01085e6i | −0.127872 | + | 0.122223i | ||||
\(771\) | 1.18821e7 | 0.719873 | ||||||||
\(772\) | 394530. | − | 683346.i | 0.0238252 | − | 0.0412665i | ||||
\(773\) | −1.01074e6 | − | 1.75066e6i | −0.0608405 | − | 0.105379i | 0.834001 | − | 0.551763i | \(-0.186045\pi\) |
−0.894841 | + | 0.446384i | \(0.852711\pi\) | |||||||
\(774\) | −2.91187e6 | − | 5.04351e6i | −0.174711 | − | 0.302608i | ||||
\(775\) | −2.10799e6 | + | 3.65114e6i | −0.126070 | + | 0.218360i | ||||
\(776\) | 960317. | 0.0572480 | ||||||||
\(777\) | 7.19328e6 | + | 2.10264e6i | 0.427439 | + | 0.124943i | ||||
\(778\) | −4.96959e6 | −0.294355 | ||||||||
\(779\) | 534297. | − | 925430.i | 0.0315456 | − | 0.0546387i | ||||
\(780\) | 8.29347e6 | + | 1.43647e7i | 0.488090 | + | 0.845397i | ||||
\(781\) | 1.55143e6 | + | 2.68715e6i | 0.0910131 | + | 0.157639i | ||||
\(782\) | 8.62296e6 | − | 1.49354e7i | 0.504243 | − | 0.873374i | ||||
\(783\) | −1.79215e7 | −1.04465 | ||||||||
\(784\) | −3.81949e6 | + | 1.98085e6i | −0.221930 | + | 0.115097i | ||||
\(785\) | 7.72763e6 | 0.447582 | ||||||||
\(786\) | −6.75389e6 | + | 1.16981e7i | −0.389940 | + | 0.675396i | ||||
\(787\) | −7.88722e6 | − | 1.36611e7i | −0.453928 | − | 0.786227i | 0.544698 | − | 0.838632i | \(-0.316644\pi\) |
−0.998626 | + | 0.0524059i | \(0.983311\pi\) | |||||||
\(788\) | 7.53207e6 | + | 1.30459e7i | 0.432114 | + | 0.748444i | ||||
\(789\) | −5.63592e6 | + | 9.76170e6i | −0.322309 | + | 0.558255i | ||||
\(790\) | −1.57409e7 | −0.897348 | ||||||||
\(791\) | −7.73672e6 | − | 2.26149e6i | −0.439659 | − | 0.128515i | ||||
\(792\) | 3.68934e6 | 0.208995 | ||||||||
\(793\) | 8.59807e6 | − | 1.48923e7i | 0.485532 | − | 0.840966i | ||||
\(794\) | −5.49124e6 | − | 9.51111e6i | −0.309115 | − | 0.535402i | ||||
\(795\) | −5.00340e6 | − | 8.66614e6i | −0.280768 | − | 0.486304i | ||||
\(796\) | −5.12010e6 | + | 8.86827e6i | −0.286415 | + | 0.496085i | ||||
\(797\) | 1.22436e6 | 0.0682750 | 0.0341375 | − | 0.999417i | \(-0.489132\pi\) | ||||
0.0341375 | + | 0.999417i | \(0.489132\pi\) | |||||||
\(798\) | −2.60321e6 | + | 2.48820e6i | −0.144711 | + | 0.138318i | ||||
\(799\) | −1.37631e7 | −0.762690 | ||||||||
\(800\) | 932551. | − | 1.61523e6i | 0.0515167 | − | 0.0892295i | ||||
\(801\) | 1.77175e7 | + | 3.06876e7i | 0.975712 | + | 1.68998i | ||||
\(802\) | 7.42670e6 | + | 1.28634e7i | 0.407718 | + | 0.706189i | ||||
\(803\) | −3.54007e6 | + | 6.13158e6i | −0.193742 | + | 0.335571i | ||||
\(804\) | −1.70398e7 | −0.929658 | ||||||||
\(805\) | 3.86221e6 | + | 1.58362e7i | 0.210061 | + | 0.861312i | ||||
\(806\) | −1.07297e7 | −0.581771 | ||||||||
\(807\) | 1.06555e7 | − | 1.84559e7i | 0.575959 | − | 0.997590i | ||||
\(808\) | −860037. | − | 1.48963e6i | −0.0463435 | − | 0.0802692i | ||||
\(809\) | 1.38662e7 | + | 2.40170e7i | 0.744882 | + | 1.29017i | 0.950250 | + | 0.311489i | \(0.100828\pi\) |
−0.205368 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(810\) | −839536. | + | 1.45412e6i | −0.0449600 | + | 0.0778731i | ||||
\(811\) | −1.19246e7 | −0.636636 | −0.318318 | − | 0.947984i | \(-0.603118\pi\) | ||||
−0.318318 | + | 0.947984i | \(0.603118\pi\) | |||||||
\(812\) | −2.78018e6 | − | 1.13996e7i | −0.147973 | − | 0.606734i | ||||
\(813\) | 3.23476e7 | 1.71639 | ||||||||
\(814\) | 725313. | − | 1.25628e6i | 0.0383676 | − | 0.0664546i | ||||
\(815\) | 1.16379e6 | + | 2.01575e6i | 0.0613735 | + | 0.106302i | ||||
\(816\) | −3.92642e6 | − | 6.80076e6i | −0.206429 | − | 0.357546i | ||||
\(817\) | 550151. | − | 952889.i | 0.0288354 | − | 0.0499444i | ||||
\(818\) | 1.50376e7 | 0.785770 | ||||||||
\(819\) | 4.02787e7 | − | 3.84993e7i | 2.09829 | − | 2.00559i | ||||
\(820\) | −2.20250e6 | −0.114388 | ||||||||
\(821\) | −8.02312e6 | + | 1.38965e7i | −0.415418 | + | 0.719525i | −0.995472 | − | 0.0950526i | \(-0.969698\pi\) |
0.580054 | + | 0.814578i | \(0.303031\pi\) | |||||||
\(822\) | −1.66152e7 | − | 2.87784e7i | −0.857682 | − | 1.48555i | ||||
\(823\) | 5.61533e6 | + | 9.72603e6i | 0.288985 | + | 0.500537i | 0.973568 | − | 0.228398i | \(-0.0733489\pi\) |
−0.684583 | + | 0.728935i | \(0.740016\pi\) | |||||||
\(824\) | 1.66129e6 | − | 2.87743e6i | 0.0852367 | − | 0.147634i | ||||
\(825\) | −7.01437e6 | −0.358801 | ||||||||
\(826\) | 2.99159e6 | + | 874460.i | 0.152564 | + | 0.0445954i | ||||
\(827\) | −2.68427e7 | −1.36478 | −0.682389 | − | 0.730989i | \(-0.739059\pi\) | ||||
−0.682389 | + | 0.730989i | \(0.739059\pi\) | |||||||
\(828\) | 1.03321e7 | − | 1.78957e7i | 0.523736 | − | 0.907138i | ||||
\(829\) | −1.40210e7 | − | 2.42850e7i | −0.708584 | − | 1.22730i | −0.965382 | − | 0.260839i | \(-0.916001\pi\) |
0.256798 | − | 0.966465i | \(-0.417332\pi\) | |||||||
\(830\) | 4.03147e6 | + | 6.98272e6i | 0.203127 | + | 0.351827i | ||||
\(831\) | 6.72813e6 | − | 1.16535e7i | 0.337981 | − | 0.585400i | ||||
\(832\) | 4.74673e6 | 0.237731 | ||||||||
\(833\) | 939564. | − | 2.07872e7i | 0.0469152 | − | 1.03797i | ||||
\(834\) | 5.76747e6 | 0.287125 | ||||||||
\(835\) | −7.99186e6 | + | 1.38423e7i | −0.396672 | + | 0.687056i | ||||
\(836\) | 348521. | + | 603656.i | 0.0172470 | + | 0.0298727i | ||||
\(837\) | 3.66665e6 | + | 6.35083e6i | 0.180907 | + | 0.313341i | ||||
\(838\) | −9.20054e6 | + | 1.59358e7i | −0.452588 | + | 0.783905i | ||||
\(839\) | −3.30603e7 | −1.62145 | −0.810723 | − | 0.585430i | \(-0.800926\pi\) | ||||
−0.810723 | + | 0.585430i | \(0.800926\pi\) | |||||||
\(840\) | 7.12416e6 | + | 2.08244e6i | 0.348366 | + | 0.101830i | ||||
\(841\) | 1.14880e7 | 0.560086 | ||||||||
\(842\) | 809728. | − | 1.40249e6i | 0.0393604 | − | 0.0681741i | ||||
\(843\) | −1.23645e7 | − | 2.14160e7i | −0.599250 | − | 1.03793i | ||||
\(844\) | −7.37495e6 | − | 1.27738e7i | −0.356372 | − | 0.617254i | ||||
\(845\) | 1.75416e7 | − | 3.03830e7i | 0.845139 | − | 1.46382i | ||||
\(846\) | −1.64910e7 | −0.792176 | ||||||||
\(847\) | −1.28291e7 | + | 1.22623e7i | −0.614450 | + | 0.587305i | ||||
\(848\) | −2.86367e6 | −0.136752 | ||||||||
\(849\) | −2.20178e7 | + | 3.81359e7i | −1.04835 | + | 1.81579i | ||||
\(850\) | 4.51005e6 | + | 7.81164e6i | 0.214109 | + | 0.370847i | ||||
\(851\) | −4.06251e6 | − | 7.03648e6i | −0.192296 | − | 0.333067i | ||||
\(852\) | 3.95677e6 | − | 6.85334e6i | 0.186742 | − | 0.323447i | ||||
\(853\) | 2.73897e7 | 1.28889 | 0.644444 | − | 0.764652i | \(-0.277089\pi\) | ||||
0.644444 | + | 0.764652i | \(0.277089\pi\) | |||||||
\(854\) | −1.82322e6 | − | 7.47575e6i | −0.0855452 | − | 0.350760i | ||||
\(855\) | 3.75306e6 | 0.175578 | ||||||||
\(856\) | 799192. | − | 1.38424e6i | 0.0372792 | − | 0.0645695i | ||||
\(857\) | 1.48360e6 | + | 2.56968e6i | 0.0690027 | + | 0.119516i | 0.898463 | − | 0.439050i | \(-0.144685\pi\) |
−0.829460 | + | 0.558566i | \(0.811352\pi\) | |||||||
\(858\) | −8.92587e6 | − | 1.54601e7i | −0.413935 | − | 0.716957i | ||||
\(859\) | 1.98980e7 | − | 3.44643e7i | 0.920081 | − | 1.59363i | 0.120794 | − | 0.992678i | \(-0.461456\pi\) |
0.799287 | − | 0.600949i | \(-0.205211\pi\) | |||||||
\(860\) | −2.26785e6 | −0.104561 | ||||||||
\(861\) | 2.90164e6 | + | 1.18976e7i | 0.133394 | + | 0.546954i | ||||
\(862\) | 379034. | 0.0173744 | ||||||||
\(863\) | −3.59799e6 | + | 6.23190e6i | −0.164450 | + | 0.284835i | −0.936460 | − | 0.350775i | \(-0.885918\pi\) |
0.772010 | + | 0.635610i | \(0.219251\pi\) | |||||||
\(864\) | −1.62209e6 | − | 2.80954e6i | −0.0739248 | − | 0.128042i | ||||
\(865\) | −1.41893e6 | − | 2.45766e6i | −0.0644794 | − | 0.111682i | ||||
\(866\) | −8.63453e6 | + | 1.49554e7i | −0.391241 | + | 0.677649i | ||||
\(867\) | 2.79940e6 | 0.126478 | ||||||||
\(868\) | −3.47084e6 | + | 3.31751e6i | −0.156364 | + | 0.149456i | ||||
\(869\) | 1.69411e7 | 0.761015 | ||||||||
\(870\) | −1.01207e7 | + | 1.75296e7i | −0.453329 | + | 0.785188i | ||||
\(871\) | 2.49063e7 | + | 4.31391e7i | 1.11241 | + | 1.92675i | ||||
\(872\) | 116357. | + | 201536.i | 0.00518203 | + | 0.00897554i | ||||
\(873\) | −2.78244e6 | + | 4.81932e6i | −0.123563 | + | 0.214018i | ||||
\(874\) | 3.90417e6 | 0.172882 | ||||||||
\(875\) | −2.22231e7 | − | 6.49594e6i | −0.981259 | − | 0.286828i | ||||
\(876\) | 1.80573e7 | 0.795045 | ||||||||
\(877\) | −1.25621e7 | + | 2.17582e7i | −0.551523 | + | 0.955266i | 0.446642 | + | 0.894713i | \(0.352620\pi\) |
−0.998165 | + | 0.0605532i | \(0.980714\pi\) | |||||||
\(878\) | 4.44734e6 | + | 7.70303e6i | 0.194699 | + | 0.337229i | ||||
\(879\) | 2.03150e7 | + | 3.51866e7i | 0.886839 | + | 1.53605i | ||||
\(880\) | 718343. | − | 1.24421e6i | 0.0312698 | − | 0.0541609i | ||||
\(881\) | 120262. | 0.00522022 | 0.00261011 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00261011 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(882\) | 1.12579e6 | − | 2.49074e7i | 0.0487289 | − | 1.07809i | ||||
\(883\) | 2.43497e7 | 1.05097 | 0.525487 | − | 0.850802i | \(-0.323883\pi\) | ||||
0.525487 | + | 0.850802i | \(0.323883\pi\) | |||||||
\(884\) | −1.14782e7 | + | 1.98808e7i | −0.494018 | + | 0.855664i | ||||
\(885\) | −2.68833e6 | − | 4.65632e6i | −0.115378 | − | 0.199841i | ||||
\(886\) | 9.36851e6 | + | 1.62267e7i | 0.400946 | + | 0.694459i | ||||
\(887\) | 1.41383e7 | − | 2.44883e7i | 0.603377 | − | 1.04508i | −0.388929 | − | 0.921268i | \(-0.627155\pi\) |
0.992306 | − | 0.123812i | \(-0.0395120\pi\) | |||||||
\(888\) | −3.69969e6 | −0.157446 | ||||||||
\(889\) | −7.90786e6 | − | 2.31152e6i | −0.335587 | − | 0.0980941i | ||||
\(890\) | 1.37989e7 | 0.583943 | ||||||||
\(891\) | 903552. | − | 1.56500e6i | 0.0381293 | − | 0.0660419i | ||||
\(892\) | 6.70160e6 | + | 1.16075e7i | 0.282011 | + | 0.488458i | ||||
\(893\) | −1.55786e6 | − | 2.69828e6i | −0.0653730 | − | 0.113229i | ||||
\(894\) | −1.40263e7 | + | 2.42943e7i | −0.586948 | + | 1.01662i | ||||
\(895\) | 1.84293e7 | 0.769042 | ||||||||
\(896\) | 1.53547e6 | − | 1.46763e6i | 0.0638955 | − | 0.0610727i | ||||
\(897\) | −9.99885e7 | −4.14924 | ||||||||
\(898\) | −1.79586e6 | + | 3.11053e6i | −0.0743161 | + | 0.128719i | ||||
\(899\) | −6.54688e6 | − | 1.13395e7i | −0.270169 | − | 0.467946i | ||||
\(900\) | 5.40398e6 | + | 9.35997e6i | 0.222386 | + | 0.385184i | ||||
\(901\) | 6.92471e6 | − | 1.19940e7i | 0.284178 | − | 0.492210i | ||||
\(902\) | 2.37045e6 | 0.0970094 | ||||||||
\(903\) | 2.98774e6 | + | 1.22506e7i | 0.121934 | + | 0.499963i | ||||
\(904\) | 3.97920e6 | 0.161948 | ||||||||
\(905\) | −398096. | + | 689523.i | −0.0161572 | + | 0.0279851i | ||||
\(906\) | 1.19699e7 | + | 2.07324e7i | 0.484472 | + | 0.839130i | ||||
\(907\) | 1.21584e7 | + | 2.10590e7i | 0.490748 | + | 0.850000i | 0.999943 | − | 0.0106507i | \(-0.00339029\pi\) |
−0.509195 | + | 0.860651i | \(0.670057\pi\) | |||||||
\(908\) | 1.06455e7 | − | 1.84386e7i | 0.428501 | − | 0.742186i | ||||
\(909\) | 9.96754e6 | 0.400109 | ||||||||
\(910\) | −5.14106e6 | − | 2.10798e7i | −0.205802 | − | 0.843847i | ||||
\(911\) | −3.36224e7 | −1.34225 | −0.671123 | − | 0.741346i | \(-0.734188\pi\) | ||||
−0.671123 | + | 0.741346i | \(0.734188\pi\) | |||||||
\(912\) | 888871. | − | 1.53957e6i | 0.0353876 | − | 0.0612932i | ||||
\(913\) | −4.33888e6 | − | 7.51517e6i | −0.172267 | − | 0.298374i | ||||
\(914\) | −1.19636e7 | − | 2.07216e7i | −0.473693 | − | 0.820461i | ||||
\(915\) | −6.63710e6 | + | 1.14958e7i | −0.262075 | + | 0.453927i | ||||
\(916\) | 1.61701e7 | 0.636759 | ||||||||
\(917\) | 1.27734e7 | − | 1.22091e7i | 0.501629 | − | 0.479468i | ||||
\(918\) | 1.56897e7 | 0.614479 | ||||||||
\(919\) | 4.06874e6 | − | 7.04727e6i | 0.158917 | − | 0.275253i | −0.775561 | − | 0.631272i | \(-0.782533\pi\) |
0.934479 | + | 0.356019i | \(0.115866\pi\) | |||||||
\(920\) | −4.02348e6 | − | 6.96887e6i | −0.156723 | − | 0.271452i | ||||
\(921\) | −2.95001e7 | − | 5.10956e7i | −1.14597 | − | 1.98488i | ||||
\(922\) | −3.25013e6 | + | 5.62939e6i | −0.125914 | + | 0.218089i | ||||
\(923\) | −2.31338e7 | −0.893807 | ||||||||
\(924\) | −7.66739e6 | − | 2.24123e6i | −0.295439 | − | 0.0863587i | ||||
\(925\) | 4.24962e6 | 0.163304 | ||||||||
\(926\) | 1.69259e7 | − | 2.93165e7i | 0.648671 | − | 1.12353i | ||||
\(927\) | 9.62688e6 | + | 1.66742e7i | 0.367948 | + | 0.637304i | ||||
\(928\) | 2.89627e6 | + | 5.01649e6i | 0.110400 | + | 0.191219i | ||||
\(929\) | −1.79027e7 | + | 3.10084e7i | −0.680580 | + | 1.17880i | 0.294224 | + | 0.955736i | \(0.404939\pi\) |
−0.974804 | + | 0.223063i | \(0.928395\pi\) | |||||||
\(930\) | 8.28261e6 | 0.314022 | ||||||||
\(931\) | 4.18173e6 | − | 2.16872e6i | 0.158118 | − | 0.0820029i | ||||
\(932\) | 2.37776e7 | 0.896661 | ||||||||
\(933\) | 1.54249e7 | − | 2.67167e7i | 0.580120 | − | 1.00480i | ||||
\(934\) | −1.53319e7 | − | 2.65556e7i | −0.575080 | − | 0.996068i | ||||
\(935\) | 3.47409e6 | + | 6.01730e6i | 0.129961 | + | 0.225098i | ||||
\(936\) | −1.37533e7 | + | 2.38213e7i | −0.513116 | + | 0.888744i | ||||
\(937\) | 4.65849e7 | 1.73339 | 0.866694 | − | 0.498840i | \(-0.166241\pi\) | ||||
0.866694 | + | 0.498840i | \(0.166241\pi\) | |||||||
\(938\) | 2.13947e7 | + | 6.25382e6i | 0.793963 | + | 0.232080i | ||||
\(939\) | 4.12029e7 | 1.52498 | ||||||||
\(940\) | −3.21093e6 | + | 5.56149e6i | −0.118525 | + | 0.205292i | ||||
\(941\) | 1.03362e6 | + | 1.79029e6i | 0.0380529 | + | 0.0659096i | 0.884425 | − | 0.466683i | \(-0.154551\pi\) |
−0.846372 | + | 0.532593i | \(0.821218\pi\) | |||||||
\(942\) | 1.06057e7 | + | 1.83697e7i | 0.389415 | + | 0.674487i | ||||
\(943\) | 6.63850e6 | − | 1.14982e7i | 0.243103 | − | 0.421067i | ||||
\(944\) | −1.53865e6 | −0.0561966 | ||||||||
\(945\) | −1.07201e7 | + | 1.02465e7i | −0.390498 | + | 0.373247i | ||||
\(946\) | 2.44078e6 | 0.0886750 | ||||||||
\(947\) | −1.18386e7 | + | 2.05051e7i | −0.428970 | + | 0.742998i | −0.996782 | − | 0.0801602i | \(-0.974457\pi\) |
0.567812 | + | 0.823158i | \(0.307790\pi\) | |||||||
\(948\) | −2.16034e7 | − | 3.74182e7i | −0.780732 | − | 1.35227i | ||||
\(949\) | −2.63936e7 | − | 4.57150e7i | −0.951334 | − | 1.64776i | ||||
\(950\) | −1.02099e6 | + | 1.76841e6i | −0.0367041 | + | 0.0635734i | ||||
\(951\) | −6.50345e7 | −2.33181 | ||||||||
\(952\) | 2.43396e6 | + | 9.97993e6i | 0.0870403 | + | 0.356891i | ||||
\(953\) | −3.40521e6 | −0.121454 | −0.0607270 | − | 0.998154i | \(-0.519342\pi\) | ||||
−0.0607270 | + | 0.998154i | \(0.519342\pi\) | |||||||
\(954\) | 8.29725e6 | − | 1.43713e7i | 0.295164 | − | 0.511239i | ||||
\(955\) | −1.00762e7 | − | 1.74525e7i | −0.357510 | − | 0.619226i | ||||
\(956\) | −7.00510e6 | − | 1.21332e7i | −0.247896 | − | 0.429368i | ||||
\(957\) | 1.08924e7 | − | 1.88663e7i | 0.384455 | − | 0.665896i | ||||
\(958\) | −9.61170e6 | −0.338366 | ||||||||
\(959\) | 1.02996e7 | + | 4.22315e7i | 0.361639 | + | 1.48283i | ||||
\(960\) | −3.66414e6 | −0.128320 | ||||||||
\(961\) | 1.16357e7 | − | 2.01535e7i | 0.406427 | − | 0.703952i | ||||
\(962\) | 5.40769e6 | + | 9.36639e6i | 0.188397 | + | 0.326313i | ||||
\(963\) | 4.63119e6 | + | 8.02145e6i | 0.160926 | + | 0.278732i | ||||
\(964\) | −1.16236e7 | + | 2.01326e7i | −0.402853 | + | 0.697762i | ||||
\(965\) | 1.78059e6 | 0.0615525 | ||||||||
\(966\) | −3.23441e7 | + | 3.09152e7i | −1.11520 | + | 1.06593i | ||||
\(967\) | 1.44238e6 | 0.0496036 | 0.0248018 | − | 0.999692i | \(-0.492105\pi\) | ||||
0.0248018 | + | 0.999692i | \(0.492105\pi\) | |||||||
\(968\) | 4.38051e6 | − | 7.58727e6i | 0.150258 | − | 0.260254i | ||||
\(969\) | 4.29880e6 | + | 7.44575e6i | 0.147075 | + | 0.254741i | ||||
\(970\) | 1.08352e6 | + | 1.87672e6i | 0.0369751 | + | 0.0640427i | ||||
\(971\) | 2.57977e6 | − | 4.46830e6i | 0.0878078 | − | 0.152088i | −0.818776 | − | 0.574113i | \(-0.805347\pi\) |
0.906584 | + | 0.422025i | \(0.138681\pi\) | |||||||
\(972\) | −1.69266e7 | −0.574651 | ||||||||
\(973\) | −7.24151e6 | − | 2.11674e6i | −0.245215 | − | 0.0716779i | ||||
\(974\) | −681206. | −0.0230081 | ||||||||
\(975\) | 2.61484e7 | − | 4.52904e7i | 0.880914 | − | 1.52579i | ||||
\(976\) | 1.89936e6 | + | 3.28978e6i | 0.0638237 | + | 0.110546i | ||||
\(977\) | 3.48825e6 | + | 6.04183e6i | 0.116915 | + | 0.202503i | 0.918544 | − | 0.395319i | \(-0.129366\pi\) |
−0.801628 | + | 0.597823i | \(0.796033\pi\) | |||||||
\(978\) | −3.19447e6 | + | 5.53299e6i | −0.106795 | + | 0.184975i | ||||
\(979\) | −1.48511e7 | −0.495225 | ||||||||
\(980\) | −8.18065e6 | − | 5.22932e6i | −0.272096 | − | 0.173932i | ||||
\(981\) | −1.34853e6 | −0.0447394 | ||||||||
\(982\) | 1.15526e7 | − | 2.00096e7i | 0.382296 | − | 0.662156i | ||||
\(983\) | 1.40784e7 | + | 2.43845e7i | 0.464696 | + | 0.804878i | 0.999188 | − | 0.0402961i | \(-0.0128301\pi\) |
−0.534491 | + | 0.845174i | \(0.679497\pi\) | |||||||
\(984\) | −3.02281e6 | − | 5.23565e6i | −0.0995228 | − | 0.172378i | ||||
\(985\) | −1.69968e7 | + | 2.94394e7i | −0.558184 | + | 0.966804i | ||||
\(986\) | −2.80142e7 | −0.917669 | ||||||||
\(987\) | 3.42725e7 | + | 1.00181e7i | 1.11983 | + | 0.327334i | ||||
\(988\) | −5.19691e6 | −0.169376 | ||||||||
\(989\) | 6.83547e6 | − | 1.18394e7i | 0.222217 | − | 0.384891i | ||||
\(990\) | 4.16268e6 | + | 7.20997e6i | 0.134985 | + | 0.233801i | ||||
\(991\) | 1.17022e7 | + | 2.02687e7i | 0.378514 | + | 0.655606i | 0.990846 | − | 0.134995i | \(-0.0431018\pi\) |
−0.612332 | + | 0.790601i | \(0.709768\pi\) | |||||||
\(992\) | 1.18513e6 | − | 2.05270e6i | 0.0382372 | − | 0.0662287i | ||||
\(993\) | 4.30825e7 | 1.38653 | ||||||||
\(994\) | −7.48330e6 | + | 7.15271e6i | −0.240230 | + | 0.229617i | ||||
\(995\) | −2.31080e7 | −0.739954 | ||||||||
\(996\) | −1.10659e7 | + | 1.91668e7i | −0.353459 | + | 0.612210i | ||||
\(997\) | 2.15142e7 | + | 3.72637e7i | 0.685468 | + | 1.18727i | 0.973290 | + | 0.229581i | \(0.0737356\pi\) |
−0.287822 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(998\) | −1.08720e6 | − | 1.88309e6i | −0.0345529 | − | 0.0598474i | ||||
\(999\) | 3.69592e6 | − | 6.40151e6i | 0.117168 | − | 0.202941i |
(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 | 14.6.c.a.9.1 | ✓ | 4 | |
3.2 | odd | 2 | 126.6.g.j.37.1 | 4 | |||
4.3 | odd | 2 | 112.6.i.d.65.2 | 4 | |||
7.2 | even | 3 | 98.6.a.h.1.2 | 2 | |||
7.3 | odd | 6 | 98.6.c.e.67.2 | 4 | |||
7.4 | even | 3 | inner | 14.6.c.a.11.1 | yes | 4 | |
7.5 | odd | 6 | 98.6.a.g.1.1 | 2 | |||
7.6 | odd | 2 | 98.6.c.e.79.2 | 4 | |||
21.2 | odd | 6 | 882.6.a.ba.1.2 | 2 | |||
21.5 | even | 6 | 882.6.a.bi.1.1 | 2 | |||
21.11 | odd | 6 | 126.6.g.j.109.1 | 4 | |||
28.11 | odd | 6 | 112.6.i.d.81.2 | 4 | |||
28.19 | even | 6 | 784.6.a.bb.1.2 | 2 | |||
28.23 | odd | 6 | 784.6.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.a.9.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
14.6.c.a.11.1 | yes | 4 | 7.4 | even | 3 | inner | |
98.6.a.g.1.1 | 2 | 7.5 | odd | 6 | |||
98.6.a.h.1.2 | 2 | 7.2 | even | 3 | |||
98.6.c.e.67.2 | 4 | 7.3 | odd | 6 | |||
98.6.c.e.79.2 | 4 | 7.6 | odd | 2 | |||
112.6.i.d.65.2 | 4 | 4.3 | odd | 2 | |||
112.6.i.d.81.2 | 4 | 28.11 | odd | 6 | |||
126.6.g.j.37.1 | 4 | 3.2 | odd | 2 | |||
126.6.g.j.109.1 | 4 | 21.11 | odd | 6 | |||
784.6.a.s.1.1 | 2 | 28.23 | odd | 6 | |||
784.6.a.bb.1.2 | 2 | 28.19 | even | 6 | |||
882.6.a.ba.1.2 | 2 | 21.2 | odd | 6 | |||
882.6.a.bi.1.1 | 2 | 21.5 | even | 6 |