Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,8,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not 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: | \(30.6137324974\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.67 |
Dual form | 98.8.c.c.79.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | + | 6.92820i | 0.353553 | + | 0.612372i | ||||
\(3\) | −41.0000 | + | 71.0141i | −0.876717 | + | 1.51852i | −0.0217948 | + | 0.999762i | \(0.506938\pi\) |
−0.854922 | + | 0.518756i | \(0.826395\pi\) | |||||||
\(4\) | −32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | ||||
\(5\) | 224.000 | + | 387.979i | 0.801407 | + | 1.38808i | 0.918690 | + | 0.394979i | \(0.129248\pi\) |
−0.117283 | + | 0.993098i | \(0.537419\pi\) | |||||||
\(6\) | −656.000 | −1.23987 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | −2268.50 | − | 3929.16i | −1.03727 | − | 1.79660i | ||||
\(10\) | −1792.00 | + | 3103.84i | −0.566680 | + | 0.981519i | ||||
\(11\) | −1204.00 | + | 2085.39i | −0.272742 | + | 0.472403i | −0.969563 | − | 0.244842i | \(-0.921264\pi\) |
0.696821 | + | 0.717245i | \(0.254597\pi\) | |||||||
\(12\) | −2624.00 | − | 4544.90i | −0.438359 | − | 0.759259i | ||||
\(13\) | −7116.00 | −0.898326 | −0.449163 | − | 0.893450i | \(-0.648278\pi\) | ||||
−0.449163 | + | 0.893450i | \(0.648278\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −36736.0 | −2.81043 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1243.00 | − | 2152.94i | 0.0613621 | − | 0.106282i | −0.833712 | − | 0.552199i | \(-0.813789\pi\) |
0.895074 | + | 0.445917i | \(0.147122\pi\) | |||||||
\(18\) | 18148.0 | − | 31433.3i | 0.733458 | − | 1.27039i | ||||
\(19\) | 18241.0 | + | 31594.3i | 0.610114 | + | 1.05675i | 0.991221 | + | 0.132217i | \(0.0422097\pi\) |
−0.381107 | + | 0.924531i | \(0.624457\pi\) | |||||||
\(20\) | −28672.0 | −0.801407 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −19264.0 | −0.385715 | ||||||||
\(23\) | 6440.00 | + | 11154.4i | 0.110367 | + | 0.191161i | 0.915918 | − | 0.401365i | \(-0.131464\pi\) |
−0.805551 | + | 0.592526i | \(0.798131\pi\) | |||||||
\(24\) | 20992.0 | − | 36359.2i | 0.309966 | − | 0.536877i | ||||
\(25\) | −61289.5 | + | 106157.i | −0.784506 | + | 1.35880i | ||||
\(26\) | −28464.0 | − | 49301.1i | −0.317606 | − | 0.550110i | ||||
\(27\) | 192700. | 1.88412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −88094.0 | −0.670739 | −0.335369 | − | 0.942087i | \(-0.608861\pi\) | ||||
−0.335369 | + | 0.942087i | \(0.608861\pi\) | |||||||
\(30\) | −146944. | − | 254514.i | −0.993636 | − | 1.72103i | ||||
\(31\) | 141318. | − | 244770.i | 0.851984 | − | 1.47568i | −0.0274306 | − | 0.999624i | \(-0.508733\pi\) |
0.879415 | − | 0.476056i | \(-0.157934\pi\) | |||||||
\(32\) | 16384.0 | − | 28377.9i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −98728.0 | − | 171002.i | −0.478235 | − | 0.828328i | ||||
\(34\) | 19888.0 | 0.0867791 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 290368. | 1.03727 | ||||||||
\(37\) | 107267. | + | 185792.i | 0.348145 | + | 0.603005i | 0.985920 | − | 0.167218i | \(-0.0534784\pi\) |
−0.637775 | + | 0.770223i | \(0.720145\pi\) | |||||||
\(38\) | −145928. | + | 252755.i | −0.431416 | + | 0.747234i | ||||
\(39\) | 291756. | − | 505336.i | 0.787578 | − | 1.36413i | ||||
\(40\) | −114688. | − | 198645.i | −0.283340 | − | 0.490759i | ||||
\(41\) | 140874. | 0.319218 | 0.159609 | − | 0.987180i | \(-0.448977\pi\) | ||||
0.159609 | + | 0.987180i | \(0.448977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36464.0 | 0.0699399 | 0.0349699 | − | 0.999388i | \(-0.488866\pi\) | ||||
0.0349699 | + | 0.999388i | \(0.488866\pi\) | |||||||
\(44\) | −77056.0 | − | 133465.i | −0.136371 | − | 0.236202i | ||||
\(45\) | 1.01629e6 | − | 1.76026e6i | 1.66254 | − | 2.87961i | ||||
\(46\) | −51520.0 | + | 89235.3i | −0.0780411 | + | 0.135171i | ||||
\(47\) | 358434. | + | 620826.i | 0.503578 | + | 0.872223i | 0.999991 | + | 0.00413639i | \(0.00131666\pi\) |
−0.496414 | + | 0.868086i | \(0.665350\pi\) | |||||||
\(48\) | 335872. | 0.438359 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −980632. | −1.10946 | ||||||||
\(51\) | 101926. | + | 176541.i | 0.107594 | + | 0.186359i | ||||
\(52\) | 227712. | − | 394409.i | 0.224582 | − | 0.388987i | ||||
\(53\) | 28473.0 | − | 49316.7i | 0.0262705 | − | 0.0455018i | −0.852591 | − | 0.522578i | \(-0.824970\pi\) |
0.878862 | + | 0.477077i | \(0.158304\pi\) | |||||||
\(54\) | 770800. | + | 1.33506e6i | 0.666137 | + | 1.15378i | ||||
\(55\) | −1.07878e6 | −0.874309 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.99152e6 | −2.13959 | ||||||||
\(58\) | −352376. | − | 610333.i | −0.237142 | − | 0.410742i | ||||
\(59\) | −1.07493e6 | + | 1.86184e6i | −0.681394 | + | 1.18021i | 0.293161 | + | 0.956063i | \(0.405293\pi\) |
−0.974555 | + | 0.224147i | \(0.928041\pi\) | |||||||
\(60\) | 1.17555e6 | − | 2.03612e6i | 0.702607 | − | 1.21695i | ||||
\(61\) | 1.54218e6 | + | 2.67113e6i | 0.869923 | + | 1.50675i | 0.862075 | + | 0.506781i | \(0.169165\pi\) |
0.00784785 | + | 0.999969i | \(0.497502\pi\) | |||||||
\(62\) | 2.26109e6 | 1.20489 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −1.59398e6 | − | 2.76086e6i | −0.719925 | − | 1.24695i | ||||
\(66\) | 789824. | − | 1.36802e6i | 0.338163 | − | 0.585716i | ||||
\(67\) | 1.51718e6 | − | 2.62784e6i | 0.616277 | − | 1.06742i | −0.373882 | − | 0.927476i | \(-0.621974\pi\) |
0.990159 | − | 0.139947i | \(-0.0446931\pi\) | |||||||
\(68\) | 79552.0 | + | 137788.i | 0.0306810 | + | 0.0531411i | ||||
\(69\) | −1.05616e6 | −0.387042 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −106624. | −0.0353550 | −0.0176775 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176775 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(72\) | 1.16147e6 | + | 2.01173e6i | 0.366729 | + | 0.635193i | ||||
\(73\) | 494465. | − | 856439.i | 0.148767 | − | 0.257671i | −0.782005 | − | 0.623272i | \(-0.785803\pi\) |
0.930772 | + | 0.365600i | \(0.119136\pi\) | |||||||
\(74\) | −858136. | + | 1.48634e6i | −0.246176 | + | 0.426389i | ||||
\(75\) | −5.02574e6 | − | 8.70484e6i | −1.37558 | − | 2.38257i | ||||
\(76\) | −2.33485e6 | −0.610114 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.66810e6 | 1.11380 | ||||||||
\(79\) | −1.70795e6 | − | 2.95825e6i | −0.389744 | − | 0.675057i | 0.602671 | − | 0.797990i | \(-0.294103\pi\) |
−0.992415 | + | 0.122933i | \(0.960770\pi\) | |||||||
\(80\) | 917504. | − | 1.58916e6i | 0.200352 | − | 0.347019i | ||||
\(81\) | −2.93949e6 | + | 5.09135e6i | −0.614574 | + | 1.06447i | ||||
\(82\) | 563496. | + | 976004.i | 0.112861 | + | 0.195480i | ||||
\(83\) | 15142.0 | 0.00290676 | 0.00145338 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145338 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11373e6 | 0.196704 | ||||||||
\(86\) | 145856. | + | 252630.i | 0.0247275 | + | 0.0428292i | ||||
\(87\) | 3.61185e6 | − | 6.25591e6i | 0.588048 | − | 1.01853i | ||||
\(88\) | 616448. | − | 1.06772e6i | 0.0964289 | − | 0.167020i | ||||
\(89\) | 87405.0 | + | 151390.i | 0.0131423 | + | 0.0227631i | 0.872522 | − | 0.488575i | \(-0.162483\pi\) |
−0.859379 | + | 0.511338i | \(0.829150\pi\) | |||||||
\(90\) | 1.62606e7 | 2.35119 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −824320. | −0.110367 | ||||||||
\(93\) | 1.15881e7 | + | 2.00711e7i | 1.49390 | + | 2.58751i | ||||
\(94\) | −2.86747e6 | + | 4.96661e6i | −0.356083 | + | 0.616754i | ||||
\(95\) | −8.17197e6 | + | 1.41543e7i | −0.977899 | + | 1.69377i | ||||
\(96\) | 1.34349e6 | + | 2.32699e6i | 0.154983 | + | 0.268439i | ||||
\(97\) | −1.35068e7 | −1.50263 | −0.751313 | − | 0.659946i | \(-0.770579\pi\) | ||||
−0.751313 | + | 0.659946i | \(0.770579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.09251e7 | 1.13162 | ||||||||
\(100\) | −3.92253e6 | − | 6.79402e6i | −0.392253 | − | 0.679402i | ||||
\(101\) | −9.38224e6 | + | 1.62505e7i | −0.906112 | + | 1.56943i | −0.0866937 | + | 0.996235i | \(0.527630\pi\) |
−0.819418 | + | 0.573196i | \(0.805703\pi\) | |||||||
\(102\) | −815408. | + | 1.41233e6i | −0.0760807 | + | 0.131776i | ||||
\(103\) | −8.10401e6 | − | 1.40366e7i | −0.730751 | − | 1.26570i | −0.956562 | − | 0.291527i | \(-0.905837\pi\) |
0.225811 | − | 0.974171i | \(-0.427497\pi\) | |||||||
\(104\) | 3.64339e6 | 0.317606 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 455568. | 0.0371520 | ||||||||
\(107\) | −3.48290e6 | − | 6.03256e6i | −0.274851 | − | 0.476056i | 0.695246 | − | 0.718771i | \(-0.255295\pi\) |
−0.970098 | + | 0.242715i | \(0.921962\pi\) | |||||||
\(108\) | −6.16640e6 | + | 1.06805e7i | −0.471030 | + | 0.815848i | ||||
\(109\) | 7.45195e6 | − | 1.29072e7i | 0.551159 | − | 0.954636i | −0.447032 | − | 0.894518i | \(-0.647519\pi\) |
0.998191 | − | 0.0601177i | \(-0.0191476\pi\) | |||||||
\(110\) | −4.31514e6 | − | 7.47403e6i | −0.309115 | − | 0.535403i | ||||
\(111\) | −1.75918e7 | −1.22090 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.60684e7 | −1.69958 | −0.849788 | − | 0.527125i | \(-0.823270\pi\) | ||||
−0.849788 | + | 0.527125i | \(0.823270\pi\) | |||||||
\(114\) | −1.19661e7 | − | 2.07259e7i | −0.756459 | − | 1.31023i | ||||
\(115\) | −2.88512e6 | + | 4.99717e6i | −0.176897 | + | 0.306395i | ||||
\(116\) | 2.81901e6 | − | 4.88267e6i | 0.167685 | − | 0.290438i | ||||
\(117\) | 1.61426e7 | + | 2.79599e7i | 0.931803 | + | 1.61393i | ||||
\(118\) | −1.71989e7 | −0.963637 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.88088e7 | 0.993636 | ||||||||
\(121\) | 6.84435e6 | + | 1.18548e7i | 0.351224 | + | 0.608337i | ||||
\(122\) | −1.23374e7 | + | 2.13691e7i | −0.615128 | + | 1.06543i | ||||
\(123\) | −5.77583e6 | + | 1.00040e7i | −0.279864 | + | 0.484738i | ||||
\(124\) | 9.04435e6 | + | 1.56653e7i | 0.425992 | + | 0.737840i | ||||
\(125\) | −1.99154e7 | −0.912019 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.13136e7 | 0.923301 | 0.461651 | − | 0.887062i | \(-0.347257\pi\) | ||||
0.461651 | + | 0.887062i | \(0.347257\pi\) | |||||||
\(128\) | 1.04858e6 | + | 1.81619e6i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.49502e6 | + | 2.58946e6i | −0.0613175 | + | 0.106205i | ||||
\(130\) | 1.27519e7 | − | 2.20869e7i | 0.509064 | − | 0.881724i | ||||
\(131\) | 5.23866e6 | + | 9.07363e6i | 0.203597 | + | 0.352640i | 0.949685 | − | 0.313207i | \(-0.101403\pi\) |
−0.746088 | + | 0.665847i | \(0.768070\pi\) | |||||||
\(132\) | 1.26372e7 | 0.478235 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.42749e7 | 0.871547 | ||||||||
\(135\) | 4.31648e7 | + | 7.47636e7i | 1.50995 | + | 2.61530i | ||||
\(136\) | −636416. | + | 1.10230e6i | −0.0216948 | + | 0.0375764i | ||||
\(137\) | −1.80990e7 | + | 3.13485e7i | −0.601359 | + | 1.04158i | 0.391257 | + | 0.920281i | \(0.372040\pi\) |
−0.992616 | + | 0.121302i | \(0.961293\pi\) | |||||||
\(138\) | −4.22464e6 | − | 7.31729e6i | −0.136840 | − | 0.237014i | ||||
\(139\) | 5.27655e7 | 1.66647 | 0.833237 | − | 0.552916i | \(-0.186485\pi\) | ||||
0.833237 | + | 0.552916i | \(0.186485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87832e7 | −1.76598 | ||||||||
\(142\) | −426496. | − | 738713.i | −0.0124999 | − | 0.0216504i | ||||
\(143\) | 8.56766e6 | − | 1.48396e7i | 0.245011 | − | 0.424372i | ||||
\(144\) | −9.29178e6 | + | 1.60938e7i | −0.259316 | + | 0.449149i | ||||
\(145\) | −1.97331e7 | − | 3.41787e7i | −0.537534 | − | 0.931037i | ||||
\(146\) | 7.91144e6 | 0.210388 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.37302e7 | −0.348145 | ||||||||
\(149\) | −3.68001e7 | − | 6.37397e7i | −0.911376 | − | 1.57855i | −0.812122 | − | 0.583487i | \(-0.801688\pi\) |
−0.0992535 | − | 0.995062i | \(-0.531645\pi\) | |||||||
\(150\) | 4.02059e7 | − | 6.96387e7i | 0.972681 | − | 1.68473i | ||||
\(151\) | −8.71444e6 | + | 1.50939e7i | −0.205978 | + | 0.356764i | −0.950444 | − | 0.310896i | \(-0.899371\pi\) |
0.744466 | + | 0.667660i | \(0.232704\pi\) | |||||||
\(152\) | −9.33939e6 | − | 1.61763e7i | −0.215708 | − | 0.373617i | ||||
\(153\) | −1.12790e7 | −0.254595 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.26621e8 | 2.73114 | ||||||||
\(156\) | 1.86724e7 | + | 3.23415e7i | 0.393789 | + | 0.682063i | ||||
\(157\) | −1.11078e7 | + | 1.92394e7i | −0.229077 | + | 0.396773i | −0.957535 | − | 0.288318i | \(-0.906904\pi\) |
0.728458 | + | 0.685091i | \(0.240237\pi\) | |||||||
\(158\) | 1.36636e7 | − | 2.36660e7i | 0.275591 | − | 0.477337i | ||||
\(159\) | 2.33479e6 | + | 4.04397e6i | 0.0460635 | + | 0.0797844i | ||||
\(160\) | 1.46801e7 | 0.283340 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.70318e7 | −0.869140 | ||||||||
\(163\) | −3.11898e7 | − | 5.40223e7i | −0.564099 | − | 0.977049i | −0.997133 | − | 0.0756711i | \(-0.975890\pi\) |
0.433033 | − | 0.901378i | \(-0.357443\pi\) | |||||||
\(164\) | −4.50797e6 | + | 7.80803e6i | −0.0798045 | + | 0.138225i | ||||
\(165\) | 4.42301e7 | − | 7.66089e7i | 0.766522 | − | 1.32765i | ||||
\(166\) | 60568.0 | + | 104907.i | 0.00102770 | + | 0.00178002i | ||||
\(167\) | −3.31238e7 | −0.550343 | −0.275171 | − | 0.961395i | \(-0.588735\pi\) | ||||
−0.275171 | + | 0.961395i | \(0.588735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.21111e7 | −0.193010 | ||||||||
\(170\) | 4.45491e6 | + | 7.71613e6i | 0.0695453 | + | 0.120456i | ||||
\(171\) | 8.27594e7 | − | 1.43344e8i | 1.26570 | − | 2.19226i | ||||
\(172\) | −1.16685e6 | + | 2.02104e6i | −0.0174850 | + | 0.0302848i | ||||
\(173\) | −3.52899e7 | − | 6.11240e7i | −0.518191 | − | 0.897532i | −0.999777 | − | 0.0211336i | \(-0.993272\pi\) |
0.481586 | − | 0.876399i | \(-0.340061\pi\) | |||||||
\(174\) | 5.77897e7 | 0.831626 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.86317e6 | 0.136371 | ||||||||
\(177\) | −8.81443e7 | − | 1.52670e8i | −1.19478 | − | 2.06942i | ||||
\(178\) | −699240. | + | 1.21112e6i | −0.00929301 | + | 0.0160960i | ||||
\(179\) | 6.05881e7 | − | 1.04942e8i | 0.789590 | − | 1.36761i | −0.136628 | − | 0.990622i | \(-0.543626\pi\) |
0.926218 | − | 0.376988i | \(-0.123040\pi\) | |||||||
\(180\) | 6.50424e7 | + | 1.12657e8i | 0.831272 | + | 1.43980i | ||||
\(181\) | −2.30550e7 | −0.288995 | −0.144498 | − | 0.989505i | \(-0.546157\pi\) | ||||
−0.144498 | + | 0.989505i | \(0.546157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.52918e8 | −3.05070 | ||||||||
\(184\) | −3.29728e6 | − | 5.71106e6i | −0.0390206 | − | 0.0675856i | ||||
\(185\) | −4.80556e7 | + | 8.32348e7i | −0.558011 | + | 0.966504i | ||||
\(186\) | −9.27046e7 | + | 1.60569e8i | −1.05635 | + | 1.82964i | ||||
\(187\) | 2.99314e6 | + | 5.18428e6i | 0.0334720 | + | 0.0579752i | ||||
\(188\) | −4.58796e7 | −0.503578 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.30751e8 | −1.38296 | ||||||||
\(191\) | 1.01463e7 | + | 1.75740e7i | 0.105364 | + | 0.182496i | 0.913887 | − | 0.405969i | \(-0.133066\pi\) |
−0.808523 | + | 0.588465i | \(0.799733\pi\) | |||||||
\(192\) | −1.07479e7 | + | 1.86159e7i | −0.109590 | + | 0.189815i | ||||
\(193\) | −1.13041e7 | + | 1.95792e7i | −0.113184 | + | 0.196040i | −0.917052 | − | 0.398767i | \(-0.869438\pi\) |
0.803869 | + | 0.594807i | \(0.202772\pi\) | |||||||
\(194\) | −5.40272e7 | − | 9.35778e7i | −0.531259 | − | 0.920167i | ||||
\(195\) | 2.61413e8 | 2.52468 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.27180e7 | −0.304898 | −0.152449 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152449 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(198\) | 4.37004e7 | + | 7.56913e7i | 0.400089 | + | 0.692975i | ||||
\(199\) | 3.62236e7 | − | 6.27411e7i | 0.325841 | − | 0.564374i | −0.655841 | − | 0.754899i | \(-0.727686\pi\) |
0.981682 | + | 0.190525i | \(0.0610192\pi\) | |||||||
\(200\) | 3.13802e7 | − | 5.43521e7i | 0.277365 | − | 0.480410i | ||||
\(201\) | 1.24409e8 | + | 2.15483e8i | 1.08060 | + | 1.87166i | ||||
\(202\) | −1.50116e8 | −1.28144 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.30465e7 | −0.107594 | ||||||||
\(205\) | 3.15558e7 | + | 5.46562e7i | 0.255823 | + | 0.443099i | ||||
\(206\) | 6.48321e7 | − | 1.12292e8i | 0.516719 | − | 0.894984i | ||||
\(207\) | 2.92183e7 | − | 5.06075e7i | 0.228959 | − | 0.396569i | ||||
\(208\) | 1.45736e7 | + | 2.52422e7i | 0.112291 | + | 0.194493i | ||||
\(209\) | −8.78487e7 | −0.665615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.38006e7 | 0.687412 | 0.343706 | − | 0.939077i | \(-0.388318\pi\) | ||||
0.343706 | + | 0.939077i | \(0.388318\pi\) | |||||||
\(212\) | 1.82227e6 | + | 3.15627e6i | 0.0131352 | + | 0.0227509i | ||||
\(213\) | 4.37158e6 | − | 7.57181e6i | 0.0309963 | − | 0.0536872i | ||||
\(214\) | 2.78632e7 | − | 4.82605e7i | 0.194349 | − | 0.336623i | ||||
\(215\) | 8.16794e6 | + | 1.41473e7i | 0.0560503 | + | 0.0970819i | ||||
\(216\) | −9.86624e7 | −0.666137 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.19231e8 | 0.779457 | ||||||||
\(219\) | 4.05461e7 | + | 7.02280e7i | 0.260853 | + | 0.451810i | ||||
\(220\) | 3.45211e7 | − | 5.97923e7i | 0.218577 | − | 0.378587i | ||||
\(221\) | −8.84519e6 | + | 1.53203e7i | −0.0551232 | + | 0.0954761i | ||||
\(222\) | −7.03672e7 | − | 1.21879e8i | −0.431653 | − | 0.747645i | ||||
\(223\) | −1.62567e6 | −0.00981671 | −0.00490835 | − | 0.999988i | \(-0.501562\pi\) | ||||
−0.00490835 | + | 0.999988i | \(0.501562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.56141e8 | 3.25496 | ||||||||
\(226\) | −1.04274e8 | − | 1.80607e8i | −0.600891 | − | 1.04077i | ||||
\(227\) | −1.23076e8 | + | 2.13174e8i | −0.698367 | + | 1.20961i | 0.270665 | + | 0.962674i | \(0.412756\pi\) |
−0.969032 | + | 0.246934i | \(0.920577\pi\) | |||||||
\(228\) | 9.57288e7 | − | 1.65807e8i | 0.534897 | − | 0.926470i | ||||
\(229\) | −5.30204e7 | − | 9.18340e7i | −0.291755 | − | 0.505335i | 0.682470 | − | 0.730914i | \(-0.260906\pi\) |
−0.974225 | + | 0.225579i | \(0.927573\pi\) | |||||||
\(230\) | −4.61619e7 | −0.250171 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.51041e7 | 0.237142 | ||||||||
\(233\) | 1.01103e8 | + | 1.75116e8i | 0.523623 | + | 0.906942i | 0.999622 | + | 0.0274960i | \(0.00875336\pi\) |
−0.475999 | + | 0.879446i | \(0.657913\pi\) | |||||||
\(234\) | −1.29141e8 | + | 2.23679e8i | −0.658884 | + | 1.14122i | ||||
\(235\) | −1.60578e8 | + | 2.78130e8i | −0.807142 | + | 1.39801i | ||||
\(236\) | −6.87956e7 | − | 1.19157e8i | −0.340697 | − | 0.590105i | ||||
\(237\) | 2.80103e8 | 1.36678 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.67523e7 | −0.174137 | −0.0870687 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870687 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(240\) | 7.52353e7 | + | 1.30311e8i | 0.351303 | + | 0.608476i | ||||
\(241\) | 2.88208e7 | − | 4.99190e7i | 0.132631 | − | 0.229724i | −0.792059 | − | 0.610445i | \(-0.790991\pi\) |
0.924690 | + | 0.380721i | \(0.124324\pi\) | |||||||
\(242\) | −5.47548e7 | + | 9.48381e7i | −0.248353 | + | 0.430159i | ||||
\(243\) | −3.03208e7 | − | 5.25171e7i | −0.135556 | − | 0.234790i | ||||
\(244\) | −1.97399e8 | −0.869923 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.24133e7 | −0.395787 | ||||||||
\(247\) | −1.29803e8 | − | 2.24825e8i | −0.548082 | − | 0.949305i | ||||
\(248\) | −7.23548e7 | + | 1.25322e8i | −0.301222 | + | 0.521732i | ||||
\(249\) | −620822. | + | 1.07530e6i | −0.00254841 | + | 0.00441398i | ||||
\(250\) | −7.96616e7 | − | 1.37978e8i | −0.322447 | − | 0.558495i | ||||
\(251\) | 2.61332e8 | 1.04312 | 0.521561 | − | 0.853214i | \(-0.325350\pi\) | ||||
0.521561 | + | 0.853214i | \(0.325350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.10150e7 | −0.120407 | ||||||||
\(254\) | 8.52543e7 | + | 1.47665e8i | 0.326436 | + | 0.565404i | ||||
\(255\) | −4.56628e7 | + | 7.90904e7i | −0.172454 | + | 0.298698i | ||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.73813e8 | + | 3.01052e8i | 0.638727 | + | 1.10631i | 0.985712 | + | 0.168437i | \(0.0538721\pi\) |
−0.346985 | + | 0.937871i | \(0.612795\pi\) | |||||||
\(258\) | −2.39204e7 | −0.0867160 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.04030e8 | 0.719925 | ||||||||
\(261\) | 1.99841e8 | + | 3.46135e8i | 0.695734 | + | 1.20505i | ||||
\(262\) | −4.19093e7 | + | 7.25891e7i | −0.143965 | + | 0.249354i | ||||
\(263\) | 8.82507e7 | − | 1.52855e8i | 0.299139 | − | 0.518124i | −0.676800 | − | 0.736167i | \(-0.736634\pi\) |
0.975939 | + | 0.218043i | \(0.0699672\pi\) | |||||||
\(264\) | 5.05487e7 | + | 8.75530e7i | 0.169082 | + | 0.292858i | ||||
\(265\) | 2.55118e7 | 0.0842133 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.43344e7 | −0.0460883 | ||||||||
\(268\) | 9.70996e7 | + | 1.68182e8i | 0.308138 | + | 0.533711i | ||||
\(269\) | −2.03944e8 | + | 3.53242e8i | −0.638821 | + | 1.10647i | 0.346871 | + | 0.937913i | \(0.387244\pi\) |
−0.985692 | + | 0.168557i | \(0.946089\pi\) | |||||||
\(270\) | −3.45318e8 | + | 5.98109e8i | −1.06769 | + | 1.84930i | ||||
\(271\) | 1.58809e8 | + | 2.75066e8i | 0.484711 | + | 0.839544i | 0.999846 | − | 0.0175649i | \(-0.00559137\pi\) |
−0.515135 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(272\) | −1.01827e7 | −0.0306810 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.89585e8 | −0.850450 | ||||||||
\(275\) | −1.47585e8 | − | 2.55625e8i | −0.427935 | − | 0.741206i | ||||
\(276\) | 3.37971e7 | − | 5.85383e7i | 0.0967605 | − | 0.167594i | ||||
\(277\) | −1.46863e8 | + | 2.54375e8i | −0.415178 | + | 0.719109i | −0.995447 | − | 0.0953156i | \(-0.969614\pi\) |
0.580269 | + | 0.814425i | \(0.302947\pi\) | |||||||
\(278\) | 2.11062e8 | + | 3.65570e8i | 0.589188 | + | 1.02050i | ||||
\(279\) | −1.28232e9 | −3.53494 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.45027e7 | −0.146536 | −0.0732682 | − | 0.997312i | \(-0.523343\pi\) | ||||
−0.0732682 | + | 0.997312i | \(0.523343\pi\) | |||||||
\(282\) | −2.35133e8 | − | 4.07262e8i | −0.624369 | − | 1.08144i | ||||
\(283\) | 1.02705e8 | − | 1.77889e8i | 0.269362 | − | 0.466549i | −0.699335 | − | 0.714794i | \(-0.746520\pi\) |
0.968697 | + | 0.248245i | \(0.0798537\pi\) | |||||||
\(284\) | 3.41197e6 | − | 5.90970e6i | 0.00883875 | − | 0.0153092i | ||||
\(285\) | −6.70101e8 | − | 1.16065e9i | −1.71468 | − | 2.96992i | ||||
\(286\) | 1.37083e8 | 0.346498 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.48668e8 | −0.366729 | ||||||||
\(289\) | 2.02079e8 | + | 3.50012e8i | 0.492469 | + | 0.852982i | ||||
\(290\) | 1.57864e8 | − | 2.73429e8i | 0.380094 | − | 0.658343i | ||||
\(291\) | 5.53778e8 | − | 9.59172e8i | 1.31738 | − | 2.28177i | ||||
\(292\) | 3.16458e7 | + | 5.48121e7i | 0.0743833 | + | 0.128836i | ||||
\(293\) | 1.18887e8 | 0.276119 | 0.138059 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138059 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.63138e8 | −2.18430 | ||||||||
\(296\) | −5.49207e7 | − | 9.51254e7i | −0.123088 | − | 0.213194i | ||||
\(297\) | −2.32011e8 | + | 4.01854e8i | −0.513879 | + | 0.890064i | ||||
\(298\) | 2.94401e8 | − | 5.09918e8i | 0.644440 | − | 1.11620i | ||||
\(299\) | −4.58270e7 | − | 7.93748e7i | −0.0991454 | − | 0.171725i | ||||
\(300\) | 6.43295e8 | 1.37558 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.39431e8 | −0.291297 | ||||||||
\(303\) | −7.69344e8 | − | 1.33254e9i | −1.58881 | − | 2.75189i | ||||
\(304\) | 7.47151e7 | − | 1.29410e8i | 0.152529 | − | 0.264187i | ||||
\(305\) | −6.90897e8 | + | 1.19667e9i | −1.39432 | + | 2.41504i | ||||
\(306\) | −4.51159e7 | − | 7.81431e7i | −0.0900129 | − | 0.155907i | ||||
\(307\) | −1.63581e8 | −0.322663 | −0.161332 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161332 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.32906e9 | 2.56265 | ||||||||
\(310\) | 5.06484e8 | + | 8.77256e8i | 0.965605 | + | 1.67248i | ||||
\(311\) | −2.16240e8 | + | 3.74539e8i | −0.407638 | + | 0.706050i | −0.994625 | − | 0.103547i | \(-0.966981\pi\) |
0.586986 | + | 0.809597i | \(0.300314\pi\) | |||||||
\(312\) | −1.49379e8 | + | 2.58732e8i | −0.278451 | + | 0.482291i | ||||
\(313\) | −2.13516e8 | − | 3.69821e8i | −0.393574 | − | 0.681690i | 0.599344 | − | 0.800491i | \(-0.295428\pi\) |
−0.992918 | + | 0.118802i | \(0.962095\pi\) | |||||||
\(314\) | −1.77726e8 | −0.323964 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.18617e8 | 0.389744 | ||||||||
\(317\) | 1.73751e8 | + | 3.00946e8i | 0.306352 | + | 0.530616i | 0.977561 | − | 0.210651i | \(-0.0675584\pi\) |
−0.671210 | + | 0.741267i | \(0.734225\pi\) | |||||||
\(318\) | −1.86783e7 | + | 3.23517e7i | −0.0325718 | + | 0.0564161i | ||||
\(319\) | 1.06065e8 | − | 1.83710e8i | 0.182939 | − | 0.316859i | ||||
\(320\) | 5.87203e7 | + | 1.01706e8i | 0.100176 | + | 0.173510i | ||||
\(321\) | 5.71195e8 | 0.963867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.06943e7 | 0.149751 | ||||||||
\(324\) | −1.88127e8 | − | 3.25846e8i | −0.307287 | − | 0.532237i | ||||
\(325\) | 4.36136e8 | − | 7.55410e8i | 0.704742 | − | 1.22065i | ||||
\(326\) | 2.49518e8 | − | 4.32178e8i | 0.398879 | − | 0.690878i | ||||
\(327\) | 6.11060e8 | + | 1.05839e9i | 0.966421 | + | 1.67389i | ||||
\(328\) | −7.21275e7 | −0.112861 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.07682e8 | 1.08403 | ||||||||
\(331\) | 4.07707e8 | + | 7.06169e8i | 0.617945 | + | 1.07031i | 0.989860 | + | 0.142045i | \(0.0453679\pi\) |
−0.371915 | + | 0.928267i | \(0.621299\pi\) | |||||||
\(332\) | −484544. | + | 839255.i | −0.000726691 | + | 0.00125867i | ||||
\(333\) | 4.86670e8 | − | 8.42938e8i | 0.722238 | − | 1.25095i | ||||
\(334\) | −1.32495e8 | − | 2.29489e8i | −0.194575 | − | 0.337015i | ||||
\(335\) | 1.35940e9 | 1.97555 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.55790e8 | −0.791054 | −0.395527 | − | 0.918454i | \(-0.629438\pi\) | ||||
−0.395527 | + | 0.918454i | \(0.629438\pi\) | |||||||
\(338\) | −4.84442e7 | − | 8.39079e7i | −0.0682392 | − | 0.118194i | ||||
\(339\) | 1.06881e9 | − | 1.85123e9i | 1.49005 | − | 2.58084i | ||||
\(340\) | −3.56393e7 | + | 6.17291e7i | −0.0491760 | + | 0.0851753i | ||||
\(341\) | 3.40294e8 | + | 5.89406e8i | 0.464744 | + | 0.804960i | ||||
\(342\) | 1.32415e9 | 1.78997 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.86696e7 | −0.0247275 | ||||||||
\(345\) | −2.36580e8 | − | 4.09768e8i | −0.310178 | − | 0.537244i | ||||
\(346\) | 2.82319e8 | − | 4.88992e8i | 0.366416 | − | 0.634651i | ||||
\(347\) | −5.38540e8 | + | 9.32778e8i | −0.691934 | + | 1.19846i | 0.279269 | + | 0.960213i | \(0.409908\pi\) |
−0.971203 | + | 0.238252i | \(0.923426\pi\) | |||||||
\(348\) | 2.31159e8 | + | 4.00379e8i | 0.294024 | + | 0.509265i | ||||
\(349\) | −1.44167e9 | −1.81541 | −0.907707 | − | 0.419605i | \(-0.862169\pi\) | ||||
−0.907707 | + | 0.419605i | \(0.862169\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.37125e9 | −1.69255 | ||||||||
\(352\) | 3.94527e7 | + | 6.83340e7i | 0.0482144 | + | 0.0835099i | ||||
\(353\) | 2.86633e8 | − | 4.96463e8i | 0.346829 | − | 0.600725i | −0.638856 | − | 0.769327i | \(-0.720592\pi\) |
0.985684 | + | 0.168602i | \(0.0539252\pi\) | |||||||
\(354\) | 7.05155e8 | − | 1.22136e9i | 0.844837 | − | 1.46330i | ||||
\(355\) | −2.38838e7 | − | 4.13679e7i | −0.0283337 | − | 0.0490755i | ||||
\(356\) | −1.11878e7 | −0.0131423 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.69410e8 | 1.11665 | ||||||||
\(359\) | 4.74667e8 | + | 8.22148e8i | 0.541451 | + | 0.937820i | 0.998821 | + | 0.0485438i | \(0.0154581\pi\) |
−0.457370 | + | 0.889276i | \(0.651209\pi\) | |||||||
\(360\) | −5.20339e8 | + | 9.01254e8i | −0.587798 | + | 1.01810i | ||||
\(361\) | −2.18532e8 | + | 3.78509e8i | −0.244478 | + | 0.423449i | ||||
\(362\) | −9.22200e7 | − | 1.59730e8i | −0.102175 | − | 0.176973i | ||||
\(363\) | −1.12247e9 | −1.23169 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.43041e8 | 0.476890 | ||||||||
\(366\) | −1.01167e9 | − | 1.75226e9i | −1.07859 | − | 1.86817i | ||||
\(367\) | −1.50885e8 | + | 2.61341e8i | −0.159337 | + | 0.275979i | −0.934630 | − | 0.355622i | \(-0.884269\pi\) |
0.775293 | + | 0.631602i | \(0.217602\pi\) | |||||||
\(368\) | 2.63782e7 | − | 4.56885e7i | 0.0275917 | − | 0.0477902i | ||||
\(369\) | −3.19573e8 | − | 5.53516e8i | −0.331114 | − | 0.573506i | ||||
\(370\) | −7.68890e8 | −0.789147 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.48327e9 | −1.49390 | ||||||||
\(373\) | 6.80910e8 | + | 1.17937e9i | 0.679374 | + | 1.17671i | 0.975170 | + | 0.221459i | \(0.0710819\pi\) |
−0.295796 | + | 0.955251i | \(0.595585\pi\) | |||||||
\(374\) | −2.39452e7 | + | 4.14742e7i | −0.0236683 | + | 0.0409947i | ||||
\(375\) | 8.16531e8 | − | 1.41427e9i | 0.799582 | − | 1.38492i | ||||
\(376\) | −1.83518e8 | − | 3.17863e8i | −0.178042 | − | 0.308377i | ||||
\(377\) | 6.26877e8 | 0.602542 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.51839e9 | −1.43267 | −0.716333 | − | 0.697758i | \(-0.754181\pi\) | ||||
−0.716333 | + | 0.697758i | \(0.754181\pi\) | |||||||
\(380\) | −5.23006e8 | − | 9.05873e8i | −0.488950 | − | 0.846885i | ||||
\(381\) | −8.73857e8 | + | 1.51356e9i | −0.809474 | + | 1.40205i | ||||
\(382\) | −8.11708e7 | + | 1.40592e8i | −0.0745037 | + | 0.129044i | ||||
\(383\) | 2.27057e8 | + | 3.93274e8i | 0.206509 | + | 0.357684i | 0.950613 | − | 0.310380i | \(-0.100456\pi\) |
−0.744103 | + | 0.668064i | \(0.767123\pi\) | |||||||
\(384\) | −1.71966e8 | −0.154983 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.80865e8 | −0.160066 | ||||||||
\(387\) | −8.27186e7 | − | 1.43273e8i | −0.0725462 | − | 0.125654i | ||||
\(388\) | 4.32217e8 | − | 7.48622e8i | 0.375657 | − | 0.650656i | ||||
\(389\) | 9.18499e8 | − | 1.59089e9i | 0.791143 | − | 1.37030i | −0.134117 | − | 0.990965i | \(-0.542820\pi\) |
0.925260 | − | 0.379334i | \(-0.123847\pi\) | |||||||
\(390\) | 1.04565e9 | + | 1.81112e9i | 0.892610 | + | 1.54605i | ||||
\(391\) | 3.20197e7 | 0.0270893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.59141e8 | −0.713987 | ||||||||
\(394\) | −1.30872e8 | − | 2.26677e8i | −0.107798 | − | 0.186711i | ||||
\(395\) | 7.65161e8 | − | 1.32530e9i | 0.624688 | − | 1.08199i | ||||
\(396\) | −3.49603e8 | + | 6.05530e8i | −0.282906 | + | 0.490007i | ||||
\(397\) | 6.18339e8 | + | 1.07099e9i | 0.495975 | + | 0.859054i | 0.999989 | − | 0.00464153i | \(-0.00147745\pi\) |
−0.504014 | + | 0.863695i | \(0.668144\pi\) | |||||||
\(398\) | 5.79578e8 | 0.460809 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.02084e8 | 0.392253 | ||||||||
\(401\) | −7.89739e8 | − | 1.36787e9i | −0.611615 | − | 1.05935i | −0.990968 | − | 0.134096i | \(-0.957187\pi\) |
0.379353 | − | 0.925252i | \(-0.376147\pi\) | |||||||
\(402\) | −9.95271e8 | + | 1.72386e9i | −0.764100 | + | 1.32346i | ||||
\(403\) | −1.00562e9 | + | 1.74178e9i | −0.765360 | + | 1.32564i | ||||
\(404\) | −6.00463e8 | − | 1.04003e9i | −0.453056 | − | 0.784716i | ||||
\(405\) | −2.63378e9 | −1.97010 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.16598e8 | −0.379815 | ||||||||
\(408\) | −5.21861e7 | − | 9.03890e7i | −0.0380403 | − | 0.0658878i | ||||
\(409\) | −9.62788e8 | + | 1.66760e9i | −0.695823 | + | 1.20520i | 0.274079 | + | 0.961707i | \(0.411627\pi\) |
−0.969902 | + | 0.243494i | \(0.921706\pi\) | |||||||
\(410\) | −2.52446e8 | + | 4.37250e8i | −0.180894 | + | 0.313318i | ||||
\(411\) | −1.48412e9 | − | 2.57057e9i | −1.05444 | − | 1.82635i | ||||
\(412\) | 1.03731e9 | 0.730751 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.67492e8 | 0.323797 | ||||||||
\(415\) | 3.39181e6 | + | 5.87478e6i | 0.00232950 | + | 0.00403481i | ||||
\(416\) | −1.16589e8 | + | 2.01937e8i | −0.0794016 | + | 0.137528i | ||||
\(417\) | −2.16339e9 | + | 3.74710e9i | −1.46103 | + | 2.53057i | ||||
\(418\) | −3.51395e8 | − | 6.08633e8i | −0.235330 | − | 0.407604i | ||||
\(419\) | 2.39996e9 | 1.59388 | 0.796938 | − | 0.604062i | \(-0.206452\pi\) | ||||
0.796938 | + | 0.604062i | \(0.206452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.20940e9 | 0.789919 | 0.394960 | − | 0.918698i | \(-0.370759\pi\) | ||||
0.394960 | + | 0.918698i | \(0.370759\pi\) | |||||||
\(422\) | 3.75202e8 | + | 6.49870e8i | 0.243037 | + | 0.420952i | ||||
\(423\) | 1.62622e9 | − | 2.81669e9i | 1.04469 | − | 1.80945i | ||||
\(424\) | −1.45782e7 | + | 2.52501e7i | −0.00928801 | + | 0.0160873i | ||||
\(425\) | 1.52366e8 | + | 2.63905e8i | 0.0962778 | + | 0.166758i | ||||
\(426\) | 6.99453e7 | 0.0438354 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.45811e8 | 0.274851 | ||||||||
\(429\) | 7.02548e8 | + | 1.21685e9i | 0.429611 | + | 0.744109i | ||||
\(430\) | −6.53435e7 | + | 1.13178e8i | −0.0396335 | + | 0.0686473i | ||||
\(431\) | 1.08143e9 | − | 1.87308e9i | 0.650618 | − | 1.12690i | −0.332355 | − | 0.943155i | \(-0.607843\pi\) |
0.982973 | − | 0.183750i | \(-0.0588236\pi\) | |||||||
\(432\) | −3.94650e8 | − | 6.83553e8i | −0.235515 | − | 0.407924i | ||||
\(433\) | −2.25750e9 | −1.33635 | −0.668174 | − | 0.744005i | \(-0.732924\pi\) | ||||
−0.668174 | + | 0.744005i | \(0.732924\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.23622e9 | 1.88506 | ||||||||
\(436\) | 4.76925e8 | + | 8.26058e8i | 0.275580 | + | 0.477318i | ||||
\(437\) | −2.34944e8 | + | 4.06935e8i | −0.134673 | + | 0.233260i | ||||
\(438\) | −3.24369e8 | + | 5.61824e8i | −0.184451 | + | 0.319478i | ||||
\(439\) | −3.72862e8 | − | 6.45816e8i | −0.210340 | − | 0.364320i | 0.741481 | − | 0.670974i | \(-0.234124\pi\) |
−0.951821 | + | 0.306654i | \(0.900790\pi\) | |||||||
\(440\) | 5.52337e8 | 0.309115 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.41523e8 | −0.0779559 | ||||||||
\(443\) | 5.51076e8 | + | 9.54492e8i | 0.301161 | + | 0.521626i | 0.976399 | − | 0.215974i | \(-0.0692925\pi\) |
−0.675238 | + | 0.737600i | \(0.735959\pi\) | |||||||
\(444\) | 5.62937e8 | − | 9.75036e8i | 0.305225 | − | 0.528665i | ||||
\(445\) | −3.91574e7 | + | 6.78227e7i | −0.0210647 | + | 0.0364850i | ||||
\(446\) | −6.50269e6 | − | 1.12630e7i | −0.00347073 | − | 0.00601148i | ||||
\(447\) | 6.03522e9 | 3.19608 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.41600e9 | 1.78097 | 0.890483 | − | 0.455017i | \(-0.150367\pi\) | ||||
0.890483 | + | 0.455017i | \(0.150367\pi\) | |||||||
\(450\) | 2.22456e9 | + | 3.85306e9i | 1.15080 | + | 1.99325i | ||||
\(451\) | −1.69612e8 | + | 2.93777e8i | −0.0870642 | + | 0.150800i | ||||
\(452\) | 8.34190e8 | − | 1.44486e9i | 0.424894 | − | 0.735938i | ||||
\(453\) | −7.14584e8 | − | 1.23770e9i | −0.361168 | − | 0.625562i | ||||
\(454\) | −1.96922e9 | −0.987640 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.53166e9 | 0.756459 | ||||||||
\(457\) | −2.13655e8 | − | 3.70061e8i | −0.104714 | − | 0.181371i | 0.808907 | − | 0.587936i | \(-0.200060\pi\) |
−0.913621 | + | 0.406566i | \(0.866726\pi\) | |||||||
\(458\) | 4.24163e8 | − | 7.34672e8i | 0.206302 | − | 0.357326i | ||||
\(459\) | 2.39526e8 | − | 4.14871e8i | 0.115613 | − | 0.200248i | ||||
\(460\) | −1.84648e8 | − | 3.19819e8i | −0.0884487 | − | 0.153198i | ||||
\(461\) | −2.18116e9 | −1.03690 | −0.518448 | − | 0.855109i | \(-0.673490\pi\) | ||||
−0.518448 | + | 0.855109i | \(0.673490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.88134e8 | 0.0880916 | 0.0440458 | − | 0.999030i | \(-0.485975\pi\) | ||||
0.0440458 | + | 0.999030i | \(0.485975\pi\) | |||||||
\(464\) | 1.80417e8 | + | 3.12491e8i | 0.0838423 | + | 0.145219i | ||||
\(465\) | −5.19146e9 | + | 8.99187e9i | −2.39444 | + | 4.14729i | ||||
\(466\) | −8.08825e8 | + | 1.40093e9i | −0.370258 | + | 0.641305i | ||||
\(467\) | 4.27267e8 | + | 7.40048e8i | 0.194129 | + | 0.336241i | 0.946615 | − | 0.322367i | \(-0.104479\pi\) |
−0.752486 | + | 0.658609i | \(0.771145\pi\) | |||||||
\(468\) | −2.06626e9 | −0.931803 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.56925e9 | −1.14147 | ||||||||
\(471\) | −9.10844e8 | − | 1.57763e9i | −0.401671 | − | 0.695715i | ||||
\(472\) | 5.50365e8 | − | 9.53260e8i | 0.240909 | − | 0.417267i | ||||
\(473\) | −4.39027e7 | + | 7.60416e7i | −0.0190755 | + | 0.0330398i | ||||
\(474\) | 1.12041e9 | + | 1.94061e9i | 0.483230 | + | 0.836980i | ||||
\(475\) | −4.47193e9 | −1.91455 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.58364e8 | −0.108998 | ||||||||
\(478\) | −1.47009e8 | − | 2.54628e8i | −0.0615669 | − | 0.106637i | ||||
\(479\) | −3.41407e8 | + | 5.91334e8i | −0.141938 | + | 0.245844i | −0.928226 | − | 0.372016i | \(-0.878667\pi\) |
0.786288 | + | 0.617860i | \(0.212000\pi\) | |||||||
\(480\) | −6.01883e8 | + | 1.04249e9i | −0.248409 | + | 0.430257i | ||||
\(481\) | −7.63312e8 | − | 1.32210e9i | −0.312748 | − | 0.541695i | ||||
\(482\) | 4.61132e8 | 0.187569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.76077e8 | −0.351224 | ||||||||
\(485\) | −3.02552e9 | − | 5.24036e9i | −1.20422 | − | 2.08576i | ||||
\(486\) | 2.42566e8 | − | 4.20137e8i | 0.0958525 | − | 0.166021i | ||||
\(487\) | −2.07560e9 | + | 3.59504e9i | −0.814313 | + | 1.41043i | 0.0955063 | + | 0.995429i | \(0.469553\pi\) |
−0.909820 | + | 0.415004i | \(0.863780\pi\) | |||||||
\(488\) | −7.89596e8 | − | 1.36762e9i | −0.307564 | − | 0.532717i | ||||
\(489\) | 5.11512e9 | 1.97822 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.99538e8 | 0.342953 | 0.171476 | − | 0.985188i | \(-0.445146\pi\) | ||||
0.171476 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(492\) | −3.69653e8 | − | 6.40258e8i | −0.139932 | − | 0.242369i | ||||
\(493\) | −1.09501e8 | + | 1.89661e8i | −0.0411579 | + | 0.0712876i | ||||
\(494\) | 1.03842e9 | − | 1.79860e9i | 0.387552 | − | 0.671260i | ||||
\(495\) | 2.44722e9 | + | 4.23871e9i | 0.906891 | + | 1.57078i | ||||
\(496\) | −1.15768e9 | −0.425992 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.93315e6 | −0.00360400 | ||||||||
\(499\) | 3.05555e8 | + | 5.29237e8i | 0.110087 | + | 0.190677i | 0.915805 | − | 0.401623i | \(-0.131554\pi\) |
−0.805718 | + | 0.592299i | \(0.798220\pi\) | |||||||
\(500\) | 6.37293e8 | − | 1.10382e9i | 0.228005 | − | 0.394916i | ||||
\(501\) | 1.35808e9 | − | 2.35226e9i | 0.482495 | − | 0.835705i | ||||
\(502\) | 1.04533e9 | + | 1.81056e9i | 0.368799 | + | 0.638779i | ||||
\(503\) | −5.23241e9 | −1.83322 | −0.916608 | − | 0.399787i | \(-0.869084\pi\) | ||||
−0.916608 | + | 0.399787i | \(0.869084\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.40649e9 | −2.90466 | ||||||||
\(506\) | −1.24060e8 | − | 2.14879e8i | −0.0425702 | − | 0.0737337i | ||||
\(507\) | 4.96554e8 | − | 8.60056e8i | 0.169215 | − | 0.293089i | ||||
\(508\) | −6.82035e8 | + | 1.18132e9i | −0.230825 | + | 0.399801i | ||||
\(509\) | 1.16765e8 | + | 2.02243e8i | 0.0392465 | + | 0.0679770i | 0.884981 | − | 0.465626i | \(-0.154171\pi\) |
−0.845735 | + | 0.533603i | \(0.820838\pi\) | |||||||
\(510\) | −7.30606e8 | −0.243886 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 3.51504e9 | + | 6.08823e9i | 1.14953 | + | 1.99104i | ||||
\(514\) | −1.39050e9 | + | 2.40842e9i | −0.451648 | + | 0.782278i | ||||
\(515\) | 3.63060e9 | − | 6.28838e9i | 1.17126 | − | 2.02868i | ||||
\(516\) | −9.56815e7 | − | 1.65725e8i | −0.0306587 | − | 0.0531025i | ||||
\(517\) | −1.72622e9 | −0.549388 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.78755e9 | 1.81723 | ||||||||
\(520\) | 8.16120e8 | + | 1.41356e9i | 0.254532 | + | 0.440862i | ||||
\(521\) | 1.11514e9 | − | 1.93149e9i | 0.345461 | − | 0.598356i | −0.639977 | − | 0.768394i | \(-0.721056\pi\) |
0.985437 | + | 0.170039i | \(0.0543893\pi\) | |||||||
\(522\) | −1.59873e9 | + | 2.76908e9i | −0.491958 | + | 0.852097i | ||||
\(523\) | 2.37398e8 | + | 4.11185e8i | 0.0725638 | + | 0.125684i | 0.900024 | − | 0.435840i | \(-0.143549\pi\) |
−0.827460 | + | 0.561524i | \(0.810215\pi\) | |||||||
\(524\) | −6.70549e8 | −0.203597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.41201e9 | 0.423047 | ||||||||
\(527\) | −3.51317e8 | − | 6.08498e8i | −0.104559 | − | 0.181102i | ||||
\(528\) | −4.04390e8 | + | 7.00424e8i | −0.119559 | + | 0.207082i | ||||
\(529\) | 1.61947e9 | − | 2.80500e9i | 0.475638 | − | 0.823830i | ||||
\(530\) | 1.02047e8 | + | 1.76751e8i | 0.0297739 | + | 0.0515699i | ||||
\(531\) | 9.75392e9 | 2.82715 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.00246e9 | −0.286762 | ||||||||
\(534\) | −5.73377e7 | − | 9.93118e7i | −0.0162947 | − | 0.0282232i | ||||
\(535\) | 1.56034e9 | − | 2.70259e9i | 0.440535 | − | 0.763029i | ||||
\(536\) | −7.76797e8 | + | 1.34545e9i | −0.217887 | + | 0.377391i | ||||
\(537\) | 4.96823e9 | + | 8.60522e9i | 1.38449 | + | 2.39802i | ||||
\(538\) | −3.26311e9 | −0.903429 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.52509e9 | −1.50995 | ||||||||
\(541\) | 4.23985e8 | + | 7.34363e8i | 0.115122 | + | 0.199398i | 0.917829 | − | 0.396977i | \(-0.129941\pi\) |
−0.802706 | + | 0.596375i | \(0.796607\pi\) | |||||||
\(542\) | −1.27047e9 | + | 2.20052e9i | −0.342743 | + | 0.593648i | ||||
\(543\) | 9.45255e8 | − | 1.63723e9i | 0.253367 | − | 0.438844i | ||||
\(544\) | −4.07306e7 | − | 7.05475e7i | −0.0108474 | − | 0.0187882i | ||||
\(545\) | 6.67694e9 | 1.76681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.55694e7 | −0.0171295 | −0.00856477 | − | 0.999963i | \(-0.502726\pi\) | ||||
−0.00856477 | + | 0.999963i | \(0.502726\pi\) | |||||||
\(548\) | −1.15834e9 | − | 2.00630e9i | −0.300679 | − | 0.520792i | ||||
\(549\) | 6.99687e9 | − | 1.21189e10i | 1.80468 | − | 3.12580i | ||||
\(550\) | 1.18068e9 | − | 2.04500e9i | 0.302596 | − | 0.524112i | ||||
\(551\) | −1.60692e9 | − | 2.78327e9i | −0.409227 | − | 0.708802i | ||||
\(552\) | 5.40754e8 | 0.136840 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.34981e9 | −0.587150 | ||||||||
\(555\) | −3.94056e9 | − | 6.82525e9i | −0.978436 | − | 1.69470i | ||||
\(556\) | −1.68850e9 | + | 2.92456e9i | −0.416619 | + | 0.721604i | ||||
\(557\) | −3.06262e8 | + | 5.30461e8i | −0.0750930 | + | 0.130065i | −0.901127 | − | 0.433556i | \(-0.857259\pi\) |
0.826034 | + | 0.563621i | \(0.190592\pi\) | |||||||
\(558\) | −5.12928e9 | − | 8.88417e9i | −1.24979 | − | 2.16470i | ||||
\(559\) | −2.59478e8 | −0.0628288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.90876e8 | −0.117382 | ||||||||
\(562\) | −2.18011e8 | − | 3.77606e8i | −0.0518085 | − | 0.0897349i | ||||
\(563\) | 3.51051e8 | − | 6.08037e8i | 0.0829068 | − | 0.143599i | −0.821591 | − | 0.570078i | \(-0.806913\pi\) |
0.904497 | + | 0.426479i | \(0.140246\pi\) | |||||||
\(564\) | 1.88106e9 | − | 3.25809e9i | 0.441495 | − | 0.764692i | ||||
\(565\) | −5.83933e9 | − | 1.01140e10i | −1.36205 | − | 2.35914i | ||||
\(566\) | 1.64327e9 | 0.380936 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.45915e7 | 0.0124999 | ||||||||
\(569\) | −1.21788e8 | − | 2.10944e8i | −0.0277149 | − | 0.0480036i | 0.851835 | − | 0.523810i | \(-0.175490\pi\) |
−0.879550 | + | 0.475806i | \(0.842156\pi\) | |||||||
\(570\) | 5.36081e9 | − | 9.28520e9i | 1.21246 | − | 2.10005i | ||||
\(571\) | −2.64459e9 | + | 4.58057e9i | −0.594474 | + | 1.02966i | 0.399147 | + | 0.916887i | \(0.369306\pi\) |
−0.993621 | + | 0.112772i | \(0.964027\pi\) | |||||||
\(572\) | 5.48330e8 | + | 9.49736e8i | 0.122506 | + | 0.212186i | ||||
\(573\) | −1.66400e9 | −0.369498 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.57882e9 | −0.346333 | ||||||||
\(576\) | −5.94674e8 | − | 1.03000e9i | −0.129658 | − | 0.224575i | ||||
\(577\) | −1.84228e9 | + | 3.19092e9i | −0.399245 | + | 0.691513i | −0.993633 | − | 0.112666i | \(-0.964061\pi\) |
0.594388 | + | 0.804178i | \(0.297394\pi\) | |||||||
\(578\) | −1.61663e9 | + | 2.80009e9i | −0.348228 | + | 0.603149i | ||||
\(579\) | −9.26933e8 | − | 1.60549e9i | −0.198460 | − | 0.343743i | ||||
\(580\) | 2.52583e9 | 0.537534 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.86045e9 | 1.86305 | ||||||||
\(583\) | 6.85630e7 | + | 1.18755e8i | 0.0143301 | + | 0.0248205i | ||||
\(584\) | −2.53166e8 | + | 4.38497e8i | −0.0525969 | + | 0.0911006i | ||||
\(585\) | −7.23191e9 | + | 1.25260e10i | −1.49351 | + | 2.58683i | ||||
\(586\) | 4.75546e8 | + | 8.23670e8i | 0.0976228 | + | 0.169088i | ||||
\(587\) | 4.23510e9 | 0.864232 | 0.432116 | − | 0.901818i | \(-0.357767\pi\) | ||||
0.432116 | + | 0.901818i | \(0.357767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.03111e10 | 2.07923 | ||||||||
\(590\) | −3.85255e9 | − | 6.67282e9i | −0.772265 | − | 1.33760i | ||||
\(591\) | 1.34144e9 | − | 2.32344e9i | 0.267309 | − | 0.462993i | ||||
\(592\) | 4.39366e8 | − | 7.61004e8i | 0.0870362 | − | 0.150751i | ||||
\(593\) | 4.85477e9 | + | 8.40872e9i | 0.956043 | + | 1.65592i | 0.731962 | + | 0.681345i | \(0.238605\pi\) |
0.224081 | + | 0.974571i | \(0.428062\pi\) | |||||||
\(594\) | −3.71217e9 | −0.726734 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.71042e9 | 0.911376 | ||||||||
\(597\) | 2.97034e9 | + | 5.14477e9i | 0.571341 | + | 0.989592i | ||||
\(598\) | 3.66616e8 | − | 6.34998e8i | 0.0701064 | − | 0.121428i | ||||
\(599\) | 2.02088e9 | − | 3.50027e9i | 0.384191 | − | 0.665438i | −0.607466 | − | 0.794346i | \(-0.707814\pi\) |
0.991657 | + | 0.128908i | \(0.0411471\pi\) | |||||||
\(600\) | 2.57318e9 | + | 4.45688e9i | 0.486341 | + | 0.842367i | ||||
\(601\) | 2.62572e7 | 0.00493387 | 0.00246694 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246694 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.37669e10 | −2.55697 | ||||||||
\(604\) | −5.57724e8 | − | 9.66007e8i | −0.102989 | − | 0.178382i | ||||
\(605\) | −3.06627e9 | + | 5.31094e9i | −0.562946 | + | 0.975051i | ||||
\(606\) | 6.15475e9 | − | 1.06603e10i | 1.12346 | − | 1.94588i | ||||
\(607\) | −3.63244e9 | − | 6.29158e9i | −0.659232 | − | 1.14182i | −0.980815 | − | 0.194942i | \(-0.937548\pi\) |
0.321583 | − | 0.946882i | \(-0.395785\pi\) | |||||||
\(608\) | 1.19544e9 | 0.215708 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.10543e10 | −1.97187 | ||||||||
\(611\) | −2.55062e9 | − | 4.41780e9i | −0.452377 | − | 0.783541i | ||||
\(612\) | 3.60927e8 | − | 6.25145e8i | 0.0636488 | − | 0.110243i | ||||
\(613\) | 5.50186e9 | − | 9.52949e9i | 0.964712 | − | 1.67093i | 0.254324 | − | 0.967119i | \(-0.418147\pi\) |
0.710387 | − | 0.703811i | \(-0.248520\pi\) | |||||||
\(614\) | −6.54325e8 | − | 1.13332e9i | −0.114079 | − | 0.197590i | ||||
\(615\) | −5.17515e9 | −0.897139 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50181e8 | 0.145718 | 0.0728590 | − | 0.997342i | \(-0.476788\pi\) | ||||
0.0728590 | + | 0.997342i | \(0.476788\pi\) | |||||||
\(618\) | 5.31623e9 | + | 9.20798e9i | 0.906033 | + | 1.56930i | ||||
\(619\) | 2.89636e9 | − | 5.01663e9i | 0.490834 | − | 0.850149i | −0.509110 | − | 0.860701i | \(-0.670026\pi\) |
0.999944 | + | 0.0105519i | \(0.00335885\pi\) | |||||||
\(620\) | −4.05187e9 | + | 7.01804e9i | −0.682786 | + | 1.18262i | ||||
\(621\) | 1.24099e9 | + | 2.14945e9i | 0.207944 | + | 0.360170i | ||||
\(622\) | −3.45984e9 | −0.576488 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.39007e9 | −0.393789 | ||||||||
\(625\) | 3.27194e8 | + | 5.66717e8i | 0.0536075 | + | 0.0928510i | ||||
\(626\) | 1.70813e9 | − | 2.95857e9i | 0.278299 | − | 0.482027i | ||||
\(627\) | 3.60179e9 | − | 6.23849e9i | 0.583556 | − | 1.01075i | ||||
\(628\) | −7.10902e8 | − | 1.23132e9i | −0.114538 | − | 0.198386i | ||||
\(629\) | 5.33332e8 | 0.0854516 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.69052e9 | −1.06012 | −0.530062 | − | 0.847959i | \(-0.677831\pi\) | ||||
−0.530062 | + | 0.847959i | \(0.677831\pi\) | |||||||
\(632\) | 8.74469e8 | + | 1.51463e9i | 0.137795 | + | 0.238669i | ||||
\(633\) | −3.84583e9 | + | 6.66116e9i | −0.602666 | + | 1.04385i | ||||
\(634\) | −1.39001e9 | + | 2.40757e9i | −0.216623 | + | 0.375202i | ||||
\(635\) | 4.77424e9 | + | 8.26923e9i | 0.739940 | + | 1.28161i | ||||
\(636\) | −2.98853e8 | −0.0460635 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.69704e9 | 0.258714 | ||||||||
\(639\) | 2.41877e8 | + | 4.18942e8i | 0.0366725 | + | 0.0635187i | ||||
\(640\) | −4.69762e8 | + | 8.13652e8i | −0.0708350 | + | 0.122690i | ||||
\(641\) | −2.38597e9 | + | 4.13262e9i | −0.357818 | + | 0.619759i | −0.987596 | − | 0.157016i | \(-0.949813\pi\) |
0.629778 | + | 0.776775i | \(0.283146\pi\) | |||||||
\(642\) | 2.28478e9 | + | 3.95736e9i | 0.340778 | + | 0.590245i | ||||
\(643\) | −4.09295e9 | −0.607153 | −0.303576 | − | 0.952807i | \(-0.598181\pi\) | ||||
−0.303576 | + | 0.952807i | \(0.598181\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.33954e9 | −0.196561 | ||||||||
\(646\) | 3.62777e8 | + | 6.28348e8i | 0.0529451 | + | 0.0917036i | ||||
\(647\) | −2.69951e9 | + | 4.67569e9i | −0.391850 | + | 0.678705i | −0.992694 | − | 0.120662i | \(-0.961498\pi\) |
0.600843 | + | 0.799367i | \(0.294832\pi\) | |||||||
\(648\) | 1.50502e9 | − | 2.60677e9i | 0.217285 | − | 0.376348i | ||||
\(649\) | −2.58843e9 | − | 4.48330e9i | −0.371690 | − | 0.643786i | ||||
\(650\) | 6.97818e9 | 0.996656 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.99229e9 | 0.564099 | ||||||||
\(653\) | 2.04893e9 | + | 3.54886e9i | 0.287960 | + | 0.498761i | 0.973323 | − | 0.229441i | \(-0.0736898\pi\) |
−0.685363 | + | 0.728202i | \(0.740356\pi\) | |||||||
\(654\) | −4.88848e9 | + | 8.46709e9i | −0.683363 | + | 1.18362i | ||||
\(655\) | −2.34692e9 | + | 4.06499e9i | −0.326328 | + | 0.565216i | ||||
\(656\) | −2.88510e8 | − | 4.99714e8i | −0.0399022 | − | 0.0691127i | ||||
\(657\) | −4.48678e9 | −0.617242 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.77455e9 | −0.513766 | −0.256883 | − | 0.966442i | \(-0.582696\pi\) | ||||
−0.256883 | + | 0.966442i | \(0.582696\pi\) | |||||||
\(660\) | 2.83073e9 | + | 4.90297e9i | 0.383261 | + | 0.663827i | ||||
\(661\) | 4.90953e9 | − | 8.50355e9i | 0.661203 | − | 1.14524i | −0.319097 | − | 0.947722i | \(-0.603380\pi\) |
0.980300 | − | 0.197515i | \(-0.0632871\pi\) | |||||||
\(662\) | −3.26165e9 | + | 5.64935e9i | −0.436953 | + | 0.756825i | ||||
\(663\) | −7.25305e8 | − | 1.25627e9i | −0.0966548 | − | 0.167411i | ||||
\(664\) | −7.75270e6 | −0.00102770 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.78673e9 | 1.02140 | ||||||||
\(667\) | −5.67325e8 | − | 9.82636e8i | −0.0740273 | − | 0.128219i | ||||
\(668\) | 1.05996e9 | − | 1.83591e9i | 0.137586 | − | 0.238305i | ||||
\(669\) | 6.66526e7 | − | 1.15446e8i | 0.00860648 | − | 0.0149069i | ||||
\(670\) | 5.43758e9 | + | 9.41817e9i | 0.698464 | + | 1.20977i | ||||
\(671\) | −7.42714e9 | −0.949058 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.98739e9 | 1.26299 | 0.631494 | − | 0.775381i | \(-0.282442\pi\) | ||||
0.631494 | + | 0.775381i | \(0.282442\pi\) | |||||||
\(674\) | −2.22316e9 | − | 3.85063e9i | −0.279680 | − | 0.484420i | ||||
\(675\) | −1.18105e10 | + | 2.04564e10i | −1.47810 | + | 2.56015i | ||||
\(676\) | 3.87554e8 | − | 6.71263e8i | 0.0482524 | − | 0.0835756i | ||||
\(677\) | 2.37780e8 | + | 4.11847e8i | 0.0294520 | + | 0.0510123i | 0.880376 | − | 0.474277i | \(-0.157290\pi\) |
−0.850924 | + | 0.525289i | \(0.823957\pi\) | |||||||
\(678\) | 1.71009e10 | 2.10724 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.70229e8 | −0.0695453 | ||||||||
\(681\) | −1.00923e10 | − | 1.74803e10i | −1.22454 | − | 2.12097i | ||||
\(682\) | −2.72235e9 | + | 4.71525e9i | −0.328624 | + | 0.569193i | ||||
\(683\) | −1.38182e8 | + | 2.39339e8i | −0.0165951 | + | 0.0287436i | −0.874204 | − | 0.485559i | \(-0.838616\pi\) |
0.857609 | + | 0.514303i | \(0.171949\pi\) | |||||||
\(684\) | 5.29660e9 | + | 9.17398e9i | 0.632850 | + | 1.09613i | ||||
\(685\) | −1.62167e10 | −1.92773 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.69534e9 | 1.02315 | ||||||||
\(688\) | −7.46783e7 | − | 1.29347e8i | −0.00874248 | − | 0.0151424i | ||||
\(689\) | −2.02614e8 | + | 3.50938e8i | −0.0235995 | + | 0.0408754i | ||||
\(690\) | 1.89264e9 | − | 3.27815e9i | 0.219329 | − | 0.379889i | ||||
\(691\) | 4.41241e9 | + | 7.64252e9i | 0.508748 | + | 0.881178i | 0.999949 | + | 0.0101311i | \(0.00322490\pi\) |
−0.491201 | + | 0.871047i | \(0.663442\pi\) | |||||||
\(692\) | 4.51711e9 | 0.518191 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.61664e9 | −0.978542 | ||||||||
\(695\) | 1.18195e10 | + | 2.04719e10i | 1.33552 | + | 2.31319i | ||||
\(696\) | −1.84927e9 | + | 3.20303e9i | −0.207906 | + | 0.360104i | ||||
\(697\) | 1.75106e8 | − | 3.03293e8i | 0.0195879 | − | 0.0339272i | ||||
\(698\) | −5.76666e9 | − | 9.98815e9i | −0.641846 | − | 1.11171i | ||||
\(699\) | −1.65809e10 | −1.83628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.61615e10 | 1.77202 | 0.886012 | − | 0.463662i | \(-0.153465\pi\) | ||||
0.886012 | + | 0.463662i | \(0.153465\pi\) | |||||||
\(702\) | −5.48501e9 | − | 9.50032e9i | −0.598408 | − | 1.03647i | ||||
\(703\) | −3.91331e9 | + | 6.77806e9i | −0.424816 | + | 0.735803i | ||||
\(704\) | −3.15621e8 | + | 5.46672e8i | −0.0340928 | + | 0.0590504i | ||||
\(705\) | −1.31674e10 | − | 2.28067e10i | −1.41527 | − | 2.45132i | ||||
\(706\) | 4.58613e9 | 0.490490 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.12825e10 | 1.19478 | ||||||||
\(709\) | 4.18051e9 | + | 7.24085e9i | 0.440522 | + | 0.763006i | 0.997728 | − | 0.0673680i | \(-0.0214602\pi\) |
−0.557207 | + | 0.830374i | \(0.688127\pi\) | |||||||
\(710\) | 1.91070e8 | − | 3.30943e8i | 0.0200350 | − | 0.0347016i | ||||
\(711\) | −7.74896e9 | + | 1.34216e10i | −0.808537 | + | 1.40043i | ||||
\(712\) | −4.47514e7 | − | 7.75116e7i | −0.00464650 | − | 0.00804798i | ||||
\(713\) | 3.64035e9 | 0.376123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.67663e9 | 0.785415 | ||||||||
\(716\) | 3.87764e9 | + | 6.71627e9i | 0.394795 | + | 0.683805i | ||||
\(717\) | 1.50685e9 | − | 2.60993e9i | 0.152669 | − | 0.264431i | ||||
\(718\) | −3.79734e9 | + | 6.57719e9i | −0.382863 | + | 0.663139i | ||||
\(719\) | −4.09445e9 | − | 7.09180e9i | −0.410814 | − | 0.711550i | 0.584165 | − | 0.811635i | \(-0.301422\pi\) |
−0.994979 | + | 0.100085i | \(0.968089\pi\) | |||||||
\(720\) | −8.32543e9 | −0.831272 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.49652e9 | −0.345745 | ||||||||
\(723\) | 2.36330e9 | + | 4.09336e9i | 0.232560 | + | 0.402806i | ||||
\(724\) | 7.37760e8 | − | 1.27784e9i | 0.0722488 | − | 0.125139i | ||||
\(725\) | 5.39924e9 | − | 9.35175e9i | 0.526198 | − | 0.911402i | ||||
\(726\) | −4.48990e9 | − | 7.77673e9i | −0.435470 | − | 0.754256i | ||||
\(727\) | 1.40657e10 | 1.35766 | 0.678832 | − | 0.734294i | \(-0.262486\pi\) | ||||
0.678832 | + | 0.734294i | \(0.262486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.88473e9 | −0.753772 | ||||||||
\(730\) | 1.77216e9 | + | 3.06948e9i | 0.168606 | + | 0.292035i | ||||
\(731\) | 4.53248e7 | − | 7.85048e7i | 0.00429165 | − | 0.00743336i | ||||
\(732\) | 8.09336e9 | − | 1.40181e10i | 0.762676 | − | 1.32099i | ||||
\(733\) | −4.76816e9 | − | 8.25870e9i | −0.447185 | − | 0.774547i | 0.551017 | − | 0.834494i | \(-0.314240\pi\) |
−0.998202 | + | 0.0599473i | \(0.980907\pi\) | |||||||
\(734\) | −2.41417e9 | −0.225336 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.22052e8 | 0.0390206 | ||||||||
\(737\) | 3.65337e9 | + | 6.32783e9i | 0.336169 | + | 0.582262i | ||||
\(738\) | 2.55658e9 | − | 4.42813e9i | 0.234133 | − | 0.405530i | ||||
\(739\) | −7.25665e9 | + | 1.25689e10i | −0.661425 | + | 1.14562i | 0.318816 | + | 0.947817i | \(0.396715\pi\) |
−0.980241 | + | 0.197805i | \(0.936619\pi\) | |||||||
\(740\) | −3.07556e9 | − | 5.32703e9i | −0.279006 | − | 0.483252i | ||||
\(741\) | 2.12877e10 | 1.92205 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.88434e9 | −0.168538 | −0.0842692 | − | 0.996443i | \(-0.526856\pi\) | ||||
−0.0842692 | + | 0.996443i | \(0.526856\pi\) | |||||||
\(744\) | −5.93309e9 | − | 1.02764e10i | −0.528173 | − | 0.914822i | ||||
\(745\) | 1.64865e10 | − | 2.85554e10i | 1.46077 | − | 2.53012i | ||||
\(746\) | −5.44728e9 | + | 9.43497e9i | −0.480390 | + | 0.832060i | ||||
\(747\) | −3.43496e7 | − | 5.94953e7i | −0.00301509 | − | 0.00522228i | ||||
\(748\) | −3.83122e8 | −0.0334720 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.30645e10 | 1.13078 | ||||||||
\(751\) | 8.59707e9 | + | 1.48906e10i | 0.740646 | + | 1.28284i | 0.952202 | + | 0.305470i | \(0.0988137\pi\) |
−0.211556 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(752\) | 1.46815e9 | − | 2.54290e9i | 0.125894 | − | 0.218056i | ||||
\(753\) | −1.07146e10 | + | 1.85583e10i | −0.914522 | + | 1.58400i | ||||
\(754\) | 2.50751e9 | + | 4.34313e9i | 0.213031 | + | 0.368980i | ||||
\(755\) | −7.80814e9 | −0.660288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.02275e10 | −0.856909 | −0.428454 | − | 0.903563i | \(-0.640942\pi\) | ||||
−0.428454 | + | 0.903563i | \(0.640942\pi\) | |||||||
\(758\) | −6.07355e9 | − | 1.05197e10i | −0.506524 | − | 0.877325i | ||||
\(759\) | 1.27162e9 | − | 2.20250e9i | 0.105563 | − | 0.182840i | ||||
\(760\) | 4.18405e9 | − | 7.24698e9i | 0.345740 | − | 0.598838i | ||||
\(761\) | 1.46903e9 | + | 2.54444e9i | 0.120833 | + | 0.209289i | 0.920096 | − | 0.391692i | \(-0.128110\pi\) |
−0.799264 | + | 0.600981i | \(0.794777\pi\) | |||||||
\(762\) | −1.39817e10 | −1.14477 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.29873e9 | −0.105364 | ||||||||
\(765\) | −2.52649e9 | − | 4.37601e9i | −0.204034 | − | 0.353398i | ||||
\(766\) | −1.81646e9 | + | 3.14619e9i | −0.146024 | + | 0.252921i | ||||
\(767\) | 7.64921e9 | − | 1.32488e10i | 0.612115 | − | 1.06021i | ||||
\(768\) | −6.87866e8 | − | 1.19142e9i | −0.0547948 | − | 0.0949074i | ||||
\(769\) | 1.49710e10 | 1.18716 | 0.593579 | − | 0.804776i | \(-0.297714\pi\) | ||||
0.593579 | + | 0.804776i | \(0.297714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.85053e10 | −2.23993 | ||||||||
\(772\) | −7.23460e8 | − | 1.25307e9i | −0.0565918 | − | 0.0980199i | ||||
\(773\) | −7.66354e9 | + | 1.32736e10i | −0.596762 | + | 1.03362i | 0.396534 | + | 0.918020i | \(0.370213\pi\) |
−0.993296 | + | 0.115602i | \(0.963120\pi\) | |||||||
\(774\) | 6.61749e8 | − | 1.14618e9i | 0.0512979 | − | 0.0888506i | ||||
\(775\) | 1.73226e10 | + | 3.00037e10i | 1.33677 | + | 2.31536i | ||||
\(776\) | 6.91548e9 | 0.531259 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.46960e10 | 1.11884 | ||||||||
\(779\) | 2.56968e9 | + | 4.45082e9i | 0.194759 | + | 0.337333i | ||||
\(780\) | −8.36523e9 | + | 1.44890e10i | −0.631170 | + | 1.09322i | ||||
\(781\) | 1.28375e8 | − | 2.22353e8i | 0.00964279 | − | 0.0167018i | ||||
\(782\) | 1.28079e8 | + | 2.21839e8i | 0.00957753 | + | 0.0165888i | ||||
\(783\) | −1.69757e10 | −1.26375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.95263e9 | −0.734335 | ||||||||
\(786\) | −3.43656e9 | − | 5.95230e9i | −0.252433 | − | 0.437226i | ||||
\(787\) | −2.82231e8 | + | 4.88839e8i | −0.0206392 | + | 0.0357482i | −0.876161 | − | 0.482019i | \(-0.839903\pi\) |
0.855521 | + | 0.517768i | \(0.173237\pi\) | |||||||
\(788\) | 1.04697e9 | − | 1.81341e9i | 0.0762245 | − | 0.132025i | ||||
\(789\) | 7.23656e9 | + | 1.25341e10i | 0.524521 | + | 0.908497i | ||||
\(790\) | 1.22426e10 | 0.883442 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.59365e9 | −0.400089 | ||||||||
\(793\) | −1.09742e10 | − | 1.90078e10i | −0.781475 | − | 1.35355i | ||||
\(794\) | −4.94671e9 | + | 8.56795e9i | −0.350707 | + | 0.607443i | ||||
\(795\) | −1.04598e9 | + | 1.81170e9i | −0.0738312 | + | 0.127879i | ||||
\(796\) | 2.31831e9 | + | 4.01543e9i | 0.162921 | + | 0.282187i | ||||
\(797\) | −2.02786e10 | −1.41884 | −0.709421 | − | 0.704785i | \(-0.751044\pi\) | ||||
−0.709421 | + | 0.704785i | \(0.751044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.78213e9 | 0.123602 | ||||||||
\(800\) | 2.00833e9 | + | 3.47854e9i | 0.138682 | + | 0.240205i | ||||
\(801\) | 3.96556e8 | − | 6.86856e8i | 0.0272641 | − | 0.0472228i | ||||
\(802\) | 6.31791e9 | − | 1.09429e10i | 0.432477 | − | 0.749072i | ||||
\(803\) | 1.19067e9 | + | 2.06230e9i | 0.0811498 | + | 0.140556i | ||||
\(804\) | −1.59243e10 | −1.08060 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.60899e10 | −1.08238 | ||||||||
\(807\) | −1.67234e10 | − | 2.89659e10i | −1.12013 | − | 1.94012i | ||||
\(808\) | 4.80371e9 | − | 8.32026e9i | 0.320359 | − | 0.554878i | ||||
\(809\) | −1.60069e9 | + | 2.77249e9i | −0.106289 | + | 0.184098i | −0.914264 | − | 0.405119i | \(-0.867230\pi\) |
0.807975 | + | 0.589217i | \(0.200564\pi\) | |||||||
\(810\) | −1.05351e10 | − | 1.82474e10i | −0.696534 | − | 1.20643i | ||||
\(811\) | 2.22219e10 | 1.46288 | 0.731439 | − | 0.681907i | \(-0.238849\pi\) | ||||
0.731439 | + | 0.681907i | \(0.238849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.60447e10 | −1.69982 | ||||||||
\(814\) | −2.06639e9 | − | 3.57910e9i | −0.134285 | − | 0.232588i | ||||
\(815\) | 1.39730e10 | − | 2.42020e10i | 0.904146 | − | 1.56603i | ||||
\(816\) | 4.17489e8 | − | 7.23112e8i | 0.0268986 | − | 0.0465897i | ||||
\(817\) | 6.65140e8 | + | 1.15206e9i | 0.0426713 | + | 0.0739088i | ||||
\(818\) | −1.54046e10 | −0.984043 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.03914e9 | −0.255823 | ||||||||
\(821\) | −1.28655e9 | − | 2.22836e9i | −0.0811381 | − | 0.140535i | 0.822601 | − | 0.568619i | \(-0.192522\pi\) |
−0.903739 | + | 0.428084i | \(0.859189\pi\) | |||||||
\(822\) | 1.18730e10 | − | 2.05646e10i | 0.745604 | − | 1.29142i | ||||
\(823\) | 2.57745e9 | − | 4.46427e9i | 0.161172 | − | 0.279159i | −0.774117 | − | 0.633043i | \(-0.781806\pi\) |
0.935289 | + | 0.353884i | \(0.115139\pi\) | |||||||
\(824\) | 4.14925e9 | + | 7.18672e9i | 0.258360 | + | 0.447492i | ||||
\(825\) | 2.42040e10 | 1.50071 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.02079e10 | 1.24237 | 0.621185 | − | 0.783664i | \(-0.286651\pi\) | ||||
0.621185 | + | 0.783664i | \(0.286651\pi\) | |||||||
\(828\) | 1.86997e9 | + | 3.23888e9i | 0.114480 | + | 0.198285i | ||||
\(829\) | −1.13460e10 | + | 1.96519e10i | −0.691676 | + | 1.19802i | 0.279613 | + | 0.960113i | \(0.409794\pi\) |
−0.971289 | + | 0.237904i | \(0.923539\pi\) | |||||||
\(830\) | −2.71345e7 | + | 4.69983e7i | −0.00164721 | + | 0.00285304i | ||||
\(831\) | −1.20428e10 | − | 2.08587e10i | −0.727987 | − | 1.26091i | ||||
\(832\) | −1.86542e9 | −0.112291 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.46142e10 | −2.06620 | ||||||||
\(835\) | −7.41974e9 | − | 1.28514e10i | −0.441048 | − | 0.763918i | ||||
\(836\) | 2.81116e9 | − | 4.86907e9i | 0.166404 | − | 0.288220i | ||||
\(837\) | 2.72320e10 | − | 4.71672e10i | 1.60524 | − | 2.78036i | ||||
\(838\) | 9.59983e9 | + | 1.66274e10i | 0.563520 | + | 0.976045i | ||||
\(839\) | 1.18283e10 | 0.691444 | 0.345722 | − | 0.938337i | \(-0.387634\pi\) | ||||
0.345722 | + | 0.938337i | \(0.387634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.48932e9 | −0.550110 | ||||||||
\(842\) | 4.83760e9 | + | 8.37897e9i | 0.279279 | + | 0.483725i | ||||
\(843\) | 2.23461e9 | − | 3.87046e9i | 0.128471 | − | 0.222518i | ||||
\(844\) | −3.00162e9 | + | 5.19896e9i | −0.171853 | + | 0.297658i | ||||
\(845\) | −2.71288e9 | − | 4.69884e9i | −0.154679 | − | 0.267912i | ||||
\(846\) | 2.60194e10 | 1.47741 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.33251e8 | −0.0131352 | ||||||||
\(849\) | 8.42177e9 | + | 1.45869e10i | 0.472309 | + | 0.818064i | ||||
\(850\) | −1.21893e9 | + | 2.11124e9i | −0.0680787 | + | 0.117916i | ||||
\(851\) | −1.38160e9 | + | 2.39300e9i | −0.0768473 | + | 0.133103i | ||||
\(852\) | 2.79781e8 | + | 4.84596e8i | 0.0154982 | + | 0.0268436i | ||||
\(853\) | −1.17141e10 | −0.646230 | −0.323115 | − | 0.946360i | \(-0.604730\pi\) | ||||
−0.323115 | + | 0.946360i | \(0.604730\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.41524e10 | 4.05736 | ||||||||
\(856\) | 1.78324e9 | + | 3.08867e9i | 0.0971746 | + | 0.168311i | ||||
\(857\) | 8.39774e9 | − | 1.45453e10i | 0.455753 | − | 0.789387i | −0.542978 | − | 0.839747i | \(-0.682703\pi\) |
0.998731 | + | 0.0503595i | \(0.0160367\pi\) | |||||||
\(858\) | −5.62039e9 | + | 9.73480e9i | −0.303781 | + | 0.526164i | ||||
\(859\) | −9.31163e9 | − | 1.61282e10i | −0.501244 | − | 0.868181i | −0.999999 | − | 0.00143758i | \(-0.999542\pi\) |
0.498755 | − | 0.866743i | \(-0.333791\pi\) | |||||||
\(860\) | −1.04550e9 | −0.0560503 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.73028e10 | 0.920113 | ||||||||
\(863\) | 9.78413e9 | + | 1.69466e10i | 0.518184 | + | 0.897522i | 0.999777 | + | 0.0211264i | \(0.00672523\pi\) |
−0.481592 | + | 0.876395i | \(0.659941\pi\) | |||||||
\(864\) | 3.15720e9 | − | 5.46843e9i | 0.166534 | − | 0.288446i | ||||
\(865\) | 1.58099e10 | − | 2.73835e10i | 0.830563 | − | 1.43858i | ||||
\(866\) | −9.02999e9 | − | 1.56404e10i | −0.472470 | − | 0.818343i | ||||
\(867\) | −3.31410e10 | −1.72703 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.22548e9 | 0.425199 | ||||||||
\(870\) | 1.29449e10 | + | 2.24212e10i | 0.666470 | + | 1.15436i | ||||
\(871\) | −1.07963e10 | + | 1.86997e10i | −0.553618 | + | 0.958894i | ||||
\(872\) | −3.81540e9 | + | 6.60846e9i | −0.194864 | + | 0.337515i | ||||
\(873\) | 3.06402e10 | + | 5.30703e10i | 1.55862 | + | 2.69961i | ||||
\(874\) | −3.75911e9 | −0.190456 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.18990e9 | −0.260853 | ||||||||
\(877\) | 4.38040e9 | + | 7.58707e9i | 0.219288 | + | 0.379818i | 0.954591 | − | 0.297921i | \(-0.0962932\pi\) |
−0.735302 | + | 0.677739i | \(0.762960\pi\) | |||||||
\(878\) | 2.98290e9 | − | 5.16653e9i | 0.148733 | − | 0.257613i | ||||
\(879\) | −4.87435e9 | + | 8.44262e9i | −0.242078 | + | 0.419292i | ||||
\(880\) | 2.20935e9 | + | 3.82671e9i | 0.109289 | + | 0.189294i | ||||
\(881\) | −3.59103e10 | −1.76931 | −0.884653 | − | 0.466250i | \(-0.845605\pi\) | ||||
−0.884653 | + | 0.466250i | \(0.845605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.42420e10 | −1.67377 | −0.836887 | − | 0.547375i | \(-0.815627\pi\) | ||||
−0.836887 | + | 0.547375i | \(0.815627\pi\) | |||||||
\(884\) | −5.66092e8 | − | 9.80500e8i | −0.0275616 | − | 0.0477381i | ||||
\(885\) | 3.94887e10 | − | 6.83964e10i | 1.91501 | − | 3.31689i | ||||
\(886\) | −4.40861e9 | + | 7.63594e9i | −0.212953 | + | 0.368845i | ||||
\(887\) | 6.66497e9 | + | 1.15441e10i | 0.320675 | + | 0.555426i | 0.980628 | − | 0.195882i | \(-0.0627569\pi\) |
−0.659952 | + | 0.751307i | \(0.729424\pi\) | |||||||
\(888\) | 9.00700e9 | 0.431653 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.26519e8 | −0.0297899 | ||||||||
\(891\) | −7.07829e9 | − | 1.22600e10i | −0.335241 | − | 0.580654i | ||||
\(892\) | 5.20215e7 | − | 9.01039e7i | 0.00245418 | − | 0.00425076i | ||||
\(893\) | −1.30764e10 | + | 2.26490e10i | −0.614480 | + | 1.06431i | ||||
\(894\) | 2.41409e10 | + | 4.18133e10i | 1.12998 | + | 1.95719i | ||||
\(895\) | 5.42870e10 | 2.53113 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.51563e9 | 0.347690 | ||||||||
\(898\) | 1.36640e10 | + | 2.36667e10i | 0.629667 | + | 1.09061i | ||||
\(899\) | −1.24493e10 | + | 2.15628e10i | −0.571459 | + | 0.989796i | ||||
\(900\) | −1.77965e10 | + | 3.08245e10i | −0.813741 | + | 1.40944i | ||||
\(901\) | −7.07839e7 | − | 1.22601e8i | −0.00322402 | − | 0.00558416i | ||||
\(902\) | −2.71380e9 | −0.123127 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.33470e10 | 0.600891 | ||||||||
\(905\) | −5.16432e9 | − | 8.94487e9i | −0.231603 | − | 0.401147i | ||||
\(906\) | 5.71668e9 | − | 9.90157e9i | 0.255385 | − | 0.442339i | ||||
\(907\) | 1.97816e9 | − | 3.42627e9i | 0.0880310 | − | 0.152474i | −0.818648 | − | 0.574296i | \(-0.805276\pi\) |
0.906679 | + | 0.421822i | \(0.138609\pi\) | |||||||
\(908\) | −7.87688e9 | − | 1.36432e10i | −0.349184 | − | 0.604804i | ||||
\(909\) | 8.51344e10 | 3.75951 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.77864e10 | 0.779426 | 0.389713 | − | 0.920936i | \(-0.372574\pi\) | ||||
0.389713 | + | 0.920936i | \(0.372574\pi\) | |||||||
\(912\) | 6.12664e9 | + | 1.06117e10i | 0.267449 | + | 0.463235i | ||||
\(913\) | −1.82310e7 | + | 3.15770e7i | −0.000792797 | + | 0.00137316i | ||||
\(914\) | 1.70924e9 | − | 2.96049e9i | 0.0740442 | − | 0.128248i | ||||
\(915\) | −5.66535e10 | − | 9.81268e10i | −2.44485 | − | 4.23461i | ||||
\(916\) | 6.78661e9 | 0.291755 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.83242e9 | 0.163502 | ||||||||
\(919\) | −1.89653e10 | − | 3.28489e10i | −0.806040 | − | 1.39610i | −0.915587 | − | 0.402120i | \(-0.868274\pi\) |
0.109548 | − | 0.993982i | \(-0.465060\pi\) | |||||||
\(920\) | 1.47718e9 | − | 2.55855e9i | 0.0625427 | − | 0.108327i | ||||
\(921\) | 6.70684e9 | − | 1.16166e10i | 0.282884 | − | 0.489970i | ||||
\(922\) | −8.72465e9 | − | 1.51115e10i | −0.366598 | − | 0.634966i | ||||
\(923\) | 7.58736e8 | 0.0317603 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.62974e10 | −1.09249 | ||||||||
\(926\) | 7.52538e8 | + | 1.30343e9i | 0.0311451 | + | 0.0539449i | ||||
\(927\) | −3.67679e10 | + | 6.36839e10i | −1.51597 | + | 2.62573i | ||||
\(928\) | −1.44333e9 | + | 2.49992e9i | −0.0592855 | + | 0.102685i | ||||
\(929\) | 2.11707e10 | + | 3.66687e10i | 0.866323 | + | 1.50052i | 0.865728 | + | 0.500515i | \(0.166856\pi\) |
0.000595086 | 1.00000i | \(0.499811\pi\) | ||||||||
\(930\) | −8.30633e10 | −3.38625 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.29412e10 | −0.523623 | ||||||||
\(933\) | −1.77317e10 | − | 3.07122e10i | −0.714767 | − | 1.23801i | ||||
\(934\) | −3.41814e9 | + | 5.92038e9i | −0.137270 | + | 0.237758i | ||||
\(935\) | −1.34093e9 | + | 2.32256e9i | −0.0536494 | + | 0.0929235i | ||||
\(936\) | −8.26503e9 | − | 1.43155e10i | −0.329442 | − | 0.570611i | ||||
\(937\) | −1.65147e10 | −0.655817 | −0.327909 | − | 0.944709i | \(-0.606344\pi\) | ||||
−0.327909 | + | 0.944709i | \(0.606344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.50167e10 | 1.38021 | ||||||||
\(940\) | −1.02770e10 | − | 1.78003e10i | −0.403571 | − | 0.699005i | ||||
\(941\) | −1.57165e10 | + | 2.72217e10i | −0.614881 | + | 1.06501i | 0.375524 | + | 0.926813i | \(0.377463\pi\) |
−0.990405 | + | 0.138193i | \(0.955871\pi\) | |||||||
\(942\) | 7.28675e9 | − | 1.26210e10i | 0.284024 | − | 0.491945i | ||||
\(943\) | 9.07229e8 | + | 1.57137e9i | 0.0352311 | + | 0.0610220i | ||||
\(944\) | 8.80583e9 | 0.340697 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.02442e8 | −0.0269769 | ||||||||
\(947\) | 1.63557e10 | + | 2.83289e10i | 0.625813 | + | 1.08394i | 0.988383 | + | 0.151983i | \(0.0485659\pi\) |
−0.362571 | + | 0.931956i | \(0.618101\pi\) | |||||||
\(948\) | −8.96331e9 | + | 1.55249e10i | −0.341696 | + | 0.591834i | ||||
\(949\) | −3.51861e9 | + | 6.09442e9i | −0.133641 | + | 0.231473i | ||||
\(950\) | −1.78877e10 | − | 3.09824e10i | −0.676896 | − | 1.17242i | ||||
\(951\) | −2.84952e10 | −1.07433 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.62655e10 | −0.983017 | −0.491509 | − | 0.870873i | \(-0.663554\pi\) | ||||
−0.491509 | + | 0.870873i | \(0.663554\pi\) | |||||||
\(954\) | −1.03346e9 | − | 1.79000e9i | −0.0385365 | − | 0.0667472i | ||||
\(955\) | −4.54556e9 | + | 7.87315e9i | −0.168879 | + | 0.292507i | ||||
\(956\) | 1.17607e9 | − | 2.03702e9i | 0.0435344 | − | 0.0754037i | ||||
\(957\) | 8.69734e9 | + | 1.50642e10i | 0.320771 | + | 0.555591i | ||||
\(958\) | −5.46251e9 | −0.200730 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.63012e9 | −0.351303 | ||||||||
\(961\) | −2.61852e10 | − | 4.53542e10i | −0.951754 | − | 1.64849i | ||||
\(962\) | 6.10650e9 | − | 1.05768e10i | 0.221146 | − | 0.383036i | ||||
\(963\) | −1.58019e10 | + | 2.73697e10i | −0.570187 | + | 0.987593i | ||||
\(964\) | 1.84453e9 | + | 3.19482e9i | 0.0663156 | + | 0.114862i | ||||
\(965\) | −1.01284e10 | −0.362825 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.58253e10 | 0.918443 | 0.459222 | − | 0.888322i | \(-0.348128\pi\) | ||||
0.459222 | + | 0.888322i | \(0.348128\pi\) | |||||||
\(968\) | −3.50431e9 | − | 6.06964e9i | −0.124176 | − | 0.215080i | ||||
\(969\) | −3.71846e9 | + | 6.44057e9i | −0.131290 | + | 0.227400i | ||||
\(970\) | 2.42042e10 | − | 4.19228e10i | 0.851509 | − | 1.47486i | ||||
\(971\) | 1.12051e10 | + | 1.94078e10i | 0.392780 | + | 0.680315i | 0.992815 | − | 0.119659i | \(-0.0381801\pi\) |
−0.600035 | + | 0.799974i | \(0.704847\pi\) | |||||||
\(972\) | 3.88106e9 | 0.135556 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.32095e10 | −1.15161 | ||||||||
\(975\) | 3.57632e10 | + | 6.19436e10i | 1.23572 | + | 2.14033i | ||||
\(976\) | 6.31677e9 | − | 1.09410e10i | 0.217481 | − | 0.376688i | ||||
\(977\) | 1.77291e10 | − | 3.07077e10i | 0.608214 | − | 1.05346i | −0.383321 | − | 0.923615i | \(-0.625220\pi\) |
0.991535 | − | 0.129842i | \(-0.0414470\pi\) | |||||||
\(978\) | 2.04605e10 | + | 3.54386e10i | 0.699407 | + | 1.21141i | ||||
\(979\) | −4.20942e8 | −0.0143378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.76190e10 | −2.28679 | ||||||||
\(982\) | 3.59815e9 | + | 6.23218e9i | 0.121252 | + | 0.210015i | ||||
\(983\) | −7.28837e9 | + | 1.26238e10i | −0.244733 | + | 0.423890i | −0.962057 | − | 0.272850i | \(-0.912034\pi\) |
0.717323 | + | 0.696740i | \(0.245367\pi\) | |||||||
\(984\) | 2.95723e9 | − | 5.12207e9i | 0.0989468 | − | 0.171381i | ||||
\(985\) | −7.32882e9 | − | 1.26939e10i | −0.244347 | − | 0.423222i | ||||
\(986\) | −1.75201e9 | −0.0582061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.66148e10 | 0.548082 | ||||||||
\(989\) | 2.34828e8 | + | 4.06734e8i | 0.00771904 | + | 0.0133698i | ||||
\(990\) | −1.95778e10 | + | 3.39097e10i | −0.641269 | + | 1.11071i | ||||
\(991\) | −6.28564e9 | + | 1.08871e10i | −0.205160 | + | 0.355347i | −0.950184 | − | 0.311691i | \(-0.899105\pi\) |
0.745024 | + | 0.667038i | \(0.232438\pi\) | |||||||
\(992\) | −4.63071e9 | − | 8.02062e9i | −0.150611 | − | 0.260866i | ||||
\(993\) | −6.68639e10 | −2.16705 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.24564e10 | 1.04453 | ||||||||
\(996\) | −3.97326e7 | − | 6.88189e7i | −0.00127421 | − | 0.00220699i | ||||
\(997\) | −5.20184e9 | + | 9.00986e9i | −0.166236 | + | 0.287929i | −0.937093 | − | 0.349079i | \(-0.886495\pi\) |
0.770858 | + | 0.637007i | \(0.219828\pi\) | |||||||
\(998\) | −2.44444e9 | + | 4.23389e9i | −0.0778435 | + | 0.134829i | ||||
\(999\) | 2.06704e10 | + | 3.58021e10i | 0.655947 | + | 1.13613i |
(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 | 98.8.c.c.67.1 | 2 | ||
7.2 | even | 3 | inner | 98.8.c.c.79.1 | 2 | ||
7.3 | odd | 6 | 14.8.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 98.8.a.b.1.1 | 1 | |||
7.5 | odd | 6 | 98.8.c.f.79.1 | 2 | |||
7.6 | odd | 2 | 98.8.c.f.67.1 | 2 | |||
21.17 | even | 6 | 126.8.a.d.1.1 | 1 | |||
28.3 | even | 6 | 112.8.a.e.1.1 | 1 | |||
35.3 | even | 12 | 350.8.c.d.99.2 | 2 | |||
35.17 | even | 12 | 350.8.c.d.99.1 | 2 | |||
35.24 | odd | 6 | 350.8.a.h.1.1 | 1 | |||
56.3 | even | 6 | 448.8.a.a.1.1 | 1 | |||
56.45 | odd | 6 | 448.8.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
98.8.a.b.1.1 | 1 | 7.4 | even | 3 | |||
98.8.c.c.67.1 | 2 | 1.1 | even | 1 | trivial | ||
98.8.c.c.79.1 | 2 | 7.2 | even | 3 | inner | ||
98.8.c.f.67.1 | 2 | 7.6 | odd | 2 | |||
98.8.c.f.79.1 | 2 | 7.5 | odd | 6 | |||
112.8.a.e.1.1 | 1 | 28.3 | even | 6 | |||
126.8.a.d.1.1 | 1 | 21.17 | even | 6 | |||
350.8.a.h.1.1 | 1 | 35.24 | odd | 6 | |||
350.8.c.d.99.1 | 2 | 35.17 | even | 12 | |||
350.8.c.d.99.2 | 2 | 35.3 | even | 12 | |||
448.8.a.a.1.1 | 1 | 56.3 | even | 6 | |||
448.8.a.j.1.1 | 1 | 56.45 | odd | 6 |