Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,5,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), 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: | \(1.03369963084\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.7 |
Dual form | 10.5.c.b.3.1 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 2.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.00000 | − | 1.00000i | 0.111111 | − | 0.111111i | −0.649365 | − | 0.760477i | \(-0.724965\pi\) |
0.760477 | + | 0.649365i | \(0.224965\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | −15.0000 | − | 20.0000i | −0.600000 | − | 0.800000i | ||||
\(6\) | 4.00000 | 0.111111 | ||||||||
\(7\) | −19.0000 | − | 19.0000i | −0.387755 | − | 0.387755i | 0.486131 | − | 0.873886i | \(-0.338408\pi\) |
−0.873886 | + | 0.486131i | \(0.838408\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 79.0000i | 0.975309i | ||||||||
\(10\) | 10.0000 | − | 70.0000i | 0.100000 | − | 0.700000i | ||||
\(11\) | 202.000 | 1.66942 | 0.834711 | − | 0.550689i | \(-0.185635\pi\) | ||||
0.834711 | + | 0.550689i | \(0.185635\pi\) | |||||||
\(12\) | 8.00000 | + | 8.00000i | 0.0555556 | + | 0.0555556i | ||||
\(13\) | −99.0000 | + | 99.0000i | −0.585799 | + | 0.585799i | −0.936491 | − | 0.350692i | \(-0.885946\pi\) |
0.350692 | + | 0.936491i | \(0.385946\pi\) | |||||||
\(14\) | − | 76.0000i | − | 0.387755i | ||||||
\(15\) | −35.0000 | − | 5.00000i | −0.155556 | − | 0.0222222i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −239.000 | − | 239.000i | −0.826990 | − | 0.826990i | 0.160110 | − | 0.987099i | \(-0.448815\pi\) |
−0.987099 | + | 0.160110i | \(0.948815\pi\) | |||||||
\(18\) | −158.000 | + | 158.000i | −0.487654 | + | 0.487654i | ||||
\(19\) | 40.0000i | 0.110803i | 0.998464 | + | 0.0554017i | \(0.0176439\pi\) | ||||
−0.998464 | + | 0.0554017i | \(0.982356\pi\) | |||||||
\(20\) | 160.000 | − | 120.000i | 0.400000 | − | 0.300000i | ||||
\(21\) | −38.0000 | −0.0861678 | ||||||||
\(22\) | 404.000 | + | 404.000i | 0.834711 | + | 0.834711i | ||||
\(23\) | 541.000 | − | 541.000i | 1.02268 | − | 1.02268i | 0.0229476 | − | 0.999737i | \(-0.492695\pi\) |
0.999737 | − | 0.0229476i | \(-0.00730510\pi\) | |||||||
\(24\) | 32.0000i | 0.0555556i | ||||||||
\(25\) | −175.000 | + | 600.000i | −0.280000 | + | 0.960000i | ||||
\(26\) | −396.000 | −0.585799 | ||||||||
\(27\) | 160.000 | + | 160.000i | 0.219479 | + | 0.219479i | ||||
\(28\) | 152.000 | − | 152.000i | 0.193878 | − | 0.193878i | ||||
\(29\) | − | 200.000i | − | 0.237812i | −0.992906 | − | 0.118906i | \(-0.962061\pi\) | ||
0.992906 | − | 0.118906i | \(-0.0379387\pi\) | |||||||
\(30\) | −60.0000 | − | 80.0000i | −0.0666667 | − | 0.0888889i | ||||
\(31\) | −758.000 | −0.788762 | −0.394381 | − | 0.918947i | \(-0.629041\pi\) | ||||
−0.394381 | + | 0.918947i | \(0.629041\pi\) | |||||||
\(32\) | −128.000 | − | 128.000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 202.000 | − | 202.000i | 0.185491 | − | 0.185491i | ||||
\(34\) | − | 956.000i | − | 0.826990i | ||||||
\(35\) | −95.0000 | + | 665.000i | −0.0775510 | + | 0.542857i | ||||
\(36\) | −632.000 | −0.487654 | ||||||||
\(37\) | 141.000 | + | 141.000i | 0.102995 | + | 0.102995i | 0.756726 | − | 0.653732i | \(-0.226797\pi\) |
−0.653732 | + | 0.756726i | \(0.726797\pi\) | |||||||
\(38\) | −80.0000 | + | 80.0000i | −0.0554017 | + | 0.0554017i | ||||
\(39\) | 198.000i | 0.130178i | ||||||||
\(40\) | 560.000 | + | 80.0000i | 0.350000 | + | 0.0500000i | ||||
\(41\) | 1042.00 | 0.619869 | 0.309935 | − | 0.950758i | \(-0.399693\pi\) | ||||
0.309935 | + | 0.950758i | \(0.399693\pi\) | |||||||
\(42\) | −76.0000 | − | 76.0000i | −0.0430839 | − | 0.0430839i | ||||
\(43\) | −759.000 | + | 759.000i | −0.410492 | + | 0.410492i | −0.881910 | − | 0.471418i | \(-0.843742\pi\) |
0.471418 | + | 0.881910i | \(0.343742\pi\) | |||||||
\(44\) | 1616.00i | 0.834711i | ||||||||
\(45\) | 1580.00 | − | 1185.00i | 0.780247 | − | 0.585185i | ||||
\(46\) | 2164.00 | 1.02268 | ||||||||
\(47\) | −459.000 | − | 459.000i | −0.207786 | − | 0.207786i | 0.595540 | − | 0.803326i | \(-0.296938\pi\) |
−0.803326 | + | 0.595540i | \(0.796938\pi\) | |||||||
\(48\) | −64.0000 | + | 64.0000i | −0.0277778 | + | 0.0277778i | ||||
\(49\) | − | 1679.00i | − | 0.699292i | ||||||
\(50\) | −1550.00 | + | 850.000i | −0.620000 | + | 0.340000i | ||||
\(51\) | −478.000 | −0.183775 | ||||||||
\(52\) | −792.000 | − | 792.000i | −0.292899 | − | 0.292899i | ||||
\(53\) | −1819.00 | + | 1819.00i | −0.647561 | + | 0.647561i | −0.952403 | − | 0.304842i | \(-0.901396\pi\) |
0.304842 | + | 0.952403i | \(0.401396\pi\) | |||||||
\(54\) | 640.000i | 0.219479i | ||||||||
\(55\) | −3030.00 | − | 4040.00i | −1.00165 | − | 1.33554i | ||||
\(56\) | 608.000 | 0.193878 | ||||||||
\(57\) | 40.0000 | + | 40.0000i | 0.0123115 | + | 0.0123115i | ||||
\(58\) | 400.000 | − | 400.000i | 0.118906 | − | 0.118906i | ||||
\(59\) | 4600.00i | 1.32146i | 0.750624 | + | 0.660730i | \(0.229753\pi\) | ||||
−0.750624 | + | 0.660730i | \(0.770247\pi\) | |||||||
\(60\) | 40.0000 | − | 280.000i | 0.0111111 | − | 0.0777778i | ||||
\(61\) | 2082.00 | 0.559527 | 0.279764 | − | 0.960069i | \(-0.409744\pi\) | ||||
0.279764 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(62\) | −1516.00 | − | 1516.00i | −0.394381 | − | 0.394381i | ||||
\(63\) | 1501.00 | − | 1501.00i | 0.378181 | − | 0.378181i | ||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 3465.00 | + | 495.000i | 0.820118 | + | 0.117160i | ||||
\(66\) | 808.000 | 0.185491 | ||||||||
\(67\) | 5081.00 | + | 5081.00i | 1.13188 | + | 1.13188i | 0.989865 | + | 0.142013i | \(0.0453575\pi\) |
0.142013 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(68\) | 1912.00 | − | 1912.00i | 0.413495 | − | 0.413495i | ||||
\(69\) | − | 1082.00i | − | 0.227263i | ||||||
\(70\) | −1520.00 | + | 1140.00i | −0.310204 | + | 0.232653i | ||||
\(71\) | −3478.00 | −0.689942 | −0.344971 | − | 0.938613i | \(-0.612111\pi\) | ||||
−0.344971 | + | 0.938613i | \(0.612111\pi\) | |||||||
\(72\) | −1264.00 | − | 1264.00i | −0.243827 | − | 0.243827i | ||||
\(73\) | −3479.00 | + | 3479.00i | −0.652843 | + | 0.652843i | −0.953677 | − | 0.300834i | \(-0.902735\pi\) |
0.300834 | + | 0.953677i | \(0.402735\pi\) | |||||||
\(74\) | 564.000i | 0.102995i | ||||||||
\(75\) | 425.000 | + | 775.000i | 0.0755556 | + | 0.137778i | ||||
\(76\) | −320.000 | −0.0554017 | ||||||||
\(77\) | −3838.00 | − | 3838.00i | −0.647327 | − | 0.647327i | ||||
\(78\) | −396.000 | + | 396.000i | −0.0650888 | + | 0.0650888i | ||||
\(79\) | − | 7680.00i | − | 1.23057i | −0.788304 | − | 0.615286i | \(-0.789041\pi\) | ||
0.788304 | − | 0.615286i | \(-0.210959\pi\) | |||||||
\(80\) | 960.000 | + | 1280.00i | 0.150000 | + | 0.200000i | ||||
\(81\) | −6079.00 | −0.926536 | ||||||||
\(82\) | 2084.00 | + | 2084.00i | 0.309935 | + | 0.309935i | ||||
\(83\) | 6081.00 | − | 6081.00i | 0.882712 | − | 0.882712i | −0.111098 | − | 0.993809i | \(-0.535437\pi\) |
0.993809 | + | 0.111098i | \(0.0354367\pi\) | |||||||
\(84\) | − | 304.000i | − | 0.0430839i | ||||||
\(85\) | −1195.00 | + | 8365.00i | −0.165398 | + | 1.15779i | ||||
\(86\) | −3036.00 | −0.410492 | ||||||||
\(87\) | −200.000 | − | 200.000i | −0.0264236 | − | 0.0264236i | ||||
\(88\) | −3232.00 | + | 3232.00i | −0.417355 | + | 0.417355i | ||||
\(89\) | − | 5680.00i | − | 0.717081i | −0.933514 | − | 0.358541i | \(-0.883274\pi\) | ||
0.933514 | − | 0.358541i | \(-0.116726\pi\) | |||||||
\(90\) | 5530.00 | + | 790.000i | 0.682716 | + | 0.0975309i | ||||
\(91\) | 3762.00 | 0.454293 | ||||||||
\(92\) | 4328.00 | + | 4328.00i | 0.511342 | + | 0.511342i | ||||
\(93\) | −758.000 | + | 758.000i | −0.0876402 | + | 0.0876402i | ||||
\(94\) | − | 1836.00i | − | 0.207786i | ||||||
\(95\) | 800.000 | − | 600.000i | 0.0886427 | − | 0.0664820i | ||||
\(96\) | −256.000 | −0.0277778 | ||||||||
\(97\) | 561.000 | + | 561.000i | 0.0596238 | + | 0.0596238i | 0.736290 | − | 0.676666i | \(-0.236576\pi\) |
−0.676666 | + | 0.736290i | \(0.736576\pi\) | |||||||
\(98\) | 3358.00 | − | 3358.00i | 0.349646 | − | 0.349646i | ||||
\(99\) | 15958.0i | 1.62820i | ||||||||
\(100\) | −4800.00 | − | 1400.00i | −0.480000 | − | 0.140000i | ||||
\(101\) | 1682.00 | 0.164886 | 0.0824429 | − | 0.996596i | \(-0.473728\pi\) | ||||
0.0824429 | + | 0.996596i | \(0.473728\pi\) | |||||||
\(102\) | −956.000 | − | 956.000i | −0.0918877 | − | 0.0918877i | ||||
\(103\) | 7021.00 | − | 7021.00i | 0.661797 | − | 0.661797i | −0.294007 | − | 0.955803i | \(-0.594989\pi\) |
0.955803 | + | 0.294007i | \(0.0949888\pi\) | |||||||
\(104\) | − | 3168.00i | − | 0.292899i | ||||||
\(105\) | 570.000 | + | 760.000i | 0.0517007 | + | 0.0689342i | ||||
\(106\) | −7276.00 | −0.647561 | ||||||||
\(107\) | −2159.00 | − | 2159.00i | −0.188575 | − | 0.188575i | 0.606505 | − | 0.795080i | \(-0.292571\pi\) |
−0.795080 | + | 0.606505i | \(0.792571\pi\) | |||||||
\(108\) | −1280.00 | + | 1280.00i | −0.109739 | + | 0.109739i | ||||
\(109\) | − | 280.000i | − | 0.0235670i | −0.999931 | − | 0.0117835i | \(-0.996249\pi\) | ||
0.999931 | − | 0.0117835i | \(-0.00375090\pi\) | |||||||
\(110\) | 2020.00 | − | 14140.0i | 0.166942 | − | 1.16860i | ||||
\(111\) | 282.000 | 0.0228878 | ||||||||
\(112\) | 1216.00 | + | 1216.00i | 0.0969388 | + | 0.0969388i | ||||
\(113\) | −8479.00 | + | 8479.00i | −0.664030 | + | 0.664030i | −0.956327 | − | 0.292297i | \(-0.905580\pi\) |
0.292297 | + | 0.956327i | \(0.405580\pi\) | |||||||
\(114\) | 160.000i | 0.0123115i | ||||||||
\(115\) | −18935.0 | − | 2705.00i | −1.43176 | − | 0.204537i | ||||
\(116\) | 1600.00 | 0.118906 | ||||||||
\(117\) | −7821.00 | − | 7821.00i | −0.571335 | − | 0.571335i | ||||
\(118\) | −9200.00 | + | 9200.00i | −0.660730 | + | 0.660730i | ||||
\(119\) | 9082.00i | 0.641339i | ||||||||
\(120\) | 640.000 | − | 480.000i | 0.0444444 | − | 0.0333333i | ||||
\(121\) | 26163.0 | 1.78697 | ||||||||
\(122\) | 4164.00 | + | 4164.00i | 0.279764 | + | 0.279764i | ||||
\(123\) | 1042.00 | − | 1042.00i | 0.0688743 | − | 0.0688743i | ||||
\(124\) | − | 6064.00i | − | 0.394381i | ||||||
\(125\) | 14625.0 | − | 5500.00i | 0.936000 | − | 0.352000i | ||||
\(126\) | 6004.00 | 0.378181 | ||||||||
\(127\) | 821.000 | + | 821.000i | 0.0509021 | + | 0.0509021i | 0.732100 | − | 0.681198i | \(-0.238541\pi\) |
−0.681198 | + | 0.732100i | \(0.738541\pi\) | |||||||
\(128\) | 1024.00 | − | 1024.00i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 1518.00i | 0.0912205i | ||||||||
\(130\) | 5940.00 | + | 7920.00i | 0.351479 | + | 0.468639i | ||||
\(131\) | −2198.00 | −0.128081 | −0.0640406 | − | 0.997947i | \(-0.520399\pi\) | ||||
−0.0640406 | + | 0.997947i | \(0.520399\pi\) | |||||||
\(132\) | 1616.00 | + | 1616.00i | 0.0927456 | + | 0.0927456i | ||||
\(133\) | 760.000 | − | 760.000i | 0.0429646 | − | 0.0429646i | ||||
\(134\) | 20324.0i | 1.13188i | ||||||||
\(135\) | 800.000 | − | 5600.00i | 0.0438957 | − | 0.307270i | ||||
\(136\) | 7648.00 | 0.413495 | ||||||||
\(137\) | −9399.00 | − | 9399.00i | −0.500773 | − | 0.500773i | 0.410905 | − | 0.911678i | \(-0.365213\pi\) |
−0.911678 | + | 0.410905i | \(0.865213\pi\) | |||||||
\(138\) | 2164.00 | − | 2164.00i | 0.113632 | − | 0.113632i | ||||
\(139\) | − | 13960.0i | − | 0.722530i | −0.932463 | − | 0.361265i | \(-0.882345\pi\) | ||
0.932463 | − | 0.361265i | \(-0.117655\pi\) | |||||||
\(140\) | −5320.00 | − | 760.000i | −0.271429 | − | 0.0387755i | ||||
\(141\) | −918.000 | −0.0461747 | ||||||||
\(142\) | −6956.00 | − | 6956.00i | −0.344971 | − | 0.344971i | ||||
\(143\) | −19998.0 | + | 19998.0i | −0.977945 | + | 0.977945i | ||||
\(144\) | − | 5056.00i | − | 0.243827i | ||||||
\(145\) | −4000.00 | + | 3000.00i | −0.190250 | + | 0.142687i | ||||
\(146\) | −13916.0 | −0.652843 | ||||||||
\(147\) | −1679.00 | − | 1679.00i | −0.0776991 | − | 0.0776991i | ||||
\(148\) | −1128.00 | + | 1128.00i | −0.0514974 | + | 0.0514974i | ||||
\(149\) | − | 9000.00i | − | 0.405387i | −0.979242 | − | 0.202694i | \(-0.935030\pi\) | ||
0.979242 | − | 0.202694i | \(-0.0649695\pi\) | |||||||
\(150\) | −700.000 | + | 2400.00i | −0.0311111 | + | 0.106667i | ||||
\(151\) | −23798.0 | −1.04373 | −0.521863 | − | 0.853029i | \(-0.674763\pi\) | ||||
−0.521863 | + | 0.853029i | \(0.674763\pi\) | |||||||
\(152\) | −640.000 | − | 640.000i | −0.0277008 | − | 0.0277008i | ||||
\(153\) | 18881.0 | − | 18881.0i | 0.806570 | − | 0.806570i | ||||
\(154\) | − | 15352.0i | − | 0.647327i | ||||||
\(155\) | 11370.0 | + | 15160.0i | 0.473257 | + | 0.631009i | ||||
\(156\) | −1584.00 | −0.0650888 | ||||||||
\(157\) | 29781.0 | + | 29781.0i | 1.20820 | + | 1.20820i | 0.971608 | + | 0.236595i | \(0.0760314\pi\) |
0.236595 | + | 0.971608i | \(0.423969\pi\) | |||||||
\(158\) | 15360.0 | − | 15360.0i | 0.615286 | − | 0.615286i | ||||
\(159\) | 3638.00i | 0.143903i | ||||||||
\(160\) | −640.000 | + | 4480.00i | −0.0250000 | + | 0.175000i | ||||
\(161\) | −20558.0 | −0.793102 | ||||||||
\(162\) | −12158.0 | − | 12158.0i | −0.463268 | − | 0.463268i | ||||
\(163\) | 12641.0 | − | 12641.0i | 0.475780 | − | 0.475780i | −0.427999 | − | 0.903779i | \(-0.640781\pi\) |
0.903779 | + | 0.427999i | \(0.140781\pi\) | |||||||
\(164\) | 8336.00i | 0.309935i | ||||||||
\(165\) | −7070.00 | − | 1010.00i | −0.259688 | − | 0.0370983i | ||||
\(166\) | 24324.0 | 0.882712 | ||||||||
\(167\) | 29981.0 | + | 29981.0i | 1.07501 | + | 1.07501i | 0.996948 | + | 0.0780632i | \(0.0248736\pi\) |
0.0780632 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(168\) | 608.000 | − | 608.000i | 0.0215420 | − | 0.0215420i | ||||
\(169\) | 8959.00i | 0.313679i | ||||||||
\(170\) | −19120.0 | + | 14340.0i | −0.661592 | + | 0.496194i | ||||
\(171\) | −3160.00 | −0.108067 | ||||||||
\(172\) | −6072.00 | − | 6072.00i | −0.205246 | − | 0.205246i | ||||
\(173\) | −4739.00 | + | 4739.00i | −0.158341 | + | 0.158341i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(174\) | − | 800.000i | − | 0.0264236i | ||||||
\(175\) | 14725.0 | − | 8075.00i | 0.480816 | − | 0.263673i | ||||
\(176\) | −12928.0 | −0.417355 | ||||||||
\(177\) | 4600.00 | + | 4600.00i | 0.146829 | + | 0.146829i | ||||
\(178\) | 11360.0 | − | 11360.0i | 0.358541 | − | 0.358541i | ||||
\(179\) | − | 32920.0i | − | 1.02743i | −0.857960 | − | 0.513717i | \(-0.828268\pi\) | ||
0.857960 | − | 0.513717i | \(-0.171732\pi\) | |||||||
\(180\) | 9480.00 | + | 12640.0i | 0.292593 | + | 0.390123i | ||||
\(181\) | −40558.0 | −1.23800 | −0.618998 | − | 0.785392i | \(-0.712461\pi\) | ||||
−0.618998 | + | 0.785392i | \(0.712461\pi\) | |||||||
\(182\) | 7524.00 | + | 7524.00i | 0.227146 | + | 0.227146i | ||||
\(183\) | 2082.00 | − | 2082.00i | 0.0621697 | − | 0.0621697i | ||||
\(184\) | 17312.0i | 0.511342i | ||||||||
\(185\) | 705.000 | − | 4935.00i | 0.0205990 | − | 0.144193i | ||||
\(186\) | −3032.00 | −0.0876402 | ||||||||
\(187\) | −48278.0 | − | 48278.0i | −1.38059 | − | 1.38059i | ||||
\(188\) | 3672.00 | − | 3672.00i | 0.103893 | − | 0.103893i | ||||
\(189\) | − | 6080.00i | − | 0.170208i | ||||||
\(190\) | 2800.00 | + | 400.000i | 0.0775623 | + | 0.0110803i | ||||
\(191\) | 33002.0 | 0.904635 | 0.452318 | − | 0.891857i | \(-0.350597\pi\) | ||||
0.452318 | + | 0.891857i | \(0.350597\pi\) | |||||||
\(192\) | −512.000 | − | 512.000i | −0.0138889 | − | 0.0138889i | ||||
\(193\) | −23199.0 | + | 23199.0i | −0.622809 | + | 0.622809i | −0.946249 | − | 0.323440i | \(-0.895161\pi\) |
0.323440 | + | 0.946249i | \(0.395161\pi\) | |||||||
\(194\) | 2244.00i | 0.0596238i | ||||||||
\(195\) | 3960.00 | − | 2970.00i | 0.104142 | − | 0.0781065i | ||||
\(196\) | 13432.0 | 0.349646 | ||||||||
\(197\) | −16899.0 | − | 16899.0i | −0.435440 | − | 0.435440i | 0.455034 | − | 0.890474i | \(-0.349627\pi\) |
−0.890474 | + | 0.455034i | \(0.849627\pi\) | |||||||
\(198\) | −31916.0 | + | 31916.0i | −0.814101 | + | 0.814101i | ||||
\(199\) | 14160.0i | 0.357567i | 0.983888 | + | 0.178783i | \(0.0572161\pi\) | ||||
−0.983888 | + | 0.178783i | \(0.942784\pi\) | |||||||
\(200\) | −6800.00 | − | 12400.0i | −0.170000 | − | 0.310000i | ||||
\(201\) | 10162.0 | 0.251528 | ||||||||
\(202\) | 3364.00 | + | 3364.00i | 0.0824429 | + | 0.0824429i | ||||
\(203\) | −3800.00 | + | 3800.00i | −0.0922129 | + | 0.0922129i | ||||
\(204\) | − | 3824.00i | − | 0.0918877i | ||||||
\(205\) | −15630.0 | − | 20840.0i | −0.371921 | − | 0.495895i | ||||
\(206\) | 28084.0 | 0.661797 | ||||||||
\(207\) | 42739.0 | + | 42739.0i | 0.997433 | + | 0.997433i | ||||
\(208\) | 6336.00 | − | 6336.00i | 0.146450 | − | 0.146450i | ||||
\(209\) | 8080.00i | 0.184977i | ||||||||
\(210\) | −380.000 | + | 2660.00i | −0.00861678 | + | 0.0603175i | ||||
\(211\) | 48842.0 | 1.09706 | 0.548528 | − | 0.836132i | \(-0.315189\pi\) | ||||
0.548528 | + | 0.836132i | \(0.315189\pi\) | |||||||
\(212\) | −14552.0 | − | 14552.0i | −0.323781 | − | 0.323781i | ||||
\(213\) | −3478.00 | + | 3478.00i | −0.0766603 | + | 0.0766603i | ||||
\(214\) | − | 8636.00i | − | 0.188575i | ||||||
\(215\) | 26565.0 | + | 3795.00i | 0.574689 | + | 0.0820984i | ||||
\(216\) | −5120.00 | −0.109739 | ||||||||
\(217\) | 14402.0 | + | 14402.0i | 0.305846 | + | 0.305846i | ||||
\(218\) | 560.000 | − | 560.000i | 0.0117835 | − | 0.0117835i | ||||
\(219\) | 6958.00i | 0.145076i | ||||||||
\(220\) | 32320.0 | − | 24240.0i | 0.667769 | − | 0.500826i | ||||
\(221\) | 47322.0 | 0.968899 | ||||||||
\(222\) | 564.000 | + | 564.000i | 0.0114439 | + | 0.0114439i | ||||
\(223\) | −35019.0 | + | 35019.0i | −0.704197 | + | 0.704197i | −0.965309 | − | 0.261112i | \(-0.915911\pi\) |
0.261112 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(224\) | 4864.00i | 0.0969388i | ||||||||
\(225\) | −47400.0 | − | 13825.0i | −0.936296 | − | 0.273086i | ||||
\(226\) | −33916.0 | −0.664030 | ||||||||
\(227\) | −68599.0 | − | 68599.0i | −1.33127 | − | 1.33127i | −0.904235 | − | 0.427034i | \(-0.859558\pi\) |
−0.427034 | − | 0.904235i | \(-0.640442\pi\) | |||||||
\(228\) | −320.000 | + | 320.000i | −0.00615574 | + | 0.00615574i | ||||
\(229\) | 98760.0i | 1.88326i | 0.336651 | + | 0.941630i | \(0.390706\pi\) | ||||
−0.336651 | + | 0.941630i | \(0.609294\pi\) | |||||||
\(230\) | −32460.0 | − | 43280.0i | −0.613611 | − | 0.818147i | ||||
\(231\) | −7676.00 | −0.143850 | ||||||||
\(232\) | 3200.00 | + | 3200.00i | 0.0594530 | + | 0.0594530i | ||||
\(233\) | 53721.0 | − | 53721.0i | 0.989537 | − | 0.989537i | −0.0104084 | − | 0.999946i | \(-0.503313\pi\) |
0.999946 | + | 0.0104084i | \(0.00331314\pi\) | |||||||
\(234\) | − | 31284.0i | − | 0.571335i | ||||||
\(235\) | −2295.00 | + | 16065.0i | −0.0415573 | + | 0.290901i | ||||
\(236\) | −36800.0 | −0.660730 | ||||||||
\(237\) | −7680.00 | − | 7680.00i | −0.136730 | − | 0.136730i | ||||
\(238\) | −18164.0 | + | 18164.0i | −0.320669 | + | 0.320669i | ||||
\(239\) | − | 45600.0i | − | 0.798305i | −0.916884 | − | 0.399153i | \(-0.869304\pi\) | ||
0.916884 | − | 0.399153i | \(-0.130696\pi\) | |||||||
\(240\) | 2240.00 | + | 320.000i | 0.0388889 | + | 0.00555556i | ||||
\(241\) | −57038.0 | −0.982042 | −0.491021 | − | 0.871148i | \(-0.663376\pi\) | ||||
−0.491021 | + | 0.871148i | \(0.663376\pi\) | |||||||
\(242\) | 52326.0 | + | 52326.0i | 0.893484 | + | 0.893484i | ||||
\(243\) | −19039.0 | + | 19039.0i | −0.322427 | + | 0.322427i | ||||
\(244\) | 16656.0i | 0.279764i | ||||||||
\(245\) | −33580.0 | + | 25185.0i | −0.559434 | + | 0.419575i | ||||
\(246\) | 4168.00 | 0.0688743 | ||||||||
\(247\) | −3960.00 | − | 3960.00i | −0.0649085 | − | 0.0649085i | ||||
\(248\) | 12128.0 | − | 12128.0i | 0.197190 | − | 0.197190i | ||||
\(249\) | − | 12162.0i | − | 0.196158i | ||||||
\(250\) | 40250.0 | + | 18250.0i | 0.644000 | + | 0.292000i | ||||
\(251\) | 39402.0 | 0.625419 | 0.312709 | − | 0.949849i | \(-0.398763\pi\) | ||||
0.312709 | + | 0.949849i | \(0.398763\pi\) | |||||||
\(252\) | 12008.0 | + | 12008.0i | 0.189090 | + | 0.189090i | ||||
\(253\) | 109282. | − | 109282.i | 1.70729 | − | 1.70729i | ||||
\(254\) | 3284.00i | 0.0509021i | ||||||||
\(255\) | 7170.00 | + | 9560.00i | 0.110265 | + | 0.147020i | ||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 31121.0 | + | 31121.0i | 0.471180 | + | 0.471180i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.431116 | + | 0.902297i | \(0.641880\pi\) | |||||||
\(258\) | −3036.00 | + | 3036.00i | −0.0456102 | + | 0.0456102i | ||||
\(259\) | − | 5358.00i | − | 0.0798736i | ||||||
\(260\) | −3960.00 | + | 27720.0i | −0.0585799 | + | 0.410059i | ||||
\(261\) | 15800.0 | 0.231940 | ||||||||
\(262\) | −4396.00 | − | 4396.00i | −0.0640406 | − | 0.0640406i | ||||
\(263\) | −60739.0 | + | 60739.0i | −0.878125 | + | 0.878125i | −0.993340 | − | 0.115216i | \(-0.963244\pi\) |
0.115216 | + | 0.993340i | \(0.463244\pi\) | |||||||
\(264\) | 6464.00i | 0.0927456i | ||||||||
\(265\) | 63665.0 | + | 9095.00i | 0.906586 | + | 0.129512i | ||||
\(266\) | 3040.00 | 0.0429646 | ||||||||
\(267\) | −5680.00 | − | 5680.00i | −0.0796757 | − | 0.0796757i | ||||
\(268\) | −40648.0 | + | 40648.0i | −0.565939 | + | 0.565939i | ||||
\(269\) | − | 63800.0i | − | 0.881690i | −0.897583 | − | 0.440845i | \(-0.854679\pi\) | ||
0.897583 | − | 0.440845i | \(-0.145321\pi\) | |||||||
\(270\) | 12800.0 | − | 9600.00i | 0.175583 | − | 0.131687i | ||||
\(271\) | −113238. | −1.54189 | −0.770945 | − | 0.636901i | \(-0.780216\pi\) | ||||
−0.770945 | + | 0.636901i | \(0.780216\pi\) | |||||||
\(272\) | 15296.0 | + | 15296.0i | 0.206747 | + | 0.206747i | ||||
\(273\) | 3762.00 | − | 3762.00i | 0.0504770 | − | 0.0504770i | ||||
\(274\) | − | 37596.0i | − | 0.500773i | ||||||
\(275\) | −35350.0 | + | 121200.i | −0.467438 | + | 1.60264i | ||||
\(276\) | 8656.00 | 0.113632 | ||||||||
\(277\) | −14739.0 | − | 14739.0i | −0.192092 | − | 0.192092i | 0.604508 | − | 0.796599i | \(-0.293370\pi\) |
−0.796599 | + | 0.604508i | \(0.793370\pi\) | |||||||
\(278\) | 27920.0 | − | 27920.0i | 0.361265 | − | 0.361265i | ||||
\(279\) | − | 59882.0i | − | 0.769286i | ||||||
\(280\) | −9120.00 | − | 12160.0i | −0.116327 | − | 0.155102i | ||||
\(281\) | −7278.00 | −0.0921721 | −0.0460860 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460860 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(282\) | −1836.00 | − | 1836.00i | −0.0230874 | − | 0.0230874i | ||||
\(283\) | 58601.0 | − | 58601.0i | 0.731698 | − | 0.731698i | −0.239258 | − | 0.970956i | \(-0.576904\pi\) |
0.970956 | + | 0.239258i | \(0.0769041\pi\) | |||||||
\(284\) | − | 27824.0i | − | 0.344971i | ||||||
\(285\) | 200.000 | − | 1400.00i | 0.00246230 | − | 0.0172361i | ||||
\(286\) | −79992.0 | −0.977945 | ||||||||
\(287\) | −19798.0 | − | 19798.0i | −0.240357 | − | 0.240357i | ||||
\(288\) | 10112.0 | − | 10112.0i | 0.121914 | − | 0.121914i | ||||
\(289\) | 30721.0i | 0.367824i | ||||||||
\(290\) | −14000.0 | − | 2000.00i | −0.166468 | − | 0.0237812i | ||||
\(291\) | 1122.00 | 0.0132497 | ||||||||
\(292\) | −27832.0 | − | 27832.0i | −0.326421 | − | 0.326421i | ||||
\(293\) | −95499.0 | + | 95499.0i | −1.11241 | + | 1.11241i | −0.119582 | + | 0.992824i | \(0.538156\pi\) |
−0.992824 | + | 0.119582i | \(0.961844\pi\) | |||||||
\(294\) | − | 6716.00i | − | 0.0776991i | ||||||
\(295\) | 92000.0 | − | 69000.0i | 1.05717 | − | 0.792876i | ||||
\(296\) | −4512.00 | −0.0514974 | ||||||||
\(297\) | 32320.0 | + | 32320.0i | 0.366403 | + | 0.366403i | ||||
\(298\) | 18000.0 | − | 18000.0i | 0.202694 | − | 0.202694i | ||||
\(299\) | 107118.i | 1.19817i | ||||||||
\(300\) | −6200.00 | + | 3400.00i | −0.0688889 | + | 0.0377778i | ||||
\(301\) | 28842.0 | 0.318341 | ||||||||
\(302\) | −47596.0 | − | 47596.0i | −0.521863 | − | 0.521863i | ||||
\(303\) | 1682.00 | − | 1682.00i | 0.0183206 | − | 0.0183206i | ||||
\(304\) | − | 2560.00i | − | 0.0277008i | ||||||
\(305\) | −31230.0 | − | 41640.0i | −0.335716 | − | 0.447622i | ||||
\(306\) | 75524.0 | 0.806570 | ||||||||
\(307\) | 38601.0 | + | 38601.0i | 0.409564 | + | 0.409564i | 0.881587 | − | 0.472022i | \(-0.156476\pi\) |
−0.472022 | + | 0.881587i | \(0.656476\pi\) | |||||||
\(308\) | 30704.0 | − | 30704.0i | 0.323663 | − | 0.323663i | ||||
\(309\) | − | 14042.0i | − | 0.147066i | ||||||
\(310\) | −7580.00 | + | 53060.0i | −0.0788762 | + | 0.552133i | ||||
\(311\) | 29162.0 | 0.301506 | 0.150753 | − | 0.988571i | \(-0.451830\pi\) | ||||
0.150753 | + | 0.988571i | \(0.451830\pi\) | |||||||
\(312\) | −3168.00 | − | 3168.00i | −0.0325444 | − | 0.0325444i | ||||
\(313\) | 1881.00 | − | 1881.00i | 0.0192000 | − | 0.0192000i | −0.697442 | − | 0.716642i | \(-0.745678\pi\) |
0.716642 | + | 0.697442i | \(0.245678\pi\) | |||||||
\(314\) | 119124.i | 1.20820i | ||||||||
\(315\) | −52535.0 | − | 7505.00i | −0.529453 | − | 0.0756362i | ||||
\(316\) | 61440.0 | 0.615286 | ||||||||
\(317\) | 83781.0 | + | 83781.0i | 0.833733 | + | 0.833733i | 0.988025 | − | 0.154292i | \(-0.0493097\pi\) |
−0.154292 | + | 0.988025i | \(0.549310\pi\) | |||||||
\(318\) | −7276.00 | + | 7276.00i | −0.0719513 | + | 0.0719513i | ||||
\(319\) | − | 40400.0i | − | 0.397009i | ||||||
\(320\) | −10240.0 | + | 7680.00i | −0.100000 | + | 0.0750000i | ||||
\(321\) | −4318.00 | −0.0419056 | ||||||||
\(322\) | −41116.0 | − | 41116.0i | −0.396551 | − | 0.396551i | ||||
\(323\) | 9560.00 | − | 9560.00i | 0.0916332 | − | 0.0916332i | ||||
\(324\) | − | 48632.0i | − | 0.463268i | ||||||
\(325\) | −42075.0 | − | 76725.0i | −0.398343 | − | 0.726391i | ||||
\(326\) | 50564.0 | 0.475780 | ||||||||
\(327\) | −280.000 | − | 280.000i | −0.00261856 | − | 0.00261856i | ||||
\(328\) | −16672.0 | + | 16672.0i | −0.154967 | + | 0.154967i | ||||
\(329\) | 17442.0i | 0.161140i | ||||||||
\(330\) | −12120.0 | − | 16160.0i | −0.111295 | − | 0.148393i | ||||
\(331\) | 106282. | 0.970071 | 0.485036 | − | 0.874494i | \(-0.338807\pi\) | ||||
0.485036 | + | 0.874494i | \(0.338807\pi\) | |||||||
\(332\) | 48648.0 | + | 48648.0i | 0.441356 | + | 0.441356i | ||||
\(333\) | −11139.0 | + | 11139.0i | −0.100452 | + | 0.100452i | ||||
\(334\) | 119924.i | 1.07501i | ||||||||
\(335\) | 25405.0 | − | 177835.i | 0.226376 | − | 1.58463i | ||||
\(336\) | 2432.00 | 0.0215420 | ||||||||
\(337\) | −142479. | − | 142479.i | −1.25456 | − | 1.25456i | −0.953654 | − | 0.300905i | \(-0.902711\pi\) |
−0.300905 | − | 0.953654i | \(-0.597289\pi\) | |||||||
\(338\) | −17918.0 | + | 17918.0i | −0.156840 | + | 0.156840i | ||||
\(339\) | 16958.0i | 0.147562i | ||||||||
\(340\) | −66920.0 | − | 9560.00i | −0.578893 | − | 0.0826990i | ||||
\(341\) | −153116. | −1.31678 | ||||||||
\(342\) | −6320.00 | − | 6320.00i | −0.0540337 | − | 0.0540337i | ||||
\(343\) | −77520.0 | + | 77520.0i | −0.658909 | + | 0.658909i | ||||
\(344\) | − | 24288.0i | − | 0.205246i | ||||||
\(345\) | −21640.0 | + | 16230.0i | −0.181811 | + | 0.136358i | ||||
\(346\) | −18956.0 | −0.158341 | ||||||||
\(347\) | −6479.00 | − | 6479.00i | −0.0538083 | − | 0.0538083i | 0.679691 | − | 0.733499i | \(-0.262114\pi\) |
−0.733499 | + | 0.679691i | \(0.762114\pi\) | |||||||
\(348\) | 1600.00 | − | 1600.00i | 0.0132118 | − | 0.0132118i | ||||
\(349\) | 32920.0i | 0.270277i | 0.990827 | + | 0.135138i | \(0.0431479\pi\) | ||||
−0.990827 | + | 0.135138i | \(0.956852\pi\) | |||||||
\(350\) | 45600.0 | + | 13300.0i | 0.372245 | + | 0.108571i | ||||
\(351\) | −31680.0 | −0.257141 | ||||||||
\(352\) | −25856.0 | − | 25856.0i | −0.208678 | − | 0.208678i | ||||
\(353\) | −53919.0 | + | 53919.0i | −0.432706 | + | 0.432706i | −0.889548 | − | 0.456842i | \(-0.848980\pi\) |
0.456842 | + | 0.889548i | \(0.348980\pi\) | |||||||
\(354\) | 18400.0i | 0.146829i | ||||||||
\(355\) | 52170.0 | + | 69560.0i | 0.413965 | + | 0.551954i | ||||
\(356\) | 45440.0 | 0.358541 | ||||||||
\(357\) | 9082.00 | + | 9082.00i | 0.0712599 | + | 0.0712599i | ||||
\(358\) | 65840.0 | − | 65840.0i | 0.513717 | − | 0.513717i | ||||
\(359\) | − | 171760.i | − | 1.33270i | −0.745638 | − | 0.666351i | \(-0.767855\pi\) | ||
0.745638 | − | 0.666351i | \(-0.232145\pi\) | |||||||
\(360\) | −6320.00 | + | 44240.0i | −0.0487654 | + | 0.341358i | ||||
\(361\) | 128721. | 0.987723 | ||||||||
\(362\) | −81116.0 | − | 81116.0i | −0.618998 | − | 0.618998i | ||||
\(363\) | 26163.0 | − | 26163.0i | 0.198552 | − | 0.198552i | ||||
\(364\) | 30096.0i | 0.227146i | ||||||||
\(365\) | 121765. | + | 17395.0i | 0.913980 | + | 0.130569i | ||||
\(366\) | 8328.00 | 0.0621697 | ||||||||
\(367\) | 152261. | + | 152261.i | 1.13046 | + | 1.13046i | 0.990100 | + | 0.140363i | \(0.0448271\pi\) |
0.140363 | + | 0.990100i | \(0.455173\pi\) | |||||||
\(368\) | −34624.0 | + | 34624.0i | −0.255671 | + | 0.255671i | ||||
\(369\) | 82318.0i | 0.604564i | ||||||||
\(370\) | 11280.0 | − | 8460.00i | 0.0823959 | − | 0.0617969i | ||||
\(371\) | 69122.0 | 0.502190 | ||||||||
\(372\) | −6064.00 | − | 6064.00i | −0.0438201 | − | 0.0438201i | ||||
\(373\) | −71339.0 | + | 71339.0i | −0.512754 | + | 0.512754i | −0.915369 | − | 0.402615i | \(-0.868101\pi\) |
0.402615 | + | 0.915369i | \(0.368101\pi\) | |||||||
\(374\) | − | 193112.i | − | 1.38059i | ||||||
\(375\) | 9125.00 | − | 20125.0i | 0.0648889 | − | 0.143111i | ||||
\(376\) | 14688.0 | 0.103893 | ||||||||
\(377\) | 19800.0 | + | 19800.0i | 0.139310 | + | 0.139310i | ||||
\(378\) | 12160.0 | − | 12160.0i | 0.0851040 | − | 0.0851040i | ||||
\(379\) | 172600.i | 1.20161i | 0.799397 | + | 0.600803i | \(0.205153\pi\) | ||||
−0.799397 | + | 0.600803i | \(0.794847\pi\) | |||||||
\(380\) | 4800.00 | + | 6400.00i | 0.0332410 | + | 0.0443213i | ||||
\(381\) | 1642.00 | 0.0113116 | ||||||||
\(382\) | 66004.0 | + | 66004.0i | 0.452318 | + | 0.452318i | ||||
\(383\) | 158421. | − | 158421.i | 1.07998 | − | 1.07998i | 0.0834683 | − | 0.996510i | \(-0.473400\pi\) |
0.996510 | − | 0.0834683i | \(-0.0265997\pi\) | |||||||
\(384\) | − | 2048.00i | − | 0.0138889i | ||||||
\(385\) | −19190.0 | + | 134330.i | −0.129465 | + | 0.906257i | ||||
\(386\) | −92796.0 | −0.622809 | ||||||||
\(387\) | −59961.0 | − | 59961.0i | −0.400357 | − | 0.400357i | ||||
\(388\) | −4488.00 | + | 4488.00i | −0.0298119 | + | 0.0298119i | ||||
\(389\) | − | 146760.i | − | 0.969859i | −0.874553 | − | 0.484929i | \(-0.838845\pi\) | ||
0.874553 | − | 0.484929i | \(-0.161155\pi\) | |||||||
\(390\) | 13860.0 | + | 1980.00i | 0.0911243 | + | 0.0130178i | ||||
\(391\) | −258598. | −1.69150 | ||||||||
\(392\) | 26864.0 | + | 26864.0i | 0.174823 | + | 0.174823i | ||||
\(393\) | −2198.00 | + | 2198.00i | −0.0142312 | + | 0.0142312i | ||||
\(394\) | − | 67596.0i | − | 0.435440i | ||||||
\(395\) | −153600. | + | 115200.i | −0.984458 | + | 0.738343i | ||||
\(396\) | −127664. | −0.814101 | ||||||||
\(397\) | −83579.0 | − | 83579.0i | −0.530293 | − | 0.530293i | 0.390366 | − | 0.920660i | \(-0.372348\pi\) |
−0.920660 | + | 0.390366i | \(0.872348\pi\) | |||||||
\(398\) | −28320.0 | + | 28320.0i | −0.178783 | + | 0.178783i | ||||
\(399\) | − | 1520.00i | − | 0.00954768i | ||||||
\(400\) | 11200.0 | − | 38400.0i | 0.0700000 | − | 0.240000i | ||||
\(401\) | −42078.0 | −0.261677 | −0.130839 | − | 0.991404i | \(-0.541767\pi\) | ||||
−0.130839 | + | 0.991404i | \(0.541767\pi\) | |||||||
\(402\) | 20324.0 | + | 20324.0i | 0.125764 | + | 0.125764i | ||||
\(403\) | 75042.0 | − | 75042.0i | 0.462056 | − | 0.462056i | ||||
\(404\) | 13456.0i | 0.0824429i | ||||||||
\(405\) | 91185.0 | + | 121580.i | 0.555921 | + | 0.741228i | ||||
\(406\) | −15200.0 | −0.0922129 | ||||||||
\(407\) | 28482.0 | + | 28482.0i | 0.171942 | + | 0.171942i | ||||
\(408\) | 7648.00 | − | 7648.00i | 0.0459439 | − | 0.0459439i | ||||
\(409\) | − | 300960.i | − | 1.79913i | −0.436789 | − | 0.899564i | \(-0.643884\pi\) | ||
0.436789 | − | 0.899564i | \(-0.356116\pi\) | |||||||
\(410\) | 10420.0 | − | 72940.0i | 0.0619869 | − | 0.433908i | ||||
\(411\) | −18798.0 | −0.111283 | ||||||||
\(412\) | 56168.0 | + | 56168.0i | 0.330898 | + | 0.330898i | ||||
\(413\) | 87400.0 | − | 87400.0i | 0.512403 | − | 0.512403i | ||||
\(414\) | 170956.i | 0.997433i | ||||||||
\(415\) | −212835. | − | 30405.0i | −1.23580 | − | 0.176542i | ||||
\(416\) | 25344.0 | 0.146450 | ||||||||
\(417\) | −13960.0 | − | 13960.0i | −0.0802811 | − | 0.0802811i | ||||
\(418\) | −16160.0 | + | 16160.0i | −0.0924887 | + | 0.0924887i | ||||
\(419\) | 208680.i | 1.18865i | 0.804226 | + | 0.594323i | \(0.202580\pi\) | ||||
−0.804226 | + | 0.594323i | \(0.797420\pi\) | |||||||
\(420\) | −6080.00 | + | 4560.00i | −0.0344671 | + | 0.0258503i | ||||
\(421\) | 86882.0 | 0.490191 | 0.245096 | − | 0.969499i | \(-0.421181\pi\) | ||||
0.245096 | + | 0.969499i | \(0.421181\pi\) | |||||||
\(422\) | 97684.0 | + | 97684.0i | 0.548528 | + | 0.548528i | ||||
\(423\) | 36261.0 | − | 36261.0i | 0.202656 | − | 0.202656i | ||||
\(424\) | − | 58208.0i | − | 0.323781i | ||||||
\(425\) | 185225. | − | 101575.i | 1.02547 | − | 0.562353i | ||||
\(426\) | −13912.0 | −0.0766603 | ||||||||
\(427\) | −39558.0 | − | 39558.0i | −0.216959 | − | 0.216959i | ||||
\(428\) | 17272.0 | − | 17272.0i | 0.0942877 | − | 0.0942877i | ||||
\(429\) | 39996.0i | 0.217321i | ||||||||
\(430\) | 45540.0 | + | 60720.0i | 0.246295 | + | 0.328394i | ||||
\(431\) | −125078. | −0.673328 | −0.336664 | − | 0.941625i | \(-0.609299\pi\) | ||||
−0.336664 | + | 0.941625i | \(0.609299\pi\) | |||||||
\(432\) | −10240.0 | − | 10240.0i | −0.0548697 | − | 0.0548697i | ||||
\(433\) | 5921.00 | − | 5921.00i | 0.0315805 | − | 0.0315805i | −0.691140 | − | 0.722721i | \(-0.742891\pi\) |
0.722721 | + | 0.691140i | \(0.242891\pi\) | |||||||
\(434\) | 57608.0i | 0.305846i | ||||||||
\(435\) | −1000.00 | + | 7000.00i | −0.00528471 | + | 0.0369930i | ||||
\(436\) | 2240.00 | 0.0117835 | ||||||||
\(437\) | 21640.0 | + | 21640.0i | 0.113317 | + | 0.113317i | ||||
\(438\) | −13916.0 | + | 13916.0i | −0.0725381 | + | 0.0725381i | ||||
\(439\) | 55280.0i | 0.286840i | 0.989662 | + | 0.143420i | \(0.0458099\pi\) | ||||
−0.989662 | + | 0.143420i | \(0.954190\pi\) | |||||||
\(440\) | 113120. | + | 16160.0i | 0.584298 | + | 0.0834711i | ||||
\(441\) | 132641. | 0.682025 | ||||||||
\(442\) | 94644.0 | + | 94644.0i | 0.484450 | + | 0.484450i | ||||
\(443\) | 63561.0 | − | 63561.0i | 0.323879 | − | 0.323879i | −0.526374 | − | 0.850253i | \(-0.676449\pi\) |
0.850253 | + | 0.526374i | \(0.176449\pi\) | |||||||
\(444\) | 2256.00i | 0.0114439i | ||||||||
\(445\) | −113600. | + | 85200.0i | −0.573665 | + | 0.430249i | ||||
\(446\) | −140076. | −0.704197 | ||||||||
\(447\) | −9000.00 | − | 9000.00i | −0.0450430 | − | 0.0450430i | ||||
\(448\) | −9728.00 | + | 9728.00i | −0.0484694 | + | 0.0484694i | ||||
\(449\) | 204880.i | 1.01626i | 0.861279 | + | 0.508132i | \(0.169664\pi\) | ||||
−0.861279 | + | 0.508132i | \(0.830336\pi\) | |||||||
\(450\) | −67150.0 | − | 122450.i | −0.331605 | − | 0.604691i | ||||
\(451\) | 210484. | 1.03482 | ||||||||
\(452\) | −67832.0 | − | 67832.0i | −0.332015 | − | 0.332015i | ||||
\(453\) | −23798.0 | + | 23798.0i | −0.115970 | + | 0.115970i | ||||
\(454\) | − | 274396.i | − | 1.33127i | ||||||
\(455\) | −56430.0 | − | 75240.0i | −0.272576 | − | 0.363434i | ||||
\(456\) | −1280.00 | −0.00615574 | ||||||||
\(457\) | −10599.0 | − | 10599.0i | −0.0507496 | − | 0.0507496i | 0.681277 | − | 0.732026i | \(-0.261425\pi\) |
−0.732026 | + | 0.681277i | \(0.761425\pi\) | |||||||
\(458\) | −197520. | + | 197520.i | −0.941630 | + | 0.941630i | ||||
\(459\) | − | 76480.0i | − | 0.363013i | ||||||
\(460\) | 21640.0 | − | 151480.i | 0.102268 | − | 0.715879i | ||||
\(461\) | 224242. | 1.05515 | 0.527576 | − | 0.849508i | \(-0.323101\pi\) | ||||
0.527576 | + | 0.849508i | \(0.323101\pi\) | |||||||
\(462\) | −15352.0 | − | 15352.0i | −0.0719252 | − | 0.0719252i | ||||
\(463\) | −243499. | + | 243499.i | −1.13589 | + | 1.13589i | −0.146707 | + | 0.989180i | \(0.546868\pi\) |
−0.989180 | + | 0.146707i | \(0.953132\pi\) | |||||||
\(464\) | 12800.0i | 0.0594530i | ||||||||
\(465\) | 26530.0 | + | 3790.00i | 0.122696 | + | 0.0175280i | ||||
\(466\) | 214884. | 0.989537 | ||||||||
\(467\) | −226919. | − | 226919.i | −1.04049 | − | 1.04049i | −0.999145 | − | 0.0413430i | \(-0.986836\pi\) |
−0.0413430 | − | 0.999145i | \(-0.513164\pi\) | |||||||
\(468\) | 62568.0 | − | 62568.0i | 0.285667 | − | 0.285667i | ||||
\(469\) | − | 193078.i | − | 0.877783i | ||||||
\(470\) | −36720.0 | + | 27540.0i | −0.166229 | + | 0.124672i | ||||
\(471\) | 59562.0 | 0.268490 | ||||||||
\(472\) | −73600.0 | − | 73600.0i | −0.330365 | − | 0.330365i | ||||
\(473\) | −153318. | + | 153318.i | −0.685284 | + | 0.685284i | ||||
\(474\) | − | 30720.0i | − | 0.136730i | ||||||
\(475\) | −24000.0 | − | 7000.00i | −0.106371 | − | 0.0310249i | ||||
\(476\) | −72656.0 | −0.320669 | ||||||||
\(477\) | −143701. | − | 143701.i | −0.631572 | − | 0.631572i | ||||
\(478\) | 91200.0 | − | 91200.0i | 0.399153 | − | 0.399153i | ||||
\(479\) | 334240.i | 1.45676i | 0.685174 | + | 0.728379i | \(0.259726\pi\) | ||||
−0.685174 | + | 0.728379i | \(0.740274\pi\) | |||||||
\(480\) | 3840.00 | + | 5120.00i | 0.0166667 | + | 0.0222222i | ||||
\(481\) | −27918.0 | −0.120669 | ||||||||
\(482\) | −114076. | − | 114076.i | −0.491021 | − | 0.491021i | ||||
\(483\) | −20558.0 | + | 20558.0i | −0.0881225 | + | 0.0881225i | ||||
\(484\) | 209304.i | 0.893484i | ||||||||
\(485\) | 2805.00 | − | 19635.0i | 0.0119248 | − | 0.0834733i | ||||
\(486\) | −76156.0 | −0.322427 | ||||||||
\(487\) | 278541. | + | 278541.i | 1.17444 | + | 1.17444i | 0.981139 | + | 0.193302i | \(0.0619196\pi\) |
0.193302 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(488\) | −33312.0 | + | 33312.0i | −0.139882 | + | 0.139882i | ||||
\(489\) | − | 25282.0i | − | 0.105729i | ||||||
\(490\) | −117530. | − | 16790.0i | −0.489504 | − | 0.0699292i | ||||
\(491\) | −84118.0 | −0.348920 | −0.174460 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174460 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(492\) | 8336.00 | + | 8336.00i | 0.0344372 | + | 0.0344372i | ||||
\(493\) | −47800.0 | + | 47800.0i | −0.196668 | + | 0.196668i | ||||
\(494\) | − | 15840.0i | − | 0.0649085i | ||||||
\(495\) | 319160. | − | 239370.i | 1.30256 | − | 0.976921i | ||||
\(496\) | 48512.0 | 0.197190 | ||||||||
\(497\) | 66082.0 | + | 66082.0i | 0.267529 | + | 0.267529i | ||||
\(498\) | 24324.0 | − | 24324.0i | 0.0980791 | − | 0.0980791i | ||||
\(499\) | − | 166840.i | − | 0.670037i | −0.942211 | − | 0.335019i | \(-0.891257\pi\) | ||
0.942211 | − | 0.335019i | \(-0.108743\pi\) | |||||||
\(500\) | 44000.0 | + | 117000.i | 0.176000 | + | 0.468000i | ||||
\(501\) | 59962.0 | 0.238891 | ||||||||
\(502\) | 78804.0 | + | 78804.0i | 0.312709 | + | 0.312709i | ||||
\(503\) | 190461. | − | 190461.i | 0.752783 | − | 0.752783i | −0.222214 | − | 0.974998i | \(-0.571328\pi\) |
0.974998 | + | 0.222214i | \(0.0713285\pi\) | |||||||
\(504\) | 48032.0i | 0.189090i | ||||||||
\(505\) | −25230.0 | − | 33640.0i | −0.0989315 | − | 0.131909i | ||||
\(506\) | 437128. | 1.70729 | ||||||||
\(507\) | 8959.00 | + | 8959.00i | 0.0348533 | + | 0.0348533i | ||||
\(508\) | −6568.00 | + | 6568.00i | −0.0254511 | + | 0.0254511i | ||||
\(509\) | 223960.i | 0.864440i | 0.901768 | + | 0.432220i | \(0.142270\pi\) | ||||
−0.901768 | + | 0.432220i | \(0.857730\pi\) | |||||||
\(510\) | −4780.00 | + | 33460.0i | −0.0183775 | + | 0.128643i | ||||
\(511\) | 132202. | 0.506286 | ||||||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −6400.00 | + | 6400.00i | −0.0243190 | + | 0.0243190i | ||||
\(514\) | 124484.i | 0.471180i | ||||||||
\(515\) | −245735. | − | 35105.0i | −0.926515 | − | 0.132359i | ||||
\(516\) | −12144.0 | −0.0456102 | ||||||||
\(517\) | −92718.0 | − | 92718.0i | −0.346883 | − | 0.346883i | ||||
\(518\) | 10716.0 | − | 10716.0i | 0.0399368 | − | 0.0399368i | ||||
\(519\) | 9478.00i | 0.0351870i | ||||||||
\(520\) | −63360.0 | + | 47520.0i | −0.234320 | + | 0.175740i | ||||
\(521\) | −297918. | −1.09754 | −0.548771 | − | 0.835973i | \(-0.684904\pi\) | ||||
−0.548771 | + | 0.835973i | \(0.684904\pi\) | |||||||
\(522\) | 31600.0 | + | 31600.0i | 0.115970 | + | 0.115970i | ||||
\(523\) | 200601. | − | 200601.i | 0.733381 | − | 0.733381i | −0.237907 | − | 0.971288i | \(-0.576461\pi\) |
0.971288 | + | 0.237907i | \(0.0764613\pi\) | |||||||
\(524\) | − | 17584.0i | − | 0.0640406i | ||||||
\(525\) | 6650.00 | − | 22800.0i | 0.0241270 | − | 0.0827211i | ||||
\(526\) | −242956. | −0.878125 | ||||||||
\(527\) | 181162. | + | 181162.i | 0.652298 | + | 0.652298i | ||||
\(528\) | −12928.0 | + | 12928.0i | −0.0463728 | + | 0.0463728i | ||||
\(529\) | − | 305521.i | − | 1.09177i | ||||||
\(530\) | 109140. | + | 145520.i | 0.388537 | + | 0.518049i | ||||
\(531\) | −363400. | −1.28883 | ||||||||
\(532\) | 6080.00 | + | 6080.00i | 0.0214823 | + | 0.0214823i | ||||
\(533\) | −103158. | + | 103158.i | −0.363119 | + | 0.363119i | ||||
\(534\) | − | 22720.0i | − | 0.0796757i | ||||||
\(535\) | −10795.0 | + | 75565.0i | −0.0377151 | + | 0.264006i | ||||
\(536\) | −162592. | −0.565939 | ||||||||
\(537\) | −32920.0 | − | 32920.0i | −0.114159 | − | 0.114159i | ||||
\(538\) | 127600. | − | 127600.i | 0.440845 | − | 0.440845i | ||||
\(539\) | − | 339158.i | − | 1.16741i | ||||||
\(540\) | 44800.0 | + | 6400.00i | 0.153635 | + | 0.0219479i | ||||
\(541\) | −288398. | −0.985366 | −0.492683 | − | 0.870209i | \(-0.663984\pi\) | ||||
−0.492683 | + | 0.870209i | \(0.663984\pi\) | |||||||
\(542\) | −226476. | − | 226476.i | −0.770945 | − | 0.770945i | ||||
\(543\) | −40558.0 | + | 40558.0i | −0.137555 | + | 0.137555i | ||||
\(544\) | 61184.0i | 0.206747i | ||||||||
\(545\) | −5600.00 | + | 4200.00i | −0.0188536 | + | 0.0141402i | ||||
\(546\) | 15048.0 | 0.0504770 | ||||||||
\(547\) | 123081. | + | 123081.i | 0.411355 | + | 0.411355i | 0.882210 | − | 0.470856i | \(-0.156055\pi\) |
−0.470856 | + | 0.882210i | \(0.656055\pi\) | |||||||
\(548\) | 75192.0 | − | 75192.0i | 0.250386 | − | 0.250386i | ||||
\(549\) | 164478.i | 0.545712i | ||||||||
\(550\) | −313100. | + | 171700.i | −1.03504 | + | 0.567603i | ||||
\(551\) | 8000.00 | 0.0263504 | ||||||||
\(552\) | 17312.0 | + | 17312.0i | 0.0568158 | + | 0.0568158i | ||||
\(553\) | −145920. | + | 145920.i | −0.477161 | + | 0.477161i | ||||
\(554\) | − | 58956.0i | − | 0.192092i | ||||||
\(555\) | −4230.00 | − | 5640.00i | −0.0137327 | − | 0.0183102i | ||||
\(556\) | 111680. | 0.361265 | ||||||||
\(557\) | 162261. | + | 162261.i | 0.523002 | + | 0.523002i | 0.918477 | − | 0.395474i | \(-0.129420\pi\) |
−0.395474 | + | 0.918477i | \(0.629420\pi\) | |||||||
\(558\) | 119764. | − | 119764.i | 0.384643 | − | 0.384643i | ||||
\(559\) | − | 150282.i | − | 0.480932i | ||||||
\(560\) | 6080.00 | − | 42560.0i | 0.0193878 | − | 0.135714i | ||||
\(561\) | −96556.0 | −0.306799 | ||||||||
\(562\) | −14556.0 | − | 14556.0i | −0.0460860 | − | 0.0460860i | ||||
\(563\) | 264081. | − | 264081.i | 0.833145 | − | 0.833145i | −0.154801 | − | 0.987946i | \(-0.549474\pi\) |
0.987946 | + | 0.154801i | \(0.0494737\pi\) | |||||||
\(564\) | − | 7344.00i | − | 0.0230874i | ||||||
\(565\) | 296765. | + | 42395.0i | 0.929642 | + | 0.132806i | ||||
\(566\) | 234404. | 0.731698 | ||||||||
\(567\) | 115501. | + | 115501.i | 0.359269 | + | 0.359269i | ||||
\(568\) | 55648.0 | − | 55648.0i | 0.172486 | − | 0.172486i | ||||
\(569\) | − | 8320.00i | − | 0.0256980i | −0.999917 | − | 0.0128490i | \(-0.995910\pi\) | ||
0.999917 | − | 0.0128490i | \(-0.00409007\pi\) | |||||||
\(570\) | 3200.00 | − | 2400.00i | 0.00984918 | − | 0.00738689i | ||||
\(571\) | 283082. | 0.868240 | 0.434120 | − | 0.900855i | \(-0.357059\pi\) | ||||
0.434120 | + | 0.900855i | \(0.357059\pi\) | |||||||
\(572\) | −159984. | − | 159984.i | −0.488973 | − | 0.488973i | ||||
\(573\) | 33002.0 | − | 33002.0i | 0.100515 | − | 0.100515i | ||||
\(574\) | − | 79192.0i | − | 0.240357i | ||||||
\(575\) | 229925. | + | 419275.i | 0.695425 | + | 1.26813i | ||||
\(576\) | 40448.0 | 0.121914 | ||||||||
\(577\) | 260401. | + | 260401.i | 0.782152 | + | 0.782152i | 0.980194 | − | 0.198042i | \(-0.0634582\pi\) |
−0.198042 | + | 0.980194i | \(0.563458\pi\) | |||||||
\(578\) | −61442.0 | + | 61442.0i | −0.183912 | + | 0.183912i | ||||
\(579\) | 46398.0i | 0.138402i | ||||||||
\(580\) | −24000.0 | − | 32000.0i | −0.0713436 | − | 0.0951249i | ||||
\(581\) | −231078. | −0.684552 | ||||||||
\(582\) | 2244.00 | + | 2244.00i | 0.00662486 | + | 0.00662486i | ||||
\(583\) | −367438. | + | 367438.i | −1.08105 | + | 1.08105i | ||||
\(584\) | − | 111328.i | − | 0.326421i | ||||||
\(585\) | −39105.0 | + | 273735.i | −0.114267 | + | 0.799869i | ||||
\(586\) | −381996. | −1.11241 | ||||||||
\(587\) | −281439. | − | 281439.i | −0.816786 | − | 0.816786i | 0.168855 | − | 0.985641i | \(-0.445993\pi\) |
−0.985641 | + | 0.168855i | \(0.945993\pi\) | |||||||
\(588\) | 13432.0 | − | 13432.0i | 0.0388496 | − | 0.0388496i | ||||
\(589\) | − | 30320.0i | − | 0.0873974i | ||||||
\(590\) | 322000. | + | 46000.0i | 0.925022 | + | 0.132146i | ||||
\(591\) | −33798.0 | −0.0967645 | ||||||||
\(592\) | −9024.00 | − | 9024.00i | −0.0257487 | − | 0.0257487i | ||||
\(593\) | 419761. | − | 419761.i | 1.19369 | − | 1.19369i | 0.217671 | − | 0.976022i | \(-0.430154\pi\) |
0.976022 | − | 0.217671i | \(-0.0698460\pi\) | |||||||
\(594\) | 129280.i | 0.366403i | ||||||||
\(595\) | 181640. | − | 136230.i | 0.513071 | − | 0.384803i | ||||
\(596\) | 72000.0 | 0.202694 | ||||||||
\(597\) | 14160.0 | + | 14160.0i | 0.0397296 | + | 0.0397296i | ||||
\(598\) | −214236. | + | 214236.i | −0.599087 | + | 0.599087i | ||||
\(599\) | 136240.i | 0.379709i | 0.981812 | + | 0.189855i | \(0.0608016\pi\) | ||||
−0.981812 | + | 0.189855i | \(0.939198\pi\) | |||||||
\(600\) | −19200.0 | − | 5600.00i | −0.0533333 | − | 0.0155556i | ||||
\(601\) | 234962. | 0.650502 | 0.325251 | − | 0.945628i | \(-0.394551\pi\) | ||||
0.325251 | + | 0.945628i | \(0.394551\pi\) | |||||||
\(602\) | 57684.0 | + | 57684.0i | 0.159170 | + | 0.159170i | ||||
\(603\) | −401399. | + | 401399.i | −1.10393 | + | 1.10393i | ||||
\(604\) | − | 190384.i | − | 0.521863i | ||||||
\(605\) | −392445. | − | 523260.i | −1.07218 | − | 1.42957i | ||||
\(606\) | 6728.00 | 0.0183206 | ||||||||
\(607\) | −406779. | − | 406779.i | −1.10403 | − | 1.10403i | −0.993919 | − | 0.110111i | \(-0.964879\pi\) |
−0.110111 | − | 0.993919i | \(-0.535121\pi\) | |||||||
\(608\) | 5120.00 | − | 5120.00i | 0.0138504 | − | 0.0138504i | ||||
\(609\) | 7600.00i | 0.0204917i | ||||||||
\(610\) | 20820.0 | − | 145740.i | 0.0559527 | − | 0.391669i | ||||
\(611\) | 90882.0 | 0.243442 | ||||||||
\(612\) | 151048. | + | 151048.i | 0.403285 | + | 0.403285i | ||||
\(613\) | 135621. | − | 135621.i | 0.360916 | − | 0.360916i | −0.503234 | − | 0.864150i | \(-0.667857\pi\) |
0.864150 | + | 0.503234i | \(0.167857\pi\) | |||||||
\(614\) | 154404.i | 0.409564i | ||||||||
\(615\) | −36470.0 | − | 5210.00i | −0.0964241 | − | 0.0137749i | ||||
\(616\) | 122816. | 0.323663 | ||||||||
\(617\) | −151959. | − | 151959.i | −0.399168 | − | 0.399168i | 0.478771 | − | 0.877940i | \(-0.341082\pi\) |
−0.877940 | + | 0.478771i | \(0.841082\pi\) | |||||||
\(618\) | 28084.0 | − | 28084.0i | 0.0735330 | − | 0.0735330i | ||||
\(619\) | − | 22440.0i | − | 0.0585655i | −0.999571 | − | 0.0292827i | \(-0.990678\pi\) | ||
0.999571 | − | 0.0292827i | \(-0.00932231\pi\) | |||||||
\(620\) | −121280. | + | 90960.0i | −0.315505 | + | 0.236629i | ||||
\(621\) | 173120. | 0.448915 | ||||||||
\(622\) | 58324.0 | + | 58324.0i | 0.150753 | + | 0.150753i | ||||
\(623\) | −107920. | + | 107920.i | −0.278052 | + | 0.278052i | ||||
\(624\) | − | 12672.0i | − | 0.0325444i | ||||||
\(625\) | −329375. | − | 210000.i | −0.843200 | − | 0.537600i | ||||
\(626\) | 7524.00 | 0.0192000 | ||||||||
\(627\) | 8080.00 | + | 8080.00i | 0.0205531 | + | 0.0205531i | ||||
\(628\) | −238248. | + | 238248.i | −0.604102 | + | 0.604102i | ||||
\(629\) | − | 67398.0i | − | 0.170351i | ||||||
\(630\) | −90060.0 | − | 120080.i | −0.226909 | − | 0.302545i | ||||
\(631\) | −199958. | −0.502204 | −0.251102 | − | 0.967961i | \(-0.580793\pi\) | ||||
−0.251102 | + | 0.967961i | \(0.580793\pi\) | |||||||
\(632\) | 122880. | + | 122880.i | 0.307643 | + | 0.307643i | ||||
\(633\) | 48842.0 | − | 48842.0i | 0.121895 | − | 0.121895i | ||||
\(634\) | 335124.i | 0.833733i | ||||||||
\(635\) | 4105.00 | − | 28735.0i | 0.0101804 | − | 0.0712629i | ||||
\(636\) | −29104.0 | −0.0719513 | ||||||||
\(637\) | 166221. | + | 166221.i | 0.409644 | + | 0.409644i | ||||
\(638\) | 80800.0 | − | 80800.0i | 0.198504 | − | 0.198504i | ||||
\(639\) | − | 274762.i | − | 0.672907i | ||||||
\(640\) | −35840.0 | − | 5120.00i | −0.0875000 | − | 0.0125000i | ||||
\(641\) | 448562. | 1.09171 | 0.545854 | − | 0.837880i | \(-0.316205\pi\) | ||||
0.545854 | + | 0.837880i | \(0.316205\pi\) | |||||||
\(642\) | −8636.00 | − | 8636.00i | −0.0209528 | − | 0.0209528i | ||||
\(643\) | 73041.0 | − | 73041.0i | 0.176663 | − | 0.176663i | −0.613237 | − | 0.789899i | \(-0.710133\pi\) |
0.789899 | + | 0.613237i | \(0.210133\pi\) | |||||||
\(644\) | − | 164464.i | − | 0.396551i | ||||||
\(645\) | 30360.0 | − | 22770.0i | 0.0729764 | − | 0.0547323i | ||||
\(646\) | 38240.0 | 0.0916332 | ||||||||
\(647\) | −90259.0 | − | 90259.0i | −0.215616 | − | 0.215616i | 0.591032 | − | 0.806648i | \(-0.298721\pi\) |
−0.806648 | + | 0.591032i | \(0.798721\pi\) | |||||||
\(648\) | 97264.0 | − | 97264.0i | 0.231634 | − | 0.231634i | ||||
\(649\) | 929200.i | 2.20607i | ||||||||
\(650\) | 69300.0 | − | 237600.i | 0.164024 | − | 0.562367i | ||||
\(651\) | 28804.0 | 0.0679659 | ||||||||
\(652\) | 101128. | + | 101128.i | 0.237890 | + | 0.237890i | ||||
\(653\) | −56019.0 | + | 56019.0i | −0.131374 | + | 0.131374i | −0.769736 | − | 0.638362i | \(-0.779612\pi\) |
0.638362 | + | 0.769736i | \(0.279612\pi\) | |||||||
\(654\) | − | 1120.00i | − | 0.00261856i | ||||||
\(655\) | 32970.0 | + | 43960.0i | 0.0768487 | + | 0.102465i | ||||
\(656\) | −66688.0 | −0.154967 | ||||||||
\(657\) | −274841. | − | 274841.i | −0.636723 | − | 0.636723i | ||||
\(658\) | −34884.0 | + | 34884.0i | −0.0805702 | + | 0.0805702i | ||||
\(659\) | 438920.i | 1.01068i | 0.862920 | + | 0.505341i | \(0.168633\pi\) | ||||
−0.862920 | + | 0.505341i | \(0.831367\pi\) | |||||||
\(660\) | 8080.00 | − | 56560.0i | 0.0185491 | − | 0.129844i | ||||
\(661\) | 593762. | 1.35897 | 0.679484 | − | 0.733690i | \(-0.262204\pi\) | ||||
0.679484 | + | 0.733690i | \(0.262204\pi\) | |||||||
\(662\) | 212564. | + | 212564.i | 0.485036 | + | 0.485036i | ||||
\(663\) | 47322.0 | − | 47322.0i | 0.107655 | − | 0.107655i | ||||
\(664\) | 194592.i | 0.441356i | ||||||||
\(665\) | −26600.0 | − | 3800.00i | −0.0601504 | − | 0.00859291i | ||||
\(666\) | −44556.0 | −0.100452 | ||||||||
\(667\) | −108200. | − | 108200.i | −0.243207 | − | 0.243207i | ||||
\(668\) | −239848. | + | 239848.i | −0.537506 | + | 0.537506i | ||||
\(669\) | 70038.0i | 0.156488i | ||||||||
\(670\) | 406480. | − | 304860.i | 0.905502 | − | 0.679127i | ||||
\(671\) | 420564. | 0.934086 | ||||||||
\(672\) | 4864.00 | + | 4864.00i | 0.0107710 | + | 0.0107710i | ||||
\(673\) | 424561. | − | 424561.i | 0.937368 | − | 0.937368i | −0.0607833 | − | 0.998151i | \(-0.519360\pi\) |
0.998151 | + | 0.0607833i | \(0.0193599\pi\) | |||||||
\(674\) | − | 569916.i | − | 1.25456i | ||||||
\(675\) | −124000. | + | 68000.0i | −0.272154 | + | 0.149246i | ||||
\(676\) | −71672.0 | −0.156840 | ||||||||
\(677\) | 229021. | + | 229021.i | 0.499687 | + | 0.499687i | 0.911340 | − | 0.411654i | \(-0.135049\pi\) |
−0.411654 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(678\) | −33916.0 | + | 33916.0i | −0.0737811 | + | 0.0737811i | ||||
\(679\) | − | 21318.0i | − | 0.0462388i | ||||||
\(680\) | −114720. | − | 152960.i | −0.248097 | − | 0.330796i | ||||
\(681\) | −137198. | −0.295838 | ||||||||
\(682\) | −306232. | − | 306232.i | −0.658388 | − | 0.658388i | ||||
\(683\) | −450999. | + | 450999.i | −0.966795 | + | 0.966795i | −0.999466 | − | 0.0326716i | \(-0.989598\pi\) |
0.0326716 | + | 0.999466i | \(0.489598\pi\) | |||||||
\(684\) | − | 25280.0i | − | 0.0540337i | ||||||
\(685\) | −46995.0 | + | 328965.i | −0.100155 | + | 0.701082i | ||||
\(686\) | −310080. | −0.658909 | ||||||||
\(687\) | 98760.0 | + | 98760.0i | 0.209251 | + | 0.209251i | ||||
\(688\) | 48576.0 | − | 48576.0i | 0.102623 | − | 0.102623i | ||||
\(689\) | − | 360162.i | − | 0.758681i | ||||||
\(690\) | −75740.0 | − | 10820.0i | −0.159084 | − | 0.0227263i | ||||
\(691\) | −432438. | −0.905665 | −0.452833 | − | 0.891596i | \(-0.649587\pi\) | ||||
−0.452833 | + | 0.891596i | \(0.649587\pi\) | |||||||
\(692\) | −37912.0 | − | 37912.0i | −0.0791707 | − | 0.0791707i | ||||
\(693\) | 303202. | − | 303202.i | 0.631343 | − | 0.631343i | ||||
\(694\) | − | 25916.0i | − | 0.0538083i | ||||||
\(695\) | −279200. | + | 209400.i | −0.578024 | + | 0.433518i | ||||
\(696\) | 6400.00 | 0.0132118 | ||||||||
\(697\) | −249038. | − | 249038.i | −0.512625 | − | 0.512625i | ||||
\(698\) | −65840.0 | + | 65840.0i | −0.135138 | + | 0.135138i | ||||
\(699\) | − | 107442.i | − | 0.219897i | ||||||
\(700\) | 64600.0 | + | 117800.i | 0.131837 | + | 0.240408i | ||||
\(701\) | −895838. | −1.82303 | −0.911514 | − | 0.411269i | \(-0.865086\pi\) | ||||
−0.911514 | + | 0.411269i | \(0.865086\pi\) | |||||||
\(702\) | −63360.0 | − | 63360.0i | −0.128570 | − | 0.128570i | ||||
\(703\) | −5640.00 | + | 5640.00i | −0.0114122 | + | 0.0114122i | ||||
\(704\) | − | 103424.i | − | 0.208678i | ||||||
\(705\) | 13770.0 | + | 18360.0i | 0.0277048 | + | 0.0369398i | ||||
\(706\) | −215676. | −0.432706 | ||||||||
\(707\) | −31958.0 | − | 31958.0i | −0.0639353 | − | 0.0639353i | ||||
\(708\) | −36800.0 | + | 36800.0i | −0.0734144 | + | 0.0734144i | ||||
\(709\) | 64360.0i | 0.128033i | 0.997949 | + | 0.0640167i | \(0.0203911\pi\) | ||||
−0.997949 | + | 0.0640167i | \(0.979609\pi\) | |||||||
\(710\) | −34780.0 | + | 243460.i | −0.0689942 | + | 0.482960i | ||||
\(711\) | 606720. | 1.20019 | ||||||||
\(712\) | 90880.0 | + | 90880.0i | 0.179270 | + | 0.179270i | ||||
\(713\) | −410078. | + | 410078.i | −0.806654 | + | 0.806654i | ||||
\(714\) | 36328.0i | 0.0712599i | ||||||||
\(715\) | 699930. | + | 99990.0i | 1.36912 | + | 0.195589i | ||||
\(716\) | 263360. | 0.513717 | ||||||||
\(717\) | −45600.0 | − | 45600.0i | −0.0887006 | − | 0.0887006i | ||||
\(718\) | 343520. | − | 343520.i | 0.666351 | − | 0.666351i | ||||
\(719\) | − | 239840.i | − | 0.463942i | −0.972723 | − | 0.231971i | \(-0.925483\pi\) | ||
0.972723 | − | 0.231971i | \(-0.0745175\pi\) | |||||||
\(720\) | −101120. | + | 75840.0i | −0.195062 | + | 0.146296i | ||||
\(721\) | −266798. | −0.513230 | ||||||||
\(722\) | 257442. | + | 257442.i | 0.493861 | + | 0.493861i | ||||
\(723\) | −57038.0 | + | 57038.0i | −0.109116 | + | 0.109116i | ||||
\(724\) | − | 324464.i | − | 0.618998i | ||||||
\(725\) | 120000. | + | 35000.0i | 0.228300 | + | 0.0665874i | ||||
\(726\) | 104652. | 0.198552 | ||||||||
\(727\) | −438339. | − | 438339.i | −0.829357 | − | 0.829357i | 0.158071 | − | 0.987428i | \(-0.449472\pi\) |
−0.987428 | + | 0.158071i | \(0.949472\pi\) | |||||||
\(728\) | −60192.0 | + | 60192.0i | −0.113573 | + | 0.113573i | ||||
\(729\) | − | 454321.i | − | 0.854885i | ||||||
\(730\) | 208740. | + | 278320.i | 0.391706 | + | 0.522274i | ||||
\(731\) | 362802. | 0.678946 | ||||||||
\(732\) | 16656.0 | + | 16656.0i | 0.0310848 | + | 0.0310848i | ||||
\(733\) | 145261. | − | 145261.i | 0.270359 | − | 0.270359i | −0.558886 | − | 0.829245i | \(-0.688771\pi\) |
0.829245 | + | 0.558886i | \(0.188771\pi\) | |||||||
\(734\) | 609044.i | 1.13046i | ||||||||
\(735\) | −8395.00 | + | 58765.0i | −0.0155398 | + | 0.108779i | ||||
\(736\) | −138496. | −0.255671 | ||||||||
\(737\) | 1.02636e6 | + | 1.02636e6i | 1.88958 | + | 1.88958i | ||||
\(738\) | −164636. | + | 164636.i | −0.302282 | + | 0.302282i | ||||
\(739\) | − | 738040.i | − | 1.35142i | −0.737167 | − | 0.675711i | \(-0.763837\pi\) | ||
0.737167 | − | 0.675711i | \(-0.236163\pi\) | |||||||
\(740\) | 39480.0 | + | 5640.00i | 0.0720964 | + | 0.0102995i | ||||
\(741\) | −7920.00 | −0.0144241 | ||||||||
\(742\) | 138244. | + | 138244.i | 0.251095 | + | 0.251095i | ||||
\(743\) | 579101. | − | 579101.i | 1.04900 | − | 1.04900i | 0.0502671 | − | 0.998736i | \(-0.483993\pi\) |
0.998736 | − | 0.0502671i | \(-0.0160073\pi\) | |||||||
\(744\) | − | 24256.0i | − | 0.0438201i | ||||||
\(745\) | −180000. | + | 135000.i | −0.324310 | + | 0.243232i | ||||
\(746\) | −285356. | −0.512754 | ||||||||
\(747\) | 480399. | + | 480399.i | 0.860916 | + | 0.860916i | ||||
\(748\) | 386224. | − | 386224.i | 0.690297 | − | 0.690297i | ||||
\(749\) | 82042.0i | 0.146242i | ||||||||
\(750\) | 58500.0 | − | 22000.0i | 0.104000 | − | 0.0391111i | ||||
\(751\) | −495318. | −0.878222 | −0.439111 | − | 0.898433i | \(-0.644706\pi\) | ||||
−0.439111 | + | 0.898433i | \(0.644706\pi\) | |||||||
\(752\) | 29376.0 | + | 29376.0i | 0.0519466 | + | 0.0519466i | ||||
\(753\) | 39402.0 | − | 39402.0i | 0.0694910 | − | 0.0694910i | ||||
\(754\) | 79200.0i | 0.139310i | ||||||||
\(755\) | 356970. | + | 475960.i | 0.626236 | + | 0.834981i | ||||
\(756\) | 48640.0 | 0.0851040 | ||||||||
\(757\) | −536979. | − | 536979.i | −0.937056 | − | 0.937056i | 0.0610771 | − | 0.998133i | \(-0.480546\pi\) |
−0.998133 | + | 0.0610771i | \(0.980546\pi\) | |||||||
\(758\) | −345200. | + | 345200.i | −0.600803 | + | 0.600803i | ||||
\(759\) | − | 218564.i | − | 0.379398i | ||||||
\(760\) | −3200.00 | + | 22400.0i | −0.00554017 | + | 0.0387812i | ||||
\(761\) | −908798. | −1.56927 | −0.784636 | − | 0.619957i | \(-0.787150\pi\) | ||||
−0.784636 | + | 0.619957i | \(0.787150\pi\) | |||||||
\(762\) | 3284.00 | + | 3284.00i | 0.00565579 | + | 0.00565579i | ||||
\(763\) | −5320.00 | + | 5320.00i | −0.00913824 | + | 0.00913824i | ||||
\(764\) | 264016.i | 0.452318i | ||||||||
\(765\) | −660835. | − | 94405.0i | −1.12920 | − | 0.161314i | ||||
\(766\) | 633684. | 1.07998 | ||||||||
\(767\) | −455400. | − | 455400.i | −0.774109 | − | 0.77 |