Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.17 | ||
Character | \(\chi\) | \(=\) | 43.7 |
Dual form | 43.7.d.a.37.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.90547i | 1.23818i | 0.785319 | + | 0.619092i | \(0.212499\pi\) | ||||
−0.785319 | + | 0.619092i | \(0.787501\pi\) | |||||||
\(3\) | 12.0709 | − | 6.96915i | 0.447071 | − | 0.258117i | −0.259521 | − | 0.965737i | \(-0.583565\pi\) |
0.706593 | + | 0.707621i | \(0.250231\pi\) | |||||||
\(4\) | −34.1183 | −0.533098 | ||||||||
\(5\) | −41.4735 | + | 23.9447i | −0.331788 | + | 0.191558i | −0.656635 | − | 0.754209i | \(-0.728021\pi\) |
0.324847 | + | 0.945767i | \(0.394687\pi\) | |||||||
\(6\) | 69.0327 | + | 119.568i | 0.319596 | + | 0.553556i | ||||
\(7\) | −415.762 | − | 240.040i | −1.21213 | − | 0.699826i | −0.248910 | − | 0.968527i | \(-0.580072\pi\) |
−0.963224 | + | 0.268701i | \(0.913406\pi\) | |||||||
\(8\) | 295.992i | 0.578110i | ||||||||
\(9\) | −267.362 | + | 463.084i | −0.366751 | + | 0.635232i | ||||
\(10\) | −237.184 | − | 410.814i | −0.237184 | − | 0.410814i | ||||
\(11\) | −1050.18 | −0.789015 | −0.394508 | − | 0.918893i | \(-0.629085\pi\) | ||||
−0.394508 | + | 0.918893i | \(0.629085\pi\) | |||||||
\(12\) | −411.839 | + | 237.776i | −0.238333 | + | 0.137602i | ||||
\(13\) | −1567.47 | + | 2714.94i | −0.713459 | + | 1.23575i | 0.250092 | + | 0.968222i | \(0.419539\pi\) |
−0.963551 | + | 0.267525i | \(0.913794\pi\) | |||||||
\(14\) | 2377.71 | − | 4118.32i | 0.866513 | − | 1.50084i | ||||
\(15\) | −333.749 | + | 578.070i | −0.0988885 | + | 0.171280i | ||||
\(16\) | −5115.51 | −1.24890 | ||||||||
\(17\) | 1146.21 | − | 1985.29i | 0.233301 | − | 0.404090i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) |
0.958778 | + | 0.284157i | \(0.0917138\pi\) | |||||||
\(18\) | −4587.07 | − | 2648.34i | −0.786534 | − | 0.454106i | ||||
\(19\) | 10015.3 | − | 5782.31i | 1.46016 | − | 0.843025i | 0.461144 | − | 0.887325i | \(-0.347439\pi\) |
0.999018 | + | 0.0442998i | \(0.0141057\pi\) | |||||||
\(20\) | 1415.00 | − | 816.953i | 0.176875 | − | 0.102119i | ||||
\(21\) | −6691.51 | −0.722547 | ||||||||
\(22\) | − | 10402.5i | − | 0.976946i | ||||||
\(23\) | −8694.71 | − | 15059.7i | −0.714614 | − | 1.23775i | −0.963108 | − | 0.269115i | \(-0.913269\pi\) |
0.248494 | − | 0.968634i | \(-0.420065\pi\) | |||||||
\(24\) | 2062.82 | + | 3572.90i | 0.149220 | + | 0.258456i | ||||
\(25\) | −6665.80 | + | 11545.5i | −0.426611 | + | 0.738912i | ||||
\(26\) | −26892.7 | − | 15526.5i | −1.53008 | − | 0.883393i | ||||
\(27\) | 17614.2i | 0.894892i | ||||||||
\(28\) | 14185.1 | + | 8189.76i | 0.646186 | + | 0.373076i | ||||
\(29\) | 23889.4 | + | 13792.6i | 0.979517 | + | 0.565524i | 0.902124 | − | 0.431477i | \(-0.142007\pi\) |
0.0773924 | + | 0.997001i | \(0.475341\pi\) | |||||||
\(30\) | −5726.05 | − | 3305.94i | −0.212076 | − | 0.122442i | ||||
\(31\) | 23677.4 | + | 41010.4i | 0.794783 | + | 1.37660i | 0.922977 | + | 0.384855i | \(0.125749\pi\) |
−0.128194 | + | 0.991749i | \(0.540918\pi\) | |||||||
\(32\) | − | 31728.0i | − | 0.968263i | ||||||
\(33\) | −12676.6 | + | 7318.86i | −0.352746 | + | 0.203658i | ||||
\(34\) | 19665.3 | + | 11353.7i | 0.500337 | + | 0.288870i | ||||
\(35\) | 22990.8 | 0.536228 | ||||||||
\(36\) | 9121.93 | − | 15799.6i | 0.195515 | − | 0.338641i | ||||
\(37\) | −62039.1 | + | 35818.3i | −1.22479 | + | 0.707131i | −0.965935 | − | 0.258786i | \(-0.916678\pi\) |
−0.258852 | + | 0.965917i | \(0.583344\pi\) | |||||||
\(38\) | 57276.5 | + | 99205.8i | 1.04382 | + | 1.80795i | ||||
\(39\) | 43695.7i | 0.736623i | ||||||||
\(40\) | −7087.45 | − | 12275.8i | −0.110741 | − | 0.191810i | ||||
\(41\) | −23687.0 | −0.343683 | −0.171842 | − | 0.985125i | \(-0.554972\pi\) | ||||
−0.171842 | + | 0.985125i | \(0.554972\pi\) | |||||||
\(42\) | − | 66282.5i | − | 0.894646i | ||||||
\(43\) | −32889.9 | − | 72385.2i | −0.413673 | − | 0.910426i | ||||
\(44\) | 35830.3 | 0.420623 | ||||||||
\(45\) | − | 25607.6i | − | 0.281016i | ||||||
\(46\) | 149173. | − | 86125.2i | 1.53256 | − | 0.884824i | ||||
\(47\) | 154554. | 1.48863 | 0.744313 | − | 0.667831i | \(-0.232777\pi\) | ||||
0.744313 | + | 0.667831i | \(0.232777\pi\) | |||||||
\(48\) | −61749.0 | + | 35650.8i | −0.558349 | + | 0.322363i | ||||
\(49\) | 56414.1 | + | 97712.1i | 0.479512 | + | 0.830539i | ||||
\(50\) | −114364. | − | 66027.9i | −0.914909 | − | 0.528223i | ||||
\(51\) | − | 31952.4i | − | 0.240876i | ||||||
\(52\) | 53479.4 | − | 92629.0i | 0.380344 | − | 0.658775i | ||||
\(53\) | 50382.4 | + | 87264.9i | 0.338416 | + | 0.586154i | 0.984135 | − | 0.177421i | \(-0.0567754\pi\) |
−0.645719 | + | 0.763575i | \(0.723442\pi\) | |||||||
\(54\) | −174477. | −1.10804 | ||||||||
\(55\) | 43554.6 | − | 25146.2i | 0.261786 | − | 0.151142i | ||||
\(56\) | 71050.1 | − | 123062.i | 0.404576 | − | 0.700747i | ||||
\(57\) | 80595.6 | − | 139596.i | 0.435198 | − | 0.753785i | ||||
\(58\) | −136622. | + | 236636.i | −0.700223 | + | 1.21282i | ||||
\(59\) | −380692. | −1.85361 | −0.926803 | − | 0.375548i | \(-0.877455\pi\) | ||||
−0.926803 | + | 0.375548i | \(0.877455\pi\) | |||||||
\(60\) | 11386.9 | − | 19722.8i | 0.0527173 | − | 0.0913090i | ||||
\(61\) | 211205. | + | 121939.i | 0.930498 | + | 0.537223i | 0.886969 | − | 0.461829i | \(-0.152807\pi\) |
0.0435288 | + | 0.999052i | \(0.486140\pi\) | |||||||
\(62\) | −406227. | + | 234536.i | −1.70449 | + | 0.984087i | ||||
\(63\) | 222318. | − | 128355.i | 0.889104 | − | 0.513324i | ||||
\(64\) | −13111.8 | −0.0500177 | ||||||||
\(65\) | − | 150130.i | − | 0.546674i | ||||||
\(66\) | −72496.7 | − | 125568.i | −0.252166 | − | 0.436764i | ||||
\(67\) | 128636. | + | 222804.i | 0.427698 | + | 0.740795i | 0.996668 | − | 0.0815630i | \(-0.0259912\pi\) |
−0.568970 | + | 0.822358i | \(0.692658\pi\) | |||||||
\(68\) | −39106.7 | + | 67734.8i | −0.124373 | + | 0.215419i | ||||
\(69\) | −209907. | − | 121190.i | −0.638967 | − | 0.368908i | ||||
\(70\) | 227734.i | 0.663949i | ||||||||
\(71\) | −240547. | − | 138880.i | −0.672085 | − | 0.388028i | 0.124781 | − | 0.992184i | \(-0.460177\pi\) |
−0.796866 | + | 0.604156i | \(0.793510\pi\) | |||||||
\(72\) | −137069. | − | 79137.1i | −0.367234 | − | 0.212023i | ||||
\(73\) | 82166.8 | + | 47439.0i | 0.211217 | + | 0.121946i | 0.601877 | − | 0.798589i | \(-0.294420\pi\) |
−0.390660 | + | 0.920535i | \(0.627753\pi\) | |||||||
\(74\) | −354797. | − | 614527.i | −0.875558 | − | 1.51651i | ||||
\(75\) | 185820.i | 0.440462i | ||||||||
\(76\) | −341703. | + | 197282.i | −0.778410 | + | 0.449415i | ||||
\(77\) | 436624. | + | 252085.i | 0.956392 | + | 0.552173i | ||||
\(78\) | −432827. | −0.912074 | ||||||||
\(79\) | −80984.1 | + | 140269.i | −0.164255 | + | 0.284498i | −0.936390 | − | 0.350960i | \(-0.885855\pi\) |
0.772135 | + | 0.635458i | \(0.219189\pi\) | |||||||
\(80\) | 212158. | − | 122490.i | 0.414371 | − | 0.239237i | ||||
\(81\) | −72150.9 | − | 124969.i | −0.135765 | − | 0.235151i | ||||
\(82\) | − | 234631.i | − | 0.425543i | ||||||
\(83\) | −98071.2 | − | 169864.i | −0.171517 | − | 0.297076i | 0.767433 | − | 0.641129i | \(-0.221533\pi\) |
−0.938950 | + | 0.344053i | \(0.888200\pi\) | |||||||
\(84\) | 228303. | 0.385188 | ||||||||
\(85\) | 109783.i | 0.178763i | ||||||||
\(86\) | 717009. | − | 325790.i | 1.12727 | − | 0.512203i | ||||
\(87\) | 384490. | 0.583885 | ||||||||
\(88\) | − | 310845.i | − | 0.456138i | ||||||
\(89\) | 227218. | − | 131184.i | 0.322309 | − | 0.186085i | −0.330112 | − | 0.943942i | \(-0.607087\pi\) |
0.652422 | + | 0.757856i | \(0.273753\pi\) | |||||||
\(90\) | 253655. | 0.347950 | ||||||||
\(91\) | 1.30339e6 | − | 752512.i | 1.72962 | − | 0.998594i | ||||
\(92\) | 296649. | + | 513811.i | 0.380960 | + | 0.659841i | ||||
\(93\) | 571616. | + | 330023.i | 0.710649 | + | 0.410294i | ||||
\(94\) | 1.53092e6i | 1.84319i | ||||||||
\(95\) | −276912. | + | 479625.i | −0.322976 | + | 0.559411i | ||||
\(96\) | −221118. | − | 382987.i | −0.249925 | − | 0.432883i | ||||
\(97\) | 27971.4 | 0.0306478 | 0.0153239 | − | 0.999883i | \(-0.495122\pi\) | ||||
0.0153239 | + | 0.999883i | \(0.495122\pi\) | |||||||
\(98\) | −967884. | + | 558808.i | −1.02836 | + | 0.593724i | ||||
\(99\) | 280778. | − | 486321.i | 0.289372 | − | 0.501208i | ||||
\(100\) | 227426. | − | 393913.i | 0.227426 | − | 0.393913i | ||||
\(101\) | −1393.95 | + | 2414.38i | −0.00135295 | + | 0.00234338i | −0.866701 | − | 0.498828i | \(-0.833764\pi\) |
0.865348 | + | 0.501171i | \(0.167097\pi\) | |||||||
\(102\) | 316504. | 0.298249 | ||||||||
\(103\) | 366787. | − | 635294.i | 0.335662 | − | 0.581384i | −0.647950 | − | 0.761683i | \(-0.724373\pi\) |
0.983612 | + | 0.180299i | \(0.0577066\pi\) | |||||||
\(104\) | −803601. | − | 463959.i | −0.714398 | − | 0.412458i | ||||
\(105\) | 277520. | − | 160226.i | 0.239732 | − | 0.138409i | ||||
\(106\) | −864400. | + | 499061.i | −0.725767 | + | 0.419022i | ||||
\(107\) | −1.98925e6 | −1.62382 | −0.811911 | − | 0.583781i | \(-0.801573\pi\) | ||||
−0.811911 | + | 0.583781i | \(0.801573\pi\) | |||||||
\(108\) | − | 600965.i | − | 0.477065i | ||||||
\(109\) | 1.11975e6 | + | 1.93947e6i | 0.864656 | + | 1.49763i | 0.867388 | + | 0.497632i | \(0.165797\pi\) |
−0.00273211 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(110\) | 249085. | + | 431428.i | 0.187141 | + | 0.324139i | ||||
\(111\) | −499247. | + | 864720.i | −0.365045 | + | 0.632276i | ||||
\(112\) | 2.12684e6 | + | 1.22793e6i | 1.51384 | + | 0.874015i | ||||
\(113\) | 850675.i | 0.589561i | 0.955565 | + | 0.294780i | \(0.0952465\pi\) | ||||
−0.955565 | + | 0.294780i | \(0.904754\pi\) | |||||||
\(114\) | 1.38276e6 | + | 798337.i | 0.933324 | + | 0.538855i | ||||
\(115\) | 721200. | + | 416385.i | 0.474201 | + | 0.273780i | ||||
\(116\) | −815066. | − | 470579.i | −0.522178 | − | 0.301480i | ||||
\(117\) | −838163. | − | 1.45174e6i | −0.523324 | − | 0.906424i | ||||
\(118\) | − | 3.77093e6i | − | 2.29510i | ||||||
\(119\) | −953100. | + | 550273.i | −0.565585 | + | 0.326541i | ||||
\(120\) | −171104. | − | 98787.1i | −0.0990187 | − | 0.0571685i | ||||
\(121\) | −668685. | −0.377455 | ||||||||
\(122\) | −1.20787e6 | + | 2.09209e6i | −0.665181 | + | 1.15213i | ||||
\(123\) | −285924. | + | 165078.i | −0.153651 | + | 0.0887103i | ||||
\(124\) | −807832. | − | 1.39921e6i | −0.423697 | − | 0.733865i | ||||
\(125\) | − | 1.38672e6i | − | 0.709998i | ||||||
\(126\) | 1.27142e6 | + | 2.20216e6i | 0.635590 | + | 1.10087i | ||||
\(127\) | 896333. | 0.437581 | 0.218790 | − | 0.975772i | \(-0.429789\pi\) | ||||
0.218790 | + | 0.975772i | \(0.429789\pi\) | |||||||
\(128\) | − | 2.16047e6i | − | 1.03019i | ||||||
\(129\) | −901475. | − | 644542.i | −0.419937 | − | 0.300249i | ||||
\(130\) | 1.48711e6 | 0.676883 | ||||||||
\(131\) | 3.26478e6i | 1.45225i | 0.687564 | + | 0.726124i | \(0.258680\pi\) | ||||
−0.687564 | + | 0.726124i | \(0.741320\pi\) | |||||||
\(132\) | 432505. | − | 249707.i | 0.188048 | − | 0.108570i | ||||
\(133\) | −5.55195e6 | −2.35988 | ||||||||
\(134\) | −2.20698e6 | + | 1.27420e6i | −0.917241 | + | 0.529569i | ||||
\(135\) | −421766. | − | 730521.i | −0.171424 | − | 0.296914i | ||||
\(136\) | 587632. | + | 339269.i | 0.233608 | + | 0.134874i | ||||
\(137\) | − | 2.03174e6i | − | 0.790145i | −0.918650 | − | 0.395073i | \(-0.870719\pi\) | ||
0.918650 | − | 0.395073i | \(-0.129281\pi\) | |||||||
\(138\) | 1.20044e6 | − | 2.07922e6i | 0.456776 | − | 0.791159i | ||||
\(139\) | −775516. | − | 1.34323e6i | −0.288766 | − | 0.500158i | 0.684749 | − | 0.728779i | \(-0.259912\pi\) |
−0.973516 | + | 0.228621i | \(0.926578\pi\) | |||||||
\(140\) | −784406. | −0.285862 | ||||||||
\(141\) | 1.86560e6 | − | 1.07711e6i | 0.665522 | − | 0.384239i | ||||
\(142\) | 1.37567e6 | − | 2.38273e6i | 0.480450 | − | 0.832165i | ||||
\(143\) | 1.64612e6 | − | 2.85117e6i | 0.562930 | − | 0.975024i | ||||
\(144\) | 1.36769e6 | − | 2.36891e6i | 0.458038 | − | 0.793344i | ||||
\(145\) | −1.32104e6 | −0.433322 | ||||||||
\(146\) | −469906. | + | 813901.i | −0.150991 | + | 0.261525i | ||||
\(147\) | 1.36194e6 | + | 786317.i | 0.428752 | + | 0.247540i | ||||
\(148\) | 2.11667e6 | − | 1.22206e6i | 0.652932 | − | 0.376970i | ||||
\(149\) | −1.44824e6 | + | 836141.i | −0.437806 | + | 0.252767i | −0.702666 | − | 0.711519i | \(-0.748007\pi\) |
0.264861 | + | 0.964287i | \(0.414674\pi\) | |||||||
\(150\) | −1.84063e6 | −0.545373 | ||||||||
\(151\) | − | 1.01384e6i | − | 0.294469i | −0.989102 | − | 0.147235i | \(-0.952963\pi\) | ||
0.989102 | − | 0.147235i | \(-0.0470372\pi\) | |||||||
\(152\) | 1.71152e6 | + | 2.96444e6i | 0.487361 | + | 0.844135i | ||||
\(153\) | 612905. | + | 1.06158e6i | 0.171127 | + | 0.296401i | ||||
\(154\) | −2.49702e6 | + | 4.32497e6i | −0.683692 | + | 1.18419i | ||||
\(155\) | −1.96397e6 | − | 1.13390e6i | −0.527399 | − | 0.304494i | ||||
\(156\) | − | 1.49082e6i | − | 0.392692i | ||||||
\(157\) | −3.83385e6 | − | 2.21347e6i | −0.990686 | − | 0.571973i | −0.0852066 | − | 0.996363i | \(-0.527155\pi\) |
−0.905479 | + | 0.424391i | \(0.860488\pi\) | |||||||
\(158\) | −1.38943e6 | − | 802186.i | −0.352261 | − | 0.203378i | ||||
\(159\) | 1.21633e6 | + | 702246.i | 0.302593 | + | 0.174702i | ||||
\(160\) | 759719. | + | 1.31587e6i | 0.185478 | + | 0.321258i | ||||
\(161\) | 8.34832e6i | 2.00042i | ||||||||
\(162\) | 1.23788e6 | − | 714689.i | 0.291161 | − | 0.168102i | ||||
\(163\) | 2.10774e6 | + | 1.21690e6i | 0.486692 | + | 0.280992i | 0.723201 | − | 0.690637i | \(-0.242670\pi\) |
−0.236509 | + | 0.971629i | \(0.576003\pi\) | |||||||
\(164\) | 808159. | 0.183217 | ||||||||
\(165\) | 350496. | − | 607077.i | 0.0780246 | − | 0.135143i | ||||
\(166\) | 1.68258e6 | − | 971441.i | 0.367835 | − | 0.212369i | ||||
\(167\) | 1.62068e6 | + | 2.80710e6i | 0.347974 | + | 0.602709i | 0.985890 | − | 0.167397i | \(-0.0535363\pi\) |
−0.637915 | + | 0.770107i | \(0.720203\pi\) | |||||||
\(168\) | − | 1.98064e6i | − | 0.417712i | ||||||
\(169\) | −2.50052e6 | − | 4.33102e6i | −0.518048 | − | 0.897285i | ||||
\(170\) | −1.08745e6 | −0.221341 | ||||||||
\(171\) | 6.18388e6i | 1.23672i | ||||||||
\(172\) | 1.12215e6 | + | 2.46966e6i | 0.220528 | + | 0.485346i | ||||
\(173\) | −2.68694e6 | −0.518943 | −0.259471 | − | 0.965751i | \(-0.583548\pi\) | ||||
−0.259471 | + | 0.965751i | \(0.583548\pi\) | |||||||
\(174\) | 3.80855e6i | 0.722957i | ||||||||
\(175\) | 5.54277e6 | − | 3.20012e6i | 1.03422 | − | 0.597107i | ||||
\(176\) | 5.37221e6 | 0.985405 | ||||||||
\(177\) | −4.59530e6 | + | 2.65310e6i | −0.828694 | + | 0.478447i | ||||
\(178\) | 1.29944e6 | + | 2.25070e6i | 0.230408 | + | 0.399078i | ||||
\(179\) | −5.62591e6 | − | 3.24812e6i | −0.980921 | − | 0.566335i | −0.0783728 | − | 0.996924i | \(-0.524972\pi\) |
−0.902548 | + | 0.430589i | \(0.858306\pi\) | |||||||
\(180\) | 873688.i | 0.149809i | ||||||||
\(181\) | 2.25816e6 | − | 3.91124e6i | 0.380819 | − | 0.659598i | −0.610361 | − | 0.792124i | \(-0.708975\pi\) |
0.991180 | + | 0.132526i | \(0.0423088\pi\) | |||||||
\(182\) | 7.45398e6 | + | 1.29107e7i | 1.23644 | + | 2.14158i | ||||
\(183\) | 3.39926e6 | 0.554665 | ||||||||
\(184\) | 4.45755e6 | − | 2.57357e6i | 0.715555 | − | 0.413126i | ||||
\(185\) | 1.71532e6 | − | 2.97102e6i | 0.270913 | − | 0.469235i | ||||
\(186\) | −3.26903e6 | + | 5.66212e6i | −0.508019 | + | 0.879914i | ||||
\(187\) | −1.20373e6 | + | 2.08491e6i | −0.184078 | + | 0.318833i | ||||
\(188\) | −5.27310e6 | −0.793583 | ||||||||
\(189\) | 4.22811e6 | − | 7.32330e6i | 0.626269 | − | 1.08473i | ||||
\(190\) | −4.75091e6 | − | 2.74294e6i | −0.692653 | − | 0.399904i | ||||
\(191\) | 6.24064e6 | − | 3.60304e6i | 0.895631 | − | 0.517093i | 0.0198511 | − | 0.999803i | \(-0.493681\pi\) |
0.875780 | + | 0.482710i | \(0.160347\pi\) | |||||||
\(192\) | −158272. | + | 91378.4i | −0.0223615 | + | 0.0129104i | ||||
\(193\) | −2.46565e6 | −0.342972 | −0.171486 | − | 0.985187i | \(-0.554857\pi\) | ||||
−0.171486 | + | 0.985187i | \(0.554857\pi\) | |||||||
\(194\) | 277070.i | 0.0379476i | ||||||||
\(195\) | −1.04628e6 | − | 1.81221e6i | −0.141106 | − | 0.244403i | ||||
\(196\) | −1.92475e6 | − | 3.33377e6i | −0.255627 | − | 0.442759i | ||||
\(197\) | 3.72684e6 | − | 6.45508e6i | 0.487464 | − | 0.844313i | −0.512432 | − | 0.858728i | \(-0.671255\pi\) |
0.999896 | + | 0.0144152i | \(0.00458866\pi\) | |||||||
\(198\) | 4.81724e6 | + | 2.78124e6i | 0.620587 | + | 0.358296i | ||||
\(199\) | 1.13404e7i | 1.43902i | 0.694481 | + | 0.719511i | \(0.255634\pi\) | ||||
−0.694481 | + | 0.719511i | \(0.744366\pi\) | |||||||
\(200\) | −3.41738e6 | − | 1.97303e6i | −0.427173 | − | 0.246628i | ||||
\(201\) | 3.10551e6 | + | 1.79297e6i | 0.382423 | + | 0.220792i | ||||
\(202\) | −23915.6 | − | 13807.7i | −0.00290153 | − | 0.00167520i | ||||
\(203\) | −6.62154e6 | − | 1.14688e7i | −0.791537 | − | 1.37098i | ||||
\(204\) | 1.09016e6i | 0.128411i | ||||||||
\(205\) | 982381. | − | 567178.i | 0.114030 | − | 0.0658351i | ||||
\(206\) | 6.29288e6 | + | 3.63320e6i | 0.719860 | + | 0.415611i | ||||
\(207\) | 9.29854e6 | 1.04834 | ||||||||
\(208\) | 8.01841e6 | − | 1.38883e7i | 0.891042 | − | 1.54333i | ||||
\(209\) | −1.05178e7 | + | 6.07246e6i | −1.15209 | + | 0.665160i | ||||
\(210\) | 1.58712e6 | + | 2.74897e6i | 0.171376 | + | 0.296832i | ||||
\(211\) | 6.14692e6i | 0.654351i | 0.944964 | + | 0.327175i | \(0.106097\pi\) | ||||
−0.944964 | + | 0.327175i | \(0.893903\pi\) | |||||||
\(212\) | −1.71896e6 | − | 2.97733e6i | −0.180409 | − | 0.312478i | ||||
\(213\) | −3.87149e6 | −0.400627 | ||||||||
\(214\) | − | 1.97045e7i | − | 2.01059i | ||||||
\(215\) | 3.09730e6 | + | 2.21453e6i | 0.311651 | + | 0.222826i | ||||
\(216\) | −5.21366e6 | −0.517346 | ||||||||
\(217\) | − | 2.27341e7i | − | 2.22484i | ||||||
\(218\) | −1.92114e7 | + | 1.10917e7i | −1.85434 | + | 1.07060i | ||||
\(219\) | 1.32244e6 | 0.125905 | ||||||||
\(220\) | −1.48601e6 | + | 857947.i | −0.139557 | + | 0.0805735i | ||||
\(221\) | 3.59330e6 | + | 6.22377e6i | 0.332902 | + | 0.576603i | ||||
\(222\) | −8.56546e6 | − | 4.94527e6i | −0.782874 | − | 0.451992i | ||||
\(223\) | 205341.i | 0.0185166i | 0.999957 | + | 0.00925830i | \(0.00294705\pi\) | ||||
−0.999957 | + | 0.00925830i | \(0.997053\pi\) | |||||||
\(224\) | −7.61600e6 | + | 1.31913e7i | −0.677615 | + | 1.17366i | ||||
\(225\) | −3.56436e6 | − | 6.17365e6i | −0.312921 | − | 0.541994i | ||||
\(226\) | −8.42634e6 | −0.729984 | ||||||||
\(227\) | −3.98116e6 | + | 2.29852e6i | −0.340355 | + | 0.196504i | −0.660429 | − | 0.750888i | \(-0.729626\pi\) |
0.320074 | + | 0.947393i | \(0.396292\pi\) | |||||||
\(228\) | −2.74978e6 | + | 4.76277e6i | −0.232003 | + | 0.401841i | ||||
\(229\) | −3.36236e6 | + | 5.82378e6i | −0.279987 | + | 0.484951i | −0.971381 | − | 0.237526i | \(-0.923663\pi\) |
0.691394 | + | 0.722478i | \(0.256997\pi\) | |||||||
\(230\) | −4.12449e6 | + | 7.14382e6i | −0.338990 | + | 0.587147i | ||||
\(231\) | 7.02728e6 | 0.570101 | ||||||||
\(232\) | −4.08250e6 | + | 7.07109e6i | −0.326935 | + | 0.566268i | ||||
\(233\) | −8.02588e6 | − | 4.63375e6i | −0.634491 | − | 0.366323i | 0.147999 | − | 0.988988i | \(-0.452717\pi\) |
−0.782489 | + | 0.622664i | \(0.786050\pi\) | |||||||
\(234\) | 1.43802e7 | − | 8.30240e6i | 1.12232 | − | 0.647972i | ||||
\(235\) | −6.40987e6 | + | 3.70074e6i | −0.493908 | + | 0.285158i | ||||
\(236\) | 1.29885e7 | 0.988154 | ||||||||
\(237\) | 2.25756e6i | 0.169588i | ||||||||
\(238\) | −5.45071e6 | − | 9.44090e6i | −0.404317 | − | 0.700298i | ||||
\(239\) | 6.59956e6 | + | 1.14308e7i | 0.483416 | + | 0.837302i | 0.999819 | − | 0.0190443i | \(-0.00606237\pi\) |
−0.516402 | + | 0.856346i | \(0.672729\pi\) | |||||||
\(240\) | 1.70730e6 | − | 2.95712e6i | 0.123502 | − | 0.213912i | ||||
\(241\) | 6.72733e6 | + | 3.88402e6i | 0.480608 | + | 0.277479i | 0.720670 | − | 0.693278i | \(-0.243834\pi\) |
−0.240062 | + | 0.970758i | \(0.577168\pi\) | |||||||
\(242\) | − | 6.62363e6i | − | 0.467359i | ||||||
\(243\) | −1.28623e7 | − | 7.42603e6i | −0.896393 | − | 0.517532i | ||||
\(244\) | −7.20596e6 | − | 4.16036e6i | −0.496047 | − | 0.286393i | ||||
\(245\) | −4.67938e6 | − | 2.70164e6i | −0.318192 | − | 0.183709i | ||||
\(246\) | −1.63518e6 | − | 2.83221e6i | −0.109840 | − | 0.190248i | ||||
\(247\) | 3.62544e7i | 2.40586i | ||||||||
\(248\) | −1.21388e7 | + | 7.00832e6i | −0.795829 | + | 0.459472i | ||||
\(249\) | −2.36762e6 | − | 1.36695e6i | −0.153361 | − | 0.0885428i | ||||
\(250\) | 1.37361e7 | 0.879108 | ||||||||
\(251\) | 1.06293e7 | − | 1.84104e7i | 0.672175 | − | 1.16424i | −0.305112 | − | 0.952317i | \(-0.598694\pi\) |
0.977286 | − | 0.211924i | \(-0.0679729\pi\) | |||||||
\(252\) | −7.58510e6 | + | 4.37926e6i | −0.473979 | + | 0.273652i | ||||
\(253\) | 9.13101e6 | + | 1.58154e7i | 0.563842 | + | 0.976602i | ||||
\(254\) | 8.87859e6i | 0.541805i | ||||||||
\(255\) | 765092. | + | 1.32518e6i | 0.0461417 | + | 0.0799197i | ||||
\(256\) | 2.05613e7 | 1.22555 | ||||||||
\(257\) | 1.11532e6i | 0.0657050i | 0.999460 | + | 0.0328525i | \(0.0104592\pi\) | ||||
−0.999460 | + | 0.0328525i | \(0.989541\pi\) | |||||||
\(258\) | 6.38449e6 | − | 8.92953e6i | 0.371764 | − | 0.519960i | ||||
\(259\) | 3.43913e7 | 1.97947 | ||||||||
\(260\) | 5.12219e6i | 0.291431i | ||||||||
\(261\) | −1.27742e7 | + | 7.37521e6i | −0.718478 | + | 0.414814i | ||||
\(262\) | −3.23392e7 | −1.79815 | ||||||||
\(263\) | −4.73899e6 | + | 2.73606e6i | −0.260506 | + | 0.150403i | −0.624566 | − | 0.780972i | \(-0.714724\pi\) |
0.364059 | + | 0.931376i | \(0.381391\pi\) | |||||||
\(264\) | −2.16633e6 | − | 3.75219e6i | −0.117737 | − | 0.203926i | ||||
\(265\) | −4.17907e6 | − | 2.41279e6i | −0.224565 | − | 0.129653i | ||||
\(266\) | − | 5.49946e7i | − | 2.92197i | ||||||
\(267\) | 1.82849e6 | − | 3.16704e6i | 0.0960636 | − | 0.166387i | ||||
\(268\) | −4.38883e6 | − | 7.60168e6i | −0.228005 | − | 0.394917i | ||||
\(269\) | 1.26283e7 | 0.648768 | 0.324384 | − | 0.945925i | \(-0.394843\pi\) | ||||
0.324384 | + | 0.945925i | \(0.394843\pi\) | |||||||
\(270\) | 7.23615e6 | − | 4.17779e6i | 0.367634 | − | 0.212254i | ||||
\(271\) | 9.98905e6 | − | 1.73015e7i | 0.501899 | − | 0.869314i | −0.498099 | − | 0.867120i | \(-0.665968\pi\) |
0.999998 | − | 0.00219398i | \(-0.000698366\pi\) | |||||||
\(272\) | −5.86345e6 | + | 1.01558e7i | −0.291371 | + | 0.504670i | ||||
\(273\) | 1.04887e7 | − | 1.81670e7i | 0.515508 | − | 0.892886i | ||||
\(274\) | 2.01254e7 | 0.978345 | ||||||||
\(275\) | 7.00029e6 | − | 1.21249e7i | 0.336603 | − | 0.583013i | ||||
\(276\) | 7.16165e6 | + | 4.13478e6i | 0.340632 | + | 0.196664i | ||||
\(277\) | −7.64152e6 | + | 4.41183e6i | −0.359534 | + | 0.207577i | −0.668877 | − | 0.743374i | \(-0.733225\pi\) |
0.309342 | + | 0.950951i | \(0.399891\pi\) | |||||||
\(278\) | 1.33054e7 | − | 7.68185e6i | 0.619287 | − | 0.357546i | ||||
\(279\) | −2.53217e7 | −1.16595 | ||||||||
\(280\) | 6.80510e6i | 0.309999i | ||||||||
\(281\) | 931596. | + | 1.61357e6i | 0.0419864 | + | 0.0727226i | 0.886255 | − | 0.463198i | \(-0.153298\pi\) |
−0.844269 | + | 0.535920i | \(0.819965\pi\) | |||||||
\(282\) | 1.06692e7 | + | 1.84797e7i | 0.475758 | + | 0.824038i | ||||
\(283\) | −1.69284e7 | + | 2.93208e7i | −0.746889 | + | 1.29365i | 0.202417 | + | 0.979299i | \(0.435120\pi\) |
−0.949307 | + | 0.314351i | \(0.898213\pi\) | |||||||
\(284\) | 8.20704e6 | + | 4.73834e6i | 0.358287 | + | 0.206857i | ||||
\(285\) | 7.71936e6i | 0.333462i | ||||||||
\(286\) | 2.82422e7 | + | 1.63056e7i | 1.20726 | + | 0.697011i | ||||
\(287\) | 9.84814e6 | + | 5.68583e6i | 0.416590 | + | 0.240518i | ||||
\(288\) | 1.46928e7 | + | 8.48286e6i | 0.615072 | + | 0.355112i | ||||
\(289\) | 9.44119e6 | + | 1.63526e7i | 0.391141 | + | 0.677476i | ||||
\(290\) | − | 1.30855e7i | − | 0.536532i | ||||||
\(291\) | 337641. | − | 194937.i | 0.0137018 | − | 0.00791071i | ||||
\(292\) | −2.80339e6 | − | 1.61854e6i | −0.112599 | − | 0.0650091i | ||||
\(293\) | −3.00894e7 | −1.19622 | −0.598109 | − | 0.801415i | \(-0.704081\pi\) | ||||
−0.598109 | + | 0.801415i | \(0.704081\pi\) | |||||||
\(294\) | −7.78884e6 | + | 1.34907e7i | −0.306500 | + | 0.530874i | ||||
\(295\) | 1.57886e7 | − | 9.11556e6i | 0.615004 | − | 0.355073i | ||||
\(296\) | −1.06019e7 | − | 1.83631e7i | −0.408800 | − | 0.708062i | ||||
\(297\) | − | 1.84980e7i | − | 0.706084i | ||||||
\(298\) | −8.28237e6 | − | 1.43455e7i | −0.312972 | − | 0.542084i | ||||
\(299\) | 5.45148e7 | 2.03939 | ||||||||
\(300\) | − | 6.33986e6i | − | 0.234810i | ||||||
\(301\) | −3.70100e6 | + | 3.79899e7i | −0.135712 | + | 1.39306i | ||||
\(302\) | 1.00426e7 | 0.364607 | ||||||||
\(303\) | 38858.5i | 0.00139688i | ||||||||
\(304\) | −5.12332e7 | + | 2.95795e7i | −1.82360 | + | 1.05286i | ||||
\(305\) | −1.16792e7 | −0.411637 | ||||||||
\(306\) | −1.05155e7 | + | 6.07111e6i | −0.366999 | + | 0.211887i | ||||
\(307\) | 1.42466e7 | + | 2.46758e7i | 0.492375 | + | 0.852818i | 0.999961 | − | 0.00878267i | \(-0.00279565\pi\) |
−0.507587 | + | 0.861601i | \(0.669462\pi\) | |||||||
\(308\) | −1.48969e7 | − | 8.60072e6i | −0.509851 | − | 0.294362i | ||||
\(309\) | − | 1.02248e7i | − | 0.346560i | ||||||
\(310\) | 1.12318e7 | − | 1.94540e7i | 0.377019 | − | 0.653016i | ||||
\(311\) | 2.94316e7 | + | 5.09770e7i | 0.978436 | + | 1.69470i | 0.668094 | + | 0.744076i | \(0.267110\pi\) |
0.310342 | + | 0.950625i | \(0.399556\pi\) | |||||||
\(312\) | −1.29336e7 | −0.425849 | ||||||||
\(313\) | −1.38711e7 | + | 8.00850e6i | −0.452354 | + | 0.261167i | −0.708824 | − | 0.705385i | \(-0.750774\pi\) |
0.256470 | + | 0.966552i | \(0.417441\pi\) | |||||||
\(314\) | 2.19255e7 | − | 3.79761e7i | 0.708207 | − | 1.22665i | ||||
\(315\) | −6.14686e6 | + | 1.06467e7i | −0.196662 | + | 0.340629i | ||||
\(316\) | 2.76304e6 | − | 4.78572e6i | 0.0875640 | − | 0.151665i | ||||
\(317\) | 1.98660e7 | 0.623638 | 0.311819 | − | 0.950141i | \(-0.399062\pi\) | ||||
0.311819 | + | 0.950141i | \(0.399062\pi\) | |||||||
\(318\) | −6.95607e6 | + | 1.20483e7i | −0.216313 | + | 0.374665i | ||||
\(319\) | −2.50882e7 | − | 1.44847e7i | −0.772853 | − | 0.446207i | ||||
\(320\) | 543793. | − | 313959.i | 0.0165953 | − | 0.00958128i | ||||
\(321\) | −2.40121e7 | + | 1.38634e7i | −0.725964 | + | 0.419136i | ||||
\(322\) | −8.26941e7 | −2.47689 | ||||||||
\(323\) | − | 2.65110e7i | − | 0.786716i | ||||||
\(324\) | 2.46167e6 | + | 4.26373e6i | 0.0723759 | + | 0.125359i | ||||
\(325\) | −2.08969e7 | − | 3.61945e7i | −0.608739 | − | 1.05437i | ||||
\(326\) | −1.20540e7 | + | 2.08782e7i | −0.347919 | + | 0.602614i | ||||
\(327\) | 2.70330e7 | + | 1.56075e7i | 0.773126 | + | 0.446364i | ||||
\(328\) | − | 7.01116e6i | − | 0.198687i | ||||||
\(329\) | −6.42575e7 | − | 3.70991e7i | −1.80441 | − | 1.04178i | ||||
\(330\) | 6.01338e6 | + | 3.47183e6i | 0.167331 | + | 0.0966087i | ||||
\(331\) | 5.64240e7 | + | 3.25764e7i | 1.55589 | + | 0.898296i | 0.997643 | + | 0.0686250i | \(0.0218612\pi\) |
0.558252 | + | 0.829671i | \(0.311472\pi\) | |||||||
\(332\) | 3.34602e6 | + | 5.79548e6i | 0.0914354 | + | 0.158371i | ||||
\(333\) | − | 3.83058e7i | − | 1.03737i | ||||||
\(334\) | −2.78056e7 | + | 1.60536e7i | −0.746265 | + | 0.430856i | ||||
\(335\) | −1.06700e7 | − | 6.16030e6i | −0.283810 | − | 0.163858i | ||||
\(336\) | 3.42305e7 | 0.902392 | ||||||||
\(337\) | 4.38948e6 | − | 7.60280e6i | 0.114689 | − | 0.198648i | −0.802966 | − | 0.596025i | \(-0.796746\pi\) |
0.917656 | + | 0.397377i | \(0.130079\pi\) | |||||||
\(338\) | 4.29008e7 | − | 2.47688e7i | 1.11100 | − | 0.641438i | ||||
\(339\) | 5.92849e6 | + | 1.02684e7i | 0.152175 | + | 0.263576i | ||||
\(340\) | − | 3.74560e6i | − | 0.0952981i | ||||||
\(341\) | −2.48655e7 | − | 4.30683e7i | −0.627096 | − | 1.08616i | ||||
\(342\) | −6.12542e7 | −1.53129 | ||||||||
\(343\) | 2.31436e6i | 0.0573519i | ||||||||
\(344\) | 2.14255e7 | − | 9.73516e6i | 0.526326 | − | 0.239148i | ||||
\(345\) | 1.16074e7 | 0.282669 | ||||||||
\(346\) | − | 2.66154e7i | − | 0.642546i | ||||||
\(347\) | −1.94170e7 | + | 1.12104e7i | −0.464724 | + | 0.268308i | −0.714028 | − | 0.700117i | \(-0.753131\pi\) |
0.249305 | + | 0.968425i | \(0.419798\pi\) | |||||||
\(348\) | −1.31181e7 | −0.311268 | ||||||||
\(349\) | −4.28834e7 | + | 2.47587e7i | −1.00882 | + | 0.582441i | −0.910845 | − | 0.412748i | \(-0.864569\pi\) |
−0.0979723 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(350\) | 3.16987e7 | + | 5.49037e7i | 0.739328 | + | 1.28055i | ||||
\(351\) | −4.78214e7 | − | 2.76097e7i | −1.10586 | − | 0.638469i | ||||
\(352\) | 3.33201e7i | 0.763974i | ||||||||
\(353\) | 2.92232e7 | − | 5.06161e7i | 0.664361 | − | 1.15071i | −0.315098 | − | 0.949059i | \(-0.602037\pi\) |
0.979458 | − | 0.201647i | \(-0.0646294\pi\) | |||||||
\(354\) | −2.62802e7 | − | 4.55186e7i | −0.592405 | − | 1.02608i | ||||
\(355\) | 1.33017e7 | 0.297319 | ||||||||
\(356\) | −7.75229e6 | + | 4.47579e6i | −0.171823 | + | 0.0992018i | ||||
\(357\) | −7.66987e6 | + | 1.32846e7i | −0.168571 | + | 0.291974i | ||||
\(358\) | 3.21742e7 | − | 5.57273e7i | 0.701226 | − | 1.21456i | ||||
\(359\) | 2.15033e7 | − | 3.72447e7i | 0.464752 | − | 0.804974i | −0.534439 | − | 0.845207i | \(-0.679477\pi\) |
0.999190 | + | 0.0402337i | \(0.0128103\pi\) | |||||||
\(360\) | 7.57966e6 | 0.162458 | ||||||||
\(361\) | 4.33473e7 | − | 7.50797e7i | 0.921383 | − | 1.59588i | ||||
\(362\) | 3.87427e7 | + | 2.23681e7i | 0.816703 | + | 0.471524i | ||||
\(363\) | −8.07164e6 | + | 4.66016e6i | −0.168749 | + | 0.0974275i | ||||
\(364\) | −4.44694e7 | + | 2.56744e7i | −0.922055 | + | 0.532349i | ||||
\(365\) | −4.54366e6 | −0.0934387 | ||||||||
\(366\) | 3.36712e7i | 0.686777i | ||||||||
\(367\) | −2.23693e7 | − | 3.87448e7i | −0.452538 | − | 0.783818i | 0.546005 | − | 0.837782i | \(-0.316148\pi\) |
−0.998543 | + | 0.0539636i | \(0.982814\pi\) | |||||||
\(368\) | 4.44779e7 | + | 7.70380e7i | 0.892485 | + | 1.54583i | ||||
\(369\) | 6.33299e6 | − | 1.09691e7i | 0.126046 | − | 0.218319i | ||||
\(370\) | 2.94293e7 | + | 1.69910e7i | 0.580999 | + | 0.335440i | ||||
\(371\) | − | 4.83752e7i | − | 0.947330i | ||||||
\(372\) | −1.95026e7 | − | 1.12598e7i | −0.378846 | − | 0.218727i | ||||
\(373\) | 7.22707e7 | + | 4.17255e7i | 1.39263 | + | 0.804035i | 0.993606 | − | 0.112906i | \(-0.0360158\pi\) |
0.399024 | + | 0.916941i | \(0.369349\pi\) | |||||||
\(374\) | −2.06520e7 | − | 1.19235e7i | −0.394774 | − | 0.227923i | ||||
\(375\) | −9.66423e6 | − | 1.67389e7i | −0.183262 | − | 0.317420i | ||||
\(376\) | 4.57467e7i | 0.860589i | ||||||||
\(377\) | −7.48919e7 | + | 4.32389e7i | −1.39769 | + | 0.806957i | ||||
\(378\) | 7.25407e7 | + | 4.18814e7i | 1.34309 | + | 0.775435i | ||||
\(379\) | 2.04585e7 | 0.375799 | 0.187899 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187899 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(380\) | 9.44775e6 | − | 1.63640e7i | 0.172178 | − | 0.298221i | ||||
\(381\) | 1.08196e7 | − | 6.24668e6i | 0.195630 | − | 0.112947i | ||||
\(382\) | 3.56898e7 | + | 6.18165e7i | 0.640256 | + | 1.10896i | ||||
\(383\) | 3.40929e6i | 0.0606831i | 0.999540 | + | 0.0303415i | \(0.00965949\pi\) | ||||
−0.999540 | + | 0.0303415i | \(0.990341\pi\) | |||||||
\(384\) | −1.50567e7 | − | 2.60789e7i | −0.265910 | − | 0.460570i | ||||
\(385\) | −2.41444e7 | −0.423092 | ||||||||
\(386\) | − | 2.44234e7i | − | 0.424663i | ||||||
\(387\) | 4.23139e7 | + | 4.12225e6i | 0.730047 | + | 0.0711216i | ||||
\(388\) | −954337. | −0.0163383 | ||||||||
\(389\) | 6.44693e7i | 1.09523i | 0.836732 | + | 0.547613i | \(0.184463\pi\) | ||||
−0.836732 | + | 0.547613i | \(0.815537\pi\) | |||||||
\(390\) | 1.79508e7 | − | 1.03639e7i | 0.302615 | − | 0.174715i | ||||
\(391\) | −3.98639e7 | −0.666882 | ||||||||
\(392\) | −2.89220e7 | + | 1.66981e7i | −0.480143 | + | 0.277211i | ||||
\(393\) | 2.27528e7 | + | 3.94090e7i | 0.374849 | + | 0.649258i | ||||
\(394\) | 6.39406e7 | + | 3.69161e7i | 1.04541 | + | 0.603570i | ||||
\(395\) | − | 7.75657e6i | − | 0.125857i | ||||||
\(396\) | −9.57966e6 | + | 1.65925e7i | −0.154264 | + | 0.267193i | ||||
\(397\) | −4.27622e7 | − | 7.40664e7i | −0.683422 | − | 1.18372i | −0.973930 | − | 0.226849i | \(-0.927158\pi\) |
0.290508 | − | 0.956872i | \(-0.406176\pi\) | |||||||
\(398\) | −1.12332e8 | −1.78177 | ||||||||
\(399\) | −6.70172e7 | + | 3.86924e7i | −1.05504 | + | 0.609125i | ||||
\(400\) | 3.40990e7 | − | 5.90612e7i | 0.532797 | − | 0.922831i | ||||
\(401\) | 1.65294e7 | − | 2.86298e7i | 0.256345 | − | 0.444002i | −0.708915 | − | 0.705294i | \(-0.750815\pi\) |
0.965260 | + | 0.261291i | \(0.0841484\pi\) | |||||||
\(402\) | −1.77602e7 | + | 3.07615e7i | −0.273381 | + | 0.473510i | ||||
\(403\) | −1.48454e8 | −2.26818 | ||||||||
\(404\) | 47559.0 | − | 82374.6i | 0.000721255 | − | 0.00124925i | ||||
\(405\) | 5.98470e6 | + | 3.45527e6i | 0.0900902 | + | 0.0520136i | ||||
\(406\) | 1.13604e8 | − | 6.55895e7i | 1.69753 | − | 0.980068i | ||||
\(407\) | 6.51522e7 | − | 3.76156e7i | 0.966376 | − | 0.557937i | ||||
\(408\) | 9.45768e6 | 0.139253 | ||||||||
\(409\) | 1.08918e8i | 1.59195i | 0.605328 | + | 0.795976i | \(0.293042\pi\) | ||||
−0.605328 | + | 0.795976i | \(0.706958\pi\) | |||||||
\(410\) | 5.61816e6 | + | 9.73094e6i | 0.0815160 | + | 0.141190i | ||||
\(411\) | −1.41595e7 | − | 2.45250e7i | −0.203950 | − | 0.353251i | ||||
\(412\) | −1.25141e7 | + | 2.16751e7i | −0.178941 | + | 0.309935i | ||||
\(413\) | 1.58277e8 | + | 9.13813e7i | 2.24682 | + | 1.29720i | ||||
\(414\) | 9.21064e7i | 1.29804i | ||||||||
\(415\) | 8.13470e6 | + | 4.69657e6i | 0.113814 | + | 0.0657108i | ||||
\(416\) | 8.61396e7 | + | 4.97327e7i | 1.19653 | + | 0.690816i | ||||
\(417\) | −1.87224e7 | − | 1.08094e7i | −0.258198 | − | 0.149071i | ||||
\(418\) | −6.01506e7 | − | 1.04184e8i | −0.823590 | − | 1.42650i | ||||
\(419\) | − | 1.24009e6i | − | 0.0168582i | −0.999964 | − | 0.00842910i | \(-0.997317\pi\) | ||
0.999964 | − | 0.00842910i | \(-0.00268310\pi\) | |||||||
\(420\) | −9.46851e6 | + | 5.46665e6i | −0.127801 | + | 0.0737858i | ||||
\(421\) | 1.05213e8 | + | 6.07449e7i | 1.41002 | + | 0.814073i | 0.995389 | − | 0.0959180i | \(-0.0305787\pi\) |
0.414627 | + | 0.909991i | \(0.363912\pi\) | |||||||
\(422\) | −6.08882e7 | −0.810206 | ||||||||
\(423\) | −4.13217e7 | + | 7.15713e7i | −0.545955 | + | 0.945623i | ||||
\(424\) | −2.58298e7 | + | 1.49128e7i | −0.338862 | + | 0.195642i | ||||
\(425\) | 1.52808e7 | + | 2.64671e7i | 0.199058 | + | 0.344778i | ||||
\(426\) | − | 3.83490e7i | − | 0.496049i | ||||||
\(427\) | −5.85407e7 | − | 1.01396e8i | −0.751925 | − | 1.30237i | ||||
\(428\) | 6.78699e7 | 0.865657 | ||||||||
\(429\) | − | 4.58884e7i | − | 0.581207i | ||||||
\(430\) | −2.19359e7 | + | 3.06802e7i | −0.275899 | + | 0.385881i | ||||
\(431\) | 1.19252e8 | 1.48948 | 0.744738 | − | 0.667357i | \(-0.232574\pi\) | ||||
0.744738 | + | 0.667357i | \(0.232574\pi\) | |||||||
\(432\) | − | 9.01055e7i | − | 1.11764i | ||||||
\(433\) | −4.06937e7 | + | 2.34945e7i | −0.501260 | + | 0.289403i | −0.729234 | − | 0.684265i | \(-0.760123\pi\) |
0.227974 | + | 0.973667i | \(0.426790\pi\) | |||||||
\(434\) | 2.25192e8 | 2.75476 | ||||||||
\(435\) | −1.59461e7 | + | 9.20651e6i | −0.193726 | + | 0.111848i | ||||
\(436\) | −3.82041e7 | − | 6.61715e7i | −0.460947 | − | 0.798383i | ||||
\(437\) | −1.74160e8 | − | 1.00551e8i | −2.08691 | − | 1.20488i | ||||
\(438\) | 1.30994e7i | 0.155894i | ||||||||
\(439\) | −1.12957e7 | + | 1.95647e7i | −0.133511 | + | 0.231248i | −0.925028 | − | 0.379899i | \(-0.875959\pi\) |
0.791516 | + | 0.611148i | \(0.209292\pi\) | |||||||
\(440\) | 7.44310e6 | + | 1.28918e7i | 0.0873767 | + | 0.151341i | ||||
\(441\) | −6.03319e7 | −0.703447 | ||||||||
\(442\) | −6.16494e7 | + | 3.55933e7i | −0.713940 | + | 0.412194i | ||||
\(443\) | 5.32924e7 | − | 9.23051e7i | 0.612991 | − | 1.06173i | −0.377742 | − | 0.925911i | \(-0.623300\pi\) |
0.990733 | − | 0.135821i | \(-0.0433672\pi\) | |||||||
\(444\) | 1.70334e7 | − | 2.95028e7i | 0.194605 | − | 0.337065i | ||||
\(445\) | −6.28235e6 | + | 1.08814e7i | −0.0712922 | + | 0.123482i | ||||
\(446\) | −2.03400e6 | −0.0229269 | ||||||||
\(447\) | −1.16544e7 | + | 2.01860e7i | −0.130487 | + | 0.226010i | ||||
\(448\) | 5.45140e6 | + | 3.14737e6i | 0.0606281 | + | 0.0350037i | ||||
\(449\) | −4.21692e7 | + | 2.43464e7i | −0.465861 | + | 0.268965i | −0.714506 | − | 0.699630i | \(-0.753348\pi\) |
0.248644 | + | 0.968595i | \(0.420015\pi\) | |||||||
\(450\) | 6.11529e7 | − | 3.53067e7i | 0.671088 | − | 0.387453i | ||||
\(451\) | 2.48756e7 | 0.271171 | ||||||||
\(452\) | − | 2.90236e7i | − | 0.314294i | ||||||
\(453\) | −7.06563e6 | − | 1.22380e7i | −0.0760074 | − | 0.131649i | ||||
\(454\) | −2.27680e7 | − | 3.94353e7i | −0.243308 | − | 0.421422i | ||||
\(455\) | −3.60374e7 | + | 6.24185e7i | −0.382577 | + | 0.662643i | ||||
\(456\) | 4.13193e7 | + | 2.38557e7i | 0.435771 | + | 0.251592i | ||||
\(457\) | 3.24332e7i | 0.339814i | 0.985460 | + | 0.169907i | \(0.0543468\pi\) | ||||
−0.985460 | + | 0.169907i | \(0.945653\pi\) | |||||||
\(458\) | −5.76872e7 | − | 3.33057e7i | −0.600459 | − | 0.346675i | ||||
\(459\) | 3.49693e7 | + | 2.01895e7i | 0.361617 | + | 0.208780i | ||||
\(460\) | −2.46061e7 | − | 1.42063e7i | −0.252796 | − | 0.145952i | ||||
\(461\) | −1.92401e7 | − | 3.33248e7i | −0.196383 | − | 0.340146i | 0.750970 | − | 0.660337i | \(-0.229586\pi\) |
−0.947353 | + | 0.320191i | \(0.896253\pi\) | |||||||
\(462\) | 6.96085e7i | 0.705889i | ||||||||
\(463\) | −2.97704e7 | + | 1.71880e7i | −0.299945 | + | 0.173174i | −0.642418 | − | 0.766354i | \(-0.722069\pi\) |
0.342473 | + | 0.939528i | \(0.388735\pi\) | |||||||
\(464\) | −1.22207e8 | − | 7.05561e7i | −1.22332 | − | 0.706286i | ||||
\(465\) | −3.16092e7 | −0.314380 | ||||||||
\(466\) | 4.58994e7 | − | 7.95001e7i | 0.453575 | − | 0.785616i | ||||
\(467\) | 8.60386e7 | − | 4.96744e7i | 0.844778 | − | 0.487733i | −0.0141076 | − | 0.999900i | \(-0.504491\pi\) |
0.858885 | + | 0.512168i | \(0.171157\pi\) | |||||||
\(468\) | 2.85967e7 | + | 4.95309e7i | 0.278983 | + | 0.483213i | ||||
\(469\) | − | 1.23511e8i | − | 1.19726i | ||||||
\(470\) | −3.66576e7 | − | 6.34928e7i | −0.353077 | − | 0.611548i | ||||
\(471\) | −6.17041e7 | −0.590543 | ||||||||
\(472\) | − | 1.12682e8i | − | 1.07159i | ||||||
\(473\) | 3.45403e7 | + | 7.60174e7i | 0.326394 | + | 0.718340i | ||||
\(474\) | −2.23622e7 | −0.209981 | ||||||||
\(475\) | 1.54175e8i | 1.43858i | ||||||||
\(476\) | 3.25181e7 | − | 1.87744e7i | 0.301512 | − | 0.174078i | ||||
\(477\) | −5.38813e7 | −0.496459 | ||||||||
\(478\) | −1.13227e8 | + | 6.53717e7i | −1.03673 | + | 0.598558i | ||||
\(479\) | −5.94155e6 | − | 1.02911e7i | −0.0540622 | − | 0.0936384i | 0.837728 | − | 0.546088i | \(-0.183884\pi\) |
−0.891790 | + | 0.452450i | \(0.850550\pi\) | |||||||
\(480\) | 1.83410e7 | + | 1.05892e7i | 0.165844 | + | 0.0957501i | ||||
\(481\) | − | 2.24576e8i | − | 2.01804i | ||||||
\(482\) | −3.84731e7 | + | 6.66373e7i | −0.343570 | + | 0.595081i | ||||
\(483\) | 5.81808e7 | + | 1.00772e8i | 0.516343 | + | 0.894332i | ||||
\(484\) | 2.28144e7 | 0.201221 | ||||||||
\(485\) | −1.16007e6 | + | 669768.i | −0.0101686 | + | 0.00587082i | ||||
\(486\) | 7.35583e7 | − | 1.27407e8i | 0.640800 | − | 1.10990i | ||||
\(487\) | −8.08963e7 | + | 1.40116e8i | −0.700393 | + | 1.21312i | 0.267936 | + | 0.963437i | \(0.413658\pi\) |
−0.968329 | + | 0.249679i | \(0.919675\pi\) | |||||||
\(488\) | −3.60931e7 | + | 6.25152e7i | −0.310574 | + | 0.537930i | ||||
\(489\) | 3.39232e7 | 0.290115 | ||||||||
\(490\) | 2.67610e7 | − | 4.63514e7i | 0.227465 | − | 0.393981i | ||||
\(491\) | −5.58436e7 | − | 3.22413e7i | −0.471769 | − | 0.272376i | 0.245211 | − | 0.969470i | \(-0.421143\pi\) |
−0.716980 | + | 0.697094i | \(0.754476\pi\) | |||||||
\(492\) | 9.75523e6 | − | 5.63218e6i | 0.0819110 | − | 0.0472913i | ||||
\(493\) | 5.47646e7 | − | 3.16183e7i | 0.457045 | − | 0.263875i | ||||
\(494\) | −3.59117e8 | −2.97889 | ||||||||
\(495\) | 2.68926e7i | 0.221726i | ||||||||
\(496\) | −1.21122e8 | − | 2.09789e8i | −0.992608 | − | 1.71925i | ||||
\(497\) | 6.66734e7 | + | 1.15482e8i | 0.543105 | + | 0.940685i | ||||
\(498\) | 1.35402e7 | − | 2.34524e7i | 0.109632 | − | 0.189889i | ||||
\(499\) | 1.31349e7 | + | 7.58344e6i | 0.105712 | + | 0.0610329i | 0.551924 | − | 0.833894i | \(-0.313894\pi\) |
−0.446212 | + | 0.894927i | \(0.647227\pi\) | |||||||
\(500\) | 4.73123e7i | 0.378499i | ||||||||
\(501\) | 3.91262e7 | + | 2.25895e7i | 0.311139 | + | 0.179636i | ||||
\(502\) | 1.82364e8 | + | 1.05288e8i | 1.44154 | + | 0.832275i | ||||
\(503\) | 1.99168e7 | + | 1.14990e7i | 0.156501 | + | 0.0903558i | 0.576205 | − | 0.817305i | \(-0.304533\pi\) |
−0.419704 | + | 0.907661i | \(0.637866\pi\) | |||||||
\(504\) | 3.79922e7 | + | 6.58043e7i | 0.296758 | + | 0.514000i | ||||
\(505\) | − | 133511.i | − | 0.00103667i | ||||||
\(506\) | −1.56659e8 | + | 9.04469e7i | −1.20921 | + | 0.698139i | ||||
\(507\) | −6.03671e7 | − | 3.48530e7i | −0.463209 | − | 0.267434i | ||||
\(508\) | −3.05813e7 | −0.233273 | ||||||||
\(509\) | 1.19132e7 | − | 2.06343e7i | 0.0903392 | − | 0.156472i | −0.817315 | − | 0.576192i | \(-0.804538\pi\) |
0.907654 | + | 0.419720i | \(0.137872\pi\) | |||||||
\(510\) | −1.31265e7 | + | 7.57859e6i | −0.0989552 | + | 0.0571318i | ||||
\(511\) | −2.27746e7 | − | 3.94467e7i | −0.170682 | − | 0.295630i | ||||
\(512\) | 6.53994e7i | 0.487263i | ||||||||
\(513\) | 1.01851e8 | + | 1.76410e8i | 0.754417 | + | 1.30669i | ||||
\(514\) | −1.10477e7 | −0.0813548 | ||||||||
\(515\) | 3.51305e7i | 0.257195i | ||||||||
\(516\) | 3.07568e7 | + | 2.19907e7i | 0.223868 | + | 0.160062i | ||||
\(517\) | −1.62309e8 | −1.17455 | ||||||||
\(518\) | 3.40662e8i | 2.45095i | ||||||||
\(519\) | −3.24338e7 | + | 1.87257e7i | −0.232004 | + | 0.133948i | ||||
\(520\) | 4.44375e7 | 0.316038 | ||||||||
\(521\) | 1.95475e8 | − | 1.12857e8i | 1.38222 | − | 0.798025i | 0.389798 | − | 0.920900i | \(-0.372545\pi\) |
0.992422 | + | 0.122875i | \(0.0392115\pi\) | |||||||
\(522\) | −7.30549e7 | − | 1.26535e8i | −0.513615 | − | 0.889608i | ||||
\(523\) | 1.34445e8 | + | 7.76217e7i | 0.939807 | + | 0.542598i | 0.889900 | − | 0.456156i | \(-0.150774\pi\) |
0.0499071 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(524\) | − | 1.11389e8i | − | 0.774190i | ||||||
\(525\) | 4.46043e7 | − | 7.72568e7i | 0.308247 | − | 0.533899i | ||||
\(526\) | −2.71019e7 | − | 4.69419e7i | −0.186227 | − | 0.322555i | ||||
\(527\) | 1.08557e8 | 0.741696 | ||||||||
\(528\) | 6.48475e7 | − | 3.74397e7i | 0.440546 | − | 0.254349i | ||||
\(529\) | −7.71782e7 | + | 1.33677e8i | −0.521348 | + | 0.903001i | ||||
\(530\) | 2.38998e7 | − | 4.13956e7i | 0.160534 | − | 0.278052i | ||||
\(531\) | 1.01782e8 | − | 1.76292e8i | 0.679813 | − | 1.17747i | ||||
\(532\) | 1.89423e8 | 1.25805 | ||||||||
\(533\) | 3.71286e7 | − | 6.43087e7i | 0.245204 | − | 0.424705i | ||||
\(534\) | 3.13710e7 | + | 1.81120e7i | 0.206018 | + | 0.118944i | ||||
\(535\) | 8.25012e7 | − | 4.76321e7i | 0.538764 | − | 0.311056i | ||||
\(536\) | −6.59482e7 | + | 3.80752e7i | −0.428261 | + | 0.247257i | ||||
\(537\) | −9.05466e7 | −0.584722 | ||||||||
\(538\) | 1.25090e8i | 0.803294i | ||||||||
\(539\) | −5.92449e7 | − | 1.02615e8i | −0.378342 | − | 0.655308i | ||||
\(540\) | 1.43899e7 | + | 2.49241e7i | 0.0913856 | + | 0.158284i | ||||
\(541\) | −4.77667e7 | + | 8.27344e7i | −0.301671 | + | 0.522510i | −0.976515 | − | 0.215451i | \(-0.930878\pi\) |
0.674843 | + | 0.737961i | \(0.264211\pi\) | |||||||
\(542\) | 1.71380e8 | + | 9.89462e7i | 1.07637 | + | 0.621443i | ||||
\(543\) | − | 6.29498e7i | − | 0.393183i | ||||||
\(544\) | −6.29894e7 | − | 3.63670e7i | −0.391265 | − | 0.225897i | ||||
\(545\) | −9.28802e7 | − | 5.36244e7i | −0.573765 | − | 0.331263i | ||||
\(546\) | 1.79953e8 | + | 1.03896e8i | 1.10556 | + | 0.638293i | ||||
\(547\) | −5.93198e7 | − | 1.02745e8i | −0.362441 | − | 0.627766i | 0.625921 | − | 0.779886i | \(-0.284723\pi\) |
−0.988362 | + | 0.152120i | \(0.951390\pi\) | |||||||
\(548\) | 6.93195e7i | 0.421225i | ||||||||
\(549\) | −1.12936e8 | + | 6.52039e7i | −0.682523 | + | 0.394055i | ||||
\(550\) | 1.20102e8 | + | 6.93411e7i | 0.721877 | + | 0.416776i | ||||
\(551\) | 3.19012e8 | 1.90700 | ||||||||
\(552\) | 3.58712e7 | − | 6.21307e7i | 0.213269 | − | 0.369394i | ||||
\(553\) | 6.73402e7 | − | 3.88789e7i | 0.398198 | − | 0.229900i | ||||
\(554\) | −4.37013e7 | − | 7.56928e7i | −0.257019 | − | 0.445170i | ||||
\(555\) | − | 4.78173e7i | − | 0.279709i | ||||||
\(556\) | 2.64593e7 | + | 4.58288e7i | 0.153941 | + | 0.266633i | ||||
\(557\) | 2.52042e8 | 1.45850 | 0.729252 | − | 0.684245i | \(-0.239868\pi\) | ||||
0.729252 | + | 0.684245i | \(0.239868\pi\) | |||||||
\(558\) | − | 2.50823e8i | − | 1.44366i | ||||||
\(559\) | 2.48075e8 | + | 2.41676e7i | 1.42019 | + | 0.138356i | ||||
\(560\) | −1.17610e8 | −0.669698 | ||||||||
\(561\) | 3.35558e7i | 0.190055i | ||||||||
\(562\) | −1.59832e7 | + | 9.22790e6i | −0.0900439 | + | 0.0519869i | ||||
\(563\) | −2.59217e8 | −1.45257 | −0.726287 | − | 0.687391i | \(-0.758756\pi\) | ||||
−0.726287 | + | 0.687391i | \(0.758756\pi\) | |||||||
\(564\) | −6.36512e7 | + | 3.67490e7i | −0.354788 | + | 0.204837i | ||||
\(565\) | −2.03692e7 | − | 3.52805e7i | −0.112935 | − | 0.195609i | ||||
\(566\) | −2.90436e8 | − | 1.67684e8i | −1.60178 | − | 0.924786i | ||||
\(567\) | 6.92765e7i | 0.380047i | ||||||||
\(568\) | 4.11073e7 | − | 7.12000e7i | 0.224323 | − | 0.388539i | ||||
\(569\) | −5.64015e7 | − | 9.76902e7i | −0.306164 | − | 0.530291i | 0.671356 | − | 0.741135i | \(-0.265712\pi\) |
−0.977520 | + | 0.210844i | \(0.932379\pi\) | |||||||
\(570\) | −7.64638e7 | −0.412887 | ||||||||
\(571\) | −1.98649e8 | + | 1.14690e8i | −1.06703 | + | 0.616051i | −0.927369 | − | 0.374148i | \(-0.877935\pi\) |
−0.139663 | + | 0.990199i | \(0.544602\pi\) | |||||||
\(572\) | −5.61629e7 | + | 9.72770e7i | −0.300097 | + | 0.519783i | ||||
\(573\) | 5.02202e7 | − | 8.69840e7i | 0.266941 | − | 0.462355i | ||||
\(574\) | −5.63208e7 | + | 9.75504e7i | −0.297806 | + | 0.515815i | ||||
\(575\) | 2.31829e8 | 1.21945 | ||||||||
\(576\) | 3.50561e6 | − | 6.07189e6i | 0.0183441 | − | 0.0317729i | ||||
\(577\) | 8.83230e7 | + | 5.09933e7i | 0.459776 | + | 0.265452i | 0.711950 | − | 0.702230i | \(-0.247812\pi\) |
−0.252174 | + | 0.967682i | \(0.581146\pi\) | |||||||
\(578\) | −1.61980e8 | + | 9.35194e7i | −0.838840 | + | 0.484304i | ||||
\(579\) | −2.97627e7 | + | 1.71835e7i | −0.153333 | + | 0.0885269i | ||||
\(580\) | 4.50715e7 | 0.231003 | ||||||||
\(581\) | 9.41641e7i | 0.480128i | ||||||||
\(582\) | 1.93094e6 | + | 3.34449e6i | 0.00979491 | + | 0.0169653i | ||||
\(583\) | −5.29106e7 | − | 9.16438e7i | −0.267016 | − | 0.462485i | ||||
\(584\) | −1.40416e7 | + | 2.43208e7i | −0.0704982 | + | 0.122106i | ||||
\(585\) | 6.95231e7 | + | 4.01392e7i | 0.347265 | + | 0.200494i | ||||
\(586\) | − | 2.98050e8i | − | 1.48114i | ||||||
\(587\) | −1.09550e8 | − | 6.32485e7i | −0.541622 | − | 0.312706i | 0.204114 | − | 0.978947i | \(-0.434569\pi\) |
−0.745736 | + | 0.666241i | \(0.767902\pi\) | |||||||
\(588\) | −4.64671e7 | − | 2.68278e7i | −0.228567 | − | 0.131963i | ||||
\(589\) | 4.74270e8 | + | 2.73820e8i | 2.32102 | + | 1.34004i | ||||
\(590\) | 9.02939e7 | + | 1.56394e8i | 0.439645 | + | 0.761488i | ||||
\(591\) | − | 1.03892e8i | − | 0.503291i | ||||||
\(592\) | 3.17362e8 | − | 1.83229e8i | 1.52964 | − | 0.883139i | ||||
\(593\) | −8.64944e7 | − | 4.99376e7i | −0.414786 | − | 0.239477i | 0.278058 | − | 0.960564i | \(-0.410309\pi\) |
−0.692844 | + | 0.721088i | \(0.743643\pi\) | |||||||
\(594\) | 1.83232e8 | 0.874261 | ||||||||
\(595\) | 2.63523e7 | − | 4.56434e7i | 0.125103 | − | 0.216684i | ||||
\(596\) | 4.94114e7 | − | 2.85277e7i | 0.233393 | − | 0.134750i | ||||
\(597\) | 7.90327e7 | + | 1.36889e8i | 0.371436 | + | 0.643346i | ||||
\(598\) | 5.39995e8i | 2.52514i | ||||||||
\(599\) | −1.34336e8 | − | 2.32677e8i | −0.625045 | − | 1.08261i | −0.988532 | − | 0.151011i | \(-0.951747\pi\) |
0.363487 | − | 0.931599i | \(-0.381586\pi\) | |||||||
\(600\) | −5.50013e7 | −0.254636 | ||||||||
\(601\) | 673740.i | 0.00310362i | 0.999999 | + | 0.00155181i | \(0.000493957\pi\) | ||||
−0.999999 | + | 0.00155181i | \(0.999506\pi\) | |||||||
\(602\) | −3.76308e8 | − | 3.66601e7i | −1.72486 | − | 0.168037i | ||||
\(603\) | −1.37569e8 | −0.627436 | ||||||||
\(604\) | 3.45906e7i | 0.156981i | ||||||||
\(605\) | 2.77327e7 | − | 1.60115e7i | 0.125235 | − | 0.0723044i | ||||
\(606\) | −384911. | −0.00172959 | ||||||||
\(607\) | −1.37075e8 | + | 7.91402e7i | −0.612903 | + | 0.353860i | −0.774101 | − | 0.633062i | \(-0.781798\pi\) |
0.161198 | + | 0.986922i | \(0.448464\pi\) | |||||||
\(608\) | −1.83461e8 | − | 3.17764e8i | −0.816270 | − | 1.41382i | ||||
\(609\) | −1.59856e8 | − | 9.22931e7i | −0.707747 | − | 0.408618i | ||||
\(610\) | − | 1.15688e8i | − | 0.509682i | ||||||
\(611\) | −2.42258e8 | + | 4.19603e8i | −1.06207 | + | 1.83956i | ||||
\(612\) | −2.09113e7 | − | 3.62194e7i | −0.0912276 | − | 0.158011i | ||||
\(613\) | 1.33078e8 | 0.577728 | 0.288864 | − | 0.957370i | \(-0.406722\pi\) | ||||
0.288864 | + | 0.957370i | \(0.406722\pi\) | |||||||
\(614\) | −2.44425e8 | + | 1.41119e8i | −1.05595 | + | 0.609650i | ||||
\(615\) | 7.90550e6 | − | 1.36927e7i | 0.0339863 | − | 0.0588660i | ||||
\(616\) | −7.46153e7 | + | 1.29238e8i | −0.319217 | + | 0.552900i | ||||
\(617\) | −2.42051e6 | + | 4.19244e6i | −0.0103051 | + | 0.0178489i | −0.871132 | − | 0.491049i | \(-0.836614\pi\) |
0.860827 | + | 0.508898i | \(0.169947\pi\) | |||||||
\(618\) | 1.01281e8 | 0.429105 | ||||||||
\(619\) | −2.59299e7 | + | 4.49119e7i | −0.109327 | + | 0.189360i | −0.915498 | − | 0.402323i | \(-0.868203\pi\) |
0.806171 | + | 0.591683i | \(0.201536\pi\) | |||||||
\(620\) | 6.70072e7 | + | 3.86866e7i | 0.281155 | + | 0.162325i | ||||
\(621\) | 2.65264e8 | − | 1.53150e8i | 1.10765 | − | 0.639503i | ||||
\(622\) | −5.04951e8 | + | 2.91534e8i | −2.09835 | + | 1.21148i | ||||
\(623\) | −1.25958e8 | −0.520910 | ||||||||
\(624\) | − | 2.23526e8i | − | 0.919972i | ||||||
\(625\) | −7.09486e7 | − | 1.22887e8i | −0.290606 | − | 0.503344i | ||||
\(626\) | −7.93279e7 | − | 1.37400e8i | −0.323373 | − | 0.560098i | ||||
\(627\) | −8.46398e7 | + | 1.46600e8i | −0.343378 | + | 0.594748i | ||||
\(628\) | 1.30804e8 | + | 7.55199e7i | 0.528133 | + | 0.304918i | ||||
\(629\) | 1.64221e8i | 0.659898i | ||||||||
\(630\) | −1.05460e8 | − | 6.08875e7i | −0.421762 | − | 0.243504i | ||||
\(631\) | −2.74828e8 | − | 1.58672e8i | −1.09389 | − | 0.631558i | −0.159281 | − | 0.987233i | \(-0.550917\pi\) |
−0.934609 | + | 0.355676i | \(0.884251\pi\) | |||||||
\(632\) | −4.15184e7 | − | 2.39707e7i | −0.164471 | − | 0.0949575i | ||||
\(633\) | 4.28389e7 | + | 7.41991e7i | 0.168899 | + | 0.292541i | ||||
\(634\) | 1.96782e8i | 0.772179i | ||||||||
\(635\) | −3.71740e7 | + | 2.14624e7i | −0.145184 | + | 0.0838220i | ||||
\(636\) | −4.14989e7 | − | 2.39594e7i | −0.161312 | − | 0.0931333i | ||||
\(637\) | −3.53710e8 | −1.36845 | ||||||||
\(638\) | 1.43477e8 | − | 2.48510e8i | 0.552486 | − | 0.956934i | ||||
\(639\) | 1.28626e8 | − | 7.42622e7i | 0.492976 | − | 0.284620i | ||||
\(640\) | 5.17319e7 | + | 8.96023e7i | 0.197342 | + | 0.341806i | ||||
\(641\) | 1.79466e8i | 0.681411i | 0.940170 | + | 0.340706i | \(0.110666\pi\) | ||||
−0.940170 | + | 0.340706i | \(0.889334\pi\) | |||||||
\(642\) | −1.37323e8 | − | 2.37851e8i | −0.518967 | − | 0.898877i | ||||
\(643\) | −9.15602e6 | −0.0344408 | −0.0172204 | − | 0.999852i | \(-0.505482\pi\) | ||||
−0.0172204 | + | 0.999852i | \(0.505482\pi\) | |||||||
\(644\) | − | 2.84830e8i | − | 1.06642i | ||||||
\(645\) | 5.28207e7 | + | 5.14582e6i | 0.196845 | + | 0.0191768i | ||||
\(646\) | 2.62603e8 | 0.974098 | ||||||||
\(647\) | 1.13727e7i | 0.0419904i | 0.999780 | + | 0.0209952i | \(0.00668347\pi\) | ||||
−0.999780 | + | 0.0209952i | \(0.993317\pi\) | |||||||
\(648\) | 3.69899e7 | − | 2.13561e7i | 0.135943 | − | 0.0784870i | ||||
\(649\) | 3.99795e8 | 1.46252 | ||||||||
\(650\) | 3.58523e8 | − | 2.06993e8i | 1.30550 | − | 0.753731i | ||||
\(651\) | −1.58437e8 | − | 2.74422e8i | −0.574268 | − | 0.994662i | ||||
\(652\) | −7.19125e7 | − | 4.15187e7i | −0.259455 | − | 0.149796i | ||||
\(653\) | 1.94540e8i | 0.698667i | 0.936998 | + | 0.349334i | \(0.113592\pi\) | ||||
−0.936998 | + | 0.349334i | \(0.886408\pi\) | |||||||
\(654\) | −1.54599e8 | + | 2.67774e8i | −0.552681 | + | 0.957272i | ||||
\(655\) | −7.81743e7 | − | 1.35402e8i | −0.278189 | − | 0.481838i | ||||
\(656\) | 1.21171e8 | 0.429227 | ||||||||
\(657\) | −4.39365e7 | + | 2.53668e7i | −0.154928 | + | 0.0894477i | ||||
\(658\) | 3.67484e8 | − | 6.36500e8i | 1.28991 | − | 2.23419i | ||||
\(659\) | −3.17062e7 | + | 5.49168e7i | −0.110787 | + | 0.191889i | −0.916088 | − | 0.400978i | \(-0.868670\pi\) |
0.805301 | + | 0.592866i | \(0.202004\pi\) | |||||||
\(660\) | −1.19583e7 | + | 2.07124e7i | −0.0415947 | + | 0.0720442i | ||||
\(661\) | 3.66297e8 | 1.26832 | 0.634160 | − | 0.773202i | \(-0.281346\pi\) | ||||
0.634160 | + | 0.773202i | \(0.281346\pi\) | |||||||
\(662\) | −3.22685e8 | + | 5.58907e8i | −1.11226 | + | 1.92648i | ||||
\(663\) | 8.67488e7 | + | 5.00845e7i | 0.297662 | + | 0.171855i | ||||
\(664\) | 5.02785e7 | − | 2.90283e7i | 0.171743 | − | 0.0991557i | ||||
\(665\) | 2.30259e8 | − | 1.32940e8i | 0.782980 | − | 0.452054i | ||||
\(666\) | 3.79437e8 | 1.28445 | ||||||||
\(667\) | − | 4.79690e8i | − | 1.61653i | ||||||
\(668\) | −5.52947e7 | − | 9.57733e7i | −0.185504 | − | 0.321303i | ||||
\(669\) | 1.43105e6 | + | 2.47866e6i | 0.00477944 | + | 0.00827824i | ||||
\(670\) | 6.10206e7 | − | 1.05691e8i | 0.202886 | − | 0.351409i | ||||
\(671\) | −2.21803e8 | − | 1.28058e8i | −0.734177 | − | 0.423877i | ||||
\(672\) | 2.12308e8i | 0.699615i | ||||||||
\(673\) | −4.18831e8 | − | 2.41812e8i | −1.37402 | − | 0.793292i | −0.382591 | − | 0.923918i | \(-0.624968\pi\) |
−0.991432 | + | 0.130626i | \(0.958301\pi\) | |||||||
\(674\) | 7.53093e7 | + | 4.34798e7i | 0.245962 | + | 0.142006i | ||||
\(675\) | −2.03364e8 | − | 1.17413e8i | −0.661247 | − | 0.381771i | ||||
\(676\) | 8.53134e7 | + | 1.47767e8i | 0.276170 | + | 0.478341i | ||||
\(677\) | 2.11180e8i | 0.680592i | 0.940318 | + | 0.340296i | \(0.110527\pi\) | ||||
−0.940318 | + | 0.340296i | \(0.889473\pi\) | |||||||
\(678\) | −1.01714e8 | + | 5.87244e7i | −0.326355 | + | 0.188421i | ||||
\(679\) | −1.16295e7 | − | 6.71427e6i | −0.0371492 | − | 0.0214481i | ||||
\(680\) | −3.24948e7 | −0.103345 | ||||||||
\(681\) | −3.20375e7 | + | 5.54906e7i | −0.101442 | + | 0.175703i | ||||
\(682\) | 4.26612e8 | − | 2.46304e8i | 1.34487 | − | 0.776460i | ||||
\(683\) | 1.76038e8 | + | 3.04906e8i | 0.552514 | + | 0.956983i | 0.998092 | + | 0.0617396i | \(0.0196648\pi\) |
−0.445578 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(684\) | − | 2.10983e8i | − | 0.659295i | ||||||
\(685\) | 4.86495e7 | + | 8.42634e7i | 0.151358 | + | 0.262160i | ||||
\(686\) | −2.29248e7 | −0.0710122 | ||||||||
\(687\) | 9.37312e7i | 0.289077i | ||||||||
\(688\) | 1.68249e8 | + | 3.70287e8i | 0.516638 | + | 1.13703i | ||||
\(689\) | −3.15892e8 | −0.965785 | ||||||||
\(690\) | 1.14977e8i | 0.349996i | ||||||||
\(691\) | 2.14509e8 | − | 1.23847e8i | 0.650147 | − | 0.375362i | −0.138366 | − | 0.990381i | \(-0.544185\pi\) |
0.788512 | + | 0.615019i | \(0.210852\pi\) | |||||||
\(692\) | 9.16737e7 | 0.276647 | ||||||||
\(693\) | −2.33473e8 | + | 1.34796e8i | −0.701516 | + | 0.405021i | ||||
\(694\) | −1.11045e8 | − | 1.92335e8i | −0.332215 | − | 0.575413i | ||||
\(695\) | 6.43267e7 | + | 3.71390e7i | 0.191618 | + | 0.110631i | ||||
\(696\) | 1.13806e8i | 0.337550i | ||||||||
\(697\) | −2.71502e7 | + | 4.70256e7i | −0.0801817 | + | 0.138879i | ||||
\(698\) | −2.45247e8 | − | 4.24780e8i | −0.721169 | − | 1.24910i | ||||
\(699\) | −1.29173e8 | −0.378217 | ||||||||
\(700\) | −1.89110e8 | + | 1.09183e8i | −0.551341 | + | 0.318317i | ||||
\(701\) | −6.55682e7 | + | 1.13568e8i | −0.190344 | + | 0.329686i | −0.945364 | − | 0.326016i | \(-0.894294\pi\) |
0.755020 | + | 0.655702i | \(0.227627\pi\) | |||||||
\(702\) | 2.73487e8 | − | 4.73693e8i | 0.790542 | − | 1.36926i | ||||
\(703\) | −4.14225e8 | + | 7.17459e8i | −1.19226 | + | 2.06505i | ||||
\(704\) | 1.37698e7 | 0.0394647 | ||||||||
\(705\) | −5.15821e7 | + | 8.93427e7i | −0.147208 | + | 0.254972i | ||||
\(706\) | 5.01376e8 | + | 2.89470e8i | 1.42479 | + | 0.822600i | ||||
\(707\) | 1.15910e6 | − | 669206.i | 0.00327991 | − | 0.00189366i | ||||
\(708\) | 1.56784e8 | − | 9.05192e7i | 0.441775 | − | 0.255059i | ||||
\(709\) | 2.01021e8 | 0.564031 | 0.282015 | − | 0.959410i | \(-0.408997\pi\) | ||||
0.282015 | + | 0.959410i | \(0.408997\pi\) | |||||||
\(710\) | 1.31760e8i | 0.368136i | ||||||||
\(711\) | −4.33041e7 | − | 7.50049e7i | −0.120482 | − | 0.208680i | ||||
\(712\) | 3.88296e7 | + | 6.72549e7i | 0.107578 | + | 0.186330i | ||||
\(713\) | 4.11736e8 | − | 7.13148e8i | 1.13593 | − | 1.96748i | ||||
\(714\) | −1.31590e8 | − | 7.59736e7i | −0.361517 | − | 0.208722i | ||||
\(715\) | 1.57664e8i | 0.431334i | ||||||||
\(716\) | 1.91946e8 | + | 1.10820e8i | 0.522927 | + | 0.301912i | ||||
\(717\) | 1.59326e8 | + | 9.19867e7i | 0.432243 | + | 0.249556i | ||||
\(718\) | 3.68927e8 | + | 2.13000e8i | 0.996705 | + | 0.575448i | ||||
\(719\) | −1.16682e8 | − | 2.02099e8i | −0.313918 | − | 0.543721i | 0.665289 | − | 0.746586i | \(-0.268308\pi\) |
−0.979207 | + | 0.202864i | \(0.934975\pi\) | |||||||
\(720\) | 1.30996e8i | 0.350963i | ||||||||
\(721\) | −3.04992e8 | + | 1.76087e8i | −0.813735 | + | 0.469810i | ||||
\(722\) | 7.43700e8 | + | 4.29375e8i | 1.97600 | + | 1.14084i | ||||
\(723\) | 1.08273e8 | 0.286488 | ||||||||
\(724\) | −7.70444e7 | + | 1.33445e8i | −0.203014 | + | 0.351630i | ||||
\(725\) | −3.18484e8 | + | 1.83877e8i | −0.835746 | + | 0.482518i | ||||
\(726\) | −4.61611e7 | − | 7.99534e7i | −0.120633 | − | 0.208943i | ||||
\(727\) | − | 1.67591e8i | − | 0.436162i | −0.975931 | − | 0.218081i | \(-0.930020\pi\) | ||
0.975931 | − | 0.218081i | \(-0.0699796\pi\) | |||||||
\(728\) | 2.22738e8 | + | 3.85793e8i | 0.577297 | + | 0.999908i | ||||
\(729\) | −1.01816e8 | −0.262806 | ||||||||
\(730\) | − | 4.50071e7i | − | 0.115694i | ||||||
\(731\) | −1.81405e8 | − | 1.76725e7i | −0.464404 | − | 0.0452425i | ||||
\(732\) | −1.15977e8 | −0.295691 | ||||||||
\(733\) | 1.41184e7i | 0.0358487i | 0.999839 | + | 0.0179243i | \(0.00570580\pi\) | ||||
−0.999839 | + | 0.0179243i | \(0.994294\pi\) | |||||||
\(734\) | 3.83785e8 | − | 2.21579e8i | 0.970511 | − | 0.560325i | ||||
\(735\) | −7.53126e7 | −0.189673 | ||||||||
\(736\) | −4.77814e8 | + | 2.75866e8i | −1.19847 | + | 0.691935i | ||||
\(737\) | −1.35091e8 | − | 2.33984e8i | −0.337461 | − | 0.584499i | ||||
\(738\) | 1.08654e8 | + | 6.27313e7i | 0.270318 | + | 0.156068i | ||||
\(739\) | 1.54801e8i | 0.383566i | 0.981437 | + | 0.191783i | \(0.0614270\pi\) | ||||
−0.981437 | + | 0.191783i | \(0.938573\pi\) | |||||||
\(740\) | −5.85237e7 | + | 1.01366e8i | −0.144423 | + | 0.250148i | ||||
\(741\) | 2.52662e8 | + | 4.37624e8i | 0.620992 | + | 1.07559i | ||||
\(742\) | 4.79179e8 | 1.17297 | ||||||||
\(743\) | 4.48460e7 | − | 2.58918e7i | 0.109334 | − | 0.0631243i | −0.444336 | − | 0.895860i | \(-0.646560\pi\) |
0.553670 | + | 0.832736i | \(0.313227\pi\) | |||||||
\(744\) | −9.76842e7 | + | 1.69194e8i | −0.237195 | + | 0.410834i | ||||
\(745\) | 4.00423e7 | − | 6.93553e7i | 0.0968390 | − | 0.167730i | ||||
\(746\) | −4.13310e8 | + | 7.15875e8i | −0.995543 | + | 1.72433i | ||||
\(747\) | 1.04882e8 | 0.251616 | ||||||||
\(748\) | 4.10690e7 | − | 7.11337e7i | 0.0981318 | − | 0.169969i | ||||
\(749\) | 8.27055e8 | + | 4.77500e8i | 1.96829 | + | 1.13639i | ||||
\(750\) | 1.65807e8 | − | 9.57287e7i | 0.393024 | − | 0.226913i | ||||
\(751\) | −4.08165e8 | + | 2.35654e8i | −0.963643 | + | 0.556360i | −0.897292 | − | 0.441437i | \(-0.854469\pi\) |
−0.0663509 | + | 0.997796i | \(0.521136\pi\) | |||||||
\(752\) | −7.90621e8 | −1.85915 | ||||||||
\(753\) | − | 2.96308e8i | − | 0.693998i | ||||||
\(754\) | −4.28301e8 | − | 7.41839e8i | −0.999160 | − | 1.73060i | ||||
\(755\) | 2.42762e7 | + | 4.20476e7i | 0.0564079 | + | 0.0977013i | ||||
\(756\) | −1.44256e8 | + | 2.49858e8i | −0.333863 | + | 0.578267i | ||||
\(757\) | −4.96517e8 | − | 2.86664e8i | −1.14458 | − | 0.660824i | −0.197020 | − | 0.980400i | \(-0.563126\pi\) |
−0.947561 | + | 0.319576i | \(0.896460\pi\) | |||||||
\(758\) | 2.02651e8i | 0.465308i | ||||||||
\(759\) | 2.20439e8 | + | 1.27271e8i | 0.504155 | + | 0.291074i | ||||
\(760\) | −1.41965e8 | − | 8.19637e7i | −0.323401 | − | 0.186716i | ||||
\(761\) | −1.77053e7 | − | 1.02222e7i | −0.0401744 | − | 0.0231947i | 0.479778 | − | 0.877390i | \(-0.340717\pi\) |
−0.519953 | + | 0.854195i | \(0.674050\pi\) | |||||||
\(762\) | 6.18763e7 | + | 1.07173e8i | 0.139849 | + | 0.242226i | ||||
\(763\) | − | 1.07514e9i | − | 2.42043i | ||||||
\(764\) | −2.12920e8 | + | 1.22929e8i | −0.477459 | + | 0.275661i | ||||
\(765\) | −5.08386e7 | − | 2.93517e7i | −0.113556 | − | 0.0655615i | ||||
\(766\) | −3.37706e7 | −0.0751368 | ||||||||
\(767\) | 5.96723e8 | − | 1.03355e9i | 1.32247 | − | 2.29059i | ||||
\(768\) | 2.48194e8 | − | 1.43295e8i | 0.547909 | − | 0.316335i | ||||
\(769\) | 9.31984e7 | + | 1.61424e8i | 0.204941 | + | 0.354969i | 0.950114 | − | 0.311903i | \(-0.100966\pi\) |
−0.745173 | + | 0.666871i | \(0.767633\pi\) | |||||||
\(770\) | − | 2.39162e8i | − | 0.523866i | ||||||
\(771\) | 7.77280e6 | + | 1.34629e7i | 0.0169596 | + | 0.0293748i | ||||
\(772\) | 8.41237e7 | 0.182838 | ||||||||
\(773\) | − | 2.80646e8i | − | 0.607603i | −0.952735 | − | 0.303802i | \(-0.901744\pi\) | ||
0.952735 | − | 0.303802i | \(-0.0982560\pi\) | |||||||
\(774\) | −4.08328e7 | + | 4.19139e8i | −0.0880616 | + | 0.903932i | ||||
\(775\) | −6.31315e8 | −1.35625 | ||||||||
\(776\) | 8.27933e6i | 0.0177178i | ||||||||
\(777\) | 4.15135e8 | − | 2.39679e8i | 0.884966 | − | 0.510935i | ||||
\(778\) | −6.38598e8 | −1.35609 | ||||||||
\(779\) | −2.37231e8 | + | 1.36965e8i | −0.501833 | + | 0.289733i | ||||
\(780\) | 3.56974e7 | + | 6.18296e7i | 0.0752233 | + | 0.130291i | ||||
\(781\) | 2.52617e8 | + | 1.45849e8i | 0.530285 | + | 0.306160i | ||||
\(782\) | − | 3.94870e8i | − | 0.825722i | ||||||
\(783\) | −2.42945e8 | + | 4.20792e8i | −0.506083 | + | 0.876562i | ||||
\(784\) | −2.88587e8 | − | 4.99848e8i | −0.598865 | − | 1.03726i | ||||
\(785\) | 2.12004e8 | 0.438263 | ||||||||
\(786\) | −3.90364e8 | + | 2.25377e8i | −0.803901 | + | 0.464132i | ||||
\(787\) | 1.74237e8 | − | 3.01787e8i | 0.357451 | − | 0.619123i | −0.630084 | − | 0.776527i | \(-0.716979\pi\) |
0.987534 | + | 0.157405i | \(0.0503127\pi\) | |||||||
\(788\) | −1.27154e8 | + | 2.20236e8i | −0.259866 | + | 0.450101i | ||||
\(789\) | −3.81360e7 | + | 6.60535e7i | −0.0776433 | + | 0.134482i | ||||
\(790\) | 7.68324e7 | 0.155834 | ||||||||
\(791\) | 2.04196e8 | − | 3.53678e8i | 0.412590 | − | 0.714626i | ||||
\(792\) | 1.43947e8 | + | 8.31081e7i | 0.289753 | + | 0.167289i | ||||
\(793\) | −6.62116e8 | + | 3.82273e8i | −1.32774 | + | 0.766573i | ||||
\(794\) | 7.33662e8 | − | 4.23580e8i | 1.46566 | − | 0.846201i | ||||
\(795\) | −6.72603e7 | −0.133862 | ||||||||
\(796\) | − | 3.86913e8i | − | 0.767140i | ||||||
\(797\) | 2.57297e8 | + | 4.45651e8i | 0.508229 | + | 0.880278i | 0.999955 | + | 0.00952803i | \(0.00303291\pi\) |
−0.491726 | + | 0.870750i | \(0.663634\pi\) | |||||||
\(798\) | −3.83266e8 | − | 6.63836e8i | −0.754209 | − | 1.30633i | ||||
\(799\) | 1.77151e8 | − | 3.06834e8i | 0.347298 | − | 0.601538i | ||||
\(800\) | 3.66316e8 | + | 2.11493e8i | 0.715461 | + | 0.413072i | ||||
\(801\) | 1.40295e8i | 0.272988i | ||||||||
\(802\) | 2.83592e8 | + | 1.63732e8i | 0.549757 | + | 0.317402i | ||||
\(803\) | −8.62899e7 | − | 4.98195e7i | −0.166653 | − | 0.0962172i | ||||
\(804\) | −1.05955e8 | − | 6.11729e7i | −0.203869 | − | 0.117704i | ||||
\(805\) | −1.99898e8 | − | 3.46234e8i | −0.383196 | − | 0.663716i | ||||
\(806\) | − | 1.47051e9i | − | 2.80842i | ||||||
\(807\) | 1.52436e8 | − | 8.80089e7i | 0.290046 | − | 0.167458i | ||||
\(808\) | −714639. | − | 412597.i | −0.00135473 | − | 0.000782154i | ||||
\(809\) | −6.98727e8 | −1.31966 | −0.659830 | − | 0.751415i | \(-0.729372\pi\) | ||||
−0.659830 | + | 0.751415i | \(0.729372\pi\) | |||||||
\(810\) | −3.42260e7 | + | 5.92813e7i | −0.0644023 | + | 0.111548i | ||||
\(811\) | 7.42276e8 | − | 4.28553e8i | 1.39156 | − | 0.803419i | 0.398074 | − | 0.917353i | \(-0.369679\pi\) |
0.993488 | + | 0.113934i | \(0.0363453\pi\) | |||||||
\(812\) | 2.25916e8 | + | 3.91297e8i | 0.421967 | + | 0.730868i | ||||
\(813\) | − | 2.78461e8i | − | 0.518194i | ||||||
\(814\) | 3.72601e8 | + | 6.45363e8i | 0.690829 | + | 1.19655i | ||||
\(815\) | −1.16554e8 | −0.215305 | ||||||||
\(816\) | 1.63453e8i | 0.300831i | ||||||||
\(817\) | −7.47954e8 | − | 5.34777e8i | −1.37154 | − | 0.980633i | ||||
\(818\) | −1.07888e9 | −1.97113 | ||||||||
\(819\) | 8.04771e8i | 1.46494i | ||||||||
\(820\) | −3.35172e7 | + | 1.93511e7i | −0.0607891 | + | 0.0350966i | ||||
\(821\) | 7.29011e8 | 1.31736 | 0.658681 | − | 0.752423i | \(-0.271115\pi\) | ||||
0.658681 | + | 0.752423i | \(0.271115\pi\) | |||||||
\(822\) | 2.42932e8 | − | 1.40257e8i | 0.437390 | − | 0.252527i | ||||
\(823\) | −3.19420e8 | − | 5.53252e8i | −0.573011 | − | 0.992484i | −0.996255 | − | 0.0864682i | \(-0.972442\pi\) |
0.423244 | − | 0.906016i | \(-0.360891\pi\) | |||||||
\(824\) | 1.88042e8 | + | 1.08566e8i | 0.336104 | + | 0.194050i | ||||
\(825\) | − | 1.95144e8i | − | 0.347531i | ||||||
\(826\) | −9.05175e8 | + | 1.56781e9i | −1.60617 | + | 2.78197i | ||||
\(827\) | −1.75383e7 | − | 3.03773e7i | −0.0310078 | − | 0.0537072i | 0.850105 | − | 0.526613i | \(-0.176538\pi\) |
−0.881113 | + | 0.472906i | \(0.843205\pi\) | |||||||
\(828\) | −3.17250e8 | −0.558870 | ||||||||
\(829\) | 2.51161e8 | − | 1.45008e8i | 0.440848 | − | 0.254523i | −0.263110 | − | 0.964766i | \(-0.584748\pi\) |
0.703957 | + | 0.710243i | \(0.251415\pi\) | |||||||
\(830\) | −4.65217e7 | + | 8.05780e7i | −0.0813620 | + | 0.140923i | ||||
\(831\) | −6.14935e7 | + | 1.06510e8i | −0.107158 | + | 0.185604i | ||||
\(832\) | 2.05524e7 | − | 3.55978e7i | 0.0356856 | − | 0.0618092i | ||||
\(833\) | 2.58650e8 | 0.447483 | ||||||||
\(834\) | 1.07072e8 | − | 1.85454e8i | 0.184577 | − | 0.319697i | ||||
\(835\) | −1.34430e8 | − | 7.76134e7i | −0.230907 | − | 0.133314i | ||||
\(836\) | 3.58850e8 | − | 2.07182e8i | 0.614177 | − | 0.354595i | ||||
\(837\) | −7.22364e8 | + | 4.17057e8i | −1.23191 | + | 0.711245i | ||||
\(838\) | 1.22837e7 | 0.0208735 | ||||||||
\(839\) | 4.62908e8i | 0.783806i | 0.920007 | + | 0.391903i | \(0.128183\pi\) | ||||
−0.920007 | + | 0.391903i | \(0.871817\pi\) | |||||||
\(840\) | 4.74258e7 | + | 8.21438e7i | 0.0800159 | + | 0.138592i | ||||
\(841\) | 8.30583e7 | + | 1.43861e8i | 0.139635 | + | 0.241855i | ||||
\(842\) | −6.01707e8 | + | 1.04219e9i | −1.00797 | + | 1.74586i | ||||
\(843\) | 2.24905e7 | + | 1.29849e7i | 0.0375419 | + | 0.0216748i | ||||
\(844\) | − | 2.09723e8i | − | 0.348833i | ||||||
\(845\) | 2.07410e8 | + | 1.19748e8i | 0.343764 | + | 0.198472i | ||||
\(846\) | −7.08947e8 | − | 4.09311e8i | −1.17085 | − | 0.675993i | ||||
\(847\) | 2.78014e8 | + | 1.60511e8i | 0.457526 | + | 0.264153i | ||||
\(848\) | −2.57732e8 | − | 4.46405e8i | −0.422650 | − | 0.732051i | ||||
\(849\) | 4.71906e8i | 0.771139i | ||||||||
\(850\) | −2.62169e8 | + | 1.51364e8i | −0.426899 | + | 0.246470i | ||||
\(851\) | 1.07883e9 | + | 6.22860e8i | 1.75050 | + | 1.01065i | ||||
\(852\) | 1.32089e8 | 0.213573 | ||||||||
\(853\) | 72047.7 | − | 124790.i | 0.000116084 | − | 0.000201064i | −0.865967 | − | 0.500101i | \(-0.833296\pi\) |
0.866083 | + | 0.499899i | \(0.166630\pi\) | |||||||
\(854\) | 1.00437e9 | − | 5.79873e8i | 1.61258 | − | 0.931021i | ||||
\(855\) | −1.48071e8 | − | 2.56467e8i | −0.236904 | − | 0.410330i | ||||
\(856\) | − | 5.88803e8i | − | 0.938748i | ||||||
\(857\) | 1.83561e8 | + | 3.17937e8i | 0.291634 | + | 0.505124i | 0.974196 | − | 0.225703i | \(-0.0724678\pi\) |
−0.682562 | + | 0.730827i | \(0.739135\pi\) | |||||||
\(858\) | 4.54546e8 | 0.719641 | ||||||||
\(859\) | 1.21800e8i | 0.192162i | 0.995374 | + | 0.0960811i | \(0.0306308\pi\) | ||||
−0.995374 | + | 0.0960811i | \(0.969369\pi\) | |||||||
\(860\) | −1.05675e8 | − | 7.55558e7i | −0.166140 | − | 0.118788i | ||||
\(861\) | 1.58502e8 | 0.248327 | ||||||||
\(862\) | 1.18125e9i | 1.84425i | ||||||||
\(863\) | 1.38254e8 | − | 7.98207e7i | 0.215102 | − | 0.124189i | −0.388578 | − | 0.921416i | \(-0.627034\pi\) |
0.603680 | + | 0.797227i | \(0.293700\pi\) | |||||||
\(864\) | 5.58863e8 | 0.866491 | ||||||||
\(865\) | 1.11437e8 | − | 6.43380e7i | 0.172179 | − | 0.0994075i | ||||
\(866\) | −2.32724e8 | − | 4.03090e8i | −0.358334 | − | 0.620652i | ||||
\(867\) | 2.27928e8 | + | 1.31594e8i | 0.349736 | + | 0.201920i | ||||
\(868\) | 7.75648e8i | 1.18606i | ||||||||
\(869\) | 8.50478e7 | − | 1.47307e8i | 0.129600 | − | 0.224473i | ||||
\(870\) | −9.11948e7 | − | 1.57954e8i | −0.138488 | − | 0.239868i | ||||
\(871\) | −8.06531e8 | −1.22058 | ||||||||
\(872\) | −5.74069e8 | + | 3.31439e8i | −0.865794 | + | 0.499866i | ||||
\(873\) | −7.47849e6 | + | 1.29531e7i | −0.0112401 | + | 0.0194685i | ||||
\(874\) | 9.96005e8 | − | 1.72513e9i | 1.49186 | − | 2.58397i | ||||
\(875\) | −3.32867e8 | + | 5.76543e8i | −0.496875 | + | 0.860613i | ||||
\(876\) | −4.51194e7 | −0.0671198 | ||||||||
\(877\) | −5.41886e8 | + | 9.38573e8i | −0.803357 | + | 1.39146i | 0.114037 | + | 0.993477i | \(0.463622\pi\) |
−0.917394 | + | 0.397979i | \(0.869712\pi\) | |||||||
\(878\) | −1.93797e8 | − | 1.11889e8i | −0.286328 | − | 0.165311i | ||||
\(879\) | −3.63207e8 | + | 2.09698e8i | −0.534795 | + | 0.308764i | ||||
\(880\) | −2.22804e8 | + | 1.28636e8i | −0.326945 | + | 0.188762i | ||||
\(881\) | −6.34879e8 | −0.928460 | −0.464230 | − | 0.885715i | \(-0.653669\pi\) | ||||
−0.464230 | + | 0.885715i | \(0.653669\pi\) | |||||||
\(882\) | − | 5.97616e8i | − | 0.870996i | ||||||
\(883\) | 2.06016e8 | + | 3.56830e8i | 0.299239 | + | 0.518297i | 0.975962 | − | 0.217941i | \(-0.0699339\pi\) |
−0.676723 | + | 0.736238i | \(0.736601\pi\) | |||||||
\(884\) | −1.22597e8 | − | 2.12344e8i | −0.177469 | − | 0.307386i | ||||
\(885\) | 1.27055e8 | − | 2.20066e8i | 0.183300 | − | 0.317486i | ||||
\(886\) | 9.14326e8 | + | 5.27886e8i | 1.31462 | + | 0.758995i | ||||
\(887\) | − | 9.31313e8i | − | 1.33452i | −0.744825 | − | 0.667260i | \(-0.767467\pi\) | ||
0.744825 | − | 0.667260i | \(-0.232533\pi\) | |||||||
\(888\) | −2.55951e8 | − | 1.47773e8i | −0.365525 | − | 0.211036i | ||||
\(889\) | −3.72661e8 | − | 2.15156e8i | −0.530406 | − | 0.306230i | ||||
\(890\) | −1.07785e8 | − | 6.22296e7i | −0.152893 | − | 0.0882728i | ||||
\(891\) | 7.57714e7 | + | 1.31240e8i | 0.107120 | + | 0.185538i | ||||
\(892\) | − | 7.00588e6i | − | 0.00987116i | ||||||
\(893\) | 1.54789e9 | − | 8.93676e8i | 2.17363 | − | 1.25495i | ||||
\(894\) | −1.99952e8 | − | 1.15442e8i | −0.279842 | − | 0.161567i | ||||
\(895\) | 3.11102e8 | 0.433943 | ||||||||
\(896\) | −5.18600e8 | + | 8.98242e8i | −0.720956 | + | 1.24873i | ||||
\(897\) | 6.58044e8 | − | 3.79922e8i | 0.911754 | − | 0.526402i | ||||
\(898\) | −2.41163e8 | − | 4.17706e8i | −0.333028 | − | 0.576822i | ||||
\(899\) | 1.30629e9i | 1.79788i | ||||||||
\(900\) | 1.21610e8 | + | 2.10634e8i | 0.166817 | + | 0.288936i | ||||
\(901\) | 2.30995e8 | 0.315812 | ||||||||
\(902\) | 2.46404e8i | 0.335760i | ||||||||
\(903\) | 2.20083e8 | + | 4.84366e8i | 0.298898 | + | 0.657825i | ||||
\(904\) | −2.51793e8 | −0.340831 | ||||||||
\(905\) | 2.16284e8i | 0.291795i | ||||||||
\(906\) | 1.21223e8 | − | 6.99883e7i | 0.163005 | − | 0.0941112i | ||||
\(907\) | 6.76391e8 | 0.906518 | 0.453259 | − | 0.891379i | \(-0.350261\pi\) | ||||
0.453259 | + | 0.891379i | \(0.350261\pi\) | |||||||
\(908\) | 1.35830e8 | − | 7.84217e7i | 0.181443 | − | 0.104756i | ||||
\(909\) | −745375. | − | 1.29103e6i | −0.000992392 | − | 0.00171887i | ||||
\(910\) | −6.18285e8 | − | 3.56967e8i | −0.820473 | − | 0.473700i | ||||
\(911\) | 5.80485e8i | 0.767778i | 0.923379 | + | 0.383889i | \(0.125416\pi\) | ||||
−0.923379 | + | 0.383889i | \(0.874584\pi\) | |||||||
\(912\) | −4.12288e8 | + | 7.14104e8i | −0.543521 | + | 0.941405i | ||||
\(913\) | 1.02992e8 | + | 1.78388e8i | 0.135329 | + | 0.234398i | ||||
\(914\) | −3.21266e8 | −0.420752 | ||||||||
\(915\) | −1.40979e8 | + | 8.13943e7i | −0.184031 | + | 0.106250i | ||||
\(916\) | 1.14718e8 | − | 1.98697e8i | 0.149260 | − | 0.258527i | ||||
\(917\) | 7.83679e8 | − | 1.35737e9i | 1.01632 | − | 1.76032i | ||||
\(918\) | −1.99987e8 | + | 3.46387e8i | −0.258507 | + | 0.447748i | ||||
\(919\) | −3.07516e8 | −0.396206 | −0.198103 | − | 0.980181i | \(-0.563478\pi\) | ||||
−0.198103 | + | 0.980181i | \(0.563478\pi\) | |||||||
\(920\) | −1.23247e8 | + | 2.13470e8i | −0.158275 | + | 0.274140i | ||||
\(921\) | 3.43939e8 | + | 1.98573e8i | 0.440253 | + | 0.254180i | ||||
\(922\) | 3.30098e8 | − | 1.90582e8i | 0.421163 | − | 0.243159i | ||||
\(923\) | 7.54099e8 | − | 4.35379e8i | 0.959010 | − | 0.553685i | ||||
\(924\) | −2.39759e8 | −0.303920 | ||||||||
\(925\) | − | 9.55031e8i | − | 1.20668i | ||||||
\(926\) | −1.70255e8 | − | 2.94890e8i | −0.214421 | − | 0.371387i | ||||
\(927\) | 1.96130e8 | + | 3.39707e8i | 0.246209 | + | 0.426447i | ||||
\(928\) | 4.37611e8 | − | 7.57965e8i | 0.547576 | − | 0.948429i | ||||
\(929\) | −6.57149e8 | − | 3.79405e8i | −0.819628 | − | 0.473212i | 0.0306604 | − | 0.999530i | \(-0.490239\pi\) |
−0.850288 | + | 0.526318i | \(0.823572\pi\) | |||||||
\(930\) | − | 3.13104e8i | − | 0.389260i | ||||||
\(931\) | 1.13000e9 | + | 6.52408e8i | 1.40033 | + | 0.808482i | ||||
\(932\) | 2.73829e8 | + | 1.58095e8i | 0.338246 | + | 0.195286i | ||||
\(933\) | 7.10533e8 | + | 4.10227e8i | 0.874862 | + | 0.505102i | ||||
\(934\) | 4.92048e8 | + | 8.52252e8i | 0.603903 | + | 1.04599i | ||||
\(935\) | − | 1.15291e8i | − | 0.141046i | ||||||
\(936\) | 4.29704e8 | − | 2.48090e8i | 0.524013 | − | 0.302539i | ||||
\(937\) | −4.52123e8 | − | 2.61034e8i | −0.549589 | − | 0.317305i | 0.199367 | − | 0.979925i | \(-0.436111\pi\) |
−0.748956 | + | 0.662619i | \(0.769445\pi\) | |||||||
\(938\) | 1.22344e9 | 1.48242 | ||||||||
\(939\) | −1.11625e8 | + | 1.93340e8i | −0.134823 | + | 0.233520i | ||||
\(940\) | 2.18694e8 | − | 1.26263e8i | 0.263301 | − | 0.152017i | ||||
\(941\) | 1.67741e7 | + | 2.90535e7i | 0.0201312 | + | 0.0348682i | 0.875915 | − | 0.482465i | \(-0.160258\pi\) |
−0.855784 | + | 0.517333i | \(0.826925\pi\) | |||||||
\(942\) | − | 6.11208e8i | − | 0.731201i | ||||||
\(943\) | 2.05952e8 | + | 3.56718e8i | 0.245601 | + | 0.425393i | ||||
\(944\) | 1.94743e9 | 2.31498 | ||||||||
\(945\) | 4.04963e8i | 0.479866i | ||||||||
\(946\) | −7.52988e8 | + | 3.42138e8i | −0.889436 | + | 0.404136i | ||||
\(947\) | −6.02282e8 | −0.709169 | −0.354584 | − | 0.935024i | \(-0.615378\pi\) | ||||
−0.354584 | + | 0.935024i | \(0.615378\pi\) | |||||||
\(948\) | − | 7.70242e7i | − | 0.0904070i | ||||||
\(949\) | −2.57588e8 | + | 1.48718e8i | −0.301389 | + | 0.174007i | ||||
\(950\) | −1.52717e9 | −1.78122 | ||||||||
\(951\) | 2.39801e8 | − | 1.38449e8i | 0.278811 | − | 0.160971i | ||||
\(952\) | −1.62877e8 | − | 2.82110e8i | −0.188776 | − | 0.326970i | ||||
\(953\) | −1.24355e9 | − | 7.17965e8i | −1.43676 | − | 0.829515i | −0.439139 | − | 0.898419i | \(-0.644717\pi\) |
−0.997623 | + | 0.0689036i | \(0.978050\pi\) | |||||||
\(954\) | − | 5.33720e8i | − | 0.614707i | ||||||
\(955\) | −1.72547e8 | + | 2.98861e8i | −0.198106 | + | 0.343130i | ||||
\(956\) | −2.25166e8 | − | 3.89998e8i | −0.257708 | − | 0.446364i | ||||
\(957\) | −4.03784e8 | −0.460694 | ||||||||
\(958\) | 1.01938e8 | − | 5.88539e7i | 0.115942 | − | 0.0669389i | ||||
\(959\) | −4.87700e8 | + | 8.44721e8i | −0.552964 | + | 0.957762i | ||||
\(960\) | 4.37606e6 | − | 7.57956e6i | 0.00494618 | − | 0.00856703i | ||||
\(961\) | −6.77485e8 | + | 1.17344e9i | −0.763360 | + | 1.32218i | ||||
\(962\) | 2.22453e9 | 2.49870 | ||||||||
\(963\) | 5.31850e8 | − | 9.21191e8i | 0.595539 | − | 1.03150i | ||||
\(964\) | −2.29525e8 | − | 1.32516e8i | −0.256211 | − | 0.147924i | ||||
\(965\) | 1.02259e8 | − | 5.90392e7i | 0.113794 | − | 0.0656990i | ||||
\(966\) | −9.98194e8 | + | 5.76308e8i | −1.10735 | + | 0.639327i | ||||
\(967\) | 5.47535e8 | 0.605526 | 0.302763 | − | 0.953066i | \(-0.402091\pi\) | ||||
0.302763 | + | 0.953066i | \(0.402091\pi\) | |||||||
\(968\) | − | 1.97926e8i | − | 0.218211i | ||||||
\(969\) | −1.84759e8 | − | 3.20012e8i | −0.203065 | − | 0.351718i | ||||
\(970\) | −6.63436e6 | − | 1.14911e7i | −0.00726916 | − | 0.0125905i | ||||
\(971\) | 4.36070e8 | − | 7.55296e8i | 0.476320 | − | 0.825010i | −0.523312 | − | 0.852141i | \(-0.675304\pi\) |
0.999632 | + | 0.0271309i | \(0.00863709\pi\) | |||||||
\(972\) | 4.38838e8 | + | 2.53363e8i | 0.477865 | + | 0.275896i | ||||
\(973\) | 7.44621e8i | 0.808345i | ||||||||
\(974\) | −1.38792e9 | − | 8.01315e8i | −1.50206 | − | 0.867215i | ||||
\(975\) | −5.04489e8 | − | 2.91267e8i | −0.544300 | − | 0.314252i | ||||
\(976\) | −1.08042e9 | − | 6.23783e8i | −1.16210 | − | 0.670940i | ||||
\(977\) | −8.00380e8 | − | 1.38630e9i | −0.858247 | − | 1.48653i | −0.873600 | − | 0.486646i | \(-0.838220\pi\) |
0.0153524 | − | 0.999882i | \(-0.495113\pi\) | |||||||
\(978\) | 3.36025e8i | 0.359215i | ||||||||
\(979\) | −2.38620e8 | + | 1.37767e8i | −0.254307 | + | 0.146824i | ||||
\(980\) | 1.59652e8 | + | 9.21753e7i | 0.169628 | + | 0.0979347i | ||||
\(981\) | −1.19752e9 | −1.26846 | ||||||||
\(982\) | 3.19366e8 | − | 5.53157e8i | 0.337251 | − | 0.584136i | ||||
\(983\) | −3.30230e8 | + | 1.90658e8i | −0.347661 | + | 0.200722i | −0.663655 | − | 0.748039i | \(-0.730996\pi\) |
0.315994 | + | 0.948761i | \(0.397662\pi\) | |||||||
\(984\) | −4.88619e7 | − | 8.46313e7i | −0.0512844 | − | 0.0888271i | ||||
\(985\) | 3.56953e8i | 0.373510i | ||||||||
\(986\) | 3.13194e8 | + | 5.42469e8i | 0.326726 | + | 0.565906i | ||||
\(987\) | −1.03420e9 | −1.07560 | ||||||||
\(988\) | − | 1.23694e9i | − | 1.28256i | ||||||
\(989\) | −8.04130e8 | + | 1.12468e9i | −0.831261 | + | 1.16263i | ||||
\(990\) | −2.66384e8 | −0.274538 | ||||||||
\(991\) | 8.04753e8i | 0.826878i | 0.910532 | + | 0.413439i | \(0.135673\pi\) | ||||
−0.910532 | + | 0.413439i | \(0.864327\pi\) | |||||||
\(992\) | 1.30118e9 | − | 7.51237e8i | 1.33291 | − | 0.769559i | ||||
\(993\) | 9.08121e8 | 0.927461 | ||||||||
\(994\) | −1.14390e9 | + | 6.60431e8i | −1.16474 | + | 0.672463i | ||||
\(995\) | −2.71542e8 | − | 4.70324e8i | −0.275656 | − | 0.477450i | ||||
\(996\) | 8.07791e7 | + | 4.66378e7i | 0.0817563 | + | 0.0472020i | ||||
\(997\) | 1.09647e9i | 1.10640i | 0.833048 | + | 0.553201i | \(0.186594\pi\) | ||||
−0.833048 | + | 0.553201i | \(0.813406\pi\) | |||||||
\(998\) | −7.51175e7 | + | 1.30107e8i | −0.0755700 | + | 0.130891i | ||||
\(999\) | −6.30910e8 | − | 1.09277e9i | −0.632806 | − | 1.09605i |
(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 | 43.7.d.a.7.17 | ✓ | 42 | |
43.37 | odd | 6 | inner | 43.7.d.a.37.5 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.17 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.7.d.a.37.5 | yes | 42 | 43.37 | odd | 6 | inner |